Answer:
1) f(x) = 4·x² - 3·x + 6
2) f(x) = -2·x² + 5·x - 1
3) y = 2·(x - 3)² + 5
Step-by-step explanation:
1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows
The general form of a quadratic function is f(x) = a·x² + b·x + c
Where, in (x, y), f(x) = y, and x = x
Therefore for the point (0, 6), we have;
6 = 0·x² + 0·x + c
c = 6
We have c = 6
For the point (2, 16), we have;
16 = a·2² + b·2 + 6
10 = 4·a + 2·b.............................(1)
For the point (3, 33), we have;
33 = a·3² + b·3 + 6
27 = 9·a + 3·b............................(2)
Multiply equation (1) by 1.5 and subtract it from equation (2), we have;
1.5 × (10 = 4·a + 2·b)
15 = 6·a + 3·b
27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;
27 - 15 = 9·a - 6·a+ 3·b - 3·b
12 = 3·a
a = 12/3 = 4
a = 4
From equation (1), we have;
10 = 4·a + 2·b = 4×4 + 2·b
10 - 4×4 = 2·b
10 - 16 = 2·b
-6 = 2·b
b = -3
The function, f(x) = 4·x² - 3·x + 6
2) Where the points are (-1, -8), (0, -1), (1, 2), we have;
For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)
For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)
For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)
Adding equation (1) to equation (3) gives
-8 + 2 = a - b + c + a + b + c = 2·a + 2·c where, c = -1, we have
-8 + 2 = -6 = 2·a + 2
2·a = -6 + 2 = - 4
a = -8/2 = -2
From equation (3), we have;
2 = a + b + c
b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5
f(x) = -2·x² + 5·x - 1
3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola
The vertex equation of a parabola is y = a(x - h)² + k
Where;
(h, k) = Vertex (3, 5)
(x, y) = (1, 13)
We have
13 = a·(1 - 3)² + 5
13 = a·(-2)² + 5
13 - 5 = a·(-2)² = 4·a
4·a = 8
a = 8/4 = 2
The equation is y = 2·(x - 3)² + 5.
how many are 9 raised to 2 ???
Answer:
[tex]\boxed{81}[/tex]
Step-by-step explanation:
9 raised to 2 is
=> [tex]9^2[/tex]
=> 9 * 9
=> 81
What is the area of the trapezoid shown below?
Answer:
180 units
Step-by-step explanation:
In order to solve this, we need to find the length of the missing side of the triangle using the Pythagorean theorem.
a²+b²=c²
a= 7
b=x
c= 25
7²+x²=25²
49+x²=625
Subtract 49 from both sides
x²=576
x=24
The length of the missing side of the triangle is 24, which is also the base of the triangle. We need to find the area of the triangle so we use the formula for the area of a triangle, A=1/2bh.
A= 1/2 (24 x 7)
A=84
Now, we need to find the area of the rectangle.
Formula for area of rectangle: A= bh
A= bh
A= 4 x 24
A= 96
Next, we add the areas of both shapes to get the area of the entire figure.
96+84=180
Area of figure= 180
Answer:
area = 180
Step-by-step explanation:
will make it simple and short
area of a trapezoid = (a + b) h/2
h = sqrt(25² - 7²) = 24
Area = (4 + 11) * 24/2
area = 180
What type of number is 17?
There may be more than one correct answer.
Select all that apply.
If only one answer is correct, select "only" and the answer that applies.
rational
only
integer
natural
whole
Rational Numbers
Answer:
Rational, integer, natural, whole, rational numbers
Step-by-step explanation:
17 is a rational, integer, natural, whole, and is a rational number. I'm not totally sure why rational is on there, since rational and rational number should be the same thing. Basically it's everything but "only". If rational is supposed to mean irrational, then it's not irrational.
Why do you think that when subtracting a negative
number, in reality you are adding it? (For example: 1-
(-1) = 1+1=2)
Answer:
See explanation
Step-by-step explanation:
When we have a positive number and a negative number, let's imagine it with a number line.
<-----------0----------->
If we have the positive number 1:
<-----------0--1-------->
And we want to subtract 1 from it, the number would move to the left
1 - 1 = 0
<-----------0----------->
However, if we were to subtract a negative number, they are opposites. It can't move to the left because that's what a positive number does. The only other way to go: right.
1 + -1 = 2
<-----------0--1--2----->
Hope this helped!
if the mean of 3 2 x 11 13 14 is 8 find the value of x
Answer:
x=5
Step-by-step explanation:
To find the mean, add up all the numbers and then divide by the number of numbers
(3+ 2+x+ 11+ 13+14)/6 = 8
Multiply each side by 6
(3+ 2+x+ 11+ 13+14) = 48
Combine like terms
43+x = 48
Subtract 43 from each side
x =5
Answer:
[tex]\huge \boxed{{x=5}}[/tex]
Step-by-step explanation:
The mean is the average value of a data set.
[tex]\displaystyle \sf mean = \frac{sum \ of \ terms}{number \ of \ terms}[/tex]
The mean is given solve for x.
[tex]\displaystyle 8 = \frac{3+2+x+11+13+14}{6}[/tex]
Multiply both sides by 6.
[tex]\displaystyle 8(6) = \frac{3+2+x+11+13+14}{6} \times (6)[/tex]
[tex]48=3+2+x+11+13+14[/tex]
Combine the numbers on the right side of the equation.
[tex]48=x+43[/tex]
Subtract 43 from both sides.
[tex]48-43=x+43-43[/tex]
[tex]5=x[/tex]
You have this information about ΔABC, ΔFDE, and ΔGIH:
AB = DF
AB = GI
BC = HI
DE = HI
m∠B = m∠D = m∠I
Which triangles must be congruent?
The triangle ABC, triangle FDE, and triangle GIH are congruent with each other.
What is a triangle?Three sides and three internal angles define a triangle, a basic shape. The symbol is used to represent one of the geometric shapes in which the three corners are connected to one another. Triangles are categorized according to their sides into numerous different forms.
As per the given data in the question,
Sides AB = DF, AB = GI, BC = HI, and DE = HI are equal to each other.
Also, the angles, m∠B = m∠D = m∠I are equal.
Then by the property of the side angle side all the triangles are congruent with each other.
To know more about Triangle:
https://brainly.com/question/2773823
#SPJ3
Answer:
A. ΔABC, ΔFDE, and ΔGIH
Meredith has $630,000 she wants to save. If the FDIC insurance limit per
depositor, per bank, is $250,000, which of these ways of distributing her
money between three banks will guarantee that all of her money is insured?
A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C
B. $200,000 in bank A, $170,000 in bank B, $260,000 in bank C
C. $160,000 in bank A, $180,000 in bank B, $290,000 in bank C
D. $160,000 in bank A, $200,000 in bank B, $270,000 in bank C
you
Answer:
$200,000 in bank A, $200,000 in bank B, $230,000 in bank C
Step-by-step explanation:
Meredith has $630,000
Limit per depositor, per bank, is $250,000
She needs to distribute her money between three Banks to guarantee that her money is insured.
A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C
It can be seen in A that her deposit per bank deposit didn't exceed the $250,000 limit in the three Banks.
B. $200,000 in bank A, $170,000 in bank B, $260,000 in bank C
Here, her deposit in bank C exceeds $250,000, so there is no guarantee for insurance in bank C
C. $160,000 in bank A, $180,000 in bank B, $290,000 in bank C
Her deposit in bank C is $290,000 which exceeds the $250,000 limit. Therefore, no guarantee for insurance of her money in bank C
D. $160,000 in bank A, $200,000 in bank B, $270,000 in bank C
you
Also, her deposit in bank C exceeds $250,000, so there is no guarantee for insurance in bank C
The way her money can be distributed between three Banks and guarantee insurance is
A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C.
That way, her deposit per bank is less than the $250,000 limit
what is the answer to (x+1)(3x+2)
Answer ASAP, will give brainliest!!
Answer:
Step-by-step explanation:
77; The formula to calculating the area of a trapezoid is (a+b)/2 * c. a+b are the 2 parallel lines, and c is the height or the altitude. So, it is (10+12)/2 * 7, which is 22/2 * 7 = 11*7=77 :)
daniel thinks of a number and subtracts 2
from it. He divides 32 by the result. If
his answer is 4, what number does he
think of
Answer:
the number is 126
Step-by-step explanation:
1) multiply each side by 32: (n-2) / 32 = 4
2) subtract 2 from each side: n-2 = 128
3) n = 126
Answer:
130
Step-by-step explanation:
So basically this number, minus 2, divided by 32 is 4, so lets write the unknown number as x.
So, (x-2)/32 = 4.
First multiply both sides by 32 to get rid of the denominator.
(32)(x-2)/32 = 4(32) x-2 = 128
Now the -2 remains to figure out x, so you add 2 to both sides to get rid of the -2.
So, x-2+2 = 128+2, -2 +2 is 0, and 128 +2 is 130, so you have x = 130.
Tuition for one year at the University of Atlantis costs $12,000 per year. Rachel would like to attend this university and will save money each month for the next 3 years. Her parents will contribute $3,000 for her first year's tuition. How much money will Rachel need to save each month to have enough money for the first year of college at the University of Atlantis?
Answer:
250 dollars per month.
Step-by-step explanation:
We first need to subtract the amount of money her parents are giving her.
12000-3000=9000.
Since she is saving money every month for 3 years we have to multiply 3×12=36 months.
We than need to divide how much money she needs by the amount of months she has to get it.
9000÷36=250
While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top of the lighthouse is 48°
What can you conclude about the height of the lighthouse, with respect to Jacob's distance from the lighthouse? Explain your answer.
Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Answer:
The height of the lighthouse is approximately 42.
Step-by-step explanation:
This situation forms a right triangle so the angles would be 90 and 48
90+48+x=180
138+x=180
x=180-138
x=42
Four witches are making a brew.Patricia puts in x frogs legs.sheila puts in five more than patricia.Anne puts double the amount that Sheila adds,and Winifred adds three times the number Sheila adds.
write down an algebraic expression for:
Sheila. Anne. Winifred
Answer:
see explanation
Step-by-step explanation:
Given Patricia puts in x frogs legs, then
Sheila puts in x + 5 ( 5 more than Patricia )
Anne puts in 2(x + 5) ( double the amount of Anne )
Winifred puts in 3(x + 5) ( three times the number of Sheila )
Someone please help! Thank you
Answer:
Hey there!
We can write a equations here:
3x+y=180
Also, since all of the angles have 3x on the outside, then y must be constant.
3y=180
y=60
Thus, for x, we have 3x+60=180, 3x=120, x=40.
2x+6y
2(40)+6(60)
80+360
440.
Let me know if this helps :)
HE SODA MACHINE
The soda machine at your school offers several types of soda. There are two buttons for your favorite drink, Blast,
while the other drinks (Slurp, Lemon Twister, and Diet Slurp) each have one button.
Describe the input and output of this soda machine.
While buying a soda, Ms. Whitney pushed the button for Lemon Twister and got a can of Lemon Twister.
Later she went back to the same machine, again pushing the Lemon Twister button, but this time she got a can
of Blast. Is the machine functioning consistently? Why or why not?
BLAST
BLAST
BLUSO
ooo
Students, write your resnonsel
Answer:
yes and no
Step-by-step explanation:
if a machine is work a lot lot LOT, then it might be jamed
or the teacher might have accidentally pressed blast and you might have not seen the buttons correctly
( also i am not a student of yours )
The tens digit of a two-digit number is three times greater than the ones digit. The difference between twice the original number and half the number obtained after reversing the digits is 108. What is the original number? Show your work.
