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The equation of the line is ,y= -9x+5.

Acc to our question-,

We should use the slope-intercept formula to solve this problem.

The point-slope formula states:= [ y = mx + c]

Where m is the slope and c is the y-intercept for the point (0,y1)

Substituting the information provided we get the equation: y= -9x+5.

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Answer:

10, 17

Step-by-step explanation:

let the number be n then the other number is n + 7 and

n + n + 7 = 27

2n + 7 = 27 ( subtract 7 from both sides )

2n = 20 ( divide both sides by 2 )

n = 10

n + 7 = 10 + 7 = 17

the numbers are 10, 17

Perimeter of triangle BCF is 19.24 units. Area of triangle BCF is 15 [tex]units^{2}[/tex].

Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]

Perimeter = a + b + c

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

      s = [tex]\frac{a+b+c}{2}[/tex]

Given, B(3,2), C(1,-2), F(-3,5).

BC = a  = [tex]\sqrt{(3-1)^{2} +(2+2)^{2} }[/tex]

            = [tex]\sqrt{2^{2} +4^{2} }[/tex]

            = [tex]\sqrt{4+16}[/tex]

            = [tex]\sqrt{20}[/tex]

            = 4.47 units

CF = b = [tex]\sqrt{(1+3)^{2} +(-2-5)^{2} }[/tex]

           = [tex]\sqrt{4^{2} +7^{2} }[/tex]

           = [tex]\sqrt{16+49}[/tex]

           = [tex]\sqrt{65}[/tex]

           = 8.06 units

BF = c = [tex]\sqrt{(3+3)^{2} +(2-5)^{2} }[/tex]

           = [tex]\sqrt{6^{2} +3^{2} }[/tex]

           = [tex]\sqrt{36+9}[/tex]

           = [tex]\sqrt{45}[/tex]

           = 6.71 units

Perimeter = a + b + c

                = 4.47 + 8.06 + 6.71

                = 19.24 units

s = [tex]\frac{a+b+c}{2}[/tex]

 = [tex]\frac{19.24}{2}[/tex]

 = 9.62

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

        = [tex]\sqrt{9.62(9.62-4.47)(9.62-8.06)(9.62-6.71)}[/tex]

        = [tex]\sqrt{9.62*5.15*1.56*2.91}[/tex]

        = [tex]\sqrt{224.91}[/tex]

        = 14.99

        ≈ 15  [tex]units^{2}[/tex]

Hence, perimeter is 19.24 units and area is 15  [tex]units^{2}[/tex].

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The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.

Comparing one quantity to another is what it is. For instance, the weight ratio is 1:3 if you weigh 30 kg and your father weighs 90 kg.

Given:

The ratio of vertical and horizontal distance = 1:12,

The vertical distance of  Mrs. Giles's business  = 28 inches,

If for every one unit of vertical distance, the ramp must have 12 units of horizontal distance, so or 28 inches vertical distance the horizontal distance would be = 28 × 12 = 336 inches,

([tex]1 feet = 12inches[/tex])

= 336 / 12 = 28 feet

Therefore, The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.

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Answer:

1/2=0.5

Step-by-step explanation:

-2+4/5°-1=1/2

Answer:

Step-by-step explanation:

Given:

2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10

factor it

I used MatLab   roots(x)  to find these so I kinda cheated :P

-2.5,  -2 ,  1

so we know  -2 is a factor and,  then

x+2=0    is a factor

so the "x+2"  answer C)

A golf club costs $342 at retail. The markup rate is 71.4% if the golf store has increased the price by $42.

Given,

The difference in prices is  $342 - $42 = $300

So, we need to find what percentage of 42 is 300

We do this by dividing: 300/42 = 7.14

which is 71.4 %.

So, the markup is  71.4 %.

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Answer:

c

Step-by-step explanation:

cause -14w-3-(5w)

-14w-5w-3

-19w-3

The runner's speed If a runner traveled a distance of d(h)=/16h4 in time t(h) = 3h^4 - 3h^3 -5h^2 is  4 /3h^2 - 3h -5h.

The concept that will be used to calculate this is the concept of speed which is the ratio of the distance per time which can be expressed as

speed = distance/time

Then we were given distance as d(h)=/16h^4

time as  t(h) = 3h^4 - 3h^3 -5h^2

Speed = [tex]\sqrt{16h^4} /3h^4 - 3h^3 -5h^2[/tex]

Then we will have 4h^2 /3h^4 - 3h^3 -5h^2

then  take h^2 from both the numerator and denominator and then cancel them , then we will have

= 4 /3h^2 - 3h -5h.

Therefore, the first option is correct.

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The completion of the following accounting ratios is as follows:

A. Profit margin on net sales is 31.6%.

B. Acid test is 86.0%.

Accounting ratios enable financial analysts to understand the relative magnitude of one financial statement account to another.

By their nature, accounting ratios compare or represent an entity's financial performance or position in relative terms.

Current assets = $13,000

Inventory = $4,400

Current liabilities = $10,000

Net income = $7,700 Net sales = $24,400

The profit margin on net sales = Net Income ÷ Net Sales x 100

= $7,700 ÷ $24,400

= 31.6%

Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities

= ($13,000 - $4,400) ÷ $10,000

= 0.86

= 86%

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No, the data provided does not give good evidence that ACME’s penetration rate for widgets is greater than 40%, Test at the

2.5% level of significance

P-value in the data is 40% and this refers to the probability that the assumed penetration rate is greater tan 40 %

The central limit theorem is frequently employed in situations when it is necessary to identify the features of the population but it is challenging to analyze the entire population.

The central limit theorem gives the formula

Z = (X - μ) / σ

Definition of variables

sample mean, X = 185

population mean, μ  = ?

standard deviation, σ = ?

sample size, n = 185

significance level = 2.5% = 0.025

confidence level = 1 - significance level = 1 -  0.025 = 0.975 = 97.5%

z score, z

Z score for 97.5% confidence level = 1.96

substituting into the formula

Z = (X - μ) / σ

The given variables are not enough for the calculation

population mean, μ  = ?

standard deviation, σ = ?

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Solution of the given inequality -18 + x < 16 is equal to x < 34.

As given in the question,

Given inequality is equal to :

-18 + x < 16

Get the value of the variable x by adding 18 both the side of the inequality we get,

-18 + x + 18 < 16 + 18

Collect all like terms together we get,

⇒ x + (-18 + 18 ) < 34

⇒ x + 0 < 34

Solution of the inequality -18 + x < 16 is given by

⇒ x < 34

For the given inequality -18 + x < 16 the value of variable x is less than 34.

Therefore, solution of the given inequality -18 + x < 16 is  x < 34.

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Answer:

14 and 15

Step-by-step explanation:

[tex]196<201<225 \\ \\ \sqrt{196}<\sqrt{201}<\sqrt{225} \\ \\ 14<\sqrt{201}<15[/tex]

Answer:

1.3% decrease

Step-by-step explanation:

% change = (9.69 - 9.56) / 9.69) x 100 = 1.3% decrease

9.69-9.56 = 0.13

0.13/0.69= 0.0134158972

Multiply by 100 and you get 1.34158927

Round to nearest tenth and you get = 1.3%

Therefore, the percentage decrease is 1.3

The cost of the sales tax in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The sales tax percentage in Texas = 5 %

                                                          = 5 / 100

                                                          = 0.05

The cost of 1 bag of dog food in Houston = $ 52

Now ,

The sales tax cost is calculated by the equation ,

The sales tax cost =
Sales tax percentage in Texas x cost of 1 bag of dog food in Houston

The sales tax cost = $ 52 x 0.05

                              = $ 2.60

And , the total cost of 1 bag of dog food = cost of 1 bag of dog food in Houston + sales tax cost

Total cost of 1 bag of dog food = $ 52 + $ 2.60

                                                   = $ 54.60

Therefore , the sales tax cost is $ 2.60

Hence , the sales tax cost to pay in Houston is $ 2.60 and the total cost of bag of dog food is $ 54.60

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Answer:

Step-by-step explanation:

I believe that the volume of the rectangular prism is 512.

Explanation: V = whl = 8 · 8 · 8 = 512

V=Volume

W= Width

H= Height

L= Length

The total number of degrees the temperature changed in the 6 hours is 12°F

Here,

The temperature dropped 2°F every hour for 6 hours.

We have to find,

The total number of degrees the temperature changed in the 6 hours.

Fahrenheit is a scale for measuring temperature, in which water freezes at 32 degrees and boils at 212 degrees. It is represented by the symbol ° F.

Now,

The temperature dropped 2°F every hour for 6 hours.

1 hour =  2°F

6 hour = 6 x 2 = 12°F

Hence, The total number of degrees the temperature changed in the 6 hours is 12°F.

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The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

As per the given,

Percentage of people who notice the speed limit = 84%

The percentage of people who notice the sign and follow the speed limit is 75%.

Therefore, 84% - 75%  = 9% are the percentage speeding and noticed.

Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".

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The critical points of the given inequality are; x=-6 and x=2

1) When the denominator is equal to zero, at that point, we will have a critical point.

We are given the inequality;

(2x + 5)/(x - 2) ≥ (x - 1)/(x - 2)

Thus, x - 2 = 0

x = 2.

Thus, x = 2 is a critical point

2) Simplify the numerator to get the expression such that p(x) ≥ 0 or p(x) ≤ 0.

Thus, at p(x) = zero, we have other critical point(s)

Multiply both sides by (x - 2) to get;

2x + 5 = x - 1

2x - x = - 1 - 5

x = - 6

Then, the two critical points are x = 2 and x = - 6.

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2x+3  x-3 those are correct

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a reflection across the line x = -3 followed by a reflection across the line y = x.

Given that both triangles are congruent, we can infer or deduce that there were no dilations or contractions. Hence, since we are moving in a clockwise direction, we can submit that this was not a rotation but a reflection.

Hence the first sequence of reflection was such that:

∆ABC reflects onto ∆A′B′C′ across the line x = -3; followed by
a reflection across the line y = x.

Note that in geometry, reflection refers to the mirror image of an image. The line through which an image reflects is called the line of reflection.

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Answer:

x=3

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!

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

So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!

The distance to the point is less than c=10, so the point is inside the circle.

Given that, (a, b) = (5, –2) and c = 10.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

Part A:

Use of the Pythagorean theorem gets you to the equation for a circle in essentially one step:

Sum of squares of sides = square of hypotenuse

(x -a)²+(y -b)² = c² circle centered on (a, b) with radius c.

Part B:

The circle will be defined for values of x in the domain f ± c, and for values of y in the range b ± c.

domain: 5 ± 10 = [5, -5]

Range: -2 ±10 = [8, -11]

Part C:

The distance from point (10, 2) to (a, b)=(5, -2) is

c² = (10-5)² +(-2-2)²

c² = 25+16

c² = 41

c=√41

c=6.4

The distance to the point is less than c=10, so the point is inside the circle.

Therefore, the distance to the point is less than c=10, so the point is inside the circle.

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Answer:

0.13 km

Step-by-step explanation:

Rearrange the formula to solve for [tex]h[/tex]:

[tex]D(h)=111.7\sqrt{h}[/tex]

[tex]\frac{D(h)}{111.7}=\sqrt{h}[/tex]

[tex](\frac{D(h)}{111.7})^2=(\sqrt{h})^2[/tex]

[tex](\frac{D(h)}{111.7})^2=h[/tex]

Then, substitute the distance of 40 km:

[tex](\frac{40}{111.7})^2=h[/tex]

[tex]0.13\approx{h}[/tex]

Answer:48

Step-by-step explanation:12x4=48

Answer:

  Andrew failed to change the direction of the inequality

Step-by-step explanation:

You want to know the mistake in Anderw's work solving the inequality ...

  −4(x + 8) + 25 ≤ −2 + 1(x − 50)

−4(x + 8) + 25 ≤ −2 + 1(x − 50)

−4x − 32 + 25 ≤ −2 + 1x − 50

−4x − 7 ≤ 1x − 52

−5x ≤ −45

x ≥ 9

Andrew's mistake was failing to reverse the inequality symbol when dividing by a negative number (-5) at the last step.

__

Additional comment

The last steps of the solution could be written ...

  -5x ≤ -45

  45 ≤ 5x . . . . . . . add 5x+45 to both sides

  9 ≤ x . . . . . . . . . divide by 5 (no reversal of ≤ is needed)

using the power rule of logarithm, the value of a is 1.1021.

In the given question we have to determine a so that [tex]A(t)=A_{0}a^t[/tex] describes the amount of nitrogen-16 left after t seconds, where [tex]A_{0}[/tex] is the amount at time t=0.

The given exponential function is [tex]A(t)=A_{0}a^t[/tex].

The amount of nitrogen-16 is approximately 7.13 seconds.

According to the question, [tex]A(t)=A_{0}/2[/tex] and t = 7.13 seconds.

Putting the value in the given function;

[tex]A_{0}/2=A_{0}a^{7.13}[/tex]

Divide by [tex]A_{0}[/tex] on both side, we get

[tex]1/2=a^{7.13}[/tex]

Taking In on both side

[tex]\text{In}(1/2)=\text{In}(a^{7.13})[/tex]

Using the power rule of logarithm

In(1/2)=7.13In(a)

Divide by 7.13 on both side

In(a)= -0.693/7.13

In(a)= -0.0972

Taking exponential on both side

[tex]e^{\text{In}(a)}= e^{-0.0972}[/tex]

a = 1.1021

Hence, the value of a is 1.1021.

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