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Leto [7]
3 years ago
13

When 43,55 and 67 are divided by a certain number, the remainder is 7 in each case. Find the number? ​

Mathematics
1 answer:
siniylev [52]3 years ago
5 0

Answer:

12

Step-by-step explanation:

First subtract 7 from 43, 55 and 67

43 - 7 = 36 ;  55 - 7 = 48  ;  67 - 7 = 60

Now find the GCF of 36 , 48 , 60

36 = 2 * 2 * 3 * 3

48 = 2 * 2 * *2*2 * 3

60 = 2 * 2 * 3 * 5

GCF = 2 * 2 * 3 = 12

The required number is 12

When you divide 43 by 12, the remainder is 7.

When you divide 55 by 12, the remainder is 7

When you divide 67 by 12, the remainder is 7

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(05.08A)Triangle ABC is transformed to similar triangle A′B′C′ below:
Romashka-Z-Leto [24]

Answer:

1st option is correct i.e., 1 over 2

Step-by-step explanation:

Given that Triangle ABC transformed to Triangle A'B'C'.

Coordinated of Triangle ABC are A(2,6) , B(2,4) and C(4,4)

Coordinated of Triangle A'B'C' are A'(1,3), B'(1,2) and C'(2,2)

Scale factor of Dilation is the no. of times coordinates of vertices of a figure increase or decrease.i.e.,

if A(a,b) ⇒ A'(c,d)

where, a.k=c & b.k=d then k is scale factor of dilation.

Value of k is same for all vertices.

For coordinates of A & A' ,we have 2.k=1\implies k=\frac{1}{2} \:\: and \:\: 6.k=3\implies k=\frac{1}{2}

For coordinates of B & B' ,we have 2.k=1\implies k=\frac{1}{2} \:\: and \:\: 4.k=2\implies k=\frac{1}{2}

For coordinates of C & C' ,we have 4.k=2\implies k=\frac{1}{2} \:\: and \:\: 4.k=2\implies k=\frac{1}{2}

Therefore, the scale factor of dilation is \:\frac{1}{2}\:  since in all cases k=\frac{1}{2}

1st option is correct i.e., 1 over 2

3 0
4 years ago
the volume of a cone is 120 cubic centimeters. the height of the cone is 4.5 centimeters. determine the radius of a cone
kolbaska11 [484]
<h3> given:</h3>

<u>v = 120 \:  {cm}^{3}</u>

<u>h = 4.5 \: cm</u>

<h3>to find:</h3>

the radius of the cone.

<h3>solution:</h3>

r =  \sqrt{3 \frac{v}{\pi \: h} }

r =  \sqrt{3  \times   \frac{120}{\pi \times 4.5} }

r = 5.04627 \: cm

r = 5.05 \: cm

<u>hence</u><u>,</u><u> </u><u>the</u><u> </u><u>radius</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>cone</u><u> </u><u>is</u><u> </u><u>5.05</u><u> </u><u>centimeters</u><u>.</u>

7 0
3 years ago
As an estimate we are told 5 miles is 8 km, what is 62.5 miles into km
Sati [7]

Answer:

≈100.5

Step-by-step explanation:

hope this helps

6 0
2 years ago
Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.
kherson [118]

Answer:

=\frac{364\pi}{3} cubic units

Step-by-step explanation:

We are to find the  volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

f(x)=2x+1, y=0, x=0, x=4.

The picture is given as shaded region.

This is rotated about x axis

Limits for x are already given as 0 and 4

f(x) is a straight line

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Volume = \pi \int\limits^a_b {(2x+1)^2} \, dx \\= \pi \int\limits^4_0 {(4x^2+4x+1)} \, dx \\=\pi [\frac{4x^3}{3} +2x^2+x]^5_0\\\\=\pi[\frac{4*4^3}{3}+2*4^2+4-0]\\=\frac{364\pi}{3}

7 0
3 years ago
If m∠A = m∠B and m∠A + m∠C = m∠D, then<br> m∠B + m∠C = m∠D.
just olya [345]

Answer:

True. The statement is also equivalent to: If m<B + m<C does not equal m<D, then m<A does not equal m<B and m<A + m<C is not equal to m<D.

8 0
3 years ago
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