A rock was thrown from a cliff. Its path can be modelled by the relation h=-0.5d^2 + d + 12, where h is the height of the rock above the ground and d is the horizontal distance, both in metres. a) How high is the cliff? b) Write the relation in intercept form. c) Determine the zeros of the relation. d) At what horizontal distance did the
rock hit the ground? e) Graph the relation.

Answer: f= [tex]x^2+4x+8+(7/3x-4)[/tex]

Step-by-step explanation:

Careful with simplifying every step.

Answer: [tex]x^{2} -7x+10[/tex]

Explanation:

Get the result ⇒ [tex]f(x)-g(x)=(x^{2} -6x+8)-(x-2)[/tex]

Remove the parentheses ⇒ [tex]x^{2} -6x+8-x+2[/tex]

Reorder and gather like terms ⇒ [tex]x^{2} +(-6x-x)(8+2)[/tex]

Collect the coefficients for the like terms ⇒ [tex]x^{2} +(-6-1)*x+(8+2)[/tex]

Calculate the sum or difference ⇒ [tex]x^{2} -7x+(8+2)[/tex]

Calculate the sum or difference ⇒ [tex]x^{2} -7x+10[/tex]

Convert to required form ⇒ [tex]x^{2} -7x+10[/tex]

Answer ⇒ [tex]x^{2} -7x+10[/tex]

Answe65

Step-by-step explanationthat the anews

Let the price be x

Price is $17 now

Answer:

y=x^2-5x+4 i am not sure but a im try

Answer:

76

Step-by-step explanation:

All steps are in the pic attached :

Answer:

Answer: 24

Step-by-step explanation:

There are 4 possibilities for the first card. After that, there are 3 possibilities for the second card. Finally, there are 2 possibilities for the third card. The total number of permutations is 4×3×2 = 24. Here's the list (in alphabetical order): ARS ART ASR AST ATR ATS RAS RAT RSA RST RTA RTS SAR SAT SRA SRT STA STR TAR TAS TRA TRS TSA TSR

428.5oz (total amount she had to put out)÷ 5(amount of bowls she wanted to use) = 85.7oz

Options A and B situation does NOT yield variability that is A. How many days are in a leap year? B. How many siblings does each person in your class have?

Statistics deals with the study of variability. The statement is said to be statistical if there would be variability in that data.

A. How many days are in a leap year?

This situation does NOT yield variability because the question is answered by a single value. It does not need any collecting data that vary.

B. How many siblings does each person in your class have?

This situation does NOT yield variability because the question is answered by a single value. It does not need any collecting data that vary.

C. How many miles do you travel in your car each day?

This situation yield variability because the question is answered by collecting data.

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Answer:

6

Step-by-step explanation:

5.7 is already immediately  6 because if a number after the whole number is 5 or more you round up.

6

Step-by-step explanation:

In Rectangle , 16 copies of ABCD fit inside A'B'C'D'.

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral.

                                       The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

DA = 3

D'A' = 12

Scale factor DA/D'A' = 3/12 = 1/4

The scale factor = 1/4

The scale factor = 1/4

area ratio = 1/16

16 copies of ABCD fit inside A'B'C'D'.

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Answer:

$4.70

Step-by-step explanation:

First, you need to divide 18.80 by 8.

18.80/8 = 2.35

2.35 is the unit price for one (1) pound bag of flour,

Multiply by 2 to find the price of a two (2) pound bag.

2.35 * 2 = 4.7

$4.70 is the price of a two-pound bag.

hope this helps :)

Answer:

The picture isnt popping up fix it and ill answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

change in time: 2

change in distance: 5.5

2:5.5

The equation that is equivalent to the considered equation of log is given by: Option E: 2^3 = x+5

When you raise a number with an exponent, there comes a result.

Lets say you get [tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]

Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.

Log with base 10 is written as [tex]\log(x)[/tex] simply.

The equation given is:

[tex]\log_3(x+5) = 2[/tex]

By using the definition of log, which says [tex]a^b = c \leftrightarrow \log_a(c) = b[/tex], we get:

[tex](x+5) = 2^3[/tex] or [tex]2^3 = x+5[/tex]

Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]

(we used the fact that the question is asked in a way that expresses that there is only one equivalent equation. Plus we used the fact that as option E is a sure equivalent version, so it is correct option).

Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]

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The probability (x s 110) is 0.975, the correct option is A.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

Mean=98

Now,

To find the probability that x is less than or equal to 110 for a normal distribution with mean 98 and standard deviation 6, we need to use the standard normal table or a calculator.

Using the standard normal table, we first need to convert x to a z-score using the formula:

z = (x - mean) / standard deviation

Plugging in x = 110, mean = 98 and standard deviation = 6, we get:

z = (110 - 98) / 6

z = 2

This means that x = 110 is equivalent to z = 2 on the standard normal distribution.

Now we look up the value of z = 2 on the table and find that it corresponds to an area of 0.9772. This means that P(z ≤ 2) = 0.9772.

However, this is not the answer we want. We want P(x ≤ 110), which is the same as P(z ≤ 2). The table gives us the area to the left of z, but we need to subtract it from 1 to get the area to the right of z. This is because P(x ≤ 110) = P(z ≤ 2) + P(z > 2) = 1.

Therefore,

P(x ≤ 110) = P(z ≤ 2)

P(x ≤ 110) = 1 - P(z > 2)

P(x ≤ 110) = 1 - (1 - P(z ≤ 2))

P(x ≤ 110) = P(z ≤ 2)

P(x ≤ 110) ≈0.9772

Therefore, by the given mean the answer will be 0.975.

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Answer:

The area is 56.52 sq. in.

Step-by-step explanation:

First to find the area of a whole circle, we do r^2(pi)- 6^2(3.14)=113.04. Since the circle is cut in half or is a semicricle, we divide the whole area by 2 to get 113.04/2=56.52.

Answer:

the slope = 0

Step-by-step explanation:

we notice that the points (13, -2) and (3, -2) have the same y-coordinate -2

Then

the slope = 0

[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]

════════════════════

1.

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

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

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

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

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

[tex]x = \sqrt \frac{2y + 6}{2}[/tex]

───────────────────

2.

[tex]y = 3x - 1[/tex]

[tex]3x - 1 = y[/tex]

[tex]3x = y + 1[/tex]

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

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

═══════════════════

Explanation:

#Carry on learning

The two person will pay the same amount of money when they both watch 9 hockey games.

A hockey season ticket holder pays $99.00 for her tickets plus $3.00 for a program for each game. Therefore,

y = 99 + 3x

where

y = total cost

x = number of game

A second person pays $14.00 for a ticket to every game but doesn't buy programs. Therefore,

y = 14x

The number of games they will have the same amount is as follows:

99 + 3x = 14x

99  = 14x - 3x

99 = 11x

x = 99 / 11

x = 9

Therefore, they will have the same amount when they watch 9 games.

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Answer:

1st, 2nd, and 5th one

Step-by-step explanation:

I got an 100 on the assignment! hope this help <3

C

Line symmetry is when a shape can be folded over an imaginary axis and have both sides be a mirror of the other. This axis is called the line of symmetry.

Letter C

In this case, if you draw a horizontal line across the middle of the letter "C" and fold the letter, each half would be the same. The top half of "C" mirrors the lower half.

Other Examples

The lowercase letter "l" also has 2 lines of symmetry. You can draw both a horizontal and vertical line across the letter and each side will mirror the other.

Step-by-step explanation:

The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle.

You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the third side.

Answer:

2 ≤ x ≤ 10

Step-by-step explanation:

4|x – 6| ≤ 16

|x – 6| ≤ 4

-4 ≤ x – 6 ≤ 4

2 ≤ x ≤ 10

The solution to 4|x – 6| ≤ 16 is 2 ≤ x ≤ 10

A polynomial expression is an expression that can be built from constants and symbols.

Polynomials are algebraic expressions that comprise exponents which can be added, subtracted, or multiplied. Polynomials are of different types. Monomial- Linear equations (A monomial is a polynomial with one term)Binomia l- quadratic equation (A binomial is a polynomial with two, unlike terms).

calculation:-

⇒4|x – 6| ≤ 16

⇒|x – 6| ≤ 4

⇒-4 ≤ x – 6 ≤ 4

⇒2≤ x ≤ 10

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Answer:

Step-by-step explanation:

Remember :

Here :

Answer:

Step-by-step explanation:

Given

2x + 9 - x + 3

What's equivalent

Solution

2x - x + 9 + 3             The terms have been rearranged. Combine

x + 12

Test.

x = 5

2(5) + 9 - 5 + 3

10 + 9 - 5 + 3

19 - 5 + 3

14 + 3

17

x + 12

5 + 12 = 17

Answer:

Jim=S-3

Steve=M-4

U figure out the last part.           I helped

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Equating Matt's Speed in both cases

Now, taking Equation 1 :

Now, taking Equation 2 :

Answer: [tex]\frac{3}{5}[/tex] of the judges were not wearing their powdered wigs.

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] out of the whole [tex]\frac{5}{5}[/tex] were wearing a wig. So subtract [tex]\frac{2}{5}[/tex] from [tex]\frac{5}{5}[/tex] to see the fraction that wasn't wearing a wig.

[tex]\frac{5}{5} -\frac{2}{5} =\frac{3}{5}[/tex]