A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.

[tex]4+ \sqrt{6x + 4 = 8} [/tex]

[tex] \sqrt{6x + 4 = 4}[/tex]

[tex]6x + 4 = 16[/tex]

[tex]6x = 12[/tex]

[tex]x = \frac{12}{6} = 2[/tex]

Option C is correct, x=2 is the solution to the equation 4+√(6x+4)=8

Two or more expressions with an Equal sign is called as Equation.

The given equation is 4+√(6x+4)=8

We have to solve for x

Subtract 4 from both sides

√(6x+4)=4

Square on both sides

6x+4=16

Subtract 4 from both sides

6x=12

Divide both sides by 6

x=2

Hence, Option C is correct, x=2 is the solution to the equation 4+√(6x+4)=8

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Answer:

it's C

Step-by-step explanation:

Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately  5.88\times 10^{12}5.88×1012 miles. Suppose a star is 2.23\times 10^22.23×102 light years from Earth.

To find : In scientific notation, how many miles away a star is from earth?

Solution :

One light-year is the distance that light can travel in one year is 5.88\times 10^{12}5.88×1012 miles.

In 2.23\times 10^22.23×102 lights year the distance is  

=5.88\times 10^{12}\times 2.23\times 10^2=5.88×1012×2.23×102

=1.31124\times10^{15}=1.31124×1015

Therefore, Option C is correct.

Answer:

-20

Step-by-step explanation:

x/5=3-7

x/5=-4

x=-4×5

x=-20

The amount of water in each pool at a particular time are illustrations of linear functions

For the first pool, we have the following parameters

So, the equation of the amount of water in the pool is:

y = 2164 + 31.75x

For the second pool, we have the following parameters

So, the equation of the amount of water in the pool is:

y = 2500 + 21.25x

When both pools have the same amount of water, we have:

2164 + 31.75x = 2500 + 21.25x

Collect like terms

31.75x - 21.25x = 2500 - 2164

Evaluate the like terms

10.5x = 336

Solve for x

x = 32

This means that they will have the same amount of water after 32 minutes

Substitute 32 for x in y = 2164 + 31.75x

This gives

y = 2164 + 31.75 * 32

y = 3180

Both pools will have 3180 liters at 32 minutes

Read more about linear functions at:

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Answer:

D

Step-by-step explanation:

as the p value is 0.45 > 0.05 so the report that men over 6 feet tall earn more then men under 6 feet tall is accepted. So the salary differences are statistically signifcant

Answer:

25th term = 701

Step-by-step explanation:

see attached

have a great day :)

Answer:

yes

Step-by-step explanation:

see the attachement

Answer:

x > -5/8

Step-by-step explanation:

Simplify by combining x and 4/5 and then moving 4 to the left side of x

-x * 4/5 + 3/10 < 8/10

-4x/5 + 3/10 < 8/10

Now we cancel the common factor of 8 and 10.

Factor 2 out of 8

-4x/5 + 3/10 < 2(4)/10

2 from 10

-4x/5 + 3/10 < 4/5

Now move all the terms not containing x to the right side

Lets subtract 3/10 from both sides

-4x/5 < 4/5 - 3/10

Now we multiply by 2/2 to write 4/5 with a common denomi.

-4x/5 < 4/5 * 2/2 - 3/10

Now write with a common denom of 10 and multiply by 1

-4x/5 < 4*2/5 * 2 - 3/10

5 by 2

-4x/5 < 4 * 2/10 - 3/10

Combine

-4x/5 < 4 * 2 - 3/10

Simplify the numerator by multiplying then subtracting

-4x/5 < 8 - 3/10

-4x/5 < 5/10

Cancel the common factor of 5 and 10...

-4x/5 < 5(1)/10

-4x/5 5* 1/5 * 2

-4x/5 < 1/2

Now we divide by -1

-4x/5)/-1 > 1/2)/-1

4x/5 > 1/2)-1

4x/5 > -1/2

Multiply both sides by 5 and cancel common factors. (5)

4x * 5 > -1/2 * 5

4x > -1/2 * 5

4x > -5/2

Now divide by 4 in each term

4x/4 > -5/2)/4

x > -5/2)/4

Multiply the numer by the reciprocal of the denom

x > -5/1 * 1/4

x > -5/4 * 2

x > -5/8

Step-by-step explanation:

Slope formula:

[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]

m = slope

Substitute the points into the formula format:

[tex] \frac{4}{5} - \frac{4}{3} = m[/tex]

Solve:

[tex] \frac{0}{2} = m[/tex]

The slope is 0.

The line doesn't increase or decrease.

Answer:

a) 35m+26

Step-by-step explanation:

5(7m+7)-9

= 35m+35-9

=35m+26

Hope this helps!

Answer:

Step-by-step explanation:

5(7m + 7) - 9

= 5*7m + 5 * 7 - 9

= 35m + 35 - 9

= 35m + 26

answers: 1st, 2nd, and 4th choices

Answer:

The cost for a towel at 4 for $17 is:

17/4 = 4.25 $/towel

The cost for a towel at 2 for $9 is:

9/2 = 4.5 $/towel

So Shaunda is correct, as the cost per towel for 4 at $17 is lower.

Answer:

a. 9m + 8×$20 = $340

b. 9×$10.50 + 8×$10.50 = $178.50

Step-by-step explanation:

Its self-explanatory

Step-by-step explanation:

the volume of the tank is

80×50×45 = 180,000 cm³

3/4 of that volume is

180000 × 3/4 = 135,000 cm³

so, we want to know how long it takes to fill 135,000 cm³.

the water intake flow is 9 l / minute.

now we need to know that a cube of 10 cm side length contains exactly 1 liter of water.

such a cube has the volume

10×10×10 = 10³ = 1000 cm³

so, 1000 cm³ = 1 liter.

and we need to fill 135,000 cm³.

how many times fit 1000 cm³ into 135,000 cm³ ?

135000/1000 = 135 times.

and that means it would take 135 minutes to fill it, if the flow was 1 l / minute.

but it is faster (9 times faster) : 9 l / minute

so, how many minutes ?

135 / 9 = 15 minutes

it takes 15 minutes to fill 3/4 of the tank.

Answer:

15 minutes

Step-by-step explanation:

The volume (V) of the tank is calculated as

V = lbh (l is the length, b the breadth and h the height (

here l = 80, b = 50, h = 45 , then

V = 80 × 50 × 45 = 180000 cm³

1 litre = 1000 cm³ , then

9 litres = 9 × 1000 = 9000 cm³

Divide the volume of the tank by 9000 for time in minutes

180000 ÷ 9000 = 20 minutes

It takes [tex]\frac{3}{4}[/tex] × 20 = 15 minutes to fill [tex]\frac{3}{4}[/tex] of the tank

Answer:

21 degrees

Step-by-step explanation:

I'm assuming that the 0 is supposed to be theta, which I'm replacing with x to make it easier for me to type.

Because these angles are acute, we can use the fact that if two angles A and B are complementary, then sinA = cosB.

So we can get that x+4+3x+2=90

4x+6=90

4x=84

x=21

Step-by-step explanation:

[tex]36 - {b}^{2} - {c}^{2} + 2bc[/tex]

Factor out -1

[tex] - ( - 36 + {b}^{2} + {c}^{2} - 2bc[/tex]

[tex] -( (b + c) { }^{2} - 36[/tex]

[tex] - (b + c + 6)( b + c - 6)[/tex]

answer:

c. y = -1/2x + 1

steps-explanation:

given sample equation:

comparing to the formula of slope intercept form: y = mx + b

                                              [ where m is the slope and b is the y-intercept ]

we can determine here that the slope is 2 and 9 is the y-intercept.

but here we need only the slope.

making the slope perpendicular using: -1/m → 1/-2 → -1/2

formula:                  

using the formula:                     [ here known that y1 is -1 and x1 is 4 ]

Answer:

C)    y = -1/2x + 1

Step-by-step explanation:

Equation of a line in slope-intercept form:  y = mx + b

(where m is the slope (gradient) and b is the y-intercept)

The slopes of two perpendicular lines are negative reciprocals of each other.  So, if the line is perpendicular to y = 2x + 9, then the slope m of the new line will be -1/2.

