A. seconds

B. cubic centimeters

C. meters

D. liters

**Answer:**

c

**Step-by-step explanation:**

The metre or meter, symbol m, is the primary unit of length in the International System of Units, though its prefixed forms are also used relatively frequently.

What is the average rate of change of f(x), represented by the graph, over the interval [-1, 2]?

The **estimate **(to one decimal place) of the **average rate **of change f is 2.3

The **interval **is given as

[-1, 2]

This can be rewritten as

x = -1 to x = 2

This can also be represented as

(a, b) = (-1, 2)

From the attached **graph**, we have

f(-1) = -5

f(2) = 2

The estimate (to one decimal place) of the **average rate **of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(2) - f(-1)]/[2 + 1]

So, we have

Rate = [2 + 5]/[2 + 1]

Evaluate

Rate = 2.3

Hence, the **average rate **of change f is 2.3

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What is the proportional relationship between a and bA B8. 324 940 15 Write a equation describing the relationship between a and b

**Explanation:**

A proportional relationship means that the two variables are related by a constant called *constant of proportionality*:

k is the constant of proportionality.

To find k we have to use the values of a and b from the table:

[tex]\begin{gathered} k=\frac{a}{b} \\ k=\frac{8}{3} \\ k=\frac{24}{9}=\frac{8}{3} \\ k=\frac{40}{15}=\frac{8}{3} \end{gathered}[/tex]**Answers:**

• equation: ,a = 8/3 b

,• constant of proportionality:, 8/3

8.12 Midpoint formula: find the endpoint EUW

Learn with an example

Submit

or Watch a video

The midpoint of PQ is M(4, 0). One endpoint is P(6, 0). Find the coordinates of the other

endpoint Q.

Write the coordinates as decimals or integers.

‹=OD

Work

The coordinates of the other endpoint **Q.=(2,0)**

**How to calculate the coordinates of the other endpoint Q ?**

**Given:**

Midpoint = PQ = M(4,0)

One endpoint = P = [tex](x_1,y_1)[/tex] = (6,0)

Other endpoint Q= [tex](x_2,y_2)[/tex]

We know that,

[tex]\text{Midpoint PQ}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\=(\frac{6+x_2}{2} ,\frac{0+y_2}{2} )=(4,0)\\\\= > \frac{6+x_2}{2} =4\\\\= > 6+x_2= 8\\\\= > x_2=2[/tex]

[tex]\text{Similarly},\\\\\frac{0+y_2}{2} =0\\\\= > y_2=0[/tex]

So, the **Other endpoint Q=(2,0)**

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Let's call a year "nice" if its number can be represented as the difference of two powers of two. What is the next nice year? What nice year will be the first one after it?

The next **nice** year will be 2 nice.

The nice year that will be the first one after it is 4 nice.

What is an exponent?It should be noted that an **exponent** is used to express the numbers that are either too big or too small. This is usually expressed in their **powers**.

Fron the information, it as stated that a year is called "**nice**" if its number can be represented as the difference of two powers of two.

The next nice year will be the **difference** which will be

= (2² - 2) × nice

= (4 - 2) × nice

= 2 nice.

The one after it will be:

= 2 × 2 nice

= 4 nice.

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can someone help me? thank you so much

image has the answers

x2 + 7x + 12 = ** Show

x² + 7x + 12 = 0

Using the factorisation method

Find two numbers such that its product gives 12 and its sum gives 7

The two numbers are 3 and 4

Replace 7 in the equation by those two numbers and then factorise

That is;

x² + 3x + 4x + 12 = 0

x(x+3) + 4(x+3) = 0

(x+3)(x+4) = 0

Either x+3 = 0 or x+4 =0

Either x = -3 or x= -4

The answer has to be a geometric proof. Thank you!

Given data:

The given triangle in which AD is on perpendicular bisector on BC.

In triangle ABD and ACD.

[tex]\begin{gathered} \angle ADB=\angle\text{ADC}=90^{\circ} \\ BD=CD(\text{given)} \\ AD=AD\text{ (common)} \\ \Delta ABD\cong\Delta ACD(\text{SAS)} \end{gathered}[/tex]Simmilary triangle BED and triangle CED.

[tex]\begin{gathered} \angle BDE=\angle CDE \\ BD=CD \\ ED=ED \\ \Delta BED\cong\Delta CED(SAS) \end{gathered}[/tex]The fisr expression can be written as,

[tex]\begin{gathered} \Delta ABD\cong\Delta ACD \\ \Delta\text{ABE}+\Delta BED\cong\Delta ACE+\Delta\text{CED} \end{gathered}[/tex]Substitute CED in place of BED.

[tex]\begin{gathered} \Delta ABE+\Delta CED\cong\Delta ACE+\Delta CED \\ \Delta ABE\cong\Delta ACE \end{gathered}[/tex]Thus, the **triangle ABE is congruent to trriangle ACE.**

Match each compound inequality on the left to the graph that represents its solution on the right. 4x + 3 > 15 or -6x > 12 -5 0 1 - 8x > - 24 and -10 < 2x - 6 -7 1 - 29 < 9x - 2 < 16 6 4

The first **compound inequality** 4x+3>15 or -6x≥12 matches the third graph, i.e x>3 or x≥-2.

The second **compound inequality **-8x>-24 and -10≤2x-6 matches the second graph, i.e x>3 or x≥-2.

The third **compound inequality** -29≤9x-2<16 matches the first graph, i.e -3≤x<2.

Given the **expressions** are:

a. 4x+3>15 or -6x≥12

**simplify.**

4x+3>15 or -6x≥12

4x>15-3 or x≥12/-6

4x>12 or x≥-2

x>3 or x≥-2

hence the** graph** is** third.**

b. -8x>-24 and -10≤2x-6

simplify.

-8x>-24 and -10≤2x-6

x>-24/-8 and -10+6≤2x

x>3 and -4≤2x

x>3 and -4/2≤x

x>3 and -2≤x

x>3 and x≥-2

hence the **second graph** matches.

c. -29≤9x-2<16

first take -29≤9x-2

simplify

-29+2≤9x

-27≤9x

-27/9≤x

-3≤x

now take 9x-2<16

simplify.

9x<16+2

9x<18

x<18/9

x<2

hence we get -3≤x<2

hence the** first graph** matches the given** inequality.**

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Use ''compound inequality'' in the main answer and ''graph'' in the explanation.

if you cant read it, it says : A - is an algebraic expression that continues a variable to power of one - is an example A- is a rational number that is multiplied by aA Variable - is a number that can be written as the ratio fraction of two integers - is the expression - is an example of coefficient - are terms who variables are their exponents are the same one example is an - 7y ( - = blank ) the things you can feel in the blank is 4x, 2y, rational coefficient, like-terms, rational-number , 4, linear expression, and 6x+5

A **Linear expression** is an algebraic expression that contains a variable to the power of one. **3 + y **is an example.

A **Coefficient** is a rational number multiplied by a variable. A **Rational Number **is a number that can be written as the ratio, or fraction or intgers.

**4** in the expresson **4x **is an example of a coefficient.

**Like Terms** are terms whose variables and their exponent are the same. One example is **9y** and -7y

** **

Find the constant of proportionality from a graph

**Answer: 2**

**Step-by-step explanation:**

The constant of proportionality is the same as the slope of the line. Using the slope formula with the points (0, 0) and (2, 4), [tex]\frac{4-0}{2-0}=2[/tex].

Given the right triangle ABC with altitude BD drawn to the hypotenuse AC. If AC=6 and DC=4, what is the length of BC in simplest radical form ?

This problem is an application of the **Geometric mean theorem**. It says that

*Comment:** In other words, it says that the length of BC (x) is the geometric mean between the lengths of AC and DC.*

Then,

[tex]x^2=6\cdot4=24[/tex][tex]x=\sqrt[]{24}=2\cdot\sqrt[]{6}[/tex]................................................................................................................................................................

Let's talk a little about the simplest radical form of a square root

[tex]\sqrt[]{a}[/tex]The first step to finding it is to write the number within the root as a product of prime powers, such product is called its integer factorization. Let's do that for 24:

Then, the integer factorization of 24 is

[tex]24=2^3\cdot3[/tex]Thus,

[tex]\sqrt[]{24}=\sqrt[]{2^3\cdot3}[/tex]The idea now is *to take out of the root all we can*. The rule is that we can only take out powers of 2 (for our root is a square root). In the expression

There is only one power of 2, within 2^3. We can write it as

[tex]2^2\cdot2\cdot3[/tex]How are we going to take out it? We are going to take out the base of the power, which is 2 in this case. Then,

[tex]\sqrt[]{24}=2\cdot\sqrt[]{2\cdot3}=2\cdot\sqrt[]{6}[/tex]**In simple terms, the simplest radical form of a root is what results after taking out the root all that can be taken out.**

Find the equation of the linear function represented by the table below in slope-intercept form. X у -1 2 -8 5 -17 8 -26 Submit Answer Answer: D attempt 1 out of 2

Slope intercept form:

y = mx + b

m = (y2 - y1)/(x2 - 1) = (-8 - 1)/(2 - (-1)) = -9/(2 + 1) = -9/3 = -3

m = -3

If we take one of the point, for example (2, -8) and use it on the equation with the slope we already found:

y = -3x + b

-8 = -3(2) + b

Solving for b:

-8 = -6 + b

b = -8 + 6 = -2

b = -2

Therefore, the equation is: y = -3x -2

**Answer:**

**y = -3x -2**

the product of 5 and y

To get the product we multiply.

[tex] = 5 \times y \\ = 5y[/tex]

Use the point-slope form to find the equation of each altitude of SABC. (Recall ! a triangle is the perpendicular drawn from any vertex to the opposite side.) (b) A(4,3), B(0,7). C- (a) A(1, -2), B(3,4), C(-2,6)

The rule of the slope of a line has 2 points is

[tex]m=\frac{y2-y1}{x2-x1}[/tex]A = (1, -2), B = (3, 4), C = (-2, 6)

We will take the altitude from A to the opposite side of BC

Then we will find the slope of BC first

x1 = 3 and y1 = 4. point B

x2 = -2 and y2 = 6. point C

We will substitute them in the rule above

[tex]\begin{gathered} m=\frac{6-4}{-2-3}=\frac{2}{-5} \\ m=-\frac{2}{5} \end{gathered}[/tex]**The slope of BC = -2/5**

Since the **product of the slopes of the perpendicular line is -1**, then if the slope of one is **m**, then the slope of the other will be **-1/m**, we reciprocal it and change its sign, then **the slope of the altitude of BC** should be **5/2**

The form of the equation in point-slope is

**y - y1 = m(x - x1)**

**m = 5/2**

Since point A is lying on the altitude from A to BC, then

**x1 = 1** and **y1 = -2** point A

Substitute m and coordinates of point A in the form of the equation above

**y - (-2) = 5/2 (x - 1)**

The equation of the altitude from A to BC is

**y + 2 = 5/2 (x - 1)**

For each scenario below, choose the graph that gives the best representation.

(a). The daily amount of calories that a rat eats increases steadily from birth to about age 3 months. Then, the amount levels off until about age 6 months, when it increases again.

(b). Jane leaves her house on her bike. She rides at a constant speed until she reaches a lemonade stand, where she parks her bike and takes a rest. Then she turns around and bikes home as fast as she can.

A) The second** graph** gives the best representation of the daily amount of calories consumed by the rat.

B)The fourth graph** **gives the best representation of Jane's journey.

The first **slope** of the graph represents the steady increase in the consumption of calories by the rat until the age of 3. The **horizontal line** represents the level off until the age of 6. The slopes after the horizontal line represent the increase in consumption of calories after age 6.

The first slope of the graph represents the steady increase in the **distance** from her home as she is traveling away from her home. The horizontal line that comes after the slope represents the time she rested at the lemonade stand. And the negative slope that comes after the horizontal line represents the decreasing distance to her home as she travels back to her home.

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What is a number that when you divide it by 2 and subtract 3.8 from the quotient, you get 7?

