choose yes or no to indicate which of the equations can be used to describe the pattern in the table (am i correct??????)​

Answer:

Step-by-step explanation:

the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)

in this case, the zeroes are 3 and 6

Answer:

A. x = 3 and x = 6

Step-by-step explanation:

Zeros occur when the function crosses the x - axis. In this case, the quadratic function crosses the function when x = 3 and x = 6.

Answer:

Kristen would be 7.5 yo and Nicole would be 24.5 years old

Step-by-step explanation:

let x= kristen's age

3x+2= nicole's age

(3x+2)+x=32

4x+2=32

4x=30

x=7.5

3(7.5)+2= 24.5

Answer:

The answer B

Step-by-step explanation:

To find the value of Lucy's house at the start of 2017, calculate a 5% increase each year from the initial £200,000 value in 2014. The compound value over the three years results in a house value of £231,525 at the start of 2017.

To calculate the value of Lucy's house at the start of 2017, we need to apply a 5% annual increase to the initial value of the house for three consecutive years (2014 to 2017).

Find the increase for the first year:

Initial value for 2014: £200,000

5% increase: £200,000 * 0.05 = £10,000

Value at the start of 2015: £200,000 + £10,000 = £210,000

Calculate the increase for the second year:

Value at the start of 2015: £210,000

5% increase: £210,000 * 0.05 = £10,500

Value at the start of 2016: £210,000 + £10,500 = £220,500

Calculate the increase for the third year:

Value at the start of 2016: £220,500

5% increase: £220,500 * 0.05 = £11,025

Value at the start of 2017: £220,500 + £11,025 = £231,525

Therefore, the value of Lucy's house at the start of 2017 would be £231,525.

Answer:

[tex]r=16\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the silo is equal to the volume of a cylinder plus the volume of a hemisphere

so

[tex]V=\pi r^{2}h+\frac{4}{6}\pi r^{3}[/tex]

In this problem we have

[tex]V=35,500\pi\ ft^{3}[/tex]

[tex]h=4D=8r[/tex] ----> 4 times the diameter is equal to 8 times the radius

substitute in the formula and solve for r

[tex]35,500\pi=\pi r^{2}(8r)+\frac{4}{6}\pi r^{3}[/tex]

Simplify pi

[tex]35,500=8r^{3}+\frac{4}{6}r^{3}[/tex]

[tex]35,500=r^{3}[8+\frac{4}{6}][/tex]

[tex]35,500=r^{3}[\frac{52}{6}][/tex]

[tex]r^{3}=35,500/[\frac{52}{6}][/tex]

[tex]r=16\ ft[/tex]

Answer:

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Step-by-step explanation:

we know that

the equation of a circle into center radius form is equal to

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( 3,-2)

radius r=3 units

substitute

[tex](x-3)^{2} +(y+2)^{2}=3^{2}[/tex]

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Answer: A on edg

Step-by-step explanation:

Answer:

2 2/5

Step-by-step explanation:

-1 3/5 ÷ -2/3

Change the mixed number to an improper fraction

-1 3/5 =  - (5*1 +3)/5 = -8/5

-8/5÷-2/3

Copy dot flip

-8/5 * -3/2

24/10

Divide top and bottom by 2

12/5

Change to a mixed number

12/5 = 2 2/5

Answer:

You had it correctly chosen, (9, infinity)

Step-by-step explanation:

Good job =)

ANSWER

[9,∞)

EXPLANATION

The given radical function is ;

[tex]f(x) = \sqrt{x - 9} [/tex]

This function is defined if and only if the expression under the radical sign is greater than or equal to zero.

