REASONING An absolute value function is positive over its entire domain. How many x-intercepts does the graph of the function have?

● None

01

02

O Infinite

A line's** x-intercep**t and** y-intercep**t are the points at which the** x- and y-axes**, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation **y = x + 5** crosses the x-axis at the location (-5, 0).

We set** y = 0 and solve the equation for x to determine the x-intercept**. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

The x-intercept is zero, right? If you can locate the x-intercept of a linear function, finding the zero should be simple**. The x-coordinate of the x-intercept is zero.**

**Summary**

Consider the numbers as being on the x-axis to help you remember this. The positive values are located to** the right of the origin**, and the negative values are located to the left of the origin.

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Write the equation of the line that passes through the points (4, -1)

and (3,-2).

Ox+y = -5

O y = x-5

O y = -x +3

Oy - 3x + 13

**Answer:**

[tex]y=x-5[/tex]

**Step-by-step explanation:**

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Given points:

(x₁, y₁) = (4, -1)(x₂, y₂) = (3, -2)Substitute the given points into the **slope formula** to find the slope of the line:

[tex]\implies m=\dfrac{-2-(-1)}{3-4}=\dfrac{-1}{-1}=1[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Point-slope Formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and the point (4, -1) into the **point-slope formula** to create the **equation of the line**:

[tex]\implies y-(-1)=1(x-4)[/tex]

[tex]\implies y+1=x-4[/tex]

[tex]\implies y+1-1=x-4-1[/tex]

[tex]\implies y=x-5[/tex]

Write the equation of a line in the form y=Mx+b that passes through the point (3,6) and has a slope of -2/3. Sketch this line

[tex]\begin{gathered} m=\frac{-2}{3} \\ P(3,6) \\ y=mx+b \\ U\sin g\text{ the given data} \\ y=\frac{-2}{3}x+b \\ 6=\frac{-2}{3}(3)+b \\ 6=-2+b \\ b=6+2 \\ b=8 \\ Hence \\ \text{The equation of the line is }y=\frac{-2}{3}x+8 \end{gathered}[/tex]

The first term of an Ap is 5 and the common difference is-3/2 Find the term whose value is 201/2

The term in the **AP **whose value is 201 / 2 is 71.3.

The first term of an** arithmetic progression** is 5 and the common difference is - 3/2.

The formula of the** arithmetic progression** can be described as follows:

nth term = a + (n - 1)d

where

a = first termn = number of termsd = common differenceTherefore, using the **arithmetic progression **formula,

a = 5

d = 3 / 2

nth term = 201 / 2

let's find the term(n)

Therefore,

- 201 / 2 = 5 + (n - 1) - 3 / 2

- 201 / 2 = 5 - 3 / 2 n + 3 / 2

- 201 / 2 - 3 / 2 - 5 = - 3 / 2 n

- 107 = -3 / 2 n

-3n = - 214

n = 214 / 3

n = 71.3

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Samantha borrowed money to buy lawn equipment to start her new lawn service business. She borrowed $800 for 9 months and paid $70.50 in interest. What was the rate of interest.

Using **simple interest**, the **rate of interest** on the amount that Samantha borrowed to buy the law equipment is 11.75%.

A **simple interest system** does not accumulate (**compound**) interest on both the principal and interest, unlike **compound interest**.

The **simple interest** uses the following formula, Interest = Principal x Rate x Period.

This **simple interest formula** can be reversed to find either the principal, rate, or period, as the case may be.

The loan amount = $800

Period of loan = 9 months

Total interest paid = $70.50

**Rate of interest** = (Interest × 100)/(Principal × Time)

= 11.75% ($70.50 x 100)/($800 x 9/12)

Check:

Interest = $70.50 ($800 x 11.75% x 9/12)

Thus, Samantha's** interest rate** on the loan is 11.75%.

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Write an equation that says that the length of the green line is equal to the length of theblack line. Combine like terms

Explanation:

Length of green line = length of black line

Length of green line = 26

Total length of black line = h + h + *

Total length of black line = 2h + 8

Equate the two expressions

**26 = 2h + 8**

Collect the like terms

26 - 8 = 2h

18 = 2h

Isolate h by dividing both sides by 2

18/2 = 2h/2

h = 18/2

h = 9

The equation is 26 = 2h + 8

Find Sin A, Cos A, Sin B, and Cos B for the following. Enter answers as fractions in simplest form, not decimals.

**Answer:**

**Explanation:**

Let x represent unknown side length

We can go ahead and find x using the Pythagorean Theorem as seen below;

[tex]\begin{gathered} (5\sqrt[]{3})^2=5^2+x^2 \\ (25\times3)=25+x^2 \\ 75-25=x^2 \\ 50=x^2 \\ x=\sqrt[]{50}=\sqrt[]{25\times2}=\sqrt[]{25}\times\sqrt[]{2}=5\sqrt[]{2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]Let's find sin A as seen below;

[tex]\begin{gathered} \sin A=\frac{opposite}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \sin A=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \sin A=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Let's find cos A as seen below;

[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \cos A=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find sin B as seen below;

[tex]\begin{gathered} \sin B=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \sin B=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find cos B as seen below;

[tex]\begin{gathered} \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \cos B=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]We have to find two partial products to add 513×46

Answer

Explanations:

The **product of two integers** using the **partial product** is expressed using the **distributive law** as shown:

**Expanding the result **using the distributive law as shown;

what is 576.984 round in to the nearest tenths

**Answer: 577**

**Step-by-step explanation:**

**Answer:**

577.0

Rounded to the nearest 0.1 or

the Tenths Place.

**Step-by-step explanation:**

576.984

You rounded to the nearest tenths place. The 9 in the tenths place rounds up to 10 because the digit to the right in the hundredths place is 8.

Because the tenths place was rounded up from 9 to 10, the tenths place becomes 0 and the ones place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0 and we add 1 to the previous place value.

577.0

When the digit to the right is 5 or greater we round away from 0.

576.984 was rounded up and away from zero to 577.0

What is the slope of a line perpendicylar to the line whose equation is 5x - 6y = 30 Fully simplify your answer.

**Answer:**

-6/5

**Step-by-step explanation:**

[tex]5x-6y=30 \\ \\ 6y-5x=-30 \\ \\ 6y=5x-30 \\ \\ y=\frac{5}{6}x-5[/tex]

Perpendicular lines have negative reciprocal slopes, so the answer is -6/5.

How many solutions does the equation 6z − 3z − 7 = −2 + 3 have? (5 points)TwoNoneInfinitely manyOne

**Answer**:

One solution.

**Explanation**:

Let us try to solve the equation and see how many solutions it has.

The first step in solving the equation is to first simplify both the right-hand and the left-hand sides. This means adding all the like terms.

[tex]\begin{gathered} 6z−3z−7=−2+3 \\ \Rightarrow3z-7=1 \end{gathered}[/tex]Next, we add 7 to both sides. This gives

[tex]3x-7+7=1+7[/tex][tex]3x=8[/tex]dividing both sides by 3 gives

[tex]\boxed{z=8/3.}[/tex]which is exactly one solution!

**Therefore, our equation had one solution. **

The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general form?answers:•x+y1=0•y-1=0•x-y+1 = 0

We will have the following:

First, we find the slope:

[tex]m=\frac{1-1}{2-(-2)}\Rightarrow m=0[/tex]So, the equation that represents the line is:

[tex]y=1[/tex]So:

[tex]y-1=0[/tex]***Explanation***

We are given the points (-2, 1) & (2. 1).

From this we cans see that the line passes both times through y = 1.

We also know that the slope (m) is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So the slope for this line will be:

[tex]m=\frac{1-1}{2-(-2)}\Rightarrow m=0[/tex]Now, we also know that the equation of the line in general form is given by:

[tex]y-y_1=m(x-x_1)[/tex]So, the equation of the line will be given by:

[tex]y-1=(0)(x+2)\Rightarrow y-1=0[/tex]So the function is a constant value, thus a horizontal line.

***Explanation for the general form of a line***

The general form of a line is given by:

[tex]y-y_1=m(x-x_1)[/tex]Here "x" & "y" are two variables; "x1" & "y1" are the component of a point that belongs to that lline and "m" is the slope of that line. We remember that (x1, y1) can be any point that belongs to the line.

So, we simply replace the values, in our case I willl solve for (-2, 1), but we could also use (2, 1), the solution at the end will be the same.

So:

[tex]y-(1)=(0)(x-(-2))\Rightarrow y-1=0\cdot x+0\cdot2[/tex][tex]\Rightarrow y-1=0[/tex]Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.figure 1: 9 cubesfigure 2: 13 cubesfigure 3: (blank)figure 4: (blank)figure 5: (blank)

Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.

figure 1: 9 cubes

figure 2: 13 cubes

figure 3: (blank)

figure 4: (blank)

figure 5: (blank)

Let

f(0)=5

so

For n=0

f(1)=5+4=9

f(1)=9

For n=1

f(2)=9+4=13

f(2)=13

For n=2

f(3)=13+4=17

For n=3

f(4)=17+4=21

For n=4

f(5)=21+4=25

For n=5

f(6)=25+4=29

therefore

theanswer is

figure 3: 17figure 4: 21figure 5: 25In a jar there are 65 red, 154 yellow and 70 green beads. You extract 54 beads at random.

Estimate the number of red beads obtained.

The number of **red beads **obtained from the **jar **is 12 **beads. **

The number of **red beads **that can be obtained from the **jar **is the ratio of red **beads **to the total number of **beads **multiplied by the total number of **beads **picked at random.

Number of **red beads **obtained = (number of red beads / total number of beads) x number of beads picked

Total number of **beads **= 65 + 154 + 70 = 289

Number of **red beads **obtained = (65 / 289) x 54 = 12.14 ≈ 12 beads

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A 25 ft ladder is leaning against a building.The base of the ladder is 6 ft away from the building.How high up is the ladder?

Applying the **Pythagorean Theorem**, the ladder's height from the ground is: 24.3 ft.

If we know any two sides of a **right triangle**, the **Pythagorean Theorem** can be used to find the length of the third side, c, if c is the longest side, and a and b are the shorter sides of the **right triangle**, we ill have the equation:

c² = a² + b².

The ladder forms a **right triangle** with the wall of the building. Therefore:

Substitute

25² = 6² + b²

b = √(25² - 6²)

b = 24.3 ft.

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Consider the graph of the function f. a) Find the domain, range, and zeros of the function. b) write an equation for the function f. (In vertex form, standard form, or intercept form)c) compare the graph of f to the graph of g(x) = x^2.

**Solution:**

Given the graph;

**(a) **The domain of a function is the set of values for which the function is real and defined. Thus, the **domain D **is;

The **range **is;

The **zeros of the function are the points y=0;**

**(b) **The equation of a parabola in vertex form is;

Thus, **the equation is;**

**(c) **Using the graph below;

The graph of **g(x) **has its intercept at **(0,0).**

**The transformation goes as;**

**Vertical stretch 2units, reflection over the x-axis, horizontal shift to the the right 3 units, vertical shift up 8 units**

Using **(5,0);**

Determine wether y varies directly with x. If so find the constant of variation k and write the equation

The given data is incorrect, k does not constitute a** constant,** but rather y does not **varies directly **to x.

We may have 11=7k for the** initial point**, implying that k=11/7.

Again for second point, we'd have 13=8k, which means k=13/8.

Using** proportions,** we can see that 11/7 doesn't really equal 13/8: cross multiply and you get 11*8=7*13, or 88=91.

Thus, this is incorrect, k does not constitute a** constant,** but rather y does not **varies directly **to x.

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The complete question is-

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

x y

7 11

8 13

9 15

10 17

could you please help me out with a question

of the circumference is 21.2, we get that the diameter is

[tex]d=\frac{21.2}{\pi}\approx6.75[/tex]and therefore the radius is

[tex]r=3.37[/tex]What is the LCM of 9 and 15?

What is the LCM of 9 and 15?

we know that

9=(3^2)

15=(3)(5)

so

the LCM=(3^2)(5)=45

the answer is

LCM=453^2=3*3=9QUIK ANSWER PLEASE!!! Solve the equationy^3 - 27 = 9y^2 - 27y

The first step is to simplify both sides of the equation. The equation can be written as

y^3 - 3^3 = 9y(y - 3)

For the left hand side, we would apply the difference of two cubes formula. it is expressed as

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

By comparing with the left hand side of the equation,

x = y and y = 3. It becomes

(y - 3)(y^2 + 3y + 3^2)

= (y - 3)(y^2 + 3y + 9)

The equation becomes

(y - 3)(y^2 + 3y + 9) = 9y(y - 3)

If we divide both sides of the equation by (y - 3), it becomes

(y - 3)(y^2 + 3y + 9)/(y - 3 = 9y(y - 3)/(y - 3)

y^2 + 3y + 9 = 9y

y^2 + 3y - 9y + 9 = 0

y^2 - 6y + 9 = 0

We would solve the quadratic equation by applying the method of factorisation. We would find two terms such that their sum or difference is - 6y and their product is 9y^2. The terms are - 3y and - 3y. The equation becomes

y^2 - 3y - 3y + 9

y(y - 3) - 3( y - 3) = 0

(y - 3)(y - 3) = 0

y - 3 = 0 twice

**y = 3 twice**

Carly has twice as many sisters as Connor.

