GRADE 8 UNIT 5 LESSON 5 OPEN UP RESOURCES
#3 A car is traveling on a small highway and is either going 55mph or 35mph, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55mph, and y being the time in hours that the car is going 35mph, an equation describing the relationship is:
55x + 35y = 200
a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?
b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?
c. If the car spends no time going 35mph, how long would the trip take?

Answer:

y=(x-2)^2+4

Step-by-step explanation:

The quadratic function that represents the parabola is y = - (x - 4)² + 4.

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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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.

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

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]

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

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.

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:

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.

Answer:

Step-by-step explanation:

Answer:I think it's 30

Step-by-step explanation:

Because 2x3=6 and 6x5= 30

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.

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)

Answer:

3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

The value of y is 6 when x is 4

Step-by-step explanation:

If x varies inversely as y, then

∵ 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:167 + 167 = 334

Step-by-step explanation:

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.

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.

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

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)

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

Answer:

635

Step-by-step explanation:

83,820 / 132 = 635

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

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.

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°

Answer:

1

Step-by-step explanation:

I think it's 1 because I never did this question before.

Answer:

r= -45

Step-by-step explanation:

trust on this one

Answer:

-189

Step-by-step explanation:

The distance (D) is 10 cm.

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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Answer: 5000

Step-by-step explanation: 5/5000

The workers tested 5000 headphones.

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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Answer:

its 26

Step-by-step explanation:

give me brainly

Answer:

D) 0,6,12,18,24

Step-by-step explanation:

Answer:

look at the picture ahown