The height of a triangle is 4 times its base. If the triangle has an area of 162ft^2, find the length of the base and the height.

As ray UW bisects ( divides the angles into two equal parts )

WUT = WUV

6x - 10° = 4x + 6°

6x - 4x = 6° + 10°

2x = 16°

x = 16° ÷ 2 = 8°

Putting the value of x in the Angle WUT

6 × 8° - 10° = 48° - 10° = 38°

Answer:

33 cm²

Step-by-step explanation:

Formula

Solving

Answer:

33 cm²

Step-by-step explanation:

Since the pyramid has a square base, the area of each of the triangular sides will be the same.

Therefore, to calculate the total surface area, find the area of one triangle, multiply it by 4, then add it to the area of the square base.

Formulae

Area of a square = x³  (where x is the side length)

Area of a triangle = 1/2 × base × height

Calculation

area of the square base = 3² = 3 × 3 = 9 cm²

area of one triangle = 1/2 × 3 × 4 = 6 cm²

Solution

Total area = area of the square base + 4 × area of one triangle

                 = 9 + (4 × 6)

                 = 9 + 24

                 = 33 cm²

Answer:

17 meters

Step-by-step explanation:

|\ angle = 60 degrees here of triangle
|   \              <-- digitaly drawn triangle
|___\

cirlcle diameter is 60 meters, since pillar is at the center then the distance of the pillar to the edge of the circlular meadow is (60/2) 30 meters.

30 meters is opposite of the angle.

The height of the pillar is adjacent to the angle so use tangent to solve

Tan(60) = 30/x

Tan(60) = 1.7; make sure that calculator is in degrees and not in radians to not get an incorrect value

1.7 = 30/x --> 1.7x = 30

x = 30/1.7

x = 17.3205 meters

using 2 significant figures gives us 17 meters

The equation that represents the amount saved by Alyssa after tt weeks is AA = 100 + $7tt

The equation that represents the amount saved by Colton after tt weeks is CC = $55 + $10tt

The amount they would have when they have same amount of money is $205.

The total amount saved: inital amount + (amount saved per week x total number of weeks

AA = 100 + $7tt

CC = $55 + $10tt

$55 + $10tt = 100 + $7tt

Combine similar terms and solve for tt

100 - 55 = 10tt - 7tt

45 = 3tt

tt = 15 weeks

100 + $7(15) = $205

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The growth of the town is an illustration of exponential growth function

The population of the town in 15 years is 125651

The given parameters are:

An exponential growth function is represented as:

y = a * (1 + r)^t

So, we have:

y =75000 * (1 + 3.5%)^15

Evaluate

y =125651

Hence, the population in 15 years is 125651

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Answer:

Option D

Step-by-step explanation:

I am taking a guess here, but since the volume of the rectangle part is 594, and it is sort of a similar size as the top part, then I assume it is D.

Let me know how it goes.

Step-by-step explanation:

Only the top player with the highest grade can be considered as MVP on the winning team.You can still be considered MVP even if you have less than 10 grade as long as you have the highest grade and your team won the matchYou can only considered MVP-loss if you have the highest grade and you qualify for a gold medalMedals for the winning teamBest case scenario: 1 MVP, 4 GoldWorst case scenario: 1 MVP, 2 Silver, 2 BronzeMedals for the losing teamBest case scenario: 1 MVP Loss, 1 Gold, 2 Silver, 1 BronzeWorst case scenario: 5 Bronze

Answer:

160 fluid ounces

Step-by-step explanation:

There are 16 ounces in one pint, therefore multiply the number of pints by 16 to get your answer.

16 * 10 = 160

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Answer:

Answer:

x= -6, -2

Step-by-step explanation:

Answer:

x=-6, x=-2

Step-by-step explanation:

Answer:

2.71

Step-by-step explanation:

Using this formula: Volume= 4 over 3 * π * r cubed.
then do R=(3V4π)⅓=(3·83.54·π)⅓≈2.71144
2.71144 rounded to the nearest 10 is 2.71

Maria and Sheila total marks are illustrations of proportions

The total marks obtained by both is 156

The given parameters are:

Sheila = 96 marks

2/5 of Maria's marks = 1/4 of Sheila's marks

The second highlight above means that:

