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3 years ago

Solve the proportional

Mathematics

1 answer:

shepuryov [24]3 years ago

7 0

Answer:

x = 7

Step-by-step explanation:

10 / 4 = x + 8 / x - 1

[cross multiply]

10 (x - 1) = 4 (x + 8)

[distribute the factors]

10x - 10 = 4x + 32

+ 10 + 10

[add 10 to both sides to cancel out -10]

10x = 4x + 42

-4x -4x

[subtract both sides by 4x to cancel out 4x]

6x = 42

÷6 ÷6

[divide both sides by 6 to simplify 6x to x]

x = 7

________

x = 7 → 10 / 4 = x + 8 / x - 1 →

(7) + 8 / (7) - 1 → 15 / 6 →

15 ÷ 3 / 6 ÷ 3 → 5 / 2 →

5 × 2 / 2 × 2 → 10 / 4 = 10 / 4

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Which two triangles are congruent ? Complete the congruence statement . Please don’t be wrong I’ll

lukranit [14]

Answer:

ΔHFG≅ΔSUT

Step-by-step explanation:

You just have to match up the sides and the angle.It's easier to color code them.

For example:

Segment SU would be congruent with HF. (both would be blue, just example color)

Angle U is congruent to angle F (red)

UT congruent to FG (green)

6 0

3 years ago

Points X and Z are on a number line, and point Y partitions

abruzzese [7]

Answer:

The coordinate of $Z$ is 13.36.

Step-by-step explanation:

According to the statement, we have the following information:

$\frac{XY}{XZ} = \frac{5}{12}$ (1)

$\frac{YZ}{XZ} = \frac{7}{12}$ (2)

$X = 0.4$ (3)

$Y = 5.8$ (4)

From (2), we have the following expression:

$YZ = \frac{7}{12}\cdot XZ$

$Y-Z =\frac{7}{12}\cdot (X-Z)$

$Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z$

$Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z$

$\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X$

$5\cdot Z = 12\cdot Y-7\cdot X$

$Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X$ (5)

If we know that $Y = 5.8$ and $X = 0.4$ , then the coordinate of $Z$ is:

$Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)$

$Z = 13.36$

The coordinate of $Z$ is 13.36.

6 0

3 years ago

3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall

Katen [24]

Answer:

The volume of the toy is $V=5.23\ ft^3$

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

$V=\frac{2}{3}\pi r^{3}$

In this problem, the wide of the toy is equal to the diameter of the hemisphere

$D=2\ ft$

$r=2/2=1\ ft$ ----> the radius is half the diameter

substitute

$V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3$

step 2

Find the volume of the cone

The volume of the cone is given by

$V=\frac{1}{3}\pi r^{2}h$

we know that

The radius of the cone is the same that the radius of the hemisphere

$r=1\ ft$

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

$h=4-1=3\ ft$

substitute the given values

$V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3$

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

$V=(\frac{2}{3} \pi+\pi)\ ft^3$

$V=(\frac{5}{3}\pi)\ ft^3$

assume

$\pi=3.14$

$V=\frac{5}{3}(3.14)=5.23\ ft^3$

5 0

4 years ago

I need help in this question

tiny-mole [99]

Answer:

C. 12/15

Step-by-step explanation:

2/3, 6/9, and 18/27 all simplify to 2/3. 12/15 does not.

8 0

3 years ago

Sarah purchased a car that was on sale for 3/4 of the original price .if the original price was 6000, what was the price that Sa

umka21 [38]

So you do 3/4 divided by 6000 which make the thing switches and so you make 4/3 times by 6000 equals to your answers so you gotten 24,000 dividend it by 3 so you get will get.

Answer: 8,000

4 0

3 years ago