Mathematics College

Line DCE is parallel to line AB
a) Find the size of angle ABC
b) Find the size of angle DCA
c) Calculate the size of angle ACB

Answers

Answer 1

Answer:

Angle DCA = Angle CAB. (Alternate Interior Angle)

Angle DCA = 68°

Angles(DCA + ACB + BCE) = 180°. (Linear Pair)

Angle ACB + 68° + 33° = 180°

Angle ACB = 79°

Therefore,

Angle ABC = 33°. (Alternate Interior Angle)

Related Questions

cuál es el resultado de 1/2 + 1/4 + 0.25

Answers

Answer:

Step-by-step explanation:

[tex]\frac{1}{2}=.5 \\ \frac{1}{4}=.25[/tex]

0.5 + 0.25 + 0.25 = 1

espero que esto ayude :)

Factor Completely;;;;;

Answers

Answer:

2x²-24x+54

2(x²-12x+27)

2(x²-9x-3x+27)

2(x(x-9)-3(x-9))

2(x-9)(x-3)

t or f i need help with this

Answers

Answer:

false 5 is an odd

Answer:

Step-by-step explanation:

false

Luis wants to buy a skateboard that usually sells for $79.91. All merchandise is discounted by %12. What is the total cost of the skateboard if Luis has to pay a state sales tax of 8.25%. Round your intermediate calculations and answer to the nearest cent.

Answers

Answer:

Luis' skateboard will cost $76.32.

Step-by-step explanation:

Divide 79.91 by 100, this is what one percent is worth, .7991.

Multiply this by 12, giving you 12 percent, 9.59 (rounded to the nearest 10th).

Now subtract 9.59 from 79.91, 70.32. That is the price BEFORE tax.

Than divide 70.32 by 100, .7032.

Multiply this by 8.25, 5.80, this is tax.

Now add the price before tax, 70.32, to the tax, 5.80.

This creates 76.12. This means that the total price of the skateboard is $76.32.

Answer:

saving $10.38

tax $5.80

total pay $76.12

Step-by-step explanation:

79.91*0.12=9.59

79.91-9.59=70.32

70.32*0.0825=5.80

70.32+5.80=76.12

Which one is prime 32,42,29,15

Answers

Answer:

Step-by-step explanation:

32 can be created from 4 x 8, so it is not.

42 can be created from 6 x 7, so it is not.

15 can be created from 5 x 3, so it is not.

29 cannot be created from any numbers multiplied.

Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow: Month Machine Hours Electricity Costs January 2,000 $ 18,950 February 2,400 $ 22,100 March 1,400 $ 14,050 April 2,600 $ 24,100 May 3,300 $ 28,800 June 2,800 $ 23,100 July 3,600 $ 25,300 August 3,000 $ 23,300 September 1,500 $ 16,600 October 3,200 $ 27,100 November 4,200 $ 32,100 December 3,700 $ 28,300 Summary Output Regression Statistics Multiple R 0.960 R Square 0.921 Adjusted R2 0.913 Standard Error 1,545.17 Observations 12.00 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7,465.99 1,566.61 4.77 0.00 3,975.37 10,956.62 Machine Hours 5.76 0.53 10.78 0.00 4.57 6.95 If the controller uses the high-low method to estimate costs, the cost equation for electricity costs is: (Round intermediate calculations to 2 decimal places.)

Answers

Answer:

If the controller uses the high-low method to estimate costs, the cost equation for electricity costs is "Total cost = $5,010 + ($6.45 * Machine hours)".

Step-by-step explanation:

Note: The data needed to estimate costs using the high-low method is merged together. It is therefore sorted before answering the question as follows:

Month Machine Hours Electricity Costs

January 2,000 $18,950

February 2,400 $22,100

March 1,400 $14,050

April 2,600 $24,100

May 3,300 $28,800

June 2,800 $23,100

July 3,600 $25,300

August 3,000 $23,300

September 1,500 $16,600

October 3,200 $27,100

November 4,200 $32,100

December 3,700 $28,300

The explanation of the answer is now provided as follows:

Step 1: Calculation of variable cost per hour

From the data above, the highest Machine Hours and Electricity Costs occur in November, while the lowest occur in March. Therefore, we have:

Variable cost per hour = (Highest Electricity Costs - Lowest Electricity Costs) / (Highest Machine Hours - Lowest Machine Hours = ($32,100 - $14,050) / (4,200 – 1,400) = $18,050 / $2,800 = 6.44642857142857

Rounding to 2 decimal places as required, we have:

Variable cost per hour = $6.45

Therefore, the variable-cost components using the high-low method is $6.45.

Step 2: Calculation of total fixed cost

The formula for calculating the total cost is given as follows:

Total cost = Total Fixed Cost + Total Variable Cost ................. (1)

Where;

Total Variable Cost = Variable cost per hour * Machine hours at a particular Electricity Costs

Using highest levels of activity and substitute into equation (1), we have:

$32,100 = Total Fixed Cost + ($6.45 * 4,200)

Total Fixed Cost = $32,100 - ($6.45 * 4,200) = $32,100 - $27,090 = $5,010

Therefore, the fixed-cost components using the high-low method is $5,010.

Step 3: Derivation of the cost equation for electricity costs

The cost equation for electricity costs can be obtained based on the total cost function given in equation (1) above, where:

Total Fixed Cost = $5,010

Total Variable Cost = Variable cost per hour * Machine hours = $6.45 * Machine hours

Substituting the values into equation (1), we have:

Total cost = $5,010 + ($6.45 * Machine hours)

Therefore, if the controller uses the high-low method to estimate costs, the cost equation for electricity costs is "Total cost = $5,010 + ($6.45 * Machine hours)".

Triangle ABC and Triangle DEF are similar. Find the unknown measures. (t = ? and u = ?)

Answers

t= 60°

It is an equilateral triangle which means all sides and angles are equal

u= 10m

It is an equilateral triangle which means all sides and angles are the same

remi and vishal start at the same point and begin jogging in different directions. remi is jogging east at a speed of 4 miles per hour. vishal is jogging South at a speed of 2 miles per hour. after how many hours will they be exactly 12 miles apart

Answers

Answer:

2.68 hours

Step-by-step explanation:

1 of 12
Eli is following this recipe to bake bread rolls.
He uses 500 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
400 g flour
6 g salt
8 g yeast
40 mL oil
360 ml water
?g salt
?g yeast
?mL oil
?mL water

Answers

Answer:

Step-by-step explanation:

I'm needing help with 4,5,6

Answers

3. Acute
4. Right
5. Acute

Hope this helps!

Answer:

4. acute

5. obtuse

6. obtuse

Step-by-step explanation:

Coordinate double equation

Answers

Answer:

????

Step-by-step explanation:

Sorry I can’t help but maybe another question

the ratio of boys to girls in the park was 4 to 5 .if 270 children were in the park.How many girl?

Answers

Answer:

150 are girls.

Step-by-step explanation:

There is an important difference between the way counts are viewed in ratio to that in fractions.

The ratio of boys : girls

4:5

so you have 4 boys and 5 girls making the whole count in its simplest form.

4+5=9

So to change the ratio proportion into fraction proportion we have:

Boys: 4/9

Girls: 5/9

It is given that the whole is 270 therefore the count of girls is:

5/9 x 270 = 150

Vonna scored 72 goals at soccer practice. Her ratio of goals to misses was 8 to 7. How many times did she miss?

Answers

8:7
72:63
The answer is 63

State the domain and range of both the function and the inverse function. f(x) = 8 x + 8 f -1(x) = Domain of f(x): Range of f(x): Domain of f -1(x): Range of f -1(x)

Answers

Answer:

[tex]f^{-1}(x) = \frac{x+8}{8}[/tex]

Domain of f(x): All real values.

Range of f(x): All real values.

Domain of f -1(x): All real values.

Range of f -1(x): All real values

Step-by-step explanation:

We are given the following function:

[tex]f(x) = 8x + 8[/tex]

Since it is a line, we have that both the domain is the range is the real set.

Inverse function:

The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.

Finding the inverse function:

Exchange x and y in the original function, and isolate y. So

Original

[tex]y = 8x + 8[/tex]

Exchanging:

[tex]x = 8y - 8[/tex]

Isolating y:

[tex]8y = x + 8[/tex]

[tex]y = \frac{x+8}{8}[/tex]

[tex]f^{-1}(x) = \frac{x+8}{8}[/tex]

What is the solution to the equation?

Answers

Answer:

32.13

Step-by-step explanation:

g = 15.3 x 2.1 = 32.13

Answer:

g= 15.3 *2.1= 32.13

Hence answer is 32.13

Simplify the following question
x+9-10=500

Answers

Step-by-step explanation:

x+9-10=500

x-1=500

x=500+1=501

Step-by-step explanation:

solution

here,

given,

x+9-10= 500

or, x-1= 500

or, x= 500-1

or, x= 499

hope this helps u...

Artificial grass sells for $10.98 per square yard final cost to buy and install 69.2 square yards if the seller charges $5.15 per square yard for labor round to the nearest cent

Answers

Answer:

$1,116.19.

Step-by-step explanation:

Given that artificial grass sells for $ 10.98 per square yard, to determine the final cost to buy and install 69.2 square yards if the seller charges $ 5.15 per square yard for labor, round to the nearest cent, the following calculation must be performed:

69.2 x (10.98 + 5.15) = X

69.2 x 16.13 = X

1,116,196 = X

Thus, the cost to purchase and install 69.2 square yards of artificial grass is $ 1,116.19.

What is the slope of the line? y-3=5(x-2)y−3=5(x−2)y, minus, 3, equals, 5, left parenthesis, x, minus, 2, right parenthesis Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac15 5 1 start fraction, 1, divided by, 5, end fraction (Choice B) B -\dfrac45− 5 4 minus, start fraction, 4, divided by, 5, end fraction (Choice C) C 111 (Choice D) D 55

Answers

Answer: A

Step-by-step explanation:

Answer:5

Step-by-step explanation:I got it wrong and decided to give you guys the right answer.

The distance between the two points is____

Answers

Answer:

7 units

Step-by-step explanation:

x + 14 = 113 x=______ solve the question

Answers

Answer:

x=99

Step-by-step explanation:

Move all terms not containing x to the right side of the equation.

I can do the previous part but I don't know what to do here

Answers

There is no picture

Answer:

25°; 115°.

Step-by-step explanation:

all the details are in the attached picture, the answers is marked with red colour.

Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3

Answers

Answer:

Step-by-step explanation:

Let the ends of the given segment are A and B.

Coordinates of A → (8, 6)

Coordinates of B → (12, 12)

If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,

(x, y) → (kx, ky)

If k = [tex]\frac{2}{3}[/tex]

(x, y) → [tex](\frac{2}{3}x, \frac{2}{3}y)[/tex]

By this rule coordinates of the image points of A and B will be,

A(8, 6) → [tex]A'(\frac{2\times 8}{3},\frac{2\times 6}{3})[/tex]

→ A'(5.3, 4)

B(12, 12) → [tex]B'(\frac{12\times 2}{3}, \frac{12\times 2}{3})[/tex]

→ B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of [tex]\frac{2}{3}[/tex].

terry has nuts and bolts 7:9 if terry has 36 bolts how many nuts does terry have

Answers

Answer:

Answer:

4 2/5 x 5 1/2 = 24.2

Step-by-step explanation:

PLZZ MARK BRAINLIEST!!!

what is the volume of a cube with 2 1/4 inch sides

Answers

Answer:11.39

Step-by-step explanation:

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Line DCE is parallel to line AB a) Find the size of angle ABC b) Find the size of angle DCA c) Calculate the size of angle ACB

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Line DCE is parallel to line AB
a) Find the size of angle ABC
b) Find the size of angle DCA
c) Calculate the size of angle ACB