What transformation will prove that these two triangles are CONGRUENT.

Answer:

[tex]\displaystyle \binom{-8}{6}[/tex]

Step-by-step explanation:

The car's starting position is 2 miles south of the town center.  If it travels 6 miles north, then it will be 4 miles north of the town center.

The car's starting position is 5 miles east of the town center.  If it travels 8 miles west, it will be 3 miles west of the town center.

Therefore, its final position is 4 miles north and 3 miles west of the town center.

If the car travels 6 miles north from it's starting position, the y-value of the vector will be 6, as the car is moving in a positive direction along the y-axis.

If the car travels 8 miles left, the x-value of the vector will be -8, as the car is moving in a negative direction along the x-axis.

Therefore, the single translation vector that moves the car from its starting position to its final position is:

[tex]\displaystyle \binom{x}{y}=\binom{-8}{6}[/tex]

Answer:

$26.2

Step-by-step explanation:

5*2.50 is 13 for video games

4*3.30 is 13.2 for DVD

Sum them up and you get 26.2

Answer:

Option B

Step-by-step explanation:

|-1| [tex]\neq[/tex] -1

|-1| = 1

Answer:b

Step-by-step explanation: bc it’s right

Step-by-step explanation:

sin60 =opp/hyp

0.86=y/20

y=17.2

cos60=adj/hyp

0.5=x/20

x=10

sin57=y/15

0.83=y/15

y=12.45

Answer:

81.055 ft²

Step-by-step explanation:

A full circle has a central angle of 360°.

A sector with a central angle is 72° is 72/360 = 1/5 of a circle.

A full circle has 5 times the area of a sector with a 72° central angle.

A = 5 × 16.211 ft²

A = 81.055 ft²

Answer:

251,991 tons of ore are need to obtain 126 tons of gold.

Step-by-step explanation:

The total cost of the Job in the question is; D: $87,500

We are given that;

Direct Labor = $25000

Cost of direct materials used = $50000

Overhead is 50% of direct labor costs. Thus;

Overhead Cost = 50% * $25000 = $12500

Total Cost of Job = Overhead Cost + Materials Cost + Labor Cost

Total Cost of Job = $87,500

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Answer:

A. 33

Step-by-step explanation:

Add 4 to each number

1. 5 is your first number

2. 5+4= 9 is your second number

3. 9+4= 13 is your third number

4. 13+4= 17 ...

5. 17+4= 21 ...

6. 21+4= 25 ...

7.25+4= 29 ...

8.29+ 4= 33 is your eight number

Answer:

[tex]They\ are\ 8.544\ feet\ apart[/tex]

Step-by-step explanation:

Step 1:  Determine the important information

Math teacher 8 feet in front

Science teacher 3 feet to the right

Step 2:  Determine how far apart the teachers are

Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]

[tex](8)^2+(3)^2=c^2[/tex]

[tex]64 + 9 = c^2[/tex]

[tex]73 = c^2[/tex]

[tex]\sqrt{73} = \sqrt{c^2}[/tex]

[tex]8.544=c[/tex]

Answer:  [tex]They\ are\ 8.544\ feet\ apart[/tex]

The probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

Total number of outcomes = C(25, 2) = 300

Total number of favorable outcomes = C(20, 2) = 190

Probability = 190/300 = 19/30 or

= 0.63

Thus, the probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

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Answer:

Step-by-step explanation :

Given :

To Find :

Solution :

Let the angles be 7x and 8x respectively

As We know that, Sum of supplementary angles is always 180°

So, Adding Both the angles,

→ 7x + 8x = 180°

→ 15x = 180°

→ x = 180/15

→ x = 12

Hence,

Therefore,

Answer:

when the sum of the squares of the sides are equal to the square of the hypotenuse

Step-by-step explanation:

we use Pythagoras, 97 is the hypotenuse, 65 and 72 the sides.

