A machine salesperson earns a base salary of $40,000 plus a commission of $300 for every
machine he sells. Write an equation that shows the total amount of income the salesperson
earns, if he sells x machines in a year.

Answer:

[tex]slope \: or \: gradient = y2 - y1 \div x2 - x1 \\ 3 - 2 \div 4 - 1 \\ 1 \div 3 \\ y = mx + c \\ 2 = 1 \div 3 \times 1 + c \\ 2 = 1 \div 3 + c \\ 2 - 1 \div 3 = c \\ c = 5 \div 3 \\ y = 1 \div 3x + 5 \div 3[/tex]

Answer:

j=10-3k

Step-by-step explanation:

here you go...i hope it's correct

If the equation is (3j+k)/2=15-4k then j=10-3k

Two or more expressions with an Equal sign is called as Equation.

The given equation is (3j+k)/2=15-4k

We need to prove j=10-3k

(3j+k)/2=15-4k

Apply cross multiplication and solve for k

3j+k=2(15-4k)

3j+k=30-8k

Subtract k from both sides

3j=30-9k

Divide both sides by 3

j=10-3k

Hence, if the equation is (3j+k)/2=15-4k then j=10-3k

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[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

In triangle ABC

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B = 125 \degree \: - - - (1) }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle B + \angle C = 150 \degree \: - - - (2)}[/tex]

We know,

Sum of all interior angles of a triangle is supplementary.

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B + \angle C = 180\degree }[/tex]

On adding equation (1) and (2), we get

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B + \angle B + \angle C = 125\degree + 150 \degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:\angle A + \angle B + \angle C + \angle B = 275\degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:180\degree + \angle B = 275\degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:\angle B = 275\degree - 180\degree \:}[/tex]

[tex] \purple{\rm :\longmapsto\:\angle B = 95\degree \:}[/tex]

On substituting the value in equation (1) and (2), we get

[tex] \purple{\rm :\longmapsto\:\angle A + 95\degree = 125\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle A = 125\degree - 95\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle A = 30\degree }[/tex]

Also, from equation (2), we get

[tex] \purple{\rm :\longmapsto\:95\degree + \angle C = 150\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle C = 150\degree - 95\degree }[/tex]

[tex] \purple{\rm :\longmapsto\:\angle C = 55\degree }[/tex]

Hence,

[tex]\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{\angle A = 30\degree } \\ \\ &\sf{\angle B = 95\degree } \\ \\ &\sf{\angle C = 55\degree } \end{cases}\end{gathered}\end{gathered}[/tex]

Answer:

angle A=30°

angle B=95°

angle C=55°

Answer:

207 cm

Step-by-step explanation:

Because ΔPQR ≅ΔSTU and the longest side in the ΔPQR is RP then the longest side in ΔSTU must be SU = 92 cm

Perimeter of triangle PQR is

P(ΔPQR) = 36+48+24 = 108 cm

Because the triangles are are similar their sides are in proportion.

But how much bigger did the second triangle get?...is (92/48) times bigger

P(ΔSTU) = 180*(92/48) = 207 cm

...you can also use proportions to find each side and then find the perimeter

TU = 24*92 /48 = 46

TS = 36*92/48 = 69

SU = 92

P(ΔSTU) = 92+69+46 =207 cm

*the triangles are not drawn to scale

The equation with only one unique solution is 9 − |2x − 1| = 9, with the solution x = 1/2. D.

To determine which equation has only one unique solution, let's analyze each equation:

|3 − x| = 3

In this equation, the absolute value term represents a distance.

By setting up two cases, where the absolute value is positive and negative, we can find the solutions.

Case 1:

3 - x = 3

Solving for x, we have x = 0.

Case 2:

x - 3 = 3

Solving for x, we have x = 6.

Thus, this equation has two solutions.

|x − 2| − 7 = 7

Similar to equation A, the absolute value term represents a distance.

By adding 7 to both sides, we have |x - 2| = 14.

This equation implies that the distance between x and 2 is 14.

There are two possible values for x: x = 2 + 14 = 16 and x = 2 - 14 = -12.

This equation has two solutions.

-4|x| + 1 = -3

To solve this equation, we isolate the absolute value term:

-4|x| = -4

Dividing both sides by -4:

|x| = 1

The absolute value of any number is always positive or zero.

The equation |x| = 1 has two solutions: x = 1 and x = -1.

9 − |2x − 1| = 9

The absolute value term represents a distance.

Subtracting 9 from both sides, we have |2x - 1| = 0.

The only way the absolute value of a real number can be equal to zero is if the number inside the absolute value is zero.

Thus, we set 2x - 1 = 0 and solve for x:

2x - 1 = 0

2x = 1

x = 1/2

Equation D has only one unique solution: x = 1/2.

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Answer:

26.6

Step-by-step explanation:

simplify -26.6 divided by -1 to 26.6

Answer:

26.6

Step-by-step explanation:

- 26.6 / - 1

- 26.6 = - 1 x 26.6

- 1 = - 1 x 1

- 26.6 / - 1

= ( - 1 x 26.6 ) / ( - 1 x 1 )

= ( - 1 / - 1 ) x ( 26.6 / 1 )

= 1 x 26.6

= 26.6

Answer:

p < 14/3

Step-by-step explanation:

Answer:

a.divide both sides with 3

Step-by-step explanation:

I hope you find this useful, Mark as Brainliest please, it's very much appreciated.

Explanation:

In one minute, Diego can type 35 words;140÷4

At this rate, it will take him 11 minutes to type 385 words;385÷35

Therefore, he can type 525 words in 15 minutes; 35×15

Answer:

Hope this helps.

Step-by-step explanation:

1. 385 x 4 = 1540/140

    =11

2. 15/4 = 3.74 x 140

    =525

Answer:

42.3

Step-by-step explanation:

add both angles then subtract by 180 and the negative number is your answer

Answer:

1) answer is 2x^2 - x + 6

2) answer is 2x^2 + 2x + 2

Step-by-step explanation:

i dont know if this is what you wanted, but i tried to follow the directions as best i could

Answer:

2x2 - 2x + 6 - (-3x)  = 2x2(tiny) + x + 6

or

-(3 - 2x2) + 5 +2x = 2x2(tiny) + 2x +2

Step-by-step explanation:

I don't remember exactly how you find the smallest, sorry...

Answer:  1 1/14

Step-by-step explanation: sorry if im wrong

Answer:

13 and 6

Step-by-step explanation:

Step-by-step explanation:

there u have it, since y is 0, we make a straight line that passes through 2 and shade the numbers that are <2

Answer:

-12 gal / min

Step-by-step explanation:

[tex] \frac{ - 60 \: gallon}{5 \: minutes} = - \frac{60}{5} = - 12[/tex]

Answer:

32

Step-by-step explanation:

The interior angles of a triangle add up to 180.

Subtract 98 and 50 from 180.

180-(98+50)=32

Step-by-step explanation:

you add all the values and equate them to 180

Answer:A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements. Curly braces are used to indicate that the objects written between them belong to a set

Answer: A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.

Curly braces are used to indicate that the objects written between them belong to a set.

A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements.

here, we have,

N={1,2,3,4,.......}

Determine the sets of natural number

Represent this set with letter N

From definition of natural numbers, they are integer numbers starting from 1;

In other words: 1,2,3,4,5, and so on.

To represent this as a set of N, we have

N={1,2,3,4,.......}

The ..... means that the counting still continues.

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Step-by-step explanation:

8

a. total cost ($)

→ 25 = 25×2.5 = $62.5

→ 50 = 50 × 2.5 = $125

→ 75 = 75 × 2.5 = $187.5

b. 2.5n

c. $400/2.5 = 160

therefore, she can make 160 crafts by $400.

9. 7x + 12 = 18

→ 7x = 18 - 12 = 6

→ x = 6/7

therefore value of x is 6/7.

hope this answer helps you dear...take care

Answer:

see explanation

Step-by-step explanation:

The vertex is the coordinates of the turning point of the parabola

The axis of symmetry is a vertical line passing through the vertex with equation

x = c ( where c is the x- coordinate of the vertex )

vertex = (0, 0 ) , axis of symmetry is x = 0 ( the y- axis )

(1)

vertex = (- 2, 4 ) , axis of symmetry is x = - 2

(2)

vertex = (7, 1 ) , axis of symmetry is x = 7

(4)

vertex = (- 3, - 2 ) , axis of symmetry is x = - 3

Answer:

I think it`s the second one

Step-by-step explanation:

Answer: The answer is the second choice. Hope this helps!

QPR is 68 degrees

triangle=180 degrees

180-44=136

136/2=68 (R=68 and S=68)

R has two angles so both are 68 degrees

QPR=68 degrees

Answer:

Step-by-step explanation:

1.

3,4,5 will make a triangle.

2.

sum of any sides > third side

difference of any two sides < third side

3+4=7>5

4+5=9>3

5+3=8>4

again

4-3=1<5

5-3=2<4

5-4=1<3

so it makes one triangle.

3.

3,4,8

4.

3+4=7 not >7

again

8-4 =4 not <3

so they do not make a triangle.

Answer:

10. put a dot on the number 10

Step-by-step explanation:

3-(-5)-(-2)

when subtracting negatives, you actually end up adding

so

3+5+2=10

3 - (5) - (-2) = 10.

The solution will be positive 10 on the line.

Inequalities are used to represent unequal expressions

The inequality that represents the number  of  seeds her apple could  have is [tex]\mathbf{A < 6}[/tex]

Represent the fruits with the first letter.

So, we have:

[tex]\mathbf{W =3A - 1}[/tex] --- watermelon is one less than three times apple

[tex]\mathbf{O =5A - 13}[/tex] --- orange is thirteen less than five times apple

[tex]\mathbf{W > O}[/tex] --- the seeds in watermelon exceeds orange

Substitute expressions for W and O in [tex]\mathbf{W > O}[/tex]

[tex]\mathbf{3A - 1 > 5A - 13}[/tex]

Collect like terms

[tex]\mathbf{13- 1 > 5A - 3A}[/tex]

[tex]\mathbf{12 > 2A}[/tex]

Divide both sides by 2

[tex]\mathbf{6 > A}[/tex]

Rewrite as:

[tex]\mathbf{A < 6}[/tex]

The inequality that represents the number  of  seeds her apple could  have is [tex]\mathbf{A < 6}[/tex]

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Answer:

y = 2/3x - 5  or   in standard form 3y = 2x - 5

Step-by-step explanation:

Remember this fact: Parallel lines have the same slope

Step 1   Solve for y  so that the equation is in the slope- intersect form

         2x - 3y = 6

          -3y = -2x + 6  

           -3y/-3  = -2x/-3 + 6/-3

             y = 2/3 x -2        

  now we know the slope is 2/3  or

   when the equation is in Standard form Ax + By = C   you can use this fact:  slope = - A/B    so  the slope = -2/-3 = 2/3

    Remember the   Parallel lines have the same slope

     Find the y-intersect "b"     use the slope = 2/3 and point (6, -1)

      y = mx + b

       -1 = 2/3(6) + b

       -1 = 4 + b

       -5 = b    

Now write the equation of line that is parallel to the given line and passes through  point (6, -1)

y = 2/3x - 5  or  in standard form 3y = 2x - 5

So a line that is perpendicular is a line that intercepts other line at a 90 degree angle.

Slope of perpendicular lines is the opposite sign and the reciprocal of the other.

So if your slope was 2 the perpendicular line would have a slope of -1/2.

So the equation, 2x + y = 3

Can be rewritten as

y= -2x+3

Perpendicular slope: 1/2

Since it intercepts/ passes the coordinates (5,4) it means that those values are included in the function input x and output y.

y=mx+b

4=1/2(5)+b

Solve for b (y intercept)

4-2.5=b

1.5=b

So the equation of the perpendicular is

y=1/2x+3/2 or y=.5x+1.5

Answer:

The answer to A is: "Angle 2 is congruent to angle 3"

The answer to B is: "Angle 3 is congruent to angle 7"

(7a*2b)+3c=3c+(7a*2b) the property for the given expression is Option A) Commutative Property of Addition.

The given expression is (7a*2b) + 3c = 3c + (7a*2b). This equation demonstrates the Commutative Property of Addition.

The Commutative Property of Addition states that the order in which numbers are added does not affect the result.

In mathematical terms, it can be written as: a + b = b + a.

In your expression, you have terms involving both addition and multiplication. However, since addition is involved on both sides of the equation, we can focus on the addition aspect.

(7a*2b) + 3c = 3c + (7a*2b)

First, we can rearrange the terms on the left side:

7a*2b + 3c = 3c + 7a*2b

Now, observe that the terms on both sides of the equation are the same: 7a*2b and 3c.

They are just arranged in a different order. This aligns with the Commutative Property of Addition, which says the order of addition doesn't matter.

Therefore, the expression is an illustration of this property, and the correct answer is the Commutative Property of Addition (A).

In summary, the expression shows that changing the order of terms within an addition does not change the result, thus demonstrating the Commutative Property of Addition.

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