Solve each equation for both variables help please

Answer:

Step-by-step explanation:

1 : 4 1/2 :: 8 1/5 : x            proportion

x = (4 1/2)(8 1/5)                product of means/extremes

x = (9/2)(41/5)                   change improper fraction

x = 369/10                         multiply

x = 36.9                              change to decimal

The actual length is 36.9 feet.

The car travels at the speed of 68 miles per hour.

Billy made error on substitution process.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

The graph shows a proportional relationship between the distance traveled in miles and time in hours.

That means,

distance traveled in miles/ time in hours = k,

where k is a proportional constant.

Here, k is the speed.

The incorrect speed is,

1/68 miles per hour.

k = 1/68.

From the graph,

distance = 272 miles

And the corresponding time is 4 hours.

So, the speed,

= distance / time

The speed = 272 / 4

The speed = 68 miles per hour.

Billy made the error of not substituting the right values to the formula.

Therefore, the speed of the car is 68 miles per hour.

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The complete question is given in the attached image.

Answer:

The first chart.

Step-by-step explanation:

The first table. The chart gives a ratio of 1:4, which is the same as the amount the teenager made.

Answer:

Step-by-step explanation:

Steps to find the equation of a line from two points:

   1) Find the slope using the slope formula. ...

   2) Use the slope and one of the points to solve for the y-intercept (b). ...

   3) Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = MX + b) to get the equation for the line.

Answer:

this is your proper answer ...

Answer:

350,000.00

Step-by-step explanation:

420,000.00 - 20% = 350,000.00
Increase percentage: 70,000.00

The correct answer in the number line is 2 and 0.888 .

A picture of numbers on a straight line is referred to as a number line in mathematics. Across the length of a number line, the numbers are arranged in a sequential manner at equal intervals. It is frequently seen horizontally and can extend indefinitely in any direction.

The addition, subtraction, division, and times table problems can all be illustrated with a number line. You can better comprehend the idea of negative numbers by using the number line.

The addition, subtraction, division, and times table problems can all be illustrated with a number line. You can better comprehend the idea of negative numbers by using the number line.

1. 9/2 in 2

2.4/9 by 2 is = 4/4.5 = 0.888 .

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The measure of angle B is 53°.

The equation used to find B is  

B = [tex]sin^{-1}[/tex](4/5).

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Right triangle ABC.

AB = 6

BC = 10

AC = 8

In order for the triangle to be a right triangle it must satisfy the Pythagorean theorem.

So,

BC² = AB² + AC²

100 = 6² + 8²

100 = 36 + 64

100 = 100

This means,

B

|        \

|             \

|                 \

A_________C

Now,

Sin B = 8/10 = 4/5

B = [tex]sin^{-1}[/tex] (4/5)

B = 53°

Sin C = 6/10 = 3/5

C = [tex]sin^{-1}[/tex] (3/5)

C = 37°

We see that,

∠A + ∠B + ∠C = 180

90 + 53 + 37 = 180

90 + 90 = 180

180 = 180

Thus,

The equation used to find B is  

Sin B = AC / BC = 8/10

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Answer:

Tangent B=8/5

Step-by-step explanation:

Just look at the answer

the answer is right there

The point (5,5/3) also lies on the line.

A point (x, y) is located on a line with slope m if and only if it satisfies the equation:

y = mx + b

where b is the y-intercept of the line. In this case, we know that the point (3, 1) is located on the line, so we can use the information to find the value of b and then write the equation of the line in slope-intercept form.

The y-coordinate of the point (3, 1) is 1, so we can substitute this into the equation and solve for b:

1 = (1/3) * 3 + b

This simplifies to:

1 = 1 + b

so, b = 0

So, the equation of the line is

y = 1/3 * x +0

Now we can use this equation to find the coordinates of any point that lies on the line. So any point (x, y) that satisfies this equation could also be located on the line.

