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Natali [406]
2 years ago
10

A three-digit number ends in number 7. If you put the number 7 in the first position, the number will increase by 324. Find the

original three-digit number.
Mathematics
1 answer:
liq [111]2 years ago
5 0

Answer:

<u>The original three-digit number is 417</u>

Step-by-step explanation:

Let's find out the solution to this problem, this way:

x = the two digits that are not 7

Original number = 10x+7

The value of the shifted number = 700 + x

Difference between the shifted number and the original number = 324

Therefore, we have:

324 = (700 + x) - (10x + 7)

324 = 700 + x - 10x - 7

9x = 693 - 324 (Like terms)

9x = 369

x = 369/9

x = 41

<u>The original three-digit number is 417</u>

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Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides
cestrela7 [59]

Answer:

Choice D - 8cm and 9cm.

Step-by-step explanation:

The other sides are not greater than 13.

A: 5 + 8 = 13

B: 6 + 7 = 13

C: 7 + 2 = 9

However, <u>D is greater than 13 and is the correct answer.</u>

D: 8 + 8 = 16.

3 0
2 years ago
Given the vectors, a=3i+4j, b=-2i+5j, c=10i-j, d=-1/3i+5/2j, find -0.4a-0.3b+0.2d=?
sveta [45]

Answer:

-\frac{2}{3}i - \frac{13}{5}j

Step-by-step explanation:

-0.4(3i + 4i) - 0.3(-2i + 5j) + 0.2(-\frac{1}{3}i + \frac{5}{2}j)

-1.2i - 1.6j + 0.6i - 1.5j - \frac{0.2}{3}i + 0.5j

Converting to fraction form;

-\frac{6}{5}i + \frac{3}{5}i - \frac{1}{15}i - \frac{8}{5}j - \frac{3}{2}j + \frac{1}{2} j

<u>Solving the i part;</u>

\frac{-18i + 9i - i}{15} = -\frac{2}{3}i

<u>Solving the j part;</u>

\frac{-16j-15j+5j}{10} = -\frac{13}{5}j

So -0.4a - o.3b + 0.2d =  -\frac{2}{3}i - \frac{13}{5}j

6 0
2 years ago
William drove 344 miles in 8 hours. If he continued at the same rate, how far would he travel in 17 hours?
DiKsa [7]

Answer:

731 miles

Step-by-step explanation:

To solve this, we can set up a proportion.

Let's name the number of miles he travels in 17 hours x for now.

8/344=17/x

Simplify 8/344

2/86=17/x

Cross multiply

86*17=2*x

2x=1462

Divide both sides by 2.

x=731

He would travel 731 miles in 17 hours.

4 0
2 years ago
Read 2 more answers
The triangles shown below must be congruent. True or false
Alex777 [14]
The correct answer to your question is false. this is because congruent triangles must have the same 3 angles and the same 3 sides, and while these triangles have the same angles, they dont have the same sides.
let me know if you have any other questions
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4 0
2 years ago
Read 2 more answers
A point is dilated with respect to the origin. Determine the value of K and state whether the dilation is an expansion or contra
vlabodo [156]
Scale Factor (K) = (new length/measure)/ (original length/measure)
for x-coordinate  = 8/2 = 4
for y-coordinate  = 16/4 = 4

K=4, expansion

K is the representation of "scale factor". Scale factor is the ratio of the lengths involved of the similar figures. It can be used to identify the kind of dilation, whether it is contraction or expansion. If the Scale Factor is greater than 1, then that means expansion and if it is less than 1, then it signifies contraction.
5 0
2 years ago
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