The value of two plums and a peanut, divided by a grape and a peanut is 11
How to solve the expression?The given parameters are:
Peanut = 1Grape = 2 Acorn + 3 grapes = 14Acorn = 1/2 PlumSubstitute Grape = 2 in Acorn + 3 grapes = 14
Acorn + 3 *2 = 14
Acorn + 6 = 14
Subtract 6 from both sides
Acorn = 8
Substitute Acorn = 8 in Acorn = 1/2 Plum
8 = 1/2 Plum
Multiply both sides by 2
Plum = 16
So, we have:
Peanut = 1
Grape = 2
Acorn = 8
Plum = 16
The value of two plums and a peanut, divided by a grape and a peanut is:
(2 plums + peanut)/(grape + peanut)
This gives
(2 * 16 + 1)/(2+ 1)
Evaluate
11
Hence, the value of two plums and a peanut, divided by a grape and a peanut is 11
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What are the solutions of the equation 6x^2-x-1=0
Answer:
x=1/2 or x=-1/3
Step-by-step explanation:
6x^2-x-1=0
6x^2+2x-3x-1=0
(6x^2+2x)+(-3x-1)=0
2x(3x+1)-1(3x+1)=0
2x(3x+1)-1(3x+1)=0
(2x-1)(3x+1)=0
(2x-1)(3x+1)=0
2x-1=0
or
3x+1=0
x=-1/3
x=1/2
Answer:
Its 1/3 and -1/2
Step-by-step explanation:
Help? It’s for scantron and I have to exempt
Answer:
A. Red/Line C
Step-by-step explanation:
Simplify the expression (4x2y3)2
Answer:
8x^2 2y^3
Step-by-step explanation:
PLEASE SOLVE FOR X AND Y!!!! I WILL MARK BRAINLIEST!!!!
opposite sides and diagonals of a parallelogram are equal
+ diagonals of a parallelogram meet eachother in the middle so:
10x+14=x+77
10x-x=77-14
9x=63
x=63÷9
x= 7
y+8=4y-19
y-4y=-19-8
-3y=-27
y=-27÷-3
y=9
2z+3=37
2z=37-3
2z=34
z=34÷2
z=17
The top three teams qualified to compete at the state competition. At the state competition, however, scoring is done differently than at the other meets. Use the following information to create a system of equations where is the points for first place, is the points for second place, and is the points for third place.
Results:
Eagles got 5 first-place, 3 second-place, and 4 third-place finishes with a team total of 67 points.
Pirates got 2 first-place, 5 second-place, and 5 third-place finishes with a team total of 56.
Devil Rays got 6 first-place, 3 second-place and 3 third-place finishes with a team total of 72.
We can’t believe the Devil Rays came from behind and won! We need to determine how many points were awarded for each place. Use Cramer’s rule or inverse method to get the answers. Explain your process.
The equations are
5x+3y+4z=672x+5y+5z=566x+3y+3z=72Lets solve them through matrix
Let
[tex]\\ \rm\Rrightarrow A=\left[\begin{array}{ccc}\rm 5&\rm 3&\rm 4\\ \rm 2&\rm 5&\rm 5\\ \rm 6&\rm 3&\rm3\end{array}\right][/tex]
[tex]\\ \rm\Rrightarrow X=\left[\begin{array}{c}\rm x\\ \rm y\\ \rm z\end{array}\right][/tex]
[tex]\\ \rm\Rrightarrow B=\left[\begin{array}{c}\rm 67 \\ \rm 56\\ \rm 72\end{array}\right][/tex]
Let solve
Determinant of A
[tex]\\ \rm\Rrightarrow |A|[/tex]
[tex]\\ \rm\Rrightarrow 5\left|\begin{array}{cc}\rm 5&\rm 5\\ \rm 3&\rm 3\end{array}\right|-3\left|\begin{array}{cc}\rm 2&\rm 5\\ \rm 6&\rm 3\end{array}\right|+4\left|\begin{array}{cc}\rm 2&\rm 5\\ \rm 6&\rm 3\end{array}\right|[/tex]
[tex]\\ \rm\Rrightarrow 5(15-15)-3(6-30)+4(6-30)[/tex]
[tex]\\ \rm\Rrightarrow 72-96[/tex]
[tex]\\ \rm\Rrightarrow -24[/tex]
