Use the given D to find the range of each function: a f(x)=3x−5, D={−1, 0, 3}

The factor outside the parentheses is -1. Distribute using that factor.

2 - (4 - x) = 7x - 5x

-1 * 4 = -4 and -1 * -x = x

2 - 4 + x = 7x - 5x

Simplify.

-2 + x = 2x

x = 2x + 2

-x = 2

x = -2

x = -2

Answer:

B. 60.03 meters.

Step-by-step explanation:

We use the equation of motion under gravity:

h = ut - 0.5gt^2      where h = height, t = time and u = initial velocity.

h = (0)(3.5) - 0.5 * -9.8 * 3.5^2

= 60.025 m.

The height of the tower is found by utilizing the equation of motion for free fall. When the given values are input into the equation, the result is 60.03 meters. Hence, the correct answer is option B (60.03 meters).

This is a question about the physics of free fall motion. In problems of free fall, we consider the motion under the gravitational force alone. We disregard air resistance to simplify our calculations. The height (h) of the tower can be calculated using the equation of motion: h = 0.5 * g * t^2, where g is the acceleration due to gravity and t is the time taken for the ball to reach the ground.

Plugging the values into the formula, h = 0.5 * -9.8 m/s^2 * (3.5 s)^2 = -0.5 * -9.8 * 12.25 = 60.03 meters. The distance is positive, because we are considering the magnitude of the height, rather than the directional displacement. So, option B (60.03 meters) is the correct answer.

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Its 70%

392/560 = 0.7

0.7 * 100 = 70%

Answer:

  11/18

Step-by-step explanation:

The fraction you spent is the ratio of the amount you spent to the amount you started with:

__

  $11/$18 = 11/18 . . . . fraction spent on movie tickets

Check the picture below.

[tex]\bf \textit{area of a trapezoid}\\\\A=\cfrac{h(a+b)}{2}~~\begin{cases}a,b=\stackrel{bases}{parallel}\\\qquad ~sides\\h=height\\\cline{1-1}a=4\\b=7\\h=7\end{cases}\implies A=\cfrac{7(4+7)}{2}\implies A=\cfrac{7(11)}{2}\\\\\\A=\cfrac{77}{2}\implies A=38\frac{1}{2}[/tex]

The area of polygon ABCD is found by dividing it into two rectangles and calculating their areas separately, which are then added together to get a total area of 77 square units.

Calculating the Area of Polygon ABCD:

The area of polygon ABCD with vertices at A(-4,2), B(3,2), C(3,-5), and D(-4,-2), we can split the polygon into two rectangles. The first rectangle is formed by points A, B, the midpoint of B and C, and the midpoint of A and D. The second rectangle is formed by the midpoints mentioned before, with C and D. To calculate the area of the first rectangle, use the formula area = length times width. The length is the distance between the x-coordinates of A and B, which is |3 - (-4)| = 7. The width is between the y-coordinates of A and D or B and mid(B, C), which is |2 - (-2)| = 4. Thus, the area of the first rectangle is 7 times 4 = 28 square units.

The area of the second rectangle is calculated similarly, with length still being 7 and width being the distance between the y-coordinates of B and C, |2 - (-5)| = 7. Therefore, the area of the second rectangle is 7 times 7 = 49 square units. Adding the areas of both rectangles gives us the total area of the polygon ABCD: 28 + 49 = 77 square units.

Answer:

0.3212, 0.332, 0.340, 0.3412, 0.342, 0.348, 0.35, 0.352

Answer:

See below.

Step-by-step explanation:

0.3212, 0.332, 0.340, 0.3412, 0.342, 0.348, 0.35, 0.352.

Answer:

.25

Step-by-step explanation:

8/32 = 1/4

1/4 = .25

Answer:

0.25

Step-by-step explanation:

Answer:

a = 15

Step-by-step explanation:

Given

3a + b = 54 ← substitute b = 9

3a + 9 = 54 ( subtract 9 from both sides )

3a = 45 ( divide both sides by 3 )

a = 15

An equation is formed when two equal expressions. The value of a in the equation 3a+b=54, when b equals 9 is 15.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given statement "3 a plus b equals 54" in terms of the equation can be written as,

3a + b = 54

Given an equation 3a+b=54. Also, the value of b in the given equation is 9. Therefore, the value of a in the given equation can be written as,

3a + 9 = 54

Subtract 9 from both sides of the equation,

3a + 9 - 9 = 54 - 9

3a = 45

Divide both the sides of the equation by a,

3a/3 = 45/3

a = 15

Hence,  the value of a in the equation 3a+b=54, when b equals 9 is 15.

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Answer:

the outlier is 3

Step-by-step explanation:

Answer:34

Step-by-step explanation:

The answers to Unit 3 Homework 1 in an AP Chemistry subject are listed with careful instruction to students to understand the related concepts and why the answers are correct.

Based on the data provided it appears you are referring to Unit 3 Homework 1 of an Advanced Placement Chemistry subject. Here's a breakdown of the answers:

Please make sure to review each question individually, understand the related concepts and why these answers are correct. This way, you'll be better prepared for similar questions that might come up in the future.

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Answer:

The statement is false. 12 ≠ -18

Step-by-step explanation:

2(3x + 6) = 3(2x - 6)

6x + 12 = 6x - 18

-6x           -6x

12 ≠ -18

Answer:

21

Step-by-step explanation:

If she does 3 pushups every morning, than you need to multiply 3x7

3 sets of 8 pushups a day (can't forget that information!! its critical the the problem!!!) 7 days a week

3*8 = 24

24*7 = 168

168 pushups a week

Answer:

Step-by-step explanation:

Answer:

The solution to 10m -28 = 6 -7m​ is m = 2.

Step-by-step explanation:

Given 10m - 28 = 6 - 7m ⇒ 10m + 7m = 6 + 28 ⇒ 17m = 34 ⇒m= 34/17

⇒ m = 2.

Answer: 47/8

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we will put our new number over our old denominator and we have our answer which is 47/8.

Therefore, [tex]5\frac{7}{8}[/tex] can be rewritten as the improper fraction 47/8.

Answer:

[tex]x^3-5x^2-2x+24[/tex]

Step-by-step explanation:

the polynomial function of least degree whose only zeros are -2, 3, and 4

Factors are -2,3 and 4

First we write the polynomial in factor form

If 'a' is a zero of the polynomial then (x-a) is a factor

Factors are -2,3 and 4

Polynomial is [tex](x-(-2))(x-3)(x-4)[/tex]

[tex](x+2)(x-3)(x-4)[/tex]

Now we multiply all the parenthesis

[tex](x+2)(x-3)(x-4)[/tex]

[tex](x^2-3x+2x-6)(x-4)[/tex]

[tex](x^2-x-6)(x-4)[/tex]

[tex]x^3-4x^2-x^2+4x-6x+24[/tex]

[tex]x^3-5x^2-2x+24[/tex]

Answer:

x>48/5 or x<-3/2

Step-by-step explanation:

Solve for x

a) 12x + 7 < -11

12x < -11-7

12x < -18

x < -18/12

⇒ Simplify: divide the numerator by 6

x < -3/2

b) 5x – 8 > 40

5x > 40+8

5x > 48

x > 48/5

Therefore, x>48/5 or x<-3/2.

Answer: 1 1/2

Step-by-step explanation: 5/8 + 7/8

= 12/8

simplifies to 1 1/2

Answer:

$58.50

Step-by-step explanation:

It is given that the the student council pays

For per french fry = $0.85

For per soda fry = $1.20

Discount on the combo of  fries and soda = $0.75

Total revenue for one combo = $0.85 + $1.20 - $0.75 = $1.30

Since the total revenue for one combo is $1.30, therefore the total revenue for 45 combo is

Total revenue for 45 combo = 45 × $1.30 = $58.50

Therefore, they will make $58.50 if they sell 45 combos.

Answer:

2^(-n^2+n+1)

Step-by-step explanation:

2^(n+2)*2^(n-1)*2^(-n(n-1))=2^((n+2)+(n-1)-(n^2-n))=2^(-n^2+3n+1)

I can do it because they have the same base, so I can add the exponents.

I can write 4^n=2^2n. So I have 2^(-n^2+3n+1) / 2^2n and they have the same base again (2), so we can subtract the exponents.

2^((-n^2+3n+1)-2n)=2^(-n^2+n+1)

Answer:

8 Cups of Sugar.

Step-by-step explanation:

3x4=12 cups of water.

2x4=8 cups of sugar

Answer is 90.49095 i think not sure yet

Answer:

B. 86.3%

Step-by-step explanation:

The correct answer is C. 88.7%.

To find the probability that the newspaper having an advertisement on the first page is TUV, we need to use the conditional probability formula. The probability that an event A occurs given that event B has occurred is given by:

[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]

In this case, event A is that the newspaper is TUV, and event B is that the newspaper has an advertisement on the front page. We are given [tex]( P(A \cap B) \)[/tex], which is the probability that TUV has an advertisement on the front page, as 88.7%. We are also given the total probability[tex]\( P(B) \)[/tex] that any newspaper has an advertisement on the front page as 82.4%.

Using the conditional probability formula, we get:

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{P(\text{TUV} \cap \text{Ad})}{P(\text{Ad})} \][/tex]

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{88.7\%}{82.4\%} \][/tex]

Now, we calculate this probability:

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{88.7}{100} \times \frac{100}{82.4} \][/tex]

[tex]\[ P(\text{TUV}|\text{Ad}) = \frac{88.7}{82.4} \][/tex]

[tex]\[ P(\text{TUV}|\text{Ad}) \approx 1.0765 \][/tex]

However, probabilities cannot be greater than 1, so we must have made a mistake in our calculation. The correct approach is to realize that the total probability of 82.4% already includes the probability of TUV having an advertisement. Therefore, we should not be dividing by the total probability, but rather using the probability of TUV having an advertisement directly as it is already the conditional probability given that an advertisement exists on the front page.

The range is the y-values.

Let r = range

r = {0, -3, -9, 5, 7}

Turtle is closest to the sea level.

In which horizontal straight line, we represent integer numbers from low value to high, from left to right, is called number line.

Zero is in the middle of that line.

If we consider the number line, then in the left side of zero, we have all the negative values, where .... < -5< -4< -3< -2< -1< 0

And in the right side of zero, we have all the positive values, where 0<1<2<3<4<5 and so on....

We know that, Level zero is called the sea level.

So, if we assume number line in vertical way, then the zero will be the sea level.

Here, if we arrange levels of animals from low to high, we get,

Sea lion(-10)<Shark(-7)<Turtle(-6)<0 <Seagull(+24)

We see that, zero is in between -6 & 24

The distance between 0 & -6 is 6 units whereas between 0 & 24 is 24 units.

So, Turtle is closest to sea level.

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Sea Lion has the lowest value indicating its proximity to sea level. Hence, the correct option is second.

Sea Lion is the animal closest to sea level with a value of -10. This means it is approximately 10 meters below sea level. In comparison, the Shark has a value of -7, the Turtle has a value of -6, and the Seagull has a value of 24, making the Sea Lion the closest to sea level.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{(3^{-2})^2}{3^{-3}}\implies \cfrac{3^{-2\cdot 2}}{3^{-3}}\implies \cfrac{3^{-4}}{3^{-3}}\implies \cfrac{1}{3^{-3}\cdot 3^4}\implies \cfrac{1}{3^{-3+4}}\implies \cfrac{1}{3^1}\implies \cfrac{1}{3}[/tex]

Answer:

x > -99/4

Step-by-step explanation:

I must assume that you meant (-2/5)x -9<9/10.

This inequality has 3 terms.  The LCD is 10.  Multiply each term by 10 and reduce the result:

10(-2/5)x - 10(9) < 10(9/10), or:

-4x - 90 < 9

Adding 90 to both sides results in:

-4x < 99

Here we must divide by a negative number (that is, by -4).  This requires reversing the direction of the inequality sign:

x > -99/4 is the final solution.

Answer:

The quantity sold by Annette was $600

The quantity sold by Barb was $480

The quantity sold by Carlita was $400

Step-by-step explanation:

Let

x ----> quantity sold by Annette

y ---> quantity sold by Barb

z ---> quantity sold by Carlita

we know that

[tex]x+y+z=1,480[/tex] ----> equation A

[tex]x=y+120[/tex] ----> equation B

[tex]y+z=x+280[/tex] ----> equation C

substitute equation C in equation A and solve for x

[tex]x+(x+280)=1,480[/tex]

[tex]2x=1,480-280[/tex]

[tex]2x=1,200[/tex]

[tex]x=\$600[/tex]

Find the value of y

[tex]x=y+120[/tex]

[tex]600=y+120[/tex]

[tex]y=600-120=\$480[/tex]

Find the value of z

[tex]x+y+z=1,480[/tex]

[tex]600+480+z=1,480[/tex]

[tex]1,080+z=1,480[/tex]

[tex]z=\$400[/tex]

therefore

The quantity sold by Annette was $600

The quantity sold by Barb was $480

The quantity sold by Carlita was $400

The solution involves setting up a system of three linear equations based on the given problem. By solving these equations methodically, we find that Barb, Annette, and Carlita sold $400, $520, and $560 of clothing respectively.

The problem involves setting up and solving a system of linear equations. Here's how we approach it:

So, Barb sold $400 of clothing, Carlita sold $560, and Annette sold $520.

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To solve, multiply 5 by 5 twenty-two times. It will equal 2384185791015625. Then, multiply 5 by 5 thirteen times. It will equal 1220703125. Finally, simplify 2384185791015625/1220703125. You should get 1953125 as your answer. Therefore, 1953125 is the answer.

Edit: 5^22 means 5²² which means to multiply 5 by 5 by 5... for 22 times. It means the exponents. (Power of)

The expression 5^22/5^13 simplifies to 5^(22-13) which equals 5^9. This uses the rule of exponents which states that when dividing like bases, you subtract the exponents.

To simplify the expression 5^22/5^13, we need to apply the exponent rule which states that when you divide two powers with the same base, you subtract the exponents. In this case, we subtract the exponent of 5^13 from the exponent of 5^22. So, 5^22/5^13 = 5^(22-13) = 5^9.

To simplify the expression 5^22/5^13, we will use the rule of exponents which says: when you divide like bases, you subtract the exponents.

Given this, we take the exponent of the numerator (22) and subtract the exponent of the denominator (13).

Therefore, 5^22/5^13 simplifies to 5^(22-13), which equals 5^9.

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Answer:

the answer is

x′ = x − 3

y′ = y − 2

Step-by-step explanation:

Answer:

x′ = x − 3

y′ = y − 2

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Answer:

After these reflections, the coordinates of P' will be P'(4,-4)

Step-by-step explanation:

The question is

After these reflections, the coordinates of P' will be?

we have

Triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1)

Part 1) Reflect triangle PQR across the x-axis

we know that

The rule of the reflection of a point across the x-axis is

(x,y) -----> (x,-y)

Applying the rule of the reflection across the x-axis at the coordinates of triangle PQR

P(-4, -4) -----> P'''(-4,4)

Q(-1, -3) -----> Q'''(-1, 3)

R(-3, -1) ----> R'''(-3, 1)

Part 2) Reflect triangle P'''Q'''R''' across the y-axis

we know that

The rule of the reflection of a point across the y-axis is

(x,y) -----> (-x,y)

Applying the rule of the reflection across the y-axis at the coordinates of triangle P'''Q'''R'''

P'''(-4,4) -----> P''(4,4)

Q'''(-1, 3) ---> Q''(1, 3)

R'''(-3, 1) ---> R''(3, 1)

Part 3) Reflect triangle P''Q''R'' across the x-axis again

we know that

The rule of the reflection of a point across the x-axis is

(x,y) -----> (x,-y)

Applying the rule of the reflection across the x-axis at the coordinates of triangle P''Q''R''

P''(4,4) ---->  P'(4,-4)

Q''(1, 3) ----> Q'(1, -3)

R''(3, 1) ----> R'(3, -1)

therefore

After these reflections, the coordinates of P' will be P'(4,-4)