We know
[tex]\boxed{\sf Area=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(4x)=36[/tex]
[tex]\\ \sf\longmapsto 4x^2=36[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto x^2=9[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{9}[/tex]
[tex]\\ \sf\longmapsto x=3[/tex]
Breadth=3mLength=4(3)=12mTranslate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)
or
Answer:
The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].
Step-by-step explanation:
Vectorially speaking, the translation of a point can be defined by the following expression:
[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)
Where:
[tex]V(x,y)[/tex] - Original point.
[tex]V'(x,y)[/tex] - Translated point.
[tex]T(x,y)[/tex] - Translation vector.
If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:
[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]
[tex]A'(x,y) = (3, 0)[/tex]
[tex]B'(x,y) = (0,1) + (6, -4)[/tex]
[tex]B'(x,y) = (6, -3)[/tex]
[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]
[tex]C'(x,y) = (2, -3)[/tex]
The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].
The combined value of the ages of Mary, Kate and Tom is 26 years. What will be their age in total after 2 years?
Answer:
32
Step-by-step explanation:
they will each age two years, 3x2 is 6, add 6 to 26
Answer:
32
Step-by-step explanation:
they will each age two years, 3x2 is 6, add 6 to 26
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F + G) (2) =
4
5
9
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Answer:
9
Step-by-step explanation:
The ordered pair (2, 4) in the relation for function F tells you F(2) = 4.
The ordered pair (2, 5) in the relation for function G tells you G(2) = 5.
Then the sum is ...
(F+G)(2) = F(2) +G(2) = 4 +5
(F+G)(2) = 9
If the rate of inflation is 2.6% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.
p(t)=600(1.026)t
Find the current price of the item and the price 9 years from today.
Round your answers to the nearest dollar as necessary.
Answer:
The current price of the item is $600.
The price of the item 9 years from today will be of $756.
Step-by-step explanation:
Price of the item:
The price of the item, in dollars, after t years, is given by:
[tex]p(t) = 600(1.026)^t[/tex]
Current price of the item
This is p(0). So
[tex]p(0) = 600(1.026)^0 = 600[/tex]
The current price of the item is $600.
9 years from today.
This is p(9). So
[tex]p(9) = 600(1.026)^9 = 756[/tex]
The price of the item 9 years from today will be of $756.
according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2
Answer:
6
Step-by-step explanation:
First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.
Expanding, we get
(x³-3x+1)² = (x³-3x+1)(x³-3x+1)
= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1
= x^6 - 6x^4 + 2x³ +9x²-6x + 1
In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots
HELP ME WITH THIS MATHS QUESTION
PICTURE IS ATTACHED
Answer:
In picture.
Step-by-step explanation:
To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.
The picture below is the answer.
A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast (in ft/s) is the tip of his shadow moving when he is 45 feet from the pole
Answer:
25/3 ft/s
Step-by-step explanation:
Height of pole , h=15 ft
Height of man, h'=6 ft
Let BD=x
BE=y
DE=BE-BD=y-x
All right triangles are similar
When two triangles are similar then the ratio of their corresponding sides are equal.
Therefore,
[tex]\frac{AB}{CD}=\frac{BE}{DE}[/tex]
[tex]\frac{15}{6}=\frac{y}{y-x}[/tex]
[tex]\frac{5}{2}=\frac{y}{y-x}[/tex]
[tex]5y-5x=2y[/tex]
[tex]5y-2y=5x[/tex]
[tex]3y=5x[/tex]
[tex]y=\frac{5}{3}x[/tex]
Differentiate w.r.t t
[tex]\frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}[/tex]
We have dx/dt=5ft/s
Using the value
[tex]\frac{dy}{dt}=\frac{5}{3}(5)=\frac{25}{3}ft/s[/tex]
Hence, the tip of his shadow moving with a speed 25/3 ft/s when he is 45 feet from the pole.
Answer:
The tip pf the shadow is moving with speed 25/3 ft/s.
Step-by-step explanation:
height of pole = 15 ft
height of man = 6 ft
x = 45 ft
According to the diagram, dx/dt = 5 ft/s.
Now
[tex]\frac{y-x}{y}=\frac{6}{15}\\\\15 y - 15 x = 6 y \\\\y = \frac{5}{3} x\\\\\frac{dy}{dt} = \frac{5}{3}\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{5}{3}\times 5 =\frac{25}{3} ft/s[/tex]
Evaluate −3w − 6p for w=2 and p = −7
-3w-6p when w=2 and p=-7
-3(2)-6(-7)
= -6 + 42
= 36
Answer:
48
Step-by-step explanation:
-3w-6p when w=2 and p--7
you want to plug in the numbers to their letters
-3(2)-6(-7)
then you want to times the numbers.
-6-42
=48
f(x)= |2x+3|-5 G(x) = 7 find (f-g)(x)
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Answer:
(f -g)(x) = |2x +3| -12
Step-by-step explanation:
The difference of the functions is ...
(f -g)(x) = f(x) -g(x) = |2x +3| -5 -7
(f -g)(x) = |2x +3| -12
PLEASE HELP please I need this done now
The total cost of a truck rental, y, for x days, can be modeled by y = 35x + 25.
What is the rate of change for this function?
Answers
A- 35$
B-25$
C-60$
D-10$
Answer:
35
Step-by-step explanation:
y = 35x+23 is in the form
y = mx+b where m is the slope and b is the y intercept
The slope can also be called the rate of change
35 is the slope
Solve for x and simplify answer as much as possible
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]4=6+2x[/tex]
Flip the equation:
[tex]2x+6=4[/tex]
Subtract 6 from both sides:
[tex]3x+6-6=4-6[/tex]
[tex]2x=-2[/tex]
Divide both sides by 2:
[tex]2x/2=-2/2[/tex]
[tex]x=-1[/tex]
Answer:
x= -1
Step-by-step explanation:
firstly group the like terms
4-6=2x
-2=2x
divide both sides by 2
-2/2=2x/2
-1=x
therefore x is -1
14. Which property is shown by 3 + 2 = 2 + 3? (1 point)
O Commutative Property of Addition
O Identity Property of Addition
O Distributive Property
O Associative Property of Addition
Answer: Commutative Property of Addition
Explanation: The problem 3 + 2 = 2 + 3 demonstrates the commutative property of addition. In other words, the commutative property of addition says that changing the order of the addends does not change the sum.
For example here, we can easily see that the sum of 3 + 2,
which is 5, is equal to the sum of 2 + 3, which is also 5.
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
3 + 2 = 2 + 3It is commutative property of additionWhich of the following statements are correct? Select ALL that apply!
Select one or more:
O a. -1.430 = -1.43
O b. 2.36 < 2.362
O c.-1.142 < -1.241
O d.-2.33 > -2.29
O e. 2.575 < 2.59
O f. -2.25 -2.46
Identify the domain of the function shown in the graph.
A. -5
B. x> 0
C. 0
D. x is all real numbers.
What is the solution to 3×^2-2×+4=0
Answer:
this has no real solution.
only in the realm of complex and imaginary numbers.
x = 1/3 ± sqrt(11)i/3
Step-by-step explanation:
I read as the equation to be solved :
3x² - 2x + 4 = 0
the solution to such a quadratic equation is
x =(-b ± sqrt(b² - 4ac))/(2a)
in our case
a=3
b=-2
c=4
so,
x = (2 ± sqrt(4 - 48))/6 = (2 ± sqrt(-44))/6 =
= (2 ± sqrt(4×-11))/6 = (2 ± 2×sqrt(-11))/6 =
= (1 ± sqrt(11)×i)/3 = 1/3 ± sqrt(11)i/3
Simplify the expression. 8x^-10 y^'6 -2x^2y^-8 Write your answer without negative exponents.
