Step-by-step explanation:
I assume the original expression is
2x² + 16x + 11
we need to get this into the form of a(x + b)² + c
let's do the generic multiplication and compare the result to the given expression :
a(x² + 2bx + b²) + c = ax² + 2abx + ab² + c
when we compare this with the original equation, we only need to look at terms with the same variable exponents.
2x² is the only term with "x²".
and ax² is the only term with "x²" in the generic form.
so ?
2x² = ax²
=>
a = 2
16x is the only term with "x" (exponent 1).
2abx is the only term with "x" in the generic form.
16x = 2abx
8x = abx = 2bx
4x = bx
=>
b = 4
11 is the only pure number (constant).
ab² + c is the only constant term in the genetic form.
11 = ab² + c = 2×4² + c = 2×16 + c = 32 + c
-21 = c
so, the solution is
2(x + 4)² - 21
A valuable collection of coins contained old nickels, dimes,quaters, and pennies. The face value of the pennies was $8. Therewere seven more than three times as many quaters as dimes andsixteen less than twice as many nickels as quaters. If the facevalue of the entire collection was $38.40, how many of each kind ofcoin was there?
Answer:A number line shows 114, −224, and −134. Which statement is NOT true?
Step-by-step number line shows 114, −224, and −134. Which statement is NOT true?
A number line shows 114, −224, and −134. Which statement is NOT true?
recipe☝️
Question: How many cups of sifted cake flour will you need for 2 cakes? Show your work.
Answer:
5 cups of flour need to make two cakes
Help pls I don’t understand this shi
Answer:
It's kind-of blurry, can you copy-paste the questions?
Step-by-step explanation:
do you think i can pass 7th grade with at least a B i have to make them 80%.
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
I passed 7th grade with a B
Wjejjejjsnsbbnxkskakksnsnsnznsmsnndndd
Answer:
whats
Step-by-step explanation:
[tex]\orange{\rule{40pt}{555555pt}} \green{\rule{40pt}{555555pt}} \blue{\rule{40pt}{555555pt}} \red{\rule{40pt}{555555pt}}\pink{\rule{40pt}{555555pt}}\yellow{\rule{40pt}{555555pt}}[/tex]
A tractor can plant a field at a rate of 2.5 acres per 5 minutes. If a mammoth farm measuring 4 square miles needs planting, how long will it take in hours to plant the field? There are 640 acres in a square mile. Determine your answer to the nearest hour. If the tractor can run 8 hours a day, what is the minimum number of days it will take to plant the farm?
The time taken by the tractor to plant the field with an area of 4 square miles is nearly 85 hours.
The minimum number of days taken by the tractor when working 8 hours a day is 11 days.
What is the area?The area is the total surface occupied within the boundary of the figure.
How to solve the question?In the question, we are given that a tractor can plant a field at a rate of 2.5 acres per 5 minutes.
We are asked the time taken by the tractor to plant a field having an area of 4 square miles.
First, we convert the area of the field from sq. miles to acres using the conversion rate, 1 square mile = 640 acres,
Thus, the area of the field = 4 sq. miles = 4*640 acres = 2560 acres.
Time taken to plant 2.5 acres is given to be 5 minutes.
Thus, the time taken to plan 1 acre = 5/2.5 = 2 minutes.
Thus, the time taken to plant the field having an area of 2560 acres = 2560*2 minutes = 5120 minutes = 85.33 hours = 85 hours and 20 minutes.
Thus, the time taken by the tractor to plant the field with an area of 4 square miles is nearly 85 hours.
The time for which the tractor can run daily is 8 hours.
Thus, the number of days taken by the tractor to plant the field = 85.33/8 = 10.66625, or 11 days.
Thus, the minimum number of days taken by the tractor when working 8 hours a day is 11 days.
Learn more about unit conversions at
https://brainly.com/question/28000115
#SPJ2
Which of the following expressions has the greatest value?
Answer:
[tex](0.1)^2[/tex]
Step-by-step explanation:
The top number known as an exponent tells you to multiply the number by its self that many times so the other number will get very small.
Hey there!
Option A.
0.01^4
= 0.01 * 0.01 * 0.01 * 0.01
= 0.0001 * 0.0001
= 0
Option B.
0.1^4
= 0.1 * 0.1 * 0.1 * 0.1
= 0.01 * 0.01
= 0.0001
Option C.
0.01^3
= 0.01 * 0.01 * 0.01
= 0.001 * 0.01
= 0.00001
Option D.
0.1^2
= 0.1 * 0.1
= 0.01
“ 0.01 > 0.0001 > 0.00001 > 0”
Therefore, your answer should be: 0.1^2 (option D)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
what is the answer to 5^-16+24 with solution
Answer:
24
Step-by-step explanation:
i used calculator. it is so easy
how did you get m in the equation
Rachel has a $23,000 six year loan with APR of 7.25%
Answer:6,000 is the answer
Step-by-step explanation:
Liam invests $3,670 in a savings account at his local bank which gives 1.9% simple annual interest. He also invests $2,040 in an online savings account which gives 5.5% simple annual interest. After five years, which one will have earned more interest, and how much more interest will it have earned, to the nearest dollar?
Step-by-step explanation:
Given:
Investment P₁ = $3670Investment P₂ = $2040Rate of interest r₁ = 1.9% SIRate of interest r₂ = 5.5% SITime t = 5 yearsFind amount of interest in both investments:
I₁ = P₁r₁t = $3670*(1.9/100)*5 = $348.65I₂ = P₂r₂t = $2040*(5.5/100)*5 = $561.00As we see the online savings account earns more interest and the difference is:
$561.00 - $348.65 = $212.35 ≈ $2122.9. What is the equation of a line parallel to 3x + 4 = y and passing through
(4,-2)?
A. 3x + 10 = y
B. 3x – 14 = y
C. -*-=y
D. --*x+10=y
Hello! (:
3x+4=y
We want to convert it into slope-intercept form:
y=mx+b
Our equation looks like this:
y=3x+4
Now, parallel lines have the same slope. So if one line has a slope of 3, the line parallel to it has a slope of 3 as well.
Now, we have the slope and a point, so we write the equation in point-slope form:
y-y1=m(x-x1)
y-(-2)=3(x-4)
y+2=3x-12
y=3x-12-2
y=3x-14
Hence, that is the required equation, Hope it helps you!
If you have any question or query, feel free to ask! (:
~An excited gal
[tex]SparklingFlower (:[/tex]
A new energy drink advertises 140 calories for 8 ounces. How many calories are in 20 ounces of the drink?
There are
calories in the 20 ounce drink.
Answer:
350
Step-by-step explanation:
in every 140 calories there is 8 ounces
what about in 20 ounce of drink
140 calories ___8 ounce
? 20 ounce
140×20 =2800÷8=350
What is the best estimate for the volume of a jug of milk?
Answer:
3.785 litres
Step-by-step explanation:
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
A) no solution
Step-by-step explanation:
These lines are parallel. Which means that they will never intersect, and since the solution to a system of equations is the point or points of intersection, this means there would be no solution to this system.
there is a bag filled with 6 blue and 5 red marbles.
a marble is taken at random from the bag the colour is noted and then it is replaced. another marble is taken at random. what is the probability of getting 2 reds
Answer:
Step-by-step explanation:
The probability of obtaining a red marble in one sample is 5/11. Since you are sampling twice the probability of picking a red marble both times is 5/11 x 5/11 = 25/121. That is slightly less than one time in five.
Please solve these.
