Triangle ABC and triangle CFG are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CG? A) 0 − 2 3 − 0 = 2 − 6 9 − 3 B) 0 − 2 3 − 0 = 6 − 2 9 − 3 C) 2 − 0 3 − 0 = 6 − 2 9 − 3 D) 3 − 0 2 − 0 = 9 − 3 6 − 2

Answer:

498

Step-by-step explanation:

38×12 + 7×6 = 498

don't worry!

Answer: B 498

Step-by-step explanation:12 times 38 because it is 12 eggs in each cartons plus 7 times 6 because she also bought 7 quail eggs equal to 498

Answer:

For this case we have an exponential function of the form:

Where,

A: original cost

b: rate of change

x: number of years

Therefore, replacing values we have:

Answer:

the value, after 7 years, of a 2014 Ford Mustang is:

y=13946

Answer:11000

Step-by-step explanation:8*25000/100 =2000 so 2000 is the 8 percent depreciation. then multiply by 7 which is 14000 then just subtract from 25,000.00 and the answer is 11000

Answer:

[tex]\boxed{\text{Degree = 4; Max. no. of terms = 5}}[/tex]

Step-by-step explanation:

(x² + x + 2)(x² – 2x + 3)

1. Degree of product

The degree of the product of two polynomials is the sum of their degrees.

Each polynomial is of degree 2, so the degree of the product is 4.

That is, the term of highest degree must come from x² × x² = x⁴.

2. Maximum number of terms

The maximum number of terms is one more than the degree of the product.

Thus, there is a maximum of five terms in the product: one for each power of x plus a constant term.

P = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Answer:

D. 21/2

Step-by-step explanation:

We simply have to evaluate the first three terms based on the progression's formula:

t= 1,  the first term is 8, as we see:

[tex]8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{1-1} = 8 * 1 = 8[/tex]

t=2, the second term is 2, as we see:

[tex]8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{2-1} = 8 * \frac{1}{4} = 2[/tex]

t=3, the third term is 1/2, as we see:

[tex]8(\frac{1}{4})^{t-1} = 8(\frac{1}{4})^{3-1} = 8 * \frac{1}{16} = \frac{1}{2}[/tex]

The sum of the first 3 terms is then: 8 + 2 + 1/2 = 10 1/2

Among the answer choices, D. 21/2, which is 10 1/2.

Answer:

Step-by-step explanation:

So all you need to do is multiply the Base by the Height so 16 multipled by 8 is simply 64. Thus the are of the triangle with a base of 16 inches and a height of 8 inches is 64 Inches.

Final answer:

To find the area of a triangle with a given base and height, use the formula Area = (1/2) × base × height. In this case, with a base of 16 inches and a height of 8 inches, the area would be 64 in².

Explanation:

The area of a triangle is calculated using the formula (1/2) × base × height. To find the area of a triangle with a base of 16 inches and a height of 8 inches, you plug the values into the formula:

Area = (1/2) × base × height

Area = (1/2) × 16 inches × 8 inches

Area = 64 in²

Answer:

7/10

Step-by-step explanation:

To make things simple, let's turn 80% into a fraction, 8/10. To get a common denominator let's turn 8/10 into 4/5. Since they are both of equal size, the first group would have 2/5 left-handed people and the second 1/5 left-handed people. Let's imagine that each group has 5 people in it. There would be 10 people in total. There is 1 person for each fifth so we can add now. 4 + 3 = 7 right handed people. To check, 2 + 1 = 3 and 3 + 7 = 10. so 7/10 of the class is right-handed.

The fraction of the class is right handed is 7/10

We have given that

80% of the second group are right-handed.

let's turn 80% into a fraction,

The fraction form of 80% can be calculated by dividing 80 by 100

So we get,

[tex]=\frac{80}{100} \\\\=\frac{8}{10}[/tex]

=8/10.

To get a common denominator let's turn

8/10 =4/5             .....(divide the numerator and denominator by 2)

Since they are both of equal size,

The first group would have 2/5 left-handed people and

The second 1/5 left-handed people.

Let's imagine that each group has 5 people in it.

There would be 10 people in total.

There is 1 person for each fifth so we can add now.

4 + 3 = 7 .....(1)

right handed people.

we can check it,

2 + 1 = 3 and 3 + 7 = 10. .........(2)

Therefore we get,

7/10 of the class is right-handed.

