Solve each system of equations by GRAPHING. Clearly identify your solution.4x - y = 33x + y = 4

The average rate of change of the function from x = 4 to x = 7 is: -1/3.

The formula used to estimate the average rate of change of a function is given as:

f(b) - f(a) / b - a.

Given the function as shown in the diagram below, we are required to find the average rate of change of the function within the interval, x = 4 to x = 7, therefore:

a = 4

b = 7

f(a) = f(4) = 4

f(b) = f(7) = 3

To find the average rate of change of the given function for the interval of x = 4 to 7, substitute the above stated values into the formula for the average rate of change, f(b) - f(a) / b - a:

Average rate of change = 3 - 4 / 7 - 4

Average rate of change = -1/3

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Answer:

20 hyenas

Step-by-step explanation:

locate number of lions 28 on the horizontal axis , then go up vertically to meet the line, then cross horizontally to meet the vertical axis at 20

that is 20 hyenas are contained

Given -

Equations:

y = -x² - 4x -3 and y = 2x + 5

To Find -

Next step =?

Step-by-Step Explanation -

We know first step:

-x² - 4x - 3= 2x + 5

-x² - 4x - 3 - 2x - 5 = 0

-x² - 6x - 8 = 0

-(x² + 6x + 8) = 0

x² + 6x + 8 = 0

x² + 2x + 4x + 8 = 0

x(x+2) +4(x +2) = 0

(x+4)(x+2) = 0

So,

x = -4 or x = -2

So,

The next step is to combine like terms onto one side of the equation.

Final Answer -

Option (d)

Combine like terms onto one side of the equation

Answer:

0.1 also 0.0636942675

B the purchase cost of the aquarium

Explanation

we have the equation

this is a linear equation in the form

hence

so, if we have the sentence

the cost in dollars, y, of purchasing and maintaining a classroom aquarium for x months

let

cost in dollars = y

as x is the variable, let x for the variable in the text, in this case, what changes is the number of months,so

number of months= x

the factor of x ( 48), is the value for the mainting the classroom ( as we can see it depends on the number of months , x)

so

the monthly cost of the aquarium=48

finally , we have 250, this values is a constant, it does not depend on the number of months, so it is

the purchase cost of the aquarium=250

so,the answer is

B the purchase cost of the aquarium

I hope this helps you

Answer: -6/5=2/9

Step-by-step explanation:

Given that the height of a tree increases as time passes.

Your friend says that is dependent because size deemds on time.

Leet's determine if your friend is correct.

Here, since the height of a tree increases as time passes, the height of the tree depends on the time.

Hence, size is the dependent variable while time is the independent variable.

Therefore, your friend is NOT correct.

ANSWER:

No, your friend is NOT correct.

In the given right triangle of the figure

we have that

sin(O)=1/d ----> by the opposite side divided by the hypotenuse in a right triangle

solve for d

d=1/sin(O)

d=4,124,966.13 AU -----> two decimal places

the expression to calculate d for any star is equal to

Answer: 85

To solve this, we need to calculate the height of the triangle. To do this, we divide the triangle verticaly, in two right triangles.

So, we have the hypotenuse of the two smaller triangles is 14. The short leg is half the side of the big triangle: 14/2=7 and the long leg is the height of the triangle and what we want to know.

By the pythagorean theorem:

And now we use the formula for the area of a triangle:

This is the area of each of the smaller triangles. To get the area of the big triangle, we add up the two smaller areas:

rounded to the nearest tenth is 85

Answer:

The probability of selecting a small or white marble is 10/13

Step-by-step explanation:

The total number of marbles is 15 + 11 = 26 marbles

The probability that we want to calculate is if the marble selected is small or white.

So we need to find the number of small marbles as well as the number of white marbles

We can construct a table to see the distribution of the marbles. Please check the attachment for this.

From the table , we can see that there are 11 small marbles and a total of 9 white marbles

The probability of selecting a white marble is;

number of white marbles/total number of marbles = 9/26

The probability of selecting a small marble will be ;

number of small marbles/total number of marbles = 11/26

In probability, whenever we have or, we tend to add

So therefore, the probability of selecting a white or small marble = Probability of selecting a white marble + Probability of selecting a small marble

Mathematically, that would be 9/26 + 11/26 = 20/26

So the probability is 10/13

Answer:

Step-by-step explanation:

Comment

Well my response is, I know how it is done and most of the time I get it right, but mistakes make me give myself about a 3.4.

