Mathematics College

B. Are the graphs of y = a|x| and y = |ax| the same when a is negative? Why?

Answers

Answer 1

The absolute value gives always a positive number.

If a is negative, then a|x| is negative and |ax| is positive.

Therefore, the graph of y=a|x| won't be the same as the graph of y=|ax|.

Another way to see it, is by using the property:

Since a is negative, then |a| = -a. So, |ax| = -a|x|, which is clearly different from a|x|.

Related Questions

Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden
treats himself to some chocolates. The number of chocolates remaining in the box t
days after Brayden's birthday can be modeled by the equation C = -3t+ 12. What
is the slope of the equation and what is its interpretation in the context of the
problem?

Answers

Answer:

Step-by-step explanation:

The slope of the function is -3 which reveals the number of chocolates Brayden eats each night.

3.In the figure. What are the coordinates of the image of point B after a translation (x+4, y-7) ?

Answers

Answer:

(5, -5)

Explanation:

The coordinate of Point B is: (1,2)

If we carry out the translation (x+4, y-7) on point B, we have:

[tex]B(1,2)\rightarrow (1+4,2-7)=B^{\prime}(5,-5)[/tex]

The coordinates of the image of point B is (5, -5)

43/1/2 divided by 1/1/4

Answers

When 43/1/2 is divided by 1/1/4 , the value will be 34 4/5.

What is a fraction?

A fraction simply means a numbers that's represented as a/b where a = numerator and b = denominator

In this case, the division of the fraction will be:

43 1/2 ÷ 1 1/4

= 87/2 ÷ 5/4

= 87/2 × 4/5

= 174 / 5

= 34 4/5

This shows the. concept of fractions.

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Alex has a $100 budget to buy food for his birthday
party. Each pizza costs $10 and each soda bottle
costs $3. Alex will buy 7 pizzas.
What is the greatest number of soda bottles Alex can
buy without going over budget?

Answers

If Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles

The total budget = $100

The cost of one pizza = $10

Number of pizza he bought = 7

The total cost of pizza = 7×10 = $70

The remaining money = 100-70

= $30

The cost of one soda bottle = $3

Number of soda bottle can he buy using the remaining money = 30/3

= 10 soda bottles

Hence, if Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles

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In parallelogram ABCD… Justify your answer with the applicable property.

Answers

Solution

For this case we have the following measures:

m <1= x+12

m < 2= 6x -18

We can set up both angles equal:

x +12 = 6x -18

Solving for x we have:

12+18 = 5x

5x = 30

x= 30/5= 6

Then the value of m< 2 is:

m< 2= 6*6 -18= 36-18= 18

the best second answer is:

If a quadrilateral is ||gram the opposite angles are congruent

4(y – 4) = 8 O A. -2 O B. 2 0 C. 4 D. 6

Answers

To find the value of y

4(y – 4) = 8

Divide both-side of the equation by 4

y - 4 = 2

Add 4 to both-side of the equation

y = 2 + 4

y = 6

D is the correct option

The figure shows two right triangles, each with its longest side on the same line. Z 3 X T y 2 R. S 1. Explain how you know the two triangles are similar 2. How long is XY? 3. For each triangle, calculate (vertical side) = (horizontal side). 4. What is the slope of the line? Explain how you know.

Answers

The triangle are similar because the ratio between 2 sides is the same as the ratio between another 2 sides.

The included angle(angle S and Y) are equal( 90 degree)

An electrician charges $25 per hour plus a one-time service fee of $50. Write an equation to
represent the cost, y, he charges for x hours of service. How much would he charge for 3 hours of
service.

Answers

The equation that represents the cost and the charges for the service is y = $25x + $50. And the he charges $125 for 3 hours of service.

Equation:

An equation state that the value of two mathematical expressions is equal.

For example,

2x + 5 = 7

is an equation.

Given,

An electrician charges $25 per hour plus a one-time service fee of $50.

Here we need to find the equation for the given situation and we have also find the charge for the 3 hour of service.

Let us consider the equation of the line y = mx + c, where m represents the constant change and c represents the fixed constant.

While we apply these equation to the given situation we can get the value of

m = $25

And the value of

c = $50.

Therefore, the equation of the situation is

y = $25x + $50.

