can someone please solve this

Width of the rectangle is 4 units

Step-by-step explanation:

Area of the rectangle = length × width

⇒ 20 = x (x + 1)

⇒ 20 = x² + x

⇒ x² + x - 20 = 0

⇒ x² + 5x - 4x - 20 = 0 (Using Product Sum rule to factorize)

⇒ x(x + 5) - 4(x + 5) = 0

⇒ (x + 5)(x - 4) = 0

⇒ x = -5, 4 (negative value is neglected)

x = 4

Final answer:

The solution reveals that the width of the rectangle is 4 units.

Explanation:

The student is asking to find the width of the rectangle when the length is given as the sum of the width and 1 unit, and the area of the rectangle is 20 square units.

To solve this, we can set up an equation using the area formula for a rectangle, A = length * width, where the area (A) is 20 square units.

Let's denote the width as w units.

Then the length can be expressed as w + 1 units. Substituting these expressions into the area formula gives us:

20 = w * (w + 1)

Expanding the right side, we get:

20 = w² + w

This is a quadratic equation, which we can solve by setting it equal to zero:

w² + w - 20 = 0

Factoring the quadratic equation, we find:

(w + 5)(w - 4) = 0

Therefore, w could be -5 or +4. Since a width cannot be negative, the only reasonable solution is w = 4 units.

Thus, the width of the rectangle is 4 units.

Solution:

Given that we have to factor -3y - 18

Use the distributive property,

a(b + c) = ab + bc

From given,

-3y - 18

Factor out the greatest common factor of 3 and 18

The factors of 3 are: 1, 3

The factors of 18 are: 1, 2, 3, 6, 9, 18

Then the greatest common factor is 3

Factot out 3 from given expression

-3y - 18 = 3( - y - 6)

Or else we can rewrite as,

-3y - 18 = -3(y + 6)

Thus the given expression is factored

Ans is -48.

Hope this will help u..

90 in terms of pi is [tex]\frac{\pi}{2}[/tex] .

Step-by-step explanation:

We know that ,

We have to convert 90 in terms of pi i.e. degree to radians:

⇒ [tex](90)\frac{\pi }{180}[/tex]

⇒ [tex]\frac{90 }{180}(\pi)[/tex]

⇒ [tex]\frac{1 }{2}(\pi)[/tex]

⇒ [tex]\frac{\pi}{2}[/tex]

Therefore, 90 in terms of pi is [tex]\frac{\pi}{2}[/tex] .

Answer:

Quotient given:

\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} }

Answer:

2 \sqrt[3]{3} - \sqrt[3]{18}

Explanation:

1) Rationalize by multiplying numerator and denominator by         \sqrt[3]{9}

2)

\frac{6-3 \sqrt[3]{6} }{ \sqrt[3]{9} } \frac{\sqrt[3]{9}}{\sqrt[3]{9}}

3) Due the operations

\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ \sqrt[3]{27} }

\frac{6 \sqrt[3]{3}-3 \sqrt[3]{6.3}}{ 3 }=2 \sqrt[3]{3} - \sqrt[3]{18}

Step-by-step explanation:

Answer:

32 inches

Step-by-step explanation:

5 + 5 + 11 + 11 = 32 inches

Answer:

Step-by-step explanation:

Linear functions are whose graph is a straight line. They contain a slope and a constant also known as the y intercept.

Example: y = 3x + 2

The slope is 3 and the y intercept is 2.

The two given angles are vertical angles and equal each other:

3x + 50 = 6x -10

Now solve for x:

Subtract 3x from both sides:

50 = 3x -10

Add 10 to both sides:

60 = 3x

Divide both sides by 3

X = 20

Answer:the slope is 3/9

Step-by-step explanation:use the y intercept form

Answer:

3

Step-by-step explanation:

Slope = change in y/change in x

That’s y2 - y1 /x2 - x1

Given

x1 = 2

y1 = 5

x2 = -1

y2 = -4

Slope = -4 - 5 /-1 - 2

= -9/-3

= 3

Answer:

the only thing i can think of is a 5K so kilometers

Step-by-step explanation:

more context in the question? all distance measures 5 units

Answer:

can you give options please

Step-by-step explanation:

The radius of the circle is approximately 7.5 cm, and the corresponding area is approximately 56.25π cm², as calculated using the formulas for circumference and area. Here option C is correct.

1: Find the radius using the circumference formula

We know the circumference C = 157 cm.

