Add the equations.

3x - y = -5
7x + y=15

A. -4x = 10
B. -4x = -20
C. 10x = 10
D. 10x-2y = -20

The GPA of the girls is 3.12

In this question, we have been given a class has 12 boys and 18 girls.

The class as a whole has a GPA (grade point average) of 2.88, and the boys have a GPA of 2.52

We need to find the GPA of girls.

Let m be the GPA of girls.

The weighted average GPA would be,

(12(2.52) + 18m)/ (12+18) = 2.88

We solve above equation to find the value of m

30.24 + 18m = 30 * 2.88

18m = 86.4 - 30.24

18m = 56.16

m = 3.12

Therefore, the GPA of the girls in the class is 3.12

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Answer: A. No, because two points with the same x-value have different y values.

Step-by-step explanation: A function is a relation in which each element in the domain (the set of x-values) is paired with exactly one element in the range (the set of y-values). If there are two points with the same x-value but different y-values, then there is more than one y-value for a given x-value, which violates the definition of a function. Therefore, the given relation is not a function.

Answer:

b = 72

Step-by-step explanation:

Since AB and AC are congruent then Δ ABC is isosceles with base angles also congruent, that is

∠ ACB = ∠ ABC = b

the sum of the 3 angles in the triangle is 180° , then

b + b + 36 = 180

2b + 36 = 180 ( subtract 36 from both sides )

2b = 144 ( divide both sides by 2 )

b = 72

Answer:

152°

Step-by-step explanation:

Circle Theorem vocabulary

Secant: a straight line that intersects a circle at two points.

Arc: the curve between two points on the circumference of a circle

Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

Angles of Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.

[tex]\implies m \angle PRD=\dfrac{1}{2}\left(m\overset{\frown}{PD}-m\overset{\frown}{QS} \right)[/tex]

From inspection of the given diagram:

Substitute these into the formula and solve for x:

[tex]\implies 50^{\circ}=\dfrac{1}{2}\left((12x+8)-(4x+4)\right)^{\circ}[/tex]

[tex]\implies 50^{\circ}=\dfrac{1}{2}\left(8x+4\right)^{\circ}[/tex]

[tex]\implies 100^{\circ}=(8x+4)^{\circ}[/tex]

[tex]\implies 96^{\circ}=8x^{\circ}[/tex]

[tex]\implies x=12[/tex]

Substitute the found value of x into the expression for arc PD:

[tex]\implies m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=(12 \cdot 12+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=(144+8)^{\circ}[/tex]

[tex]\implies m\overset{\frown}{PD}=152^{\circ}[/tex]

Therefore, the measure of arc PD is 152°.

The probability that  is more likely between selecting a tube of blue or yellow paint, OR selecting a tube of green or red paint id; Both are equally lilkely.

We are given;

Number of blue tubes = 7

Number of red tubes = 4

Number of yellow tubes = 3

Number of green tubes = 6

Thus;

Total number of painted tubes = 7 + 4 + 3 + 6 = 20

Probability of selecting a blue tube = 7/20

Probability of selecting a red tube = 4/20

Probability of selecting a yellow tube = 3/20

Probability of selecting a green tube = 6/20

Thus;

P(selecting a tube of blue or yellow paint) = (7/20) + (3/20) = 10/20

P(selecting a tube of green or red paint) = (6/20) + (4/20) = 10/20

Thus, they are equally likely.

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Answer: 2.666666etc..

Step-by-step explanation:

Answer:

2.64

Step by step explanation

4/9=0.44

0.44×6=2.64

In the online auction for an autograph, losing bid is 10 less than the winning bid.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Losing bid in online auction of Autograph = $40,

Also, Losing bid is 80% of the winning bid,

Let winning bid is 100%.

Therefore, winning bid is 20% more than losing bid.

Since,

80% = 40

20 % = 10

Hence, losing bid is 10 less than the winning bid.

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Answer:

Step-by-step explanation:

2x - 3y = 6

-3y = -2x + 6

y = 2/3x - 2

correct answer is A

Answer: x=26

Step-by-step explanation:

a^2+b^2=c^2

28.2^2-16^2=539.24

square root 539.24=23.2

23.2^2+11^2=659.24

square root 659.24=25.7

x=25.7 or 26

Answer:

Step-by-step explanation:

[tex]P(t)=400cos(30t-180)+1100[/tex]

a.  What was the population of arctic foxes in Yukon in 1992?

t' represents the number of years since 1992. So plugging in 0 gives the population in 1992.

[tex]P(0)=400cos(30*0-180)+1100[/tex]

Subtract 180 from 0.

[tex]P(0)=400cos(-180)+1100[/tex]

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

[tex]P(0)=400(-cos(0))+1100[/tex]

The exact value of cos (0) is 1.

[tex]P(0)=400(-1*1)+1100[/tex]

[tex]P(0)=400*-1+1100[/tex]

Multiply 400 by −1. Then add −400 and 1100.

[tex]P(0)=700[/tex]

D. What will be the population of arctic foxes in 2030?

[tex]P(38)=400cos(30(38)-180)+1100[/tex]

[tex]P(38)=900[/tex]

The equations of the line that passes though points (2,-1) and (8,4) are

The linear function written in the slope intercept form  form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (2,-1) and (8,4)

m = (y₂ - y₁) / (x₂ - x₁)

substituting the values

= (-1 - 4 ) / (2 - 8 )

= -4 / -6

= 2/3

using the point slope formula which is

(2, -1)

(y - y') = m(x - x')

(y - (-1)) = 2/3(x - 2)

y + 1 = 2x/3 - 4/3

y = 2x/3 - 4/3 - 1

y = 2x/3 - 7/3

(8,4)

(y - 4) = 2/3(x - 8)

y - 4 = 2x/3 - 16/3

y = 2x/3 - 16/3 + 4

y = 2x/3 - 28/3

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Answer:

YES

Step-by-step explanation

it is just vocab words you probably have to study

567 feet does the car travel before coming to a complete stop .

What is the definition of a velocity simple?

The direction of the movement of the body or the object is defined by its velocity. In its basic form, speed is a scalar quantity.

                        In essence, velocity is a vector quantity. It measures how quickly a distance changes. It is the displacement change rate.

vo = 48     v(t) = integral of a(t) plus vo, the initial velocity

a(t) = -2

v(t) = -2t + 48 = 0 when t= 21 seconds, the time to stop

s(t) = -t^2 +48t  

s(21) = -(21)^2 + 48(21) = 1008-441 = 567 feet

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The equation of the line is y = -2x + c

What is an equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another.

To find the slope, use the two points (4.5,0) and (0,9) and substitute these in the slope formula:

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

   = (9 - 0) / (0 - 4.5)

   = -2

The equation of the line is

y = mx + c

y = -2x + c

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Answer:

[tex]2x^2+7x+6[/tex]

Step-by-step explanation:

Use the FOIL method to multiply these two expressions:

[tex](x+2)(2x+3)\\x(2x)+2(2x)+3(x)+2(3)\\2x^2+4x+3x+6\\2x^2+7x+6[/tex]

The area of the circle-shaped rug is 379.94 square inches

The formula for calculating the area of a circle is expressed as;

Area = πr^2

Where;

From the information given, we have the value of the circumference as 69.08 inches

We need to find the value of the radius.

The formula for calculating the circumference of a circle is mathematically expressed as;

Circumference = 2πr

Where: r is the radius of the circle and π takes the value 3. 14

Now, substitute the value into the formula for circumference of a circle, we have;

69.08= 2(3.14)r

Divide both sides by the coefficient of r

r = 69.08/6. 28

r = 11 inches

Then, area = 3.14 × (11)^2

Area = 3.14 × 121

Area = 379.94 square inches

Hence, the value is 379.94 square inches

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Complete question:

Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 69.08 inches. Find the area

The interpretations of the equations are

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

The function `P` gives the number of people, in millions,

Years = t

The function P(17) = 2320

Recall that, we have

P(t) = the number of people, in millions,

This means that the year is

Year = 2000 + 17

Year = 2017

So, the interpretation is there are 2320 million people in 2017

The function P(-10) = 0

So, we have

Year = t + 2000

Substitute the known values in the above equation, so, we have the following representation

Year = -10 + 2000

Evaluate

Year = 1990

So, the interpretation is there are 0 million people in 1990

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Complete question

The function gives the number of people , in millions. who own smarphone t years alter the year 2000

What does each equaton tell us about smartphone ownership?

(a) P(17) = 2320

(b) P(-10) = 0

118°

The overall shape is a quadrilateral. meaning total angles on the inside = 360°

each side is equal and therefore both CDE and CFE are the same. 90 + 34 = 124

360 - 124 = 236

236/2 = 118 therefore you answer is 118°

After the linear equation method the answer is 6 Zoomas and 5 Popsies.

What is an linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

There is a linear equation in one variable and a linear equation in two variables.

It is given that there are two types of alien live on the planet Starlight Zoomas and Popsies.

Zoomas have 3 eyes and 2 legs

Popsies have 4 eyes and 5 legs

There are total 38 eyes and 37 legs

Let there are x number of Zoomas and y number of Popsies.

According to question:

3x + 4y = 38 ..........(1)

2x + 5y = 37 ...............(2)

Solve the above system of equation.

Find the value of x from the equation(1)

3x + 4y = 38

3x = 38 - 4y

x = [tex]\frac{38-4y}{3}[/tex]

Substitute this value of x in equation(2)

2( [tex]\frac{38-4y}{3}[/tex]) + 5y = 37

⇒ [tex]\frac{76-8y}{3}+5y = 37[/tex]

⇒ [tex]\frac{76-8y+15y}{3}=37[/tex]

⇒ 76 + 7y = 111

⇒ 7y = 111 - 76

⇒ 7y = 35

⇒ y = 35/7 = 5

Substitute this value of y in the value of x

x = [tex]\frac{38-4y}{3}[/tex]

x = [tex]\frac{38-4(5)}{3}=\frac{38-20}{3}=\frac{18}{3}=6[/tex]

Therefore, there are 6 Zoomas and 5 Popsies.

