The missing equations are;
a + 2b + 3c = 12
3a + 2b + 5c = 22
2a + 4b + 4c = 18
Answer:
a = 2
b = 0.5
c = 3
Step-by-step explanation:
We are told that;
a represent the price per pound of apples
b represent the price per pound of bananas
c represent the price per pound of oranges
The equations system is;
a + 2b + 3c = 12 - - - (eq 1)
3a + 2b + 5c = 22 - - - (eq 2)
2a + 4b + 4c = 18 - - - (eq 3)
Divide through equation 3 by 2 to get
a + 2b + 2c = 9 - - - (eq 4)
Subtract eq 4 from eq 1 to get;
3c - 2c = 12 - 9
c = 3
Put 3 for c in eq(2) and eq 4;
3a + 2b + 5c = 22
3a + 2b + 5(3) = 22
3a + 2b + 15 = 22
3a + 2b = 7 - - - (5)
a + 2b + 2(3) = 9
a + 2b + 6 = 9
a + 2b = 3 - - - (eq 6)
Subtract eq 6 from eq 5 to get;
2a = 7 - 3
2a = 4
a = 2
Put 2 for a in eq 6;
2 + 2b = 3
2b = 3 - 2
2b = 1
b = 1/2
b = 0.5
Answer:
It's A
Step-by-step explanation:
edge 2021
express 5√72 in simplest radical form.
Answer:
30*sqrt(2)
Step-by-step explanation:
5*sqrt(72)=5*sqrt(36*2)=5*6*sqrt(2)=30*sqrt(2)
A rectangular garden has links twice as great as it's with a second rectangular garden has the same link as the first garden and with that is for meters greater than the width of the first garden the second Gordon has area of 120 m² what is the length of the two gardens
Solution :
For the bigger rectangle
Width of bigger rectangle = W
Length of bigger rectangle, L = 2W
For the smaller rectangle
Width , w = W+4
Length, l = L = 2W
Area, a =120 [tex]m^2[/tex]
Now we know,
Area = length x width
[tex]$a=l \times w$[/tex]
[tex]$120=(2W) \times (W+4)$[/tex]
[tex]$120=2W^2 + 8W$[/tex]
[tex]$2W^2+8W-120=0$[/tex]
[tex]$W^2+4W-60=0$[/tex]
[tex]$(W+10)(W-6) = 0$[/tex]
We get, either [tex]W=-10[/tex] (rejecting)
or [tex]W=6[/tex]
∴ length of the bigger rectangle, [tex]$L=2W $[/tex]
= 2(6)
= 12 m
Length of the smaller rectangle, [tex]$L=2W$[/tex]
= 2(6)
= 12 m
Hence, the length of the two gardens is 12 m.
There are 4512 marbles which will be divided equally among 48 students how many marbles will each student get
Answer:
94 marbles
Step-by-step explanation:
4512/48 = 94
4. Determine all unknown sides and angles to 1 decimal place.
a.
b.
32°
12 cm
30°
38 cm
The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees
4a) Given the following
Opposite side = 38cm (side facing the given angle)
Required
Adjacent and hypotenuse side
According to SOH CAH TOA
[tex]tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp= 60.81cm[/tex]
Next is to get the adjacent
[tex]Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm[/tex]
Next is to get the missing angle
Since sum of angle in the triangle is 180degrees
32 + 90 + x = 180
122 + x = 180
x = 180 - 122
x = 58degrees
The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees.
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HELPHELPHELPHELPHELP
Answer:
2¼ mph
Step-by-step explanation:
It takes ⅓hour to walk to the library.
⅓ •3 = 1 hour
¾ • 3 = 9/4 = 2¼ miles/hour
The function f is defined by f(x) = x^2 - 2x - 24. If f(x+3) = x^2 - kx - 21, what is the value of k?
Answer:
k = 4
Step-by-step explanation:
In the equation: x² - 2x - 24
Replace the x with x + 3
(x+3)² - 2(x+3) - 24
x² + 6x + 9 - 2x - 6 -24
Let's rearrange it
x² + 6x -2x - 24 + 9 - 6
x² - 4x - 21
f(x+3) = x² - 4x - 21
The equivalent value of k from the function is k = -4
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = x² - 2x - 24
Let the second function be represented as B
Now , the value of B is
f ( x + 3 ) = x² - kx - 21
On simplifying , we get
f ( x + 3 ) = ( x + 3 )² - 2 ( x + 3 ) - 24
f ( x + 3 ) = x² + 6x + 9 - 2x - 6 - 24
f ( x + 3 ) = x² + 4x - 21
So , from the equations , we get
-kx = 4x
Divide by -x on both sides , we get
k = -4
Hence , the equation is k = -4
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Tess created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triple 3, 4, and 5 by 8. Is Tess correct? Can a Pythagorean triple be created using multiples of a known Pythagorean triple.
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Yes, as long as each number in the Pythagorean triple is multiplied by a different whole number.
No, Pythagorean triples only exist with small numbers.
No, multiplying a known Pythagorean triple by a whole number will not create a Pythagorean triple.
Answer:
Hello,
Answer A
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Step-by-step explanation:
(a,b,c) is a Pythagorien triple : c²=a²+b²
and k is a naturel.
[tex](ka)^2+(kb)^2\\\\=k^2*a^2+k^2*b^2\\\\=k^2(a^2+b^2)\\\\=k^2c^2\\\\=(kc)^2\\[/tex]
Answer:
Yes, as long as each number in the Pythagorean Triple is multiplied by the same whole number.
General Formulas and Concepts:
Pre-Algebra
Equality PropertyTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
In order for it to remain a Pythagorean triple, we must follow the equality rules. To make it the exact same expression, all parts of an equation must be multiplied or divided by the same number. If this is done, then it would also remain a Pythagorean triple, and hence we arrive at our answer.
Find the missing length of the following with midsegment drawn
Answer:
18
Step-by-step explanation:
RQ = (22+14)/2 = 36/2 = 18
Answer:
QR = 18
Step-by-step explanation:
The midsegment QR is half the sum of the parallel bases, that is
QR = [tex]\frac{JM+KL}{2}[/tex] = [tex]\frac{22+14}{2}[/tex] = [tex]\frac{36}{2}[/tex] = 18
Please hurry I will mark you brainliest
Answer:
the answer is 120
Step-by-step explanation:
a trapezoid should measure 360 when all sides are added together
180-125=55
65+55=120
360-120=240
240÷2=120
Please help !!!!!!!!!!!
Answer:
98°+62°+6x = 180
160+6x = 180
6x = 180 - 160
6x = 20
x= 20/6
x= 3.33
therefor your answer is 3.33
in a data ,range is 17 and coefficient of range is 0.2 find the smallest term of the data.
I will make brainelist to the best answer
Answer:
Step-by-step explanation:
Let largest value of data be L
and smallest value of data be S.
We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.
Range formula is given by = Largest value - Smallest value
17 = L - S
L = 17 + S ---------- [Equation 1]
Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)
0.2 = l-s/l+s
0.2 = 17/l+s
L + S = 17/0.2 = 85
So, L + S = 85
17 + S + S = 85 {using equation 1}
2*S = 80
S = 80/2 = 40
Putting value of S in equation 1, we get L = 20 + 40 = 60
Therefore, Largest value, L = 60
smallest value, S = 40
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Step-by-step explanation:
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after how many years will Rs 21000 give Rs 5040 as interest at 6% pa simple interest
Answer:
within 4 years it will give the required interest
Given 2 ||
m
|| n, find the value of x.
142°
m
(3x+8)°
n
PLSSSS HELP MEEEE
Answer:
x = 10Step-by-step explanation:
Given,
l || m
Therefore,
142° + (3x+8)° = 180° [Since Co-exterior angles]
=> 3x + 8 = 180 - 142
=> 3x + 8 = 38
=> 3x = 38 - 8
=> 3x = 30
[tex] = > x = \frac{30}{3} [/tex]
=> x = 10 (Ans)
Given that QR¯∥ST¯, identify the length of PT¯.
Answer:
PT = 16.3 units
Step-by-step explanation:
From the picture attached,
From ΔPQR and ΔPST,
QR ║ST [Given]
PQ is a transversal line.
Therefore, ∠PST ≅ ∠PQR [Corresponding angles]
∠P ≅ ∠P [Common angle]
ΔPQR ~ ΔPST [By AA property of similarity of two triangles]
Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.
[tex]\frac{PQ}{PS}=\frac{PR}{PT}[/tex]
[tex]\frac{12+28}{28}= \frac{PT+7}{PT}[/tex]
[tex]\frac{40}{28}=1+\frac{7}{PT}[/tex]
[tex]\frac{10}{7}-1=\frac{7}{PT}[/tex]
[tex]\frac{10-7}{7}=\frac{7}{PT}[/tex]
PT = [tex]\frac{49}{3}[/tex]
PT = 16.3 units
1. You buy rice at $0.71 a pound. One batch of fried rice requires 6.5 pounds of rice. How much does the rice for one batch cost? Round to the nearest cent.
Select one:
a. $4.60
b. $4.65
c. $4.61
d. $4.62
The cost for one batch of fried rice will be $4.62.
Since the rice is bought at $0.71 a pound and one batch of fried rice requires 6.5 pounds of rice, then the cost of one batch of rice will be:
= $0.71 × 6.5
= $4.615
= $4.62 approximately.
In conclusion, the cost for one batch of fried rice will be $4.62.
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Write an equation in point-slope form of the line that passes through the given point and has the given slope.
