Manny took home a couple of his friends after soccer practice. He originally had 5 gallons of gas in his car. He used 1.03 gallons of gas to take one friend home and four fifths gallon to take the other friend home. How much gas did he have left in his car after taking both friends home?

1.04 gallons
3.17 gallons
5.8 gallons
6.03 gallons

In a triangle of EFG we have ∠E+∠F = 120°,E=(8x-2)° and F=(7x+2)°.

Option B is true and angle of G is 60°.

Given that,

∠E+∠F = 120°

In the figure we have a triangle with EFG.

E=(8x-2)°

F=(7x+2)°

We know

∠E+∠F = 120°

8x-2+7x+2=120

15x=120

x=120/15

x=8

We got x =8

∠E=8[tex]\times[/tex]8-2=62°

∠F=7[tex]\times[/tex]8+2=58°

Now, we know in a triangle all angles are equal to 180°.

∠E+∠F+∠G=180°

62°+58°+G=180°

120°+G=180°

G=180°-120°

G=60°

We have 4 option

a) (7x)° which is false

b) (7x+4)° which is true (7[tex]\times[/tex]8+4=60°)

c)(8x)° which is false

d) (8x+4)° which is false

Therefore, option B is true and angle of G is 60°.

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k = -3 is the value in straight line.

What is  straight line?

Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.

Different  type

On putting the values of the point in the equation of line, the value of X = 2 and Y = -8

When a line passes through a point, the point satisfies the equation of the line.

The line   y = kx + 4 goes through the point (2, -2)

So, ( 2 , -2 )  must satisfy the equation of the line.

Put  x = 2 y= - 2 in equation y = kx + 4

-2 = k * 2 + 4

- 2 = 2k + 4

-2 -4 = 2k

-6 =2k

k = -6/2

k = -3

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The total distance travelled by the body is 48 meters

According to the question we have been given an equation of the position of  a body moving along x-axis as

                    s = t³ - 12t² + 36t

where,    s = distance in meters

             t = time in seconds

We need to find the total distance traveled by the body from t=0s to t=4s

The formula for the total distance is given as :

            S = |s(1) - s(0)| + |s(2) - s(1)| + |s(3) - s(2)| + |s(4) - s(3)|

Now we will find out the distance travelled in time 0s to 4s

when t = 0s ,  s = (0)³ - 12(0)² + 36*0

                         = 0m

         t = 1s ,  s = (1)³ - 12(1)² + 36*1

                         =  25m

         t = 2s ,  s = (2)³ - 12(2)² + 36*2

                         =  32m

         t = 3s , s = (3)³ - 12(3)² + 36*3

                         = 27m

         t = 4s , s = (4)³ - 12(4)² + 36*4

                         = 16m

Putting the required values in the above formula we get ,

  S = |25-0|+|32-25|+|27-32|+|16-27|

  S = 25 + 7 + 5 + 11 meters

   S = 48 meters

Hence the total distance travelled by the body is 48 meters

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The coordinates of B is (-5, 6).

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space

What is section formula ?

The section formula helps in determining the coordinates of a point which facilitates division of the line joining two points in a ratio. This takes place either internally or externally.

P (x, y)= (c*m + a*n)/(m + n) , (d*m + b*n)/(m + n ).

Given:

let the coordinates of B (x, y)

M is midpoint M(-6,4) and coordinates of A are (-7, 2)

Using section formula

-6 = (x -7)/2

-12 = x -7

x = -5

and, 4 = y+2/2

8 = y+2

y = 6

Hence, the coordinates of B is (-5, 6)

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Answer:

Sub in the numbers given to x, y, z and use calculator to solve

a = amount invested at 2%

how much is 2% of "a"? (2/100) * "a", namely 0.02a.

b = amount invested at 7%

how much is 7% of "b"? (7/100) * "b", namely 0.07b.

We know that fund A is less than fund B by 8000, that is a = b - 8000.

we also know that the yielded amount in interest is $1730, so if we simply add their interest, that'd be 0.02a + 0.07b = 1730.

[tex]\boxed{a = b - 8000} \\\\\\ 0.02a~~ + ~~0.07b~~ = ~~1730\implies 0.02(\stackrel{a}{b-8000})~~ + ~~0.07b~~ = ~~1730 \\\\\\ 0.02b-160+0.07b=1730\implies 0.02b+0.07b=1890\implies 0.09b=1890 \\\\\\ b=\cfrac{1890}{0.09}\implies \blacksquare~~ b=21000 ~~\blacksquare[/tex]

Answer:

5 is the answer to that question

Answer:

D. √45

Step-by-step explanation:

(4, -1) (7, 5)

(x₁, y₁)  (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(7 - 4)² + (5 - (-1))²

d = √(3)² + (6)²

d = √9 + 36

d = √45

I hope this helps!

Answer:

7000 panels.

Step-by-step explanation:

Let x be the number of panels produced by Plant B.

Therefore:

Given information:

Create an equation with the given information and defined variables, remembering to write the percentages in their decimal form:

[tex]\implies 0.03(4x) + 0.02x = 980[/tex]

To find the number of panels Plant B produced, solve the found equation for x:

[tex]\implies 0.03(4x) + 0.02x = 980[/tex]

[tex]\implies 0.12x + 0.02x = 980[/tex]

[tex]\implies 0.14x = 980[/tex]

[tex]\implies \dfrac{0.14x}{0.14} = \dfrac{980}{0.14}[/tex]

[tex]\implies x=7000[/tex]

Therefore, Plant B produced 7000 panels.

The ounces of herbs costing $1 per ounce that should be mixed with these 50 oz of herbs to produce a mixture costing $2.50 per ounce?

is 50 ounces.

Let x = the amount of herb that costs $1 per ounce.

Based on the information,the total weight will be:

x + 50 = y.

At $2.50, the cost of the mixture will be:

1x + 4(50) = 2.50y

x + 200 = 2.50y

x + 200 = 2.50(x + 50)

x + 200 = 2.50x + 125

Collect like terms

2.5x - x = 200 - 125

1.5x = 75

Divide

x = 75/1.5

x = 5.

Therefore, the correct option is 50

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Definition: n math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given,

Points scored per game by 35 NBA players during the 2017 basketball season.

Context: Points scored per game by 35 NBA players

Shape: dotted, no gaps

Outliers: none

Center: 14(Median)

Spread: Data varies from somewhere between (12-14) to somewhere between (24-26)

context is about the graph

shape is about the representation

outliers is whether any point is farther

center is the median

spread is till where the graph is extended with gaps in between

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Answer:

Step-by-step explanation:

comment on the comment section with a complete question I will help you there please

Answer: IK=14

Step-by-step explanation:

IK=IJ+JK

IL=IJ+JL

IL-JL=IJ+JL-JL

IJ=IL-JL

IK=IL-JL+JK

IK=31-25+8

IK=6+8

IK=14

The area of the rectangular backyard is 804.37

The area of a rectangle can be calculated by multiplying the length and the width

Area= length × width

Length= 35.75 feet

Width= 22.5 feet

Area= 35.75 × 22.5

= 804.37

Hence the area of the rectangular backyard is 804.37

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The number of street lights that will be needed is 3 street lights.

From the information, it was stated that the city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long,

The number of street lights needed will be:

= 7/8 ÷ 3/8

= 7/8 × 8/3

= 7/3

= 3 street lights.

Therefore, the number of street lights that will be needed is 3 street lights.

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Answer:

39 hours

Step-by-step explanation:

52 × 45 = 2340

2340 mins into hours = 39 hours

hope this helps :)

Answer:

Step-by-step explanation:

Given an oval track in the shape of a 48 m by 96 m rectangle with semicircular ends, you want the length of the track and the area enclosed.

If you remove the rectangle, you see that what remains is a circle of diameter 48. The length of that circular portion of the track is the circumference of the circle:

  C = πd

  C = π(48 m) = 48π m ≈ 151 m

Added to that length are the two 96 m sides of the rectangle. So, the total length of the track is ...

  track length = curved length + straight length

  track length = 151 m + 2×96 m = 343 m

The length of the track is 343 meters.

The area enclosed by the track includes the area of the circle we saw above, and the area of the rectangle.

The radius of the circular portion is half the diameter, or 24 m. Then the area is ...

  A = πr²

  A = π(24 m)² = 576π m² ≈ 1810 m²

The area of the rectangular portion is the product of length and width:

  A = LW

  A = (96 m)(48 m) = 4608 m²

The enclosed area is the sum of these areas:

  enclosed area = area of circle + area of rectangle

  enclosed area = 1810 m² +4608 m² = 6418 m²

The area enclosed by the track is 6418 square meters.

The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.

In this problem we have a composite figure generated by a rectangle and two semicircles, of which we must determine its perimeter and area. The perimeter is the sum of the contour lengths of the semicircles and the rectangle and the enclosed area is the sum of areas of the two semicircles and a rectangle.

