Work out m and c for the line: 5 x − 3 y + 4 = 0

Answer:

(B) -6x + 4y = 11

Step-by-step explanation:

Two lines are parallel if they have the same slope

In the line equation, y = mx + b, m = slope

For y = 3/2*x - 7/4, slope = 3/2

(B) can be written as

4y = 6x +11

Dividing by 4 on both sides gives y = 6/4*x + 11/4 which is 3/2*x + 11/4 so the coefficient of x (the slope) is 3/2 which is the slope of the line in the question

Using same strategies for the other lines, you will see
(A) has slope -3/2

(C) has slope 1/2

(D) has slope -3/2

Answer:

36

Step-by-step explanation:

We know all angles in a triangle must add up to 180°

The square in the triangle that angle is equal to 90°

We can now solve for x

90 + 54 + x = 180

144 + x = 180

x = 36

That is your answer

- Kan Academy Advance

Answer:

The volume of the box is 250cm³

Step-by-step explanation:

V = Length * Width * Height

V = 5cm * 5cm * 10cm

V = 250cm³

The volume of the given box (rectangular prism).

[tex]V = whl[/tex]

[tex]V = 10 \times 5 \times 5[/tex]

[tex]\large\boxed{\sf{V = 250 \: {cm}^{3}}}[/tex]

Therefore, the volume of the given box (rectangular prism) is 250 cubic centimeters.

The volume of the biggest candle given the volume of the smallest candle is  90.75cm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder =πr²h

Volume of the smallest candle = 3.14 x 5 x 1.7² = 45.37 cm³

Volume of the largest candle =  45.37 cm³ x 2 = 90.75cm³

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Answer:

I think it's just water bro

Answer:

B & C

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

2. a. Combination (as there is no particular order in which they are selected)

3. b. 5 (As there are 5 letters present)

4. Ways in which the word can be arranged :

5. No. of ways :

6. P (Honda) :

Answer:

21 m^2

Step-by-step explanation:

0.5 x 14 x 3

hope this helps

have a good day

Answer:

The answer is 21 m^2

cmiller did it first so giver her brainlliest if you were going to do it to me.

Answer:

Claro esta:

139 x 1

Pero tambien

69.5 x 2

Y

46.3 x 3

Y muchos mas

Answer:

Here is the answer...hope it helps

Answer:

y= -3/2x - 3/2

Step-by-step explanation:

So you know the gradient of the line is -3/2x since that is the gradient.

So the equation so far is y=-3/2x +c

Then, substitute the co-ordinates to find c so:

-3 = -3/2 +c

-3/2 = c

The equation is y = -3/2x -3/2

Answer:

B and C are functions.

Step-by-step explanation:

B and C are functions because they satisfy the Vertical Line Test. A and D are not functions because they do not satisfy the Vertical Line Test.

Answer:

750 cm^3

Step-by-step explanation:

VOLUME  = base * height  = 50 cm^2 x 15 cm = 750 cm^3  

The balance of the loan at 14 months= $10,561.25

It would take a total 23 months to pay off the loan.

The total amount of money paid for the car is = $9,052.5

The total loan for the car = $8,500

The rate at which the loan is compounded monthly is

= 6.5%

The monthly payment for the loan = $390

Find the simple interest

= P×T×R/100

= 8,500 × 1 × 6.5/100

= 55,250/100

= $552.5

If 12 months = 8,500 + 552.5

14 months = X

make X the subject of formula,

X = 14 × 9052.5/12

X= 126,735/12

X = $10,561.25

The amount paid monthly = $390

The amount to be paid for the loan with interest = 8,500 + 552.5 = $9,052.5

If 1 month = $390

× month = $9,052.5

Make X the subject of formula,

X = $9,052.5/$390

X= 23 months

The total amount of money paid for the car is already calculated which is through the simple interest

= P×T×R/100

= 8,500 × 1 × 6.5/100

= 55,250/100

= $552.5

= 8,500 + 552.5

= $9,052.5

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Applying the Pythagorean theorem, the distance between the Earth's horizon and the satellite would be 5756.70 miles.

To calculate the distance from the satellite to the Earth's horizon, it is necessary to use the Pythagorean Theorem as follows:

We must identify the data we have:

To calculate the distance from the satellite to the Earth's horizon, we must first establish the distance from the center of the Earth to the satellite, for this we calculate the radius of the Earth and add the distance to the satellite:

With these data we can draw an imaginary triangle from the center of the Earth, one of its legs would be the distance between the center of the Earth and the satellite, the other leg would be the distance between the center of the Earth and the Earth's horizon (at 90° to the other leg).

