Select all equations that are equivalent to x² + 6x = 16

Answer: $9.57

Step-by-step explanation: 47.85/5 = 9.57. Therefore each book costs $9.57.

Answer:

379 liters

Step-by-step explanation:

3.79  L / gal   * 100 gal = 379 Liters

Kendra's fish tank can hold 379 liters of water under the given conditions.

Given that,
There are about 3.79 liters in 1 gallon. Kendra’s fish tank contains 100 gallons of salt water.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
3.79 liters = 1 gallon,
Now,
in the fish tank
100 gallon of water = 3.79× 100 liters
                                 = 379 liters

Thus, Kendra's fish tank can hold 379 liters of water under the given conditions.

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Answer: look at explanation

Step-by-step explanation:

1. It helps you learn and listen to minor details in music better.

2. He had a handicap (partially deaf/deaf) but still managed to overcome and lay his mark in the music world.

3. Pay attention, eye contact, listen, pay attention to nonverbal cues, and show that you are listening

4. A foundation on which notes are drawn on. The lines represent a sound in music. A musical form is the structure of musical compositions. It makes music more interesting because it makes it organized and not jumbled up.

Step 1

The given equation is

Required: To find the real zeroes by factorization and the turning points.

Step 2

Find the number of real zeroes

Step 3

Find the number of turning points.

Therefore, there are 7 real zeroes and 6 turning points; 0, 2 and 4

The answer is option A

If the ratio the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5 and the new version of the Flash added 14 miles per gallon and now the ratio is 24:27, then the miles per gallon of the Thunderbolt is  15.27 miles per gallon

The ratio the Thunderbolt and the Flash, in terms of their miles per gallon = 6:5

Then the miles per gallon of the Thunderbolt and the Flash is 6x and 5x respectively

The new version of the Flash added 14 miles per gallon

New ratio of the cars = 24:27

Therefore the equation is

5x+14 = 27x

27x-5x = 14

22x = 14

x = 7/11

The miles per gallon of the Thunderbolt = 24x

= 24×7/11

= 15.27 miles per gallon

Hence, If the ratio the Thunderbolt and the Flash, in terms of their miles per gallon was 6:5 and the new version of the Flash added 14 miles per gallon and now the ratio is 24:27, then the miles per gallon of the Thunderbolt is 15.27 miles per gallon

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Answer:

-12

Step-by-step explanation:

plug in and solve

1. 12(-1/4) - 3(3)

2. -12/4 - 9

3. -3 - 9

4. -12

we have that

the best description of the data is

Given:

First, we arrange the equation:

Further simplification of the given equation will give us a result with an imaginary number, making the equation a nonreal circle, or not a conic section.

ANSWER:

STEP-BY-STEP EXPLANATION:

The equation of the line in its slope and intercept form is as follows:

The slope can be calculated as follows:

Replacing the points (-1 , 1) and (5 , -3) :

Now, we calculate the value of b, with the help of the slope and the point (-1,1)

Therefore, the equation would be:

Step-by-step explanation:

substitution means to use one equation to express one variable only in terms of the other variable and constants.

let's use

6f + 11b = 317

for that purpose.

6f = 317 - 11b

f = (317 - 11b)/6

now we use that my substituting "f" by its identical expression in b in the second equation :

7(317 - 11b)/6 + 5b = 221

to avoid handling fractions we multiply everything by 6 :

7(317 - 11b) + 30b = 1326

2219 - 77b + 30b = 1326

893 - 47b = 0

893 = 47b

b = 893/47 = 19 cents

f = (317 - 11b)/6 = (317 - 11×19)/6 = (317 - 209)/6 =

= 108/6 = 18 cents

a piece of fudge is 18 cents.

a piece of bubble gum is 19 cents.

Given:

The function is

Required:

Find the inverse of the function.

Explanation:

The given function is:

Put

Interchange x and y.

Take the square on both sides.

Substitute

Final Answer:

Option A is the correct answer.

Answer:16

Step-by-step explanation:

I think is confused

6A.- h(0) = 100 - 16(0)^2

= 100 - 0

h(0) = 100

h(0) = 100 ft

The result is the value starting height 100 ft

6B.- h(2) = 100 - 16(2)^2

h(2) = 100 - 64

h(2) = 36 ft

No, the equation does ot predict that the ball is going to hit the ground after 2 seconds because the height was 32 ft, that is the height necessary to hit the ground.

John recieved the greater discount and the original price of the bike is $120

John purchased the bike at a 20% discount off the original

price.

Let the price of the bike be x

The price at which John purchased the bike is x - 20% of x

= x - (20/100)x

=(80/100)x

Raul brought the bike at original price.

Raul's cost price is x

x is greater than (80/100)x

Raul purchased at a greater price than John, so the greater discount is recieved by John.

John got discount = (20/100) x

He saved = $24

(20/100)x = 24

20x =2400

x = 2400/20

x = 120

The original price is $120

Therefore, John recieved the greater discount and the original price of the bike is $120

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The slope of the line that passes through the points (4, -2) and (4, 10) is 0. The slope of a line is 0 if it is horizontal. This function is constant.

The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.

The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.

If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.

If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.

The slope of a line is 0 if it is horizontal. This function is constant.

A line's slope is ambiguous if it is vertical.

In other terms, the rise is (y2 y1) = y. The rise of a road between two points is the difference in the altitude of the road at those two sites, say y1 and y2. The run, or (x2 x1) = x, is the difference in distance from a given point measured along a level, horizontal line for relatively small distances where the Earth's curvature may be disregarded. Here, the ratio of the altitude change to the horizontal distance between any two places on the line is used to define the slope of the road between the two points.

In mathematical language, slope m of the line is

slope = [tex]\frac{x-x1}{y-y1} =\frac{4-4}{-2+10} = 0[/tex]

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For there to be a profit,

From the question,

Concept: The formula for the percent profit is given below as

Answer: [tex](0, 3.6)[/tex]

Step-by-step explanation:

When rotating -270 degrees, which is the same as 90 degrees, we are going to the topmost point of the graph.

Since the radius is 3.6, this point has coordinates [tex](0, 3.6)[/tex].

Answer:

8

Step-by-step explanation:

4[tex]\sqrt{4}[/tex]

The [tex]\sqrt{4}[/tex] is 2

4x2 = 8

Answer:The square root of 4 is simply just 2 or in other words, 4 = 2.

Step-by-step explanation:

The value of root 4 is equal to exactly 2. But the roots could be positive or negative or we can say there are always two roots for any given number.

Answer:

-16,777,216

Step-by-step explanation:

4 to the fifth power =1024

-4 to the seventh power = 16, 384

1024 × -16, 384 =

- 16,777,216

ANSWER:

52 shrubs

STEP-BY-STEP EXPLANATION:

We know the number of trees planted in a given area, so to calculate the number of total trees, we must calculate the area of the entire figure and thus calculate by means of a proportion

We calculate the total area if we divide the figure in two, as follows:

The area of zone A, which is a rectangle, is calculated as follows:

The area of zone B, which is a triangle, is calculated as follows:

To calculate the value of the height of the triangle, we apply the Pythagorean theorem on the right triangle that is formed:

Where the hypotenuse is 25 meters and the other leg is 15 meters, just like this:

Now, the total area would be the sum of both areas:

Which means that if in an area of 400 square meters (20 * 20) they can plant 16 shrubs, in an area of 1300 square meters they would be:

In other words, a total of 52 shrubs can be raised throughout the region.

The vector along which a translation of the plane would map point A to its image T(A) is: C. vector MN.

In Geometry, there are different types of transformation and these include the following:

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

In this context, we can reasonably infer and logically deduce that vector MN is a translation of the given plane which would map point A to its image point T(A) because they both move in the same direction.

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We see that the unique point that lie on both the x-axis and the y-axis is the pont (0,0)!

Using the distance between a point and a line and the conversion of the units to yards, it is found that the minimum distance from the giant pumpkin is of  8.9 yards.

Suppose that we have a linear function defined according to the following rule, in standard notation:

Ax + By + C = 0.

And a point with coordinates given by:

P(x*,y*)

The shortest distance between the line and the point is given by:

[tex]d = \frac{|Ax^\ast + By^\ast + C|}{\sqrt{A^2 + B^2}}[/tex]

The line of the path in this problem has:

Hence:

y = 0.5x.

-0.5x + y = 0

-x + 2y = 0.

The coefficients are:

A = -1, B = 2.

The giant pumpkin has coordinates given by:

(x*, y*) = (-4, -3).

Hence the distance in units is given by:

d = |(-1)(-4) + 2(-3)|/sqrt(5)

d = 2/sqrt(5)

d = 0.89 units.

Each unit is equivalent to 10 yards, hence the shortest distance in yards is given by:

0.89 x 10 = 8.9 yards.

The problem is given by the image at the end of the answer.

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Step-by-step explanation:

that means we need to calculate the function result with x having a specific value.

for this we replace any appearance of x in the function expression by that specific value, and then we calculate.

g(x) = -3x + 1

g(7) means x = 7, and that gives us

-3×7 + 1 = -21 + 1 = -20

so, g(7) = -20

Answer:

-20

Step-by-step explanation:

Substitute 7 into the function g(x)

Since negatives "rule" positives,

7 * -3 = -21,

-21 + 1 = -20

Part a:

In this study, we have only a reference value of 16% (the proportion of people that can wiggle ears) and a population of 342 millionaires whose results we want to compare with this reference value. Since there is a relativelly high number of millionaries that were surveyed, we should use the z-test for a population proportion.

Part b:

It p is the sample proportion, the null hypothesis, in this case, is given by:

Therefore, the alternative hypothesis is given by:

Part c:

According to the data, the z-score is given by:

Part d:

According to the normal table, the p-value related to z-score given by:

0.638

Part e:

Therefore, we can check that this p-value is > a

Part f:

Based on this, we should ACCEPT the null hypothesis.

Part g:

Thus, the final conclusion is that the data suggest the population proportion is not significantly different from 16% at a = 0.01, so there is statistially significant evidence to conclude that the population proportion of millionaries who can wiggle their ears is equal to 16%.

In this problem we have to use the convertion factor that is equal to 1 so:

so we can made the transormation:

So in one minute it fills 24 pints

The sum of the first 12 terms is s(12) = -624 if the sequence is series −5 − 14 − 23 − 32 option (B) is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

It is given that:

The sequence is:

−5 − 14 − 23 − 32 −

s(12) means the sum of the 12 terms

s(12) = (12/2)[-5 + (12-1)(-9)]

s(12) = 6[-5 -99]

s(12) = 6[-104]

s(12) = -624

Thus, the sum of the first 12 terms is s(12) = -624 if the sequence is series −5 − 14 − 23 − 32 option (B) is correct.

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Solution

For this case we can use the following formula:

where

A= future value, P= present value= 400800.00

r= 5.5%=0.055, n =1 , t= 4 years

n= represent the number of times that the interest is compounded each year =1 for this case

Replacing we got:

then we can find the interest in the following way:

1) In this division, we need to turn that decimal number into a fraction: