Find the zeros of the function
f(x)=x^2+5x+6

Answer:

Left box: Outlier in this data set is (57,132)

Right box: because the finish time looks faster than expected for the age.

Step-by-step explanation:

As per the given table shows the [tex]age[/tex] and [tex]finish \ time[/tex] of [tex]10[/tex] runners.

It is clear that people of age around [tex]35[/tex] are finishing at around [tex]142 \ minutes[/tex]

and person with older age takes longer to finish.

One person of age [tex]57[/tex] finishes in [tex]175 \ minutes[/tex] , that looks as expected.

Another person of same age [tex](57)[/tex] finishes it too fast which is unexpected.

Therefore [tex](57,132)[/tex] is an outlier, because it looks a faster finish as per expected.

Answer:

The left box = (57 , 132)

The right box= The finished time is expected for the age.

Step-by-step explanation:  

Answer:

1st and 2nd graph are decreasing functions

Step-by-step explanation:

Increasing function means, as we go from left to right, the function goes "ABOVE" and thus, increases.

Decreasing function means, as we go from left to right, the function goes "DOWN" and thus, decreases.

We will look at all the 4 graphs given. We look from "LEFT-TO-RIGHT".

The first one goes "DOWN", so its decreasing.

The second one also goes "DOWN, so this is decreasing as well.

The third one goes "UP", so it is increasing.

The fourth function stays the same, so it is neither increasing nor decreasing. It is constant.

Thus,

1st and 2nd graph are decreasing functions, only

Answer:

Only Elijah's model is correct

Step-by-step explanation:

The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play

This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play

Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.

Elijah's model is correct .

Elijah and Jonathan play on the same soccer team. They have played 3 of their 15 games.  

x is the number of games that are left to be played.

Elijah and Jonathan have 12 games left on their soccer team.

Elijah  and Jonathan  both try to simulate the situation which are shown in figure.

Creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance.

On the other side Elijah placed 15 cubes.

The value of each cube = 1

so  15 [tex]\times 1 = 15[/tex] which are equal to total number of games.  

Since 3 games are already played so on the left hand side

3 boxes of magnitude 1 each are placed.

[tex]x[/tex] is the number of  games that are left.

Jonathan uses a table  with  three x values  in a row and a 15 is the total number of games to be played are represented in the second row trying to model the same situation.

This table doesn't show the number of games left to play.

Which are 12 in number

According to Jonathan's model

[tex]3x = 15 \\x =5[/tex]

This does not model the number of games left which are 12 in number and hence

Jonathan's model  does not explains the situation

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Answer:

7x-2y≤5

7x-2y≤5

Step-by-step explanation: Graph is down below!!

Hope this helps you out!☺

Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.

We need to find the graph which represents the inequality 7x−2y≤5.

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Now,

Write in y=mx+b form.

y≥7/2x-5/2

Use the slope-intercept form to find the slope and y-intercept.

Slope: 7/2

y-intercept:(0, -5/2)

Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.

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Answer:

I'd say C.60but because of the half units its possibly B. but definitely not A or D.

Step-by-step explanation:

Because the short sides are approximately 6 units long and the long sides are 10 units long. You multiply it to find the area and you get 60.

hope this helps

The area of the graph rectangle is 60 sq. units.

The correct option is D) 60 sq. units.

The area of a rectangle is expressed as:

Area = length × width

First, we use the distance formula to find the length and width of the rectangle.

[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

From the graph, the length is between the points (-1,1) and (8,-2):

Hence;

[tex]Length = \sqrt{(8-(-1))^2 + (-2 - 1)^2}\\\\Length = \sqrt{(8+1)^2 + (-2 - 1)^2}\\\\Length = \sqrt{(9)^2 + (-3)^2}\\\\Length = \sqrt{81 + 9}\\\\Length = \sqrt{90}\\\\Length = 3\sqrt{10}[/tex]

Next, we find the width which is between the points (-1,1) and (-3,-5):

[tex]Width = \sqrt{(-3 - (-1))^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-3 + 1)^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-2)^2 + (-6)^2}\\\\Width = \sqrt{4 + 36}\\\\Width = \sqrt{40}\\\\Width = 2\sqrt{10}[/tex]

Now, plug the values for the length and width into the above formula and solve for the area:

Area = length × width

Area = 3√10 × 2√10

Area = 3 × 2 × 10

Area = 60 sq. units

Therefore, the area measures 60 sq. units.

