Question 22
The sum of two numbers is 107. The difference of the two numbers is 53. What are the two
numbers.
Let z be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 107."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 53."
Solve the system you have written above.
The larger number, a is
> Next Question
The smaller number, y is

Answer: Depends On the Numbers

Step-by-step explanation: State The Numbers

The limit exists and is equal to 6.

The limit exists and is equal to 4.

Now, let's use this concept to evaluate the limits of the given function F(x). Looking at the graph of F(x), we see that it approaches different values as x approaches different points. We will evaluate each limit separately:

lim F(x) as x → 1

As x approaches 1 from the left side, the function appears to be approaching a value of 2. Similarly, as x approaches 1 from the right side, the function appears to be approaching a value of 4. However, the limit does not exist as the function is not approaching a single value as x approaches 1.

lim F(x) as x → 3

As x approaches 3, the function appears to be approaching a value of 4.

lim F(x) as x → ∞

As x approaches infinity, the function appears to be approaching a value of 6.

To know more about limit here

https://brainly.com/question/12211820

#SPJ1

As per the Pythagorean theorem, the length of the missing side, c, is approximately 8.06 units.

Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Now, let's use the Pythagorean Theorem to find the length of the missing side in your problem. You have a right-angled triangle with side a = 4 and side b = 7. To find the length of the missing side, let's call it c, we need to use the Pythagorean Theorem, which is:

c² = a² + b²

In this case, we know the values of a and b, so we can substitute them into the equation:

c² = 4² + 7²

Simplifying the right-hand side, we get:

c² = 16 + 49

c² = 65

To solve for c, we need to take the square root of both sides of the equation:

c = √65

c ≈ 8.06

To know more about Pythagorean Theorem here

https://brainly.com/question/343682

#SPJ1

The height and width of the prism are x and 3x - 2

From the question, we have the following parameters that can be used in our computation:

V(x) = 3x^3 + x^2 - 2x + 3

Length = x + 1

This means that

Side area = Volume/Length

So, we have

Side area = (3x^3 + x^2 - 2x + 3)/(x + 1)

When evaluated, we have

Side area = 3x^2 - 2x + 3/(x + 1)

Ignoring the remainder, we have

Side area = 3x^2 - 2x

Factorize

Side area = x(3x - 2)

This means that

height = x and width = 3x - 2

Read more about polynomial at

https://brainly.com/question/7693326

#SPJ1

Emma has $5,000 total invested.

Let's call the total amount Emma has invested "x".

Emma has half of her investments in stock paying a 10% dividend, so that portion of her investment earns 0.10(x/2) = 0.05x in annual interest.

The other half of her investments are in a stock paying 14% interest, so that portion of her investment earns 0.14(x/2) = 0.07x in annual interest.

The total annual interest Emma earns is $600, so we can set up the following equation:

0.05x + 0.07x = 600

0.12x = 600

x = 5000

Therefore, Emma has a total of $5000 invested.

Learn more about compound interest here:

https://brainly.com/question/29335425

#SPJ1

Answer:

Step-by-step explanation:

7 + 4 = 11 kites

So you add the kites together because they ask you how much Khalid and Annie got together.

Answer:

  B.  28%

Step-by-step explanation:

You want to know the percent of the mixture that is fruit juice, if the mixture is 6 L of 52% juice and 9 L of 12% juice.

The total amount of juice in the 6+9 = 15 L of mix is ...

  0.52·(6 L) +0.12(9 L) = 3.12 L +1.08 L = 4.2 L

Then the fraction of the mix that is fruit juice is ...

  (4.2 L)/(15 L) = 0.28 = 28%

The percent of the mixture that is fruit juice is 28%, choice B.

__

Additional comment

Effectively, the fraction is the weighted average of the fractions of the constituents. The weights are the number of liters of each constituent.

<95141404393>

The percentage of saline solution in brand B is 3%. Then the correct option is C.

Let x be the percent of saline solution in brand B.

Since Danielle combined brands A and B to create a total of 18 gallons of 8% saline solution, we know that the total volume of saline solution in the combination is 18% of 6 gallons + x% of (18 - 6) gallons.

Thus, we can set up the equation:

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ1

Answer:

third answer option

Step-by-step explanation:

[tex] \sqrt[3]{ {x}^{2} } = {x}^{ \frac{2}{3} } [/tex]

[tex] \sqrt[3]{x} = {x}^{ \frac{1}{3} } [/tex]

[tex] \frac{1}{ {x}^{ \frac{1}{3} } } = {x}^{ - \frac{1}{3} } [/tex]

[tex] \frac{ {x}^{ \frac{2}{3} } }{6 {x}^{ \frac{1}{3} } } = \frac{1}{6} \times {x}^{ \frac{1}{3} } [/tex]

[tex] \frac{13}{6 {x}^{ \frac{1}{3} } } = \frac{13}{6} \times {x}^{ - \frac{1}{3} } [/tex]

so, the result is

[tex] \frac{1}{6} \times {x}^{ \frac{1}{3} } + \frac{13}{6} \times {x}^{ - \frac{1}{3} } [/tex]

The total of miles mark ran last week is 10.75 miles.

