ABCD is a rhombus with diagonals intersecting at E. If the measure of angle ABC is 3 times the measure of angle BAD, find the measure of angle EBC.

Hope this helps

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

I did this already

The probabilities are:

1. P(yellow) = 2/5

2. P(red) = 3/10

3. P(blue) = 3/10

4. P(blue or yellow) = 7/10

5. P(red or blue) = 3/5

To find the probability that a person in each color seat would receive the free tickets, we need to calculate the probabilities of each event.

1. P(yellow): There are 8 yellow seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a yellow seat at random is P(yellow) = 8/20 = 2/5.

2. P(red): There are 6 red seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a red seat at random is P(red) = 6/20 = 3/10.

3. P(blue): There are 6 blue seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a blue seat at random is P(blue) = 6/20 = 3/10.

4. P(blue or yellow): To calculate the probability of selecting a blue or yellow seat, we add the individual probabilities of selecting a blue seat and a yellow seat: P(blue or yellow) = P(blue) + P(yellow) = 3/10 + 2/5 = 7/10.

5. P(red or blue): To calculate the probability of selecting a red or blue seat, we add the individual probabilities of selecting a red seat and a blue seat: P(red or blue) = P(red) + P(blue) = 3/10 + 3/10 = 6/10 = 3/5.

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Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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Answer:

b^20/a^12

Step-by-step explanation:

b to the power of 20 over a to the power of 12

According to SAS Congruence Theorem and the reflexive property of congruence, it can be proved  that ΔSPQ ≅ ΔTPQ.

It is given to us that -

PQ bisects ∠SPT

SP ≅ TP

We have to prove that ΔSPQ ≅ ΔTPQ

Now, as PQ bisects ∠SPT,

∠SPQ = ∠TPQ

Also, according to the Reflexive Property of Congruence, PQ is a common side of both triangles - ΔSPQ and ΔTPQ.

Thus, according to SAS Congruence Theorem,

"If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent."

Therefore, according to SAS Congruence Theorem, we have proved that ΔSPQ ≅ ΔTPQ.

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Answer:

127 degree

Step-by-step explanation:

because angle 6 is alternate to 127 degree. Alternate makes a=b which is angle 6 is equal to 127 degree

Coefficient of 'x'= 5a

Coefficient of 'x square'= -17

Constant term = 14a

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:

To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:

0.05 x 3.8 = 0.19

So, 0.19 gallons of engine oil should be added to the jerry can.

Answer:

8

Step-by-step explanation:

in right angle triangle

h^2=p^2+b^2

5^2=3^2+b^2

25-9=b^2

b=√16=4

radius=4

diameter=4×2=8

Answer:

your answer is C i hope this helps sorry if i am wrong

Step-by-step explanation:

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

3

Step-by-step explanation:

Simplify: (-7x2 - 3x) - (4x2 - x) ... -11x2 – 2x ... 3x – 5 + 23x – 9 = 3x + 23x – 5 – 9 = 26x – 14 = 2(13x – 7) Answer: 2(13x – 7). 11 . ... 2x - 3 + 3 = - 9 + 3, (Adding 3 on both sides) 2x = -6 2x/2 = -6/2

Answer: 9x power of 2+x-16

Step-by-step explanation:

(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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Answer:

x=18

36/2=18

all good.

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

\(x=-4\)

\(y=3\)

\(z=-5\)

Step-by-step explanation:

Given:

\(x+y+z=-6\)

\(x-6y-7z=-29\)

\(-7y-5z=4\)

Solve for \(x\) in the 1st equation:

\(x+y+z=-6\)

\(x+y=-z-6\)

\(x=-y-z-6\)

Substitute the value of \(x\) into the 2nd equation and solve for \(z\):

\(x-6y-7z=-29\)

\((-y-z-6)-6y-7=-29\)

\(-7y-z-13=-29\)

\(-7y-z=-16\)

\(-z=-16+7y\)

\(z=16-7y\)

Substitute the value of \(z\) into the 3rd equation and solve for \(y\):

\(-7y-5z=4\)

\(-7y-5(16-7y)=4\)

\(-7y-80+35y=4\)

\(28y-80=4\)

\(28y=84\)

\(y=3\)

Plug \(y=3\) into the solved expression for \(z\) and evaluate to solve for \(z\):

\(z=16-7(3)\)

\(z=16-21\)

\(z=-5\)

Plug \(z=-5\) into the solved expression for \(x\) and evaluate to solve for \(x\):

\(x=-(3)-(-5)-6\)

\(x=-3+5-6\)

\(x=2-6\)

\(x=-4\)

Therefore:

\(x=-4\)

\(y=3\)

\(z=-5\)

Answer:

I believe the answer is 13/18

Step-by-step explanation:

if is not sorry but this is for 5th grade exit ticket only

Answer:

  3. (5x600)+(5x80)

Step-by-step explanation:

You want to choose an expression that shows how to evaluate 5×680 using mental math.

As with many multiple-choice problems, you can eliminate the choices that are false or not consistent with problem requirements. This leaves you with choosing between options 1 and 3.

  1. 5 × (600 +80) = 5×680, the original problem. Offers no gain in speed or simplicity

  2. = 5×608 . . . . incorrect result

  3. (5 × 600) +(5 × 80) reduces to single-digit products, an appropriate approach

  4. (5 × 600) +(6 × 80) = 3480 . . . . incorrect result

  5. (5 × 70) -(5 × 20) = 250 . . . . incorrect result

The only choice that makes any sense is ...

  3. (5 × 600) +(5 × 80)

__

Additional comment

For almost anything involving multiplication or division by 5, it works well to use 10/2 instead. That is ...

  5 × 680 = 10 × (680/2) = 10 × 340 = 3400

Usually, doubling or halving a number is easier than multiplication or division by 5.

The expression of choice 3 is identical to the "long multiplication" approach usually taught for multiplying multi-digit numbers. Yes, you can do it mentally, but there is no particular saving of effort.

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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The slope of a line is the rate of change of the line. The slope of the line is 1

The slope of a line is the rate of change of the line. The slope os calculated as:

Slope = y2-y1/x2-x1

Using the coordinate points (-1, 0) and (0, 1)

Substitute

Slope = 1-0/0-(-1)

Slope = 1/1

Slope = 1

Hence the slope of the line is 1

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Given the expression

The above expression can be rewritten as

Determine the Least Common Multiple (LCM) of the denominators.

The LCM of 2 and 1 is 2.

Thus, we have

Answer:

15,894.06

Step-by-step explanation:

HI there!

This is a compound interest question, so we will use the formula

\(x = p(1+\frac{r}{n})^n^t\)

P being our principle amount, $15,000 in this case,

R being our rate, or 1.25

N being our compound rate, which is semiannually, or twice a year.

T is our time, being 3.

After plugging these values in, we get

15,894.06

I hope this helps!

The value of x in the pentagon JKLMN is 7.2.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The pentagons ABCDE and JKLMN are similar.

when two figures have the same shape but their sizes are different, then such figures are called similar figures.

We need to find the value of x.

1/1.8=4/x

Apply cross multiplication

x=4×1.8

x=7.2

Hence, the value of x in the pentagon JKLMN is 7.2.

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The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

\(Area = \int\limits^b_a {y} \, dy\)

\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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Answer:

2.25 cars are waxed with one bottle

Step-by-step explanation:

1/3 * 3 = 1

3/4 * 3 = 9/4

9/4 = 2.25

Answer:

P(8) = 1/9

Step-by-step explanation:

There are 9 balls, 1,2,3,4,5,6,7,8,9

We want to get ball 8

P(8) = number of balls marked 8/ total number of balls

       = 1/9

Answer:

P = 1/9

Step-by-step explanation:

Probability of selecting the ball marked with 8

\(\sf Probability = \dfrac{Number\: of \:favorable\: outcomes }{ Total \:number\: of\: possible\: outcomes}\\\\\sf Probability = \dfrac{1 }{9}\)