I need help on this problem, it’s from my act prep guide

-7(w - 4) + 3w - 27

Expand

-7w + 28 + 3w - 27

Simplify like terms

-7w + 3w + 28 - 27

Result

-4w + 1

The probability that the test-taker doesn't use drugs is the ratio of the number of people who take drugs to the total number of people. Hence the probability that the test-taker doesn't take drug is

= 194/450

= 0.4311

2.

The triangles that cannot be proved congruent are the triangles in option D. We are not told that the other side is congruent to the corresponding side of the other triangle.

To prove they are congruent, we need to know the other side is congruent and prove this using the SSS postulate.

In the other cases, we can be proved they are congruent by:

• Case A ---> SAS postulate.

• Case B ---> ASA postulate.

• Case C ---> SSS postulate (the triangles share a common side)

In summary, we only have that the triangles in D cannot be proved congruent since we have two corresponding congruent sides, and one angle (vertical angle) to be congruent corresponding parts. It would be an SSA method. However, this method is not Universal, and it is not enough to demonstrate they are congruent.

In order to plot an ordered pair into the cartesian plane, we need to use the first coordinate in the x-axis and the second coordinate in the y-axis.

Then, we draw the point that has these coordinates in the plane.

For example, plotting the point (2, 3), we have:

Now, plotting the points (4, 3) and (3, 1) in the plane, we have:

rhombus STUV is located at S(-5, 4), T (-1, 5), U(-2, 1), and V(-6, 0). If STUV is translated along the rule (x, y) (x + 7 , y - 8). in which quadrant will the new rhombus be located​

we have that

the rule of the translation is

7 units at right and 8 units down

Verify each ordered pair

S(-5,4) -------> S'(-5+7,4-8) ------> S'(2,-4) (IV quadrant)

T(-1,5) ------> T'(-1+7,5-8) -----> T'(6,-3) (IV quadrant)

U(-2,1) -----> U'(5,-7) (IV quadrant)

V(-6,0) ----> V'(1,-8) (IV quadrant)

therefore

Answer:

07:45 pm

Explanation:

Steven landed in Orlando after the sum of the following time

3 hours and 45 minutes

2 hours and 30 minutes

1 hour and 30 minutes

If we add the hours and the minutes, we get:

3 hours + 2 hours + 1 hour = 6 hours

45 minutes + 30 minutes + 30 minutes = 105 minutes

But 1 hour = 60 minutes, so

6 hours and 105 minutes = 7 hours and 45 minutes

because

105 - 60 = 45

Since the flight left Boston at 12:00 pm, it was 07:45 pm when Steven landed in Orlando.

We are asked to solve the following system of equations via the addition method:

x + 2 y = - 2

6 x + 3 y = - 30

so via the addition method we will try to eliminate one of the variables by multiplying for the appropriate factor that would ease tha process. We notice that if wemultiply the whole first eqaution by the factor (-6), we will be able to in the second step eliminate the term in "x" by combining both equations term by term.

So we do that: Multiply the whole first equation by "-6":

(-6) (x + 2 y ) = (-6) (-2)

- 6 x - 12 y = 12

now we combine this with the second equation term by term to eliminate the term in x:

- 6 x - 12 y = 12

+

6 x + 3 y = - 30

_______________

0 - 9 y = - 18

Now divide both sides by "-9" to isolate y:

y = - 18 / (-9)

y = 2

Now we use y = 2 in the very first equation to solve for the variable x:

x + 2 y = - 2

x + 2 (2) = -2

x + 4 = - 2

subtract 4 from both sides:

x = - 2 - 4

x = - 6

In order to find the fraction of the amount that the discount represents, we just need to divide the discount amount by the total value:

Now, to simplify this fraction, we can divide the numerator and denominator by 40:

So the discount is 1/50 of the value paid.

Answer:

C

Step-by-step explanation:

2x-8y = 32

2/2 x - 8/2 y = 32/2

x - 4y = 16

if x = 0

-4y = 16

-4/-4 y = 16/-4

y = -4

If x = 16

16-4y = 16

-4y = 0

-4/-4 y = 0/-4

y = 0

Notice that the problem is described by a right angle triangle for which we know the length of the hypotenuse (400 ft), and also know one of the triangle's acute angles (25 degrees)

Base on this knowledge, we can start by finding the other acute angle of the triangle (

This means : 25 + 90 +

Then we can solve for angle

115 +

subtract 115 degrees from both sides to isolate

< B = 180 - 115 = 65

then we have the measure of angle < B = 65 degrees.

Now we can find the value of the side adjacent to the angle 25 degrees by using the cosine trigonometric ratio:

Then the side named "b" measures 362.52 ft

We can do something similar to find the measure of side a, but using the trigonometric ratio for the sine function:

Then the measure of side a is 168.05 ft

Now, notice that the problem wants you to round the side measures to the nearest whole number, so you need to type the following:

a = 169 ft

b = 363 ft

angle

We have to fill the blank to have an equivalent fraction:

Answer: 6

The values of x for which g(x) = 23 are x = 2.53 and x = -0.53

From the question, we are to determine the value(s) for which g(x) = 23

From the given information,

The function is

g(x) = 9x² - 18x + 11

Now, we will substitute g(x) = 23

That is,

23 = 9x² - 18x + 11

Rearranging

9x² - 18x + 11 - 23 = 0

9x² - 18x - 12 = 0

Divide through by 3

3x² - 6x - 4 = 0

Now, solve the quadratic equation

3x² - 6x - 4 = 0

Using the general formula,

x = [-b±√(b²-4ac)]/2a

a = 3, b = -6, c = -4

x = [-(-6)±√((-6)²-4(3)(-4))]/2(3)

x = [6±√(36 + 48)]/6

x = [6±√(84)]/6

x = [6 ± 9.17]/6

x = [6 + 9.17]/6 OR x = [6 - 9.17]/6

x = 15.17/6 OR x = -3.17/6

x = 2.53 OR x = -0.53

Hence, the values of x are x = 2.53 and x = -0.53

Learn more on Determining the values of x here: https://brainly.com/question/24334139

#SPJ1

To find the zeros of the polynomial given, we will first have to find some simpler zeros first then factor the polynomial so we can use the quadratic equation.

Since we can assume this question is to be solved without external tools, it is likely that two of the roots are simple ones.

So, we can try to use the rational root theorem to find these simpler ones.

Since the leading coefficient is 1 and the constant term is -18, if there are rational roots, they can be written as a fraction of a factor of -18 divided by a factor of 1.

The only factor of 1 is 1, so we now that if there are rational roots, they have to have denominator equal to 1.

The factors of 18 are 1, 2, 3, 6, 9 and 18.

Also, we have to consider the possibilities of positive and negative.

It is easier to test the lower ones, so let's start by testing 1/1 and -1/1. For either to be a zero, the polynomial has to result in 0:

So, x = 1 is a zero of the polynomial.

So, x = -1 is not a zero.

Now, let's try the next factor, 2/1 and -2/1:

So, x = 2 is not a zero.

So, x = -2 is also a zero of the polynomial.

We could continue, by we only need 2 zeros, so this is enough.

Now we know x = 1 and x = -2 are zeros of the polynomial, we can use synthetic division to factor the polynomial:

1 | 1 1 7 9 -18

| 1 2 9 18

| 1 2 9 18 0

Using the last line, we have that the remainder is 0 and the quotient is:

So, we have that:

Now, we can use synthetic division again on the quotient, but now use the other zero, x = -2:

-2 | 1 2 9 18

| -2 0 -18

| 1 0 9 0

Since x = -2 is a zero, we also got a remainder of 0, and the quotient is:

So, we can rewrite the polynomial as:

Now, we can just find the zeros of the remainer factor, x² + 9, so:

This means that the complex zeros of the given polynomial are:

And the factored usinf complex factors is:

We know that segment RS is a diameter of the circle, this means that arcs RS an RST measure 180°. Now that we know that an using the ratio for arcs RT and TS given we have:

Now, we know that an angle inscribed in a circle is half its intercepted arc, then we have:

Therefore, we have that arc RT is 30° and angle RST is 15°

Answer: We want to find angle 'theta' for which:

In general, the following is always true:

Therefore we have the following:

Therefore the angles that we were interested in is:

From congruence triangles, it is possible to see ED is congruent to DS because they are in the same line.

Answer: DS

The area of the figure will be the area of the rectangle of the top, plus the area of the rectangle of the bottom:

The area of the rectangle of the top is:

The area of the rectangle of the bottom is:

so, the total area is:

1 - The right and the left side must weight the same, and the weight of both the right and the left side would be 24, therefore each side must weight 12.

2 - Since the heart = 2, and 2*heart + square = 12 , then square = 8

3 - Now, since square = 8 and square + moon = 12, then moon=4

To summarize

heart = 2, square = 8 , moon = 4.

this is a question that involves angle of elevation and right angled triangles.

first, a diagram deoicting the scenerio is drawn below;

using the SOHCAHTOA rule for right angled triangles, we would name he distance of the ramp to the platform; x

y is length of the ramp up to the platform (the side opposite the right angle), H

8ft is the height from the ground to the platform ( the distance of the side opposite the angle), O

x is the length of the end of the ramp to the base of the platform( is the adjacent) A

THEREFORE, we will be applying TOA

the end of the ramp is 9.24ft from the base of the platform

the ramp is 16ft long up to the top of the platform

We need to calculate the time of thr flight, so we have to calculate the different between the landing time and the take off time:

The flight is 3 hours 38 minutes long.

Step 1

eliminate the parenthesis, use distributive property

Step 2

add similar terms

Step 3

add 10 in both sides

Step 4

divide each side by 4

so, the answer is x=4

To answer this question we will use the following properties of exponents:

Now, notice that:

Therefore:

Using the first property we get that:

Now, notice that x=1+x-1, then:

Answer: Options A, E, and F.

To find how many servings John can make we need to write as a relationship, this means that

to find the missing value we need to solve the relationship

he can make 20 servings with 30 cups of ice cream

Answer:

16 m

Step-by-step explanation:

If the perimeter of an equilateral pentagon is 80 m and it has five sides, the length of each side must be 16 m:

[tex]x=\frac{80}{5}[/tex]

[tex]x=16[/tex]

Therefore, if each side is 16 m in length, 2½ sides must equal 40 m:

[tex]2.5x=2.5(16)[/tex]

[tex]2.5x=40[/tex]

we can write 2 equations

where x is the wide and y the long

we can replace y=x+12 from the second equation on the first

and solve x

factor ussing

where a is 1, b is 12 and c -92

replacing

the two solutions are

the solution must be positive because it is a measure

so x=5.31feet

now we can replace the value of x on any equation to solve y(I will replace on the second equation)

so the measurements are x=5.31 and y=17.31

EXPLANATION:

To convert a fraction to a mixed number we must follow the following steps:

1.First we divide the numerator by the denominator.

2.The quotient becomes the integer part.

3.The remainder that the division gives, becomes the new numerator, and the quotient becomes the whole part, the denominator if it remains the same.

The exercise is as follows: 21/8

Now since 7/8 is a proper fraction, that is to say that its numerator is less than the denominator, it cannot be converted into a mixed fraction.

2/6 = 1/3 = 0.3333

0.333 is less than 1 so it should be on the left side of the graph.

4/3 = 1.333

1.333 is greater than 1 so it should be on the right side of the graph .

So the bigger dot on the left hand side which is before 1 should be 2/6 while the smaller dot on the right hand side which is after 1 should be 4/3 .

First Quartile is = 6

Median = 15

Range = 30 - 0

=30

Third Quatile = 24

Given:

A = 37.2°

b = 10.1 in

c = 6.2 in

Let's find the area of the traingle.

To find the area, apply the formula below:

Hence, we have:

Solving further:

Therefore, the area of triangle ABC is 19 square inches

ANSWER:

A. 19 in²

Neither

1) Firstly, we can start filling in the blanks.

2) The products xy are:

We're simply multiplying each x-entry by its output y.

The ratios y/x are:

So, x and y show:

Note that xy is not constant, for their product differs. So it is not an

inverse variation.

On the other hand, y/x is not constant as well. So it is not a direct variation.

3) Hence, it's neither direct nor inverse.