Mathematics High School

The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?

Answers

Answer 1

24*16 = 384

384*2 = 768

24+d * 16+d =768

384 + 40d+d^2 = 768

d^2 + 40d-384 =0

(d+48) (d-8) = 0

d=-48, d=8 can't use a negative number so d = 8

check:

24+8=32, 16+8=24, 32x 24 = 768

so 8 feet is added to each side

Related Questions

A comic-strip writer churns out a different number of comic strips each day. For 16 days, the writer logged the number of comic strips written each day (sorted low to high): {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7}. What type of skew can be observed in this distribution?

positive skew

negative skew

zero skew

skew cannot be observed

Answers

One way to observe the skewness of a data set is to find the quartiles: Q₁, Q₂, Q₃ and then sketch the box plot

We have the data set already in ascending order, so finding the quartiles is quite straight forward.

We have Q₁ = 2, Q₂ = 3, Q₃ = 5 (refer to the first picture below)

The box plot is given in the second picture and from this plot, we can see that the data tail slightly on the right, and this shows a positive skew.

How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?

Answers

13571.68 cube feet of water can be held

A model for a company's revenue is R=-15p^2+300p+12,000, where p is the price in dollars of the company's product. What prize will maximize revenue?

Answers

check the picture below.

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} R = &{{ -15}}p^2&{{ +300}}p&{{ +12,000}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]

so the Revenue will be the highest at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex] and that will happen at the price of [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}[/tex]

In order to do this you have to complete the square to get the vertex of the equation. The vertex will tell you the max value or the min value of whatever it is we are looking for. Here, our x values are the prices of whatever we are selling and the y values are the revenue dollars. Completing the square looks like this for us:
[tex]R(p)=-15 p^{2}+300p+12,000[/tex]
Move the 12,000 over to the other side and set the equation equal to 0:
[tex]-15 p^{2}+300p=-12,000[/tex]
In order to complete the square, the leading coefficient on the squared term has to be a 1 and it's a -15, so we have to factor that out:
[tex]-15( p^{2}-20p)=-12,000 [/tex]
Now it's ready to complete the square on it. Do this by taking half the linear term, squaring it, and then adding it in. Our linear term is 20p. Half of 20 is 10 and 10 squared is 100, so we will add in 100 on the left. Let's do this next step in two parts:
[tex]-15( p^{2}-20p+100)=-12,000 [/tex]
That's not quite complete yet because if we add in 100 inside the parethesis on the left we have to add in that same amount on the right. But on the left, we didn't just add in 100, we added in -15 TIMES 100 cuz we can't just forget about the -15 we factored out. That looks like this then:
[tex]-15( p^{2}-20p+100)=-12,000-1,500 [/tex]
The whole reason for doing this is to create a perfect square binomial on the left which is what we have done. The perfect square binomial is this (and we are going to do the subtraction on the right at the same time):
[tex]-15(p-10)^{2}=-13,500[/tex]
If we move the right side over to the left we get this:
[tex]-15(p-10) ^{2}+13,500=0 [/tex]
which gives us a vertex of (10, 13,500). That means that at a price of $10, the max revenue will be $13,500. See how beautifully that works out!??

Accuracy is a measure of how close an answer is to the actual or expected value

Answers

That statement is true

this statement is accurate having 100 % accuracy .

:)

What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?

Answers

u can find the common ratio by dividing the 2nd term by the first term
r = -9/3 = -3

an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==

Answer: [tex]\ a_{n}=3(-3)^{n-1}[/tex]

Step-by-step explanation:

Given: A geometric sequence with its first term [tex]a_1=a=3[/tex]

and second term [tex]a_2=-9[/tex]

We know that the common ratio in of a geometric sequence=[tex]\frac{a_{n}}{a_{n-1}}[/tex]

Thus, common ratio [tex]r=\frac{-9}{3}=-3[/tex]

We know that the explicit rule for geometric sequence is written as

[tex]a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }][/tex]

Thus, the explicit rule for the given geometric sequence is [tex]\ a_{n}=3(-3)^{n-1}[/tex] for every n ,a natural number.

How do I solve this

Answers

[tex]\bf \cfrac{x+2}{x^2+6x-7}[/tex] so, that function is "defined", ok, what values of "x" are not in the domain, namely, what values can "x" take on and not make the function "undefined", well, you know, if we end up with a 0 at the denominator, like [tex]\bf \cfrac{x+2}{0}[/tex] then, we'd have an "undefined" expression...so... any values of "x" that make the denominator 0, are not really the ones we want, and thus they'd be excluded from the domain.

so, hmm which are those? let's check, let's set the denominator to 0, and solve for "x".

[tex]\bf x^2+6x-7=0\implies (x+7)(x-1)=0\implies x= \begin{cases} -7\\ 1 \end{cases} \\\\\\ \textit{let's check, } x=-7\quad \cfrac{(-7)+2}{(-7)^2+6(-7)-7}\implies \cfrac{-5}{49-42-7}\implies \cfrac{-5}{0} \\\\\\ x=1\quad \cfrac{(1)+2}{(1)^2+6(1)-7}\implies \cfrac{3}{1+6-7}\implies \cfrac{-3}{0}[/tex]

It costs $35$35 per hour to rent a boat at the lake. You also need to pay a $25$25 fee for safety equipment. You have $200$200. For how long can you rent the boat?

Answers

5 hours because 35+25 divided by 200

Explain what needs to happen to the inequality sign when dividing or multiplying by a negative number. a. nothing happens c. change the inequality sign to an equals sign b. flip the inequality sign d. the inequality needs to be graphed on a number line

Answers

flip the inequality sign
so the answer is B

Answer:

(B) flip the inequality sign.

Step-by-step explanation:

If we consider an inequality such that [tex]-x\leq7[/tex], then if we multiply the inequality with a negative number such as [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].

Also, if we divide the above inequality [tex]-x\leq7[/tex], by a negative number that is [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].

Therefore, if we multiply or divide an inequality by a negative number, then it flips the inequality sign.

Hence, option (B) is correct.

Sophie has a hard rubber ball whose circumference measures 13 inches. she wants to store it in a box. what is the number of cubic inches in the volume of the smallest cube- shaped box with integer dimensions that she can use?

Answers

Let r = radius of the hard rubber ball.

Because the circumference of the ball is 13 inches, therefore
2πr = 13
r = 13/(2π) = 2.069 in

In order to fit the ball into a cube-shaped box with integer dimensions, each side of the box should measure 3 inches (the next integer greater than 2.069).

The volume of the cube-shaped box is 3³ = 27 in³.

Answer: The volume is 27 in³.

Which expression is equivalent to (cos x)(tan(–x))?

A. -sin x
B. sin x
C. -csc x
D. csc x

Answers

The tan(-x) is the same thing as -tan(x). The tangent function is also the same thing as sin(x)/cos(x), right? So let's rewrite that tan in terms of sin and cos:
[tex][cos(x)][tan(-x)][/tex] is the same as [tex][cos(x)][ -\frac{sin(x)}{cos(x)}] [/tex]
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.

the answer to this is A

Write 5000 = 12 as an order pair

Answers

Hejejdjshdjsjskskskskskskskskskkskskskdkdjdkddkkd

If you guess an answer on two multiple choice questions with the options a, b, or c, what is the probability of you guessing the answer to both questions correctly?

Answers

first, you find the probability of getting each question right individually, then you multiply the two probabilities together.

(1/3) x (1/3) = 1/9

what is the slope of a line that passes through (-4,-13) and (19,11)

Answers

the slope of the line is the gradient, which you can find through rise over run

m (gradient) = (y1 - y2) / (x1 - x2)

where (x1, y1) is the coordinate of the first point, and (x2, x2) is the coordinate of the second point

in your question:
x1 = -4
x2 = 19
y1 = -13
y2 = 11

m = (-13 -11) / (-4 -19) = -24 / -23 = 24/23 or 1.04 (2d.p.)

hope that helps :)

Answer:

24/23

Step-by-step explanation:

- vs - = + after -24,-23 =

Answer = 24, 23

What is the prime factorization of -96? tell me how do u get the answer

Answers

hello :
the prime factorization of -96 is : - 3×2^5

Answer: -1 x 2^5 x 3

Step-by-step explanation: To find the prime factorization of -96, we need to first factor out -1, which gives us 1 x (-1) x 2 x 2 x 2 x 2 x 2 x 3. Then, we can rewrite -1 as -1^1, and combine the 2's to get 2^5. So the prime factorization of -96 is -1^1 x 2^5 x 3.

