Mathematics High School

The length of a rectangle is 3 m longer than its width.
The area of the rectangle is 154m^2
What is the width of the rectangle?

___m

Answers

Answer 1
Sometimes when you're given dimensions that differ by some amount, it is easier to work with their average value. Let x represent the average of length and width of the rectangle. The length and width differ from this average value by 1.5 m. Then the area is
.. (x +1.5)*(x -1.5) = 154
.. x^2 -2.25 = 154
.. x^2 = 156.25
.. x = 12.5
The width is 1.5 m shorter than this, or 11 m.

_____
Solved in the conventional way, you are looking for factors of 154 that differ by 3. This means you have to find the factors of 154, or use the quadratic formula.
.. 154 = 1*154 = 2*77 = 7*22 = 11*14 (the pair we want)
Once you have the factorization of 154, you have the answer. No equations are necessary, really.

Related Questions

Between which 2 consecutive numbers is radical 46

Answers

[tex]\bf \sqrt{46}\approx 6.78239983 \\\\\\ \boxed{6}\text{\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash}6.78239983\text{\textemdash\textemdash\textemdash}\boxed{7}[/tex]

My jar has 25 dimes and some quarters, nickels, and pennies. The number of quarters plus dimes equals the number of pennies. I have 4 nickels for every dime and 2 pennies for every nickel. How many quarters are there? A. 175 B. 150 C. 125 D. 75

Answers

d = dimes = 25
q = quarters
p = pennies
n = nickels
1. q + n = p
2. 4n = 1 d
3. 2p = 1n

1 d = 4n
25 d = x 
x = 4 * 25 = 100 nickels

1 n = 2 p
100 n = x  p
100 n = 200 p

q + n = p
There are 100 nickels. there are 200 pennies
q + 100 = 200
q = 200 - 100
q = 100

Answer
There are 100 quarters,<<<<======


Answer:

Quarters = 175

Step-by-step explanation:

Let the number of dimes in the jar = 25

number of Nickels = n

number of quarters = q

number of pennies = p

Now we will form the equation

Number of quarters plus dimes equal the number of pennies.

q + 25 = p  --------(1)

You have 4 nickles for every dime

n = 4d

n = 4 × 25 = 100

and you have 2 pennies for every nickels

p = 2n

p = 2 × 100 = 200

Now we replace p = 200 in equation (1)

q + 25 = 200

q = 200 - 25

q = 175

Option A. 175 will be the answer.

Find the area of the following circle. (Round answer to the nearest hundredth.)
d = 15 in
area = _____ square inches
circumference = ______ inches

Answers

The area of the circle is 176.63 inches

The area of circle is,

⇒ 176.62 in²

And, ⇒ Circumference = 47.1 in.

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The diameter of circle is,

d = 15 in.

Hence, Radius of circle is.

r = 15 / 2

r = 7.5 in,

Thus, Area of circle is,

⇒ πr²

⇒ 3.14 × 7.5²

⇒ 176.62 in²

And, Circumference = 2πr

⇒ Circumference = 2 × 3.14 × 7.5

⇒ Circumference = 47.1 in.

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Write a quadratic function f whose zeros are 3 and 8

Answers

The standard form of a quadratic equation is: ax²+bx+c=0, and it is represented with a polynomial of degree 2, that's why it is also called "Equation of degree 2".
 
 1. So, if 3 and 8 are zeros of the quadratic function, then they are factors of it. Therefore, you have:
 
 (x+3)(x+8)=0
 
 2. When you write it in the standard form, you have:
 
 x²+11x+24=0
 
 a=1
 b=11
 c=24

Given: ABCD is a rectangle, AC ∩ BD = O, m∠ABD=30°, AC=16 in. Find BC.
I need the answer to this question ASAP!


Thanks!

