Question 11
Solve the simultaneous equations
4x + 2y = 9
x - 2y = 1

The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the  point where the velocity the body is zero.

Given the function that represent the height of the swimmer as  h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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Answer:

x³ - x² + 4x - 7

Step-by-step explanation:

(x³ + 2x - 3) - (x² - 2x + 4)

remove first parenthesis and distribute second parenthesis by - 1

= x³ + 2x - 3 - x² + 2x - 4 ← collect like terms

= x³ - x² + 4x - 7 ← in standard form

So trees after 1 year

Trees after 2 years

Trees after 3 years

Trees after 4years

Trees after 5 years

Trees after 6 years

Answer:

177

Step-by-step explanation:

This scenario can be modeled as an exponential function.

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

If the number of trees increase by 10% each year, then the number of trees each year will be 110% of the number of trees the previous year.  Therefore, the growth factor is 110%.

Given:

Substituting the given values into the function:

[tex]\implies y=100(1.10)^x[/tex]

(where x is time in years and y is the number of trees in the orchard)

To find how many trees are in the orchard in the 6th year, input x = 6 into the found equation:

[tex]\implies 100(1.10)^6=177.1561=177\: \sf (nearest\:whole\:number)[/tex]

Therefore, Martin had 177 trees in his orchard in the sixth year.

Slope:-

The slope of the given function is -3/4.

Slope is a value that describes the steepness and direction of a line.

Given are the points that lie on line, we need to find the slope of the line,

So,

m = y₂ - y₁ / x₂ - x₁

The ordered pairs are :-

(-3, 1) and (1, -2)

So, the slope (m) = -2-1 / 1+3 = -3/4

Hence, the slope of the given function is -3/4.

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To find differences in the angles of the intersections we must know how many degrees each angle corresponds to. We must also take into account that the sum of the internal angles must equal 180°.

A triangle is a polygon that is characterized by having three sides, three vertices, and three angles. An indispensable rule of the interior angles of the triangles is that they must add up to 180º.

Triangles are classified according to their characteristics as shown below:

According to the above, depending on the measurements of the length of the sides and the angles of a triangle, its characteristics and classification change.

Note: This question is incomplete because the image is missing. However I can answer it based on my general prior knowledge.

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Explanation:

Let x = length of side BC

This is the height of the cylinder. Think of a can that is laying on its side. The radius of this can or cylinder is CD

If point B has x coordinate of 12, and BC is 12 units long, this must mean point C has x coordinate of 12-x. This is plugged into the function to show that CD has a length of exactly [tex]\sqrt{12-x}[/tex]

This is the radius of the cylinder

The volume of a cylinder is [tex]V = \pi*r^2*h[/tex]

Plug in the radius and height mentioned to get this function in terms of x

[tex]V = \pi*\left(\sqrt{12-x} \ \right)^2*x[/tex]

That simplifies to

[tex]V = \pi(12-x)x[/tex]

or

[tex]V = \pi(12x-x^2)[/tex]

Ignore the pi portion for now.

We wish to maximize the function f(x) = 12x-x^2

Use either calculus (specifically derivatives) or a graphing calculator to find that the vertex is at (6, 36)

This means x = 6 leads to the largest f(x) value being 36.

Therefore, the volume V is maxed out when x = 6 and we get a max volume of 36pi cubic units.

Answer:

see the attachment photo!

Answer:

the answer is 7! hope this helps

Step-by-step explanation:

Step-by-step explanation:

7red marbles,3 blue marbles,4 green marbles

The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.

Probability can be defined as the likeliness of

If you use the formula P(r)=[tex]^nC_r P^rq^{n-r}[/tex]

P is the probability of success =  3/4 = .25

the total number of questions is n = 8

the total number of questions that Johnni got correct is r  = 3

the probability of getting an answer wrong is q = 1-0.25 = 0.75

Substituting all of these values

[tex]^8C_3 P^3 (0.75)^{8-3}[/tex]

=  .208.

The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.

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Answer:

B. 0.208

Step-by-step explanation:

edge 2023

Answer:

1:3

1 to 3

Step-by-step explanation:

The other notations a ratio [tex]\frac{a}{b}[/tex] can be written in are a:b and a to b.

From what we are given, a = 1 and b = 3, so in the form a:b, the ration would be 1:3 and in the form a to b it would be 1 to 3.

The statement that verifies that quadrilateral WXYZ is a parallelogram is C)The opposite sides have the same slope.

This refers to a four-sided figure that is used in geometry and has parallel opposite sides.

Hence:

Remember that the opposite sides of a parallelogram are parallel.

We would solve:

Slope WX = 0

Slope XY= 5/2

Slope XZ= 0

Slope ZW= 5/2

The next step would be:

Slope WX= Slope YZ

Slope XY = Slope ZW

Based on the fact that the opposite sides have the same slopes, we can conclude that quadrilateral WXYZ is a parallelogram

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[tex]\huge\purple{Hi!}[/tex]

renters insurance is a Fixed expenses

Answer:

a reduction

Step-by-step explanation:

this is because its growing smaller

The function is an increasing linear function

The function is given as:

f(x) = 4.2x

The above function is a linear function, because linear functions are represented as:

f(x) = mx + b

Where m represents the slope.

A positive slope represents an increasing linear function.

By comparison;

m = 4.2

4.2 is positive

Hence, the function is an increasing linear function

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Answer:The entire area would be 12 square meters.

Step-by-step explanation:

2 x 6 square meters =  12 square meters. which is the entire area.

Answer:

Step-by-step explanation:

6x + 15y = -39

-6x + 8y = 16

23y = -23

y = -1

2x - 5 = -13

2x = -8

x = -4

(-4, -1)  

Option 4

Answer:

(−4, −1)

Step-by-step explanation:

I got it right on the test

The effect of this circled point is that: A. it will increase the value of the standard deviation of the residuals because it has a large positive residual.

The standard deviation of residuals is also referred to as root mean square deviation and they are typically used in statistics to calculate the rate at which data points spread around a given regression line.

By critically observing the scatter plot shown in the image attached below, we can infer and logically deduce that the circled point will increase the value of the standard deviation of the residuals because it has a large positive residual.

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Complete Question:

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the standard deviation of the residuals?

Answer:

257/16

Step-by-step explanation:

Given :

Then :

Answer:

6x+2y=52

Step-by-step explanation:

If you just drop down the answers, like for the first set x+5x=6x, so thats the first term and so on.

Answer:

555

Step-by-step explanation:

If each side of a square is 15 miles, we can find the total distance travelled by finding how many sides of squares were travelled.

You could either count the boxes, or, as I'm going to do, you could calculate the length of each straight line.

I switch between the y axis and the x axis, because we are travelling in different directions (if moving up/down we pay attention to y-axis, if moving right/left we pay attention to x-axis)

From 'Home' to the 'Restaurant', we are travelling from 6 to -7 on the grid. So, if we want to know the distance between them, we need to figure out how far apart they are. This is similar to figuring how far apart any two numbers are--we find the difference. (6) - (-7) [6 + 7] = 13. So, the amount of squares travelled from home to the restaurant is 13.

[I pay attention to the values along the x-axis for these two points because we are considering the distance along the x-axis]

[y-axis because it is vertical travel]

Restaurant (at -5) to campground (at 2) has a distance of : 7

[x-axis because it is horizontal travel]

Campground (at -7) to Rest Area (at -3) has a distance of : 4

[y-axis travel]

Rest Area (at 2) to the endpoint of that line segment (at 8) has a distance of: 6

[x-axis travel]

Endpoint of line segment (at -3) to endpoint below destination (at 3)  has a distance of : 6

[y-axis travel]

Endpoint below destination (at 8) to destination (at 9) has a distance of : 1

We can then add all of the distance travelled:

13 + 7 + 4 + 6 + 6 + 1

= 37

37 sides of boxes were travelled, so we can multiply:

37 x 15

= 555

because each box length is 15 miles.

So, the family travelled 555 miles

The town manager's sample is not representative of population as he only picked females.

It should be noted that a sample representative simply means a subset of a population which seeks to reflect the characteristics of the larger group.

In this case, the town manager's sample is not representative of populationas he only picked females. The males too ought to be given an equal chance.

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The correlation coefficient between the student's height and the distance they were able to jump is 0.86.

The correlation coefficient is a number that ranges from -1 to 1. It shows the strength of the relationship between two variables. It also shows the direction of the relationship.

Positive correlation is when the two variables move in the same direction. If one variable increases, the other variable also increases. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. Zero correlation is when there is no relationship between the variables.

The correlation coefficient is calculated using a financial calculator.

Here is the complete question:

A group of students want to determine if a person's height is linearly related to the distance they are able to jump.

To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.

Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.

Enter the correlation coefficient. Round your answer to the nearest hundredth.

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Answer:

It's 0.92

Step-by-step explanation:

I took the test already

Exact form is x = 86/11

Mixed number form is x = 7 whole number 9/11

Answer:

[tex]\mathsf{y-8=\cfrac{3}{4}(x-4)}[/tex]

Step-by-step explanation:

Hi student, let me help you out!

.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ..... ........   ......  ... ......... .... ....

First, let's recall the point-slope form equation: ↪ [tex]\mathrm{y-y_1=m(x-x_1)}[/tex].

where: y₁ = y-coordinate of the point (the second coordinate), m=slope, x₁=x-coordinate (the first coordinate).

Let's stick in the values accordingly. We obtain the following: [tex]\mathrm{y-8=\cfrac{3}{4}(x-4)}[/tex], which is our point-slope form equation.

Hope this helped you out, ask in comments if any queries arise.

Best Wishes!

[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{4}}[/tex]

answer: 14.385

Add the numbers as if they were whole numbers.Place the decimal point in the sum  so that it lines up vertically with the numbers being added.

hope this helps:)

Answer:

the tangent ratio should be the length of the leg opposite to angle D to the length of the leg adjacent to angle D

Step-by-step explanation:

tangent is opposite over adjacent

Answer:

[tex]f(x) = {x}^{2} + 4x[/tex]

Step-by-step explanation:

The graph is concave up, this means that the leading term x^2 is positive.

[tex]f(x) = {x}^{2} + 4x[/tex]

[tex]y = {x}^{2} + 4x[/tex]

[tex] {x}^{2} + 4x = 0[/tex]

[tex]x(x + 4) = 0[/tex]

[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]

(0 , 0) and (-4 , 0)

For the y intercept, let x = 0

[tex]y = {0}^{2} + 4(0) = 0[/tex]

(0, 0)

[tex]t.p = \frac{x1 + x2}{2} [/tex]

[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]

[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]

(-2 , -4)

If you connect all these coordinates you will get the parabola shown in the picture.