The fraction of the class is right handed is 7/10

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Answer:

V =144 pi units^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

where r is the radius and h is the height

V = pi (6)^2 *4

V = pi 36*4

V =144 pi units^3

Answer:

V=452.16 units^2

Step-by-step explanation:

The formula to find the volume of a cylinder is ...

V=(3.14)r^2×h

(3.14)=pie

r^2=radius squared

h=height

So....

Let's plug in what we know

V=(3.14)6^2×4

V=(3.14)36×4

V=(3.14)144

V=452.16 units

Answer:

Step-by-step explanation:

xy = 300

x + y = 50                       Solve for y

y = 50 - x                        substitute into xy = 300

x(50 - x) = 300               Remove the brackets.

50x - x^2 = 300             Bring the left to the right.

0 = x^2 - 50x + 300

This is a quadratic. It will have 2 solutions.

a=1

b = - 50

c = 300

Put these into the quadratic equation.

It turns out that x has two values -- both plus

x1 = 42.03

x2 = 6.97

x1 + y1 = 50

42.03 + y = 50

y = 50 - 42.03

y = 7,97

(42.03 , 7.97)

====================

x2 + y2 = 50

6.97 + y2 = 50

y2 = 50 - 6.97

y2 = 43.03

(6.97 , 43.03)

Answer:

x ≈ 6.97, y ≈ 43.03; x ≈ 43.03, y ≈ 6.97

Step-by-step explanation:

System: x + y = 50, xy = 300

Alter 1st equation: y = 50 - x

Substitute: x(50 - x) = 300

Distribute: -x² + 50x = 300

Subtract: -x² + 50x - 300 = 0

Quadratic formula: x = (-50 ± √(2500 - 4 * -1 * -300))/(-2)

Simplify: x = (-50 ± √1300)/-2

Distribute: x = 25 ± (10√13)/-2

Simplify: x = 25 - 5√13 --> x ≈ 6.97, x = 25 + 5√13 --> x ≈ 43.03

Substitute: 6.97 + y = 50 --> y ≈ 43.03, 43.04 + y = 50 --> y ≈ 6.97

Answer:

A:5

Step-by-step explanation:

Both W and A have to equal each other. 5*4=20-7=13.

5*2=10+3=13

4 desserts

The number of meals can be expressed by c * s * d = m, where c is main courses, s is salads, d is desserts, and m is meals.

Fill in the variables.

6 * 2 * d = 48

Simplify.

12 * d = 48

Divide both sides by 12.

d = 4

So, there are 4 desserts.

Answer:

The answer to your question is 20 ft squared

Step-by-step explanation: when you hear the word "side length", it means that whatever the side length is on one side, then this means that the other side lengths are gonna be the same side length as well. For example, we already know that a square garden has a side length of 5 ft. So, since we are trying to the find the area of the square garden, you can either multiply the side length of the square garden by 4, or you can add the side length of the square garden 4 times, which will look like this:

5ft*4ft=20ft2

or 5ft+5ft+5ft+5ft= 20ft2

Answer:

the answer is 25 ft2

Step-by-step explanation:

Let's solve your inequality step-by-step.

x+11>2

Step 1: Subtract 11 from both sides.

x+11−11>2−11

x>−9

Answer:

x>−9

Answer:

Second option: multiply input number by 4.

Step-by-step explanation:

You need to remember that the "input numbers" are the values of "x" and the "output numbers" are the values of "y".

You can observe in the table that each output number is always four time its corresponding input number. This means that to find the missing numbers on the given table, you need to multiply the corresponding input number by 4.

Therefore, you get:

For [tex]x=3[/tex] :

[tex]y=4x\\y=(4)(3)\\y=12[/tex]

For [tex]x=6[/tex] :

[tex]y=4x\\y=(4)(6)\\y=24[/tex]

To find the missing numbers in the table, square the input for the first missing number, and multiply the input by 4 for the second missing number. The missing numbers are 9 and 24.