Answer:
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]
Step-by-step explanation:
Given
[tex]8x^{-10}y^6 - 2x^2y^{-8}[/tex]
Required
Simplify
Rewrite as:
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6}{x^{10}} - \frac{2x^2}{y^8}[/tex]
Take LCM
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^6*y^8 - 2x^2 * x^{10}}{x^{10}y^8}[/tex]
Apply law of indices
[tex]8x^{-10}y^6 - 2x^2y^{-8} = \frac{8y^{14} - 2x^{12}}{x^{10}y^8}[/tex]
C=r(5-d)/y We need to solve for d.
Answer:
5-Cy/r = d
Step-by-step explanation:
C=r(5-d)/y
Multiply each side by y
Cy=r(5-d)/y *y
Cy=r(5-d)
Divide each side by r
Cy/r=r(5-d)/r
Cy/r=(5-d)
Subtract 5 from each side
Cy/r - 5 = 5-d-5
Cy/r - 5 = -d
Multiply by -1
-Cy/r + 5 = d
5-Cy/r = d
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]C=\dfrac{r(5-d)}{y}\\\\cy=r(5-d)\\\\5-d=\dfrac{cy}{r}\\\\-d=\dfrac{cy}{r-5}\\\\d=-\dfrac{cy}{r}+5\\\\d=5-\dfrac{cy}{r}[/tex]
The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm
Answer:
The volume is increasing at a rate of 33929.3 cubic millimeters per second.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this question:
We have to derivate V and r implicitly in function of time, so:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
The radius of a sphere is increasing at a rate of 3 mm/s.
This means that [tex]\frac{dr}{dt} = 3[/tex]
How fast is the volume increasing when the diameter is 60 mm?
Radius is half the diameter, so [tex]r = 30[/tex]. We have to find [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3[/tex]
The volume is increasing at a rate of 33929.3 cubic millimeters per second.
Please help due tomorrow
Answer:
10x8=80 that would be the area for the picture 14x11=154 for the boards area
A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)
Answer:
A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.
Step-by-step explanation:
bisects ∠EDG. Find the value of x
Answer:
where is the question? please attatch the angle
What is the slope of a line thal is perpendicular to the line 2y - 3x = 8?
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Answer:
-2/3
Step-by-step explanation:
The slope of the given line can be found by solving for y.
2y -3x = 8
2y = 3x +8 . . . . add 3x
y = 3/2x +4 . . . . divide by 2
The slope is the coefficient of x: 3/2. For the perpendicular line, the slope is the opposite reciprocal of this:
-1/(3/2) = -2/3
The slope of a perpendicular line is -2/3.
Matthew actually drew the 10 of hearts and the 3 of clubs. If he keeps those to one side and selects two more from the pack, what is the chance that he'll get a pair of 10s this time? As before, give your answer in its simplest form. 2nd Attempt: Probability of getting a pair of 10s
Log6^(4x-5)=Log6^(2x+1)
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Given
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Required
Solve for x
We have:
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Remove log6 from both sides
[tex](4x-5) = (2x+1)[/tex]
Collect like terms
[tex]4x - 2x = 5 + 1[/tex]
[tex]2x = 6[/tex]
Divide by 2
[tex]x = 3[/tex]
Develop the estimated regression equation that can be used to predict the price given the weight. Also report the standard error of the estimate, , and . The regression equation is (to 1 decimal) (to 4 decimals) (to 4 decimals) (to 4 decimals) Test for the significance of the relationship at the .05 level of significance. -value is (to 4 decimals). We _________ that the two variables are related. Did the estimated regression equation provide a good fit
Answer:
Following are the response to the given question:
Step-by-step explanation:
For question 1:
Following are the regression equation:
[tex]price = 2044.03 - 28.35 \ \ (weight)[/tex]
[tex]\sigma = 94.353\\\\R^2 = 0.7647\\\\R^2\ (adj.) = 0.75\\\\[/tex]
For question 2:
Test of connection importance at 5 percent significance:
[tex]p-value < 0.000001\\\\p-value< 0.05[/tex]
Two variables could be said to be connected.