Answer:
Now solve these two equations.ull get andwer
The original number will be "63".
Let,
The ten's digit be "x".One's digit be "y".The equation will be:
→ [tex]x=y+3[/tex]...(equation 1)
Original number will be:
→ [tex]10x+y[/tex]
then,
→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]
→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]
→ [tex]40x+4y-10y-x = 216[/tex]
→ [tex]39x-6y=216[/tex]...(equation 2)
By using (equation 1) and (equation 2), we get
→ [tex]39(y+3)-6y=216[/tex]
→ [tex]39y+117-6y=216[/tex]
→ [tex]33y=99[/tex]
→ [tex]y = \frac{99}{33}[/tex]
→ [tex]= 3[/tex]
Now,
[tex]x = y+3[/tex]
[tex]=3+3[/tex]
[tex]=6[/tex]
hence,
The original number will be:
= [tex]10x+y[/tex]
= [tex]10\times 6+3[/tex]
= [tex]60+3[/tex]
= [tex]63[/tex]
Thus the above approach is right.
Learn more:
https://brainly.com/question/285966
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
What is the value of x in the equation 3x-4y=65, when y =4 will give brainliest
Hello!
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given:
3x - 4y = 65 where y = 4;
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
Hope this helped you! :)
Answer:
x=27
Step-by-step explanation:
3x-4y=65
Let y=4
3x - 4(4) = 54
3x -16 = 65
Add 16 to each side
3x -16+16 = 65+16
3x = 81
Divide each side by 3
3x/3 =81/3
x =27
Please help I did the first 2 already.
The answer to C is 1.5 or 3/2
Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2
the product 9f 2 numbers is 16/9 . if one number is 5 /2 find the other number
Answer:
The answer is 32/45Step-by-step explanation:
Let the number be x
The product of two numbers is 16/9
That's
x × y = 16/9
One of the numbers is 5/2
That's
y = 5/2
So we have
[tex] \frac{5}{2} x = \frac{16}{9} [/tex]
Multiply through by the LCM
The LCM of 2 and 9 is 18
That's
[tex]18 \times \frac{5}{2} x = \frac{16}{9} \times 18[/tex]
9 × 5x = 16 × 2
45x = 32
Divide both sides by 45
we have the final answer as
[tex]x = \frac{32}{45} [/tex]
Hope this helps you
A pyramid has a square base with an area of 169 ft.² what is the perimeter of the base of the pyramid
Answer:
52
Step-by-step explanation:
Square root of 169 is 13.
SInce it is a square all sides are same length. So you could do 13x4 or 13+13+13+13. Both will equal to 52.
The perimeter of the base of the pyramid is 52 square feet.
Given that,
The pyramid contains a square base having an area of 169 square feet.
We know that,
Area of the square = side^2
169 = side^2
So, the side is 13 feet.
So, the perimeter should be
= 4 × sides
= 4 × 13
= 52 feet
Therefore, we can conclude that The perimeter of the base of the pyramid is 52 square feet.
Learn more about the square here: brainly.com/question/14198272
Simplify
(3x + 14) + (19x - 35)
Answer:
22x -21
Step-by-step explanation:
(3x + 14) + (19x - 35)
Combine like terms
3x+19x + 14-35
22x -21
2. The ratio of
the profit, cost of
materials and labour
in the production of
an article is 5:7:13
respectively. If the
cost of materials is Le
840 more than that of
labour, find the total
cost of producing the
article
Answer:
3500Step-by-step explanation:
Given the ratio of the profit, cost of materials and labour in the production of
an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25
If the cost of labour is x, the cost of material will be 840+x (since the cost of materials is Le 840 more than that of labour) .
Let the total cost of producing the article be y.
Cost of labour = 13/25 * y = x
Cost of labour = 13y/25 = x.................... 1
Cost of material = 7/25*y = 840+x
Cost of material = 7y/25 = 840+x ..................... 2
From 1, 13y = 25x
x = 13y/25 ................... 3
Substituting equation 3 into 2:
7y/25 = 840+x
7y/25 = 840+13y/25
collect the like terms:
7y/25 - 13y/25 = 840
-6y/25 = 840
-6y = 25*840
y = 25*840/6
y = 3,500
Hence the total cost of producing the article is 3500
A carpenter has a 10 1/2 foot wood plank. He cuts off 4 1/4 feet to replace a deck board as well as 3 2/3 feet to repair a step. He uses the rest of the plank for a shelf. How many feet of wood does the carpenter have for the shelf? PLEASE SHOW YOUR WORK AND EXPLAIN HOW YOU GOT THE ANSWER PLEASE I WILL MARK YOU BRAINIEST.
Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Question 9(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x - 9)?
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answer: D) right 9 units
Step-by-step explanation:
The Vertex form of a quadratic equation is: y = a(x - h)² + k where
a is the vertical stretch or shrink(x, h) is the vertex→ h is the horizontal shift (+ is right, - is left)
→ k is the vertical shift (+ is up, - is down)
y = f(x - 9)
↓
h=9
Since h is positive, the graph moves 9 units to the RIGHT
Answer:
The graph of y = f(x) will shift right 9 units.
Step-by-step explanation:
If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.
A sprinter run 400 meter in 54 second.what about s the runner's average running rate in meter per second?round to the nearest tenth
Answer:
7.4
Step-by-step explanation:
400 ÷ 54 =7.407407...
7.407407... rounded to the nearest tenth is 7.4
I hope this helps... and plz mark me brainliest!!!
I got this wrong please help me get the right answer in the first little box marked in red. thx
Answer:
The inverse is 1/2x +2
Step-by-step explanation:
f(x) = 2x-4
y= 2x-4
To find the inverse
Exchange x and y
x = 2y-4
Solve for y
Add 4 to each side
x+4 = 2y
Divide by 2
x/2 + 4/2 = 2y/2
1/2x +2 = y
The inverse is 1/2x +2
Write 3.6 as a percent.
Answer:
360%
Step-by-step explanation:
You have to multiply 3.6 by one hundred to get the percentage. When you multiply decimals by numbers that are multiples of ten, you move the decimal place to the right of the number by the number of zeroes that is in your number. Sorry if its confusing.
Examples: 3.76 * 100 = 376. You move the decimal to the right two spaces
46.263 * 1000 = 46263. You move the decimal to the right three spaces. Hope you understand.
Okay I need ur help pls very urgent..
So I have to match the following: .complement of 50degres
Supplement of 145degress
.complement of 27degress
Supplement of 50 degrees to either
130degress
63degress
35degress
And 40degress
So I gotta match the following the first ones on top match them to these ones here on the bottom hope you can help me and very sorry..I’m just really bad with maths.
Thanks..
Supplementary angles are those which sum upto 180°
[tex] \angle 1+\angle2=180^{\circ}[/tex]
Complementary are those which sum to 90°
[tex] \angle 1+\angle2=90^{\circ}[/tex]
so if you know one angle, you can find other.
Answer:Look at my explaination
Step-by-step explanation:The complement of 50 is 90-50 giving us 40degrees
The supplement of 145 is 180-145=35 degrees
The compliment of 27 degrees is 90-27=63 degrees
The supplement of 50 degrees is 180-50=130 degrees
4x3+ 13x2 + 5x- 4 is divided by x+ 1?
Answer:
The quotient to this equation is 4x² + 13x + 1
Step-by-step explanation:
When we divide exponents, we subtract the exponential numbers.
4x³ + 13x² + 5x - 4 / x + 1
Now, we divide. For this problem, we are only dividing the like terms of x because anything divided by 1 will equal to itself.
4x² + 13x + 5 - 4
Now, we combine like terms.
4x² + 13x + 1
