the length of a rectangle is 5 cm more than twice a number. the width is 4cm less than the same number. if the area of the rectangle is 15cm2, find the number

Answers

Answer 1
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number

Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5

Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15

Related Questions

Name a diameter.
8
G
E
A
FG
С
CE
B.
AB
D
BO

Answers

Answer:

FG

Step-by-step explanation:

FG is the only line which goes straight across the circle through the centre

Aliya lined up the interior angles of the triangle along line p below
When the measure of angle A increases in the triangle, what happens to angle A on line p?
It also increases.
Olt decreases
It stays the same.
It may increase, or it may stay the same.

Answers

Answer:

it also increases

Step-by-step explanation:

Solve:
5 = p/4




SOMEONE PLEASE HELP IM SO CONFUSED AND THEIR IS 90 QUESTIONS AND IM ONLY ON 50 AND ITS DUE THIS FRIDAY

Answers

Answer:

p = 20

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtraction

~

Isolate the variable, p, by multiplying 4 to both sides of the equation:

[tex]5 = \frac{p}{4}\\ 5 (* 4) = \frac{p}{4} (* 4)\\ 5 * 4 = p\\p = 20[/tex]

p = 20 is your answer.

~

5 = p/4

You have to put unknowns (p) on 1 side and knowns on other side.

To get p alone you have to move the 4. Since p divides 4, you have to multiple by 4 to cancel it out. BUT Remember if you have to change one side, you have to change other side by same amount too, so the equality stays true. So multiply BOTH sides by 4

4* 5 = (p/4)*4

the 4s on the right side cancel each other because 4/4=1
So,

20 = p

Thursday: For the equation y=3x+5 what is the value of x when y=11? * * ​

Answers

Answer:

[tex]\huge\boxed{\bf\: 2 = x}[/tex]

Step-by-step explanation:

Given,

y = 11

We need to find x.

Equation: y = 3x + 5.

On solving,

[tex]y = 3x + 5\\(11) = 3x + 5\\11 - 5 = 3x\\6 = 3x\\6 \div 3 = x\\\boxed{\bf\:2=x}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

help pls
I'm not good with this stuff lol​

Answers

Answer:
40 square feet

Steps:
Formula for the area of a triangle.
A = B*H/2

Formula for the area of a rectangle.
A = L*W


1. Break up the shape into 1 triangle and 1 rectangle.

2. The length of the rectangle is 8 ft and the width is 3 ft. Plug-in these values into the formula for the area of a rectangle.

A = 8 * 3
A = 24

3. The base of the triangle is 8 ft and the height is 4 ft. Plug-in these values into the formula for the area of a triangle.

A = (8 * 4) / 2
A = 32 / 2
A = 16

4. Now add the two areas together to find the amount of carpet needed.

24 + 16 = 40


Answer:

38 ft²

Step-by-step explanation:

You can take it as combination of two figures, a trapezoid and a triangle.

Trapezoid has bases 12 ft and 8 ft and height 3 ft

Its area is

A = 1/2(8 + 12)(3) = 30 ft²

Triangle has height 4 ft and base 4 ft,

Its area is

A = 1/2(4*4) = 8 ft²

Total area is

30 + 8 = 38 ft²

find the lateral area and surface area of each prism. please show your work. ​

Answers

I think the lateral area is based on the surface area of each prism that make up for it

[tex]\stackrel{\textit{\Large Lateral Area}}{\stackrel{\textit{area of the 6 sides}}{6(12)(15)}\implies 1080} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ p=\stackrel{6\times 12}{72}\\ a=10.39 \end{cases}\implies A=\cfrac{1}{2}(10.39)(72)\implies 374.04 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{lateral}{1080}~~ + ~~\stackrel{two~hexagons}{2(374.04)}}\implies 1828.08\qquad \leftarrow \textit{total surface area}[/tex]

What is the length of the Radius if AB is tangent to OB

Answers

Answer:

r = 5 units

Step-by-step explanation:

One way is to use the Pythag Theroem

12 ^2 + r^2 = (8+r)^2

144 + r^2 = 64 + 16r + r^2

80 = 16 r      r = 5

Which expression is equivalent to -7 + 5a ?
-2a
-12a
5a - 7
-5a + 7

Answers

Hey there!

-7 + 5a


We DO NOT have any LIKE TERMS so we can NOT do much to this equation


So, the one that seems about right would be: -5a + 7


Answer: -5a + 7 (Option D)


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Which is a larger volume, a candle with a height of 6. 3 inches and a radius of 3. 1 inches, or a candle with both a height and a radius of 3. 9 inches?

Answers

Step-by-step explanation:

such candles are cylinders.

the volume of a cylinder is

pi×r²×height

the volume of candle 1 is

pi×3.1²×6.3 in³ = pi × 60.543 in³

the volume of candle 2 is

pi×3.9²×3.9 in³ = pi × 59.319 in³

so, candle 1 has the larger volume.

Due yesterday

Even if ur sure its correct j send it, ill turn in anything

Answers

Answer:

A)8000

B) 1296a^4

C) 9x^2

D)100000000

E)0.00097656

F)x^⁶

G)y^11

Step-by-step explanation:

» Look at this scatter plot.
60
54
48
42
36
.
30
24
18
12
6
х
6
6
12
.
18
24
30
36
42
48
54
60
)) Which equation could represent the line of best fit for this data?
II
y = -3x + 42
-X
+ 18
y = kx +
+ 24
y = 3x + 30
y = -x + 36
y
y = x + 12

Answers

Answer:

The mean for the data in the dot plot is 5. What is the

absolute deviation for the data point at 7?

2

Step-by-step explanation:

On an average day 1/40 of the students at Brown Middle School are absent during an outbreak of flu twice as many students are absent what fraction of students is this

Answers

First:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
140×21
1
40
×
2
1
Applying the fractions formula for multiplication,
=1×240×1
=
1
×
2
40
×
1
=240
=
2
40
Simplifying 2/40, the answer is
=120

In January 2015, the Pew Research Center reported results from one of their surveys. "Asked about whether vaccines for childhood diseases such as measles, mumps, rubella (MMR) and polio should be required or left up to parental choice, 68% of adults say such vaccines should be required while 30% say that parents should be able to decide whether or not to vaccinate their children. "
The following is an excerpt from the press release:
The survey of the general public was conducted using a probability-based sample of the adult population by landline and cellular telephone Aug. 15-25, 2014, with a representative sample of 2,002 adults nationwide. The margin of sampling error for results based on all adults is plus or minus 3. 1 percentage points. What is 95% confidence interval for these findings

Answers

Considering the margin of error, it is found that the 95% confidence interval for the percentage of adults who say vaccines should be required is (64.9%, 71.1%).

What is a confidence interval?

It is given by the sample statistic plus/minus the margin of error.

In this problem, 68% of adults say such vaccines should be required, with a margin of error of 3.1%, hence:

68% - 3.1% = 64.9%.

68% + 3.1% = 71.1%.

The 95% confidence interval for the percentage of adults who say vaccines should be required is (64.9%, 71.1%).

More can be learned about confidence intervals at https://brainly.com/question/25890103

Use the portion of the exponential graph below to answer questions 7-8.

What is the domain?

What is the range?

Answers

Answer:

See below ~

Step-by-step explanation:

Domain = range of x values

Lowest value = -1Highest value = 3Domain ⇒ -1 ≤ x ≤ 3

Range = range of y-values

Lowest value = 6Highest value = 27Range ⇒ 6 ≤ y ≤ 27

Jared sold 194 Boy Scout chocolate bars. Matthew sold three times as many as Jared. Gary sold 297) few than Matthew. How many bars did Gary sell?​

Answers

Answer:

285 choclate bars

Step-by-step explanation:

Jared: 194 choc. bars

Mathew: 3*jared=3*194=582

Gary: matthew-297=582-297=285 choc. bars

round 256.709 to the nearest tenth place

Answers

Answer: 256.7

Step-by-step explanation: the tenth place, (7) is rounded to 7 because when you round the number after the tenth place (7) the number has to be at 5 or greater inorder to change values.

Which statement is true?
A. |-2.5| >|-3|
B. |-2.5| <|-3|
C. |-2.5| = |-3|

Answers

Answer:

A. |-2.5| >|-3|

Step-by-step explanation:

I GOT THIS WRONG!! So what is the answer??

BOTS=BAN/REPORT

TROLL=BAN/REPORT

Answers

Use one of the sets and divide them to find the proportional relationship.

3 / 43.5 = 0.06896

Now since it's not in the answer choices, you round it.

0.06896 rounded to the nearest tenths is 0.7

I’m not sure but I belive that the correct answer was/ is A sorry if you get it wrong

sam has $37 to spend at a festival the price of admission is $10 and tickets to each attraction cost $0.75. how many tickets can he get

Answers

Answer:

37-10=27 then 27 / 0.75 = 36

Step-by-step explanation:

36 is your answer

Matt wants to start zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint? Use specific numbers from the situation to justify or refute whether Matt’s design meets the slope constraint

Answers

There is no difference in height that is not sufficient to meet the slope constraint if Matt wants to start a zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint.

What is the slope?

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

We know the slope can be evaluated using:

[tex]\rm Slope = \frac{Change \ in \ y \ axis}{Change \ in \ x \ axis}[/tex]

Change in y-axis = difference in height

Change in y-axis = 16 - 10

                            = 10 feet

Change in x-axis = distance between tress

Since the data is not given.

So, the height difference is insufficient to keep the slope constraint.

Thus, there is no difference in height that is not sufficient to meet the slope constraint if Matt wants to start a zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint.

Learn more about the slope here:

https://brainly.com/question/3605446

#SPJ1

A quadrilateral has two angles that measure 222° and 81°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?

Answers

[tex]\sf\huge\underline{\star Solution:-}[/tex]

[tex]\rightarrow[/tex] Ratio of two angles are 6:13.

So, let the one angle be [tex]\sf{6x}[/tex] and another be [tex]\sf{13x.}[/tex]

As we know that,

Sum of all interior angles of a quadrilateral = [tex]\sf\pink{360°.}[/tex]

So let's sum up the given angles,

[tex]\rightarrow[/tex] [tex]\sf{222°+81°+6x+13x \:=\: 360°}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{303+19x \:=\: 360°}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 360-303}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 57}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{x \:=\: \frac{19}{57}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{x \:=\: 3}[/tex]

Hence, [tex]\sf{x \:=\: 3}[/tex]

So, First angle [tex]\sf{= \:6x\: = \:6×3 \:=}[/tex] [tex]\sf\purple{18°.}[/tex]

Second angle [tex]\sf{= \:13x\: = \:13×3 \:=}[/tex] [tex]\sf\purple{39°.}[/tex]

_________________________________

Hope it helps you:)

HELP ASAP
The table shows how the number of sit-ups marla does each day has changed over time. At this rate, how many sit-ups will she do on day 12? Explain your steps in solving this problem

Day 1 - 12
Day 2 - 21
Day 3 - 25
Day 4 - 29
Day 5 - 33

Answers

Answer:

177

Step-by-step explanation:

just answered this for someone else but the number of sit-ups is going up in 4s so just add four to 33 7 times since thats how many days she has left til 12th day

if you invest 1500 today in a bank that gives you 5% annual interest eats, which of these items can you buy in two years

Answers

1500 dived by 5% should give u ur answer

if the prisms below are similar what is the ratio of the surface area of the smaller prism to the surface area of the larger prism
v=24
v=375

Answers

The ratio between the surfaces areas of the two prisms is equal to 6.25.

How to get the ratio of the surface areas?

The ratio between the volumes of the prisms is:

[tex]R_v = \frac{375 in^3}{24 in^3} = 15.625[/tex]

This number is equal to the cube of the scale of dilation applied to the dimensions of the smaller prism, so the scale factor is:

[tex]\sqrt[3]{15.625} = 2.5[/tex]

And the ratio between the areas should be the square of the scale factor, then we will have that the ratio between the surface areas of the two prisms is:

[tex]2.5^2 = 6.25[/tex]

If you want to learn more about scale factors, you can read:

https://brainly.com/question/3457976

Some of the dimensions of a square pyramid are shown in the diagram. The height of the pyramid is 7.5 meters.

square pyramid

What is the volume of the square pyramid in cubic meters?

Question 8 options:

40 m3

120 m3

360 m3

60 m3

DIGRAM BELOW

Answers

Answer:

40 m^3.

Step-by-step explanation:

Volume = 1/3 * 4^2 * 7.5

=  40 m^3.

i dont know this and i think its going to be in our FSA please help THANK YOU.....

Answers

Answer:

You never put a screenshot

Step-by-step explanation:

Pls put screenshot :)

Solve the equation 1.37w=0

Answers

1.37w=0
Divide by 1.37 on both sides
w=0

Hey there!

1.37w = 0

DIVIDE 1.37 to BOTH SIDES

1.37w/1.37 = 0/1.37

CANCEL out: 1.37w/1.37 because it give you 1

KEEP: 0/1.37 because it help solve for the w-value


NEW EQUATION: w = 0/1.37


SIMPLIFY IT!


w = 0


Therefore, your answer is: w = 0

Good luck on your assignment & enjoy your day!



~Amphitrite1040:)

HELP! BRAINLIEST!
Which of the following represents vector w = 11i − 60j in trigonometric form?

w = 61❬sin 280.389°, cos 280.389°❭
w = 61❬cos 280.389°, sin 280.389°❭
w = 61❬cos 79.611°, sin 79.611°❭
w = 61❬sin 79.611°, cos 79.611°❭

Answers

Answer:

  w = 61❬cos 280.389°, sin 280.389°❭

Step-by-step explanation:

The "trigonometric form" of a vector is ...

  (magnitude)❬cos(angle), sin(angle)❭

This is sometimes abbreviated ...

  magnitude cis(angle)

__

This form immediately eliminates choices A and D, as those have the trig functions reversed. The signs on the unit vectors i and j tell you the vector has a 4th-quadrant angle, so will be between 270° and 360°. Only answer choice B makes any sense.

  w = 61❬cos 280.389°, sin 280.389°❭

_____

Additional comment

The angle is computed from ...

  θ = arctan(y/x) = arctan(-60/11) = -79.611°

Expressed as a positive angle in the range [0, 360°), that will be ...

  360° +(-79.611°) = 280.389°

__

The abbreviation "cis" is mentioned as an aid to remembering the (x, y) coordinates are the cosine and sine of the angle, in that order.


Please help me find the angles marked in the above diagrams The first figure is 8cm,5cm
2. 8m,15m
3. 8.4m,6.3m
4. 105m,123m

Answers

I can not see it very well.

Help! Khan academy geometry practice

Answers

33.51, or 33.5.

V = 4/3πr³ = 4/3π2³= 33.5 (rounded)
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