The sum of three times a and four is the same as 5
times a.

30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute.

Rectangle's area is equal to its length times its width.

Given,

A rectangle has a 10 cm side.

Consequently, 30 is the area of the rectangle that changes at the instant when the other side is 12 cm and growing at a rate of 3 cm per minute.

To learn more on Rectangle click here:

brainly.com/question/20693059

#SPJ4

You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent the price of the shirt and y represent the price of the pants.

Let

x ----> the price of the shirt

y ---> he price of the pants

we have that

The price of three shirts plus the price of two paints must be equal to $300

so 3x+2y = 300 this is the equation of the line in standard form

Convert to slope intercept form

y = mx+b

Isolate the variable y

3x+2y = 300

subtract 3x both sides

3x+2y-3x = -3x+300

2y = -3x+300

Divide by 2 both sides

y = -1.5x+150

----> equation of the line in slope intercept form

Find out the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero

Using the Standard Form, identify the x-intercept of the graph

The standard form is

Ax+By = C

The x-intercept is C/A

we have

3x+2y = 300

so

300/3 = 100

The x-intercept is the point (100,0)

That means---> The price of the shirt is $100 when the price of the paints is equal to $0

Alternative method to find out the x-intercept (equation in slope intercept form)

y = -1.5x+150

For y=0

0 = -1.5x+150

solve for x

1.5x = 150

x = $100

Hence the x-intercept is the point (100,0)

To learn more about intersects click here https://brainly.com/question/24363347

#SPJ4

Answer:

Tan A = Opposite/ Adjacent

Tan A = 40/9

option D

Step-by-step explanation:

On the second page, last question

Tan is given by a formula opposite divided by the adjacent

Based on the position of the angle, our opposite will be 40 and the adjacent, 9 leaving us with and equation

tan A = 40/9

Answer:

5

Step-by-step explanation:

The straight line distance between the two friends is 12 meters.

Given, On a school playground, a math teacher draws a number line with values from -10 to 10.

Also, the distance between each consecutive number is 1 meter.

Now,  Rebecca is standing at +4, and her friend Cedric is standing at -8.

We have to find the straight-line distance between the two friends, in meters.

As, the distance of Rebecca from the origin is 4 m and the distance of Cedric from the origin is 8 m.

Therefore, the distance between Rebecca and Cedric is 4 + 8 i.e. 12 m

Hence, the straight line distance between the two friends is 12 meters.

Learn more about Coordinate Geometry here https://brainly.com/question/18269861

#SPJ1

Answer:

f(3)=-11

f(-1)=1

f(-2)=4

Explanation:

For each question you would replace the x in the main equation (f(x)=-3x-2) for the number given within f(x).

Therefore,

f(3)=-3(3)-2

=-9-2

=-11

f(-1)=-3(-1)-2

=3-2

=1

f(-2)=-3(-2)-2

=6-2

=4

The amount of money (principal)  that Hsu-Mel would need to invest in an account now with 7.4% APR, compounded daily, in order to reach her goal in 3 years is $7206.24.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Note: The annual percentage interest (APR) rate would be divided by 365 since it is compounded daily.

Substituting the given parameters into the formula, we have;

9,000 = P(1 + 0.074/265)^{365 × 3}

9,000 = P(1.00023)^{1095}

9,000 = P(1.2489)

Principal, P = 9000/1.2489

Principal, P = $7206.24.

Read more on interest rate here: https://brainly.com/question/26343258

#SPJ1

An equilateral triangle is not a right triangle for which the formula A = 1/2 bh applies. where A is the area, b is the length of the base, and h is the height. This formula does not work because all sides and angles of an equilateral triangle are equal.

Hence, An equilateral triangle is not a right triangle for which the formula A = 1/2 bh applies. where A is the area, b is the length of the base, and h is the height. This formula does not work because all sides and angles of an equilateral triangle are equal.

learn more about equilateral triangle click here:

https://brainly.com/question/17264112

#SPJ4

The value of the final result when 19 is subtracted from 26 will be positive value (7).

According to the question,

We have the following expression:

26-19

Now, we have to find whether the value of this expression will be positive or negative.

We know that when two integers are of different signs then the smaller one is subtracted from the larger one but in the final result the sign remains that of the larger integer.

In this case, 26 is greater than 19 and it is positive.

So, the result will also be positive.

26-19

7

Hence, the value of the final result when 19 is subtracted from 26 will be positive (7).

To know more about positive value here

https://brainly.com/question/14392983

#SPJ9

The compound interest earned on an account with $700 invested at 4.5% for 2 years is $64.42.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

To calculate the compound interest earned, we use the formual below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the compound interest earned is $64.42.

Learn more about compound interest here: https://brainly.com/question/24924853

#SPJ1

Answer: We on da same question i do not know

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

add the numbers up

1+2+5+5+6+6+7+8=40

divide it by 8 (because there are 8 numbers)

40/8=5

Answer:

Perimeter is the sum of length of the sides used to made the given figure. The length of each side of the yield sign is 78 centimeters.

Step-by-step explanation:

Nadia made $975 last week and $50, 700 in 2011.

The amount earned last week = Percentage of comission × earnings

The amount earned last week = 13% × 7500

The amount earned last week = 13 × 75

Performing multiplication on Right Hand Side of the equation

The amount earned last week = $975

As per the known fact, 1 year has 52 weeks. So, the commission earned in 2011 = 52 × 975

Performing multiplication on Right Hand Side of the equation

The commission earned in 2011 = $50, 700

Thus, the amount earned last week is $975 and comission earned in 2011 is $50, 700.

Learn more about percentage -

https://brainly.com/question/24877689

#SPJ4

5.37 divided by 3 equal to 1.79

The calculation can be done simply by calculator however to so it manually the decimal is converted to fraction

converting to fraction

5.37 = 537 / 100

dividing by three

= 537/100 / 3

= 537/100 * 1/3

= 537/300

= 1.79

Learn more about division here:

https://brainly.com/question/29401139

#SPJ1

1.2113 ft/s is the speed at which the radius of the sphere is changing when the radius is 6 feet .

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.

Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.

The rate of change of volume will be the product of the rate of change of radius and the area of the sphere. The area of the sphere is ...

 A = 4πr² = 4π(6 ft)² = 144π ft²

Then the relationship above is ...

dV/dt = A·dr/dt

548 ft³/s = (144π ft²)·dr/dt

dr/dt = (548 ft³/s)/(144π ft²) = 137/(36π) ft/s ≈ 1.2113 ft/s

learn more about mensuration here :

brainly.com/question/14312097

#SPJ4

The triangles are congruent using a two-column proof and triangle congruency theorems. For that please refer to the image also and reasons are mention below.
Math congruent meaning?

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

Since the statements are already presented in your figure, only the reasons need be stated here.

1)Given

2)Given

1)Given

4)Congruent line segment definition5)

5)symmetry as a congruence trait

6) Addition and substitution aspects of equality

7)Segment addition theorem

8)Congruent line segment definition

9)Congruence postulate for AAS

According to the property of addition, if A=B, then A+C=B+C. According to the substitution property, if C=D, then A+C=B+D. (D can be substituted for C). I believe that in order to move from A=B and C=D to A+B=C+D, both qualities must be present.

Learn More about congruent at
https://brainly.com/question/11949261
#SPJ1

Answer:

x=80 degrees

Step-by-step explanation:

all 3 angles of a triangles equals 180

We add the 2 angles 70+30=100

Now we subtract from 180

180-100=80

x=80 degrees

Hopes this helps please mark brainliest

Marques played songs in Number of movies = 5 and Number of commercials = 10

A mathematical statement proving the equality of two mathematical expressions is the essence of an equation.  For example, 8x + 3 = 12 is an equation in which the expressions 8x + 3 and 12 are separated by a 'equal' sign.

The system of equations that could be used to determine the number of commercials and the number of movies on which Marques songs were played is illustrated as 30(x + 5) + 120(x) = 900.

The variable x represents the number of times the song has been played in movies.

According to the information, Marques is a songwriter who collects royalties on his songs whenever they are used in a commercial or a movie, and she will earn $30 every time one of his songs is used in a commercial, while he will earn $120 every time one of his songs is used in a movie.

Let x be the number of times the song was heard in movies.

Marques' songs were heard in five times more commercials than in movies. x+5 will be the answer.

As a result, the equation to solve the problem will be:

30(x + 5) + 120(x) = 900

30x + 150 + 120x = 900

150x + 150 = 900

150x = 900 -150

150x = 750

x = 750/150

x = 5

Number of movies = 5

Number of commercial = x + 5

5 + 5 = 10

Therefore Marques played songs in Number of movies = 5 and Number of commercials = 10

To learn more about equations visit

https://brainly.com/question/17149704

#SPJ4

Making x the subject of the formula x/y -z=w is

x = y(w+z)

The subject of a formula is the variable which is expressed in terms of the other variable. For example the volume of a cylinder is V = πr^2h.

where V is the volume and r is the radius and h is the height . In the formula V is expressed in term of other variables like radius and height. Therefore V is said to be the subject of the formula

Relating the explanation with the formula x/y -z= w, here w is the subject and we need to make x the subject.