The perimeter of the composite figure is:

p = 2π · r + 2 · l

p = 2π · (24 m) + 2 · (96 m)

p ≈ 342.796 m

A = π · r² + l · (2 · r)

A = π · (24 m)² + (96 m) · (48 m)

A ≈ 6417.557 m²

The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.

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The distance between the two points are-9.87 units.

The distance formula is;

d² = (y₂ - y₁)² + (x₂ - x₁)²

Let the two given points be;

A(x₁, y₁) = (-1,-9)

B(x₂, y₂) = (6, - 16)

Put the values in the formula;

d² = (-16 + 9)² + (6 + 1)²

d² = (-7)² + (7)²

d² =2 (7)²

d = 7√2

d = 7×1.41

d = 9.87

Therefore, the distance between the two points is found as 9.87 units.

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The exponential equation to model this after t time periods is:

N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]

Given,

Melatonin is fast-acting and has a half-life of approximately 30 minutes.

10-milligram tablet is taken.

We need to write an exponential equation to model this after t time periods.

Half-life is the time required for a quantity to reduce to half of its initial value.

The formula is given as:

N(t) = [tex]N_{0} ~(\frac{1}{2})~^\frac{t}{t_{1/2}}[/tex]

Where

N(t) = quantity of the substance remaining

[tex]N_{0}[/tex] =  initial quantity of the substance

[tex]t_{1/2}[/tex] = half-life of the substance

We have,

Half-life = 30 minutes

[tex]N_{0}[/tex] = 10 mg

The exponential equation to model this after t time periods is:

N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]

Thus the exponential equation to model this after t time periods is:

N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]

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Answer:

x = 10/9

Step-by-step explanation:

Solve:

27^(3x-2) = 81

When solving equations in exponential form make sure the two bases on both sides are the same.

3^3(3x-2) = 3^4

Once the two bases are the same you cancel them out and used its exponent to solve the equation.

3(3x-2) = 4

9x-6 = 4

Add 6 to both sides.

9x-6+6 = 4+6

9x = 10

Divide both sides by 9.

x = 10/9

Therefore x = 10/9.

Answer:

15+90=3×18

Step-by-step explanation:

GCF= 5

Answer:

3:1 = 6:2 = 12:4

Hope this helps :)

Answer:

3.1=12.4

Step-by-step explanation:

12.4

12/12+4=12/16=3/4.

so 3.1=12.4

Step-by-step explanation:

if I understand you correctly, then we have the 4 described cards. 3 of these 4 cards are face cards (Jack, Queen, King).

a probability is always desired cases over totally possible cases.

so, for the first pull we have a probability of

3/4 = 0.75

we have 4 total possibilities, and 3 of them are the desired outcome.

for the second pull we have then only 3 cards left (we did not replace the first pulled card). and because the first pulled card was in this scenario a face card, 2 out of these 3 cards are face cards.

so, the probability to pull a face card here is

2/3 = 0.66666...

when we combine these 2 events into one connected event (we are creating event 1 AND event 2), we multiply the probabilities, giving us

3/4 × 2/3 = 6/12 = 1/2 = 0.5

The amount Trey invested in Fund B is $8,000.

Profit is a residual income, It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. while return is a total revenue. Profits may be negative, whereas returns, such as wages and interest are always positive.

amount invested in Fund A = $12,000            (given)

profit returned by Fund A =  1% of $12,000    (given)

= 1/100*$12,000

= $120

Let amount invested in Fund B = x                   (assumption)

profit returned by Fund B =  6% of x                 (given)

= 6/100*x

= $ 6x/100

Given that both funds A and B together returned a 3% profit, So the equation we get is

120+6x/100 = 3% of (12,000+x)

(12,000+6x)/100 = 3/100* (12,000+x)

12,000+6x = 3(12,000+x)

12,000+6x = 36,000+3x

6x-3x = 36,000-12,000                       (bringing like terms on same side)

3x = 24,000

x = 24,000/3

x = $8,000

Therefore, we can conclude that the amount Trey invested in Fund B is $8,000  

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Answer:

-3 will be on the -x axis n the -6 will be on the -y axis so both will meet at a point.

Step-by-step explanation:

that is all I understand am not sure if I am ryt

Answer:

7.112 x [tex]10^{-5}[/tex]

Step-by-step explanation:

You need to re-write the number so that it is 1 or larger but less than 10.  To do that, we need to move the decimal 5 spaces to the right.  The actually number is smaller.  The [tex]10^{-5}[/tex] is telling me how much smaller the number actually is.  To get the number in standard notation I would have to take 7.112 and divide it by 100,000.

Answer:

f(1) = 1

f(4) = -2

f(0) = 2

Step-by-step explanation:

y = f(x)