!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

The viewer represents the correct answers with x and the incorrect ones with y.

x+y = 20

for every correct answers 2 points;

and for every incorrect answers, -1 point

This can be written as

2x-y = 28

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

now

2x-y = 28

x+y = 20

On adding the equations

]3x = 48

x = 16

y = 4

This means that the contestant answered 16 questions correctly and 4 questions incorrectly

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

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The integral of [tex]f(x)[/tex] over the interval [tex][-a,a][/tex] corresponds to the area of a semicircle of radius [tex]a[/tex], so

[tex]\displaystyle \int_{-a}^a f(x) \, dx = \frac{\pi a^2}2[/tex]

The integral over [tex][a,3a][/tex] corresponds to the negative area of a trapezoid with height [tex]a[/tex] and base lengths [tex]2a[/tex] and [tex]a[/tex], so

[tex]\displaystyle \int_a^{3a} f(x) \, dx = -\frac{a(2a+a)}2 = -\frac{3a^2}2[/tex]

Then combining the integrals, we have

[tex]\displaystyle \int_{-a}^{3a} f(x) \, dx = \frac{\pi a^2}2 + \left(-\frac{3a^2}2\right) = \frac{(\pi-3)a^2}2[/tex]

When [tex]a=9[/tex], the integral evaluates to

[tex]\displaystyle \int_{-9}^{27} f(x) \, dx = \frac{(\pi-3)\times81}2 \approx \boxed{5.7345}[/tex][/tex]

Answer:

6, -2

Step-by-step explanation:

basically It asks you what's x when y=2, which on the graph is 6, -2, and -5 I think. but there is no point on the -5 so we don't need to talk about that one.

Answer:

1. 65

2. 52

3. 13

Step-by-step explanation:

For these answers, we can look at the graph:

Question 1:

For the helmet that costs 35 dollars, we look at the x-axis until we find the helmet that aligns with 35.

Then, we look at the y-axis and find the blue dot. The blue dot is the actual consumer rating that was recorded, NOT the red line. The red line is the predicted consumer rating in correlation to the price.

Hence, the consumer rating is 65.

Question 2:

For this, we can look back at the graph and apply the same concept as above. Notice how the 65 plot is 13 points away from the point predicted by the red line.

Therefore, 65 - 13 = 52

Question 3:

Just like the last two questions, we can look at the graph for this. The green line gives us this answer flat out, displaying the distance from the actual rating to the predicted rating.

Hence, the actual consumer rating was 13 above the predicted rating.

I assume you meant [tex]f(x)=100(0.7)^{x}[/tex]. The graph is shown in the image below.

Answer:

Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

Step-by-step explanation:

Edge

Answer:

A, D, E

Explanation:

It's right on edge lol

Answer:

x = [tex]\frac{7}{5}[/tex]

Step-by-step explanation:

To solve for x, we need to isolate it [get it alone on one side]

We should start by simplifying (combining the like-terms of our equation):

5 + 5 = 5x + 5 - 2

10 = 5x + 3

- 3         - 3        (subtract 3 from both sides to isolate x)

7 = 5x

÷5  ÷5   (divide both sides by 5 to find "1"x)

[tex]\frac{7}{5}=x[/tex]  

So, x = [tex]\frac{7}{5}[/tex]

(x = 7/5)

hope this helps!!

5 + 5 = 5x + 5 - 2

Answer :

[tex]x = \frac{7}{5} [/tex]

Step-by-step explanation:

5 + 5 = 5x + 5 - 2

10 = 5x + 3

Take 3 to the other side

10 - 3 = 5x

7 = 5x

[tex] \frac{7}{5} = x[/tex]

[tex]x = \frac{7}{5} [/tex]

Annette's age will be twice Josefin's age 10 years ago.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

Given that:-

Josefin is 32 years younger than Annette. How many years ago was Annette's age twice Josefins age if Annette is 74 now.

So we can see that their present age Annette is 74 so the present age of Josefin will be 32 years lesser.

J = 74 - 32 = 42 years

The before 10 years ages of both the Josefin and Annettes will be:-

J = 42 - 10 = 32

A = 74 - 10 = 64

The ratio of the ages is:-

A / J = 64 / 32 = 2

A = 2 J

Therefore Annette's age will be twice Josefin's age 10 years ago.

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The amount of the extra snow would a child need to take a snowball will be 636.71 cubic cm.

Let d be the diameter of the sphere.

Then the volume of the sphere will be

V = 1/6 πd³ cubic units

Then the amount of the extra snow would a child need to take a snowball with a diameter of 8 cm and increase its size to a snowball with a diameter of 12 cm will be

Amount of snow = 1/6 π x 12³ - 1/6 π x 8³

Amount of snow = 288 π - 85.33π

Amount of snow = 636.71 cubic cm

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Answer:

x = 5 (If solved algebraically)

No Solution (If the parentheses are absolute value lines)

Step-by-step explanation:

Result when solving this way: 3|-3x + 9| = -18

1) Divide both sides by 3
|-3x + 9| = -18/3

2) Simplify 18/3 to 6

|-3x + 9| = -6

3)  Break down the problem into these 2 equations.

-3x + 9 = -6

- (-3x + 9) = -6

4) Solve the 1st equation: -3x + 9 = -6

- Subtract 1 from both sides.

-3x = -6 - 9

-Simplify -6 - 9 to -15.

-3x = -15

-Divide both sides by -3.

x = -15/-3

- Two negatives make a positive.

x = 15/3

- Simplify 15/3 to 5.

x = 5

6)  Solve the 2nd equation:  - (-3x+ 9) = -6

1 - Remove parentheses

3x - 9 = -6

2 - Add 9 to both sides

3x = -6 + 9

3 - Simplify -6 + 9 to 3.

3x = 3

- Divide both sides by 3.

x = 1

6) Collect all solutions.

x = 1,5

7) Check solution.

When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 1 from the solution set.

8) Check solution.

When x = 5, the original equation 3|-3x + 9| = -18  does not hold true.

We will drop x = 5 from the solution set.

9) Therefore,

No solution exists.

Result when solving algebraically:

Simplifying

3(-3x + 9) = -18

Reorder the terms:

3(9 + -3x) = -18

(9 * 3 + -3x * 3) = -18

(27 + -9x) = -18

Solving

27 + -9x = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + -9x = -18 + -27

Combine like terms: 27 + -27 = 0

0 + -9x = -18 + -27

-9x = -18 + -27

Combine like terms: -18 + -27 = -45

-9x = -45

Divide each side by '-9'.

x = 5

Simplifying

x = 5

Step-by-step explanation:

3x8=24

24x30=720

720÷18=40 cents

At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. is mathematically given as

Generally, the equation  for the temperature at Portland, Maine is mathematically given as

PoT=-PhT

Since  Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix.

In conclusion, the temperature in each city is

PoT=-PhT

PhT =+PoT

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The function is [tex]y = (x +2)^2 + 5.[/tex]

we use the vertex form of the quadratic equation

We have given a graph,

y = a(x - h)^2 + k.

Therefore the vertex of the given graph is

See the vertex at (-2, 5)

Since the general way to write the vertex is (h, k), we compare (h, k) to (-2, 5).

[tex]y = a(x - (-2))^2 + 5.\\y=a(x+2)^2+5......(1)[/tex]

Now we have given that (-4,1) use this value in the above equation so we get,

[tex](1)=a(-4+2)^2+5[/tex]

[tex]1=a(-2)^2+5[/tex]

[tex]1=4a+5[/tex]

[tex]1-5=4a[/tex]

[tex]-4=4a[/tex]

[tex]a=-4/4[/tex]

[tex]a=-1[/tex]

Using the value of an in equation (1) we get,

Therefore the function is [tex]y = (x +2)^2 + 5.[/tex]

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Blank 1: 3

Blank 2: 27

Blank 3: 21

you have to distribute the three to everything inside the parenthesis, and because it's directly in front of the parenthesis it's being multiplied.

3(x - 9) = 3x - 27

Now you need to isolate the y, in this e ample you need to add 6 to both sides

the final equation should be:

y = 3x - 21

Arturo receives $90 more in the first week of work than the second.

The time a person spends engaged in compensated work is referred to as working time.

Given,

First Week Working hours = 40 hours,    per hour rate = $12

The second-week working hours = 30,   per hour rate = $13 (With raise of $1)

Calculation of Wages

First Week wages = Total Weekly Hours ×  Per Hour rate

                                     = 40 × 12 =$480

Second Week wages = Total Weekly Hours ×  Per Hour rate

                                    = 30 × 13 =$390

The difference between the First week's wages and the Second week's wages is $90 ($480 - $390).      

Thus, Arturo earn $90 more in the first week as compared to the second week.

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If the graph of a line  in an x y plane and its corresponding equation is given then , all the coordinates of every point on that line will satisfy the equation is a true statement.

An equation of a straight line is given by

y = mx+c

where m is the slope and c is the intercept on y axis.

If the graph of a line  in an x y plane and its corresponding equation is given then , all the coordinates of every point on that line will satisfy the equation .

