What is the value of x?

The equation of the quadratic function that contains the point (1,1) is

y = 2x² - 1.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree. A quadratic function must contain at least one term of the second degree.

Given  the quadratic function that contains the point (1,1)

x = 1 and y = f(x) = 1

the shape of the equation is the same as f(x) = 2x²

a quadratic equation is given by

y = a(x - k)² + h

here (k, h) is the vertex of the function

given vertex is on the y-axis,

so k = 0

y = ax² + h

and a = 2 from f(x) = 2x²

y = 2x² + h

substitute x= 1 and y = 1

1 = 2 + h

h = 1 - 2 =  -1

equation of function is y = 2x² - 1

Hence equation of the function is y = 2x² - 1.

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The 95% confidence interval estimate of the change in occupancy for the one year period is given as follows:

(0.1441, 0.1815).

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The percent change is given by the change divided by the initial value, hence the parameters are given as follows:

[tex]n = 1505, \pi = \frac{1750 - 1505}{1505} = 0.1628[/tex]

Hence the lower bound of the interval is of:

[tex]0.1628 - 1.96\sqrt{\frac{0.1628(0.8372)}{1505}} = 0.1441[/tex]

The upper bound of the interval is of:

[tex]0.1628 + 1.96\sqrt{\frac{0.1628(0.8372)}{1505}} = 0.1815[/tex]

Only the confidence interval can be calculated as the remainder of the problem is incomplete

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According to the problem the domain of this function is all real numbers x greater than or equal to 0.

Real numbers are any number that can be used to represent a quantity on the number line. They include both rational numbers (integers, fractions, and decimals) and irrational numbers (numbers that cannot be expressed as a fraction). Real numbers can be positive, negative, or zero and include the number line's endpoint values of positive and negative infinity. Real numbers are used in many areas of mathematics, including algebra and calculus. They are also found in everyday life, in the measurements of length, temperature, and in currency values.

The domain of this function is all real numbers x greater than or equal to 0. The range of this function is all real numbers y greater than or equal to 3. This is because all values of x are mapped to values of y that are greater than or equal to 3.

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Answer:

n = 30

Step-by-step explanation:

Since it is not a right-angle triangle, you will need to use sine or cosine rule;

We have two side lengths and the angle between, this means you need to use the cosine rule:

a² = b² + c² - 2bc.cosA

[tex]{a}^{2} = ({4 \sqrt{3} })^{2} + {( \sqrt{6} )}^{2} - 2( 4\sqrt{3})( \sqrt{6} ). \cos(45) \\ {a}^{2} = 48 + 6 - 8 \sqrt{18}(0.707...) \\ {a}^{2} = 54 - 24 \\ {a}^{2} = 30 \\ a = \sqrt{30}[/tex]

Answer:

n = 30

Step-by-step explanation:

For this question, use the cosine law formula:

[tex]a=\sqrt{c^2+b^2-2cb*cosA} \\a=\sqrt{(\sqrt{6})^2+(4\sqrt{3})^2-2(\sqrt{6})(4\sqrt{3})*cos45 }\\a =\sqrt{6+48-(8\sqrt{18})*\frac{\sqrt{2} }{2} }\\a=\sqrt{54-\frac{8\sqrt{36} }{2} }\\a=\sqrt{54-24}\\a=\sqrt{30}[/tex]

If a = [tex]\sqrt{n}[/tex], then n must be 30

Answer:

your answer is going to be 390625

Step-by-step explanation:

do 5x5x5x5x5x5x5x5 and you will get 390625

Answer:

x = 13

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

sum the 6 exterior angles and equate to 360

3x + 6 + 41 + 6x - 5 + 4x + 7 + 62 + 7x - 11 = 360

20x + 100 = 360 ( subtract 100 from both sides )

20x = 260 ( divide both sides by 20 )

x = 13

Answer:

6x + y

Step-by-step explanation:

Remove the parenthesis

8x−6y−2x+7y

Add like terms

(8x−2x)+(−6y+7y)

Simplify

6x+y

Answer:

(-6x-y)

Step-by-step explanation:

We would subtract like terms

2x and 8x are like terms

2x-8x = -6x

-7y and -6y

-7y+6y = -y

Giving us...

(-6x-y)

Answer:

y = 5

Step-by-step explanation:

The angle formed is a right angle which has a measure of 90 degrees. This means that the sum of the two angles is 90 degrees. Using this information we can set up an equation and solve for y

Set up equation

7y + 8 + 8y + 7 = 90

==> combine like terms

15y + 15 = 90

==> subtract 15 from both sides

15y = 75

==> divide both sides by 15

y = 5

Answer:

the answer will be 19/8

Step-by-step explanation:

pls give brainlyest

Answer:

If Joe invested x dollars in company A, he invested x + 40 dollars in company B.

The probability of P(X=10) is  [tex]\frac{27}{216}[/tex]

To get a sum of 10 , the possible triples are

Set1      Set2

136        226

145        244

235       334

If a ≠ b ≠ c  there exist 3 !=b number of permutations of (a, b, c).

If a = b ≠  c then there exist 3 unique permutations of (a, b, c).

In set 1 in each combinations, there are different numbers. joe [tex]$a \neq b \neq c$[/tex]. Thus for each combination there exist 6 permutations.

For example (1 3 6) can be written in 6 different ways.

(1 3 6), (1 6 3), (6 1 3), (3 1 6), (6 3 1)

This, we can get a sum of 10 from the numbers 136 in 6 ways.

There are 3 different combinations in set 1 , thus total number ways =3*16-18.

In set of 2 each combination can be obtained in a 3 ways.

So, total number of ways in set 2 is 3*3=9.

The total is 18+9=27 number of possible ways to get sum of 10 in three dice.

⇒P(X=10)=[tex]\frac{27}{6^{3} }[/tex]

⇒P(X=10)=[tex]\frac{27}{216}[/tex]

Therefore, the P(X=10) is [tex]\frac{27}{216}[/tex].

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Answer: 214.008

Step-by-step explanation: hope this helped :)

The unknown measures in similar triangles in which x is 24 in.

What is a similar triangle?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

We have given,

ΔABC ≈ ΔXYZ

In ΔABC

AC = 36 in, BC = 18 in and AB = x in

In ΔXYZ

XY = 16in, ZY = 12in and  XZ = 24in

We know that,

the side and angles of a similar triangle are in proportion to each other.

AC / XZ = 36 / 24 = 3/2

BC / ZY = 18 / 12 = 3/2

AB / XY = x / 16

AC / XZ = BC / ZY = AB / XY   --------(similar triangle)

x / 16 = 3/2

x  = 3/2 * 16

x = 3 * 8

x = 24

hence, the unknown measures in similar triangles in which x is 24 in.

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Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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Answer:

7 times 4 equals 28

Step-by-step explanation:

Answer:

The answer will be 2

Step-by-step explanation:

x = 14 y = 4

x = ? y = 28

= 14 × 4 = x × 28

= 56 = x × 28

= x = 28/56

= x = 2

The average speed is 75.33 miles per hour.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Distance = 565 miles

Time.

= 5:00 pm t0 12:30 am

= 7.5 hours

Now,

Average speed.

= 565 / 7.5

= 75.33

Thus,

75.33 miles per hour is the average speed.

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[tex]-\frac{263}{6}[/tex] or [tex]-43.8333.[/tex]

[tex]\frac{7}{6} -(18+27)[/tex]

[tex]\frac{7}{6} -(45)\\ \\\frac{7}{6} -45[/tex]

This can be done by multiplying number 45 by the denominator of the fraction (6) and adding 6 as a denominator of 45.

[tex]\frac{45}{6}*6\\ \\ \frac{270}{6}[/tex]

[tex]\frac{7}{6} -\frac{270}{6}[/tex]

[tex]\frac{7-270}{6}=\\ \\-\frac{263}{6}[/tex]

Since the numerator of this fraction (263) is a prime number, the fraction cannot be further simplified and it's the final result.

Answer:

The x intercept is going to be (-43/4) and the y intercept is going to be (0,-43)

Step-by-step explanation:

hope this helped

At the clothing store, the number of customers that one employee can help is 4 customers.

At the coffee shop, the number of customers that one employee can help is 6 customers.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the clothing shop with these points (2, 4) and (3, 6) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (6 - 4)/(3 - 2)(x - 2)

y - 4 = 2(x - 2)

y = 2x + 2

When x = 1, we have:

y = 2(1) + 2

y = 4 customers.

Furthermore, a linear equation which models the coffee shop is given by:

y = kx

Where:

k = y/x

k = 6/1

Therefore, the required linear equation which models the coffee shop is y = 6x.

When x = 1, we have:

y = 6(1)

y = 6 customers.

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If Steve just got a new job working at a bank.  Steve's gross monthly income is $5,000, Steve's monthly net income is  $3,277 and Seve can afford the suit based on the 5% spending guideline for clothing.

a. Steve's gross monthly income is

Gross income = $60,000 / 12

Gross income = $5,000

b.  Steve's monthly net income

His deductions are:

Medicare: $72.50

Social Security: $310

Federal Tax: $500

State Tax: $262.50

Health insurance: $553

Dental insurance: $127

Total deductions = $72.50 + $310 + $500 + $262.50 + $553 + $127 = $1723.00

Steve's monthly net income = $5,000 - $1,723 = $3,277

c. In order to  see if Steve can afford the suit using the 5% spending guideline for clothing, we need to find the 5% of his monthly net income:

5% of $3,277 = $163.85

Since  the amount of $150 is less than $163.85, Steve can afford the suit based on the 5% spending guideline for clothing.

Therefore  Steve's gross monthly income is $5,000, Steve's monthly net income is  $3,277 and Seve can afford the suit based on the 5% spending guideline for clothing.

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Answer:

Step-by-step explanation:

You want the measures of 5 marked angles in the figure showing two transversals crossing parallel lines.

Angle 1 forms a linear pair with the angle marked 88°, so is supplementary to it.

  Angle 1 = 180° -88°

  Angle 1 = 92°

Angle 3 is a corresponding angle to the one marked 64° where the horizontal transversal crosses the parallel lines. Corresponding angles are congruent.

  Angle 3 = 64°

Angles 2 and 3 are "remote interior angles" with respect to the exterior angle marked 88°. Hence their sum is 88°.

  Angle 2 = 88° -Angle 3 = 88° -64°

  Angle 2 = 24°

Angles 3, 4, and 81° combine to form a straight angle of 180°.

  Angle 4 = 180° -64° -81°

  Angle 4 = 35°

Angle 5 is an alternate interior angle with respect to the one marked 81° where the downward-sloping transversal crosses the parallel lines. Alternate interior angles are congruent.

  Angle 5 = 81°

Answer:

answer is D

Step-by-step explanation:

A={h,I,j,k l} and B={h,j,l m,n}

n(A U B)={h,I,j,k,l,m,n }

number is 7

Answer:

pls give brainiest

Step-by-step explanation:

a）2（x＋5）＋4（x-1）

＝2x＋10＋4x-4

＝6x＋6

＝6（x＋1）

b）3（y-2）＋2（y-1）

＝3y-6＋2y-2

＝5y-8

c）7（r＋3）-2（r-1）

＝7r＋21-2r＋2

＝5r＋23

Answer:

9

30

2.5

4

Step-by-step explanation:

I hope you understand cause I did it mentally but if you need and explanation just text here

Answer:

Step-by-step explanation:

Answer is A

The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

h(x) = √(x - 7) + 5

The value inside the square root should be greater than or equal to zero. Then we have

x - 7 ≥ 0

x ≥ 7

The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

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Answer:

(f - g)(x) = f(x) - g(x) = (x² - 8x + 12) - (x - 2) = x² - 8x + 12 - x + 2 = x² - 9x + 14. So, (f - g)(x) = x² - 9x + 14.

The number of guitars sold each year in Montana is given as follows:

7075 guitars.

The number of guitars sold per year in Montana is obtained applying the proportions in the context of this problem.

Ohio's average is seven times Montana's average, hence Montana's amount is obtained dividing Ohio's amount by 7.

Ohio's amount is given as follows:

49525 guitars.

Hence Montana's amount is obtained as follows:

49525/7 = 7075 guitars.

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Answer:

Step-by-step explanation:

The number is 75,146.

This can be arrived at by breaking down the number as follows:

7 ten thousands: 70000

5 fewer thousands than ten thousands: 10000 - 5000 = 5000

1 more hundred than thousands: 5000 + 100 = 5100

6 more tens than hundreds: 5100 + 60 = 5160

5 more ones than ten hundreds: 5160 + 5 = 5165

So, 70000 + 5000 + 5100 + 60 + 5 = 75,165

a) The transformations applied to the graph of f to obtain the graph of g are given as follows:

b) The rule for g(x) is given as follows: g(x) = 2x³ - 6x² + 3.

The parent function f(x) is defined as follows:

f(x) = x³ - 3x² + 2.

The transformed function is given as follows:

g(x) = 2f(x) - 1.

The meaning of each transformation is given as follows:

The rule for g(x) is then obtained as follows:

g(x) = 2(x³ - 3x² + 2) - 1

g(x) = 2x³ - 6x² + 4 - 1

g(x) = 2x³ - 6x² + 3.

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