Mathematics College

If g is an odd function, which pair of points could be found on the graph of g?
A) (-1,16) and (1,16)
B) (3,-5) and (-3,-5)
C) (4,28) and (4,-28)
D) (-2,32) and (2,-32)

Answers

Answer 1
An odd function is such that -f(x)=f(-x). D is the only option that satisfies this. f(2)=-32 and f(-2)=-f(2)=32.
Answer 2

Answer:

D is the only option that satisfies this. f(x)=-32 and f(-2)=-f(x)=32.

Step-by-step explanation:


Related Questions

John has painted 4/5 of his house the next day he painted 2/3 of what he had left what fraction of the house is left to paint

Answers

a whole, is whatever/whatever.

so... he painted 4/5 of the house first..... now the whole house is 5/5,  from 4/5 to 5/5 is just 1/5, so 1/5 was left for the next day.

the next day, he painted only 2/3 of what was left, what is 2/3 of 1/5?  well is just their product.

[tex]\bf \cfrac{2}{3}\cdot \cfrac{1}{5}\implies \cfrac{2}{15}\impliedby \textit{only painted the next day the slacker} \\\\\\ \textit{so he has painted in total }\cfrac{4}{5}+\cfrac{2}{15}\impliedby \textit{LCD of 15}\implies \cfrac{12+2}{15} \\\\\\ \stackrel{painted}{\cfrac{14}{15}}\qquad \qquad \stackrel{whole}{\cfrac{15}{15}}-\stackrel{painted}{\cfrac{14}{15}}\implies \stackrel{unpainted}{\cfrac{1}{15}}[/tex]

A certain airplane has two independent alternators to provide electrical power. the probability that a given alternator will fail on a one-hour flight is 0.019. (a) what is the probability that both will fail? (round your answer to 4 decimal places.) probability (b) what is the probability that neither will fail? (round your answer to 4 decimal places.) probability (c) what is the probability that at least one fails? (round your answer to 4 decimal places.) probability referencesebook & resources

Answers

The probability that both alternators fail is approximately 0.0004, the probability that neither fails is approximately 0.9612, and the probability that at least one fails is approximately 0.0388, all rounded to four decimal places.

(a) The probability that both Alternator will fail is calculated by multiplying the probabilities of each failing:
P(Both Fail) = P(Alternator 1 Fails) x P(Alternator 2 Fails) = 0.019 x 0.019 ≈ 0.000361 = 0.0004 (rounded to four decimal places).

(b) The probability that an alternator does not fail is 1 minus the probability that it fails.
P(Neither Fail) = (1 - P(Alternator Fails))^2 = (1 - 0.019)^2 ≈ 0.9612 (rounded to four decimal places).

(c) To find the probability of at least one alternator failing, we subtract the probability of neither failing from 1:
P(At Least One Fails) = 1 - P(Neither Fail) = 1 - 0.9612 ≈ 0.0388 (rounded to four decimal places)

Find three distinct fractions between -7/8 and -4/5

Answers

first off,  you'd want to put both fractions with the same denominator, and we simply do so by multiplying each other by the other's denominator.

[tex]\bf -\cfrac{7\cdot 5}{8\cdot 5}\implies -\cfrac{35}{40}\qquad \qquad\qquad \qquad -\cfrac{4\cdot 8}{5\cdot 8}\implies -\cfrac{32}{40} \\\\\\ \textit{since there's no enough room for three fractions there,}\\\\ \textit{let's multiply each by 2, to make room for three fractions}[/tex]

[tex]\bf -\cfrac{35\cdot 2}{40\cdot 2}\implies -\cfrac{70}{80}\qquad \qquad \qquad \qquad -\cfrac{32\cdot 2}{4\cdot 20}\implies -\cfrac{64}{80} \\\\\\ \boxed{-\cfrac{70}{80}}\qquad\qquad -\cfrac{67}{80}\qquad -\cfrac{66}{80}\qquad -\cfrac{65}{80}\qquad\qquad \boxed{-\cfrac{64}{80}}[/tex]

Solve the simultaneous equations
5x-4y=19
x+2y=8

Answers

the answer are x= 5 and y = 3/2
So to solve for x and y you need to add the two equations together, and to do this when you add them either the x or the y need to cross out.

