a. It spends 2.04 hours going 55 mph.
b. It will spend 1 hour going 35 mph.
c. The trip will take 3.64 hours.
Step-by-step explanation:
Given equation is;
55x + 35y = 200
Where
x represent the time when speed is 55 mph
y represent the time when speed is 35 mph
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
Putting y=2.5 in given equation
[tex]55x+35(2.5)=200\\55x+87.5=200\\55x=200-87.5\\55x=112.5\\[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{112.5}{55}\\x=2.04\ hours[/tex]
It spends 2.04 hours going 55 mph.
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
Putting x=3 in given equation
[tex]55(3)+35y=200\\165+35y=200\\35y=200-165\\35y=35[/tex]
Dividing both sides by 35
[tex]\frac{35y}{35}=\frac{35}{35}\\y=1[/tex]
It will spend 1 hour going 35 mph.
c. If the car spends no time going 35mph, how long would the trip take?
Putting y=0 in given equation
[tex]55x+35(0) = 200 \\55x+0=200\\55x=200[/tex]
Dividing both sides by 55
[tex]\frac{55x}{55}=\frac{200}{55}\\x=3.636[/tex]
Rounding off
x = 3.64
The trip will take 3.64 hours
Keywords: linear equation, division
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usually 1/1000 of the headphones cannot pass the tests . if they found 5 headphones failing, how many headphones did the workers test?
Answer: 5000
Step-by-step explanation: 5/5000
The workers tested 5000 headphones.
Explanation:To find out how many headphones the workers tested,
We can set up a proportion to solve the problem:
1/1000 = 5/x
Cross multiplying, we get:
x = 5 * 1000
x = 5000
Therefore, the workers tested 5000 headphones.
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a new stadium will seat 83,820. There will be 132 different sections. If each section seats same number of people, how many people will each section seat?
Answer:
635
Step-by-step explanation:
83,820 / 132 = 635
9+3x=6(3-x) what is the answer
Answer:
x = 1
Step-by-step explanation:
9 + 3x = 18 - 6x
3x + 6x = 18 - 9
9x = 9
X = 1
Answer:
Step-by-step explanation:
9+3x =6(3-x)
9+3x =6 ×3 - 6x
9+3x =18 -6x
Collect like terms
9-18= -6x-3x
-9 =-9x
Divide both sides by -9
-9/-9 =-9x/-9
Minus cancels minus and 9 divided by 9 is 1 on both sides
1 =x
x =1
For abc shown with vertices at A(-2,6),B(8,-2) and C(-8,-4), shown using coordinate geometry that the segment connecting the midpoint of sides Ac and BC is half the length of side AB.
Answer:
It is proved that AB = 2 × DE.
Step-by-step explanation:
The three vertices of triangle ABC are A(-2,6), B(8,-2) and C(-8,-4).
So, the mid point of AC (say D) has coordinates [tex](\frac{- 2 - 8}{2},\frac{6 - 4}{2}) = (-5,1)[/tex].
And the mid point of BC (say E) has coordinates [tex](\frac{8 - 8}{2}, \frac{- 2 - 4}{2}) = (0, - 3)[/tex].
Now, the length of DE will be [tex]\sqrt{(- 5 - 0)^{2} + (1 + 3)^{2}} = \sqrt{41}[/tex] units.
Again, the length of AB will be [tex]\sqrt{(- 2 - 8)^{2} + (6 + 2)^{2}} = 2\sqrt{41}[/tex] units.
So, it is proved that AB = 2 × DE. (Answer)
Solve for X (simple)
Answer:
156°
Step-by-step explanation:
This is simply angle on a straight and this angle is 180°
X + 24 = 180
Collect like terms
X = 180 — 24
X = 156°
WORTH 100 POINTS
A plane is racing a helicopter to a runway traveling 31 mph and it tends to burn 5 gallons of gas ever 3 minutes. Whilst the helicopter is traveling at a speed of 45 mph burning 7 gallons of gas every 5 minutes. They both started with the same amount of fuel (80 gallons) and both have the same amount to travel ( 640 miles) Who will make it first using the less amount of fuel?
Does this problem work?
If so what is the answer?
Show your work please
Answer:
The problem does not work.
Step-by-step explanation:
The plane with speed of 31 mph will cover 640 miles in [tex]\frac{640}{31} = 20.64[/tex] hours.
Now, it burns 5 gallons of gas every 3 minutes i.e. 0.05 hours.
So, it will burn in 20.64 hours [tex]\frac{5 \times 20.64}{0.05} = 2064[/tex] gallons.
Now, the helicopter with speed of 45 mph will cover 640 miles in [tex]\frac{640}{45} = 14.22[/tex] hours.
Now, it burns 7 gallons of gas every 5 minutes i.e. 0.083 hours.
So, it will burn in 14.22 hours [tex]\frac{7 \times 14.22}{0.083} = 1194.48[/tex] gallons.
But both of them starts with only 80 gallons of fuel.
Therefore, the problem does not work. (Answer)
2 Points
Which equation represents the slope-intercept form of the line below?
y-intercept = (0,2)
slope =
O A. y= 2x-}
O B. y=-x-2
O C. y=-_x+2
O D. y= 2x+
Answer:
the answer is C
Step-by-step explanation:
In the y intercept formula which is y=Mx+b the b in the formula represents the y intercept
Solve write or draw to explain Saul and Luisa each scored 167 points on computer games How many points did they score together
Answer:167 + 167 = 334
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Solve for r
-13 = r/9 + 8
r=
Answer:
r= -45
Step-by-step explanation:
trust on this one
Answer:
-189
Step-by-step explanation:
what is the a, b, and r for y=3.6(1.25)^x
Answer:
a=3.6, v=1.25 and r=25%
Step-by-step explanation:
The given exponential function is
[tex]y = 3.6 {(1.25)}^{x} [/tex]
We compare to the form:
[tex]y = a{(b)}^{x} [/tex]
We have a=3.6, b=1.25
The r is the percentage of increase or decrease.
We realized there is a 25% increase because
[tex]y = 3.6 {(1 + 25\%)}^{x} [/tex]
Hence
[tex]r = 25\%[/tex]
A degree may seem like a very small unit but an error of one degree in measuring an angle may be very significant. For example, suppose a laser beam directed toward the visible center of the moon misses its assigned target by the amounts specified below. How far is it (in miles) from its assigned target in each case? (Use 234,000 miles as the distance from the surface of the earth to the surface of the moon.)
a: 1 degree
b: 30” (that’s 0 degree 0’ 30”)
To calculate the distance by which a laser beam misses its target on the moon due to an angular error, one can use the tangent function with the Earth-moon distance. For an error of 1 degree, it would miss by approximately 4,080 miles, and for an error of 30 arcseconds, by about 34 miles.
To find out how far a laser beam directed toward the center of the moon misses its target by 1 degree, we can use a simple trigonometric calculation. Since we are dealing with a right-angled triangle with the Earth-moon distance as one leg (the adjacent leg in this case), and we want to find the opposite leg which represents the distance on the moon's surface from the intended target, we can use the tangent function.
For an error of 1 degree:
Convert the degree to radians, because trigonometric functions in calculators usually use radians. There are π radians in 180 degrees, so 1 degree is (π/180) radians.
Use the formula distance = tangent of the angle in radians × Earth-moon distance. So distance = tan(1° × (π/180)) × 234,000 miles.
Calculate the tangent of 1° in radians (approximately 0.01745) and multiply by 234,000 miles.
The result is approximately 4,080 miles.
For an error of 30 arcseconds (30″):
There are 60 arcseconds in 1 arcminute and 60 arcminutes in 1 degree, hence 30 arcseconds is 30/60/60 degrees, which equals 1/120 degrees.
