100 POINTS I WILL MARK BRAINLIST
Solve this equation using the method of completing the square:
3x^2 + 24x - 24 = 0
Potential answers:
x = -2 +/- 4sqrt6
x = 4 +/- 2sqrt6
x = 2 +/- 4sqrt6
x = -4 +/- 2sqrt6
Answer:
[tex]\boxed{\sf x = -4 \pm 2\sqrt{6} }[/tex]
Explanation:
3x² + 24x - 24 = 0
factor the coefficient
3(x² + 8x) -24 = 0
Halve the second term and square it
3(x + 4)² -24 -3(4)² = 0
simplify the answer
3(x + 4)² -72 = 0
add 72 on both sides
3(x + 4)² = 72
divide both sides by 3
(x + 4)² = 24
square root both sides
x + 4 = ±√24
subtract both sides by 4
x = -4 ± 2√6
Answer:
[tex]x=-4\pm2\sqrt{6}[/tex]
Step-by-step explanation:
Completing the square for quadratic in the form [tex]ax^2+bx+c=0[/tex]
Given equation:
[tex]3x^2+24x-24=0[/tex]
Factor out 3:
[tex]\implies 3(x^2+8x-8)=0[/tex]
Divide both sides by 3:
[tex]\implies x^2+8x-8=0[/tex]
Add 8 to both sides:
[tex]\implies x^2+8x=8[/tex]
[tex]\textsf{Add }\: \left(\dfrac{b}{2}\right)^2\: \textsf{ to both sides}:[/tex]
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=8+\left(\dfrac{8}{2}\right)^2[/tex]
[tex]\implies x^2+8x+16=8+16[/tex]
[tex]\implies x^2+8x+16=24[/tex]
Factor the left side:
[tex]\implies (x+4)^2=24[/tex]
Square root both sides:
[tex]\implies x+4=\pm2\sqrt{6}[/tex]
Subtract 4 from both sides:
[tex]\implies x=-4\pm2\sqrt{6}[/tex]
Find the statement Pk + 1 for the given statement Pk
Step-by-step explanation:
k has to be replaced by k+1.
so,
4 / ((k+1)(k+1 + 3)) = 4 / ((k+1)(k+4))
I am not sure how far your teacher expects you to go with this.
just in case, I will do also the full multiplications
4 / ((k+1)(k+4)) = 4 / (k² + 4k + k + 4) = 4 / (k² + 5k + 4)
and if you need the factor to go from Pk to Pk+1 :
Pk+1 / Pk = (4/((k+1)(k+4))) / (4/(k(k+3)) =
= (4/((k+1)(k+4))) × (k(k+3))/4 =
= (k(k+3)) / ((k+1)(k+4))
A person's salary is $2000 per month. 20% of this is spent on their rent, $590 is
spent on food and $650 on other expenses. DETERMINE the percentage of their salary
has he spent in total.
Answer:
the person earned one summer = $3,600
We have to show the amount in fraction that Paula spent during the following semester,
they spent for tuition = $2,500 = × 100
=0.6944 × 100
= 69.44%
they spent for rent = $650 = × 100
= 0.1806 × 100
= 18.06%
they spent for food = $430 = × 100
=0.1194 × 100
= 11.94%
they Spent in tuition, rent and food = 2,500 + 650 + 430 = $3580
Now they spent in miscellaneous expenses = 3600 - 3580 = $20.00 × 100
= 0.056 × 100
= 0.56%
Find the value of x.
31.5
68.3
26.7
11.
Answer:
26.7
Step-by-step explanation:
Using trigonometric ratio, we find:[tex]\sin 67\degree= \frac{x}{29}[/tex][tex]\implies x = 29\sin 67\degree[/tex][tex]\implies x =26.69464075[/tex][tex]\implies x \approx 26.7[/tex]What are the values of a and b? a = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8
The value of a and b given that the opposite side are equal are 17 and 6 respectively
Properties of a kiteThe kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;
2a - 4 = 30
2a = 34
a = 17
Similarly
3b+6 = 24
3b = 18
b = 6
Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively
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An ice cream shop has a make-your-own sundae bar. If there are 20 different flavors of ice cream to choose from, 5 different toppings to choose from, and 3 different sizes, how many different sundaes are possible
There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.
To find the total number of different sundaes possible, we need to multiply the number of choices for each category: ice cream flavors, toppings, and sizes.
Number of ice cream flavors = 20
Number of toppings = 5
Number of sizes = 3
Total number of sundaes = Number of ice cream flavors × Number of toppings × Number of sizes
Total number of sundaes = 20 × 5 × 3
Total number of sundaes = 300
There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.
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Two angles that form a right angle are supplementary is true or false?
X/3 + 1 = ×/8 + 1/11
solve the question please pls
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
the following expression can be solved as follows ~
[tex] \frac{x}{3} + 1 = \frac{x}{8} + \frac{1}{11} \\ [/tex]
Taking LCM on both the sides ,
[tex] \frac{x + 3}{3} = \frac{11x + 8}{88} \\ [/tex]
On cross multiplying ,
[tex]( x + 3)88 = (11x + 8)3 \\ \\ \implies \: 88x + 264 = 33x + 24[/tex]
let's now gather the like terms at either sides of the equation and solve ~
[tex]88x - 33x = 24 - 264 \\ \\ \implies \: 55x = - 240 \\ \\ \implies \: x = \cancel\frac{ - 240}{55} \\ [/tex]
on further simplifying ,
[tex]\implies x = \frac{ - 48 }{ 11} \\ [/tex]
hope helpful ~
HELP <3333333333333333333333333333333333333333
Answer:
$30
Step-by-step explanation:
since 7 = 28
and 1 = 4
divide 1 in half to find the half hour amount
1/2 hr = 2
28 + 2 = 30
your answer is $30
hope this helps:)
3x^2 + 14x +8 find magic x
x = -2/3 or -4
see the attachment for solution
hope it helps...!!!
Can someone help me with this geometry problem
Answer:
Step-by-step explanation:
Write an equation for a line parallel to the line y=1/3x - 4 through (-3, 2)
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 1/3 and passes through (-3 , 2)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-2=\cfrac{1}{3}(x+3)\implies y-2=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+3[/tex]
Find the gradient of the line segment between the points (-5,-2) and (4,3).
Give your answer in its simplest form.
Answer:
5/9
Step-by-step explanation:
Solution
The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points
m =
[tex] \frac{y2 - y1}{x2 - x1 } [/tex]
Here two points given, (-5,-2) and (4,3)
gradient (m):
[tex] \frac{3 - ( - 2)}{4 - ( - 5)} [/tex]
Which function has the same minimum value as ? f(x) = 3x 3 f(x) = |x| 3 f(x) = –x2 3
The function that has the same minimum value as fx= 3x³ is f(x) = x + 3.
What is a function?It should be noted that a function simply means a relation or expression that involves two or more variables.
In this case, the function that has the same minimum value as the expression of 3x³ is f = x + 3.
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Answer:
B. f(x) = /x/ + 3
Step-by-step explanation:
edg 22'
Mariana ha tirado 20 veces a la canasta y ha fallado la quinta parte de los tiros ¿cuantas canastas a metido?
plissssssssssssssssssssss
Veremos que de los 20 intentos, Mariana metio 16 canastas.
¿Cuantas canastas a metido Mariana?
Sabemos que ella tiro 20 veces, y sabemos que ella ha errado 1/5 de los tiros.
Entonces los otros 4/5 tiros entraron. Para obtener el numero de canastas que ha metido, debemos multiplicar la fracción por la cantidad total de tiros al aro:
C = 20*(4/5) = 16
Así, podemos concluir que Mariana ha metido 16 canastas.
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Enter an equation for which the solution is the speed of the train, in miles per hour, where the train's distance from the departing station is 162 miles and it has traveled for 3 hours. what is the equation for the speed of the train?
Answer:
Step-by-step explanation:
Formula
speed = distance / time
Givens
speed = ?
distance = 162 miles.
Time = 3 hours.
Solution
speed = 162 / 3
speed = 54 miles per hour.
which company would cost the most to serve 300 students
Answer:
Company "A"
Step-by-step explanation:
its the highest line on the graph from the 300 point.
Based on the information in the two-way table, what is the probability that a person selected at random is Ages 16-18 and has prepared a meal for their family? Round your answer to the nearest tenth of a percent.
The probability that a person selected at random is Ages 16-18 and has prepared a meal for their family
How to determine the experimental probability?From the table of values, we have:
Age 16 - 18 that has performed meal = 8
Total = 30
The probability is then calculated using:
P(16 - 18) = n(16 - 18)/Total
This gives
P(16 - 18) = 8/30
Simplify
P(16 - 18) = 4/15
Hence, the probability is 4/15
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what is the rate change of the table?
The rate of change is $27 per month if the change in y values is 54 and change in x values is 2.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
From the data given in the table, we can find the rate of change per month:
To find the rate of change:
= change in y/ change in x
= (138-84)/(4-2)
= 54/2
= 27 per month
Thus, the rate of change is $27 per month if the change in y values is 54 and change in x values is 2.
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Teresa changed number shr used for her internet password every day. This is how she figured her password:A whole number that is equal to four times the fourth power of the day of the month divided by two times the square day of the month. If today id the 7th day of the month, What is teresa's password?
Using a system of equations, it is found that Teresa's password in the 7th day of the month is of 98.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The rule for her password is defined as follows: A whole number that is equal to four times the fourth power of the day of the month divided by two times the square day of the month. Hence, considering n as the day of the month, the equation is given by:
[tex]P = \frac{4n^4}{2n^2} = 2n^2[/tex]
Hence, for the 7th day, the password is given by:
P = 2 x 7² = 98.
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Which statements are true? select three options. milk was requested for 16 of the large-sized meal orders. soda was requested for 280 of the kids’ meal orders. a juice box was requested for 82 of the regular-sized meal orders. sixty-three of the orders of soda came with a regular-sized meal. a total of 124 large-sized meals were ordered.
The true statements are:
A. Milk was requested for 16 of the large-sized meal orders;D. Sixty-three of the orders of soda came with a regular-sized meal; andE. A total of 124 large-sized meals were ordered.Calculations and Parameters:Given:
Total no of meals with milk= 71Regular size meals= 55Regular sized meals with soda= 63To find the large size meals that came with milk,
71-55= 16.
Therefore, the total number of large size meals ordered was:
16+22+86 = 124.
Hence, options A, D and E are correct.
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Find the zeros of the function. State the multiplicity of multiple zeros.
y = 12x³ - 12x
Answer: the zeros are the xintercepts which are shown on the graph
Step-by-step explanation:
What is the solution to this equation?
log + log 3 =
log(+1)
OA I=
OB.
I=
OC
I=
D. = 1
312
NIT
13
Answer:
[tex]\textsf{B.} \quad x=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Log laws
[tex]\textsf{Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\textsf{Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y[/tex]
Therefore:
[tex]\large \begin{aligned}\log_6 x+ \log_6 3 & =\log_6 (x+1)\\\log_6 (3x) & =\log_6 (x+1)\\3x & =x+1\\2x & =1\\x & =\dfrac{1}{2}\end{aligned}[/tex]
(√3+√7) (√3-√7) pl and me
[tex]\left( \sqrt 3 + \sqrt 7\right) \left( \sqrt 3 - \sqrt 7\right)\\\\=\left(\sqrt 3 \right)^2 - \left(\sqrt 7 \right)^2\\ \\=3-7\\\\=-4[/tex]
Answer:
- 4
Step-by-step explanation:
([tex]\sqrt{3}[/tex] + [tex]\sqrt{7}[/tex] )([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] )
each term in the second factor is multiplied by each term in the first factor.
[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) + [tex]\sqrt{7}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) ← distribute parenthesis
= 3 - [tex]\sqrt{21}[/tex] + [tex]\sqrt{21}[/tex] - 7 ← collect like terms
= - 4
Find the volume of this right triangular prism 5cm 8 cm 3 cm
Answer:
I can help, but can you label which is base, height, and length
Step-by-step explanation:
help help help help help
Answer:
∠ T = 76°
Step-by-step explanation:
RSTU is a cyclic quadrilateral
the opposite angles of a cyclic quadrilateral sum to 180°
∠ T + ∠ R = 180°
∠ T + 104° = 180° ( subtract 104° from both sides )
∠ T = 76°
Find the nth term of this number sequence 2, 4, 6, 8, ...
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The given sequence is in Arithmetic progression, and we have to find its nth term ~
So, let's get it solved ~
First term of the sequence is :
a = 2Common difference is :
d = 6 - 4 = 4 - 2 = 2Now, if we have to write the 2nd Term with respect to first one, we can write :
2nd Term = a + (2 - 1)d = a + d = 2 + 2 = 4similarly ~
3rd Term = a + (3 - 1)d = a + 2d = 2 + 4 = 64th Term = a + (4 - 1)d = a + 3d = 2 + 6 = 8Therefore, I similar pattern ~
[tex] \qquad \sf \dashrightarrow \: nth \: term = a + (n - 1)d[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2 + (n - 1)2[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2(1 + (n - 1))[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2(1 + n - 1)[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2 n [/tex]
Feel free to ask your doubts, if you have any ~
Answer:
2nStep-by-step explanation:
from the number sequence above, each term except the first is generated by adding 2 to the term immediately preceding it.
the nth term of the sequence is usually designated Tn, and it's usually a function of n
from the number sequence
T1= 2
T2 = 2+2= 4
T3= 4+2= 6
T4= 6+2= 8
therefore, Tn= 2+2×(n-1)
= 2+2n-2
=2-2+2n= 2n
therefore, the nth term of the number sequence= 2nAustin worked 28 hours last month and won $8 per hour. he was already spent $19 of your income. How much money does he have left?
Answer:
[tex]\huge\boxed{\sf \$\ 205}[/tex]
Step-by-step explanation:
Work hours = 28 hours
Earning = $8 per hour
1 hour = $8
28 hours = $8 × 28
28 hours = $224
He has earned $224 last month.
Spent = $19
Left:
= Earning - Spent
= $224 - $19
= $205
[tex]\rule[225]{225}{2}[/tex]
If you roll a die twice what is the probability of rolling a 3 the first time and then rolling a 4 the second time? write your answer as a fraction
Answer:
Step-by-step explanation:
P(3 and 4)= 1/6×1/6
=1/36
3.3 Factorise fully: 3.3.1 x²-x-6
Answer:
(x-3)(x+2)
Step-by-step explanation:
¹ you open brackets.
² you put the "x" in both brackets
³ you then check for factors, that will give you a "6" when you multiply them and give you the "x" when you add or subtract them.