We have the dot plot.

So, the total number of miles Mark ran

= 1 1/4 x 1 + 2 x 2 + 2 2/4 x 1 + 3 x 1

= 5/4 x 1 + 4 + 10/4 x 1 + 3

= 5/4 + 4 + 10/4 + 3

= 15/4 + 7

= 15/4 + 28/4

= 43/4

= 10 3/4

= 10.75

Thus, the total number of miles Mark ran is 10.75 miles.

Learn more about Dot plot here:

https://brainly.com/question/22746300

#SPJ1

Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.

To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):

2y = 3x + 5

y = (3/2)x + 5/2

Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes (coefficients of x) of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

Line 1 and Line 3:

To determine whether these two lines are parallel or perpendicular, we can convert Line 3 into slope-intercept form (y = mx + b):

6x - 4y = 4

-4y = -6x + 4

y = (3/2)x - 1

Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

Line 2 and Line 3:

To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):

2y = 3x + 5

y = (3/2)x + 5/2

Next, we can rearrange Line 3 into the slope-intercept form:

6x - 4y = 4

-4y = -6x + 4

y = (3/2)x - 1

Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.

To know more about the equation of the lines follow

https://brainly.com/question/18831322

#SPJ1

The best interpretation of v(9) = 277 is a cube with side lengths of 9 feet has a volume of 277 cubic feet

From the question, we have the following parameters that can be used in our computation:

The volume of a cube depends on the length of its sides.

And this is represented  in function notation as v(s)

The function notation v(s) means

The volume of cube with side length s is v

Using the above as a guide, we have the following:

A cube with side lengths of 9 feet has a volume of 277 cubic feet

Read more about functions at

https://brainly.com/question/28532394

#SPJ1

Answer:

19.1

I found it out after I got the ansewer wrong on IXL

It is false that the vector u is formed according to the given linear combination.

If the statement regarding the linear combination is true, we have that the following equality is true:

u = 2v1 - 2v2 - v3.

The vectors are given as follows:

Hence we verify the equation as follows:

(6,8) = 2(1,2) - 2(3, 4) - (-1, 0)

(6,8) = (2, 4) - (6, 8) + (1,0)

(6,8) = (2 - 6 + 1, 4 - 8 + 0)

(6, 8) = (-3, -4).

The statement is false, as the sides of the equality are different.

More can be learned about linear combination at brainly.com/question/24219860

#SPJ1

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

Here, we have,

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

To know more about solution visit :-

brainly.com/question/16989201

#SPJ1

The value of DF would be,

DF = 1.38

We are given that triangle ABC is similar to triangle DEF.

Therefore, we can set up the following proportion:

AB/DE = BC/EF = AC/DF

We are given the lengths of AB, AC, and BC, so we can substitute those values into the proportion:

11/2 = 7.9/EF = 7.6/DF

We are asked to find the length of DF, so we can isolate DF by cross-multiplying:

11/2 = 7.6/DF

DF = 7.6 x 2 / 11

DF = 1.38

Thus, The value of DF would be,

DF = 1.38

To know more about triangles visit :-

brainly.com/question/17335144

#SPJ1

The composite function f(f(x)) has a solution of - (1 - x)/x

From the question, we have the following parameters that can be used in our computation:

f(x) = 1/1 - x

To calculate f(f(x)), we replace the occurence of x in the function f(x) = 1/1 - x with f(x)

Using the above as a guide, we have the following:

f(f(x)) = 1/1 - f(x)

Substitute the known values in the above equation, so, we have the following representation

f(f(x)) = 1/(1 - 1/(1 - x))

Evaluate

f(f(x)) = - (1 - x)/x

Hence, the solution is f(f(x)) = - (1 - x)/x

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

Answer:

Faster cyclist = 37.5km/h

Slower cyclist = 32.5km/h

Step-by-step explanation:

Let's call the rate of the slower cyclist "r" (in km/h). Then the rate of the faster cyclist is "r+5" (in km/h), since they are traveling 5 km/h faster.

We know that the two cyclists are traveling towards each other and will meet in 2 hours. We can use the formula:

distance = rate × time

Let's call the distance each cyclist travels "d". Since they are traveling towards each other, their distances will add up to the total distance between the two towns, which is 130 km. So we can write:

d + d = 130

2d = 130

d = 65

Now we can use the formula again to find the rates of the two cyclists:

For the slower cyclist:

distance = rate × time

65 = r × 2

r = 32.5 km/h

For the faster cyclist:

distance = rate × time

65 = (r+5) × 2

r+5 = 32.5 + 5 = 37.5 km/h

So the rate of the slower cyclist is 32.5 km/h, and the rate of the faster cyclist is 37.5 km/h.

