The amount in dollars an electrician charges in terms of the number of hours worked is represented by the function y = 22x + 42. From the function, identify all the phrases that hold true for the situation. Options attached!
15 POINTS!

Let the shorter piece be x. The longer piece is 4 times the length of the other, so it is 4x.

4x + x = 160.

5x = 160

x = 32

4x = 128

The length of the shorter piece is x, which is 32.

Answer:

14x cannot be simplified any further.

Answer:

No, 14x can not be further simplified.

Step-by-step explanation:

I hope this helps.

If you reflect the rectangle across either the horizontal or the vertical line going straight through the middle, you will reflect it onto itself (see image).

The equation for the horizontal line is y = -1. The equation for the vertical line is x = -1.

Answer: Small correction from the bottom one its 35, 22

Step-by-step explanation: Edginuity 2021 just got is right.

Answer:

35 and 22

Step-by-step explanation:

Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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Answer: yes, Rachelle is correct.

Step-by-step explanation:

first, if you're moving left, you're subtracting from the x value.

4-4=0

next, if you're moving down then you're subtracting from the y value.

2-2=0

if you subtract more than the given numbers, like said in the problem, you would have coordinates like (-1,-1) or (-3,-4)

therefore, you would be in the third quadrant.

Answer:

400

Step-by-step explanation:

too lazy

Answer:

A.) 9.09

B.) 1.1

Step-by-step explanation:

The velocity in meters per second is equal to the distance in meters divided by time in seconds.

100 meters/ 11 seconds

100 meters is .1 kilometers

.1 kilometers x11 seconds =1.1

The graph with a line y+3=2(x+3) is

A coordinate plane with a line passing through the points (0, 3) and (-2, -1) with a slope of 2.

The answer is the fourth option: the slope of the line y - 4 = 5/2(x - 2), is

To find the graph that matches the equation y+3=2(x+3), we need to rewrite the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

y + 3 = 2(x + 3)

y + 3 = 2x + 6

y = 2x + 6 - 3

y = 2x + 3  slope-intercept form

The equation is now in slope-intercept form, y = 2x + 3,

where

The graph of this equation should be a line that passes through the y-axis at 3 and has a slope of 2. From the attached graph we can see point (-2, -1)

To find the slope of the line whose equation is y - 4 = 5/2(x - 2), we can rewrite the equation in slope-intercept form.

y - 4 = 5/2(x - 2)

y - 4 = 5/2x - 5

y = 5/2x - 5 + 4

y = 5/2x - 1  slope-intercept form

The equation is now in slope-intercept form, y = 5/2x - 1,

where the slope is 5/2.

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The additive inverse is:

(a) 4   (b) 18   (c) -620  (d) -60  (e) 244  (f) 8921

The additive inverse of a number x is the number that, when added to x  yields zero.

It is shown as \(x+(-x)=0\)

To find the additive inverse of a number we just change the sign of the given number which means positive changes to negative and vice versa.

The additive inverse of the given numbers are:

(a) 4

(b) 18

(c) -620

(d)-60

(e) 244

(f) 8921

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Answer:

B. (negative infinity, -1)

the average number of pairs of consecutive integers in a randomly selected subset of 5 distinct integers chosen from the set{1,2,3,...,30} is 2/3

There are 29 possible pairs of consecutive integers namely p1 = { 1,2} ....... ,p29= {29,30}

define a random variable Xi with Xi =1 if pi is a part of the 5 elements subset and 0 otherwise then the number of pairs of consecutive integers in a 5 selection is given by the sum X1+ .........+X29

E[ Xi]= 28C3/ 30C5

        = 2/3

Hence ,  the average number of pairs of consecutive integers in a randomly selected subset of 5 distinct integers chosen from the set{1,2,3,...,30} is 2/3

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To maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129.

If Talisa hits rock at 30 feet, then the depth of the pond will be limited to 30 feet. Therefore, she needs to modify the radius of the pond to maintain the original volume.

To do this, Talisa can use the formula for the volume of a circular cylinder, which is:

V = πr^2h

where V is the volume of the cylinder, r is the radius, and h is the height (or depth) of the cylinder.

