Use the list method to write "The odd integers between 2 and 15". {2, 3, 5, 7, 9, 11, 13, 15} {3, 5, 7, 9, 11, 13} {3, 5, 7, 9, 11, 13, 15}

Answer:

t=6

Step-by-step explanation:

We are solving for [tex]t[/tex]. To do this, let's fill in the known variables.

[tex]h=vt-16t^2[/tex]

[tex]v=80\\h=96[/tex]

[tex]96=80t-16t^2[/tex]

[tex]16t^2-80t+96=0\\16(t^2-5t+6)=0[/tex]

Since the product must equal 0, that means that the factor in the parentheses hasto be equal to 0. Therefore,

[tex]t^2-5t+6=0\\(t+1)(t-6)=0\\\\t+1=0 OR t-6=0\\t=-1 OR t=6[/tex]

However, since the time cannot be negative, [tex]t=-1[/tex] cannot be a valid answer.

Therefore, the only valid time is t=6.

I hope this helps.

Let's start with the projectile motion formula which is h = vt - 16t².

In this formula, h is the height of the object,

v is the initial velocity, and t is the time.

We know that the initial velocity is 80 feet per second

so we can plug an 80 in for v in our formula.

We also know that the object reaches a height of 96 feet above the

ground which means we can plug an 96 in for h in our formula.

So we have 96 = 88t - 16t².

To solve this equation, we set it equal to 0 by subtracting

88t and adding 16t² to get 16t² - 88t + 96 = 0².

Now we can divide both sides by 8 to get 2t² - 11t + 12 = 0.

Now we can factor the left side to get (2t - 3)(t - 4) = 0.

So this means that 2t - 3 = 0 or t - 4 = 0.

So t = 3/2 or t = 4.

Now, the reason there are two answer is because the object will be

96 feet off the ground on its way up and on its way down.

Answer:

[tex]3 \frac{3}{4} \times 3 \frac{1}{3} = \frac{15}{4} \times \frac{10}{3} = \frac{25}{2} = 12 \frac{1}{2} [/tex]

The area of this room is 12 1/2 yd².

The area of the rectangular room is (12.5) square yards, calculated by multiplying length and width.

To find the area of a rectangular room, you multiply its length by its width. Given that the length is [tex]\(3 \frac{3}{4}\)[/tex] yards and the width is  [tex]\(3 \frac{1}{3}\)[/tex] yards, you can calculate:

[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]

First, let's convert the mixed numbers to improper fractions:

[tex]\[ 3 \frac{3}{4} = \frac{4 \times 3 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \text{ yards} \]\[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \text{ yards} \][/tex]

Now, plug these values into the formula:

[tex]\[ \text{Area} = \frac{15}{4} \times \frac{10}{3} \]\[ \text{Area} = \frac{15 \times 10}{4 \times 3} \]\[ \text{Area} = \frac{150}{12} \]\[ \text{Area} = 12.5 \text{ square yards} \][/tex]

So, the area of the rectangular room is [tex]\(12.5 \, \text{square yards}\).[/tex]

For this case we must find an expression equivalent to:

[tex]4,325,000,000[/tex]

To express in scientific notation we must take into account that the power will be positive, that is, the decimal is run to the right.

We test each option.

Option A:

[tex]4,325 * 10^{-9}[/tex]

If we run the decimal 9 spaces to the left we have:

[tex]0.000000004325[/tex]

Option B:

We discard it because the exponent is negative.

Option C:

[tex]4,325 * 10 ^ 6[/tex]

We run the decimal 6 spaces to the right

[tex]4,325,000[/tex]

Option D:

[tex]4,325 * 10 ^ 9[/tex]

We run the decimal 9 spaces to the right

[tex]4,325,000,000[/tex]

Answer:

Option D

Final answer:

The expression that is equivalent to 4,325,000,000 is 4.325 × 10^9.

Explanation:

The expression that is equivalent to 4,325,000,000 is 4.325 × 109.

When we write a number in scientific notation, we express it as a product of a coefficient and a power of 10. In this case, the coefficient is 4.325 and the power of 10 is 9. This means that we move the decimal point 9 places to the right, resulting in a value of 4,325,000,000.

