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3 years ago

Solve for x:

Mathematics

1 answer:

spayn [35]3 years ago

7 0

Answer: A. -14. x=-14 and -14=x. *The answer should be the negative sign.*

Step-by-step explanation:

subtraction property of equality is subtracting the same number from both sides of an equation does not change the equation.

switch sides of an equation.

x+19=5

subtract by 19 both sides of an equation.

x+19-19=5-19

simplify.

19-5=14

x=-14 and -14=x

Hope this helps!

Thanks!

Have a great day!

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PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

hichkok12 [17]

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD = $\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8$ units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = $\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4$

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

$Slope = \frac{y_2-y_1}{x_2-x_1}$

$Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2$

Similarly,

$Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2$

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

If k > 1, then the image is an enlargement.

if 0<k< 1, then the image is a reduction.

If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

$(x, y) \rightarrow (kx , ky)$

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

$(-2, 0) \rightarrow (-4k , 0)$

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

$k = \frac{1}{2}$

∴ The Scale factor is, $k = \frac{1}{2}$

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

6 0

3 years ago

Help please asap

padilas [110]

These are 2 questions and 2 answers:

1. Question 1: The area of a rectangular carpet is given by the trinomial 5x^2 - 3x - 14. What are the possible dimensions of the carpet? Use factoring.

Answer: 5x^2 -3x -14

Explanation:

You might probe the different pairs of factors given in the answer choices to check wich product is equal to the oirginal polynomial or you can factor from zero.

I will show you how to factor that polynomial from zero:

1) given: 5x^2 - 3x - 14

2) multiply and divide by the leading coefficient =>

5 [5x^2 - 3x -14 ]
----------------------
 5

3) Enter the the factor 5 inside the parenthesis:

5.5x^2 - 5.3x - 5.14
--------------------------
 5

4) rearrange conviniently to show (5x) as a common factir of the first two terms

(5x)^2 - 3(5x) - 70
--------------------------
 5

5) factor the numerator using 5x as common term of the two binomials:

(5x ) ( 5x ) <----> open the parenthesis
(5x - ) (5x + ) <-----> include the signs
(5x - 10) (5x + 7) <---> two numbers that add up - 3 and their product is - 70

=>

(5x - 10)(5x + 7)
---------------------
 5

6) divide (5x - 10) by 5 => x - 2

7) factored expression

(x - 2) (5x + 7)

8) Conclusion: the answer is the option B. (5x + 7) and (x - 2)

2. Question 2. The area of a rectangular barnyard is given by the trinomial 6x^2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring

Answer: option C. (2x + 5)(3x - 4)

Explanation:

The procedure is the same of the question 1.

1) given: 6x^2 + 7x - 20

2) multiply numerator and denominator by 6 and rearrange to show (6x) as common factor ot the first two terms =>

(6x)^2 + 7(6x) - 120
--------------------------
 6
3) factor the numerador using 6x as common factor ot two binomials, and simplify:

(6x + )(6x - )
(6x + )(6x - )
(6x + 15) (6x - 8)

=>

(6x + 15)(6x -8)
---------------------
 6

(6x + 15)(6x - 8)
---------------------- =
 3.2

(6x + 15) (6x - 8)
------------- . ------------ =
 3 2

(2x + 5)(3x - 4)

4) answer: option C. (2x + 5)(3x - 4)

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3 years ago

What happens to F(x) when x is a very large negative number?

Anuta_ua [19.1K]

Essentially the question is answering itself here > F(x) is very large negative number.

7 0

3 years ago

A small bag of flavor weighed 13 ounces. A large bag was 5 percent heavier.How much does the large bag weigh?

Novay_Z [31]

13+5=18
The large bag would be 18 because you have to add 5 more ounces than 13

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3 years ago

Part of a tiling design is shown. The center is a regular hexagon. A square is on each side of the hexagon, and an equilateral t

VMariaS [17]

1,119.6 in. the answer is c my diddle.

Find the area of the hexagon which is 259.81

Find the area of the squares which is (6)100

Find the area of the triangles which was (6)43.3

259.81 + 600 + 259.8

519.6 + 600 = 1119.6

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3 years ago