Option D) 60 sq. units is the correct answer.

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Answer:

The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  

Step-by-step explanation:

Given as :

The total money earn by Katelynn in tow weeks = $ 1240

The money earn by Katelynn in first week = $ 480

Let The money earn by Katelynn in second week = $x

Now,

From equation

The total money earn by Katelynn in tow weeks = The money earn by Katelynn in first week  + The money earn by Katelynn in second week

Or,  $ 1240 =  $ 480 + $ x

Or, $ x =  $ 1240 - $ 480

So, x = $ 760

So, The money earn in second week is $ 760

∴ The algebraic equation to model the situation is $ x = $ 1240 - $ 480

Hence ,  The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  Answer

Answer:

Initial value for Mrs. White is $600 more than Mrs. Brown.

The rate of change is same for both.

Step-by-step explanation:

Cost of car purchased by Mrs. White = $3,000

Rate at which she pays for the car = $300 per month

Cost of car purchased by Mrs. Brown = $2,400

Rate at which she pays for the car = $300 per month

So,

Initial value for Mrs. White was =$3,000

Initial values for Mrs. Brown was =$2,400

difference in initial values  [tex]=3000-2400[/tex]  =$600

∴ Initial value for Mrs. White is $600 more than Mrs. Brown.

Rate of change of payment due for  Mrs. White = $300 per month

Rate of change for payment due for Mrs. Brown = $300 per month

∴ The rate of change is same for both.

Since Mrs White had a higher initial value than Mrs Brown and both having same rates of change, therefore Mrs. White will take a longer time to pay the due.

Answer:

c then b

Step-by-step explanation:

2 - The elevation at Point E is 50 feet, marked by a contour line, 3 - Point F is at 70 feet elevation, illustrating the informative nature of topographic maps.

On Map 1, Point E is situated at an elevation of 50 feet, as it lies directly on the contour line representing this specific elevation. Contour lines on a topographic map connect points of equal elevation, allowing us to visualize the three-dimensional terrain on a two-dimensional surface.

In this context, every point on the contour line labeled "50 feet" shares the same elevation—50 feet above a reference point, typically sea level. Moving to Point F on Map 1, it is positioned on the contour line corresponding to an elevation of 70 feet.

This indicates that Point F is situated 70 feet above the same reference point. Topographic maps are invaluable tools for understanding the landscape's elevation variations, aiding hikers, geologists, and cartographers in navigating and representing the Earth's surface features accurately.

The contour lines on such maps provide a detailed depiction of the elevation changes, and by closely following them, one can trace the undulations of the terrain.

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Answer:

It can be solve this in two ways,

1) as if the h(x) = 5x and 2) as if h(x) = 5 + x

1) If h(x) = 5x and k(x) = 1/x

Then (k o h) (x) = k ( h(x) ) = k(5x) = 1/(5x)

2) If h(x) = 5 + x and k (x) = 1/x

Then (k x h)(x) =k ( h(x) ) = k (5+x) =  1 / [5 + x]

1/(5+x) is the correct answer

Step-by-step explanation:

Answer:

not 100% sure of this but I think its a4=192

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Step-by-step explanation:

Required output is:

h(x) = 5x-6

In order to find the required f and g functions we will see that which of the two functions add up to h(x)

In order to make our work easier we can see the functions f and g whose coefficients of  add up to 5x

Then we can select from the functions that produce h(x)

So,

Pair 1 whose coefficients of x add up to 5 is:

f(x) = -2x+6 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+6+7x-9\\= 5x-3[/tex]

Pair 2 that adds up to 5x

f(x) = 8x+9 and g(x) = -3x-3

Adding both functions:

[tex](f+g)(x) = 8x+9-3x-3\\= 8x-3x+9-3\\=5x+6[/tex]

Pair 3 is:

f(x) = -2x+3 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+3+7x-9\\= -2x+7x+3-9\\=5x-6[/tex]

Hence,

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Keywords: Functions, Sum of functions

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Answer:

The volume of sphere is 500 in³

Step-by-step explanation:

Given:

Diameter of sphere is 10 in.