To find the missing numbers in the table, you can follow the pattern provided in the instructions:

1. Multiply the input number by itself to get the output number.

2. Multiply the input number by 4 to get the second output number.

Let's calculate the missing numbers using this pattern:

For the first missing number:

Input: 3

Output: 3 * 3 = 9

For the second missing number:

Input: 6

Output: 6 * 4 = 24

So, the missing numbers in the table are:

3 (for the first missing input)

24 (for the second missing input)

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Step-by-step explanation:

| x - 2 | < 4

Start at x=2.  Go 4 units in either direction: x=-2 and x=6.  Draw empty circles around each.  Since it's less than, the line goes between the circles, connecting them.  The result should look like this:

desmos.com/calculator/k2bujixjtx

| x + 2 | > 4

Start at x=-2.  Go 4 units in either direction: x=-6 and x=2.  Draw empty circles around each.  Since it's greater than, the line goes outside of the circles.  The result should look like this:

desmos.com/calculator/sk1cxob0tg

Answer:

Step-by-step explanation:

3.

|x-2|<4

-4<x+2<4

subtract 2 from each inequality

-4-2<x+2-2<4-2

-6<x<2

4.

|x+2|>4

x+2<-4 and x+2>4

or x+2-2<-4-2 and x+2-2>4-2

or x<-6 and x>2

ANSWER

300,000 cm³

EXPLANATION

We want to round

[tex]257, 166 {cm}^{3} [/tex]

to the nearest hundred thousand.

The digit in the hundred thousand position is '2'

The immediate digit to it's right is 5.

So we round up to obtain

300,000 cm³

Therefore, 257,166 cm³ rounded to the nearest hundred thousand is 300,000 cm³

The number present at hundred thousand places is 2 can be turned to 3 and rest all will zero to obtain 257, 166 rounded to the nearest hundred thousand. Thus, the nearest hundred thousand of 257,166 is 3,00,000.

The number is 2,57,166 that is needs to be rounded to the nearest hundred thousand.

In the image, each and every position is mentioned clearly.

Therefore,

The number present at hundred thousand places is 2.

The next number present to the left from 2 is 5 that is neutral, so, we need to check the number left to the 5 that is 7.

Now,

7 is a large number so we can consider 5 as a large number.

Thus,

The number present at hundred thousand places is 2 can be turned to 3 and rest all will zero to obtain 257, 166 rounded to the nearest hundred thousand. Thus, the nearest hundred thousand of 257,166 is 3,00,000.

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[tex]x \div y = 3 \div 5 \\ it \: means = \\ 3y = 5x \\ x - y = 18 \\ [/tex]

To solve we multiply the last equation by 5 and we get the following:

5x-5y=90

But 5x=3y and we replace it in this equation:

3y-5y=90

-2y=90

y=-45

and x-(-45)=18 , x+45=18

x=-27

Answer:

x = 3 and y = 3

Step-by-step explanation:

2 x + 3 y = 15 { Equation 1 }

x + y = 6 { Equation 2 }

( Multiply the x variable by 2 so equation 1 and 2 have the same x variable )

2 x + 3 y = 15 { Equation 1 }

2 x + 2 y = 12 { Equation 2 }

( Minus equation 2 from 1 so we are left with an independent variable )

y = 3

( Substitute y = 3 into equation 1 to solve for x )

2 x + 9 = 15

( Solve )

2 x + 9 = 15

[ Subtract 9 from both sides ]

2 x = 6

[ Divide by 2 from both sides ]

x = 3

Answer: x=3

y=3

Step-by-step explanation:

2x+3y=15

x+y=6

2x+3y=15

x=6-y

2(6-y)+3y=15

y=3

x=6-3

x=3

(3,3)

Answer:

1.) b/19

Step-by-step explanation:

a/b=12/19

you can always swap the b and the 12 (quick SAT trick)

To find the ratio that completes the equivalent proportion for a/12 using the given proportion a/b = 12/19, you will need to use cross multiplication.
Let's denote x as the unknown value that we are trying to find such that a/12 = b/x. To solve for x, we set up the proportion like this:
a/12 = b/x
Now let's cross multiply:
a * x = 12 * b
Since we know from the initial proportion that a/b = 12/19, we can substitute 12/19 for a/b in the equation:
(12/19) * b * x = 12 * b
Now we have b on both sides of the equation, and assuming b is not equal to zero, we can divide both sides of the equation by b to solve for x:
(12/19) * b * x / b = 12 * b / b
12/19 * x = 12
Now we need to isolate x:
x = 12 / (12/19)
To simplify this, you can multiply 12 by the reciprocal of 12/19, which is 19/12:
x = 12 * (19/12)
The 12s cancel each other out:
x = 19
Therefore, the ratio that completes the equivalent proportion is b/19.
The correct answer is:
1.) b/19

Answer:

Step-by-step explanation:

the graph of f(x)=3x becomes the graph of g(x)=3x-2 if the entire graph of f(x) = 3x is translated down by 2 units.

Answer:

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have r = 10cm and H = 25 cm.

Substitute:

[tex]V=\dfrac{1}{3}\pi(10^2)(25)=\dfrac{1}{3}\pi(100)(25)=\dfrac{250\pi}{3}\ cm^3[/tex]

[tex]\pi\approx3.14\to V\approx\dfrac{(250)(3.14)}{3}\approx261.67\ cm^3[/tex]

Answer:

c

Step-by-step explanation:

PI times radius squared

Statement C describes how to find the area. Area of the circle is obtained by dividing the diameter in half and multiply by π.

Area describes the region or the space of the given figure. If the circle has a radius of 'r' units, the area is calculated as;

A = π r² sq. units.

Because the radius of a circle is half its diameter, if the diameter is 'd', then,

r= d/2,

The area may be represented as;

A = π r² sq. units.

Area of the circle is obtained by dividing the diameter in half and multiply by π.

Hence,statement C describes how to find the area.

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Answer:

A

Step-by-step explanation:

First express [tex]\sqrt{2}[/tex] + i[tex]\sqrt{2}[/tex] in trig form

| z | = [tex]\sqrt{(\sqrt{2})^2+(\sqrt{2})^2  }[/tex] = [tex]\sqrt{4}[/tex] = 2

Θ = [tex]tan^{-1}[/tex]( [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]) = [tex]tan^{-1}[/tex]( 1) = [tex]\frac{\pi }{4}[/tex]

Thus

[tex]\sqrt{2}[/tex] + i[tex]\sqrt{2}[/tex] = 2 [ cos[tex]\frac{\pi }{4}[/tex] + isin[tex]\frac{\pi }{4}[/tex] ]

Hence

([tex]\sqrt{2}[/tex] + i[tex]\sqrt{2}[/tex] )³

= 2³ [ cos ([tex]\frac{\pi }{4}[/tex] × 3) + isin([tex]\frac{\pi }{4}[/tex] × 3 ) ]

= 8 [ cos([tex]\frac{3\pi }{4}[/tex] ) + isin([tex]\frac{3\pi }{4}[/tex]) ] → A

The standard form of the give complex number is

8 [ cos(\frac{3\pi }{4} ) + isin(\frac{3\pi }{4}) ]

We have given that,

First express  [tex]\sqrt{2} + i\sqrt{2}[/tex]  in trig form

[tex]| z | = \sqrt{(\sqrt{2})^2+(\sqrt{2})^2 } = \sqrt{4} = 2[/tex]

[tex]\theta = tan^{-1}( \frac{\sqrt{2} }{\sqrt{2} }) = tan^{-1}( 1) = \frac{\pi }{4}[/tex]

Thus, [tex]\sqrt{2} + i\sqrt{2} = 2 [ cos\frac{\pi }{4} + isin\frac{\pi }{4} ][/tex]

[ r(cos θ + i sin θ) ]^n = r^n(cos nθ + i sin nθ)

Hence, [tex](\sqrt{2} + i\sqrt{2} )^3[/tex]

[tex]= 2^3 [ cos (\frac{\pi }{4} \times 3) + isin(\frac{\pi }{4} \times 3 ) ][/tex]

[tex]= 8 [ cos(\frac{3\pi }{4} ) + isin(\frac{3\pi }{4}) ] \implies A[/tex]

Thererefore the standard form of the give complex number is

8 [ cos(\frac{3\pi }{4} ) + isin(\frac{3\pi }{4}) ].

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Answer:

34n

Step-by-step explanation:

The product of 34 and the number of pounds

The product means multiply

So the product of 34 and the number of pounds = 34 × n = 34n

The question involves mathematical conversion of units from pounds to ounces and calculating percent composition. Multiplying by 16 converts pounds to ounces, while percent composition is found by dividing the mass of the component by the total mass and then multiplying by 100. Exact numbers, like the number of bags, do not affect significant figures.

The student appears to be dealing with a conversion problem within a mathematics context, specifically involving the units of pounds and ounces. When converting from a larger unit (pounds) to a smaller unit (ounces), the correct operation is multiplication since there are 16 ounces in one pound. A clear example of this is provided where 4.5 pounds, written as 4(1/2) pounds, is converted to ounces resulting in 72 ounces.

Furthermore, the problem addresses the percent composition of a substance by mass, which is a concept commonly encountered in chemistry but framed here within a mathematical question. Using the provided formula and mass values, we calculate the percent composition by dividing the mass of the desired product by the total mass of the product and then multiplying by 100 to get a percentage. The percentages indicate the fraction of the total mass that is made up of a specific component. The key information given in the example is that the mass of the desired product is 73.0, and the total mass of the product is 215, therefore, the percent composition is 34.0%.

Lastly, the question states that because the number of bags is an exact value, it is not considered in the significant figures. This means we are not to worry about the precision of measurement when it comes to counting items, which is a principle applied to exact numbers in significant figure rules.

Answer: 12 bricks

Step-by-step explanation:

To find how many 6" bricks are needed to fit the 72" gap, just divide.

72/6=12

12 bricks are needed.

Answer:

A: x= -18, B: y= 10, C: x= 42, D: 14

Step-by-step explanation:

Note: The photo you used was hard to read, so I just assumed what the equations were.

A) x+14=-4

-14      -14

x=-18

B) y-14=-4

+14      +14

y=10

C) z/14=3

times 14         times 14

x=42

D) 2/7x=4

times 7/2      times 7/2

x=14

Answer:

The cost is less than $1.30

Step-by-step explanation:

Let

y-----> the total cost of a mobile phone call

x----> the time in minutes

we know that

if time were x=5 minutes

the cost would be

y=0.30+0.20(5)=$1.30

but

the time is less than 5 minutes

therefore

the cost would be

y< $1.30

Answer:

The possible cost of a call if it is shorter than 5 minutes ranges between 30 cents and maximum 130 cents

Step-by-step explanation:

Define a function as

Y: Cost of a call in cents

X: Number of minutes of call

So using the statement we can find that

Y=30+20X

because the cost of the call has a fix cost of 30 cents plus 20 cents per minute used. If the calls is shorter than 5 minutes for x = 5

Y=30+20X = 30 + (20*5) = 30 + 100 = 130 which is the cost of a call of max 5 minutes

Because you pay a fixed cost of 30 even if you spend very little time. X= 0 then the possible cost of a call if it is shorter than 5 minutes ranges between 30 cents and maximum 130 cents

Answer:

The answer is A. Was this a test question or a normal lesson?

Step-by-step explanation:

Answer:

the correct answer is B. 10%

Step-by-step explanation:

From the given question, we recall the following,

The probability of Wayne making a three pointer = 21%

Now, what is the the probability he makes his first three pointer on the fourth shot.

The next step is to find a solution to the question

The probability of not shooting a 3 pointer is  1- 0.79 = 1-p=q

All the throws of wayne are independent of each other

If two or  ore event are independent we have,

P (AnB) = P(A) * P(B)

P (AnBnC) = P(A) *P (B) *P (C)

P (AnBnCnD) = P(A) * P(B)* P(C) *P(D)

Now, let make first 3 pointer on the 4th shot, we have:

q³= p (0.79)³ (0.21) =10% or (1-0.21) x (1-0.21)x (1-0.21) x 0.21=(0.79) x (0.79) x (0.79) x(0.21)=0.1

which is =10%

See the attached picture.

The Y values would remain the same, the X values become the negative of the original values.

You would multiply outcomes 3 times to get the total number of elements in the sample space because the experiment has three stages.

4^3 = 64

Note: You can also multiply 4 three times.

Answer: C. 64

Step-by-step explanation:

We know that the number of total elements in the sample space is given by :_

[tex]N^n[/tex], where N is the number of total possible outcomes for an event and n is the number of times event is repeated.

Given: The number of equally likely sample outcomes of a single stage of an experiment = 4

The number of stages in the experiment = 3

Then , the total number of elements in the sample space :-

[tex](4)^3=64[/tex]

Hence, the total number of elements in the sample space = 64.