The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the
rectangle is y= x(10- x). The y value of the vertex gives the
value of the
of the rectangle.

Answers

Answer 1

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

[tex]y=x\,(10-x)=10x-x^2[/tex]

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

[tex]y=ax^2+bx+c[/tex]

is given by the formula:

[tex]x_{vertex}=-\frac{b}{2\,a}[/tex]

which in our case gives:

[tex]x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5[/tex]

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

[tex]y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25[/tex]


Related Questions

solve for x
please help !!

Answers

Answer:

34

Step-by-step explanation:

j

Answer:

it would be 31

Step-by-step explanation:

How many observations are accounted for in the stem and leaf graph? What did you do to find the answer?

Answers

Answer:

i put 2

Step-by-step explanation:

What is the exponential regression equation for the data set?
WILL GIVE BRAINLIEST!
THIS IS URGENT EMERGENCY \

Answers

Answer:

Exponential Regression. An exponential regression is the process of finding the equation of the exponential function that fits best for a set of data. As a result, we get an equation of the form y=abx where a≠0 .

Step-by-step explanation:

25 POINTS +BRAINLIEST Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she gave, but she was penalized 1 point for every incorrect answer. In the end, Thalia had a total of 28 points. In order to determine the number of correct and incorrect answers that she gave, a viewer at home used the system of linear equations x + y = 20 and 2 x + y = 28, with x being the number of correct answers and y being the number of incorrect answers. The viewer solved the system by using the linear combination method as shown. x + y = 20. + StartFraction Negative 2 x minus y = negative 28 over Negative x = negative 8 EndFraction. StartFraction negative x Over negative 1 EndFraction = StartFraction negative 8 Over negative 1 EndFraction. X = 8. 8 + y = 20. 8 + y minus 8 = 20 minus 8. y = 12. The viewer calculated that the contestant answered 8 questions correctly and 12 questions incorrectly. What went wrong? The viewer mistakenly determined that one of the equations in the system should be x + y = 20.Instead modifications should have been made before applying the equation. The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation. The viewer multiplied the equation 2 x + y = 28 by –1 incorrectly. The viewer added the equations x + y = 20 and Negative 2 x minus y = negative 28 incorrectly.

Answers

Answer:

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

Step-by-step explanation:

No of questions= 20

Right= x, Wrong= y, right= 2 points, wrong= -1 point, total points= 28

Correct pair of equations:

x+y= 20 and 2x-y= 28

solution:

x= 20-y,2(20-y)- y= 2840-2y-y=283y= 40-283y=12y=4 and x= 20-y= 20-4= 16right= 16, wrong= 4

======

The mistake is:

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

Answer:

Step-by-step explanation:

Finished on edge 2020

Q5) (2.00 marks)
The sum of two numbers is 16 and their product is 48. What are the two numbers?

Answers

12 and 4
12 + 4 = 16
12 x 4 = 48

Two pupils each drew a triangle with one side of 6 cm , one side of 10 cm and one side of 7 cm. Must their triangles be congruent? (Answer ‘yes’ or ‘no’).

Answers

Answer:

no

Step-by-step explanation:

they can be either side because the numbers are different in the angles

If £25 = 850 rubles, how many £ are in 1,088 rubles?

Answers

Answer:

There are £32.64 are in 1,088 rubles.

Step-by-step explanation:

To solve this

step 1: find cost of 1 rubble

step 2: multiply number of rubble with cost of one rubble.

cost of 850 rubles = £25

we need to find cost of 1 rubles, for that we divide lHS and RHS with 850

cost of 850/850 rubles = £25/850 = £0.03

cost of 1 rubles = £0.03

Therefore cost of 1088 rubles = 1088* cost of 1 rubles

                                                  = 1088 * £0.03 = £32.64.

Thus, there are £32.64 are in 1,088 rubles.

What is the difference of the two polynomials (9x^2+8)-(2x^2+3x)

Answers

Answer:

7x^2 -3x +8

Step-by-step explanation:

(9x^2+8)-(2x^2+3x)

Distribute the minus sign

(9x^2+8)-2x^2-3x)

Combine like terms

9x^2 -2x^2 -3x+8

7x^2 -3x +8

Answer:

[tex]5x {?}^{2} + 8 - 3x [/tex]

[tex]9x {?}^{2} + 8 - (4x {?}^{2} + 3x) \\ 9x {?}^{2} + 8 - 4x - 3x \\ 5x {?}^{2} + 8 - 3x[/tex]

PLEASE HELP, I WILL MARK BRAINLIEST!

Answers

Answer:

hope this helps you

write down in terms of n 4 ,1 -2, -5 ,-8

Answers

Answer:

aₙ= 3n+1

Step-by-step explanation:

4 ,1 -2, -5 ,-8

AP with a₁=4 and d= -3

----------------

aₙ= 4+3*(n-1)= 4+3n-3= 3n+1

aₙ= 3n+1

help meeeeeeeeeeeeeee

Answers

Answer:

184 square inches

Step-by-step explanation:

Bases: 4 in × 5 in × 2 bases = 40 in²

Smaller pair of lateral faces: 4 in × 8 in × 2 faces = 64 in²

Larger pair of lateral faces: 5 in × 8 in × 2 faces = 80 in²

40+64+80=184 in²

The surface area of the box is 184 in² or 184 square inches.

Answer: B) 184 Square Inches

Step-by-step explanation:

To find the surface area of the box we have to use the formula, the formula is  A = 2wl + 2lh + 2hw....

To find the front and the back we have to multiply the width and the length...

8 * 5 = 40 + 40 = 80

To find the right and the left we have to multiply the length and the height...

8 * 4 = 32 + 32 = 64

To find the bottom and the top we have to multiply the height and the width...

4 * 5 = 20 + 20 = 40

40 + 64 + 80 = 184

The surface is 184 square inches, I hope this helps!

factorise x^2-5x-6 please!??!?

Answers

Answer:

(x - 6)(x + 1)

Step-by-step explanation:

Given

x² - 5x - 6

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1 , since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) ← in factored form

Answer:

(x+1) (x-6)

Step-by-step explanation:

factorice la expresion

x^2 + x - 6x- 6

x(x + 1) -6(x + 1)

la solucion es:

(x + 1) (x - 6)

A phone plan has a limit of $25 that can be spent on text messages. The base cost of the text plan will cost a user $5. Each text will cost $0.05. How many text messages (t) can a user send without exceeding the plan limits?

Answers

Answer:

400 texts

Step-by-step explanation:

Answer:

The answer is A)

Step-by-step explanation:

If x2=y3, what is the value of z does x3z=y9?

Answers

If x² = y³ , for what value of z does [tex]x^{3z}[/tex] =  [tex]Y^{9}[/tex]  ?

Answer:

z= 2

Step-by-step explanation:

To solve the question given, we will follow the steps below;

[tex]X^{3z}[/tex] =  [tex]Y^{9}[/tex]   -----------------------------------------------------------------(1)

but   applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

[tex]Y^{9}[/tex]  = [tex](Y^{3})^{3}[/tex]

replace  [tex]Y^{9}[/tex]  by  [tex](Y^{3})^{3}[/tex]  in equation (1)

[tex]X^{3z}[/tex] =  [tex]Y^{9}[/tex]

[tex]X^{3z}[/tex] =   [tex](Y^{3})^{3}[/tex]   --------------------------------------------------------------------(2)

but  from the question x² = y³

replace y³ by x²  in equation (2)

[tex]X^{3z}[/tex] =   [tex](Y^{3})^{3}[/tex]

[tex]X^{3z}[/tex] =   [tex](X^{2})^{3}[/tex]

[tex]X^{3z}[/tex] =   [tex]X^{6}[/tex]

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3  at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2

(100 POINTS & BRAINLIEST!!! HURRY) A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.
If you take one spin, what is your expected value?
What changes could you make to values assigned to outcomes to make the game fair?
Prove that the game would be fair using expected values.

Answers

Answer:

The game is not fair

Step-by-step explanation:

A wheel with seven sectors:

Red Sectors  = 2   |  Probability  = 2/7

Purple sectors  = 2  |  Probability  = 2/7

Yellow sectors  = 2 |   Probability  = 2/7

Blue sectors  = 1  |  Probability  = 1/7

Landing on the blue sector will give 3 points,  => 3 * 1/7  = 3/7    points

landing on a yellow sector will give 1 point => 1 * 2/7 = 2/7   points

landing on a purple sector will give 0 points => 0 * 2/7  = 0   points

landing on a red sector will give –1 point.  =>  - 1 * 2/7  = -2/7 points

Expected value  =  3/7 + 2/7 + 0 - 2/7

= 3/7

Expected value  =  3/7

3/7   < 1/2

=> game is not fair

If expected value = 3.5/7 = 1/2  then game will be fair

hence if we make 3.5 points for Landing on the blue sector

then game will be fair.

Answer: well i'm too young to answer this lol

1. 7

2. change the value of the colors. each color should have at least 1 or 2 points for each sector.

Step-by-step explanation:

1. two are red (red=1) =2, two are purple (purple=0) =2, two are yellow (yellow=1) =4, one is blue (blue=3) =7

2. dk how to explain this i'm running out of time

Need help ASAP please

Answers

Answer: choice D) 5

Step-by-step explanation:

22.5/9=2.5

23.5/2.5=9.4

9.4-4.4=5=x

what is the y-intercept of y=-3x-2

Answers

Answer:

the answer is 2.

Step-by-step explanation:

the basic form of this equation is y=mx+c where c is the y intercept and m is the gradient. c=2 so 2 is the y intercept

The answer is 2. The y intercept follows the slope of the equation

What is the range of the function g(x) = |x – 12| – 2?

Answers

Answer:

[-2 , +∞[

Step-by-step explanation:

g(12) = |12 - 12| - 2 = -2

if x ≠ 12 then |x - 12| ≥ 0 because the absolute value I should always positive.

then |x – 12| – 2 ≥ -2

then g(x) ≥ -2

then the range is [-2 , +∞[

Answer:

B

Y is greater than or equal to -2

Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!!

Answers

Answer:

Step 1

Step-by-step explanation:

I believe it's step 1 because he subtracted 6 from 86 before distributing the five. In math, you must follow PEMDAS (parentheses, exponents, multiplication & division, addition & subtraction.) This person skipped the parentheses.

please help for brainliest answer

Answers

Answer:

a) An event with probability 0 is said to be impossible

b) An event with probability 1 is said to be certain

c) The probability of getting a head when flipping an unbiased coin is shown by the letter A

Step-by-step explanation:

a) If something has a 0 on a probability scale, it will never happen. The word used to describe this outcome is impossible.

b) If something has a 1 on a probability scale, it will always happen. The word used to describe this outcome is certain.

c) The probability of getting a head on an unbiased coin is [tex]\frac{1}{2}[/tex] or [tex]0.50[/tex]. This means that we are looking for the letter that is in the exact center of 0 and 1. It can be seen that A is in the dead center of these two numbers, so this is our answer.

The time it takes to set up a circus tent varies inversely with the number E of elephants used. If 4 elephants can set up a tent in 30 hrs how long will it take 2 elephants?

Answers

Answer:

It will take 60 hours for 2 elephants to set up the tent.

Step-by-step explanation:

Represent set-up time by T and the number of elephants by E.  T varies inversely with E:

T  = k/E, or TE = k

If 4 elephants can set up a tent in 30 hours, then 30(4) = k, and

T = 120/E

Now let E = 2.  We get T = 120/2, or 60

It will take 60 hours for 2 elephants to set up the tent.

Pat's potato farm grew 490 pounds of potatoes. Pat delivered 3/7 of the potatoes to a vegi stand. The owner of the vigi stand delivered 2/3 of the potatoes he bought to a local grocery store, witch packaged half of the potatoes that were delivered into 5 pond bags. How many 5 pound bags did the grocery store package.

Answers

Answer:

14 bags

Step-by-step explanation:

Total potato grown on Pat's potato farm = 490 pound

Fraction of potato delivered to vegi stand = 3/7 of total potato

Therefore,

Potato delivered to Vegi stand in pound = 3/7 of Total potato grown

                                                                     =  3/7 of 490 = 3/7 * 490

                                                                     = 210

Thus, 210 pound potato is delivered to vegi stand

___________________________________________

Fraction of potato delivered to local grocery store = 2/3 of  potato delivered to Vegi stand

Therefore,

Potato delivered to local grocery store in pound = 2/3 of  potato delivered to Vegi stand

                                                                     =  2/3 of 210 = 2/3 * 210

                                                                     = 140

Thus, 140 pound potato is delivered to local grocery store.

____________________________________________________

Half of the potatoes delivered were packaged into 5 pound bags

Half of 140 pound potato is delivered to local grocery store will be

140/2 = 70 pounds.

Thus, 70 pounds potatoes were packed in 5 pound bags.

Let the the no of 5 pounds bag be x.

if one bag has 5 pound potatoes then

x bag will have 5*x = 5x pound potatoes,

but it is given that  70 pounds potatoes were packed in 5 pound bags.

thus,

5x = 70

x = 70/5 = 14

Thus, 14 bags were packed by grocery store package.

help!!! an experiment consists of randomly choosing a colored card from a box. use the results in the table to find the experimental probability of each event. simplify all answers. red : 7, yellow: 12, orange: 8, white: 13

Answers

Answer:

chance of:

red 7/40 = 17.5%

yellow 3/10 = 30%

orange 1/5 = 20%

white = 13/40 = 32.5%

Step-by-step explanation:

7+12+8+13 = 40 total cards

7 red/ 40 possible

12 yellow/40 possible = 3/10

8 orange/40 possible = 1/5

13 white/40possible

Using it's concept, it is found that the experimental probability of each outcome is given by:

Red: 0.175 = 17.5%.Yellow: 0.3 = 30%.Orange: 0.2 = 20%.White: 0.325 = 32.5%.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In an experimental probability, these numbers are taken from previous outcomes.

In this problem, there are 40 cards.

7 are red, hence P(red) = 7/40 = 0.175 = 17.5%.12 are yellow, hence P(yellow) = 12/40 = 0.3 = 30%.8 are orange, hence P(orange) = 8/40 = 0.2 = 20%.13 are white, hence P(white) = 13/40 = 0.325 = 32.5%.

More can be learned about probabilities at https://brainly.com/question/14398287

The sum of two numbers is 10. The larger number is 4
times the smaller number. What are the two numbers?
Original system: x + y = 10,
y = 4x
Slope-intercept form:
y = -x + 10
y = 4x

Answers

Answer:

x=8 and y=2

Step-by-step explanation:

x+y=10

x=4y

x+y=10

4y+y=10

5y=10(divide both sides by 5)

y=2

x=4y=4*2=8

Answer:

2 and 8.

Step-by-step explanation:

y = -x + 10

y = 4x

If we subtract we eliminate y:

0 = -x + 10 - 4x

0 = -5x + 10

5x = 10

x = 2.

and y = 4 * 2 = 8.

Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Zeros:  Set g(r) = (r + 14)^2 - 49 = to 0, obtaining

(r + 14)^2 = 49

Taking the square root of both sides, we get:

r + 14 = ± 7, which results in:

r = -14 + 7 = -7 and r = -14 - 7 = -21

The smaller root is -21 and the larger one is -7.

Vertex:  Compare g(r) = (r + 14)^2 - 49 to y = (x - h)^2 + k, where (h, k) represents the vertex.  We see that h = -21 and k = -49, so that we know the vertex to be (-21, -49).

Angles A and B are supplementary. Angle A has a measure of 80°. What is the measure of angle B?
The measure of angle B is

Answers

Answer:

The measure of angle B would be 100°

Step-by-step explanation:

Supplementary means two angles add up to 180 degrees. Let's say A+B=180. Since we know what A is, we can substitute that in, B+80=180. Now solve. B=100

Answer is 100. Supplementary basically means 2 angles ,when added form 180. If angle 1 is mentioned as 80. Angle 2 will be whole - angle 1
=180 - 80
=90 degrees

Just In case you are wondering what complementary means it’s the same thing but instead of the angles forming 180 it will form 90.

Hope you have understood

Solve the exponential equation using logarithmic properties y=3^2x-4

The 2x is an exponent

Answers

Answer:

[tex]\frac{log(y+4)}{2log3}[/tex]

Step-by-step explanation:

Given the exponential equation [tex]y = 3^{2x}+4[/tex], to get 2x, we will make 2x the subject of the formula as shown;

[tex]y = 3^{2x}-4\\y+4 = 3^{2x}\\taking\ log\ of\ both\ sides\\log(y+4) = log3^{2x}\\ log(y+4) = 2xlog3\\dividing\ both\ sides\ by\ 2log 3\\\ x = \frac{log(y-4)}{2log3} \\[/tex]

The last expression gives the required value of x

Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!

Answers

Answer:

No, x = -12/23 , y = -14/23

Step-by-step explanation:

Solve the following system:

{-3 x - 4 y = 4 | (equation 1)

y - 5 x = 2 | (equation 2)

Swap equation 1 with equation 2:

{-(5 x) + y = 2 | (equation 1)

-(3 x) - 4 y = 4 | (equation 2)

Subtract 3/5 × (equation 1) from equation 2:

{-(5 x) + y = 2 | (equation 1)

0 x - (23 y)/5 = 14/5 | (equation 2)

Multiply equation 2 by 5:

{-(5 x) + y = 2 | (equation 1)

0 x - 23 y = 14 | (equation 2)

Divide equation 2 by -23:

{-(5 x) + y = 2 | (equation 1)

0 x+y = (-14)/23 | (equation 2)

Subtract equation 2 from equation 1:

{-(5 x)+0 y = 60/23 | (equation 1)

0 x+y = -14/23 | (equation 2)

Divide equation 1 by -5:

{x+0 y = (-12)/23 | (equation 1)

0 x+y = -14/23 | (equation 2)

Collect results:

Answer: {x = -12/23 , y = -14/23

What is the measure of U

Answers

Answer:

U = 48

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

x+21 + x+23 + x+61 = 180

Combine like terms

3x + 105 = 180

Subtract 105 from each side

3x+105-105 = 180-105

3x = 75

Divide by 3

3x/3 = 75/3

x = 25

We want angle u

x+23

25+23

48

Answer:

48

Step-by-step explanation:

All interior angles of a triangle add up to 180.

[tex](x+21)+(x+23)+(x+61)=180[/tex]

If you wanted to you could subtract 21, 23, and 61 from 180.

[tex](x+21)+(x+23)+(x+61)=180\\x+21+x+23+x+61=180\\3x+105=180\\3x=75[/tex]

Then take then number that's left and divide it by three, since they are all in addition to the same variable.

[tex]\frac{3x}{3}=\frac{75}{3}\\ x=25[/tex]

Then add 25 to 23 which is 48.

Each week Danny eats 540 grams of cereal over 8 weeks. He finishes a total of 12 boxes of cereal. Each box contains the same amount of cereal. How many grams of cereal are in each box?

Answers

Answer:

360 grams of cereal

Step-by-step explanation:

First you have to do 540 times 8 to find out how many grams of cereal he ate over the eight weeks.

Then you have to divide the answer by 12 to get 360 grams of cereal.

I hope this helped ;)

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Discuss how st. Clairs defeat was a pivotal event for both Indians and white Americans. Steve Drake sells a rental house on January 1, 2019, and receives $100,000 cash and a note for $50,000 at 7 percent interest. The purchaser also assumes the mortgage on the property of $25,000. Steve's original cost for the house was $170,000 on January 1, 2011 and accumulated depreciation was $27,000 on the date of sale. He collects only the $100,000 down payment in the year of sale.If Steve elects to recognize the total gain on the property in the year of sale, calculate the taxable gain. I am doing a PowerPoint on environmental pollution and the effects it has on the environment, I couldn't find any information on the positive effects caused by environmental pollution.I need POSITIVE Long-Term effects and the Short-Term effects caused by environmental pollution.-=- 30 pts and brainliest for the best answer -=- !!!PLEASE HELP!!!the exponential function g, represented in the table, can be written as g(x)=ab^x. complete the equation for g(x).please and thank you Help ASAP plz will give brainly There are 25 students in a class. 16 of those students are boys. What percent of the class are girls?The percent of girls in the class is ____ % what is the answer to he equation to of x+3 x 4x-7 A school must select one student from the honors program to send to the annual math convention. Which of the following is NOT a mathematically fair way to select the student? A) Use a random number generator to choose a student ID number. B) Have the students play a game that involves flipping a coin. Heads is worth 2 points and tails is worth 1 point. The first student to reach 40 points wins the trip. C) Have each teacher select their favorite student and then randomly draw one of those names. D) Line the students up alphabetically. Each student selects a playing card. A card is then drawn from another deck. The student with the matching card wins. What is the mechanical advantage of a wheel barrel that is 4cm long with 0.75m between the wheel and the center of the load? Does examining victim behavior when attempting to identify causes of victimization lead to victim blaming? Is is wrong to consider the role of the victim? How might considering the role of the victim in efforts to understand and explain victimization contribute to victim blaming?