State the domain and range in interval notation​

Answer: She purchased 72 cones, 32 balls, and 60 vests.

Step-by-step explanation:

The total number of items is 164.

The price of the vests is $2.50 each.

The price of the soccer balls is $9.25 each.

The price of the cones is $0.75 each.

The total budget was  $500.

If V is the number of vests, B the number of balls, and C the number of cones, we have that:

V + B + C = 164.

V*$2.50 + B*$9.25 + C*$0.75 = $500.

and:

"She purchased 40 more cones than  balls."

C = B + 40.

Then we have a system of 3 equations and 3 variables:

V + B + C = 164.

V*$2.50 + B*$9.25 + C*$0.75 = $500.

C = B + 40.

Here the first step is to replace the third equation into the other two, in this way we eliminate one variable and one equation:

V + B + (B + 40) = 164

V*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500.

Now we want to isolate one variable in one of the equations, i will isolate V in the first equation:

V = 164 - 2*B - 40 = 124 - 2*B

Now i can replace this into the other equation:

(124 - 2*B)*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500

Now let's solve this for B.

$310 - $5*B + B*$9.25 + B*$0.75 + $30 = $500

B*( $9.25 - $5 + $0.75) = $500 - $310 - $30

B*$5 = $160

B = 160/5 =  32

Now we know the value of B.

And by the equations above:

V = 124 -2*B = 124 - 2*32 = 60

C = B + 40 = 32 + 40 = 72.

Then:

She purchased 72 cones, 32 balls and 60 vests.

Answer:

2nd Account has $19,000

1st Account has $42,000

Step-by-step explanation:

First let's split the money invested.

x is money in account 1

y is money in account 2

1st equation

$61,000=x+y

5%=0.05

7%=0.07

2nd equation

0.05*x+0.07*y=$3,430

x=61,000-y

substitute into 2nd equation

0.05(61,000-y)+0.07y=3430

Solve.

3050-0.05y+0.07y=3430

0.02y=3430-3050

0.02y=380

y=380/0.02

y=$19,000

There are 2(two) ways to solve for the 1st account, but I will do it the long way.

y=61,000-x

substitute into 2nd equation

0.07(61,000-x)+0.05x=3430

Solve.

4270-0.07x+0.05x=3430

-0.02x=3430-4270

-0.02x=-840

x=-840/-0.02

x=$42,000

The short way...

x=61,000-y

x=61,000-19,000

x=$42,000

Answer:

Step-by-step explanation:

Rotation is counterclockwise

It means the angle is negative

We can see point C of the original figure is making a vertical line with point P

If we connect P to C' it is going to make more than 90 degree angle as it is above the horizontal line passing through the point P

Therefore we can estimate the angle as -105°

Answer:

23

Step-by-step explanation:

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.

The number of hours required to tutor to have enough money to pay for the trip is 23 hours.

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 of days for the summer vacation = 6

Savings = $840

Earnings per hour = $45

Airfare cost = $525

Food and sightseeing = $780

Hotel cost per night = $95

Number of hours = x

We can make an expression.

525 + 780 + 6 x 95 = 840 + 95x

525 + 780 + 570 = 840 + 45x

1875 = 840 + 45x

1875 - 840 = 45x

1035 = 45x

1035/45 = x

x = 23

This means 23 hours.

Thus,

The number of hours required to tutor to have enough money to pay for the trip is 23 hours.

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Answer:

3 and 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

A/b = c for b

A/b = c

A = bc

bc = A

b = A/c

Answer:

See below

Step-by-step explanation:

[tex]\frac{A}{b}=c\\\frac{A}{b} * b = c * b\\ A = c * b\\\frac{A}{c} = \frac{c*b}{c}\\\frac{A}{c} = b\\ b =\frac{A}{c}[/tex]

Answer:

if you do 6-8

Step-by-step explanation:

6-8 = -5 because if you subtract 8 from 6 you will still have -5

Answer:

The following are the answer:

In option a  "No".

In option b  "Yes".

Step-by-step explanation:

In choice a:

Ax = 0 has no nontrivial solution. A would be the three-pivot matrix, it may assume, that the function has no free variable, and only if the function has had at least one free factor are their nontrivial formulas for the equations of the form Ax=0.  

It implies that since A is a 3x3 matrix, has no free variables so that it has no non-trivial choices, and Ax = 0.

In choice b:

we assume that every potential has at least one solution that is Ax=b . If A does have a three-pivot matrix, It will be a pivot element for each row and column, and for each possible b∈ R³, Ax = b has at least one solution.

Step-by-step explanation:

3(2x + 1) - 2(x + 5) - 5(5 - 2x) = 16

6x + 3 - 2x - 10 - 25 + 10x = 16

6x - 2x + 10x = 16 - 3 + 10 + 25

14x = 48

x = 48/14

x = 24/7

Answer:

40,000

Step-by-step explanation:

because of the 5 in the thousands place means were rounding up

Answer:

x = 32

Step-by-step explanation:

9x=288

divde both side by 9

Answer:4,05

Step-by-step explanation:

Answer:

√10,−√10

Step-by-step explanation:

award brainliest

Answer:

2

Step-by-step explanation:

The required measure of the numerical length of RS is 4.

Given that,
Point S is on line segment RT.
ST = 2x, and RT = 4x, and RS = 4x – 4,
To determine the numerical length of RS.

A line is a curve showing the shortest distance between 2 points.
Standard equation of the line, y = mx + c, where m is slope of the equation and c is y-intercept of the equation.

Here,

Point S is on line segment RT
The total length of RT,

RT = RS + ST
4x = 4x - 4 + 2x
4x  = 6x - 4
2x = 4
x = 2

RS = 4 x - 4
RS = 4 * 2 - 4
RS = 4

Thus, the required measure of the numerical length of RS is 4.

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Answer:

188 miles or 188.5 miles

Step-by-step explanation:50-17.95/17

Answer:

TU = 6

Step-by-step explanation:

Using the Segment Addition Postulate, we know that TU + UV = TV, and since UV = 6 and TV = 12, we know that TU + 6 = 12, therefore, TU = 6.

Answer:12.5 mike he walked to practice last week

Step-by-step explanation:

2.5 miles everyday

5 practices last week

2.5 miles x 5 practices

Answer:

x and y

Step-by-step explanation:

you have to put 5 on the x axes and 3 on the y axes to cordanate 15

The table showing the data is missing, so i have attached it.

Answer:

0.8

Step-by-step explanation:

We want to find the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30.

Now, we are told that the government agency has 6000 employees. Also, from the attached table, we see that the  number of people who prefer a 4 day work week are a total of:

600 + 1200 + 2100 = 3900

Thus, probability of people who prefer a 4 day work week = 3900/6000 = 39/60

Also, we see that total number of people aged under 30 = 600 + 300 = 900

Thus, probability of people aged under 30 is;

900/6000 = 3/20

Thus;

probability that a randomly selected employee at this government agency prefers a four day work week or is under 30 = 39/60 + 3/20 = 48/60 = 4/5 = 0.8

Answer:

Step-by-step explanation:

1)expand out the bracket

-15y+6=21

2) get the y to one side

6=21+15y

3) solve

15=15y

1=y

Answer:

Y= -1

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(−5y+2)=21

(3)(−5y)+(3)(2)=21(Distribute)

−15y+6=21

Step 2: Subtract 6 from both sides.

−15y+6−6=21−6

−15y=15

Step 3: Divide both sides by -15.

−15y −15 = 15 −15

Y= -1

Answer:

the answer is B

Step-by-step explanation:

The question is incomplete. Here is the complete question

The ratio of the width to the length of a rectangle is 1:3. Which of the following ratios represents a rectangle with this same ratio?

Answer:

21:63

Step-by-step explanation:

The ratio of the width to the rectangle is 1:3

= 1/3

= 0.333333

From the options given we have the following ratios

=5:7

= 5/7

= 0.71428

= 6:9

= 6/9

= 0.666666

= 33:100

= 33/100

= 0.33

= 21:63

= 21/63

= 0.3333333

Hence the ratio which represents the rectangle given above is 21:63

Answer:

  denominators are zero for x=1

  there is no solution

Step-by-step explanation:

We suspect your equation is supposed to be ...

  10/(5x -5) +1/5 = 2/(x -1) . . . . . parentheses are required on denominators

The denominators will be zero for x=1.

This version of the equation has no solution. It simplifies to ...

  2/(x-1) + 1/5 = 2/(x -1)

  1/5 = 0 . . . . . subtract 2/(x-1) from both sides

There is no value of x that will make this equation true.

_____

Alternative interpretation

The way your equation is written, it must be interpreted according to the order of operations to be ...

  (10/5)x -5 +1/5 = (2/x) -1 . . . . x=0 makes the denominator zero

  2x -3.8 = 2/x

  2x^2 -3.8x = 2 . . . . multiply by x

  2(x^2 -1.9x +.95^2) = 2 +2(0.95^2)

  (x -0.95)^2 = 1.9025

  x = 0.95 ± √1.9025 ≈ {-0.4293, 2.3293}

Answer:

[1, 3]

Step-by-step explanation:

g(x) = f(2x), so g(x) is f(x) compressed horizontally by a factor of 2.  Vertically, it is not changed.

Therefore, the ranges are identical.

Answer:

The middle two terms cancel out each time, and the final product is x2 plus the product of the positive coefficients of i in the original expression. All imaginary parts either cancel out or get replaced with -1, leaving an expression that doesn’t include imaginary numbers.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer: B. Sandwich Town's Dipping Sauce

Step-by-step explanation: Sandwich town has 1/2 more spoonful than Burger Barn so Sandwich Town has a stronger mustard flavor.

Hope this helps! : )