Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options
Answer:
The answers are A and E
A taxi cab driver charges a $2.00 initial fee and $1.75 for each mile.
1) Shannon wants to keep her fare under $35. How many miles can she travel in the taxi?
2) Samantha has $70 for her taxi fare. If she plans on traveling 20 miles in the taxi, does she have enough money to cover the fare? Explain your answer.
1. She can travel 18 miles. Subtract 35 - 2 (initial fee) to have 33. divide 33 by 1.75 to get 18.85. To check how much her total would be, use inverse operations. 18.85 * 1.75 = 32.9875. 32.9875 + 2 = 34.9875. It is barely under $35 but still in her budget.
2. 20m * $1.75 = $35. $70 - $35 = $35. Yes, she can cover the fare. Samantha has more than needed. She can afford the taxi fare and still have money left for future use.
Answer:
Step-by-step explanation:
1) Shannon can travel exactly 18 miles.
2) Yes, Samantha has enough money for her taxi. The ride would cost her $37. She would have $33 left over.
What are the slope and y intercept of the relationship shown in the table? X 10000 y 2500; x 20000 y 3000; x 30000 y 3500
Answer: slope ; increasing by 10000, y - intercept ; increasing by 500.
Step-by-step explanation:
y = mx+b
x is increasing by 10000
y is increasing by 500
The slope of the table is 1/200 and the y-intercept is 2550.
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The table is given below;
x y
10000 2500
20000 3000
30000 3500
To find the slope:
m = (3500 - 2500)/(30000 - 10000)
m = 1000/20000
m = 1/200
Now, the equation of the line that passes through points (10000, 2500) and has a slope of 1/200 is,
y - 2500 = 1/200(x - 10000)
To find the y-intercept:
Put x = 0,
we get,
y - 2500 = 50
y = 2550
Therefore, 2550 is the y-intercept.
To learn more about the slope;
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The perimeter of a triangle is 65 meters. The second side is 5 meters less than the first side The third side is 7
meters more than the first side. What is the length of each side?
Answer:
x=21
y=16
z=28
Step-by-step explanation:
Let
The first side=x
The second side =y
The third side=z
The rest is in the attached file
Answer:
First side (x)[tex]=21m[/tex]
Second side[tex]=x-5=21-5=16m[/tex]
Third side[tex]= x+7=21+7=28m[/tex]
Step-by-step explanation:
Perimeter of the triangle= Sum of all the three sides
Let the First side be [tex]'x'[/tex]
Then, Second side [tex]=x-5[/tex]
Third side= [tex]x+7[/tex]
Perimeter[tex]=65 m[/tex]
Perimeter of the triangle= First side + Second side + Third side
[tex]65=x+(x-5)+(x+7)\\\\65=x+x+x-5+7\\\\65=3x+2\\\\3x=65-2\\\\3x=63\\\\x=63/3\\\\x=21 m\\\\[/tex]
First side (x)[tex]=21m[/tex]
Second side[tex]=x-5=21-5=16m[/tex]
Third side[tex]= x+7=21+7=28m[/tex]
If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?
Answer:
28
Step-by-step explanation:
(k + k)(4)
2k(4)
2[5(4) - 6]
2(14)
28
3
4
x +
1
4
(x + 12) − 12 = 4x − 21
Answer:
x = -4.02
Step-by-step explanation:
3 4 x + 1 4 (x + 12) − 12 = 4x − 21
Open bracket
34x + 14x + 168 - 12 = 4x - 21
Collect like terms
34x + 14x - 4x = -21+12-168
44x = -177
Divide both sides by 44
x = -177/44
x = -4.02
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Which statement is FALSE for this situation?
A) A linear function represents Company A's payments.
B) An exponential function represents Company B's payments.
C) Company A's payments grow by a factor of 2.
D) Company B's payments grow by a factor of 2.
Option C: Company A's payments grow by a factor of 2
Explanation:
We need to determine the statement which is false.
Option A: A linear function represents Company A's payments.
From the table, it is obvious that the y - value increases by adding 5000.
Thus, the payments of company A can be written in linear function.
Hence, the statement a linear function represents Company A's payments is true.
Therefore, Option A is not the correct answer.
Option B: An exponential function represents Company B's payments.
From the table, it is obvious that the y - value increases by a factor of 2.
Thus, the payments of company B can be written in exponential function.
Hence, the statement an exponential function represents Company B's payments is true.
Therefore, Option B is not the correct answer.
Option C: Company A's payments grow by a factor of 2.
From the table, it is obvious that the y - value increases by adding the 5000.
Hence, the statement Company A's payments grow by a factor of 2 is false.
Therefore, Option C is the correct answer.
Option D: Company B's payments grow by a factor of 2.
From the table, the y - value increases by a factor of 2.
Hence, the statement Company B's payments grow by a factor of 2 is true.
Therefore, Option D is not the correct answer.
value Rent-A-Car rents a luxury car at a daily rate of $37.25 plus 20 cents per mile. A business person is allotted $110 for car rental each day. How many miles can the business person travel on the $110
Answer:
110- 37.25=72.25
72.25 divided by .20 =361.25
but since you can not drive part of a mile it would be 361 miles in one day.
Step-by-step explanation:
Final answer:
After subtracting the fixed daily rental rate from the daily budget and dividing the remainder by the cost per mile, it is calculated that the business person can travel 363.75 miles with the $110 budget.
Explanation:
To calculate how many miles the business person can travel on the $110 budget using the daily car rental rate provided, we can set up an equation based on the cost structure of Value Rent-A-Car. The rental cost consists of a fixed daily rate plus a variable cost per mile.
The fixed daily rate is $37.25, and the cost per mile is $0.20 (20 cents). With a daily budget of $110, we first subtract the fixed rate from the daily budget to find out how much money is left for the variable cost per mile:
Daily budget for miles = Total daily budget - Fixed daily rate
Daily budget for miles = $110 - $37.25
Daily budget for miles = $72.75
Now, we divide the money left for miles by the cost per mile to find the number of miles the business person can travel:
Number of miles = Daily budget for miles / Cost per mile
Number of miles = $72.75 / $0.20
Number of miles = 363.75 miles
The business person can travel 363.75 miles on the daily budget of $110, given the cost structure of the car rental.
what is the opposite of-5.5
Answer:
5.5
Step-by-step explanation:
think of a numberline that might help
hope this helps!
Susan invests 3 times as much money at 10% as she does at 6%. If her total interest after 1 year is $1800, how much does she have invested at each rate?
Susan has $5000 invested at 6% and $15000 invested at 10%.
To solve the problem, let's use algebra to define the amount Susan has invested at each rate. Let the amount invested at 6% be represented by x, and consequently, the amount invested at 10% will be 3x, as it is three times the amount invested at 6%. The total interest from both investments is $1800 after one year.
The interest from the investment at 6% is 0.06x, and the interest from the investment at 10% is 0.10(3x), which is 0.30x. The equation representing the total interest is:
Total Interest = Interest from 6% + Interest from 10%
1800 = 0.06x + 0.30x
Combining like terms gives us:
1800 = 0.36x
Dividing both sides of the equation by 0.36 to solve for x:
x = 1800 / 0.36
x = $5000
This is the amount invested at 6%. The amount invested at 10% is 3 times that, so:
3x = 3 * $5000
3x = $15000
Therefore, Susan has $5000 invested at 6% and $15000 invested at 10%.
1.)
What is the solution to the system of equations below?
y = 2x + 8
3(-2x + y) = 19
Answer:
y = 2x + 8
6x + 3y = 19
6x + 3(2x + 8) = 19
6x + 6x + 24 = 19
12x = -5
x = -5/12
y = 2(-5/12) + 8
y = -5/6 + 48/6
y = 43/6
At the end of a baseball game, the players were given the choice of having a bottle of
water or a box of juice. Of all of the players, 12 chose a bottle of water, which was three-fourths of the total number of players. Write and solve an equation to determine p,
the total number of players at the baseball game.
Answer:
16 players
12(3/4) = p
Step-by-step explanation:
12/[tex]\frac{3}{4}[/tex] = 16
or 12/3 = 4 x 4 = 16
Answer:16 players
Step-by-step explanation:
Joni’s hair is 13 inches long and grows at an average rate of ⅔ in per month. Her friend Kate’s hair is 16 inches long and grows at an average rate of ½ in per month. How many months will pass before the two friends have the same hair length?
Answer:
18
Step-by-step explanation:
13 + (⅔)t = 16 + (½)t
(⅔ - ½)t = 3
t/6 = 3
t = 18
A line with a slope of 3 passes through the points (-3, 4) and (a, -8). What is the value of a?
using the slope formula:
m = y2-y1/x2-x1
3 = -8 - 4/a- -3
3 = -12/a+3
multiply each side by a +3
3a + 9 = -12
move the 9 over by subtraction
3a = -21
divide by 3
a = -7
check it:
3 = -8 - 4/-7 - -3
3 = -12/-4
3 = 3
what is the solution to the equation 5a^2-44=81
Answer:
5
Step-by-step explanation:
[tex]5a^{2} -44=81\\5a^{2} -44+44=81+44\\5a^{2} =125\\\frac{5a^{2} }{5} =\frac{125}{5}\\a^2=25\\\sqrt{25} =x=5[/tex]
Alicia can paint a small room 21 hours faster than Nina aloneness 4 hours slower than Alicia and Nina together. How long will it take them to paint the room together? Express your answer in decimal form
Answer:
11.413 Hours.
Step-by-step explanation:
Alicia can paint a house in 21 hours; Which means in 1 hour she can paint 1/24 of the house.
Nina can paint the same house in (21+4) hours. Which means in 1 hour she can paint 1/25 of the house.
Together in 1 hour they can paint: 1/21 + 1/25 = 46/525 of the house.
Total Hours for painting the house together will be 525/46 = 11.413 Hours.
Blanca has 3/4 pound of tuna salad. She uses 1/3 of the tuna salad to make sandwiches. How much of the tuna salad did Blanca use?
Answer:
33.33% or 1/3
Step-by-step explanation:
3/4 = 9/12
1/3 = 4/12
9/12 pounds is the total and 4/12 pounds were used were us
1/12 is equal to 8.333% because 9/12 is the 100%, so, the total tuna salad used was 33.33% = 1/3 of the total.
Brainliest please ;)
Answer:
3/12
Step-by-step explanation:
3/4 x 1/3 = 3/12 (3x1) = 3 (1x3) = 12
Radius=6 in.
Height=3 in.
Answer:
[tex]V = 108π {units}^{2} [/tex]
Step-by-step explanation:
Assuming you are looking for the volume of a cylinder with radius=6in and height =3 in.
First , write the formula for the volume of a cylinder.
[tex]V = \pi {r}^{2} h[/tex]
Next, substitute the radius , r=6 and the height , h=3 .
[tex]V = \pi \times {6}^{2} \times 3[/tex]
[tex]V = \pi \times 36 \times 3[/tex]
[tex]V = 108\pi {units}^{2} [/tex]
Use the ratio table to solve the percent problem.
What percent is 12 out of 20?
Answer:
It would be 60%.
Step-by-step explanation:
To find the answer, you would have to do x/100 = 12/20. You would cross multiply leaving you with 20x=1200 you would then divide by 20. This would leave you with the answer of 60. Therefore, your answer is 60%.
Answer: 60%.
Step-by-step explanation:
From the question, 12 : 20 = x
Let the missing value be x.
12/ 20 x 100/1 = 60%
Therefore 12 out of 20 is 60%.
What is the solution to 3/4(x+8)>1/2(2x+10)
Answer:
x < 4
Since you have to simplify on both sides and then divide or multiply the coefficient on both sides to get the answer.
Everly needs to order stock for her store and wants to order the items that have the greatest probability of having repeat customers. She has to decide between the national brand and the store brand for both cereal and crackers. She has recorded the sale of each type and the probability that a customer bought the same item again. Which should she stock?
Answer:
B) National Brand Cereal and Store Brand Crackers
Step-by-step explanation:
Since she wants to order the items that have the greatest probability of repeat customers she needs to order the items with the larger probability. That is National Brand Cereal and Store Brand Crackers
Answer:
b
Step-by-step explanation:
In the xy-plane, line h passes through the points
(0,5) and (4,0). Which of the following is an
equation of line h?
A) 4x + 5y = 20
B) 5x + 4y = 20
C) 4x - 5y = 20
D) 5x – 4y = 20
Answer:
5x + 4y = 20
Step-by-step explanation:
(x1,y1) and (x2, y2)
(0, 5) and (4 ,0).
From equation of a line
y2 - y1/x2 - x1 = y - y1/ x - x1
Where x1 = 0, y1 =5 , x2 = 4 , y2 = 0
Imputing values,
0- 5/4-0 = y - 5 / x - 0
-5/4 = y -5/x
Multiply both sides by 4x I. E lcm of 4 and x
4x × -5/4 = y-5/x × 4x
-5x = 4(y - 5)
-5x = 4y - 20
Add 5x to both sides
-5x + 5x = 5x + 4y - 20
5x + 4y - 20 = 0
Add 20 to both sides
5x + 4y - 20 +20 = 0+20
5x + 4y = 20
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To solve for z, you divide each side of the equation by what number?
3/4z = 15
a. 4/3
b. 3/4
c. 15
d. 4
Answer:
B
Step-by-step explanation:
PLEASE GIVE BRAINLYEST
Jack has a summer job caddying at a golf course. Jack earns $120
a week. By rounding his weekly income to the nearest hundred
dollars, find a reasonable estimate for his total income during the
12 week summer.
OA) $700
O B) $800
OC) $1200
OD) $1700
Answer:
His total income during the summer is $1200 ⇒ C
Step-by-step explanation:
To round a number to a nearest given digit
Look to the number right to this digitIf the digit is 1, 2, 3, 4 keep the given digit as it and put all the digits right to it 0If the digit is 5, 6, 7, 8, 9 add the given digit by 1 and put all the digits right to it 0Examples:
1. Round 1235 to the nearest hundred, the hundred digit is 2 and the digit right to it is 3, then keep the hundred digit 2 and put all the digit right to it 0, so the answer is 1200
2. Round 1265 to the nearest hundred, the hundred digit is 2 and the digit right to it is 6, then add the hundred digit 2 by 1 and put all the digit right to it 0, so the answer is 1300
Now let us solve the problem
∵ Jack earns $120 a week
- By rounding his weekly income to the nearest hundred dollars
∵ The hundred digit is 1
∵ The digit right to it is 2
- Keep the hundred digit 1 and put the digits right to it 0
∴ The rounded number is 100
∴ Jack earns $100 per week
- To estimate his total income during the 12 week summer
multiply 100 by 12
∴ His total income during the summer = 100 × 12
∴ His total income during the summer = $1200
Answer:
1200
Step-by-step explanation:
A hotel charges $90 per day for a double room $80 per day for a single room. If a total of 80 single and double rooms are occupied and a total revenue of $6930 is taken in, how many of each type of room are there?
Answer:
the number of single room is 27 and the number of double room is 53
Step-by-step explanation:
Let x is the number of single room
Let y is the number of double room
We know that:
x + y = 80 <=> x = 80 -y (1)
80x +90y= 6930 (2)
Substitute (1) in (2) we have:
80 (80 - y) + 90y = 6930
<=> 6400 - 80y +90y = 6930
<=> y = 53
> x = 80 - 53 = 27
the number of single room is 27 and the number of double room is 53
Determine whether the point is on the graph of the equation 2x+3y=8.
(1,2)
The point [tex](1,2)[/tex] is on the graph of the equation.
Explanation:
The equation is [tex]2x+3y=8[/tex]
We need to determine the point [tex](1,2)[/tex] is on the graph.
To determine the point [tex](1,2)[/tex] is on the graph, we need to substitute the point in the equation and find whether the LHS is equal to RHS.
Thus, substituting the point [tex](1,2)[/tex] in the equation [tex]2x+3y=8[/tex], we get,
[tex]2(1)+3(2)=8[/tex]
Multiplying the terms within the bracket, we have,
[tex]2+6=8[/tex]
Adding the LHS, we have,
[tex]8=8[/tex]
Thus, both sides of the equation are equal.
Hence, the point [tex](1,2)[/tex] is on the graph of the equation [tex]2x+3y=8[/tex]
Wha rid the value of n very confused and need help
Answer:
n = 6
Step-by-step explanation:
Two intersecting chords. The product of the parts of one chord is equal to the product of the parts of the other chord, that is
7(n + 4) = 5(n + 8) ← distribute parenthesis on both sides
7n + 28 = 5n + 40 ( subtract 5n from both sides )
2n + 28 = 40 ( subtract 28 from both sides )
2n = 12 ( divide both sides by 2 )
n = 6
How do you find an equal ratio for example is 63:27 14:6 a equivalent ratio?
Answer:
Step-by-step explanation:
Find a common denominator or greatest common factor. 63 and 27 are both multiples of 9. When you divide each by 9 you get 7:3. 14 and 6 are both multiples of 2. When you divide each by 2 you get 7:3 again. So these ratios are equivalent.
Start with any set of numbers. Multiply them each by the same factor and the new set will be an equivalent ratio.
Two times the difference of -10 and 4 amounts to -28
Answer:
True
Step-by-step explanation:
We want to determine whether the given statement is true or false.
The difference of -10 and 4 is
[tex] - 10 - 4 = - 14[/tex]
We multiply the result by 2 to obtain;
[tex]2( - 14) = - 28[/tex]
Therefore two times the difference of -10 and 4 amounts to -28 is a true statement.
Allowance $10
Earn $18
Spend $3.28, $7.15, and $9.54
Save?
Answer:
8.03
Step-by-step explanation:
10+18 = 28
28 - 3.28 - 7.15 - 9.54 = 8.03