The table represents a quadratic function. Write an equation of the function in standard form.

x -9 -7 -5 -3
y 0 8 8 0

y = ?

The length of the Hypotenuse is, [tex]\sqrt{5}x[/tex] units.

What is Pythagoras Theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Let the one leg of a right triangle is twice as long as the other.

Suppose the shorter leg is x.

So the longer leg is 2x.

Let, the hypotenuse is h.

By Pythagoras Theorem,

[tex]x^2 + (2x)^2 = h^2\\x^2 + 4x^2 = h^2\\5x^2 = h^2\\h = \sqrt{5} x[/tex]

Hence, the hypotenuse as a function of the length of the shorter leg, is [tex]\sqrt{5}x[/tex] units.

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Answer: $931

Step-by-step explanation:

Since $980 is 100% of the price and the cash discount is 5% we can calculate the cash price of the portrait like this:

$980 full price* (1 - .05 discount) = $931

ok I will help you

A=hbb

2

b Base

hb Height

The final price of the car when Mark sells a car that has been marked up $450 is $2452.50.

From the information, Mark sells a car that has been marked up $450, which was 25% of the buying price.

He also has to charge a 9% sales tax on the selling price of the car. The final price of the car will be:

= Original price + Mark up + Tax

= $1800 + $450 + (9% × $1800 + $450)

= $1800 + $450 + $202.50

= $2452.50

The price is $2452.50.

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Answer:

2:45

Step-by-step explanation:

1 hour has 60 minutes so:

number of hours in 1000minutes:

1000/60=16.6666hours

so 16 hours + 0.6666 hours

convert 0.6666 hours to minutes;

0.6666x60=39.99minutes=40 minutes(rounded)

10:05+16hours+40 minutes

2:05+40minutes=2:45

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Answer:

12 - D = X

Step-by-step explanation:

Im not REALLY x2 sure but hope its helpful

Answer:

9

Step-by-step explanation:

y = x - 4

y = 13 - 4

y = 9

By evaluating the function in x = 1 we get:

C(1) =  95.16

This means that the per capita consumption of all poultry in 2015 was 95.16 pounds.

Here we have the linear function:

C(x) = 2.97*x+ 92.19

We know that it models the consumption of all poultry in a country as a function of x, the number of years since 2014.

Then C(1) will be the consumption of all poultry in that country one year after 2014 (this would be on 2015).

To evaluate we just need to replace the variable x in the equation by 1, we will get:

C(1) = 2.97*1+ 92.19 = 95.16

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Answer:

Y= x+1

Step-by-step explanation:

m=2-1/ 1-0; m=1

Y-2= 1(x-1)

Y= x-1+2

Y= x+1

9 servings are there in 22.5 ounces of trail mix.

Given:

The weight of one serving of trail mix is 2. 5 ounces.

1 serving = 2.5 ounces

Number of servings = 22.5 ounces / 1 serving

= 22.5 / 2.5

= 225/10/25/10

= 225/25

= 9 servings.

Therefore 9 servings are there in 22.5 ounces of trail mix.

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Answer:$1031$

Step-by-step explanation: $980 is the worth of the portrait right? That means that 5%-100%=95% of the portrait is 980 so if we multiply by the reciprocal which is 980*100/95=$1031$

Answer:

[tex]68 = 2 \times 2 \times 17[/tex]

The angle W equal to 24.3

In a triangle sum of three angles is equal to 180

W = (3x-24) degree

C = (4x-11) degree

T = 2x degree

3x-24+4x-11+2x=180

9x-35=180

9x=180-35

9x= 145

x=16.1

substitute the value of x in W equation

W = 3(16.1)-24 = 24.3

The value of angle W is 24.3

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Answer: The answer should be a 27-degree difference

Step-by-step explanation:

If you add -11 and 11 you get 0 then add 16. 11+16 is 27 so a 27-degree difference!!!

Answer:

x>-4

Step-by-step explanation:

There are 28 landscapes.

From the question, we have

In five photos = 2 landscapes.

In 70 photos = 2/5*70

=28 landscapes.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

First, know that this is a downwards parabola graph.

Answer:

Answer number 3

y=-9x+5

The value of n/p is 8.

What is quadratic equation?

A quadratic equation in algebra is any equation that can be written in standard form as where x is an unknown and where a, b, and c denote known numbers, where a ≠ 0.

Let, for x^2 + mx + n = 0

⇒ x = 2α or 2β

From the given condition,

for x^2 + mx + n = 0 ⇒ x = α or x = β

Then,

2(α + β) = -m           ..(1)

4αβ = n                    ..(2)

and α + β = -p         ..(3)

αβ = m                     ..(4)

From equation (1) and (3),

-m/2 = -p

⇒ p = m/2

and from equation (2) and (4),

n/4 = m

⇒ n = 4m

Therefore,

n/p = 4m / (m/2) = 4 x 2 = 8

Hence, n/p = 8.

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Answer:

Two consecutive numbers can be written as x and x+1

if we add those two equations together we get 2x+1

And since any number times two is an even number if you add one to any even number you always get an odd number

Answer:

the cheaper plan is Mike's until month 10.  At month 10 the plans are equal after month 10 All Day is cheaper

Step-by-step explanation:

30x = 22x + 80  Set the equations equal to each other and subtract 22 from both sides of the equal sign

8x = 80  Divide both sides by 8

x = 10

At 10 months the plan are equal.

Answer:

Step-by-step explanation:

Probability that the arrow will stop on the same letter twice = 1/3 (c).

What is probability?

The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that an announcement is true.

Main body:

Given : Maria will spin the arrow on the spinner 2 times.

To find : What is the probability that the arrow will stop on the same letter twice.

Solution : We have given a spinner that spin twice and stop on the same letter.

Formula for probability = no. of favourable outcome/ total outcomes

Here, total part of spinner = 3 and it spin two times

So, total possible outcome = 6.  Arrow stay on same letter twice( favorable outcome) =2.

Plugging the values in formula :

Probability =  2/6

Probability =  1/3

Therefore,  probability that the arrow will stop on the same letter twice =  (c).

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Answer: 2x3-1

Step-by-step explanation:

The smallest angles of the triangle is angle A

In triangle ABC

The length of the side AB = 6.2 units

The length of the side AC = 9.5 units

The length of the side BC = 5.1 units

The opposite angle of AB is angle C, the opposite angle of AC is angle B and the opposite angle of BC is angle A

We know length of the line is BC which is 5.1 units which is the smallest side of the triangle. Then the opposite angle of BC will be the smallest angle in the triangle ABC

The opposite angle of the side BC is angle A, which is the smallest angle in the triangle

Hence, the smallest angles of the triangle is angle A

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The expected population of a city in 4 years is 581,000.

Current population (P) = 528 000.

Rate of growth (r) = 2.4%

Time t = 4 years

Expected population (A) = ?

The formula used is-

A = P(1 + r/100)∧t

Put the values.

A = 528 000(1 + 2.4/100)∧4

A = 528 000 x (1.042)∧4

A = 581,000

Thus, the expected population  of a city in 4 years is 581,000.

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The cost per ticket is $9, the cost of 5 ice cream cones is $14.58 and the cost of 12 bananas is $4.8.

a.

4 movie tickets cost $36.

cost per ticket = 36/4

= $9,

The cost per ticket is $9.

b.

3 ice cream cones cost $8.75.

1 ice cream cost = 8.75/3

= 2.916

5 ice cream cost = 2.916*5

= $14.58.

The cost of 5 ice cream cones is $14.58.

c.

5 bananas cost $2.00.

1 banana cost = 2/5

= 0.4

12 bananas cost = 0.4*12

= $4.8.

The cost of 12 bananas is $4.8.

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Answer:

He will read C. 38 pages on the 11th day.

Step-by-step explanation:

First day = 8 pages

2nd day = 8+3 = 11 pages

Sequence = (8,11,14.......)

a+(n-1)d

a = first term

nth term = 11

d(difference) = +3 or 3

8+(11-1)3

=38

The claim of invertible metrix is true and others are false.

In the given value we have to check which is true and which is false for the eigenvalues.

The eigenvalues are 2, 2, 5.

(1) First check the matrix is certainly invertible.

The matrix is invertible when the probuct of eigenvalues does not equal to zero.

invertible of A = 2*2*5

invertible of A = 20 which is not equal to zero.

So the matrix is certainly invertible. The claim is true.

(2) Now we check the matrix is certainly diagonalizable.

We note that the eigen value 2 has an algebraic multiplicity of 2 (number of repetitions), but we are unsure if the accompanying eigen vectors likewise have a count of two (geometric multiplicity)

The sum of the algebraic multiplicities must equal the sum of the geometric multiplicities in order for A to be diagonalizable.

In this instance, there is no evidence to support the geometric multiplicity of the eigenvalue 2. Therefore, we are unable to affirm that A is diagonalizable.

Consequently, the claim is false.

(3) Now we check the matrix is certainly not diagonalizable.

If the homogeneous equation from (A-⋋I)x=0 when the eigen value ⋋=2 is substituted x+y+z=0, then the solution set is x=-k-m where y=k, z=m are the parameters.

So it can be written as

[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =k\left[\begin{array}{ccc}-1\\1\\0\end{array}\right] +m\left[\begin{array}{ccc}-1\\0\\1\end{array}\right][/tex]

Putting k=1 and m=1, then the corresponding eigen vectors for ⋋=2 are [tex]\left[\begin{array}{ccc}-1\\1\\0\end{array}\right],\left[\begin{array}{ccc}-1\\0\\1\end{array}\right][/tex]

So the geometric multiplicity of the eigen value ⋋=2 is 2.

The algebraic multiplicity = Geometric multiplicity we can see the given matrix A is diagonalizable.

So the statement is false.

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