The equation that models the amount of gas left in the car as Phan drives is [tex](g = 18 - 2h)[/tex] and the total amount of gasoline does it take to fill her tank is 18 gallons.
Given :
The table below shows the amount of gas left in her tank as she drives.Number of Hours Spent Driving (h) 3 5 7 9 Amount of Gas Left in Tank, in gallons (g) 12 8 4 0The following steps can be used in order to determine the equation that models the amount of gas left in the car as Phan drives and the total amount of gasoline:
Step 1 - The two-point form of the line can be used in order to determine the equation that models the amount of gas left in the car as Phan drives.
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 2 - Now, substitute the value of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above expression.
[tex]\dfrac{g-12}{h-3}=\dfrac{8-12}{5-3}[/tex]
Step 3 - Simplify the above equation.
[tex]\begin{aligned}\\(g - 12)&=-2(h-3)\\g - 12&=-2h+6\\g &= 18-2h\\\end{aligned}[/tex]
Step 4 - Now, substitute the value of (h = 0) in the above equation.
[tex]g = 18-2(0)\\g = 18 \; {\rm gallons}[/tex]
Therefore, the correct option is A).
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Answer:
g = 18 – 2h; 18 gallons
Step-by-step explanation:
The answer above is correct.
Each small square on this scale weighs 1 unit. Each larger square weighs 10 units. The weight of the triangle x is unknown. The scale is balanced. Look at the image. A balanced scale. On one side there are four small squares and three large squares each labeled ten. On the other side there are two small squares, two large squares each labeled ten, and a triangle labeled x. Question 1 Part A Write an equation to represent relationship of the weights shown on the scale. Enter the correct answer in the box.
The equation to represent the relationship of the weights shown on the scale s [tex]22 + x = 34[/tex]
The weights are given as:
[tex]Small\ Square = 1[/tex]
[tex]Larger\ Square = 10[/tex]
The total weight on one side, where there are 4 small squares and 3 large squares is:
[tex]Total =4\times Small\ Square + 3 \times Larger\ Square[/tex]
[tex]Total =4\times 1 + 3 \times 10[/tex]
[tex]Total =34[/tex]
The total weight on the other side, where there are 2 small squares, 2 large squares and 1 triangle is:
[tex]Total =2\times Small\ Square + 2 \times Larger\ Square + 1\times triangle[/tex]
[tex]Total =2\times 1+ 2 \times 10+ 1\times triangle[/tex]
[tex]Total =2+ 20+ 1\times triangle[/tex]
[tex]Total =22+ 1\times triangle[/tex]
[tex]Total =22+ triangle[/tex]
The weight of the triangle is x.
So, we have:
[tex]Total =22+ x[/tex]
The weights on both sides are equal, because the scale is balanced.
So, we have:
[tex]22 + x = 34[/tex]
Hence, the equation is [tex]22 + x = 34[/tex]
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Please help me π_π π_π
Lea worked for 3 hours 20 minutes and rested for 30 minutes. The she continued worked for 2 hours till 3.40 pm. What time did she start working?
Answer:
9.50 am
Step-by-step explanation:
3.40pm minus 2 hours = 1.40pm
1.40 minus 30 min = 1.10pm
1.10am minus 3 hours = 10.10am
10.10 am minus 20 min = 9.50 am
start at 9.50 .... works for3hrs and 20 min which ends at 1.10... 30min break which ends at 1.40...works for 2hrs that finally ends at 3.40pm
hope this helps☆☆☆
Slope
What is the slope of the line through (-7, -2) and (-6.7)?
Choose 1 answer:
Answer:
9
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(7-(-2))/(-6-(-7))
m=(7+2)/(-6+7)
m=9/1
m=9
A person swims 6.4 meters per
second north while being
pushed by a current moving
west at 2.1 meters per second.
What is the magnitude of the
swimmer's resultant vector?
Answer:
4.3
im not sure
correct me if im wrong
Answer
6.7
Step-by-step explanation:
Works on acellus
Bryce wrote the linear regression equation y = 1. 123 x minus 6. 443 to predict the armspan, y, of a person who is x inches tall. Riley has an armspan of 67. 5 inches. Which is the best prediction of Riley’s height? 54. 36 inches 65. 84 inches 66. 55 inches 69. 36 inches.
The best prediction of Riley’s height is 65.84 inches and it can be determined by using the linear regression equation.
Given that,Bryce wrote the linear regression equation,
[tex]\rm y=1.123x-6.443[/tex]
To predict the arm span, y, of a person who is x inches tall.
Riley has an arm span of 67.5 inches.
We have to find,Which is the best prediction of Riley’s height?
According to the question,To predict the arm span, y, of a person who is x inches tall.
Riley has an arm span of 67.5 inches.
The linear regression equation is,[tex]\rm y=1.123x-6.443[/tex]
Where the arm span, y, of a person who is x inches tall.
Riley has an arm span of 67.5 inches,
Then,
The best prediction of Riley’s height is,
[tex]\rm 67.5 = 1.123x -6.443\\\\67.5+6.443=1.123x\\\\ 73.943 = 1.123x\\\\ x = \dfrac{73.943}{1.123}\\\\ x = 65.84 \ inches[/tex]
Hence, The best prediction of Riley’s height is 65.84 inches.
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What is the simplified form of the following expression? Assume x not-equals 0. RootIndex 5 StartRoot StartFraction 10 x Over 3 x cubed EndFraction EndRoot StartFraction RootIndex 5 StartRoot 10 x EndRoot Over 3 x EndFraction StartFraction RootIndex 5 StartRoot 30 EndRoot Over 3 x EndFraction StartFraction RootIndex 5 StartRoot 120 x cubed EndRoot Over 3 x EndFraction StartFraction RootIndex 5 StartRoot 810 x cubed EndRoot Over 3 x EndFraction.
Equivalent expressions are expressions of different forms that have the same value
The equivalent simplified expression of [tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex] is [tex]\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
The equation is given as:
[tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex]
Multiply the fraction by 810x^2.
So, we have:
[tex]\sqrt[5]{\frac{10x}{3x^3}} =\sqrt[5]{\frac{10x \times 81x^2}{3x^3\times 81x^2}}[/tex]
Evaluate the products
[tex]\sqrt[5]{\frac{10x}{3x^3}} =\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
Hence, the equivalent simplified expression of [tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex] is [tex]\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
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Answer:
d
Step-by-step explanation:
PLEASE HELP MEH!!!!!!!!!!!!!
Answer:
A) 15+ (-13) + (-2) = 0
Step-by-step explanation:
we start off with 15 cupcakes in total. Our number of cupcakes decreases when we give 13 to our friends. 15-13=2 so we have 2 cupcakes left. If we then give the remaining 2 cupcakes to our teachers, then we are left with 0 cupcakes.
The way to express this as an equation is 15 - 13 - 2 = 0 , which is equivalent to 15+(-13)+(-2)=0
Answer:
The first option.
Step-by-step explanation:
She originally has 15 cupcakes, if she gives 13 away to her friends and 2 away to her teacher then she would end up with 0, which rules out two options, but the second down would be someone giving her cupcakes, due to the addition symbol, so it's the first option.
Hope this helps and have a good day!:)
. . . .. . . .. . . .. so easy
Answer:
i aint smart but im a the last one 4/8
Answer:
The answer is 4/8.
Step-by-step explanation:
Because 4 is half of 8 while the others are either 1 more or 1 less then half or just don't make half at all. So the only answer here that makes sense is 4/8
(pls do tell me if I'm wrong)
Ankita height is 135 cm and Nita height is 150 express Ankita height as a percentage of Nita height
Answer: 90%
135/150 * 100
45*2
90
helpppp im failing math
Answer:
i think 4.4n+3-3.4n = n+3
Answer:
n+3
Step-by-step explanation:
If Im not incorrect you have to combine like terms in the equation which would only leave you with 1n (Just N basically) then you just plug in the three and equation done.
Help please due today!
Answer:
36.87 degrees
Step-by-step explanation:
Use the law of sines
sin(90)/70 = sin(x)/42
Multiply each side by 42
42 * sin(90)/70 = sin(x)
use a calculator to get 0.6
Use inverse sin to find angle sin^-1 = 0.6
The angle is approximately 36.87 degrees
у
(x, y) (?x, ?y)
A'
3-4-3-2-10
1
2
B
C
B
с
Answer:c
Step-by-step explanation:
anser :c
the picture is there
Answer:
Step-by-step explanation:
Because CB = 6 cm, we can find CD
Use Triangle CDB.
<BCD = <BCA - <ACD
<BCD = ?
<BCA = 90
<ACD = 60
<BCD = 90 - 60
<BCD = 30
Cos 30 = CD / CB
CD = Cos(30) * BC
CD = 5.196 cm
<A = 90 - ACD
<ACD = 60
<A = 90 - 60
<A = 30
Sin(<A) = CB / AB
AB = CB / sin(<A)
AB = 6 / 0.5
AB = 12
Area =1/2 CD * AB
Area = 1/2 * 5.196 * 12
Area = 31.18
Divide.
(2x² - 2x-7) divided by (x+2)
Your answer should give the quotient and the remainder.
Answer:
2x³-2x²-3x-14
Hope it helps you
How many solutions does the following equations have |6x+12|= 12 |6x+12|= -1 |6x+12|= 0 show steps to sloving. How do you know the number or solutions?
Answer:
|6x+12|= 12 has 2 solutions --> x = -4 or x = 0
|6x+12|= -1 has No solutions
∣6x+12∣=0 has 1 solution --> x = -2
Explanation:
|6x+12|= 12
- Break |6x+12| = 12 down into two equations -
↓
6x + 12 = 12
6x + 12 = −12
- Solve both equations to x -
6x + 12 = 12
6x + 12 = −12
↓
6x = 0
6x = −24
↓
x = 0
x = −4
|6x+12|= -1
The absolute value function is always positive or 0 so false.
∣6x+12∣=0
- Because its 0, we simply just solve the equation -
6x + 12 = 0
↓
6x = -12
↓
x = -2
~That's All Folks~
-Siascon
what is the vertex of the porabola
Answer:
what is the vertex of the porabola by nagla 3by 7
1) The height, h, in feet of a ball above the ground is given by h = -16t2 + 64t+ 80, where t is the time in seconds. How long does it take the ball to hit the ground? es A) 3 seconds B) 4 seconds 95 seconds D) 6 seconds
Answer:
C) 5 seconds
Step-by-step explanation:
[tex]h = - 16t {}^{2} + 64t + 80[/tex]
When the ball hits the ground, the height is 0.
[tex]0 = - 16t {}^{2} + 64t + 80[/tex]
Factor out the greatest common factor: 16
[tex]0 = - 16(t {}^{2} - 4t - 5)[/tex]
Find numbers whose sum is -5 and product is - 4.
Those numbers are - 5 and 1: - 5 × 1 = - 5, - 5 + 1 = - 4
[tex]0 = - 16(t - 5)(t + 1)[/tex]
[tex]t - 5 = 0[/tex]
Or
[tex]t + 1 = 0[/tex]
So,
[tex]t = 5[/tex]
Or
[tex]t = - 1[/tex]
Since time cannot be a negative value the correct answer is 5 seconds.
Find the coordinates of the point 7/10 of the way from A to B
Answer:
D = (9,4) - (-4, -7) = (13,11) where D is length of line between A and B
.7 D = (9.1, 7.7) since .7 * 13 = 9.1 and .7 * 11 = 7.7
Thus we merely need to add these amounts to point A
(-4, -7) + (9.1, 7.7) = (5.1, .7) for the final coordinates
Use the table from a random survey about the preferred service for streaming movies. Out of 750 people, how many would you expect to prefer Company B?
Answer:
The correct answer option is 192
Step-by-step explanation:
We are given the results of a random survey about the preferred service for streaming movies.
We are to find the number of people we would expect to prefer Company B.
Number of people using service B = 32
Total number of people = 125
Number of people expected to prefer Company B =32/125 x 750 = 192
help me on this question. would be nice if you could also graph it as well
What is the slope of the line that connects the points (5, 4) and (-3, 3)?-1/8 1/8 8 -8
Answer: 1/8
Step-by-step explanation: 3-4 = -1
-3-5= -8
-1/-8=1/8
PLS ANSWER THE FOLLOWING QUESTION
I WILL MARK AS BRAINLIST
Answer:
Simplfy 823543000000
Exponential form 8.23543 × 10^11
Which number line and equation show how to find the distance from -2 to - 5?
