Line A (y= x + 2) is transformed into Line B (y=3x + 1) . which best describes the new slope and y-intercept? the slope is ___, and the line is shifted ____. a) steeper b) flatter -----a) upward b) downward

Answer:

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Step-by-step explanation:

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Answer:

16

Explaination:

Answer:n the metric system, "milli" means 1/1,000 and "kilo" means 1,000. This means that a milligram is 1/1,000 of a gram, and a kilogram is 1,000 grams. So a kilogram is much heavier than a milligram; in fact, a kilogra

Step-by-step explanation:

The total amount of wood to build the shelves will be;

⇒ 17\(\frac{1}{4}\) feet

A fraction is a piece of a whole number and a technique to divide a number into pieces that are each the same.

Or, a fraction is a number that is stated as a quotient.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

To build the bookshelf, Tim want the three horizontal length of each length 3\(\frac{2}{3}\) feet and two vertical length with each length 2\(\frac{5}{8}\) feet.

Now, Find the total lengths for the amount of wood as;

The length of each horizontal = 3\(\frac{2}{3}\) feet

And, The vertical length = 2\(\frac{5}{8}\) feet

So, Total horizontal length = 3 × 3\(\frac{2}{3}\)

                                        = 3 x 11/3

                                       = 11 feet.

And, Vertical length = 2 × 2\(\frac{5}{8}\) feet.

                                  = 2 × 21/8

                                  = 5\(\frac{1}{4}\) feet

Thus, Total length of wood = 11 + 21/4 feet

                                        = ( 44 + 21 ) / 4

                                        = 69 / 4 feet

                                       = 17\(\frac{1}{4}\) feet

Therefore,

The total amount of wood to build the shelves will be;

⇒ 17\(\frac{1}{4}\) feet

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Answer: B: 20

Step-by-step explanation: We can take 40% as a fraction to make it 4/10, simplifying gives 2/5. 2/5 of 50 is 20!

Hope this Helps!

Answer:

Step-by-step explanation:

Hey, I'm not sure if I am right, but I hope it can create a spark or something.

8. Find x

10x - 1 = 14x - 37      Combine like terms

     +37        +37

10x + 36 = 14x          Combine like terms

-10x          -10x

    36 = 4x                Divide to isolate x

    36 = 4x

     4      4

    9 = x        

You can also do this method with the others.

PS: I am still not sure if this is the right method, lol. I just really want to help.

Answer:

8% is the sales tax rate

Step-by-step explanation:

I'm not the best with math but the way I found the answer was by first using my local sales tax rate and determining how much the tax would be.

490 * 8.75% = 42.875

Knowing that this amount was higher than in the equation, I lowered the sales tax to 8% (0.08)

490 * 8% = 39.2

Hope this was somewhat helpful

Answer:

\(8.3125\)pounds

Step-by-step explanation:

We are given that

Density of ethyl acetate at 25 degrees =\(0.902g/ml\)

We have to find the number of pounds in 133 ounces weigh.

To find the number of pounds in 133 ounces we will use unitary method

By using unitary method

We know that

1 ounce=0.0625 pounds

133 ounce=\(133\times 0.0625\)pounds

133 ounce=\(8.3125\)pounds

Hence,8.3125 pounds would 133 ounces weigh.

Answer:

x =35

y=72.5 and the 2nd y also equals 72.5

Step-by-step explanation:

x=35- it is a vertical angle

both ys + 35 makes a straight line (180)

2y+35=180

2y=145 (subtract 35 from both sides)

y=72.5 (divide by 2)

Answer: 1

Step-by-step explanation:

First you need to multiply 3 x 3 (9), because that's all 3 squared means.

Now the equation should be 9x-6x+3=0

Next we need to combine like terms. Do 9x - 6x which should give you 3x

Now your equations should be 3x+3=0

Now for the somewhat harder part...

Under the three (the one without the x) write -3 and under the zero write the same thing.  the +3-3 cancels out so just put a line or something across it.

0-3= -3

so now you should have...

3x=-3    ignore the 3x, at this point it's useless in getting the answer because it would cancel out.

-3 divided by -3  is 1 because a negative (-)  divided by a negative (-) equals a positive (+).

The answer should be  x = 1

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

Answer:

The right solution is:

(a) 0.8849

(b) 12.28%

(c) 4.9935

(d) 28004

Step-by-step explanation:

Given:

Mean,

= 4.5

Standard deviation,

= 0.3

(a)

P(x > 4.14)

As we know,

⇒ \(z = \frac{4.14-4.5}{0.3}\)

      \(=-1.20\)

then,

⇒ \(P(z>-1.20) = P(z<1.20)\)

                          \(=0.8849\)

(b)

P(4.8 < x < 5.04)

= \(P(\frac{4.8-4.5}{0.3} < \frac{x-\mu}{\sigma} < \frac{5.04-4.5}{0.3} )\)

= \(P(1<z<1.80)\)

= \(P(z<1.80)-P(z<1)\)

= \(0.9641 -0.8413\)

= \(0.1228\)

or,

= \(12.28\) (%)

(c)

P(x > x) = 0.05

z value will be,

= 1.645

⇒ \(1.645 = \frac{x - 4.5}{0.3}\)

         \(x = 4.9935\)

(d)

P(x < 5.01)

⇒ \(z = \frac{x- \mu}{\sigma}\)

      \(=\frac{5.01-4.5}{0.3}\)

      \(=1.7\)

P(z < 1.70) = 0.9554

⇒ \(n = \frac{27875}{0.9954}\)

       \(=28004\)

\( \frac{2}{5} \: \: \: of \: \: \: \frac{9}{10} \\ = \frac{9}{25} \)

Answer:

9/25

Step-by-step explanation:

(2/5) x (9/10) = 18/50

= 9/25

Answer:

The ratio of a unit rate of kilometers to miles of the distance measured by the odometer is 1 km : 0.63 miles.

Step-by-step explanation:

Given;

distance measured by odometer in kilometer, = 810 km

distance measured by odometer in miles, = 510 miles

The  ratio of a unit rate of kilometers to miles of the distance measured by the odometer is calculated as;

\(d = \frac{810 \ km}{510 \ miles} \\\\d = \frac{810 \ km \ \times \ \frac{1}{810 \ km} }{510 \ miles \ \times \frac{1}{810 \ km} } \\\\d = \frac{1 \ km}{\frac{510}{810} \ miles } \\\\d = \frac{1 \ km}{\frac{17}{27} \ miles} \\\\d = 1 \ km : \frac{17}{27} \ miles\\\\d = 1 \ km : 0.63 \ miles\)

Therefore, the ratio of a unit rate of kilometers to miles of the distance measured by the odometer is 1 km : 0.63 miles.

Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

Answer:

Step-by-step explanation:

This is the formula to find the sum of the first

n

terms of the sequence. To evaluate it, the values of the first and

n

the terms must be found .Sn=n2⋅(a1+an)

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

6

to the previous term in the sequence gives the next term. In other words,

an=a1+d(n−1)x Arithmetic Sequence:

d=6 This is the formula of an arithmetic sequence X an=a1+d(n−1)Substitute in the values of a1=4 and d=6 x an=4+(6)(n−1)Simplify each term.

an=4+6n−6 Subtract 6 from 4 x an=6n−2 Substitute in the value of N to find the N the term x a5=6(5)−2 Multiply 6 by 5 x a5=30−2 Subtract 2 from 30 x a5=28 Replace the variables with the known values to find

S5 x S5=52⋅(4+28)Add 4 and 28 x S5=52⋅32

Cancel the common factor of

2.

S5=5⋅16 Multiply 5 by 16 x S5=80

Convert the fraction to a decimal.

S5=80

Answer:

  1 1/2 miles

Step-by-step explanation:

The problem statement tells us Mara ran 4/5 of 1 7/8 miles.

The procedure usually recommended for multiplying mixed numbers is to convert them to improper fractions first. Doing that, we find the product to be ...

  \(\dfrac{4}{5}\times1\dfrac{7}{8}=\dfrac{4}{5}\times\dfrac{1\times8+7}{8}=\dfrac{4}{5}\times\dfrac{15}{8}\\\\=\dfrac{4\cdot3\cdot5}{5\cdot4\cdot2}=\dfrac{3}{2}=\boxed{1\dfrac{1}{2}}\)

Mara ran 1 1/2 miles.