I hope this answers your question. It will likely be taken down.

The history of integers begins with the natural numbers (1,2,3,...), which are also called the counting numbers. They arise naturally by the need of counting things. But there is a problem. "There is a missing number". If you have a number n of things and you subtract all of them, what remains? Intuitively, it must be a number, a number representing nothing (to have nothing). This is the origin of zero.

Now, as time passes, the man began to do trades and arose the money. This leads to a problem. Other numbers are missing now. How do you express how much money you owe someone? counting numbers are not useful here, for they mean "the money you have". Th

The profit for te corporation is 235,00 million.

The revenue for the corporation is 6700e million.

To determine th fractio in lowest terms for thr e profit and revenue is

ANSWER:

The ramp does meet federal standards

STEP-BY-STEP EXPLANATION:

The first thing we must do is sketch the situation of the statement in order to better understand it.

Now, we need to convert feet to inches, so they are the same units. We know that 1 foot is equal to 12 inches, so:

1 ft = 12 in

20 ft = 20 ft *12 in/ft = 240 in

Now, we calculate the angle of the ramp by means of the trigonometric sine function that relates the side opposite the angle to the hypotenuse.

Therefore:

The value of the angle is 3.58°, which is less than 5°, which means that it meets federal standards.

Given the radius of a circle as r = 2 and centre = (3,1)

We want to find the equation

Solution

First, the equation of a circle centre (a,b) and radius r is given by

From the question

We put the parameters into the equation ans simplify

Therefore the correct option is Option B

Answer: [tex]15x + 10[/tex]

Step-by-step explanation:

[tex]7x + 4 + 8x + 6[/tex]

First you have to combine like terms. You combine like terms by adding them so u would add 7x and 8x and get 15x. Then u would add 4 and 6 and get 10.

[tex]15x + 10[/tex]

15x + 10 would be your final answer in simplest form.

Answer:

a) -15 (b)25/2 (c)-31.2 (d)15

Step-by-step explanation:

(a)f(-24)=5/6×24+15

-15

(b)f(9)=5/6×9+15

25/2

(c)f(x)=5/6x+15

5/6x+15=-11

5x+90=-66

5x=-66-90

5x=-156

5x/5=-156/5

x=-31.2

(d)f(0)=5/6×0+15

0+15

15

A: (-3,-5)

B: (-1,8)

To find the midpoint we have to add each coordinate and divide by 2:

Midpoint: (-3-1)/2 , (-5+8)/2 = -4/2, 3/2 = -2,1.5

Midpoint: (-2, 1.5)

Explanation:

The volume formula is:

We know that the radius is r = 5 and the volume is V = 50pi. We have to replace these values into the formula above and solve for h:

Answer:

h = 2

Answer:

136 m

Step-by-step explanation:

Let w = the width of the rectangular field.

Let l = the length of the rectangular field.

The formula for the perimeter P of the rectangular field is:

P = 2w + 2l

Since the length l is 7 m less than 4 times the width w, then we can write the following equation that relates l and w:

l = 4w - 7 m

Since l = 4w - 7 and it's given that perimeter P = 136 m, then we can substitute this information into the perimeter formula as follows:

P = 2w + 2l

136 m = 2w + 2(4w - 7 m)

136 m = 2w + 2(4w) - 2(7 m)

136 m = 2w + 8w - 14 m

136 m + 14m = 10w - 14 m + 14 m

150 m = 10w + 0

10w = 150 m

(10w)/10 = 150 m/10

(10/10)w = 150 m/10

(1)w = 15 m

w = 15 m

Therefore, l = 4w - 7 m

l = 4(15 m) - 7 m

l = 60 m - 7m

l = 53 m

CHECK:

P = 2w + 2l

136 m = 2(15 m) + 2(53 m)

136 m = 30 m + 106 m

136 m = 136 m

y = 6x + 35

y = 9x + 14

Combining these equations, we get:

6x + 35 = 9x + 14

35 - 14 = 9x - 6x

21 = 3x

21/3 = x

x = 7

Substituting this result in the first equation:

y = 6*7 + 35

y = 42 + 35

y = 77

Answer: 3

Step-by-step explanation:

if x = 1 then 2(1) +1 is 2+1 which is 3

f(1) means that in the place of x you plug in 1 and simplify.

[tex]f(1) = 2(1) + 1 \\ f(1) = 2 + 1 \\ f(1) = 3[/tex]

ATTACHED IS THE SOLUTION

→

r

=

13.5

mi

, at a bearing angle of

50.4

o

Explanation:

We're asked to find the total displacement, both the magnitude and direction, of the ship after it leaves the port with the given conditions.

First, I'll explain what a bearing is.

A bearing is NOT a regular angle measure; normally, angles are measured anticlockwise from the positive

x

-axis, but bearing angles are measured clockwise from the positive

y

-axis.

Therefore, a bearing of

34.0

o

indicates that this is an angle

90.0

o

−

34.0

o

=

56.0

o

measured normally. We'll use this angle in our calculations.

We're given that the first displacement is

10.4

mi

at an angle of

56.0

o

(as calculated earlier). Let's split this up into its components:

x

1

=

10.4

cos

56.0

o

=

5.82

m

y

1

=

10.4

sin

56.0

o

=

8.62

m

Our second displacement is a simple

4.6

mi

due east, that is, the positive

x

-direction. The components are thus

x

2

=

4.6

mi

y

2

=

0

mi

To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:

Δ

x

=

x

1

+

x

2

=

5.82

mi

+

4.6

mi

=

10.42

mi

Δ

y

=

y

1

+

y

2

=

8.62

mi

+

0

mi

=

8.62

mi

r

=

√

(

x

total

)

2

+

(

y

total

)

2

=

√

(

10.42

mi

)

2

+

(

8.62

mi

)

2

=

13.5

mi

The direction of the displacement vector is given by

tan

θ

=

Δ

y

Δ

x

so the angle is then

θ

=

arctan

(

Δ

y

Δ

x

)

=

arctan

(

8.62

mi

10.42

mi

)

=

39.6

o

The question asked for the bearing angle, which is just this angle subtracted from

90

o

:

Bearing angle

=

90

o

−

39.6

o

=

50.4

o

Children's academic success, literacy, numeracy, and scientific knowledge are all directly impacted by their schooling. A child's education in school helps them learn all the fundamentals that will benefit them in the future.

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Data:

Estimate: E= 475 songs

Actual amount: A=380

To find the percent of error you use the next formula:

x² + 3 / (x-1)(x-3) is simplest form of the given expression

Given: x-3/x-1 + 6/x-3

First, find the LCM of x-1 and x-3. The LCM is c

(x-3)(x-3) + 6(x-1) / (x-1)(x-3)            

Remove the bracket of the numerator

x² - 6x + 9 + 6x - 6 / (x-1)(x-3)        

Add and subtract like terms

x² + 3 / (x-1)(x-3)

Therefore, the expression has the simplest form of x² + 3 / (x-1)(x-3). This shows the concept of expression.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given values

STEP 2: Get the inequality

Hence, the answer is:

The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.

A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.

Given Information

The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.

These transformational skills are all possessed by Matt:

Reflection

The reason a reflection maintains its original form Similar spots from the pre-image to the image remain apart from the line of reflection.

The transformation of rotations into congruence

Any rotating figure will twist. Although it is the same size and shape as before, the figure appears to have toppled over. A clock is a perfect example of how rotation works in real life. A clock's connecting arms turn around its axis every hour or every day. A rotation's degree determines what kind of rotation it is; typical rotations include 90, 180, and 270 degrees. Before turning around and going back to where it started, the figure does a full 360-degree turn. the direction of a rotation, whether it be clockwise or counterclockwise. The degree, amount, and other factors can be determined using this information .a revolution's speed, direction, etc.

Transformative translational congruence

When an object or shape is moved without altering its size, shape, or orientation, the movement is referred to as a translation. When doing a translation, also known as a slide, every point on an object or shape is moved uniformly and in one direction.

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Given:

Area of base of the prism, B = 96 square centimeters

Height of prism, H = 9 centimeters

Let's find the volume of the prism.

To find the volume of the prism, apply the formula below:

Where:

V is the volume in cubic units

B is the area of the base = 96 square centimeters

H is the height = 9 centimeters

Hence, we have:

Therefore, the volume of the prism is 864 cubic centimeters

ANSWER: