The graph of function f is shown. An exponential function on a coordinate plane passes through (minus 1, 7), (1, 2), (10, minus 1) and also intercepts the x-axis at 3 units and the y-axis at 4 units. Function g is represented by the table. x -1 0 1 2 3 g(x) 24 4 0 Which statement correctly compares the two functions? A. They have the same x- and y-intercepts. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same x-intercept and the same end behavior as x approaches ∞. D. They have the same y-intercept and the same end behavior as x approaches ∞.

I WILL USE THE LAWS OF EXPONENTS

[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]

AND

[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]

[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]

ATTACHED IS THE SOLUTION.

Answer:

i hope this one is good for you

Length of the resulting box will be of (16-x) inches

A rectangle can be made into a cuboid by cutting squares of equal length from each corners and then joining the edges.

Given, length of cardboard= 16inches

Width of cardboard= 12 inches

If squares of side x is cut out of the corners and the sides are bent  upwards to make a box,

The dimensions of the resulting box will be,

Length= (16-x) inches

Width= (12-x) inches        

Height= x inches

Therefore the length of the resulting box will be of (16-x) inches.

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The largest possible whole-number length for the third side of the triangle is 23.

The total of any two sides in a triangle with sides a, b, and c MUST be less than the length of the third side.  

You have a line segment, not a triangle if the third side's length equals the sum of the other two sides' lengths.  

Here, the sum of the two sides of the triangle is 12 + 12 = 24.  

Therefore, the length of the third side should be less than 24, and the whole number which is less than 24 is 23.  

Hence, the length of the third side is 23.

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The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.

Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,

13 · x + 7 · x = 180°

Now we clear the variable x:

20 · x = 180°

x = 9

And the missing angles are:

13 · 9 = 117°

7 · 9 = 63°

The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.

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The hypotenuse of a right triangle = 19.31cm

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Let the measure be,

Perpendicular = 18cm

Base = 7cm

Hypotenuse = ?

To find the Hypotenuse we can Pythagoras Theorem:

Hypotenuse² = Perpendicular²+ Base²

H² = (18)² + (7)²

H² = 324 + 49

H² = 373

H = [tex]\sqrt{373}[/tex]

H = 19.31cm

Hence, The measure of the other leg is²

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Answer:Given : f(x)=x

4

−3x

2

+4

f(2)=(2)

4

−3(2)

2

+4

=16−12+4=8

This can also be verified by the actual divison

Answer:

92 over 100

Step-by-step explanation:

According to Table B, There is a series that is being followed next, i.e.,

m = (m+1) * (m-1)

In the given data,

Input is 5, then given output is 6 * 4, similarly

Input is 10, then given output is 11 * 9 which implies that

Output is the products of one more than input and one less than input

⇒5 = (5+1) * (5-1)

⇒5 = 6 * 4

again with 15 = (15+1) * (15-1) ⇒ 16 * 14

with 300 = (300+1) * (300-1) ⇒ 301 * 299

At last, we can construct a series from these data,

m = (m+1) * (m-1)

Where m is input and (m+1) * (m-1) is output of data.

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The number of ounces of meat were used is 52 ounces.

Given that, a sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

There are 7 ounces of combined meat and cheese in each sandwich (4+3 =7)

Number of sandwiches can make with 91 ounce of meat and cheese

= 91/7

= 13 sandwiches

Number of ounces of meat = 13 × 4 = 52 ounces

Number of ounces of cheese = 13 × 3 = 39 ounces

Therefore, the number of ounces of meat were used is 52 ounces.

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The cost for a year is cheaper in Gym A.

The value of k for the cheaper membership is $10.

An equation in the form y = kx is known as a linear equation. A linear equation is an equation that increases at a constant rate.

In the equation : y = kx

k = y/x

Cost per month at Gym A = $50 / 5 = $10

Cost per month at Gym B = $40 / 3 = $13.33

Membership cost at Gym A for a year = $10 x 12 = $120

Membership cost at Gym B for a year = $13.33 x 12 = $160

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The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

Therefore, the p-value for study b exists 0.080.

The P value is the likelihood, for a particular statistical model, that the statistical summary would be either equal to or more extreme than the actual observed results if the null hypothesis were to hold.

In a two tailed test the probability of occurrence exists the total area beneath the critical range of values on both the sides of the curve (negative side and positive side)

Therefore, the probability values for a two tailed test as compared to a one tailed test exists given by the under given relation -

[tex]$p-\text { value }=P\left(Z < -\frac{\alpha}{2}\right)+P\left(Z > \frac{\alpha}{2}\right)$$[/tex]

simplifying the above equation, we get

[tex]$P \frac{\alpha}{2}=0.040$[/tex]

Substituting the given value in above equation, we get -

Probability values for a two tailed test

= 0.040 + 0.040

= 0.080

Therefore, the p-value for study b exists 0.080.

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A function is called bijective if it is one-to-one and onto.

To check one to one, let x1 = x2 , where x1, x2 belongs to R.

so, we can say that:

and

Given the condition that x1 and x2 are not equal to 2. So, the above equation implies that

So, it is a one-to-one function.

For onto function, let y= (3x + 4) / (x-2). Now, interchange x and y, and solve the equation fo y:

Here, the domain of the inverse of the function is R - {3}. But the function is R - {2} => R. So, it is not onto.

thus, the given function is not a bijection.

For example, if there are 5 blue balls and 7 red balls. the ration of the blue balls with the red balls is

it can also be written as a fraction :

It is important to put the one that was mentioned first in the numerator. in this case is blue ball, that's why 5 came first. If we are asked what is the ratio of the red balls with the blue balls , then we will have to indicate 7 first. The ratio will have to be

The sequence is important.

EXPLANATION

Let's see the facts:

The increasing rate is:

The increasing rate is 1.67

In percentage this is:

The percentage of increasing is of 60%.

The shows the expression below simplified 0.0042 - (1.2 x 10-6) as D. 4.1988 x 10^-3.

The concept that is been used is subtraction of the first expression from second expression.

The given expression is 0.0042 - (1.2 x 10-6) and this can be expressed in standard form as ( 4.2 *10^-3) - (1.2 x 10-6)

Then then the subtraction can be done as [ ( 4.2 *10^-3) ] - [ (1.2 x 10^-6) ] = 4.1988 x 10^-3

In conclusion, iif we go through the options., then we can see that the forth option is the best option that match the expression.

Therefore, option D is correct.

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Answer:

27

Step-by-step explanation:

Divide 270 by 10

The equation for finding the length between two points is:

where point 1 has coordinates (x1, y1) and point 2 has coordinates (x2, y2).

We assign A to be point 1 and B be point 2

Therefore,

Neither parallel nor perpendicular

The points are:

A(3, 1), B(3,-4), C(-4,1), D (-4,5)

The slope of a line is given as:

The slope of the line AB, m(AB), with gthe points A(3, 1), B(3,-4) is given as:

The slope of the line CD, m(CD), with the points C(-4,1), D (-4,5) is given as:

A line that has an infinite slope is a vertical line

For the two lines to be parallel, m(AB) should be equal to m(CD)

For the two lines to be perpendicular, m(AB) = -1 / m(CD)

None of the conditions for paralleleism and perpendicularity is met, the lines AB and CD are neither parallel nor perpendicular

The decimal figure that would be added to 1/5 to give 3/6 = 0.3

A decimal form is defined as the expression of figures that are more than a whole number with the use of decimal point.

Examples of figures that are in decimal form include the following: 0.2, 0.3, 0.4, 0.5, 1.2, 2.2,3.3 and 4.4.

To represent the given fractions in decimal form;

1/5 = 0.2

3/6 = 0.5

Therefore, X + 0.2 = 0.5

make X the subject of formula,

X = 0.5 - 0.2

X= 0.3

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Answer:

2

Step-by-step explanation:

512÷2=256

256÷2=128

128÷2=64

64÷2=32

32÷2=16

16÷2=8

8÷2=4

4÷2=2

2÷2=1

=(2^2)+(2^2)+(2^2)+(2^2)+2

When 2 is multiplied it will make it a perfect square.