Remember, negative numbers can also have prime factorizations.

PLEASE CAN SOMEONE HELP!!!????

Use elimination to solve for x and y:

−2x−y=9

2x−9y=1

My Choices are....

a. (−4,−1)
b. (−1,−4)
c. (5,1)
d. (−1,−7)

Answers

add them 2 equations to eliminate x's

-2x-y=9
2x-9y=1 +
0x-10y=10

-10y=10
divide by -10
y=-1

sub back

-2x-y=9
-2x-(-1)=9
-2x+1=9
-2x=8
divide by -2
x=-4

y=-1

(x,y)
(-4,-1)

A

The values of x and y after solving both the equations by the elimination method are -4 and -1. So option A is correct

What is an Equation ?

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Two linear equations

−2x − y = 9

2x − 9y = 1

by using elimination method,

−2x − y = 9

2x − 9y = 1

0 - 10y = 10

y = -1

2x − 9× -1 = 1

2x = -8

x = -4

Hence, the values are, -4 and -1

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Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?

Answers

52% = 0.52

78/0.52 =150

150 students voted

150 students voted in Toby's grade.

Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved about the vertical axis.

Answers

[tex]4-x^2=x\\ x^2+x-4=0\\ \Delta=1^2-4\cdot1\cdot(-4)=1+16=17\\ x_1=\dfrac{-1-\sqrt{17}}{2}\\ x_2=\dfrac{-1+\sqrt{17}}{2}\\\\ \displaystyle V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(4-x^2-x)^2\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(16-4x^2-4x-4x^2+x^4+x^3-4x+x^3+x^2)\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(x^4+2x^3-7x^2-8x+16)\,dx\\ V=\pi \left[\dfrac{x^5}{5}+\dfrac{x^4}{2}-\dfrac{7x^3}{3}-4x^2+16x\right]_0^{\dfrac{-1+\sqrt{17}}{2}}\\ [/tex]

The rest of solution in the attachment.

There's a mistake in the picture
It shoud be
[tex]V=\pi\left(\dfrac{289\sqrt{17}-521}{60}\right)\approx35[/tex]

Solve the following system by graphing.

x - y = 4
x + y = 2

What is the solution of the system?

(3, -1)
(3, 1)
(-1, 3)

Answers

hello :
the solution is : (3, -1)
put x= 3 and y = -1
you have : 3-(-1) = 4 and 3+(-1) = 2 ..... right

The solution for the system of equation x - y = 4 and x + y = 2 is (3, -1).

What is an equation ?

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given pair of equations,

x - y = 4 (1)

And x + y = 2 (2)

To find the solution of the equations,

Add both the equations,

x - y + x + y = 4 + 2

2x = 6

x = 3,

Substitute the value of x = 3 in equation (1),

3 - y = 4

y = -1

The values of x and y are 3 and -1 respectively.

Hence, option (A) is correct.

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If XYZ measures 75, what is the measure of XWZ ? A. 285 B. 210 C. 75 D. 150
(Its a circle, and its saying that the arc is 775 and wants to know what the rest of the circle is)

Answers

Your answer is 285. ADD ME!!!!!!!!!!!

The measure of XWZ is 285

what is arc?

The arc of a circle is defined as the part or segment of the circumference of a circle.

Given:

<XYZ = 75

As, we know central angle of 360

So, arc(XWZ) + <XYZ = 360

arc (XWZ) = 360 - 75

arc(XWZ) = 285

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Factor completely 36x2− 121.

Answers

The expression 36x² - 121 is in the 'difference of two squares form' which is (a² - b²)

Factorising (a² - b²) gives (a+b)(a-b)

Factorising 36x² - 121 gives (6x+11)(6x-11)

What is the factored form of the expression k^2 - 9h^2

Answers

The equation which is supposed to help you is this one:
a^2 - b^2 = (a+b) (a-b)

So, what we need to do here is apply this equation:
k^2 - 9h^2 =
k * k - (3h)^2 =
(k + 3h) (k - 3h)

in a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?

