List the angle measures of △VWX in order from smallest to largest. Assume that t is a positive number.

The angles are 22.5°, 67.5° and 90°.

Let the smallest angle = x

Total angles in a triangle = 180°

One angle is three times the smallest angle. This will be 3x.

The third angle is 45 more than twice the smallest angle. This will be:

= (2 × x) + 45

= 2x + 45

The angles will be:

x + 2x + 45 + 3x = 180

6x + 45 = 180

Collect like terms

6x = 180 - 45

6x = 135

Divide

x = 135 / 6

x = 22.5°

Smallest angle = 22.5°

The other angles will be calculated by substitutibg 22.5° for x. This will be:

3x = 3 × 22.5 = 67.5°

Also, 2x + 45 = 2(22.5) + 45 = 90°

This illustrates the concept for angles in a triangle.

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Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared​

we have that

F=m*a

we have

m=30 kg

F=60 N

substitute in the formula

60=30*a

solve for a

a=60/30

a=2 m/s^2

therefore

Using the Pythagorean theorem, the distance between two points (x1, y1) and (x2, y2) is gotten as follows:

Since we have the two coordinates: (2, 8) and (-8, 2)

where:

(x1, y1)= (2, 8)

(x2, y2) = (-8, 2)

Therefore, the distance between them is:

Therefore, the distance between the two p is: 11.7

Correct option is: Option D

Hello. This is an exercise about polynomials.

In this specific question, we will see about the division of polynomials:

We have two polynomials:

• First: 2x

• Second: 6x²-10x

Now, we'll have to divide the first by the second. We have some ways to write this:

The third and fourth options are wrong because it divides the second polynomial by the first, while the question asks the first divided by the second.

Let's begin by identifying key information given to us:

To know if the vertex is the maximum or minimum point, we will follow this below:

Hence, the answer is B.(0,4); minimum

Answer:

D) 5 minus a number M

hope this helps!

Answer:

Yep. You got it right. Good job!

Step-by-step explanation:

The required Dimensions are 6'' x 8'' x 30'' , That is option A

In this problem, we have a population with a normal distribution with:

• mean μ = 85,

• standard deviation σ = 24.

We must compute the z-score for different samples.

The standard deviation of a sample with mean M and size n is:

The z-score of the sample is given by:

Using these formulas, we compute the z-score of each sample:

(a) M = 91, n = 4

(b) M = 91, n = 9

(c) M = 91, n = 16

(d) M = 91, n = 36

a. z = 0.5

b. z = 0.75

c. z = 1

d. z = 1.5

ANSWER

The cofunction of tan 36 degrees is cot 54 degrees

STEP-BY-STEP EXPLANATION

Given information

Co function of tan can be written below as

Therefore,

tan 36 = 0.7265

cot 54 = 0.7265

Hence, the cofunction of tan 36 is cot 54

Answer: We need to find the doubling time for population growth:

Population growth is given by

Where:

For the population to double, it implies that:

Therefore:

Solving for time "t" gives:

Notice that the number of students that got a grade below 80 is:

and the total number of students is:

Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:

Finally, we get that 7 represents the

of 20.

Answer:

Answer: 38.033

5.21 x 7.3

= 38.033

The decimal notation of percentage is the quotient of the percentage divided by 100.

So it follows that :

The answer is 1

The equation is

n + 2 = - 16 - 5n

By collecting like terms, we have

n + 5n = - 16 - 2

6n = - 18

Dividing both sides of the equation by 6, we have

6n/6 = - 18/6

n = - 3

It has only one solution

Answer:

[tex]x^{4}[/tex]

Step-by-step explanation:

Whenever it comes to the division of the same variable, we subtract their powers in order to get the correct answer:

[tex]x^{9}/x^{5}[/tex]
[tex]x^{9-5}[/tex]
[tex]x^{4}[/tex]

Answer:

A. (0, 3)

C. (1, 1.5)

Explanation:

A point is a solution to the system if it satisfies both inequalities.

So for each option, we get:

Replacing (x, y) = (0, 3)

y ≥ -2x + 3

3 ≥ -2(0) + 3

3 ≥ 3

y ≤ -x² - x + 4

3 ≤ -0² - 0 + 4

3 ≤ 4

Since both inequalities are satisfied, (0, 3) is a solution.

For (x, y) = (-1, 5)

y ≥ -2x + 3

5 ≥ -2(-1) + 3

5 ≥ 2 + 3

5 ≥ 5

y ≤ -x² - x + 4

5 ≤ -(-1)² - (-1) + 4

5 ≤ -1 + 1 + 4

5 ≤ 4

Since 5 is not lower than 4, (-1, 5) is not a solution

For (x, y) = (1, 1.5)

y ≥ -2x + 3

1.5 ≥ -2(1) + 3

1.5 ≥ -2 + 3

1.5 ≥ 1

y ≤ -x² - x + 4

1.5 ≤ -(1)² - (1) + 4

1.5 ≤ -1 - 1 + 4

1.5 ≤ 2

Since both inequalities are satisfied, (1, 1.5) is a solution.

Therefore, the answers are

A. (0, 3)

C. (1, 1.5)

Given:

Since it is given that triangles PQR and STR are congruent, the corresponding angles of the triangles are equal.

Hence,

Therefore, option D is correct.

Answer:

19

Explanation:

We know that the diagonals of a rectangle are always equal, therefore RT = SW.

So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;

to be a parallelogram we need to have the 2 pairs of sides to be parallel so the correct option is C

The 35% of 125 is computed as follows:

ANSWER

Exactly one solution.

EXPLANATION

We are given the equation:

-6(x + 7) = -4x - 2

To find the number of solutions, we have to solve for x:

-6x - 42 = -4x - 2

Collect like terms:

-6x + 4x = 42 - 2

-2x = 40

x = 40 / -2

x = -20

Therefore, the equation has exactly one solution.

The image of the point (1, 6) after the translation is (0, 4).

For the given question,

The image of point P(-3, 5) after a translation is P'(-4, 3).

In this, there is a shift of 1 units to the left of x axis and shift of 2 units up on the y axis.

Thus, do the same translation for the point (1, 6).

After translation image will be (0, 4)

Thus, image of the point (1, 6) after the translation is (0, 4).

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For the given right cylinder:

Radius = r = 4 in

Height = h = 12 in

The volume of the cylinder =

So, the answer will be the volume is 192π in^3

The 95% confidence interval (in minutes) for the population mean is of:

(2.55, 3.83).

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the parameters are described as follows:

The distribution is used when the standard deviation of the population is not known, only for the sample.

In the context of this problem, the values of the parameters are given as follows:

[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.

Then the lower bound of the confidence interval is calculated as follows:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]

The upper bound is calculated as follows:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]

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The slope = 3

Note that:

The slope - Intercept form of the equation of a line takes the form y = mx + c

where m is the slope and

c is the intercept

The given equation is:

6x - 2y = -6

The equation can be re-written as:

2y = 6x + 6

2y / 2 = 6x/2 + 6/2

y = 3x + 3

The slope, m = 3

The intercept, c = 3

We recall that the area of a triangle is defined by the product of the triangle's base times its height divided by 2.

So we notice that in our image, we know the height (6 cm), and we also know the base of the triangle (2 cm)

Therefore the triangles are is easily estimated via the formula:

Then the area is 6 square cm.

Answer:

1/4

Step-by-step explanation:

it can be simplified by dividing both the numerator and denominator with 9.

[tex] \displaystyle \large{ \sf{ \frac{9}{36}}} [/tex]

[tex]\displaystyle \large{ \sf{ \frac{9}{36} = \frac{ \cancel9}{ \cancel3 \cancel6} }}[/tex]

[tex]\displaystyle \large{ \bf{ = \frac{1}{4} }}[/tex]

simplest form is 1/4

The first step to solve this problem is to solve the substraction between the first two fractions:

We will have the following:

So, the equation in vertex form is:

And in standard form:

***Explanation***

We know that the quadratic expression in vertex form follows:

Where (h, k) is the vertex of the expression. Now, we know that the vertex is (2, -8), so we replace those values and we obtain:

Now, in order to determine "a" we must replace one point (That is not the vertex) in the expression and solve for "a", and we are told that the point (4, 3) is in one of the solutions, so:

Thus, the expression in vertex form is then:

And to determine the standard form, we simply expand the equation in vertex form: