Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this firm use the method of completing the square
Factor out - 1 from each term
y = - (x² - 9x + 12)[tex]\frac{33}{4}[/tex]
To complete the square
add/subtract (half the coefficient of the x- term )² to x² - 9x
y = - (x² + 2( - [tex]\frac{9}{2}[/tex])x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 12 )
= - ( (x - [tex]\frac{9}{2}[/tex])² - [tex]\frac{33}{4}[/tex] )
y = - (x - [tex]\frac{9}{2}[/tex] )² + [tex]\frac{33}{4}[/tex] ← in vertex form
Please answer this correctly
Answer:
Emmett
Step-by-step explanation:
Kira is younger than Nila
So Nila>Kira
Nila is older than Mike and Mike is older than Kira
Nila>Mike>Kira
Nila is younger than Emmett
Emmett>Nila>Mike>Kira
Answer:
Emmett is older
Nila is older than Kira.
Nila is older than Mike.
Nila is younger than Emmett.
Therefore, Emmett is older than Nila.
And if Nila is older than Kira, and Emmett is older than Kira, Emmett is oldest.
Jim believes he will receive 50 pieces of candy for Halloween. If Jim actually
received 75 pieces of candy, what is Jim's percent error? Round your answer to
the nearest tenth of a percent.
Y is inversely proportional to x. If y= 400 when x =2 find y when x= 200
Answer: 4
Step-by-step explanation:
Inversely proportional means xy = k, where k is the constant of proportionality
First, find k when x = 2 and y = 400 ----> 2(400) = k --> 800 = k
Then, find y when x = 200 (knowing that k = 800)
200y = 800
y = 4
Ms. Thornton's class visited five freshwater lakes to learn more about the crocodiles and alligators living in them. The class counted the number of species in each lake as shown in the table.
Lake Crocodiles Alligators
A 4 5
B 21 35
C 3 9
D 6 16
E 24 30
The relationship between the number of crocodiles and the number of alligators is not proportional across all lakes. Only two of the lakes have crocodiles and alligators in the same proportion. Which two lakes are they?
A.
lake A and lake B
B.
lake B and lake C
C.
lake A and lake E
D.
lake C and lake D
Answer:
It's C. If you divide them you get 1.25 for both of them and its proportional
0.03 x 5=
How is this solved?
Answer: 0.15
Step-by-step explanation:
Multiply 0.03 by 5.
Answer:0.15
Step-by-step explanation:
First multiply 3 and 5. Then you will get 15. In the question it says 0.03 and its 2 digit from decimal so in 15 you will put a decimal 2 digit from the left and you will get 0.15
what is the answer to number 16
Answer:
b ≈ 13.80 in
Step-by-step explanation:
Since the triangle is right use the tangent ratio to solve for b
tan17.71° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{43.21}[/tex]
Multiply both sides by 43.21
43.21 × tan17.71° = AC, hence
AC = b ≈ 13.80 ( to 2 dec. places )
Mr. Yueng graded his students’ math quizzes.
Students came up with four different answers when solving the equation x3 = 22.
Which answer is correct?
A. x=22 3
B. x=22−−√3
C. x=±22−−√3
D. x=22−−√
For this case we must solve the following equation:
[tex]x ^ 3 = 22[/tex]
If we apply cubic root to both sides of the equation, then we eliminate the exponent on the left side:
[tex]\sqrt [3] {x ^ 3} = \sqrt [3] {22}\\x = \sqrt [3] {22}[/tex]
That is the exact solution of the equation. Its decimal solution is given by:
[tex]x = \sqrt [3] {22} = 2.8020[/tex]
ANswer:
The solution to the equation is [tex]x = \sqrt [3] {22} = 2.8020[/tex]
Option B. x = [tex]\sqrt[3]{22}[/tex] is the correct answer, by solving x³ = 22, where we found the cube root of 22. Other options are incorrect.
We will determine a number that, when raised to the power of 3, equals 22.
Option A: x = [tex]22^{3}[/tex] is incorrect because this represents 22 cubed, not the cube root of 22.Option B: x = [tex]\sqrt[3]{22}[/tex] is correct because it accurately represents the cube root of 22.Option C: x = ± [tex]\sqrt[3]{22}[/tex] is incorrect because cube roots can include negative values, but in the context of this problem we are looking for a single, positive value.Option D: x = [tex]\sqrt{22}[/tex] is incorrect because this represents the square root of 22, not the cube root.Therefore, the correct choice is option B. x = [tex]\sqrt[3]{22}[/tex]
Corrected question:
Mr. Yueng graded his students’ math quizzes. Students came up with four different answers when solving the equation [tex]x^{3}[/tex] = 22.
Which answer is correct?
A. x = [tex]22^{3}[/tex]
B. x = [tex]\sqrt[3]{22}[/tex]
C. x = ±[tex]\sqrt[3]{22}[/tex]
D. x = [tex]\sqrt{22}[/tex]
What is the equation of the line passing through the points (–2, 2) and (3, –1)
Answer:
3x + 5y = 4 or y = -⅗x + ⅘
Step-by-step explanation:
First, find the Rate of change [Slope]:
-y₁ + y₂\-x₁ + x₂ = m
-2 - 1\2 + 3 = -⅗
Apply the Point-Slope Formula, y - y₁ = m(x - x₁), since we are given points. It does not matter which one you choose. NOTE: All negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the coordinates into the formula with their CORRECT signs:
y + 1 = -⅗(x - 3)
y + 1 = -⅗x + 1⅘
- 1 - 1
_________________
y = -⅗x + ⅘ >> Line in Slope-Intercept Form
If you want it in Standard Form:
y = -⅗x + ⅘
+⅗x +⅗x
____________
⅗x + y = ⅘ [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]
5[⅗x + y = ⅘]
3x + 5y = 4 >> Line in Standard Form
__________________________________________________________
y - 2 = -⅗(x + 2)
y - 2 = -⅗x - 1⅕
+ 2 + 2
________________
y = -⅗x + ⅘ [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]
5[⅗x + y = ⅘]
3x + 5y = 4 >> Line in Standard Form
I am joyous to assist you anytime.
** You see? I told you it did not matter which ordered pair you choose because you get the EXACT SAME RESULT. :]
write 0.3232323232... as a fraction
write 2.555555... as a mixed number
Answer: I believe first one is 32/99 and the second one is 2 whole numbers and 5/9
Step-by-step explanation:
The number 0.323232... can be written as a fraction 32/99, while the number 2.55555... can be written as the mixed number 2 5/9.
To write 0.323232... as a fraction, you can use the method for converting repeating decimals to fractions. Let's say X = 0.323232... Then 100X = 32.323232..., and subtracting the first equation from the second gives 99X = 32, or X = 32/99.
For the number 2.55555..., we will have our whole number as '2' and we need to convert .55555... into a fraction. Let's use the same method: if Y = .55555..., then 10Y = 5.55555.... Subtracting these gives 9Y = 5, which simplifies to Y = 5/9. So, 2.55555... as a mixed number is 2 5/9.
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A town has accumulated 3 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated 6 inches, and the depth is increasing by 3 inches every hour. In about how many hours will the snowfall of the towns be equal?
Answer:
1 hour
Step-by-step explanation:
set town one equation to 3 + 6x and town two equation to 6+3x
set these two equations equal to each other and solve for x
3 + 6x = 6 + 3x
3x = 3
x = 1
1 hour
9x+11y=-14
6x-5y=-34
Resolver por regla de cramer
Answer:
x=-4 y=2
Step-by-step explanation:
y=-14-9x÷9
6x-5 (14-9x÷9)=-34
6x-(70+45x÷9)=-34
Take LCM
and then do it
This equation graphed
I answered this question already.
As Laura's mother rushed off to work, she quickly gave Laura some instruct
me, try my cell ... if I don't answer it means I'm in a meeting, but don
neaps I'm in a meeting, but don't worry, the meeting
won't last more than 30 minutes and I'll call you back when it's over." Later than
needed her mother, but her mother was stuck in a meeting and couldn't answer ih
Laura concludes that she will have to wait no more than 30 minutes before she gete
from her mother. What law of logic did Laura use to draw this conclusion?
Answer:
I don't actually know the answer to this question please
Use Order of Operations to simplify
8 + 7(4 exoponet 2 -3)
a salesman receives a salary rs 1000 per month and 10%commission on sales in excess of rs 5000.what is the amount of sales if he earns rs.2000. in a particular month
Answer:
Amount of sales = rs 10,000.
Step-by-step explanation:
He earns 2000 - 1000 = rs 1000 from sales.
This equals 10% ( = 0.10 as a fraction) of his sales so his sales must have been 1000 / 0.10
= rs 10,000.
200 principal, 4% compounded annually for 5 years
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$200\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=200\left(1+\frac{0.04}{1}\right)^{1\cdot 5}\implies A=200(1.04)^5\implies A=243.33058048[/tex]
what is 2^√(3) answer fast an step by step ,please?
Answer:
2 √2
Step-by-step explanation:
2^√(3) = {(2)³}¹/²
= (8)¹/² = √8
= √2 * 2 *2 = 2 √2
Round 17139.554963 to the nearest whole number.
menurut whole number.
Answer:
17140
Step-by-step explanation:
The number in the tenths place is 5 or higher so you need to round it up to 17140.
Answer:
17140
Step-by-step explanation:
If the number in the tenths place is 5 or more, round the number up.
Maya has 3 times as many dimes as nickels. She has 4 more quarters than nickels. if she has a total of $9.40, how many of each type of coin does she have?
Answer: nickels = 14, dimes = 42, quarters = 18
Step-by-step explanation:
Let n represent nickels which has a value of $0.05
Let d represent dimes which has a value of $0.10
Let q represent quarters which has a value of $0.25
It is given that:
n = n
d = 3n
q = n + 4
and their total value is $9.40 ⇒ n + d + q = $9.40
Use substitution to find the quantity of nickels:
.05(n) + .10(3n) + .25(n + 4) = 9.40
5n + 10(3n) + 25(n+4) = 940 multiplied by 100
5n + 30n + 25n + 100 = 940 distributed
60n + 100 = 940 added like terms
60n = 840 subtracted 100
n = 14 divided by 60
n = 14
d = 3n
= 3(14)
= 42
q = n + 4
= (14) + 4
= 18
Find the slope of the line passing through each of the following pair of points. (4, 0), (-2, 8)
Answer:
-4
-----
3
Step-by-step
x1,y1
(4,0),
x2,y2
(-2,8)
y2-y1/x2-x2
8-0/(-2)-4=8/-6= -4
-----
3
Is 73 rational or irrational
Answer:
it's rational
Answer:
rational.
Step-by-step explanation:
If it can be written as a fraction it is rational. If it cannot be written as a fraction it is irrational.
Sis I can’t do math... this has to be 20 characters so soosksksksdmksjsjdjdsjdj
Answer:
45mph.
15 x 3 = 45
20 x 3 = 60
so 60 ÷20 = 3
15 × 3 = 45
since 1 hour is 60 minutes
60 divided by 20 is 3
And 15 miles in 20 minutes times 3 is 45 miles in one hour
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In the lab, Tom has two solutions that contain alcohol and is mixing them with each other. He uses 500 milliliters less of Solution A than Solution B. Solution A is
14% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 440 milliliters of pure alcohol?
Answer:
22 milliliters
step by step
solution B x 22
20 x 22 = 440 milliliters
Final answer:
Tom uses 1,500 mL of Solution B. By setting up equations using the volume percentage of alcohol in each solution and solving for 'x', the volume of Solution A, we find the required volume for Solution B.
Explanation:
To solve for the volume of Solution B that Tom uses, we first establish the equations based on the information given. Let's denote the volume of Solution A as x mL. Thus, the volume of Solution B will be x + 500 mL. The total amount of pure alcohol in the final mixture is 440 mL.
Using the volume percentage for alcohol content in each solution, we can set up two equations to find x. The first equation is based on Solution A (14% alcohol) and the second on Solution B (20% alcohol):
The total volume of alcohol combined from both solutions is equal to 440 mL, which gives us the equation:
0.14x + 0.20(x + 500) = 440
Solving for x we get:
Since x is the volume of Solution A and we know that Solution B is 500 mL more than Solution A, we calculate the volume of Solution B as follows:
x + 500 = 1,000 + 500 = 1,500 mL
Therefore, Tom uses 1,500 mL of Solution B.
Help me please I don’t understand
Answer:
She stopped to rest for 45 minutes.
Step-by-step explanation:
It's where the line is straight. What's the second question?
Answer:
0.75 (45 mins) for both
Step-by-step explanation:
It's because the rest is the time where no activity is happening (the straight line). That line when measured from its start to end is mins 45 to mins 90, and when subtracted, gives 45 mins. For the initial ride it is from where the line moves upward until it stops. That goes from mins 0 to mins 45 ad when subtracted gives 45 mins.
Use rounding to estimate $6.79 − $3.95 to the nearest half-dollar.
A : $ 3.50
B : $ 3.00
C : $ 4.00
D : $ 4.50
B, i honestly just subtracted them... and got $2.84 and rounded up to $3.00
Answer:
B : $ 3.00
Step-by-step explanation:
Round $6.79 to $7.00 and round $3.95 to $4.00 then do $7.00 - $4.00 = $3.00. You get the answer of B : $ 3.00
Mr. Smith donated $378 to 2 charities. Charity A received 5 times as much as Charity B. How much did Charity B received from Mr Smith?
Answer:
$63
Step-by-step explanation:
let x represent Charity B then Charity A = 5x
Sum the two and equate to 378, that is
x + 5x = 378
6x = 378 ( divide both sides by 6 )
x = 63
Thus Charity B received $63
Write the equation of the line in either point-slope form or slope-intercept form.
Write the equation of a line that has a slope of -3 and passes through the point (1.25, -4).
Use the drop-down menus to select the appropriate values in the equation.
25 POINTS!
Answer:
the answer is y = -3x + ( -0.25)
Step-by-step explanation:
The equation of a line with a slope of -3 passing through the point (1.25, -4) can be derived by using the point-slope form (y - y1 = m(x - x1)). Substituting the given values, we get the line's equation as y = -3x - 0.25.
Explanation:The given problem requires us to write the equation of a line in either point-slope form or slope-intercept form. We are provided with a bit of information to get started: the slope of the line (-3) and a point the line passes through (1.25, -4).
The point-slope form of a line's equation is: y - y1 = m(x - x1), where (x1, y1) are coordinates of a point on the line and m is the slope. Substituting the given values, we get y - (-4) = -3(x - 1.25), which simplifies to y + 4 = -3x + 3.75. Finally, rearranging, we get the slope-intercept form: y = -3x - 0.25.
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Find the slope of the line with the equation 12x - 8y + 7 = 9.
-3/2
312
2/3
Final answer:
The slope of the line represented by the equation 12x - 8y + 7 = 9 is 3/2. To find this, the equation was rearranged into slope-intercept form, revealing the slope as the coefficient of x.
Explanation:
To find the slope of the line with the given equation 12x - 8y + 7 = 9, you first need to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
First, subtract 12x from both sides of the equation to isolate terms with y on one side:
-8y = -12x + 2
Next, divide each term by -8 to solve for y:
y = (12/8)x - 2/8
Simplify the fractions:
y = (3/2)x - 1/4
Now the equation is in slope-intercept form, and you can see that the slope m is 3/2 or 1.5. Therefore, the slope of the line is 3/2.
Mrs. Fronkos class for evry 6 boys there are 8 girls. Write the ratio of boys to girls in simplest form
Final answer:
The ratio of boys to girls in Mrs. Fronko's class in simplest form is 3:4, obtained by dividing both sides of the given ratio, 6:8, by the greatest common divisor, which is 2.
Explanation:
To find the ratio of boys to girls in Mrs. Fronko's class in its simplest form, we will start with the ratio given, which is 6 boys for every 8 girls. This can be written as 6:8. To simplify ratios, we divide both sides of the ratio by the greatest common divisor. In this case, the greatest common divisor of 6 and 8 is 2. Therefore, we divide both numbers by 2 to find the simplest form of the ratio.
6 ÷ 2 = 3 and 8 ÷ 2 = 4.
After dividing both numbers by 2, the ratio becomes 3:4. This indicates that for every 3 boys, there are 4 girls in Mrs. Fronko's class, and this is the simplest form of the ratio.
2. To get to the semi finals, a dancer has to score at least an average of 8 points. There are 4 judges in the
competition. The first three judges gave the dancer 8.9 points, 7.1 points and 8.3 points. What is the lowest
score 4th judge can give this dancer in order for her to move to the semi finals? Show all your work and justify
all your steps. You will not receive credit unless you justify the step. Please be sure to answer the question.
Answer:
The lowest score 4th judge can give this dancer in order for her to move to the semi finals is 7.7.
Step-by-step explanation:
Let x points be the score that 4th judge gave to the dancer.
The first three judges gave the dancer 8.9 points, 7.1 points and 8.3 points.
In total, the dancer got
[tex]8.9+7.1+8.3+x=24.3+x[/tex] points
The average score is
[tex]\dfrac{24.3+x}{4}[/tex]
This average score must be at least of 8 points, so
[tex]\dfrac{24.3+x}{4}\ge 8\\ \\24.3+x\ge 32\\ \\x\ge 32-24.3\\ \\x\ge 7.7[/tex]
The lowest score 4th judge can give this dancer in order for her to move to the semi finals is 7.7.