Now, to find the volume we need radius.

Radius(r) = half of the diameter

[tex]r=\frac{10}{2}[/tex]

[tex]r=5[/tex]

And, now putting the formula to get the volume of sphere:

[tex]volume(v)=\frac{4}{3}\pi r^{3}[/tex]

Putting the value of π = 3.

[tex]v=\frac{4}{3} \times 3.14\times 5^{3}[/tex]

[tex]v=1.33\times 3.14\times 125[/tex]

[tex]v=522.025[/tex]

So, the volume is 522.025 in³.

By estimating the value the volume is 500 in³.

Therefore, the volume of sphere is 500 in³.

Answer:

B

Step-by-step explanation:

for those that didnt understand like me

Answer: 4) 7c ^2d - 7c + 4d - 10

Explanation:

First write equastion as seen:

5c^2d - 4c + 3d - 3 + 2c^d - 3c+ d - 7

Next add the c^2d’s together:

7c^2d - 4c + 3d - 3 + 3c + d - 7

Add the c’s together:

7c^2d - 7c + 3d - 3 + d - 7

Add the d’s:

7c^2d - 7c + 4d - 3 - 7

Lastly add the normal numbers:

7c^2d - 7c + 4d - 10

Thus, that is your answer!

Hope this helps! :)

The correct answer is A

Answer: B. 239 Square Feet

Step-by-step explanation:

Let y be the size of a kitchen that costs $3,824.00.

Given : The price of tiling a room varies directly as the size of the room.

Equation of direct variation between x and y : [tex]\dfrac{x_1}{x_2}=\dfrac{y_1}{y_2}[/tex]

If the tiling costs 4,224.00 for 264 square feet , to find the  size of a kitchen that costs $3,824.00.

We put [tex]x_1= 4224 \ \ ; \ y_1=264\ ; \x_2=3824\ ; \ y_2=y[/tex] , we get

[tex]\dfrac{4224}{3824}=\dfrac{264}{y}\\\\\Rightarrow\ y=\dfrac{264\times3824}{4224}=239[/tex]

Hence, the size of a kitchen that costs $3,824.00 is 239 Square Feet

The correct answer is B. 239 Square Feet

Answer:

D) (x^-3*y^-12)/(x^15*y^-15)

Step-by-step explanation:

If you simplify that further, then you'll get x^(-18)*y^3.

Answer:

Nick gave 3 marbles to each of his 4 friends.

Step-by-step explanation:

Given:

Total Number of Marbles = 12

Number of Friends = 4

Let the number of marbles to be divided in each friend be x

Solution:

To find the number of marbles to be divided in each friend we have to divide Total Number of Marbles by  Number of Friends.

Hence number of marbles to be divided in each friend x = [tex]\frac{\textrm{Total Number of Marbles}}{\textrm{Number of friends}}= \frac{12}{4}=3[/tex]

Hence we can say that Nick gave 3 marbles to each of his 4 friends.

Answer:

The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]

Step-by-step explanation:

Given as :

The net force = F Newton

The mass of the object = m kg

The acceleration = a  m/s²

Now, As The force is define as the product of mass and velocity

So, F = m × a

Now, Again , if the acceleration = 8 a

and The force decrease to [tex]\frac{F}{2}[/tex] = 0.5 F

So, Let The mass = M

∵ F = m × a

∴ mass = [tex]\frac{\textrm Force}{\textrm acceleration}[/tex]

Or. M = [tex]\frac{\textrm 0.5 F}{\textrm 8 a}[/tex]

or, M =0.0625 × [tex]\frac{F}{a}[/tex]

∴ M = 0.0625 × m = [tex]\frac{m}{16}[/tex]

so, The mass =  [tex]\frac{m}{16}[/tex]

Hence The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]  Answer

Final answer:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). If the force is decreased to F/2, the mass that would accelerate at a rate 8a can be found by rearranging the equation and solving for mass.

Explanation:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), expressed as F = ma.

If the force is decreased to F/2, the new force is now (F/2). To find the mass (m) that would accelerate at a rate 8a, we need to rearrange the equation as follows:

(F/2) = m * (8a)

To solve for the mass (m), we divide both sides of the equation by (8a), which gives us:

m = (F/2)/(8a)

Therefore, the mass that would accelerate at a rate 8a when the force is decreased to F/2 is (F/2)/(8a).

Answer:

1. The car is slowing down at a rate of 2.5mph/s

2. The greatest acceleration is 10 mph/s.

3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.

Step-by-step explanation:

1. The deceleration of the car is from 16 seconds to 24 seconds is the slope [tex]m[/tex] of the graph from 16 to 24:

[tex]m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s[/tex]

the negative sign indicates that it is deceleration.

2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.

From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope [tex]m[/tex]:

[tex]m= \dfrac{45-5}{28-24}= 10mph/s[/tex]

3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.

The speed of the automobile in that interval, as we see from the graph, is 25 mph.

Answer:

[tex]d=8.9\ units[/tex]

Step-by-step explanation:

we know that

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

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

we have

(-3, 2) and (5, -2)

substitute the values in the formula

[tex]d=\sqrt{(-2-2)^{2}+(5+3)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(8)^{2}}[/tex]

[tex]d=\sqrt{80}\ units[/tex]

[tex]d=8.94\ units[/tex]

Round to the nearest tenth

[tex]d=8.9\ units[/tex]

Answer:

(-3, 3).

Step-by-step explanation:

4x^2-36= 0

4x^2 = 36    Taking square roots of both sides:

2x = +/- 6

x = +/- 3.

Answer:

(-3, 3)

Step-by-step explanation:

The equation is:

[tex]4x^2-36=0[/tex]

to clear for x, first we move the -36 to the right as a +36 (or you can also say that we add 36 to both sides):

[tex]4x^2=36[/tex]

dividing by 4:

[tex]x^2=36/4\\x^2=9[/tex]

taking the square root:

[tex]x=[/tex] ± [tex]\sqrt{9}[/tex]

we add the ±  because a square root has two solutions, a positive one, and a negative one.

Then we get:

[tex]x=[/tex] ± 3

The solutions are -3 and +3

which is represented in the option (-3, 3)

Answer: y+3 = 4( x + 1)

Step-by-step explanation:

The equation in point slope form is given as :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) , where m is the slope

slope = 4

point given : (-1,-3)

Using the formula :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

and substituting the value , we have

y - (-3) = 4 (x -{-1} )

y+3 = 4( x + 1)

Answer:

B

Step-by-step explanation:

When you dilate a shape you change the size, changing the composition of isometries.

Option B is not a composition of isometries.

The composition of isometries refers to combining multiple isometries (transformations that preserve distance) to create a new transformation. To determine which of the options is not a composition of isometries, we need to verify if each option preserves distance. If any option does not preserve distance, it is not a composition of isometries. Let's analyze each option:

A. Reflection over x=2 then rotation 90 degrees clockwise about the origin: Both reflection and rotation are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin: Dilation, when the scale factor is not 1, does not preserve distance. Therefore, this option is not a composition of isometries.

C. Translation (x,y)-> (x-2, y+1) then reflection over the y-axis: Both translation and reflection are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

D. Reflection over the x-axis then reflection over the y-axis: Both reflections are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

In summary, option B is the only one that is not a composition of isometries.

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Answer:

21 miles

Step-by-step explanation:

Jeff drove [tex]=\dfrac{1}{2}[/tex] of the trip

Jason Joe drove [tex]=\dfrac{1}{4}[/tex] of the trip

Together Jeff and Jason Joe drove [tex]=\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}[/tex] of the trip

All trip [tex]=1[/tex]

Remaining trip [tex]=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}[/tex]

Susan and Sharon divided the rest of the drive equally, so

Susan drove = Sharon drove [tex]=\dfrac{1}{4}:2=\dfrac{1}{4}\cdot \dfrac{1}{2}=\dfrac{1}{8}[/tex] of the trip.

The entire trip was 168 miles, then

Sharon drove [tex]=\dfrac{1}{8}\cdot 168=21\ miles[/tex]

Answer:

The annual interest rate was 4.5% in Angela's college fund.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment when Angela was 10= US$ 5,000

Duration of the investment = 8 years

Balance of the account when Angela turned 18 = US$ 6,800

2. Let's find the annual interest rate of this investment after 8 years or 20 quarters, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment when Angela turned 10 = US$ 5,000

FV = Balance of the account when Angela turned 18 = US$ 6,800

number of periods (n) = 8

Replacing with the real values, we have:

6,800 = 5,000 * (1 + r) ⁸

6,800/5,000 = (1 + r) ⁸ (Dividing by 5,000 at both sides)

34/25 = 1⁸ + r⁸

34/25 - 1 = r⁸ (1⁸ = 1)

34/25 - 25/25 =r⁸ (1 = 25/25)

9/25 =  r⁸

0.36 = r⁸ (9/25 = 0.36)

⁸√0.36 = ⁸√r⁸

0.045 = r

r = 4.5%

The annual interest rate was 4.5% in Angela's college fund.

Answer:

The answer is 4.5

Step-by-step explanation:.

To determine the interest rate, substitute the numbers for the values in the I equals Prt formula. I equals one thousand eight hundred, P equals five thousand and t equals eight because the money was in the bank for eight years.

Multiply five thousand by eight.

Divide both sides by forty thousand and evaluate.

Finally, convert the decimal zero point zero four five to four point five percent.

Answer:

7.92 Feet

Step-by-step explanation:

Since area is Length × Height in comparison to perimeter being Length + Length + Height + Height, the equation is simply:

3 × 2.64 = 7.92 Feet

Final answer:

The area of Richard's painting is calculated by multiplying the length of 3 feet by the width of 2.64 feet, which equals 7.92 square feet.

Explanation:

To calculate the area of Richard's rectangular painting, we use the formula for the area of a rectangle, which is the product of its length and width. In this case, the length of the canvas is 3 feet and the width is 2.64 feet. So, the calculation to find the area will be as follows:

Area = Length × Width

Area = 3 feet × 2.64 feet

Area = 7.92 square feet

Therefore, the area of Richard's painting is 7.92 square feet.

Answer:

x is more than or equal to 35

Answer:

2x² + 2x + 3

Step-by-step explanation:

x = 3 is a zero of both the numerator and the denominator, so the denominator will factor completely into the numerator with no remainder.  Using grouping to factor:

(2x³ − 4x² − 3x − 9) / (x − 3)

(2x³ − 4x² − 6x + 3x − 9) / (x − 3)

(2x (x² − 2x − 3) + 3x − 9) / (x − 3)

(2x (x − 3) (x + 1) + 3 (x − 3)) / (x − 3)

2x (x + 1) + 3

2x² + 2x + 3

To use long division instead, see image.

Answer:

There was 62.23% change in radius as the ion formed.

Step-by-step explanation:

Given

Radius of Aluminium [tex](Al)[/tex] atom  = 143 pm

Radius of Aluminium [tex](Al^{3+})[/tex] atom  = 54 pm

Change is the radius =  Radius of Aluminium [tex](Al)[/tex] atom - Radius of Aluminium [tex](Al^{3+})[/tex] atom = 143 -54 = 89

Now to find % Change is the radius we will divide Change is the radius by Radius of Aluminium [tex](Al)[/tex] atom and multiply by 100 we get

% Change is the radius = [tex]\frac{\textrm{Change is the radius}}{\textrm{Radius of Aluminium (Al) atom}} \times 100 = \frac{89}{143}\times100= 62.23\%[/tex]

Hence there was 62.23% change in radius as the ion formed.

Answer:

34, 35, 36

Step-by-step explanation:

34 + 35 + 36 = 105

Answer:

34

35

36

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 105.

We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 105. Therefore, you can write the equation as follows:

X + X + 1 + X + 2 = 105

To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 105

3X + 3 = 105

3X + 3 - 3 = 105 - 3

3X = 102

3X/3 = 102/3

X = 34

Which means that the first number is 34, the second number is 34+1 and third number is 34+2. Therefore, three consecutive integers that add up to 105 are:

34

35

36