Answers

Answer:

There are [tex]26[/tex] alternative schools in the country

Step-by-step explanation:

Let

x------> the number of charter schools

y-----> the number of alternative schools

we know that

[tex]x=48[/tex]

[tex]x=2y-4[/tex] -----> equation A

substitute the value of x in the equation A and solve for y

[tex]48=2y-4[/tex]

[tex]2y=48+4[/tex]

[tex]2y=52[/tex]

[tex]y=26[/tex]

Find the probability of at least 2 girls in births. Assume that male and female births are equally likely and that the births are independent events. Round to three decimal places.

Answers

we assume that male and female births are equally likely, it means that the probability of birth of male= probability of birth of female = 100%/2=50% or 0.5We have 2 independent events. So what will be the variants:
Male and FemaleMale and Male Female and Male Female and Female
All four variants are equally likely.Probability of each one is 1/4 = 0.25.So, Result "Female and Female"
are probability = 0.250 --- if round to three decimal places.

Permutations!!
If 9 actors must sit together how many ways are there to seat 13 people around the table?

Answers

Final answer:

To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.

Explanation:

The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.

Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.

Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.

Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.

Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.

Indicate the equation of the given line in standard form. The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)

Answers

the equation given has a slope of 2/3. A parallel line will have the same slope.

y = mx + b
slope(m) = 2/3
(1,-2)...x = 1 and y = -2
sub and find b, the y int
-2 = 2/3(1) + b
-2 = 2/3 + b
-2 - 2/3 = b
-6/3 - 2/3 = b
- 8/3 = b

equation is : y = 2/3x - 8/3...but we need it in standard form

y = 2/3x - 8/3
-2/3x + y = -8/3...multiply by -3
2x - 3y = 8 <== standard form

Find the area of a square with apothem 9 in. Round to the nearest whole number.

281 in2

305 in2

458 in2

324 in2

Answers

The apothem is the line from the center of the polygon (square) to the midpoint of a side.

So, if the apothem is 9in, the length of the side is 2 * 9in = 18 in.

And, the area of the square is (length of the side)^2 = (18 in)^2 = 324 in^2

Answer: 324 n^2

Answer:

The area of the square is 324 square inches.

Step-by-step explanation:

The apothem of the square is 9 inches.

The side of the square is twice the length of the apothem.

Hence, the side of the square is given by

[tex]a=2\times 9=18\text{ in}[/tex]

The area of a square is the given by

[tex]A=a^2\\A=18^2\\A=324\text{ in}^2[/tex]

Therefore, the area of the square is 324 square inches.

Line LJ is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain.

Answers

A tangent line to a circle is perpendicular to the radius drawn to the tangent point.

If tangents are constructed through points L and J, then the tangents are perpendicular to the diameter and parallel to each other.

Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
A He showed that an explicit formula could be created.
B He showed that a recursive formula could be created.
C He showed that f(n) ÷ f(n − 1) was a constant ratio.
D He showed that f(n) − f(n − 1) was a constant difference.

Answers

The defining characteristic of any geometric sequence is the common ratio, which is the constant found when dividing any term by the term preceding it.

C. He showed that f(n)/(f(n-1) was a constant ratio.

The answer to your question is : C. He showed that f(n) ÷ f(n − 1) was a constant ratio.

5⁄6 · n = 10 (solve for n)

Answers

You divide 5/6 from the equation.
When you divide 5/6 and 10 you get 12.
To check your answer multiply 5/6 and 12 and you will get 10.
N=12

[tex]\frac{5}{6}n=10\ | \div \frac{5}{6} \\\\ n= \frac{\not10^2}{1}\cdot \frac{6}{\not5^1}\\\\n=2 \cdot 6=12 \\\\ or \\\\ \frac{5}{6}n=10 \ | \times 6 \\\\ 5n=60 \ |\div 5 \\\\ n=12[/tex]

A ship travels 10 miles from Point A to Point B, makes a turn of 112, and travels 16 miles to Point C. If the ship travels directly from Point C back to Point A, how many miles will it travel on the last leg of the trip (from Point C to Point A)? Round your answer to the nearest tenth of a mile.

Answers

This is Pythagorean's Theorem, with one leg being 10 and the hypotenuse being 16. Using those values in the theorem looks like this:
[tex] 10^{2} + b^{2} = 16^{2} [/tex]
and [tex]100+ b^{2} =256[/tex]
and [tex] b^{2} =256-100[/tex]
so [tex] b^{2} =156[/tex]
Take the square root of both sides to find that b = 12.5

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