Tom is in charge of the track and field games at his school. He was given two boxes of prizes. He has given out 7/5 boxes. He estimates he will give out another 4/5 box. Does he have enough? If he does not have enough, how much more does he need?​

The equation of the line that passes through the point (-9, 2) and is perpendicular to the line 10x - 5y = 6 is y = - 1 / 2 x - 5  /2

The equation of a line can be represented in slope intercept form.

Therefore,

y = mx + b

where

Therefore, the equation of the line is perpendicular to 10x - 5y = 6.

5y = 10x - 6

y = 2x - 6 / 5

Perpendicular lines follows the rule below:

m₁m₂ = -1

Therefore,

2m₂ = -1

m₂ = -1 / 2

The slope of the line is - 1 / 2. Now, let's find the equation of the line as it passes through (-9, 2)

y = - 1 / 2 x + b

2 = - 1 / 2 (-9) + b

2 = 9 / 2 + b

b = 2 - 9 / 2

b = 4 - 9 / 2

b = - 5 / 2

Therefore, the equation of the line is as follows:

y = - 1 / 2 x - 5  /2

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Answer:

Add the expressions.

11x2−3x−3

Step-by-step explanation:

Simplification of polynomials.

Polynomials are mathematical expressions made up of many terms.To simplify a polynomial the most, you must collect all like terms and rearrange them from highest to lowest power.

The justification for each step in the solution of the equation (5x−4)/2=2x−1 is:

Step 1: (5x-4)/2 = 2x-1   (As Given)

Step 2: ((5x-4)/2) × 2 = 2 × (2x-1)

The Multiplication Property of Equality asserts that when both sides of an equation are multiplied by the same number, the two sides remain equal.

Step 3: (5x-4) = 4x-2

The Distributive Property of Equality asserts that equality holds after distributing by multiplication.

Step 4: 5x - 4 + 4 = 4x - 2 + 4

The Addition Property of Equality states adding the same number on both sides of an equation yields equivalent results.

⇒ 5x = 4x + 2

Step 5: 5x - 4x = 4x + 2 - 4x  

The Subtraction Property of Equality states that you can get an equivalent equation by subtracting the same integer from both sides of an equation.

⇒ x = 2

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According to the solving each step in the solution of the equation (5x−4)/2=2x−1 is:

Step 1: (5x-4)/2 = 2x-1  

Step 2: ((5x-4)/2) × 2 = 2 × (2x-1)

Step 3: (5x-4) = 4x-2

Step 4: 5x - 4 + 4 = 4x - 2 + 4

Step 5: 5x - 4x = 4x + 2 - 4x  

The four properties of equality—addition, subtraction, multiplication, and division—can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.

(5x-4)/2 = 2x-1   (As Given)

((5x-4)/2) × 2 = 2 × (2x-1)

According to the Multiplication Property of Equality, an equation's two sides stay equal even after being multiplied by the same number.

Step 3: (5x-4) = 4x-2

According to the distributive property of equality, multiplicative distribution still maintains equality.

Step 4: 5x - 4 + 4 = 4x - 2 + 4

According to the Addition Property of Equality, an equation produces equivalent outcomes when the same integer is added to both sides.

⇒ 5x = 4x + 2

Step 5: 5x - 4x = 4x + 2 - 4x  

According to the "Subtraction Property of Equality," subtracting the same number from both sides of an equation will result in an identical equation..

⇒ x = 2

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Answer:

[tex]-2<x<-1, 1<x<2[/tex]

Step-by-step explanation:

[tex]|x|>1 \implies x<-1[/tex] or [tex]x>1[/tex]

[tex]|x|<2 \implies -2<x<2[/tex]

Taking the union of the intervals, [tex]-2<x<-1, 1<x<2[/tex]

Each gets [tex]\frac{1}{4}[/tex] pieces of toast.

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

Given Data

LeeAnn is taking care of her 3 brothers. She has four pieces of toast and wants to divide them equally among her brothers.

So,

Total pieces of toast = 4

Each gets = 1

Fraction of toast each gets = [tex]\frac{1}{4}[/tex]

Each gets [tex]\frac{1}{4}[/tex] pieces of toast.

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The rational numbers - 1 3/4 (-2 1/7) are multiplied to give 105/28

A fraction can be defined as the part of a whole element.

There are several types of fractions, which includes;

Rational numbers are defined as types of real numbers that are in form of fractions.

For instance: a/b where a is not equal to zero.

Given the rational numbers;

- 1 3/4 (-2 1/7)

To determine the product, take the following steps

Turn into improper fractions

-7/4 × -15/ 7

Now, multiply the numerators and denominators

105/28

Hence, the value is 105/28

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Answer:

6

Step-by-step explanation:

Let the required input be y.

[tex]h(y)=y-11=-5 \\ \\ y=6[/tex]

Answer:

gradient= y2-y1/x2-x1

-8+10/-8-c=-1/8

2/-8-c=-1/8

-1(-8-c)=8(2)

8+c=16

c=16-8

c=8

Answer:The time of Trip 2 is

⇒ 0.8 hours.

The distance of Trip 1 is

⇒ 4 km.

The time of Trip 2 is 0.8 hours

The distance of trip 1 is 32 km

Given,

The speed of the bus = 40 km/h

Talia's walked at a speed = 5 km/h

To determine the time,x for her walk here used the equation; 40(0.9 – x) = 5x.

We have to find the time from Talia's home to bank in bus and the distance.

Here,

Equation is already given, we can simplify it and get x which is the time.

40(0.9 – x) = 5x.

36 - 40x = 5x

36 = 40x + 5x

36 = 45x

x = 36/45

x = 0.8 hours = 0.8 x 60 = 48 minutes

Now,

Distance from Talia's home to bank;

Speed = distance/time

Distance = speed x time = 40 x 0.8 = 32 km

That is,

The time of Trip 2 is 0.8 hours

The distance of trip 1 is 32 km

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If Lisa and Joey put the same amount of money every month in the savings account for David's future and the situation is plotted in a graph where time is on the x-axis, then there will be straight line with a constant slope.

As per the question statement, Lisa and Joey just became parents to their son, David and they decided to start a savings account for their newborn's future, where they agreed to put an equal amount of money every month.

We are required to determine the condition of the variables if the above-mentioned situation is plotted into graph and the account gets constantly filled with money as David grows older.

To solve this question, first let us consider the time to be plotted on the X-axis (As mentioned in question statement that "Time" is almost always on the x-axis) and the money collected to be plotted on the Y-axis.

Since, an equal amount of money is put into the account every month, therefore, taking 1 month as unit time to plot our graph, the money will grow diagonally in a straight line with a constant slope. Hence, both the variables (abscissa and ordinates) will increase on a constant ratio along the first quadrant.

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EXPLANATION:

Given;

We are given a parallel pair of lines m and n, and a transversal that cuts both lines.

Required;

We are required to find the value of x.

Step-by-step solution;

When a pair of parallel lines are cut by a transversal, the angle formed by the point of intersection of one line and the transversal is equal to that formed by the other line and the transversal when they both lie on the same side of the transversal.

This means on the diagram given;

This means angle 167 on line n is equal to angle 167 on line m. These are called corresponding angles.

The same applies to angle x on the line m and the other angle on line n. They both are also corresponding angles.

Next, take note that angles that lie on either side of a vertex where two lines intersect are called vertically opposite angles (or just opposite angles).

Therefore, angle x = 167 and angle 167 = x.

ANSWER:

Step-by-step explanation:

did you change the reference number ?

I think the original question was "90 is how many % of 80 ?"

now it is 81.

in % calculations the most important things to identify :

what are 100% (or any other reference % level).

then what is 1%.

and then multiply this 1% by the desired number of % or divide the target number by this 1% to find out how many % the target number is.

in our case here

100% = 81

1% = 100%/100 = 81/100 = 0.81

how many % are 90 ?

well, as many as how often 1% fits into these 90 :

90/0.81 = 111.111111111... %

when the reference was 80, then we had

90/0.8 = 112.5%

From the calculations using the data provided, the acceleration of the ball is 10 m/s^2

We know that the acceleration is the rate at which there is an increase or a decrease in the velocity of a body. In this case, we are told that A ball is released from rest and falls 125 meters in 5 seconds.

We have the following;

Distance of the object = 125 meters

Time taken =  5 seconds

Given that;

s = ut + 1/2at^2

u = 0 m/s because it was released from rest

s = 1/2at^2

a = 2s/t^2

a = 2(125)/(5)^2

a = 250/25

a = 10 m/s^2

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Answer:

Since the moon has no atmosphere, all wavelengths of sunlight reach the ground by traveling straight through space. Our sun appears white because it produces all visible wavelengths approximately equally. The sun will appear the same size whether viewed from Earth or the Moon since Earth and the moon are relatively close to the sun. The sun and moon both have an apparent size of one-half of a degree when viewed from Earth.

Step-by-step explanation:

Answer:

about 22 square units

Step-by-step explanation:

Count the number of squares which is completely inside the border. Then count the number of squares which is half or more than half inside the border as 1 square.

Answer:

20

Step-by-step explanation

We need to find the multiples of 10 and 20 (multiples of 10 = 10, 20, 30, 40; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 10 and 20, i.e., 20.

Answer:

20

Step-by-step explanation:

First, find the factors of both 10 and 20

Factors of 10: 1, 2, 5, 10

Factors of 20: 1, 2, 4, 5, 10, 20

Notice any common factors?: 1, 2, 5, 10

Now multiply the greatest common factor, 10, with another even number to hopefully get 20: 10*2=20.

