Samantha purchased a package of sugar cookies. The nutrition label states that each serving size of cookies contains 160 calories. Samantha creates the graph below showing the number of cookies eaten and the number of calories consumed.

Part A: Write an equation that represents the data graphed by Samantha.

Part B: What is the slope of the line? What does it mean in the context of the problem?

Part C: Provide a verbal description of the graph.​

If we use the method of completing the square to solve the quadratic equation x² + 5x - 1 = 0, we have to add (-25/4) to convert it to (x + 5/2)²  - 29/4 = 0

The standard form of a quadratic equation is:

ax² + bc + c = 0

In this case, the quadratic function is:

x² + 5x - 1 = 0

To solve it using the "complete the square" method, write the equation as:

(x + 5/2)² - 1 + .... = 0

The blank part in the above equation means we need to add a number to make the equality still holds.

Note that:

(x + 5/2)² = x² + 5x + 25/4

Hence,

(x + 5/2)²  - 1  =  x² + 5x + 25/4 - 1

Hence, we need to add (-25/4) to make the original equality holds:

(x + 5/2)² - 1 + (-25/4) = 0

(x + 5/2)²  - 29/4 = 0

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The solution of the given inequality is x < 0  or x > 6. [ And the Graph is given below]

It is quite similar to graphing linear equations to draw inequalities. Two further steps must be taken while concentrating on the inequality sign.

When you graph linear inequalities, you must perform two more steps i.e Choosing between a solid borderline and a dashed boundary line will be the first stage.

We can identify the boundary line with the inequality symbol.

We use a dotted boundary line if the inequality symbol is greater than or less than. This indicates that the answers are not part of the borderline.

We will use a solid line to denote that the solutions are included on the boundary line if the inequality symbol is greater than or equal to or less than or equal to.

Here we have

3 |x - 3| > 9    

Divide by 3 into both sides

=> [ 3|x - 3| ]/3 > 9/3

=> |x - 3| > 3  

As we know

=> |x - 3| > 3    

=>  (x - 3) < -3  or  (x - 3) > 3  

=>   x < 0         or    x > 6

Therefore,

The solution of the given inequality is x < 0  or x > 6. [ And the Graph is given below]

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if A triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length then the other angle is 43 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that a triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length

We have to find the measure of the third angle.

By angle sum property the sum of three angles is equal to 180 degrees.

43+94+x=180

137+x=180

Subtract 137 from both the sides

x=43 degrees.

Hence, if A triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length then the other angle is 43 degrees.

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(3, 4, 5), (5, 12, 13), (6, 8, 10), (9, 12, 15), and (15, 20, 25) are the five most common Pythagorean triples.

Any three positive integers that completely satisfy the Pythagorean theorem are considered Pythagorean triples. According to the theorem, the hypotenuse's square is equal to the sum of the squares of the other two legs of any right triangle. The Pythagorean triples are made up of the right triangle's three sides. In this article, we will learn how to make a few Pythagorean triples.

A set of three positive numbers known as Pythagorean triples conforms to the Pythagoras theorem's formula, which reads as follows: a2 + b2 = c2, where a, b, and c are positive integers. "c" denotes the "hypotenuse," or longest side, and "a" and "b" denote the remaining two legs of the right-angled triangle. (a,b,c) is how the Pythagorean triples are shown. Three, four, and five are the most well-known Pythagorean triples. We are able to demonstrate that the equations 3, 4, and 5 are correct. Find out how! 32 + 42 = 52 ⇒ 9 + 16 = 25. The Pythagorean triples 3, 4, and 5 are depicted in the right-angled triangle below.

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The  waiting time represents the 5th percentile is 160.852 days and the waiting time represents the third quartile is 220.22 days

The parameters that will help us to understand the solution are

Let X be the random variable representing the waiting time.

Here the mean = 203 days

Standard deviation (∑∝) = 25.7 days

For calculating the 5th percentile, we need to find the z- score having area 0.05.

By Z-score table we have Z= -1.64

Now, Using formula X=Z\standard deviation +mean

X = (-1.64)*(25.7)+203

 = 160.852 days

Waiting time representing 5th percentile = 160.852 days.

For calculating third quartile, we know that third quartile represents the area to the left of 75% = 0.75

we need to calculate the Z score when the area is 0.75. Using the table we get Z= 0.67

X = (0.67)*(25.7)+203

  = 220.22 (days)

Waiting time representing third quartile = 220.22 days

Conclusively, 160.852 days and 220.22 days represent the 5th and 3rd percentile and quartiles of the waiting time

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Correct question:

Assume the time spent (in days) waiting for a heart transplant for people ages 35-49 can be approximated by a normal distribution with mean of 203 days and a standard deviation of 25.7 days. what waiting time represents the 5th percentile? what waiting time represents the third quartile?

Theoretically, Usain Bolt can complete a kilometer in 96.9 seconds, and he also moves at an average speed of 1.032 * 10 m/s.

speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.

Given that, At the 2008 Summer Olympics, Usain Bolt won the 100 m sprint with a time of 9.69 sec.

Thus,

The average speed of the athlete = 100/9.69

The average speed of the athlete = 10.319 m/sec.

Also theoretically he can run 1 km in 96.9 seconds.

therefore, theoretically Usain bolt can run 1 km in 96.9 seconds, and also his average speed is  1.032 * 10 meters per second.

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"She" is the right pronoun to finish the phrase. The pronoun "she" is used to refer to the victorious candidate since she is considered to be female. The pronoun "they" is commonly used when referring to someone whose gender is unclear or undetermined.

A pronoun is a term that is used in a phrase in place of a noun. In order to avoid using the same nouns again and to refer to someone or something without using their name, pronouns are utilised. Pronouns can be classified into a variety of categories, such as personal pronouns (like I, me, you, him, her, it, we, us, and they), possessive pronouns (like my, mine, your, yours, his, her, hers, it, our, ours, and their, theirs), reflexive pronouns (like I, myself, you, him, her, it, ourselves, ourselves, and ourselves), and interrogative pronoun (such as who, whom, whose, which, what).

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Answer:

  False

Step-by-step explanation:

You want to know if it is true or false that "the number 0.3333... repeats forever; therefore it is irrational."

Any repeating decimal is a form of rational number. A number will only be irrational if it has an infinite number of decimal digits and never repeats.

The number 0.3333... is rational.

The offered statement is false.

__

Additional comment

There are enough typos in your statement that we cannot be certain what the statement is. We can be certain that 0.3333... is rational.

Check to make sure the question being answered here is the one you want the answer for.

The triangle ΔSTW is similar to the triangle ΔUVW. Then the value of the variable 'x' is 12.5 meters.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔSTW and ΔUVW, we have

∠T = ∠V      (Given)

∠W = ∠W    (Common angle)

Then the triangles ΔSTW and ΔUVW will be similar to each other. Then the ratio of the corresponding sides will be constant. Then the equation is given as,

ST / UV = VW / TW

ST / UV = VW / (TV + VW)

5 / x = 6 / (9 + 6)

x = 5 (9 + 6) / 6

x = 5(15) / 6

x = 75 / 6

x = 12.5

The triangle ΔSTW is similar to the triangle ΔUVW. Then the value of the variable 'x' is 12.5 meters.

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The area of rectangle is  19.58 m.

The equation for calculating a rectangle's area. Rectangle's surface area. A = l × b. Once the length and breadth of a rectangle are known, its area may be computed. The area of the rectangle can be calculated as a square unit by multiplying the length and width.

The surface of a shape's area is measured. You must multiply the length and breadth of a rectangle or square in order to determine its area. A has an area of x times y.

length of the rectangle = 2 2/4 m

width of rectangle = 7 5/6 m

Area of rectangle = Length × Breadth

⇒ 10/4 × 47/6

⇒ 5/2 × 47/6

⇒ 19.58 m

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C)The greatest number is 8.2 × 10-3. It is 2,000 times greater than the smallest number.

In scientific notation, a number is written as the product of a number between 1 and 10 and a power of 10. The power of 10 tells us how many places to move the decimal point to the right (if the exponent is positive) or to the left (if the exponent is negative).

In this case, 8.2 × 10-3 means 8.2 × (10^-3) = 0.0082, 5.2 × 10-6 means 5.2 × (10^-6) = 0.0000052 and 4.1 × 10-6 means 4.1 × (10^-6) = 0.0000041.

To compare the numbers, we can compare the coefficient or the number in front of the 10 power. We can see that 8.2 is greater than 5.2 and 4.1. To check how many times greater the smallest number is, we can use the following formula: (greatest number / smallest number) = (8.2 / 0.0000041) = 2,000

Therefore, the greatest number is 8.2 × 10-3 and it is 2,000 times greater than the smallest number.

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]

For a specific distance between two places, a grid scale factor is determined and referred to as a "line scale factor."

The ratio of the two equivalent side lengths of comparable figures is known as the scale factor, sometimes known as the linear scale factor. The shapes of similar figurines are the same, yet they come in various sizes. Geometrical problems are solved using the scale factor. To determine a figure's missing side lengths, apply the scale factor.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.

A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.

A figure's size may enlarge or contract by dilation.

The diagram shows:

scaling factor of BA = AC/CA' = 4/(4 + 16)=1/5

Line segment BA's elongation is scaled by a factor of 1/5.

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a) The ratio of the number of white tiles to the number of blue tiles = 3:1

b) The ratio of the total cost of the white tiles to the total cost of the blue tiles = 3:2.

a)Since they are 48 white tiles and 16 blue tiles, the ratio of the number of white tiles to the number of blue tiles is the number of white tiles divided by the number of blue tiles. Therefore-

The ratio of white tiles to the blue tiles = number of white tiles/number of blue tiles = [tex]\frac{48}{16}[/tex] = 3

b)Total cost of the white tiles = number of white tiles × cost of each white tile = 48 tiles × £2 per tile = £96

Total cost of the blue tiles = number of blue tiles × cost of each blue tile = 16 tiles × £4 per tile = £64

The ratio of the total cost of the white tiles to the total cost of the blue tiles = total cost of the white tiles/total cost of the blue tiles = [tex]\frac{96}{64} = \frac{3}{2}[/tex]

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The complete question is:

Ewen has 48 white tiles and 16 blue tiles.

(a) Write down the ratio of the number of white tiles to the number of blue tiles.

Give your ratio in its simplest form.

The cost of each white tile was £2

The cost of each blue tile was £4

(b) Work out the ratio of the total cost of the white tiles to the total cost

of the blue tiles

The sum of the interior angles for a Polygon of 5 angles is 540°

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

The sum of the interior angles of a Polygon is calculating by the formulation:

Sum of Interior Angles = (n-2) x 180°

Replacing the number of angles (n = 5) in the equation we get:

Sum of Interior Angles = (n-2) x 180°

Sum of Interior Angles = (5-2) x 180°

Sum of Interior Angles = 3 x 180°

Sum of Interior Angles = 540°

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The given equation  "x⁴- 52x² + 576 = 0" does not have any imaginary solution , the real solutions are  x = 4 or x = -4 or x = 6 or x = -6    .

The real solution in algebra is simply a solution of the equation which is a real number.

the equation is : x⁴ -52x² + 576 = 0 ;

we rewrite the equation as : ⇒  (x²)² - 52x² + 576 = 0;

let x² = u ;

the equation becomes ⇒u² - 52u + 576 = 0 ;

the equation in factor form is written as : ⇒ (u - 16)(u - 36) = 0  ;

this implies that ; ⇒ x² = 16   or   x² = 36  ;

that means that the real solutions are  ⇒ x = ±4  or x = ±6  .

The given question is incomplete , the complete question is

What are the real or imaginary solutions of the polynomial equation x⁴ -52x² + 576 = 0 ?

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The values of the constants for the given quadratic equation are a=2, b=3, and c=7.

The values of the constants for the given quadratic equation are a=2, b=3, and c=7.

The quadratic equation is defined as a polynomial with a degree of two or with a maximum power of a variable in a polynomial of 2, which will cut two intercepts on the graph at the x-axis.

Here is an equation to consider:

2x²+3x+7 = 0

Using the general equation as a comparison to the previous equation:

ax²+bx+c = 0

Thus, the constants' values will be as follows:

a=2, b=3 c=7

Therefore, for the following quadratic equation, the values of the constants are a=2, b=3, and c=7.

The values of the constants for the given quadratic equation are a=2, b=3, and c=7.

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Answer:

3

Step-by-step explanation:

The ratio of x to y is constant

And as you can see

X×6 = y

6×6= 36

8×6=48

10×6= 60

Therefore

X×6 =18

18÷6= 3

X=3

The average speed of Keddy based on time of travel and distance covered is 160 km/hr.

The time taken to reach the destination = 13:51 - 12:36

Performing subtraction

Time taken to reach the destination = 1:15 or 1 hour and 15 minutes

As we know, 1 hour has 60 minutes.

So, total time in hour = 1 + 15/60

Total time in hour = 1.25 hours

The speed, distance and time are related as -

Average speed = total distance travelled ÷ total time taken

Keep the values in formula -

Average speed = 200/1.25

Performing division

Average speed = 160 km/hr

Thus, the average speed of Keddy is 160 km/hr.

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The area of square A is 25 in² and each side measures 5 inches

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

For square B:

Area = side²

144 = side²

side = 12 in

For square C:

Area = side²

169 = side²

side = 13 in

To find the length of each square A side, we use Pythagoras theorem. Hence:

(Side C)² = (Side A)² + (side B)²

13² = (side A)² + 12²

169 = (side A)² + 144

(side A)² = 25

Side A = 5 in

Area of square A = (side A)² = 5² = 25 in²

The area of square A is 25 in²

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The standard deviation is 6.

What a standard deviation means?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Standard deviation in statistics is a measure of dispersion of a set of data relative to the mean of the data set.

The square root of the variance of the data set gives the standard deviation of the data set.

In this case, the variance,

s²=36 ( as given, variance of the set of values is 36 )

The standard deviation,

s=√36 =6

Therefore, the standard deviation is 6.

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In the trigonometric functions angles are,

1) 53.13°

2) 48.19°

3) 36.87°

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given ,

1) sin x = [tex]\frac{4}{5}[/tex]

=> x= [tex]sin^{-1}\frac{4}{5}[/tex]

=> x = 53.13°

2) cos x = [tex]\frac{2}{3}[/tex]

=> x = [tex]cos^{-1}\frac{2}{3}[/tex]

=> x = 48.19°

3) tan x = [tex]\frac{3}{4}[/tex]

=> x = [tex]tan^{-1}\frac{3}{4}[/tex]

=> x = 36.87°

Hence the angles are,

1) 53.13°

2) 48.19°

3) 36.87°

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The ratio between of the two legs of a 30-60-90 triangle:

√3 : 2.

The correct option is D.

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Given:

A triangle is a 30-60-90 triangle.

So, the sides of a 30-60-90 triangle are always in the ratio of 1:√3: 2.

The side opposite is 60° is √3.

And The side opposite to 90° is 2.

So, the ratio,

= s/h

= √3 : 2.

Therefore, the ratio is √3 : 2.

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Addition symbols are called plus signs. They are used to indicate a mathematical operation or expression that adds two numbers or values together. They are represented by a cross or a plus sign (+) and are usually placed between the two values being added.

The plus sign is often used in algebra and other mathematical equations to indicate that two numbers should be added together. It is also used in programming languages to indicate the addition of two values. Additionally, the plus sign is used to indicate the inclusion of something, such as a plus sign in front of a movie title to indicate that it is an extended edition.

The plus sign is an important part of mathematics and programming and is used in many different contexts. It is a versatile symbol that is used to indicate the addition of two values. Knowing how to use the plus sign correctly is an important part of understanding basic mathematics and programming.

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The 29th term in the given arithmetic sequence is −170.

An arithmetic sequence can be defined in one of two ways. In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term," or "each term is obtained where the differences between every two successive terms are the same." The arithmetic sequence that comes next is created by adding 4 to the term that comes before it.

