Mathematics High School


5. A w-foot wide path is to be built around a rectangular space that is 80
feet by 50 feet. Write and simplify an expression for the total area.

Answers

Answer 1

To find the area of the path, we'll need to find the area of the space with the path and subtract the area of the inner space.

Total area: (80 + w)(50 + w)

Inner area: 80 x 50

Area of the path: (80 + w)(50 + w) - (80 x 50)

(4000 + 80w + 50w + w^2) - (4000)

4000 + 130w + w^2 - 4000

w^2 + 130w

w(w + 130)

Expression for the total area: (80 + w)(50 + w)

Expression for the area of the path: w(w + 130)

Hope this helps!! :)

Related Questions

literally the only question I'm struggling to understand rn...i hate puzzles :C.
​

Answers

Answer:

It's 2 4 7

Step-by-step explanation:

The first column says "one number is correct and well placed," so it's number two, because the third column says "One number is correct but incorrectly placed," which means number 2 is in the same place, and number 4 is in the last, but the fourth column says "Two numbers are correct but incorrectly placed," means 4 and 7 are in the first and second columns, but supposed to be in the 2nd and 3rd place, respectively. As a result, it's 2, 4, 7, and I hope you understand because I'm terrible at explaining things.

calculate log 1.125 please​

Answers

Answer:

0.05115

Step-by-step explanation:

Plug it into your calculator and you'll get the same value

Rolling a six sidded die and getting a I or 5

Answers

Answer:

probability is the same

mathematics algebra sat

Answers

Answer:

D

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] w = [tex]\frac{4}{3}[/tex] , that is

[tex]\frac{3w}{5}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )

9w = 20 ( divide both sides by 9 )

w = [tex]\frac{20}{9}[/tex] → D

Multiply both sides of the equation by 5/3; 5/3 * (3/5 * w) = 5/3 * 4/3 Simplify both sides of the equation. Simplify both sides of the equation . Simplify both sides of the equation .... Simplify the left side . ... Simplify Simplify 5/3 * (3/5 * w)... w = 5/3 * 4/3 Simplify the right side .. Multiply 5/3 * 4/3
the answer is w = 20/9

what is 26 divided by 9 as an improper fraction

Answers

Answer:

26/9

Step-by-step explanation:

26/9 is correct because it cannot be simplified so it is left as 26/9

Marie is reading a 271-page book. She has already read 119 pages. If she reads
at about 8 pages per hour, how long will it take her to finish the book?
Which equation helps to solve this problem?

Answers

Answer:

119+8h=271

Step-by-step explanation:

We already know she has read 119 pages out of 271. And we know the constant proportionality in this is 8 pages every hour. If we were able to find out how long it took for her, then we would add that with 119, because that, in total, will be 271/the whole book, with 152 pages of it in hours.

sorry if this doesn't make sense, if you want me to explain more on it go ahead and ask!

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

Answers

Answer:

5678

Step-by-step explanation:

yeeeeeeeeeeeeeeeeeeeeeeee

Please help me with this. Please dont just type in the wrong answer to get points. I will give 30 points to anyone who answers correctly and i will mark you as the brainliest so you will get rewarded.

Answers

it is 53cm because it says beside the d 53cm and it the length

jeqndc[ppppppppi21111112fffffffffffffffffffffffffffffffffffffffffffffffff

please need help asap

Answers

Answer:

30 = 6 x 5

g = 5

I think that might be the answer

Step-by-step explanation:

Answer: g x 6 = 30

5 times 6 is 30, so g is 5.

Wrong and silly answer will be reported .​

Answers

I HOPE IT WILL HELP YOU.

Thank you.

2²×2³×2⁸×2⁹+10+20²+10+10+10

Answers

>> Answer

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

2² × 2³ × 2⁸ × 2⁹ + 10 + 20² + 10 + 10 + 10

= 2²² + (10 × 4) + 400

= 4.194.304 + 40 + 400

= 4.194.304 + 440

= 4.194.744✔

Answer:

(2²×2³×2⁸×2⁹)+10+20²+10+10+10=

=2²+³+⁸+⁹ + 10 + (20 x 20) +(10+10+10)

=2²² + 10 + 400 + 30

=4.194.304 + (410 + 30)

=4.194.304 + 440

=4.194.744

Homework Progress
579 Marks
Aplo of sand has a weight of 90 kg.
The sand is put into a small bag, a medium bag and a large bag
in the ratio 2:3:7.
Work out the weight of sand in each bag.

Answers

Answer:

77

Step-by-step explanation:

2:3:7.

What is the smallest distance between the origin and a point on the graph of:y=1/sqrt(2)*(x^2-8)

Answers

What we are being asked here is to simply minimize distance. Also, note that we can write
f
(
x
)
=
√
x
as
y
=
√
x
.
Now, what is this "distance?" How do we find it? Well, if you think back to Algebra I or Geometry, you'll remember that the distance between two points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is given by:
√
(
y
2
−
y
1
)
2
+
(
x
2
−
x
1
)
2
. For example, the distance between the points
(
4
,
0
)
and
(
0
,
3
)
would be:
√
(
3
−
0
)
2
+
(
4
−
0
)
2
=
√
9
+
16
=
√
25
=
5
Ok, so what is
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
in our example?
(
x
1
,
y
1
)
is simple - it's just the point given in the problem,
(
4
,
0
)
. Because we don't know what
x
2
is, we'll just call it
x
for now. As for
y
2
, we don't know that either; and since
y
=
√
x
, we'll call it
√
x
.
Our formula then becomes:
√
(
√
x
−
0
)
2
+
(
x
−
4
)
2
=
√
(
√
x
2
)
+
x
2
−
8
x
+
16
=
√
x
+
x
2
−
8
x
+
16
=
√
x
2
−
7
x
+
16
We are being asked to minimize this distance, which we'll call
s
to make the following calculations easier. To minimize something, we have to take its derivative, so let's start there:
s
=
√
x
2
−
7
x
+
16
=
(
x
2
−
7
x
+
16
)
1
2

d
s
d
x
=
(
2
x
−
7
)
⋅
1
2
(
x
2
−
7
x
+
16
)
1
2
→
Using power rule and chain rule
d
s
d
x
=
2
x
−
7
2
√
x
2
−
7
x
+
16
Now we set this equal to
0
and solve for
x
:
0
=
2
x
−
7
2
√
x
2
−
7
x
+
16
0
=
2
x
−
7
x
=
7
2
This is known as the critical value, and it represents the
x
-value for which the function is minimized. All we need to do now is find the corresponding
y
-value, using the definition of
y
:
y
=
√
x
. Substituing
7
2
for
x
:
y
=
√
7
2

y
≈
1.87
And voila, the
y
-value. We can now say that the minimum distance between
f
(
x
)
=
√
x
and the point
(
4
,
0
)
(the place where these two are closest) occurs at
(
7
2
,
1.87
)
. For a little extra fun, we can use the distance formula to see what the actual distance between the points is:
s
=
√
(
1.87
−
0
)
2
+
(
7
2
−
4
)
2
≈
1.8
units

A- 63
B- 125
C-44
D-45

Answers

Answer:

So, the sum of the 3 angles in a triangle is 180.

What you would do is:

180= 73+6x-4+7x+7.

Then, you add the common coefficients:

180=76+13x

Then you subtract:

104=13x

Then you divide:

x=8.

Then substitute the x value into the A value to get 44, meaning that C is the correct answer.

what are the two integers

Answers

Answer:

3 and 4

Step-by-step explanation:

2^3 = 8

2^4=16

14 lies in between them

leanna finds a buy two get one free sale at her favorite store. her purchases cannot exceed $100. A skit orginally sells $22. What is the greatest number of skirts that she can get.

Answers

6

her order can't exceed 100

and if she buys 2 she gets 1 free

each one costs 22

so she can get 6 skirts for 88 which is the highest it can go

Evaluate the expression −t/u+vw , where t = 2, u=−2/3 , v=−1 , and w=−1/3 .3 1/31 2/3−2 2/3

Answers

Answer:

The answer is 3 1/3

The value of the expression  −t/u+vw is 3 1/3 after pluggin the values of t, u, v, and w in the expression.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

It is given that,

The expression is:

= −t/u+vw

The values of t = 2, u=−2/3 , v=−1 , and w=−1/3

After pluggin the values of t, u, v, and w in the above expression we get:

= -2/(-2/3) + (-1)(-1/3)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

= 3 + 1/3

= 3 1/3 (in mixed fraction)

Thus, the value of the expression  −t/u+vw is 3 1/3 after pluggin the values of t, u, v, and w in the expression.

Learn more about the expression here:

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3 1/3

5n + 34 = -2 ( 1 - 7n)
this is due by midnight.

NO LINKS PLEASE!

Answers

Answer :

n = 4

Step-by-step explanation:

5n + 34 = -2(1-7n)

first distribute

5n + 34 = -2(1) -2(-7n)

5n + 34 = -2+14n

-5n

+2

then get all of n to the same side

36 = 9n

isolate the variable

36/9 = 9n/9

4 = n

Answer:

n=4

Step-by-step explanation:

Hi there!

We are given the following equation:

5n + 34 = -2(1-7n)

And we want to solve it for n

To do that, we want to isolate n (also written as 1n) on on side by itself.

In this equation, on the right side, we have -2(1-7n), which is in the way. We'll need to open it up.

In order to open up the parenthesis, we'll need to do the distributive property, where we will multiply -2 to both 1 and -7n, then add them together.

-2(1-7n)=-2+14n

That's for the right side.

The equation now looks like this:

5n + 34 = -2 + 14n

Remember that we will be trying to isolate n on one side

Subtract 5n from both sides to remove it from the left side:

5n + 34 = -2 + 14n

-5n                  -5n

__________________

34 = -2 + 9n

Add 2 to both sides to remove it from the right side:

34 = -2 + 9n

+2    +2

______________

36 = 9n

Now, we have numbers on one side and variables on the other, but we're not done yet, since remember; we want just n (or 1n), not 9n. We need to divide both sides by a number that will result in 1n

If we divide a number by itself, then the result is 1

So we should divide both sides by 9

4 = 1n, also written as 4=n , or n=4

Hope this helps!

9.6 + 7.9u − 0.16 = –9.31 − 4.6u?

Answers

Answer:

u = -1.5

9.6 + 7.9(-1.5) − 0.16 = –9.31 − 4.6(-1.5)

-2.41 = -2.41

Step-by-step explanation:

I used a calculator, pls let me know if im incorrect

Pls help will mark brainliest, no fake answers

Answers

Step-by-step explanation:

b = what Bernie earns per day = Php 1000

m = what Mitch earns on a given day

e = what Eugene earns on a given day

r = what Rowan earns on a given day

a.

t = the total earnings of Bernie and Mitch on a given day

t = m + 1000 (or m + b)

b.

e = m/2

c.

r = 2×(m + 1000) or 2×t

2(3x-5y)+3(x^(2)-4y) for x=3, y=-5

Answers

Answer:

-38

Step-by-step explanation:

this is the answer

brainlist please

2(3x-54) +3(x-44)
2(3(3)-5(-5))+3(3^2-4(-5))
2(9+25)+3(9+20）
2(34)+3(29)
68+87
155

1. What is the equation, in standard form, of a parabola that contains the following points? (1 point)
(-2, 18), (0.2). (4, 42)
Oy=-222 - 2x - 3
Oy=-3x2 + 2x - 2
Oy = 3x2 - 2x + 2
Oy=-2x2 + 3x + 2

Answers

Answer:

y=3x2−2x+2

Step-by-step explanation:

Standard form of equation of a parabola is [tex]y=ax^2+bx+c[/tex]

As it passes through points (−2,18), (0,2) and (4,42), each of these points satisfies the equation of parabola and hence

18=a⋅4+b⋅(−2)+c or 4a−2b+c=18 ........(A)

2=c ........(B)

and 42=a⋅16+b⋅4+c or 16a+4b+c=42 ........(C)

Now putting (B) in (A) and (C), we get

4a−2b=16 or 2a−b=8 and .........(1)

16a+4b=40 or 4a+b=10 .........(2)

Adding (1) and (2), we get 6a=18 or a=3

and hence b=2⋅3−8=−2

Hence equation of parabola is [tex]y=3x^2 -2x+2[/tex] and it appears as shown below

graph{3x^2-2x+2 [-10.21, 9.79, -1.28, 8.72]}

Solve for x in terms of h and k:
2(2x - h) - k = 6

Answers

Answer:

Well what i got was x= 3/2 + h/2 + k/4= 6+ 2h+k=4

I'm not sure if that exactly helps but it's what i got

Step-by-step explanation:

Can someone help me I’m doing a khan academy and need help ASAP marking brainliest

Answers

Answer:

x = 180 - 89 = 91

Step-by-step explanation:

From the fig. find the angle which is equal to 110˚. *
1 point

∠A
∠C
∠D
none of the above

Answers

Answer:

∠C is equal to 110⁰ (alternate interior angles)

Step-by-step explanation:

Pls mark as brainliest

C! They are alternate interior angles :)

HELP ASAP I NEED THIS IN ONE HOUR WILL REPORT WRONG ANSWERS

A new drill is used to dig a hole in the ground. At noon, the hole is 13.2 feet deep when the new drill is turned

on for the first time that day. At 2 p.m., the drill has dug the hole to be 42 1/4 feet deep. The new drill dug

1.5 times as much of the hole as the old drill would have in the same length of time.

(a) What expression represents the number of feet the new drill dug?

(b) How many feet would the old drill have dug in the same length of time? Show your work. Answer the
question in a complete sentence.

Answers

Answer:

(a) 42.25 - 13.2

(b)  The old drill would have dug 19.367 ft in the same length of time (2 hours).

Step-by-step explanation:

(a) In the two hours, 12 Noon to 2 p.m., the new drill dug

42.25 - 13.2 =

29.05 feet.  

(b) Let r = the old drill dig rate in units of ft/hour

Then, 1.5r = the new drill dig rate.

So, 1.5r (2 hours) = 29.05, so that

r = (29.05)/(1.5 * 2) = 9.6833333 ... ft/hour.

So, the answer is: 9.683333 ... * 2 = 19.367 ft, rounded to the nearest 1000th.  Thus, the old drill would have dug 19.367 ft in the same length of time (2 hours).  

The required expression and the length of hole are 1.5( 42(¹/₄) - 13.2) and 43.57 feet respectively.

What is Unitary method?

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

The given problem can be solved by unitary method as follows,

(a) The expression that represents the length of hole dug by new drill is given as,

The length of hole dug by old drill in 2 hours is given as,

42(¹/₄) - 13.2

For new drill it is  1.5( 42(¹/₄) - 13.2) feet.

(b) The length of drill dug by old drill is,  

42(¹/₄) - 13.2

=  42.25 - 13.2

=  43.57 feet.

Hence, the expression for hole length by the new drill and the length of hole dug by old drill are given as  1.5( 42(¹/₄) - 13.2) and 43.57 feet respectively.

To know more about unitary method click on,

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Given: PQ = RS; PQ|| RS
Prove: PQRS is a parallelogram

Answers

Answer:

If PQRS is a parallelogram, then — PQ ≅ — RS and — QR ≅— SP . If a quadrilateral is a parallelogram, then its opposite angles are congruent. If PQRS is a parallelogram, then ∠P ≅ ∠R and ∠Q ≅ ∠S.

PQ=RS and PQ||RS implies PQRS is a parallelogram by showing that the diagonals bisect each other at O.

What is a parallelogram?

A quadrilateral with opposite sides equal and parallel but the angles are not right angle is called parallelogram.

Given that PQ=RS and PQ||RS .

Draw the parallelogram PQRS as in figure

To prove: PQRS is a parallelogram.

Construction: Join PS and QS as diagonals.

From the ΔORS and ΔOPQ,

PQ=RS (Given)

∠SOR=∠POQ   (opposite angles)

∠PQO=∠OSR  (since PQ=RS and PR is a traversal)

∴ΔOQS≅ΔOPQ

Hence, Op=OR and OQ=OS

Therefore , the diagonal of quadrilateral PQRS bisects each other.

Hence the given quadrilateral PQRS is a parallelogram.

To learn more about parallelogram click here:

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The basketball court in the park is rectangular two of the size of 84 feet long and the other two sides of 50 feet long what is the permit perimeter of the basketball

Answers

Answer:

8400

Step-by-step explanation:

84 x 50= 4200

84 x 50 = 4200

4200+4200= 8400

B is the midpoint of AC. C is the midpoint of AD. Find the coordinates of B and D given the coordinates of A (-2,5) and the coordinates of C (8,7). ​

Answers

B= (3,6) and D= (18,9)

Step-by-step explanation:

To find the midpoint of two given points add X1 and X2 together, then divide by 2 to get the X value of the midpoint and do the same thing for the Y value. That will get you B. From there you can see to get from point A to point C you add 10 to the x value and add 2 to the y value. Because C is the midpoint just double what you had to add to get point D (add 20 to x and add 4 to y)

Find the equation of the line with slope m=−5/3 that contains the point (9,−15).

Answers

Answer:

y=-5/3x

Step-by-step explanation:

y = -5/3x+b

-15 = -5/3(9)+b

-15=-15+b - Add 15 to both sides

0 = b

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