The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998. choose the equivalent expression that is most useful for finding the year where the population was at a minimum. 8(x2 − 18x 108) 8(x2 − 18x) 108 8(x − 9)2 − 216 8(x − 9)2 216
The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.
Given expression 8x² − 144x + 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given expression is 8x² − 144x + 864
Let y = 8x² − 144x + 864
also, y - 864 = 8x² - 144x
by Extracting common factor 8 on the right side
y - 864 = 8(x² - 18x)
Add (18/2)² on both sides, we get
y - 864 + 8(18/2)² = 8 (x² - 18x + 81²)
y - 864 + 648 = 8 (x² - 8x + 9)
on simplification
y - 216 = 8 (x - 9)²
y = 8(x - 9)² + 216
therefore, y = 8 (x - 9)² + 216
The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.
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i will mark brainliest rn
Answer:
65 is the correct answer
Mr. Jones has a cylindrical water storage
tank. The tank has a diameter of 6 feet and
a height of 12 feet. Mr. Jones wants to
paint the tank but since the tank rests on a
concrete slab, he will not need to paint the
bottom of the tank. How much paint will
he need to paint the water storage tank?
Answer:
254.47sqft (square feet) of paint
Step-by-step explanation:
The surface area of the cylinder (282.74) minus the area of the one circle that doesn't need to be painted (28.27) is 254.47sqft which is the amount of paint he will need Mr. Jones.
if 10x+6 = 21 then what is 15
Answer:
The answer is
→ 1.5 or 10x = 15
Step-by-step explanation:
Since 10x + 6 = 21 and we supposed to find what 15 is, we would have to use these steps;
First subtract 6 on both sides
10x + 6 - 6 = 21 - 6
= 10x = 15
Another way I know the other answer is by multiplying 10 by 1.5 which equals 15.
Finding the Range
Find the range of the following set of numbers: 3, 16, 4,
17, 42, 12, 12, 16, 92, 14, 5.
After you find the range, explain how you came to that
calculation in the box below.
Answer:
89
Step-by-step explanation:
92 - 3 =89
subtract smallest from largest
Using the BOX and WHISKER above, what is the LOWER QUARTILE of the information?
Answer:
Lower Quartile is 8 according to the diagram.
What is the answer to this question????
Answer:
Yes, its a linear function
Step-by-step explanation:
See, all the results here are one-one which means for a distinct input there will be a distinct output.
That's why its a linear function
paul says x/y can result in either positive or negative quotient. is paul correct? explain why or why not.
Answer:
Dividing by same signs give a positive answer.
Dividing by different signs give a negative answer.
Step-by-step explanation:
Quotient is just a term for the answer given by a division problem.
positive/positive = positive
positive/negative = negative
negative/positive = negative
negative/negative = positive
x - 3y = 4
2x - 5y = 8
solve by substitution
Answer:
y = 0
x = 4
Explanation:
x - 3y = 42x - 5y = 8make x the subject,
x - 3y = 4
x = 4 + 3y __ equation 1
2x - 5y = 8
x = (8+5y)/2 __ equation 2
using substitution method:
(8+5y)/2 = 4 + 3y
8 + 5y = 8 + 6y
6y - 5y = 8 - 8
y = 0
Find x,
x = 4 + 3y
x = 4 + 3(0)
x = 4
Answer:
x = 4
y = 0
Step-by-step explanation:
Step 1. Pick one equation and rewrite in the form of x= OR y=x - 3y = 4 (original)
x = 4 + 3y (rewritten)
Step 2. Substitute for x in the other equation2x -5y = 8 (second equation)
2(4 + 3y) - 5y = 8 (substitute 4 + 3y for x)
Step 3. Solve for the unknown variable, y2(4 + 3y) - 5y = 8 (distribute)
8 + 6y - 5y = 8 (combine like terms)
y = 0 (first variable)
Step 4. Find x by plugging y into an equationx - 3y = 4 (original)
x - 3(0) = 4 (substitute 0 for y)
x = 4 (second variable)
FINAL SOLUTION: x = 4, y = 0You can double check this by plugging these numbers back into each equation; x = 4 and y = 0 is true for both.
I hope this helps!
Anita is 42 1/2 feet below jared. Steph is 67 3/7 feet above anita. What is stephs position compared to jared. Explain
Check the picture below.
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{42\frac{1}{2}}\implies \cfrac{42\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{85}{2}} ~\hfill \stackrel{mixed}{67\frac{3}{7}}\implies \cfrac{67\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{472}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{472}{7}~~ - ~~\cfrac{85}{2}\implies \cfrac{(2)472~~ - ~~(7)85}{\underset{\textit{using this LCD}}{14}}\implies \cfrac{944~~ - ~~595}{14}\implies \cfrac{349}{14}\implies 24\frac{13}{14}[/tex]
Can someone help me on this question? I’ll give brainliest if you answer soon!!!
