A worker on the production line is paid a base salary of ​$170 per week plus ​$1.21 for each unit produced. Write an equation to represent his earnings of ​$491.86 for a week when he produced x units. How many units did he ​produce? Use pencil and paper. If the worker had produced twice that number of​ units, what would his earnings have​ been? Show your work.

Step-by-step explanation:

LINE K is linear equation

y = mx + b

m = delta y/ delta x

= 6/3

= 2

b = y-intercept (at x = 0, y = 0)

y = 2x

Answer:

6cm , 12cm

Step-by-step explanation:

Answer:

A. Frozen yogurt

Step-by-step explanation:

The frozen yogurt costs less than the frozen custard, even though you get the same amount (3 ounces)

No matter how much money Marco has, he would be able to buy more of the frozen yogurt because it has a cheaper unit rate.

So, the answer is A, frozen yogurt

Answer:

True

Step-by-step explanation:

Cuz if u substitute (3,-3/2) it would work

Y = 1/2x - 3

-3/2 = 1/2(3)-3

-3/2 = 1.5 - 3

-3/2 = -1.5

& -3/2 is -1.5 as a decimal lol

Answer:

(a) [tex]j = 4k[/tex]

(b) [tex]4k - 18 = 18 + k[/tex]

(c) Jim initially had 48; Kirk initially had 12

Step-by-step explanation:

Given

[tex]j = Jim[/tex]

[tex]k=Krik[/tex]

Solving (a): An equation for the amount they originally had.

From the question, we understand that j is 4 times as many as k.

Mathematically, this is:

[tex]j = 4 * k[/tex]

[tex]j = 4k[/tex]

Solving (b): Equation after Kirk wins

Initially Kirk had k.

To get the new expression, we add 18 to k.

This gives: 18 + k

In the same vein, Jim's number of chirps will reduce by 18.

Initially, Jim had j chirps (or 4k chirps)

To get the new expression, we subtract 18 from j.

This gives: j - 18

So, the equation is:

[tex]j - 18 = 18 +k[/tex]

Solving (c): Number of chirps they started with.

In (b), we have:

[tex]j - 18 = 18 +k[/tex]

Substitute 4k for j

[tex]4k - 18 = 18 + k[/tex]

Collect Like Terms

[tex]4k - k = 18 + 18[/tex]

[tex]3k = 36[/tex]

Divide both sides by 3

[tex]k =12[/tex]

Substitute 12 for k in [tex]j = 4k[/tex]

[tex]j = 4 * 12[/tex]

[tex]j = 48[/tex]

Answer:

x = 2/3 and y = 8/9

Step-by-step explanation:

If a parallelogram INDY has diagonals that intersects at P, then O bisects ID and YN

Hence IP = PD and NP = YP

Given

IP=3x

DP = 6x - 2

NP = 3y and

YP=7x-2,

Substitute

3x = 6x-2

3x-6x = -2

-3x = -2

x = 2/3

x = 0.67

Also NP = YP

3y = 7x-2

3y = 7(2/3) - 2

3y = 14/3 - 2

3y = 14-6/3

3y = 8/3

9y = 8

y = 8/9

Hence x = 2/3 and y = 8/9

I mist that one its not the first one

Step-by-step explanation:

Answer:

The correct answer is the last image...I just got it right on the quiz.

Step-by-step explanation:

Answer:

2√5

Step-by-step explanation:

Using the formula for calculating resultant

R = √Fx + Fy

\sum Fx = -2sin 45 + 4 cos 45

\sum Fx =  2cos45

\sum Fx = 2(1/√2)

\sum Fx   = 2/√2

Similarly;

\sum Fy = 2 cos 45 + 4 sin45

\sum Fx  = 2(1/√2) + 4(1/√2)

\sum Fx = 6/√2

Magnitude = √(2/√2)²+6/√2)²

Magnitude = √4/2 + 36/2

Magnitude = √2+18

Magnitude = √20

Magnitude = 2√5

Hence the magnitude of their sum is 2√5

Answer:

2√5

Step-by-step explanation:

Answer:

2-4=4+7=11 so that is the answer begginer

Answer:

First: 3 units Second: 7 units Third: 9 units

Step-by-step explanation:

19=x+(x+4)+3x

19=5x+4

15=5x

x=3

first side is 3 units

3+4=7

second side is 7 units

3*3=9

third side is 9 units

Answer:

£125000

Step-by-step explanation:

Original cost of house = £100 000

Percent increase = 25%

Increase in price = 25% of 100,000

Increase in price = 0.25 * 100,000

Increase in price = 25000

New cost = original cost + Increment

New cost = 100,000 + 25,000

New cost = 125,000

Hence it now cost  £125000

Answer:

10

Step-by-step explanation:

Answer:

$5.61

Step-by-step explanation:

So, first of all, 15% off of 1.20 is 1.02. Then, multiply that by 5 1/2 to get $5.61.

D) -3

because the number should be less than -2 and greater than -6

so here only -3 satisfies the condition

Answer:

B.f(x)=4x

Step-by-step explanation:

Multiply x value by 4

Answer:

it has 5 hopefully this helps you with work

Answer:

Step-by-step explanation:

Given lines:

These have same slopes of 2/3 and therefore are parallel, so no intersection. There is no solution if lines don't intersect.

The graph is attached as well to show lines are parallel.

Answer:

5

Step-by-step explanation:

Answer:

Because it bears an equal sign

Expressions don't have a definite solution to the problem.

Answer:

B

Step-by-step explanation:

3 x X = 3x 3 x 2 = 6 so 4x + 3x = 7x +6

Answer:

4 is greater than -5

Step-by-step explanation:

positive are greater than negative

Answer:

Step-by-step explanation:

1 in = 2.54 cm

Part (a)

Answer: 8.268 in

Part (b)

Answer: 11.693 in

Part (c)

In SI units standard-sized paper is 21.0 cm by  29.7 cm, which is equivalent to 8.268 in by 11.693 in.

Answer: 8.268 in by 11.693 in.

Part (d)

The U.S sized standard paper is 8.0 in by  11.0 in. Therefore the SI (internationally) sized paper is longer.

Part (e)

If the U.S> adopts the SI standard for letter-sized paper, both the width and length of standard paper will have to be increased. Therefore letter-sized paper will occupy a larger area and will be heavier if the thickness and density do not change.

Answer:

Explanation  below

Step-by-step explanation:

1/2 =0.5

1/3 = 0.333

4/6 = 0.667

2/5 = 0.4

5/8 = 0.625

7/12 = 0.583

The fractions less than 1/2 are:

1/3 and 2/5.  (A and C).

Answer:

X = 12.21

Step-by-step explanation:

Since this is a right triangle, use the formula A^2 + B^2 = C^2 and plug in appropriate values.

(10)^2 + (7)^2 = C^2

100 + 49 = C^2

149 = C^2

12.2065 = C

Rounded to two decimal places, this makes X equal to 12.21.

The required value of x is 12.21 for the given right triangle.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

Since this is a right triangle, use the formula A² + B² = C² and substitute appropriate values.

(10)² + (7)² = x²

100 + 49 = x²

149 = x²

x = √149

x = 12.2066

Rounded to two decimal places,

x = 12.21

Therefore, the required value of x is 12.21.

Learn more about Pythagoras's theorem here:

brainly.com/question/343682

#SPJ2

Answer:

i. x² + 7x - 16800 = 0 ii. x = 126.16 km/h or -133.16 km/h iii. 5.01 h

Step-by-step explanation:

i. If he drove at an average speed of x km/h on his journey from City P to City Q formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.

For the first journey from City P to City Q, with Mr Lee moving at an average speed of x km/h, he reaches there in time, t and covers the distance, d = 600 km

So, xt = 600 (1)

On his return journey from City Q to CIty P, his average speed increases by 7 km/h, so it is (x + 7)km/h and his time is 15 minutes less than his first journey. 15 min = 15/60 h = 0.25 h, we have that his time for the journey is (t - 0.25) h. Since the distance covered is the same d = 600 km,

We have (x + 7)(t - 0.25) = 600  (2)

Expanding the brackets, we have

xt - 0.25x + 7t - 0.25(7) = 600

xt - 0.25x + 7t - 1.75 = 600

From (1) t = 600/x and xt = 600

Substituting these into the equation, we have

600 - 0.25x + 7(600/x) - 1.75 = 600

simplifying

-0.25x + 4200/x - 1.75 = 600 - 600

-0.25x + 4200/x - 1.75 = 0

multiplying through by x, we have

-0.25x² + 4200 - 1.75x = 0

dividing through by -0.25, we have

-0.25x²/-0.25 + 4200/-0.25 - 1.75x/-0.25 = 0

x² - 16800 + 7x = 0

re-arranging, we have

x² + 7x - 16800 = 0

ii. Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to  2 decimal places.

Using the quadratic formula, we solve x² + 7x - 16800 = 0 for x

So, [tex]x = \frac{-7 +/-\sqrt{7^{2} - 4 X 1 X -16800} }{2 X 1}\\x = \frac{-7 +/-\sqrt{49 + 67200} }{2} \\x = \frac{-7 +/-\sqrt{67249} }{2} \\x = \frac{-7 +/- 259.32}{2} \\x = \frac{-7 + 259.32}{2} or x = \frac{-7 - 259.32}{2} \\x = 252.32/2 or x= -266.32/2\\x = 126.16 km/hor x = -133.16 km/h[/tex]

So, x = 126.16 km/h or -133.16 km/h

iii. Find the time taken for the return journey

The time taken for the return journey is t' = t + 0.25. Now. t = 600/x

Since x cannot be negative, we use x = 126.16 km/h.

So, t = 600/x = 600/126.16 = 4.76 h

t' = t + 0.25

t' = 4.76 + 0.25

t' = 5.01 h

Answer:

3:8

Step-by-step explanation:

The ratio of Mina's age to Naomi's age is 3 : 4

Multiplying the above ratio by 2 = 6:8

The ratio of Lev's age to Mina's age is 1 : 2

Multiplying the above ratio by 3

= 3:6

Therefore, ratio of Lev's age to Naomi's age in simplest form.

= 3:8

Answer:

3:8

Step-by-step explanation:

Let L, M, and N stand for the three ages.

The given ratios tell us that

M = 2L

and

N = 4/3M.

Therefore,

N = 4/3 x 2L = 8/3L.

This means that Lev's and Naomi's ages are in the ratio 3:8.