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gogolik [260]
3 years ago
8

the sum of three numbers is twenty. the second number is four times the first and the sum of the first and third is eight. what

are the three numbers?
Mathematics
1 answer:
8090 [49]3 years ago
4 0
Let's call the three numbers x, y, and z. 


The numbers are 3, 12, and 5.
x + y + z = 20
y = 4x
x + z = 8
We can rewrite the first equation because y is 4x, so 
x + 4x + z = 20
5x + z = 20
And now we can use simultaneous equation rules to solve

5x + z = 20
x + z = 8

5x + z = 20
5x + 5z = 40
(subtract)
-4z + -20
÷ -4
z = 5

x + z = 8
x + 5 = 8
x = 3

y = 4x
y = 4 × 3
y = 12

I hope this helps!
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3 years ago
find the coordinates of point Z that splits the segment XY located 3/7 of the way between X(-2,1) and Y(4,5)
Drupady [299]

Answer:

Z(-0.2, 2.2).

Step-by-step explanation:

We will use section formula when a point, say P, divides any segment ,say AB, internally in the ratio m:n.

[x=\frac{mx_2+nx_1}{m+n}, y= \frac{my_2+ny_1}{m+n}]

We have been given the points of segment XY as X at (-2,1) and Y at (4,5) and ratio is 3:7.

(x_1, y_1)=(-2,1)

(x_2, y_2)=(4,5)  

m:n=3:7    

Upon substituting coordinates of our given points in section formula we will get,

[x=\frac{(3*4)+(7*-2)}{3+7}, y= \frac{3*5+7*1}{3+7}]

[x=\frac{12-14}{10}, y= \frac{15+7}{10}]

[x=\frac{-2}{10}, y= \frac{22}{10}]

[x=-0.2, y= 2.2]

Therefore, coordinates of point Z will be (-0.2, 2.2).

7 0
3 years ago
Solve:<br> -3/4+p=1/2<br> Thank you so much!
shepuryov [24]

-3 / 4 + p = 1/2

LCD 4 and 2 = 4

Multiply by LCD = 4

p. (4)- 3/4 .( 4 ) = 1/2.(4)

4 p - 3 = 2

Add 3 to both sides:

4 p - 3 + 3 = 2 + 3

4 p = 5

Divide both sides by 4 :

4p / 4 =  5 /4

p = 5/4

3 0
3 years ago
In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.
OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse           Soh

<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse          Cah

<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent                Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = d*\frac{41ft}{d}     Multiply both sides by "d"

dcos77° = 41 ft                          

dcos77° / cos77° = 41 ft / cos77°        Divide both sides by cos77°

d = 41 ft / cos77°                      Input into calculator

d = 182.261874....... ft           Unrounded answer

d ≈ 182 ft                       Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0
3 years ago
Anyone know how to do this
blsea [12.9K]

Answer:

A B C D E MIGHT BE UR ANSWER

7 0
3 years ago
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