Answer:
x² - 49
Step-by-step explanation:
(x - 7)² =
(x - 7) * (x - 7) =
x * x - 7 * 7 =
x² - 49
In a 7-sided figure, three of the angles are equal
and each of the other four angles is 150 greater
than each of the first three. Find the angles.
The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).
So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:
3x + 4(x+15) = 900
7x + 60 = 900
7x = 840
x = 120
The figure has three angles of 120 degrees, and four angles of 135 degrees.
Find the value of the expression x+|x| if x=7, 10, 0, -3, -8. write the expression without the absolute value symbol for these values of x: x≤0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
What does the expression mean?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).
For x =7,x+|x| =7+|7| =14
For x =10,x+|x|= 10+|10| =20
For x = 0,x+|x| =0+|0| =0
For x = -3, x + |x| = -3 + |-3| = 0
For x = -8, x + |x| = -8 + |-8| = 0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
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Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 180 gallons of orange juice last year. This year, the hotel served 70% more orange juice than it did the previous year. How much was served this year?
The hotel served 306 gallons of orange juice this year.
To find the amount of orange juice served this year, we need to add 70% more of the amount served last year to the amount served last year. Let's denote the amount served last year as "x". Then we can set up the equation:
Amount served this year = x + 0.7xSimplifying this equation gives us:
Amount served this year = 1.7xWe know from the problem that the amount served last year was 180 gallons. Plugging this into our equation, we get:
Amount served this year = 1.7(180)Simplifying this equation gives us:
Amount served this year = 306Therefore, the hotel served 306 gallons of orange juice this year.
In summary, we used the information given in the problem to set up an equation and solve for the amount of orange juice served this year. We first found the amount served last year, and then added 70% more of that amount to get the total amount served this year.
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Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
Solve: 3√x-√9x-17 =1
The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.
What is the solution to the given equation?Given the equation in the question (3√x) - √(9x-17) = 1.
To solve for x in the given equation:
(3√x) - √(9x-17) = 1
We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:
(3√x) = √(9x - 17) + 1
Squaring both sides of the equation, we get:
(3√x)² = (√(9x - 17) + 1)²
9x = -16 + 2√(9x - 17) + 9x
Solve for 2√(9x - 17)
2√(9x - 17) = 16
36x - 68 = 256
Add 68 to both sides
36x - 68 + 68 = 256 + 68
36x = 324
x = 324/36
x = 9
Therefore, the solution is x = 9.
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Calculate the amount of interest on $4,000. 00 for 4 years, compounding daily at 4. 5 % APR. From the Monthly Interest Table use $1. 197204 in interest for each $1. 00 invested
The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.
To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:
A = $4,000.00(1 + 0.045/365)^(365*4)
A = $4,000.00(1.0001234)^1460
A = $4,889.68
The final amount is $4,889.68, which means that the interest earned is:
Interest = $4,889.68 - $4,000.00 = $889.68
We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:
$1.197204 / $1.00 = 1.197204
Interest earned = $889.68 x 1.197204 = $1,064.08
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A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.
Find the probability that a 0 is received. (Enter the value of the probability in decimal format and round the final answer to one decimal place.)
P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).
0.5333
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly
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n+d=21
0.05n + 0.10d= 1.70
Answer:
To solve the system of equations:
n + d = 21 ---(1)
0.05n + 0.10d = 1.70 ---(2)
We can use the substitution method by solving for one variable in terms of the other from equation (1) and substituting it into equation (2).
Solving equation (1) for n:
n = 21 - d
Substituting this expression for n into equation (2):
0.05(21 - d) + 0.10d = 1.70
Distributing the 0.05:
1.05 - 0.05d + 0.10d = 1.70
Combining like terms:
0.05d = 0.65
Dividing both sides by 0.05:
d = 13
Substituting this value of d into equation (1):
n + 13 = 21
Solving for n:
n = 8
Therefore, the solution to the system of equations is n = 8 and d = 13.
The interest rate of an auto
loan is 4%. Express this
number as a decimal.
Answer: 0.04
Step-by-step explanation:
In order to get 4% as a decimal, you must divide 4 by 100.
4/100 = 0.04
Thus, the answer to your question is 0.04
in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g
The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040
A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.
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The Turners have purchased a house for $170,000. They made an initial down payment of $34,000 and secured a mortgage with interest charged at a rate of 3.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 15 years. (Round all answers to the nearest cent.)
(a) What monthly payment will the Turners be required to make?
$
(b) What will be their total interest payment?
$
(c) What will be their equity (disregard depreciation and inflation) after 10 years?
$
(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).
What monthly payment will the Turners be required to make?Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).
Applying the values provided, we obtain:
(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.
Amount paid: $1,054.63
Hence, the installment will be $1,054.63 per month.
What will be their total interest payment?(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:
Total interest equals PV minus (Payment x n)
Applying the values provided, we obtain:
$1,054.63 multiplied by 180 equals $136,000 in interest.
Interest totaled $88,833.40.
The total interest payment will therefore be $88,833.40.
What will be their equity (disregard depreciation and inflation) after 10 years?(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:
The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i
Where n denotes how many payments are still due (180 - 120 = 60).
Applying the values provided, we obtain:
The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917
Balance remaining: $71,587.90
As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.
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an inner city revitalization zone is a rectangle that is twice as long as it is wide. the width of the region is growing at a rate of 32 m per year at a time when the region is 220 m wide. how fast is the area changing at that point in time?
The area is changing at a rate of 28,160 m²/year at that point in time.
The area of the rectangular region is given by:
A = lw
Where l is the length of the rectangular region and w is the width of the rectangular region.
The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:
l = 2w
l = 2 x 220
l = 440
Therefore, the length l of the rectangular region is 440 m.
At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.
A = lw
dA/dt = w dl/dt + l dw/dt
dA/dt = 220 d/dt(2w) + 440 dw/dt
dA/dt = 220 x 2 dw/dt + 440 dw/dt
dA/dt = 880 dw/dt
Substitute the value of dw/dt to get:
dA/dt = 880 x 32
dA/dt = 28,160 m²/year
Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.
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6. 4 The point Q (3, -1) has been translated from P by the vector (3) What are the coordinates of the point P?
The coordinates of the point P is (-1,2) .
What is translation?
In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.
Finding the coordinates of the point P :
The coordinates of point P can be found by subtracting the vector from point Q.
To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).
Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:
3 - 4 = -1
Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:
-1 - (-3) = 2
Therefore, the coordinates of point P are (-1, 2).
So, the correct answer is (C) (-1, 2).
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Charles is 10 years old what is the best estimate of the length of his shoe
Answer:
Size 3 ♀️
Step-by-step explanation:
In the US, the average shoe size for 10-Year-Old is USA Size 3.
-Jul 12, 2020
ABCD is a quadrilateral in which BD = 15 cm., perpendiculars from A and Con BD are 6 cm and 8 cm respectively. Calculate the area of the quadrilaterals
The area of the quadrilateral is 161.24 cm².
How to deal with quadrilateral?We can see that we can divide the quadrilateral into two triangles: ABD and CBD. We know that the height of ABD is 6 cm and the height of CBD is 8 cm. We also know that BD is 15 cm. To find the area of each triangle, we need to find the base of each triangle. We can do this using the Pythagorean theorem.
For triangle ABD:
AB² = AD² + BD²
AB² = (6 cm)² + (15 cm)²
AB² = 261 cm²
AB = [tex]\sqrt(261) cm[/tex]
For triangle CBD:
BC² = CD² + BD²
BC² = (8 cm)² + (15 cm)²
BC² = 289 cm²
BC = 17 cm
Now we can find the areas of the triangles:
Area of ABD =[tex]\frac{1}{2}[/tex] * AB * 6 cm
Area of ABD = [tex]\frac{1}{2}[/tex] * [tex]\sqrt(261) cm[/tex] * 6 cm
Area of ABD = 93.24 cm^2
Area of CBD = [tex]\frac{1}{2}[/tex] * BC * 8 cm
Area of CBD = [tex]\frac{1}{2}[/tex] * 17 cm * 8 cm
Area of CBD = 68 cm²
Finally, we can find the area of the quadrilateral by adding the areas of the triangles:
Area of ABCD = Area of ABD + Area of CBD
Area of ABCD = 93.24 cm² + 68 cm²
Area of ABCD = 161.24 cm²
Therefore, the area of the quadrilateral is 161.24 cm².
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Qual o resultado do problema 3528÷98?
Answer:
36
Step-by-step explanation:
How do you do this I need help please
Answer:
30,000 grams
Step-by-step explanation:
multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g
Answer:
hi I'm really sorry I can't help
After heating up in a teapot, a cup of hot water is poured at a temperature of
201°F. The cup sits to cool in a room at a temperature of 73° F. Newton's Law
of Cooling explains that the temperature of the cup of water will decrease
proportionally to the difference between the temperature of the water and the
temperature of the room, as given by the formula below:
T = Ta + (To-Ta)e-kt
Ta
the temperature surrounding the object
To the initial temperature of the object
t = the time in minutes
=
T =
the temperature of the object after t minutes
k = decay constant
The cup of water reaches the temperature of 189°F after 3 minutes. Using
this information, find the value of k, to the nearest thousandth. Use the
resulting equation to determine the Fahrenheit temperature of the cup of
water, to the nearest degree, after 6 minutes.
The temperature of the cup of water is approximately 180°F after 6 minutes.
How to find temperature and time?Using the given formula, we can write:
T = Ta + (To - Ta) * e^(-kt)
where Ta = 73°F (the temperature of the room), To = 201°F (the initial temperature of the water), and T = 189°F (the temperature of the water after 3 minutes).
We can solve for the decay constant k as follows:
(T - Ta) / (To - Ta) = e^(-kt)
ln[(T - Ta) / (To - Ta)] = -kt
k = -ln[(T - Ta) / (To - Ta)] / t
Substituting the given values, we get:
k = -ln[(189°F - 73°F) / (201°F - 73°F)] / 3 minutes
k = -ln[116 / 128] / 3 minutes
k ≈ 0.0434 minutes^-1 (rounded to the nearest thousandth)
Now we can use this value of k to find the temperature of the water after 6 minutes:
T = Ta + (To - Ta) * e^(-kt)
T = 73°F + (201°F - 73°F) * e^(-0.0434 minutes^-1 * 6 minutes)
T ≈ 180°F (rounded to the nearest degree)
Therefore, the temperature of the cup of water is approximately 180°F after 6 minutes.
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Smoothie Activity
6. Using the relative frequency table, create a segmented bar graph by employee type using technology or by hand. If using Excel technology the columns may need to be switched after inserting the chart. Click on the chart and the "Chart Design" ribbon will pop up. Then select "Switch Row/Column." (10 points)
By answering the presented question, we may conclude that I used the following procedures to produce this graph.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I made the segmented bar graph using these percentages.
The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.
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Can anyone please help with this math problem? Thanks!
Answer: Yes Sofia will have enough money
=======================================================
Explanation:
Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.
The area of the rectangle is 16*7 = 112 square meters.
The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be
sum of the exterior sides = perimeter
6+7+16+7+6+x = 54
42+x = 54
x = 54-42
x = 12
The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.
area of the trapezoid = 0.5*height*(base1+base2)
area = 0.5*5.66*(16+12)
area = 79.24 square meters
----------------
Recap so far
area of the rectangle at the bottom = 112 square metersarea of the trapezoid up top = 79.24 square metersThe total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.
Let's convert that to square decimeters.
Recall that 1 decimeter = 10 centimeters
Multiply both sides by 10
1 decimeter = 10 centimeters
10*(1 decimeter) = 10*(10 centimeters)
10 decimeters = 100 centimeters
10 decimeters = 1 meter
Then,
[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]
The entire lawn is 19124 square decimeters.
----------------
We have one final block of calculations to determine the total price.
x = number of rolls
1 roll covers 90 square decimeters
x rolls cover 90x square decimeters
90x = 19124
x = 19124/90
x = 212.489 approximately
Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).
In short, Sofia needs 213 rolls.
1 roll costs $4.50
213 rolls will cost 213*4.50 = 958.50 dollars.
This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).
Sofia will have enough money to pay for all of the grass.
the dog eats 8 ounces of dog food each day his owner bought 28 pound bag at the 8 ounces cost $3.50 so how much did the owner spend for 28 bag
Answer:
$196
Step-by-step explanation:
1 lb = 16oz
28 lbs x 16 = 448 ozs (in 28 lb bag)
448/8 = 56 (8 oz portions)
56 x $3.50= $196
3
The ratio of desktop computers to laptop computers sold by
a mail-order company last week was 8 to 3. What could be
the numbers of computers sold by the company last week?
A
B
C
D
448 desktops, 168 laptops
448 desktops, 165 laptops
440 desktops, 168 laptops
400 desktops, 165 laptops
using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.
How to Calculate Ratios?To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.
Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:
A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168
B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165
C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168
D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165
Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.
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Ñamandu es un genio dibujó un cuadrado de x cm cada lado en la parte superior del cuadrado partió en tres partes iguales quedando el corte expresado de esta manera x bajo 3 unió el primer punto de corte con el vértice del lado paralelo trazando un segmento a lo que llamó y Descubre que figuras se forman y entra el perímetro de cada figura formado
The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).
When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.
Using the Pythagorean theorem, we can solve for y:
y^2 = (x/3)^2 + x^2
y^2 = x^2/9 + x^2
y^2 = (10x^2)/9
y = x×sqrt(10)/3
Now we can find the perimeter of each figure that is created
Perimeter of the original square = 4x
Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3
Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Hence, 28 toy soldiers are the correct answer.
In mathematics, how is a group defined?A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.
Let's refer to the quantity of toy soldiers as "x".
We are aware that x is within the range of 27 and 54 thanks to the problem.
x can be divided by 4 without any remainders.
The residual is 6 when x is divided by 7.
The leftover after dividing x by five is three.
These criteria allow us to construct an equation system and find x.
Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:
x = 4k, where k is some integer.
Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:
x ≡ 6 (mod 7)
This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:
4k ≡ 6 (mod 7)
We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:
4(1) ≡ 6 (mod 7)
4 ≡ 6 (mod 7)
It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.
k = 2:
4(2) ≡ 6 (mod 7)
1 ≡ 6 (mod 7)
k = 3:
4(3) ≡ 6 (mod 7)
5 ≡ 6 (mod 7)
k = 4:
4(4) ≡ 6 (mod 7)
2 ≡ 6 (mod 7)
k = 5:
4(5) ≡ 6 (mod 7)
6 ≡ 6 (mod 7)
k = 6:
4(6) ≡ 6 (mod 7)
3 ≡ 6 (mod 7)
k = 7:
4(7) ≡ 6 (mod 7)
0 ≡ 6 (mod 7)
We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:
x = 4(7) = 28
This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.
28 toy soldiers are the correct response.
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Help please & thanks
The function f(t)=−5t^2+20t models the approximate height of an object t seconds after it is launched. Which of the following equations correctly shows the quadratic formula being used to determine the number of seconds it will take for the objects to be at a height of 18 feet after launch?
The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
What is trigοnοmetric equatiοns ?Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.
Accοrding tο the given infοrmatiοn:
The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.
Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].
Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].
In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
Plugging in the values οf a, b, and c, we get:
[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]
Simplifying this expressiοn, we get:
[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
[tex]t = 2 \± 0.632[/tex]
Therefοre, the twο pοssible values οf t are:
t = 2 + 0.632 = 2.632 secοnds
t = 2 - 0.632 = 1.368 secοnds
Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
t = 2 ± 0.632
Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
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what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9
Answer:
I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.
for the first equation y=-x+6, y intercept is (0,6)
for equation two 2x-y=-9, y intercept is (0,9)
In both of the equations the x value is 1.
Solving for y without graphing. Y=9+2x
and x=-1
Step-by-step explanation:substitute i
HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5
It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.
One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?
Answer:
2x - 13
Step-by-step explanation:
If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:
x + (x - 13) = 2x - 13
Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
Use the following function to find d(0)
d(x)=-x+-3
d(0)=
When the function d(x) = -x +(-3), then the value of d(0) is -3
In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.
In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.
To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:
d(0) = -(0) - 3
The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as
d(0) = -3
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a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 32.083. what is the value of the additional data point?
The value of the additional data point is [tex]$19.17$[/tex].
What is the value of the additional data point?Let us first find the mean of the given data:
[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]
Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is
[tex]$(39+45+43+42+44+x)$[/tex].
Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:
[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]
Multiplying both sides of the equation by 6 we get:
[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]
We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].
Therefore, substituting all the values, we get:
[tex]193.83 + x = 213[/tex]
On subtracting [tex]$193.83$[/tex] from both sides, we get the value of
[tex]x. x = 213 - 193.83 = 19.17[/tex]
Therefore, the value of the additional data point is [tex]$19.17$[/tex]
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