Given that 89th term in an arithmetic sequence is -590

And 8th term is -23

-590 = a₁ + (89 - 1)d

-590 = a₁ + 88d

a₁ = -590 - 88d

and

-23 = a₁ + (8 - 1)d

-23 = a₁ + 7d

a₁ = -23 - 7d

Factor out a₁ in both equations

-590 - 88d =  -23 - 7d

-88d + 7d = 590 - 23

-81d = 567

d = -567.81

d = −7

As we have the d lets find fist term

a₁ = -23 - 7(-7)

a₁ = -23 + 49

a₁ = 26

Now, find  29th term

a₂₉ = 26 + (29 - 1)(−7)

a₂₉ = −170

Thus, the 29th term in the given arithmetic sequence is −170.

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Answer:

x=99°

Step-by-step explanation:

total angle :

(n-2)×180°

=360°

x= 360°- 101° - 92°- 68°

x= 99°

Answer:

The value of X is 99 ( being the sum of all angle of quadrilateral is 360)

Answer:

The ratio of boys to girls in von's class is 2:3, which means for every 2 boys there are 3 girls.

The following can represent the number of boys and girls in her class:

If there are 12 students in the class, there would be 8 boys and 4 girls (2:3 ratio)

If there are 15 students in the class, there would be 10 boys and 5 girls (2:3 ratio)

If there are 18 students in the class, there would be 12 boys and 6 girls (2:3 ratio)

And so on.

It is important to note that as long as the ratio of boys to girls is 2:3, the numbers will represent the number of boys and girls in the class.

Step-by-step explanation:

It means that the area of the gingerbread house Hillary will cover with icing is 0 cm^2.

To find the area of the gingerbread house that Hillary plans to cover with icing, we need to subtract the area of the window and the door from the total area of the front of the house.

The window measures 2 cm x 2.5 cm, so the area of the window is 2 cm x 2.5 cm = 5 cm^2

The door measures 2 cm x 3 cm, so the area of the door is 2 cm x 3 cm = 6 cm^2

The total area of the front of the house is the sum of the areas of the window and door, so we can find it by adding 5 cm^2 + 6 cm^2 = 11 cm^2

To find the area of the gingerbread house Hillary will cover with icing, we need to subtract the area of the window and the door from the total area of the front of the house:

Area of gingerbread house covered with icing = Total area of front of house - Area of window - Area of door

Area of gingerbread house covered with icing = 11 cm^2 - 5 cm^2 - 6 cm^2 = 0 cm^2

It means that the area of the gingerbread house Hillary will cover with icing is 0 cm^2. This means that the area of the window and door are equal to the total area of the front of the house and there's no space left to put icing on.

Thus, It means that the area of the gingerbread house Hillary will cover with icing is 0 cm^2.

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The window is 2 cm by 2.5 cm, so its surface is 2 cm by 2.5 cm, or 5 cm2.

The door is 2 cm by 3 cm in size, so its surface is 2 cm by 3 cm, or 6 cm2.

We can calculate the area of the front of the house by adding the areas of the window and entrance (5 cm2 + 6 cm2 = 11 cm2)

The area of the window and door must be subtracted from the overall front-of-the-house area in order to determine how much of the gingerbread house Hillary will ice:

Total frontage of the home divided by the size of the gingerbread house covered in frosting

The theoretical probability of getting a blue color is 1/4.

The experimental probability of landing a blue color is 35%.

Option A is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of times the blue color is recorded = 7

The total number of times each color is recorded = 20

Now,

Number of sections = 4

Number of blue sections = 1

So,

The theoretical probability of getting a blue color.

= 1/4

Now,

Experimental probability of landing a blue color.

= 7/20

= 7/20 x 100

= 35%

Thus,

Theoretical probability of getting a blue color is 1/4.

Experimental probability of landing a blue color is 35%.

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The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

Answer:

B and E

Step-by-step explanation:

A translation is a slide.  If your only moves was a slide, y would slide right over B and E.  The others would you have to flip or rotate or expand.

Answer:

B and E.

Step-by-step explanation:

A translation is a slide.  If your only moves was a slide, y would slide right over B and E.  The others would you have to flip or rotate or expand.