Partial results of a survey about students who wear glasses are shown in the two-way table.

Which of the following statements are true? Check all that apply.
225 students were surveyed.
25 girls always wear glasses.
15 girls sometimes wear glasses.
52 boys never wear glasses.
75 boys were surveyed.
65 students sometimes wear glasses.

To solve a function like this, simply put the numerical value in place of the unknown variable for which you have to find the solution, for instance '-3' in this case.

g(x) = 2x-2

so to find g(-3), we just need to replace the x in the given expression by '-3'. Working is shown below:

g(x) = 2x-2

putting '-3' in place of x

g(-3) = 2(-3) - 2

g(-3) = -6 -2

g(-3) = -8

Answer:

What does the multiplication property of equality allow us to do while solving equations?

C. The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.

~batmans wife dun dun dun...

The multiplication property of equality in Mathematics allows us to multiply both sides of an equation by the same value without affecting the equality. This property is useful for simplifying equations and finding unknown variables.

The multiplication property of equality is a crucial concept in solving equations. It states that if you have an equation, you can multiply the same quantity to both sides of the equation without affecting the equality. Essentially, what it says is captured in option C: The multiplication property of equality allows us to multiply both sides of the equation by the same value to maintain equivalent equations.

For example, if we have an equation 2x = 8, we can apply the multiplication property of equality by multiplying both sides of the equation by 1/2 (the reciprocal of 2) to find the value of x, without changing the balance of the equation. So, 2x * 1/2 equals 8 * 1/2, simplified gives us x = 4. This helps in simplifying complex equations and reaching the solution.

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(I have answered this question about half an hour before - repeating here)

In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.

The shortest interval of time after which the clock will show the correct time is 1.5 hours.

To find the shortest interval of time after which the clock will show the correct time, we need to determine the total time it takes for the clock to lose 2 minutes and reset to the correct time. Since the clock loses 2 minutes every 3 hours, it loses 1 minute per 1.5 hours. Therefore, it will take 1.5 hours for the clock to lose 2 minutes and show the correct time again. So, the shortest interval of time is 1.5 hours.

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Answer:

The maximum height is reached after 3.75 seconds.

Step-by-step explanation:

Assuming the deceleration due to gravity is unaided by air resistance, gravity causes the ball to lose vertical speed at the rate of 32 ft/s every second. The initial vertical speed of 120 ft/s will decline to zero when t satisfies ...

... 120 ft/s - (32 ft/s²)t = 0

... (120 ft/s)/(32 ft/s²) = t = 3.75 s

The ball will not go any higher after its vertical speed is zero.

Answer:

Maximum value of the expression = 5

X value it occurs at = 2

Step-by-step explanation:

Please view the image I provided.

Answer:

Cylinder C is the right answer.

Step-by-step explanation:

We have to find the storage capacity or the volume of cylindrical silos.

A. radius 6 feet; height 60 feet

Volume = [tex]\pi r^{2} h[/tex]

V = [tex]3.14\times6\times6\times60=6782.40[/tex] cubic feet

B. radius 8 feet; height 50 feet

V = [tex]3.14\times8\times8\times50=10048[/tex] cubic feet

C. radius 10 feet; height 34 feet

V = [tex]3.14\times10\times10\times34=10676[/tex] cubic feet

D. radius 12 feet; height 20 feet

V = [tex]3.14\times12\times12\times20=9043.20[/tex] cubic feet

Comparing all the volumes, we can see that cylinder C has the heighest volume.

Therefore, cylinder C is the right answer.

∠ a and ∠ d ( 2 arcs at angles indicate corresponding angles ) ;

∠ b and ∠ c ( single arc at angles indicate corresponding )

Rewrite the equation so both sides have the same base, then equate exponents and solve for c.

[tex]\displaystyle\left(\frac{1}{4}\right)^{c-2}=64\\\\\left(4^{-1}\right)^{c-2}=4^{3}\\\\-(c-2)=3\\\\-1=c[/tex]

The value of c is -1.

g=1

Add like terms on both sides. That would lead to 2+6g=11-3g

Add -6g to both sides or add 3g  to both sides so that g is on one side. Also get the whole numbers on the opposite side to get 9g=9 or -9g=-9. That makes g=1

It is convenient to start with the point-slope form and then simplify it to the desired form.

The point-slope form of the equation for a line with slope m through point (h, k) can be written as ...

... y = m(x -h) +k

You have m=-7 and (h, k) = (-3, 16), so you can fill in the numbers to get ...

... y = -7(x +3) +16

... y = -7x -21 +16 . . . eliminate parentheses

... y = -7x -5 . . . . the form you are looking for

A 2x + 6 is the quotient

Answer:

The quotient in polynomial form is 2x+6

Step-by-step explanation:

use the synthetic division

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

-1             2          8        6

               0          -2       -6            

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

               2          6         0

Now we use the quotient we got.

quotient is 2  and 6. Remainder is 0

In quotient we have only two numbers

So we write it as 2x+6

The quotient in polynomial form is 2x+6

5/50 = x / 170

solve for x by multiplying both sides by 170

Jesse used 5 gallons of gasoline to drive 50 miles. the gasoline he will need to travel 170 miles will be 17 gallons.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Jesse used 5 gallons of gasoline to drive 50 miles.

Let x be the gasoline he will need to travel 170 miles

5/50 = x / 170

x = 170 (1/10)

x = 17

Hence, the gasoline he will need to travel 170 miles will be 17 gallons.

Learn more about the unitary method;

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{(−7, 2), (−2, 2), (0, 1), (4, 5)} = B

Element x contains negative 4, negative 3, negative 1, and 1. Element Y contains negative 3, negative 1, and 4. = C

i hope this helps, i got kinda confused :/

Answer:

1) Domain -7, -2, 0, 4

Range 1, 2, 5

2) Domain -4, -3, -1, 1

Range -3, -1, 4

Step-by-step explanation:

1) Given relation,

{(−7, 2), (−2, 2), (0, 1), (4, 5)}

That, has the input values, -7, -2, 0, 4,

And, has the output values 2, 1, 5

We know that the set of all possible input values of a relation is called the domain of the relation,

While the set of all possible output values is called the range of the relation,

Thus, the domain of the above relation would be,

{ -7, -2, 0, 4 }

And, the range of the function,

{ 1, 2, 5 }

2) In the second relation,

Negative four maps to negative 1. Negative three maps to negative 3 and 4. Negative one maps negative 1. One maps to 4.

Let g(x) be the relation,

⇒ g(x) = {(-4, -1), (-3, -3), (-3, 4), (-1,-1), (1,4)}

Input values are -4, -3, -1, 1,

⇒ Domain = { -4, -3, -1, 1 }

Also, output values are  -1, -3, 4,

⇒ Range = { -3, -1, 4 }

- 28[tex]p^{5}[/tex] - 7[tex]p^{4}[/tex] + 7p³

distributing and adding exponents of like terms gives

- 28[tex]p^{3+2}[/tex] - 7[tex]p^{3+1}[/tex] + 7p³

= - 28[tex]p^{5}[/tex] - 7[tex]p^{4}[/tex] + 7p³

Answer:

-5/3

Step-by-step explanation:

The slope of the line between two points is the "rise" divided by the "run". That is, it is the ratio of the vertical change to the horizontal change.

It is usually convenient (but not necessary) to choose the horizontal change to be positive when finding slope from a graph.

When finding slope from a pair of point coordinates, you can do the math with the points in any order. The x- and y-values need to correspond, meaning if you subtract the first y-value from the second, you must also subtract the first x-value from the second.

slope = (change in y)/(change in x) = ∆y/∆x

... = (3-8)/(-4-(-7)) . . . . . . . . (difference of y-values)/(difference of x-values)

slope = -5/3

a no the corresponding angles are not congruent

∠A ≠ ∠E and ∠D ≠ ∠H

Answer:

No, the corresponding angles are not congruent.