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The probability that their average score is between 200 and 250 is 42.49%.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree

Given:

Mean = 240

and standard deviation = 27

So, P( 200 < x < 250) =  P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] < x <  x- [tex]\mu[/tex])/ [tex]\sigma[/tex])

                                    = P (200- 240 / 27  < x < 250- 240 /27)

                                    = P( -1.481 < x < 0.370)

                                    = 0.42499

Hence, the probability that their average score is between 200 and 250 is 42.49%.

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Answer: 1/2

Step-by-step explanation:

Let N be any number and M be the additive inverse of N

N + M = 0 = M + N

that additive inverse of N is - N

x + ( - 1/2 ) = 0

x - 1/2 = 0

x = 1/2

the additive inverse of -1/2 is 1/2

Answer:

x (in simple terms)< -11/7 or -1 4/7

Step-by-step explanation:

1) Place x on one side: The point of this is to islolate x (and to keep things simple make x a positive variable if you can). One way of doing this is adding 8x on both sides what we now get is 14 < 14x + 36

2) Subtract 36 on both sides: We doing this for the same reason as the 1st step which is to islolate x so after this the new equation is -22 < 14x

3) Divide 14 on both sides: Since we aren't dividing by a negative number the sign remains the same the answer is -22/14 < x or x> -22/14 but to simply find the greatest common factor for both the numberator and demonationr which is 2 and divide from there the answer is x> -11/7 or x> -1 4/7

An elevator stop for 23 floor.

it went up so +18

it came down so -11

again it went upward +16

so... 18-11+16

=18+16-11

=34-11

=23

An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They are typically powered by electric motors that drive traction cables and counterweight systems such as a hoist, although some pump hydraulic fluid to raise a cylindrical piston like a jack.

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Answer:

  24th floor

Step-by-step explanation:

You want to know where an elevator stopped if it started at the first floor, went up 18, down 11, and back up 16.

If it started at the first floor and went up 1, it would be at the 2nd floor. Starting from the first floor and going up 18, it would be at the 19th floor.

Down 11 floors from there is the 8th floor. Back up 16 floors from the 8th floor puts the elevator at the 24th floor.

The elevator stopped at the 24th floor.

__

Additional comment

If there is no 13th floor, then it may have stopped at the 25th floor.

Answer: $4

Step-by-step explanation: To find how much each family paid, we must do this:

80-44

That gets us to 36. Now, we do 36 / 9, and get 4!

TIP: Don't worry about the negative signs, It won't be used in this. I hope this helped!

Answer:

q = -9

Step-by-step explanation:

(3, -15), (4, -21)

(-21 + 15)/(4 - 3) = -6/1 = -6

y + 15 = -6(x - 3)

y + 15 = -6x + 18

y = -6x + 3

q = -6(2) + 3 = -12 + 3 = -9

The required equation is y = -(x + 1)² + 9.

Parabola is a curve like shape, in which any point is equal distance from a fix point.

The standard equation of parabola,

y = a(x-h)² + k.

Here, h = horizontal coordinate of the vertex,

k = vertical coordinate of the vertex.

In the given graph, the vertical coordinate of the vertex k = 9,

The horizontal coordinate of the vertex h = -1.

And the focus of the parabola = -1,

The required equation,

y = -1(x - (-1))² + 9

y = -(x + 1)² + 9

The required equation of the given graph is y = -(x + 1)² + 9.

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Answer:

25

Step-by-step explanation:

9/x = 36/100

9 x 4 = 36

? x 4 = 100

100 ÷ 4 = 25

One way to solve 2(a - 1.1) = 5.8 is divide both sides by 2 and then add 1.1 on both sides to find a = 4.

To solve 5/2 b - 2 3/4= 7 1/4, add 2 3/4 on both sides, and then multiply both sides by 2/5 to find b = 4.4

In the equation a and b divide the same value.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

2(a - 1.1) = 5.8

divide both sides by 2

a - 1.1 = 5.8/2

a - 1.1 = 2.9

Add 1.1 on both sides:

a - 1.1 + 1.1 = 2.9 + 1.1

a = 4.

Another equation is

5/2 b - 2 3/4= 7 1/4

add 2 3/4 on both sides:

5/2 b= 7 1/4 + 2 3/4

Convert the mixed fraction to improper fraction:

5/2 b  = 29/4 + 15/4

5/2 b  = 44/4

Multiply both sides by 2/5:

b = (44/4) × (2/5)

b = 11× (2/5)

b = 22/5

b = 4.4

Both number 4 a and 4.4 is divisible by 4.

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Answer:

54 is the answer

Step-by-step explanation:

hope this helps

Answer:

54 is your answer

Step-by-step explanation:

the person above is right