1. The table represents a quadratic function. Write an equation of the function in standard form. X f(x) -4 -3 -2 0 0 1 2 0
Answers
An equation of the function in standard form is equal to -x²/4 + 1 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-3 = a(-4)² + b(-4) + c ⇒ -3 = 16a - 4b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
1 = a(0)² + b(0) + c ⇒ 1 = c .......equation 3.
Substituting the value of c into eqn. 1 and eqn. 2, we have:
-4 = 16a - 4b .......equation 4.
-1 = 4a - 2b .......equation 5.
Multiplying eqn. 5 by 2 and solving simultaneously, we have:
-4 = 16a - 4b
-2 = 8a - 4b
-2 = 8a
a = -2/8
a = -1/4
For the value of b, we have:
-1 = 4a - 2b
-1 = 4(-1/4) - 2b
-1 = -1 - 2b
2b = 0
b = 0
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-1/4x² + (0)x + 1 = 0
-x²/4 + 1 = 0
Check:
When x = 2, we have:
-x²/4 + 1 = 0
-2²/4 + 1 = 0
-4/4 + 1 = 0
-1 + 1 = 0
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Related Questions
(e) For what value(s) of x is f(x) = 0?
Answers
Step-by-step explanation:
For the value of x = 0 then the f(x) will became f(o) = 0
100 POINTS!!! Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Multiply or divide as indicated. Leave your answer with no factors in the denominator.
p^-4 q^5 r^6 / p^-3 qr^-2
Answers
Answer:
[tex]\dfrac{q^{4} r^8}{p}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}[/tex]
Separate the variables:
[tex]\implies\dfrac{p^{-4}}{p^{-3}} \times \dfrac{q^5}{q} \times \dfrac{r^6}{r^{-2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies p^{(-4-(-3)} \times q^{(5-1)} \times r^{(6-(-2)}[/tex]
[tex]\implies p^{(-4+3)} \times q^{(5-1)} \times r^{(6+2)}[/tex]
[tex]\implies p^{-1} \times q^{4} \times r^8[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{p} \times q^{4} \times r^8[/tex]
Simplify:
[tex]\implies \dfrac{q^{4} \times r^8}{p}[/tex]
[tex]\implies \dfrac{q^{4} r^8}{p}[/tex]
What is f(g(x) of f(x)=9x+2 and g(x)=x-2 over 9
Answers
The value of the composite function f(g(x)) is calculated as f(g(x)) = 65.
What is termed as the composite function?Composite functions is one in which one function is placed within another.
A composite function defines one that is reliant on another. A composite function is defined whenever one function is replaced for another. For example, the composite function constituted by substituting g(x) for x in f is f(g(x)) (x).f(g(x)) is spoken as "f оg(x)."For, the given values in the question;
f(x) = 9x+2 and g(x) = x-2
We have to find the value of f(g(x)) for x = 9.
First estimate the value of g(x) by substituting x = 9 in it.
g(x) = x-2
g(9) = 9-2 = 7
Now,
f(x) = 9x+2 and
f(g(x)) = f(7) = 9x+2, (substitute x = 7)
f(g(x)) = 9×7 + 2
f(g(x)) = 65.
Thus, the value of the composite function f(g(x)) = 65.
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Construct an angle of measure 45° with the help of a protractor. Bisect it and find the measure of the bisected angles .
Answers
Answer:
See attachment
Step-by-step explanation:
Draw a 45o angle
Bisecting means dividing the angle into 2 halves, which is 22.5o each
Select the lesser of The two given numbers -152, 12
Answers
Answer:
-152
Step-by-step explanation:
-152 < 12
-152 is negative, which means it is less than 1.
12 is positive, which means it is greater than 1.
Therefore, -152 is the lesser of the two given numbers.
Have a great rest of your day! :)
Hi!
-152 is less than 12, because:
It's negative, and 12 is positive!It's to the left of 12 on the number line![tex]\mathbb{NUMBER \ LINE}[/tex]
[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]
[tex]-152[/tex] [tex]12[/tex]
Cheers!
Have a nice day!
I hope this helps!
QUESTION 8 Nigel received a student loan for $9467. If his tuition was $4997.94, textbook costs $854.84, student fees $702.88, and school supplies $80.41, how much did Nigel have left after paying all his school related expenses? Round your answer to the nearest cent. 3 poin
Answers
4997.94
+ 854.84
——————
5852.78
+ 702.88
—————-
6555.66
+ 80.41
—————
6636.07
2. Subtract
9467.00
-6636.07
——————
2,830.93
If a family has 5 children, in how many ways can the parents have 2 boys and 3 girls as children?
Answers
Considering the definition of combination, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.
What is combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following expression is applied:
[tex]mCn=\frac{m!}{n!(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
Ways the parents have 2 boys and 3 girlsIf a family has 5 children, you can know that:
Among the 5 children, 3 are boys = 5C3 = [tex]\frac{5!}{3!(5-3)!}[/tex]= [tex]\frac{5!}{3!2!}[/tex]Among the 5 children, 2 are girls = 5C2 = [tex]\frac{5!}{2!(5-2)!}[/tex]= [tex]\frac{5!}{2!3!}[/tex]So, you can observe that 5C3 is equal to 5C2. Then:
5C3 = 5C2 = [tex]\frac{5!}{3!2!}[/tex]= 10
Finally, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.
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How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mpb? What is always true about the product speed x time?
Answers
The times associated with each speed are:
20 h10 h6.667 h5 h4 hIt is always true that the speed is inversely proportional to time.
How to analyze the motion of a bicycle at constant speed
In this case we find the situation of bicycle moving at constant speed, where the traveled distance (s), in miles, is equal to the following expression:
s = v · t (1)
Where:
v - Speed, in miles per hour.t - Time, in hourNow we proceed to calculate time needed for each speed:
t = s / v
Case 1
t = 100 mi / 5 mi / h
t = 20 h
Case 2
t = 100 mi / 10 mi / h
t = 10 h
Case 3
t = 100 mi / 15 mi / h
t = 6.667 h
Case 4
t = 100 mi / 20 mi / h
t = 5 h
Case 5
t = 100 mi / 25 mi / h
t = 4 h
According to the model for rectilinear uniform motion, the speed is inversely proportional to time.
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The dividen is greater that 1,000, The quotient of 52 with a remainder of 18
Answers
The minimum divisor such that the dividend is greater than 1000 and a quotient of 52 with a remainder of 18 is 18.86.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variable called division.
Let's consider a division problem.
5/2 → 2 + 1
Here 5 is called the dividend,2 is the divisor,2 is the quotient, and 1 is the remainder.
Now,
2 × 2 + 1 = 5
Therefore,divisor × quotient + remainder = dividend
So,
Let's suppose the divisor in the given case is x
Now,
52x + 18 ≥ 1000
52x ≥ 982
x ≥ 18.86
Hence "The minimum divisor such that the dividend is greater than 1000 and a quotient of 52 with a remainder of 18 is 18.86".
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The given question is incomplete complete question is ;
What is the minimum divisor such that The dividend is greater than 1,000, The quotient of 52 with a remainder of 18
At the movie theatre, child admission is $5.90 and adult admission is $9.00. On Saturday, 137 tickets were sold for a total sales of $1003.60. How many adult tickets were sold that day?
Answers
The number of adult tickets, that were sold that day at the movie theatre was 62
What are simultaneous equations?
Simultaneous equations are two or more equations that must be solved concurrently in order to derive the values of the unknown, the total sales, as well as the total number of tickets sold, can be modeled into equations as below:
let x be the number of adult tickets
let y be the number of children's tickets
9x+5.90y=1000.60....... equation 1
x+y=137.................. equation 2
solve for y in equation 2
y=137-x
substitute for y in equation 1
9x+5.90(137-x)=1000.60
9x+808.30-5.90x=1000.60
9x-5.90x=1000.60-808.30
3.10x=192.30
x=192.30/3.10
x=adult tickets=62
children tickets=137-62
children tickets=75
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express the following as percents a)15 girl out of 75 pupils
Answers
Zoey needs to order some new supplies for the restaurant where she works. The restaurant needs at least 711 glasses. There are currently 281 glasses. If each set on sale contains 10 glasses, use the drop-down menu below to write an inequality representing
s
s, the number of sets of glasses Zoey should buy
Answers
The inequality that represents the number of sets of glasses Zoey should buy is s ≥ 43
What is the inequality?The first step is to determine the number of glasses needed.
The number of glasses needed = 711 - 281 = 430
The second step is to determine the number of sets Zoey needs to buy.
Number of sets needed = 430 / 10 = 43 sets
The third step is to determine the appropriate inequality sign to use
Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe ≥ (greater than or equal to ) would be used since the number of sets can either be equal to or greater.
s ≥ 43
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How to solve x+5/-6= -4
Answers
x+5/-6= -4
multiply each side by -6
x-5/6= -4
*-6 *-6
x+5=24
subtract 5 from each side
x=19
Ronnie is playing a card game where the goal is to get the lowest possible score. In
the first round, Ronnie scored -6 points. In the second round, he scored -12 points.
What is Ronnie's total score
Answers
Buster's dog house is 3 feet long, 2 feet wide, and 2 feet high. how much space would there be if buster's house were twice as long
Answers
there woldbe 96 volume
Step-by-step explanation:
to find the volume you have to multiply width x lenghth x height
so set up your equation like this -
3 x 2 x 2
the times everything by 2 so it will now look like this -
6 x 4 x 4
then solve and get the answer 96
How long does it take $450 to double at a simple interest rate of 14%? Express your answer in months. Round to the nearest whole number.
Answers
The number of months so that the investment gets double will be 86 months.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on. The amount is given as,
A = P + (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
The principal amount is $450 and if the amount gets doubled, then the value of the amount will be $900. The simple interest rate is 14%. Then the time is given as,
A = P + (PRT)/100
900 = 450 + [450 x 14 x T] / 100
450 = 450 x 14 x T / 100
T = 100 / 14
T = 7.14 years
T = 7.14 x 12
T = 85.7 ≈ 86 months
The number of months so that the investment gets double will be 86 months.
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Write the expression. Then, check all that apply.
twice the difference of a number and six
Answers
The algebraic expression for the given statement is: 2(n - 6).
How to Write an Algebraic Expression?To translate the statement, "twice the difference of a number and six", follow the steps below:
The two operations we would use are multiplication and subtraction.
The constants are 2 and 6.
Twice is translated as 2 ×, (-) is "difference".
Let the number be "n" .
The difference of a number, n, and 6, would be: n - 6.
Therefore, we would have the following algebraic expression: 2(n - 6).
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The city of Raleigh has 10,300 registered voters. There are two candidates for City Council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 300 randomly selected registered voters was conducted. 9595 said they'd vote for Brown, 182 said they'd vote for Feliz, and 23 were undecided.
Answers
Answer:
What do I solve for?
Step-by-step explanation:
In the word grapefruit , the ratio of vowels to consonants is 2 : 3
Answers
Answer:
pineapple: 4:5strawberry: 3:7Step-by-step explanation:
You want the ratio of vowels to consonants in each of the words "pineapple" and "strawberry."
RatioTo form the reduced ratio vowels:consonants, we need to identify the type of letter each is. Here we use bold to identify the vowels.
pineapple ⇒ 4:5
strawberry ⇒ 3:7 . . . . counting "y" as a vowel
what is an equation of the line that passes through the points (0,8) and (5,2)
Answers
y=-3/2x+6
Step-by-step explanation:
You will need to find the equation of the line in slope-intercept form y=mx+b.
First, find the slope m using slope formula m = (y_2-y_1)/(x_2-x_1) which is m=(6-(-6))/(0-8)=-12/8=-3/2
Now that you found the slope, your equation intercept form looks like y=-3/2 x+b.
Both points (8, -6) and (0.6) belong to this line, therefore both points coordinates satisfy line above which means: 6=-3/2(0)+b (i used second point here)
Solving for b we will get y intercept which is b=6
Finally, the line that passes through points (8,-6) and (0,6) has equation: y=-3/2 x + 6
hopefully this helps! :)
1. The price of one kg grapes is 60p, find the total price of 30 kg grapes in pounds.
2. The price of one kg carrots is 35p, find the total price of 40-kg carrots in pounds.
3. The price of one kg grapes is 60p and the price of one kg bananas is 40p per kg, find the total price of 30 kg grapes and 40kg bananas in pounds.
4. The price of one kg oranges is 90p and the price of bananas is 30p per kg, find the total price of 30 kg oranges and 40kg bananas in pounds
Answers
Maths:
Round 1
1) Grapes cost £1.50 per kg and carrots cost £1.00 per kg. How much would it costs for 3kg of
grapes and half a kilogram of carrots? £5
2) Jenny decides to share her sweets between herself and her 3 friends. She has 212 green
sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jenny and her friends
get each? 256
3) Large chocolate bars come with 32 pieces. Medium chocolate bars come with 24 pieces.
Barry buys 8 large bars of chocolate and 6 medium bars. How many pieces of chocolate will he
have altogether? 400
4) A flower shop sells roses for £1.79, carnations for £1.25 and buttercups for £1.30. Holly
decides to buy 3 roses and a buttercup. How much does she spend? £6.67
5) Pencils come in packs of 12 and each pack costs £1.19. Mr Green needs to buy a pencil for
each of the 50 children in his class. How much will he spend on pencils? £5.95
Round 2
1) Mrs Orange decides to share her savings between her six grandchildren. She has £350 in
her savings tin and £1450 in her savings account. How much will each of her grandchildren get?
£300
2) Green lollipops come in packs of 5, yellow lollipops come in packs of 6 and blue lollipops
come in packs of 4. A school buys 32 packs of blue lollipops and 18 packs of green lollipops.
How many lollipops will they buy altogether? 218
3) The baker’s oven can bake 28 loaves of bread at a time. In a day, it can go through 30 full
bakes. How many loaves of bread would be baked after 1 week? 5880
4) Ms Purple sells cars for a living. In one day, she sells 2 blue cars (at £4500 each), 7 yellow
cars (at £6000 each) and 12 black cars (at £8000 each). How much money does she take in car
sales in that one day? £147,000
5) Coaches carry 58 people. A school decides to take its 300 pupils and 38 staff on a visit to the
beach. A single coach costs £128. How much will the total cost of the coaches come to? £768
Topic:
Fruit Veg
Quince
raspberry
Lettuce
garlic
tomato
strawberry
grape
pumpkin
blackberries
nashi
kiwi
chilli
pear
passion fruit
cantaloupe
fig
eggplant/aubergine
cucumber
lemon
peach
lime
watermelon
pineapple
Zucchini/courgette
grapefruit
persimmons
mango
plum
cauliflower
Broccoli
Leeks
Fennel
Carrots
Coriander
Silverbeet
Snow peas
Beans
Celery
Beetroot
Peas
Artichoke
Sweet potato
A rental car company charges $71.02 per day to rent a car and $0.12 for every mile
driven. Lily wants to rent a car, knowing that:
She plans to drive 475 miles.
. She has at most $390 to spend.
.
What is the maximum number of days that Lily can rent the car while staying within
her budget?
Answers
Answer:
Step-by-step explanation:
4 is the maximum number of days.
Using Inequality, the maximum number of days that Lily can rent the car while staying within her budget is 4 days.
How to find the maximum number of days she can rent the car?The rental car company charges $71.02 per day to rent a car and $0.12 for every mile driven.
Lily wants to rent a car and she plans to drive 475 miles. She has a budget of $390.
Therefore, the maximum number of days that Lily can rent the car while staying within her budget can be calculated as follows:
Using inequality,
total cost = 71.02(x) + 0.12(y)
where
x = number of days
y = number of miles
Therefore,
71.02x + 0.12(475) ≤ 390
71.02x ≤ 390 - 57
71.02x ≤ 333
x ≤ 333 / 71.02
x ≤ 4.68882005069
Therefore,
she can drive maximum of 4 days.
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If angle YXZ measures 90 degrees, which statement is true?
(answers are below)
segment XZ is perpendicular to segment WY
WX =XY
segment XZ is a perpendicular bisector of segment WY
X is the midpoint of segment WY
Answers
The true statement about the given diagram is: A. segment XZ is perpendicular to segment WY.
What are Perpendicular Segments?Perpendicular segments are line segments that intersect at a point to form right angles which is equal to 90 degrees. The point where perpendicular segments meet have an angle measure of 90 degrees.
In the given diagram, we are told that angle YXZ is equal to 90 degrees. This means that at the point where segment XZ and segment WY meet have an angle measure of 90 degrees.
