Answer:
width=5yd and length=10yd
Step-by-step explanation:
To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)
We know that Area (A) = Length (L) * Width (W)
You know Area (A) = 50 sq. yds.
You don't know anything about the width, so let's just say Width (W) = x
And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd
Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.
Well, now just plug in. What does W equal and L equal?
From above we plug in and can say that 50 sq yd = x * (x + 5 yd).
Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).
Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:
0 = x^2 + 5x - 50
Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.
I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that
0 = x^2 + 5x - 50 = (x + 10)(x - 5)
And so you know that x = -10 or 5.
Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.
mark me brainlistArun took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4 plus $4.25 per mile. The total fare was $110.25, not including the tip. How many miles was the taxi ride?
Answer:
Answer = 25 miles
Step-by-step explanation:
We can make an equation based off of this information in the form of 4.25x+4=110.25. When we solve for x we find that it equals 25.
Hope that helps! :)
I need help asap!!!!!!!!!
Find the value of x.
6
14
8
0
21
x = [ ? ]
3x-12
Answer: 7
Step-by-step explanation:
By the angle bisector theorem,
[tex]\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}[/tex]
Jessie is painting a cardboard box for a school project and needs to know much paint she needs to cover the box.
6n
10 in.
Answer:
incomplete question
Step-by-step explanation:
in order to calculate for the surface area of a rectangular box we would need 3 measurements:
length
width
height
you only provided 2
b) How many more 18-year
old students than 12-year
old students spent
between 25 and 35 mins
on social media?
The number if 18-year old 12-year old students that took part in the survey is 320.
The number of more 18-year old students than 12-year old students that spent between 25 and 35 mins on social media is 20.What is the survey about?Looking at the survey chart one can see that the total number of 18year old that partook of the survey are:
30 + 20 + 60 + 70 + 40 + 60 + 40
= 340
From the diagram , 18 year old = 60
12 year old = 40
The differences will be:
= 60 - 40
= 20
Therefore, The number if 18-year old 12-year old students that took part in the survey is 320 and the number of more 18-year old students than 12-year old students that spent between 25 and 35 mins on social media is 20.
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A square has a triangular hole in it. What is the area of the figure?
9 in. 3 in.
76.5 in 2
89 in 2
72 in 2
3 in.
9 in.
Answer:
76.5in²
Step-by-step explanation:
First we will find the area of the square. This is done by multiplying the side length (9in) by itself.
[tex]9 * 9 = \boxed{81}[/tex]
The area of the square is 81in².
Next we will find the area of the triangular hole. We can use the formula [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle (3) and h is the height of the triangle (3).
[tex]\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}[/tex]
The area of the triangle is 4.5in².
Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.
[tex]81 - 4.5 = \boxed{76.5}[/tex]
The area of the figure is 76.5in².
That is the answer
- Kan Academy Advance
Identify the zeros given the quadratic equation y= -16(x+7)(x-5)
Answer:
wouldn't it be -7 and 5? I'm pretty sure that you switch the signs around.
Step-by-step explanation:
set y=0 and solve. -7 + 7 = 0 and 5 - 5 = 0. my teacher told me to switch the signs for each factored term. hope this helps.
Answer:
x = -7
x = 5
Step-by-step explanation:
Hello!
We can use the Zero Product Property to solve for the Zeroes.
Zero product PropertyThe zero product property stars by factoring a quadratic. You then set each of the factors to zero, and solve for the variable in the factor.
Factored form: y = a(x - h)(x - k)
0 = a(x - h)(x - k)0 = (x - h)(x - k) Divide by aNow, let's call each factor, A and B. To get to 0, either A, B, or both have to be 0. We prefer to solve for both.
Solvey = -16(x + 7)(x - 5)0 = -16(x + 7)(x - 5)0 = (x + 7)(x - 5) Divide by -16x + 7 = 0, x = -7x - 5 = 0, x = 5The zeroes of the Quadratic is -7 and 5.
Why do we replace it with 0?
Zeroes means the x-intercepts, or the roots of a quadratic. An x-intercet is when y is equal to 0. So we replace y with 0, and solve for x.
Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.
Answer: AAS
Step-by-step explanation:
We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.