We achieve this by evacuating other variables attached to x

x/y -z= w

add both sides by z

x/y-z+z= w+z

x/y= w+z

multiply both sides by y

x/y×y=(w+z)y

therefore x= y(w+z)

learn more about subject of formula from

https://brainly.com/question/657646

#SPJ1

By evaluating the exponential equation we will see that:

a) On 2001 the population is 150.38 thousands.

b) on 2018 the population is 409.13 thousands.

We know that the population (in thousands) x years after 1998 is given by the exponential equation:

y = 123.1*(1.069)^x

a) We want to find the population in 2001, this is 3 years after 1998, so x = 3, replacing that we will get:

y = 123.1*(1.069)^3 = 150.38

So the population on 2001 will be 150.38 thousands.

b) If the equation still works for 2018, then we can use x = 20 (2018 is 20 years after 1998) then the population will be:

y = 123.1*(1.069)^18 = 409.13

So the population is 409.13 thousands.

Learn more about exponential equations:

https://brainly.com/question/11832081

#SPJ1

The system of inequalities that represents this scenario is;

x² - 2y ≥ 7000

2x + 5y < 1000

We are given that;

Value of company's stock = x² - 2y

Now, purchases by the company is modeled by; 2x + 5y

We are now told that the company’s goal is to maintain a stock value of at least $7,000. This means the stock value must be greater than or equal to $7000. Thus, this inequality is;

x² - 2y ≥ 7000

Now, we are told that the purchases must be kept below $1000. This means less than $1000 and as such the inequality is;

2x + 5y < 1000

Read more about system of Inequalities at; https://brainly.com/question/28230245

#SPJ1

Answer:

72.6%

Step-by-step explanation:

Percentages are simple

(Number given / Total given ) × 100 = ?%

(363 / 550 ) × 100 =

0.726 × 100 = 72.6

This should be our final answer of 72.6%

Hope this helped and have a good day

Answer:

∴ g(x) = -2x + 10

Step-by-step explanation:

Since f(x) = -x + 5,

g(x) = 2[f(x)]

      = 2(-x + 5)

      = -2x + 10

Answer:

The answer to your problem is 540

Step-by-step explanation:

The answer is 180 because all triangles have 3 sides and a pentagon is 3 triangles formed as one so you need to do 180 x 3 which is 540

Answer:

m = -27/13

Step-by-step explanation:

Given equation,

→ (2m - 27)/3 = 5m

Now the value of m will be,

→ (2m - 27)/3 = 5m

→ 2m - 27 = 5m × 3

→ 2m - 15m = 27

→ -13m = 27

→ [ m = -27/13 ]

Hence, value of m is -27/13.

Answer:

See below

Step-by-step explanation:

By "gradient of the given line" the question is asking to find the slope of the line.  If we rearrange each equation inrto slope-intercept format of y = mx + b, we can find the slope easily, since m is the slope (b is the y-intercept).

y = 4x + 3

 The slope is 4.

y= -8x + 6

  The slope is -8

4y = 8x +3

y = 2x + (3/4)   Rearrange to y = mx + b

  The slope is 2

y+x=8

y = -1x + 8       Rearrange

    The slope is -1

y -x = 5

      y = x + 5   Rearrange

      The slope is 1

4y + 5x = 30

       y = -(5/4)x + (30/4)

       The slope is -(5/4)

Di-ane plans to walk 6000 steps on day 100.

Given, Di-ane walks 5000 steps each day. She keeps her goal to increase the 10 number of steps. The increase has been modelled using the function.  

A re-lation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a re-lationship between inputs in which each input is connected to precisely one output.

We have to write what does f(100)=6000 represent.

As given in question the function represents the number of steps. and x represent the day.

100 represents the number 100th day, f(100)=6000 represents that Di-ane walks 6000 steps on the 100th day.

To learn more on function here:

https://brainly.com/question/5975436#

#SPJ9

Length of KM using distance formula is √53.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In math, what is a distance? The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.

Given,

Coordinates of K = (8,-4)

Coordinates of M = (1,-2)

Distance formula:

D = √(x₂ - x₁)² + (y₂ - y₁)²

D = √(8-1)² + (-4+2)²

D = √49 + 4

D = √53

Length of KM using distance formula is √53.

To learn more about distance, visit:

https://brainly.com/question/28956738

#SPJ13