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1 year ago

What are the domain and range of the function?

Mathematics

1 answer:

kolbaska11 [484]1 year ago

8 0

Answer:

$x$ = - 2/7

Alternate form: - 0.285714

Step-by-step explanation:

1- Substitute f ( x ) = 0

Reorder

f ( $x$ ) = $x$ x 2 - 16 $x$ - 4

2- Collect like terms

0 = 2 $x$ - 16 $x$ - 4

3- Move the variable to the left

0 = - 14 $x$ - 4

4- Divide both sides

14 $x$ = - 4

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Solve:

Misha Larkins [42]

Answer:

convert 3 1/3 to an improper fraction

3*3 = 9

9+1 = 10

10/3

multiply the numerator by 4

(10/3) * 4 = 40/3

40/3 = 13 1/3

5 0

2 years ago

Read 2 more answers

A painter starts with a blank 24-inch by 12-inch piece of rice paper. The painter wants to leave a uniform border x inches wide

ddd [48]

Answer:

a. A = x² - 36x + 288

b. If x = 2; A = 220 in²

Step-by-step explanation:

In this scenario, 'x' represents the width of the border. A "uniform border" means that the border has the same width all around.

The area of the paper that can be painted does not include the border. Since the border is on the original rice paper (not added to it), you subtract 'x' from each side of the rice paper.

The area of a rectangle is A = lw (Area is length times width). <u>Each length and width is reduced by 'x'.</u>

If the original rice paper's area is: 24 X 12, then,

the Area that can be painted is:

A = (24 - x) (12 - x)

A polynomial in standard form means the most expanded version of an expression, ordering the terms (numbers) from greatest to least degree. (The degree of a term is the value of its exponent).

Expand the expression. Multiply the numbers from each bracket in the order FOIL (first, outside, inside last):

A = (24 - x) (12 - x)

= 288 - 24x - 12x + x² Collect like terms (-24x - 12x = -36x)

= 288 - 36x + x² Rearrange ordering greatest to least exponent value

= x² - 36x + 288 Standard form polynomial

The width of the margin is the same thing as the width of the border. Since 'x' is the width of the border,

x = 2

Using either the expanded or factored equation for area of that can be painted, substitute 'x' for 2.

I will use the factored form.

A = (24 - x) (12 - x) Substitute x for 2

= (24 - 2) (12 - 2) Solve inside each bracket first by subtracting

= (22) (10) Multiply

= 220 Area that can be painted

Remember to include the units: 220 in²

Therefore if the margin is 2 inches wide, then the area that can be painted in 220 square inches.

5 0

2 years ago

The intelligence quotient (iq) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15

Mrrafil [7]

<span>0.9818 is the answer </span>

3 0

2 years ago

Evaluate 3 – 24 - 8 + 32

UNO [17]

Answer:

Step-by-step explanation:

Evaluate the calculation from left to right, that is

3 - 24 - 8 + 32

= - 21 - 8 + 32

= - 29 + 32

= 3

6 0

2 years ago

Read 2 more answers

2. The coordinates of the vertices of ABC are A (5, 2), B (2, 4), and C (7, 5). Determine whether ABC is a right triangle.

Amiraneli [1.4K]

Answer:

Part 2) Triangle ABC is a right triangle (see the explanation)

Part 3) Quadrilateral QRST is not a parallelogram (see the explanation)

Step-by-step explanation:

Part 2) we have

A (5, 2), B (2, 4), and C (7, 5)

Plot the figure to better understand the problem

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the length side AB

A (5, 2), B (2, 4)

substitute the values in the formula

$d=\sqrt{(4-2)^{2}+(2-5)^{2}}$

$d=\sqrt{(2)^{2}+(-3)^{2}}$

$d_A_B=\sqrt{13}\ units$

step 2

Find the length side BC

B (2, 4), C (7, 5)

substitute the values in the formula

$d=\sqrt{(5-4)^{2}+(7-2)^{2}}$

$d=\sqrt{(1)^{2}+(5)^{2}}$

$d_B_C=\sqrt{26}\ units$

step 3

Find the length side AC

A (5, 2), C (7, 5)

substitute the values in the formula

$d=\sqrt{(5-2)^{2}+(7-5)^{2}}$

$d=\sqrt{(3)^{2}+(2)^{2}}$

$d_A_C=\sqrt{13}\ units$

step 4

Verify if the triangle ABC is a right triangle

we know that a right triangle must satisfy the Pythagorean Theorem

$BC^2=AB^2+AC^2$

Remember that the hypotenuse is the greater side

substitute the values

$(\sqrt{26})^2=(\sqrt{13})^2+(\sqrt{13})^2$

$26=13+13$

$26=26$ ----> is true

therefore

Triangle ABC is a right triangle

Part 3) we have

Q (5, 1), R (8, 7), S (14, 10) and T (10, 2)

we know that

The opposite sides of a parallelogram are parallel and congruent

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Step 1

Find the length side QR

Q (5, 1), R (8, 7)

substitute in the formula

$d=\sqrt{(7-1)^{2}+(8-5)^{2}}$

$d=\sqrt{(6)^{2}+(3)^{2}}$

$d_Q_R=\sqrt{45}\ units$

Step 2

Find the length side RS

R (8, 7), S (14, 10)

substitute in the formula

$d=\sqrt{(10-7)^{2}+(14-8)^{2}}$

$d=\sqrt{(3)^{2}+(6)^{2}}$

$d_R_S=\sqrt{45}\ units$

Step 3

Find the length side ST

S (14, 10), T (10, 2)

substitute in the formula

$d=\sqrt{(2-10)^{2}+(10-14)^{2}}$

$d=\sqrt{(-8)^{2}+(-4)^{2}}$

$d_S_T=\sqrt{80}\ units$

Step 4

Find the length side QT

Q (5, 1), T (10, 2)

substitute in the formula

$d=\sqrt{(2-1)^{2}+(10-5)^{2}}$

$d=\sqrt{(1)^{2}+(5)^{2}}$

$d_Q_T=\sqrt{26}\ units$

Step 5

Compare the length of the opposite sides

QR and ST

$\sqrt{45}\ units \neq \sqrt{80}\ units$

$d_Q_R \neq d_S_T$

RS and QT

$\sqrt{45}\ units \neq \sqrt{26}\ units$

$d_R_S \neq d_Q_T$

Opposite sides are not congruent

therefore

Quadrilateral QRST is not a parallelogram

5 0

2 years ago