2/5 * Maria = 1/4 * 96

Multiply both sides by 5/2

Maria = 1/4 * 96 * 5/2

Evaluate the product

Maria = 60

Their total mark is then calculated as:

Total = Sheila + Mark

This gives

Total = 96 + 60

Evaluate the sum

Total = 156

Hence, the total marks obtained by both is 156

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Answer: Times it

Step-by-step explanation:

Answer:

90 square feet

Step-by-step explanation:

area of this figure = area of 1 rectangle + area of 2nd rectangle

= L×B + l × b

= 18 × 3 + 12 × 3

= 54 + 36

= 90 feet²

Answer:

[tex]\huge{\boxed{\bf\:1.79 * p}[/tex]

Step-by-step explanation:

Given,

If pounds of peaches = p, then,

Cost of p pounds of peaches

= Cost of 1 pound × p pounds of peaches (p)

= 1.79 × p

[tex]\rule{150pt}{2pt}[/tex]

Answer:

4) a = 6

5) m = 1

Step-by-step explanation:

4) use FOIL, First Inside Outside Last, when you cross multiply.

[tex]\frac{a+4}{a-1} =\frac{a-2}{a-4}[/tex]

[tex](a+4)(a-4) = (a-1)(a-2)[/tex]

I'm going to do the left side first.

[tex](a+4)(a-4)\\a^2-4a+4a-16\\a^2-16[/tex]

Now I'm going to do the right side.

[tex](a-1)(a-2)\\a^2-2a-1a+2\\a^2-3a+2[/tex]

Next I'm going to rewrite back as the equation and solve for a.

[tex]a^2 - 16 = a^2 -3a +2\\a^2 - a^2 -16 = a^2-a^2-3a+2\\-16-2=-3a+2-2\\-18=-3a\\-18/-3=-3a/-3\\a=6[/tex]

5) I'm going to use distributive propoerty when I cross multiply. Then I will setup an equation like number 4 and solve for m.

[tex]\frac{5m-2}{3}=\frac{8-3m}{5} \\[/tex]

[tex]5(5m-2)=3(8-3m)\\25m-10=24-9m\\25m+9m-10=24-9m+9m\\34m-10=24\\34m-10+10=24+10\\34m=34\\34m/34=34/34\\m=1[/tex]

Answer:

Pierre has  £ 146 and

Alex has  £ 106

Step-by-step explanation:

Let the money with Pierre be = p

Let the money with Alex = a

If Pierre gave Alex £20, they would have the same amount.

So, we should subtract £ 20 from p and add £ 20 to a

p - 20 = a + 20

     p    = a + 20 + 20

 p    = a + 40 ----------------(I)

If Alex gave Pierre £22, then Pierre would have twice as much as Alex.

p + 22 = 2*(a -22)

 p + 22 = 2a - 44      

         p  = 2a - 44 - 22

         p = 2a - 66

p -2a    = - 66   -----------------(II)

Substitute p = a + 40 in equation (II)

a + 40 - 2a = -66

 a - 2a + 40 = -66

     -a            = - 66 - 40

              -a  = - 106

      Multiply both sides by (-1)

[tex]\boxed{a = \£ \ 106}[/tex]

Substitute a = 106 in equation (I)

p = 106 + 40

[tex]\boxed{p = \£ 146}[/tex]

Answer:

53

Step-by-step explanation:

You get the perimeter by adding up all of the sides. I added them up and got 53

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Complementary angles add to 90 degrees, so the measure of its complement is 90-88=2 degrees.

Supplementary angles add to 180 degrees, so the measure of its supplement is 180-88=92 degrees.

Answer:

15 percent of 20 is 3. so there are 3 boys and 17 girls in the class.

Step-by-step explanation:

Answer:

863432

Step-by-step explanation:

Add all numbers You will get answer

Answer:

863432.00

Step-by-step explanation:

800000

60000

3000

400

30

2

--------------

863432

_______

The rule y = -3 - x is an illustration of a linear equation

The points on the coordinate plane with the rule y = -3 - x are (0,-3), (1,-4) and (2,-5)

The rule of the points is given as:

y = -3 - x

When x = 0, we have:

y = -3 - 0

y = -3

When x = 1, we have:

y = -3 - 1

y = -4

When x = 2, we have:

y = -3 - 2

y = -5

From the above computation, we have the following points

(0,-3), (1,-4) and (2,-5)

Hence, the points on the coordinate plane with the rule y = -3 - x are (0,-3), (1,-4) and (2,-5)

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Answer:

  $42,782.40

Step-by-step explanation:

You want to know how much more Glados paid than Shaq on a 30-year mortgage if their monthly payments were $755.99 and $637.15, respectively.

