This room has an oil stain on the floor. Tyler wants to rotate the rug so that it covers the stain. What kind of rotation should be performed on the kite-shaped rug? Be sure to specify the center of rotation and the direction (clockwise or counter-clockwise).

To know if 2 triangles are similar, we would need at least 2 angles, why?

Since a triangle has 3 angles, and those angles add up to 180°, we can easily determine the third angle.

Example: If 2 angles of a triangle were 13 and 97, we would know that 13 + 97 = 110, then 180° - 110° = 70°, so the missing angle is worth 70°.

Hope this helped! c:

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.

Answer:

B) 68

Step-by-step explanation:

56*2=112

180-112=68.

The required √5 on the number line is shown in the image attached.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here

To locate √5 on a number line, we can begin by locating the integers that √5 lies between. We know that 2² = 4 and 3² = 9, so √5 must be between 2 and 3.

To get a more accurate estimate, we can divide the distance between 2 and 3 into 10 equal parts (tenths). Each tenth represents 0.1 units on the number line. We know that 0.5 is halfway between 0 and 1, so √5 must be a little more than halfway between 2 and 3.

By estimating the position of √5 on the number line, we can approximate it as being around 2.2 to 2.3.

Thus, the required √5 is shown in the image attached.

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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 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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Answer:

Transactional service - APEX

Step-by-step explanation:

Answer:

the answer is 5.

Step-by-step explanation:

The expression 12(43−6⋅32) evaluates to -132 by following the order of operations, first calculating the exponent, then the multiplication and subtraction inside the parentheses, and finally multiplying the result by 12.

To evaluate the given expression 12(43−6⋅32), we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

First, solve the exponent 32 which is 9.
Then, perform the multiplication within the parentheses: 6⋅9 equals 54.
Now, subtract that result from 43: 43 - 54 which gives us -11.
Finally, multiply the result by 12: 12 ⋅ (-11) equals -132.

Therefore, the expression 12(43−6⋅32) evaluates to -132.

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 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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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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