Now, to identify the distance between the horizon and the satellite, we apply the Pythagorean Theorem:

According to the above, the distance between the satellite and the horizon would be 5756.70 miles.

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Answer:

15

Step-by-step explanation:

Just add the number of kids disregarding their age

Answer:

The correct answer is 15.

Step-by-step explanation:

To get this answer, all we have to do is add up the data from the graph.

3 + 4 + 2 + 5 + 1 = 15

Hope this helps:) Goodluck!

Answer:

[tex]27c^3-27c^2d+9cd^2-d^3[/tex]

Step-by-step explanation:

Binomial Theorem

[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]

[tex]\textsf{If }(a+b)^n=(3c-d)^3 \: \textsf{ then}:[/tex]

Substitute the given values into the formula:

[tex]\begin{aligned}(3c-d)^3 & =(3c)^3+\dfrac{3!}{1!(3-1)!}(3c)^{3-1}(-d)+\dfrac{3!}{2!(3-2)!}(3c)^{3-2}(-d)^2+(-d)^3\\\\& =(3c)^3+3(3c)^2(-d)+3(3c)^1(-d)^2+(-d)^3\\\\& =27c^3-27c^2d+9cd^2-d^3\end{aligned}[/tex]

Answer:

x=3

Step-by-step explanation:

X^2*x^3 → x^5

x^5 = 243 means x = 3

Answer:

The number is 3.

Step-by-step explanation:

Let "The square of the number" be x^2.

Let "the cube of the same number" be x^3.

"product" means multiplication.

x^2 • x^3 = 243

Multiply. To multiply, add the exponents.

x^5 = 243

Take the 5th root of both sides. You can do this on many scientific calculators with a x^y button. Or raise 243^ (1/5)

1/5 power is the same as 5th root.

You might do it in your head by thinking "what number to the 5th power is 243"

x = 3

Check 3^5 = 243

also

3^2 • 3^3 = 43

9 • 27 = 243

243 = 243 check

   [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

    Find the slope using the following points:

        (20, -10) (6, -20)

[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Use the slope formula:-

                    [tex]\LARGE\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]

Replace letters with numbers as follows:-

                             [tex]\Large\text{$\displaystyle\frac{-20-(-10)}{6-20}$}[/tex]

On simplification,

                                  [tex]\Large\text{$\displaystyle\frac{-20+10}{-14}$}[/tex]

On further simplification,

                                        [tex]\Large\text{$\displaystyle\frac{-10}{-14}$}[/tex]

Reducing the fraction,

                               [tex]\large\text{$\displaystyle\frac{10}{14}$}[/tex]

               [tex]\large\text{$\displaystyle\frac{5}{7}$}\leftarrow\:slope[/tex]

[tex]\rule{300}{1}[/tex]

The volume of a cylinder with a height of 12 millimeters and diameter of 18mm is 972π mm^3

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h where:

r is the radius

h is the height

Given the following parameters

h = 12mm

r = 18/2 = 9mm

Substitute

V = π(9)²(12)
V = 972π mm^3

Hence the volume of a cylinder with a height of 12 millimeters and diameter of 18mm is 972π mm^3

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Answer: The answer would be (-2,0),(-4,0), and (5,0)

Step-by-step explanation:

Guessing the answer choices are

(-2,0)

(4,0)

(0,10)

(-4,0)

(0,-2)

(0,-10)

(5,0)

The amount of paint needed to cover all parts of the table will be 3703 square inches. Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.

The table is shown below.

The surface area of the cylinder will be

SA of cylinder = 2πr² + 2πrh

SA of cylinder = 2π (18² + 18 × 3)

SA of cylinder = 2375 square inches

Then the surface area of the prism will be

SA of prism = 4 [WL + 2(WH + LH)]

SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]

SA of prism = 4 [12 + 2 x 160]

SA of prism = 4 [12 + 320]

SA of prism = 1328 square inches

Then the total surface area of the table will be

Total surface area = SA of prism + SA of cylinder

Total surface area = 1328 + 2375

Total surface area = 3703 square inches

Thus, the amount of paint needed to cover all parts of the table will be 3703 square inches.

Then the correct option is B.

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Based on the lengths of the given triangles and the length of segment BD, the length of segment AD is 22.20.

The triangle ABC is a right angled triangle with segment AB being the hypothenuse.