Let the number x.

Then the number divided by 2 gives

[tex]\frac{x}{2}[/tex]Subtract 3.8 from the quotient gives

[tex]\frac{x}{2}-3.8[/tex]Hence,

[tex]\frac{x}{2}-3.8=7[/tex][tex]\begin{gathered} \frac{x}{2}-3.8=7 \\ \frac{x}{2}=7+3.8=10.8 \\ \Rightarrow x=2\times10.8=21.6 \end{gathered}[/tex]x = 21.6

Why the answer to 12am=4, for a is a=1/3m help please

We can solve the given expression for [tex]a=\frac{1}{3m}[/tex] by using the **division method**.

The given **expression **is [tex]12am=4[/tex].

We have to solve the given expression for [tex]a=\frac{1}{3m}[/tex].

Now we solving the expression.

[tex]12am=4[/tex]

We can easily solve the expression by seeing the value that we have to solve.

We using the division method to solve the given expression.

In the division method we divide the both side by same variable to find to value of particular variable.

For solving the expression for [tex]a[/tex] we eliminate [tex]12m[/tex].

We divide the given expression by [tex]12m[/tex] on both side

[tex]\frac{12am}{12m}=\frac{4}{12m}\\a=\frac{4}{3\times4m}\\a=\frac{1}{3m}[/tex]

Now we solve the given expression for [tex]a=\frac{1}{3m}[/tex].

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A line that includes the point (1, 10) has a slope of 1. what is its equation in slope-intercept form?

Considering the definition of a line, the **equation in slope-intercept** of the line that passes through the point (1, 10) and has a slope of 1 is y=x+9.

A linear equation o line can be expressed in the form **y = mx + b**

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Equation in slope-intercept form in this caseIn this case, you know:

The line has a slope of 1.The line passes through the point (1, 10).Substituting the value of the slope m, the line has a form: y=1x + b or what is the same y=x +b.

Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:

10= 1×1 + b

10= 1 + b

10 -1 = b

*9= b*

Finally, the **equation of the line** is y=x +9.

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Please answer this quickly, I don’t need no explanation or work, just the letter, thank you!

**Solution:**

Given the graph;

If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function.

**ANSWER: ****B**

Independent Practice7. The original quantity is 10 and the new quantityis 13. What is the percent change? Is it anincrease or decrease?8. The original quantity is 5 and the new quantityis 3. What is the percent change? Is it an increaseor decrease?7%1310100%100%poP.P Р-P%.The percent increase is%The percent decrease is

The percentage increase or decrease can be calculated by :

[tex]\%change=\frac{New-Orig}{Orig}\times100[/tex]7. New = 13, Orig = 10

% change = [(13 - 10)/10] x 100 = **30% (Increase)**

8. New = 3, Orig = 5

% change = [(3 - 5)/5] x 100 = -40% or **40% (decrease)**

I'd angle 5=42° and angle 1=117° find the measure of angle CDF.

If angle 5= 42° and angle 1 = 117°

angle CDF = angle 5 + angle 1

=42° + 117°

=159°

a spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 9? Give your answer in fraction form.

**Answer:**

[tex]\frac{9}{10}[/tex]

**Step-by-step explanation:**

multiplies of 9, 18,27,36, and 45. Every number has a change to be selected, but these 5. There are 50 numbers

[tex]\frac{50-5}{50}[/tex]

[tex]\frac{45}{50\\}[/tex]

[tex]\frac{9}{10}[/tex]

5. The following stem-and-leaf plots compare the ages of 30 actors and 30 actresses at the time they won the Oscar award for Best Actor or Actress.ActorsStemsActresses2146667987532213001133444557788877654332210041112966515210601167480(a) What is the age of the youngest actor to win an Oscar? years(b) What is the age difference between the oldest and the youngest actress to win an Oscar? years(c) What is the oldest age shared by two actors to win an Oscar? years

Answer:

(a) 31 years

(b) 59 years

(c) 56 years

Step-by-step explanation:

In general, when reading a stem and leaf plot, we read firstly the number in the steam (middle) and then in the leaf.

Now, let's move on to the question:

(a) As we can see in the graph, the youngest actor has** 31 years**.

(b) The youngest actress is 21 years old and the oldest is 80.

So, the difference is 80 - 21 = **59 years**.

(c) In this exercise, we have to look for actors who had the same age. That means, when evaluating the steam, we will have to find similar values in the leaf. The oldest age shared is **56 years**.

Line c has an equation of y = -5x + 3. Parallel to line c is line d, which passes through the

point (2, -6). What is the equation of line d?

**Answer:**

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so equation of line d is y = -5x + c.

Substitute (2,-6) into the equation to find c.

-6 = -5(2) + c

c = 4

Hence equation of line d is y = -5x + 4.

Solve the following equation 12+5x=2x+3

**Answer:**

-3

**Step-by-step explanation:**

im assuming u want to find x

1. move all the numbers with x to the left side to make life easier

2. 5x-2x= 3x

3. 3-12= -9

4. you want the x to be solo

5. -9/3 = -3

The wheels on noah’s bike have a circumference of about 5 feet how many time do the wheels rotated if noah rides 40 feet

Answer is 8 rotations

Step by step

If the wheel is 5 feet around, we can divide the 40 feet by the 5 feet per rotation, = 8 rotations

Step by step

If the wheel is 5 feet around, we can divide the 40 feet by the 5 feet per rotation, = 8 rotations

please help tutor I will give you a good rating

**Answer**

**Options A, D and E are correct.**

**The two functions are increasing.**

**The function for plan II has a greater unit rate.**

**The function for plan I has a greater y-intercept.**

**Explanation**

The slope and y-intercept form of the equation of a straight line is given as

**y = mx + b**

where

**y = y-coordinate of a point on the line.**

**m = slope of the line.**

**x = x-coordinate of the point on the line whose y-coordinate is y.**

**b = y-intercept of the line.**

For the first plan, there's a one time investment of **15,000 dollars **and subsequent monthly payments of **500 dollars.**

**y = 15,000 + 500x**

**y = 500x + 15,000**

**Slope = unit rate of increase = 500**

**y-intercept = 15,000**

For the second plan, the function is just given as

**y = 12,000 + 520x**

**y = 520x + 12,000**

**Slope = unit rate of increase = 520**

**y-intercept = 12,000**

We can see that

**The two functions are increasing.**

**The function for plan II has a greater unit rate.**

**The function for plan I has a greater y-intercept.**

**Hope this Helps!!!**

7. Which state had a population of eight

hundred four thousand, one hundred

ninety-four?

**Answer:**

I read it's south Dakota but not sure of it.

I found it from this picture

(03.06) 5.)Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2OPTIONS: A.) y-6 = 1/2(x+3)B.) y = 1/2x - 6C.) y+3 = 1/2(x-6)D.) y-2y = 12I NEED THIS DONE ASAP!

Answer the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2

A linear equation can have the form

y = mx + b

The slope is m

The point-slope form is

(y- y1) = m(x -x1) (1)

the point (x1, y1) = (6, -3)

______________

Replacing in (1) the slope and the point (x1, y1)

(y- y1) = m(x -x1)

(y- (-3)) = 1/2(x -6)

y+3 = 1/2(x-6)

__________________

So, checking the options the correct answer is C

A.) y-6 = 1/2(x+3)

B.) y = 1/2x - 6

C.) y+3 = 1/2(x-6)

D.) y-2y = 12

A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Which diagram best represents this information?

The diagram which best represents the **hiking** track of the hiker is attached below.

As time increases, speed is constant, i.e., 214 miles per hour

So, the distance increases with an increase in time.

**Speed** = Distance/Time

Let, Distance = D and Time = T,

214 = D / T

D = 214T

Let, D = Y coordinate, Time = X coordinate

y = 214 x→→Equation of the line passing through the origin and slope 214.

For the given situation, the equation is a **linear equation** and the equation will be on the y-axis.

Hence, a diagram that represents this information is:

Correct question :

A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Draw the diagram which best represents this information?

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1. The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?
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