Triangle cde maps to triangle lmn with the transformation (x,y) —> (x+3,y-2)

The glee club has $90 to spend on pens and pencils. Each pen costs $0.75 and each pencil costs $0.15. Let x represent the number

Deffense [45]

Answer:

part a: answer b. 0.75x + 0.15y = 90

8 0

2 years ago

Read 2 more answers

Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum dista

algol [13]

Answer: The minimum and maximum distances that Morgan's dog may be from the house are 508 meters and 492 meters.

Step-by-step explanation:

Hi, to answer this question we have to solve the given equation: |x – 500| = 8.

The modulus can take a positive value (x - 500) or a negative value (-x+500).

For the positive value:

x -500 = 8

x = 8+500

x =508

For the negative value:

- (x -500) =8

-x +500 =8

500 -8 = x

492 =x

So, the minimum and maximum distances that Morgan's dog may be from the house are 508 meters and 492 meters.

Feel free to ask for more if needed or if you did not understand something.

5 0

1 year ago

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. How many cups of trail mix will she make if she uses 8 cup

alexgriva [62]

Answer:

48

Step-by-step explanation:

8 divided by 2 = 4

4 times 12 = 48

5 0

1 year ago

Suppose that a high school marching band has 125 members. Of these 125 band members, 41 are seniors, 24 play the trumpet, and 10

Alborosie

Answer:

The probability is 42%

Step-by-step explanation:

Conditional Probability

It's the probability of the occurrence of an event B knowing that an event A has already occurred and A and B are related (not independent).

If P(A) is the probability of occurrence of A, $P(A\cap B)$ is the probability of both events to occur, and P(B|A) is the required probability occurrence of B:

$\displaystyle P(B|A)=\frac{P(A\cap B)}{P(A)}$

We know a high school marching band has 125 members, from which 41 are seniors (event B), 24 play the trumpet (event A), and 10 are seniors who play the trumpet.

The probability that a randomly selected band member plays the trumpet is

$\displaystyle P(A)=\frac{24}{125}$

The probability that he or she has both attributes is

$\displaystyle P(A\cap B)=\frac{10}{125}$

Thus, the required conditional probability is

$\displaystyle P(B|A)=\frac{\frac{10}{125}}{\frac{24}{125}}$

$\displaystyle P(B|A)=\frac{10}{24}=\frac{5}{12}=0.42$

The probability is 42%

5 0

2 years ago

1) Proiectiile catetelor unui triunghi dreptunghic pe ipotenuza au lungimile 9 cm si 25 cm. Aflati lungimea inaltimii din varful

Flauer [41]

Answer:

1) 15cm

2) left projection/h = h/right projection

Step-by-step explanation:

Question:

1) The projections of the legs of a right triangle on the hypotenuse have lengths of 9 cm and 25 cm. Find the length of the height at the top of the right angle.

2) In a right triangle the length of the hypotenuse is 34 cm, and the lengths of the projections of the legs on the hypotenuse are directly proportional to the numbers 0, (6) and 0.75. Calculate the length of the height corresponding to the hypotenuse.

Solution

1) The length of the height of a right angle triangle is also called the altitude.

Since there are no diagrams in the question, I sent a diagram of the right angle as an attachment to the solution.

The projections of the legs are 25cm and 9cm.

Hence, the longer projection length AD = 25cm and the shorter projection length DB = 9cm

In a right triangle, the altitude (height) drawn from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the

geometric mean of these two segments (the two projections) and it's given by:

left projection/h = h/right projection

AD/h = h/DB

25/h = h/9

Cross multiply

h^2 = 25×9

h =√225 = 15cm

The length of the height at the top of the triangle = 15cm

2) Length of hypotenuse = 34

From the question, the lengths of the projections of the legs on the hypotenuse are directly proportional to the numbers 0, (6) and 0.75.

There is an error with the figures because the sum of the length of the projection of the legs should be equal to the hypotenuse but it isn't in this case.

To calculate the length of the height corresponding to the hypotenuse, we would use the same formula above.

left projection/h = h/right projection

To find each leg using question 1 above, each leg of the triangle is the mean proportional between the hypotenuse and the part of the hypotenuse directly below the leg.

Hypotenuse =34cm

Hyp/leg = leg/part

To find leg y, part for leg y = 25cm

34/y = y/25

y^2 = 34×25 = 850

y = √850 = 29.2cm

To find leg x, part for leg x = 9cm

34/y = y/9

y^2 = 34×9 = 306

y = √306 = 17.5cm

8 0

1 year ago

Triangle cde maps to triangle lmn with the transformation (x,y) —> (x+3,y-2) —> (2/3x, 2/3y)