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2 years ago

If QR=x+29 and PS=x–16, what is the value of x?

Mathematics

1 answer:

Juli2301 [7.4K]2 years ago

6 0

Answer:

Step-by-step explanation:

PS is a midsegment of the triangle, so is half the length of the parallel base segment.

2PS = QR

2(x -16) = x +29 . . . . . substitute given expressions

2x -32 = x +29 . . . . . eliminate parentheses

x = 61 . . . . . . . . . . . . add 32-x

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An architect is planning to make two triangular prisms out of iron. The architect will use ∆ABC for the bases of one prism and ∆

____ [38]

a) 5/7

b) 4459 cm cube

c) 2275 cm cube

Step-by-step explanation:

Step 1 :

The Side AB (28 cm) has been scaled to side DE (20 cm)

Let x b the scale factor.

Then we have 28 *x = 20

=> x = 20/28 = 5/7

Hence the scale factor is 5/7

Step 2 :

Given the height of the triangular prism is 15 cm

Volume = ( 1/2 ) * base* height of the triangle * height of the prism

= (1/2)* 21*28*15 = 4410 cm cube.

Step 3 :

Given volume of the triangular prism with base ABC is 4459 cm cube

The scale factor is 5/7

Hence the volume of the prism with DEF as base is

4459 * (5/7)*(5/7) = 2275 cm cube.

4 0

3 years ago

Calculate the sum of 45 and 39

Jlenok [28]

Answer:

Step-by-step explanation:

45 + 39 = 84

4 0

3 years ago

Read 2 more answers

If P= (-3,5) and Q= (1,9), find the equation of the circle that has segment PQ as a diameter

Alex777 [14]

Answer:

The equation of the circle is;

(x - [(-1))² + (y - [7])² = 8

Step-by-step explanation:

The given coordinates of the points P and Q are;

P = (-3, 5) and Q = (1, 9)

To find the equation of the circle that has segment PQ as a diameter

The equation of a circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

Given that segment PQ is the diameter of the circle, we have;

The center of the circle, O = The midpoint of PQ

The coordinates of the midpoint of segment PQ, O = ((-3 + 1)/2, (5 + 9)/2) = (-1, 7)

∴ The coordinates of the center of the circle, O = The coordinates of the midpoint of segment PQ = (-1, 7)

Therefore;

h = -1, k = 7

From PQ = The diameter of the required circle, we also have;

The length of PQ = 2 × (The radius of the circle) = 2 × r

The length of segment PQ = √((1 - (-3))² + (9 - 5)²) = √32 = 4·√2

Therefore;

The length of PQ = 4·√2 = 2 × r

r = (4·√2)/2 = 2·√2

r = 2·√2

r² = (2·√2)² = 8

r² = 8

The equation of the circle is therefore;

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - 7)² = 8.

6 0

3 years ago

$8000 principal earning 5% compounded annually, after 6 years

Verdich [7]

Future amount after 6 years will be: $10720.76

Step-by-step explanation:

Principal = $8000

Interest= 5% compounded annually

Time = 6 years

We need to find A (future amount)

The formula used is:

$A=P(1+\frac{r}{n})^{nt}$

A= Future amount

P= Principal amount

r= interest rate

n= no of times interest is applied

t= time

Putting values and finding A

P=8000. r=0.05, n=1, t=6

$A=P(1+\frac{r}{n})^{nt}\\A=8000(1+\frac{0.05}{1})^{1*6}\\ A=8000(1+0.05)^{6}\\ A=8000(1.05)^{6}\\A=10720.76$

So, Future amount after 6 years will be: $10720.76

Keywords: Compound Interest

Learn more about Compound Interest at:

#learnwithBrainly

8 0

3 years ago

Write a function rule for the table.

Sati [7]

Answer:

p = 7.50h

Step-by-step explanation:

The answer has to be in the form of p =, since p is the pay which represents our y value, and the hours worked represents our x value. You can find the slope of the line by using the formula and any two points on the table:

$m=\frac{30-15}{4-2}=\frac{15}{2}$

That simplifies to 7.5. So the slope of the line is 7.5. We also know that the line goes through the origin (0, 0), which means, according to our data (and any data in the real world) that if you work 0 hours (x) you get 0 pay (y). So the y intercept of the line is 0. The equation, then, in slope-intercept form, is

p = 7.50h, the first choice. This means that the employee makes $7.50 per hour and should probably consider a new job.

8 0

3 years ago