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3 years ago

The points (–4, –3) and (–1, –8) are on a line. Find the intercepts to the nearest tenth.

1 answer:

4 0

The intercepts are the points where the line meets with the x axis and the y axis. First let us find the equation of the line.

Finding slope:

slope=change in y/change in x (y2-y1/x2-x1)

slope=-3-(-8)/-4-(-1)=5/-3=-5/3

Finding y-intercept:

y=mx+b

-8=-5/3(-1)+b

b=-9 2/3

y intercept: (0,-9 2/3)

Equation: y=-5/3x-9 2/3

Since we already have the y intercept let us find the x intercept by plugging 0 in the place of y in the equation.

0=-5/3x-9 2/3

x=29/3x(-3/5)

x=-29/5

x intercept: (-29/5,0)

answers: (0,-9 2/3) and (-29/5,0)

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Marissa bought four bottles of water Each bottle of water is 0.95 cents Write an equation with the same product as the total cos

zysi [14]

Answer: Total cost = Cost of each bottle × Number of bottles

Step-by-step explanation: If each bottle of water Marissa bought cost 0.95cents. This means four bottles will cost = 0.95 + 0.95 + 0.95 + 0.95 = 3.80 cents

This can be written simply as 0.95 × 4 = 3.80 cents

Therefore, a general equation for calculating the total cost of bottle water will be;

Total cost = Cost of each bottle × Number of bottles.

8 0

3 years ago

Recall that the volume of a sphere is given by the formula V = 4/3pi to the 3rd

Kisachek [45]

9514 1404 393

Answer:

1. (256/3)π ft³

2. 33.49 ft³

Step-by-step explanation:

1. Put 4 ft into the formula where r is, then simplify.

V = (4/3)π(4 ft)³ = (256/3)π ft³

2. The radius is half the diameter, so is 2 ft. Put that in the formula, along with the value for π, and do the arithmetic.

V = (4/3)(3.14)(2 ft)³ ≈ 33.49 ft³

4 0

3 years ago

Value of p,q and r if (2^p)*(3^q)*(7^r)=1176

koban [17]

Answer:

p=3 , q=1 , r=2

Step-by-step explanation:

1176=2*2*2*3*7*7

1176=(2^3)*(3^1)*(7^2)

given that 1176 = (2^p)*(3^q)*(7^r)

Comparing Equation 1 & 2

we get p=3 , q=1, r=2

5 0

3 years ago

Using long division, what is the quotient of this expression?<br> X^4+4x^3-5x^2+x-3/x^2+x-3

Paladinen [302]

Answer:

Using long division method the answer is B

Step-by-step explanation:

x²+3x-5+(15x-18)/x²+x-3

7 0

2 years ago

PLEASE HELP 100 POINTS!!!!!!

horrorfan [7]

Answer:

A) See attached for graph.

B) (-3, 0) (0, 0) (18, 0)

C) (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.

Given piecewise function:

$g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}$

Therefore, the function has two definitions:

$g(x)=x^3-9x \quad \textsf{when x is less than 3}$

$g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}$

When <u>graphing</u> piecewise functions:

Use an open circle where the value of x is <u>not included</u> in the interval.
Use a closed circle where the value of x is <u>included</u> in the interval.
Use an arrow to show that the function <u>continues indefinitely</u>.

<u>First piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=(3)^3-9(3)=0 \implies (3,0)$

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

<u>Second piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)$

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the <u>first piece</u> of the function to zero and solve for x:

$\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}$

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the <u>second piece</u> to zero and solve for x:

$\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}$

$\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b$

$\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}$

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation: (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0

2 years ago