For this equation we’re going to multiply the bottom equation by 2 so that the y’s will cancel out when we ad the equations together so that we can solve for x

5x-4y=19
2(x+2y=8)

Distribute the 2

5x-4y=19
2x+4y=16

Next add the two equations together

7x=35

As you can see the y was cancelled out. Now divide each side by 7 to solve for x

x=5

Now take this answer and plug it back into either equation to solve for y. I am going to plug it into the second equation, but you can choose either

x+2y=8

Replace x with its value, 5

5+2y=8

Subtract 5 from each side

2y=3

Divide each side by 2

y=3/2 (or 1.5)

ANSWER:

x = 5

y = 3/2 (or 1.5)

Of all the rectangles with a perimeter of 168 feet, find the dimension of the one with the largest area

Answers

The rectangle with the largest area with a given perimeter will be a square - so the sides will be equal. So we need to find length of side, L, such that 4*L=168. L = 168/4 L=42. So the dimensions of the rectangle that maximizes the area with a perimiter of 168 feet are: 42 feet by 24 feet.

Final answer:

The largest area for a rectangle with a fixed perimeter of 168 feet is achieved by a square, and the dimensions of that square are 42 feet by 42 feet.

Explanation:

To find the dimensions of a rectangle with the largest area given a fixed perimeter, we need to understand that the rectangle with the largest area for a given perimeter is a square.

In this problem, the perimeter is 168 feet, which can be expressed by the formula 2l + 2w = 168, where l is the length and w is the width of the rectangle. Knowing that a square has all four sides equal, we simply divide the perimeter by 4 to get the side length, which gives us l = w = 168/4 = 42 feet.

Therefore, the dimensions of the rectangle with the largest area, which in this case is a square, are 42 feet by 42 feet.

What is 2x-4y=20 for y

Answers

okay so you need to get the y by itself

2x - 4y = 20

subtract the 2x over

-4y = -2x + 20

divide everything by -4

y = 1/2x - 5        <-------   this is your answer


The shadow of a vertical tower is 50 m long when the angle of elevation of the sun is 35°. find the height of the tower. © k12 inc. 2. an airplane is flying 12,330 feet above level ground. the angle of depression from the plane to the base of a building is 11°. how far must the plane fly horizontally before it is directly over the building?

Answers

1.  To find the shadow of the tower, you must calculate the tangent of 35. Tan. (35) = x/ 50. X= tan (35) (50) = 35. The tower is 35 m.

2. To find how far the plane must fly, you must calculate the tangent of 11. Tan. (11) = 12,330 / x. X = 12,330/ tan (11). X = 63,432. The plane must fly 63,432 feet before it is directly over the building.

Hope this helps.

What is 1.5 x 10^-1 in standard form?

Answers

Here is your answer:

Its scientific notation:

Its negative so your going to the left:

1.5×10^-1
=0.015

Answer:

the answer is .15

Step-by-step explanation:

THe cost of a hamburger is $2.50. Each additional hamburger cost $2.00. Sully wrote this explicit rule to explain the sequence of costs: f(n) = 2 + 2.5(n-1). Using the rule, he found the cost of 12 hamburgers to be 29.50. Is this number correct?

Answers

Answer:

Yes, the number is correct.

Step-by-step explanation:

The cost of a hamburger is $2.50.

Each additional hamburger cost $2.00.

Sully wrote this explicit rule to explain the sequence of costs:

[tex]f(n) = 2+2.5(n-1)[/tex]

Using the rule, he found the cost of 12 hamburgers to be 29.50.

Lets check by putting n = 12.

[tex]f(12) = 2+2.5(12-1)[/tex]

= [tex]2+2.5(11)[/tex]

=  [tex]2+27.5 [/tex]

= $29.50

So, yes Sully is correct.

please help me with this

Answers

So basically what you want to do is put the number on the left into the variable slot on the right, and solve the equation.

I'll do the first chart as an example. 

The equation is n + 6.

So taking the first number, 4, you can just put it in as n,

or 4 + 6.

Then the output would be 10.

Then 8 + 6 = 14

12 + 6 = 18

16 + 6 = 22

20 + 6 = 26

24 + 6 = 30

And you can complete the rest of the charts by doing this.

Hope this helped :D

The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.

Answers

If you've started pre-calculus, then you know that the derivative of  h(t)
is zero where h(t)  is maximum.

