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Anika [276]
3 years ago
10

What value of x satisfies the system of equations {2x+5y=35x=−10−15y? Enter your answer as the correct value for x, like this: 4

2
Mathematics
1 answer:
Nata [24]3 years ago
7 0

Answer:

x = 23

Step-by-step explanation:

2x + 5y = 35 * (-3) ------>  -6x -15y = -105 (A)

x = -10 - 15y -----> x + 15y = -10 (B)

(A) + (B)

-5x = -115

x = 23

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What is the volume of this square pyramid? <br> 1296 cm^3<br> 1620cm^3<br> 3888cm^3<br> 11,664cm^4
vampirchik [111]

\bf \textit{volum of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{18\times 18}{324}\\ h=12 \end{cases}\implies V=\cfrac{1}{3}(324)(12)\implies V=1296

3 0
3 years ago
The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
Frankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft. what will be
ira [324]

The length of his path to the nearest tenth of a foot is 37.7 ft option fourth is correct.

<h3>What is the Pythagoras theorem?</h3>

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have:

Frankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft.

From the Pythagoras theorem:

Perpendicular(P) = 32 ft

Base(B) = 20 ft

H = √(32²+20²)

H = √1424

H = 37.7 ft

Thus, the length of his path to the nearest tenth of a foot is 37.7 ft option fourth is correct.

Learn more about Pythagoras' theorem here:

brainly.com/question/21511305

#SPJ1

5 0
2 years ago
What is the perimeter?
DanielleElmas [232]

Answer:

Step-by-step explanation:

jest mutply it

7 0
3 years ago
Cory made 4,500 g of candy. He saved 1 kg to eat later. He divided the rest of the candy over 7 bowls to
Olenka [21]

Answer: 500 g of candy in each bowl

Step-by-step explanation:

1,000 g = 1Kg

4,500 g - 1,000 g =  3,500 g of candy were divided over 7 bowls:

Each bowl contains = 3,500 g➗7 bowls = 500 g candy/bowl

Answer: 500 g of candy in each bowl

<h2><em>Spymore</em></h2>
4 0
3 years ago
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