97² = 65² + 72²

97² = 97²

it is a right triangle

The solution is 62. We have to multiply the mixed number by the whole number. 12 1/2 is 25/2 so we now multiply by flipping the 25/2 to 2/25 and when you multiply you get 1550/25, which is 62

Answer:

Mean: 80

Mode: 81

Median:81

Step-by-step explanation:

First, let's get the set of numbers from this Stem-and-Leaf plot:

[60,61,73,75,79,81,81,81,92,96,98]. From here we can solve for the mean by adding all the numbers up and dividing it by the number of terms that we have: [tex]\frac{60+61+73+75+79+81+81+81+92+96+98}{11} = 80[/tex] when rounded to the nearest whole number. The median is the middle number of the set when arranged from least to greatest, in this case, the median is 81.

Hope this helps! :)

The values for the highlighted variables that show how to subtract the rational expressions correctly are a = 6, x^2 + 6x is equal to x(x+6), and b=2.

From the informaation, the denominator and numerator of the first term are multiplied by x.

The second term is multiplied by (x-6)/(x-6).

Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term. In the same way as d is carried over from b, e is carried over from c.

We factor out the (x+6) from the numerator and denominator.

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Answer:

y ≤ 4

Step-by-step explanation:

Solving :

Answer:

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{10}~,~\stackrel{y_1}{-18})\qquad W(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y -18}{2} \right)~~ = ~~\stackrel{M}{(12~~,~~0.5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=12\implies x+10=24\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -18}{2}=0.5\implies y-18=1\implies \boxed{y=19}[/tex]

Answer:

$38696.84

Step-by-step explanation:

7% interest

so *1.07 per year

10,000*1.07^x=y

10,000*1.07^20=$38696.84

The equation that represent the  value of Alizeh’s investment after 20 years is y = 1000(b)^20

The increase in the amount of his money can be represented using the exponential function as shown:

y = ab^x

Given the following

a = 1000

x = 20 years

Substitute

y = 1000(b)^20

Hence the equation that represent the  value of Alizeh’s investment after 20 years is y = 1000(b)^20

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A confidence interval is the mean of the estimate plus and minus the variation in that estimate.

From the excel, Confidence.T(0.10,1.45,15)

Margin of error = 0.659414066

Lower limit will be;

= mean-0.659414066

= 5.3 - 0.659414066

= 4.640585934

Upper limit will be:

= mean+0.659414066

= 5.3+0.659414066

= 5.959414066

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Answer:

Coordinates of the midpoint are ( 9/2 , -6 )

Step-by-step explanation:

always remember, equations and inequalities are like a scale with 2 pans (left and right).

a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.

for an equation the scale has to stay balanced all the time.

and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.

A

so, in our case here

2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.

2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?

2×5 - 5 >= 3

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = 5 is also a valid solution.

what else ?

let's simplify the inequality

2x - 5 >= 3

2x >= 8

x >= 4

so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.

B

-2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.

-2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?

-2×-5 - 5 >= 3

remember, -×- = +

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = -5 is also a valid solution.

what else ?

let's simplify the inequality

-2x - 5 >= 3

-2x >= 8

x <= -4

a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.

so, really every value of x that is less or equal to -4 is a valid solution for the inequality.

Answer:

672 litres.

Step-by-step explanation:

Convert the measurements to cm:

14 m = 1400 cm

The capacity = 1400 * 8 * 60

= 672,00 cm^3

There are 1000 cm^3 in 1 litre so the answer is

672 litres.

Answer:

y12111097

Step-by-step explanation:

because I know the answer

Answer:

(33+7)-(15/3) = 35

Step-by-step explanation:

35

Step-by-step explanation:

fancy way of saying (33+7) - (15/3)

33 + 7 = 40

15 / 3 = 5

40 - 5 = 35

[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]

Answer:

7.5

Step-by-step explanation:

you take the largest number (9.8) and subtract with the smallest number (2.3)