Question 3: Solve this system. Use the substitution method
.A
.B
.C
.D

the graph of Andrew's distance from home will look like this: Time (x-axis)  0  1  2  3  4  5  6  7  8  9  10 Distance (y-axis)  0  5  10 10 15 20 20 24 28 32  0

Graph is a data structure which is used to represent relationships between objects or data points. It is composed of nodes and edges, where nodes are the objects and edges are the connections between the objects. Graphs are used to represent mathematical equations, networks, and data structures such as trees. They are also used to represent relationships between data points in large datasets. Graphs can be used to represent both directed and undirected relationships, and are commonly used in many fields including computer science, engineering, mathematics, and data science.

From the given information, we can create a graph that shows Andrew's distance from home as he drives to the store, to the bank, and back again. The x-axis will represent time (in minutes), and the y-axis will represent the number of blocks away from home.

At time zero, Andrew is at his home, so the graph will begin with a point at (0, 0). As he travels to the store, the graph will move up 5 blocks for every minute he drives. Therefore, after 2 minutes, he will be 10 blocks away from home, so the graph will be at (2, 10). After he stops at the store for 2 minutes, he will still be 10 blocks away from home, so the graph will stay at (2, 10).

When he leaves the store and drives to the bank, he will move 5 blocks each minute. After 5 minutes, he will be 25 blocks away from home, so the graph will be at (5, 25). After he stops at the bank for 3 minutes, he will still be 25 blocks away from home, so the graph will remain at (5, 25).

Finally, when he drives home, he will move 4 blocks for each minute he drives. After 5 more minutes, he will be back at his home, so the graph will be at (10, 0).

Therefore, the graph of Andrew's distance from home will look like this:

Time (x-axis)  0  1  2  3  4  5  6  7  8  9  10

Distance (y-axis)  0  5  10 10 15 20 20 24 28 32  0

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Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Answer:

1) the most direct way is to use the normal volume formula for cubes/rectangular prisms

2)60 inches cubed

Step-by-step explanation:

Volume=length x width x height

V=4x5x3

V=20x3

V=60

therefore the volume is 60 inches ^3

Answer:

C and D is correct

Step-by-step explanation:

C: Debit is negative, and if you add 27 to -14, you get 13 which is Maria's account.

D: Its the same thing but opposite. 13 minus 27 is -14.

♡ Hope it helps ♡

Answer:

both c and d

Step-by-step explanatioin

nobody is answering my question so im saving up like 100 points so someone will actually do it so ye

Answer:

-3,-2,-1 is less than -4 and not greater than

Step-by-step explanation:

Answer:

The probability of spinning yellow or blue is \(\frac{4}{5}\) or 80%.

Step-by-step explanation:

Since the circle is split evenly into 5 parts, and 4 parts are either blue or yellow, that means the probability of spinning blue or yellow is the number of blue or yellow sections divided by the total sections, which is \(\frac{4}{5}\) or 80%.

Answer:

\(cosC = \frac{\sqrt{161} }{15}\)

Step-by-step explanation:

\(cosC = \frac{\sqrt{161} }{15}\)

CosC = adj/hyp

The 99 percent confidence interval for the true mean length of the bolt is CI = (2.8712, 3.1288)

Confidence Interval is used to tell us the degree of certainty or uncertainty that is existent in a sampling method.

The general formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

z is z-score at confidence level

s is sample standard deviation

n is sample size

We are given;

sample size; n = 36

Sample mean; x' = 3 inches

standard deviation; s = 0.3 inches

confidence level = 99%

z at 99% CL = 2.576

Thus;

CI = 3 ± 2.576(0.3/√36)

CI = 3 ± 0.1288

CI = (2.8712, 3.1288)

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Answer:

1

Step-by-step explanation:

i am not sure but that is what i got.

Answer:

b). Commutative property

Step-by-step explanation:

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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Answer:

E. 15

Step-by-step explanation:

Use the Pythagorean theorem: a²+b²=c²

Answer:

Step-by-step explanation:

15

Answer:

222.80

Step-by-step explanation:

My keyboard won't do pounds. I'll leave the units off and just use pure numbers.

Magazines

Number of magazines = 50

Commission                  = 10/100

Price of magazines       = 7

Books

Number of books    =      21

Cost per book          =     12

Commission             =      15/100

Solution

Income from magazines = 10/100 * 7 * 50 =                                      35

Income from books         = 15/100 * 12 * 21                                        37.80

Basic Pay                                                                                            150

Take home pay                                                                                  222.80

Answer:

\( \frac{ {6}^{7} }{ {6}^{3} } = {6}^{7 - 3} = {6}^{4} \)

Answer:

\(E\approx14,962\text{ feet}\)

Step-by-step explanation:

Please refer to the attachment below.

As shown, we can split the diagram into a scalene triangle and a right triangle.

The strategy here is to use the Law of Sines to find x, then use right triangle ratios to find h, the height of Matterhorn (with respect to our elevation).

Let’s start with the scalene triangle.

To use the Law of Sines, we will need two angles and the sides opposite to the angles.

Since we need to find x, we need the angle opposite to x. This is already given to us as 30°.

We can use the side that measures 1,500. The angle opposite to it θ is unknown.

So, we will need to determine θ. From supplementary angles, we know that:

\(\alpha+35=180\)

So, it follows that:

\(\alpha=145^\circ\)

The interior angles of a triangle always sum to 180°. Hence:

\(30+\alpha+\theta=180\)

By substitution:

\(30+145+\theta=180\)

Hence:

\(\theta=5^\circ\)

Now, we can use the Law of Sines, given by:

\(\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}\)

It is important to align the angles correctly with the sides.

So, we will substitute θ = 5° for A and 1,500 for a.

And we will substitute 30° for B and x for b. Hence:

\(\displaystyle \frac{\sin(5^\circ)}{1,500}=\frac{\sin(30^\circ)}{x}\)

Solve for x. Cross-multiply:

\(x\sin(5^\circ)=1500\sin(30^\circ)\)

Hence:

\(\displaystyle x=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}\)

When doing trigonometry (or any math, really), try not to round intermediate values, as this may result in inaccuracies in the final answer. Hence, we will leave this as is.

Now, we can use the right triangle.

We know that an angle is 35°.

The height h is opposite to our angle.

And x was our hypotenuse. Therefore, we can use the sine ratio given by:

\(\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}\)

In this case, our angle is 35°.

The opposite side is h.

And the hypotenuse is x. Hence, by substitution:

\(\displaystyle \sin(35^\circ)=\frac{h}{x}\)

Solve for h. Multiply both sides by x:

\(h=x\sin(35^\circ)\)

Since we already know the value of x:

\(\displaystyle h=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}\cdot\sin(35^\circ)\)

Simplify. So, the height of Matterhorn with respect to our current elevation is:

\(\displaystyle h =\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}\)

The total elevation of Matterhorn will be the current elevation of the surveyor plus the height with respect to the current elevation or simply h. So, the elevation height is:

\(E=9756+h\)

By substitution:

\(\displaystyle E=9756+\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}\)

Now we may approximate. Use a calculator. So, the total elevation of Matterhorn is:

\(E=14961.78867...\approx14,962\text{ feet}\)

Answer:

a. The given equation is (y - 3)^2 -10 = 71. To determine the number and type of solutions, we need to use the discriminant, which is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0). In this case, the equation can be rewritten as (y - 3)^2 = 81, which is in the form of (y - k)^2 = r^2, where k = 3 and r = 9. Therefore, the equation can be written as (y - k)^2 - r^2 = 0, which is a quadratic equation with a = 1, b = -6, and c = -72. The discriminant is then b^2 - 4ac = (-6)^2 - 4(1)(-72) = 300. Since the discriminant is positive, there are two real solutions.

b. To solve the equation (y - 3)^2 -10 = 71, we first add 10 to both sides to get (y - 3)^2 = 81. Then, we take the square root of both sides to get y - 3 = ±9. Adding 3 to both sides, we get y = 3 ± 9, which gives us two solutions: y = 12 and y = -6.

Therefore, the equation (y - 3)^2 -10 = 71 has two real solutions, which are y = 12 and y = -6.

Step-by-step explanation:

Answer:  type: real   number of solutions:2   y=12,-6

Step-by-step explanation:

see images for explanations

The volume of the solid whose base is the semicircle y = √(16 - x²), where -4 < x < 4 and whose cross section perpendicular axis are squares is 256/3 unit³

To obtain the volume of a 3D shape, the cross-section area is discovered and then integrated across a predetermined limit. This technique is known as the cross-sectional method of volume fining. The area of the square base is determined in the given problem, and it is then integrated to determine the overall volume.

To find the volume we will first find the cross-sectional area and then integrate it with respect to x from -4 to 4.

Thus the volume is given as follows:

y = √(16 - x²)

V = ₋₄∫⁴ (√(16 - x²))² dx

V = ₋₄∫⁴ (16 - x²) dx

V = [16x - x³/3]₋₄⁴

V = (64 - 64/3 + 64 -64/3)

V = 256/3 unit³

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Answer: It is Yes

Step-by-step explanation:

The y-intercept of the line representing Beatrice's monthly music is 20

From the question, we have the following parameters that can be used in our computation:

y = -.95x + 20

To calculate the y-intercept of the line, we set x = 0

So, we have

y = -.95 * 0 + 20

Evaluate

y = 20

Hence, the y-intercept of the line representing Beatrice's monthly music is 20

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Question

What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?

The equation is y = -.95x + 20

Answer:

a)29

b)70

Step-by-step explanation:

The sum of the interior angles in a triangle is 180.

a)95+56+a=180        b)40+2b=180

151+a=180                     2b=180-40

a=180-151                      2b=140  /2

a=29                              b=70

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.

From the given dot plot.

The number of minutes Charles spent on homework.

15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.

Here, lower quartile = 20

Upper quartile = 50

Median = 30

Range = 60-15

= 45

The number of minutes Jermod spent on homework.

15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.

Here, lower quartile = 20

Upper quartile = 50

Median = 45

Range = 55-15

= 40

Therefore, options C and D are the correct answer.

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If you're looking for the cube roots of √(3 + i ), you first have to decide what you mean by the square root √(…), since 3 + i is complex and therefore √(3 + i ) is multi-valued. There are 2 choices, but I'll stick with 1 of them.

First write 3 + i in polar form:

3 + i = √(3² + 1²) exp(i arctan(1/3)) = √10 exp(i arctan(1/3))

Then the 2 possible square roots are

• √(3 + i ) = ∜10 exp(i arctan(1/3)/2)

• √(3 + i ) = ∜10 exp(i (arctan(1/3)/2 + π))

and I'll take the one with the smaller argument,

√(3 + i ) = ∜10 exp(i arctan(1/3)/2)

Then the 3 cube roots of √(3 + i ) are

• ∛(√(3 + i )) = ¹²√10 exp(i arctan(1/3)/6)

• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + π/3))

• ∛(√(3 + i )) = ¹²√10 exp(i (arctan(1/3)/6 + 2π/3))

On the off-chance you meant to ask about the cube roots of 3 + i, and not √(3 + i ), then these would be

• ∛(3 + i ) = ⁶√10 exp(i arctan(1/3)/3)

• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/3 + 2π/3))

• ∛(3 + i ) = ⁶√10 exp(i (arctan(1/3)/6 + 4π/3))

Answer:

16 teachers.

Step-by-step explanation:

84 / 21 = 4

4 * 4 = 16

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Answer:

\( \huge \colorbox{blue}{16 students}\)

Step-by-step explanation:

we are given the ratio of students and teachers:

\( \displaystyle \: \frac{21}{4} \)

which means if the number of students is 21 then the number of teachers should be 4

to find how many teachers should go if students 84 we have to divide 84 by \(21/4\) :

\( \displaystyle \: 84 \div \frac{21}{4} \)

simplify division:

\( = \displaystyle \: 84 \times \frac{4}{21} \)

simplify multiplication:

\( = \displaystyle \: \cancel{ 84} \: ^{4} \times \frac{4}{ \cancel{21}} \\ = 4 \times 4 \\ = 16 \)

Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)