Find the area of a triangle bounded by the
y
axis, the line
f
(
x
)
=
4
−
1
5
x
, and the line perpendicular to
f
(
x
)
that passes through the origin.

The equation of line passing that has a slope of One-half and passes through point (2, –3) is y = 0.5x - 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The equation of line passing that has a slope of One-half and passes through point (2, –3) is:

y - (-3) = (1/2)(x - 2)

y + 3 = 0.5x - 1

y = 0.5x - 4

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Based on the fact that the data for the average CO₂ over the whole year was smoother than the daily and monthly level, the term for the phenomenon is called Smoothing.

Smoothing refers to a process in statistics where the messier points of a data distribution is removed. In other words, the data points that give the data set a varied distribution are removed so that the data set appears smoother.

There are several methods to engage in smoothing but most of them use averaging over a longer period of time. They would for instance, use the averages of a period over a month or weekly and convert it to an annual measure like the scatterplot of CO₂ for the year.

In conclusion, the fact that the average CO₂ scatterplot for the year was smoothly than monthly or daily is due to smoothing.

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The value of x in the similar triangles is x = 3.375

The triangles represent the given parameter

On the triangle, we have the following corresponding sides

AB to BC and AD to DE

This means that

AB : BC = AD : DE

Express as fractions

So, we have

AB/BC = AD/DE

Substitute the known values in the above equation

x/3 = x + 9/11

This gives

11x = 3x + 27

So, we have

8x =27

Divide

x = 3.375

Hence, the value of x is x = 3.375

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According to the given function,

Domain = [tex]\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)[/tex]

Vertical Asymptote = 4

Horizontal Asymptote = 0

X - intercept = No x - intercepts

Y - intercept = 1/4

Domain:

The  the domain of a function referred as the set of inputs accepted by the function

Given,

The function is,

[tex]f(x)=\frac{x-2}{x^2+2x-8}[/tex]

Here we need to find the domain, vertical asymptote, horizontal asymptote,  x - intercept, and y-intercept.

To find the domain and intercepts, we have to plot the graph for the given function.

So, the graph of the function is attached below. It can be drawn using the graphing calculator.

As per the graph,

Domain = [tex]\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)[/tex]

And the values of

x - intercept = No x-intercepts

y - intercept = 1/4

Now, the vertical asymptote is calculated as,

The line x=L is a vertical asymptote of the function f(x), if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x = -4

Then,

[tex]\lim_{x \to -4^+} \frac{1}{x + 4}=\infty[/tex]

Since the limit is infinite, then x=−4 is a vertical asymptote.

And the horizontal asymptote is,

Line y=L is a horizontal asymptote of the function y=f(x), if either '

[tex]\lim_{x \to \infty} f{\left(x \right)}=L[/tex] or [tex]\lim_{x \to -\infty} f{\left(x \right)}=L[/tex]  and L is finite.

When we calculate the limits:

[tex]\lim_{x \to \infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0\\\\\lim_{x \to -\infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0[/tex]

Thus, the horizontal asymptote is y=0.

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The first step we need to do is to convert the measures from inches to feet (12 inches is 1 foot):

8 inches = 8/12 feet = 0.667 feet

6 inches = 6/12 feet = 0.5 feet

So the measures are 12.667 ft and 14.5 ft.

Now, to find the area of the rectangular living room, we just need to multiply these measures:

Since we expect a waste of 10%, we need to increase this area by 10%, that is, we multiply it by 110% or 1.1:

Since she cannot buy part of a square yard, we need to round up our answer (if we round down, the amount of carpet will not be enough). So rouding up, she will have to buy 203 in2 of carpet.

[tex](x + \frac{1}{3} ) + (x + \frac{1}{5} ) = 1 \\ x + x + \frac{1}{3} + \frac{1}{5} = 1 \\ 2x(15) + \frac{1}{3} (15) + \frac{1}{5} (15) = 1(15) \\ 30x + 5 + 3 = 15 \\ 30x = 15 - 5 - 3 \\ 30x = 7 \\ \frac{30x}{30} = \frac{7}{30} \\ x = \frac{7}{30} [/tex]

ATTACHED IS THE SOLUTION

If f(x) = x^5 + 4x - 5,  is divided by x - 3  the remainder is 220.

What is a remainder ?

In mathematics, the term "remnant" refers to the amount that is "left over" after performing a calculation. In mathematics, the integer that is left over after dividing two integers to produce an integer quotient is known as the residual (integer division). In algebra of polynomials, the "remainder" is the polynomial that is left over after dividing one polynomial by another. The operation that yields such a remainder when a dividend and a divisor are both present is the modulo operation.

How are functions divided?

Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2580\\ P=\textit{original amount deposited}\dotfill & \$2400\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 2580=2400[1+(\frac{r}{100})(1)] \implies \cfrac{2580}{2400}=1+\cfrac{r}{100}\implies \cfrac{43}{40}\implies \cfrac{100+r}{100} \\\\\\ \cfrac{4300}{40}=100+r\implies \cfrac{215}{2}=100+r\implies \cfrac{215}{2}-100=r\implies \boxed{\stackrel{\%}{7.5}=r}[/tex]

Answer:

7.5%

Step-by-step explanation:

Answer:

[tex]x + 53 + 86 = 63 \\53 - 86 = 33[/tex]

Based on the rate that the team is rescuing people per hour, the total number of people that the team can rescue in another two hours is 6 people.

First, find the rate at which people are being rescued by the search and rescue team per hour.

The rate of people rescued is:
= Number of people rescued / Number of hours

= 15  / 5

= 3 people per hour

The number of people rescued in 2 hours is:

= Number of hours x People rescued per hour

= 2 x 3

= 6 people

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Answer:

The Convention of 1818 was a treaty between the United States and Britain that set the 49th parallel as the boundary between British North America and the US across the West.Forty-Ninth ParallelCutting on the 49th parallel, on the right bank of the Moyie River, looking west, 1860.(courtesy North American Boundary Commission)The Convention of 1818 was a treaty between the United States and Britain that set the 49th parallel of latitude as the boundary between British North America and the US across the West. This remains the boundary today between the two nations.

hope that helps! Have a good day

48.50 U.S. dollars = 281 Egyptian pounds

What is a dollar?

The United States dollar (symbol: $; code: USD; often abbreviated US$ or U.S. Dollar to differentiate it from other dollar-denominated currencies; known colloquially as the dollar, U.S. dollar, American dollar, or buck) is the official currency of the United States and numerous other nations. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, split it into 100 cents, and permitted the minting of coins denominated in dollars and cents. Federal Reserve Notes, generally known as greenbacks owing to their predominately green hue, are the currency of the United States.

Given, 1 U.S. dollar = 5.8 Egyptian pounds

so, 48.50 U.S. dollars = 5.8 x 48.50 = 281.30 Egyptian pounds

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ANSWER

The graph of y = sin θ shifted to the left by π/2 units

EXPLANATION

This is the graph of y = sin θ shifted to the left π units. In function notation, this shift is represented by adding π to the variable: y = sin (θ + π).

Also, we know that the graph of y = cos θ is like the graph of y = sin θ but shifted π/2 units to the left. So, if we shift the graph of y = cos θ π/2 units to the left, we get the given graph.

Therefore, the only description that does not match the graph is the graph of y = sin θ shifted to the left by π/2 units.

Answer:

1.) -4

2.) 3/5 and 6/10 are both equal to 0.6

Step-by-step explanation:

1.) 16(1/4 - 1/2)

For this one you can either distribute the 16 and solve or just subtract the fractions and solve.  I like the first method personally:

16/4 - 16/8

4 - 8

-4

2.) Fractions can be looked at as dividing the top (numerator) by the bottom (denominator).  If we put each of the answer choices into our calculator and divide, we get 3/5 and 6/10.  Note that 2/3 = 0.66, but that is not the same as 0.6.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +8}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=1\implies x+8=2\implies \boxed{x=-6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=4\implies y+7=8\implies \boxed{y=1}[/tex]

Answer:

B

Step-by-step explanation:

SOLUTION:

Step 1:

In the question, we are considering the equation:

Step 2:

The details of the solution are as follows:

OCONCLUSION:

The final answer is:

Expressing the final answer in decimal, we have that:

Answer:

x = a/2 + 9/2

Step-by-step explanation:

Solve for x:

x^2 - 18 x + 81 = (x - a)^2

Expand out terms of the right hand side:

x^2 - 18 x + 81 = x^2 - 2 a x + a^2

Subtract x^2 - 2 a x + a^2 from both sides:

2 a x - 18 x - a^2 + 81 = 0

Collect in terms of x:

81 - a^2 + x (2 a - 18) = 0

Factor constant terms from the left hand side:

-(a - 9) (-2 x + a + 9) = 0

Divide both sides by -a + 9:

-2 x + a + 9 = 0

Subtract a + 9 from both sides:

-2 x = -a - 9

Divide both sides by -2:

Answer: x = a/2 + 9/2

Given

s: silk flowers

r: ribbon

f: foam

v: vase

Procedure

s = 3r

r = 2f

v = 3f

s: silk flowers $24

r: ribbon $ 8

f: foam $ 4

v: vase $12

Answer:

0.25.2

Step-by-step explanation:

1.51/2

So,halves

0.25.2

the radius of of circle V is 2

XZ is the diameter of circle Y (bigger circle)

UW is the diameter of circle V (smaller circle)

We are to find the radius of the smaller circle. To find the radius, we use the formula relating diamter to radius:

Diameter = 2(radius)

UW = 4, diameter =4

4 = 2(radius)

radius = 4/2

radius = 2

Hence, the radius of of circle V is 2

Answers:

x = 108

y = 111/5 = 22.2

========================================================

Explanation:

The angles 72 and x form a 180 degree straight line.

72+x = 180

x = 180-72

x = 108

Angles x and 5y-3 are congruent corresponding angles assuming the lines pointing to the northwest are parallel

5y - 3 = x

5y - 3 = 108

5y = 108+3

5y = 111

y = 111/5

y = 22.2

Answer:

x = 108°

y = 22.2°

Step-by-step explanation:

Angles on a straight line sum to 180°.

[tex]\implies 72^{\circ} + x = 180^{\circ}[/tex]

[tex]\implies 72^{\circ} + x - 72^{\circ} = 180^{\circ} - 72^{\circ}[/tex]

[tex]\implies x = 108^{\circ}[/tex]

Corresponding Angles Theorem

When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.

Assuming the two lines that appear parallel in the given diagram are parallel:

[tex]\implies (5y - 3)^{\circ} = x^{\circ}[/tex]

[tex]\implies 5y - 3 = 108[/tex]

[tex]\implies 5y - 3 + 3 = 108 + 3[/tex]

[tex]\implies 5y = 111[/tex]

[tex]\implies 5y \div 5 = 111 \div 5[/tex]

[tex]\implies y = 22.2^{\circ}[/tex]

Answer:

x = 3 ± 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

x² - 6x - 41 = 0 ( add 41 to both sides )

x² - 6x = 41

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 41 + 9

(x - 3)² = 50 ( take square root of both sides )

x - 3 = ± [tex]\sqrt{50}[/tex] = ± 5[tex]\sqrt{2}[/tex] ( add 3 to both sides )

x = 3 ± 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

a distance on a coordinate grid is always the Hypotenuse of a right-angled triangle with the differences of the x coordinates and the y coordinates as the legs.

so, per Pythagoras

distance² = (x diff)² + (y diff)²

we have here a distance 17. 17² = 289.

to get integer coordinates the lengths of the legs must be integer numbers.

what 2 squared integer numbers can be added to get 289 ?

I found after subtracting 4, 9, 16, 25, 36, 49 and finally 64 (the squares of 2, 3, 4, 5, 6, 7, 8) that

289 - 64 = 225, which is also a square number (15²).

so, we get the possible integer coordinates of Q to be

(-4 + 8, 7 + 15) = (4, 22)

in this case the shorter leg has the length 8, and the longer leg the length 15.

the shorter leg is in this case horizontal, because it is the x coordinate difference. and Q is again as described (4, 22).

if we make the shorter leg vertical, that means it is the y coordinate difference. and Q is then

(-4 + 15, 7 + 8) = (11, 15)

The ellipse has 2 axis, the minor and the major axis,

The major axis is denoted in blue color and the minor axis in purple color. By comparing our equation with the general equation of the ellipse:

where the lenght of the major axis is given by

Fron the given equation, we can note that

Therefore, the lenght of the major axis is 36 feet. Therefore, the maximum distance between any two persons is 36 feet corresponding to the major axis, which is option 3 from top to bottom

The Vertex form of y= (x+9/2)² - 89/4 hence, vertex=(-9/2 , -89/4),

Given,y=x²+9x-2

Take out the leading coefficient.

y=(x²+9×x)-2

Complete the square.

y = (x² +(2×9/2) × x × (9/2)²) + (-2-(9/2)²)

Express the function in vertex form.

y=(x+9/2)² - 89/4

Hence the vertex form is y=(x+9/2)² - 89/4

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The  graphed piecewise function is conformed of two lines, it can be written as::

Notice that we have two lines that conform the piecewise function.

The linear equation in the left passes through the points (-8, 8) and (-1, 1), so the slope is:

m = (1 - 8)/(-1 + 8) = -7/7 = -1

Then it is something like:

y = -x + b

To find the value of b we use the point (-1, 1), we will get:

1 = -(-1) + b

1 - 1 = b

0 = b

Then the first line is:

y = -x   if x < -1.

The second line passes through points (-1, -3) and (4, 2), then the slope is:

m = (2 + 3)/(4 + 1) = 1

And we can see that it intercepts the y-axis at y = -1, so the linear equation here is:

y = x - 1

Finally, the piecewise function is:

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Answer:

You can follow these steps to multiply a fraction by a whole number:

Write the whole number as a fraction with a denominator of 1.

Multiply the numerators.

Multiply the denominators.

Simplify. , if needed. If your answer is greater than 1, you may want to write your answer as a mixed number.

There are 11 red counters left so the difference is −11.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Add some zero pairs because need to remove 7 yellow counters}$.

Since you need to remove 7 yellow counters, add 7 zero pairs.

When you remove yellow counters, there are 11 red counters left so the difference is:

−4−7=−11

​There are 4 red counters so you should add 7 zero pairs in order to eliminate 7 yellow counters. There are 11 red counters left so the difference is −11.

Therefore, there are 11 red counters left so the difference is −11.

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