Convert 1/120 degrees to radians similarly as before.
Use the same tangent formula: distance = tan((1/120)° × (π/180)) × 234,000 miles.
Calculate the tangent of (1/120)° in radians (approximately 0.000145444) and multiply by 234,000 miles.
This results in approximately 34 miles from the assigned target.
7.8 dividend by 0.03
Answer:
its 26
Step-by-step explanation:
give me brainly
Write an equation that relates y, and the dependent quantity, to x, the independent quantity, if the slope is 2/3 and the y-intercept is -7.
Answer:
Step-by-step explanation:
y = mx + b....in this form, the slope will be in the m position and the y int will be in the b position
so ur equation is : y = 2/3x - 7
what is the range of the function f(x)=12-3x for the domain {-4,-2,0,2,4}
A) 24,18,12,6,20
B) 6,12,18,24,30
C) -12,-6,0,6,12
D) 0,6,12,18,24
Answer:
D) 0,6,12,18,24
Step-by-step explanation:
What is the solution 4x+6<18
Answer:
x < 3
Step-by-step explanation:
4x +6 < 18
add and subtract 6 from both sides
4x + 6 - 6 < 18 -6
4x < 12
x< 12/4
X < 3
Answer:
x < 3
Step-by-step explanation:
I took the test its, the right answer, trust me.
Josie's dog weighs 122 pounds. This is about 7 times as much as Len's dog weighs. About how much does Len's dog weigh? Select the numbers that correctly complete the sentence. Len's dog weighs between pounds.
Divide the weight of Josies dog by 7:
122 / 7 = 17.43
It weighs between 17 and 18 pounds.
Final answer:
Len's dog weighs about 17 pounds, calculated by dividing Josie's dog's weight (122 pounds) by 7 since her dog is approximately 7 times heavier than Len's.
Explanation:
Josie's dog weighs 122 pounds, which is about 7 times as much as Len's dog weighs. To find the weight of Len's dog, we need to divide the weight of Josie's dog by 7. Here's the calculation:
122 pounds by 7 = approximately 17.43 pounds
Therefore, Len's dog weighs about 17 pounds. This is a unit of weight that makes sense for the size of a dog. We choose pounds because ounces would be too small and tons would be too large to represent the weight of a large dog accurately. Thus, using pounds is appropriate to express the weight of a dog, such as Len's dog in this case.
3 is 50% of what number
What is (8×^2+4×+6)(6×^2-5×+6)
Answer:
1
Step-by-step explanation:
I think it's 1 because I never did this question before.
2×1 1/2 -1 1/2×1 1/2
Answer:
3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
how to solve 6x-9 = 3x + 4
Subtract 3x on both sides: 6x-3x-9=3x-3x+4 which is 3x-9=4
Add 9 to both sides: 3x+9-9=4+9 which is 3x=13
Divide both sides by 3 to get x=13/3 or 4 1/3
Hope this helped!
Answer:
x = 13/3 = 4.333
Step-by-step explanation:
6*x-9-(3*x+4)=0
Step 1 :
Solving a Single Variable Equation :
Solve : 3x-13 = 0
Add 13 to both sides of the equation :
3x = 13
Divide both sides of the equation by 3:
x = 13/3 = 4.333
If x varies inversely as y, and x = 3 when y= 8, find y when x=4
The value of y is 6 when x is 4
Step-by-step explanation:
If x varies inversely as y, then
x = [tex]\frac{k}{y}[/tex] , where k is the constant of variationxy = k, you can find k by using the initial values of x and y[tex]\frac{x_{1}}{x_{2}}=\frac{y_{2}}{y_{1}}[/tex]∵ x varies inversely as y
∴ x = [tex]\frac{k}{y}[/tex]
∵ When x = 3, y = 8
- Substitute these values in the equation to find k
∴ 3 = [tex]\frac{k}{8}[/tex]
- Multiply both sides by 8
∴ 24 = k
∴ The equation of variation is x = [tex]\frac{24}{y}[/tex]
∵ x = 4
- Substitute the value of x in the equation to find y
∴ 4 = [tex]\frac{24}{y}[/tex]
- Multiply both sides by y
∴ 4y = 24
- Divide both sides by 4
∴ y = 6
The value of y is 6 when x is 4
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ANSWER THIS FAST
BRANLIEST IS ON THE LINE in
Answer:
Option A.) is correct [tex]\triangle XYZ \sim \triangle WVZ[/tex] by AA similarity. There are two angles that are congruent given by [tex]\angle ZXY = \angle ZWV \hspace{0.2cm} and\hspace{0.2cm} \angle ZYX = \angle ZVW[/tex].
