If five pounds of potatoes cost $3.45, then 2 lb cost $.89.

Answers

Answer 1

Answer: if this a true or false question, that is false you will see that 2 lbs of potatos cost $1.38 (:

Answer 2

Answer: False. $3.45 divided by 5 times two equals $1.38 not $.89

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A train travels with a constant speed of 108 km/h. How long will it take to travel a distance of 270 kilometers? PLEASE HELLLLLLPPPP THERE BRAINLIEST
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What is the oblique asymptote of the function f(x) = the quantity x squared plus 5x plus 6 over the quantity x plus 4?

Answers

Answer:

$x+1$

Step-by-step explanation:

A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.

We are given a function:

$f(x)=(x^2+5x+6)/(x+4)$

Since in the given function the polynomial in the numerator is a higher degree than the polynomial in the denominator.

So, now to find oblique asymptote we will divide the numerator by the denominator

So, on dividing we get :

$f(x)=(x^2+5x+6)/(x+4)=x+1+\frac2{x+4}$ j

Now, As $x\to\pm\infty$ the remainder term disappears

So the oblique asymptote is the line $y=x+1$

Thus, the oblique asymptote of the function $f(x)=(x^2+5x+6)/(x+4)$ is $x+1$

$f(x)=(x^2+5x+6)/(x+4)=x+1+\frac2{x+4}$

As $x\to\pm\infty$ , the remainder term disappears, so the oblique asymptote is the line $y=x+1$ .

Solve for x 8/9x= 32

Answers

The solution to the given equation is 36.

The given equation is 8/9 x=32.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 8x=32×9

x=(32×9)/8

x=4×9

x=36

Therefore, the solution to the given equation is 36.

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8/9x*9=32*9 8/x = 288 8/8x = 288/8 1/x = 35 X=1/35 is the answer

To determine the appropriate landing speed of an airplane, the formula D = .1x 2 − 3x + 22 is used, where x is the initial landing speed in feet per second and D is the distance needed in feet. If the landing speed is too fast, the pilot may run out of runway; if the speed is too slow, the plane may stall. What is the appropriate landing speed if the runway is 800 feet long? Show all of your work or explain how you came up with your solution

Answers

$800=0.1x^2-3x+22\n0.1x^2-3x-778=0\n\Delta=(-3)^2-4\cdot0.1\cdot(-778)=9+3112=3121\n√(\Delta)=√(3121)\nx_1=(-(-3)-√(3121))/(2\cdot0.1)=(3-√(3121))/(0.2)=15-5√(3121)\approx-264.3\nx_2=(-(-3)+√(3121))/(2\cdot0.1)=(3+√(3121))/(0.2)=15+5√(3121)\approx294.3$

Approx. 294.3 ft/s

Your new job guarantees you an eight percent raise for each year with the company. If your initial salary is $42,200, write an equation to model your salary after t years

Answers

initial salary is $42,200

eight percent raise for each year = 1.08

salary after t years

equation :

Y(t) = $42,200 x (1.08)^t

$42,000
× 0.08
$3,360
+42,000
= $45,360

Henri bought 3 jars of spaghetti sauce. He used a coupon that reduced the cost of each jar by $0.75. If he paid $6.72 altogether, what was the regular price?

Answers

Answer: $8.97

Step-by-step explanation:

he bought three jars and lowered the price by 75 cents for each, so multiply $0.75 by three

$0.75 * 3 = $2.25

so henri saved $2.25 in total

we can add that to what he paid to find the original cost

$6.72 + $2.25 = $8.97

so the original price was $8.97 :)

Graph y = 5x and y = log5x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. Explain also.

Answers

Answer:

1) For $y=5x$

A) Domain= $(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]$

B) Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

C) y-intercept = 0

D) Asymptote= No asymptote

2) For $y=log_5x$

A) Domain=Domain= $(0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]$

B) Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

C) y-intercept = None

D) Vertical Asymptote: x=0

Step-by-step explanation:

Given : $y=5x$ and $y=log_5x$

Refer the graph attached.

1) In equation (1) $y=5x$

→The domain is the set of all possible values in which function is defined.

y=5x is a linear polynomial defined on all real numbers.

Domain= $(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]$

→Range is the set of all values that function takes.

It also include all real numbers.

Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

→y-intercept- Value of y at the point where the line crosses the y axis.

put x=0 in equation y=5x we get, y=0

Therefore, y-intercept = 0 (We can see in the graph also)

→An asymptote is a line that a curve approaches, but never touches.

Asymptote= No asymptote

2) Now in equation (2) $y=log_5x$

Domain= $(0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]$

because log function is not defined in negative.

Range= $(-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]$

y-intercept - None

Vertical Asymptote: x=0

A) Domain= (-∞, ∞) for all x

B) Range= (-∞, ∞) for all y

C) y-intercept = 0

D) Asymptote= No asymptote

A) Domain=(0, ∞) for all x > 0

B) Range= (-∞, ∞) for all y

C) y-intercept = None

D) Vertical Asymptote: x=0

Here, we have,

Function 1: y = 5x

Domain: The domain of this function is all real numbers because there are no restrictions on the values that x can take.

Range: The range of this function is also all real numbers because for every value of x, we can find a corresponding y value by multiplying it by 5.

Y-intercept: To find the y-intercept, we set x = 0 and solve for y. Substituting x = 0 into the equation, we get y = 5(0) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: There are no asymptotes in this linear function.

Function 2: y = log₅x

Domain: The domain of this function is all positive real numbers because the logarithm function is only defined for positive values of x.

Range: The range of this function is all real numbers because the logarithm function can produce any real number output.

Y-intercept: To find the y-intercept, we set x = 1 and solve for y. Substituting x = 1 into the equation, we get y = log₅(1) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: The logarithmic function has a vertical asymptote at x = 0 because the logarithm is undefined for x ≤ 0. Additionally, there is no horizontal asymptote.

When plotting these functions on the same set of axes, we will observe that the graph of y = 5x is a straight line passing through the origin (0, 0) with a slope of 5.

The graph of y = log₅x will appear as a curve that starts at the point (1, 0) and approaches the vertical asymptote x = 0 as x approaches zero.

The two graphs will intersect at the point (1, 0) because log₅1 = 0.

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