Answers

∠BAC = ∠ABD = 30°
BC/AC = sin(∠BAC)

BC = AC*sin(∠BAC)
.. = (16 in)*sin(30°)
.. = 8 in
It is 8 inches as I have calculated

help with geometry please! will mark brainliest

Answers

1. The segment LO bisects one of the angles of the triangle shown in the figure attached, and divide the segment NM in two segments: NO and OM. Therefore, you must apply the Triangle Angle Bisector Theorem, which is shown below:

 LN/LM=NO/OM

 LN=10
 LM=18
 NO=4
 OM=x (The value you want to find)

 2. When you substitute this values in LN/LM=NO/OM, you have:

 10/18=4/x
 10x=(18)(4)
 x=(18)(4)/10
 x=72/10

 3. Finally, you obtain:

 x=7.2

 The answer is: The value of "x" is 7.2

**HELP!**

El Generico public high school got a new flag pole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janoitor set up a 5-foot stick next to the flagpole and compared shadows. The 5 foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.

Use rules of similar polygons to figure out how tall the flagpole is! HINT: this will involve proportions!

Answers

if two figures or lengths are similar, then the ratios of the corresponding lengths are equal.
Thus, 8/32 =5/x
          8x = 160
            x = 20 feet
Therefore, the length of the flag pole was 20 feet long

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase or decrease per time period.

y=12(2)^t

Plz help!

Answers

See also https://brainly.com/question/8975313

The growth factor is 2.

The increase is (2 -1)*100% = 100% per period.

Please help me Idk what I’m doing thanks

Answers

check the picture below.

A large statue is in the shape of a square pyramid. Each side of the base of the square pyramid is 723 feet long and the height is 341 feet.

What is the volume of the statue?

___ft³

Answers

Simple. First write down the equation.
(a^2)h/3
Next, plug in the variables you know.
(723^2)341/3
(522,729)(113.67)
= 59,416,863 is your answer.
Hope this helps!

Answer:

The volume is[tex]=59,416,863ft^3[/tex]

Step-by-step explanation:

Given A large statue is in the shape of a square pyramid. Each side of the base of the square pyramid is 723 feet long and the height is 341 feet.

Base edge=a=723 feet.

Height=h=341 feet

As, [tex]\text{Volume of square pyramid is=}(a^2)\frac{h}{3}[/tex]

Substitute the values of a and h, we get

[tex]V=(723^2)\frac{341}{3}[/tex]

    [tex]=(522,729)(113.67)[/tex]

    [tex]=59,416,863ft^3[/tex]

What is the equation of the line that is perpendicular to the line and passes through the point (6, 2)?

Answers

Hey there! :D

So, when you find something perpendicular, you are finding the opposite reciprocal. 

The slope is 1/2 because:

y=mx+b <== it is in this form; m is equal to slope. 

Flip the 2 and 1 and make it negative. 

2/1= -2

We already know "C" and "D" aren't the options. Now, we can just plug in the points given to see if it works. Plug in the set of points (6,2)

y=-2x+14

2=-2(6)+14

2=-12+14

2=2 <== this works. This is our answer. Let's just make sure by checking the other one. 

y=-2x-2

2=-2(6)-2

2=-12-2

2=-14 <== that is not true. 

The first option is correct.

I hope this helps!
~kaikers


Step [tex]1[/tex]

Find the slope of the line perpendicular to the given line

we have

the equation of the given line is

[tex]y=\frac{1}{2}x+7[/tex]

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

in this problem the slope m1 of the given line is

[tex]m1=\frac{1}{2}[/tex]

so

[tex]m2=-\frac{1}{m1}[/tex]

[tex]m2=-2[/tex]

Step [tex]2[/tex]

Find the equation of the line with slope m2 and passes through the point [tex](6, 2)[/tex]

we know that

the equation of the line is

[tex]y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14[/tex]

therefore

the answer is the option A

the equation of the line is [tex]y=-2x+14[/tex]

see the attached figure to better understand the problem

Sabastian is driving 400 miles to meet his friend. He travels 100 miles in the first two hours of his trip. If he continues at the same rate, how long will it take to drive the remaining distance?

