Answer: The min value of Q is Q = 84 and it happens when x = 4 and y = 3
===========================================================
Explanation:
x+y = 7 turns into y = 7-x after subtracting x from both sides
Replace y with 7-x in the other equation to get
Q = 3x^2 + 4y^2
Q = 3x^2 + 4( y )^2
Q = 3x^2 + 4(7-x)^2
Q = 3x^2 + 4(49 - 14x + x^2)
Q = 3x^2 + 196 - 56x + 4x^2
Q = 7x^2 - 56x + 196
We have a function with one variable. Graphing 7x^2-56x+196 produces a parabola in which the vertex point is what we're after
Anything in the form p(x) = ax^2+bx+c will have a vertex (h,k) such that
h = -b/(2a)
k = p(h)
Let's find the x coordinate of the vertex
h = -(-56)/(2*7)
h = 4
Use this to find the y coordinate of the vertex
k = p(h)
p(x) = 7x^2-56x+196
p(h) = 7h^2-56h+196
p(4) = 7(4)^2-56(4)+196
p(4) = 84
The vertex is the lowest point in this case (since a = 7 is positive) and the vertex is (4,84)
Therefore, the minimum value of Q is Q = 84 and this happens when x = 4 and y = 3. Recall that y = 7-x.
We can see that,
Q = 3x^2 + 4y^2
Q = 3(4)^2 + 4(3)^2
Q = 3(16) + 4(9)
Q = 48 + 36
Q = 84
Which helps us verify we have the right Q value.
does this graph represents a function? why or why not?
Answer:
Yes, it passes the vertical line test
Step-by-step explanation:
This graph has a one to one correspondence and will pass the vertical line test, there fore it is a function
A quadrilateral has angle measures of 120 degrees ,37 degrees and 48 degrees what is the measure of the forth angle
Answer:
Let the fourth angle be x
Angles in a quadrilateral add up to 360°
To find the fourth angle add all the known angles and subtract them from 360°
That's
x + 120+37+48=360
x + 205 = 360
x = 360-205
x = 155°
Therefore the fourth angle is 155°
Hope this helps
Type SSS, SAS, ASA, SAA, or HL to justify why the two larger triangles are congruent.
Answer:
Step-by-step explanation:
PLEASE HELP!! I will give BRAINLIEST!! What is the range of possible sizes for side x?
Answer:
.5 < x < 16.5
Step-by-step explanation:
The smallest x can be is greater than the difference of the other two sides
8.5 -8 = .5
The largest x can be the less than the sum of the two sides
8.5+8 = 16.5
.5 < x < 16.5
Find the coordinates of a point that divides the directed line segment PQ in the ratio 5:3. A) (2, 2) B) (4, 1) C) (–6, 6) D) (4, 5)
Answer:
The answer is explained below
Step-by-step explanation:
The question is not complete we need point P and point Q.
let us assume P is at (3,1) and Q is at (-2,4)
To find the coordinate of the point that divides a line segment PQ with point P at [tex](x_1,y_1)[/tex] and point Q at [tex](x_2,y_2)[/tex] in the proportion a:b, we use the formula:
[tex]x-coordinate:\\\frac{a}{a+b}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{a}{a+b}(y_2-y_1)+y_1[/tex]
line segment PQ is divided in the ratio 5:3 let us assume P is at (3,1) and Q is at (-2,4). Therefore:
[tex]x-coordinate:\\\frac{5}{5+3}(-2-3)+3 \\\\While \ for\ y-coordinate:\\\frac{5}{5+3}(4-1)+1[/tex]
Isabel purchased bananas and apples at a grocery store. She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas. If the apple cost 3 times as much per pound as bananas, what is the cost per pound of apples??
A) $0.90
B) $1.80
C) $2.70
D) $3.60
Answer:
C. $2.70
If one pound of apples cost 3 times the amount of a pound of bananas, then a pound of apples costs; $2.70.
The cost per pound of apples will be $2.70, which is the correct answer would be option (C).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the cost per pound of apples be x, and the cost per pound of banana be y
She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas.
So, 3x + 2y = 9.90 ....(i)
And the apple cost 3 times as much per pound as bananas.
So, x = 3y
y = x/3 ....(ii)
Substitute the value of y = x/3 in the equation (i), and solve
3x + 2(x/3) = 9.90
3x + 2x/3 = 9.90
11x/3 = 9.90
11x = 2.97
x = 2.97/11
x = 2.70
Thus, the cost per pound of apples will be $2.70.
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For the function defined by [Image Displayed], What is the constant of proportionality?
a.
120
c.
12
b.
undefined
d.
1200
Answer:
I think the answer is undefined because the question above is an expression of f of x not a statement of variation which should have a constant of proportionality
Please Help!
Consider the graph of f(x) on the interval [−6,2] shown.
The local minimum of f(x) is at the point _[blank ]_.
Enter your answer the ordered pair that correctly fills in the blank in the previous sentence, like this: (42, -53)
Expand to write an equivalent expression: -1/4(-8x+12y)
Answer:
8x -12
Step-by-step explanation:
Use the distributive property. 16 outside wishes to go inside and multiply each term; you get 16x/2 which is 8x minus ¾ of 16 which is 12.
Answer:
2x-3y
Step-by-step explanation:
To expand this expression, use the distributive property.
[tex]-\frac{1}{4}(-8x+12y)[/tex]
To distribute, multiply each term inside the parentheses by the number outside the parentheses.
[tex](-\frac{1}{4}*-8x)+(-\frac{1}{4} *12y)[/tex]
Multiply -1/4 and -8x first.
[tex]((-\frac{1}{4}*-8)x)+(-\frac{1}{4} *12y)[/tex]
[tex]2x+(-\frac{1}{4} *12y)[/tex]
Next, multiply -1/4 and 12y.
[tex]2x+ ((-\frac{1}{4} *12)y)[/tex]
[tex]2x+ -3y[/tex]
A +- becomes a -
[tex]2x-3y[/tex]
Please answer this question now
Answer:
C = (2,2)
Step-by-step explanation:
B = (10 ; 2)
M = (6 ; 2)
C = (x ; y )
|___________|___________|
B (10;2) M (6;2) C ( x; y)
So:
dBM = dMC
√[(2-2)^2 + (6-10)^2] = √[(y-2)^2 + (x - 6)^2]
(2-2)^2 - (6-10)^2 = (y-2)^2 + (x - 6)^2
0 + (-4)^2 = (y-2)^2 + (x - 6)^2
16 = (y-2)^2 + (x - 6)^2
16 - (x - 6)^2 = (y-2)^2
Also:
2*dBM = dBC
2*√[(2-2)^2 + (6-10)^2] = √[(y-2)^2 + (x - 10)^2]
4*[(0)^2 + (-4)^2] = (y-2)^2 + (x - 10)^2
4*(16) = (y-2)^2 + (x - 10)^2
64 = (y-2)^2 + (x - 10)^2
64 = 16 - (x - 6)^2 + (x - 10)^2
48 = (x - 10)^2 - (x - 6)^2
48 = x^2 - 20*x + 100 - x^2 + 12*x - 36
48 = - 20*x + 100 + 12*x - 36
8*x = 16
x = 2
Thus:
16 - (x - 6)^2 = (y-2)^2
16 - (2 - 6)^2 = (y-2)^2
16 - (-4)^2 = (y-2)^2
16 - 16 = (y-2)^2
0 = (y-2)^2
0 = y - 2
2 = y
⇒ C = (2,2)
is this right? someone help i’ll give brainliest!
Answer:
yes this is right
Step-by-step explanation: i dont even no the answer i just said its right
Answer:
-10< x< 3
Step-by-step explanation:
Please see attached picture for full solution.
*Sign changes when you divide inequality with a negative number.
Further explanation:
When you add, subtract, divide or multiply an inequality, it applies throughout. This means that from step 1 to 2, if you subtract 1 from the constant 58 to obtain 57, your inequality should be:
19< -6x -3< 57
Note that you do not subtract 1 from the coefficient of x (which means -6x does not become -7x since -7 is not a constant here).