(16,-4);m=-3/4
If x²+1/4x²=8 ,find the value of x+1/2x
Answer:
16/31
Step-by-step explanation:
x²+1/4x²=8
x²+1=32x²
1=32x²-x²
1=31x²
√1=√31x²
31x=1
x=1/31
Now x+1/2x
=31+1/2×31
=32/62
=16/31
Audrey Baker bought 4 new tires for her
car. The cost of each tire was $75. The
Federal Excise tax was $5.10 per tire, and
the state sales tax was 7% of the cost of the
tires, excluding the excise tax. Find the
total cost of the tires.
Please show work
Answer:
the cost of the tire=341.4$
Solve inequality problem (urgent help please)
Answer:
B
Step-by-step explanation:
|3m-2|=>1
1 <= 3m-2 or 3m-2 <= -1
3 <= 3m or 3m <= 1
1 <= m or m <= (1/3)
ITS TIMED HELP!!!
Assuming x and y are two odd numbers and x/y is an integer. Which of the following statements are true?
1: x + y is odd.
2: xy is odd.
3: x/y is odd.
4: x-y is odd.
A: 1 and 2 only.
B: 1 and 3 only.
C: 2 and 3 only.
D: 2, 3, and 4 only.
E: 2 and 4 only.
Answer:
C
Step-by-step explanation:
1: x + y is even. Try it. 3 + 5 = 8. 2x + 1 + 2y + 1 = 2x +2x + 2. That's even no matter what 2 odd numbers you use.
2: xy is again try it 3 * 5 = 15 which is odd. (2x + 1)(2y + 1) = 4xy + 2x + 2y + 1. The first 3 terms are even. The last one is odd. So xy is odd.
3. 9/3 = 3. Three should be true. The numerator is greater than the denominator. And x/y is given as an integer. So the statement should be true.
4. x - y is This can't be right. 2x + 1 - 2y - 1 = 2x + 2y. The result is even.
2 and 3 only
Question 13 of 46
What is the remainder for the synthetic division problem below?
Answer:
Step-by-step explanation:
Let's do this out as best as we can here. Here's the problem:
2 | 3 1 2 -7
___________
The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:
2 | 3 1 2 -7
6
3
Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):
2 | 3 1 2 =7
6 14
3 7
And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:
2 | 3 1 2 -7
6 14 32
3 7 16 25
The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.
What is the inequality?
Answer:
The best option would be the second one.
Step-by-step explanation:
This is the only option that shows that x can only be greater than -8. The circled dot means x cannot be the number the dot is sitting on, in this case, -8.
20. What is the transformation?:
a. rotation
b. reflection
c. translation
Please help me with this! It’s due in a few hours
Answer:
Reflection
Step-by-step explanation:
A rotation would be to rotate a figure around the origin
A reflection would be to reflect the figure around one of the axes.
A translation would be to move a figure a certain amount of units.
Since A and A' are 2 units away from the y-axis, and C, B, B', and C' are all one unit away from the y-axis, this could not be a translation because the position of A'B'C' is not the same position of ABC.
It could not be a rotation around the origin or any point because it would result the figure in either Quadrant 2 or 3, and in the one occasion it would be in Quadrant 1, the figure cannot be in that position.
This reveals only one option, that which is a reflection. A reflection about the x-axis would not make sense, since it would result in Quadrant 3, so a reflection around the y-axis would make the most sense.
The data we have above also accounts for a reflection, since all points are a certain distant away from the y-axis.
The segments shown below could form a triangle.
BRAINLEST IF CORRECT
Answer:
422.39
Step-by-step explanation:
[tex]A = \pi r^2\\A = 144\pi \\\\144\pi -30 = 422.39[/tex]
use a calculator for the above and round
Someone please help me. Asap ?
Answer:
Graph A
Step-by-step explanation:
A directly proportional relationship must create a straight line that goes through the origin (0,0) ( note that the slope can be negative or positive in a proportional relationship. )
All graphs show a straight line going through the origin except Graph A.
Graph A shows a straight line however that line does not go through the origin therefore it is not a proportional relationship
c) The GCF and LCM of two numbers are 2 and 70 respectively. If one of the numbers is 10, find the other number? [3m] solution: of too numbers
Their LCM is
70
hope it helps you.
Answer:
Their L.C.M IS
70....
IT IS YOUR ANSWER
SOMEONE HELP ME PLEASE
A standard die has numbers = 1,2,3,4,5 and 6
Total outcomes = 6
P = Number of outcomes/Total Outcomes
Even and less than 4 = 1,2,3,4 and 6
P = 5/6
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The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. (Help ASAP)
Is it a, b, c or d?
Answer:
C.
Step-by-step explanation:
212/4 = 53, so 53/1, or 53 miles are driven every hour.
Find the area of the shaded regions:
Answer:
84.78
Step-by-step explanation:
Used calculator and formula
