write an equivalent expression

We will investigtate the application of scale factors to re-size any image or figure.

The figure at hand is described as a triangle. Every triangle has two distinct side lengths namely:

The original side-length for each of the distinct sides is given as follows:

We are to re-size the original triangle as per the scale factor given:

A general rule for re-sizing any figure either enlarging or shrinking can be given by the numerical value of scale factor as follows:

The scale factor given is expressed as a fraction (1/4). This lies in the third category. Hence, we will be reducing the size of the original triangle.

By re-sizing any figure we apply the scale factor to every distinct side-length of the figure. For the case of triangle these side lengths are base and height. The general formulation used while re-sizing is:

We will use the above relation for each of the side-lengths of a triangle as follows:

Therefore the base of the reduced triangle would be:

9514 1404 393

Answer:

Step-by-step explanation:

1) Divide both sides by the coefficient of x.

  x = (7.2/(-14/9))/((-108/35)/(-2/3))

  x = -1

__

2) Multiply both sides by the factor x is being divided by.

  x = (-3.18/5.3)/((-20/3)/(-2))

  x = -2

_____

Your calculator can help you with this.

Answer:

x + (4x-20) = 180

by linear pair

therefore x= 70

Applying the definition of linear pair, the value of x is: D. 40.

Therefore:

x + (4x - 20°) = 180°

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 40

Therefore, applying the definition of linear pair, the value of x is: D. 40.

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This is the same question as 17042785 (the question number in the site URL), with the exception of using the other identity,

\(\sin^2x=\dfrac{1-\cos(2x)}2\)

We have

\(2\sin^4(2x)=2(\sin^2(2x))^2=2\left(\dfrac{1-\cos(4x)}2\right)^2=\dfrac12(1-\cos(4x))^2\)

Expand the binomial:

\(2\sin^4(2x)=\dfrac12(1-2\cos(4x)+\cos^2(4x))\)

Using the identity in the previous question,

\(\cos^2x=\dfrac{1+\cos(2x)}2\)

we get

\(\cos^2(4x)=\dfrac{1+\cos(8x)}2\)

So,

\(2\sin^4(2x)=\dfrac12\left(1-2\cos(4x)+\dfrac{1+\cos(8x)}2\right)\)

\(2\sin^4(2x)=\dfrac14\left(3-4\cos(4x)+\cos(8x)\right)\)

Answer: 2 = |x − 47|

Step-by-step explanation:The total weight of the container and the nuts is x ounces. The desired weight of the container and the nuts is (45 + 2), or 47 ounces. The absolute error allowed is 2 ounces.

absolute error = |actual weight − desired weight|

Substituting the values, the equation obtained is 2 = |x − 47|.

(a) The probability that a point chosen randomly inside the rectangle is in the square is 0.6.

(b) The probability that a point chosen randomly inside the rectangle is outside the square is 0.4.

The probability that a point chosen randomly inside the rectangle is in each given shape is calculated as follows;

The area of the triangle is calculated as follows;

area = ¹/₂ x base x height

area = ¹/₂ x 4 x 5

area = 10 sq.units

The area of the rectangle is calculated as follows;

area = 4 x 4

area = 16 sq.units

The probability that a point chosen randomly inside the rectangle is in the square is calculated as;

P = outcome / total possible outcome

P = ( 10 ) / 16

P = 0.625 ≈ 0.6

The probability that a point chosen randomly inside the rectangle is outside the square;

P = 1 - p(inside)

P = 1 - 0.6

P = 0.4

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To find the equation of a line that passes through the points;

(10, 2) and (2, -2)

we will use the formula;

From the question;

x₁ = 10 y₁=2 x₂ = 2 y₂ = -2

substiuting the above values into the formula;

Then we will go ahead and simplifies

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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The solution to the arithmetic operations by using the PEMDAS method is -336.5

There are various phases to solving arithmetic operations, whether they are simple calculations using only fundamental operations like addition and subtraction or more difficult issues requiring the use of several operations and the application of more sophisticated mathematical ideas.

Using the PEMDAS approach to solving the given arithmetic operations, we have:

= 9 + 10 + 9 - 23 × 30 - 5

= 9 + 10 + 9 - 690 - 5

= 28 - 695

=  - 667

In addition to that, we are to divide the above answer by 2, then subtract 3 from the answer;

i.e.

= - 667/2 - 3

= -333.5 - 3

= -336.5

Therefore, the solution to the arithmetic operations by using the PEMDAS method is -336.5.

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Answer:  

y = x - 3

y = -5x +2

Step-by-step explanation:  for The "missing" coefficient of x (m in the y=mx+b format) is an implied +1. So the slope is "up-one & over one." y-intercept is -3

y = -5x +2   The slope is -5 so "down 5 & over 1" on the graph, The y-intercept is +2

Answer:

Step-by-step explanation:

1 semester = 4474

8 semester = 8* 4474                    35792

1 semester books = 389

8 semester books = 8* 389             3112

Total                                                38904  

If he is going to pay this off in 10 years, he would have to have an increase of 3890.40 (after all income taxes) to pay it off. Fewer years would mean dividing by the number of years.

