solve the literal equation l ax + b l = c

Answer:

C. 150

Step-by-step explanation:

Given:

m<8 = 11y + 7

m<3 = y + 17

Required:

Find m<2

Solution:

m<8 + m<3 = 180 (supplementary angles and linear pair theorem)

11y + 7 + y + 17 = 180 (substitution)

Collect like terms

12y + 24 = 180

Subtract 24 from each side

12y = 180 - 24

12y = 156

Divide both sides by 12

y = 156/12

y = 13

m<2 = m<8 (alternate exterior angles are congruent)

m<2 = 11y + 7

Substitute y = 13 into the equation

m<2 = 11(13) + 7 = 143 + 7

m<2 = 150°

The length of the rectangle-shaped classroom is 15 meters.

We have a classroom. The shape of the classroom is rectangular. The length of the classroom is 3 meters more as compared to its width. The area of the rectangular classroom is 180 square meters. We need to find the length of the classroom.

Let the width of the rectangle be represented by the variable "x". The length of the rectangle is "x + 3". We will use the formula for the area of a rectangle. The area of a rectangle is the product of its length and width.

A = x*(x + 3)

180 = x² + 3x

x² + 3x - 180 = 0

We will use the quadratic formula to solve for the values of "x".

x = [-3 ± √(3² - 4(1)(-180))]/2(1)

x = [-3 ± √(9 + 720)]/2

x = [-3 ± √729]/2

x = [-3 ± 27]/2

The values of the variable "x" are -15 and 12. The negative value is rejected because the measure of a dimension cannot be negative. Hence, the value of "x" is 12. The length of the rectangular classroom is x + 3 = 12 + 3 = 15 meters.

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Answer:

5/(8+4+5) = 5/17

Step-by-step explanation:

total has (8 red +4 white+5 blue）= 17

we looking for blue , so is 5.

5/17

To calculate the percentage of the free throws that were successful:

To get the percentage you multiply it by 100:

Answer: The player made 71% of the free throws attempted.

The measure of the angle BCA is 50 degrees.

The angles at the circumference subtended by the same arc are equal.

The angles at the circumference on the same segment theorem states that angles in the same segment of the circle are equal.

Therefore, let's use the theorem to find the angle ∠BCA in the circle.

Hence,

∠BCA = ∠BOA

Finally,

∠BCA =  50 degrees.

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The measure of angle D is 45°

Similar triangles have the same corresponding angle measures and proportional side lengths. When two triangles are similar, the corresponding angles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

To know the corresponding angles

side AC is corresponding to side EF, therefore angle D is congruent to angle A

angle D = 45°

OR , we can use the sum of angles In a triangle , which is 180°

angle D = 180 -( 72+63)

= 180 - 135

= 45°

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Answer:

She is correct because 30 percent of 30 is 9 or in other words if you multiply 30 by 30 percent you get 9.

Step-by-step explanation:

Answer:

Yes she is correct cause 30 times 30 percent is 9

Step-by-step explanation:

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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The mean, median, range, and standard deviation  for the new data set must all be 7 greater than for the original data set.

The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.

The formula for the mean is: Mean = (Sum of Values)/(Number of Values)

For the original data set: Mean = (Sum of Values)/30

For the new data set: Mean = (Sum of Values + 6)/31

Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.

The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.

The formula for the median is: Median = (n+1)/2

For the original data set: Median = (30+1)/2 = 15.5

For the new data set: Median = (31+1)/2 = 16.5

Therefore, the median for the new data set must be 7 greater than the median for the original data set.

The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.

The formula for the range is: Range = (Largest Value) - (Smallest Value)

For the original data set: Range = (Largest Value) - 13

For the new data set: Range = (Largest Value + 6) - 13

Therefore, the range for the new data set must be 7 greater than the range for the original data set.

The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)

For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)

For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)

Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set

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The difference in the addition of both fractions is that they have different lowest common multiples.

We want to add the fraction expression given as:

¹/₂ + ¹/₄

Taking the Lowest common multiple of 8, we have:

(4 + 2)/8 = 6/8

However, for the second fraction expression, we have:

¹/₂ + ¹/₃

Taking the lowest common multiple which is 6, we have:

(3 + 2)/6 = 5/6

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Answer:

pounds

Step-by-step explanation:

pounds : ounces

   10      :      \(x\)

    1        :     16

\(x=160\)

The numerator would be pounds. \(\frac{10 pounds}{160 ounces}\)

Let:

a = 13.5

b = 12.1

x = unknown percent

so:

Answer:

89.6%

Your answer is 89.6%

Answer:

Step-by-step explanation:

Let's solve for g.

gx=(−14(x−21))(2)+47

Step 1: Divide both sides by x.

gx

x

=

−28x+635

x

g=

−28x+635

x

Answer:

g=

−28x+635

x

The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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Answer:

X=33 degrees

Y= 45

Step-by-step explanation:

The x would've been 90 degrees but the 57 degrees got in the way so if you subtract the 57 from 90 you get 33.