Cofactor[tex]\\ \rm\Rrightarrow A_{11}=0[/tex]
[tex]\\ \rm\Rrightarrow A_{12}=24[/tex]
[tex]\\ \rm\Rrightarrow A_{13}=-24[/tex]
[tex]\\ \rm\Rrightarrow A_{21}=3[/tex]
[tex]\\ \rm\Rrightarrow A_{22}=-9[/tex]
[tex]\\ \rm\Rrightarrow A_{23}=3[/tex]
[tex]\\ \rm\Rrightarrow A_{31}=-5[/tex]
[tex]\\ \rm\Rrightarrow A_{32}=-17[/tex]
[tex]\\ \rm\Rrightarrow A_{33}=19[/tex]
Cofactor of A[tex]\\ \rm\Rrightarrow \left[\begin{array}{ccc}\rm 0&\rm 24&\rm -24\\ \rm 3&\rm -9&\rm 3\\ \rm -5&\rm -17&\rm 19\end{array}\right][/tex]
Adjacent of A[tex]\\ \rm\Rrightarrow \left[\begin{array}{ccc}\rm 0&\rm 24&\rm -24\\ \rm 3&\rm -9&\rm 3\\ \rm -5&\rm -17&\rm 19\end{array}\right]^T[/tex]
[tex]\\ \rm\Rrightarrow \left[\begin{array}{ccc}\rm 0&\rm 3&\rm -5\\ \rm 24&\rm -9&\rm -17\\ \rm -24&\rm 3&\rm 19\end{array}\right][/tex]
Inverse of A[tex]\\ \rm\Rrightarrow \dfrac{1}{|A|}\times Adj.A[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{-24}\left[\begin{array}{ccc}\rm 0&\rm 3&\rm -5\\ \rm 24&\rm -9&\rm -17\\ \rm -24&\rm 3&\rm 19\end{array}\right][/tex]
Now
[tex]\\ \rm\Rrightarrow AX=B[/tex]
[tex]\\ \rm\Rrightarrow X=A^{-1}B[/tex]
[tex]\\ \rm\Rrightarrow X=\dfrac{1}{-24}\left[\begin{array}{ccc}\rm 0&\rm 3&\rm -5\\ \rm 24&\rm -9&\rm -17\\ \rm -24&\rm 3&\rm 19\end{array}\right]\left[\begin{array}{c}\rm 67\\ \rm 56\\ \rm 72\end{array}\right][/tex]
[tex]\\ \rm\Rrightarrow X=\dfrac{1}{-24}\left[\begin{array}{c}\rm -192\\ \rm -120\\ \rm -72\end{array}\right][/tex]
[tex]\\ \rm\Rrightarrow X=\left[\begin{array}{c}\rm 8\\ \rm 5\\ \rm 3\end{array}\right][/tex]
So
[tex]\\ \rm\Rrightarrow \left[\begin{array}{c}\rm x\\ \rm y\\ \rm z\end{array}\right]=\left[\begin{array}{c}\rm 8\\ \rm 5\\ \rm 3\end{array}\right][/tex]
We get
x=8y=5z=3Multiply.
[tex]\frac{\sqrt{2}}{6}cis (\frac{3\pi }{5})[/tex]·[tex]\frac{\sqrt{6}}{4}cis (\frac{2\pi }{3})[/tex]
A.[tex]\frac{\sqrt{3}}{12}cis(\frac{19\pi }{15})[/tex]
B. [tex]\frac{\sqrt{3}}{12}cis(\frac{2\pi }{5})[/tex]
C. [tex]\frac{\sqrt{2}}{8}cis(\frac{2\pi }{5})[/tex]
D. [tex]\frac{\sqrt{2}}{8}cis(\frac{19\pi }{15})[/tex]
Multiply the moduli and add the arguments:
√2/6 cis(3π/5) × √6/4 cis(2π/3)
= (√2/6 × √6/4) cis(3π/5 + 2π/3)
= √3/12 cis(19π/15) … [A]
help please <33 i’m struggling if anyone sees this please help this girl <3333
Answer:
2 15/28
Step-by-step explanation:
First we will convert both mixed fractions into improper fractions.
5 1/4 becomes 21/4
2 5/7 becomes 19/7
21/4 - 19/7 does not work, so we must make the denominator the same
147/28 - 76/28 = 71/28
Now we convert back to a mixed number:
2 15/28
Answer: [tex]-11\frac{15}{28}[/tex]
Step-by-step explanation:
Convert to Improper fractions
[tex]5\frac{1}{4} = \frac{21}{4} \\2\frac{5}{7} = \frac{19}{7} \\[/tex]
Find a lowest common multiple
lcm(4,7) = 28 (7 * 4)
since they are just multiplying each other, we can cross multiply
[tex]\frac{(21*7) - (19*4)}{4*7} = \frac{147-76}{28} \\= \frac{71}{28} \\=2\frac{15}{28}[/tex]
I'll give brainiest to the first person to respond BUT only if the answer is correct
Answer:
115 and 1/2
Step-by-step explanation:
B•W•H
Hope this helps! ;-)
Thanks for correcting my mistake!!!
