Solve the following equation by factoring.
y²-8y=0

The option that correctly replaces the question mark in Aisha's proof is SAS (Option C). See it explained below.

Mathematical proofs are statements that are used to demonstrate that a mathematical expression or logic of true.

Since the portion of the question that shows the question mark is missing, we can rewrite the proof as follows:

Step 1

AB Dissects BC

AE ║ BD

Reason - It is given

Step 2

BC ≅ BE

Reason -  Definition of Segment Bisector

Step 3

∠ABE ≅ ∠CBD

Step 4

∠BCD ≅ ∠BEA

Reason

Alternative Interior Angles

Step 5

ΔBCD ≅ ΔBEA

Reason

SAS Postulate

Step 6

QED

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The dot product of the two matrices D and n is determine as (4, - 7).

The dot product of the two matrices is calculated as follows;

n = (-2, -1), and D = [-4   2]

                               [4    3]

D.n =  (-2, -1). [-4   2]  = (-2 x -4) + (-1 x 4) = 4

                     [4    3]  = (-2 x 2) + (-1 x 3) = -7

D.n = (4, - 7)

Thus, the dot product of the two matrices D and n is determine as (4, - 7).

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Answer:

x = 23.0

Step-by-step explanation:

To solve, you have to make the equation:

[tex]cos(64)=\frac{9}{x}[/tex]

Now multiply x to both sides:

[tex]cos(64)*x=9[/tex]

Next divide both sides by cos(64):

[tex]x=\frac{9}{cos(64)}[/tex]

x = 22.9675486404

Round to the tenth:

x = 23.0

Hope it helps and have a nice day!

The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.

The time the investment lasted= 12 years.

Simple interest = 1579.05 - 800= $779.05

The principal capital= $800

Rate of the both capital invested;

= SI × 100/P ×T

= 779.05 × 100/800 × 12

= 77,905/9600

= 8.11%

To find the amount of money that Phyllis invested at each given rate,

Rate 1 = 4/8.11× 800

= 3200/8.11

= $394.57

Rate 2 = 6/8.11× 800

= 4800/8.11

= $591.86

The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.

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Answer:

[tex]31.8\%[/tex]

Step-by-step explanation:

The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]

The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]

Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

Here we have the functions:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

So the y-intercepts are equal, meaning that the correct option is D.

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Answer:

Both f(x) and g(x) have the same y-intercept of (0, 1).

Step-by-step explanation:

I got it right on the test.

Step-by-step explanation:

a linear relationship is simply a straight line relationship.

any equation that can be pot in the form of y = mx + b is a linear relationship.

linear = straight

hope this helps

Answer:

19i

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-361}[/tex]

= [tex]\sqrt{361(-1)}[/tex]

= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]

= 19 × i

= 19i

Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

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The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

We have ABCD is a parallelogram.

BE is perpendicular to FC

FA is perpendicular to FC

As we know in the parallelogram ABCD:

AB ≅ DC

AD ≅ CB

As the DC is extended to F

So, AB ≅ FE

And BE is perpendicular to FC

       FA  is perpendicular to FC  (given)

∴ FA ≅ BE

∴ ABEF is a parallelogram.

Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

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Step-by-step explanation:

please mark me as brainlest

The total volume of this squared-base pyramid based on the information provided is 2666 micrometers.

The general formula to calculate the volume of a squared-based pyramid is:

Base area: 20 x 20 = 400

400 micrometers x 20/ 3 = 2666 micrometers.

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Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.

The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]

Thus, we can compute the confidence interval:

[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]

Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.

Part B

The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]

Answer:

40 dollars

Step-by-step explanation:

We can use a ratio to solve the problem

5 pounds         50 pounds

----------------  = -----------------

4 dollars            x dollars

Using cross products

5 * x = 4 * 50

5x = 200

Divide by 5

5x/5 = 200/5

x = 40

40 dollars

Step-by-step explanation:

[tex]\sf 5 \: pounds \longrightarrow 4 \: dollars[/tex]

[tex]\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars[/tex]

[tex]\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars[/tex]

[tex]\sf \longmapsto 40 \: dollars[/tex]

Answer:

your answer will be 85 1/3ins

Step-by-step explanation:

16x 5 1/3 = 85.3333333333

then I took the 85 and the 1/3

and just put em together

Answer:

y₁ - y₂ = (-7/9)(x₁ - x₂)

Step-by-step explanation:

The general structure for an equation in point-slope form is:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope and the "x" and "y" values come from each point. To find "m", plug the values of each point into the equation.

Point 1: (4, -3)                   Point 2: (-5,4)

y₁ - y₂ = m(x₁ - x₂)                                  <---- Original equation

-3 - 4 = m(4 - (-5))                                 <---- Plug values in for "x" and "y"

-7 = m(4 - (-5))                                      <---- Simplify left side

-7 = m(9)                                               <---- Simplify within parentheses

-7/9 = m                                              <---- Divide both sides by 9

I don't exactly understand what "fully simplified point-slope form" means because if all of the variables are plugged in, you wouldn't be left with an equation. It may just be asking for the slope, which in this case would make the equation look like this:

y₁ - y₂ = (-7/9)(x₁ - x₂)  

It may want you to find the equation in slope-intercept form (y = mx + b), and you would have to find "b". Sorry I don't quite understand what exactly you are looking for.

Answer:

Paul and Krystal spent 13 hours at the pool

Step-by-step explanation:

I Thank

The choice in the solution set of the equation 4x = 30 is x = 7.5

The equation is given as:

4x = 30

Divide both sides of the equation by 4

4x/4 = 30/4

Evaluate the quotients

x = 7.5

Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5

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Answer:

x=6, y=4

Step-by-step explanation:

x - y = 2

2x = 3y => 2x - 3y = 0

x - y = 2 | ×(-2) => -2x + 2y = -4

2x - 3y = 0

-2x + 2y = -4

2x - 3y = 0

___________

0 - y = - 4 | ×(-1)

y = 4

Substitution in x - y = 2:

x - 4 = 2 | +4

x = 2+4 = 6

Answer:

4500

Step-by-step explanation:

all of them were admitted.

The point at which three or more lines intersect is the point of concurrency.

The point were three lines meet or intersect is a point of concurrency.

In other words, a point of concurrency is where three or more lines intersect in one place.

This point of concurrency is a single point shared by three or more lines.

Perpendicular bisectors, and altitudes are concurrent in every triangle.

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Answer:

concurrency

Step-by-step explanation:

Look above for more

By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.

We know that the average temperature is given by the equation:

f(x)=31cos(0.0055πx)+88

And it is in Fahrenheit degrees.

To get the lowest average temperature, we just need to find the minimum of the above function.

Remember that the minimum of the cosine function is:

cos(x) = -1

Then the lowest value of the above function is:

f(x₀) = 31*(-1) + 88 = 57

From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.

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Answer:

  318

Step-by-step explanation:

The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.

__

The amount of the penalty is 5.3% of 6000:

  0.053 × 6000 = 318

Wendy paid a penalty of 318 for her early withdrawal.

Answer:

  B

Step-by-step explanation:

A box and whisker plot is a graphical representation of the 5-number summary of a data set. It shows the minimum, maximum, median, and the values of the 1st and 3rd quartiles. Here, you're asked to identify the data set having the same 5-number summary as that shown in the plot.

__

The minimum of the data set is shown by the end of the left "whisker." The plot shows a minimum value of 41. Choice C has a minimum of 40, so is not the data set we're looking for.

The maximum of the data set is shown by the end of the right whisker. The plot shows a maximum of 50, matching all of the answer choices shown.

The median of the data set is shown by the vertical line in the middle of the box. Here, the median of the data set is indicated as 44. This will be the middle value, or the average of the two middle values of the set of data.

These sets of data have 10 values, an even number, so the median is the average of the middle two.

Choices A and B have a middle pair of 43 and 45, which means their median is (43+45)/2 = 44. Choice D has a middle pair of 43 and 47, so a median of (43+47)/2 = 45. Choice D is not the data set we're looking for.

The 1st and 3rd quartiles of the data set are shown by the left and right ends of the box, respectively. They are indicated as being 43 and 48.

The median divides the data set into two parts. It is not considered to be a member of either part. The 1st quartile is the median of the lower (left) part. The 3rd quartile is the median of the upper (right) part.

Here, each part has 5 data values, so the quartile values are 3rd from the ends of the data set. In choice A, they are 43 and 49, not a match to the given plot. In choice B, they are 43 and 48, matching the values in the given box plot.

The data set in choice B could be represented by the box plot shown.

Answer:

x = - 6 , x = 1

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

x² + 5x - 6 = 0

consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)

the factors are + 6 and - 1 , since

6 × - 1 = - 6 and 6 - 1 = + 5 , then

(x + 6)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 1 = 0 ⇒ x = 1

Answer:

19 cents or 0.199

Step-by-step explanation:

Hope it helped!

Answer:

19 cents

Step-by-step explanation:

divide total cost by amount of items

Answer:

L = 16

w = 10

Step-by-step explanation:

Givens

Area = 160 sqr inches

width = x

length = x + 6

Equation

Area = L * w

Solution

Substitute in the equation all of the givens.

160 = x(x + 6)                     Remove the brackets

160 = x^2 + 6x                   Subtract 160 from both sides.

160-160 = x^2 + 6x - 160

0 = x^2 + 6x - 160

This equation factors. Turn it around first

x^2 + 6x - 160 =  0

(x - 10)(x + 16) = 0

Answer

x (width) = 10

x + 16 = 16

Answer:

The length is 16 inches and the width is 10 inches.

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

divide 43.75 by 3.5 to get your answer

Step-by-step explanation:

it is not important that the triangle is right-angled.

but the distance between each pair of points is calculated via Pythagoras

c² = a² + b²

with c being the Hypotenuse (baseline opposite of the 90° angle) = distance between the end points, and a and b are the legs (= the x and y coordinate differences of the 2 end points) of the virtual right-angled triangles between each pair of points.

so,

AB² = (6 - -3)² + (-4 - -4)² = 9² + 0² = 81

AB = 9 ft

BC² = (6 - 6)² + (8 - -4)² = 0² + 12² = 144

BC = 12 ft

and now for AC, which is because of the special case of how the main triangle is placed and oriented, the same calculation as with Pythagoras for the main right-angled triangle. but I keep showing you the point distance calculation, because this is what you will need in the future for more general triangle or other shapes calculations :

AC² = (6 - -3)² + (8 - - 4)² = 9² + 12² = 81 + 144 = 225

AC = 15 ft

so, Nasir will need

9 + 12 + 15 = 36 ft

of fencing.