Connor has twice as many sisters as Alicia.

Alicia has 3 sisters.

How many sisters does Carly have?

Answer:

12

Step-by-step explanation:

Alicia has 3 sisters.

Connor has twice as many sisters.

Twice means "two times".

Connor has 2×3, that is 6 sisters.

Carly has twice (two times) as many sisters as Connor.

Carly has 2×6, or 12 sisters.

I'll give brainliest!

The **scientific notation** is [tex]5.72 * 10^{6}[/tex]

Factor out 1 of the powers of 10

[tex]= (5.5 * 10^{6}/10^{6} + 2.2 * 10^{5}/10^{6}) * 10^{6}[/tex]

Perform division of exponents:

[tex](5.5 * 10^{0} + 2.2 * 10^{-1}) * 10^{6}[/tex]

Convert **Scientific notations** to real numbers:

[tex]= (5.5 + 0.22) * 10^{6}[/tex]

Combine real numbers:

[tex]= (5.72) * (10^{6})[/tex]

Convert to proper **Scientific notations**:

[tex]= 5.72 * 10^{6}[/tex]

Manually check answer

= (5.5 x 1000000) + (2.2 x 100000)

= 5500000 + 220000

= 5720000

[tex]= 5.72 * 10^{6}[/tex]

What are **Scientific notations**?

**Scientific notation** is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place following the decimal. This makes it challenging to express a small number of integers in their enlarged form. We thus employ **scientific notations**. Learn general forms for numbers as well.

Rules for **Scientific Notation**

We must adhere to the following rule in order to calculate the power or exponent of 10:

The base must always be 10.

Exponents that are non-zero integers must be either positive or negative in order to be used.

The coefficient's absolute value is more than or equal to 1, but it must be less than 10.

Positive and negative numbers, including whole and decimal values, can be coefficients.

The remaining significant digits of the number are represented by the mantissa.

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Identify the graph of the ellipse given by the equation below.

Answer options are also attached :)

The required **graph **below which represents the given **equation **of the **ellipse **is (x +7)²/49 + (y-5)²/25 = 1. Which is the correct **answer **would be **option **(**C**).

An **ellipse **can be defined as a shape that looks like an **oval **circle.

The **equation **of the **ellipse **is (x +7)²/49 + (y-5)²/25 = 1 which is given in the question.

An **asymptote **is a line that a curve approaches, but never touches. Find the **horizontal**, **vertical**, and oblique asymptotes.

Center of the **ellipse **: (−7,5)

Vertex 1: (0,5)

Vertex 2: (−14,5)

We have attached the required **graph **below which represents the given

**equation **of the **ellipse **is (x +7)²/49 + (y-5)²/25 = 1.

Hence, the correct **answer **would be an **option **(**C**).

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Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.

I need the Equation.

The **equation **that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".

So, the **equation **for P will be:

Now, the equation can be:

P = 20x + 80(Refer the table attached below)

Therefore, the **equation **that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".

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find the remainder for the given division. (z^2+3z+1)/(z-2)

**Explanation**

Given the expression

[tex]\frac{z^{2}+3z+1}{z-2}[/tex]We are asked to find the remainder. We can use the remainder theorem. This can be seen below.

According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

**All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.**

**Therefore, we will have;**

[tex]\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}[/tex]

three fifths of thr tshirts in a tshirt shop are on sale. five eighths of those tshirts are on sale. one third of those blue tshirts that are on sale are size medium. what fraction of the shops tshirts are blue tshirts that are on sale and are size medium? explain

3/5 of the T-shirts of the shop are on sale

5/8 of those on sale are blue

1/3 of the blue shirts on sale are medium size.

First calculate how many of the shirts on sale are blue:

[tex]\frac{5}{8}\frac{\div3}{5}=\frac{5}{8}\cdot\frac{5}{3}=\frac{25}{24}[/tex]25/24 of the shirts on sale are blue

Then divide that number by three to know how many are medium size:

[tex]\frac{25}{24}\div3=\frac{25}{72}[/tex]25/72 are blue and medium size

Find the slope of the linear regression line for the given data below. Round your

answer to two decimal places.

x y

2 25

3 19

48

5 11

6 15

7 14

Round your final result to two decimal places.

**Answer:**

hey bro listen

**Step-by-step explanation:**

you can't always

get the answers

here try to

do yourself and

see your potential.

1. It costs $9.81 for 9 pounds of grapefruit. How much would it cost for 1 pound of grapefruit?

It’s dividing 9.81 by 9,

9.81 / 9 = 1.09

$1.09

9.81 / 9 = 1.09

$1.09

**Answer:**

**the anser is 1.09**

**Step-by-step explanation:**

9.81 divided by 9 = 1.09

is this triangle possible?

**Answer: The triangle is not possible.**

**Step-by-step explanation:**

**1) Find the missing angle **

62+59+x=180

x=59

**2) Use the Law of Sine to check if the triangle sides are the same.**

The Law of sine means that Sine the angle and divide with the side across it will equal to same.

[tex]\frac{sin(x)}{x} =\frac{sin(y)}{y}[/tex]

Substitute the numbers.

[tex]\frac{sin(59)}{10} =\frac{sin(62)}{10}[/tex]

0.0636 = -0.0739

**3) Solve**

**Since the decimals aren't the same, the triangle is not possible.**

Fill in the blank to make equivalent rational expressions.

2/y^2=_/3y^5

The **expression **that can complete the blank is 6y^3

**Expressions **are mathematical statements that are represented by variables, coefficients and operators

The **expression **is given as

2/y^2=_/3y^5

Replace the blank with x

So, we have

2/y^2 = x/3y^5

Multiply both sides of the **equation **by 3y^5

So, we have

x = 3y^5 * 2/y^2

Evaluate the products

x = 6y^3

This means that the blank is 6y^3

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Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets ofcardboard from which she cuts out 2-in squares from eachPLEASE CHECK PHOTO

**Solution:**

**Given:**

When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;

[tex]\begin{gathered} l=(x+4)-2-2=x+4-4=x \\ w=x-2-2=x-4 \\ h=2 \\ \\ The\text{ volume }V=792in^3 \end{gathered}[/tex]The volume of a cuboid is given by;

[tex]\begin{gathered} V=lwh \\ 792=(x)(x-4)(2) \\ Dividing\text{ both sides by 2;} \\ \frac{792}{2}=x(x-4) \\ 396=x^2-4x \\ \\ Collecting\text{ all sides to one side to form a quadratic equation;} \\ 0=x^2-4x-396 \\ x^2-4x-396=0 \end{gathered}[/tex]Solve the quadratic equation by factorization;

[tex]\begin{gathered} x^2-4x-396=0 \\ x^2+18x-22x-396=0 \\ x(x+18)-22(x+18)=0 \\ (x-22)(x+18)=0 \\ x=22,x=-18 \\ \\ Since\text{ the dimension of a box can not be negative, then;} \\ x=22in \end{gathered}[/tex]Hence, the dimension of the original piece of cardboard is;

[tex]\begin{gathered} (x+4)\text{ by }x \\ \\ Substitute\text{ the value of x, the dimension of the cardboard is;} \\ (22+4)\text{ by }22 \\ 26in\text{ by }22in \end{gathered}[/tex]**Therefore, the dimensions of the original piece of cardboard are 26 in by 22in**