Answer: The answer is 115 1/2
Explanation: Just multiply all the dimensions
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 33 feet up. The ladder makes an angle of 74 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
HOPE IT HELP (≧▽≦)(≧▽≦)(≧▽≦)
Answer:
Step-by-step explanation:
the answer is wrong its 34.3
Jim works as a manager at a local supermarket in dallas. jim worked 36 hours and his paycheck for this week was $1,620.51. how much does jim make per hour? round your answer to the nearest cent.
324
Step-by-step explanation:
roughly about that much
Find the minimum value of
\[\frac{x^2 + 9}{x}\]for $x > 0.$
I tried this but I didn't get it, could someone explain?
I hope this will help you a lot
Which answers describe the shape below? Check all that apply.
Answer:
Step-by-step explanation:
A: Not a Rhombus. Adjacent sides are unequal
B: True. Opposite sides are parallel
C: True. Adjacent sides are unequal in length but it has two sets of parallel lines and at least 1 right angle.
D: Not a square. Not all 4 sides are of equal length
E: It is a quadrilateral. A quadrilateral only requires 4 sides.
F: Not true. It does not have the properties of a trapezoid.
Tara made a scale drawing of a boarding school. she used the scale 1 centimeter : 7 meters. a building at the school is 12 centimeters long in the drawing. how long is the actual building?
Answer:
84cm
Step-by-step explanation:
Given that;
1cm = 7m
12cm = x
Cross Multiply
x = 12×7
x = 84m
A baby is born weighing 120 ounces. At 1 year, the same baby weighs 14 pounds. How many pounds did the bay gain?
Given the equations and the graph below, how many solutions are there to the system of equations?
Explain your answer.
Answer:
One, since the lines are not parallel (you can tell by either the graph, or the coefficient of the x term, called "slope", and it's (3;4)
discuss why area: perimeter for a square ÷ 4.
Step-by-step explanation:
because its formula is 4L
whats 55 + 55? I've been struggling and I can't take it anymore. I saw the memes and I need the real absolute final answer. pls help
Answer:
110
50+50=100
5+5=10
100+10=110
(thats how i do mental math)
HELP ME PLEASEEEEE
Answer:
x = 4
Step-by-step explanation:
x(x + 8) = 48
x² + 8x = 48
x² + 8x - 48 = 0
times into -48
add into 8
(x - 4)(x + 12) = 0
x - 4 = 0
x = 4
or
x + 12 = 0
x = -12
A length cannot be a negative number therefore x = 4
A line passes through the points (-4,3) and (0, 0). What is the slope of the line?
Answer:
-3/4
Step-by-step explanation:
ΔY / ΔX, or change in y divided by change in x
(-4,3) and (0, 0)
x increases by 4
y decreases by 3
-3/4
Answer:
It is -3/4
Step-by-step explanation:
Mason has a business selling perfume at the mall. Currently his business has a
balance of -$20.
Which amounts of sales would give Mason's business a positive balance?
Choose ALL that apply.
$15 $35 $21 $29 $30 $19
Answer:
21, 29, 30, 35
Step-by-step explanation:
anything greater than 20 would break even and then give a position balance
Can someone help please?
Answer Quickly and Correctly for Brainlist!!! Marcelle and Megan realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate their difference in their ages. Marcelle is 15 1/2 years old, and Megan is 7 7/12. What is the difference in their ages? Express your answer as a simplified mixed number.
Answer:
the difference in their ages is 31/2
Step-by-step explanation:
151/2=2x15+1/2=31/2
In a company which services air-conditioner units, the revenue,
$r, is given by the equation r = 20x, where x is the number of
units serviced. The operating cost, $c, is given by the equation
c= 3600 + 4x.
The profit, $P, is given by the expression, r — c.
(a) Find a formula for P in terms of x only.
(b) For each of the following cases, find the value of x if
(i) the revenue earned is twice that of the cost,
(ii)the profit earned is $292 more than one third of the revenue
earned.
Answer:
p(x) = 16x -3600600 units417 unitsStep-by-step explanation:
The problem statement gives expressions and relations for revenue, cost, and profit. Substitute and simplify or solve, as appropriate.
__
(a)Given: r(x) = 20x; c(x) = 3600+4x; p(x) = r(x) -c(x)
The formula for p(x) is ...
p(x) = (20x) -(3600 +4x) . . . . substitute for r(x) and c(x)
p(x) = 16x -3600 . . . . . . . . simplify
__
(b-i)r(x) = 2·c(x) . . . . given relation for revenue and cost
20x = 2(3600 +4x) . . . . substitute for each
12x = 7200 . . . . . . . simplify and subtract 8x
x = 600 . . . . . . . divide by 12
Revenue is twice the cost when x = 600 units.
__
(b-ii)p(x) = 292 +1/3r(x) . . . . given relation for profit and revenue
16x -3600 = 292 +1/3(20x) . . . . . substitute for each
28/3x = 3892 . . . . . . . . add 3600 -20/3x
x = 417 . . . . . . . . multiply by 3/28
Profit is $292 more than 1/3 the revenue earned for 417 units.
You are playing a game that uses two fair number cubes. If the total on the number cubes is either 2 or 5 on your next turn, you win the game. What is the probability of winning on your next turn? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
The probability of winning the game on your next turn is; 14%
How to find the Probability of Winning?The sample size of the two number cubes, when rolled is:
n = 36
The number of outcomes that give a sum of 2 or 5 is 5,
And the outcomes are (1, 1) (2, 3) (3, 2) (1, 4) (4, 1)
The probability is the quotient of the number of outcomes of the sum of 2 or 5 and the total outcomes.
Thus,
Probability = 5/36 * 100% = 13.89% ≈ 14%
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Which of the following BEST describes how to use the addition property of equality to isolate the variable y
below?
y-12 = 14
A. add 12 to the left side of the equation only
B. subtract 12 from the left side of the equation only
C. add 12 to both sides of the equation
D. subtract 12 from both sides of the equation
Please select the best answer from the choices provided
Ο Α
ОВ
С
Answer: C) add 12 to both sides
Reason:
We add 12 to the left side to undo the -12, which will get y by itself.
We must do the same thing to both sides to keep things balanced.
please help meh I give brainliest
What are the ratio of the perimeters and the ratio of the areas?
Check the picture below.
the ratio of the sides will be the same ratio of their perimeters
[tex]\stackrel{\textit{\LARGE ratio of their}}{\stackrel{perimeters}{\cfrac{6}{15}\implies \cfrac{2}{5}}\hspace{5em}\stackrel{areas}{\cfrac{2^2}{5^2}\implies \cfrac{4}{25}}}[/tex]
Please help me
Which equation has the same solutions as x²+6x-7=0 ?
A) (x+3)²=2
B) (x-3)²=2
C) (x-3)²=16
D) (x+3)²=16
Answer:
[tex]D)~(x+3)^2 = 16[/tex]
Step-by-step explanation:
[tex]~~~~~~x^2 +6x -7 = 0\\\\\implies x^2+6x = 7\\\\\implies x^2 +2 \cdot 3 \cdot x +3^2 -3^2 = 7\\\\\implies x^2 +2 \cdot 3 \cdot x+3^2 = 7+3^2\\\\\implies (x+3)^2 = 7+9\\\\\implies (x+3)^2 = 16[/tex]
If v₁ = (3,-4) and v₂ = (2,6), then v₁v₂ is equal to which of the following?
O A. (-12,-24)
OB. 30
O C. -18
OD. (6,-24)
Answer:
C. -18
Step-by-step explanation:
Scalar Product (Dot Product) of two vectors
[tex]\displaystyle \vec{a} \cdot \vec{b}=\sum_{i=1}^na_ib_i[/tex]
[tex]\textsf{If }\: \vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \quad \textsf{and } \quad \vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}[/tex]
[tex]\textsf{then }\quad \vec{a} \cdot \vec{b}=a_1b_1+a_2b_2+a_3b_3[/tex]
Given:
v₁ = (3, -4)v₂ = (2, 6)⇒ v₁ · v₂ = (3 · 2) + (-4 · 6)
⇒ v₁ · v₂ = 6 + (-24)
⇒ v₁ · v₂ = 6 - 24
⇒ v₁ · v₂ = -18
What happens to warm air when it cools?
A) It sinks back down to Earth.
B) It is absorbed into clouds.
C) It remains in Earth’s upper atmosphere.
D) It breaks apart and disappears.
Answer:
b
Step-by-step explanation:
hj
Answer:Its B,dude
Step-by-step explanation: