A rectangular swimming pool is twice as long as it is wide. A small concrete sidewalk surrounds the pool and is a constant 2 feet wide. The total area of the pool and sidewalk is 160 square feet. Find the dimensions of the pool

Answer:

The equation of the line that goes through points (1,1) and (3,7) is [tex]\mathbf{y=3x-2}[/tex]

Step-by-step explanation:

Determine the equation of the line that goes through points (1,1) and (3,7)

We can write the equation of line in slope-intercept form [tex]y=mx+b[/tex] where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have [tex]x_1=1, y_1=1, x_2=3, y_2=7[/tex]

Putting values and finding slope

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3[/tex]

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

[tex]y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2[/tex]

We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

[tex]y=mx+b\\y=3x-2[/tex]

The equation of the line that goes through points (1,1) and (3,7) is [tex]\mathbf{y=3x-2}[/tex]

Answer:

0

Step-by-step explanation:

tan0 •sin 0+ cot0 •sin0 =

tan(0) • sin(0) + cot(0) • sin(0) =

(tan(0) × sin(0)) + (cot(0) × sin(0)) =

(0 × 0) + (0 × 0) = 0 + 0 = 0

Answer:

The answer is 3/4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

9 × 4 =36 - 8 = 28.

hope this helps. :)

Answer:

a. 1:5

b 1:4

Step-by-step explanation:

The ratios are as follows

a. For money withdrawn to total money deposited

₹410 : ₹ 2050

₹41:₹205

1:5

b. For money withdrawn to the remaining amount

₹410: (₹2050 - ₹410)

₹410:₹1640

₹41:₹164

1:4

Answer:

45900

Step-by-step explanation:

that is rounding the hundreds place

Answer:

45,800

Rounded to the nearest 100 or

the Hundreds Place.

Step-by-step explanation:

Hope this helps. Sorry if its wrong

Answer:

19

Step-by-step explanation:

Answer:

5/-6

Step-by-step explanation

use rise/run to get 4-(-1)/-5-1 to get 5/-6

The possible values of the expression 2 - a are -5, -6, and -7.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To find all possible values of the expression 2 - a, we need to use the information that is given in the inequality 6 < a < 10.

We know that a is a value between 6 and 10, but not equal to 6 or 10. So, we can substitute each of the values between 6 and 10 (excluding 6 and 10) into the expression 2 - a and find the result.

We can start with the smallest possible value for a, which is 6 + 1 = 7.

So, 2 - 7 = -5

Next, we can use the value of a = 8,

so, 2 - 8 = -6

And, we can use the value of a = 9,

so, 2 - 9 = -7

Therefore, the possible values of the expression 2 - a are -5, -6, and -7.

Learn more about inequalities here:

brainly.com/question/20383699

#SPJ2

[tex]\boxed{\boxed{\pink{\bf \leadsto Hence \ the\ correct \ option \ is \ B \ \bigg\{ x | x \in R , x \leq 7\dfrac{5}{6}\bigg\} }}}[/tex]

A inequality is given to us and we need to find the solution set . The inequality given to us is :-

[tex]\bf \implies x - 6\dfrac{1}{3} \leq 1\dfrac{1}{2} \\\\\bf\implies x \leq 6\dfrac{1}{3} + 1\dfrac{1}{2} \\\\\bf\implies x \leq \dfrac{19}{3} + \dfrac{3}{2}\\\\\bf\implies x \leq \dfrac{38+9}{6} \\\\\bf\implies x \leq \dfrac{47}{6} \\\\\bf\implies\boxed{\red{\bf x \leq 7\dfrac{5}{6}}} [/tex]

This means that x belongs to Real Numbers. Hence final answer would be :-

[tex]\boxed{\red{\bf \bigg\{ x | x \in R , x \leq 7\dfrac{5}{6}\bigg\}}}[/tex]

Answer:

B. Principal

Step-by-step explanation:

A principal is defined in economics as a sum of money lent or invested, on which interest is paid.

Hope this helps!

Answer:

A.24

Step-by-step explanation:

3cm × 4cm = 12 × 2 = 24 that's why my answer is A pls tell me if you get it right or I make a mistake.

Answer:

i think the answer is A but it might be D

Answer:

33

Step-by-step explanation:

33= 11 * 3

99= 11 * 3 * 3

Answer:

33.

Step-by-step explanation:

33 = 3*11

99 = 3*3*11

The common factors are 3 and 11 so the GCF = 3*11 = 33.

Answer:

184

Step-by-step explanation:

Answer:

oo i got hac ked on this acount but thir gone off now OωO

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

density= mass/volume

25/50=0.5

Step-by-step explanation:

3a + 6 + 5a - 2

8a + 4

4(2a+1)

or

Easy

3a + 6 + 5a - 2

8a +4

Answer:

Please check explanations

Step-by-step explanation:

Using the difference of two squares, the lowest common multiple becomes;

1-sin^2 a

Thus, we have that;

cos a (1-sin a) + cos a (1 + sin a) /1 - sin^2 a

1 - sin^2 a = cos^2 a

That means;

{cos a - cos a sin a + cos a + cos a sin a}/ cos^2 a

= 2cos a / cos^2 a

= 2/cos a

but 1/cos a = sec a

Thus;

2/ cos a = 2 sec a

Answer:

Gwendolyn is faster than Francine by 2.9 seconds.

Step-by-step explanation:

15 3/4= 15.75

18.65- 15.75= 2.9

Answer:

94+41=135.

180-135=45.

45+111=156

180-156=24

x=24.

Answer:

x=24

Step-by-step explanation:

Answer:

36

8 times 9 equals 72 and then you just divide that by two and it would be 36

Answer:

[tex]\sin \left(90^{\circ \:}-x\right)=\cos \left(x\right)[/tex]

Hence, option D is correct.

Step-by-step explanation:

Given the expression

[tex]sin\:\left(90^{\circ }\:-\:x\right)[/tex]

Using the angle difference identity

[tex]\sin \left(s-t\right)=\sin \left(s\right)\cos \left(t\right)-\cos \left(s\right)\sin \left(t\right)[/tex]

so the expression becomes

[tex]sin\:\left(90^{\circ }\:-\:x\right)=\sin \:\left(90^{\circ \:\:}\right)\cos \:\left(x\right)-\cos \:\left(90^{\circ \:\:}\right)\sin \:\left(x\right)[/tex]

as sin 90° = 1

so sin 90° cos x = cos x

also

cos 90° = 0

so con (90°) sin x = 0

Thus, the expression becomes

[tex]\sin \:\left(90^{\circ \:\:}\right)\cos \:\left(x\right)-\cos \:\left(90^{\circ \:\:}\right)\sin \:\left(x\right)=\cos \:\left(x\right)-0[/tex]

                                                           [tex]= cos (x)[/tex]      ∵ [tex]\cos \left(x\right)-0=\cos \left(x\right)[/tex]

Therefore,

[tex]\sin \left(90^{\circ \:}-x\right)=\cos \left(x\right)[/tex]

Hence, option D is correct.

Answer:

y = -x - 1

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

On the graph, the point on the y-axis is the y-intercept. That point is (0, -1). So the y-intercept is -1.

To find the slope, find two points and put it in the slope equation.

Point A: (0, -1)

Point B: (-1, 0)

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]

Point A: [tex](x_{1}, y_{1})[/tex]

Point B: [tex](x_{2}, y_{2})[/tex]

m = [tex]\frac{0 - (-1)}{-1 - 0}[/tex]

m = [tex]\frac{1}{-1}[/tex]

m = -1

y = -1x - 1

In other words, y = -x - 1

Hope this helped! <3

Answer:  y = -1x - 1

This means -1 goes in the first box, and -1 goes in the second box.

y = -1x - 1 is the same as y = -x - 1

========================================================

Explanation:

The two points (0,-1) and (1,-2) are on the red diagonal line.

Let's use the slope formula to compute the slope

m = (y2-y1)/(x2-x1)

m = (-2-(-1))/(1-0)

m = (-2+1)/(1-0)

m = -1/1

m = -1

The slope is -1.

The y intercept is -1 because the red line crosses the y axis at -1.

Since the y intercept is -1, this means b = -1.

With m = -1 and b = -1, we go from y = mx+b to y = -1x + (-1). This is the same as y = -1x - 1

Furthermore, that equation simplifies to y = -x - 1.

Side note: the slope and y intercept aren't always the same value.

Answer:

87.5%

Step-by-step explanation:

The answer would be 87.5 because there are a total of 26 students and 14 of them like chocolate. So, you would set up the fraction of 14/26 and x/100. You would then multiply 14 times 100 and divide that by 26. The answer would be 87.5. And that would be 87.5%.

Hope this helped!! :)

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