This is because both pairs represent alternate interior angles formed by lines intersecting two parallel lines.
Step-by-step explanation:
From the given figure we can say that
i) Option A.) is correct [tex]\triangle XYZ \sim \triangle WVZ[/tex] by AA similarity. There are two angles that are congruent given by [tex]\angle ZXY = \angle ZWV \hspace{0.2cm} and\hspace{0.2cm} \angle ZYX = \angle ZVW[/tex].
This is because both pairs represent alternate interior angles formed by lines intersecting two parallel lines.
How do you evaluate 2x3x5
Answer:
Step-by-step explanation:
Answer:I think it's 30
Step-by-step explanation:
Because 2x3=6 and 6x5= 30
What is 129 multiply by 75
The graph below is a parabola, so it can be represented by a quadratic function. Which of the following quadratic functions could represent this graph.
y=-(x-2)^2-4
y=(x-2)^2+4
y=-(x+2)^2+4
y=-(x-2)^2+4
Answer:
y=(x-2)^2+4
Step-by-step explanation:
The quadratic function that represents the parabola is y = - (x - 4)² + 4.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
From the graph of the function, the parabola intersects the x-axis
at 0 and 4, and we also know when a parabola opens downwards the equation is negative.
So, The required equation is y = - (x - 0)(x - 4).
y = - (x² - 4x).
y = - {x² - 4x + 4 - 4}.
y = - { (x - 2)² - 4}.
y = - (x - 4)² + 4.
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Given that S is the centroid of triangle MNO, find SQ.
Answer:
|SQ|=5
Step-by-step explanation:
If S is the median, then OP is a median of triangle OMN.
This implies that:
|MP|=|NP|
[tex]3x-4=x+4[/tex]
We group like terms and solve for x.
[tex]3x-x=4+4[/tex]
[tex]\implies 2x=8[/tex]
[tex]\implies x=4[/tex]
Now we know that: MN:SQ=2:1
But MN=2x+2
This implies that:
2x+2:SQ=2:1
Put x=4
2(4)+2:SQ=2:1
10:SQ=2:1
Therefore |SQ|=5
Find A n B if A = {4, 7, 10, 13, 17) and B = {3, 5, 7, 9)
Answer:
look at the picture ahown
Write a system of equations to describe the situation below. Sparkles the Clown makes balloon animals for children at birthday parties. At Jenny’s party, she made 2 balloon poodles and 2 balloon giraffes, which used a total of 12 balloons. For Roger’s party, she used 27 balloons to make 4 balloon poodles and 5 balloon giraffes. How many balloons does each animal require?
A system of equations to represent the situation with Sparkles the Clown is: 2p + 2g = 12 for Jenny's party and 4p + 5g = 27 for Roger's party. We can use substitution or elimination methods to solve for 'p' and 'g' to determine the number of balloons needed for each animal.
Explanation:To write a system of equations based on the given situation with Sparkles the Clown, we will let 'p' represent the number of balloons needed for a poodle and 'g' represent the number of balloons needed for a giraffe. From Jenny's party, we know that 2 poodles plus 2 giraffes used a total of 12 balloons. From Roger’s party, we learn that 4 poodles plus 5 giraffes used a total of 27 balloons. Therefore, our system of equations to represent this situation is:
2p + 2g = 12 (Jenny's party)4p + 5g = 27 (Roger's party)To solve this system of equations, we could use methods such as substitution or elimination to find the values of 'p' and 'g' which would tell us how many balloons are required for each balloon animal.