Answers

His rate so far is (100 mi)/(2 h), so 50 mi/h. The remaining 300 miles will take
.. (300 mi)/(50 mi/h) = 6 h

An antique car was purchased for $7400 and is not worth $10,600. What is the approximate percent of change

Answers

I assume you meant "is now worth," right?

% CHANGE FORMULA:
(New # - Original #) ÷ Original # x 100

%= ($10600 - $7400)/7400 x 100
%= $3200/$7400 x 100
%= 0.432 x 100
%= 43.2% increase

ANSWER: 43% increased change

Hope this helps! :)



The approximate percentage of change will be 43.24%.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

An antique car was purchased for $7400 and is not worth $10,600.

Then the approximate percent of change will be given as,

P = [(10600 - 7400) / 7400] x 100

P = (3200 / 7400) x 100

P = 0.4324 x 100

P = 43.24%

The approximate percentage of change will be 43.24%.

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The surface area of a cube is 150 cm2. what is the area of each face of the cube?

Answers

the area of each face is 25 cm

Answer:

6 25 5 these r the answers

Step-by-step explanation:

edge2021

Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0. h(t) = · sin( t + ) +

Answers

Answer:

the correct answer is

h(t)= 25 * sin (1 pi t + (-0.5) pi) + 29

Step-by-step explanation:


What type of association does the scatter plot show?

Answers

Scatter plots show how much one point or variable affects the other (or another point). 

Answer:

wheres the scatter plot

Step-by-step explanation:

.help me please thank you.

Answers

it should be the second option which is the SAS postulate
it is the SAS postulate

The corners of a fence are at a (11,3), b (3,-11), c (-13,-9), and d (-5,9). let q be the midpoint of ????????⎯⎯⎯⎯⎯, r be the midpoint of ????????⎯⎯⎯⎯⎯, s be the midpoint of ????????⎯⎯⎯⎯⎯, and t be the midpoint of ????????⎯⎯⎯⎯⎯. what are the midpoints of the sides of this fence?

Answers

The midpoints and their coordinates are shown in the attached figure.

The midpoint between two points (a, b) and (c, d) can be found by averaging their coordinates:
.. midpoint = ((a+c)/2, (b+d)/2)

Nial is signing a lease for an apartment that rents for $1020/month. How much will he pay to move in if he must pay the first and last months' rent and a security deposit equal to 60% of his monthly rent?

2040


$2448


$2652


$2856

Answers

1020 + 1020 = 2040
%60 of 1020 is:612
2040+612=2652
so third one is true

Answer:

Option (c) is correct.

He pays $ 2652.

Step-by-step explanation:

Given :   Nial is signing a lease for an apartment that rents for $1020/month.

We have to find the amount he pay to move in if he must pay the first and last months' rent and a security deposit equal to 60% of his monthly rent.

Since, given he must pay the first and last months' rent and a security deposit equal to 60% of his monthly rent.

Given monthly rent is $ 1020

That is 60% of his monthly rent = [tex]\frac{60}{100}\times 1020=612[/tex]

Thus, total amount he needs to pay is  first month rent + last month rent + 60% of his monthly rent.

That is 1020 + 1020 + 612 = 2652.

Thus, He pays $ 2652.

In a hockey club there are 5% more boys than there are girls. If there is a total of
246 members in the club, what is the number of boys and the number of girls?
HOW WOULD I WORK THIS OUT

Answers

Determine the percentage of boys and the percentage of girls in the club.
For an instance, pb stands for percentage of boys, and pg stands for percentage of girls.
pb + pg = 100%

There are 5% more boys, pb = pg + 5%
Input to the previous equation to find the percentage of the girls
pb + pg = 100%
pg + 5% + pg = 100%
2pg + 5% = 100%
2pg = 100% - 5%
2pg = 95%
--------------- divide each side by 2
pg = 47.5%

Substitute the percentage of girls to either equations to find the percentage of the boys
pb = pg + 5%
pb = 47.5% + 5%
pb = 52.5%

Find the number of the boys and the girls
The boys
b = pb × total members
b = 52.5% × 246
b = 0.525 × 246
b = 129.15
Because the number of people couldn't be a fraction, round to the nearest whole number
b = 129

The girls
g = total - b
g = 246 - 129
g = 117

There are 129 of boys, and 117 of girls

The number of boys and the number of girls are 126 and 120 respectively.

What is percentage?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, there are 5% more boys than there are girls, there is a total of

246 members in the club,

We need to find the number of boys and the number of girls,

Here we will use the concept of percentage as well as equation solving,

Let the number of girls be x, so, the number of boys = 105% of x = 1.05x

According to the question,

x+1.05x = 246

2.05 x = 246

x = 120

1.05x = 126

Hence, the number of boys and the number of girls are 126 and 120 respectively.

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Jennifer wants to rent a car for 5 days, and she’s interested in a the loss damage waiver but not the collision damage wavier.If the daily rate is $39 and LDW is $65 for the rental period,what is her total cost?

Answers

T= total cost
n= number of days

Total cost equals the cost per day times the number of days plus the fee.

T= $39n + $65
substitute 5 for n
T= 39(5) + 65
T= 195 + 65
T= $260 total cost

Hope this helps! :)

APEX  $260 is correct answer.

solve the following question: |x|=3/4

Answers

Answer:  "x = [tex] \frac{3}{4} [/tex]" or "x = - [tex] \frac{3}{4} [/tex]" .
____________________________________________________
 
Or, write as:  " x = ± [tex] \frac{3}{4} [/tex] " .

____________________________________________________
Answer: x = ¾, -¾

Process:Remove the absolute value term. This create a _ On the right side of the equation because |x| = _x.
x = _ ¾

Set up the positive portion of the _ solution.
x = ¾

Set up the negative portion of the _ solution.
x = -¾

The solution to the equation includes both the positive and negative portions of the solution.
x = ¾, -¾

I hope this helps!
Please Rate & Thank!
Please mark as Brainliest!

Have a wonderful day! : )

i need to know the equations

Answers

Let l, t, b represent the numbers of lions, tigers, bears, respectively.

2l +3t +3b = 156 . . . . . . . 156 meals per day are supplied
l +t = 3b . . . . . . . . . . . . . . there are 3 times as many great cats as bears
l +t +b = 68 . . . . . . . . . . . there are a total of 68 animals

_____
The last 2 equations tell you
.. 4b = 68
.. b = 17
Subtracting 3 times the last equation from the first gives
.. -l = -48
There are 48 lions, 3 tigers, and 17 bears.
Let L = number of lions
Let T = number of tigers
Let B = number of bears

If one lion eats 2 meals per day, then L number of lions eat 2L meals per day.
Tigers eat 3T meals per day, and bears eat 3B meals per day.

In one day, all animals combined ate 156 meals.

That gives us our first equation.

2L + 3T + 3B = 156

The lions and tigers are considered great cats. The bears are not cats.
There are 3 times as many great cats as bears.
This gives us our second equation.

L + T = 3B

In all there are 68 animals in the zoo.
From here we get our third equation.

L + T + B = 68

Our system of equations is:

2L + 3T + 3B = 156
L + T = 3B
L + T + B = 68

Now we solve the system of equations.

Subtract the second equation from the third equation.

B = -3B + 68

4B = 68

B = 17

Substitute B = 17 into the first and second equations.

2L + 3T + 3B = 156

2L + 3T + 3(17) = 156

2L + 3T + 51 = 156

2L + 3T = 105      New Equation A

L + T = 3B

L + T = 3(17)

L + T = 51   Equation B

Equations A and B have only two variables, so we can solve them as a system of two equations in two unknowns.

2L + 3T = 105
L + T = 51

Rewrite equation A. Multiply Equation B by -2 and write underneath Equation A. Then add the equations.

       2L + 3T = 105
+    -2L - 2T = -102
-------------------------
                T = 3

Now use B = 17 and T = 3 in the original third equation to solve for L.

L + T + B = 68

L + 3 + 17 = 68

L + 20 = 68

L = 48

Answer: There are 48 lions, 3 tigers, and 17 bears

Check:
"Lions eat 2 meals per day, tigers and bears eat 3 meals each per day."
Number of meals:
2 * 48 + 3 * 3 + 3 * 17 = 96 + 9 + 51 = 156

"There are 3 times as many great cats in the zoo as bears."
48 + 3 = 51, and 51 is 3 times 17

"There are 68 animals in the zoo."
48 + 3 + 17 = 68

All statements are satisfied by our solution, so the answer above is correct.

Determine whether each pair of angles is a pair of vertical angles, a linear pair of angles, or neither. Select the correct answer for each lettered part.

Answers

A)  ∠AFC and ∠CFD are neither.  They share more than a vertex, so they are not vertical angles.  Also, they do not form a straight line so they do not make a linear pair.
B)  ∠AFB and ∠CFD are neither.  Vertical angles are also known as vertically opposite angles.  While these two only share a vertex, they are not opposite each other.  They also do not form a linear pair, as they do not form a straight line.
C)  ∠BFD and ∠AFE are vertical angles.  They are opposite each other and share only a vertex.

Answer:

Linear Pair, Neither, Vertical.

Its also in the attached PNG just in case the question you have decides to put them out of order. You are all welcome! I hope this helps you people in the future

Describe how you would estimate the square root of a number that is not a perfect square without using a calculator. lets say n was the imperfect square number and the square root is w. the square root of n = n+w squared/ 2w.

Answers

To get the square root of imperfect square we can use the formula , which is usually accurate to about two decimal places,
√X =√S +(X-S)2√S
Where, X = the number you want the square roof of, and S is the closest square you know to x.
For example 75 is an imperfect square
Thus, X=75 and thus the nearest number S = 81, this ,means √81 =9.
Putting this into the formula;
√75= 9+(75-81)/2/2(9)
      =  9 + -6/18 
      = 9-0.33333 = 8.667
= 8.667, thus the square root of 75 is 8.66

Then net folds into s cube. Which two letters appear on the opposite faces?

Answers

Out of the choices given, B and E will be opposite of each other when the folding occurs. You have to imagine what it would look like, once folded.
B and E i'm confident

Kelly is hanging shelves in her closet. She can buy shelves for $1.25 a foot. Kelly buys one 5-foot shelf and a shelf that measures 24 inches. The rest of her materials cost $90. How much change will she get it she pays with $100?

Answers

Hello!

There are 12 inches in a foot.

Kelly buys two shelves that measure 7 feet altogether, and the cost of each foot is $1.25.

Multiply the number of feet by the cost per foot.

7 × 1.25 = 8.75

Add this to the cost of the rest of her items.

90 + 8.75 = 98.75

Finally, subtract this from the $100 Kelly will use to pay.

100 - 98.75 = 1.25

ANSWER: Kelly will receive $1.25 change after her payment.

In the diagram, △ABC ≅ △WRS. What is the perimeter of △WRS?

10 units
11 units
12 units
13 units

Answers

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

△ABC ≅ △WRS

So, Perimeter of △ABC is given by

AB+BC+CA

here, AB = 3 units

BC = 4 units

AC = x

By pythagorus theorem, we get that

[tex]AC^2=AB^2+BC^2\\\\x^2=3^2+4^2\\\\x^2=9+16\\\\x^2=25\\\\x=\sqrt{25}\\\\x=5\ units[/tex]

So, perimeter of △ABC is

3+4+5=12 units

So, the perimeter of △WRS is also 12 units as they are similar triangles .

Hence, Third option is correct.

Answer:

The Answer Is 12

Step-by-step explanation:

Jarrod walked 3 miles due north before turning left and walking 3.5 miles due west. He turned again and returned to his starting point by walking a straight path. What was the angle of the last turn? Round to the nearest degree.

Answers

see the attached figure

the angle of the last turn was angle alfa in the point C
tan(alfa)=3/3.5=0.8571
alfa=arctan(0.8581)=40.60°
Round to the nearest degree---------> alfa=41°

the answer is 41°

Find the volume of this

Answers

V = 4 cm * 5 cm * 3 cm = 60 cm³
3cm * 4cm * 5cm = 60 cm^3
Answer is C

Other Questions
Read the following paragraph and answer the question. 1Poe really was the inventor of the detective story, which he called the "ratiocinative" tale. 2Here believing the effect intended was "to perplex the reader and whet his desire for elucidation," he originated two devices useful to this day. 3One might be called "the device of the baffled friend": He gave his brilliant detective a companion not good at solutions and had him tell the story. 4Viewing the happenings through this narrator's eyes, the reader shares his growing puzzlement. 5Poe used his second device at the tale's end: He had the detective disclose his surprising solution and then "elucidate" step by step the reasoning which led to it. 6"The Purloined Letter" demonstrated Poe's use of these two devices in a detective story. (From: United States in Literature by Walter Blair, Paul Farmer, Theodore Hornberger, and Margaret Wasson. C. 1963 by Scott, Foresman and Company. Reprinted by permission.) Type the essential words which must be included in a paragraph summary of Sentences 1-6. AB BC and AD CD What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem? What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem? Can someone help me? A spherical model of planet Earth has a radius of 3 ft.What is the approximate volume of the model of planet earth?Use 3.14 to approximate pi. Round to the nearest hundredth if necessary.Enter your answer in the box. 226in is equal to how many ft and in (show work pls help me!!Which of the following is a large body in space that orbits a star and does not produce its own light?MoonPlanetSunUniverse Will Upvot!!!!!In the Vedic Age, what types of goods were traded most often? A. goods that there is a shortage of B. goods that are expensive and rare C. goods that there is a surplus of D. goods that are cheap but rare which statement correctly describes an example of the cohesive property of water How did the magna carta inspire later documents? A.It stated that a social contract was violated if a monarch was in power. B.It clarified that the justice system was subject to the approval of government leaders. C.It declared the monarch to be an illegal position of authority. D.It argued that all people were subject to the rule of law. write the number in scientific notation 0.0000024please help This Southeast Asian country was once a French colony, was split by war from 1954 to 1975, and currently exists as a unified, socialist state. How does the reader know that the narrator's mental state has begun to deteriorate? dan saved $463 over the 12 weeks of summer break. He saved $297 of it during the last 4 weeks.How much did he save during the first 8 weeks? How did the Catholic Church respond to the Scientific Revolution? Subtract: 12 3/8 - 8 1/5 A)4 2/3 B)4 1/20 C)4 2/13 D)4 7/40 Suppose (b c)d = 0, where b and c and m n matrices and d is invertible. show that b =c. What is the quotient of 22,389 and 13? Mary is giving a persuasive speech about the benefits of adoption over abortion and wants to engage her audience early on. Which of the following supporting materials would probably be the most effective choice to use during the introduction of her speech? a. A total of 820,151 legal induced abortions were reported in 2005, the abortion ratio (number of abortions per 1,000 live births) was 233, and the abortion rate was 15 per 1,000 women aged 15--44 years. - (www.cdc.gov) b. According to Lisa M. Koonin, M.N., M.P.H. and Jack C. Smith, M.S., Legal induced abortion is one of the most frequently performed surgical procedures in the United States. Abortion rates for teenagers are much higher in the United States than in most Western European countries and in some Eastern European countries. c. My name is Allie J. A few years ago I was working as an outreach worker in Vancouver, BC, Canada. One of my clients asked me to go with her while she got an abortion. I sat holding her hand wondering how I ever thought that this was not going to affect me. I was ashamed to think I had condoned this. Never will I encourage abortion over adoption again. There is a better way. d. A young teenage girl who becomes pregnant and is faced with the choice of whether to give her child up for adoption or to have an abortion. Rhetorical questions are used to strengthen a point in speaking or writing. true or false No democrat has won texas in a presidential race since ________.