Find the amount of money
accumulated after investing a
principle P for years t at interest
rate r, compounded continuously.
t = 6
P = $1,500 r = 7%
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500e^{0.07\cdot 6}\implies A=1500e^{0.42}\implies A\approx 2282.94[/tex]
PLEASE HELP ME I WILL GIVE BRAINLYEST
Answer:
your answer will be 85 1/3ins
Step-by-step explanation:
16x 5 1/3 = 85.3333333333
then I took the 85 and the 1/3
and just put em together
PLEASE HELP! ITS DUE SOON IM SO CONFUSED SOMEONE PLEASE HELP ME!
Answer:
40.6°
Step-by-step explanation:
formula of area of triangle
1) √[(s)(s-a)(s-b)(s-c)] , s= (a+b+c)/2
2) 1/2ab sin c
calculate the area first
s= (9.6+6.3+8.1)/2
=12
area= √[(12)(12-9.6)(12-6.3)(12-8.1)]
= √640.224
= 25.3026
1/2(9.6)(8.1) sin c = 25.3026
sin c = 25.3026(2)/(9.6*8.1)
sin c = 0.6508
c = sin-¹ 0.6508
c = 40.6 (nearest tenth)
A survey asked people how many siblings they have, and the results were recorded in this line plot.
How many people surveyed have 4 or more siblings?
dot plot
Answer:
we need a pic of the graph to be able. to work this out.
THANK YOU
Answer:
It's 5.
Step-by-step explanation:
8-3= 5
1) - 6z+2+3= 15
How do I solve this question
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to solve the equation [tex]\mathrm{-6z+2+3=15}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The goal is to isolate x.Notice that we can add 2+3 right off the bat:
[tex]\star~\mathrm{-6z+5=15}[/tex]
Subtract 5 from both sides of the equal sign:
[tex]\star~\mathrm{-6z=10}[/tex]
Divide both sides by -6:
[tex]\star~\mathrm{z=\cfrac{10}{-6}}[/tex]
Simplify!
[tex]\star~\mathrm{z=-\cfrac{5}{3}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
A picture frame has a perimeter of 40 inches. Its length is 2 inches greater than one-half its width. Let w represent the width in inches of the picture frame, and let l represent the length in inches. Which system of equations can be used to find the dimensions of the picture frame?
Equations can be used to find the dimensions of the picture frame:
Length = 2 +1/2w
and, 2(l+b)=40
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Perimeter = 40 inches.
let the width be w
length= 1/2w+2
So.
Perimeter of rectangle
40= 2 (l+b)
40= 2(0.5w+2+w)
20=1.5w+2
18=1.5w
w= 12
length= 8
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Can someone tell me what is 9x46288
write a rule for the nth term of the arithmetic sequence
-11, -4, 3, 10...
Answer: aₙ = -11 + 7(n - 1)
Step-by-step explanation: The equation of an arithmetic sequence is
aₙ = a₁ + d(n - 1).
a₁ is the first term.
d is the common difference.
Solve for X.
6
X = [?]
Enter the number, in decimal form,
that belongs in the green box.
Answer:
By proportional method
[tex] \frac{4}{6} = \frac{5}{x} [/tex]
4x= 30
x= 7.5
help what is
thr circumference of a circle is 36π cm
what is the radius of teh circle?
Let's consider the relationship between the circumference and the radius:
⇒ first, consider the equation for finding the circumference
[tex]Circumference = 2\pi *radius[/tex]
Let's consider the known information
Circumference ⇒ 36πLet's plug the known information to find the radius:
[tex]Circumference = 2\pi *radius\\36\pi =2\pi *radius\\radius = 18[/tex]
Thus the radius is 18 cm
Answer: 18 cm
Hope that helps!
A circle has a radius of 7 in. Find the radian measure of the central angle 0 that intercepts an arc of length 15 in. Do not round any intermediate computations, and round your answer to the nearest tenth.
The measure of the central angle is 2.15 radians if the radius of the circle is 7 in.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
The radius of the circle = 7 in
Arc length = 15 in
We know,
s = rθ
s is the arc length, θ is the central angle, and r is the radius of the circle.
15 = 7θ
θ = 15/7
θ = 2.142 radians ≈ 2.15
Thus, the measure of the central angle is 2.15 radians if the radius of the circle is 7 in.
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interest rate of 2.99% compounded monthly for a 4 year loan, find the regular monthly payments required to repay the loan.
Using it's formula, considering a loan of $10,000, the regular monthly payments required to pay off the loan will be of $221.3.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, we have that the parameters are given as follows:
P = 10,000, r = 0.0299, n = 4 x 12 = 48.
Then:
r/12 = 0.0299/12 = 0.00249167.
Hence, the monthly payment will be given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 10000\frac{0.00249167(1+0.00249167)^{48}}{(1+0.00249167)^{48} - 1}[/tex]
A = 221.3.
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Pls help me with no26
Answer:
a) 8
Step-by-step explanation:
The prime factors for 24 are 2, 2, 2, 3 -> The greatest is 3
The prime factors for 35 are 5, 7 -> The smallest is 5
So the sum is 3+5=8
Find the degree of the polynomial b5 + 2b3 + 7.
Answer:
5
Step-by-step explanation:
b^5 + 2b^3 + 7
Here,
degrees are 5 and 3.
The degree of the polynomial is the highest / greatest number in the degree.
Out of 3 and 5
5 is the highest / greatest number.
Hence,
the degree of the given polynomial is 5.
When 2(3/5 x + 2 3/4 y - 1/4 x - 1 1/2 y + 3) is simplified, what is the resulting expression?
Answer:
6 + 7/10x + 2/y
Step-by-step explanation:
Hope this helps :)
Which of the following points is not coplanar with points C, D and E?
The point R is the point which is not coplanar with points C, D and E.
We need to find the point which is not coplanar with points C, D and E.
What are coplanar points?The points that lie on the same plane are called coplanar points.
In the given figure there are five planes which are as follows:
BCUD, BRAE, BRAC, BTDE, ACUDE
Now, points C,D and E lie in plane ACUDE.
In the plane ACUDE points A, C, U, D, E and S lies.
From the options point, R is not lining in the same plane as C, D and E lies.
Therefore, the point R is the point which is not coplanar with points C, D and E.
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Select the best definition of repeating decimal.
A. any number that does not repeat, or terminate, that can not be written as a fraction.
B. a decimal that has a recurring sequence of numbers that follow a pattern
C. any number that can be written as a fraction, repeating or terminating decimal
D. a decimal which has digits that do not go on forever.
The correct option that defines repeating decimals correctly is Option B;
a decimal that has a recurring sequence of numbers that follow a pattern.
What is a Repeating Decimal?A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.
From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.
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Aaron solved an inequality and then graphed the solution as shown below.
-8-7
1 0 1 2 3 4 5
Which inequality did Aaron solve?
|x+2| <3
Ox+2| >3
|x+3| <2
|x+31 > 2
Based on the graph that Aaron made, we can infer that the inequality he solved is | x + 2 | < 3.
What inequality was solved by Aaron?
The value of x in the graphed inequality is:
-5 < x < 1
If 2 was added to both sides, the least value would be - 3 and the highest value would be 3.
The inequality then becomes:
-3 < x < 3
This in line with the first option which is that when 2 is added to any value of x, it will be less than 3.
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I'd appreciate the help!!
Answer:
B
Step-by-step explanation:
look at the graph. y is negative from x>2, so interval is 2<x<infinity.
in other case y=0 for x=2, y<0 for infinity<x<2
Answer:
The intervel that describes where the graph is negative is C :)
I hope this helps you!
Step-by-step explanation:
what is the answer divided
Answer:
4m/9
Step-by-step explanation:
Which expression is a perfect cube
Answer: some perfect cubes are
8 (2^3)
27 (3^3)
64 (4^3)
there are many perfect cubes
maybe there is more to this question?
Step-by-step explanation:
A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.
Directions: Follow the instructions for the following inequalities. 1. 4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10 2. 11>-2 Add 5 to both sides, then add 3, then add (-4) 3. -4<-2 Subtract 6 from both sides, then 8, and then 2 4. -8<8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
In the given question, we have to perform this experiment and test if the inequality is true or not.
Adding the same value to both sides of the inequality will not change the inequality sign
Inequalitydata;
4 < 711 > - 2-4 < - 2-8 < 8In the first case, we would do follow the process
[tex]6 * 7 * 4 < 7 * 7 * 6\\168 < 294[/tex]
In the second case;
[tex]11 > - 2\\\\5 + 11 > -2 + 5\\3 + 16 > 3 + 3\\4+ 19 > 6 + 4\\23 > 10[/tex]
In all the scenarios, the operations did not affect the inequality sign because we are doing it equally to all side and at the end of the day nullifies each other.
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