[tex]x - 9 \geqslant 0[/tex]

[tex]x \geqslant 9[/tex]

Or

In interval notation, we have

[9,∞)

Answer:

D. 33

Step-by-step explanation:

√(x-8) + 2 = 7

subtract 2 from both sides

√(x-8)  = 5

square both sides

(√(x-8))²  = 5²

x-8 = 25

add 8 to both sides

x = 33

ANSWER

D. 33

EXPLANATION

The given radical equation is

[tex] \sqrt{x - 8} + 2 = 7[/tex]

Group similar terms,

[tex]\sqrt{x - 8} = 7 - 2[/tex]

[tex]\sqrt{x - 8} = 5[/tex]

Square both sides:

[tex] {(\sqrt{x - 8})}^{2} = {5}^{2} [/tex]

Simplify

[tex]x - 8 = 25[/tex]

Solve for x

[tex]x = 25 + 8 = 3[/tex]

Answer:

-13 < 16

Step-by-step explanation:

(4 is x, -5 is y)

-5 - 8 < 4(4)

-13 < 16

It is true and is a solution

Answer:

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Step-by-step explanation:

Step 1: Plug x and y into the inequality

-5 - 8 < -4(4)

Step 2: Simplify the inequality

-13 < -16

Step 3: Interpret and conclude

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Answer:

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Step-by-step explanation:

Let

x-----> Shravan's age

y-----> Gaurav’s age

we know that

x=y+10 -----> equation A

(1/7)(x-5)=(1/5)(y-5) ----> equation B

substitute equation A in equation B and solve for y

(1/7)(y+10-5)=(1/5)(y-5)

(1/7)(y+5)=(1/5)(y-5)

5(y+5)=7(y-5)

5y+25=7y-35

7y-5y=25+35

2y=60

y=30 years

Find the value of x

x=y+10  ----> x=30+10=40 years

therefore

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Answer:

p=0.125

Step-by-step explanation:

2p+6p=1

Add like terms

8p=1

Divide both sides by 8 to get p by itself

8p/8=1/8

p=0.125

11 is the base, meaning that it is the number being multiplied

3 is the exponent, meaning it tells you how many times you must multiply the base together

For this question we must multiply 11 together 3 times:

11*11*11 = 1331

Hope this helped!

Answer:

Step-by-step explanation:

Add the square of half the x-coefficient to both sides.

 x² -12x +(-6)² = 61 +(-6)²

Answer:

x² - 12x + 36 = 97

Step-by-step explanation:

Given

x² - 12x = 61

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 6)x + (- 6)² = 61 + (- 6)², so

x² - 12x + 36 = 61 + 36

x² - 12x + 36 = 97

Final answer:

To solve the equation ax - y = bx for x, add y to both sides, combine x terms, factor x out, and divide by (a - b) resulting in the solution x = y / (a - b).

Explanation:

To solve the given equation ax - y = bx for x, we aim to isolate x on one side of the equation:

First, we add y to both sides of the equation: ax = bx + y.

Next, we group the x terms together: ax - bx = y.

Then, we factor out x: x(a - b) = y.

Finally, we divide both sides by (a - b) to solve for x: x = y / (a - b).

So, the solution is x = y / (a - b).

ANSWER

a. 16

b. 1

c. 64

d. 64

EXPLANATION

We want to simplify the following exponential expressions

a.

[tex] {2}^{4} [/tex]

This implies that

[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]

[tex] {2}^{4} = 16[/tex]

b. Any non-zero number exponent zero is 1.

This implies that,

[tex] {3}^{0} = 1[/tex]

c. The given exponentiial expression is,

[tex] {4}^{6} \times {4}^{ - 3} [/tex]

The bases are the same so we add the exponents.

