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2 years ago

Find the sum of all 3 digit whole numbers that arw divisible by 13 ?

1 answer:

7 0

We have an arithmetic sequence with

a0 = 1st 3-digit number divisible by 13 
a0 = 104 
d = 13 (why?) 
last term is largest divisible by 13 = 988 
how many terms? (988-104)/13 + 1 = 69 

S = 69/2(104+988) = 37674

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Novosadov [1.4K]

What’s the given information?

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Answer for points

givi [52]

B=area of the base and 12cm
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Volume= 216cm

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How to do this math exercise 4x-2y=60 4x-3y=26

igomit [66]

4x -2y = 60
4x -3y = 26
(-) (+) (-)
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1y = 34
y = 34

To find x
4x -2y = 60
4x -(2)(34) = 60
4x -68 = 60
4x = 60 + 68
4x = 128
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Answer:
x=32 ; y=34

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3 years ago

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What is the value of x?

guajiro [1.7K]

Answer:

x ≈ 8.66

Step-by-step explanation:

Using the sine ratio in the right triangle

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{10}$

Multiply both sides by 10

10 × sin60° = x, thus

x ≈ 8.66 ( to 2 dec. places )

4 0

3 years ago

In the diagram below, ST is parallel to PQ. If ST is 4 more than PS,SR = 12, and PQ = 15, find the length of PS. Figures are not

Tpy6a [65]

Since segments ST and PQ are parallel, triangles SRT and PRQ are similar due to the AAA postulate. In general, the ratio between the corresponding sides of two similar triangles is constant; therefore,

$\frac{SR}{PR}=\frac{RT}{RQ}=\frac{TS}{QP}$

Furthermore,

$PS=PR-RS$

Finding PR and RS,

$\begin{gathered} ST=4+PS \\ SR=12 \\ PQ=15 \end{gathered}$

Then,

$\frac{12}{PR}=\frac{TS}{15}$ $\begin{gathered} \Rightarrow\frac{12}{PR}=\frac{4+PS}{15} \\ \Rightarrow\frac{12}{PS+12}=\frac{4+PS}{15} \end{gathered}$

Solving for PS,

$\begin{gathered} 12\cdot15=(PS+12)(PS+4) \\ \Rightarrow180=PS^2+16PS+48 \end{gathered}$

Solve the quadratic equation in terms of PS, as shown below

$\begin{gathered} \Rightarrow PS^2+16PS-132=0 \\ \Rightarrow PS=\frac{-16\pm\sqrt[]{16^2-4(-132)}}{2}=\frac{-16\pm28}{2} \\ \Rightarrow PS=-22,6 \end{gathered}$

And PS is a segment; therefore, it has to be positive.

Hence, the answer is PS=6

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11 months ago