Answer:
4g² - 36gh + 81h²
Step-by-step explanation:
Apply the perfect square formula: (a - b)² = a² - 2ab + b²
(2g - 9h)² = (2g)² - 2(2g)(9h) + (9h)²
Simplify:
2g² = 4g²
-2 · 2g = -4g · 9h = -36gh
9h² = 81h²
= 4g² - 36gh + 81h²
hope this helps!
Work out the area of the shape drawn below.
6 m
Answer:
28.3 m²
Step-by-step explanation:
The formula to find the area of a quadrant: 1/4 x π x r², where r is radius (diameter ÷ 2) and π is 3.14 or 22/7 or 3.142.
1) Substitute the values into the formula.
= 1/4 x 22/7 x 6²
2) Solve it.
= 1/4 x 22/7 x 36
= 1/4 x 113.14
= 28.285
2) Round the answer to one decimal place.
= 28.3
the axis of symmetry for a parabola with x intercepts (-8,0) & (12,0)
12-(-8)=20
x axis = 20:2 = 10
Find the product. 5(4v + 1)
Answer: 20v+5
Step-by-step explanation:
5(4v+1)
Use the distributive property to multiply 5 by 4v+1.
20v+5
Answer:
20v+5
Step-by-step explanation:
You would multiply using the distributive property
Distributive property formula examples:
AB=BA
A+B=B+A
(AB)C=A(BC)
(A+B)+C=A+(B+C)
A(B+C)=AB+AC
Please Help Me!!!
The ratio of men to women working for a company is 4 to 3. If there are 161 employees total, how many men work for the company?
Answer:
I dont know
Step-by-step explanation: I hope someone can help you
Write the equation of a line that passes through the point (-5,-4) and has a slope of 1/5
Typically, linear equations are written in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-intercept (the value of y when the line crosses the y-axis)To find the equation of a line given a point and the slope:
Plug the slope into y=mx+b as mPlug the point into y=mx+b as (x,y)Solve for bPlug b back into y=mx+b along with mSolving the Question
We're given:
[tex]m=\dfrac{1}{5}[/tex]Passes through (-5,-4)[tex]y=mx+b[/tex]
⇒ Plug in the slope, [tex]\dfrac{1}{5}[/tex]:
[tex]y=\dfrac{1}{5}x+b[/tex]
⇒ Plug in the point (-5,-4) and solve for b:
[tex]-4=\dfrac{1}{5}(-5)+b\\\\-4=-1+b\\\\b=-3[/tex]
⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:
[tex]y=\dfrac{1}{5}x-3[/tex]
Answer[tex]y=\dfrac{1}{5}x-3[/tex]
Which of the following solutions are represented correctly on their number line? Select all that apply. A. Katie's dog weighs more than 9 pounds. The number line that represents this amount is: B. Owen's suitcase weighs less than 10 kilograms. The number line that represents this amount is: C. The bag of cotton weighs less than 75 grams. The number line that represents this amount is: D. Riley's tennis racket weighs less than 16 ounces. The number line that represents this amount is
As a result of inflation, the purchasing power of a fixed quantity of money decreases by 5% every year. If a certain quantity of money can buy 940 frozen dinners this year, how many frozen dinners can it buy in 16 years?
There would be 413 frozen dinners in the next 16 years.
How to solve an exponential function?Let y represent the amount of frozen dinners after x years.
If a certain quantity of money can buy 940 frozen dinners this year, and it decreases by 5% every year, hence:
y = 940(0.95)ˣ
In 16 years:
y = 940(0.95)¹⁶
y = 413.71
There would be 413 frozen dinners in the next 16 years.
Find out more on exponential function at: https://brainly.com/question/12940982
What would be the slope intercept form for the inequality 3x-2y>5?
Answer:
y<3/2x-5/2
Step-by-step explanation:
You just have to know how to get y on one side and the rest of the problem on the other.
First you would subtract 3x from both sides, which leaves you with -2y>5-3x.
Lastly you would divide both sides by -2.
To get the final answer of y<3/2x-5/2
An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graph can be used to determine approximately how many years will it take for the balance to be $282?
Answer:
D. Graph 4 In an account with 250$ balance that accrues 2% annually, with no deposits or withdrawals, it takes 6 years and 6 months for the balance to be 282$
Step-by-step explanation:
if the balance accrues 2% annually, then that means every year the amount increases by 100% + 2% = 102%
102%= 102/100 = 1.02
if we multiply the balance in the account with 102% or by 1.02 at the beginning of each year we will get the amount accrued at the end of the year
First year: $250 x 1.02 = $260.1
Second year: 260.1 x 1.02 = $265.302
Third year: 265.302 x 1.02 = $270.60802
we can use these points to create a graph that will help us estimate at what year the amount will be 282$
Answer:
D
Step-by-step explanation:
70 students choose to attend one of three after school activities: football, tennis or running. There are 30 boys. 13 students choose football, of which 9 are girls. 31 students choose tennis. 9 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answer:
9/70
Step-by-step explanation:
Given that:
70 students choose to attend one of three after school activities: football, tennis or running.
There are 30 boys. 13 students choose football, of which 9 are girls. 31 students choose tennis. 9 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Since it asking for the probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.
Therefore, we also know 70 students is the total
Hence, the answer is 9/70
9/70 is in simplest form already.
~lenvy~
Answer:
9/70
Step-by-step explanation:
Important info:
70 students choose to attend one of three after school activities: football, tennis or running.There are 30 boys. 13 students choose football, of which 9 are girls. 31 students choose tennis. 9 girls choose running.A student is selected at random.What is the probability this student chose running?Solution:
Probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.
Thus, 70 students is the total
Therefore, the answer is 9/70
9/70 can't be simplify.
[RevyBreeze]
How much would
$550 invested at 9%
interest compounded
annually be worth
after 8 years?
After 8 years the worth would become $1,095.91
How to find the compound interest?If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We are given that $550 invested at 9% interest compounded annually be worth after 8 years.
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
a = 550 (1 + 0.09)^8t
a = 550 (1.09)^8t
a =1,095.91
Hence, the worth would be; $1,095.91
Learn more about compound interest here:
https://brainly.com/question/1329401
#SPJ2
Help picture below problem 23
Answer: 7 hours.
Step-by-step explanation: Randall can assemble 5 race car tracks in an hour and Diggery can assemble 4 race car tracks in an hour. To see how many hours it takes to make 63 race car tracks, you need to add 5 and 4, since Randall and Diggery are working together. Both of them combined can make 9 race car tracks in total every hour. 63 can be divided by 9, which is 7. Therefore, it'll take 7 hours for both of them to make 63 race car tracks.
Let me know if this is right! :)
9. A bag of candy weighs 11 3/4 ounces. You get 1/8 of the bag. What is the weight of your share in ounces?
Answer:12 1/8
Step-by-step explanation:
you add the denomunator in order to get your answer
Is the data set approximately periodic? If so, what are it's period and amplitude?
Day| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Books Borrowed 102 | 76 | 91 | 140 | 98 | 74 | 88 | 137 | 100 | 75 | 92 | 139
• not periodic
• periodic with a period of 4 and an amplitude of about 20
• periodic with a period of 4 and an amplitude of about 30
• periodic with a period of 5 and an amplitude of about 25
NO LINKS!!!
At the dance the DJ is blaring music at 110 decibels. As he fades the music, the sound level decreases about 16% every second.
How long until the sound level falls below 30 decibels? (SHOW WORK!)
Equation:_____________________
Answer: ______________________
We are given:
Initial sound Intensity: 110 dB
Rate of decreasing sound level: 16% every second
Constructing the equation:
Since the Intensity decreases by 16% of it's current value every second.
Intensity(t) = [tex]110 * (\frac{84}{100})^{t}[/tex] [where t is the time elapsed]
In this equation, we multiply the initial sound intensity by 84% (since 16% was diminished).
because we are multiplying the same value by 84%, it will keep taking that percentage of the new value, which is what we need here because the music's intensity keeps becoming 84% of the previous value.
Time at which sound level falls to 30 dB:
replacing intensity by 30 in the equation we made.
[tex]30 = 110 * (\frac{84}{100})^{t}[/tex]
[tex]\frac{3}{11} = (\frac{84}{100})^t[/tex]
taking log of both sides.
[tex]log(\frac{3}{11}) = t*log(\frac{84}{100})[/tex]
[tex]\displaystyle \frac{log(\frac{3}{11})}{log(\frac{84}{100})} = t[/tex]
t = 7.452 seconds
Answer:
Equation: [tex]y=110(0.84)^x[/tex]
(where x is the time in seconds, and y is the sound level in decibels)
Answer: The sound level falls below 30 decibels after 7.452 seconds (3 dp)
Step-by-step explanation:
We can model this as an exponential equation.
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is growth factorx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
If the sound decreases by 16% each second, then the growth (decay) factor will be 100% - 16% = 84% → 0.84
Given:
a = 110 decibelsb = decreases by 16% each second = 0.84x = time (in seconds)y = sound level (in decibels)Substituting these values into the equation:
[tex]\implies y=110(0.84)^x[/tex]
To find how long until the sound level falls below 30 decibels, set y < 30 and solve for x:
[tex]\begin{aligned}110(0.84)^x & < 30\\\\(0.84)^x & < \dfrac{3}{11}\\\\\ln (0.84)^x & < \ln \left(\dfrac{3}{11}\right)\\\\x \ln (0.84) & < \ln \left(\dfrac{3}{11}\right)\\\\x & > \dfrac{\ln \left(\dfrac{3}{11}\right)}{\ln (0.84)}\\\\x & > 7.452008851\end{aligned}[/tex]
Therefore, the sound level falls below 30 decibels after 7.452 seconds (3 dp)
When was the model rocket 600 feet above the ground? Answers:4.5 seconds. 7 seconds. 7 and 9.5 seconds. 4.5 and 12 seconds.
Answer:
D. 4.5 and 12 seconds
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
It was correct on the quiz
Select all the correct locations on the image. Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
The parabolae b, d and f seen in the real coordinate plane have complex roots.
What is the graphical criterion to determine what second order polynomial has complex roots?
Second order polynomials are algebraic equations of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
a, b, c - Coefficientsx - Independent variabley - Dependent variableA value of x is a root of the polynomial for y = 0, which can real or complex but not both according to the discriminant of the quadratic formula. If the polynomial has no real roots, then it does not pass through the x-axis in the real coordinate plane.
Therefore, the parabolae b, d and f seen in the real coordinate plane have complex roots. [tex]\blacksquare[/tex]
To learn more on quadratic functions, we kindly invite to check this verified question: https://brainly.com/question/4119540
What is x? If necessary, round to the nearest tenth (one decimal place):
Answer:
x = 10
Step-by-step explanation:
Both right triangles are similar.
-> Corresponding sides of similar triangles are in proportion.
[tex] \implies \: \frac{x + 6}{16} = \frac{x}{10} \\ \\ \implies \: 10(x + 6) = 16x \\ \\ \implies \: 10x + 60= 16x \\ \\ \implies \: 10x - 16x = - 60 \\ \\ \implies \: - 6x = - 60 \\ \\ \implies \: x = \frac{ - 60}{ - 6} \\ \\ \implies \: x = 10[/tex]
At the market, 2.4 pounds of peas cost
$1.68. How much does one pound of
peas cost?
$0.7
Step-by-step explanation:Given sentence:
2.4 pounds of peas cost $1.68.Writing as an equation:
[tex]\implies 2.4 \ \text{pounds} = \$1.68[/tex]
To obtain the cost per pound of peas, divide 2.4 both sides. This will convert the value on the L.H.S to 1 pound. The value obtained on the R.H.S will be the the cost (answer).
[tex]\implies \dfrac{2.4 \ \text{pounds}}{2.4} = \$\dfrac{1.68}{2.4}[/tex]
[tex]\implies 1 \ \text{pounds}}= \$\dfrac{1.68}{2.4}[/tex]
[tex]\implies 1 \ \text{pound} = \$0.7[/tex]
A team from the high school went on a science-and-math quiz show. The science questions were worth 3 points and the math questions were worth 1 point. The team answered a total of 16 questions and earned 36 points. How many questions did the team answer in each category?
Answer:
5 science questions and 1 math question
Step-by-step explanation:
i literally just counted on my fingers by 3
Which of the following is a root of the polynomial function below?
F(x) = x2-3x2+x+5
O A. -2+1
O B. 2
O C. 2+1
O D. 1
PLEASE HELP, I missed a bunch of school and I dont know how to do this.
Answer:
(2, -4)
Step-by-step explanation:
Answer:
(2, -4)
Step-by-step explanation:
The solution to a system of equations is always going to be the point(s) where they intersect. To solve, use substitution and find each variable, x and y. Our final answer will be a set of coordinates (x, y). To plot this system, see the help image attached.
y = -x - 2
2x - y = 8
Substitute y to find x
2x - (-x - 2) = 8
2x + x + 2 = 8
3x = 6
x = 2
Substitute x to find y
y = -(2) - 2
y = -2 - 2
y = -4
Solution: (2, -4)
I hope this helps and God bless!
Find the product of 40 and
100.
Answer:
4000
Step-by-step explanation:
Product just means multiply!
40 × 100 = 4000
Answer:
4000
Step-by-step explanation:
40 times 100 is 4000
take the 4 and put the amount of 0's in the equation behind it ( there are 3 in total, 2 from the 100 and 1 from the 40): 4000
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AEC ≅ DEB, given that CA is parallel to DB and E is the midpoint of AD. Submit the entire proof to your instructor.
Given:
CA || DB
E is the midpoint of AD
Prove:
AEC ≅ DEB
A two column proof for ΔAEC ≅ ΔDEB is as shown below.
What are congruent triangles?"Two triangles are congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure."
What are interior angles?"These angles formed on the inside of two straight lines when crossed by a transversal."
What is midpoint?"It is point which divides a line segment into two equal parts."
What is AAS postulate of triangle congruence?"AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent."
For given question,
Given that CA is parallel to DB and E is the midpoint of AD.
CA is parallel to DB
CB is transversal.
∠ACB and ∠CBD are alternate interior angles.
We know that when a transversal intersects a parallel line then alternate interior angles formed are congruent.
So, ∠ACB ≅ ∠CBD ................(i)
Similarly for CA || DB and AD is transversal.
∠CAD ≅ ∠ADB ..................(ii)
Also, E is the midpoint of AD.
By definition of midpoint,
⇒ AE = ED ..................(iii)
From (i), (ii) and (iii),
By AAS postulate of triangle congruence,
ΔAEC ≅ ΔDEB
Therefore, a two column proof for ΔAEC ≅ ΔDEB is as shown below.
Learn more about AAS postulate of triangle congruence here:
https://brainly.com/question/1593616
#SPJ2
The Ruiz family is exchanging euros for US dollars. The exchange rate is 1 euro equals 1.35261 USD. Since the Ruiz family knows that USD are stated to the nearest hundredth of a dollar, they used the conversion ratio. Will this give the Ruiz family the correct
The Ruiz family using a rounded figure for exchange rate will not give the correct exchange.
Exchange rate:
1 euro = 1.35261 USD
1.35261 rounded to the nearest hundredth = 1.35
If Ruiz family is exchanging 50 euros for instance
Original exchange rate
1 euro = 1.35261 USD
50 euro = 67.6305
Rounded exchange rate:
1 euro = 1.35 USD
50 euro = 67.5 USD
Therefore, the Ruiz family using a rounded figure for exchange rate will not give the correct exchange.
Read more:
https://brainly.com/question/17985441
PLEASE HELP PLEASE PLEASE HELP
Answer:
D. is correct.
Look at 2 × [tex]\frac{1}{3}[/tex] as 2 × 1 for now.[tex]2 * 1 = 2[/tex]
Multiply 4 by 1(third)[tex]4 * 1=4[/tex]
Now, add.[tex]4 + 2 = 6[/tex]
________________________________________________________
The product of answer choice D.(6) is not equal to the product of [tex]\frac{2}{3}[/tex] × 4, because [tex]\frac{2}{3}[/tex] × 4 is actually [tex]2\frac{2}{3}[/tex]
________________________________________________________
What have we learned?We learned how to find whole numbers through an expression with fractions.
Questions related to the topic? Ask me in the comments box.
estimate 62% of 700 help me please
Answer:
anywhere around 420-450
Step-by-step explanation:
the actual answer is 434, a good estimation would be in that range
select the place where the digit 2 sits in this number 428,031
Answer:
The 2 is in the ten thousands place.
Answer:
In this case the number 2 would be located in the tens of thousands.
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
If you flip three fair coins, what is the probability that you'll get a tail on the first flip, a head on the second flip, and another tail on the third flip?
Answer:
75%
Im happy to help you
Answer:
1/8
Step-by-step explanation:
I think so
The solution of the equation 3(x + 3) = 12 is
Question 5 options:
1
2
3
4
Answer:
x=1
Step-by-step explanation:
1) Distribute 3x+9=12
2) Subtract 9 from both sides 3x=3
3) Divide by three x=1