This means they are perpendicular segments.
Therefore, the true statement about the given diagram is: A. segment XZ is perpendicular to segment WY.
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Vicente is investing money into a savings account that pays 3% simple interest, and plans to leave it there for 10 years. Determine what Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years.
Answers
The amount Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years is $15,384.62
What is simple interest?
The simple interest on the savings is determined as the deposit multiplied by the annual interest rate and the number of years that deposit would last in the account
I=PRT
I=simple interest
P=principal=deposit=unknown
R=annual simple interest=3%
T=number of years=10
A(amount in 10 years)=P+PRT
A=P(1+RT)
$20,000=P(1+3%*10)
$20,000=P*1.30
P=$20,000/1.30
P=$15,384.62
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Please help solve number 24
Answers
Check out the attached photo
expressions that have 2\3 as a product.
Answers
The expression that have 2\3 as a product are 4/5 × 5/6 and 6/7 × 7/9 which is option (a) and (e) .
An expression in maths could be a sentence with a minimum of 2 numbers/variables and a minimum of one maths operation in it.An expression could be a combination of terms that are combined by victimization mathematical operations like subtraction, addition, multiplication, and division.(a) 4/5 × 5/6 = 20/30
= 2 /3
(b) 7/8 × 9/10 = 63 / 80
(c) 1/3 × 2/3 = 2 /9
(d) 3/4 × 7/12 = 21 / 48
= 7 / 16
(e) 6/7 × 7/9 = 42 /63
= 6 / 9
= 2 / 3
Only the expression (a) and (e) have 2\3 as a product.
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The complete question is given below :
Choose all the expressions that have 2\3 as a product.
(a) 4/5 × 5/6
(b) 7/8 × 9/10
(c) 1/3 × 2/3
(d) 3/4 × 7/12
(e) 6/7 × 7/9
It is the end of the budgeting period for John Smith, and he has $500 left in his budget for car rental expenses. He plans to spend this budget on a sales trip throughout the country. He will rent a car that costs $50 per day and $ 0.50per mile, and he can spend no more than 500
Answers
The number of miles that John Smith can travel with his budget if he has $500 left in his budget for car rental expenses is 900 miles.
How to calculate the expression?Amount left in the budget = $500
Since he will rent a car that costs $50 per day and $ 0.50per mile, the expression will be:
50 + 0.50m = 500
where m = number of miles
Collect like terms
0.5m = 500 - 50
0.5m = 450
Divide
m = 450/0.5
m = 900
Therefore, the number of miles that John Smith can travel with his budget is 900 miles.
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Answer for this please see image attached m
Answers
3x+18
-18. -18
3x=162
x=54
54+11=65=a
54+7=61=c
b=54
If it is asking you for the whole triangle then 180, all triangles equal 180 degrees
Answer:
angle A=125 angle B= 114 angle C= 121
Step-by-step explanation:
first you have to find x so that you can find each angle
the interior angles of a triangle is equal to 360
add the angles together x+x+7+x+11=360
combine like terms 3x+18=360
subtract 18 on both sides 3x=342
divide by 3 on both sides x=114
to find angles:
plug in X to each side
(114)+7 = angle C
(114)+11= angle A
114= angle B
Identify the y-intercept for each function and determine which function has the greater y-intercept. Please help me!
Answers
In Florida, as of Nov 19, 1,020,000 had people tested positive for corona virus. This was a
0.18% increase from the previous day. If that percent increase continued, how many people
would be infected on Dec 19th?
Answers
The number of people that would be infected on Dec 19th, based on the daily growth rate of 0.18% is 1,076,542
What is interval in days between Nov. 19th and Dec.19th?
The interval between November 19th and December 19th is a period of 30 days, since there are 11 more days in November and 19days in December, in essence, using the future value formula, we can compute the number of people tested positive for corona virus on 19th December as shown below:
FV=PV*(1+g)^N
FV=number of people tested positive for corona virus on 19th Dec.=unknown
PV=number of people tested positive for corona virus on Nov. 19th=1,020,000
g=growth rate=0.18%
N=number of days between 19th Nov. and Dec.
FV=1,020,000*(1+0.18%)^30
FV= 1,076,542
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