Since Talisa wants to maintain the original volume of the pond, she can set the equation for the new cylinder equal to the equation for the original cylinder, and solve for the new radius, r2:

πr1^2h1 = πr2^2h2

where r1 is the original radius (unknown), h1 is the original height (36 ft), r2 is the new radius (unknown), and h2 is the new height (30 ft).

Simplifying this equation, we can cancel out the π and h1 terms:

r1^2 = r2^2(30/36)

Taking the square root of both sides, we get:

r1 = r2(√(30/36))

Thus, to maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129. In other words, she needs to multiply the original radius by 0.9129 to get the new radius.

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The area of triangle A"B"C" is 1/9 of the area of triangle ABC.

In this problem, we are given a triangle ABC and asked to construct a new triangle A'B'C' by taking points on each side of the original triangle such that they divide the sides into thirds. We then repeat this process to create another triangle A"B"C" using points on the sides of A'B'C'. The objective is to show that the sides of triangle A"B"C" are parallel to the corresponding sides of triangle ABC. Additionally, we need to determine the fraction of the area of triangle ABC that is occupied by triangle A"B"C".

Let's start by examining triangle ABC and the construction of triangle A'B'C'. We are given that point A' is located one-third of the way from point B to point C. This means that the distance from B to A' is one-third of the distance from B to C. We can express this mathematically as AB' = (1/3)BC. Similarly, we can determine the other side lengths of triangle A'B'C' as BC' = (1/3)CA and CA' = (1/3)AB.

To demonstrate that the sides of triangle A"B"C" are parallel to the corresponding sides of triangle ABC, we need to show that the ratios of the side lengths are equal. Let's consider one side as an example. We know that AB' = (1/3)BC in triangle A'B'C'. Now, let's examine the corresponding side in triangle A"B"C". Denote the side length in triangle A"B"C" as A"B''. Using a similar logic, we can express A"B'' as (1/3)B"C".

To compare the ratios, we can set up a proportion:

AB' / BC = A"B'' / B"C"

Substituting the values we obtained earlier:

(1/3)BC / BC = (1/3)B"C" / B"C"

Simplifying the equation, we find:

1/3 = 1/3

Since the ratio of the side lengths is the same for all corresponding sides, we can conclude that the sides of triangle A"B"C" are parallel to the sides of triangle ABC.

Now, let's determine the fraction of the area of triangle ABC that is occupied by triangle A"B"C". Since triangle A"B"C" is created by taking one-third of each side length of triangle A'B'C', we can conclude that the ratio of their areas will be the square of the ratio of their side lengths.

The ratio of the side lengths is 1/3, so the ratio of the areas will be (1/3)^2 = 1/9.

Therefore, the area of triangle A"B"C" is 1/9 of the area of triangle ABC.

In summary, we have shown that the sides of triangle A"B"C" are parallel to the sides of triangle ABC, and the area of triangle A"B"C" is 1/9 of the area of triangle ABC.

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Using the concepts of equation it is concluded that Theo was saving money from 6 weeks and he had $6 in savings when he started to save the money.

An equation is a mathematical expression comprised of two expressions linked by an equal sign.

Let Theo have x amount of money in the savings where 0 < x > 8.

He saves $8 per week until he has $52 including his savings.

Let y be the no. of weeks.

So, this given condition can be written as:

8y + x = 52

8y = 52 - x

As we know, y can't be negative or have decimal values, as here weeks can only be in natural numbers (y = 1, 2, 3...…).

From the obtained equation and above statement it is clear that the value of 52 - x must be a multiple of 8.

The closest multiples of 8 for the above condition are 48 or 56.

The value of x to obtain 48 is 4 and value of x to obtain 56 is - 4.

Since 0 < x > 8, we get that:

x = 6

Put the value of x = 6 in the equation 8y = 52 - x to obtain:

8y = 52 - 6

8y = 48

y = 6

Therefore, Theo was saving money from 6 weeks and he had $6 in savings when he started to save the money.

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Answer:

800'000

Step-by-step explanation:

this is near to hundred thousand bro

After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

Answer:

183in^2

Step-by-step explanation:

Given that the length is 15 in and the width is 26 in we can figure out the area of a full rectangle.