For example, we can pick any x, calculate corresponding y.

x=5, y=5/3

So point (5,5/3) also lies on the line.

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Step-by-step explanation:

please refer to the sketch

Answer:

245 miles

Step-by-step explanation:

210 = 6 gallons

210/6 = how far you can travel with one gallon

210/6 = 35

7*35 = how far you can travel with 7 gallons

7*35 = 245

Answer:

Ann drove 245 miles during her drive last weekend.

Step-by-step explanation:

If Ann used 7 gallons of gas during her drive last weekend, we can use the car's MPG to find out how far she drove by multiplying the number of gallons used by the MPG:

7 gallons * 35 miles/gallon = 245 miles

Answer: 2.) Blue and red

Step-by-step explanation:

The slope of the red and blue ones is - 3 while the green one's slope is -4

3(5 - 12) + 4 ÷ 2 = - 19

A must be the answer

You need 2 tablespoons of vinegar for every 1 tablespoon of oil.

What are a ratio and proportions?

A ratio is a way of comparing two or more values by division. A ratio expresses a relationship between two or more quantities. It is a comparison of one quantity to another. For example, the ratio of 3:2, 3 is being compared to 2.

A proportion is an equation that states that two ratios are equal. It can be written as:

a/b = c/d or a:b = c:d, where a,b,c,d are numerical values.

The ratio of tablespoons of vinegar to tablespoons of oil in the salad dressing is given by the ratio of the number of tablespoons of vinegar to the number of tablespoons of oil.

In this case, the ratio is 22 tablespoons of vinegar to 11 tablespoons of oil, or 22/11.

You can simplify this ratio by dividing both numerator and denominator by their greatest common divisor, that is 11

So the ratio of tablespoons of vinegar to tablespoons of oil is 2:1

Another way to express this is that for every 1 tablespoon of oil, 2 tablespoons of vinegar are needed.

So, If you want to know how many tablespoons of vinegar are needed for every tablespoon of oil you can use the proportion:

vinegar/oil = 22/11 = 2/1

Hence, you need 2 tablespoons of vinegar for every 1 tablespoon of oil.

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In the right triangle in the figure the value of x is solved to be 4.5

Using SOH CAH TOA for the right triangle

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figures show that

hypotenuse = 6

adjacent = x

given angle = 41 degrees

The value of x will be calculated using cos, CAH let the angle be y

cos y = adjacent / hypotenuse

cos 41 = x / 6

x = 6 * cos 41

x = 4.528

x = 4.5

Hence the value of x is 4.5

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Answer:

a and c are both congruent to each other i just learned about rhombuses the other day so if a and c are congruent then b and d are congruent too

In the sample compound interest rate tables presented in your reading material, the first column on the left-hand side of each table shows you the number of periods. Option C

When interest is computed, it is done so on the initial principal as well as all of the accrued interest from prior periods.

The ability of compound interest is defined as producing "interest on interest."

Any frequency schedule, including continuous, daily, and yearly, can be used to compound interest.

Money increases more quickly when compounded.

Formula is given as :
[tex]A = P(1 + \frac{r}{n})^n^t[/tex]

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The value of x=70 and y=40

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Here, 2x+y=180

x-y= 30

Here, the coefficient of y in these two equations are equal and have opposite signs. so,

                             2x+y= 180

                             x-y= 30

     Now adding equation 1 and equation 2

We get,

               3x= 210

                  x= 210/3

                  x= 70

Now, to find y:

Putting the value of x in equation 2

          x-y= 30

         70-y= 30

          y= 70-30

           y= 40

so, the value of x and y are 70 and 40

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As a result, the first term of the answer to the given arithmetic mean problem is 14.

The Arithmetic Mean or Average of the Group is the product of the sum of all the numbers in a group and the amount of items in that list, divided by both. The Geometric progression is also same as this .This average of the numbers 5, 7, and 9 is, for instance, 4, as 5 + 7 + 9 is 21, and 21 split by 3 [there really are three numbers] equals 7.