We have already now that the y represents the cost and the x represents the hour of service.

Now we have to find the service charge for 3 hours,

So we have to apply the value of x as 3 then we get,

=> y = $25 (3) + $50

=> y = $75 + $50

=> y = $125

Therefore, the cost for 3 hours is $125.

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A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?

Answers

A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?

we know that

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

[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]

we have

D(-10, -1), E(-10,6)

substitute the given values in the formula

[tex]\begin{gathered} d=\sqrt[]{(6+1)^2+(-10+10)^2} \\ d=\sqrt[]{(7)^2+(0)^2} \\ d=\sqrt[]{49} \\ d=7\text{ units} \end{gathered}[/tex]

therefore

the distance DE is 7 units

3t^2-2t+5; find the company revenues last month if t=-1

Answers

Given revenue function is:

[tex]R=3t^2-2t+5[/tex]

Now revenue at t=(-1)

[tex]\begin{gathered} R=3(-1)^2-2(-1)+5 \\ R=3+2+5 \\ R=10 \end{gathered}[/tex]

So the revenue at t=-1 is 10.

The cost of 5 gallons of ice cream has a varianceof 36 with a mean of 36 dollars during the summer.What is the probability that the samplean would differ from the true mean by more than 0.6 dollars if a sample of 107 5-gallon pails is randomly selected? Roundyour answer to four decimal places.

Answers

Given:

[tex]\begin{gathered} Variance=36 \\ mean=36 \end{gathered}[/tex]

To Determine: The samplean would differ from the true mean by more than 0.6 dollars

Solution

Please note that standard deviation is the square root of variance

[tex]\begin{gathered} SD=\sqrt{Variance} \\ SD=Standard-deviation \\ SD=\sqrt{36}=6 \end{gathered}[/tex][tex]\begin{gathered} S.E=\frac{SD}{\sqrt{n}} \\ S.E=Standard-Error \\ n=107 \\ S.E=\frac{6}{\sqrt{107}}=0.5800 \end{gathered}[/tex]

Please note that Z is the number of SE(standard error away from the mean. Therefore

[tex]\begin{gathered} Z=\frac{0.6}{0.5800} \\ Z=1.0345 \end{gathered}[/tex][tex]P(|Z|<1.0345)[/tex][tex]P(|Z|<1.0345)=1-P(Z<-1.0345)=1-0.1515=0.8485[/tex]

Hence the probability is 0.8485

Evaluate when n=5 4n

Answers

We are given an expression "4n"

The question says to evaluate this expression when n = 5

Here, evaluation simply means, finding the value of "4n" when n = 5. This is a simple problem of substitution. By substitution I mean replacing every occurence of n in the given expression by 5. This would be done as follows:

Given expression = 4n

Note that here 4 is being multiplied to n.

Replacing n by 5, we get the result as:

[tex]4\text{ }\times\text{ 5 = 20 }[/tex]

From here, we can conclude that the value of expression "4n" for n = 5 will be 20.

Consider the polynomial function q ( x ) = − 2 x 8 + 5 x 6 − 3 x 5 + 50

Answers

The function has an end behaviour of x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞

How to determine the end behaviour of the function?

The equation of the polynomial function is given as

q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50

To determine the end behaviour of the function, we calculate

q(∞) and q(-∞)

So, we have

q(∞) = -2(∞)⁸ + 5(∞)⁶ - 3(∞)⁵ + 50

Evaluate the exponents

q(∞) = -2(∞) + 5(∞) - 3(∞) + 50

This gives

q(∞) = -∞ + ∞ - ∞ + 50

q(∞) = -∞

Also, we have

q(-∞) = -2(-∞)⁸ + 5(-∞)⁶ - 3(-∞)⁵ + 50

Evaluate the exponents

q(-∞) = -2(∞) + 5(∞) - 3(-∞) + 50

This gives

q(-∞) = -∞ + ∞ + ∞ + 50

q(-∞) = -∞

Hence, the end behaviour of the graph is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞

Answers

We have the following triangles:

And we need to determine if they are similar by identifying the similarity statement.

To determine that similarity statement, we can proceed as follows:

1. Check the measures of the internal angles of the triangles. We need to remember that the sum of the internal angles of a triangle is 180 degrees. Then we have:

2. We can see that to find the angles in the first triangle, EFG, and in the second triangle, JKL, we have that the sum of the three angles must be 180 degrees, and we obtained the other angles as follows:

[tex]\begin{gathered} \text{ Triangle EFG}\rightarrow50+70+x=180 \\ \\ x=180-(50+70)=180-120=60 \\ \\ \text{ Triangle JKL}\rightarrow50+60+y=180 \\ \\ y=180-(50+60)=180-110=70 \end{gathered}[/tex]

3. Then we can redraw the triangles as follows:

4. Now, since we can see that, at least, two of the angles of the triangles are congruent (then the third one is also congruent, that is, has the same measure), we also have that to prove that if two triangles are similar it is sufficient that two of the corresponding angles of one triangle are congruent to the two corresponding angles of the other triangle, and this is known as the Angle-Angle method for proving similar triangles, then we can conclude that:

Triangle EFG is similar to triangle JKL by the Angle-Angle method.

Therefore, in summary, we have that:

Triangle EFG is similar to Triangle JKL by Angle-Angle similarity

[tex]\text{ Triangle EFG \textasciitilde Triangle JKL by Angle-Angle similarity}[/tex]

[Last option]

A loaf of bread is cut into slices size. Some of the loaf us used in a recipe and 4/8 of the loaf is used to make a sandwich. The remaining 2/8 of the loaf is put into the remaining

Answers

We have

[tex]\frac{7}{10}-\frac{2}{10}[/tex]

in order to know what expression is equivalent, we need to solve and simplify the expression above

[tex]\frac{7}{10}-\frac{2}{10}=\frac{5}{10}=\frac{1}{2}[/tex]

Then we will solve the next expressions in order to find the equivalent expression

[tex]undefined[/tex]

As Mars revolves around the sun, it travels at a rate of approximately 15 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mars travel in 3 minutes? Do not round your answers. Rate:mi/minDistance traveled in 3 minutes:mi

Answers

We have:

1 minute = 60 seconds

Then, 15 miles per second to miles per minute is:

[tex]15\frac{miles}{second}\times\frac{60\text{ seconds}}{1\text{ minute}}=15\times60=900\frac{miles}{minute}[/tex]

Next, Distance traveled in 3 minutes is given by:

[tex]distance=900\times3=2700\text{ miles}[/tex]

Answer:

rate = 900 mi/min

distance = 2700 miles

helpppppp plssssssssssssssssssss

Answers

Answer:

No.

Step-by-step explanation:

Pre-Solving

We are given the following inequality:

[tex]76 < 5-\frac{136}{s}[/tex]

And we want to know if s=2 is a solution, meaning if s is 2, will the inequality still be true?

Solving

We can substitute 2 for s in the inequality to test it.

Replace s with 2.

[tex]76 < 5-\frac{136}{2}[/tex]

First, let's divide 136 by 2.

136/2 = 68

The inequality is now:

76 < 5 - 68

Subtract 68 from 5.

76 < -63

The inequality reads "76 is less than -63", which is a false statement (76 is positive, -63 is negative, and positive numbers are greater than negative numbers).

Ergo, s = 2 is not a solution to the inequality.

Find the length of the missing side. Round answers to the nearest tenth if necessary. * S sva Your answer

Answers

Question:

Solution:

Notice that the angle between the sides of the square is 90 degrees:

Therefore, the angle of the vertex of the triangle measures 45 degrees:

thus, we obtain the following right triangle:

Now, apply the following trigonometric identity:

[tex]\cos \text{ (45) = }\frac{s}{5\sqrt[]{2}}[/tex]

solving for s, we get:

[tex]s\text{ = cos(45) . 5 }\sqrt[]{2}\text{ = 5}[/tex]

then, we can conclude that the correct answer is:

[tex]s\text{ = 5}[/tex]

what is 3 to the negative 8th power divided by 3 to the negative 4th power

Answers

Answer

Answer = 3⁻⁴ = (1/3⁴) = (1/81)

The answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.

Explanation

The law of indices is usually applied when questions that involve same numbers with (different or the same) powers are considered.

When a number carrying a particular power is divided by the same number also carrying another power, the result is that same number raised to the power of the difference between the power of the numerator and the power of the denominator.

It'll be clearer in practice now.

[tex]\frac{3^{-8}}{3^{-4}}=3^{-8\text{ - (-4)}}=3^{-8+4}=3^{-4}[/tex]

Hence, the answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.

Hope this Helps!!!

im confused on premtier

Answers

we have to calculate the perimeter of the semicircle which radius is 16 mm

[tex]P_{sc}=\frac{2\pi\cdot r}{2}=\pi\cdot r=16\pi\approx50.26\operatorname{mm}[/tex]

Now we have to add the outter sides of the triangle

[tex]P=20+20+50.26=90.26\operatorname{mm}[/tex]

Assuming a fixed hourly pay rate, how much would an employee earn for working 4 hours based on this wage table? Hourly Pay Table Hours Worked 2 Money Earned $12.00 $24.00 $36.00 ? A. $36.00 B. $45.00 C. $64.00 D. $48.00

Answers

We have the following table

hour pay

1 12

2 24

3 36

4 ?

It seems that for each hour we work, we end up earning $12. Then, we know that if we work 3 hours we earn 36. So, if we work one more hour (4) we should add 12 to what we earn for working 3 hours. That is

[tex]12+36\text{ = 48 }[/tex]

So we aren 48 for working 4 hours.

Which type of statically graphic uses bars to describe the data ?Dot plot Box plot Histogram

Answers

Answer:

HISTOGRAM

Explanations:

Data are reported using visuals to make reporting easier and ease the understanding of the audience.

Some of the graphic used in statistics to report data and make inference include:

• Bar charts

• line charts

• Dot plot

• Box plot

• Histogram etc.

Bar charts and histograms make use of bars to report data. This charts are important to detect outliers that may be present in our data.

We can therefore conclude that the type of statically graphic that uses bars to describe data is the HISTOGRAM

Suzanne is designing a garden for the Gateway Botanical Center. She used a scale of 1 : 600 to make the drawing below. 5 cm 15 cm What is the actual area of the garden, in square meters? (1m = 100 cm)

Answers

The given scale is 1:600.

The dimensions of the drawing are 5 by 15.

We just have to multiply each dimension by 600.

[tex]\begin{gathered} 5\times600=3000 \\ 15\times600=9000 \end{gathered}[/tex]

So, the dimensions of the actual area are 3,000 cm and 9,000 cm. But, we know that 1 meter equals 100 centimeters, let's transform.

[tex]\begin{gathered} 3000cm\cdot\frac{1m}{100\operatorname{cm}}=30m \\ 9000\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}}=90m \end{gathered}[/tex]

Then, we multiply the dimensions to find the area.

[tex]A=30m\times90m=2700m^2[/tex]Hence, the actual area is 2,700 square meters.

Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 190 pounds of blended coffee beans selling for
$4.55 per pound. She plans to do this by blending together a high-quality bean costing $5.50 per pound and a cheaper
bean at $3.50 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee
bean she should blend.
She should blend lbs of high quality beans.
(Round to the nearest pound as needed.)

Answers

By solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.

What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the total pounds Sarah needs to blend:

Let the number of pounds by 'x'.

Now form an equation as:

5.50x + 3.50x = 190 × 4.55

Then, solve equation for 'x' as follows:

5.50x + 3.50x = 190 × 4.559x = 864.5x = 864.5/9x = 96 pounds

Therefore, by solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.

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A delivery company uses robot dogs to deliver packages in anoffice building. The graph shows how long a robot dog can operatetor each hour its battery is charged.Pickany two points on the line. Find the slope of the line betweenInesetwo points. Can you find another pair of points on the linehat gives you a different slope?

Answers

Given:

Let the two points from the graph are

[tex](1,30)\text{ and (}2,60)[/tex][tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{60-30}{2-1} \\ =30 \end{gathered}[/tex]

No, its impossible to find the another pair of points to give a different slope.

Only one slope from a line.

Michael wants to save $55,000.00 for a down payment on a home. How much will he need to invest in anaccount with 8.5% APR, compounding daily, in order to reach his goal in 3 years?

Answers

Step 1. The information that we have is:

The final amount that Michael wants to save is:

[tex]A=55,000[/tex]

We will call that amount A.

The annual percentage rate of the investment, which we will label as r, is:

[tex]r=8.5[/tex]

We will need this annual percentage rate represented as a decimal number, therefore, we divide it by 100:

[tex]\begin{gathered} r=8.5/100 \\ r=0.085 \end{gathered}[/tex]

The time of the investment, t, is 3 years:

[tex]t=3[/tex]

And it is compounded daily, let n be the number of times of compounding in a year:

[tex]n=365[/tex]

Step 2. We need to find the initial amount of the investment, which will be called P or principal.

The formula we will use to find it is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Step 3. Substituting the known values:

[tex]55,000=P(1+\frac{0.085}{365})^{(365)(3)}[/tex]

From this equation, we need to solve the operations and solve for P, the principal amount of the investment.

Step 4. Simplifying the equation:

[tex]55,000=P(1+0.0002328767)^{1095}[/tex]

Continue simplifying:

[tex]\begin{gathered} 55,000=P(1.0002328767)^{1,095} \\ 55,000=P(1.2904233) \end{gathered}[/tex]

Then, we solve for P:

[tex]\begin{gathered} \frac{55,000}{1.2904233}=P \\ 42,621.6726=P \end{gathered}[/tex]

Rounding to the nearest cent (2 decimal places) The amount that he needs to invest is $42,621.67

Answer: $42,621.67

I’ve been stuck for a while and it logged me out:(

Answers

Solution

A polynomial is a function in the form of ; where n is non- negative integers which is known as the degree of polynomial. from this definition, it is clear that only option (2) √2 x -1 , is polynomial. because coefficient of variables ; √2, -1 are real number and also power of variable is non-negative integer.

I have selected the options , the ones I have ticked are polynomials, while the one cancelled are none polynomials:

Find the equation of a line passing through (-7,9) with a slope of -5.

Answers

y=-5x-26

Explanation

the equation of a line can be written as:

[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ and\text{ b is the y-intercept} \end{gathered}[/tex]

now, when we have the slope and a passing point, we need to use the slope-point formula , it says

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope and \lparen x}_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]

Step 1

a)let

[tex]\begin{gathered} slope=-5 \\ (x_1,y_1)=(-7,9) \end{gathered}[/tex]

b) now replace in the slope-point formula and solve for y

[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ replace \\ y-9=-5(x-(-7)) \\ y-9=-5(x+7) \\ y-9=-5x-35 \\ add\text{ 9 in both sides} \\ y-9+9=-5x-35+9 \\ y=-5x-26 \end{gathered}[/tex]

therefore, the equaton of the line is

y=-5x-26

I hope this helps you

Cameron has 21 coins in his pocket, all of which are dimes and quarters. If the total value of his change is315 cents, how many dimes and how many quarters does he have?

Answers

Given:

Cameron has 21 coins in his pocket, all of which are dimes and quarters.

Let, x be the number of quarters and y be the number of dimes.

The total cost is 315 cents.

The equations are,

[tex]\begin{gathered} x+y=21\ldots\ldots\ldots\text{.}(1) \\ 25x+10y=315\ldots.\ldots\ldots....\ldots(2) \end{gathered}[/tex]

Solve the equation,

[tex]\begin{gathered} x+y=21 \\ x=21-y\text{ put this value in equation (2)} \\ 25(21-y)+10y=315 \\ 525-25y+10y=315 \\ 525-315=15y \\ y=\frac{210}{15} \\ y=14 \end{gathered}[/tex]

Put the value of y in equation (1),

[tex]\begin{gathered} x+y=21 \\ x+14=21 \\ x=21-14 \\ x=7 \end{gathered}[/tex]

Thus, the number of quarters are 7 and dimes are 14 .

Joe earned 2,100$. He spent 1/5 on rent and 1/4 on food. How much money did he have left?

Answers

The amount of money that Joe has left is $1155

How to calculate the amount of money left ?

Joe earned $2100

He spent 1/5 of the money on rent

1/5 × 2100

= 420

$420 was spent on rent

He spent 1/4 of the money on food

= 1/4 × 2100

= 525

$525 was spent on food

The amount of money left can be calculated as follows

Total amount spent = 525 + 420

= 945

Amount left= 2100 - 945

= 1155

Hence Joe has $1155 left