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3 years ago

In order for RECT to be a rectangle, what must the value of x be?

Mathematics

1 answer:

Readme [11.4K]3 years ago

6 0

Answer:

x = 21

Step-by-step explanation:

If RECT is a rectangle, each of its interior angles are right angles, 90°. Since ∠RTC is split into two angles, the sum of the two angles must be 90°. (Angles that add to 90° are called complementary angles).

∠RTC = ∠RTE + ∠ETC Formula for complementary angles

90 = 2x + 6 + 42 Substitute the angles

90 = 2x + 48 Combined like terms to simplify

Now isolate "x" to solve

90 - 48 = 2x + 48 - 48 Subtract 48 from both sides

42 = 2x

42/2 = 2x/2 Divide both sides by 2

x = 21

Therefore x is 21.

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Ray has found that his new car gets 31 miles per gallon on the highwayand 26 miles per gallon in the city. He recently drove 285

Mkey [24]

Answer:

$Highway = 155\ miles$

$City = 130\ miles$

Step-by-step explanation:

Given

$Highway = 31mi/gallon$

$City = 26mi/gallon$

$Total\ Miles = 285$

$Total\ Gallons = 10$

Required

Determine the number of miles driven on the highway and on the city

Represent the gallons used on highway with h and on city with c.

So, we have:

$c + h = 10$ ---- gallons used

and

$31h + 26c = 285$ --- distance travelled

In the first equation, make c the subject

$c = 10 - h$

Substitute 10 - h for c in the second equation

$31h + 26c = 285$

$31h + 26(10 - h) = 285$

Open bracket

$31h + 260 - 26h = 285$

Collect like terms

$31h - 26h = 285 - 260$

$5h = 25$

Make h the subject

$h = \frac{25}{5}$

$h = 5$

Substitute 5 for h in $c = 10 - h$

$c = 10 - 5$

$c = 5$

If on the highway, he travels 31 miles per gallon, then his distance on the highway is:

$Highway = 31 * 5$

$Highway = 155\ miles$

If in the highway, he travels 26 miles per gallon, then his distance on the highway is:

$City = 26 * 5$

$City = 130\ miles$

8 0

2 years ago

Set of the equation <br> X+9=26

trapecia [35]

Answer:

Step-by-step explanation:

subtract 9 from 26 and you should get the answer

8 0

3 years ago

Five sevenths times seven thirds

lord [1]

5/7 x 7/3

Multiply the numerators together and the denominators:

(5 x 7) / (7 x 3)

35/21 reduces to 5/3 = 1 2/3

3 0

3 years ago

Fizzbos sells only sandwiches. They offer five choices of bread, five types of meat toppings, four types of cheese and eight veg

sineoko [7]

Answer:

<em>800 possible combinations</em>

Step-by-step explanation:

We can reach the answer by simple logic reasoning. Knowing Fizzbos' sandwiches have one type of bread, one meat, one type of cheese and one vegetable for their sandwiches, we can find the possible combinations like this:

We have 5 choices of bread, there are, of course, 5 different kinds of sandwiches to offer.

We also know there are 5 types of meat toppings which, combined with the 5 possible choices we already have, will make

5*5 possible combinations

Now we consider the 4 types of cheese combined with our previous kinds of sandwiches to get

5*5*4 possible combinations

Finally, we have 8 vegetable toppings, making our final result

5*5*4*8 = 800 possible combinations

5 0

3 years ago

Graph the linear equation by plotting three points. 2y=-3+2

Ksivusya [100]

Answer:

Step-by-step explanation:

Convert 2y=-3x+2 into y=mx+b form

$\frac{2y}{2} =\frac{-3x+2}{2}$

$y=\frac{-3x}{2} +1$

Y intercept is 1, slope is -3/2

Graph looks like this:

3 0

2 years ago