Thus, the easiest way to solve an inequality with 2 inequality signs is to split them up into 2 different inequalities first and solving them separately before combining them into 1 to solve the question.
This set of 3 numbers are measurements of a right triangle. 26, 24, 10
True
False
Answer:
True
Step-by-step explanation:
24^2 = 576
10^2 =100
576+100=676
26^2=676
Answer:
True
Step-by-step explanation:
Use the pathagorean theorum:
a squared +b squared=c squared
(the numbers squared)
676, 576, 100
a=576 b=100 c=676
because 676=576+100
Help please, I'm not timed
Answer:
B 30% you can divide 160 the total by 10then multiply and you can check B and C
Alex purchased a motorbike that costs $3,500. He'll pay for the motorbike through an installment plan. The installment plan requires him to
make a 10% down payment and pay the remaining amount in 12 monthly installments of $276 each. How much will Alex pay in finance charges?
ОА.
$162
ОВ.
$188
O c.
$512
OD.
$538
O E.
$552
Answer:
Option A.) $162
Alex pays $162 in finance charges.
What is Installment Plan ?An installment plan is a way of buying goods gradually. You make regular payments to the seller until, after some time, you have paid the full price and the goods belong to you.
According to the question
The cost Price of the motor bike is $3,500.
10% down payment = $350
The amount that needs to be financed = $3500-350=$3150
Time Period = 12 months
Each installment = $276
Total amount paid = $276* 12 = $3312
Therefore Alex pays $3312-3150 = $162 in finance charges.
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Which Anna quality graft is the solution to X/ < -3
Answer:
Well the following inequality [tex]x<-3[/tex] as a graph is in the image below.
Which of the following best describes the slope of the line below?
O A. Undefined
O B. Negative
O c. Positive
O D. Zero
Answer:
zero or undefined
Answer:
it's d zero.
Step-by-step explanation:
just took the test
These cylinders are similar. Find the surface area of the smaller cylinder. Round to the nearest tenth.
Thank you in advance for your help!
Answer:
Surface area = 80.4 cm²
Step-by-step explanation:
The diagram of both cylinders is attached below for a better understanding.
First find the radius of larger cylinder:Surface area = 2πrh + 2πr²
236 = 2(3.14)(5)r + 2(3.14)r²
236 = 31.4r + 6.28r²
236 = 6.28(r² + 5r)
35.58 = r² + 5r
r = 3.97 cm
Find the radius of Smaller cylinder:
Two cylinders are in proportion if their heights and radius are in proportion:
Ratio of height of small cylinder to big cylinder = 3/5 = 0.6
So ratio of radius of both is also 0.6
Let R be the radius of small cylinder
ratio of radius of small cylinder to big cylinder = R / 3.97
R = (0.6)(3.97)
R = 2.38
Surface Area for small cylinder:R = 2.38cm and h = 3 cm
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2.38)(3) + 2(3.14)(2.38)²
Surface area = 80.4115cm²
Round of to nearest tenth
Surface area = 80.4 cm²
Please help with this
Find the area of this circle. Area = _______ in2. Use 3.14 for pi and round to the nearest tenth. A. 35.8 B. 28.3 C. 254.3 D. 1017.4
Answer:
A ≈ 254.5 in²
Option C
Step-by-step explanation:
Area of a Circle Formula: A = πr²
d = 2r
Since we are given diameter d, we simply divide by 2 to get radius r:
r = 18/2 = 9
Then we simply plug it into the formula:
A = π(9)²
A = 81π
A = 254.469
A circle with a radius of 9 inches has an area of 254.3 square inches. The of aarea circle is calculated using the formula πr², where π is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.
Hence, the correct option is C.
The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius of the circle. In this case, the radius is 9 inches, so the area is given by:
In this case, the radius is 9 inches, so the area of circle is given by,
Area = pi × [tex]9^{2}[/tex]
Area = 3.14 × 81
Area= 254.3
The value of pi is approximately 3.14, so the area of the circle is approximately 254.3. However, the question asks for the area rounded to the nearest tenth, so the answer is 254.3.
