If p represents a number, which expression represents "p divided by 7, increased by 8"?

Answer:

We know that the factors of the number 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

Step-by-step explanation:

so it would be 1,2,3,5,6,9 hope it helps :)

I agree, that is correct

Answer:

the answer would be the letter A

The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.

Given the quadratic equation in the question:

6x² = -3x + 1

To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:

6x² + 3x - 1 = 0

Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:

\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\)

Here; a = 6, b = 3, and c = -1.

Let's substitute these values into the quadratic formula:

\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23\)

Therefore, the values of x are -0.73 and 0.23.

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Answer:

72.3

Step-by-step explanation:

Given that:

The arithmetic sequence:

\(\sum \limits ^{14}_{k=0} (3 + 0.26k)\)

The first term of the sequence \(a_0\) = 3 since k = 0

i.e (3 + 0.26(0)) = 3

The last term of the sequence \(a_{14}\) = 6.64

i.e (3+ 0.26(14)

= (3 + 3.64)

= 6.64

Total no of terms = 15 i.e from 0 to 14

∴

The partial sum of the arithmetic sequence = \(\dfrac{Total \ no \ of \ terms }{2} \times (a_o+a_{15})}\)

\(=\dfrac{15 }{2} \times (3+6.64)}\)

= 72.3

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

His weekly exercise time goal is 168 minutes.

Step-by-step explanation:

This question can be solved using a rule of three.

42 minutes is 25% = 0.25 of the total

x minutes is 100% = 1 of the total.

Then

42 minutes - 0.25

x minutes - 1

\(0.25x = 42\)

\(x = \frac{42}{0.25}\)

\(x =  168\)

His weekly exercise time goal is 168 minutes.

Answer:

(-3,5)

Step-by-step explanation:

I got it right on khan academy

Answer:

6417

Step-by-step explanation:

if A = b*h then when we substitute b for 93 and h for 69

A=93*69 = 6417

Answer:

A ratio can be expressed as a word description, with a colon or as a fraction.

Step-by-step explanation:

A ratio can be expressed as a word description, with a colon or as a fraction.

Quantitatively, a ratio is a number representing a comparison between two named values. It is the relative magnitude of two quantities usually expressed as a quotient.

Thus, a ratio can be expressed as a word description between two quantities, for example:

four to five.

It can be represented with a colon. i.e  4:5

Or as a fraction i.e. \(\dfrac{4}{5}\)

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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The ordered pair that makes both inequalities true is (4,0).

we have

y<3x-1 ----> inequality A

y > –x + 4----> inequality B

we know that

If an ordered pair is a solution to the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

Verify each ordered pair

case 1) (4,0)

Inequality A

0<3(4)-1 ----> is true

Inequality B

0> –4 + 4 ----> is true

A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

So, The ordered pair makes both inequalities true

case 2) (1,2)

Inequality A

2< 3(1) – 1

2<3-1

2<2----> is not true

So the ordered pair does not make both inequalities true

case 3) (0,4)

Inequality A

0 < 3(4) – 1

0<12-1

0<11 ----> is not true

So, the ordered pair does not make both inequalities true

case 4) (2,1)

Inequality A

1< 3(2) – 1

1<6-1

1<5----> is true

Inequality B

\(1\geq -2+4\)

\(1\geq 2\) ----> is not true

So the ordered pair does not make both inequalities true.

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Answer:

The system of equation that models the projectile of the two balls is option;

C. y = -16·x² + 12·x + 3

y = -16·x² + 9·x + 3.25

Step-by-step explanation:

The general equation for vertical (upward) motion under gravity is presented as follows;

h - h₀ = u·t + 1/2·g·t²

Where;

h = The final height reached

h₀ = The initial height

u = The initial velocity

g = The acceleration due to gravity ≈ -32 feet/second

t = The time taken

We can rewrite the above equation with different letters for the variables as follows;

h = y,

h₀ = y₀, and

t = x

Therefore, we have;

y - y₀ = u·x - 1/2 × 32 × x²

y = u·x - 1/2 × 32 × x² + y₀ = u·x - 16· x² + y₀

y = u·x - 16· x² + y₀ = -16·x² + u·x + y₀

y = -16·x² + u·x + y₀

For Tara, we have;

u = 12 feet/second

y₀ = 3 feet

Therefore, we get;

y = -16·x² + 12·x + 3

For Mallory, we have;

u = 9 feet/second

y₀ = 3.25 feet

Therefore, we get;

y = -16·x² + 9·x + 3.25

The correct option is therefore;

y = -16·x² + 12·x + 3

y = -16·x² + 9·x + 3.25

Answer:

160 meters

Step-by-step explanation:

Before I begin, note that distance = rate * time (or d = r * t)

To solve this problem, we need to find what point these two people have the same distance. (so Janiyah covers the same distance as Connor)

So, let's set the time that Janiyah takes as x (in seconds). So, he covers

d = r * t, or 8x meters

Then, Connor's equation would be

d = r * t

d = 5x + 60 (because he got a 60 meter headstart)

Because d is the same in both equations, to solve for the amount of time they run:

8x = 5x + 60

Subtract 5x from both sides.

3x = 60

x = 20

Then, to find Janiyah's distance (you can also use Connors because the two distances are equal), put x = 20 into 8x

8x = 8 * 20 = 160

So, Janiyah ran 160 meters.

Just in case, let's check if this is correct. Connor's distance equals Janiyah's, so

5x + 60 = 160

5 * 20 + 60 = 160

100 + 60 = 160

160 = 160

True.

So, the answers are correct.

I hope this helps! Feel free to ask any questions!

Answer: 160 meters

Step-by-step explanation:

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

When you're reading a study that reports selecting a random sample of hospitals and estimating admission delay times, it's an example of C. probability sampling.

Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling.

Using a method based on probability theory, probability sampling is a strategy in which the researcher selects samples from a larger population.

Researchers can produce a sample that accurately represents the relevant real-world population by using probability sampling.

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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:

a. Quota sampling

b. Convenience Sampling

c. Probability sampling

d. Sampling bias

The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

From the question, we have the following parameters that can be used in our computation:

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

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Answer:

So the first step is asking you to write the explanation on your own paper (Easy! :)

The whole equation is designed for you to get the variable "x" by itself so that you know what number it is equal to. In order to do this you need to follow the steps.

So for the second step you need to add 1 to both sides. This step is so that you can get rid of the 1 on the left side, to do this you need to add 1 because this will cancel out on the left side since you are substracting it. BUT if you add one on the left side, you also need to add it to the right side!!! (Whatever you do on one side of the equal sign you need to do on the other side)! So add one on both sides this will get rid of the 1 on the left and turn the 6 to a 7 on the right side.

NEXT STEP (Multiply both sides by -2) So (-1/2) is the same as saying 1 divided by -2 which is -0.5 as a decimal. If you want to cancel out a fraction you want to multiply it by the denominator (aka bottom number), in this case that number is -2. So if you multiply (-1/2) by -2 this cancels that fraction out on the left side and it disappears, BUT you must do it on the right side too! So you multiply 7 by -2 which is equal to -14.

Now you're left with 5x = -6! Your final step is to get rid on the 5 on the left side. To do this you simply divide it by 5 so that it cancels out on the left side and you're left with x. BUT you still divide on the right side, so x is equal to (-6/5).

I hope this helps!

It is all about getting x by itself.

The gradient of  y = 16 - 8x is - 8

The gradient of y - 5 = 6x is 6

y = mx + c form of y - 5 = 6x is

The slope is another name for the gradient. Any straight line's gradient illustrates or demonstrates how steep it is. The gradient is said to be bigger if any line is steeper.

In other words, the ratio of vertical change to horizontal change is known as Gradient.

The gradient of line y = mx + c is 'm'  

Here we have

Equation (1) y = 16 - 8x

Compare the given equation with y = mx + c

=> Gradient / Slope (m) = - 8

Equation (2) y = 7x + 8

Compare the given equation with y = mx + c

=> Gradient/ Slope (m) = 7

Equation (3) y - 5 = 6x

Convert the given equation in the form of y = mx + c

=> y - 5 = 6x  

Add 5 on both sides

=> y = 6x + 5

When we compare the given equation with y = mx + c

=> Gradient / Slope (m) = 6

Therefore,

The gradient of  y = 16 - 8x is - 8

The gradient of y - 5 = 6x is 6

y = mx + c form of y - 5 = 6x is y = 6x + 5.  

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On each roll of a 6-sided die, we have 6 possible outcomes.

Then if we roll it twice, we will have 36 outcomes.

The outcomes where the sum is 4 are:

roll 1     roll 2    sum

1             3           4

3            1            4

2           2           4

Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:

P = 3/36

P = 1/12

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Answer: 28.25%

Step-by-step explanation:

113/400=0.2825=28.25%

₋2.3 < ₋8/3 is the correct answer.

Given, we need to compare the terms.

₋8/3 = ₋2.67

therefore, 2.3 is less than 2.667

hence we form it as ₋2.3 < ₋2.67

we form: ₋2.3 < ₋8/3

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Answer:

65/100 that is the answer to this question

The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q

We are given the algebraic expression as:

¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃

Combining Like terms gives us:

(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)

Solving both brackets individually gives us:

((11 - 4)/12) + ⁴/₆q

= ⁷/₁₂ + ⁴/₆q

Thus, we conclude that is the solution of the given algebraic expression problem

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Answer:

x³=8

x³=27

x³=64

Step-by-step explanation:

A rational number is one formed by dividing integers. This means a rational number can be expressed as a ratio of two integers. Examples of rational numbers are;

Given in the question;

x³=8 ----- x=∛8 = 2 -------can be formed from 2/1 ⇒ equation has rational number

x³=16 -----x=∛16 = 2.5198421 ----- irrational

x³=27-------x=∛27 = 3--------rational

x³=64------x=∛64 =4---------rational

Answer:

Option B.

Step-by-step explanation:

The given equation is

\(17h+6=40\)

We need to find the property of equality to move the constant term to the right side of the equation.

In the given equation 6 is the constant term on the left side.

Using subtraction property of equality, subtract 6 from both sides.

\(17h+6-6=40-6\)

\(17h=34\)

So, the appropriate property of equality to move the constant term to the right side of the equation is Subtraction Property of Equality.

Therefore, the correct option is B.

Answer:

136 times

Step-by-step explanation:

If the park lets you swim 8 times in one month, there are 12 months in one year, therefore you could swim eight times each of those twelve months.             8 x 12 = 96. Then, you have 5 more months left to swim. So, if you swam eight times each month that would be 8 x 5 = 40. So, 96 + 40 = 136.

Answer:4.2

Step-by-step explanation:

128 Bales of hay

Step-by-step explanation:

Take 64 and multiply it by 2 since 4 is half of 8 and 2 is double which make 64 so the answer is 128

X 2

___

128