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yulyashka [42]
2 years ago
13

{x - 4} " alt="g(x) = \frac{3}{x - 4} " align="absmiddle" class="latex-formula">find the domain, range and zeros/intercepts.The domain would be all real numbers not equal to 4. Right?How do I find the range and intercepts?
Mathematics
1 answer:
liberstina [14]2 years ago
6 0

You are right about the domain

it is all real values of x except 4

So about the range we must make x subject of the formular so we know the values of y in which g(x) is defined

undefined

u

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Noah has $50. He wants to buy a cell phone case for $20 and some accessories. Each accessory costs $8. How many accessories (x)
levacccp [35]

Answer:

Noah can buy 2 accessories.

Step-by-step explanation:

Given:

Money Noah has = $50

Cost of Cell phone case = $20

Cost of each accessory =$8

Amount he wants to be left = $8

So Total Amount he he wants to spend on accessories and Cell phone case will be equal to Money Noah has minus Amount he wants to be left.

framing in equation form we get;

Total Amount he he wants to spend on accessories and Cell phone case = \$50-\$8 =\$42

No we need to find the number of accessories Noah can buy.

Let the number of accessories be 'x'.

Now we can say that;

Cost of Cell phone case plus Cost of each accessory multiplied by number of accessories should be less than or equal to Total Amount he he wants to spend on accessories and Cell phone case.

framing in equation form we get;

20+8x\leq 42

Subtracting both side by 20 we get using Subtraction property of Inequality.

20+8x-20\leq 42-20\\\\8x\leq 22

Now Dividing both side by 8 using Division property of Inequality we get;

\frac{8x}{8}\leq \frac{22}{8}\\\\x\leq 2.75

Now rounding to whole number we get ;

x\leq 2

Hence Noah can buy 2 accessories.

8 0
3 years ago
PLS HELP ME (i will give brainliest) I’m not very smart.
Rufina [12.5K]

Answer:

1) 6(3.14) = 18.84 in

2) 9(2)(3.14) = 56.52 cm

3) 1.5(3.14) = 4.71 ft

3 0
3 years ago
write and show on a number line the set of all the numbers that are less than 0 and greater than (-5)
vodka [1.7K]

Answer:

0 i think................??????

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3 years ago
Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.
wel

Answer:

Ellipse

Step-by-step explanation:

Given the equation

4x^2 +9y^2 =36

Divide this equation by 36:

\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=\dfrac{36}{36}\\ \\ \\\dfrac{x^2}{9}+\dfrac{y^2}{4}=1

The equation of the form

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1

represents an ellipse, so given equation is the equation of the ellipse.

5 0
3 years ago
Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral
Stella [2.4K]

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

l_{AB} = \sqrt{\left (6-4  \right )^{2}+\left (6-1  \right )^{2}} = \sqrt{29}

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

l_{BC} = \sqrt{\left (1-6  \right )^{2}+\left (4-6  \right )^{2}} = \sqrt{29}

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

l_{CD} = \sqrt{\left (-1-1  \right )^{2}+\left (-1-4  \right )^{2}} = \sqrt{29}

The length of side DA, with D = (-1, -1) and A = (1,4)   gives;

l_{DA} = \sqrt{\left (4-(-1)  \right )^{2}+\left (1-(-1)  \right )^{2}} = \sqrt{29}

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

Therefore;

Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

5 0
3 years ago
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