Final answer:
To find out how many balloons are required for each balloon animal, we set up a system of equations with p representing the number of balloons for a poodle, and g for a giraffe. The system is based on the balloon usage at two parties, resulting in the equations 2p + 2g = 12 and 4p + 5g = 27.
Explanation:
To solve the problem of how many balloons Sparkles the Clown needs for each type of balloon animal, we need to set up a system of linear equations based on the given information. We will let p represent the number of balloons needed for a poodle, and g represent the number for a giraffe.
From Jenny's party, we have the first equation:
2p + 2g = 12
From Roger's party, we have the second equation:
4p + 5g = 27
Now, we have established our system of equations:
1) 2p + 2g = 12
2) 4p + 5g = 27
Solving this system will give us the number of balloons needed to make each type of balloon animal.
MAPS On a map, Wilmington Street, Beech Drive, and Ash Grove Lane appear to all be parallel. The on
ilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and
ove along Magnolia is 280 feet, what is the distance between the two streets along Kendall?
The distance between the two streets along Kendall is 347.9 feet.
Solution:
The image of the problem is attached below.
Distance between Wilmington to Ash Grove along Kendall = 820 feet
Distance between Wilmington to Ash Grove along Magnolia = 660 feet
Distance between Beech and Ash Grove along Magnolia = 280 feet
Distance between Wilmington to Beech along Magnolia
= 660 feet – 280 feet
= 380 feet
Let us x be the distance between Wilmington to Beech along Kendall and
820 – x be the distance between Beech and Ash Grove along Kendall.
The given streets are parallel.
By proportionality theorem, parallel lines cut by a transversal are in proportion.
[tex]$\Rightarrow\frac{380}{280} =\frac{x}{820-x}[/tex]
Do cross multiplication.
[tex]$\Rightarrow{380}({820-x}) =280x[/tex]
[tex]$\Rightarrow 311600-380x =280x[/tex]
[tex]$\Rightarrow 311600 =280x+380x[/tex]
[tex]$\Rightarrow 311600 =660x[/tex]
[tex]$\Rightarrow x=472.1[/tex]
Distance between Beech and Ash Grove along Kendall
= 820 – x
= 820 – 472.1
= 347.9
Hence the distance between the two streets along Kendall is 347.9 feet.
Final answer:
By analyzing the given distances along two parallel paths and using proportional reasoning, it is determined that the distance between Beech Drive and Ash Grove Lane along Kendall is approximately 547.33 feet.
Explanation:
Since Wilmington Street, Beech Drive, and Ash Grove Lane are parallel, and given the distances along Kendall and Magnolia, we can deduce the relationships between these distances to find the desired measurement. Utilizing the ratio of distances along Magnolia, we can apply the same ratio to the distances along Kendall.
We know that the total distance along Magnolia (660 feet) minus the distance between Beech and Ash Grove (280 feet) gives the distance between Wilmington and Beech along Magnolia, which is 380 feet. Assuming the distance distribution is proportional along Kendall, the distance between Beech and Ash Grove along Kendall would be given by:
(280 feet / 660 feet) * 820 feet = (2/3) * 820 feet = 547.33 feet.
Therefore, the distance between Beech Drive and Ash Grove Lane along Kendall is approximately 547.33 feet.
Find the distance (D) Round your answer the nearest tenth.PLEASE HELP!!
The distance (D) is 10 cm.
Explanation:To find the distance (D), we can use the formula D = do + di, where do is the actual distance and di is the apparent image distance.
In the given information, it states that 2do must be less than 20 cm, so we can set do = 10 cm.
Therefore, the distance (D) is 10 cm.
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