Here,

In this case, t(n) = (a + ((n — 1) * d)),

The value of the nth term is t(n),

The first term of the AS is a.

The position of a value in the A.S. is represented by the positive whole integer n, and

The constant common difference among A.S. words is d.

In light of the question, we can say:

11 = (5 + ((4 — 1) * d)),

Take 5 away from both sides.

11 — 5 = (5 + ((4 — 1) * d)) — 5,

On the RHS, the fives cancel one another out.

6 = 3d,

d = 2.

In summary, the common distinction is: 2.

=> 20 = a + 3d

=> 20 - 6

=> a =14

As a result, the first term of the answer to the given arithmetic mean problem is 14.

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On solving the provided question we can say that the it will 4 hrs to walk all the way around the crater, on doing the radius.

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter

here,

D= 1

r = 1/2 = .5

A = 40

T = 40/10 4 hrs.

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Find time needed to drive 200 miles:

50 miles = 1 hour

1 mile = 1/50 hour

200 miles = 1/50 x 200 = 4 hours

Find time of arrival:

7:00am + 4 hours = 11am

Answer: She will arrive at 11am

Answer:

The woman will arrive at New York City at 11 am.

Step-by-step explanation:

At an average speed of 50 miles per hour, it will take the woman 4 hours to reach New York City. If she leaves at 7 am, she will arrive at 11 am. Here's the math:

200 miles / 50 miles per hour = <<200/50=4>>4 hours

7 am + 4 hours = 11 am

So the woman will arrive at New York City at 11 am.

Answer:

$28.29

Step-by-step explanation:

1 pound: $6.15
4.6 pounds: 6.15 x 4.6 = $28.29

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given : PQRS has the length 12

and TUVW has length 15.

thus ,

To find the perimeter of PQRS:

we find,

TUVW = 35 units

and

PQRS = 35 - 6

=> PQRS  = 29

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

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The rate based on the information will be 590 kilometers per hour and 1010 kilometers per hour

Rate in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that rate contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the an airplane travels 4720 kilometers in 8 hours. The rate is:

= 4720 / 8

= 590 kilometers per hour

Flying with the wind, the same plane travels 4040 kilometers in 4 hours. The rate will be:

= 4040 / 4

= 1010 kilometers per hour

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Answer:

Marita had a $10-off coupon, so she paid $50 - $10 = $40 for the item

Step-by-step explanation:

To find the original price of the item, we need to work backwards through the discounts and find the price of the item before any discounts were applied.

We'll call the original price of the item "x."

First, we know that Marita received a 25% discount on the item, which means she paid 100% - 25% = 75% of the original price.

Then, Marita received an additional 20% discount on the sale price, which means she paid 100% - 20% = 80% of the 75% discounted price.

So, Marita paid 80% of the original price, which was reduced by a 25% discount. That means she paid 0.8 * 0.75 = 0.6 * original price = $30.

Therefore, the original price of the item was $30 / 0.6 = $<<30/0.6=50>>50.

Finally, Marita had a $10-off coupon, so she paid $50 - $10 = $40 for the item.

Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

The word "mathematics" has 11 letters, so there are 11 letters in the bowl. The probability of drawing the letter "O" is 1/11, since there is only 1 "O" in the 11 letters. Similarly, the probability of drawing the letter "B" is 1/11, and the probability of drawing the letter "J" is 1/11 as well.

Since the events of drawing the letter "O", "B", and "J" are independent of each other, the probability of drawing all three letters in order is the product of their individual probabilities.

Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331

It is a very low probability, the chances of drawing that sequence are very low.

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Answer:

  True

Step-by-step explanation:

You want to know if it is true or false that "two angles add up to 180° if and only if they are supplementary."

Two supplementary angles have a sum of 180°. That is the definition of supplementary angles. The offered statement is True.