The y is if you look on the opposite side of the y there is a blank space that is the same exact size as the y size. So that would've been a 90 degrees as well but the other 90 degrees cut in the middle of it. Making you divide 90 in half.

Answer:

It means his IQ score is better than 91% of the other students scores and scored less than only 9% of the other students.

Step-by-step explanation:

Percentile is not the same as percentage. While percentage is the score gotten out of 100, whereas, percentile means that you are scored better than that percentage of people.

Thus, for his IQ score to be in 91st percentile, it means he scored above 91% of the other students, and only scored lesser than 9% of the students.

Answer: (6x+1)(7x+3)

Step-by-step explanation:

Step-by-step explanation:

a quadratic

use sum factor pattern

42x^2+25x+3

=42x^2+18x+7x+3

common factor

6x(7x+3)+7x+3

rewrite in factored form

(6x+1)(7x+3)

Answer:100,000

Step-by-step explanation:

Answer:

hold yo ablo espanol

Step-by-step explanation:

Answer:

y = 3/5x - 6

Step-by-step explanation:

Slope intercept Form: y = mx + b

m = slope

b = y-intercept

Slope = 3/5

Y-intercept = -6

y = 3/5x - 6

Answer:

y = 3/5 -6

Step-by-step explanation:

You have the y and constant value already

plz give brainliest

Answer:

8

Step-by-step explanation:

8-3=5

8x5=40

Answer:

x3−2x2−5x+10=(x2−5)(x−2)

Step-by-step explanation:

i hope i helped u

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Step-by-step explanation:

No she won't have enough money saved.

This is so because at the end of 30 weeks she would have saved only $450 and short by 115.

Answer:

2.02955

Step-by-step explanation:

Given that:

Susan invests $Z as each year ends for seven years.

So we assume that Z = 1

Susan's accrued value comprises $7 invested each year at a 6 percent annual effective rate.

The cashflow interest:

The cashflow of Susan interest payments are:

Payments   Time

0                     1

0.05               2

2(0.05)           3

3(0.05)           4

4(0.05)            5

5(0.05)            6

6(0.05)            7

The accumulated value of this cash flow is:

\((0.05)I_{6\%} = (0.05) \dfrac{((1+0.06)_{6\%} - 6)}{0.06} \\ \\ \implies 1.1653\)

So Susan accumulated values is:

X = 7 + 1.1653

X = 8.1653

Lori's accumulated value is $14, which she has set aside to plan her cash flow for interest.

The cashflow of Lori interest payments are;

Payments    0     0.025     2(0.025)       3(0.025)    .........   13(0.025)

Time             1        2              3                    4            ..........  14

The accumulated value of cash flow is:

\((0.025 )(I)_{3\%} =(0.025) \dfrac{(1+0.03)_{3\%}-13}{0.03}\\ \\= 2.5719\)

Now, Lori's accumulated value is:

Y = 14 + 2.5719

Y = 16.5719

Since; Susan value X = 8.1653

Lori's value Y = 16.5719

∴

\(\dfrac{Y}{X}= \dfrac{16.5719}{8.1653}\)

= 2.02955

It would cost approximately $241.29 to travel 1935.0 miles with a Honda car that gets 33mpg and holds 13 gallons of gas.

It is important to note that this calculation is based on the assumption

Cost = (distance ÷ mpg) × price per gallonFirst, we need to calculate how many gallons of gas the car would use to travel 1935.0 miles.

We can do this by dividing the distance by the car's mpg:

Gallons used = distance ÷ mpg= 1935.0 ÷ 33= 58.63636364 gallonsSince the car can hold 13 gallons of gas, we would need to refill the tank about 5 times:5 × 13 = 65 gallons

Now, we can calculate the total cost of the gas by multiplying the gallons used by the price per gallon:Cost = gallons used × price per gallon= 58.63636364 × $4.12= $241.29Therefore, it would cost approximately $241.29 to travel 1935.0 miles with a Honda car that gets 33mpg and holds 13 gallons of gas.

It is important to note that this calculation is based on the assumption that the car would consume gas at a constant rate of 33mpg, which may not always be the case due to factors such as driving conditions and habits.

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