The quadratic function has an equation of f(x) = -2x² - 4x - 3
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(−1,−1), (2,−19), and (3,−33).
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (-1, -1), we have
a(-1)²+ b(-1) + c = -1
So, we have
a - b + c = -1
Using the point (2, -19), we have
a(2)²+ b(2) + c = -19
So, we have
4a + 2b + c = -19
Using the point (3, -33), we have
a(3)²+ b(3) + c = -33
So, we have
9a + 3b + c = -33
So, we have
a - b + c = -1
4a + 2b + c = -19
9a + 3b + c = -33
Using a graphing tool, we have
a = -2, b = -4 and c = -3
Substitute a = -2, b = -4 and c = -3 in f(x) = ax²+ bx + c
So, we have
f(x) = -2x² - 4x - 3
Hence, the equation is f(x) = -2x² - 4x - 3
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victor had a goal of making a 90 on each of his math tests. at the end of the year, he was within 5 points of his goal for each test. what are the maximum and minimum scores that he could have received?
Answer: he could have gotten 100 or 0
Step-by-step explanation: he could have had alot of tests and gotten 100 on all of them to even out the one zero.
its takes 8 lemons and 18 cups of water to make lemonade. You have one lemon. How many water do you need to make lemonade?
How many cups of water do you need to make lemonade? 9/4 cups
How is the number of cups calculated?
Given:
8 lemons need =18 cups of water
1 lemon needs= x cups of water
By cross- multiplication method,
[tex]\frac{8}{1} =\frac{18}{x}[/tex]
8x = 18
x = 18/8
= 9/4 cups of water is needed to make lemonade
What is the cross- multiplication method?
In the cross multiplication method, we multiply the numerator of one fraction by its denominator and the first term's denominator by its numerator. We employ the cross multiplication approach to locate the answers to two linear equations.Cross-multiplication can be used to compare unlike fractions.To learn more about cross- multiplication method, refer:
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how is a circle square and triangle related?
In order to depict alchemy and the philosopher's stone, which is the ultimate goal of alchemy, a sign of a circle within a square within a triangle within a larger circle started to be used in the 17th century.
What do the symbols for a circle, triangle, and square mean?
It has deep philosophy where a circle symbolizes heaven and represents number one, a square represents earth and represents number two, and a triangle represents people and represents number three.
An enduring representation of good fortune, the triangle enclosed within a circle was thought to stave off evil spirits. It was accepted by Alcoholics Anonymous as a symbol of a person's transition from an alcohol preoccupation to a life saturated with the triangle of Recovery, Unity, and Service.
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Angel and his children went into a restaurant and will buy hotdogs and drinks. Each
hotdog costs $5 and each drink costs $1.50. Angel has a total of $50 to spend on
hotdogs and drinks. Write an inequality that would represent the possible values for
the number of hotdogs purchased, h, and the number of drinks purchased, d.
Considering the definition of an inequality, an inequality that represent the possible values for the number of hotdogs purchased and the number of drinks purchased is 5h + 1.50d≤ 50.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values, in addition to certain known data.
Inequality in this caseIn this case, you know that:
Each hotdog costs $5 and each drink costs $1.50. Angel has a total of $50 to spend on hotdogs and drinks.Being:
"h" the number of hotdogs purchased."d" the number of drinks purchased.the inequality that expresses the previous relationship is
5h + 1.50d≤ 50
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Tia rounds a number, x, to 3 sf.
The result is 7.68.
Write the error interval for x in the form a ≤
x < b.
If Tia rounds a number, x, to 3 sf and the result is 7.68. the error interval for x in the form a ≤ x < b is 7.685 ≤ x ≤ 7.684
What is error interval?The accuracy thresholds that apply when a number has been rounded or truncated are known as error intervals. In other words, they represent the range of values that a number might have taken had it not been rounded off or truncated.
To do this, we consider the smallest and largest numbers that could be rounded or truncated to a value while maintaining a certain level of accuracy.
We know that if this digit is smaller than 5, then we round down.
