All categories

4 years ago

Solve each quadratic equation. Show your work 15. x2 + 3x = 10

Mathematics

2 answers:

Margarita [4]4 years ago

5 0

X^2+3x-10=0
(x+5)(x-2)=0
x=-5 or x=2
Hope this helps.

OLEGan [10]4 years ago

4 0

X² + 3x = 10

Convert to standard form.
x² + 3x - 10 = 0

factor x² = x * x
factor -10 = 5 * -2

(x + 5) (x - 2) = 0
x(x -2) + 5(x-2) = 0
x² - 2x + 5x - 10 = 0
x² + 3x - 10 = 0

x + 5 = 0   x² + 3x = 10
x = -5 -5² + 3(-5) = 10
25 - 15 = 10
10 = 10

x - 2 = 0 x² + 3x = 10
x = 2 2² + 3(2) = 10
   4 + 6 = 10
   10 = 10

You might be interested in

If h (x) = -5x-7 then what is h (x-1) ?

goldenfox [79]

Answer:

h(x - 1) = -5x - 2

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Terms/Coefficients

Functions

Function Notation

Step-by-step explanation:

Step 1: Define

Identify

h(x) = -5x - 7

Step 2: Find

Substitute in x [Function h(x)]: h(x - 1) = -5(x - 1) - 7
[Distributive Property] Distribute -5: h(x - 1) = -5x + 5 - 7
Combine like terms: h(x - 1) = -5x - 2

6 0

3 years ago

A square pyramid is 6 feet on each side. The height of the pyramid is 4 feet. What is the total area of the pyramid?

Temka [501]

Answer is C, 96 ft squared.

4 0

3 years ago

Read 2 more answers

Calculate volume of hemisphere with radius 3.2 cm

Olin [163]

Answer:

V ≈ 68.63 cm³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = $\frac{4}{3}$ πr³

the volume of a hemisphere is half the volume of a sphere, so

V = $\frac{1}{2}$ × $\frac{4}{3}$ πr³ = $\frac{2}{3}$ πr³ , then

V = $\frac{2}{3}$ π × 3.2³

= $\frac{2}{3}$ π × 32.768

≈ 68.63 cm³ ( to 2 dec. places )

5 0

2 years ago

Determine whether the lines given in each box are parallel, perpendicular, or neither

andrey2020 [161]

Answer/Step-by-sep explanation:

To determine whether the lines given in each box are parallel, perpendicular, or neither, take the following simple steps:

1. Ensure the equations for both lines being compared are in the slope-intercept form, y = mx + b. Where m is the slope.

2. If both lines have the same slope value, m, then both lines are parallel.

3. If the slope of one line is the negative reciprocal of the other, then both lines are perpendicular. That is, x = -1/x.

4. If the slope of both lines are not the same, nor the negative reciprocal of each other, then they are neither parallel nor perpendicular.

1. y = 3x - 7 and y = 3x + 1.

Both have the same slope value of 3. Therefore, they are parallel.

2. ⬜ $y = -\frac{2}{5}x + 3$ and $y = \frac{2}{5}x + 8$

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⅖ and the slope of the other is ⅖. Therefore, they are neither parallel nor perpendicular.⬜

3. $y = -\frac{1}{4}x$ and $y = 4x - 5$

The slope of the first line, ¼, is the negative reciprocal of the slope of the second line, 4.

Therefore, they are perdendicular.

4. 2x + 7y = 28 and 7x - 2y = 4.

Rewrite both equations in the slope-intercept form, y = mx + b.

2x + 7y = 28

7y = -2x + 28

y = -2x/7 + 28/7

y = -²/7 + 4

And

7x - 2y = 4

-2y = -7x + 4

y = -7x/-2 + 4/-2

y = ⁷/2x - 2

The slope of the first line, -²/7, is the negative reciprocal of the slope of the second line, ⁷/2.

Therefore, they are perdendicular.

5.⬜ y = -5x + 1 and x - 5y = 30.

Rewrite the second line equation in the slope-intercept form.

x - 5y = 30

-5y = -x + 30

y = -2x/-5 + 30/-5

y = ⅖x - 6

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -5 and the slope of the other is ⅖. therefore, they are neither parallel nor perpendicular.⬜

6.⬜ 3x + 2y = 8 and 2x + 3y = -12.

Rewrite both line equations in the slope-intercept form.

3x + 2y = 8

2y = -3x + 8

y = -3x/2 + 8/2

y = -³/2x + 4

And

2x + 3y = -12

3y = -2x -12

y = -2x/3 - 12/3

y = -⅔x - 4

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -³/2 and the slope of the other is -⅔ therefore, they are neither parallel nor perpendicular.⬜

7. y = -4x - 1 and 8x + 2y = 14.

Rewrite the equation of the second line in the slope-intercept form.

8x + 2y = 14

2y = -8x + 14

y = -8x/2 + 14/2

y = -4x + 7

Both have the same slope value of -4. Therefore, they are parallel.

8.⬜ x + y = 7 and x - y = 9.

Rewrite the equation of both lines in the slope-intercept form.

x + y = 7

y = -x + 7

And

x - y = 9

-y = -x + 9

y = -x/-1 + 9/-1

y = x - 9

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -1, and the slope of the other is 1, therefore, they are neither parallel nor perpendicular.⬜

9. y = ⅓x + 9 And x - 3y = 3

Rewrite the equation of the second line.

x - 3y = 3

-3y = -x + 3

y = -x/-3 + 3/-3

y = ⅓x - 1

Both have the same slope value of ⅓. Therefore, they are parallel.

10.⬜ 4x + 9y = 18 and y = 4x + 9

Rewrite the equation of the first line.

4x + 9y = 18

9y = -4x + 18

y = -4x/9 + 18/9

y = -⁴/9x + 2

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⁴/9, and the slope of the other is 4, therefore, they are neither parallel nor perpendicular.⬜

11.⬜ 5x - 10y = 20 and y = -2x + 6

Rewrite the equation of the first line.

5x - 10y = 20

-10y = -5x + 20

y = -5x/-10 + 20/-10

y = ²/5x - 2

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is ⅖, and the slope of the other is -2, therefore, they are neither parallel nor perpendicular.⬜

12. -9x + 12y = 24 and y = ¾x - 5

Rewrite the equation of the first line.

-9x + 12y = 24

12y = 9x + 24

y = 9x/12 + 24/12

y = ¾x + 2

Both have the same slope value of ¾. Therefore, they are parallel.

5 0

3 years ago

Which set of values could be from a direct proportion

mr Goodwill [35]

Answer: