MATHEMATICS HIGH SCHOOL

Solve |x + 3| = 7.
A. x= -4
B. x= 10
C. x= 4
D. x= -10

Answers

Answer 1
Answer:

Answer:

C. x= 4

Step-by-step explanation:

|x + 3| = 7

x + 3 = 7

x = 7 - 3

x = 4
Answer 2
Answer:

Answer:

x = 4

Step-by-step explanation:

|x + 3| = 7

=> x + 3 = 7

=> x = 7 - 3

=> x = 4

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Classify triangle ABC by its sides if side AB = 6x, side AC = 4x + 6 and side BC = 8x + 3. The perimeter of triangle ABC is 63. Show all your work.
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Explain how a number and its reciprocal are related

Answers

A number's reciprocal when multiplied by the original form of the number is, and always will be, 1.

The sum of two numbers is 67. The larger number is 4 more than 2 times the smaller. What are the two numbers?a) 23 and 44
b) 21 and 46
c) 19 and 48
d) 17 and 50

Answers

x,y - two numbers (x > y)

(1)    x + y = 67 ⇒ x = 67 - y
(2)    x - 4 = 2y

subtitute (1) to (2)

67 - y - 4 = 2y
63 - y = 2y    |add y to both sides
63 = 3y    |divide both sides by 3
y = 21

subtitute the value of y to (1)

x = 67 - 21 = 46

Answer: 21 and 46.

Find the product. x 3(x 2 5x 1) x 6 5x 4 x 3 x 5 5x 4 x 3 x 5 5x 3 x 3

Answers

x^(3) ( x^(2) +5x+1)= x^(5) +5 x^(4) + x^(3)

PLEASE HELP ASAP!!!!Hugo is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram. He starts by assigning coordinates to the vertices of quadrilateral RSTV and labeling the midpoints of the sides of the quadrilateral as A, B, C, and D. Quadrilateral R S T V in a coordinate plane with vertex R at 0 comma 0, vertex S in the first quadrant at 2 a comma 2b, vertex T also in the first quadrant at 2 c comma 2 d, and vertex V on the positive side of the x-axis at 2 c comma 0. Point A is between points R and S, point B is between points S and T, point C is between points T and V, and point D is between points R and V. Enter the answers, in simplified form, in the boxes to complete the proof. The coordinates of point A are ( , ). The coordinates of point B are ( , ). The coordinates of point C are (2c, d) . The coordinates of point D are (c, 0) . The slope of both AB¯¯¯¯¯ and DC¯¯¯¯¯ is . The slope of both AD¯¯¯¯¯ and BC¯¯¯¯¯ is −bc−a . Because both pairs of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Answers

Answer:

Step-by-step explanation:

R(0,0)

A=((0+2a)/2,(0+2b)/2)=(a,b)

S(2a,2b)

B=((2a+2c)/2,(2b+2d)/2)=(a+c,b+d)

T(2c,2d)

C=((2c+2c)/2,(2d+0)/2)=(2c,d)

V(2c,0)

D=((2c+0)/2,(0+0)/2)=(c,0)

R(0,0)

slope of AB=(b+d-b)/(a+c-a)=d/c

slope of DC=(d-0)/(2c-c)=d/c

slope of AD=(0-b)/(c-a)=-b/(c-a)

slope of BC=(d-b-d)/(2c-a-c)=-b/(c-a)

Which of the following statements is always true of similar polygons?A. Corresponding angles of similar figures have the same measure.

B. The lengths of corresponding sides form equivalent ratios.
C. The lengths of corresponding sides have the same measure.
D. both (a) and (b)

Answers

In this question, there are two correct choices. The corresponding angles of a similar figures have the same measure and the lengths of corresponding sides form equivalent ratios will be the correct choices. 

How do you find the surface area of this figure?

Answers

Answer:

SA=158cm²

Step-by-step explanation:

To find surface area, you find the area for all the surfaces and add them together. Let's start with the red rectangular prism first.

The top has measurements of 5 and 2. The area of that is 10.

The bottom is the same so it's area is also 10 but we don't want to add it since it's not on the surface.

The side facing us has measurements of 4 and 2, the area is 8.

The side opposite to this is the same so it's area is also 8

Now the right face of this shape is 4 and 4 so 16.

The left face will have the same area. It'll also be 16.

The surface area of the red shape is 10+8+8+16+16= 58

Now the orange shape.

The side facing us is 5 and 3 so area=15

The side opposite to this will have the same area.= 15

The right face is also 5 and 3 so 5x3=15

The opposite face to this will also have an area of 15

Now the top face, it's 5 and 5 = 25. We have to subtract the area covered by the red shape. So 25 - 10 = 15

The bottom face's area will be 25.

The surface area of this shape will be : 15+15+15+15+25=100

Now add the areas of both shapes

58+100 = 158

SA=158cm²

Hope this helps :)
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