Mathematics High School

Please answer with clear instructions so that i can apply this to other questions.

Answers

Answer 1

Answer:

length = 50 cm

Step-by-step explanation:

let width be w then length = w + 10

area = w(w + 10) = 2000 , that is

w² + 10w = 2000 ( subtract 2000 from both sides )

w² + 10w - 2000 = 0 ← in standard form

Consider the factors of the constant term (- 2000 ) which sum to give the coefficient of the w- term ( + 10)

the factors are + 50 and - 40 , since

50 × - 40 = - 2000 and sum = 50 - 40 = + 10

(w + 50)(w - 40) = 0 ← in factored form

equate each factor to zero and solve for w

w + 50 = 0 ⇒ w = - 50

w - 40 = 0 ⇒ w = 40

Since w > 0 then w = 40 and

length = w + 10 = 40 + 10 = 50 cm

Related Questions

How many solutions exist for the given equation?3x + 13 = 3(x + 6) + 1

Answers

Answer:

Step-by-step explanation:

3x+13=3(x+6)+1
Expand:

3x+13=3x+18+1
Simplify:

3x+13=3x+19
Subtract 13 from both sides:
3x+13-13=3x+19-13
Simplify:

3x=3x+6

Subtract 3x from both sides:
3x-3x=3x-3x+6

0=6

Since the sides are not equal there are no solutions to this problem

The Hamden board of education wants to know how the community feels about building a new media center for the middle school. They called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. Which of the following are true of the sample of 40 voters? Check all that apply.

Answers

Answer:

The true statements about the sample described in the scenario above are:

The sample should be larger to give more reliable information.

The sample size is too small to represent the population.

The sample size is too small and can lead to false inferences.

Step-by-step explanation:

The sampling technique employed is a systematic random sampling where samples are chosen at every specified interval. Hence, the sample is randomly selected.

Alexandra is following a recipe that requires three fourths cup of water. She needs to make 10 servings. How many cups of water does Alexandra need?

one and one fifth cups
three and one fourth cups
seven and two fourths cups
eight and two thirds cups

Answers

So if one batch needs 3/4 of a cup and she needs to make 10 batches then you multiply how many batches by how many water cups required for one batch:

3/4 • 10 = 30/4 = 7 2/4

So she needs seven and two fourths cups of water.

Answer:

3/4 • 10 = 30/4 = 7 2/4

i am not smart pls help!!!

Answers

Answer:

yes, the 10 ft wave is an outlier

Step-by-step explanation: smarts

hope this helps :))

Answer:

the 10ft wave is the outlier

Step-by-step explanation:

hope this helps

I need help asap the question is in the picture.

Answers

Answer:

The second one between 2 and 3

Step-by-step explanation:

Sq root of 7 = 2.65

Answer:

2nd number line represents √7 best

Step-by-step explanation:

Method 1

√7 ≈ 2.65

Therefore, the 2nd number line represents √7 best

(the one with the dot between 2 and 3)

Method 2

√1 = 1

√4 = 2

√9 = 3

Therefore, as √7 is between √4 and √9, the solution is somewhere between 2 and 3.

There were 24 teams at a soccer tournament. In all, 12 teams wore red shirts, 6 teams wore blue shirts, 4 teams wore orange shirts, and 2 teams wore white shirts.

Answers

Answer:

1rst one is 3:2 the second one is 1:2 and third is 1:12 if i remember

Step-by-step explanation:

The total number of teams at the soccer tournament was 24.

The information about the number of teams and the shirts they wore at the soccer tournament.

To summarize:

12 teams wore red shirts

6 teams wore blue shirts

4 teams wore orange shirts

2 teams wore white shirts

To find the total number of teams, add up the number of teams for each shirt color:

Total Teams = 12 (Red) + 6 (Blue) + 4 (Orange) + 2 (White) = 24 teams

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A small airplane can hold 13 people per trip. How many trips would it take the airplane to transport 9,165 people?

Answers

You have to divide

its 9,165 divided by 13

[tex]\frac{9165}{13}[/tex] = 205

Teddy it takes 205 trips

to transfer 9,165 in a plane that can hold 13 people per trip

Hope I helped ^-^

Please help me due today

Answers

Answer:

if m∠1 = 30° then m∠3 = 30° as they are parallel to each other and that is why they will have same angles.

therefore m∠3 = 30°

extra's:

→ m∠2 = m∠4 =

→ (360-30*20)/2

→ 150°

...............................

See here

m<1 and m<3 are opposite angles to eachother.

And we know that opposite angles are equal

m<1=m<3 m<3=30°

Learning Task 5 : In your answer sheet , prove the theorem , using the given below . if a quadrilateral is inscribed in a circle , then its opposite angles are supplementary." Given : Quadriateral ABCD is inscribed in OE Prove : ∠ABC and ∠ABC are supplementary ∠DAB and ∠DCB are supplementary

Answers

Answer: quadrilateral is inscribed in a circle , then supplementary . " its opposite angles are Given : Quadriateral ABCD is inscribed in OE Prove : ABC

Step-by-step explanation:

(SHOW UR WORK I DONT FEEL LIKE DOING THIS XDD BUT THANKSS) 98.73 ÷ 15 =

Answers

Answer:

Answer 6.582

Step-by-step explanation:

0 6. 5 8 2

1 5 9 8. 7 3 0

− 0

9 8

− 9 0

8 7

− 7 5

1 2 3

− 1 2 0

3 0

− 3 0

Hope its understandable ._.

Grace got a haircut for $26.95, bought three shirts on sale for $18.50 each and a pair of jeans for $48, and purchased two CDs for $18.50 each. Round each amount to the nearest ten dollars to find a reasonable estimate of how much Grace spent.

Answers

26.95 + 18.5 * 3 + 48 + 18.5 * 2

18.5 * 3 = 55.5

18.5 * 2 = 37

37 + 55.5 + 48 + 26.95 = 167.45

= $167.5

please help me quick with it

Answers

Answer:

is there any examples/

Step-by-step explanation:

What are the factors of x2 – x – 6? Check all that apply. X – 6 x 6 x – 3 x – 2 x 2 x 1 x – 1.

Answers

Answer:

The factors are x-3 and x+2, and the roots are 3 and -2.

Step-by-step explanation:

x^2-x-6 can be factored in the following way:

(x-3)(x+2)

The factors are x-3 and x+2, and the roots are 3 and -2.

Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: (x-3) and (x+2)

How to factorize a quadratic polynomial with single variable?

Quadratic polynomial with single variables are expressible in the form

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

where x is the variable and a,b,c are constants.

Its factored form is

[tex]\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})[/tex]

For the given case, the expression given to us is [tex]x^2 - x - 6[/tex]

Comparing it with the standard form of quadratic expression [tex]ax^2 + bx + c[/tex], we get: a = 1. b = -1. and c = -6

Using the aforesaid formula, we get:

[tex]=\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})\\\\=\dfrac{1}{4}\times(2x -1 - \sqrt{1 +24})(2a -1 + \sqrt{1 + 24})\\\\=\dfrac{1}{4} \times (2x - 1-5)(2x - 1 + 5)\\\\=(x -3)(x+2)[/tex]

Thus, The factors of given expression are: (x-3) and (x+2)

Learn more about factors here;

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What is the surface area of the sphere, in square meters?

Possible answers:

A. Not enough information is given to calculate this surface area.

B. 804

C. 2144

D. 201

Answers

[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies SA=4\pi (8)^2\implies \stackrel{using~\pi =3.14}{SA\approx 804}[/tex]

1. A pound of fertilizer pellets will cover about 300 square feet of lawn. Find how many pounds of fertilizer will be
needed for a rectangular patch of grass that measures 45 feet by 45 feet.

Answers

Answer:

6.75 if exact 7 if rounding up

Step-by-step explanation:

1lb=300ft^2

45x45=2,025

2,025/300=6.75

how much is 20 cookies for 15.25 dollars

Answers

Answer:

305 cookies

Step-by-step explanation:

Well, we know that each cookie is $15.25( that is expensive!?) so we multiply it and get 305 (15.25 x 20)

YW!! Have a nice day!

The height of a cone is 10ft. The area of the base is 22ft. Compute the volume of the cone

Answers

[tex] {73.33ft}^{3} [/tex]

Step-by-step explanation:

[tex]v = \pi {r}^{2} \frac{h}{3} [/tex]

[tex]\pi {r}^{2} = {22ft}^{2} [/tex]

[tex]v = 22 \times \frac{10}{3} [/tex]

[tex]v = 22 \times 3.33[/tex]

[tex]v = {73.33ft}^{3} [/tex]

The question is in the picture please give me all the answers

Answers

Answer:
a) 1/4
b) 1/8
c) 1/81
Step-by-step explanation:
I used the negative exponent rule:
b^-n = 1/b^n

∠1 and ∠2 are vertical angles. ∠2 has a measure of 63°.

What is the measure of ∠1?

Answers

Answer:

63 degrees

Step-by-step explanation:

vertical angles are conruent

Hope this helps! :)

I need help finding x

Answers

Answer:

Step-by-step explanation:

#19.

(7x - 2)° + (10 - 3x)° = 180°

(7x - 3x) + (10 - 2) = 180

4x = 172

x = 43

#21.

(6x - 144)° = (2x)°

4x - 2x = 144

2x = 144

x = 72

the top answer is correct

Please help me asap
I will give you 50 points

Answers

Answer: C

Step-by-step explanation:

Find the value of x if the figure is a regular polygon.

Answers

taking a peek at this regular polygon hmm is has 6 sides, so is a hexagon, ok.

[tex]\textit{sum of all interior angles in regular polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies 6\theta =180(6-2) \\\\\\ 6\theta =180(4)\implies 6\theta =720\implies \theta =\cfrac{720}{6}\implies \boxed{x=\theta =120}[/tex]

Which set of points is a function?

A- (0,3),(2,4),(0,6)
B- (1,2),(2,2),(3,2)
C- (1,4),(2,5),(1,6)
D- (2,3),(-2,4),(2,6)

Answers

Answer:

Step-by-step explanation:

This is a really simple topic. All you need to do when seeing these ordered pairs is see which has x-values that don't repeat. Over here, we can see that that is B, so B is the correct option.

Helpppp asapppppppppppp

Answers

Answer:

the first one

4a + 3a =7a

the second one

4a+4b

Answer:

1. 7a

2. 4a + 4b

Step-by-step explanation

1. (a x 4) = 4a

(a x 3) = 3a

4a + 3a = 7a

2. question 2 is correct

The answer for y = -x + 4

Answers

Answer:

x=4

y=4

m=-1

b=4

no relatibe extrema

no horizontal asymtotes

netheir even nor odd

Step-by-step explanation:

what does "what is the difference between ½+¼ and ¾+¼" mean

Answers

Answer:

It means: 1/2+1/4 - 3/4+1/4

Help !! To avoid working with messy fractions when solving a quadratic equation by completing the square, the b value should be:

negative

zero

odd

even

Answers

Answer
Even

Step-by-step explanation:

I got the answer from my teacher.

Find the two numbers whose sum is 67 and whose difference is 3.

Answers

Answer:

32;35

Step-by-step explanation:

a+b=67

a-b=3 => a=3+b

=>instead of a we write 3+b =>

a+b=67 => 3+b+b=67 => 2b=64 => b=32

=> a = 3+b=> a=32+3=35

What is the range of the function F(x)= 2cos(x-3)?

Answers

Answer:

The range is −5≤y≤−1 - 5 ≤ y ≤ - 1 .

Answer:
range: [-2, 2]

Solving Steps:
Find properties of the trigonometric
function: → range: [-2, 2]

I hope this helps you :)

Lainley wraps a cube-shaped present in a box that has a volume of 729 inches. Neglecting any overlap, how many square inches of wrapping paper does Lainey use to cover all of the sides of the box? Marking brainliest
A. 81 in.^2
B. 162 in^2
C. 324 in^2
D. 486 in^2

Answers

Driving home from school today at

The area of a cube-shaped present in a box Lainley wraps is A. 81 in²

What is a cuboid?

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, A box that has a volume of 729 inches.

First we'll prime factorize 729.

729 = 3×243 = 3×3×81 = 3×3×3×3×3×3.

If we take the cube root of 729 it would be 3×3 = 9.

So, It is a cube with a side length 9.

Now, We know area of a cube is side².

Therefore, The area of this cube is 9² = 81 in².

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