15x26=390in

We now want to figure out the small rectangle on the bottom of the image.

The area of a triangle is A=hb/2

A=6x15/2=45

In the image, you can see that the rectangle is incomplete and missing part of it. It's missing a triangle so in order to complete the rectangle you multiply 45x2.

45x2=90

Finally, we can solve for the remaining triangle.

A=9x26/2=117

Add up the triangles and subtract the sum from the area of the rectangle to get the shaded area.

390-(90+117)=183in^2

Hope this helps :)

Thomas packed 1.6 L1.6 L1, point, 6, start text, space, L, and end text of the soup in his kids' lunches and  had firmed 7100 ml of haze.

What's meant by equation?

Given that;

He made 8700 ml haze and he packed1.6 liter haze.

1 liter = 1000 milliliters

liter = 1.6 × 1000

litre = 1600 ml

Chancing the firmed haze-

8700 ml- 1600 ml

7100 ml.

Hence

Frozen haze = 7100 milliliters.

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The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1)

Any quadratic function represented graphically by a parabola

1. If the coefficient of x² is positive, then the parabola open upward

  and its vertex is a minimum point.

2. If the coefficient of x² is negative, then the parabola open

  downward and its vertex is a maximum point

3. The standard form of the quadratic function is: f(x) = ax² + bx + c

   where a, b , c are constants

4. The vertex form of the quadratic function is: f(x) = a(x - h)² + k,

  where h , k are the coordinates of its vertex point

∵ The function f(x) = 3(x - 2)² + 1

∵ The f(x) = a(x - h)² + k in the vertex form

∴ a = 3 , h = 2 , k = 1

∵ h , k are the coordinates of the vertex point

∴ The coordinates of the vertex point are (2 , 1)

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1)

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If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

Answer:

D) x-3

Step-by-step explanation:

\(x^2-13x+30=\\(x-3)(x-10)\)

So the answer choices were:

A )x-5

B) x+3

C) x+5

D) x-3

The correct answer is D) x-3.

The correct binomials which is a factor of this trinomial is,

⇒ x - 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x² - 13x + 30

Now, We can simplify as;

⇒ x² - 13x + 30

⇒ x² - 10x - 3x + 30

⇒ x (x - 10) - 3 (x + 10)

⇒ (x - 3) (x + 10)

Thus, The correct binomials which is a factor of this trinomial is,

⇒ x - 3

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A slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

The slope of a linear relationship represents the rate of change between two variables. In this case, a slope of b = 0.007 suggests a weak positive relationship between the variables. The positive sign indicates that as the independent variable increases, the dependent variable also tends to increase. However, the small value of 0.007 indicates that the increase in the dependent variable is relatively small for each unit increase in the independent variable.

To illustrate, let's consider an example where the independent variable represents time and the dependent variable represents the number of customers in a store. With a slope of 0.007, it means that for every unit increase in time (e.g., one hour), we can expect a small increase of 0.007 customers on average. This indicates a weak positive relationship, as the increase in customers is relatively modest for each unit increase in time.

In summary, a slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

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Answer:

x = - \(\frac{b}{a}\) ( a ≠ 0 )

Step-by-step explanation:

To find the zero, let the polynomial equal zero, that is

ax + b = 0 ( subtract b from both sides )

ax = - b ( divide both sides by a )

x = - \(\frac{b}{a}\)

Given:

Base salary = $1700

Additional salary = $60 for each copy of English Pleasure she sells.

Total wage = P

Number of copies of English is Fun she sells = N

To find:

The equation relating P to N.

Step-by-step explanation:

Let P represent her total wage (in dollars), and N represent the number of copies of English is Fun she sells.

Additional salary = $60N

Base salary = $1700

Total wage = Base salary + Additional salary

\(P=1700+60N\)

Therefore, the required equation is \(P=1700+60N\).

Substitute N=26 to find the gross wage if she sells 26 copies of English is Fun.

\(P=1700+60(26)\)

\(P=1700+1560\)

\(P=3260\)

Therefore, the gross wage if she sells 26 copies of English is Fun is $3260.