PQRS is a parallelogram. Find the values of a and b. Solve for the value of c, if c=a+b.

Answer:

[tex]\large \boxed{\mathrm{B. \ 6}}[/tex]

Step-by-step explanation:

Length AB is similar to length DE.

Scale factor = DE/AB

Scale factor = 12/2

Scale factor = 6

The required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF which is the correct option (B).

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

Length AB is similar to length DE.

Here triangle ΔABC is dilated to form triangle ΔDEF

Length of the side DE = 12

Length of the side AB = 2

As we know scale factor is the ratio of sides in the original image and the image after dilation.

Scale factor = DE/AB

Substitute the values of the length of the side DE and AB,

Scale factor = 12/2

Apply the division operation, and we get

Scale factor = 6

Therefore, the required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF.

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Answer:

Musah's final point from the centre = 60.355 steps

Step-by-step explanation:

From the given information:

Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°

The sketch for this information can be seen in the attached file below.

How far west is Musah's final point from the centre?

In order to determine how far west  is Musah's,

Let d be the distance of how far;

Then d = QR + RS cos θ

In the North West direction,

cos θ = cos 45°

d = 25 + 50( cos 45°)

d = 25 + 50( [tex]\dfrac{1}{\sqrt{2}}[/tex] )

d = 25 + 50( 0.7071)

d =25 + 35.355

d = 60.355 steps

Musah's final point from the centre = 60.355 steps

Answer: The solution of these inequalities are similar because they begin at two, however they are different because in the first inequality two cannot be an answer hence the open circle ⭕️, but the second inequality can have two as a solution hence the closed circle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a parabola. If we plot the vertex and the focus, we see that the focus is below the vertex. What this tells us is that the parabola opens "upside down" since the parabola wraps itself around the focus. If it opens upside down, then the format for the equation is

[tex]4p(y-k)=-(x-h)^2[/tex]

where p is the distance between the vertex and the focus (4), h is the first coordinate of the vertex (0), and k is the second coordinate of the vertex (0). Filling in the formula then:

[tex]4(4)(y-0)=-(x-0)^2[/tex] which simplifies down to

[tex]16y=-x^2[/tex] and then finally,

[tex]y=-\frac{1}{16}x^2[/tex]

Answer:

A = 62.35 cm²

Step-by-step explanation:

Use the area formula A = [tex]\frac{\sqrt{3}a^2}{4}[/tex], where a is the side length.

Plug in the values:

A = [tex]\frac{\sqrt{3}(12^2)}{4}[/tex]

A = [tex]\frac{\sqrt{3}(144)}{4}[/tex]

A = 62.35 cm²

Hi there! :)

Answer:

[tex]\huge\boxed{\frac{1}{25}}[/tex]

When evaluating an expression with a negative exponent, the reciprocal will need to be taken. Therefore:

[tex]5^{-2} = \frac{1}{5^{2} } = \frac{1}{25}[/tex]

Answer:

x = 300

Step-by-step explanation:

of means multiply and is means equals

25% * x = 75

Change to decimal form

.25x = 75

Divide each side by .25

.25x/.25 = 75/.25

x = 300

Answer:

300

Step-by-step explanation:

Assume the unknown value is 'Y'

75 = 25% x Y

75 = 25/100 x Y

Multiplying both sides by 100 and dividing both sides of the equation by 25 we will arrive at:

Y = 3 x 100/25

Y = 300%

Answer: 75 is 25 percent of 300

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar and ratios of corresponding sides are equal, that is

[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values

[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

Answer:

The lateral area of the figure = 480 m²

The surface area = 720 m²

Step-by-step explanation:

By definition, we have;

The lateral area is the area of the vertically facing sides of or the area of the triangular faces of a pyramid

The surface area is the area of the entire surface = Lateral area + The other surface areas of the object

For a pyramid, the surface area =   Lateral area  + Area of base

The figure in the question is a pentagon based pyramid with five triangles on the sides

The lateral area of the figure = 5 × area of the 5 triangles = 5 × Base × Height

The lateral area of the figure = 5 × 12 × 8 = 480 m²

The lateral area of the figure = 480 m²

The surface area = Area of the base + Lateral surface area

Area of the regular pentagon base = 1/2 × Perimeter of the pentagon × Apothem

Perimeter of the pentagon = 5 × 12 = 60 m

Apothem = Perpendicular distance from the pentagon's side to the center = 8.3 m

∴ Area of the regular pentagon base = 1/2 × 60 × 8 = 240 m²

∴ The surface area = 240 +480 =720 m²

The surface area = 720 m²

Answer:

  d) m - 2 l = - 6; m - l = 5

Step-by-step explanation:

Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...

  m = 2l -6

Subtracting 2l from both sides gives the equation ...

  m -2l = -6 . . . . . matches choice D

Answer:

y=-2x+4

x | y

0 | 4

2 | 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

the x after the 10 is literally just 1

so 10 x 1  =10

-10 + 10 = 0

Answer:

The positive integer factors of 15552 that are perfect squares are;

1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184

Step-by-step explanation:

The positive integer factors of 15552 are;

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 864, 972, 1296, 1728, 1944, 2592, 3888, 5184, 7776, 15552

The perfect square integers are;

1 = 1 × 1

4 = 2 × 2

9 = 3 × 3

16 = 4 × 4

36 = 6 × 6

64 = 8 × 8

91 = 9 × 9

144 = 12 × 12

324 = 18 × 18

576 = 24 × 24

1296 = 36 × 36

5184 = 72 × 72

Therefore, the positive integer factors of 15552 that are perfect squares are;

1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184.

Complete question:

One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.

Answer:

111 students

Step-by-step explanation:

Given the following :

Margin of Error (E) = 0.28

Population standard deviation (sd) = 1.5

Recall:

Margin of Error(E) = Z * (sd/√n)

Taking a confidence interval of 95%

The Z value at a 95% confidence interval is 1.96

Plugging our values, we have :

Margin of Error(E) = Z * (sd/√n)

0.28 = 1.96 * (1.5/√n)

0.28 = 2.94 / √n

√n × 0.28 = 2.94

√n = 2.94 / 0.28

√n = 10.5

Square both sides to obtain n

n = 10.5^2

n = 110.25

Answer:

english i think u need hekp

Answer:  4/7

Step-by-step explanation:

the number of chairs = 7

the number of cushions = 11

Every chair has at least 1 cushion. There are 7 chairs so 7 cushions are used.

There is a total of 11 cushions and 7 cushions are already distributed to the chairs so there are 4 chairs with a 2nd cushion.

Chairs with 2 cushions ÷ Total chairs = 4/7

Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

Area = 6.76 cm²

To find the radius substitute the value of the area into the above formula and solve for the radius

That's

[tex]6.76 = \pi \: {r}^{2} [/tex]

Divide both sides by π

We have

[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]

r = 1.46689291

We have the final answer as

radius = 1.47 cm

Hope this helps you

Answer:

If we have a system of linear equations:

y = a*x + b

y = c*x + d

And the graphs of the equations are the same line, this means that both lines have the same equation, then:

a = c and b = d.

Then we have only one equation (but repeated) and two variables, then we have infinite solutions for our system.

Another way to see this is:

When we have a system of linear equations, the solution is the point where the lines intersect.

But if both lines are the same line, then the lines intersect in infinite points, then we have infinite solutions.

Answer:

0.02

Step-by-step explanation:

Answer:

.02

Step-by-step explanation:

The first four terms of the given sequence are 18, 10, 6, and 4 respectively.

A sequence is an ordered list object which related and connected by a common value.

There are many sequences. They are Arithmetic sequence, Geometric sequence, and so on.

It is given that,

The first term of the sequence is a1 = 18

And the terms of the sequence are related by,

a(n + 1) = (2 + an)/2

For n = 1;

a(1 + 1) = (2 + a1)/2

⇒ a2 = (2 + 18)/2 = 10

For n = 2;

a(2 + 1) = (2 + a2)/2

⇒ a3 = (2 + 10)/2 = 6

For n = 3;

a(3 + 1) = (2 + a3)/2

⇒ a4 = (2 + 6)/2 = 4

Thus, the first four terms of the given sequence are a1 = 18, a2 = 10, a3 = 6, and a4 = 4.

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Answer:

Step-by-step explanation:

To evaluate the expression substitute the values of a , b , c and d into the above expression

a = - 9

b = - 7

c = 9

d = 3

So we have

2cd + 3ab = 2(9)(3) + 3(-9)(-7)

= 2(27) + 3( 63)

= 54 + 189

We have the final answer as

Hope this helps you

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          Hi my lil bunny!

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A) Let's solve for x.  [tex]2x + 3y = 40[/tex]

Step 1: Add -3y to both sides.

[tex]2x + 3y + -3y = 40 + -3y[/tex]

[tex]2x = -3y + 40[/tex]

Step 2: Divide both sides by 2.

[tex]\frac{2x}{2} = \frac{-3y + 40}{2}[/tex]

[tex]x = \frac{-3}{2} y + 20[/tex]

Answer : [tex]\frac{-3}{2} y + 20[/tex]

~~~~~~~~~~~~~~~~~

B) Let's solve for x. [tex]5x + 2y = 30[/tex]

Step 1: Add -2y to both sides.

[tex]5x + 2y + -2y = 30 + -2y[/tex]

[tex]5x = -2y + 30[/tex]

Step 2: Divide both sides by 5.

[tex]\frac{5x}{5} = \frac{-2y + 30}{5}[/tex]

[tex]x = \frac{-2}{5} y + 6[/tex]

Answer : [tex]\frac{-2}{5} y + 6[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

[tex] x(x {}^{2} + xy + y {}^{2})[/tex]

Step-by-step explanation:

[tex]x {}^{3} + x {}^{2}y + xy {}^{2} = x(x {}^{2} + xy + y {}^{2})[/tex]

Hope this helps ;) ❤❤❤

Answer:

12.57

Step-by-step explanation:

The formula to solve the circumference of a circle is:

2 x PI x R (radius)

=> 2 x PI x 2

=> 4 PI or 12.57

Answer:

y² + x²

Step-by-step explanation:

Given

(y + x)² - 2xy ← expand (y + x)² using FOIL

= y² + 2xy + x² - 2xy ← collect like terms

= y² + x²

Ans2x + 2y -2xy

Step-by-step explanation:

First You need to distribute 2 to both x and y. 2x + 2y-2xy

Answer:

$11,280

Step-by-step explanation:

Plug in 150 as p into the equation to solve for the cost, C:

C = 30 + 75p

C = 30 + 75(150)

C = 30 + 11,250

C = 11,280

= $11,280

Answer:

There are seven seventh roots of unity, e2πki7 , all on the unit circle, r=1 above.

The first one is at θ=2π7=360∘7=5137 ∘ , and there are others at 4π7,6π7,8π7,10π7,12π7 and of course at 0 radians, i.e. unity itself.

How to find?

There are 4 fourth roots of unity and they are 1, i,−1 and−i

Each of the roots of unity can be found by changing the value of k k k in the expression e 2 k π i / n e^{2k\pi i/n} e2kπi/n. By Euler's formula, e 2 π i = cos ⁡ ( 2 π ) + i sin ⁡ ( 2 π ) = 1.

Answer:

1.417

Step-by-step explanation:

102/72=1.417

Answer:

t=0.64

Step-by-step explanation:

h = -16t^2 +4t +4

We want h =0 since it is hitting the ground

0 = -16t^2 +4t +4

Using the quadratic formula

a = -16  b = 4  c=4

-b ± sqrt( b^2 -4ac)

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

         2a

-4 ± sqrt( 4^2 -4(-16)4)

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

         2(-16)

-4 ± sqrt( 16+ 256)

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

         -32

-4 ± sqrt( 272)

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

         -32

-4 ± sqrt( 16*17)

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

         -32

-4 ± sqrt( 16) sqrt(17)

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

         -32

-4 ± 4 sqrt(17)

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

         -32

Divide by -4

1 ±  sqrt(17)

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

         8

To the nearest hundredth

t=-0.39

t=0.64

Since time cannot be negative

t=0.64

Answer:

0.64  

Step-by-step explanation:

0 = -16t^2 + 4t + 4

-4(4t^2 - t -1) = 0

t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)

t = 0.64, -0.39

answer is 0.64

Answer:

Answers

product, and assign a number to each person. ... 0.82. 12–13. 9. 0.18. 1.00. Total. 50. 1.00. F requency. 0. 1. 2. 3. 4. 5. 6. 7. 8 ... 3.12 (a) x = 25661.3333, ˜x = 25514.5 (b) Skewed ... N(8.25, 0.0002857).

Answer:

the answer is c

Step-by-step explanation:

i just took the test