which one is equivalent?

11) Since the triangle has a pair of congruent base angles, it is an isosceles triangle which means that the two pairs of legs are congruent.

Make them equal to each other in an equation.

5x = x + 20

Subtract x from both sides.

4x = 20

Divide both sides by 4.

x = 5

12) The two legs are congruent so that means the base angles must be congruent. First find the measure of the base angles. Create an equation:

x + x + 50 = 180

Combine like terms.

2x + 50 = 180

Subtract 50 from both sides.

2x = 130

Divide both sides by 2.

x = 65

Now make the base angle plus x equal 180, because they form a straight line.

65 + x = 180

Subtract 65 from both sides.

x = 115

13) You know the vertex angle (top angle) is 90 degrees because it is supplementary to a right angle. The triangle is isosceles because the two legs are congruent, so make the base angles plus 90 add up to 180 in an equation.

x + x + 90 = 180

Combine like terms.

2x + 90 = 180

Subtract 90 from both sides.

2x = 90

Divide both sides by 2.

x = 45

The required number of lunch that contains 55% of ham sandwich is given as 23.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The total number of lunches is given as,
= 3 × 14
= 42 lunch in the 3 ice chests,

Now, 55% of the lunch consists the ham sandwich,
The number of lunch that contains the ham sandwich is given as,
= 0.55 × 42
= 23.1
≈ 23

Thus, the required number of the lunch that contains 55% of the ham sandwich is given as 23.

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Final answer:

To multiply 5 by the expression (2a-7b-2), each term inside the parentheses is multiplied by 5, resulting in the final expression 10a - 35b - 10.

Explanation:

To use the distributive property to multiply 5(2a-7b-2), multiply each term inside the parentheses by 5.

Multiply 5 by 2a which gives 10a.

Multiply 5 by -7b which gives -35b.

Multiply 5 by -2 which gives -10.

Now, combine these results to get the final expression: 10a - 35b - 10.

the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).

To solve the quadratic equation[tex]\( x^2 - 7x - 8 = 0 \)[/tex]by completing the square, we follow these steps:

1. Move the constant term to the other side of the equation:

[tex]\[ x^2 - 7x = 8 \][/tex]

2. To complete the square, take half of the coefficient of ( x ) (which is -7), square it, and add it to both sides of the equation:

[tex]\[ x^2 - 7x + \left( \frac{-7}{2} \right)^2 = 8 + \left( \frac{-7}{2} \right)^2 \]\[ x^2 - 7x + \frac{49}{4} = 8 + \frac{49}{4} \][/tex]

3. Simplify the right side of the equation:

[tex]\[ x^2 - 7x + \frac{49}{4} = \frac{32}{4} + \frac{49}{4} \]\[ x^2 - 7x + \frac{49}{4} = \frac{81}{4} \][/tex]

4. Write the left side of the equation as a perfect square:

[tex]\[ \left( x - \frac{7}{2} \right)^2 = \frac{81}{4} \][/tex]

5. Take the square root of both sides to solve for ( x ):

[tex]\[ x - \frac{7}{2} = \pm \sqrt{\frac{81}{4}} \]\[ x - \frac{7}{2} = \pm \frac{9}{2} \][/tex]

6. Solve for ( x ) by adding [tex]\( \frac{7}{2} \)[/tex]to both sides:

[tex]\[ x = \frac{7}{2} \pm \frac{9}{2} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{7}{2} + \frac{9}{2} = \frac{16}{2} = 8 \]\[ x = \frac{7}{2} - \frac{9}{2} = \frac{-2}{2} = -1 \][/tex]

So, the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).

The length of one side of Colin's square garden, which has an area of 97 square feet, is approximately 9.85 feet.

Colin has a square garden with an area of 97 square feet. The area of a square is calculated by squaring the length of one side (Side length * Side length = Area). Therefore, to find the length of one side of the square when you know the area, you would take the square root of the area.

In Colin's case, the area of the garden is 97 square feet, so the length of one side would be the square root of 97, which is approximately 9.85 feet.

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Answer:

The number of spots in the parking lot if there are 32 parking spots in the first row =111.

Step-by-step explanation:

We are given that a new parking lot is being built for a medical office.

We are given that

The expression representing the number of parking spots in the new lot =[tex]\frac{15x}{4}-9[/tex]

Where x= The number of parking lots in the first row

We have to find number of spots in the parking lot when parking spots in the first row is 32.

The number of parking spots in the first row =x=32

Substitute the value of x in the given expression then we get

Number of spots in the parking lot =[tex]\frac{15\times 32}{4}-9[/tex]

Number of spots in the parking lot=[tex]\frac{480}{4}-9[/tex]

The number of spots in the parking lot=120-9

The number of spots in the parking lot=111.

Hence, the number of spots in the parking lot if there are 32 parking spots in the first row=111.

Which expression represents the area of the triangle drawn below?

Base of the triangle=4x+2

Height of the triangle=2x+1

Area of triangle=[tex] \frac{1}{2} [/tex]*b*h

Area=[tex] \frac{1}{2} [/tex]*(4x+2)(2x+1)

Simplifying 4x+2 we get, 2(2x+1)

So, we have, Area=[tex] \frac{1}{2} [/tex]*2(2x+1)(2x+1)

Area=[tex] \frac{1}{1} [/tex]*1(2x+1)(2x+1)

=(2x+1)(2x+1)

FOILing the two we get, 2x*2x +2x*1 +1*2x+1*1

(2x+1)(2x+1)=4x²+2x+2x+1

Area=4x²+4x+1

So, Area of the triangle=4x²+4x+1

Answer:Option C

Answer:

It is C

Step-by-step explanation:

I just took the same quiz. I saw that this was the answer.

Hope this helps!

The correct answer is option B: [tex]\( y = -2x + 7 \).[/tex] To write the equation of a line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation.

The point-slope form is given as:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.

Given that the point is [tex]\( (2, 3) \)[/tex] and the slope is [tex]\( -2 \)[/tex], we can substitute these values into the point-slope form:

[tex]\[ y - 3 = -2(x - 2) \][/tex]

Now, we can simplify and rewrite the equation in various forms to match the options provided:

Option A: [tex]\( 2x + y = 7 \)[/tex]

To match this option, let's rearrange the equation:

[tex]\[ y - 3 = -2(x - 2) \][/tex]

[tex]\[ y - 3 = -2x + 4 \][/tex]

[tex]\[ 2x + y = 7 \][/tex]

So, option A is equivalent to the given equation.

Option B: [tex]\( y = -2x + 7 \)[/tex]

Let's solve the equation for [tex]\( y \):[/tex]

[tex]\[ y - 3 = -2(x - 2) \][/tex]

[tex]\[ y - 3 = -2x + 4 \][/tex]

[tex]\[ y = -2x + 7 \][/tex]

This matches option B.

Option C: [tex]\( y - 3 = -2(x - 2) \)[/tex]

This is already in point-slope form and matches the given equation.

Option D: [tex]\( y = -\frac{1}{2} x + 5 \)[/tex]

Let's solve the equation for [tex]\( y \):[/tex]

[tex]\[ y - 3 = -2(x - 2) \][/tex]

[tex]\[ y - 3 = -2x + 4 \][/tex]

[tex]\[ y = -2x + 7 \][/tex]

This does not match option D.

Therefore, the correct answer is option B: [tex]\( y = -2x + 7 \).[/tex]

The complete question is:

A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?

A) 2x + y = 7

B) y = -2x + 7

C) y - 3 = -2(x - 2)

D) y = - 1 2 x + 5.

When we divide a circle into 4 equal parts, the angles formed are the right angles.

When a circle is divided into 4 equal parts, we get 4 quarters of the circle.

The area that is intercepted by two radii that are at 90° to each other and a quarter portion of the circumference of a circle is known as a quarter circle.

In a quarter of a circle, the angle between radii is 90 degrees.

So, When we divide a circle into 4 equal parts, the angles formed are the right angles.

Hence, When we divide a circle into 4 equal parts, the angles formed are the right angles.

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Answer:

Transactional service - APEX

Step-by-step explanation:

1. The student that wrote a statistical question is Lisa. This is because there can be many answers to the question

2. The score of each student is: 4.5 points.

A statistical question is a question whose answer can be gotten by collecting data that has variability. That is, the answers to the question may be many.

1. The question that is more statistical in nature is Lisa's. This is because there can be many answers to the question

2. The average of a data is the mean, which is the sum of all data points divided by the number of data points.

Therefore, if all students had the same score and the mean score was 4.5, it means the score of each student is: 4.5 points.

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The cardboard is used to make each box is 90 in²

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given that, pyramid-shaped gift boxes have a square bases that measure 5 inches on each side, the slant height is 6.5 inches.

We need to find that how much cardboard is used to make each box,

For the same we will simply find the surface area of the box,
So,

SA = b² + 2bs

= 5²+2(5)(6.5)

= 25+65

= 90 in²

Hence, the cardboard is used to make each box is 90 in²

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Given that all helmets in the bin are red, the probability of randomly selecting a red helmet is 1, which corresponds to answer C.

The question is asking for the probability that a randomly selected helmet from a bin of four is red. Since all the helmets in the bin are red, no matter which one you pick, it will be red. In probability, this is represented as the total number of favorable outcomes divided by the total number of outcomes. In this scenario, both favorable outcomes (red helmets) and total outcomes (helmets in the bin) are four. Mathematically, 4/4 results in 1. So, the correct answer is C which symbolize the probability to be 1.

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