Answer:

If I am not mistaken, the answer is:

x1: 4.436

x2: 0.564

Step-by-step explanation:

Answer is

5 + √15    or 4.43649 decimal

  2

and

5 - √15  or .56350 decimal

  2

Step by step

Given 2x^2 -10x +5 = 0

Quadratic formula

-b +- √ b^2 - 4 a c

2a

- -10 +- √ -10^2 (-4)(2)(5)

2(2)

Simplify

10 +- √ 100 - 40

2(2)

10+- √ 60

2(2)

Factor out √60 = 2^2 * 3 * 5

Rewrite after moving 2 outside √

10 +- 2 √15

2(2)

Divide out one of the “2’s” with terms outside the √

5 +- √15

2

Solve

5 + √15

2

5 - √15

2

The quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

The quadratic equation is the polynomial having the highest power of 2. If 5i and -5i are the solutions to the quadratic equation, then the quadratic equation can be written as:

(x - 5i)(x + 5i) = 0

Expanding this equation, we get:

x² - (5i)² = 0

x² - 25i² = 0

Since i² = -1, we can substitute -1 for i², giving us:

x² - 25(-1) = 0

x² + 25 = 0

Therefore, the quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

To know more about quadratic equations follow

https://brainly.com/question/11704385

#SPJ1

The area of the shaded region is equal to 12.5π or 39.27 square centimeters.

In Mathematics and Geometry, the area of a semicircle can be calculated by using this formula:

Area of semicircle, As = πr²/2

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 20/2 = 10 centimeters.

By substituting the radius into the formula for the area of a semicircle, we have the following;

Area of semicircle = 1/2 × π × 10²

Area of semicircle = 50π square centimeters.

For the circle, we have:

Area of circle, Ac = πr²

Area of circle, Ac = π(10/2)²

Area of circle, Ac = 25π square centimeters.

Now, we can determine the area of the shaded region as follows;

Area of shaded region = (As - Ac)/2

Area of shaded region = (50π - 25π)/2

Area of shaded region = 12.5π or 39.27 square centimeters.

Read more on area of semicircle and circle here: https://brainly.com/question/28697311

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A

Step-by-step explanation:

Goes down to the integer 1. B is the only one that makes sense subtracting doesn't work 87654321 goes from the 2 half line.

1.  A limit imposed by the government on the quantity of a good or product that can be brought into the country is called a quota. The Option B.

2. An option that is not be an effective argument for the U.S. to enact trade restrictions is hey make foreign products cheaper to U.S. shoppers. The Option D is correct.

3. If a country is on the gold standard, this means that it sets the value of its currency in relation to a specific amount of gold. The Option A is correct.

4. An economists tend to classify a country as less developed if the country's average level of Income is less than $3.040 per person. The Option C is correct.

5. The option that would not be considered a barrier to economic development is low population growth. The Option B is correct.

Read more about trade

brainly.com/question/17727564

#SPJ1

Answer: 6(a) - 6(3)

Step-by-step explanation:

Answer: Its B

Step-by-step explanation:

The expression 6(a-3) can be simplified by applying the distributive property of multiplication over addition, which gives 6a - 18. Therefore, the expression is equivalent to 6a - 18. The answer is (b) –2. All other options do not simplify to the same expression as 6(a-3). For example, 18a is not equivalent to 6(a-3) and neither is 6(a)-6(3). Option (d) 1 simplifies to 6a - 18a + 18, which is not equivalent to the original expression. Similarly, 6(a)-3 simplifies to 6a - 3, which is also not equivalent.

Answer:

0.90

Step-by-step explanation:

Just like a decimal to a percentage number, you must multiply by 100. By converting a percentage number to a decimal point, you must divide it by 100. Which means, the decimal must move 2 times.

For example,

0.90 x 100 = 90%

This is decimal to percentage number, but in this case it is percentage to decimal.

90%.

Since the number ended at 0, put the decimal there and move it 2 times to get to your decimal point.

.90 = 0.90

There you'll get your answer! ^^

90% = 0.90

Answer:

Simplifying the expression `n + n - 0.18n`, we get:

n + n - 0.18n = 2n - 0.18n

Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.

Looking at the answer choices:

a. 1.18n

b. 1.82n

c. n- 0.18

d. 2n - 0.82

We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.

Therefore, the answer is d. 2n - 0.82.

Step-by-step explanation:

The value c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.

To find the value of c for which P(z < c) = 0.0234 for a standard normal distribution, we can use a standard normal distribution table or a calculator with a built-in normal distribution function.

Using a standard normal distribution table, we can look up the area to the left of c and find the corresponding z-score. This z-score will be the value of c for which P(z < c) = 0.0234.

Looking up the area 0.0234 in the table, we find that the corresponding z-score is approximately -2.07.

Therefore, c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.

To know more about standard normal distribution follow

https://brainly.com/question/4079902

#SPJ1

Answer: $6,320.25

Step-by-step explanation:

Mrs. Cowley's broker fee is calculated by multiplying the purchase price by the broker fee percentage: $32,000 x 0.0075 = $240. Her total cost for the purchase is then $32,000 + $240 = $32,240. When she sells the stock for $25,100, she incurs another fee of $17 for using the discount broker. To calculate her net loss, we subtract her total cost from her selling price and subtract the two broker fees: $25,100 - $32,240 - $17 - $17 = -$6,320.25, which is rounded to $6,320.25 as a net loss.