(b) A line has the equation y = 6x + 11
Does the point (-3,15) lie on the line? Explain you answer as fully as possible

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle

Perimeter of rectangle = 2(L + B)

Substituting the required values:

→ 168 = 2(3x + x)

→ 168 = 2(4x)

→ 168/2 = 4x

→ 84 = 4x

→ 84/4 = x

→ 21 = x

Hence,

Answer:

⠀

Step-by-step explanation :

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As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .

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Now, According to the Question :

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[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

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[tex]{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}[/tex]

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[tex]{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}[/tex]

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[tex]{\longrightarrow \qquad { {\sf{12 w = 168 }}}}[/tex]

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[tex]{\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}[/tex]

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[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar[/tex]

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Therefore,

⠀

Now, we are to find the length of the rectangle :

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[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: [/tex]

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[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: [/tex]

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[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar[/tex]

⠀

Therefore,

Answer:

19

Step-by-step explanation:

(5x+37)+(3x-9)=180

8x= 152

x=19

Answer:

(a) To find the missing angle, we would do inverse tan.

[tex]angle =tan^{-1}\frac{opp}{adj}[/tex]

[tex]angle = tan^{-1}\frac{17}{21}[/tex]

angle= 39.0 degrees or 0.7 radians

(b) To find the missing angle, we would do inverse sin.

[tex]angle= sin^{-1}\frac{opp}{hyp}[/tex]

[tex]angle= sin^{-1}\frac{12.7}{22.1}[/tex]

angle= 35.1 degrees or 0.6 radians

Answer:

Step-by-step explanation:

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

STEP 1: Define box plot.

In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread, and skewness groups of numerical data through their quartiles.

STEP 2: Choose the correct statement

The box plot shows the minimum height, maximum height, first and third quartiles, and the median.

Therefore,

The box plot does not show the number of vases recorded

The box plot does not show the heights of mugs, just vases.

The height is measured in inches, not centimeters.

Answer:

x∈[20/3;+∝).

Step-by-step explanation:

3x+10≥30; ⇔ 3x≥20; ⇔ x≥20/3

Answer:

Area of shaded rectangle = 42 cm²

55%

Step-by-step explanation:

The length of the shaded area is equal to the length of the white rectangle.

Therefore, length of shaded rectangle = 7 cm

The width of the shaded rectangle is equal to the length of the white rectangle minus two widths of the white rectangle.

Therefore, width = 7 - (2 x 0.5) = 6 cm

Area of shaded rectangle = width x length

                                          = 6 x 7

                                          = 42 cm²

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Perimeter of a square = 4 × side length

If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm

Area of a square = side length x side length

⇒ area of this square = 10 x 10 = 100 cm²

To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.

Area of a triangle = 1/2 x base x height

⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²

⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²

Therefore, shaded area = 100 - 15 - 30 = 55 cm²

To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:

(55 ÷ 100) × 100% = 55%

Answer:

A

Step-by-step explanation:

(1.7x10²³) and (3.4x10²³) cancel into 0.5.

0.5(8x10^-14) = 4x10^-14

Answer:

13.6x/3.4 x 10^14 This is a fraction by the way hope this helps

Step-by-step explanation:

13.6

x

3.4

⋅

10

14

Answer:

1/72

Step-by-step explanation:

multiple the numerators and denominators by each other so 1*1 = 1 and 8*9 = 72

Answer:

81

Step-by-step explanation:

27 total of pupils.

girls 1×27=27

boys 2×27=54

total 54+27=81

Answer:

IV

In the fourth quadrant (IV).

Step-by-step explanation:

In the IV quadrant the x coordinate is always positive and the y coordinate is always negative. So the x coordinate is always larger than the y coordinate.

Answer:

no solution

Step-by-step explanation:

Solve:

6(2k + 1) = 12k + 1

Expand brackets:

⇒  12k + 6 = 12k + 1

Subtract 12k from both sides:

⇒  6 = 1

As 6 ≠ 1 there is no solution

Answer:

No solution

Step-by-step explanation:

Simplify the L.H.S and the R.H.S

⇒ [tex]6(2k + 1) = 12k + 1[/tex]

⇒ [tex]12k + 6 = 12k + 1[/tex]

Cancel out the "12k"

⇒ [tex]12k + 6 = 12k + 1[/tex]

⇒ [tex]6 = 1 (\text{False})[/tex]

Henceforth, this equation has no solution.

The true statement about the equation of the line of best fit (d) For every year a person gets older, their screen time decreases by 3.2 minutes

The equation of the line of best fit is given as:

y = -3.2x + 274.4

Where:

A linear equation is represented as:

y = mx + b

Where:

By comparison, we have:

m = -3.2 and b = 274.4

This means that:

For every year a person gets older, the average screen time decreases by 3.2 minutes

Hence, the true statement is (d)

Read more about line of best fit at:

https://brainly.com/question/17261411

Answer:

She has about 2 choices

Step-by-step explanation:

7 ÷ 3 ≈ 2.3

≈ 2

To find which fractions are equal to each other, we must simplify or multiply to both denominator and numerator:

          [tex]\frac{2}{6} =\frac{1*2}{3*2} =\frac{1}{3}*\frac{2}{2}=\frac{1}{3}*1= \frac{1}{3} \\\\\frac{8}{1}=8\\ \\\frac{2}{4} =\frac{1*2}{2*2} =\frac{1}{2}*\frac{2}{2} =\frac{1}{2} *1= \frac{1}{2} =\frac{1}{2}*1 =\frac{1}{2}*\frac{4}{4} =\frac{1*4}{2*4}=\frac{4}{8} \\\\\frac{2}{8} =\frac{1*2}{4*2}=\frac{1}{4}*\frac{2}{2} =\frac{1}{4} *1 =\frac{1}{4} \\\\\frac{4}{4} =1[/tex]

Hope that helps!

Answer:

2/6 = 1/3

8/1 = 8

2/4 = 4/8

2/8 = 1/4

4/4 = 1

Step-by-step explanation:

2/2 = 1 and 6/2 = 3 so that would make the equivalent fraction 1/3

for 8/1 it is the same as just 8

2*2 = 4 and 4*2 = 8 so that would make the equivalent fraction 4/8

and 2/8 is 1/4

and 4/4 is just 1  

PLEASE RATE!! I hope this helps!!

If you have any questions let me know

Answer:

70p

Step-by-step explanation:

Amy-

£2.00 - £0.15 = £1.85

so Amy payed £1.85

Tina-

£5.00 - £2.45 = £2.55

so Tina payed £2.55

£2.55 - £1.85 = £0.70

which means tina payed 70p more

the expression represents a quadratic polynomial with 2 terms.The constant term is 1, the leading tern is x and the leading coefficient is 1

Answer: Side length E D corresponds to Side length B A because they are in the same position.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

After the sequencing of transformations, reflection over the y-axis.

dilation with a scale factor of 0.5

translation 2 units left and 2 units up

Step-by-step explanation:

The circumference of a circle that was computed when the diameter is 3cm will be 9.426cm.

The circumference of a circle of gotten by the formula:

C = 2πr or πd

where,

r = radius

d = diameter

Since the diameter is given as 3cm, the circumference will be:

= πd

= 3.142 × 3

= 9.426cm

In conclusion, the circumference of the circle is 9.426cm.

Learn more about circle on:

https://brainly.com/question/25938130

Answer:

Step-by-step explanation:

Answer: She.Was.Playing.By.Ear

Answer:

the answer is c

Step-by-step explanation:

45% of 1500=675

38% of 1500=570

675+570=1245

1500-1245=255

Answer:

(5,1)

is one of infinitely many possible order pairs.

Step-by-step explanation:

There are an infinite amount of x values that give you an answer to this question. You get to choose. But first let's start off with isolating y.

[tex]-x + 6y = 1\\6y = 1 + x\\y = \frac{1+x}{6}[/tex]

Now the equation is easier to interpret. [tex]y = \frac{1+x}{6}[/tex]

Now here's the part where you actually get to choose. Take any x, value, I'll choose 5.

I'll sub it into the equation and get my y value, [tex]y = \frac{1 + (5)}{6}= 1[/tex]

Okay, we get that y = 1, when x = 5. That's an ordered pair:

(5,1)

Remember you could follow this same procedure for any x value you choose.

Break it down gently

f(x) = 1 - sin⁴3x + cos6x/6

let's break ( - sin⁴3x) and (Cos6x/6) and 1 separately

the derivative of ( -sin⁴3x) = 12cos3xsin³3x

the derivative of (cos6x/6) = -sin6x

the derivative of (1) = 0

f'(x) = 0

12cos3xsin³3x - sin6x = 0

Answer:

what is 2dimes and one nickle and one quarter makes

Answer: $1500

Step-by-step explanation:

Did the quiz on this hope you have a great day.

Answer:

The required angles are 15, 75 and 90

Step-by-step explanation:

1x + 5x+ 6x = 180
or 12x = 180
180 ÷ 12 = 15
hence,
15, 75, 90.

Using the z-distribution, as we are working with a proportion, it is found that the buyers need a sample of 1505.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.

There is no estimate of the percentage, hence [tex]\pi = 0.5[/tex], and the margin of error is of M = 0.03, hence we solve for n to find the desired sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 2.327(0.5)[/tex]

[tex]\sqrt{n} = \frac{2.327(0.5)}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.327(0.5)}{0.03}\right)^2[/tex]

[tex]n = 1504.2[/tex]

Rounding up, the buyers need a sample of 1505.

More can be learned about the z-distribution at https://brainly.com/question/25890103

Answer:

The maximum profit is $854

Step-by-step explanation:

Profit is the difference between the revenue and the cost price of an item. It is given by:

Profit = selling price - cost price

Since x represent the profit made by the company, is related to the selling price of each widget, x and it is given by the formula:

y = -3x² + 155x - 1148

At maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 155

0 = -6x + 155

6x = 155

x = 25.83

The maximum profit is at gotten when the selling price of each widget is 25.83. Hence:

y = -3(25.83)² - 155(25.83) - 1148

y = $854

Therefore the maximum profit is $854

Answer:

Step-by-step explanation:

605/11 = x/5

11x = 3025

x = 275 miles

Answer:

275 miles

Step-by-step explanation:

Bill drove 605 miles in 11 hours , so by the formula , Speed = Distance/ time

We can find that ,

Speed = 55 miles/hours

So , In 5 hours he will drive

Distance = Speed × Time

Distance = 55 × 11

Distance = 275 miles