A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250. How much would he have to sell in a month if he needed to have a monthly income of $2900?

He would need to sell $
to reach his needed monthly income needs.

The solutions for the given equations are x=2 and x=-4

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Fo question 5.

1/2x-2=9-5x

Take the variable terms on one sides\

x/2+5x=11

x+10x=22

11x=22

Divide both sides by 11

x=22/11

x=2

For question 6:

-5+x/4=3x+6

-20+x=12x+24

-20-24=12x-x

-44=11x

x=-4

Hence, the solutions for the given equations are x=2 and x=-4

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Answer:

x = √52

Step-by-step explanation:

Triangle PLM and JLK are connected together at L, which means that they share the same vertex L and therefore, the angle at L is the same for both triangles.

Since PLM and JLK are both triangles, we know that the sum of the angles in each triangle is always 180 degrees.

Let's call the angle at L as a. So we have:

a + (180-a) = 180

We know that PL = 6 and PM = 12, so we can use the Law of Cosines to find the value of the angle a:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the hypotenuse, a and b are the other two sides and C is the angle opposite to c.

c = PL = 6

a = PM = 12

b = JL = 4

c^2 = 12^2 + 4^2 - 2124cos(a)

36 = 144 - 48cos(a)

cos(a) = (144 - 36)/48 = (108/48) = 9/4

a = arccos(9/4)

Now we know the measure of angle a and we can use it in the equation of the sum of angles in a triangle.

a + (180-a) = 180

We also know that JL = 4 and JK = x and we can use the Law of Cosines again to find the value of x.

x^2 = 4^2 + 6^2 - 246cos(a)

x^2 = 16 + 36 - 24(9/4)

x^2 = 52

x = √52

Answer:

14 inches is to 56 miles

Step-by-step explanation:

First, let's convert the question into an "equation"

1in : 4mi as xin:56mi

Since we need to multiply 4mi by 14 to 56mi, we will multiply 1in by 14 to find the value of x. 1 * 14 = 14. So, x must be equal to 14 and 1 inch is to 4 miles as 14 inches is to 56 miles.

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It is given to us in the question that we have a proportion of 1 inch is to 4 miles.

The proportion we need to solve is, 1 : 4 :: x : 56  as given in the question.

To solve this,

If 1 inch is equal to 4 miles, that means 4 miles is equal to 1/4 inch.

i.e. 1x = 4y; where x is inches and y is miles

1y = 1x/4....................(i)

Similarly, from the above-given proportion, we see that

x = 56y;

Taking the value of y from (i),

x = 56 * (1/4)

= 14

So the proportion becomes,

1 inch : 4 miles :: 14 inch : 56 miles

Hence, it can be determined that 1 inch is to 4 miles as 14 inches is to 56 miles.

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Answer:

Step-by-step explanation:

The solutions to the equation −2x+2=(1/3)^x+1 can be found by finding the values of x that make the two sides of the equation equal. To solve this equation, we need to find the x values where the graphs of f(x) and g(x) intersect.Since the two functions are not linear and have different forms, it's hard to find the exact solutions. One way to find the solution is to graph the functions and find the x values where the two graphs intersect.It's not possible to find the exact values of x that make the two sides of the equation equal, because the two functions don't intersect at any specific point. It's not possible to find an exact solution to this equation, so none of the options are correct.

The height of the radio tower observed by the person is approximately 554.75 feet.

The tangent function is a mathematical function that maps an angle to its corresponding tangent value. It is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.

We can use trigonometry to solve this problem. The angle of elevation from the window to the top of the tower is 38°, and the angle of depression from the window to the bottom of the tower is 29°. We can use these angles to form two similar right triangles, one with the tower and the window and one with the height of the tower and the difference between the height of the window and the height of the tower.

Let H be the height of the tower. Then the difference between the height of the window and the height of the tower is H - 300.

Using the tangent function, we can write:

tan(38°) = H / 300

and

tan(29°) = (H - 300) / 300

Solving for H, we find:

H = 300 * tan (38°) = 554.75 feet

So, the height of the tower is approximately 554.75 feet.

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Answer:

To determine the amount of the investment after 7 years, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (the amount after 7 years)

P = the initial principal or investment amount ($2750)

r = the annual interest rate (3.5%)

n = the number of times the interest is compounded per year (quarterly)

t = the number of years the investment is held (7)

First, we convert the annual interest rate to a decimal: 3.5% = 0.035

Then we convert the interest rate to a quarterly rate by dividing by the number of times it is compounded per year: 0.035 / 4 = 0.00875

We can now substitute these values into the formula:

A = $2750(1 + 0.00875)^(4*7)

A = $2750(1.00875)^28

A = $2750(1.3471)

A = $3710.82

So, the amount of the investment after 7 years is $3710.82, rounded to the nearest hundredth.

Therefore , the solution of the given problem of scatter plot comes out to be Line 3 to the right of the graph is best fit line.

Line of best fit refers to a line through a scatter plot of data points that best expression the relationship between those points.The graphs that show the association between two variables in a data set are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.

Here,

In the xy plane, a scatter plot is displayed. The x-axis has values from 0 to 9 with 1 increments, while the y-axis has values from 0 to 9 with 1 increments.

On the x-axis, data points range from 0 to 3; on the y-axis, they range from 0 to 8.5. There are three lines marked Line 1, Line 2, and Line 3. Line 1 connects the points in a way that places the majority of the points on the left of the line,

Line 2 connects the points in a way that places the majority of the points on both sides of the line, and Line 3 connects the points in a way that places the majority of the points on the right of the line.

Line 3 to the right of the graph is best fit line

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The correct brackets for the equations are added as follows:

a) (42 - 8) x 3 - 22 = 80

b) 75+ (5 x 4) -70 = 25

c) (160 ÷ 4) x (3 + 2) = 200

d) 120 ÷ (2 x 3) + 5 = 25.

Equations are mathematical statements that equate or show that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to show the equality of the algebraic expressions.

Using parentheses in equations enable the use of the distributive property to solve the equation.

Thus, the correct parentheses have been added to the equations to prove them correct when solved.

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Answer:

The bus journey takes 25 minutes (5 minutes per stop x 5 stops). The bus leaves the Railway Station every 10 minutes (the wait time between circuits).

The first departure is at 09:15, so the bus will arrive back at the Railway Station at:

09:15 + 25 minutes = 09:40

Bart will drive the bus for 4 circuits, so the bus will arrive back at the Railway Station for the final time at:

09:40 + (4 x 25 minutes + 4 x 10 minutes) = 09:40 + 130 minutes =

11:50.

So the final arrival time will be D 11:55.

Answer:

Step-by-step explanation:

Each circuit takes 25 minutes (5 destinations times 5 minutes) plus the 10 minute wait at the Railway Station.  So the entire circuit is 35 minutes with the wait.  Bart drives 4 circuits - 4 times 35 minutes is 140 minutes.

140 minutes equals 2 hours and 20 minutes.

Add 2 hrs and 20 minutes to 9:15 and the sum = 11:35

The answer is B -  11:35

it would take 12 weeks to save and buy the iphone.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Johny is saving money to buy an Iphone X which cost $1000.

He started saving money $300 he receieved for a birthday gift.

He saved allowance of $60 per week.

We need to find how long will it take for him to save and the Iphone X.

1000=300+60x

Subtract 300 from both sides

700=60x

Divide both sides by 60

700/60=x

11.66=x

Hence, it would take 12 weeks to save and buy the iphone.

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Answer:

Step-by-step explanation:

set up the composite function and simplify: first one is -3, second is -2

The mass per cup for the objects will be 320g and 272g respectively.

What is mass?

Mass simply means the weight that an object contains.

The mass of a teapot and 4 cups is 1,280 grams. The mass per cup will be:

= Mass / Number of cups

= 1280 / 4

= 320g

The mass of the same teapot and 10 cups is 2,720 grams. The mass per cup will be: = 2720 / 10 = 272g

Hence, the mass per cup for the objects will be 320g and 272g respectively.

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Complete questions:

The mass of a teapot and 4 cups is 1,280 grams. The mass of the same teapot and 10 cups is 2,720 grams. Each cup has the same mass. What is the mass?

The fraction is 0.001545/5 =0.00309/1 .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

2 in² and 5 yd²

now,

1 inch =0.0278yard

so, we get,

2in^2=0.001545 yd^2

i.e. 0.001545/5

=0.00309/1

hence, The fraction is 0.001545/5 =0.00309/1 .

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The simplified expression as a product of polynomials is given as follows:

(c - d)(p + 1).

The expression for this problem is defined as follows:

p(c - d) + c - d.

The expression can be defined as an addition in which the terms are given as follows:

The common factor to both of the terms of the addition is given as follows:

(c - d).

The quotients of each term relative to the common factor are given as follows:

Hence the simplified expression is given as follows:

(c - d)(p + 1).

(the plus sign for p + 1 is because the expression is an addition and not a subtraction).

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The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

Step-by-step explanation:

Solving by factoring is a strategy used to solve quadratic in form polynomials, which are equations that can be written in the form of ax^2 + bx + c = 0. The goal of this strategy is to factor the equation into two binomials that are equal to zero. Once the equation is factored, we can use the zero product property to set each binomial equal to zero and solve for the roots or solutions of the equation.

The process of factoring begins by finding the greatest common factor of all the terms in the equation. Once the GCF is identified, it can be factored out of the equation. Next, we look for two binomials that multiply to give the remaining terms in the equation and add to give the remaining constant term.

For example, consider the equation: 3x^2 + 6x - 9 = 0.

To factor this equation, we first find the GCF of all the terms, which is 3. We can factor out 3 from all the terms, giving us: 3(x^2 + 2x - 3) = 0.

Now, we look for two binomials that multiply to give x^2 + 2x - 3 and add to give -2. We can see that (x-3)(x+1) satisfies this condition.

By factoring the equation, we have now factored the polynomial into (x-3)(x+1) = 0. We can use the zero product property to set each binomial equal to zero and solve for the roots: x-3 = 0 and x+1 = 0. The solutions are x=3 and x=-1.

By using the factoring strategy, we were able to solve the quadratic in form polynomial 3x^2 + 6x - 9 = 0 and find the roots x=3 and x=-1. This strategy can be applied to any quadratic in form polynomial and is a useful tool in solving equations.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{b + b + b + b + b}\\\mathsf{= 1b + 1b + 1b + 1b + 1b}\\\mathsf{= 2b + 2b + 1b}\\\mathsf{= 4b + 1b}\\\mathsf{= 5b}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{5b}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

b+b+b+b+b is 5b

The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).

A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.

To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.

Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC :

Let the equation be Distance [tex]$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex] substitute the values in the above equation, we get

[tex]$\mathrm{AC}=\sqrt{\left((2-(-2))^2+(4-1)^2\right)}$$[/tex]

simplifying the equation, we get

[tex]$A C=\sqrt{ }(4+9)=\sqrt{ }(13)$$[/tex]

We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).

Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))

Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.

The complete question is:

Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.

The coordinates are and D.

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Answer:

A, B and E

Step-by-step explanation:

Answer:

64 mph

Step-by-step explanation:

46 x 5 = 230

710 - 230 = 480 is the distance that he has left

distance = rate x times

480 = rate x 7.5       (12.5 -5 = 7.5)

480 = r(7.5)  Divide both sides b y 7.5 to find the rate

480/7.5 = [ r(7.5) ]/7.5

64 = r

The conversion from cents to Dollar we get :

4 cent  = 4/100 = $ 0.04

70 cents = 70/100 = $ 0.7

58 cents = 58/100 = $.58

204 cents = 204/100 = $ 2.04 = $2 and 4 cents

.75 cents = .75 / 100 = $ 0.0075

3009 cents = 3009/100 = $ 30.09 = $30 and 9 cents

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.

Cents are equivalent to one dollar. Dollars are represented by paper banknotes, which come in denominations of $100, $50, $20, $10, $5, and $1. Coins include cents.

The act of converting one value into another, such as from inches to millimeters or from liters to gallons, is known as conversion. The following measurements: length, weight, capacity, temperature, and speed are all measured in units.

The values in cents

4 cent  = 4/100 = $ 0.04

70 cents = 70/100 = $ 0.7

58 cents = 58/100 = $.58

204 cents = 204/100 = $ 2.04 = $2 and 4 cents

.75 cents = .75 / 100 = $ 0.0075

3009 cents = 3009/100 = $ 30.09 = $30 and 9 cents.

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From the coordinates we can see the rule for this transformation:

This is a rotation by 180 degrees and translation 5 units down, therefore shape or size remain as is. So this is a congruence transformation.

Answer:

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

Congruence transformation.

Step-by-step explanation:

Given vertices of ΔPQR:

Given vertices of ΔSTU:

From observation, the mapping rule the transforms ΔPQR to ΔSTU is:

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

This is a congruence transformation as the two triangles have the same shape and same size.

The slope of the line is C) [tex]\frac{6}{5}[/tex].

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line. Any two distinct places along the line can be used to determine the slope of any line.

Here the given point is [tex](x_1,y_1)=(-5,-1)[/tex] and [tex](x_2,y_2)=(5,11)[/tex]

Now using slope formula then,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{11-(-1)}{5-(-5)}[/tex]

=> slope m = [tex]\frac{11+1}{5+5}[/tex]

=> slope m = [tex]\frac{12}{10}[/tex]

=> slope m = [tex]\frac{6}{5}[/tex]

Hence the slope of the line is C) [tex]\frac{6}{5}[/tex].

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well, the subtotal cost will be 48.30 + 17.75 = 66.05, now let's add the tax to that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 66.05}}{\left( \cfrac{6}{100} \right)66.05} ~~ \approx ~~ 3.96~\hfill \underset{total~cost}{\stackrel{66.05~~ + ~~3.96}{\approx \text{\LARGE 70.01}}}[/tex]

The total cost of the purchase is $70.013.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Set of baseball cleats = $48.30

Baseball gloves = $17.75.

Sales tax = 6%.

This means,

6% of (48.30 + 17.75)

= 6/100 x 66.05

= $3.963

Now,

Total cost.

= 48.30 + 17.75 + 3.963

= $70.013

Thus,

The total cost is $70.013.

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The arithmetic sequence's fifth term is therefore 84.

An arithmetic sequence's nth term is determined by a = a + (n - 1)d. So, enter the values a = 2 and d = 3 into the formula to determine the nth term.

The formula to determine the nth term of an arithmetic series is a = a1 + (n - 1)d if a1 is the first term and d is the common difference.

In the mathematical sequence, 84 is the fifth term.

The process for calculating value

An arithmetic sequence's nth term can be calculated using the following formula:

Tn = a + (n -1)d

Where;

First term is a.

N words are present.

d is the typical difference

We must substitute nas 5's value in order to find the fifth term.

T5 = 4 + (5-1) 20

T5 = 4 + 4(20) (20)

the bracket be expanded

T5 = 4 + 80

T5 = 84

The arithmetic sequence's fifth term is therefore 84.

The complete question is,

4 is the initial term and 20 is the constant difference in an arithmetic series. Discover the sequence's sixth phrase.

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Answer: Timespan is 410 minute(s).

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

rise over run

Answer:

Step-by-step explanation:

The general formula for finding the antiderivative of a polynomial function is to add one to the exponent of each term and divide by that new exponent.

To find the antiderivative of y = 5x -6x² +9x³, we need to integrate each term individually, using the general formula:

∫ (5x) dx = (5/1)x^(1+1) = 5x^2 + C

∫ (-6x²) dx = (-6/2)x^(2+1) = -3x^3 + C

∫ (9x³) dx = (9/4)x^(3+1) = (9/4)x^4 + C

So the antiderivative of y = 5x -6x² +9x³ is:

∫ y dx = 5x^2 - 3x^3 + (9/4)x^4 + C

Where C is the constant of integration, which can take any real value.

A counterexample to show that the statement is false is -1<x<0 or >1

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

EXPLANATION;

Rearrange unknown terms to the left side of the equation: x^3-x>0

Factor the expression:x(x+1)(x-1)>0

Convert inequality to equation:x(x+1)(x-1)=0

Apply Zero Product Property: x=0 or x+1=0 or x-1=0

Rearrange unknown terms to the left side of the equation:x=-1

Rearrange unknown terms to the left side of the equation:x=1

Combine the results: :x=0 or :x=1  or- :x=1

Order x-intercepts from smallest to greatest: x1=-1or x2=0  or x3=1

EXPLANATION;

Rearrange unknown terms to the left side of the equation:

Factor the expression:

Convert inequality to equation:

Apply Zero Product Property: or  or

Rearrange unknown terms to the left side of the equation:

Rearrange unknown terms to the left side of the equation:

Combine the results: or  or

Order x-intercepts from smallest to greatest: or  or

Plot: As shown in figure

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Answer:

It may

Step-by-step explanation:

Vertically shift the graph of f(x) up 7 units.

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