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Tanzania [10]
4 years ago
12

Before her shopping spree, Lemon owned 11 shirts. Then she bought some more and now she owns 33 of them. What is the ratio of sh

irts before the purchase to the total number of shirts after the purchase
Mathematics
1 answer:
qwelly [4]4 years ago
4 0

Answer:

So the ratio of shirts before the purchase to the total number of shirts after the purchase is 1:3

Step-by-step explanation:

In this question we have to find the ratio of before and after so It will be written like this

Before : After

11: 33

Dividing both sides with 11

11/11:33/11

1: 3

So the ratio of shirts before the purchase to the total number of shirts after the purchase is 1:3

Which means that if we have total of 4 shirts then the number of shirts before the purchase were 1 and after the purchase were 4 meaning there are 3  new shirts in place for every single old shirt.

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Given that ΔPQR is similar to ΔPTS, which statement MUST be true? A) m∠PST = m∠QPR B) m∠TPS = m∠RPQ C) m∠SPT = m∠PTS D) m∠PRQ =
skelet666 [1.2K]

Answer: B) m∠TPS = m∠RPQ


Step-by-step explanation:

Given that ΔPQR is similar to ΔPTS

We know that of two triangles are similar then their corresponding angles are equal in measure and corresponding sides are proportional.

Therefore, If ΔPQR is similar to ΔPTS, then

m∠TPS=m∠RPQ

m∠STP=m∠RQP

m∠PTS=m∠PQR

Therefore, from the given options, only B is the right options, i.e. m∠TPS = m∠RPQ


3 0
4 years ago
Stacy wants to build a patio with a small, circular pond in her backyard.The pond will have a 6-foot radius. She also wants to i
solong [7]
First we are going to find the Area of the pond using the area of a circle formula: A= \pi r^2
where
A is the area of the circle 
r is the radius of the circle 
We know for our problem that the pond will have a 6-foot radius, so r=6. Lets replace that value on our area formula:
A= \pi r^2
A= \pi (6)^2
A=113.1ft^{2}
We know that the <span>cost of installing the pond is $0.62 per square foot, so lets multiply the area we just found by the cost:
Total cost of pund=</span>(0.62)(113.1)=70.12 dollars

Now, let x be the width the rectangle, so its length will be x+13. Remember that the area of a rectangle is width times length, so:
A=x(x+13)
A=(x^2+13x)ft^2
Since the cost of installing ties is $1, the cost of installing ties in our rectangle will be x^2+13x dollars.

<span>Stacy can spend no more than $536 on this project, so we can setup an inequality relating the cost of the pound and the cost of installing ties:
</span>70.12+x^2+13x \leq 536
x^2+13x \leq 465.88

We can conclude that the inequality that can be used to fin the width, x, of the patio is x^2+13x \leq 465.88
6 0
3 years ago
Rewrite the expression as a simplified expression containing one term cos alpha - beta
Vesna [10]

The given question seem incomplete

Rewrite the expression as a simplified expression containing one term

cos (α + β)cos(β) + sin( α + β)sin(β)

Answer:

The simplified form of the given expression is cos(α)

Step-by-step explanation:

We are given the expression

cos (alpha + beta)cos(beta) + sin( alpha + beta)sin(beta)

we will proceed by expanding the given expression as

(cos(alpha)cos(beta) - sin(alpha)sin(beta))cos(beta) + (sin(alpha)cos(beta)+cos(alpha)sin(beta))sin(beta)

cos(alpha)cos^2(beta) -sin(alpha)sin(beta)cos(beta) + sin(alpha)cos(beta)sin(beta) + cos(alpha)sin^2(beta)

The two middle terms will cancel each other so we are left with

cos(alpha)cos^2(beta) + cos(alpha)sin^2(beta)

cos(alpha)[cos^2(beta) + sin^2(beta)]

cos(alpha) (1) = cos(alpha)          [cos^2(beta) + sin^2(beta) = 1]

Therefore the simplified form of the given expression is cos(α)

8 0
3 years ago
Round 7300 correct to one significant figure.
notsponge [240]
The answer is 7000. 

Any zero that isnt trapped between two non-zero numbers (on the left side of the decimal) is insignificant, therefore the 3 rounds down. hope this helped!

3 0
3 years ago
Read 2 more answers
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Firdavs [7]
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sin(2(2x)) - sin(2(4x))
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7 0
3 years ago
Read 2 more answers
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