A graph of f(x) = 6x2 + 7x – 3 is shown on the grid.

What are the zeros of f ?

Answer:

in fractions

16/18 = 8/9

4/18 = 2/9

Answer:

8/9 and 2/9

Step-by-step explanation:

for 16/18

divide the numerator and denominator by 2 to option it's simplest form

16/18÷2/2 = 8/9

for 4/18

also divide the numerator and denominator by 2 to get the simplest form.

4/18 ÷2/2= 2/9

Answer:

To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:

V = l * w * h

In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft3 because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:

21,904 ft3 = l * w * (8ft)

You are also told that the length is 2 times the width. Written as an equation, you would say that

l = 2w

Now, you can substitute that 2w for l to get the equation:

21,904 ft3 = (2w) * w * 8ft

We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w2 and that

21,904 ft3 = 2w2 * 8ft

Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get

2738 = 2w2

Then divide both sides by 2 to get

1369 = w2

Finally, for this portion, take the square root of 1369 to get

w = 37 feet.

But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.

The final answer is that the width of the pool is 37 feet and the length is 74 feet.

You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft3.

If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft3 and you know that you answer is correct.

Step-by-step explanation:

Answer:

0.182

Step-by-step explanation:

2 / 11 = 0.181818...repeating

0.1818 round up since the 4th number 8 > 5

Answer:

0.182

Step-by-step explanation:

:)

Answer:

y=14; x=72

Step-by-step explanation:

y=(21×2)/3; x=(48×21)/14

Using a calculator, it is found that the correlation coefficient for this data is given by:

B. -0.901.

To find the coefficient, which has symbol r², we input in a calculator the values of x and the values of y, hence:

r² = -0.901.

Which means that option B is correct.

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Answer:

It should move three places to the left :3

Step-by-step explanation:

Answer: 9 cups

Step-by-step explanation: 8 multiply it by 9 .

The equation of the line that passes through the points (7, 450) and (14, 401) is y + 7x = 499

The equation of a line  can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, (7, 450)(14, 401)

m = 401 - 450 / 14 - 7 = -49 / 7 = -7

Therefore, using (7, 450)

y - 450 = -7(x - 7)

y - 450 = -7x + 49

y + 7x = 49 + 450

y + 7x = 499

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Put u=17

Answer:

59.5.

Step-by-step explanation:

h = 3.5u

When u = 17,

h = 3.5*17

= 59.5

Answer:

A = 8 and B = 6

Step-by-step explanation:

Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".

(A - 5)² + (B - 3)² = 18                                 ----->  Original equation

(A - 5)² + ((A - 2) - 3)² = 18                         ----->  Plug in B = A - 2

(A - 5)² + (A - 5)² = 18                                ----->  Subtract

(A² - 10A + 25) + (A² - 10A + 25) = 18       ----->  Expand parentheses

2A² - 20A + 50 = 18                                 ------>  Add like terms

2A² - 20A + 32 = 0                                   ----->   Subtract 18 from both sides

2(A² - 10A + 16) = 0                                   -----> Remove common factor

2(A - 2)(A - 8) = 0                                      -----> Factor within parentheses

A = 2                                                         -----> Find A - 2 = 0

A = 8                                                        -----> Find A - 8 = 0

Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.

When A = 2:

B = A - 2                           -----> Original equation

B = 2 - 2                           -----> Plug in A = 2

B = 0                               -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(2 - 5)² + (B - 3)² = 18       ------>  Plug in A = 2

(-3)² + (B - 3)² = 18           -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

When A = 8:

B = A - 2                         -----> Original equation

B = 8 - 2                         -----> Plug in A = 8

B = 6                             -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(8 - 5)² + (B - 3)² = 18       ------>  Plug in A = 8

(3)² + (B - 3)² = 18            -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.

Step-by-step explanation:

the photo should explain

Answer:

2

Step-by-step explanation:

-3 log₂ (-n + 10) = -16+7

-3 log₂ (-n + 10) = -9

log₂ (-n + 10) = -9/-3

log₂ (-n + 10) = 3

-n + 10 = 2^3

-n + 10 = 8

n=2

The smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.

The divisible rule of 9 and 5 are:

Two digits of the 6-digit number are missing.

[tex]X = 345 * 8*[/tex]

The smallest possible number from this is divisible by 45. The factors of 45 are 9 and 5.

[tex]45=9\times5[/tex]

Thus, the 6-digit number which is divisible by 45, must be divisible by 9 and 5.  

To be divisible with 5, the number has 0 or 5 in last. So the numbers can be,

[tex]X = 345 * 85\\X=345 * 80[/tex]

For first number, when the blank is filled with number 2 to make sum 9 and for second the blank number should be 7. Thus, the numbers,

[tex]X = 345 285\\X=3457 80[/tex]

Thus, the smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.

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Answer:

0.91 g/cm³

Step-by-step explanation:

Density Formula

Solving

In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

In the first triangle, we need to use trigonometric ratio to find the missing side in the triangle

Data;

To find the adjacent side, we need to use cosine rule on this problem.

[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]

The adjacent side is equal to 8 units

In the second triangle, we also need to use trigonometric ratio, but let's write down our data

We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.

[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]

The adjacent side is equal to 8.660, let's find the opposite side using sine rule

[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]

And lastly, the value of the other angle is

[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]

From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

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Answer:

5/8

Step-by-step explanation:

There are 8 sections, and 4 sections that are 1, and 1 pink section. So adding these up, we get 5/8.

Hope this helped! :)

All real numbers

1. f(x) = 2x

2. g(x) = 2x

Substitute g(x) to the 2x in the first statement.

You'll get: f(x) = g(x)

Therefore, x ∈ all real numbers (any value of x would make it a true statement)

Answer & step-by-step explanation:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign. As you can clearly see here, there is no equal sign connecting anything here, thus, it is an expression.

Because for it to be called an equation you need to have the equal symbol (=) comparing two epressions.

Example of expression:

 2x - 4y + 14

Example of equation:

   -3y - 2 = -2x - 8

⇔ -3y = -2x + 6

⇔ -y = -[tex]\frac{2}{3}[/tex]x + 2

⇔ y = [tex]\frac{2}{3}[/tex]x - 2

Answer:

The answer is D. Hope this helps :)

To solve this problem, we have to understand and establish some basic mathematical facts on a cone.

The answer to this question are option b and c only.

This is a solid figure that has the base of a circle and the top is made up round triangle.

The formula of volume of a cone is given as

[tex]v = \frac{1}{3}\pi r^2 h[/tex]

where;

In the given question, the first fact given is if the radius doubles the diameter and that false.

[tex]diameter = 2 * radius[/tex]

If we have the value of the the radius, we can calculated the base area using area of a circle

[tex]area = \pi r^2[/tex]

The volume of a cone is actually one-third the volume of a cylinder

we can only calculate the volume of the cone is we have the value of the height of the cone.

The answer to this question are option b and c only.

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Answer:

B, C, D, E

Step-by-step explanation:

Got it wrong the first time.

The amount of co2 that Harry's vehicle would release to the atmosphere in a year is 12,000 pounds.

The first step is to determine the gallons of gasoline that the car would need in a year: 15,000 / 25 = 600 gallons

The second step is to determine the total emissions when the car uses 600 gallons: 600 x 20 = 12,000 pounds

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An estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.

The percentage of a defective item out of a total item can be calculated as follows:

% defective item = no of defective item/total no of items × 100

According to this question, in a random sample of 200 items, 5 items were defective.

% defective item = 5/200 × 100

% defective item = 2.5%

Therefore, an estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.

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Using geometric sequence concepts, it is found that:

a) The rule is: [tex]P_n = 750000(0.5)^{n-1}[/tex].

b) An exponential relationship exists between the two variables.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

A geometric sequence represents an exponential relationship between the variables.

In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:

[tex]a_1 = 750000, q = 0.5[/tex].

Hence the nth term of the sequence is given by:

[tex]P_n = 750000(0.5)^{n-1}[/tex]

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Answer:

6.75$

Step-by-step explanation:

because 15% of 45$ is 6.75$

Step-by-step explanation:

there are 13 out of 52 diamond cards.

and there are 26 out of 52 black cards.

so, for the first card to be diamond the probability is

13/52 = 1/4 = 0.25

but now, he does not put the card back.

he pulls the second card out of 51 possible cards.

the desired cases are still 26.

so, the probability to pull a black card as the second card under the restriction that the first card was a diamond is

26/51 = 0.509803922...

the probability for that combined event is then

1/4 × 26/51 = 26/204 = 13/102 = 0.12745098...

so, c. is the right answer.