[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]

This simplifies to,

[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]

[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]

d. We want to simplify:

[tex] { ({2}^{3}) }^{2} [/tex]

This is the same as

[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]

We add the exponents now to get:

[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]

Answer:

12x^2+3x+6 and  -7x^2-4x-2 -> 5x^2-x+4

2x^2-x and -x-2x^2-2 -> -2x-2

x^3+x^2+2 and x^2-2-x^3 -> 2x^2

x^2+x and x^2+8x-2 -> 2x^2+9x-2

hope this helps :)

so, the cost will increase 2.8% per annum... so that simply means is a compound interest rate, so let's use the compound interest formula for this one.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$33741\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=\textit{years after 2015}\dotfill &t \end{cases} \\\\\\ A=33741\left(1+\frac{0.028}{1}\right)^{1\cdot t}\implies b(x)=33741(1.028)^x[/tex]

The complete expression for the compounding tuition fee function is [tex]b(x) = 33741(1.028) {}^{x} [/tex]

Using the compound interest relation :

[tex] b = P(1 + \frac{r}{n} ) {}^{nx} [/tex]

Where ;

The function b(x) can be written as :

[tex]b(x) = 33741(1 + \frac{0.028}{1} ) {}^{x} [/tex]

Therefore, the expression for the function b(x) is :

[tex]b(x) = 33741(1.028) {}^{x} [/tex]

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Answer:

The Average rate of change (the slope) is -4/3

Step-by-step explanation:

Find two Exact point like point A (-1,4) and point B (2,0)

Then count how many spaces does point A have to move left to right and down to get to point B.

since it moves down the number will be negative.

You will have to go 3 spaces to the right and 4 spaces down.

therefore giving you a slope of -4/3

To find the average rate of change for a given function, evaluate the function at the two given points and use the formula (f(2) - f(-1)) / (2 - (-1)).

To find the average rate of change for a given function, we need to calculate the difference in the values of the function between the two given points, and then divide that difference by the difference in the x-coordinates of the points. In this case, we are given x=-1 and x=2.

Let's evaluate the function at these two points:

f(-1) = ?, f(2) = ?

Once we have the values, we can calculate the average rate of change using the formula:

Average Rate of Change = (f(2) - f(-1)) / (2 - (-1))

Substitute the values and calculate to find the answer.

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Answer:

D. Even

Step-by-step explanation:

Given function is [tex]f\left(x\right)=-2x^4+3x^2[/tex].

Now we need to check if the given function is Even/Odd.

we know that if f(-x)=f(x) then function is called Even.

we know that if f(-x)=-f(x) then function is called Odd.

[tex]f\left(x\right)=-2x^4+3x^2[/tex]

[tex]f\left(-x\right)=-2(-x)^4+3(-x)^2[/tex]

[tex]f\left(-x\right)=-2x^4+3x^2[/tex]

[tex]f\left(-x\right)=f\left(x\right)[/tex]

Hence given function is an Even function.

So the correct choice is D. Even.

Answer:

At 11:30 am they will arrive at their starting point together

Step-by-step explanation:

we know that

One of them completes one lap in 6 minutes

The second one in 9 minutes

The third one in 15 minutes

step 1

Find the least common multiple (LCM)

6=2*3

9=3²

15=3*5

so

LCM=(3²)*(2)*(5)=90 minutes

step 2

Find the number of laps of each jogger for the LCM

jogger 1

90/6=15 laps

jogger 2

90/9=10 laps

jogger 3

90/15=6 laps

If they start at 10:00 am

then

10:00 am + 90 minutes=11:30 am

Answer:

2x - 3y = -2 AND 4x + y = 24

Step-by-step explanation:

Simply plug in the coordinates into each answer choice, evaluate them, and you will have your answer.

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

The area under the curve y = x^2 + 4 on the interval [-3,2] can be found using definite integration. The definite integral of a function gives us the net area between the function and the x-axis across the specified interval. To compute the area, we set up the integral from -3 to 2 of the function x^2 + 4.

To solve this, we integrate the function with respect to x:

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

Answer:

The point was reflected over the y-axis.

The point was translated left 6 units

Step-by-step explanation:

step 1

we know that

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite

In this problem

If you apply a reflection across the y-axis

(x.y)------> (-x,y)

(3,-2) ------> (-3,-2)

step 2

If you apply a translation to the left 6 units

The rule of the translation is equal to

(x,y)------> (x-6,y)

(3,-2) ------> (3-6,-2) ----> (-3,-2)

Answer:

Simplify 4y + 7x = 2t and there you go that's your answer☺

Step-by-step explanation:

Bucket = y

Jars = x

Tubs = t

y + 5x = t

3y + 2x = t

Answer:

Number of jars in one tub is:

13

Step-by-step explanation:

Let b denote the buckets, j denotes the jars and t denotes the tubs

One bucket + 5 jars equal one tub

b+5j=t   ----------------(1)

Three buckets plus two jars equal two tubs

3b+2j=2t   ------------------(2)

equation (1)×3- equation (2)

3(b+5j)-(3b+2j)= 3t-2t

3b+15j-3b-2j= t

13j= t

Hence, Number of jars in one tub is:

13

Answer:

D

Step-by-step explanation:

[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Question \: and \: Choices:\:\:\:\:\:\:\:\:\:}}}}[/tex]

Find the height of a rectangular prism if the surface area is 868, the width is 7 and the length is 31.

A.) 434

B.) 2.85

C.) 76

D.) 5.7

[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}[/tex]

[tex]\huge\colorbox{pink}{\color{black}{\boxed{D.) 5.7}}}[/tex]

[tex]\large\purple{ChaEunWoo2009}[/tex]

#CarryOnLearning

Answer:

x = -3 , y = 2

Step-by-step explanation:

Solve the following system:

{y - 2 x = 8 | (equation 1)

{-3 x - y = 7 | (equation 2)

Swap equation 1 with equation 2:

{-(3 x) - y = 7 | (equation 1)

{-(2 x) + y = 8 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{-(3 x) - y = 7 | (equation 1)

{0 x+(5 y)/3 = 10/3 | (equation 2)

Multiply equation 2 by 3/5:

{-(3 x) - y = 7 | (equation 1)

{0 x+y = 2 | (equation 2)

Add equation 2 to equation 1:

{-(3 x)+0 y = 9 | (equation 1)

{0 x+y = 2 | (equation 2)

Divide equation 1 by -3:

{x+0 y = -3 | (equation 1)

{0 x+y = 2 | (equation 2)

Collect results:

Answer:  {x = -3 , y = 2

The solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2). The correct answer is option A.

Let's use the elimination method:

-2x + y = 8

-3x - y = 7

By adding the two equations together, we can eliminate the y variable:

(-2x + y) + (-3x - y) = 8 + 7

-2x - 3x + y - y = 15

-5x = 15

Dividing both sides by -5, we get:

x = -3

Now, substitute this value of x back into one of the original equations. Let's use -2x + y = 8:

-2(-3) + y = 8

6 + y = 8

y = 8 - 6

y = 2

Therefore, the solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2).

Therefore, the correct answer is option A.

Learn more about the linear equations here:

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The complete question is as follows:

The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations?

A. (–3, 2)

B. (–2, 3)

C. (2, –3)

D. (3, 2)

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5, hence

sum = 180° × 3 = 540°

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Answer:

Option A. [tex]10\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of the rectangle is equal to

A=LW

where

L is the length of rectangle

W is the width of rectangle

we have

[tex]A(-3,1),B(-2,-1),C(2,1),D(1,3)[/tex]

Plot the vertices

see the attached figure

L=AD=BC

W=AB=DC

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AD

[tex]A(-3,1),D(1,3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(3-1)^{2}+(1+3)^{2}}[/tex]

[tex]AD=\sqrt{(2)^{2}+(4)^{2}}[/tex]

[tex]AD=\sqrt{20}[/tex]

[tex]AD=2\sqrt{5}\ units[/tex]

Find the distance AB

[tex]A(-3,1),B(-2,-1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(-1-1)^{2}+(-2+3)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(1)^{2}}[/tex]

[tex]AB=\sqrt{5}[/tex]

[tex]AB=\sqrt{5}\ units[/tex]

Find the area

[tex]A=(2\sqrt{5})*(\sqrt{5})=10\ units^{2}[/tex]