Answers
Answer:
Step-by-step explanation:
(x+y)/2 - (x-y)/6 = 16
x/3 + (x+2y)/3 = 14
Multiply first equation by 6
3(x+y) - (x - y) = 96
2x + 4y = 96
x + 2y = 48 (A)
Multiply second equation by 3
x + x + 2y = 42
x + y = 21 (B)
Subtract A - B:-
y = 27
So:
x + 27 = 21
x = -6.
The quadratic relation
is f(x) = a(x - 27)(x + 6)
= a(x^2 - 21x - 162) where a is some constant
Vertex form:
f(x) = a[(x - 10.5)^2 - 110.25 - 162]
f(x) = a[(x - 10.5)^2 - 272.25]
f(x) = a[(x - 10.5)^2 - 272.25a.
Related Questions
Write each quadratic equation in general form.
I need help direly
Answers
Answer:
9. 3x² +x -2y +5 = 0
10. 4x² +x -y +4 = 0
11. 9x² -6x -3y -12 = 0
Step-by-step explanation:
"General form" of a polynomial equation is ...
f(x, y) = 0
where the terms are arranged in lexicographical order and decreasing degree. That is, for terms of the same degree, x-terms are listed before y-terms, and xy terms are listed before y-only terms.
The leading coefficient can be positive or negative, your choice. (Positive is generally preferred.) For linear equations, "standard form" has the coefficients mutually prime. Making that happen for a general form polynomial would be your choice.
__
9.The highest-degree term is 3x². If we keep the leading coefficient positive, we can get general form by subtracting the expression on the left side of the equal sign.
3x² +x -2y +5 = 0
__
10.Subtracting the right side gives ...
4x² +x -y +4 = 0
__
11.Subtracting the left side gives ...
9x² -6x -3y -12 = 0
or
3x² -2x -y -4 = 0 . . . . . . remove a common factor of 3
A total of 643 tickets were sold for the school play. They were either adult tickets or student tickets. There were 57 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
Answer:
350 adult tickets
Step-by-step explanation:
If x is the number of adult tickets sold, then x-57 is the number of student tickets sold (57 fewer). The total number sold is ...
x +(x -57) = 643
2x = 700 . . . . . . . . collect terms, add 57
x = 350 . . . . . . . divide by 2
There were 350 adult tickets sold.
You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 24cm3 . Determine the minimum surface area necessary to construct a box of this volume. Enter an exact answer.
Answers
What is value of x?
Enter your answer in the box.
X=
Answers
Answer: 10
Step-by-step explanation:
What is 4,321,109,432 rounded to the nearest billion?
Answers
Answer:
I think 4000000000
Answer: 4,321,109,432 rounded to the nearest billion is 4,000,000,000
Step-by-step explanation:
First, you find the billions place which is right here:
4,321,109,432
Look to the number to the right of it. Is it greater or less than 5? Since it's less, you round down to 0, leaving a 4 and 3 sets of 3 zeroes.
Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B?
-Dilate circle A by scale factor of 2
- Translate circle A using the rule (x+1, y-1)
-Rotate circle A 180 degrees about the center.
-Reflect circle A over the Y axis
Answers
Answer:
-Dilate circle A by scale factor of 2
Got it right on the test (see picture)
Circle A is translated using the rule (x + 1, y - 1). Then the correct option is B.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10.
Circle B is translated as 1 unit leftward in the x-direction and 1 unit upward in the y-direction.
Then circle B is dilated by a factor of 2.
More about the circle link is given below.
https://brainly.com/question/11833983
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Isabel wants a coat that costs $60. She has saved $42. What fraction of the
amount she needs has she saved?
A) 21/30
B) 4/6
C) 8/12
D) 1/3
Answers
coat cost= $60.
to find:the fraction of amount she needs to save.
solution:saved/ actual cost
= $42/ $60 ÷ 2/2
= 21/30
answer= option a) 21/30
An amount of 47,000 is borrowed for 12 years at 8.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
Answers
Answer:
$121,683.79
Step-by-step explanation:
A= P(1+ r)^t
A= Amount, P = Principal, r = Rate (decimal form), t= time
A = 47000(1+0.0825)^12
A = 47000(1.0825)^12
A = 47000(2.589016751)
A = 121683.7873
Rounded Answer = $121,683.79
(If there is meant to be no cents then $121,684). Good luck :)
f ( x ) = x 2 + 6 x and g ( x ) = x − 8 , calculate. f ( g ( − 5 ) ) =
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
First we have to calculate g (-5) :
[tex]\qquad \tt \dashrightarrow \:x - 8[/tex]
[tex]\qquad \tt \dashrightarrow \: - 5 - 8[/tex]
[tex]\qquad \tt \dashrightarrow \: - 13[/tex]
Now, let's find f (g (-5)) :
[tex]\qquad \tt \dashrightarrow \: {x}^{2} + 6x[/tex]
[tex]\qquad \tt \dashrightarrow \:( - 13) {}^{2} + (6 \times - 13)[/tex]
[tex]\qquad \tt \dashrightarrow \:169 + ( - 78)[/tex]
[tex]\qquad \tt \dashrightarrow \:169 - 78[/tex]
[tex]\qquad \tt \dashrightarrow \:91[/tex]
Which description most accurately describes the motions for the calculation -5+ (-37)?
Answers
The motions for the calculation -5+ (-37) is given as a small movement to the left followed by a large movement to the left.
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
The expression -5+ (-37) can be solved using a number line. The motions for the calculation -5+ (-37) is given as a small movement to the left followed by a large movement to the left.
Find out more on equation at: https://brainly.com/question/2972832
Answer:
small movement to the left followed by a large movement to the left.
Step-by-step explanation:
The product of 4 and 3 is raised to the 5th
power. Which expression shows this?
A (4 X 3) 5
B(4/3)5
C 4 X 35
D 4/35
Answers
It raised the product first
Because the equation is (4x3), and this still represents the product, so it would be (4x3) to the 5th power, or (4x3)^5 to be exact
NEED HELP ASAP!!!!
A) 12 sq. cm.
B) 6 sq. cm.
C) 12 cm
D) 6 cm
Answers
Answer:
its B- 6 sq. cm.
Step-by-step explanation:
1/2 times base times height
1/2 x 4 x 3
6
Answer:
The answer is given below
Step-by-step explanation:
[tex]area = \frac{1}{2} \times base \times perpendicular[/tex]
[tex]area = \frac{1}{2} \times 3 \times 4[/tex]
Area = 1/2 * 12
Area = 6
Why is it wrong to draw y=ln(2x-5) this way?
Answers
well because he did not do it
Notice how
2x-5 = 2x - 2*2.5 = 2(x-2.5)
This means we can replace x with x-2.5 in the second step, in the "wrong way" column.
So,
y = ln(2x)
y = ln( 2(x-2.5) )
y = ln( 2x - 2*2.5 )
y = ln( 2x - 5 )
In the second step, the x-2.5 tells the reader to shift the curve 2.5 units to the right. Therefore, the 1/2 = 0.5 would shift to 0.5+2.5 = 3 as indicated by the correct graph.
Predicted distance traveled in 10 minutes: 3 km
(b) Lena is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
4
8
9
Cost (in dollars)
36
64
72
O The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $80:
Explanation
Check
Answers
Answer:
Cost for person is not always the same
For 80 dollars predicted would be 10 people
Step-by-step explanation:
4 people 36 dollars = 9 each
8 people 64 dollars = 8 each
9 people 72 dollars = 8 each seems to flatten at 8 dollars each
Help me with this question about vectors.
Answers
Answer:
parallelogram
Step-by-step explanation:
sr/pq=sp/rq
ab/dc=ad/bc
Answer:
Proven.
Step-by-step explanation:
So, fasten your seatbelts, we're about to go on a long ride(◠‿・)—☆
» In a parallelogram, opposite sides are equal in length.
This can be represented (in the vector way) by
'QR = '-SP = 'PS and 'RS = 'QS (let “'” represent a vector)
'QR + 'SP= 0 and 'RS-'QS = 0
Note the signs. The signs are determined by the arrows in the diagram. [A reminder: If you walk from a point A to a point B, your displacement vector is 'AB. If you walk back, that is, from B to A; your displacement vector is 'BA which is also equal to '-AB.]
This means: to prove that PQRS is a parallelogram, we must prove that
'QR + 'SP= 0 and/or 'RS-'QS = 0.
In this solution, we will only work on the first equation.
Permit me to remove this ' sign.
QR = QC+CR ...1
QR= QB+BA+AD+DR...2
ADD 1 TO 2
2QR= QC+CR+QB+BA+AD+DR
[LOOK CLOSELY, QC+QB=0 ; CR+DR=0. This is because BQ+QC = BC
BUT, BQ=QC= (BC)/2
QC-BQ= 0
AND, -BQ= QB
QC+QB= 0 ;)]
2QR= BA+AD...3
★
SP = SA+AP...4
SP= SD+DC+CB+BP...5
ADD 4 TO 5
2SP = SA+AP+SD+DC+CB+BP
[AGAIN, SA+ SD = 0 ; AP+ BP = 0]
2SP= DC+CB...6
3+6
2QR+2SP= BA+AD+DC+CB
[ BA+AD+DC+CB, IN A SIMPLE WAY, MEANS:
you start from B, and move to A (BA); from A to D (AD); from D to C (DC); and from C to B (CB). Therefore, you have gone from B to B (from your starting point and back). Hence, your total DISPLACEMENT is zero (you haven't changed your position).
2(QR+SP) = 0
'QR+'SP= 0
PROVEN
You can work out the other equation, but it is evident that PQRS is a parallelogram.
3x⁵. 2xy - x²y. 4x⁴ simplified
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:(3 {x}^{5} \times 2xy) - ( {x}^{2} y \times 4 {x}^{4} )[/tex]
[tex]\qquad \tt \dashrightarrow \:6 {x}^{6} y - 4 {x}^{6} y[/tex]
[tex]\qquad \tt \dashrightarrow \:2 {x}^{6} y[/tex]
= (3x^5× 2xy) — (x^2y × 4x^4)
= 6x^6y - 4x^6y
= 2x^6y
Use ABC to find the value of sin A
12/35
35/37
37/12
12/37
Answers
Answer:
The correct answer is 12/37
Complete the following sentence.
13 cm
8 cm
8 cm
The composite figure is made up of a rectangular prism and a
Answers
Answer:
Triangular prism
Step-by-step explanation:
There is one rectangular prism at the bottom and one triangular prism at the top.
Answer:
It is a square pyramid
Step-by-step explanation:
I hate math. Can someone pls help me?
Answers
Answer:
∠s = 158
Step-by-step explanation:
Since lines a and b are parallel,
∠s and 158 are alternate exterior angles.
Alternate exterior angles are equal if two lines are parallel.
So,
∠s = 158
Answer: 22°.
Step-by-step explanation: We're given the angle 158°, which is all we need. Angle u and 158°, have to add up to 180°. 180° - 158° = 22°, which is the angle measure of u. You're probably wondering how this will help us. The answer to that is it gives us the measurement of angle t, which is 158°. Now, we'll do the same thing we did with angle u, which was to make angle u add up with 158° to make 180°. We'll apply this to angle t and angle s. We already know that angle t is 158°, so angle s has to be 22° in order to add up to 180°. Therefore, your answer is 22° for angle s.
Let me know if this is right! :)
If you drive 23 miles south, make a turn and drive 39 miles east, how far are you, in a straight line, from
your starting point? Round your answer to the nearest tenth of a mile.
Answers
Answer:
45.27 miles
Step-by-step explanation:
Pythagorean theorem
23^2 + 39^2 = d ^ 2
d = 45.27 miles
If a person drives 23 miles south and make a turn to east and drive 39 miles then the distance between starting point and person is 45.27 miles.
What is pythagoras theorem?Pythagoras theorem applies in a right angled triangle. It says that in a right angled triangle the square of hypotenuse is equal to sum of squares of perpendicular and base of that triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
How to find distance?When person drives towards south and then east , it forms a right angled triangle. We have to find the distance of person from the starting point. If we see the figure then we will come to know that we are require to find hypotenuse of triangle.
H=[tex]\sqrt{P^{2} +B^{2} }[/tex]
Distance=[tex]\sqrt{23^{2} +39^{2} }[/tex]
=[tex]\sqrt{1521+529}[/tex]
=[tex]\sqrt{2050}[/tex]
=45.27
Hence the distance of person from starting point is 45.27 miles.
Learn more about pythagoras theorem at https://brainly.com/question/343682
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Noah writes the equation 3(x+7)=57 to represent the situation. Use the distributive property to write this equation another way.
Answers
Answer:
3x+21=57
Step-by-step explanation:
When we use distributive property we do
[tex]3*x[/tex] and [tex]3*7[/tex] which will like this when rewritten [tex]3x+21=57[/tex]
Check answer:
[tex]3x+21=57\\-21=-21\\3x=36[/tex] [tex]\frac{3x}{3} =\frac{36}{3}[/tex]
x=12 3(12)+21=57
36+21=57
Henry has 1.20 pounds of cat food. He uses 0.15 pound of cat food to feed one cat. How many cats can Henry feed with the cat food he has?
Answers
Divided 1.20/0.15
Given the same type of golf ball scenario with an equation
y=-0.005x2 +1.8x, horizontal distance of 360 feet, maximum
height of 162 feet, and using the helpful projectile motion formulas
below, answer the following.
x(t)=v, cos(6)y(t)= h, + v, - sin(0).4-1612
. 0
a.) What is the angle at which the ball takes off?
[ Select]
b.) How long is the ball in the air? (Select]
c.) What is the ball's speed when it hits the ground?
[ Select
Answers
The angle at which the ball takes off, distance the ball in the air, the ball's speed is mathematically given as
theta=60d=6.3658vo=116.486What is the angle at which the ball takes off?Generally, the equation for the verticle component is mathematically given as
[tex]y=xtan\theta-\frac{16x^2}{v0cos^2\theta}\\\\Therefore\\\\\theta=tan^{-1}(1.8)[/tex]
theta=60
b)
hmax=vo^2sin^2\theta/2g
vo=116.486
Therefore, distance the ball in the air
[tex]d=\frac{2*114.486*0.874*2}{32}[/tex]
d=6.3658
c)
The ball's speed when it hits the ground will be vo
vo=116.486
Read more about Angle
https://brainly.com/question/14362353
The cost of a barrel of beans, b, fluctuates (changes) by 17% in both
directions during a three-month period.
Match the verbal description of the high cost of a barrel of beans with all equivalent expressions for b is increased by 17%.
A. b + 0.17b
B. b - 0.17b
C. b - 1.17b
D. -0.17b
E. 0.83b
F. 1.17b
Answers
Answer:
b increased by 17% =b + 17% of b =b + 0.17b =1.17bCorrect ones A and F
------------------------------------------
b decreased by 17% =b - 17% of b =b - 0.17b =0.83bCorrect ones H and K
Yan had 5 trading cards, and then his friend gave him more cards. Now he has 16 trading cards. Let t represent the number of cards his friend gave him. Write both an addition equation and a subtraction equation to model the problem.
PLEASE ANSWER IN THE NEXT 1 MINUTE.
Answers
Explanation:
5+11=16
16-11=5
∣_7x+4∣=<18 absolute value
Answers
Step-by-step explanation:
|7x+4|≤18
7x+4≤ 18. 7x+4≥-18
x≤2. x≥-22/7
2≤x≤-22/7
Help will give thanks to the first to answer
Answers
our number is x
we add seven (+7) to x
x+7
1. Quinn's test scores are 95, 90, and 83. What must she score on the next test to have an average
score of 90 on the four tests?
Answers
Answer:
92
Step-by-step explanation:
Add 95, 90, and 83 all together
add 92 to that total
divide by 4
A boat is heading towards a lighthouse, where Meena is watching from a vertical
distance of 120 feet above the water. Meena measures an angle of depression to the
boat at point A to be 18º. At some later time, Meena takes another measurement and
finds the angle of depression to the boat (now at point B) to be 44º. Find the distance
from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Answer:
245 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle in which Meena's height is the side opposite the angle of depression, and the distance to the boat is the side adjacent to the angle of depression. The mnemonic SOH CAH TOA reminds us of the relation ...
Tan = Oppsite/Adjacent
__
The more useful trig function for this problem is the inverse of the tangent function, the cotangent. Using that function, we have ...
cot(angle) = (distance to boat)/(Meena's height)
Then the distance to the boat is ...
distance to boat = (Meena's height)×cot(angle)
The change in distance from A to B is then ...
A -B = (120 ft)(cot(18°) -cot(44°))
= (120 ft)(3.0777 -1.0355) ≈ 245.06 ft
The distance from point A to point B is about 245 feet.
While on vacation, the Garner family paid $120 for 3 tickets to a water park. How much money would they have spent on 5 tickets?
Answers
Answer:
$ 200
Step-by-step explanation:
$ per ticket = $ 120 / 3 tix
Price for 5 $120 / 3 tix * 5 tix = $ 200