Answer:
Step-by-step explanation:
The diagonal ^2= 13^2+7^2
=169+49=218
diagonal = V218
the lengh of the square=l
l^2+l^2= 218
2l^2=218
l^2= 218/2= 109
l= ✓109
Find the coordinates of point G that lies along the directed line segment from F(-1, -1) to H(-8, 20) and partitions the segment in the ratio of 5:2.
Answer:
coordinates of point g is ( -6, 14)
Step-by-step explanation:
The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).
___________________________________________
given point
F(-1, -1) to H(-8, 20)
ratio : 5:2
the coordinates of point g is
(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)
=> (-2 -40/7 , -2+100/7)
=> (-42/7, 98/7)
=>( -6, 14)
Thus , coordinates of point g is ( -6, 14)
A delivery truck company just bought a new delivery truck and they need to know the maximum volume it can carry. In the front of the truck, there is an extra ledge that sticks out over the driver's cab for extra storage space. What is the maximum amount of cargo that can fit into the new truck?
Answer:
The answer is below
Step-by-step explanation:
To find the maximum amount of cargo the truck can carry, we need to find the volume of the truck.
Volume = length × width × height.
Firstly 1 feet (1') = 12 inches (12"),
For the extra ledge that sticks out, the height = 7'8" = 7.667 feet, the width = 16'9" - 14'3" = 16.75 - 14.25 = 2.5 feet, the length = 2'7" = 2.583 feet
Volume of extra ledge = length × width × height = 2.583 × 2.5 × 7.667 = 49.5 feet³
For the truck, the height = 7'8" = 7.667 feet, the length = 14'3" = 14.25 feet, the width = 6'6" = 6.5 feet
Volume of truck = length × width × height = 14.25 × 6.5 × 7.667 = 710.16 feet³
The maximum volume = volume of extra ledge + volume of truck = 49.5 + 710.16 = 759.66 feet³
Please answer ASAP!!
plssss
Answer:
86°
Step-by-step explanation:
b = 29× 2 = 58
d= [180-(86+29)]×2 = 130
a=c=x
a+b+c+d = 360
2x+188= 360
2x= 172
x= 86
a = c = 86°
In 1 through 3, what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
Answer:
7000 (7 thousand)
700 (7 hundred)
20 (2 tens)
2 (2 units)
Step-by-step explanation:
what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
From the knowledge of place values;
7,700 could be broken down thus :
7000 + 700 + 0 + 0
The first 7 depicts thousands as it has 3 trailing digits (7000)
The second 7 depicts hundred as it has 2 trailing digits (700)
522 could be broken down thus :
500 + 20 + 2
From 522
The first '2' has one trailing digit = tens
The ending / last digit ia always = Unit value
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = −7.126 + .0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the critical value for a right-tailed test to see if the slope is positive, using α = .05.A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = −7.126 + .0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the critical value for a right-tailed test to see if the slope is positive, using α = .05.
Answer:
1.734
Step-by-step explanation:
Given that:
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles).
The fitted regression is Time = −7.126 + .0214 Distance
Based on a sample size n = 20
And an Estimated standard error of the slope = 0.0053
the critical value for a right-tailed test to see if the slope is positive, using ∝ = 0.05 can be computed as follows:
Let's determine the degree of freedom df = n - 1
the degree of freedom df = 20 - 2
the degree of freedom df = 18
At the level of significance ∝ = 0.05 and degree of freedom df = 18
For a right tailed test t, the critical value from the t table is :
[tex]t_{0.05, 18} =[/tex] 1.734
Solve the system by substitution.
y = -2
y =
5x + 40
Answer:
x = 8.4
y = -2
Step-by-step explanation:
Step 1: Sub y=-2 into y=5x + 40
-2 = 5x + 40
Step 2: Solve for 'x'
-2 = 5x +40
-42 = 5x
x = 42/5
x = 8.4
Step 3: Solve for 'y'
y is given in the question, y=-2
Please Help me with this math question
–14=–(-2x+2)8)51=7(-1+2v)+2
Answer:
x = -6; v = 4.
Step-by-step explanation:
–14 = –(-2x + 2)
-14 = 2x - 2
2x - 2 = -14
2x = -12
x = -6.
51 = 7(-1 + 2v) + 2
51 = -7 + 14v + 2
51 = 14v - 5
14v = 56
v = 4.
Hope this helps!
what is the discriminant and how many solutions?
Step-by-step explanation:
[tex]\text{Discriminant} =\Delta = b^2-4ac\\
\implies \Delta = 7^2-4(1)(10)=49-40=9\\
\therefore \Delta >0\\[/tex]
Since the discriminant is greater than zero, there are two real solutions.
Also, the solutions are $x=5$ and $x=2$
find the co efficient of m in the expression of ( m/2-3/2) ( m+2/3)
Answer:
Step-by-step explanation:
We will get m when we multiply (m/2)*(2/3) & m *(-3/2)
[tex]\frac{m}{2}*\frac{2}{3}+m*\frac{-3}{2}=\frac{m}{3}-\frac{3m}{2}\\\\\\=m(\frac{1}{3}-\frac{3}{2})\\\\\\=m(\frac{2}{6}-\frac{9}{6})\\\\\\=\frac{-7}{6}m[/tex]
Coefficient of m = -7/6
find the slope between (0, 6) and (-3,9)
Answer:
-1
Step-by-step explanation:
The formula for finding a slope is: m = (change in y)/(change in x)
Find the change in each value
Y: 9 - 6 = 3
X: -3 - 0 = -3
Input the values
m = 3/-3
m = -1
I would start this problem by setting up a table.
In the left column, we will have our x values
and in the right column, we have our y values.
Put our first ordered pair on the top and second on bottom.
We can see the y values go from 6 to 9 so change in y is 3.
The x values go from 0 to -3 so change in x is -3.
The slope is equal to the rate of change or change in y / change in x.
So our slope is 3/-3 of -1.
Each packet of the cooking oil weighs 2/5th of a kilogram and one kilogram of the cooking oil costs $6.5. Sara went to the grocery shop to buy some items to stock her kitchen. If she bought 8 packets of the cooking oil, how much money did she spend? A $19.60 B $18.20 C $20.80 D $23.40
Answer:
C) $20.80
Step-by-step explanation:
1 kg of cooking oil = $6.5
1 packet of cooking oil =2/5 kg
If 1 kg of cooking oil = $6.5
2/5kg of cooking oil = $X
Cross Multiply
1kg × $X = 2/5kg × $6.5
$X = 13/5
$X = 2.6
Hence 2/5kg of oil cost $2.6
Since 1 packet of oil = 2/5kg of oil , 1 packet of oil cost $2.6
The amount she spent if she bought if she bought 8 packets of the cooking oil is calculated as:
1 packet of oil = $2.6
8 packets of oil =
$2.5 × 8
= $20.80
Therefore,if Sara bought 8 packets of oil, the amount she would spend = $20.80
Kelly bought a crate of floor tiles for $95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles.
Write and solve an equation to determine the cost per box, b. Then write and solve a second equation to determine the cost per tile, t, to the nearest cent.
Answer:
$1.60 a crate
Step-by-step explanation:
t= 95.94/(6x20)
(6x20)= 60
95.94/60
$1.60
Answer:
Step-by-step explanation:
i) Cost per box = cost of a crate ÷ Number of boxes in the crate
b = 95.94 ÷ 6
b = $ 15.99
ii) Cost per tile = Cost per box ÷ Number of tiles in a box
t = b ÷ 20
t = 15.99 ÷20
t = $ 0.7995
convert 0.129 into a percentage
Answer:
12.9%
Step-by-step explanation:
Answer:
0.129%
Step-by-step explanation:
Just add the percent sign
Find the 9th term of the geometric sequence whose common ratio is 23 and whose first term is 3
Answer:
2.35 x 10^11
Step-by-step explanation:
The formula for finding the nth term in a geometric sequence is ar^n-1.
a = 3, r = 23, and n = 9:
3(23)^9-1 = 3(23)^8 = 2.35 x 10^11.
Consider the equation: x 2 − 6 = 2 − 18 x x 2 −6=2−18xx, squared, minus, 6, equals, 2, minus, 18, x 1) Rewrite the equation by completing the square. Your equation should look like ( x + c ) 2 = d (x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or ( x − c ) 2 = d (x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation? Choose 1 answer: Choose 1 answer: (Choice A) A x = 9 ± 89 x=9±89x, equals, 9, plus minus, 89 (Choice B) B x = − 9 ± 89 x=−9±89x, equals, minus, 9, plus minus, 89 (Choice C) C x = 9 ± 89 x=9± 89 x, equals, 9, plus minus, square root of, 89, end square root (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Answer:
1. (x+9)^2 = 89
2. (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Step-by-step explanation:
x^2 - 6 = 2 - 18x
1) rewrite the equation by completing the square
x^2 - 6 = 2 - 18x
x^2 + 18x = 2+6
x^2 + 18x = 8
Find the half of the coefficient of x and square it
18x
Half=9
Square half=(9)^2
=81
Add 81 to both sides
x^2 + 18x = 8
x^2 + 18x + 81 = 8 + 81
x^2 + 18x + 81 = 89
(x+9)^2 = 89
Check:
(x+9)(x+9)=89
x^2 + 9x + 9x + 81=89
x^2 + 18x +81 =89
2) (x+9)^2 = 89
√(x+9)^2 = √89
x+9=√89
x=√89 - 9
It can be rewritten as
x= -9 ± √89
(Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
A container in form of a frustum of a cone is 16 cm in diameter at the open end and 24 cm diameter at the bottom. If the vertical depth of the container is 8 cm calculate the capacity of the container.
Answer:
The capacity of the container is 2546.78 cm³.
Step-by-step explanation:
The volume of the frustum of a cone is:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
The information provided is:
r = 16/2 = 8 cm
R = 24/2 = 12 cm
h = 8 cm
Compute the capacity of the container as follows:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
[tex]=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78[/tex]
Thus, the capacity of the container is 2546.78 cm³.
Imagine that you have plotted many data points on an xy-plane. Your points seem to align into a clear best-fit line. Do you think this best-fit line can help you make predictions about future data? Explain your answer, and give one or more examples to support it.
It depends really. If you stay close to the present, then predicting future results isn't too bad. The further you go out, the more unpredictable things get. This is because the points may deviate from the line of best fit (aka regression line) as time wears on. Of course, it also depends on what kind of data we're working with. Some pairs of variables are naturally going to correlate very strongly together. An example would be temperature versus ice cream sales.
A best-fit line shows an association between two variables and can therefore be used to make predictions.
An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.
(see attachment below).
Recall:
A best-fit line is a line drawn on a scatterplot showing a trend or an association between two variables.A best-fit line can either show a weak association or a strong association.A best-fit line is often applied in various situations to make predictions based on current trend revealed.Therefore, a best-fit line shows an association between two variables and can therefore be used to make predictions.
An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.
(see attachment below).