Even for a scatter plot the line of the best fit is drawn and every point on the line will satisfy the equation.

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Answer:

c

Step-by-step explanation:

answer is C . First last digits are forty you will have down 2 answers

Answer:

the answer to the question is C

The slope of the line and describe is the negative 0.5 which means in this situation will be negative 0.5 miles per minute.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall, and the difference between the abscissa is called run.

Joseph drove from his summer home to his place of work.

To avoid the road construction, Joseph decided to travel the gravel road.

After driving 20 minutes, he was 62 miles away from work, and after driving 40 minutes, he was 52 miles away from work.

This situation is shown in the graph below.

Then the slope of the line and describe what it means in this situation will be

Slope = (52 – 62) / (40 – 20)

Slope = – 10 / 20

Slope = – 0.5 miles per minute

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Answer:

Step-by-step explanation:

she has 7 servings. Add 1/2 + 1/2 until you get 3 1/2 and it equals 7

Answer:

1/2

Step-by-step explanation:

First parabola  f(x1)   =  a ( x+4)(x-6)    use point 0,-12 to find a = 1/2

                                = 1/2 (x+4)(x-6)

Second parabola    a ( x+4) (x-6)       using point  0, -24    shows a = 1

                       f(x2)       = (1)(x+4)(x-6)

Difference between the 'a' values =  1 - 1/2 = 1/2

Answer: x = 130, y = 130

Step-by-step explanation:

By the corresponding angles theorem, x = 130

Thus, by the vertical angles theorem, y = 130

Answer:

[tex]1.9 \times {10}^{7} meters[/tex]

is the right answer

The quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

The quadratic equation that takes the form ax^2+bx+c can be determined from a given set of factors by applying the rule:

Let us expand the eqaution: 2(x-1) (2x+3)

So, we have:

2(x - 1)(2x + 3) ⇒ 4x² + 2x - 6.

= 4x² + 2x - 6 + x² - 4x + 2

Now, let us group like terms, we have:

= 4x² + x² + 2x - 4x - 6 + 2

= 5x² - 2x - 4

Therefore, we can conclude that the quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.

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[tex]z_{2}-3i=(-4+i)-3i=-4-2i\\\\z_{1}+2=(3-4i)+2=5-4i\\\\(z_{1}+2)-(z_{2}-3i)=(5-4i)-(-4-2i)=9-4i+4+2i=9-2i[/tex]

which corresponds with point C

The expression which is the result of subtracting (z2-3i) from (z1+2) is 9-2i.

Given On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, -2), B is (1, -6), C is (9,- 2), D is (9, - 6), z 1 is (3, - 4), and z 2 is (- 4, 1).

Coordinate plane is a two dimensional plane formed by the intersection of two number lines. One is horizontal line and one is vertical. On horizontal line x values are denoted and on vertical line y values are written. There can be three dimensional plane also.

z2-3i=(-4+i)-3i=-4-2i

z1+2=(3-4i)+2=5-4i

(z1+2)-(z2-3i)=(5-4i)-(-4-2i)

=9-4i+4+2i

=9-2i

Hence for the expression (z1+2)-(z2-3i)=9-2i

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Answer:

Step-by-step explanation:

2/x-5

Answer:

(x-1) and (x-5)

Answer:

x is 130°,y is 60°

Step-by-step explanation:

x is corresponding to 130° therefore they are equal to find y since the angle on a straight line is 180° you subtract 180 from 130 and get 50 then you have gotten the other interior angle then add both interior angles and subtract by180 then you get the y

Answer:

both the lines are parallel

therefore, X= 130° ( if two lines are parallel their corresponding angles are equal)

Y + 70° = X ( sum of tow interior angle is equal to exterior)

Y + 70= 130

Y = 130 - 70

Y = 60°

The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}

What are the domain and range of the function f(x) = x^2 + 8x + 7/x + 1

We have the function to be

[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]

Set the denominator to 0

x + 1 = 0

Solve for x

x = -1

This means that the domain of the function is the set of all real numbers except -1

Hence, the domain of the function is {x ∊ ℝ | x ≠ -1}

We have the function to be

[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]

Factorize the numerator

[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1}[/tex]

Simplify

f(x) = x + 7

The function is undefined at x= -1.

So, we have:

f(-1) = -1 + 7

f(-1) = 6

This means that the range of the function is the set of all real numbers except 6

Hence, the range of the function is {y ∊ ℝ | y ≠ 6}

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Answer:

It is d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}

Step-by-step explanation:

I took the test