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

The sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A′′B′′C′′D′′ is: Trapezoid ABCD was reflected across the y-axis and then translation till 7 units up.

A translation relocates a figure without changing its size or orientation. The trapezoid was translated 7 units up and 12 units left in this case, which means that every point on the original trapezoid was moved 7 units up and 12 units left.

The trapezoid was reflected across the y-axis after translation, which means that each point was moved to the opposite side of the y-axis.

When these two transformations are combined, they produce a new figure that is congruent with the original but in a different position.

Thus, the correct transformation sequence to produce trapezoid A''B''C''D'' involves a translation followed by a reflection across the y-axis.

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Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b.  For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).

Given the equation 17v = 62, we can take the logarithm base 17 of both sides:

log(17^v) = log(62)

v*log(17) = log(62)

Dividing both sides by log(17) gives us:

v = log(62) / log(17)

This is the solution for v, the unknown variable in the equation.

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Answer:

B. 35

Step-by-step explanation:

180° - 125° = 55° (value of the inside of the triangle)

180° - 90° = 90°

p + 90° + 55° = 180° (total angle in triangle)

p + 145° = 180°

p = 180° - 145°

p = 35°

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

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a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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The eighth grade class has a more consistent time spent on math homework. This can be seen in the histogram, which shows that the eighth grade class has a peak at 20 minutes.

Consistent refers to something that remains unchanged or is regular and dependable over time. It is a dependable and steady quality or state. Consistency is important in many areas of life, from professional and personal relationships to commitments and expectations. Consistent behavior is sometimes a sign of reliability, trustworthiness, and dependability.

Consistent actions are important for maintaining relationships and for achieving goals. Consistency helps to create stability, reliability, and predictability. Without consistency, it would be difficult to know what to expect from people and situations.

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Mr. Sullivan's class typically spends more time on math homework, as the mean of their sample is slightly higher than that of Mrs. Farrington's class.

Spend is an action that involves exchanging money for goods, services, or other items of value. When someone spends money, they take money out of their account or wallet and use it to purchase something.

Mrs. Farrington's class has a more consistent time spent on math homework, as the range of the sample is smaller than that of Mr. Sullivan's class.
For Mr. Sullivan's class:
The mean of the sample is 11.6, so the mean of the population is expected to be 11.6 as well. The standard deviation of the sample is 3.41. Therefore, the expected standard deviation of the population is 3.41.
Using the 68-95-99.7 rule, we can calculate the following:
68% of the population is expected to spend between 8.79 and 14.41 minutes on math homework.
95% of the population is expected to spend between 5.38 and 17.82 minutes on math homework.
99.7% of the population is expected to spend between 1.97 and 21.23
minutes on math homework.
Therefore, we can expect approximately 82 (68% of 120) students in Mr. Sullivan's class to spend between 9 and 12 minutes on math homework.

For Mrs. Farrington's class:
The mean of the sample is 11 and the standard deviation is 2.87. Therefore, we can expect the mean and standard deviation of the population to be 11 and 2.87, respectively.
Using the 68-95-99.7 rule, we can calculate the following:
68% of the population is expected to spend between 8.26 and 13.74 minutes on math homework.
95% of the population is expected to spend between 5.39 and 16.61 minutes on math homework.
99.7% of the population is expected to spend between 1.72 and 19.48 minutes on math homework.
Therefore, we can expect approximately 68 (68% of 100) students in Mrs. Farrington's class to spend between 9 and 12 minutes on math homework.

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Answer: x=-4

Step-by-step explanation:

-4x=16

Divide by -4 on each side to cancel it out

x=-4

x-intercept means the value of x at y = 0

y-intercept means the value of y at x = 0

the equation is

Substitute y by 0 to find the x-intercept

Divide both sides by 7 to find x

The ordered pair of x-intercept is (3, 0)

Substitute x by 0 to find the y-intercept

Divide both sides by -3 to find y

The ordered pair of the y-intercept is (0, -7)