Choose the best Spanish equivalent to the phrase. The car is far away from the park.
which number is the closest approximation to the value of 3/94?
what are the 4 types of graphs and when do we use each type?
Question 28Identify the underlined parts of speech in the following sentence:I hope it doesn't rain again on Saturday because I am so tired of the rain.Group of answer choicesA. first noun, then verbB. first pronoun, then nounC. first verb, then nounD. first adjective, then nounE. first adverb, then nounF. first verb, then prepositionG. first conjunction, then verb acting as a nounQuestion 29If Ive told you once Ive told you a million times: watch out for run-ons theyll get you.Group of answer choicesA. If Ive told you once, Ive told you a million times: watch out for run-ons theyll get you.B. If Ive told you once, Ive told you a million times: watch out for run-ons, theyll get you.C. If Ive told you once, Ive told you a million times: watch out for run-ons. theyll get you.D. If Ive told you once, Ive told you a million times: watch out for run-ons; theyll get you.Question 30Of the four sentence purposes, the sentence purpose used most often in expository writing is _____________________.Question 31The prompt is: "You have decided to go to college; what reasons would you present in a paragraph or essay to help someone deliberating over whether or not to go?"What would be the best choice for a thesis statement?Group of answer choicesA. As many of us know, there are many reasons for going to college.B. I decided to go to college for many reasons; you can decide to go for many reasons too.C. Although there are many incentives for going to college, three stand out as the primary reasons for getting a college education.D. There are several reasons why you should get a college education.E. Several good reasons why you should get a college education: better jobs, greater knowledge, and strong social support.Question 32Pick the correct answer which corrects the underlined portion of the following sentences in the simplest way possible for grammar and/or style, without changing the basic meaning of each sentence. (Hint: think: formal standard English and third person)As you can see, obesity is nothing to mess around with as it causes you health problems that are detrimental to our bodys health.Group of answer choicesA. As you can see, obesity is nothing to mess around with as it causes us health problems that are detrimental to our bodys health.B. As you can see, obesity is nothing to mess around with as it can cause health problems that are detrimental to our bodies health.C. Obesity is nothing to be concerned with because it can cause health problems that are detrimental to a person's bodys health.D. Obesity is nothing to trifle with because it can cause health problems that are detrimental to a person's health.Question 33OK, so this sentence really needs some work. Take your time and determine which correction is the clearest, makes the most sense, and is grammatically correct (... and yes, this was an actual sentence submitted by a student).People commit crimes of all races and dresses differently or the same as people who don't commit crimes and are doctors and lawyers, so criminal profiling is not a good thing.Group of answer choicesA. People of all races and dresses commit crimes differently or the same as people who don't commit crimes and are doctors and lawyers, so crimminal profiling is not right.B. It is difficult to tell who fits a crimminal profile because people of all races and manners of dress commit crimes differently or the same as people, such as doctors and lawyers who don't commit crimes.C. It is difficult to tell who fits a crimminal profile because people of all races and manners of dress commit the same crimes as people such as doctors and lawyers.D. It is difficult to tell who fits a crimminal profile because both law-breakers and law-abiding people come in all races, professions, and manners of dress.
the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours it is observed that 400 bacteria are present. after 10 hours 2000 bacteria are present. what was the initial number of bacteria?
BCD is a straight line. Triangle ABC is equilateral. CE=DEWork out the size of angle x.
Question 10The table below shows the amount of water that is in a bathtub that is being filled.Minutes1234Gallons ofWater12172227Which of the following functions could model the amount of gallons of water, f(x), that the bathtub will contain after x minutes of being filled?f(x) = 5x + 7Bf(x) = 5x + 12f(x) = 7x + 5Df%) = 12x + 5No
When sodium hydroxide reacts with sulfuric acid a solution of sodium sulfate is produced.a.) Describe how crystals of sodium sulfate can be obtained from a solution of sodium sulfate.
If a substance conducts electricity when dissolved in water, turns litmus from blue to red, and tastes sour, would you expect it to be acidic, basic, or neutral? Justify your answer.
Which statement below best describes the purpose of settling colonies as shown in the diagram?
How many times larger is 8.1 than 2.7
What scientific principle do bulletproof vests worn by law enforcement officers best illustrate when they protect personnel from impact injury in the line of duty?
The figures below are congruent. Name the corresponding sides.
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Great Britain's empire in the late 1800s included colonies in Africa and a sphere ofinfluence in China. Which of the following statements is true?
Your exercise program only needs to include cardio activities. A. True B. False
Is Monotheism in the Jewish religion different fromthe Monotheism in the Christian and Muslimreligions?
Please help me please
Write a paragraph please How do Noah's choices regarding how Born A Crime begins to contribute to the reader's understanding of Noah's perspective and the system of Apartheid?
Rajan climbed to a height of 15 ft from the bottom of a climbing wall. He then climbed up an additional 10 ft.What must he do to return to the bottom of the climbing wall?In the first blank, say whether Rajan must climb up or down. In the second blank, state the number of feet Rajan must travel up or down.Rajan must climb_____ft to return to the bottom of the climbing wall.