Learn more here:
https://brainly.com/question/2396661
HELP!!! Monica measures the number of bacteria that are living on her petri dish. Each day, she measures the amount of change in the number of bacteria. These amounts create a geometric sequence. Use the data in the table to determine the sum of the amounts of change in the bacteria after the seventh day. Day Amount of Change in Bacteria 1 2 2 −8 3 32 4 −128 A) −6553.2 B) −10.8 C)6554 D)11.6
Answer:
The correct option is;
C) 6554
Step-by-step explanation:
The given data are;
Day, Amount of change in Bacteria
1, 2
2, -8
3, 32
4, -128
Given that the data follows a geometric sequence, we have;
The first term of the series = 2, the common ratio = -4, the sum of a geometric progression is given by the following formula;
[tex]S_n = \dfrac{a \times \left (r^n - 1\right )}{r - 1}[/tex]
Which gives;
[tex]S_7 = \dfrac{2 \times \left ((-4)^7 - 1\right )}{(-4) - 1} = \dfrac{2 \times \left (-16384- 1\right )}{-4 - 1} = \dfrac{2 \times \left (-16385\right )}{-5} = 6554[/tex]
Therefore, the correct option is C) 6554.
select the shape of the graph of this two variable equation. y=4x^(2)-1
Answer:
The highest power of the equation is 2, since the equation is y = 4x^2 - 1. That means that the graph is a parabola. And because the 4 is positive, the parabola curves into a smile.
You can use the Math is Fun Function and Calculator to graph the parabola.
Hope this helps!
6 + x is an example of _____.
a formula
an expression
a constant
a variable
Answer:
An expression
Step-by-step explanation:
The constant in this case would be 6 because it never changes.
The variable would be x because the value of x can change.
A formula is a mathematical rule, which 6 +x is not.
Therefore, 6+x is an expression.
Solve the system of equations.
y=-2x
y= x2 - 8
A. (-4, 8) and (2, -4)
B. (-2,-4) and (4,8)
C. (-4,-8) and (2, 4)
D. (-2, 4) and (4, -8)
Answer:
A. (-4,8) and (2,-4)
Step-by-step explanation:
Because you already have a value for "y" you can plug in that value of "y" into the next equation and then solve for Y and X
please solve this fast.
Answer:
- 24 - 70i
Step-by-step explanation:
Given
([tex]\sqrt{5}[/tex] - 7i)²
= ([tex]\sqrt{5}[/tex] - 7i)([tex]\sqrt{5}[/tex] - 7i)
= 5 - 7[tex]\sqrt{5}[/tex] i - 7[tex]\sqrt{5}[/tex] i + 49i² ( note that i² = - 1 )
= 5 - 14[tex]\sqrt{5}[/tex] i - 49
= - 44 - 14[tex]\sqrt{5}[/tex] i
Answer:
Step-by-step explanation:
(a - b)² = a² - 2ab + b²
[tex][\sqrt{5} - 7i]^{2}= (\sqrt{5})^{2} - 2*\sqrt{5}*7i + (7i)^{2}\\\\\\= 5 - 14i\sqrt{5}+7^{2}*i^{2}]]= 5 -14i\sqrt{5} +49 * -1\\\\= 5 -14i\sqrt{5} - 49\\\\= -44 - 14i\sqrt{5}[/tex]
what number times itself 3 times go into 343
Answer:
According to an expert your answer is 7.
Step-by-step explanation:
since the unkown number is multiplied by itself what we need to do to get out answer is to work backwards. Thats where we cube root 343 to get 7
HOPE IT HELP!!!!!!!!!!!!IF IT REALLY HELPS SO PLZ MARK ME AS BRAINIESTkind of urgent!! Please describe a real-world scenario in which it would be important to know how to apply scale factors.
One example is that you're given blueprints and you want to find out how large the object is in real life, rather than just on paper. The scale factor will help find those real life measurements. Let's say a house on paper is 2 inches long, and also let's say the scale factor is labeled "1 inch = 20 feet". This means the real life house is 2*20 = 40 feet long.
You could think of it as 1 inch = 20 feet, so 2 inches = 40 feet (multiply both sides by 2).
Scale factors are also used in maps. Look at the bottom corner of any map and it will show you how each distance on paper corresponds to a real life distance (in miles or kilometers maybe). Usually it shows a checkered "ruler" of sorts.
Answer:
everyday living
Step-by-step explanation:
Scale factors are involved in virtually every aspect of the logistics of everyday life. Scale factors of number of units, price per unit, and tax rate are applied to every shopping experience. Scale factors of miles per gallon, or daily rate, or number of travelers are applied to most travel experiences. Scale factors of number of people and/or serving size are applied to food planning--even when ordering pizza.
Scale factors are involved in virtually every aspect of engineering, from specifying or estimating a job, to scheduling, material choice, purchase, and application. Sometimes, these are "rules of thumb", and sometimes they are based on careful calculation.
Much of modern technology is based on the observation that computing power doubles every 2 years or so--a scale factor consistently seen for more than 50 years. This has informed systems planning in many different industries.
If the product of two matrices is AB=1/-3/5 over 2/5/7, what are the dimensions of Matrix B if A is a 2x3 matrix?
Answer:
Matrix multiplication is associative: ( A B ) C = A ( B C ) \displaystyle \left(AB\right)C=A\left(BC\right) (AB)C=A(BC).
Matrix multiplication is distributive: C(A+B)=CA+CB,(A+B)C=AC+BC. C ( A + B ) = C A + C B , ( A + B ) C = A C +
The expression f(x) = 12(1.035)* models the monthly growth of membership in the new drama club at a school. According to the function, what is the monthly growth rate?
Answer:
The monthly growth rate is 3.5%.
Step-by-step explanation:
The exponential growth function is given as follows:
[tex]y=a(1+r)^{x}[/tex]
Here,
y = final value
a = initial value
r = growth rate
x = time taken
The provided expression for the monthly growth of membership in the new drama club at a school is:
[tex]f(x) = 12\cdot(1.035)^{x}[/tex]
Comparing this function with the exponential growth function:
[tex]a(1+r)^{x}=12(1.035)^{x}\\\\a(1+r)^{x}=12(1+0.035)^{x}[/tex]
Then value of r is 0.035 or 3.5%.
Thus, the monthly growth rate is 3.5%.
Find the exact value of cos A in simplest radical form.
Answer:
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Step-by-step explanation:
Since we are finding cos A we have
[tex] \cos(A) = \frac{AC}{AB} [/tex]From the question
AC = √96
AB = 14
Substitute the values into the above formula
That's
[tex] \cos(A) = \frac{ \sqrt{96} }{14} [/tex]We have the final answer as
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Hope this helps you
The 4th term of an exponential sequence is 108 and the common ratio is 3. Calculate the value of the eighth term of the sequence.
Answer:
The eighth term is 8748Step-by-step explanation:
Since the sequence is a geometric sequence
For an nth term in a geometric sequence
[tex]A (n) = a ({r})^{n - 1} [/tex]
where
a is the first term
r is the common ratio
n is the number of terms
To find the eighth term we must first find the first term
4th term = 108
common ratio = 3
That's
[tex]A(4) = a ({r})^{4 - 1} [/tex]
[tex]108 = a ({3})^{3} [/tex]
[tex]27a = 108[/tex]
Divide both sides by 27
a = 4The first term is 4For the eighth term
[tex]A(8) = 4 ({3})^{8 - 1} [/tex]
[tex]A(8) = 4({3})^{7} [/tex]
The final answer is
A(8) = 8748The eighth term is 8748Hope this helps you
Bruno is designing his next skateboard. The skateboard store has 3 types of grip tape, 13 types of decks, 7 types of trucks, 4 types of bearings, and 2 types of wheels. How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.
Answer:
2184 different combinations
Step-by-step explanation:
To find how many different combinations are possible, multiply all of the values:
3 * 13 * 7 * 4 * 2 = 2184 different combinations
Answer:
2,184 different skateboards.
Step-by-step explanation:
You would have to multiply
3 x 13 x 7 x 4 x 2 = 2184
If it helps you then please mark it as brainliest!