The derivative is            h'(t) = -32 t  +  96 .

At the maximum ...        h'(t) = 0

                                       32 t = 96 sec

                                           t  =  3 sec . 
___________________________________________

If you haven't had any calculus yet, then you don't know how to
take a derivative, and you don't know what it's good for anyway.

In that case, the question GIVES you the maximum height.
Just write it in place of  h(t), then solve the quadratic equation
and find out what  't'  must be at that height.

                                       150 ft = -16 t²  +  96  t  +  6 

Subtract 150ft from each side:    -16t²  +  96t  -  144  =  0 .

Before you attack that, you can divide each side by  -16,
making it a lot easier to handle:

                                                         t²  -  6t  +  9  =  0

I'm sure you can run with that equation now and solve it.    
The solution is the time after launch when the object reaches 150 ft.
It's 3 seconds.  
(Funny how the two widely different methods lead to the same answer.)

The answer is from AL2006

Salespeople make an average of $1,000 per week. There are nine salespeople. What would the ninth person need to earn for the mean to be $1,000 if the other eight salespeople earned $550, $600, $600, $800, $950, $950, $1,000, and $1,100?

Answers

all numbers equal 6550
(6550+x)/9=1000
6550+x=9000
x=2450
Final answer:

To get an average earnings of $1,000 for all nine salespeople, the ninth salesperson needs to earn $2,450.

Explanation:

The subject of this question is mathematics, specifically statistics, and it involves the concept of 'mean' or 'average'. To find out what the ninth person needs to earn to keep the average earn of $1,000, we first need to calculate the total earnings of all nine people. Since the average earnings of a salesperson is $1,000, we multiply $1,000 by 9, which gives us $9,000. Then we need to subtract the sum of the earnings of the first eight salespeople from $9,000 to find out the earnings of the ninth person.  

Here is the breakdown with the given figures:

The sum of the earnings of the first eight salespeople is: $550 + $600 + $600 + $800 + $950 + $950 + $1,000 + $1,100 = $6,550Subtract this from the total ($9,000): $9,000 - $6,550 = $2,450

So, the ninth person would need to earn $2,450 for the average earnings to remain at $1,000.

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Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3). Question 1 options: The rate of change is 3, and the y -intercept is –6. The rate of change is –3, and the y -intercept is 18. The rate of change is −1/3 and the y intercept is 7 1/3 The rate of change is 1/3 and the y intercept is 4 2/3

Answers

First of all, the rate of change is simply the slope. You can find the slope by dividing the y values of the given points over the x values to get a slope of -3. Then you can use the point-slope formula to find your y-intercept. It should be (0,18). So, to answer your question it should be the second choice.

The savings account offering which of these APRs and compounding periods offers the best APY?
4.0784% compounded monthly
4.0798% compounded semiannually
4.0730% compounded daily

Answers

[tex]\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~\textit{4.0784\% compounded monthly}\\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0784\%\to \frac{4.0784}{100}\to &0.040784\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12 \end{cases} \\\\\\ \left(1+\frac{0.040784}{12}\right)^{12}-1\\\\ -------------------------------\\\\ ~~~~~~~~~~~~\textit{4.0798\% compounded semiannually}\\\\ [/tex]

[tex]\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2 \end{cases} \\\\\\ \left(1+\frac{0.040798}{2}\right)^{2}-1\\\\ -------------------------------\\\\ [/tex]

[tex]\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0730\%\to \frac{4.0730}{100}\to &0.040730\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\to &365 \end{cases} \\\\\\ \left(1+\frac{0.040730}{365}\right)^{365}-1[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

The formula is = [tex](1+\frac{r}{n})^{n}-1[/tex]

r = rate of interest

n = number of times its compounded

1. 4.0784% compounded monthly

here n = 12

[tex](1+\frac{0.040784}{12})^{12} -1[/tex] = 1.0403-1 = 0.0403

2. 4.0798% compounded semiannually

here n = 2

[tex](1+\frac{0.040798}{12})^{2} -1[/tex] = 1.0066-1 = 0.0066

3. 4.0730% compounded daily

here n = 365

[tex](1+\frac{0.040730}{12})^{365}[/tex] = 3.328-1 = 2.328

Find the area of the surface. the part of the cylinder y^2+z^2=9 that lies above the rectangle with vertices (0,0),(4,0),(0,2), and (4,2)

Answers

Final answer:

To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

Explanation:

To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.

numbers in order from least to greatest. -5.25, 1.002, -5.09

Answers

-5.25, -5.09, 1.002

hopes this help please mark me as brainliest. :)

Robert can swim the first 50 meters of a race in 1 minute. Then he slows down by 12 seconds for each of the next 50 meters of a race. How long will it take Robert to swim a 400 meter race?

Answers

Final answer:

It takes Robert 13 minutes and 36 seconds to complete a 400 meter swimming race when he swims the first 50 meters in 1 minute and slows down by 12 seconds for each subsequent 50 meters.

Explanation:

In this mathematical problem, Robert swims the first 50 meters in 1 minute. He slows down by 12 seconds for each subsequent 50 meters of the race. The total distance Robert needs to swim is 400 meters. The 400 meters is split into eight 50 meter increments.

For the first increment, it takes Robert 1 minute (or 60 seconds). For the next seven increments, Robert swims each in 12 seconds slower than the previous increment.

Therefore, the total time in seconds for Robert to complete the 400 meters swimming race is:

60 + 72 + 84 + 96 + 108 + 120 + 132 + 144 = 816 seconds

This is equivalent to 13 minutes and 36 seconds.

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whats the slope of (0,1) and (2,7)

Answers

7-1/2-0=6/2 the slope would be 3/1
The slope formula is y2-y1/x2-x1=m. You have to use the points given to you respectively.
7-1/2-0 or 1-7/0-2, the answer will equal 3 in either form as long as the y-coordinates are on the top and the x-coordinates are on the bottom. 

A rocket is launched with an initial velocity of 360 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds. h(t)=‒10t2 + 360t Which statement is true?
A. The rockets maximum height is 324 feet.
B. The rockets maximum height is 3240 feet.
C. In the interval from 9 seconds to 18 seconds, the rocket is descending.
D. The rocket hits the ground in 18 seconds.

Answers

the answer for this question is d 
hope it helps

Cours hero a simple random sample of 64 8th graders at a large suburban middle school indicated that 89% of them are involved with some type of after school activity. find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.
a.[0.799, 0.981]
b.[0.699, 0.931]
c.[0.849, 0.854]
d.[0.799, 0.781]
e.[0.719, 0.981] f) none of the above

Answers

Final answer:

Using the formula for the confidence interval of a proportion, and after calculating standard error and margin of error, the 98% confidence interval for the proportion of 8th graders involved in after school activities is [0.799, 0.981]. Therefore, option a is correct.

Explanation:

To find the 98% confidence interval for the proportion of 8th graders involved in some type of after school activity, we can use the formula for the confidence interval of a proportion:

CI = ± z * √((p*(1-p))/n), where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the confidence level.

In this case, we have p = 0.89 (since 89% of the sample is involved in after school activities), n = 64, and for a 98% confidence interval, the z-score (from z-tables or statistical software) is approximately 2.33.

First, let's calculate the standard error (SE): SE = √((0.89*(1-0.89))/64) = √((0.89*0.11)/64) = √(0.0989/64) = 0.0392.

Next, calculate the margin of error (ME): ME = z * SE = 2.33 * 0.0392 = 0.09136.

Now we can calculate the confidence interval: the lower limit is p - ME = 0.89 - 0.09136 = 0.79864 and the upper limit is p + ME = 0.89 + 0.09136 = 0.98136.

After rounding to three decimal places, the 98% confidence interval for the proportion is [0.799, 0.981]. Hence, option a is correct.

Trina's employer purchased a health insurance plan that cost $550 per month Trina pays $85 toward the plan each month what is the annual value of the employer's contribution

Answers

$ 5580.00 this isn't the correct answer from apex

The annual value of the employer's contribution towards Trina's health insurance plan is $5,580.

Here, we have to find the annual value of the employer's contribution, we need to determine how much the employer pays towards the health insurance plan in one month.

Trina's employer purchased a health insurance plan that costs $550 per month, and Trina pays $85 toward the plan each month.

Therefore, the employer's contribution is the difference between the total cost of the plan and what Trina pays:

Employer's contribution = Total cost of the plan - Trina's contribution

Employer's contribution = $550 - $85

Employer's contribution = $465 per month

Now, to find the annual value of the employer's contribution, we multiply the monthly contribution by 12 (since there are 12 months in a year):

Annual employer's contribution = $465 * 12

Annual employer's contribution = $5,580

So, the annual value of the employer's contribution towards Trina's health insurance plan is $5,580.

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Use the distributive property in two different ways to find the product of 127 and 32.

Answers

1.)   127(30+2) = 3810+254=4064

2.) 32(100+20+7)= 3200+640+224=4064

Answer and explanation:

Use the distributive property in two different ways to find the product of 127 and 32.

Distributive property says that,

[tex]a(b+c)=ab+ac[/tex]

We have to find product of 127 and 32,

1) Split 127 as 100+27

[tex]127\times32=(100+27)\times 32[/tex]

Apply distributive property,

[tex]127\times32=100\times 32+27\times 32[/tex]

[tex]127\times32=3200+864[/tex]

[tex]127\times32=4064[/tex]

2) Split 32 as 30+2

[tex]127\times32=127\times (30+2)[/tex]

Apply distributive property,

[tex]127\times32=127\times 30+127\times 2[/tex]

[tex]127\times32=3810+254[/tex]

[tex]127\times32=4064[/tex]

Tony and some friends went to the movies. They bought 4 drinks and 2 tubs of popcorn and spent a total of $32.50 on the food. Each drink cost $3.50 less than a tub of popcorn. Define a variable. Write and equation that can be used to find the cost of one tub of popcorn.

Answers

1 tub of popcorn = t
1 drink = t - 3.5

4(t - 3.5) + 2t = $32.50
4t - 14 + 2t = 32.5
6t = 32.5 + 14
6t = 46.5
t = 46.5 / 6
t = $7.75

"THIS IS A 90 POINT QUESTION"
A) F IS A INCREASING ON THE INTERVAL X < 0
B) F IS A DECREASING ON THE INTERVAL X < 0
C) F IS A INCREASING ON THE INTERVAL 0 < X < 1
D) F IS A DECREASING ON THE INTERVAL 0 < X < 1
E) F IS A INCREASING ON THE INTERVAL 1 < X < 3
F) F IS A DECREASING ON THE INTERVAL 1 < X < 3
G) F IS A INCREASING ON THE INTERVAL X > 3
H) F IS A DECREASING ON THE INTERVAL X > 3
"SELECT ALL THAT APPLY"

Answers

that would be letter F and letter B
F) F IS A DECREASING ON THE INTERVAL 1 < X < 3

A) F IS A INCREASING ON THE INTERVAL X < 0 

hope this helps

Which expression shows how to multiply 5 times 381 by using place value and expanded form

Answers

5 * 1 + 5 * 80 + 5 * 300

A major league baseball pitcher throws a pitch that follows these parametric equations:

x(t) = 143t
y(t) = –16t2 + 5t + 5.
Recall that the speed of the baseball at time t is

s(t)=√ [x '(t)]2 + [y ' (t)]2 ft/sec.

What is the speed of the baseball (in mph) when it passes over homeplate?

Answers

97.67 mph The distance between the pitches plate and homeplate is 60.5 ft. So the time t at which the ball passes over home plate will be 60.5 = 143t 0.423 = t Now calculate the first derivative of each equation. So x(t) = 143t x'(t) = 143 y(t) = -16t^2 + 5t + 5 y'(t) = -32t + 5 So at 0.423 seconds, the respective velocities will be x'(0.423) = 143 y'(0.423) = -32 * 0.423 + 5 = -13.536 + 5 = -8.536 And the speed will be sqrt(143^2 + (-8.536)^2) = sqrt(20449 + 72.8633) = sqrt(20521.86) = 143.2545 ft/s Now convert from ft/s to mile/hour 143.2545 ft/s * 3600 s/hour / 5280 = 97.67 mile/hour = 97.67 mph

The speed of the baseball when it passes over the home plate is 97.67 mph.

Given :

[tex]x(t) = 143t[/tex]    ---- (1)[tex]y(t) = -16t^2+5t+5[/tex]    ---- (2)The distance between the pitcher's plate and the home plate is 60.5 ft.

Differentiate the function x(t) and y(t) with respect to t.

[tex]x'(t)=143[/tex]

[tex]y'(t)= -32t+5[/tex]   ---- (3)

Now, put the value of x(t) in equation (1).

60.5 = 143t

t = 0.423 sec

Now, put the value of t in equation (3).

[tex]y'(t) = -32(0.423)+5=-8.536[/tex]

Now, [tex]s(t) = \sqrt{(x'(t))^2+(y'(t))^2}[/tex]

[tex]s(t)=\sqrt{143^2+(-8.536)^2}[/tex]

[tex]\rm s(t)=\sqrt{20521.8633} = 143.2545\;ft/sec[/tex]

[tex]\rm s(t) = 97.67 mph[/tex]

Therefore, the speed of the baseball when it passes over the home plate is 97.67 mph.

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Two worded maths questions. Even if you know one answer it would help! Please also give working out if possible.

Answers

Answer:

675 litres 80 mL

Step-by-step explanation:

1. The total amount of oil in the two tanks at the start is ...

  total oil = n + (n +150) + 0 = 2n+150 . . . . litres

The amount of oil in tank C at the end is 1/3 this amount, or

  oil in tank C = (total oil)/3 = (2n+150)/3 . . . . litres

The amount pumped into tank C was 500 litres, so we have ...

  (2n +150)/3 = 500

  2n +150 = 1500 . . . . . . multiply by 3

  2n = 1350 . . . . . . . . . . . subtract 150

  1350/2 = n = 675 . . . . . divide by the coefficient of n

___

2. Let x represent the amount remaining in container A. Then 4x is the amount in tank B. Before the transfer, the amount in each container was the same, so ...

  x +120 = 4x -120 . . . . . A had 120 more than remains; B had 120 less

  240 = 3x . . . . . . . . add 120-x

  240/3 = x = 80 . . . divide by the coefficient of x

The amount of liquid left in container A is 80 mL.

Given: 2x + 11 = 15 Prove: x = 2 Statements Reason 1. 2x + 11 = 15 1. Given 2. 2x = 4 2. 3. x = 2 3. Division Property of Equalit

Answers

2x + 11 = 15 ⇒  Given

2x + 11 - 11 = 15 - 11 ⇒ Subtracting 11 from both sides, this is the Property of Equality

2x = 4 ⇒ Carried on from the previous line of working out

2x ÷ 2 = 4 ÷ 2 ⇒ Divide both sides by 2, this is the property of division equality

x = 2 ⇒ Proved as required

David is playing a trivia game where he gains points for correct answers and loses points for incorrect answers. At the start of round 3 his score is −1500 points. During round 3 he answered five 1000 point questions correctly and three 500 points questions incorrectly. What is his score at the end of round 3?
A) −2000
B) −500
C) 2000
D) 3500

Answers

start of round 3....score is -1500
he answered 5 one thousand point questions....5 * 1000 = 5000
so he now has -1500 + 5000 = 3500
he answered 3 five hundred point question incorrectly...3 * -500 = -1500
3500 + (-1500) = 3500 - 1500 = 2000

so he ended up with 2000

Answer:

2000 points

Step-by-step explanation:

Topic: Substraction, Addition and Products

You have to organize the problem, as you can see

at Start of Round 3 David Has: - 1500

During Round 3:

5 Questions: 1000 each correctly

so 5 x 1000 = 5000

3 Questions: - 500 each incorrectly

so 3 x -500 = -1500

at the End of Round 3:

Starting: -1500

During Round 3: 5000 - 1500 = 3500

the end of round 3: -1500 + 3500 = 2000

Find the distance between the points given. (2, 5) and (6, 8) √(37) 5 √(22)

Answers

The answer is given by Pythagoras’ Theorem. √((8-5)²+(6-2)²)=√(9+16)=√25=5, answer option 2.

Answer:  The correct option is (B) 5.

Step-by-step explanation:  We are given to find the distance between the points (2, 5) and (6, 8).

We will be using the following formula :

DISTANCE FORMULA :  The distance between the points (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points (2, 5) and (6, 8) is given by

[tex]D\\\\=\sqrt{(6-2)^2+(8-5)^2}\\\\=\sqrt{4^2+3^2}\\\\=\sqrt{16+9}\\\\=\sqrt{25}\\\\=5.[/tex]

Thus, the required distance between the given points is 5 units.

Option (B) is CORRECT.

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