All categories

3 years ago

ASAP!!!!

Mathematics

1 answer:

ELEN [110]3 years ago

3 0

Answer:

The value of x is 45

Step-by-step explanation:

Statement 1: Segment ST is parallel to segment RQ.

Reason: Given

Statement 2: Angle QRS is congruent to angle TSP.

Reason : Corresponding angles formed by parallel lines and their transversal are congruent.

Statement 3: Angle SPT is congruent to angle RPQ.

Reason: Reflexive property of angles

Statement 4: Triangle SPT is similar to triangle RPQ.

Reason: Angle-Angle Similarity Postulate

So, ΔSPT≈ΔRPQ

5. Corresponding sides of similar triangles are in proportion.

$\frac{SP}{PR}=\frac{PT}{PQ}\\\frac{60}{60+x}=\frac{48}{48+36}\\60(48+36)=48(60+x)\\5040=2880+48x\\5040-2880=48x\\2160=48x\\\frac{2160}{48}=x\\45=x$

Hence The value of x is 45

You might be interested in

Miss Robinson and Miss Gibson recorded the hours and distance they drove their results formed ratios presented in the tables Bel

Ludmilka [50]

Where are the tables and what are the ratios?

6 0

3 years ago

Q(x)= 1/2x - 3; q(x) =-4. Find the value of x

Lelu [443]

Answer:

$q(x) =-5$

Step-by-step explanation:

I am solving this using Function Notation.

We are given:

$q(x)= \frac{1}{2}x - 3$

While we are to find:

$q(x) =-4$

In Function Notation, replace all the " $x$ " you see with the value you are given.

So, in this case,

$q(x)= \frac{1}{2}x - 3\\\\=\frac{1}{2}x - 3$

Would become

$q(x)= \frac{1}{2}x - 3\\\\=\frac{1}{2}(-4) - 3$

Now we can solve.

$\frac{1}{2}(-4) - 3$

Use PEMDAS; Parenthesis first;

$\frac{1}{2}(-\frac{4}{1})$

Cross divide: 1 cancels 1, -4 ÷ 2 = -2

Hence, we are left with

$(-2) - 3$

$-5$

Therefore, the value of x is -5

8 0

2 years ago

A local garden contains 1/12 lettuce, 3/12 carrots, 4/12 of corn and the rest red radishes. How much of the garden is radishes?

melamori03 [73]

Answer:

The answer to your question is a) 4/12 b) 5/12

Step-by-step explanation:

Data

Lettuce = 1/12

Carrots = 3/12

Corn = 4/12

Red radishes = ?

The total of the garden is 12/12

Red radishes = 12/12 - 1/12 - 3/12 - 4/12

= 12/12 - 8/12

= 4/12

4/12 of the garden are red radishes.

Corn of lettuce = 1/12 + 4/12

= 5/12

5/12 of the garden are corn or lettuce.

3 0

2 years ago

Find the slope of a line through (4, 5) and (4, -5). Determine if the line is vertical, horizontal, or neither.

oksian1 [2.3K]

Answer:

Its a straight line

Step-by-step explanation:

4 0

3 years ago

The equation of the line that is parallel<br> to 4x+2 and passing through (5,15)

Mila [183]

Answer:

y=4x-5.

Step-by-step explanation:

slop-interception form of the required line is y=kx+b, where k - slop, b - intercept;

1) to find value of k:

if the required line is parallel to the given line, then slop of the given line = slop of the required line, it means k=4 and the required line is y=4x+b;

2) to find the value of 'b':

if to substitute the given coordinates into the equation of the given line, then:

15=4*5+b, b= -5.

3) finally, y=4x-5

8 0

2 years ago