Step-by-step explanation:

In the bigger model, the corresponding angles are 1 degree bigger

If a square has an area of 45 square units its side has a length of

[tex]s=\sqrt{45} = 3 \sqrt{5}[/tex]

units.  Is that a perfect length?  I don't know, but I know it's perfect for a square whose area is 45.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad(\stackrel{x_2}{4}~,~\stackrel{y_2}{-6})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\d=\sqrt{[4-(-2)]^2+[-6-2]^2}\implies d=\sqrt{(4+2)^2+(-6-2)^2}\\\\\\d=\sqrt{6^2+(-8)^2}\implies d=\sqrt{100}\implies d=10[/tex]

EF = 10

to calculate the distance use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (4, - 6 )

EF = √(4 + 2 )² + (- 6 - 2 )² = √(36 + 64 ) = √100 = 10

the function has only 2 points of discontinuity. Both a jump and removable discontinuity

The data shown in the graph states that the graph is continuous at point  [tex][-2,1][/tex]  and  [tex][-1, 2.5][/tex] and discontinuous at [tex](-2,2)[/tex] and [tex](-1,3)[/tex].

The graph is a systematic representation of data in pictorial form. The definition of continuity states that the function is defined at that point, and discontinuity defines that the function is not defined at that point.

The information provided in  the given graph states that the function is defined at the point[tex][-2,1][/tex] and[tex][-1, 2.5][/tex] and discontinuous at [tex](-2,2)[/tex] and [tex](-1,3)[/tex] which is represented in the form of holes.

The graph is continuous at point  [tex][-2,1][/tex]  and  [tex][-1, 2.5][/tex] and discontinuous at [tex](-2,2)[/tex] and [tex](-1,3)[/tex].

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24 rows of seats

let n be the number of rows

then the number of seats per row = n + 4

number of seats = number of rows × number of seats per row

n(n + 4 ) = 672

n² + 4n - 672 = 0 ← in standard form

the factors of - 672 which sum to + 4 are + 28 and - 24

(n + 28)(n - 24) = 0

equate each factor to zero and solve for n

n + 28 = 0 ⇒ n = - 28

n - 24 = 0 ⇒ n = 24

number of rows n > 0

number of rows = 24 and number of seats per row = 28

24 × 28 = 672 as a check

620,000 = 620,000 it remains the same because of the 0.

it will be 600,000 your welcome

5 nine-hour days is a total of 5×9 = 45 hours.

If 45 hours are worked in 4 days, the daily average is

... 45/4 = 11 1/4 . . . hours

They will need to work 11 hours 15 minutes daily if they switch.

Answer: 9x - y = -7

Step-by-step explanation:

Ax + By = C

9x + 7 = y

9x + 7 - y = 0

9x - y = -7

Hope this helps! :)

9x - y = - 7

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearrange y = 9x + 7 into this form ( subtract y from both sides )

0 = 9x - y + 7 ( subtract 7 from both sides )

9x - y = - 7 ← in standard form

There might be two ways to go about this

(1) I am going to assume that we can construct a second (reference) triangle - and you confirmed that it is ok to use trigonometry on that, and then we use the relationship between areas of similar triangles to get what we want. I choose a triangle DEF with same angles, 15, 75, and 90 degrees, and the hypotenuse DE a of length 1 (that is a triangle similar to ABC). I use sin/cos to determine the side lengths: sin(15)=EF and cos(15)=DF and then compute the area(DEF) =EF*DF/2. This turns out to be 1/8 = 0.125.

Now one can use the area formula for similar triangles to figure out the area of ABC - this without trigonometry now: area(ABC)/area(DEF)=(12/1)^2

so area(ABC)=144*area(DEF)=144*0.125=18

(2) Construct the triangle ABC geometrically using compass, protractor, and a ruler. Draw a line segment AB of length 12. Using the compass draw a (Thales') semi-circle centered at the midpoint of AB with radius of 6. Then, using the protractor, draw a line at 75 degrees going from point B. The intersection with the semicircle will give you point C. Finally. draw a line from C to A, completing the triangle. Then, using ruler, measure the length BC and AC.

Calculate the area(ABC)=BC*CA/2, which should come out close to 18, if you drew precisely enough.

Answer: 18 square cm

Step-by-step explanation:

*picture very note to scale im sorry lol*

Given: △ABC, m∠C=90°, m∠B=75°, AB=12 cm

m∠A = 15° (sum of all angles in a triangle is 180 degrees and 180-90-75=15)

CM - median to hypotenuse

CL - altitude

m<CLB = m<CLM = 90 degrees (def of altitude)

CM=MA=MB=1/2 AB = 6 cm (median to hypotenuse theorem)

m<MBC=m<BCM=75 degrees (base angles theorem of iso triangle)

m<BMC = 30 degrees (sum of all angles in a triangle, 180-75-75 = 30)

m<LCM = 60 degrees (sum of all angles in a triangle of triangle LCM, 180-90-30=60)

so now we know that triangle LCM is a 30-60-90 triangle with a hypotenuse of CM (6 cm)

LC = 1/2 of MC = 3 cm (leg opposite to 30 degree <)

So now we know that the height (altitude) of the triangle is 3 cm and the length is 12 cm.

Then, we can find the area by doing the (height * length)/2 = (3*12)/2, which brings us to our answer of 18 cm.

lmk if you don't understand anything in here i'm happy to clarify!

hope this helps!

c is the correct equation

given ΔABC is similar to ΔPQR

then the ratios of corresponding sides are equal.

the sides a, b and c inΔABC correspond to the sides p, q and r in ΔPQR

thus the following ratios are equal

[tex]\frac{a}{p}[/tex] = [tex]\frac{b}{q}[/tex] = [tex]\frac{c}{r}[/tex]

from this we can see that [tex]\frac{c}{r}[/tex] = [tex]\frac{a}{p}[/tex] → c

Answer:

The answer would be 0.99/1 pound

Step-by-step explanation:

The figures in a plane can be reflected, rotated, translated or dilated to produce new figures or images.

A transformation that moves all points to the same distance and in the same direction. The final figure looks the same, just moved over. It does not flip or gets rotated. It also does not change size.This type of translation is called glide reflection. Its the summation of translation and reflection.

Answer:

Glide Reflection

Step-by-step explanation:

x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))

     = (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )

     = x³ - 3x² + 4x - 2

Answer:

f(x) = x3 – 3x2 + 4x – 2

Step-by-step explanation:

If there are any three points on the graph that are not on the same line, the function is nonlinear. Such points might be ...

... (-5, 1), (-4, 0), (-3, 1)

Given rational expression is

[tex]-\frac{8x}{8x^2+2x}[/tex]

Now we need to find the restricted values if any for this rational expression.

Restricted values means the possible values of the used variable (x) that will make denominator 0 as division by 0 is not defined.

So to find the restricted values, we just set denominator equal to 0 and solve for x

[tex]8x^2+2x=0[/tex]

[tex]2x(4x+1)=0[/tex]

2x=0 or 4x+1=0

x=0 or 4x=-1

x=0 or x=-1/4

Hence final answer is x=0, -1/4

To find the restricted values of a rational expression, set the denominator equal to zero and solve for x.

To find the restricted values of the rational expression, we need to determine the values of x that will make the denominator of the expression equal to zero. When the denominator is zero, the expression is undefined.

In this case, the denominator is 8x2 + 2x. We set this equal to zero and solve for x:

8x2 + 2x = 0

Factor out 2x:

2x(4x + 1) = 0

Set each factor equal to zero:

2x = 0, 4x + 1 = 0

Solve each equation:

x = 0, x = -1/4

Therefore, the restricted values of x for the given rational expression are 0 and -1/4.

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