Solve and show your work for each question.
What is 0. 45 expressed as a fraction in simplest form?
What is 0.45 expressed as a fraction in simplest form?
What is 0.45 expressed as a fraction in simplest form?

SHOW YOUR WORK

we can simplify it to this:

[tex]y = - 2 {x}^{2} - 12x - 16 [/tex]

so we know it , the intercept in a standard equation of a parabola is C:

[tex]a {x}^{2} + bx + c[/tex]

so the intercept is (-16) and for the vertex use:

x=-b/2a

[tex]x = \frac{12}{ - 4} = - 3 [/tex]

so now put it in the equation and get the y of vertex:

y=-18+36-16=2 ==>vertex(-3,2)

Final answer:

The vertex of the function y=-2(x+3)²+2 is (-3, 2). The y-intercept is at (0, -16).

Explanation:

To identify the vertex and the y-intercept of the graph of the function y=-2(x+3)2 +2, we need to understand the structure of a quadratic function in vertex form, which is y=a(x-h)2+k, where (h, k) is the vertex of the parabola and a determines the direction and width of the parabola.

For the given function, the vertex can be found by looking at the values inside the parentheses and the constant term outside. In this case, the vertex is at x = -3 and y = 2, so the vertex is (-3, 2). The y-intercept occurs where x = 0. Substituting x = 0 into the function, we get y = -2(0+3)2+2 = -2(9)+2 = -18+2 = -16. Therefore, the y-intercept is at (0, -16).

.25 is the answer for you

Answer:

Dividing two binomials will not always result in a polynomial. For instance, divide (x+2) over (x+3) and we won't get a polynomial. The result is known to be a rational expression but not a polynomial. So that's why division is not closed for polynomials.

Contrast that with addition, subtraction and multiplication. For any of those operations taking two polynomials and adding them, subtracting them, or multiplying them will lead to another polynomial. That's why these operations are closed for polynomials.

~ Therefor the answer is B.

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Answer:

The answer will Be B

Step-by-step explanation:

Oxygen and silicone

Answer:

A. 1/8

Step-by-step explanation:

Let

P(A) be the event that white marble is drawn

P(B) be the event that black marble is drawn

P(A) = 1/4

P(B) = 1/2

Both events A and B are independent as the first marble is put back before drawing the second marble. So the probabilities of two independent events are multiplied.

P(A and B) = P(A) * P(B)

= 1/4 * 1/2

=1/8

Option A is the correct answer..

The rational number equivalent to 0.9375 is 15/16, obtained by converting the decimal to a fraction and then simplifying it.

The rational number that is equivalent to 0.9375 can be determined through a process known as converting a decimal to a fraction. To do this, you associate the number with the place value of the last digit. In the case of 0.9375, the last digit is in the ten-thousandth place, so we write it out as 9375/10000.

Simplifying this fraction by dividing both the numerator and denominator by the greatest common divisor (in this case, 625), we get 15/16. Therefore, out of the given options, 0.9375 is equivalent to the rational number 15/16.

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Answer:

22. Perimeter = 52 units

     Area = 160 Square Units

23. Notation form :  [tex] 2 \times 10^{5}[/tex]

     Standard Form : 200000

Step-by-step explanation:

22.

The formula for perimeter is

P = 2 (length + Width )

  = 2 ( 2x+3x+1)

  =  2(5x+1)

The Formula for Area of a rectangle is

A= length x width

A= [tex]2x \times (3x+1)[/tex]

A=[tex]6x^2+2x[/tex]

Now we have to find the Perimeter and Area for x = 5

P = 2(5 x 5 +1)

P= 2(26)

P=52 units

A= 6 x 5 x 5 + 2 x 5

A= 150 + 10

A= 160 square units

23.

A. By using rule of exponents , we can determine that both the results will be same.

B.

Miriam's calculation

[tex]\frac{2.8 \times 10^{9}}{1.4 \times 10^{4}}[/tex]

[tex]\frac{2.8}{1.4} \times 10^{9-4}[/tex]

[tex]2 \times 10^5[/tex]

Priya's calculation

[tex]\frac{2.8 \times 10^{2}}{1.4 \times 10^{-3}}[/tex]

[tex]\frac{2.8}{1.4} \times 10^{2-(-3)}[/tex]

[tex]2 \times 10^5[/tex]

Standard notation

[tex]2 \times 10^5 = 200000[/tex]

Answer: The answer would be D. 64

Step-by-step explanation: Understanding that the question noted that the second rectangle was dilated from PQRS, which has a perimeter of 16. With the coordinates of point P for the first rectangle being (2,0.5) whilst the second rectangle has point P at (8,2). To figure out the perimeter, divide point P from the second rectangle with point P from the first. The result would be 4. Thus, the scale factor is 4, which you then multiply the perimeter of PQRS by, which was 16. 16 times 4 equals 64.

Answer: D

Explanation: It is D

Answer:

2 1/3 yds

Step-by-step explanation:

We need to subtract 1 1/6 yds from 3 1/2 yds to answer this question.

The LCD is 6:

3 1/2 - 1 1/6 becomes 3 3/6 - 1 1/6.  This results in 2 2/6, or 2 1/3, yds

Jim must purchase 2 1/3 yds more of burlap.

For this case we must subtract the amounts to know how many yards of burlap Jim should buy:

[tex]3 \frac {1} {2} = \frac {6 + 1} {2} = \frac {7} {2}\\1 \frac {1} {6} = \frac {6 + 1} {6} = \frac {7} {6}[/tex]

We subtract the amounts:

[tex]\frac {7} {2} - \frac {7} {6} = \frac {42-14} {12} = \frac {28} {12} = \frac {14} {6} = \frac { 7} {3}[/tex]

We convert to a mixed number:

[tex]2 \frac {1} {3}[/tex]

ANswer:

Option B

The answer is:

[tex]Sin(A)=0.93[/tex]

To solve the problem, remember to set your calculator in "degree mode"

So, we are given that the angle A is equal to 68°

So, we have that:

[tex]Sin(A)=Sin(68\°)=0.93[/tex]

Hence, we have that:

[tex]Sin(A)=0.93[/tex]

Have a nice day!

Answer:

B) 3/2

Step-by-step explanation:

a doesn't work because 2 x 1/2 = 1 which is less that 2

c doesn't work because 4/2 = 2 and 2 x 2 = 4 which is equal to 4 when we want less than 4

d doesn't work because it is greater than c

b works because 2 x 3/2 = 6/2 = 3

54 students on each bus

Answer:  26.67%

Step-by-step explanation:

32 touchdowns divided by 12 interceptions

32/12 = 26.66666%

26.66666 rounds up to 26.67%

Final answer:

The simplified ratio of touchdowns to interceptions that Max threw is 8:3, found by dividing both the number of touchdowns (32) and interceptions (12) by their greatest common divisor, which is 4.

Explanation:

To find the most simplified form of the ratio of touchdowns to interceptions that Max threw, we divide the number of touchdowns by the number of interceptions. Max threw 32 touchdowns and 12 interceptions. To simplify this ratio, we need to find the greatest common divisor (GCD) that both numbers share. In this case, the GCD of 32 and 12 is 4.

Dividing both numbers by the GCD, we get: 32 ÷ 4 = 8 and 12 ÷ 4 = 3. Therefore, the simplified ratio of touchdowns to interceptions is 8:3.

Answer:

The length is 24, width is 6

Step-by-step explanation:

Since we know the length and width cannot both be 12 (to make 144), other factors of 12 can be tested to be a product of 144. Half of 12 is 6, and 24 * 6 = 144. If we add up 12 + 12 + 6 + 6, we get 60, or the given perimeter.

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The length and width of the rectangle, set up and solve a system of equations based on the given area and perimeter. By factoring the quadratic equation obtained from the area and perimeter formulas, it is determined that the rectangle's width is 12 inches and its length is 18 inches.

The length and width of a rectangle with an area of 144 square inches and a perimeter of 60 inches, we can set up a system of equations using the formulas for area and perimeter of a rectangle, which are Area = length  imes width and Perimeter = 2  imes (length + width), respectively. Let the length be represented by 'l' and the width by 'w'.

Step 1: Set up the equations

Area = l  times w = 144
Perimeter = 2l + 2w = 60

Step 2: Solve the system of equations

First, simplify the perimeter equation to get l + w = 30. Then, express l in terms of w: l = 30 - w. Now substitute l in the area equation: (30 - w)w = 144.

Step 3: Solve the quadratic equation

Expand the equation: 30w - w² = 144.
Rearrange to form: w²- 30w + 144 = 0.
Factoring the quadratic equation gives: (w - 12)(w - 18) = 0.

Step 4: Find w and l

Setting each factor equal to zero gives us two possible widths: w = 12 or w = 18. If w = 12, then l = 30 - w = 18. If w = 18, then l = 30 - w = 12. Since both options give us the same pair of numbers, and a rectangle's sides can be switched without changing its shape, the rectangle's width is 12 inches and its length is 18 inches, or vice versa.

Answer:

y³ - 3y² + 1/y+3

Step-by-step explanation:

y² - 9 = (y - 3) ( y + 3)

y-3/(y-3)(y+3) = 1/y+3

Answer:

y^2+1/y^2+3

Step-by-step explanation:

For this case we have by definition, that the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

They tell us that the radius of the circle is 125 meters, then the diameter is 250 meters.

Substituting:

[tex]C=3.14*250\\C=785\m[/tex]

Thus, the circumference of the circle is 785 meters

ANswer:

785 meters

Option B

Answer:

The correct answer is option B.  785 m

Step-by-step explanation:

Points to remember

Circumference of a circle = 2πr

Where r is the radius of circle

To find the circumference of circle

Here r = 125 m and π = 3.14

Circumference = 2πr

 = 2 * 3.14 * 125 = 785 m

The answer is  785 m

Therefore the correct answer is option B.  785 m

Answer:

you bought a large cheese pizza

with 2 additional toppings on your pizza

Step-by-step explanation:

large cheese pizza = $13.99

Large pizza total = $16.49

each additional topping = $1.25

subtract $13.99 from $16.49

which equals $2.50

now subtract $1.25 from $2.50

which equals $1.25

now if you subtract $1.25 from $1.25

it equals 0

this shows you bought a large cheese pizza

with 2 additional toppings on your pizza

Answer:

The solution set is { (3, 4), (5 , 0) }.

Step-by-step explanation:

x^2 + y^2= 25

2x   +   y =  10

We use substitution:

From the second equation y = 10 - 2x.

Substituting for y in the first equation:

x^2 + (10 -2x)^2 = 25

x^2 + 100 - 40x + 4x^2 - 25 = 0

5x^2 - 40x  + 75 = 0

Divide through by 5:

x^2 - 8x + 15 = 0

(x - 3)(x - 5) = 0

x = 3, 5.

when x = 3 , y = 10 - 2(3) = 4.

when x = 5, y = 10 - 2(5) = 0.

Answer:

(3,4) (5,0)

Step-by-step explanation:

ANSWER

(-2,4] and [7,∞).

EXPLANATION

The domain refers to the interval on which the function is defined.

In the case of the graph, the domain refers to all the x-values for which the graph exists.

The graph is defined for x-values greater than 2 but less than or equal to 4 and

x-values greater than or equal to 7.

In interval notation, we have:

(-2,4] and [7,∞).

The second choice is correct:

Answer:

(-2,4] and [7, infinity)

Step-by-step explanation:

Answer:

3(x+6)

Step-by-step explanation:

3x+18

Both the 3 and the 18 are multiples of 3, so factor out a 3

3(x+6)

The answer is:

In 2036 there will be a population of 32309 rabbits.

We can calculate the exponential decay using the following function:

[tex]P(t)=StartAmount*(1-\frac{percent}{100})^{t}[/tex]

Where,

Start Amount, is the starting value or amount.

Percent, is the decay rate.

t, is the time elapsed.

We are given:

[tex]StartAmount=144,000\\x=7.2(percent)\\t=2036-2016=20years[/tex]

Now, substituting it into the equation, we have:

[tex]P(t)=StartAmount(1-\frac{percent}{100})^{t}[/tex]

[tex]P(t)=144000*(1-\frac{7.2}{100})^{20}[/tex]

[tex]P(t)=144000*(1-0.072)^{20}[/tex]

[tex]P(t)=144000*(0.928)^{20}[/tex]

[tex]P(t)=144000*(0.928)^{20}[/tex]

[tex]P(t)=144000*0.861=32308.888=32309[/tex]

Hence, we have that in 2036 the population of rabbis will be 32309 rabbits.

Have a nice day!

The population of rabbits in 2036 is 32309 and this can be determined by using the exponential decay function.

Given :

The formula for the exponential decay function is given by:

[tex]\rm A = P(1-\dfrac{r}{100})^t[/tex]

Now, substitute the value of known terms in the above formula.

[tex]\rm A = 144000(1-\dfrac{7.2}{100})^{20}[/tex]

Simplify the above expression.

[tex]\rm A = 144000\times (0.928)^{20}[/tex]

[tex]\rm A = 32308.888[/tex]

A [tex]\approx[/tex] 32309

So, the population of rabbits in 2036 is 32309.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=3x+2&(1)\\y=5x&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\5x=3x+2\qquad\text{subtract 3x from both sides}\\2x=2\qquad\text{divide both sides by 2}\\x=1\\\\\text{Put the value of x to (2):}\\\\y=5(1)=5[/tex]

Answer:

4.3

Step-by-step explanation:

Answer:

the mode is 3 and 5

Step-by-step explanation:

If there is a tie between the modes, it is called bimodal. There can be 2 modes in a data set.

Answer:

the mode is 3 AND 5 which means it is a bimodal

Step-by-step explanation:

TLDR: The answer is -2.

What you have here is a function with a point on the graph. It is understood that “x” represents the input and “y” represents the output, so we’re looking for the right “x” that will give y = 1/100.

To start, we can substitute the y-value into the function like this:

y = 10^x

1/100 = 10^x

From here, we can take two different pathways; one requires conceptual knowledge while the other relies on the knowledge of logarithms.

Conceptual

For the conceptual, we know that 100 = 10^2, so 1/100 is the same as 1/10^2. We also know that the inverse of a fraction is the same as the number to the negative of its power (for example, 1/2 is equal to 2^-1), so we know that 1/10^2 is the same as 10^-2. So far, we have learned that:

1/100 = 10^x

1/10^2 = 10^x

10^-2 = 10^x

So, to satisfy this, “x” must equal -2.

Logarithms

For logarithms, we can use powers and math to actually calculate the value of “x”. We know that:

1/100 = 10^x

To solve this, we need “x” to be by itself on one side of the equation. To do this, we can perform the inverse function of an exponent, which is a logarithm. In this case, the base of 10^x is 10, so we need a “base 10” logarithm to solve this function. Apply this function to both sides and simplify:

1/100 = 10^x

log10(1/100) = log10(10^x)

log10(1/100) = x

The log10 function is the inverse of 10^x, so they cancel out to leave “x”. Plug log10(1/100) into a calculator, and you find that x = -2.

Hope this helps!

B is the correct answer.

Look at the picture of it then match it .. the answer is B

Answer:

1) Point A is on 1.40

Change 1.40 to fraction. 1.40 = 1 40/100

Simplify the fraction. Divide common multiples: (40/100)/(20/20) = 2/5

1 2/5 is your answer.

2) Point B is on 1.15

Change 1.15 to fraction. 1.15 = 1 15/100

Simplify the fraction. Divide common multiples: (15/100)/(5/5) = 3/20

1 3/20 is your answer

Find out which one is greater, Point A (1 2/5) or Point B (1 3/20). Change both into a decimal, and compare:

Point A = 1 2/5 = 7/5 = 1.4

Point B = 1 3/20 = 23/20 = 1.15

Point A is greater than Point B

~

Answer:

Option C - Simplify the right side using the "difference of two logs is the log of the quotient" property.

Step-by-step explanation:

Given : Expression [tex]\ln (x-1)=\ln 6-\ln x[/tex]

To find : What is the first step in solving  the expression ?

Solution :

Expression [tex]\ln (x-1)=\ln 6-\ln x[/tex]

Step 1 - Simplify the right side using the "difference of two logs is the log of the quotient" property.

i.e. [tex]\ln a-\ln b=\ln(\frac{a}{b})[/tex]

Apply the first step we get,

[tex]\ln (x-1)=\ln(\frac{6}{x})[/tex]

Therefore, Option C is correct.

Answer is provided in the image attached.