Answer:
B
Step-by-step explanation:
If you're concerned with the points -2 and -5, you would be looking for a number line with those points plotted on it. The only one is ...
number line B
8. Determine the slope of each line,
f(x) = 3x + 6
Answer:
3
Step-by-step explanation:
Pick 2 x values to plug in:
x = 0: 3(0)+6 = 6
x = 2: 3(2)+6 = 12
slope = (y2 - y1) / (x2 - x1)
slope = (12 - 6) / (2 - 0)
slope = 6 / 2
slope = 3
(50 points) Here are descriptions of four situations in which the volume of water in a tank is
a function of time. Match each description to a corresponding graph. Each graph
is used only once.
Available Responses:
Graph 1
Graph 2
Graph 3
Graph 4
Situation A: An empty 20-gallon water tank is filled at a constant rate for 3
minutes until it is half full. Then, it is emptied at a constant rate for 3 minutes.
Situation B: A full 10-gallon water tank is drained for 30 seconds, until it is half
full. Afterwards, it gets refilled.
Situation C: A 2,000-gallon water tank starts out empty. It is being filled for 5
hours, slowly at first, and faster later.
Situation D: An empty 100-gallon water tank is filled in 50 minutes. Then, a dog
jumps in and splashes around for 10 minutes, letting 7 gallons of water out. The
tank is refilled afterwards.
Answer:
A = 3
B = 1
C = 2
D = 3
Situation A is graph 3, situation B is graph 1, situation C is graph 2 and situation D is graph 4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Situation A :
The water tank is empty at first. So the graph must start at origin.
Tank is filled at a constant rate for 3 minutes until it is half full, that is until it is 10 gallons.
Then the tank is emptied at a constant rate for 3 minutes, which is also 10 gallons.
So the slope must be equal.
And the graph must start from 0 and ends at zero which is graph 3.
Situation B :
Water tank is already full. So the graph must start at higher value in the Y axis.
The only possibility for this is graph 1, since all others starts at origin.
Situation C :
Water tank starts at empty. So the graph starts at 0.
First the rate is slower, then it becomes faster. So there will be an increase in the slope, which is graph 2.
Situation D :
Graph starts at origin since the tank is empty.
Then there is a slight decrease in the water for some time. So the graph turns down slightly, again tank is refilled, so the graph goes up.
Hence each of the graph corresponds to the situation is found.
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Which type of laboratory is not required to have coved floors (where the floor runs continuous for the wall for a few inches)
The type of laboratory that is not required to have coved floors is a BSL2.
Safety in laboratories is measured through the Biosafety Level scale. This scale evaluates how much protection do people working in the laboratory need to avoid any risks while working with pathogens or toxins.
This scale goes from 1 to 4 and the 4 level represents labs in which extremely dangerous pathogens are studied, and therefore labs with the highest safety protocols.
In this context, coved floors are not required for labs classified in Biosafety level 2 because in these labs pathogens have only a moderate risk, therefore some precautions such as the coved floors are not required.
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Can anyone help me with my homework
Answer:
x = the number
Step-by-step explanation:
15.) 2x + 9 = 25
16.) 3x - 6 = 21
17.) 7x = 12 + 3x
18.) 4x = 18 + x
19.) 2x + 24 = 8x
20.) 30 - x = 4x
23. What lines intersect to form the circumcenter of a triangle?
angle bisectors
midsegments
altitudes
perpendicular bisectors
Answer:
(d) perpendicular bisectors
Step-by-step explanation:
The circumcenter is the center of the circumcircle of the triangle. Each vertex of the triangle lies on that circle. The sides of the triangle are chords of the circle.
The perpendicular bisector of a chord is a line that intersects the center of the circle containing the chord. Hence, the perpendicular bisectors of the sides of a triangle will intersect the circumcenter.
Solve please! :) The values of m n k respectively.
Answer:
1,6,2 and 5
Step-by-step explanation:
(2x/5)² . (1x⁴/4)^-1
=(2²x²/5²) . (4/x⁴)
=4x²/25 × 4/x⁴
= 16/25x²
X- 7y = -21 2x -14y =-42
Solve by substitution.
This is the possible solution. If the question isn't set up right Please tell me and I'll fix what needs to be changed. All the best
the given system of equations has no Solution.
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given, a system of equations:
X- 7y = -21......(1)
2x -14y =-42.....(2)
From equation 1
x = -21 + 7y
Substitute the value in equation 2
2(-21 + 7y) -14y-14y = -42
Since the given equation are same
Therefore, given equations have no Solution.
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