Katie has $150 in her savings account.
She wants to buy a new iPad that
costs $375. How many weeks will it
take her to have enough to buy the
iPad if she saves $25 each week?

Answer:

9. x = 31°

10. m∠ABC = 62°

11. m∠BCA = 60°

Step-by-step explanation:

We are given the following values for ΔABC, and its exterior angle, ∠ACD:

In ΔABC, the two nonadjacent interior angles are:  

While the exterior angle, m∠ACD = (5x - 35)°.

In order to solve for questions 9 through 11, we must apply the Exterior Angle Theorem which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent or remote interior angles.

In order to find the value of x, we can use the Exterior Angle Theorem:

m∠ACD = m∠A + m∠B

(5x - 35)° = 58° + 2x°

5x° - 35° = 58° + 2x°

Subtract 2x from both sides:

5x° - 2x - 35° = 58° + 2x° - 2x

3x - 35° = 58°

Next, add 35° to both sides:

3x° - 35° + 35° = 58° + 35°

3x° = 93°

Divide both sides by 3 to isolate x:

[tex]\displaystyle\mathsf{\frac{3x}{3}\:=\:\frac{93}{3} }[/tex]

x = 31°

Therefore, the value of x = 31°.

In order to find m∠ABC, we must first substitute the value of x into m∠B:

m∠B = 2x° = 2(31)° = 62°

Therefore, m∠ABC = 62°.

In order to find m∠BCA, we must first find the value of its supplement, m∠ACD, by substituting the value of x derived from question 9.

m∠ACD = 5x° - 35° = 5(31)° - 35° = 120°

Next, substitute the value of m∠ACD into the following equation:

m∠BCA + m∠ACD = 180°

m∠BCA + 120° = 180°

Subtract 120° from both sides:

m∠BCA + 120° - 120° = 180° - 120°

m∠BCA = 60°

Therefore, m∠BCA = 60°.

In order to verify whether we have the correct values for each interior angles, we can apply the Triangle Sum Theorem which states that the sum of all interior angles of a triangle is equal to 180°.  In other words:

m∠A + m∠B + m∠C = 180°.

58° + 62° + 60° =  180°

180° =  180° (True statement).

Answer:

1867

Step-by-step explanation:

What do you need it for?

Answer:

Yes

Step-by-step explanation:

They are equal acute triangles, are congurent. Your welcom

From the question, we are asked to find the row arrangement of a stack of boxes. Let us take a look at each one of the aforelisted answers

Since we are told that the total number of boxes to be stacked is 64, then for the first arrangement, we can deduce that the "x" is going to be 4. This is because multiplying 4 by 16 gives 64. For the second row, using the same calculation, we find that "x" is 8. And that of the third gives our "x" to be 4 as well. We can then adjudge that;

Bearing this in mind, we can see that each of the 3 answers fits into the requirements we are asked.

Hence, all of the options are correct.

To learn more about rows and columns, see here https://brainly.com/question/13196178

Answer:

13 ft, 17 ft, 22 ft

Step-by-step explanation:

let x be the shortest side, then second side is x + 4 and the third side is

2x - 4

sum the 3 sides and equate to 52

x + x + 4 + 2x - 4 = 52 , simplify

4x = 52 ( divide both sides by 4 )

x = 13

x + 4 = 13 + 4 = 17

2x - 4 = 2(13) - 4 = 26 - 4 = 22

lengths of 3 sides are 13 ft, 17 ft and 22 ft

Answer:

B

Step-by-step explanation:

A is 3-2 which is 1, not 5.

C is 3(2), which is 6, not 5.

D is 6, which is not 5.

-hope it helps

Answer:

B

Step-by-step explanation:

Answer:

n (m + p) + r (o + t)

Step-by-step explanation:

You have to split the expression in half.

First, focus on mn + np, the common factor would be n.

So the first part of the answer would be mn ÷ n and np ÷ n.

Leading to it being n(m + p).

Then you focus on the second half or + rt.

You find the common factor, which is r.

You divide both sides by r.

Hence why you get r(o + t).

Lastly, you put them together, n(m + p) + r(o + t).

Hope this helps :)

Based on the way the piecework pay is calculated, Margit's piecework pay will be $90.60

The piecework pay is 12 cents for every unit that is produced.

Margit was able to produce 755 units in that week so her piecework pay will be:

= Number of units produced x Pay per unit

= 755 x 0.12

= $90.60

In conclusion, Margit should get a piecework pay of $90.60

Find out more on piecework pay at https://brainly.com/question/4692318.

Answer:

- 1 1/3 degree

Step-by-step explanation:

- 16 / 12

Answer:

-35.2

Step-by-step explanation:

-68.4-(-15.6)= (-52.8)

-52.8÷3=(-17.6)

-52.8-(-17.6)=-35.2

Answer:-35.2

Step-by-step explanation:

Answer:

2500

Step-by-step explanation:

a² + 2ab + b²

49² + 98 + 1

Comparing terms

a²= 49²

a= 49

2ab = 98

2× 49 × b = 98

98b = 98

b= 98/98

b = 1

or

b²= 1

b=√1

b= 1

a=49 and b= 1

Hence (a+b)²= (49+1)²

50²= 2500

Step-by-step explanation:

the surface area of that object consists of

2 triangles (one left, one right)

1 rectangle at the top

1 rectangle at the bottom

1 rectangle in the back

so, we need to calculate the area of each of these 5 areas and sum them up. that's it.

the area of such a triangle is

6×8/2 = 24 m²

we have 2 such triangles, so in total they are 48 m².

the rectangle at the top

10×12 = 120 m²

the rectangle at the bottom

12×8 = 96 m²

the rectangle in the back

12×6 = 72 m²

so the total surface area is

48 + 120 + 96 + 72 = 336 m²

now, we're assuming that the prism has a volume of 10³ and is filled with cubes of sides 1/2 long, Check the picture below.

now notice the bottom-right part of the picture, if we put two small cubes next to each other, they add up to 1, so to get 10 units from that, we'll need 20 of those halves, or 20/2 = 10, meaning we'll need 20 cubes side by side to make a length of 10 horizontally.

The same will be true for getting cubes to make up 10 vertically, we'll need 20, the same is true to fill up from back to front, we'll need 20 cubes.

so we can say that the rectangular prism will need 20 cubes from front to back, 20 horizontally and 20 vertically, that'll be 20*20*20 cubes, or 20³ or 8000 cubes.

mind you that we used a Cube for the prism, but the same will be true if we were to rearrange the cubes and make the prism taller or wider, same 8000 cubes will fill it in.

Answer:

-1.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

36 inches  = 3 ft

max height of lumber stack is 7 - 3 = 4 ft.

4 ft = 48 inches

48 inch / 1.5 inch/board = 32 boards

Answer:

-5.1

Step-by-step explanation:

Since we know the starting temperature was -12.6 and the decrease was 7.5, that gives an equation.

-12.6 - 7.5.

Since we are working in temperature we need to be careful when subtracting.

-12.6 - 7.5 = -5.1

In a calculator, -12.6 - 7.5 would be 20.1 but since we are using temperature the answer is -5.1.

Hope that helps. x

Answer:

Step-by-step explanation:

if x is the number of times you go swimming

100 + 4x < 6x

Out of an 98 day season

If you attend 50 days, the cost is $300 either with or without the membership

Less than 50 days, it's less expensive to just pay the daily rate.

More than 50 days, it's less expensive to have the membership.

Answer:

I feel like something is wrong with the equation but the answer is a = 3

Step-by-step explanation:

a + 3a - 3 = 6 + 3 = 9

--> 4a = 12 --> a = 3

Answer: C. (1/6)

Step-by-step explanation: If you split the circle in half horizontally, the top part would be 1/3 and the bottom part would be 3/3. 1/3 + 3/3 = 4/6 and 4/6 simplified is 1/6.

Answer:

x= 131⁰

Step-by-step explanation:

the angles add up to 180⁰ so 180-49=131

131+49=180

hope this helps!!

Answer:

131 degrees. since it's going through 2 parallel lines, 49 is equal to the angle to the left of x, so we subtract 49 from 180 (half of 360) and we get 131

Step-by-step explanation:

let's create the corresponding equation.

it is linear, because the cost per hour is constant, no matter how many hours the car parks.

t is the variable indicating the amount of hours parking.

every hour costs $2.

and $8 is the starting value (we have to pay that, even if we have 0 hours parking time).

cost(t) = 2t + 8

so, the cost after 3 hours is

cost(3) = 2×3 + 8 = 6 + 8 = $14

Answer: [tex]\frac{(y+2)^{2} }{4} - \frac{(x-4)^{2} }{9} =1[/tex]

Step-by-step explanation: Big brain

ANSWER:

y= -1/5x - 5

Since it is parallel, that means that the slope (-1/5x) is the same.

Since it is passing through the point (-10, 3), substitute the numbers in for x and y which means: -3= -1/5*(-10) + b

b stands for the new y-intercept

do the equation, and you should get the answer above!

Answer:

Step-by-step explanation:

C

Answer:

1: $32. 2: 4 weeks. 3: 5 weeks

Step-by-step explanation:

1: 8+24=32$

2: 32/8=4=4 weeks

3: 32+8=$40

    40/8=5=5 weeks

Answer:

Multiply each coordinate point by 1.5, y=1.5x

Step-by-step explanation: