Mathematics High School

The area of a rectangle is 33 m2 , and the length of the rectangle is 5 m less than double the width. find the dimensions of the rectangle.

Answers

Answer 1
By definition, a rectangle is a quadrilateral (4-sided polygon) containing two sets of equal and parallel sides called the length and the width. For determining the area of a rectangle, you simply have to multiply length times width. In this problem, let L be the length and W be the width. Then, we formulate the two independent formulas: formula for area, and formula relating L and W

A = LW = 33
L = 2W-5

Substituting the second equation to the first,

A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3

Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,

L = 2(5.5)-5
L = 6 m

Therefore, the dimensions of the rectangle is 6 m by 5.5 m.

Related Questions

A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is

a-36
b-18
c-288
d-5

Answers

B. 18 because you divide the total number of cans by the number of sheets used to make them. 36/2 = 18, 180/10 = 18

enter an equation in slope-intercept form that describes a line that contains the points (4,1) and (4,2)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 1}})\quad % (c,d) &({{ 4}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-1}{4-4}\implies \cfrac{1}{0}\leftarrow unde fined[/tex]

so... the slope is undefined, the graph of it is just a vertical line, check the picture below, and that's the equation.

now... you can't quite put it in y = mx + b, or slope-intercept form, since it has no defined slope and it doesn't have an y-intercept either.

HOW DO YOU MOVE A VARIABLE FROM ONE SIDE OF AN EQUATION TO ANOTHER? I need to know as I'm reviewing module 7 algebra and i want to know please

Answers

The easiest way to do this is to add or subtract the value of the variable.
For example in the equation 5+a=7, subtract a from both sides to get 5=7-a.
If the initial equation was 5-a=7, add from both sides (5=a+7).
Basically, if the initial value is negative, add its value to cancel to zero.
Do the opposite if the initial value is positive.

Write a possible function rule for the following sequence.

11, 15, 19, 23, 27, ...

a(n)=?

Answers

a(n) = 4(n - 1) + 11 is the equation because a(1) = 11 and the common difference (d) = 4. Then you just plug it into the arithmetic sequence formula which is a(n) = d(n - 1) + a(1). I hope this was helpful.
This is an arithmetic sequence because a common difference exists.  The common difference is a constant found when taking any term and subtracting the previous term from it.  In this case the common difference is 4, meaning that each term is 4 units greater than the previous term.  Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

In this case we know a=11 and d=4 so

a(n)=11+4(n-1)  which can be simplified...

a(n)=11+4n-4

a(n)=4n+7

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x^5 + 9x^4 + 5x^3 + 3

Answers

The leading term is -3x^5.  The end behavior of any function is the behavior that the highest powered term has as x approaches ±oo.

In this case because the highest order term is -3x^5, as x approaches -oo, y approaches +oo.  And as x approaches +oo, y approaches -oo.

Divide 35b^5 +20ab^3 +20a^2b^2 by 5b^2

Answers

Basically, you just divide each term in the equation by b^2.
So 35b^5 / b^2 = 35b^3, 30ab^3 / b^2 = 30ab, and 20a^2b^2 / b^2 = 20a^2.
So your final answer is 35b^3 + 30ab + 20a^2.

Point r is located at (3,0). point s is located at (0,-4). what is the equation of the line through these two points

Answers

(3,0)(0,-4)
slope = (-4 - 0) / (0 - 3) = -4/-3 = 4/3

y = mx + b
slope(m) = 4/3
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 4/3(0) + b
-4 = b
so ur equation is : y = 4/3x - 4....or 4x - 3y = 12 <==

The vertical ______ of the function secant are determined by the points that are not in the domain.

Answers

The word that goes in the blank is asymptote.

When 332 college students are randomly selected and surveyed, it is found that 113 own a car. find a 99% confidence interval for the true proportion of all college students who own a car?

Answers

Given:
n = 332, sample size
p = 113/332 = 0.3404, sample proportion
99% confidence interval

The confidence interval for the population is calculated from
[tex]p \pm z^{*} \sqrt{ \frac{p(1-p)}{n} } [/tex]
where z* = 2.58 for the 99% confidence level (from tables)..

[tex]2.58 \sqrt{ \frac{0.3404(1-0.3404)}{332} } =0.0671[/tex]
Therefore the 99% confidence interval is
(0.3404 - 0.0671, 0.3404 + 0.0671) = (0.2733, 0.4075)

Answer:
The 99% confidence interval is (0.273, 0.408) or (27%, 41%).
That is, between 27% and 41% of the students own cars.

How many cans of paint are needed to cover an area of 2,200 square units if one can of paint covers an area of 400 square units? 4 5 6 8?

Answers

In this case, one can of paint can covers an area of 400 square units. You are asked how much cans needed to cover an area of 2,200 square units.

Then you just need to divide 2,200 square units with 400 square units.
The equation will be : (2,200 square units / 400 square units) x 1 can=  4.5 cans
After you round up the result it would be 5 cans.

Answer: 5 cans

What percent of 210 is 70?

Answers

if we take 210 to be the 100%, what is 70 off of it in percentage then?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 210&100\\ 70&x \end{array}\implies \cfrac{210}{70}=\cfrac{100}{x}\implies x=\cfrac{70\cdot 100}{210}[/tex]
percent means parts out of 100
so x%=x/100

'of' means multiply

so

what percent of 210 is 70 translates to
x/100 times 210=70
210x/100=70
21x/10=70
times 10 both sides
21x=700
divide both sides by 21
x=33.333333


33.33333333% of 210 is 70

Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption? 4:9 ≠ 6:13 4:9 ≠ 6:7 4:13 ≠ 6:9 4:5 ≠ 6:13

Answers

Please see attached file for the triangle’s figure:

 

Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).

Therefore, the inequality that she will use to contradict the assumption is 4:9 ≠ 6:13.

To add, a relation that holds between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.



Inequalities are governed by the following properties:

Transitivity
 Converse
 Addition and subtraction
 Multiplication and division
 Additive inverse
 Multiplicative inverse
Applying a function to both sides

Answer:

4:9 ≠ 6:13.

Step-by-step explanation:

If BC = 5 and CD = 26, find AC.

Answers

Answer:

[tex]AC=\sqrt{130}[/tex]

Step-by-step explanation:

AC is the geometric mean.  Solve it using this proportion:

[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]

Now fill in the values we know:

[tex]\frac{5}{AC}=\frac{AC}{26}[/tex]

Cross multiply to get

[tex](AC)^2=130[/tex]

That means that

AC = [tex]\sqrt{130}[/tex], which, in decimal form is

AC = 11.40175425

A given line has the equation 10x + 2y = −2.

What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?

Answers

y = -5x + 12 since the slope of that line is -5x and in order to pass through that point the y intercept must be 12

Step 1

Find the slope of the given line

we have

[tex]10x+2y=-2[/tex]

Isolate the variable y

Subtract [tex]10x[/tex] both sides

[tex]2y=-10x-2[/tex]

Divide by [tex]2[/tex] both sides

[tex]y=-5x-1[/tex]

The slope of the given line is

[tex]m=-5[/tex]

Step 2

Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]

we know that

If two lines are parallel. then their slope are equal

In this problem we have

[tex]m=-5[/tex]

[tex](0, 12)[/tex]

The equation of the line into slope-intercept form is equal to

[tex]y=mx+b[/tex]

substitute the values

[tex]12=-5*0+b[/tex]

[tex]b=12[/tex]

the equation of the line is

[tex]y=-5x+12[/tex]

therefore

the answer is

[tex]y=-5x+12[/tex]

Find the missing length.

Answers

Find this using the pythagoream theorem for right triangles.

a^2+b^2=c^2
12^2+9^2=c^2

144+81= c^2
225=c^2
15=c

Final answer: c=15

The population of a type of local frog can be found using an infinite geometric series where a one equals 84 and the common ratio is one over five find the sum of the infinite series that will be the upper limit of this population. 87,105,425, or this series is divergent

Answers

a=84 and r=1/5

Since r, the common ratio squared is less than one, the sum will converge to a limit.  Rule:  if  r^2<1 infinite series converges, otherwise it diverges.

Since the sum of any geometric sequence is:

s(n)=a(1-r^n)/(1-r)

And if r^2<1, (1-r^n) becomes 1-0=1 as n approaches infinity.

So whenever r^2<1 the sum of the infinite series is just:

s(n)=a/(1-r)

Since a=84 and r=1/5 this infinite series has a sum of:

s(n)=84/(1-1/5)

s(n)=84/(4/5)

s(n)=5(84)/4

s(n)=105

Match the perfect square trinomials with their factors 4a2 + 4a + 1 (2 + a)(2 + a) 4a2 − 4a + 1 (2a + 1)(2a + 1) 4 − 4a + a2 (2a − 1)(2a − 1) 4 − 4a − a2 (2 − a)(2 − a) 4 + 4a + a2

Answers

4a2 + 4a + 1 = (2a +1)^2 = (2a + 1)(2a + 1)
4 − 4a + a2  = (2 - a)^2 = (2 − a)(2 − a)
4a2 − 4a + 1 = (2a -1)^2 = (2a − 1)(2a − 1)
4 + 4a + a2 = (2 + a)^2 = (2 + a)(2 + a) 

How do I set up this equation and solve ?

Answers

angles in a triangle need to equal 180 degrees

 so x = 180 - 47 - 58

x = 180-105

 x= 75 degrees

Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13. 0 1 2

Answers

Given:
m∠C = 85°, a= 10,  c = 13

From the Law of Sines,
sin(A)/a = sin(C)/c
sin(A) = (a/c)*sin(C)
          = (10/13)*sin(85°)
          = 0.7663
m∠A = sin⁻¹ 0.7663 = 50°, or 130°

When m∠A = 50°, obtain
m∠B = 180° - (m∠A + m∠C) = 180 - (50+85) = 45°
Again from the Law of Sines, obtain
b = (sinB/sinC)*c = 9.2

When m∠A = 130°, obtain
m∠B = 180° - (130 + 85) = -35° (not possible)
Therefore this triangle does not exist.

Answer:
There is only one possible triangle, with
A=50°, B=45°, C=85°, a=10, b=9.2, c=13.

Final answer:

Correcting for the apparent typo in the question, assuming 'c' refers to an angle and a side length respectively, there can only be one possible triangle formed given the angle and two sides. This is based on geometric principles where a unique triangle can be determined from an angle opposite and its respective side length.

Explanation:

The question presents a probable typo since it mentions two different values for 'c'. Assuming 'c = 85°' refers to an angle, and 'c = 13' refers to the length of a side opposite this angle, the proper interpretation involves finding possible triangles given an angle and two sides. However, the principles of geometry dictate that with one angle and two sides specified, especially in this non-ambiguous manner where one side length and the angle opposite are known, one can determine a unique triangle, assuming the given information leads to a viable geometric figure.

By using the Law of Sines, one might attempt to find the other angles or sides, but since we only have one angle and one side length, we directly know there's no ambiguity - geometrically speaking, there's only one way to construct such a triangle, thus, only one possible triangle can be formed given the corrected assumptions.

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -(x-4)2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answers

There is only one x-intercept for f(x) and g(x), f(x) having a minimum value of zero and g(x) having a maximum value of zero. f(x)=0 when x=0, g(x)=0 when x=4.

g(x) is f(x) reflected about the about the x-axis and shifted to the right by 4 units. 
Since x^2 = 0 implies x = 0 with multiplicity 2, there is one x-intercept
Since -x^2-5 = 0 implies x = +-sqrt(5)i, there are no x-intercepts
Transformations:
Reflect f(x) in the x-axis,
then vertically shift the result down by 5 units,
to get g(x).

What is the circumference of this circle, in millimeters? use 22/7 for pi

r = 49

Answers

Circumference=[tex]2\pi r=2\times \dfrac{22}{7} \times 49 = \boxed{308 \text{ mm}}[/tex]

Answer: circumference = 308mm

Step-by-step explanation: the formula for the circumference of a circle is given by

C=2πr

Given that r=49mm

Pi=22/4

C=2*22/7*49

C=44*7=308mm

In geometry, the circumference of a circle is the distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge of a disk, circumference is a special case of perimeter.

Redo, Answers please?

Answers

11) ?=12
10) ?=13
14) ?=13
11)

11+15+13 = 39

39 - 27 = 12

so 

answer
? = 12

10)

18 - 11 + 13 = 20

33 - 20 = 13

so 

answer

? = 13

14)

16+17+12=45

45 - 27 = 18

answer

? = 18

Find the area of the circle with the given radius or diameter. Use = 3.14.

r = 6

A =

37.68 sq. units
113.04 sq. units
226.08 sq. units

Answers

Radius [ r ] = 6 units

Area of a circle = [tex] \pi r^{2} [/tex] = [tex]3.14 * 6 * 6 = 3.14 * 36 = 113.04 [/tex] sq. units.

Hence, the answer is B.

Answer: 113.04 sq. units

Find the area under the standard normal curve between z = -1.5 and z = 2.5

Answers

Final answer:

To area under the standard normal curve between z = -1.5 and z = 2.5 is 0.927

Explanation:

A standard normal curve, also known as the standard normal distribution, is a bell-shaped, symmetrical probability distribution with a mean of 0 and a standard deviation of 1. It serves as a reference for many statistical analyses and is often denoted as the Z-distribution.

To find the area under the standard normal curve between z = -1.5 and z = 2.5, we need to use the z-table. The z-score of -1.5 corresponds to an area of 0.0668 and the z-score of 2.5 corresponds to an area of 0.9938. To find the area between these two z-scores, we subtract the smaller area from the larger area:

= 0.9938 - 0.0668

= 0.927

Learn more about Standard Normal Curve here:

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The area between these z-scores is 0.9270.

The area under the standard normal curve between z = -1.5 and z = 2.5 can be found using the z-table.

First, find the area to the left of

z = -1.5, which is 0.0668.

Next, find the area to the left of

z = 2.5, which is 0.9938.

Subtract these two values to get the area between z = -1.5 and z = 2.5 :

0.9938 - 0.0668

 = 0.9270.

A square garden plot has an area of 75 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot..

Answers

Hello.


The area of a square is calculated by the formula:

A = l²

As A = 75 ft², we have:

75 = l² 

l = √75

Now, note that: 75 = 3 . 25 = 3 . 5²

So:

l = √(3 . 5²) = √3 . √(5²)

l =  5√3 ft


Now, we can assume √3 = 1.73

l ≈ 5 * 1.732

l ≈ 8,7 ft   (Note that I have already put it in the nearest tenth)


OK :)

Simplify 5 − (−1).

a. 6
b. −6
c. 4
d. −4

Answers

Hi!

Subtracting a negative number is the same as adding a positive.

So instead of

5 - (-1)

We could write

5 + 1

5 + 1 = 6

The answer is 6.

Hope this helps! :)

Answer: it is  a

Step-by-step explanation: :) :v :B

4n-3<12 solve and please don't give me the answer just the equation

Answers

just as with an equation with an = sign, we want to isolate the variable, n.
So first bring -3 to the right hand side:

4n-3<12 => 4n < 12+3 => 4n < 15

Then divide by 4

4n/4 < 15/4 => n < 15/4

You can't simplify it beyond that.

if you subtract 23.47 km from 560.589 km, how many significant digits would your answer have?

Answers

560.589 - 23.47 is hmm 537.119  <---- 6 significant digits

alrite... looks good, however, when it comes to dealing with significant digits, for addition/subtraction, we go with the lowest significant amount for decimals, in this case,

560.589  <--- has 6 significant digits, accurate to the 1000th place
23.47     <--- has 4 significant digits, and is accurate to the 100th place

thus, our answer will have to be rounded up in 2 significant decimals, or 537.12
and that only has 5 significant digits, since is rounded up to the 100th place.

Smallville’s town council has records of the town’s budget over a 10-year period. Create a best fit and model for the data. What does the model predict the town’s budget will be in the year 2011?

Answers

I found the missing image and choices.
If these were the missing choices:

A)$391,000

B)$417,000

C)$404,000

D)$411,000

My answer is D) $411,000 in 2011.

There is an average increase of 4% from the previous budget to arrive at the amount of the current year. 

2009 budget $381,700

381,700 * (1.04)² = 381,700 * 1.0816 = 412,846.72  only Choice D. is nearest to the amount

2000 budget $265,100

265,100 * (1.04)¹¹ = 265,100 * 1.540 = 408,254 only Choice D. is nearest to the amount.





The circle given by x^2+y^2-4x-10=0 can be written in standard form like this: (x-h)^2+y^2=14. What is the value of h in this equation??

Answers

Answer: H=2

Step-by-step explanation:

we just need to complete the square for the x terms

gropu x terms

x^2-4x

take 1/2 of linear coefient and square it

-4/2=-2, (-2)^2=4

x^2-4x+4

factor

(x-2)^2

h=2

The value of h is 2.

Completing the square for the x terms by grouping x terms

x^2-4x

Taking 1/2 of linear coefficient and squaring it.

-4/2=-2, (-2)^2=4

x^2-4x+4

Factorizing the equation.

(x-2)^2

h=2.

What is an equation?

An equation is a mathematical statement this is made of two expressions related with the aid of an identical sign. As instance, 3x – 5 = 16 is an equation. To fix this equation, we get the value of the variable x as x = 7.

Learn more about the equation here: https://brainly.com/question/2972832

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