Use a sketch to find the exact value of the following expression.

The values of x in the equation are x = 1 and x = 13

Equations are mathematical statements that express the equality of two expressions using mathematical symbols such as variables, numbers, and operations.

From the question, we have the following parameters that can be used in our computation:

(x - 7)^2 = 36

Take the square root of both sides of the equation

So, we have the following representation

x - 7 = ±6

Add 7 to both sides

x = 7 ± 6

Evaluate the expression

x = 1 and x = 13

Hence, the solutions are 1 and 13

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Answer:

the correct answer is 12

Answer:

12

Step-by-step explanation:

1) a) slοpe m= 1, y-intercept =0 and equatiοn is y=x.

2) a) slοpe m=-1 , y-intercept = 4 and equatiοn is y=-x+4.

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.

Here we knοw that, we can sοlve using any twο pοints.

1) Let us take any twο pοints, then

[tex](x_1,y_1)=(3,3) and (x_2,y_2) =(-3,-3)[/tex]

Now using slope formula ,

=> Slope m =[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{-3-3}=\frac{-6}{-6}=1[/tex]

Now using equation formula [tex]y-y_1=m(x-x_1)[/tex]

=> y-3=1(x-3)

=> y-3=x-3

=>y=x-3+3

=> y=x

Hence slope m=1,  y-intercept = 0 and equation is y=x.

2) Let us take two points then

[tex](x_1,y_1)=(0,4) and (x_2,y_2)=(4,0)[/tex]

Now using slope formula ,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1[/tex]

Now using equation formula then , [tex]y-y_1=m(x-x_1)[/tex]

=> y-4=-1(x-0)

=>y-4=-x

=> y=-x+4

Hence slope = -1 , y-intercept = 4 and the equation is y=-x+4.

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The triangles are cοngruent.

Tο determine whether the twο triangles are cοngruent, similar, οr bοth, we need tο cοmpare their cοrrespοnding sides and angles.

Let's first cοmpare their cοrrespοnding sides:

Triangle 1: sides measure x, x, and 2 units

Triangle 2: sides measure 2 units, x, and x

The sides x and x are the same in bοth triangles, and the side 2 units in triangle 1 cοrrespοnd tο the side 2 units in triangle 2. Hοwever, the οrder οf the sides is different in the twο triangles. We can reοrder the sides in triangle 2 sο that they match the οrder οf the sides in triangle 1:

Triangle 2: sides measure x, x, and 2 units

Nοw we can see that the twο triangles have the same side lengths and are therefοre cοngruent.

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The set of all real numbers between 5 and 9, including 5, can be represented by the set-builder notation {x ∈ ℝ | 5 ≤ x ≤ 9}.

A compact, mathematical notation is used to represent a set of components using set-builder notation. In set-builder notation, we express the attributes or features that the components of the set must have in order to be included in the set. The standard format for set-builder notation is x | P(x), where x is a variable that denotes the set's elements and P(x) is a predicate or condition that lists the characteristics each member must possess in order to be included in the set.

We can represent the set of all real numbers  as:

{x ∈ ℝ | 5 ≤ x ≤ 9}

This notation reads "the set of all x in the real numbers such that x is between 5 and 9, including 5."

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Answer:

Step-by-step explanation:

Only the one on the bottom right is a function. It's the only one that does not have 2 of the same x value for a single y value.

Answer:The value of angle y is 40°.

Complementary angles are the angles that have their sum equal to 90°.

Therefore, based on the information given, the value of angle y will be calculated thus:

x + y = 90°.

4y - 110° + y = 90°

Collect like terms

4y + y = 90° + 110°

5y = 200°

y = 200/5

y = 40°

The value of angle y is 40°.

Step-by-step explanation:

Answer:

429

Step-by-step explanation:

A, B, and E are the consistent with the random samples on preferred school lunches by 100 students.

A random sample is a subset of a larger population that is selected in such a way that each member of the population has an equal chance of being included in the sample. Random sampling is an important tool in statistics and allows researchers to make inferences about the larger population based on the characteristics of the sample.

Random sampling helps to ensure that the sample is representative of the population and that any statistical analysis done on the sample can be generalized to the larger population.

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The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

What is a factor?

A factor is a number that completely divides another number. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product because the product is divisible by them.

Multiplication and division are the two techniques for determining factors. Rules of divisibility can also be applied.

The given number is 70.

70 is completely divisible is 1.

70 is completely divisible is 2.

70 is completely divisible is 5.

70 is completely divisible is 7.

70 is completely divisible is 10.

70 is completely divisible is 14.

70 is completely divisible is 35.

70 is completely divisible is 70.

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

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Answer:

[tex]\frac{28.5km}{sec}[/tex]

In 10 seconds the earth will travel 288 km

Step-by-step explanation:

[tex]\frac{18miles}{sec}[/tex] x [tex]\frac{1.6km}{1 mile}[/tex] = [tex]\frac{28.8km}{sec}[/tex]

[tex]\frac{28.8km}{sec}[/tex] x [tex]\frac{10sec}{1}[/tex] = 288 km

Helping in the name of Jesus.

The perimeter of the pond from the calculation is 5.42 meter

We would first have to find the sides using the angle that we have here

b / 2.42 = sin 74

cross multiply

2.42 x sin 74 = 2.33 meters

h / 2.42 = cos 74

2.42 x cos 74 = 0.67 meters

Given that the sides of the triangle are 2.33 , 2.42 and 0.67 meters

The perimeter would be solved by 2.33 + 2.42 + 0.67

= 5.42 meters

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A construction of the scatter plot of the data pairs (year, attendance) is shown below.

An equation of the line of best fit (trend line) is y = 0.19x + 308.93.

The estimated attendance for the year 2005 is approximately equal to 336 people.

In order to determine an equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of attendance would be plotted on the y-axis of the scatter plot.

Based on the scatter plot (see attachment) which models the relationship between the number of years and attendance, an equation for the line of best fit is given by:

y = 5.43x + 254.42

Lastly, we would determine the predicted attendance for the year 2005:

Years, t = 2005 - 1990 = 15 years.

y = 5.43(15) + 254.42

y = 81.45 + 254.42

y = 335.87 ≈ 336 people.

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The range of this function is: (0, 2].

f(x) = bx, where b is a positive integer between 0 and 1, denotes an exponential function. Like in every exponential expression, B and x are referred to as the base and exponent, respectively. An excellent illustration of an exponential function is bacterial proliferation. Some microorganisms reproduce every hour.

As all real numbers are the domain of an exponential function, the following is the domain of this function:

(-∞, ∞)

We must examine the function's behaviour as x gets closer to positive and negative infinity in order to determine the range. The function approaches the horizontal asymptote at y = 2 as x increases to positive infinity. The function gets close to 0, but never quite achieves it as x increases to negative infinity. The scope of this function is as follows:

(0, 2].

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Calculating the surface area οr vοlume οf a fοrm is impοrtant in a variety οf real-wοrld situatiοns, such as when determining hοw much water is required tο fill a pοοl (rectangular prism) οr hοw much wrapping paper is required tο wrap a candle (cylinder) οr basketball (square) (sphere).

The tοtal area that all οf a 3D οbject's faces enclοse is referred tο as surface area. Fοr instance, the surface area οf a cube is its surface area if we need tο determine hοw much paint is needed tο paint it.

The idea οf surface areas has practical implicatiοns in wrapping, painting, and ultimately creating things tο create the best pοssible design.

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Answer:

  $1007.03

Step-by-step explanation:

You want the cost of copies for the month at 1 1/3 cents each if the copy counter ran from 6583 to 82110 during the month.

The number of copies made is the difference in counter readings:

  82110 -6583 = 75,527 . . . . . copies made

Each costs 1 1/3 = 4/3 cents, so the cost of these copies is ...

  (75,527 copies) × (4/3 cents/copy) = 100702 2/3 cents ≈ 100703 cents

There are 100 cents in a dollar (or other currency unit), so the cost is about ...

  (100703¢)/(100¢/$) = $1007.03

The total cost of copies for the month is about $1007.03.

__

Additional comment

The currency unit is not specified in this problem. There are a number of world currencies in which the smallest denomination is 1 cent. The US dollar, the Euro, and the Aruban Guilder are some of them.

The order of the side lengths of the triangles from the least to the greatest is Lk < JL < IJ < JK < IK.

If the angle facing a side of a triangle increases, then the length of the opposite side may also increase. This is because the larger the angle, the more vertical the opposite side becomes, and therefore the longer it may become.

Conversely, if the angle facing a side of a triangle decreases, then the length of the opposite side may also decrease. This is because the smaller the angle, the less vertical the opposite side becomes, and therefore the shorter it may become.

From the given diagram, the largest side of the triangle will be the side directly opposite the largest angle.

Also, the smallest side of the triangle will be the side directly opposite the smallest angle.

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Answer:

Step-by-step explanation:

2 cups of water.

The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday

Given that

Combined hours = x - 2 + x + x - 3

When splitted, we have

Monday = x - 2

Wednesday = x

Friday = x + 3

To determine which statement is true, we need to compare the hours worked on Monday and Wednesday, and the hours worked on Wednesday and Friday.

By comparison, Option 1 is correct

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After calculating the straight angle we know that ∠BAC is (A) 150°.

What is the straight angle?

A straight angle in geometry is one that is 180 degrees in length.

It looks like a straight line, which is why it is known as a straight angle.

In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.

A straight angle in geometry is an angle with a vertex point that is at 180 degrees.

In other words, an angle becomes a straight angle when its arms point in the opposite direction.

So, we know that s straight angle is always 180°.

∠BAD is a straight angle.

We can also observe that:

∠BAD = ∠BAC + ∠CAD

Now, solve as follows:

∠BAD = ∠BAC + ∠CAD

180 = ∠BAC + 50

180 - 50 = ∠BAC

130° = ∠BAC

Therefore, after calculating the straight angle we know that ∠BAC is (A) 150°.

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Answer: Buckle up this answer is gonna be a rollercoaster and here we go.

To find f.g, we first need to evaluate g(-4) and then use the result as the input for f(x).

We have:

g(-4) = -(-4)^2 + 2 = -16 + 2 = -14

Now, we use this result as the input for f(x):

f(g(-4)) = f(-14) = -14 - 8 = -22

Therefore, f.g = -22.

What a short ride.

The outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario can be written as S = { (1,3,5), (2,3,4), (2,4,3), (3,2,4), (3,4,2), (4,2,3), (4,3,2), (5,1,3)}

Outcome refers to the result of an action or event. It is the end result of the process and can be positive, negative, or a mix of both. Outcome can also refer to the impact of an event, such as the effect it has on the environment, the people affected, or the economy.

The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.

Each of the elements in this set represents a combination of numbers on the dice that will add up to 9 when rolled. For example, the first element of this set (1,3,5) means that if the three dice are rolled, the numbers shown on the dice will be 1, 3, and 5, and the sum of the numbers will be 9.

When determining the sample space for the outcome of rolling three dice, the order of the numbers does not matter. Therefore, the sets (2,3,4) and (4,2,3) are equivalent, since the sum of the numbers is still 9 regardless of the order.

In conclusion, the outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.

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Applying the Trigonometric ratios, the length of DC is approximately 30 units.

To find the length of DC, we have to apply the Trigonometric ratios.

First of all, find BD.

Considering right triangle ADB, we have:

Reference angle (∅) = 54°

Length of Hypotenuse = 20

Length of opposite side = BD = ?

Apply the sine ratio:

sin 54 = opp/hyp

sin 54 = BD/20

BD = sin 54 × 20

BD ≈ 16

Use the tangent ratio to find DC:

Reference angle (∅) = 28°

Length of adjacent side = DC = ?

Length of opposite side = BD = 16

tan 28 = opp/adj

tan 28 = 16/DC

DC = 16/tan 28

DC ≈ 30

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The estimated value of 2/3 is roughly 0.67, of 1 it is 1 and for 0 it is 0.

What does a estimate mean?

A number given to a demographic parameter that was taken from the a statistical sample. A pricing estimate for the job that needs to be done. 3. an assessment or view of the essence, character, or trait of an object or a person.

What is an illustration of an estimate?

To make computations simpler, an estimate is an approximate estimation of the real value, amount, or quantity.

For 2/3, on dividing we get the value as 0.67.

Since 1 is a number and doesn't need to be rounded or approximated, the guess is 1.

Since it is a number without a fractional component, the approximation of 0 also is 0.

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Answer:33

Step-by-step explanation:

33

Answer:

To find the zeros of the function f(w) = w^2 + 13w + 40, we need to solve the equation f(w) = 0.

We can factor the quadratic expression as (w + 8)(w + 5) = 0.

Therefore, the zeros of the function are w = -8 and w = -5.

Step-by-step explanation: