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3 years ago

If the solutions to an equation are 2 and –3, which of the following could be the equation?

Mathematics

2 answers:

vagabundo [1.1K]3 years ago

6 0

For this case we must find an equation, whose solutions are given by:

$x = 2\\x = -3$

Or equivalently:

$(x-2) (x + 3) = 0$

Applying distributive property we have:

$x ^ 2 + 3x-2x-6 = 0\\x ^ 2 + x-6 = 0$

Now, if we multiply both sides of the equation by 2, we have:

$2x ^ 2 + 2x-12 = 0$

Thus, the equation that has the solution $x = 2\ and\ x = -3$ is:

$2x ^ 2 + 2x-12 = 0$

Answer:

$2x ^ 2 + 2x-12 = 0$

Option D

wlad13 [49]3 years ago

4 0

All my work is shown in the image below.

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What is the total volume of this compound shape?

Alex787 [66]

Answer:

This is very easy. First find the volume of the cube, and then add it to the volume of the hemisphere to find the total volume.

The volume of the cube is length x width x height: 8 x 8 x 12 = 768 cm

The volume of the hemisphere is (2/3)πr³ : (2/3)π(4)³ = 134.04 cm

*Radius is 4

Now add: 768 + 134.04 = 902.04 cm

6 0

3 years ago

Q4. The diagram shows a triangle inside a rectangle.

Yanka [14]

The prove to show that the area of the shaded portion is 18x - 30 is as follows: 3x² + 13x - 30 - 3x² + 5x = 18x - 30

<h3>How to find the area of the shaded region?</h3>

The area of the shaded region can be represented as follows:

area of the shaded region = area of rectangle - area of triangle

Therefore,

area of the rectangle = (x + 6)(3x - 5)

area of the rectangle = 3x² - 5x + 18x - 30

area of the rectangle = 3x² + 13x - 30

area of triangle = 1 / 2 × 2x × 3x - 5

area of triangle = 3x² - 5x

Therefore,

area of the shaded portion = 3x² + 13x - 30 - 3x² + 5x

area of the shaded portion = 18x - 30

learn more on area here: brainly.com/question/21208569

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4 0

2 years ago

I’m trying to figure out what the answer is to these questions?

hram777 [196]

To find corresponding angles and sides, you look at the name of the figure and see which one correlates.

QUESTION 6
ABC and DEF
Corresponding Angles-
A,D
B,E
C,F
Corresponding Sides-
AB, DE
BC, EF
AC, DF

QUESTION 7
FGHI and KLMN
Corresponding angles-
F,K
G,L
H,M
I,N
Corresponding Sides-
FG,KL
GH,LM
HI,MN
FI,KN

8-
x=12

9-
y= 25.6

10-
z= 23 1/3

11-
36=k

6 0

3 years ago

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS.

Olenka [21]

The measure of Arc Q P is 96°. We also know that ∠QTP is central angle, then the measure of arc QP is 96°.

Step-by-step explanation:

Step 1

If QS is a circle diameter,

then m∠QTS=180°.

Let x be the measure of angle RTQ: ∠RTQ =x.

so, let ∠RTQ = x

Step 2

According to the question,

∠RTQ = ∠RTS - 12°

⇒ ∠RTS = x + 12°

∴ ∠QTS = ∠RTQ + ∠RTS

= x + x + 12° = 2x + 12° = 180°

⇒ 2x = 168°

⇒ x = 84°

⇒ ∠RTQ = 84°

Step 3

Now,

∵∠QTP and ∠RTS are vertical angles

∴ ∠QTP = 84° + 12° = 96°

As ∠QTP is the central angle, hence the measure of arc QP is 96°

Step 4

The Measure of arc QP = 96°

7 0

3 years ago

Read 2 more answers

Checkpoint Quiz 1 1. Write a formula for finding the area of a parallelogram. le

azamat

Answer:

The formula for area of a parallelogram is either $A=bh$ or $A=\dfrac{d_1d_2}{2}$ .

Step-by-step explanation:

If base and vertical height of a parallelogram are given, then the area of the parallelogram is:

$A=bh$

Where, b is base and h is the vertical height of the parallelogram.

If measures of both diagonals are given, then the area of the parallelogram is:

$A=\dfrac{d_1d_2}{2}$

Where, $d_1,d_2$ are the two diagonals of the parallelogram.

5 0

3 years ago