512×2=1024

√1024

=32

a. The equation for h is h = 100/x²

b. The function for the volume of the box V, in terms of x is:

v(x) = x²×h

Given, the prism has a square base and a total surface area of 100 cm².

A) let x = the side length of the base and

h = the height of the prism.

equation for h = ?

Volume = b × h

100 cm² = x² × h

h = 100/x²

B) a function for the volume of the box, V, in terms of x.

we know that x is the base and h is the height.

So, volume in terms of x :

v = b×h

v = x² × h

Hence we get the required answers.

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The domain of the function will be; [0 ∞) and the domain is continuous.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The number c of calories consumed is a function of the number b bars

eaten is represented by the linear function b = 130c

The domain of the linear function would be [0 ∞).

A whole number or a decimal number may be c.

Any data which can be expressed as a decimal is continuous data.

Therefore, the domain of the function will be; [0 ∞) and the domain is continuous.

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1.2(3x+5)=3.6x+6

We move all terms to the left:

1.2(3x+5)-(3.6x+6)=0

We multiply parentheses

3.6x-(3.6x+6)+6=0

We get rid of parentheses

3.6x-3.6x-6+6=0

We add all the numbers together, and all the variables

=0

x=0/1

Hence, x = 0

Answer:

See below

Step-by-step explanation:

The  equation is

y = [tex]x^{2}[/tex] + x

x equals the step

We see steps: 1, 2,3 and 4

y equals the number of squares that you see in each step.

If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2

Step 2: [tex]2^{2}[/tex] + 2 = 6

Step 3: [tex]3^{2}[/tex] + 3 = 12

Step 4: [tex]4^{2}[/tex] + 4 = 20

Can you see at each step there is a square of the number and then a little extra?  That little extra equals the number of the stop.

In the equation

y = 4x -2

Step 1

y = 4(1) -2

y = 2  It works!

Step 2:

y = 4x -2

y = 4(2)  - 2

y = 8 - 2

y = 6  It works!

Step 3:

y = 4x -2

y = 4(3) - 2

y = 12 - 2

y = 10  It does not work!

Step 4:

y = 4x -2

y  = 4(4) - 2

y = 16 - 2

y = 14  It does not work!

The equation y= 4x -2  only worked for the first 2 steps.

The equation of the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

The given parameters are

Leading coefficient = 1

Zeros =  − 2 , − 4 , 3 , and 3 .

Polynomial equations have their multiplicities to add up to their degree.

This means that the multiplicity of the zeros is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

From the question, the polynomial is to be factored

This means that we represent it as

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

Hence, the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

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Polynomial is an expression consisting of indeterminates and coefficients the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3)

Polynomial is an expression consisting of indeterminates and coefficients, which involves  the operations like addition, subtraction, multiplication, and positive-integer powers of variables

Factors are the numbers which divide the expression or number with a remainder zero.

We need to write the factored form of the polynomial functions with real; coefficients and zeros minus two comma  minus four comma three and 3.

The leading coefficient of the polynomial is 1. Leading coefficient means coefficient of leading term.

Zeros =  − 2 , − 4 , 3 , and 3 .

Let the polynomial is of variable x.

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

(x-(-2))=x+2

(x-(-4))=x+4

(x-3)=x-3

So the factored form is (x+2)(x+4)(x-3)(x-3)

the polynomial is P(x)=(x+2)(x+4)(x-3)(x-3)

Hence the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3).

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Mei Mei's age if the sum of Mei Mei's age and 5 times Xin's age is 143. is 23 years.

Let the ages be x and x+1 since they're consecutive numbers.

In this case the sum of Mei Mei's age and 5 times Xin's age is 143. This will be:

x + 5(x + 1) = 143

x + 5x + 5 = 143

Collect like terms

6x + 5 = 143

6x = 143 - 5

6x = 138

Divide

x = 138 / 6

x= 23

Mei Mei is 23 years.

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Answer:

The second graph (B: X?)

Step-by-step explanation:

The second graph (B?) is a function because the graphed line passes the vertical line test (no two points are vertically on top of each other).