Answer:d=(16-x)30
Step-by-step explanation:
The car traveled 600 miles if it has 10 gallons of gas left in the tank.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.
To determine the equation that represents the relationship between the distance traveled by car and the amount of gas left in the tank.
Let the distance traveled by car would be d miles,
and the amount of gas left in the tank would be x gallons
Since the car had a 16-gallon fuel tank
So the amount of gas left in the tank would be 16 - x
When driven on a highway, it has a gas mileage of 30 miles per gallon.
To find the equation of the distance we have to calculate the product of gas left in the car and the mileage of the car.
So the required equation as:
⇒ d = (16-x)30.
If it has 10 gallons of gas left in the tank
Substitute x = 10 in the above equation, we get
⇒ d = (16-10)30.
⇒ d = (20)30.
⇒ d = 600.
Therefore, the car traveled 600 miles if it has 10 gallons of gas left in the tank.
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2. Two bicyclists on a 75-mile trail ride toward each other. One bicyclist
begins at the 45-mile marker. The other begins at the end of the trail. The
expressions shown represent the distance from the Parking Lot for each
A. Write an equation to represent the bicyclists' meeting after x hours.
plify.
bicyclist when they meet.
B. After how many hours do the bicyclists meet?
Parking
Lot
75 - 10x
45 + 10x
75 mi
C. How far away are the bicyclists from the
parking lot when they meet?
Answer:
A. The equation representing the bicyclist with equal speed, v, meeting after x hours is 75 - v·x = 45 + v·x
B. The bicyclist meet after 1.5 hours
C. They were 60 miles from the parking lot when they meet
Step-by-step explanation:
A. The starting location of the one of the bicyclist = 75-mile marker
The starting location of the other bicyclist = 45-mile marker
The direction of motion of the bicyclist = Towards each other
The time after which the bicyclist meet = x hours
The expression for the distance from the parking lot are
75 - 10x and 45 + 10x
Whereby the bicyclist are have the same speed, v, we have;
The location where they meet is 75 - v×x = 45 + v×x
B. Solving for x, we have;
75 - v×x = 45 + v×x
75 - 45 = v×x + v×x = 2×v×x
30 = 2×v×x
x = 30/(2×v)
Taking the speed of the bicyclist as 10 mph from the equation of their distance from the parking lot, by dimensional analysis, we have;
x = 30/(2×v) = 30/(2×10) = 1.5
x = 1.5 hours
The bicyclist meet after 1.5 hours
C. Their distance from the packing lot is given by substituting the time, x, it took them to meet into the expression for the distance from the parking lot as follows;
75 - 10 × 1.5 = 60 miles
45 + 10 × 1.5 = 60 miles
Therefore, they were 60 miles from the parking lot when they meet.
Answer:
A. The equation representing the bicyclist with equal speed, v, meeting after x hours is 75 - v·x = 45 + v·x
B. The bicyclist meet after 1.5 hours
C. They were 60 miles from the parking lot when they meet
Step-by-step explanation:
A. The starting location of the one of the bicyclist = 75-mile marker
The starting location of the other bicyclist = 45-mile marker
The direction of motion of the bicyclist = Towards each other
The time after which the bicyclist meet = x hours
The expression for the distance from the parking lot are
75 - 10x and 45 + 10x
Whereby the bicyclist are have the same speed, v, we have;
The location where they meet is 75 - v×x = 45 + v×x
B. Solving for x, we have;
75 - v×x = 45 + v×x
75 - 45 = v×x + v×x = 2×v×x
30 = 2×v×x
x = 30/(2×v)
Taking the speed of the bicyclist as 10 mph from the equation of their distance from the parking lot, by dimensional analysis, we have;
x = 30/(2×v) = 30/(2×10) = 1.5
x = 1.5 hours
The bicyclist meet after 1.5 hours
C. Their distance from the packing lot is given by substituting the time, x, it took them to meet into the expression for the distance from the parking lot as follows;
75 - 10 × 1.5 = 60 miles
45 + 10 × 1.5 = 60 miles
Therefore, they were 60 miles from the parking lot when they meet.
Which shows the image of triangle WXY after the transformation R0, –90°(x, y)?
On a coordinate plane, 2 triangles are shown. The first triangle has points W (negative 4, negative 1), Y (negative 2, negative 1), X (negative 4, negative 4). The second triangle has points Y prime (2, negative 1), W prime (4, negative 1), X prime (4, negative 4).
On a coordinate plane, 2 triangles are shown. The first triangle has points W (negative 4, negative 1), Y (negative 2, negative 1), X (negative 4, negative 4). The second triangle has points Y prime (negative 4, 4), W prime (negative 4, 2), X prime (negative 1, 2).
On a coordinate plane, 2 triangles are shown. The first triangle has points W (negative 4, negative 1), Y (negative 2, negative 1), X (negative 4, negative 4). The second triangle has points Y prime (negative 1, 2), W prime (negative 1, 4), X prime (negative 4, 4).
On a coordinate plane, 2 triangles are shown. The first triangle has points W (negative 4, negative 1), Y (negative 2, negative 1), X (negative 4, negative 4). The second triangle has points Y prime (5, negative 3), W prime (5, negative 1), X prime (2, negative 1).
Answer:
its c
Step-by-step explanation:
trust me
Answer:
c
Step-by-step explanation:
Use f(x) = 1/2x and f -1(x) = 2x to solve the problems.
f(2) =
f−1(1) =
f−1(f(2)) =
[tex]f(2) = \frac{1}{2} \times 2 = 1\\f^{-1}(1) = 2 \times 1 = 2\\f^{-1}(f(2)) = f^{-1}(1) = 2[/tex]
Note: [tex]f^{-1}(f(x)) = x[/tex] because f -1 and f cancel each other out.
Answer:
f(2) =
⇒ 1
f−1(1) =
⇒ 2
f−1(f(2)) =
⇒ 2
f−1(−2) =
⇒ -4
f(−4) =
⇒ -2
f(f−1(−2)) =
⇒ -2
Step-by-step explanation:
Solve the following equation for D:
fD-7=q2
The expression that represents D is (q²+7)/f
The subject of formula is a way of representing a variable to represent all other variables in a function
Given the expression
fD - 7 = q²Add 7 to both sides
fD - 7 + 7 = q² + 7
fD = q² + 7
Divide both sides by f
fD/f = (q²+7)/f
D = (q²+7)/f
Hence the expression that represents D is (q²+7)/f
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Help me !!!!!!!!!!!!!!!!
Answer:
c/9 >= 15
Step-by-step explanation:
c divided by 9 is greater than or equal to 15
-10, -7, -4, -1, ...
Answer:
2
Step-by-step explanation:
The pattern is +3 each time so -1 + 3 = 2
-10, -7 ,-4 , -1 ,2
This is the table of values of a function. Write the output when the input is n.
Input= 4 6 9 n
Output= 2 4 7 ?
Answer:
n-2
Step-by-step explanation:
1. Find what has been done to the input value to give the output value. Here, we can see that each input value is two more than each output value, so two has been subtracted from each input value to give the output. This means that the rule for this function is: take the input value and subtract two.
2. Express this in terms of n. We can then express this in terms of n (using n to show the rule that we have found). Since n is the input value we have, to find the output when the input is n, we subtract two from n. This gives us our answer of n-2.
What is the equation in point-slope form of the line that passes through (-9, 12) with a slope of 5/6?
A. y-12=6/5(x+9)
B. y-12=5/6(x+9)
C. y-9=5/6(x-12)
D. y-12=6/5(x-9)
Answer:
B (lmk if you want me to explain)
Step-by-step explanation:
the point slope form is
y-y1=m(x-x1)
y-12=5/6(x--9)
y-12=5/6(x+9)
Which process do we use in reverse to solve two-step equations?
Answer: Inverse Operation
Step-by-step explanation:
Number 4. I need help finding the value please help
Answer:
Step-by-step explanation:
Triangle A'B'C' is a rotation of triangle ABC by 60 degrees using Q as the center.
Select ALL statements that MUST be true. *
A. Angle ABC is 60 degrees.
B. Angle AQA' is 60 degrees.
C. Points C and C' coincide.
D. Triangles ABC and A'B'C' are congruent.
E. Angle ABC is congruent to angle A'B'C'
F. Segment BC is congruent to segment B'C'
G. Segment BQ is congruent to segment C'Q.
H.Segment AQ is congruent to segment A'Q.
Answer:
The correct options are;
D. Triangles ABC and A'B'C' are congruent
E. Angle ABC is congruent to angle A'B'C'
F. Segment BC is congruent to segment B'C'
H. Segment AQ is congruent to segment A'Q'
Step-by-step explanation:
The given information are;
The angle of rotation of triangle ABC = 60°
Therefore, given that a rotation of a geometric figure about a point on the coordinate plane is a form of rigid transformation, we have;
1) The length of the sides of the figure of the preimage and the image are congruent
Therefore;
BC ≅ B'C'
2) The angles formed by the sides of the preimage are congruent to the angles formed by the corresponding sides of the image
Therefore;
∠ABC ≅ ∠A'B'C'
3) The distances of the points on the figure of the preimage from the coordinates of the point of rotation are equal to the distances of the points on the figure of the image from the coordinates of the point of rotation
Therefore;
Segment AQ ≅ A'Q'.
A.The human race evacuate earth and inhabit mars. Each space shuttle can hold
1700 people.6,840,507,000 people on the planet. How many space shuttle trip will
need to be made?
Answer:
4,023,828
Step-by-step explanation:
I simply divded the two. I got 4,023,827.6470598824. I rounded it up after.
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 101010 denarius per day to support 333 legionaries and 333 archers. It only costs 333 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables.
Complete question :
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?
Answer:
No unique solution
Step-by-step explanation:
Given that:
Cost of supporting 3 legion aries and 3 archers = 10 denarius daily
Cost of supporting one legionary and one archer = 3 denarius
Let:
Legionaries = l ; archers = a
Equation for the first sentence :
3l + 3a = 10 - - - (1)
Second sentence :
l + a = 3 - - - - - (2)
From (2)
l = 3 - a
Substituting l = 3 - a into (1)
3(3 - a) + 3a = 10
9 - 3a + 3a = 10
9 - 0 = 10
The variable cancels out, Hence, ( there is no unique solution to find the cost of each soldier)
Answer:
No; the system has no solution.
Step-by-step explanation:
We'll use L to represent the cost per day of a legionary, and we'll use A to represent the cost per day of an archer. So we have the following system of equations:
3L+3A=10
L+A=3
If we multiply both sides of the second equation by 3, we get the equation 3L+3A=9
But this indicates that the cost to support 3 legionaries and 3 archers is 9 denarius. The first equation indicates that it costs 10 denarius to support 3 legionaries and 3 archers.
The cost cannot be 9 denarius and 10 denarius at the same time.
Henceforth the answer is:
No; the system has no solution.
How many groups of 1/4 are in 3/4
you buy a rack of 40 cds you have 23 cd
Answer:
um... what.
WHAT'S THE QUESTION
bruuh
bruh
Step-by-step explanation:
Struggling with geometry
Answer:
43 degrees. b and the other angle being compared too are vertical angles- vertical angles are AND have to be identical to each other.
I HAVE 5 MINUTES PLZ HELP!
(Multiple choice)
Answer:
i think its B or A
Step-by-step explanation:
3.) How fast does Greg type per minute___
Answer:
is there more to this question?
Step-by-step explanation:
pls answer asap with a picture of your work:) i’m being timed
Answer:
x = 7
Step-by-step explanation:
Evaluate: 5/8 - (1/4)²
Answer:
5/8 - (1/4)^2 = 0.5625, hope this helps!
I need help in this, the result should give 17
someone please help me
Answer:
X= 20
Step-by-step explanation:
x/5 + 13 = 17
x/5 + 13 =17
- 13. -13
x/5×5 4×5=20
So X=20
What is arccos(−1) in Radians.
Answer:
π radians
Step-by-step explanation:
The arc cos(- 1) in degrees is 180° and 180° = π radians
#1 Describe the translation of the point to its image.
(-15, 22) - (25, 15)
type here
Answer:
40 units to the right and 7 units down
Add.
(3x + 4) + (5x - 7)
Answer:
The answer is 8x - 3
Describe the relationship between volume, mass, and density. If a
marble with a density of 2.4 g/cm^3 was cut in half, what would be the
the density of half the marble?
Answer:
2.4 g/cm^3
Step-by-step explanation:
Density is the ratio of mass to volume (as the units g/cm^3 tell you). If you cut the marble in half, each piece will have half the mass and half the volume, so the density remains unchanged. It will still be ...
2.4 g/cm^3
Sue Ling gave her dad a $50 gift certificate. He plans to buy a $12 book on home repair
and as many drill bits as he can for $1.79 each. Choose the inequality that shows x, the
number of drill bits he can buy.
I
Answer:
12 + 1.79(x) ≤ 50
Number of drill bits = 21
Step-by-step explanation:
Given:
Total amount = $50
Amount of book = $12
Price of each bit = $1.79
Find:
Number of drill bits
Computation:
Assume, Number of drill bits = x
So,
12 + 1.79(x) ≤ 50
1.79(x) ≤ 38
x ≤ 21.220
Number of drill bits = 21
(a) Books to authors
(b) SIM cards to cell phone numbers
(c) True or False questions to answers
(d) Books to its ISBN
are one to one fuction?
Answer:Letter D.
Step-by-step explanation:
Daisy decides to go on a hike to a picnic area. Her map shows that when she reaches the giant oak tree she will have completed 60% of the hike. When Daisy reaches the giant oak tree she has walked 18 kilometers.
Answer:
12 kmStep-by-step explanation:
Question:How many kilometers does Daisy have left to reach the picnic area?Given
60% of the hike = 18 kmLet the distance be x, then
0.6x = 18x = 18/0.6x = 30 kmRemaining distance is:
30 - 18 = 12 km
The sum of two consecutive odd integers equals 12. What are they?
xrepresents
integer
X+ 2 represents
integer
Answer:
x = 5
The two consecutive odd integers are: 5, 7
And...checking
sum = 12
Step-by-step explanation:
2= 5 j -28 one or two step equation
Answer:
j=6
Step-by-step explanation:
2=5j-28
+28 +28
30=5j
/5 /5
j=6