Hence, the least common multiple is 20.

Answer:

If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?

Step-by-step explanation:

Answer: If I understood correctly, the answer would be A, adults who buy any clothes. I'm not too sure though that would make sense.

Answer:

It is a quadratic funcion with vertex in (4,0)

Step-by-step explanation:

15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days. The average rate of the change is 24.

Given that,

The paving of a bike route by a city. Every day, the same amount of the path is paved. 15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days.

We have to find the average change rate.

1st we find the slope with the points (4,15) and (6,12).

Slope =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Slope=[tex]\frac{12-15}{6-2}[/tex]

Slope=-3/4

Now,

y=mx+b

15=-3/4(4)+b

b=15+3

b=18

We got the equation of line as y=-3/4x+18

Now take y=0

0=-3/4x+18

-3/4x=-18

x=(18×4)/3

x=72/3

x=24

Therefore, the average rate of the change is 24.

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Number of outfit outcomes are possible with the choices of 3 pairs of pants , 4 shirts and 3 pairs of shoes are equal to 36 outfits.

As given in the question,

Number of choices given

Possibilities with the choices

Number of pairs of pants 'n' = 3 pairs

Number of shirts 'p' = 4 shirts

Number of pairs of shoes 'r' = 3 pairs of shoes

Using Fundamental counting of Principle

Total number of outfit outcomes with the given choices

= n × p × r

= 3 × 4 × 3

= 36 outfits.

Therefore, number of outfit outcomes are possible with the choices of 3 pairs of pants , 4 shirts and 3 pairs of shoes are equal to 36 outfits.

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Answer:

Step-by-step-learn is 4

The new dimensions of the box are 5 feet, 4 feet, and 6 feet.

Given:

A rectangular box has dimensions of 4 feet by 3 feet by 5 feet.

So, Length = 4 feet ,width = 3 feet and height = 5 feet.

Volume of rectangular box = length × width × height

                                             = 4 × 3 × 5 = 60 feet³

Now, increasing each dimension by the same amount yields a new box.

Let the increase in dimension be x feet.

The dimensions of the new box are,

Length = (4 + x) feet ,width = (3 + x) feet and height = (5 + x) feet.

Volume of new box = length × width × height

                                 = (4 + x) (3 + x) (5 + x)

It is given that the volume of the new box is twice the volume of the old box, 2 × 60 feet³ = 120 feet³

So, equate the volume to find the value of x.

(4 + x) (3 + x) (5 + x) = 120    

(12 + 7x + x²) (5 + x) = 120

60 + 12x + 35x + 7x² + 5x² + x³ = 120

60 + 47x + 12x² + x³ = 120

x³ + 12x² + 47x - 60 = 0  

x = 1

Hence each dimension was increased by 1 foot.

The new dimensions of the box are 5 feet, 4 feet, and 6 feet.

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Answer: 1/2

Step-by-step explanation:

The rate of change is the same as the slope.

Taking the points (2, 4) and (6,6), the slope is [tex]\frac{6-4}{6-2}=\frac{1}{2}[/tex]

The container's strawberry lemonade that had a stronger strawberry flavor is the more compact bottle and has a more robust taste.

This is further explained below.

Generally,  in a bid to understand the context of the scenario we must first write the rato of the flavor's relationship

x=8:40

y=5:20

Therefore

x=8:40

y=10:40

In conclusion, This helps us decipher that Larger container: We add eight ounces of strawberry puree for every forty ounces of lemonade that we make.

We have 10 ounces of strawberry puree for every 40 ounces of lemonade that we have.

Therefore, the more compact bottle has a more robust taste.

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The surface area of this cylinder is 6.28y? + 2rh square units.

What does a cylinder's smooth surface look like?

A cylinder has a curving surface that unfolds into a rectangle and two flat surfaces that are both circular.

Given:

The surface area of a cylinder = 2ny? + 2rh.

n = 3.14

therefore putting the value of n

we get,

=2  .  3.14  .  y? + 2rh

=6.28y? + 2rh

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Answer:

the answer to the question is 7(35.8-m)53.4)

Answer:

the answer to the question is 7(35.8-m)53.4)

Step-by-step explanation:

Answer:

5 m/s

Step-by-step explanation:

1. 3² + 4² = 25

2. √25 = 5

Answer:

Store B

Step-by-step explanation:

Since the lowest common multiple of 2 and 3 is 6, so let's find the cost of 6 bags of chips from each store.

Store A

cost for 6 bags of chips

= 3(2.5)

= $7.50

Store B

cost for 6 bags of chips

= 2(3.25)

= $6.50

Since store B offers a cheaper price for 6 bags of chips, it offers a better deal.

Alternatively, you could work out the cost of each bag of chips for both stores.