Therefore, y = -(1/2)x + b

We are told that the line passes through point (4, -1).  

Substituting the found value for m the the point (4, -1) into point-slope form:

y - y1 = m(x - x1)

y - -1 = -(1/2)(x -4)

y = -(1/2)x + 1

A rectangular fraction model can be drawn based on this idea: Annie had a total of cookies 20 but she gave 9 cookies to her friends, how many cookies does she have?

A rectangular fraction model refers to using a rectangle and dividing it to represent and understand fractions. This might be easier than representing fractions by only using numbers.

The first step is to think about a possible situation or word problem. After this, you can draw the fraction model. For example:

For this, divide a rectangle in the total of parts (20) and color the total of parts that Annie has (11). This means the total of cookies she has is 11/20.

Learn more about rectangles in: https://brainly.com/question/10046743

here u go, if u need it clearer I will re write just tell me

Answer:10.4 or -0.4

Step-by-step explanation:

The explanation is in the attached file below

Answer:

y = -4x + 15

Step-by-step explanation:

slope of y = x/4 - 2 is 1/4

slope of line perpendicular to above line is -4

so y = -4x + b

use (4, -1)

-1 = -4(4) + b

b = 16 - 1 = 15

so

y = -4x + 15

Put value of y in Equation 1 in Equation 2.

[tex] \looparrowright \sf y + 1 = - 4x[/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf (x + 2) + 1 = - 4x[/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf x + 2 + 1 = - 4x[/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf x +3= - 4x[/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf x + 4x= - 3[/tex]

[tex] \\ \\ [/tex]

[tex]\looparrowright \sf 5x= - 3[/tex]

[tex] \\ \\ [/tex]

[tex]\looparrowright \sf x= \dfrac{ - 3}{5} [/tex]

[tex] \\ \\ [/tex]

Let's find value of y :

[tex] \\ \\ [/tex]

[tex]\looparrowright \sf y=x+2[/tex]

[tex] \\ \\ [/tex]

[tex]\looparrowright \sf y= \dfrac{ - 3}{5} +2[/tex]

[tex] \\ \\ [/tex]

[tex]\looparrowright \sf y= \dfrac{ - 3 + 10}{5} [/tex]

[tex] \\ \\ [/tex]

[tex]\looparrowright \sf y= \dfrac{7}{5} [/tex]

Solution:

[tex]\looparrowright \sf \bigg( \dfrac{ - 3}{5} , \dfrac{7}{5} \bigg)[/tex]

a = 29 / 12

b = 56 / 24

c = 129 / 50

a = 2.42

b = 2.33

c = 2.58

b is cheapest, 24 for $56

Answer:

203,000

Step-by-step explanation:

You need to find the pattern first, so you need to subtract 213,000 from 209,000 to get 4,000. Now that is the pattern for 2 years we need it for 1 year. So divide 4,000÷2=2,000 for 1 year. Next, you need to multiply 2,000×3=6,000. That is the decrease of the population for 3 years. Finally, subtract 6,000 from 209,000.

Hope you get an A! <3

Answer: x < 18

Step-by-step explanation:

x - 2 < 16

We eliminate 2 to isolate the variable, x by adding 2 to both sides. -2 + 2 = 0.

x < 18

We can test this because 17 is less than 18. Pretend x = 17

17 < 18✅

Mason subtracted 2, instead of adding 2.

In order to graph this, put an open circle at 18, and the arrow should point to the left.

Answer:

total sum (s)= 6

probability of getting a 3 = 3÷6

= 1÷2

Step-by-step explanation:

probability of getting a 7 =0÷7

=0

probability of getting less than 5 =4÷6

2÷3

Answer:

1.6

Step-by-step explanation:

area of a semicircle is A = pi * r^2/2

So pi*1^2/2

3.14/2

1.57079632679

Rounded to the nearest tenth

1.6

Answer:

D) 57

Step-by-step explanation:

180 - 123

Answer:

18

Step-by-step explanation:

20% = .20

90 x .20=18

Hence, 18 kids own their own instruments

[RevyBreeze]