Answer:
81
Step-by-step explanation:
Knowing that;
∠ EHD and ∠FHC are vertical angles.
since, ∠FHC = 81 Thus, ∠EHD = 81
Look at picture below for more information;
~Learn with Lenvy~
Answer:
81
Step-by-step explanation:
Given;
If m ∠FHC = 81 °, then what is m ∠ EHD?
Solve;
∠ EHD and ∠FHC are vertical angles.
Vertical angles ⇒ a pair of opposite angles formed by intersecting lines.
Since, ∠FHC = 81 hence, ∠EHD also = 81
[RevyBreeze]
Which quadratic function in standard form has the values a = –3. 5, b = 2. 7, and c = –8. 2? f(x) = 2. 7x2 – 8. 2x – 3. 5 f(x) = 2. 7x2 – 3. 5x – 8. 2 f(x) = –3. 5x2 – 8. 2x 2. 7 f(x ) = –3. 5x2 2. 7x – 8. 2.
Maria wants to determine which students is favored for president of the student council. Which of the following samples are biased and not freedom? Select all that apply.
O Surveying the boys in the freshman class.
O Surveying every other student in the cafeteria.
O Surveying all the students in her math class.
O Surveying 20 students from each grade at random.
O Surveying the students in the chess club.
Answer:
A, C, E,
Step-by-step explanation:
A)Surveying the boys in the freshman class.
C)Surveying all the students in her math class.
E)Surveying the students in the chess club.
In exercises, 4 and 5, find the unknown or marked angles.
Answer:
alternate angle and counter
good afternoon, please help me with this question and if u get it correct ill give u the brainlest
Answer:
3/5
Step-by-step explanation:
Hope that this helped :)
(h(1) = 9
h(2) = 3
h(n) = h(n - 2)•h(n - 1)
h(3) =
Answer: 27
Step-by-step explanation:
How do solve this
h(x)=1/2x-14; h(4)
Answer:
-12
Step-by-step explanation:
h(x) = ½x - 14 where x = 4:
h(4) = ½(4) - 14
= 2 - 14
= -12
Please help I'm extremely confused. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale. (picture of diagram included )
Answer:
x=8.4
Step-by-step explanation:
use tangent to solve the equation which is opposite/adjacent and set up the proportion
[tex] \frac{ \tan(35) }{1} = \frac{x}{12} [/tex]
the cross multiply to get x=tan(35)×12 then multiply that to get x=8.4
Olivia has a beaded necklace business. She can make 12 necklaces in 2 hours. How long will it take her to make 9 necklaces?
Answer:
1.5hours
Step-by-step explanation:
Help me on this question please!
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
═════════════════════
[tex]x+5[/tex]
[tex]x^{1-1} [/tex]
[tex]x^{0} [/tex]
[tex] = 1 [/tex]
─────────────────────┈
[tex](2x + 3)[/tex]
[tex]2x^{1-1} [/tex]
[tex]2x^{0} [/tex]
[tex]2\times 1 [/tex]
[tex] = 2[/tex]
══════════════════════
Step-by-step explanation:
#Carry on learning
Find the Area. First person that answers this and gets it correct gets brainliest.
Answer:
Step-by-step explanation:
Break up the shape into a trapezoid and rectangle:
Trapezoid area = (Top + Bottom) * Height / 2
= (9 + 20) * (21-16) / 2
= 29 * 5 / 2
= 72.5
Rectangle area = Length * Width
= 20 * 16
= 320
Combining, the total area = 72.5 + 320
= 392.5 in^2
Answer:
A = 392.5 in²
Step-by-step explanation:
The composite figure is made up of a rectangle and a trapezoid.
Calculate the area of the rectangle:
[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=20 \times 16\\&=320\; \sf in^2\end{aligned}[/tex]
Calculate the area of the trapezoid:
[tex]\begin{aligned}\textsf{Area of a trapezoid}&=\dfrac{\text{base}\;a+\text{base}\;b}{2} \times \text{height}\\&=\dfrac{9+20}{2} \times (21-16)\\&=\dfrac{29}{2} \times 5\\&=72.5\; \sf in^2\\\end{aligned}[/tex]
Therefore, the area of the composite figure it the sum of the area of the rectangle and the area of the trapezoid:
[tex]\begin{aligned}\textsf{Total area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of trapezoid}\\&=320+72.5\\&=392.5 \; \sf in^2\end{aligned}[/tex]
Therefore, the area of the composite figure is 392.5 in².
Can someone please help me with this? I need to turn it in tomorrow and I don't understand what to do.
Answer:
Step-by-step explanation:
Slope intercept form
y + 7 = 3(x + 4) Change all the double minuses to pluses.
y + 7 = 3x + 12 Remove the brackets.
y + 7 - 7 = 3x + 12-7 Subtract 7 from both sides
y = 3x + 5
Slope
Whatever number is in front of the x is the slope Answer: 3
y intercept
Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number. Answer: 5
x intercept.
This occurs when y = 0
0 = 3x + 5 Subtract 5 from both sides
-5 = 3x + 5 -5
-5 = 3x Divide by 3
-5/3 = 3x / 3
-5/3 = x
Answer: x_intercept = -5/3
Diego and Lin have savings accounts. Diego had $40 in his account 6 months ago. Now Diego has $250 in his savings account. Lin currently has $100 in her account. She plans to add $50 per month. 1. Write a system of equations to represent Diego and Lin’s savings accounts.
The equation that can be used to represent Diego's and Lin's savings account is 250 = 40 + 6x and Total savings= 100 + 50x respectively.
How to write equationlet
x = amount added each monthDiego:
6 months ago = $40
Now = $250
250 = 40 + 6x
250 - 40 = 6x
210 = 6x
x = 210/6
x = $35
Lin:
Now = $100
Future = $50 per month
let
x = number of monthsTotal savings= 100 + 50x
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for each pair of lines, determine whether they are parallel, perpendicular, or neither
2. The back of Nico’s truck is 7.5 feet long, 4 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 2.5 feet on each side.
How many boxes of papers can Nico pack into the back of his truck? Show your work.
Answer:
Answer:
9 boxes
Step-by-step explanation:
As the truck is 7.5 ft long, we can fit 3 boxes of paper along the length since 7.5 ÷ 2.5 = 3
As the truck is 4 ft wide, we can only fit 1 box of paper along the width
since 4 ÷ 2.5 = 1.6
As the truck is 8 ft tall, we can fit 3 boxes of paper high
since 8 ÷ 2.5 = 3.2
Therefore, the number of boxes of paper is:
3 × 1 × 3 = 9
Answer:
9 boxes
Step-by-step explanation:
Look above me ;)
Sandy is designing a circular garden as shown in this image. Her plan is to fill the rectangular region with hyacinths. She will need 78 square feet of space per hyacinth bulb. The hyacinth bulbs are sold in packages of 8.
What is the minimum number of packages Sandy must purchase to complete her plan?
Select from the drop-down menu to correctly complete the statement.
Sandy must purchase a minimum of _________
packages of hyacinth bulbs to complete her plan.
options are, 5,6,7,8
With one package (less actually) she can fill the 48ft^2 of the rectangular area.
How many packages does Sandy need?
We know that Sandy needs 7.8 square feet of space per hyacinth bulb, and the hyacinth bulbs are sold in packages of 8.
The rectangular region has a surface area of:
A = 8ft*6ft = 48 ft^2
The number of hyacinth bulbs that she can put in that surface is:
N = (48 ft^2/7.8 ft^2) = 6.15
So with 6 hyacinth bulbs, she can almost complete the rectangular area, and on each package there come 8 of them, so with one package she should be fine.
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Answer:
The answer is 7 PACKAGES
Step-by-step explanation:
I took the test!
look figure and give exact answer.
Answer:
Those two lines are equal
I need help on this I don't get it please help me on this
Correct answer: 9x -14y = -6
Linear equation: y = ax + b
Let's replace (x,y) with (1/2, 3/4) and (4,3) and have the following equations:
1/2a + b = 3/4 (1)
4a + b = 3 (2)
=> (2) b = 3 - 4a
(1) 1/2a + 3 - 4a = 3/4
=> (1) 7/2a = 9/4
(2) b = 3- 4a
=> (1) a = 9/14
(2) b = 3/7
So we have the equation: y= 9/14x + 3/7
Multiple both sides with 14
=> 14y = 9x + 6
=> 9x -14y = -6
Please help me solve this
Answer:
x = 24
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]
consider left side
[tex]5^{\frac{x}{6} }[/tex] × [tex]5^{\frac{x}{2} }[/tex]
= [tex]5^{\frac{x}{6} }[/tex] × [tex]5^{\frac{3x}{6} }[/tex]
= [tex]5^{\frac{4x}{6} }[/tex]
then
[tex]5^{\frac{4x}{6} }[/tex] = [tex]5^{16}[/tex]
since the bases on both sides are equal, both 5 then equate exponents
[tex]\frac{4x}{6}[/tex] = 16 ( multiply both sides by 6 )
4x = 96 ( divide both sides by 4 )
x = 24
Scott earns $16. 85 per hour at his job. He works 7 hours per day, 4 days per week. What is Scott’s gross monthly income for 4 weeks? a. $471. 80 b. $943. 60 c. $1,415. 40 d. $1,887. 20.
The gross monthly income for 4 weeks is $1,887.20
We have given that Scott earns $16. 85 per hour at his job.He works 7 hours per day then,
What is the computation of the gross monthly income for 4 weeks?Gross income= Earning per hour × number of hours works per day × number of days works per week × number of weeks
Gross income= $16.85 × 7 × 4 × 4
Gross income= $1,887.20
Therefore, the gross monthly income for 4 weeks is $1,887.20.
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