So the correct expression is 4.325 × 109.

y=8(x^2 + 4x + 4) +17 + -32

Simplify:

y = 8(x^2 + 4x + 4) + 15

Use distributive property:

y = 8x^2 + 32x +32 - 15

Simplify:

y = 8x^2 + 32x +17

Complete the square using  form ax^2+bx+c:

a = 8, b = 32, c = 17

vertex form = a(x+d)^2+e

d = b/2a and e = c-b^2/4a

d = 32/2*8 = 32/16 = 2

e = 17 - 32^2/4*8 = 17-1024/32 = 17-32 = -15

Vertex form = y = 8(x+2)^2 + -15

Answer:

10 times larger

Step-by-step explanation:

To solve this you need to divide 80 amd 8.

80/8

if 10* 8 = 80 then 80/8 = 10

Therefore 10 times larger is the answer

80 is 10 times larger than 8. This is determined by dividing the larger number (80) by the smaller number (8). The result of this division gives us the times one number is larger than the other.

The comparison of two numbers can be done by looking at the ratio, or division result of those two numbers. In this case, we are comparing 80 and 8. We can do this by dividing 80 by 8, which equals 10. Therefore, 80 is 10 times larger than 8.

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Answer:

This quantity is already simplified.

Perhaps there was a typographical error?

Answer: This quantity is already simplified.

Perhaps there was a typographical error?

Step-by-step explanation:

Answer:

I think it is 4.52 × 10^-4

Answer:

See attached graph

Step-by-step explanation:

The graph of distance from home as a function of time starts at the origin of coordinates (0,0) since at time zero minutes Varun is at home.

Then we represent his driving at constant speed (although it has not been specified in the problem) as a line with positive slope equal to his speed, that goes on for the first five minutes. After that, he reaches the traffic light that keeps him at the same distance from home for three minutes (notice the line representing the distance covered is flat from minute 5 to minute 8, while he is not moving).

Then he starts moving again (we assume at the same speed as before - so the line representing his position is again a line with positive slope and with the SAME inclination as that which represents the first 5 minutes of his trip.

The line ends at minute 15 which is the time it took him to get to work.

Answer:

Step-by-step explanation:

f(x) = a(x+2)² +k

Answer:

f(x) = (x + 2)2 − 1

Step-by-step explanation:

HEY LUVS

Answer:

A

Step-by-step explanation:

Answer: D. X<7

Step-by-step explanation:

In the given inequality, x represents the number of games Colby can finish. Use opposite operations to isolate x.

Therefore, the solution set for how many more games Colby can finish this week is x < 7.

Answer:

U.S.= 9

France= 2

Step-by-step explanation:

2×4=8 +1=9

9-7=2

Hope this helps!!!

Brady

  Number of Gold medals won by USA are 9 and gold medals won by France are 2.

   Let the gold medals won by USA = x

And the gold medals won by France = y

It's given in the question "gold medals won by USA are 1 more than 4 times the number of gold medals won by France"

Therefore, equation for this situation will be,

x = 4y + 1 --------(1)

Second statement of the question states "USA won 7 gold medals more than France"

Therefore, equation will be,

x = y + 7 -------(2)

By substituting the value of 'x' in equation (1) from equation (2),

y + 7 = 4y + 1

4y - y = 7 - 1

3y = 6

y = 2

By substituting the value of 'y' in equation (1),

x = 4(2) + 1

x = 9

      Therefore, USA won 9 gold and France won 2 gold medals in the Winter Olympic Games.

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The required line parallel to y = - 7x - 2 through (- 4, 6) is y = -7x - 22.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know parallel lines have the same slope.

Given line is y = - 7x - 2, hence the required line will also have a slope of - 7

which is passing through the point (-4, 6).

∴ 6 = (-7)(-4) + b.

6 = 28 + b.

b = - 22.

Hence the required line is y = -7x - 22.

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Answer:

D

Step-by-step explanation:

The absolute value always returns a positive value, that is

| - a | = | a | = a, thus

| 7 | = 7 → D

Answer:

Step-by-step explanation:

|7|=7 answer : D

Answer:

Step-by-step explanation:

students = x

non-students=y

x+y=410

y=410-x

3x+7y=1650

3x+7(410-x)=1650

3x+2870-7x=1650

-4x=-1220 (divide both sides by -4)

x=305 y=410-305=105

Hence, 305 students attended and 105 non-students attended

The problem can be represented by two linear equations, s + n = 323 and 2s + 3.5n = 790. After putting these equations into the format y = mx + b, they can be graphed to find the solution at the point where the two lines intersect.

First, let's define two variables, s for the number of students and n for the number of non-students. From the information we have:

To solve the problem by graphing, we need to convert these equations into y = mx + b format. Our first equation then becomes s = -n + 323 and the second becomes s = (790 - 3.5n) / 2. Plotting these equations on a graph and finding the point where the lines intersect will give us the value of s and n. The x-values corresponds to n (non-students) and y-values to s (students).

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Answer:

x>-33/8

Step-by-step explanation:

9+8x>-24

1) Subtract 9 from both sides:

8x>-33

2) Divide both sides by 8:

x>-33/8

The algebraic representation of the problem is 9 + 8x > -24. After isolating 'x', the solution to the inequality is x > -4.125, which means any number greater than -4.125 satisfies the equation.

The problem presented is a linear inequality, a topic of mathematics. The sentence 'Nine increased by the product of a number and 8 is greater than -24' can be represented algebraically as 9+8x > -24, where 'x' is the number in question.

To solve it, as we aim to find the value for 'x', you first isolate 'x' on one side of the inequality. Start by subtracting 9 from both sides to get 8x > -24 - 9, which results in 8x > -33. Then, you divide both sides by 8 to solve for 'x'. As a result, x > -33/8, or x > -4.125.

This means that any number greater than -4.125 will satisfy the equation 'Nine increased by the product of a number and 8 is greater than -24'. So, the solution to this inequality is x > -4.125.

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ascended 28 ft!

10 - (-18) = 28

Answer:

32+q

Step-by-step explanation:

The complete question is

Jake has 32 quarters on his desk, molly has q quarters in her purse.  

Which algebraic expression represents the total number of quarters that Jake and Molly have?  

we know that

To find out the total number of quarters that Jake  and Molly have, sum the amount of quarters that Jake has plus the amount of quarters that Molly has

Let

x ----> the amount of quarters that Jake has

y ----> he amount of quarters that Molly has

so

x+y

we have

[tex]x=32\ quarters\\y=q\ quarters[/tex]

substitute

32+q

Answer:

Slope:

[tex]m = -\displaystyle\frac{1}{2}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]y = -\displaystyle\frac{1}{2}x + \displaystyle\frac{1}{4}[/tex]

Comparing this equation to the slope-intercept form:

[tex]y = mx + c[/tex]

where m is the slope of line and c is the y-intercept that is the value of y when x is zero.

on comparing, we get:

[tex]m = -\displaystyle\frac{1}{2}\\c = \displaystyle\frac{1}{4}[/tex]

The slope of the given line is

[tex]m = -\displaystyle\frac{1}{2}[/tex]

The slope of the given line is -1/2

The standard equation of a line is expressed as y = mx +b

where

m is the slope

b is the y-intercept

Given the equation y = -1/2x + 1/4

Compare the equations

mx = -1/2 x

m = -1/2

Hence the slope of the given line is -1/2

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Answer:

2^x

64 bacterium

10 hours

Step-by-step explanation:

doubles every hour

if x = hours

2^x

2^x --> 2⁶ = 64

2^x = 1024

1024 = 2^10 ---> x=10

Answer:

Whole numbers are positive numbers (this includes 0) that do not have decimals or fractions to them.

Example:

1, 2, 3, 4, 5,etc are all whole numbers, because they are positive and do not have decimals or fractions

1.25 would not be a whole number, because although it is positive, it has a decimal.

Hey!

-------------------------------------------------

Steps To Solve:

~Coordinates of the line

(0, -1) and (-1, 0)

~Find slope

[tex]m = \frac{0 - (-1)}{-1 - 0} = \frac{1}{-1} = -1[/tex]

~Find the equation of the line

y = mx + b

m = slope

b = y-intercept

m = -1 or -x

b = -1

y = -x - 1

~Check using zero rule (substitute x and y for (0, 0))

y = 0 - 1

y = -1 (Correct)

0 = -x - 1

-x = 1 - 0

-x = 1 (Incorrect)

~Check

{x<−3y≤−x−1

0 < -3(0) ≤ 0 - 1

0 < 0 ≤ -1

*Note* Since the line isn't near the origin, the points (0, 0) don't satisfy the equation.

-------------------------------------------------

Answer:

{x<−3y≤−x−1

-------------------------------------------------

Hope This Helped! Good Luck!

Answer:

Perimeter = 89mm

area= 528 or 220

Step-by-step explanation:

hope this is useful

Answer:

Perimeter is 99 because 22+44+15+18=99

Area is 396 because 22+44=66÷2=33x12=396

The formula for the calculating the are of trapezium is a+b÷2xheight I hope this helped I gave you the formula to calculate the area of trapezium as well just to give extra help! Your welcome!

Final answer:

To simplify an algebraic equation, combine like terms, reduce fractions, and cancel factors; multiply or divide both sides by the same number if needed, and check your work by substituting values back into the original equation.

Explanation:

Simplifying Algebraic Equations

To simplify an algebraic equation, you need to eliminate terms wherever possible. This process may involve combining like terms, reducing fractions, and canceling out factors. Multiplication or division by the same number on both sides of the equation does not change the equation's equality, so apply these operations carefully to all terms. Often, you'll want to collect constants inside the parentheses to consolidate them into a single value, making the equation simpler. After simplifying, it's important to check your answer to ensure that it is reasonable, which may involve plugging the solution back into the original equation or assessing the steps you've taken to make sure no errors were made.

Let's consider an example:

Simplify the equation by dividing both sides by a common factor, if applicable.

Collect like terms together and simplify further.

Check the simplified equation by substituting numbers to see if both sides remain equal or by ensuring logical algebraic steps were taken.

Remember, solving for an unknown variable requires doing the same operation on both sides of the equation, thereby maintaining balance. Systematic simplification and attentive checking are your keys to mastering algebraic equations.

Answer:

-4 and 6

Step-by-step explanation:

sum means +

-4+6=2

difference means -4-6=10

The sum of two integers is 2 and their difference is 10 then the two integers will be -4 and 6 and this can be determined by using the arithmetic operations.

Given :

Let the two integers be 'a' and 'b'. Then the sum of the two integers will be:

a + b = 2   ---- (1)

The difference between the two integers will be:

a - b = 10  ----- (2)

Now, solve the equation (1) for 'a'.

a = 2 - b --- (3)

Now, put the value of 'a' in equation (2).

2 - b - b = 10

2 - 2b = 10

2b = -8

b = -4

Put the value of 'b' in equation (3).

a = 2 - (-4)

a = 2 + 4

a = 6

Therefore, the correct option is D) -4 and 6.

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Answer:

32,470

Step-by-step explanation:

since there is a 7 in the ones place it will chnage the 6 to a 7 to make it 32,470

In order to find the answer to this question you must find the tenth place value and look to the right of the tenth place value and if the value next to the tenths higher then five you round up.

[tex]32,467[/tex]

[tex]Tenths=67[/tex]

[tex]7>5[/tex]

[tex]32470[/tex]

[tex]=32,470[/tex]

Therefore the answer is "32,470."

Hope this helps.

Step-by-step explanation:

The easiest thing to do here is:

4x + 2 = -2 and 4x + 2 = 26

Just know whaever you get for x is greater or less than the actual answer.

4x + 2 = -2

      - 2  - 2

 4x = -4

 [tex]\frac{4x}{4} = \frac{-4}{4}[/tex]

x = -1 <--- Because -2 is supposed to be greater than x, x equals any number less than -1 but not -1.

4x + 2 = 26

     - 2    - 2

  4x = 24

  [tex]\frac{4x}{4} = \frac{24}{4}[/tex]

x = 6 <--- Because 26 is supposed to be less than x, x equals any numbey greater than 6 but not 6

Answer:

-1 > x OR 6 < x

Step-by-step explanation:

4x + 2 > 26

- 2 - 2

___________

4x > 24

__ ___

4 4

x > 6

__________________________________________________________

4x + 2 < −2

- 2 - 2

___________

4x < -4

__ __

4 4

x < -1

The above answers are written in reverse, which are the exact same result.

I am joyous to assist you anytime.

Answer:$825. 00

Add $25.+50. For week 1 then add $25.each additional week for 6weeks.

Step-by-step explanation:

Answer:

4x - 9y = 3

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

4x - 8 = 9y - 5 ( subtract 9y from both sides )

4x - 9y - 8 = - 5 ( add 8 to both sides )

4x - 9y = 3 ← in standard form

The original equation 4x - 8 = 9y - 5 can be rearranged to the standard form by initially adding 8 to both sides and then subtracting 9y from both sides. The final equation in standard form is 4x - 9y = 3.

The given equation is in the form of 4x - 8 = 9y - 5. To convert the equation to standard form, we'll need to rearrange it so all variables and constants are on one side of the equation. Standard form is typically written as Ax + By = C. Here are the steps to do that:

So, the

standard form

of the given equation is 4x - 9y = 3.

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