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Solve the system of equations and choose the correct ordered pair. 3x-5y+2=21 and 2y=7x+4
Answer:
(-2 ; -5)
Step-by-step explanation:
2*y = 7*x + 47*x - 2*y = -4
(7/2)*x - (2/2)*y = -4/2
(7/2)*x - y = -2
(7/2)*x + 2 = y
3*x - 5*y + 2 = 213*x - 5*y = 21 - 2
3*x - 5*y = 19
3*x - 5*[(7/2)*x + 2] = 19
3*x - 35/2*x - 10 = 19
- 29/2*x = 29
- 1/2*x = 1
x = -2
⇒ y = -5
Answer : (-2 ; -5)
Gabe can wrap 1 2/3 presents in 1/3 hour. how many presents can Gabe wrap per hour?
Answer:
5.06
Step-by-step explanation:
1 2/3 = 1/3
x = 1 (cross multiply)
1/3 x = 1 2/3 (divide both sides by 1/3)
x = 5.06
Sorry the final answer is in decimal. I think better in decimal.
Answer:
Gabe can wrap 5 presents in an hour.
Step-by-step explanation:
So, to find the answer all you have to do is just multiply how many presents he can wrap in 1/3 hours and multiply that by 3. That is then your answer.
Brainliest would be appreciated.
I hope that I was able to help you.
Three points, P, Q, and R, lie on the same line such that Q lies between P and R. Find PR if PQ = 11 and QR = 13. Question 17 options: A) 2 B) 13 C) 11 D) 24
The distance between points P and R is 24 units.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
Three points P, Q and R lie on the line.
The distance between PQ = 11,
And the distance between QR = 13.
Since, All the points are on same line,
Therefore, The distance between points P and R,
PR = PQ + QR
PR = 11 + 13
PR = 24
The required distance of PR is 24 units.
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is this right? someone please help! i’ll give brainliest :)
Answer:
you're right
Step-by-step explanation:
2 + 5x ≥ 52
5x ≥ 50
x ≥ 10
7 - x > -2
-x > -9
x < 9
Answer: Yes
The only difference between simplifying equations and inequalities is that if you ever divide both sides by a negative, flip the sign.
Hope it helps <3
Sam always has eggs for breakfast. He either has boiled,
poached or fried eggs.
The probability that he has fried eggs is 0.65 and the
probability that he has poached eggs is 0.25.
a) What is the probability that he has boiled eggs?
b) Work out the probability that
i)He has boiled eggs on the first day and fried
eggs on the second
ii) He has fried eggs both days
iii) He has boiled eggs on at least one day
Answer:
a) 0.1 [ 0.10 ] probability
Step-by-step explanation:
Workout for a) question
Propability of hving boiled eggs + Propability of hving poached eggs + Propability of hving fried eggs = 100
x + 25 + 65 = 100
x=10
Writing as decimal
x=0.10=0.1
b)
i) 10 percent of hving boiled eggs on first day 65 percent of hving fried eggs in second day
ii) 65 percent of hving fried eggs on both days
iii) 10 percent propability of hving atleat one boiled egg in 1 day
Hope this helps....
Pls mark my answer as brainliest :)
Heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp
Answer:
1. not possible, 2. a. 65 b. 115 c.115
Step-by-step explanation:
def. sup. <
vertical angles post.
corresponding angles thm.
Answer:
Step-by-step explanation:
(a) 27 degrees: complementary angle is (90 - 27) degrees, or 63 degrees; recall that complementary angles add up to 90 degrees.
(b) Since supplementary angles add up to 180 degrees, we subtract 105 degrees from 180 degrees, obtaining the supplementary angle 75 degrees. There's no complementary angle here, because 105 degrees is greater than 90 degrees.
(c) complementary angle is (90 - 18) degrees, or 72 degrees; supplementary angle is (180 - 18) degrees, or 162 degrees.
A father requires his son to do chores for 4 to 6 hours a week. If the son wants to do
chores daily, how many hours per day is this (in interval notation)?
Answer: 5 hours and 15 mins
Step-by-step explanation: 45 mins x 7 = 5 hours and 15 mins. I checked so it should be correct. [tex]45x2= 1[/tex]hour and 30 mins.So I multiplied 1 hr 30 x 3 which gave me 4 hr 30 then added 45 mins, then I got 5 hr 15 min.
So in conclusion the answer is 5 hours and 15 mins.
Thank You
40 points!!! please tell me how to do it not what the answer is :D
Answer:
C
Step-by-step explanation:
You first distribute within the parentheses which is -(-z-2). This is going to make everything positive as everything in the parentheses is negative. You should get z+2. Next, you plug that back in. It should be-3z+z+2. You simplify to get -2z+2. Hope this helps!
Answer:
see below
Step-by-step explanation:
-3z -( -z -2)
The first step is to distribute the minus sign
-3z --z --2
A negative negative is a positive
-3z +z +2
Then combine the like terms
-3z+z +2
Answer
-2z+2
The triangular prisms are similar. Find the volume of the larger prism. Round your answer to the nearest hundredth.
A. 85.33 in³
B. 86.38 in³
C. 87.07 in³
D. 88.16 in³
A store ships books by weight. A small box can hold 4−6 pounds. A medium box can hold 5−7 pounds. A large box can hold 8−9 pounds. The weights of the books are given below. Drag books into each box to show what it can hold.
Answer:
4-6
3.1+2.4
5-7
3.1+2.4+.75+.75
8-9
3.1+2.4+2.4+.75
add them to see which one is close that's i got my answer because i got it right
In 4-6 pounds, the blue and green book can be added., 5-7 pounds, the blue, green and red books can be added. and n 8-9 pounds, two green books, blue book and red book be added
What is Unit of Measurement?Unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 1 lb.
In 4-6 pounds, the blue and green book can be added.
4-6
3.1+2.4
In 5-7 pounds, the blue, green and red books can be added.
3.1+2.4+.75+.75
In 8-9 pounds, two green books, blue book and red book be added.
3.1+2.4+2.4+.75
Hence, In 4-6 pounds, the blue and green book can be added., 5-7 pounds, the blue, green and red books can be added. and n 8-9 pounds, two green books, blue book and red book be added.
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Mr. Maddox asked four students to create a number line to help find the sum of the fractions.
Negative StartFraction 7 over 10 EndFraction + StartFraction 4 over 10 EndFraction
Which number line would be best to find this sum?
A number line going from Negative StartFraction 8 over 10 EndFraction to 0 in increments of StartFraction 1 over 10 EndFraction
A number line going from Negative StartFraction 3 over 10 EndFraction to positive StartFraction 3 over 10 EndFraction in increments of StartFraction 1 over 10 EndFraction
A number line going from StartFraction 4 over 10 EndFraction to StartFraction 11 over 10 EndFraction in increments of StartFraction 1 over 10 EndFraction
A number line going from 0 to StartFraction 15 over 10 EndFraction in increments of StartFraction 1 over 10 EndFraction
Answer:
A number line going from Negative StartFraction 8 over 10 EndFraction to 0 in increments of StartFraction 1 over 10 EndFraction
(2nd option)
Step-by-step explanation:
When you add the 2 fractions together: -7/10 + 4/10 = -3/10
We need to find a number line that has -3/10 in it. The best answer choice is the 2nd option because we can go backwards to find the answer from positive 3/10 to our answer -3/10 (we are going -7 units backwards).
Answer:
First choice
Step-by-step explanation:
Sum of fractions:
-7/10 + 4/10= - 3/10the interval required on the line from the left of - 7/10 to the right of -3/10
Which number line would be best to find this sum?
-8/10 to 0
yes, this is good as covers the interval from -7/10 to - 3/10-3/10 to 3/10
no, it doesn't include the left half of required section4/10 to 11/10
no, it doesn't include the required interval0 to 15/10
no, it doesn't include the required interval