Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-3=-1/5(x+2); (-2, 7)
A. y=5x+7
B. y=5x+17
C. y=(1/5)x-2
D. y=-2x+3

Plz answer quickly!! Thank you :) <3

∠8=180°-92°=88°

===================

Answer:

Step-by-step explanation:

The answer is 88 degrees i got that question right.

Can you please provide the diagram.

Answer:

154 square inches

Step-by-step explanation:

Watch the attached figure of the square pizza box and the largest pizza that can fit into it.

Let the each side of the square pizza box be a inches.

Radius of the largest pizza that can fit into it = Half of the side of the pizza box = [tex]\frac{a}{2}[/tex]

So, area of the square box = Side * Side

                                             = a * a

                                             = a² square inches

It has also been given that the large box has an area of 196 square inches.

So,

Area of the box = a²

=> 196 = a²

Flipping the sides of the equation, we get

=> a² = 196

Taking square root on both the sides,

√a² = √196

a = 14 inches

So,

Side of square box = 14 inches

Radius of the largest pizza that can fit into it = [tex]\frac{a}{2}[/tex]

                                                                          = [tex]\frac{14}{2}[/tex]

                                                                          = 7 inches

Area of the largest possible pizza that could be placed into the box

= π *radius²                                       [since pizza is circular in shape]

= [tex]\frac{22}{7}[/tex] * 7²

= [tex]\frac{22}{7}[/tex] * 7 * 7

Cancelling out a pair of 7's from the top and bottom, we have

= 22 * 7

= 154 square inches

Answer:

Yes (under certain conditions)

Step-by-step explanation:

Binomial probability formula can be used if there are success and failure been discussed in the question.

The formula is given by

P(X=x) = \binom{n}{x}p^{x}q^{n-x}

where n= no. trials

p  = success

q= failure

x= point at which we need to find the probability

Here, 85 customers are surveyed, then n= 85

we will take, p= live entertainment had increased the amount of money they spent (success)

q = live entertainment had not increased the amount of money they spent (failure)

x should be defined, then only we can use binomial probability formula

Example, x= 10 customers said that the money they spent increased if the live entertainment provided.

Answer:

Yes

Step-by-step explanation:

Binomial distribution is valid for trials which consist of only two outcomes, and each trial is independent of the other.

Here 85 mall customers were randomly surveyed.  We have that each customers is independent of the other for the state o determine if the live entertainment provided had increased the amount of money they spent

Hence probability for each person  to say yes  can be taken as p and q =1-p for no reply.

There are only two outcomes.  

Also n =85 is sufficiently large to have np or nq >5

Hence the probability can be found using binomial probability formula provided p = probability for success of a single trial is given.

Answer:

80 degrees.

Step-by-step explanation:

The real question was:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The angle measurements in the diagram are represented by the following expressions.

(angle)∠A= 8x −8 and (angle)∠B= 5x +25

Solve for x and then find the measure of (angle)∠B.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x= 11 and then since both angles equal the same......we know that angle B equals 80 degrees!

Hope that helps and maybe earns a brainliest! :)

Answer: C: y = 250x + 2000; the independent variable, x, represents the number of months after buying the car and the dependent variable, y, represents the amount of money paid on the car.

Step-by-step explanation:

The equation representing the total cost of the car over time is C(t) = 2000 + 250t, where 't' (the number of months) is the independent variable and 'C(t)' (the total cost) is the dependent variable.

To write an equation for the financing offer of a car company where customers pay a $2000 down payment and then $250 a month, we use a linear equation to represent the total cost of the car (C) over time (t):

C(t) = 2000 + 250t

Here, the independent variable 't' represents the number of months, and the dependent variable 'C(t)' represents the total cost of the car at a particular time. The independent variable is the one we have control over or choose values for, and the dependent variable is the one that changes in response to the independent variable.

A recursive rule for a geometric sequence

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=-64;\ a_2=-16;\ a_3=-4;\ a_4=-1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\\\\r=\dfrac{-16}{-64}=\dfrac{1}{4}\\\\\boxed{a_1=-64;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]

Answer:

Radical form of the  expression [tex]4^{\frac{3}{2} }[/tex] is, 8

Step-by-step explanation:

Given the expression: [tex]4^{\frac{3}{2} }[/tex]

Since,  [tex]\sqrt{4^3}[/tex] is same as [tex]4^{\frac{3}{2} }[/tex]

Now, to write an exponent in radical form,

then the  denominator or the index goes in front of the radical and

the numerator goes inside of the radical.

we raise the base to the power of the numerator then:

[tex]4^{\frac{3}{2} }[/tex] = [tex]\sqrt{64}[/tex] = [tex]\sqrt{8 \times 8}[/tex] = [tex]\sqrt{8^2} = 8[/tex]

therefore, the radical form of the given expression is, 8

To qualify for the special summer camp for accelerated students, a student must score at least approximately 978 on the standardized test, considering a score within the top 16% of all scores, given a mean score of 800 and a standard deviation of 120.

In a bell-shaped or normal distribution, the mean [tex]\(\mu\)[/tex] represents the central tendency of the data, and the standard deviation [tex]\(\sigma\)[/tex] measures the dispersion or spread of the scores. To find the score required to qualify for the top 16%, we use the z-score formula: [tex]\(z = \frac{X - \mu}{\sigma}\)[/tex], where X is the score, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.

Given the mean score [tex]\(\mu = 800\)[/tex] and standard deviation [tex]\(\sigma = 120\)[/tex], the z-score corresponding to the top 16% is found using a standard normal distribution table or statistical software. The z-score associated with the top 16% is approximately z = 1.04.

Next, use the z-score formula to solve for the score X required to be in the top 16%: [tex]\(z = \frac{X - \mu}{\sigma}\)\\[/tex]. Rearranging the formula to solve for X gives us [tex]\(X = z \cdot \sigma + \mu\)[/tex]. Substituting the z-score value and the given mean and standard deviation into the equation yields [tex]\(X = 1.04 \cdot 120 + 800 = 978\)[/tex]. Hence, a student needs to score at least approximately 978 to qualify for the special summer camp for accelerated students, given the distribution of scores on the standardized test.

[tex]\mathsf{We\;know\;that : Density = \frac{Mass\;of\;the\;Object}{Volume\;of\;the\;Object}}[/tex]

[tex]\mathsf{Given : Mass\;of\;the\;Object = 20\;Grams}[/tex]

[tex]\mathsf{Given : Volume\;of\;the\;Object = 3.5\;cm^3}[/tex]

[tex]\mathsf{\implies Density = \frac{20}{3.5}(\frac{g}{cm^3})}[/tex]

[tex]\mathsf{\implies Density = 5.71\;(\frac{g}{cm^3})}[/tex]

To find the density of an object, we will use the formula for density which is \( d = \frac{m}{v} \), where:
- \(d\) represents the density of the object,
- \(m\) is the mass of the object, and
- \(v\) is the volume of the object.

Substituting the given values into the formula:
\(m = 20 \, \text{g}\) (mass of the object),
\(v = 3.5 \, \text{cm}^3\) (volume of the object),

we get:
\(d = \frac{20 \, \text{g}}{3.5 \, \text{cm}^3}\).

Dividing 20 grams by 3.5 cubic centimeters, we obtain:
\(d ≈ 5.71 \, \text{g/cm}^3\).

Therefore, the correct answer is:

C.5.71 G/CM3

When the pack of 80 stickers is divided evenly among the three friends, each friend receives 26 stickers, with the remaining 2 stickers going to their teacher.

In order to find out how many stickers each friend will get from a pack of 80, we can divide the total number of stickers by the number of friends. In this case, that's 80 stickers ÷ 3 friends. This division gives us a result of 26 stickers with a remainder of 2.

However, the question states that the remainder is given to their teacher. So while the remainder division resulted in each friend getting 26 stickers with an extra 2 left over, those extra 2 stickers are given to the teacher. Therefore, each friend ends up with 26 stickers.

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Answer: WZ

The sequence ABCD has AD as the first and last letters of that sequence, so this pattern applies to WXYZ as well to pull out WZ. Angle A pairs up with angle W because they are both the first letters of the sequences. These angles are congruent from the fact that the parallelograms are similar. The same can be said for angle D and angle Z.

note: WZ is the same as ZW. The order doesn't matter when it comes to labeling segments based on endpoints.

[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}=-\Bigg[\left(\dfrac{1}{3}\right)^{-1}\Bigg]^x=-(3)^x\\\\f(x)<0\ \text{for any real values of x}\ (III\ and\ IV\ quadrant)\\\\a^x\ \text{is increased for}\ a>1.\ \text{Therefore}\ 3^x\ \text{is increased}.\\\\\text{We have}\ -3^x,\ \text{therefore the graph is decreased}.[/tex]

Only bottom left graph satisfy the conditions of the end behaviour and y-intercept. The bottom left option is correct.

Given:

The given function is:

[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}[/tex]

To find:

The graph of the given function.

Explanation:

The given function can be rewritten as:

[tex]f(x)=-\dfrac{1}{3^{-x}}[/tex]

[tex]f(x)=-3^{x}[/tex]

For [tex]x=0[/tex], we get

[tex]f(0)=-3^{0}[/tex]

[tex]f(0)=-1[/tex]

So, the y-intercept of the graph is [tex]-1[/tex].

End behaviour of the graph:

[tex]f(x)\to 0[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

Only bottom left graph satisfy the above conditions.

Therefore, the bottom left option is correct.

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Answer:

There would be no solution im pretty sure but not 100%

Step-by-step explanation:

Answer:

Well if you are trying to find the length of each side you Divide 24 by 4 so your answer would be 6

Step-by-step explanation:

Answer:

2√6 inches

Step-by-step explanation:

Since the picture is a square the lengths of each side are equal and their measure is √24

= √4*√6

= 2√6  in simplest form

Answer:

true/ true/ false/ true

Step-by-step explanation:

4x² is a term in both the numerator and denominator → Correct

factorise numerator and denominator

4x² - 4 = 4(x² - 1) ← common factor of 4

x² - 1 ← is a difference of squares and factors as

(x - 1)(x + 1)

4x² - 3x - 1 = (4x + 1)(x - 1) ← in factored form

Hence (x - 1) is a common factor in the numerator and denominator → Correct

4 is only a common factor in the numerator not the denominator

the denominator has three terms → Correct

being 4x² , - 3x and - 1

Answer: Negative infinity

note: if your teacher won't allow negative infinity, then try DNE for "does not exist"

=======================================================

Explanation:

As x gets closer to x = 4 from the left side of this value, then x starts at something like x = 3 and moves to x = 3.5, then to x = 3.9, then to x = 3.99, then to x = 3.999, etc

We get closer to x = 4 but never actually get there. If you look at the table attached, then f(x) = 1/(x-4) will keep getting more negative with larger and larger negative values. This growth goes on forever without any bound. So the limit is equal to negative infinity.

As you can see on the graph below, the curve heads downward as you approach x = 4 from the left hand side. Imagine you are a point on the curve, or this point is on a rollercoaster (the curve being the track itself). As you get closer to 4 from the left side, you go downhill. There is on limit to how far downhill you can go.

note: the graph and table in the attachment below were made by the free graphing calculator program GeoGebra

Answer with explanation:

The given rational function is

      [tex]y= \lim_{x \to 4^{-}} \frac{1}{x-4}[/tex]

To find the vertical Asymptotes , put

→  Denominator =0

→ x-4=0

→x=4, is the Vertical Asymptote.

Emery initially borrowed $608. Each week, she paid off $76. After 2 weeks she had $456 left to pay and after 5 weeks she owed $228.

To find out the original amount borrowed, we need to determine how much Emery is paying off each week. If we look at the information given, after 2 weeks Emery still owes $456, and after 5 weeks, she owes $228. That's a difference of $228 over the span of 3 weeks, which means she is paying off $76 each week ($228 / 3 weeks = $76 per week).

Knowing this, we can figure out that she owed $608 before she started making payments (that is, $456 + $76*2 weeks = $608). Therefore, the original amount Emery borrowed from her brother was $608.

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the complete Question is given below

Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks, she will owe $228. a. What was the original amount Emery borrowediginal amount borrowed?

Answer:

$1,250

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. If 1200 is 4% less than last year, it's 96% of what he raised last year.

[tex]\frac{96}{100}=\frac{1200}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

96(y)=100(1200)

96y=120000

y=1250

Answer:  We can plot the graph with help of below explanation.

Step-by-step explanation:

Since, given equation of polynomial,

[tex]P(x) = x^4 - 3x^3 - 8x^2 + 12x + 16[/tex]

End behavior : Since, the leading coefficient of the polynomial is positive and even.

Therefore, the end behavior of the polynomial is,

[tex]f(x)\rightarrow -\infty[/tex] as [tex]x\rightarrow -\infty[/tex]

And, [tex]f(x)\rightarrow +\infty[/tex]  as  [tex]x\rightarrow +\infty[/tex]

Points of the curve : since, P(4) = 0

Therefore, (x-4) is the multiple of P(x),

And we can write,  [tex]x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x^3+x^2-4x-4)[/tex]

[tex]x^4 - 3x^3 - 8x^2 + 12x + 16=(x-4)(x+1)(x^2-4)[/tex]

[tex]x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x+1)(x+2)(x-2)[/tex]

Thus, the roots of equation are 4, 2, -1 and -2.

Therefore, x-intercepts of the polynomial are (4,0) (2,0) (-1,0) and (-2,0)

Also, the y-intercept of the polynomial is ( 0,16)

Thus, we can plot the graph with help of the above information.

Answer:

11.33333...(keeps repeating)

Step-by-step explanation:

8.5 ÷ 3/4 = 11.33333...(keeps repeating)

Answer:

(4,-3) and (-2,5)

Step-by-step explanation:

The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).

(x,y)--->(y,x) in the new function.

If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).

Answer:

PLATO users, use this order:

(-2,5) and (4,-3)

Step-by-step explanation:

Answer:

The Rosita investment worth in 2025 is $83486.4 .

Step-by-step explanation:

The expontential increase function is given by.

[tex]y = a(1 + r)^{t}[/tex]

Where a is the initial value , r is the rate of interest in the decimal form and t is the time.

As given

Rosita invested in a precious mineral.

The value of the mineral tends to increase by about 12% per year.

She invests $24,000 in 2014.

As

a = 24000

12% is written in the decimal form.

[tex]= \frac{12}{100}[/tex]

= 0.12

r = 0.12

As Rosita invested from 2014 to 2025.

Than

t = 2025 - 2014

t = 11 years

Put in the expontential increase function.

[tex]y = 24000(1 + 0.12)^{11}[/tex]

[tex]y = 24000(1.12)^{11}[/tex]

y = 24000 × 3.4786 (Approx)

y = $83486.4

Therefore the Rosita investment worth in 2025 is $83486.4 .

[tex]10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}[/tex]

Answer:

B is the correct option choice !

QUESTION 1

The given function is

[tex]h(x)=-4x-72[/tex]

If [tex]x[/tex] decreases by [tex]11[/tex], then the new value is [tex]x-11[/tex].

We need to find the value the function at [tex]x-11[/tex] which is

[tex]h(x-11)=-4(x-11)-72[/tex]

This simplifies to

[tex]h(x-11)=-4x+44-72[/tex]

The increment in [tex]h(x)[/tex] is given by;

[tex]h(x-11)-h(x)=-4x+44-72-(-4x-72)[/tex]

This simplifies to,

[tex]h(x-11)-h(x)=-4x+44-72+4x+72[/tex]

This further simplifies to

[tex]h(x-11)-h(x)=44[/tex]

Therefore the corresponding increment in [tex]h(x)[/tex] is [tex]44[/tex].

QUESTION 2

The given function is

[tex]f(x)=\frac{3}{17}x+2[/tex].

If [tex]x[/tex] increases by [tex]51[/tex], then the new value of [tex]x[/tex] is [tex]x+51[/tex].

The increment in [tex]f(x)[/tex] is given by

[tex]h(x+51)-h(x)=\frac{3}{17}(x+51)+2-(\frac{3}{17}x+2)[/tex]

We expand the brackets to get,

[tex]h(x+51)-h(x)=\frac{3}{17}x+9+2-\frac{3}{17}x-2[/tex]

We simplify further to obtain,

[tex]h(x+51)-h(x)=9[/tex]

Therefore the corresponding increment in [tex]f(x)[/tex] is [tex]9[/tex].

When x decreases by 11, function h(x) increases by -100. When x increases by 51, f(x) increases by 9.

To find how much Function h(x) increases when x decreases by 11, we can calculate h(x) for the original value of x and the new value of x and then find the difference.

Original h(x) for h(x) = -4x - 72:

h(x) = -4x - 72

For x decreased by 11, the new x is x - 11:

New h(x) for h(x) = -4x - 72:

h(x - 11) = -4(x - 11) - 72

Now, we calculate the difference in h(x) values:

Δh = h(x - 11) - h(x)

Δh = [-4(x - 11) - 72] - (-4x - 72)

Now, simplify:

Δh = -4x + 44 - 72 + 4x - 72

The -4x and +4x cancel out:

Δh = 44 - 72 - 72

Now, calculate the difference:

Δh = -100

So, when x decreases by 11, h(x) increases by -100.

For the second part, to find how much f(x) increases when x increases by 51, we can use a similar approach.

Original f(x) for f(x) = (3/17)x + 2:

f(x) = (3/17)x + 2

For x increased by 51, the new x is x + 51:

New f(x) for f(x) = (3/17)x + 2:

f(x + 51) = (3/17)(x + 51) + 2

Now, calculate the difference in f(x) values:

Δf = f(x + 51) - f(x)

Δf = [(3/17)(x + 51) + 2] - [(3/17)x + 2]

Now, simplify:

Δf = (3/17)x + (3/17)(51) + 2 - (3/17)x - 2

The (3/17)x and - (3/17)x cancel out, and 2 - 2 also cancels:

Δf = (3/17)(51)

Now, calculate the difference:

Δf = 3 * 3

Δf = 9

So, when x increases by 51, f(x) increases by 9.

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Answer:

the tank can hold 12.5 gallons when it is full

Step-by-step explanation:

Let's assume

tank can hold 'x' gallons when it is full

we are given

The gas gauge in a car shows it has 40% of a tank of gas

So, gas in car is

[tex]=\frac{40}{100}\times x[/tex]

and we have

the car has about 5 gallons

so, we can set it equal

and then we can solve for x

[tex]5=\frac{40}{100}\times x[/tex]

[tex]5=\frac{4}{10}\times x[/tex]

[tex]5=\frac{2}{5}\times x[/tex]

Multiply both sides 5

[tex]5\times 5=5\times \frac{2}{5}\times x[/tex]

[tex]5\times 5=2x[/tex]

[tex]25=2x[/tex]

we get

[tex]x=12.5[/tex]

So, the tank can hold 12.5 gallons when it is full

Answer:

B

Step-by-step explanation:

q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

[tex]2q(0.1)+q(0.25)=9\\\\0.2q+0.25q=9\\\\0.45q=9\qquad\text{divide both sides by 0.45}\\\\q=20[/tex]

Paul has 20 quarters.

To find quarters does Paul have.

The branch of mathematics dealing with the properties and manipulation of numbers.

Let the q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

2q(0.1)+q(0.25)=9

0.45q=9

q=20

So, Paul has 20 quarters.

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Answer:

ok first get each corner make a line to the dot with each point

Step-by-step explanation:

Answer:

⇒[tex]6b=95.94[/tex]    (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒[tex]120t = 95.94[/tex]    (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Step-by-step explanation:

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒[tex]6b=95.94[/tex]     (equation to determine cost of one box)

⇒[tex]b=\frac{95.94}{6}[/tex]

⇒[tex]b=15.99[/tex]

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒[tex]120t = 95.94[/tex] (equation to determine cost of per tile)

⇒[tex]t=\frac{95.94}{120}[/tex]

⇒[tex]t=0.7995[/tex]

Thus cost of one tile t = $0.7995.