We also know the formula for circumference of a circle: C = 2πr, where r is the radius.

Rearranging the formula to solve for r, we get: r = C / (2π).

Substituting C with 157, we get: r = 157 / (2π) ≈ 7.5 cm.

2: Calculate the area using the area formula

Now that we know the radius, we can use the formula for the area of a circle: A = πr², where A is the area.

Substituting r with 7.5, we get: A = π * (7.5)² ≈ 56.25π cm².

Therefore, the area of the circle is 56.25π cm². Here option C is correct.

Complete question:

The circumference of a circle is 157 centimeters. What is the area of the circle in terms of t?

A - 7.570 cm?

B - 157 cm

C - 56.251 cm

D - 2257 cm

Answer:

2

Step-by-step explanation:

1/4 times 8 = 2

Answer: She jogged 2 miles

Step-by-step explanation: 1\4 x 8 which will give you 8\4, then you simplify it and you get 2.

Answer:

we can write

3 as a percent of 5 as

as is = to sign

percent is 100

and of is multiplication sign that gives us

3=x/100×5

x=(3×100)/5

x=300/5

x=60

so 3 is 60% of 5

Answer:

The answers would be 60%

Step-by-step explanation:

Step-by-step explanation:

√17= 4.12

Therefore, we need to find an irrational no. between 4.1 and 4.12

So, the correct option is a

4.1001000100001000001....

Answer:

25.4 feet tall

Step-by-step explanation:

254 divided by 10 equals 25.4

The height of the apple tree that you expect an apple tree to be ​25.4 feet.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A coast redwood tree is about 10 times as tall as an apple tree.

Let 'x' and 'y' be the height of redwood and apple trees. Then the equation is given as,

y = x / 10

One of the tallest coast redwoods even measured 254 feet tall. Then we have

y = 254 / 10

y = 25.4 feet

The height of the apple tree that you expect an apple tree to be ​25.4 feet.

More about the solution of the equation link is given below.

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The total number of books based on the given percentage will be 20 including 15 paperback books.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

Suppose Mr. Sanchez bought a total of x number of books.

75% of x = (75/100)x

This is the paperback thus,

(75/100)x = 15

x = 1500/75 = 20

Thus, the number of total books = 20 including 15 paperback books.

Hence "The total number of books based on the given percentage will be 20 including 15 paperback books".

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Mean: 175/5 = 35.

Median: 0, 25, 25, 25, 100 - 25 is in the middle.

Mode: 25, it appears the most.

The outlier 100 affects the data, because the number 100 still farthest from the main cluster. (Sorry if this is wrong)

2 x 7 x 7 or in exponential form, 2 x 7². 98 turns into 2 times 49, then 49 turns into 7 times 7.

The prime factorization of 98 is equal to 2 x 7².

The prime factorization of 98 involves breaking it down into prime numbers that multiply together to give the original number, 98.

The process for finding the prime factors of 98 is as follows:

Start with the smallest prime number, 2.

Since 98 is an even number, it is divisible by 2. So, divide 98 by 2 to get 49.

Now, 49 is not divisible by 2, so we try the next prime number, which is 3.

Since 49 is not divisible by 3 either, we move to the next prime number, 5, and so on until we reach 7, which does divide 49.

Divide 49 by 7 to get 7. So, 49 is 7 multiplied by 7, both of which are prime numbers.

Putting it all together, the prime factorization of 98 is 2 × 7 × 7 or 2 × 7².

Time taken by the car to cover 260 km is 2.6 hrs

Step-by-step explanation:

Speed = Distance/Time = 150/1.5 = 100 km/hr

Time = Distance/Speed = 260/100 = 2.6 hrs

Answer:

[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]

Step-by-step explanation:

We want to find the inverse of

[tex] y = \sqrt[3]{ \frac{x}{3} + 1} [/tex]

We interchange x and y to get:

[tex]x= \sqrt[3]{ \frac{y}{3} + 1} [/tex]

We solve for y;

[tex] {x}^{2} = \frac{y}{3} + 1[/tex]

Multiply through by 3

[tex]3 {x}^{2} = y + 3[/tex]

Subtract 1 from both sides:

[tex]y = 3 {x}^{2} - 3[/tex]

Therefore the inverse is

[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]

Answer:

4(4)= 16

4(5)= 20

4(6)=24

4(7)= 28

4(8)= 32

4(9)= 36

4(10)= 40

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

I think you misses attaching the photo, so please have a look at my photo for your better understanding.

We know the formula for rate of change of the  parabola line:

[tex]\frac{f(b)- f(a)}{b-a}[/tex]

Given here:

a= 2 => f(a) = 2

b=6 => f(b) = 2

Substitute all the values into the function, we have:

[tex]\frac{14-2}{6-2} = 3[/tex]

So the rate of change is 3

Answer:

D.) 3

Step-by-step explanation:

Got it right on the assignment

Answer:

{ - 9, - 7, - 3, - 1 }

Step-by-step explanation:

To obtain the range substitute the values of x from the domain into f(x)

f(- 2) = - 2(- 2) - 5 = 4 - 5 = - 1

f(- 1) = - 2(- 1) - 5 = 2 - 5 = - 3

f(1) = - 2(1) - 5 = - 2 - 5 = - 7

f(2) = - 2(2) - 5 = - 4 - 5 = - 9

range is { - 9, - 7, - 3, - 1 }

Answer:

a. - 1 3/4

b. 6

Step-by-step explanation:

For each, plug in the given number to the corresponding variable:

a. When x = -2. Plug in -2 for  x in the given expression:

2^(-2) - 2

Simplify. Note that when a negative sign is located in the power sign, you would do the normal power, and then put the number over 1.

2^(-2) = 1/(2 x 2) = 1/4

Simplify:

1/4 - 2 = - 1 3/4

- 1 3/4, or -7/4 is your answer.

b. When x = 3. Plug in 3 for x in the given expression:

2^(3) - 2

Simplify. First solve the power, then subtract:

2^3 = 2 * 2 * 2 = 4 * 2 = 8

8 - 2 = 6

6 is your answer.

~

Answer:

a. - 1 3/4

b. 6

The height of an object off the ground h after t seconds is [tex]h(t)=-16t^2+128t[/tex] and the rate of change of h is 192.

Given data:

The average rate of change of a function over an interval [a,b] is given by the formula:

[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]

Now, the function [tex]h(t)=-16t^2+128t[/tex] represents the height of an object off the ground at time t seconds. We are asked to find the average rate of change of h over the interval [4,8].

So, the value of a = 4 and b = 8.

[tex]h(8)=-16(8)^2+128(8)[/tex]

[tex]h(4)=-16(4)^2+128(4)[/tex]

On simplifying the equation:

[tex]R=\frac{h(8)-h(4)}{8-4}[/tex]

[tex]R=\frac{768}{4}[/tex]

[tex]R=192[/tex]

Hence, the average rate of change of h over the interval is 192 feet per second.

To learn more about rate of change of function, refer:

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The average rate of change of h over the interval [4,8] is -64 feet per second. This is found by substituting the values of a = 4 and b = 8 into the equation h(t) = -16t² + 128t and into the formula for average rate of change.

To find the average rate of change of h over the interval [4, 8], we use the formula for the average rate of change: (h(b) - h(a)) / (b - a). Here, a = 4 and b = 8.

First, calculate h(a) and h(b) using the given equation h(t) = -16t² + 128t:

Substitute h(a) and h(b) into the formula to get:
(0 - 256) / (8 - 4) =-256/4 = -64.

So, the average rate of change of h over the interval [4, 8] is -64 feet per second.

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There are quite a few possible combinations that are minimum 8 sodas, and under $20.

1. 4 Dr. Peppers and 4 Sprites. $2.98 times 4 = $11.92. $1.99 times 4 = $7.96. $7.96 + $11.92 = $19.88.

2. 3 Dr. Peppers and 5 Sprites. $2.98 times 3 = $8.94. $1.99 times 5 = $9.95. $9.95 + $8.94 = $18.89.

3. 2 Dr. Peppers and 6 Sprites. $2.98 times 2 = $5.96. $1.99 times 6 = $11.94. $11.94 + $5.96 = $17.90.

4. 2 Dr. Peppers and 7 Sprites. $2.98 times 2 = $5.96. $1.99 times 7 = $13.93. $5.96 + $13.93 = $19.89.

5. 1 Dr. Pepper and 7 Sprites. $2.98 times 1 = $2.98. $1.99 times 7 = $13.93. $2.98 + $13.93 = $16.91.

6. 1 Dr. Pepper and 8 Sprites. $2.98 times 1 = $2.98. $1.99 times 8 = $15.92. $15.92 + $2.98 = $18.90.

I hope this helps!