Answer:
d = distance
(x_1, y_1) = coordinates of the first point
(x_2, y_2) = coordinates of the second point
Step-by-step explanation:
Answer:
The distance formula itself is actually derived from the Pythagorean Theorem which is a 2 + b 2 = c 2 {a^2} + {b^2} = {c^2} a2+b2=c2
Step-by-step explanation:
16 divided by a number minus four is 40
Answer:
16/x - 4 = 40
16/x = 44
16 = 44x
16/44 = 44x
Hope this helps! pls rate me!
Step-by-step explanation:
At the zoo, the Spencer family bought 3 adult tickets and 2 children's tickets for $23.50. The Yang family bought 2 adult tickets and 4 children's tickets for $25. How much would the Diaz family spend if they bought 3 adults tickets and 1 children's ticket?
Diaz family spend $ 20 if they bought 3 adults tickets and 1 children's ticket
Solution:
Let "a" be the cost of each adult ticket
Let "c" be the cost of each student ticket
The Spencer family bought 3 adult tickets and 2 children's tickets for $23.50
Therefore, we frame a equation as:
[tex]3 \times a + 2 \times c = 23.50[/tex]
3a + 2c = 23.50 --------- eqn 1
The Yang family bought 2 adult tickets and 4 children's tickets for $25
Therefore, we frame a equation as:
[tex]2 \times a + 4 \times c = 25[/tex]
2a + 4c = 25 ----------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
6a + 4c = 47 ---------- eqn 3
Subtract eqn 2 from eqn 3
6a + 4c = 47
2a + 4c = 25
( - ) --------------
4a = 47 - 25
4a = 22
Divide both sides of equation by 4
a = 5.5
Substitute a = 5.5 in eqn 1
3(5.5) + 2c = 23.50
16.5 + 2c = 23.50
2c = 23.50 - 16.5
2c = 7
Divide both sides of equation by 2
c = 3.5
Thus, cost of each adult ticket = $ 5.5
Cost of each student ticket = $ 3.5
How much would the Diaz family spend if they bought 3 adults tickets and 1 children's ticket?
Total cost = 3a + 1c
Total cost = 3(5.5) + 1(3.5) = 16.5 + 3.5
Total cost = 20
Thus Diaz family spend $ 20
Final answer:
The Diaz family would spend $20 for 3 adult tickets and 1 children's ticket at the zoo after solving the system of linear equations given by the Spencer and Yang families' purchases.
Explanation:
Let A be the price of an adult ticket and C be the price of a children's ticket. We are given:
3A + 2C = $23.50 (Spencer family)
2A + 4C = $25 (Yang family)
To solve this system, we can multiply the first equation by 2 and the second equation by 3:
6A + 4C = $47 (Spencer family doubled)
6A + 12C = $75 (Yang family tripled)
Subtracting the first equation from the second gives us:
8C = $28
Dividing both sides by 8 yields:
C = $3.50
Now that we know the price of a children's ticket, we can substitute this value back into one of the original equations to find the price of an adult ticket.
3A + 2(3.50) = $23.50
3A + $7 = $23.50
3A = $16.50
A = $5.50
With the price of both ticket types known, we can now calculate the cost for the Diaz family:
3A + 1C = 3($5.50) + 1($3.50)
3A + 1C = $16.50 + $3.50
3A + 1C = $20
Therefore, the Diaz family would spend $20 if they bought 3 adult tickets and 1 children's ticket.
You are on your way to work. You drive 3.9 miles to a gas station and buy gas. Your workplace is 1.39 miles from the gas station. What is the distance of your commute to work?
Your commute is
( ?????) Miles.
Answer:
Approx. 5.3 miles
Step-by-step explanation:
A curtain measuring 6ft wide was bought for a window. However, when it hung, the curtain covered only 2/3 of the window. How wide was the window?
Answer:
9ft wide
Step-by-step explanation:
First we convert it to ratios
[tex]\frac{6}{x} \frac{2}{3}[/tex]
Then we cross-multiply
6*3=2x
Multiply 6 and 3
18=2x
Solve for x
x=18/2
x=9
Han is planning to ride his bike 24 miles.
a. If he rides at a rate of 3 miles per hour, how long will it take?
At 4 miles per hour?
At 6 miles per hour?
b. Write an equation that Han can use to find t, the time it will take to ride 24 miles, if his rate in miles
per hour is represented by r.
c. On graph paper, draw a graph that shows t in terms of r for a 24-mile ride.
Answer:
Please read the answers below.
Step-by-step explanation:
a. If he rides at a rate of 3 miles per hour, how long will it take?
Time = Distance/Rate
Time = 24/3 = 8 hours
At 4 miles per hour?
Time = 24/4 = 6 hours
At 6 miles per hour?
Time = 24/6 = 4 hours
b. Write an equation that Han can use to find t, the time it will take to ride 24 miles, if his rate in miles per hour is represented by r.
The equation is the same we used in the part a of the problem:
t = 24/r
c. On graph paper, draw a graph that shows t in terms of r for a 24-mile ride.
The graph is attached.
The sum of four and three multiplied by the quotient of four and two
Answer:
14
Step-by-step explanation:
4+3=7
4/2=2
7•2=14
A square coaster has a side length of 512 feet on each side.
What is the area of the coaster?
Answer:
do u mean 5/12
Step-by-step explanation:
Explain why dividing by a fraction results in the same answer as multiplying by its reciprocal.
Answer:
lets consider an example like
20 divided by 2/4 so we can rewrite as
2/4* x =20
so , 2* x =20*4
2* x =80
x=80/2
x=40
similarly,we can write the fraction as (20*4/2)-we can see that reciprocal of the fraction 2/4 is 4/2
x=20*4/2=80/2=40
so, we can say that dividing by a fraction results in the same answer as multiplying by its reciprocal.
Find the midpoint between two points on a number line if one of the points is at -7, and the other point is at 12.
Answer:
The middle point is 3
Step-by-step explanation:
Yo sup??
The mid point can be found out by taking the sum of the two values and dividing it by 2
mid point=(12+(-7))/2
=5/2=2.5
Hope this helps
i really need help i cant fail this
Answer:
[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex] [tex]or\ 0.42x^2[/tex]
Step-by-step explanation:
Given:
Height of the triangle [tex]h = x[/tex]
Base of the triangle [tex]b=\frac{5}{6}x[/tex]
We need to find the area of the triangle.
Solution:
Using given Formula:
[tex]Area\ of\ a\ trinagle = \frac{1}{2}bh[/tex]
Where:
b = Base of the triangle.
h = Height of the triangle.
Substitute [tex]h = x[/tex] and [tex]b=\frac{5}{6}x[/tex] in equation in given formula.
[tex]Area\ of\ a\ trinagle = \frac{1}{2}(\frac{5}{6})x\times x[/tex]
[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex]
[tex]Area\ of\ a\ trinagle =0.42x^2[/tex]
Therefore, Area of the triangle is [tex]\frac{5}{12}x^2[/tex] or [tex]0.42x^2[/tex].
Jaqueline buys 4 bracelets and 2 necklaces each bracelet cost $8 and jaqueline’s total is $70
Answer:
1 necklace is $19!
Step-by-step explanation:
4•$8=$32
$70-$32=$38
$38/2=$19
Simplify the expression 6s + 9c - 2s
Answer:
4s+9c
Step-by-step explanation:
6s+9c-2s
-2s. -2s
4s+9
A skating rink sold 66 tickets. Of these, 2/3 were children’s tickets, and the rest were adult tickets. What total number of adult tickets were sold
Answer:22
Step-by-step explanation:
66/3=22 so each part is 22 1 part for adults is 22
Alex flies airplanes. His plane ascends 100 feet above the ground
level in 20 seconds. What is the rate of ascension in feet per second?
Answer: the answer is 5 feet per second
Step-by-step explanation:
HELPPP....PLEASE...........
Answer:
9 1/3, 12 1/2, 14 3/4
Step-by-step explanation:
I assume the formula you’re working with is A=b*h since nothing says otherwise...
((Patio 1))
So you have your area (147) and your base (15 3/4), now you need to plug them in, which should look like this:
147= 15 3/4*h
You need to isolate your h in order to get the missing number, so you should divide both sides by 15 3/4 OR 63/4 ((15*3—>60+3=63))
Dividing by a fraction is the equivalent of multiplying by its reciprocal... so
147 * 4/63 = 588/63 which can be simplified to 84/9 once both the numerator and denominator are divided by 7
In mixed number for it is 9 3/9 which simplified becomes 9 1/3
You solve the other similarly
-3t-8+7t =34 +9t -2
Solve for t
Please give an exposition
Answer:
t = -8
Step-by-step explanation:
combine like terms, so -3t + 7t = 4t and 34 - 2 = 32
so 4t - 8 = 32 + 9t
then subtract 4t from both sides and subtract 32 from both sides. You will get: -40 = 5t.
Then divide both sides by 5 so you will get -8 = t
Answer: t= -8
Step-by-step explanation:
3t-8+7t=34+9t-2-3t+7t-8=9t+32-24t-8=9t+32t= -8The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6).
Which of the following is the graph of (g – f)(x)?
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).
Answer:
Option C
Step-by-step explanation:
We are given that
[tex]f(x)=-x[/tex]
The line passing through the points (0,0),(-6,6) and (6,-6).
[tex]g(x)=2x[/tex]
The line passing through the points (-3,-6),(0,0) and (3,6).
We have to find the graph of (g-f)(x).
[tex](g-f)(x)=g(x)-f(x)=2x-(-x)=2x+x[/tex]
[tex](g-f)(x)=3x[/tex]
Substitute x=0
[tex](g-f)(0)=3(0)=0[/tex]
[tex](g-f)(2)=3(2)=6[/tex]
[tex](g-f)(-2)=3(-2)=-6[/tex]
[tex](g-f)(-6)=3(-6)=-18[/tex]
Option C is true.
Frankie and his family go out to dinner. Dinner cost $32.43 and she gave an 18% tip. Along with 7% tax, what is the final bill?
Answer:
40.54
Step-by-step explanation:
32.43×3%=2.27
32.43×18%=8.107.
2.27+5.84=8.11.
32.43+8.11=40.54 total paid.
Given the system of equations, what is the solution?
3x - 2y + 10 = 0
5y = 4x + 8
{(-34/7, -16/7)}
{(-34/7, 16/7)}
{(34/7, -16/7)}
Answer:
{(-34/7, -16/7)}
Step-by-step explanation:
Rearrange values, multiply to solve for x.
(5) 2y = 3x + 10
(-2) 5y = 4x + 8
Solve for x.
10y = 15x + 50 ↓
-10y = -8x -16
Combine and evaluate.
0 = 7x + 34
Subtract 34 from both sides.
7x = -34
Divide both sides by 7.
x = [tex]\frac{-34}{7}[/tex]
Plugin x value into either equation to solve for y.
2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10
2y = [tex]\frac{-102}{7}[/tex] + 10
2y = [tex]\frac{-32}{7}[/tex]
y = [tex]\frac{-16}{7}[/tex]
I need accurate answer please this is my last attempt
Step-by-step explanation:
In order to rationalise the denominator, numerator and denominator must be multiplied by [tex] \sqrt[3]{9x^{10}}[/tex]
Ava’s aquarium is 95% filled with water. The tank holds 1,120 gallons of water. Which is the remaining number of gallons of water needed to fill the aquarium to the top?
Answer:
The aquarium needs 56 more gallons to be completely filled.
Step-by-step explanation:
To get the amount remaining you have to first divide 1120 by 100
1120/100=11.2
Then multiply it by 95
11.2*95=1064
You take the maximum amount (1120) and subtract the amount in the tank (1064) to get the amount left.
1120-1064= 56
With 56 gallons as your final answer.
a woman making$25 an hour gets a 30% raise how much is her new salery
Answer:
32.5
Step-by-step explanation:
Take 30% of $25, and get 7.5, then add $7.50 to $25. Now she's making $32.50 an hour.
The ratio of faculty members to students at a college is 1:15. If there are 675 students, then how many faculty members are there?
Answer:
The number of faculty member is 45.
Step-by-step explanation:
Ratio of faculty members to students = 1 : 15
Number of students = 675
Total = Number students + faculty members
Let the total be t
Let the faculty member be f
Representing the ratio, we have:
[tex]\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720[/tex]
Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:
Total = Number students + faculty members
[tex]720 = 675 + f\\f = 720 - 675\\f = 45[/tex]
The number of faculty member is 45.
-4/3x-3=1/3x+3/4 solve for X
Answer:
-9/4
Step-by-step explanation:
-4/3x-3=1/3x+3/4
-4/3x-1/3x-3=3/4
-5/3x=3/4+3
-5/3x=3/4+12/4
-5/3x=15/4
x=(15/4)/(-5/3)
x=(15/4)(-3/5)
x=-45/20
simplify
x=-9/4
A circular cone has volume 1200 cubic inches and radius 5 inches. What is the height of the cone, to the nearest tenth inch?
I multiply 1200 times 5 and yet 6000 because it says what is the height
If you have 470 apples and the price is 67 apples how much is each apple
Answer:
Each apples cost about $0.14
Step-by-step explanation:
cost / amount = price per piece
67 / 470 = 0.14
So every apple costs about $0.14
1) What percent of 29 is 3?
Answer: It's about 10.34%
Step-by-step explanation:
Which describes the relationship between
A. adjacent angles
B. complementary angles
C. supplementary angles
D. vertical angles
Answer:
d
Step-by-step explanation:
Della Ahkta has a whole life policy for $50,000. She pays an annual premium rate of $13.47 per
$1,000. When she signed her insurance contract she chose to use the annual dividend to reduce the
annual premium. When she gets a notice that her insurance premium is due, she is notified that her
policy has paid an annual dividend of $27.94. What amount will Della need to send the insurance
company to pay the balance due on the annual premium?
Answer:
645.56
Step-by-step explanation:
50000/1000 13.37=673.50
673.50
-27.94
Together, teammates Pedro and Ricky got 2693 base hits last season. Pedro had 283 more
hits than Ricky. How many hits did each player have?
Answer: Pedro= 1205. Ricky= 1488
Step-by-step explanation:
It is found that Ricky hits 1202 base and Pedro hits = 1485 base
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that
Pedro + Ricky = 2693 hits
Let Ricky hits = x
So, the Pedro hits will be = x + 283
( x + 283 ) + x = 2693
2 x + 283 = 2693
2 x = 2693 - 283
2 x = 2404
x = 1202
So, the Ricky hits 1202 base
Thus Pedro hits (1202 + 283) = 1485 base
Learn more about equations here;
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