Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?
No solutions
Infinite solutions
(32)
(9,2)

The value of the expression [tex]2 \div 6.3[/tex] is 0.32

The expression is given as:

[tex]2 \div 6.3[/tex]

Rewrite as:

[tex]2 \div 6.3= \frac{2}{6.3}[/tex]

Multiply the expression by 10/10

[tex]2 \div 6.3= \frac{20}{63}[/tex]

Divide 20 by 63

[tex]2 \div 6.3= 0.31746031746[/tex]

Approximate to the nearest hundredth

[tex]2 \div 6.3= 0.32[/tex]

Hence, the value of the expression [tex]2 \div 6.3[/tex] is 0.32

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The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

The weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

We assume the weight of the cow to be x kg.

The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.

Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.

But, we are given that together, they weigh 360 kg.

This can be shown as the linear equation in the one variable:

x/8 + x = 360.

Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

To solve the problem, we solve the equation as follows:

x/8 + x = 360,

or, (9/8)x = 360 {Simplifying},

or, x = 360*8/9 {Cross-Multiplying},

or, = 320.

Thus, the weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

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Step-by-step explanation:

you multiply both sides by the same factor, so that the main message or information, the ratio, stays the same :

3:6 × 2/2 = 6:12

3:6 × 1/3 / 1/3 = 1:2

3:6 × 4/3 / 4/3 = 4:8

3:6 × 100/100 = 300:600

so, these are all equivalent ratios. and there are infinitely more, as you can see.

The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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The area of Entire roof is 12 feet².

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)

Given:

As, the roof peak with a 3 and the roof overhang the sides is 4.

Now, Using Pythagorean theorem.

a² + b² = c ²

15² + 13² = c²

c² = 225+ 169

c = 19.8 (or 20)

So, the length of diagonal is 24.

Roof Dimension 36 x 24 or (

Area of Roof = 3 x 2

                      = 6 unit²

and, area of the entire roof = 2 x6 = 12 ft²

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The result of the evaluation of the equation given in the task content is; x =-2.

It follows from the task content that the equation given whose solution is to be determined is;

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

The equation can be solved as follows;

-3x + 6x +3 = x-1

2x = -4

x = -2

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Answer:

Step-by-step explanation:

(7x-3)(12x-7)

we are solving for x and we are multiplying.

we start with the x's 7x*12x=  84x

-3*-7=21

so now we have

84x+21=0

the 0 is a placer for answering the question

we minus 21 to both sides

84x=-21

now we divide

84/-21= -4

x=-4

Answer:

One side is 40 cm and the adjacent side is 50 cm

Step-by-step explanation:

We can use a rectangle because a rectangle is a parallelogram.  Draw a rectangle.  Write the width as x and the length as x + 10.  We find the perimeter by adding all 4 side lengths.

Two side lengths are x and two side lengths are x + 10.  If we add all of this together we get 180

x +x +x+10+x+10 = 180

4x + 20 = 180  Combine the like terms.  There are 4 x's and 10+10 is 20

4x = 160  Subtract 20 from both sides

x  = 40  Divide both sides by 4

So, two sides are 40 and two sides are 50, this will add up to 180

Answer:

40 cm & 50 cm

Step-by-step explanation:

one side = X cm (??)

the other side =X+10 cm

Solve

2(x+x+10)=180

x+x+10=90

2x=80

x = 80/2

x=40

therefore

x+10=50cm

Answer:

[tex]0,35[/tex]

Step-by-step explanation:

In view of the fact that our events are independent of each other, we should multiply their probabilities: [tex]P(A \cap B) = P(A) * P(B) = 0,7 * 0,5 = 0,35[/tex].

Answer:

Step-by-step explanation:

The area of a circle is πr²

so your area is 114.99

Answer:

The water in pot X is hoter than that of pot Y

Answer:

A is the answer

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

i'm 99% sure

Answer:

A. y = 0.5x

Step-by-step explanation:

i got it right

The volume of the igloo is 523.43 m^3

We know that the volume of a sphere of radius R is:

[tex]V = (4/3)*pi*R^3[/tex]

Where pi = 3.14

Then the volume of a hemisphere is half of that.

In this case, we have a hemisphere with a radius of 6.3m, then the volume will be:

[tex]V = (1/2)*(4/3)*3.14*(6.3m)^3 = 523.43 m^3[/tex]

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Answer:

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m represents the slope and b represents the intercept.

x - 3y = 6

3y = x - 6

y = [tex]\frac{1}{3}[/tex]x - 2

4x - y = 1

y = 4x - 1

6x + 5y = -15

5y = -6x - 15

y = -[tex]\frac{6}{5}[/tex]x - 3

13x - 11y = -12

11y = 13x + 12

y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]

The center and radius of the circle is (b) center: (-5, 1) radius: 2

The circle equation is given as:

(x-5)^2 + (y+1)^2 = 4

The circle equation is represented as:

(x-a)^2 + (y-b)^2 = r^2

Where:

Center = (a,b)

Radius = 4

By comparison, we have:

(a, b) = (-5, 1)

r^2 = 4

This gives

(a, b) = (-5, 1)

r = 2

Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2

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Answer:

c = 10

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)

Here given: a = 8 cm, b = 6 cm, c = ?

Substituting values:

8² + 6² = c²

c² = 64 + 36

c² = 100

c = √100

c = 10

Answer:

10 cm

Step-by-step explanation:

[tex]a^2=b^2+c^2[/tex]

[tex]a^2=6^2+8^2[/tex]

[tex]a^2=100[/tex]

[tex]\sqrt{a^2}=\sqrt{100[/tex]

a=10

The correct statement based on the data is: A. Mean, because there are no outliers to affect the data.

Outliers are data point that appears extreme from other data values of a data distribution. When there is an outlier in a data distribution, the median is a better measure of center, while the mean is best when outliers are absent.

From the data distribution for both bakeries, no data seem extreme from the rest of the data, therefore, the mean is a better measure of center.

The answer is: A. Mean, because there are no outliers to affect the data.

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Answer:

The system of equations y=14-2x and 6x+3y=42.

Step-by-step explanation:

Please see attachment to see the answer as a graph.

Hope this helps!

The function to calculate the speed is S = 260.52/t.

From the information given, there are 78 laps through the Monte Carlo and each lap has a distance of 3.34 km. Therefore, the total length of the race will be:

= 78 × 3.34

= 260.52km

The function to calculate the speed will be:

Speed = Distance/Time

S = 260.52/t

Complete question:

The famous Grand Prix has 78 laps through the Monte Carlo and each lap has a distance of 3.34 km.

a. What is the total length of the race?

b. Write a function that can be used to model the race where the independent variable represent the average speed.

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Answer:

There are 36 members in the Science Club.

Step-by-step explanation:

25 minus one is 24 and half of 24 is 12. 12 times 3 is 36, which is the full 3/3 of the Science Club.

The value of the probability P(A and C) is 0.18

The complete question is added as an attachment

From the attached tree diagram, we have:

P(A) = 0.6

P(C) = 0.3

The required probability is then calculated as:

P(A and C) = P(A) * P(C)

This gives

P(A and C) = 0.6 * 0.3

Evaluate

P(A and C) = 0.18

Hence, the value of the probability P(A and C) is 0.18

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Answer:

8.

Step-by-step explanation:

P/Q = 3.125 = 3 1/8

- looks like the denominator Q could be 8.

It could not be any of the other choices.

25/8 = 3.125.

Each junior  receives 93 score on the test. It is also the average score of the juniors.

Given Information

It is given that 10% of the strength of the class consists of juniors and 90% consists of seniors.

Let us assume the total strength of the class is 100, then,

Number of seniors = 90

Number of juniors = 10

It is also given that the average score of the class = 84

And, average score of the seniors = 83

Another given information is that all the juniors all received the same score, which is their average score. Let it be x.

Average Score of Juniors

Total marks obtained by the seniors = Number of seniors × Average score of seniors

= 90 × 83

= 7470

Total marks obtained by the juniors = Number of juniors × Average score of juniors

= 10x

Average marks on the test = Total marks / Total number of students

⇒ 84 = (7470 + 10x)/100

⇒ 84 × 100 = 7470 + 10x

⇒ 10x + 7470 = 8400

⇒ 10x = 8400-7470

⇒ 10x = 930

⇒ x = 930/10

⇒  x = 93

Thus, each junior scores 93 on the test.

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Answer:

y = |x + 8|

Explanation:

Please see the table attached below.

Answer:y=|x+8|

Step-by-step explanation:

No digit with the format 90x0y07 is divisible by 2017

The given parameters are:

Dividend = 90x0y07

Divisor = 2017

The dividend is a 7-digit number, and the divisor is a 4-digit number

So, the quotient must be 3 to 4 digits.

Comparing the first and last digits of 90x0y07 and 2017;

The first and last digits of the quotient must be 4 and 1, respectively

So, we have:

90x0y07 = 2017 * 4a1

Assume a = 9.

So, we have:

90x0y07 = 2017 * 491

90x0y07 = 990347

The above is 6-digit.

So, we make use of a 4-digit quotient

This gives

90x0y07 = 2017 * 4ab1

Next, we make use of trial by error.

After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017

The closest attempt is

90x0y07 = 2017 * 4471

90x0y07 = 9018007

Where:

x = 1, y = 0 and the digit between x and y is 8, not 0

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Answer:

The speed of the boat in still water is 18 mph.

The speed of the current is 2 mph

Step-by-step explanation:

Let x constitute the charge of the boat in nonetheless water.

Let y constitute the rate of the contemporary.

When the boat is going against the modern-day, the rate is sixteen mph. Assuming it traveled against the modern at the equal time as going upstream, its general speed may be (x - y) mph. It way that

x - y = 16  (equation 1)

Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its standard pace would be (x + y) mph. It way that

x + y = 20  (equation 2)

Adding each equation, it becomes

2x = 36

x = 36/2

x = 18 mph

Substituting x = 18 into equation 1, it will become

18 - y = 16

y = 18 - 16

y = 2 mph

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0,2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-1)}[/tex] = [tex]\frac{2}{0+1}[/tex] = [tex]\frac{2}{1}[/tex] = 2

The quadrants of the points are

The points are given as:

A(2, 4)    B(0, -3)   C(1, -1)

E(-4,1)     G(-3,-2)   I(0, 2)

D(3, 3)     F(2,0)    H(-2, 3)

J(-1,-4)

Next, we plot each coordinate on a graph (see attachment)

From the attached graph, we have the following categories

Quadrant 1: Points A and D

Quadrant 2: Points E and H

Quadrant 3: Points G and J

Quadrant 4: Points C

x-axis: Point F

y-axis: Point B and I

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Answer:

tan 33° = 0.6494

C = 65°

Step-by-step explanation:

Use a calculator.

tan 33° = 0.6494

cos C = 0.4226

Use the inverse cosine function on a calculator.

C = 65°

The distance of the top of the building from a is 163m and that from b is 115m .

Calculating the Perpendicular Distance of the Top From Ground

It is given that the angle of elevations of the building top from a and b are 25° and 37° respectively.

ab = 57m

Let the top of the building be point c and the distance between the building and the point b be x. Then, from the figure, we can deduce the following,

In Δacd, tan 25° = cd/ad

⇒ 0.4663 = cd /(x+57)

⇒ cd = 0.4663(x+57)             ......................... (1)

In Δbcd, tan 37° = cd/x

⇒ 0.7536 = cd/x

⇒ x =cd / 0.7536                   .......................... (2)

Solving for the Distance cd

Substitute the value of in equation (2) to equation (1) to get,

cd = 0.4663 ((cd/0.7536)+57)

cd = 0.4663(cd+42.9552)/0.7536

0.7536cd = 0.4663cd + 20.03

0.7536cd - 0.4663cd = 20.03

0.2906cd = 20.03

cd = 20.03/0.2906

Thus, the distance cd ≈ 68.93m

Finding the Distance cb and Distance ca

In Δacd, sin25° = cd/ca

⇒ 0.4226 = 68.93/ca

ca = 68.93/0.4226

ca = 163.10

∴ The distance ca ≈ 163m

Similarly, in Δbcd, sin37° = cd/cb

⇒ 0.6018 = 68.93/cb

cb = 68.93/0.6018

cb =114.54m

∴ The distance cb ≈ 115m

Therefore, the points a and b are at a distance of 163m and 115m respectively from the top of the building.  

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