We can therefore find this length using the Pythagoras Rule:

Hypothenuse ² = a² + b²

Hypothenuse ² = 28.6² + 23.2²

Hypothenuse ² = 1,356.20

Hypothenuse = √1,356.20

= 36.83

Length of AD:
= AB - BD

= 36.83 - 14.60

= 22.2

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Answer:

a) 20r + 20w = 500, 10r + 35w = 500

b) r = 15, w = 10

c) 900 calories

Explanation:

Let running time be r, walking time be w

a) Hence, make equation's:

20r + 20w = 500... equation 1

10r + 35w = 500... equation 2

b) Determine the value of the variables by solving simultaneously.

⇒ (500 - 20w)/20 = (500 - 35w)/10

cross multiply

⇒ 10(500 - 20w) = 20(500 - 35w)

multiply

⇒ 5000 - 200w = 10000 - 700w

shift sides

⇒ -200w + 700w = 10000 - 5000

simplify

⇒ 500w = 5000

divide both sides by 500

⇒ w = 10

Now find the value of variable r,

⇒ r = (500 - 20w)/20

insert w = 10

⇒ r = (500 - 20(10))/20

simplify

⇒ r = 15

Hence the value of r is 15 and w is 10

c) Find calories burnt after one hours of running:  [1 hours = 60 minutes]

calories = 60r = 60(15) = 900 calories

Hence, he can burn 900 calories after one hours of running.

c=√a2+b2 I really hope this helps

The side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.

The length of the side of the square and the height will be

6.98 cm and 13.96 cm.

Pyramid is a three dimensional Structure ,having square , rectangle , hexagonal base , the faces for a square pyramid and hexagonal pyramid are triangle meeting at one point .

It is given in the question that

A toy is being constructed in the shape of a pyramid.

the maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters.

the height of the toy is double the side length

Let us assume the side length to be x

and therefore the height of the toy is 2x

The surface area of the toy is given = 250 sq.cm

First let us consider for a square base

The surface area of a square pyramid is given by

[tex]\rm A = a^2 + 2 a\sqrt {\dfrac{a^2}{4}+h^2}[/tex]

Here a is the side length which x for us and h = 2x

[tex]\rm 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+(2x)^2}\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+4x^2}\\\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{17 x^2}{4}}\\\\\\250 = x^2 + x^2 \sqrt{17}\\\\\\250 = 5.132 x^2\\\\\\48.71 = x^2\\\\\\x = 6.98 cm .[/tex]

Therefore the length of the side of the square and the height will be

6.98 cm and 13.96 cm.

For a hexagonal base

The total surface area is given by

[tex]A =6ah + 3 \sqrt{3}a^2\\\\\\A = 6 \times x \times 2x + 3\sqrt{3} (x)^2\\\\250= 12x^2 + 3\sqrt{3} x^2\\\\\\250 = 17.196 x^2\\\\\\14.54 = x^2\\\\x = 3.81 cm\\\\[/tex]

Therefore the side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.

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Answer:

[tex] \frac{8}{5} = \frac{2}{m - 3} \\ \\ \implies \: 8(m - 3) = 2 \times 5 \\ \\ \implies \: 8m - 24 = 10 \\ \\ \implies \: 8m = 10 + 24 \\ \\ \implies \: 8m = 34 \\ \\ \implies \: m = \frac{34}{8} \\ \\ \implies \: \boxed{m = 4.25}[/tex]

therefore , second option is correct.

hope helpful ~

Taking into account the definition of a system of linear equations, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The tickets to gone with the wind, at the classic movie house, cost $4.50 for adults and $2 for children.

45 people attended the Saturday matinee showing and the Classic movie House sold $162.50 worth of tickets.

So, the system of equations to be solved is

[tex]\left \{ {{x+y=45} \atop {4.50x+2y=162.5}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation you get:

x=45 - y

Then, substituting the expression in the second equation you get:

4.50×(45 - y) +2y=162.5

Solving:

4.50×45 - 4.50y +2y=162.5

4.50×45 - 4.50y +2y=162.5

202.5 -2.5y= 162.5

-2.5y= 162.5 -202.5

-2.5y= -40

y= (-40)÷ (-2.5)

y=16

Now, replacing in the expression x=45 - y you get:

x=45 -y

x= 45-16

x= 29

Finally, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.

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Answer:

2[tex]n[/tex] = [tex]\alpha n[/tex] and [tex]n + n[/tex] = [tex]\alpha n[/tex]

Step-by-step explanation: