Select the correct answer.
Determine which equation has the same solutions as the given equation.

x2 − 10x − 11 = 0

A.
(x − 10)2 = 21
B.
(x − 5)2 = 21
C.
(x − 5)2 = 36
D.
(x − 10)2 = 36

Answer:

C) 12/9 = 4/3

Step-by-step explanation:

it is a right-angled triangle.

Pythagoras applies.

cos(theta) = 9/15

that is the horizontal leg in relation to the baseline (Hypotenuse).

since we are only dealing with ratios here, to get the vertical leg and its relation to the Hypotenuse, we can simply use the numbers of the ratio.

15² = vleg² + 9²

225 = vleg² + 81

vleg² = 144

vleg = 12

therefore,

sin(theta) = 12/15

tan(theta) = sin(theta)/cos(theta) = 12/15 / 9/15 = 12/9 = 4/3

FYI : to prove to you how irrelevant the absolute lengths in ratios are, here a variation with simplified fractions or ratios :

cos(theta) = 9/15 = 3/5

5² = vleg² + 3²

25 = vleg² + 9

vleg² = 16

vleg = 4

therefore,

sin(theta) = 4/5

tan(theta) = sin(theta)/cos(theta) = 4/5 / 3/5 = 4/3

as you see, all as above.

for these kind of calculations we only need ratios (or relative sizes)

The value of "c" in this triangle is approximately 154.2 units long.

The given information is a side length of 61 and two angles, one of which is 142 degrees. To solve for the unknown side length "c", we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

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

Where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.

In this problem, we know the side length "a" is 61 and the angle opposite that side is 63 degrees. We also know the angle opposite the unknown side "c" is 142 degrees. Using the law of sines, we can write:

61/sin(63) = c/sin(142)

Now we can solve for "c" by multiplying both sides by sin(142) and then dividing by sin(63):

c = (61*sin(142))/sin(63)

Using a calculator, we find that c is approximately 154.2. Rounding to the nearest tenth, we get:

c ≈ 154.2 to the nearest tenth.

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Answer:

117.25

Step-by-step explanation:

Ik this is late but I need the answer for my test later so I’m answering here so I can find it. Also this was right on acellus.

The bar graph that correctly displays the data from the list and the table is Graph D.

A bar chart, often known as a bar graph, is a diagram that displays categorical data as rectangular bars with heights or lengths proportional to the values they stand for.

You can plot the bars either vertically or horizontally.

Considering the data given:

The correct bar graph is D.

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The surface area of the rectangular prism is 2600 square inches.

Surface area is the total area that the surface of a 3-dimensional object covers. In order to find the surface area of a rectangular prism, we need to find the area of each of its faces and add them together.

The rectangular prism in question has dimensions of 23 inches by 8 inches by 18 inches. Looking at the net, we see that there are three pairs of identical rectangles: the top and bottom faces, the front and back faces, and the left and right faces. Each of these rectangles has dimensions of 23 inches by 8 inches.

Therefore, the surface area of the rectangular prism can be calculated as:

Area of top and bottom faces = 2 * (23 in. * 8 in.) = 368 square inches

Area of front and back faces = 2 * (18 in. * 8 in.) = 288 square inches

Area of left and right faces = 2 * (23 in. * 18 in.) = 828 square inches

Total surface area = 368 + 288 + 828 = 2600 square inches

Correct Question :

what is the surface area, in square inches, of the rectangular prism formed by folding the net below?

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The coordinates of the reflected triangle are (-1,3) (-3,1) and (-4,5)

Given that we have the graph of the triangle ABC

With the coordinates (1,3) (3,1) (4,5)

The transformation is given as

Triangle ABC is reflected over the y-axis

The rule of this transformation is

(x, y) = (-x, y)

So, we have

Image = (-1,3) (-3,1) and (-4,5)

In (a), we have

The rule of this transformation is (x, y) = (-x, y)

This means that the y-coordinate remains unchanged while the x-coordinate is negated as a result of this reflection.

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Answer:

90° counterclockwise

Step-by-step explanation:

Find the center of rotation. This is the point that is equidistant from each vertex and its image. You can do this by drawing the perpendicular bisectors of the segments that connect each vertex and its image, and finding their intersection point. In this case, the center of rotation is the origin (0,0).

Choose a vertex and its image to measure the angle of rotation. For example, you can use A and A’. Draw a line segment from the center of rotation to each point, forming an angle.

Use a protractor or estimate the angle of rotation by comparing it to benchmark angles. In this case, the angle of rotation is about 90 degrees.

Determine the direction of rotation by observing which way the figure moved around the center of rotation. In this case, the direction of rotation is counterclockwise (positive).

Answer:

see below

Step-by-step explanation:

the quotient is 1 and the remainder is 565.

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

Option C is the correct answer.

We have,

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

This will give us a single equation in y, which we can then solve for y, and use to find the value of x.

In this case, we can eliminate the x term by adding the equations.

3x + 2y = 4

-3x + y = 2

If we add the two equations, the x term will cancel out:

3x + 2y = 4

(-3x + y = 2)

0x + 3y = 6

Simplifying, we get:

3y = 6

y = 2

Now that we have found the value of y, we can substitute it into one of the equations to find the value of x.

Let's use the second equation:

-3x + y = 2

-3x + 2 = 2

-3x = 0

x = 0

Therefore, the solution to the system of equations is (x, y) = (0, 2).

Thus,

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

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The side length ZW is 6 units and the side length WX is 10.392 units. Then the area of the rectangle is 62.352 square units.

Given that:

Diagonal, d = 12

Angle, α = 30°

The rectangle's area will be given as,

Area of the rectangle = L × W square units

The measure of the side length ZW is calculated as,

sin 30° = ZW / 12

ZW = 6 units

The measure of the side length WX is calculated as,

cos 30° = WX / 12

ZW = 10.392 units

The area of the rectangle is calculated as,

A = 6 x 10.392

A = 62.352 square units

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Answer:

The answer to your problem is, [tex]ft^3[/tex]

Step-by-step explanation:

In the problem we will use the area formula:

l × w × h

Multiply:

16.5 × 12 × 5 = 990

We look at the options:

990 [tex]ft^3[/tex] is in Option D.

Thus the answer to your problem is, 990 [tex]ft^3[/tex]

As we have shown that both line segments PN and PM are equal to (1/2)MN, and hence they are equal in length to each other.

Given that point P lies on the perpendicular bisector l of line segment MN, we know that line segment PN and line segment PM are both equal in length to the distance between point P and the midpoint of MN, which we will call point O. This is because the perpendicular bisector of a line segment passes through the midpoint of the segment, and any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Let us call the length of line segment PM "x". Then, we can express the lengths of line segments PN and PO in terms of x as well. Since P is equidistant from the endpoints of MN, we know that line segment PN has the same length as line segment PO, which is half the length of MN. We can express this relationship mathematically as:

PN = PO = (1/2)MN

Similarly, we can express the length of line segment PM in terms of the length of PO, which is also equal to (1/2)MN. Since line segment PM is equal in length to the distance between point P and the midpoint of MN, we know that:

PM = PO = (1/2)MN

Therefore, we have proved that PM = PN.

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Using the law of detachment and the law of syllogism,

We can conclude that Sally is too heavy for the bridge, but we cannot conclude that she can cross the bridge.

We have,

Using the law of detachment, we can conclude from statements 1 and statement 3:

If something weighs more than 2,000 pounds, then it weighs more than Jill's car. (Statement 1)

Sally the elephant weighs 2,325 pounds. (Statement 3)

Therefore, Sally weighs more than Jill's car.

Using the law of syllogism, we can then use the conclusion above and statement 2 to conclude:

Sally weighs more than Jill's car.

If something weighs more than Jill's car, then it is too heavy for the bridge. (Statement 2)

Therefore, Sally is too heavy for the bridge.

Therefore,

We can conclude that Sally is too heavy for the bridge, but we cannot conclude that she can cross the bridge.

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The simplified value for the vectors  u = (-6, 4) and w= (-4, -6) in the expression v = u + 4w is equal to v = (-22, -20).

Vectors are ,

u = (-6, 4)

and w= (-4, -6).

To find the vector v = u + 4w,

we need to multiply the vector w by 4 and add it to the vector u component-wise,

v = u + 4w

Substitute the value of the vectors we have,

= (-6, 4) + 4(-4, -6)

Now, add component wise vector  we get,

= (-6, 4) + (-16, -24)

= (-6 - 16, 4 - 24)

= (-22, -20)

Therefore, the value of the vectors v = u + 4w is equals to v = (-22, -20).

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The Mayan notation is shown below.

1. 234

The highest power of 20 that will divide into 3575 is 20² = 400

So, 234/ 400 = 0.585

0.585 x 20=11.7

0.7 x 20= 14

So, 234₁₀= 11,14₂₀

Now, the Mayan notation will be

14 in the ones position three bars at the bottom of the number.

11 the 20s place, so that’s three bars and three dots in the second position.

2. 10503

The highest power of 20 that will divide into 3575 is 20² = 400

So, 10503/ 400 = 26.2575

0.2575 x 20= 5.15

05.15 x 20= 3

So, 234₁₀= 26, 5,3₂₀

Now, the Mayan notation will be

3 in the ones position three dots at the bottom of the number.

5 the 20s place, so that’s one bars and three dots in the second position.

and, 26 shows by 2 vertical dots and bar.

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Answer:  

552 students are going to the picnic

The number of minutes of local landline calls is 132 min.

We are given that;

Time= 36min

Bill= 13119

Now,

To find the number of minutes of local landline calls, we need to rearrange the tariff structure formula to solve for n in terms of Total and m. We also need to substitute the given values of Total and m.

Total = nx 12c/min +mX R1,10/min + R75,75

n = (Total - m x R1,10/min - R75,75) / (12c/min)

Total = R131.19

m = number of minutes of calls to cellphones = 36 min

n = (131.19 - 36 x 1.10 - 75.75) / 0.12

= (131.19 - 39.60 - 75.75) / 0.12

= (15.84) / 0.12

= 132 min

Therefore, by algebra the answer will be 132 min.

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The value of the arithmetic operation; 0.79 × 12 as required in the task content is; 9.48.

The value of the arithmetic operation; 12.45 × 11 as required in the task content is; 136.95

It follows from the task content that the value of the given arithmetic expressions are to be determined.

By the use of a mathematical calculator; we have that;

0.79 × 12 = 9.48

Also; 12.45 × 11 = 136.95.

Ultimately, the result of the evaluations as required are such that;

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The solution is, PV= $45,879.68.

Here, we have,

Explanation:

Giving the following information:

Cash flow= $4,000 annually

n= 20

i= 6% compunded annually

The maximum that an investor should pay is the present value (PV).

First, we need to calculate the future value using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual cash flow

FV= {4,000*[(1.06^20) - 1]} / 0.06

FV= $147,142.36

Now, we can calculate the present value, we need to use the following formula:

PV= FV/(1+i)^n

PV= 147,142.36/(1.06^20)

PV= $45,879.68

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complete question:

Assuming you are a rational investor, the amount you should be willing to pay for a 20-year ordinary annuity that makes payments of $4,000 per year and you require a 6% rate of return per year is closest to:

Answer:

D

Step-by-step explanation:

The statement that is true about histograms is that data is organized in equal intervals. Histograms are graphical representations of data that use bars to show the frequency of values in a continuous range. The bars are of variable heights depending on the frequency of data within each interval, but the width of each bar represents the same interval size. This allows for easy comparison between different intervals and helps to visualize the distribution of data. It is important to note that the bars in a histogram do touch, as they represent continuous data ranges.

Answer:

d

Step-by-step explanation:

got it right on homework

Answer:

800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits

160 biscuits × 3 grams butter/biscuit = 480 grams butter

160 biscuits × 2 grams sugar/biscuit = 320 grams sugar

Katie needs 320 grams sugar.

Kate needs 270g of sugar to make the maximum number of biscuits possible.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;

⇒ 800g + 550g

= 1350g of the mixture.

Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.

We can do this by adding up the ratio numbers;

(5+3+2) = 10.

Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.

So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:

2/10 = x/1350

We can solve for x by cross-multiplying:

2 × 1350 = 10x

2700 = 10x
x = 270

Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.

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If the 2 boxes are stacked on top of other, then the total volume of both boxes will be (b) 224m³.

To find the total volume when two boxes are stacked on top of each other, we need to add the volume of both boxes. The formula for the volume of a rectangular box is : Volume = Length x Width x Height,

Using the dimensions, that Length = 8m, Width = 7m and height = 2m,

The volume of the first-box is:

⇒ Volume1 = 8m × 7m × 2m = 112 cubic meters,

The volume of the second-box will be the same, because it has the same dimensions;

So, Volume2 = 8m × 7m × 2m = 112 cubic meters,

To find the total volume when the boxes are stacked, we add the volumes:

⇒ Total Volume = Volume1 + Volume2,

⇒ Total Volume = 112 cubic meters + 112 cubic meters,

⇒ Total Volume = 224 cubic meters,

Therefore, the total-volume when the two boxes are stacked on top of each other is 224 cubic meters, correct option is (b).

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The reasonable domain to plot the growth function is {x : 0 ≤ x ≤10}.

y intercept of the graph of the function represents the initial height of the plant.

Average rate of change of the function f(n) from n = 3 to n = 10 is 0.43.

Given a growth function,

f(n) = 12 (1.03)ⁿ

Part A :

When the scientist concluded his study, the height of the plant was approximately 16.13 cm.

12 (1.03)ⁿ = 16.13

(1.03)ⁿ = 1.344

Taking logarithms on both sides,

n log (1.03) = log (1.344)

n = log (1.344) / log (1.03)

n = 10.006 ≈ 10 days

Domain = {x : 0 ≤ x ≤10}

Part B :

The y intercept of the graph of the function is the height of the plant in 0 days, that is the initial height of the plant.

Part C:

Average rate of change of the function f(n) from n = 3 to n = 10 is,

f(10) - f(3) / 10 - 3

f(10) = 12(1.03)¹⁰ = 16.127

f(3) = 12(1.03)³ = 13.113

Average rate of change = (16.127 - 13.113) / 7 = 0.43

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Answer:

-9/20 is greater than -0.5

Step-by-step explanation:

-9/20 also just means -9 divided by 20

-9 divided by 20 is -0.45

in negative numbers, the closer the number is to 1, the greater value it is. So, since -9/20 = -0.45, and -0.45 is closer to 1 than -0.5 is, -9/20 is greater than -0.5.

Answer:

Set your calculator to degree mode.

Using the Law of Cosines:

37^2 = 23^2 + 20^2 - 2(23)(20)(sin C)

1,369 = 929 - 920sin(C)

440 = -920sin(C)

sin(C) = -11/23

C = sin^-1 (-11/23) = 151.4°

Answer:

Step-by-step explanation:

-119

The value of 2x+y when X =4al and y = 3​ is 8al + 3

to find the value of of 2x+y

If X = 4al and y = 3, then:

2x + y = 2(4al) + 3

Simplifying the expression:

2x + y = 8al + 3

Therefore, the value of 2x+y is 8al+3.

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The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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The proportion of the tapestries' height to width is 3:2, which means the height is 1.5 times the width.

To find the proportion of the tapestries' height to width using whole numbers and ratio notation, we need to divide the height of the tapestry by its width.

The height of the tapestry is 1.5 meters, and the width is 1 meter. Therefore, the proportion of the tapestry's height to width is

1.5 meters / 1 meter = 1.5 : 1

We can simplify this ratio by dividing both sides by 1, which gives

1.5 : 1 = 3/2 : 1

Therefore, the proportion of the tapestry's height to width using whole numbers and ratio notation is 3:2.

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