So for 8 years for example, he would need 4863 every year.

That number is obtained by dividing 38904 / 8

In 6 years he would need

38904/6 = 6484 extra dollars.        

Answer:

Answer is C. $11,700

Step-by-step explanation:

The surface area of the two hemispheres combined is 100π square meters, and the volume of the two hemispheres combined is (500/3)π cubic meters.

The circumference of a great circle on a sphere is given by the formula C = 2πr, where r is the radius of the sphere.

In this case, we are given that the circumference of the great circle is 10π meters, so we can set up an equation:

10π = 2πr

Dividing both sides by 2π, we get:

r = 5

So the radius of the sphere is 5 meters.

When the sphere is cut in half, we get two equal hemispheres. The surface area of a closed hemisphere is given by the formula A = 2πr^2, where r is the radius of the hemisphere.

Since we are dealing with a radius of 5 meters, the surface area of one hemisphere is:

A = 2π(5^2) = 50π

Therefore, the surface area of the two hemispheres combined is:

2A = 2(50π) = 100π

The volume of a closed hemisphere is given by the formula V = (2/3)πr^3. Again, since we are dealing with a radius of 5 meters, the volume of one hemisphere is:

V = (2/3)π(5^3) = (2/3)π125 = (250/3)π

Therefore, the volume of the two hemispheres combined is:

2V = 2(250/3)π = (500/3)π

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Answer:

A

Step-by-step explanation:

they are complementary, they add to 90

The slope of the line passing through given points is 5/7

We know that the slope is the ratio of the change in y-values to the change in x-values.

We use slope formula,

m = (y2 - y1)/(x2 - x1)

For pair of points (1, 3) and (8, 8),

m1 = (8 - 3)/(8 - 1)

m1 = 5/7

For pair of points (8, 8)  and (15, 13),

m2 = (13 - 8)/(15 - 8)

m2 = 5/7

For pair of points (22,18)  and (29, 23),

m3 = (23 - 18)/(29 - 22)

m3 = 5/7

For pair of points (15, 13)  and (22, 18),

m4 = (18 - 13)/(22 - 15)

m4 = 5/7

Since the rate of change of output values to the input values is constant i.e., 5/7, the slope of the line is 5/7

Therefore, the slope of the line passing through given points is 5/7

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Answer:

proportional

Step-by-step explanation:

your going up by an even number at a steady pace in a straight line

Answer: c.)2 g/ml is the correct answer.

Answer:

39.8

Step-by-step explanation:

5 + 25 = 30

3.14 * 2.5^2 ( divide it in two since its a semi circle)

add that result with 30

Answer:

D. n = 10 or 20 they have the same probability

Responder:

1

Explicación paso a paso:

cuando una variable no tiene exponente, el grado siempre es uno. Ej: 8x es lo mismo que 8x elevado a 1

Answer: r = -2.4

Step-by-step explanation:

Simplifying 6r + 4 = r + -8 Reorder the terms: 4 + 6r = r + -8 Reorder the terms: 4 + 6r = -8 + r Solving 4 + 6r = -8 + r Solving for variable 'r'. -8 + -4 = -12

5r = -12

Answer:

C 835Which of the following is equal to the expression below

Answer:

Move 5 decimal places to the right. 231,000. If it was 10^-5, you would have to move 5 decimal places to the left.

Answer:

\(y - 4 = - 3(x - 2)\)

Answer:

$620.30

Step-by-step explanation:

We multiply 593.59 by .045 to get the amount we add to the original price. This gives us 620.30

Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

\(H_0: p = 0.4\)

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

\(H_1: p > 0.4\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that \(\mu = 0.4, \sigma = \sqrt{0.4*0.6}\)

Random sample of 15 adults, 8 favor capital punishment.

This means that \(n = 15, X = \frac{8}{15} = 0.5333\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}\)

\(z = 1.05\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Answer:

Step-by-step explanation:

Gallons, 1, 2

Quarts, 4, 8

Pints, 8, 16

Cups, 16, 32

Fluid ounces, 128, 256

Dude, it's conversation rates, you could have just looked up gallons to quarts etc.

Answer:

m=4

Step-by-step explanation:

First subtract 5 from 2m and 13. This gives you 2m=8. Then divide by 2 on both sides. This gives you m=4

Answer:

m=4

Step-by-step explanation:hope it helps

5-13=2m+5-5

2/2m=8/2

m=4

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:

40°

Step-by-step explanation:

<CAB=70°

<ABC=70°

<ACB+ <CAB+ <ABC=180(sum of angles in a triangle)

<ACB +70+70=180

<ACB+140=180

<ACB=180-140

<ACB=40°