Each month, Glados paid this amount more:

  $755.99 -637.15 = $118.84

Over the 360-month life of the 30-year loan, this excess amount adds up to ...

  360 × $118.84 = $42,782.40

Glados pays $42,782.40 more than Shaq for the same loan amount.

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Answer:

197

Step-by-step explanation:

to solve Hypotenuse:

a^2+b^2=c^2

Plug in:

28^2+195^2=c^2

Solve:

784+38025=c^2

38809=c^2

sqrt 38809=sqrt c^2

c=191

I hope it helps!!!

Answer:

can you clear more I don't understand

The water of the cylinder cannot fill the container, since the cylinder has less volume. Lastly, there is no apparent mistakes.

The rectangular container ([tex]V_{R}[/tex]), in cubic inches, is full whether its volume is equal to the volume of the cylinder ([tex]V_{C}[/tex]), in cubic inches. The volume formulae for both containers are described below:

[tex]V_{R} = w\cdot l \cdot h[/tex]   (1)

Where:

[tex]V_{C} = \pi\cdot r^{2}\cdot h[/tex]   (2)

Where:

Now we proceed to determine the volume of each figure:

[tex]V_{R} = (3.6\,in)\cdot (3.6\,in)\cdot (5.3\,in)[/tex]

[tex]V_{R} = 68.688\,in^{3}[/tex]

[tex]V_{C} = \pi\cdot (1.8\,in)^{2}\cdot (5.3\,in)[/tex]

[tex]V_{C} \approx 53.947\,in^{3}[/tex]

The volume of the water in the cylinder is approximately 53.947 cubic inches. The water of the cylinder cannot fill the container, since the cylinder has less volume. Lastly, there is no apparent mistakes. [tex]\blacksquare[/tex]

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[tex] \huge\boxed { \frak{Answer : }}[/tex]

Given :

[tex] \: \: \: [/tex]

[tex] \: \: \: [/tex]

We Have To Find The Value Of " b ".

[tex] \: \: \: [/tex]

[tex] \: \: [/tex]

Now , Put the given value of x & y in the above eqn ~.

[tex] \: \: [/tex]

[tex] \sf \large \: \: \: \: ⇝5x + by = 17[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: \: \: \: ⇝5( - 3) + b(8) = 17[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: \: \: \: ⇝ - 15 + 8b = 17[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: \: \: \: ⇝8b = 17 + 15[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: \: \: \: ⇝8b = 32[/tex]

[tex] \: \: [/tex]

[tex]\sf \large \: \: \: \: ⇝b = \cancel\frac{32}{8} [/tex]

[tex] \: \: [/tex]

[tex] \boxed{\sf \large \: \: \: \: \underline{ \: \: ⇝b = 4 \: \: \: \: }}[/tex]

[tex] \: \: [/tex]

Hope Helps!:)

The value of the coefficient b in the linear equation 5x +by =17 is -4

The pair of values are given as:

(x,y) = (-3,-8)

The equation is given as:

5x +by =17

Substitute values for x and y in the equation

-5 * 3 - 8 * b =17

Evaluate the product

-15 - 8b =17

Add 15 to both sides

-8b = 32

Divide both sides by -8

b = -4

Hence, the value of the coefficient b is -4

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The sequence Tn = an + b is an arithmetic sequence.

b represents the first term, and a represents the common difference

The general term is given as:

Tn = an + b

The above term is an arithmetic sequence.

An arithmetic sequence is represented as:

Tn = T1 + (n - 1)d

Where T1 represents the first term, and d represents the common difference

By comparing Tn = an + b and Tn = T1 + (n - 1)d, we have:

b = T1

a = d

This means that b represents the first term, and a represents the common difference

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Answer: 170

Step-by-step explanation: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.