You will get all of my points if you get all of them correct
Answer:
Step-by-step explanation:
1) Area of triangle= 1/2 x b x h
b = 7.6cm h= 3.4cm
Area= 1/2 x 7.6 x3.4 = 12.92cm²
2)Divide the shape into a triangle and a rectangle
Area of rectangle : l x b
L= 20cm, b= 7cm
= 20 x 7 = 140 cm²
Area of triangle =1/2 x b xh
B = 20cm, h= 16 - 7 = 9cm
1/2 x 20x 9= 90cm²
Total area = 140 + 90 = 230cm²
3) area of triangle = 1/2 x b x h
B = 12cm, h= 5cm
= 1/2 x 12 x 5 = 30cm²
4) area of triangle = 1/2 x b x h
B = 15cm, h= 8cm
= 1/2 x 15 x 8 = 60cm²
5) divide the shape into two rectangles; the lower and the upper
Area of rectangle= l x b
Upper rectangle, l= 10cm, b= 27 - 9 = 18cm
Area= 10 x 18= 180cm²
Lower rectangle, l= 24cm, b= 9cm
Area = 24 x 9= 216cm²
180 + 216 = 396cm²
The lengths of the sides of a triangle are square root 139, square root 73, and 6. Classify the trianglo as “acute", "right", or "obtuso".
Choose the correct type of triangle below.
O acute
obtuse
Oright
Answer:
It's obtuse.
Step-by-step explanation:
Mumble. Smells al-kashi laws of cosine to me.
[tex]a^2-b^2-c^2 = -2bc cos\alpha\\b^2-c^2-a^2=-2ca cos \beta\\c^2-a^2-b^2=-ab cos \gamma[/tex]
Now, we don't need to calculate the RHSs, and then:
If at least one of the three LHSs is greater than zero, the triangle is obtuse
If at least one is zero, it's a right triangle (pythagorean theorem anyone?)
if all three numbers are less than zero, the triangle is acute
Start crunching numbers.
[tex]139-73-36 = 30[/tex] First try was the charm. finding 30 means that the product [tex][-2(\sqrt{73})(6) ]cos \alpha[/tex] is positive, and since the product in the large bracket is negative, the cosine has to be 0, thus the angle has to be greater than 90°, QED
omg please help idek
Can someone help me with this I’m not getting it
Answer:
n = 3.5
Step-by-step explanation:
basically it's saying that 2.8 is proportional to 4.8 as n is proportional to 6. therefore:
2.8/4.8 = n/6
0.583 = n/6
3.5 = n
HELP ME OUT PLEASE I RLLY NEED IT ASAP. ):
(a) Slope is rise over run, or change in y over change in x.
1 -> 3 ( [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{4 - -8}{-1 - -5} = \frac{4 + 8}{-1 +5}= \frac{12}{4} =\frac{12}{4}[/tex] )
2 -> 3 ( [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{1 - 7}{0 - 2} = \frac{-6}{- 2} =\frac{6}{2}[/tex] )
3 -> -1/3 ( [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-7 - -3}{6 - -6}= \frac{-7+3}{6+6}=\frac{-4}{12}=-\frac{1}{3}[/tex] )
(b) If a line is parallel, the slopes will be the same. If they are perpendicular, the slopes will be are negative reciprocals of one another. If they are neither, then their slopes don't match up in any way.
1 & 2 -> Parallel
1 & 3 -> Perpendicular
2 & 3 -> Perpendicular
Note - Since 1 & 2 are parallel, then both 1 and 2 will be perpendicular to 3!
Have a nice day!
If this is not what you are looking for - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
Line 1: slope: 1
Line 2: slope: -3/2
Line 1 and line 2: neither
Line 3 slope: - 1/3
Line 1 and 3: neither
Line 2 and 3: neither
Step-by-step explanation:
Line 1: (-5,-8) and (-1,4)
Slope: (4 - - 8)/(-1 - - 5) = 12/4 = 3
Line 2: (2,7) and (0,10)
Slope: (10 -7)/(0 - 2) = 3/-2 = -3/2
Line 3. ((-6,-3) and (6,-7)
Slope: (-7 - - 3)/(6 - -6)= -4/12= -1/3
1. The table shows the number of pages a
student reads in various amounts of time.
2. The dou
rate at
Dollars
Time (h)
3
5
9
10
Pages
195
325
585
650
Hours
Tell whether the relationship is a proportional relationship. Ex
Answer:
Please post the chart
Step-by-step explanation:
Pls answer the questions, I would really appreciate it, thx, :)
Answer:
7V
The average amount of minutes exercised on each day
Step-by-step explanation:
We are given that every day "V" amount of vegetables are eaten everyday.
If there are 7 days in a week then the amount of vegetables eaten in 1 week would be 7V
E = ( M + W + F ) / 3
M = # of minutes exercised on Monday
W = # of minutes exercised on Wednesday
F = # of minutes exercised on Friday.
Note that to find the average of something you find the sum of the values and divide that by the number of values.
The equation "E" is adding up the # of minutes exercised on Monday, Wednesday and Friday and dividing the sum of that by 3, which happens to be the number of values being added( those values being the # of minutes exercised on Monday, Wednesday and Friday) . So we can conclude that the equation E represents an average, more specifically the average # of minutes exercised on each day.
The 5th term of an arithmetic sequence is 30, while the 13th term is 70
Answer:
a = 10
d = 5
Step-by-step explanation:
[tex]a_{n}=a + (n-1)d\\\\a_{5}=30\\\\a + (5-1)*d=30\\\\[/tex]
a + 4d = 30 ------------------(I)
[tex]a_{13}=70\\\\a + (13-1)d=70[/tex]
a + 12d =70 -------------(II)
Multiply equation (II) by (-1) and then add.So, 'a' will be eliminated and you can find the value of d
(I) a + 4d = 30
(II)*(-1) -a - 12d = -70 {Now add}
- 8d = - 40
Divide both sides by (-8)
d = -40/-8
d = 5
Plugin d = 5 in equation (I)
a + 4*5 = 30
a + 20 = 30
a = 30 - 20
a = 10
What is the stimated difference of 31,523 - 23,589
Answer:
8000 (Estimated) and the real difference would be 7934
Step-by-step explanation:
An estimated difference would be 8000, we get this number by subtracting 23,000 from 31,000 to make the subtraction much faster. The real answer to this would be 7934 which is pretty close to 8000 which is the estimation
1.
What is the sum of
4 |
22 (1 point)
+
+
3
011
o
어
IN IN NII am |
0
0 0
Answer:
B. One whole number one over two. 1½
Solve the equations.
[tex]\sqrt{x^{2} } =14[/tex]
[tex]\sqrt{x^{2} } =17[/tex]
[tex]\sqrt{y^{2} } =5[/tex]
Answer:
[tex]x=\pm14\\x=\pm17\\y=\pm5[/tex]
Step-by-step explanation:
Generally, equations in the form [tex]\sqrt{x^2}=c[/tex] where [tex]c[/tex] is some constant, would have [tex]x=\pm c[/tex] as its solution.
This is because the square of a number is always positive regardless of the sign of [tex]x[/tex].
Wendy was riding her bike along a trail and travelled 63 miles in 6 hours. When Iman was riding on the same trail she travelled 10.1 miles per hour. What was Wendy's unit rate for her bike ride? (Miles per Hour) Who was riding faster?
can someone please help me! :)
Rewrite the equation below so that it does not have fractions.
3/4x-5=3/8
Do not use decimals in your answer.
Answer:
x=
6
43
Step-by-step explanation:
pasos
4
3
x−5=
8
3
Agrega 5 a ambos lados.
4
3
x=
8
3
+5
Convertir 5 a la fracción
8
40
.
4
3
x=
8
3
+
8
40
Como
8
3
y
8
40
tienen el mismo denominador, sume sus numeradores para sumarlos.
4
3
x=
8
3+40
Suma 3 y 40 para obtener 43.
4
3
x=
8
43
Multiplica los dos lados por
3
4
, el recíproco de
4
3
.
x=
8
43
×(
3
4
)
Multiplica
8
43
por
3
4
(para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).
x=
8×3
43×4
Realiza las multiplicaciones en la fracción
8×3
43×4
.
x=
24
172
Reduzca la fracción
24
172
a su mínima expresión extrayendo y anulando 4.
x=
6
43
