14. Construction workers are laying out the rectangular foundation for a new building.They want to check that the corner is 90°. They measure the diagonal as shown to be 9.5 m. Is the angle 90° Explain your reasoning.

We are asked to find 1/3 of 3/7 using a rectangular fraction model.

Let us draw a rectangular fraction model.

1/3 means make 3 rows

3/7 means make 7 columns

Three 3 filled boxes represent the numerator and the total 21 boxes represent the denominator.

Therefore, the result is 3/21

We are given the following coordinates.

We are asked to reflect them across the x-axis.

Recall that the rule for reflection across the x-axis is given by

As you can see, the y-coordinate gets reversed.

Let us apply this rule on the given coordinates S, T, U

Therefore, the above coordinates are reflected over the x-axis.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve for x as follows:

In the  Polynomial  function  f(x)= [tex]2x^{3} -11x^{2} -12x+36 =0 then[/tex]

So all the zeros of f(x) algebraically

[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex].

Step: 1

Given[tex]$f(x)=2 x^3-11 x^2-12 x+36$and $f(6)=0 \Rightarrow(x-6)$ is factor of $f(x)$now $f(x)=2 x^3-11 x^2-12 x+36$$$[/tex]

[tex]\begin{aligned}&\Rightarrow \mathrm{f}(\mathrm{x})=\left(2 \mathrm{x}^2-12 \mathrm{x}^2\right)+\left(\mathrm{x}^2-\right. \\&\Rightarrow \mathrm{f}(\mathrm{x})=2 \mathrm{x}^2(\mathrm{x}-6)+(\mathrm{x}-6)^2 \\&\Rightarrow \mathrm{f}(\mathrm{x})=(\mathrm{x}-6)\left(2 \mathrm{x}^2+\mathrm{x}-6\right)\end{aligned}$$[/tex]

Step: 2

Now consider [tex]$2 x^2+x-6=2 x^2+4 x-3 x-6$$$\begin{aligned}&\Rightarrow 2 x(x+2)-3(x+2) \\&\Rightarrow 2 x^2+x-6=(2 x-3)(x+2)\end{aligned}$$[/tex]

[tex]$5 \circ f(x)=(x-6)\left(2 x^2+x-6\right)$$$\Rightarrow \mathrm{f}(\mathrm{x})=(x-6)(2 \mathrm{x}-3)(\mathrm{x}+2)$$[/tex]

Step: 3

so for finding zeros of

[tex]$f(x) \rightarrow f(x)=0$$$\Rightarrow(x-6)(2 x-3)(x+2)=0$$$$\Rightarrow(x-6)=0 ;(2 x-3)=0 ;(x+2)=0$$[/tex]

[tex]$$\Rightarrow x=6, x=\frac{3}{2} ; x=-2$$[/tex]

Explanation: Please refer to solution in this step.

Answer:

So required zeros of

[tex]\mathrm{f}(\mathrm{x}) \ are\ \mathrm{x}=-2, \mathrm{x}=\frac{3}{2}, \mathrm{x}=6$[/tex]

A polynomial consists of two words, poly and nominal. "Poly" means many and "nomial" means  term, and so when  combined, polynomials can be said to be "algebraic expressions with many terms." Let's go ahead and start by defining polynomial functions and their types.

The polynomial function in standard form is:

f(x) =  [tex]a_{n}x^{n} +a_{n-1} x^{n-1} +.....a_{2} x^{2} +a_{1} x+a0[/tex]

This algebraic expression is called a polynomial function of the variable x. The name of a polynomial is determined by the number of terms it contains.

The three most common polynomials we usually encounter are

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We must solve the following equation for x:

We can square both sides of the equation so we can get rid of the radical:

We expand the squared binomial on the left:

Then we substract (3-x) from both sides:

Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:

In our case a=1, b=7 and c=6 so we get:

So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:

Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:

From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.

Then the answer is option A.

Answer:

y=-1x/4+5/2

Step-by-step explanation:

use the slope formula

Answer:

C. y = 1.60 +.08x

Explanation:

The cost of the ice cream will be equal to the fixed cost of $1.60 plus the cost that depends on the number of toppings. So, if Natasha chooses x number of topping, the total cost of the toppings will be 8 cents times x or $0.08x

So, the total cost for the ice cream is represented by the equation:

y = 1.60 +.08x

The most appropriate choice for subtraction of natural numbers will be given by-

Jenny needs $1172.95 to earn her goal.

What is subtraction?

At first, it is important to know about natural numbers.

Natural numbers are integers which are greater than or equal to 1

One of the operations on natural number is subtraction

The process of reducing one number from another number is called subtraction. Subtraction is used to find the difference between two numbers. The larger number is called minuend and the smaller number is called subtrehend.

Amount of money Jennyy had before = $127.05

Amount of money Jenny wants to earn = $1300

Amount of money Jenny needs to earn her goal = $(1300 - 127.05)

                                                                                 = $1172.95

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Complete Question

Jenny wants to earn $1,300 by the end of the summer. How much more will she need to meet her goal?

(Jenny had $127.05 before.)

To calculate the volume, w will use the formula:

where r is the radius and h is the height

From the question,

diameter = 10

This implies that; r=d/2 = 10/2 = 5

h = 17

susbtitute the values into the formula

If we substitute the value of pie= 22/7

Let's begin by identifying key information given to us:

Thale's method shows that angles in a triangle opposite two sides of equal length are equal

As such, the answer is A (The distance between points A and Z is the same as the distance between X and Z)

Answer:

-7

Step-by-step explanation:

Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).

Given the expression:

Let's simplify the expression and convert its decimal form to get its approximation.

We get,

In decimal form:

Therefore, the approximate equivalent of 3√200 is 5.8.

Given:

To find- the simplification.

Explanation-

We know that the distribution property of multiplication over addition says

Use this property to simplify, and we get

Multiply by opening the bracket, and we get

Now, open the bracket and combine the like terms.

On further solving, we get

Thus, from the distributive property of multiplication over addition, we get v⁴+13v³+37v²-7v-44.

The answer is v⁴ + 13v³ + 37v² - 7v - 44.

The volume from tanks A and B are taken as 3 and 5 gallons respectively.

Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B =  1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40  + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3

Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.

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The given quadratic equation is

y = - x^2 + 25

a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.

Leading coefficient = - 1

Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is

Down

b) The standard form of a quadratic equation is

y = ax^2 + bx + c

By comparing both equations,

a = - 1

b = 0

c = 25

The formula for calculating the x coordinate of the vertex of the graph is

x = - b/2a

By substituting the given values,

x = - 0/2 * - 1 = 0

We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have

y = - 0^2 + 25

y = 25

The coordinate of the vertex is (0, 25)

c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have

- x^2 + 25 = 0

x^2 = 25

Taking the square root of both sides,

x = square root of 25

x = ± 5

Thus, the x intercepts are

(5, - 5)

d) The y intercept is the value of y when x = 0

Substituting x = 0 into the orignal equation,

y = - 0^2 + 25

y = 25

y intercept = (0, 25)

e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have

y = - (6)^2 + 25 = - 36 + 25

y = - 11

We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below

Answer:

The range of z-score is given below as

The final answer is

Solution:

Given that the initial cost price of the jewelry is $2,200.

The rate at which it decreases each year is 12%.

Thus, the exponential decay function is;

The graph of the function is;

From the graph;

CORRECT OPTION:

Answer: 14

Step-by-step explanation:

1/4 of a pumpkin is required to make a pie. The easiest way to complete this is to convert 3.5 pumpkins into the same fraction.

1 pumpkin = 4/4

3.5 pumpkins = 14/4

If only 1/4 of a pumpkin is required to make a pie and we have 14/4 then we can make 14 pumpkin pies.

ANSWER

x = 10.2

EXPLANATION

In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.

With the given information, we can use the cosine of the angle to find the missing value,

In this problem,

Solving for x,

Hence, the value of x is 10.2, rounded to the nearest tenth.

The given points are A(-3, 1), B(2, 1), C(2, 4), D(-3, 4).

The image below shows the figure formed by these points.

As you can observe, the shape formed by the given points is a rectangle with dimensions 5 times 3.

Out of 200 students surveyed, 38 said that soccer was their favorite sport.

The total number of students surveyed represents 100% of the sample, to determine which percentage does 38 represent, you can use cross multiplication:

200 students____100%

38 students _____ x%

Both relationships are at the same ratio so that:

To determine the percentage multiply both sides by 38:

The percentage of students surveyed that like soccer is 19%

x = 8, y = 21

The given equation is:

y = 4x - 11 = x + 13

This can be splitted into two equations as:

y = 4x - 11..........(1)

y = x + 13..........(2)

Substitute equation (1) into equation (2)

4x - 11 = x + 13

4x - x = 13 + 11

3x = 24

x = 24/3

x = 8

Substitute the value of x into equation (1)

y = 4x - 11

y = 4(8) - 11

y = 32 - 11

y = 21

x = 8, y = 21

Given the word problem, we can deduce the following information:

1. Jan draws a card from the set below, replaces it and then draws another card.

Based on the given information, there is a replacement happening. It means that Jan put a card back in the set before selecting another card. So the tree diagram that shows all the possible outcomes is Diagram A.

Therefore, the answer is A.

There would be 91.8 calories in 27 grams.

The unitary approach involves determining the value of a single unit, from which we can calculate the values of the necessary number of units. We must first determine the number of objects at the unit level in order to answer questions based on the unitary technique, after which we must determine it for higher values. For instance, if the price of 5 chocolates is $10, it is preferable to first determine the price of 1 chocolate in order to get the price of 6 chocolates. Once we get the price for 6 chocolates, we multiply it by 6.

Given,

Calories per serving = 25

Serving size = 85 grams

Calories per serving using unitary method:

Dividing,

[tex]\frac{85}{25}[/tex]

3.4

Calories per serving using unitary method is 3.4 calories.

Now, we have 27 grams,

Multiplying:

27 (3.4)

91.8

There would be 91.8 calories in 27 grams.

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The given equation is

Where a = 2, b = 8, and c = 8.

The discriminant formula is

Let's replace the values

The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.

This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.

In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.

Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.

Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.

The difference is however $2.79 - $2.36 = $0.43.

Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.

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Solution

The volume for a triangular pyramid is given by:

And the Base is given by:

And since h= 1.5 ft we have this:

And then we can find the total cost like this:

Then the final answer would be 12$

The values of the variables are x = 2, y = -2 and z =0

From the question, the system of equations is given as

x – y - 3z = 4

2x + 3y – 3z = -2

x + 3y – 2z = -4

Subtract the second equation from the third

This action will eliminate (y)

So, we have

x + 3y – 2z = -4 - (2x + 3y – 3z = -2)

Evaluate

-x + z = -2

Make x the subject

x = z + 2

Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4

z + 2 – y - 3z = 4

z + 2 + 3y – 2z = -4

Evaluate

-2z - y = 2

-z + 3y = -6

Double -z + 3y = -6

-2z + 6y = -12

Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z

7y = -14

Divide

y = -2

Substitute y = -2 in -z + 3y = -6

-z + 3(-2) = -6

Evaluate

-z - 6 = -6

Evaluate

z = 0

Recall that x – y - 3z = 4

So, we have

x + 2 - 3(0) = 4

Evaluate

x = 2

Hence, the solution is x = 2, y = -2 and z =0

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ExplanatIon

Step 1

let x represents the number

hence,

four times a number =4*x=4x

the difference of four times a number and seven=4x-7

is can be written as equal or "="",so

the difference of four times a number and seven is 13​

Step 2

solve for x

so, the number is 5.

I hope this helps you

To determine the fraction of cousins, you have to divide the number of cousins she invited by the total number of guests.

She invited 12 cousins, 6 aunts, 4 brothers, and 2 sisters, a total of 24 guests.

Then:

Both, 12 and 24 are divisible by 12, to simplify the fraction, divide the numerator and denominator by 12

The fraction