For question 3:
[tex]R^2 = 0.7647[/tex]
The computed equations of the regression fit well.
What the distance between -6,2 -6,-15
Answer:
The answer is 17
Step-by-step explanation:
-15-2= -17
3 st Post Office charges for an ordinary telegram are sh 4 for the first 10 words and 40 cents for each extra word. Calculate the cost of sending this telegram: MR KAMAU ARRIVING AT 0630 EAST AFRICAN TIME ON BOARD KQ 46 INFORM THE WIFE
Answer:
The cost of sending the telegram is $6.
Step-by-step explanation:
Since 3 St. Post Office charges for an ordinary telegram are $ 4 for the first 10 words and 40 cents for each extra word, to calculate the cost of sending this telegram: MR KAMAU ARRIVING AT 0630 EAST AFRICAN TIME ON BOARD KQ 46 INFORM THE WIFE must perform the following calculation:
The telegram has 15 words.
4 + ((15 - 10) x 0.40) = X
4 + (5 x 0.40) = X
4 + 2 = X
6 = X
Therefore, the cost of sending the telegram is $ 6.
Determine la razón de la siguiente progresión geométrica: 81,27,9,3,1,....
Answer:
BẠN BỊ ĐIÊN À
Step-by-step explanation:
CÚT
what is the vertical change from point a to point b
what is the horizontal change from point a to point b
Answers:
Vertical change = 1Horizontal change = 2Rate of change = 0.5====================================================
Explanation:
Imagine that we have point A as a buoy in the water. So the horizontal line through 1 on the y axis is the water line. How much should the water line go up so that points A and B are on the same horizontal level? That would be 1 unit up. This is the vertical change. Another term for this is "rise".
After the water goes up, and A and B are on the same level, the question is now: how far to the right do we go from A to B? That would be 2 units. This is the horizontal change. Another term for this is "run".
Using those two values, we can compute the rate of change aka slope.
slope = rise/run = 1/2 = 0.5
So each time we go up 1 (rise) we move to the right 2 (run).
The slope is positive since we're moving uphill while moving to the right.
Rita earns scores of 70, 76, 86, 87, and 85 on her five chapter tests for a certain class and a grade of 85 on the dass project.
The overall average for the course is computed as follows: the average of the five chapter tests makes up 60% of the course
grade; the project accounts for 10% of the grade; and the final exam accounts for 30%. What scores can Rita earn on the final
exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90? Assume
that 100 is the highest score that can be earned on the final exam and that only whole-number scores are given.
To obtain a "B", Rita needs to score between and inclusive.
Answer:
To obtain a "B", Rita needs to score between 76.7 and 100.
Step-by-step explanation:
Chapter tests mean:
[tex]M = \frac{70 + 76 + 86 + 87 + 85}{5} = 80.8[/tex]
Grades:
80.8 worth 60% = 0.6
85 worth 10% = 0.1
x worth 0.3.
So her grade is:
[tex]G = 80.8*0.6 + 85*0.1 + 0.3x = 56.98 + 0.3x[/tex]
What scores can Rita earn on the final exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90?
G has to be greater than or equal to 80 and less than 90, so:
[tex]80 \leq G < 90[/tex]
Lower bound:
[tex]G \geq 80[/tex]
[tex]56.98 + 0.3x \geq 80[/tex]
[tex]0.3x \geq 80 - 56.98[/tex]
[tex]x \geq \frac{80 - 56.98}{0.3}[/tex]
[tex]x \geq 76.7[/tex]
Upper bound:
[tex]G < 90[/tex]
[tex]56.98 + 0.3x < 80[/tex]
[tex]0.3x < 90 - 56.98[/tex]
[tex]x < \frac{90 - 56.98}{0.3}[/tex]
[tex]x < 110[/tex]
Highest grade is 100, so:
To obtain a "B", Rita needs to score between 76.7 and 100.