Then the largest number that can be rounded down to 7.68 is:
7.684
Now we want to find the smallest number that can be rounded up to 7.68
We know that if the next digit is 5 or bigger, then we round up.
Then the number 7.685 is rounded up to 7.68
Then the error interval is:
7.685 ≤ x ≤ 7.684
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Match the ratio of side lengths to its corresponding anglemeasure.
Consider the formulae from Inverse Trigonometry,
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Hypotenuse}}) \\ \theta=\tan ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Adjacent Leg}}) \\ \theta=\cos ^{-1}(\frac{\text{ Adjacent Leg}}{\text{ Hypotenuse}}) \end{gathered}[/tex]Solve for the first angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.139) \\ \theta\approx82^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 82 degrees approximately.
Solve for the second angle as,
[tex]\begin{gathered} \theta=\tan ^{-1}(0.249) \\ \theta\approx14^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 14 degrees approximately.
Solve for the third angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.469) \\ \theta\approx28^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 28degrees approximately.
Solve for the fourth angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.682) \\ \theta\approx47^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 47 degrees approximately.
Solve for the fifth angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.848) \\ \theta\approx58^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 58 degrees approximately.
Using the SSS congruence criterion, what additional information is needed to show that ARST AUTS?
51 points composite functions need help soon
Answer:
(f∘g)(12) = 24
Step-by-step explanation:
Pre-SolvingWe are given the functions f(x)=4x+8 and [tex]g(x)=\sqrt{x+4}[/tex]. We want to find (f∘g)(12).
(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).
SolvingFirst, we find g(12). To do this, substitute x as 12.
[tex]g(12) = \sqrt{12 + 4}[/tex]
Add 12 and 4 together under the radical.
[tex]g(12) = \sqrt{16}[/tex]
Take the square root of 16.
g(12) = 4
Now, substitute 4 as x in f(x) = 4x + 8.
f(4) = 4(4) + 8
Multiply.
f(4) = 16 + 8
Add 16 and 8 together.
f(4) = 24
f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).
Therefore, (f∘g)(12) is 24.
The Federal form 1040 is used by whom to file taxes?
O Individuals
O Companies
O Law Enforcement
O Nonprofit Organizations
Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent.
From 68 to 63
The percentage increase is 7.9 %.
The given numbers are 68 and 63.
What is the percent change?Percentage change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.
Here, old value = 63 and new value = 68
Difference = 68-63 =5
Percentage increase = Difference of old value and new value ÷ old value
= 5/63 × 100
= 0.0793 × 100
= 7.93 %
≈ 7.9 %
Therefore, the percentage increase is 7.9 %.
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mcdonald's claims that their monopoly game has a win rate of 25%. if you play the game 500 times, what is the probability that your win rate will be between 21% and 23%?
The required probability is 0.132 .
What is normal approximation?
The sampling distribution of averages or proportions from a large number of independent trials approximately and the expectation of a sample proportion or average is the corresponding population value.
On solving using mean sampling method, we get
P(E) = 0.132
Hence, the required probability is 0.132 .
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what two numbers make a product of 50 and a sum of -15?
the diagram shows triangle ABC. D is on the point AB such that CD is perpendicular to AB. AC=9.4cm, AD=5.2cm and BD=7.8cm. Work out the size of angle ABC.
Answer:
45°
Step-by-step explanation:
Triangles ADC and BDC are right triangles, since CD⊥AB.
Use Pythagorean to find the length of CD:
CD² + AD² = AC²CD² + 5.2² = 9.4²CD² = 9.4² - 5.2²CD² = 61.32CD = √61.32CD = 7.83Use trigonometry to find the angle ABC:
tan (∠ABC) = CD/BDtan (∠ABC) = 7.83/7.8tan (∠ABC) = 1.0 (rounded)m∠ABC = arctan 1m∠ABC = 45°The accurate scale drawing shows a car and a lamp post.
The car has a real width of 1.5 metres.
Find an estimate for the real height, in metres of the lamp post.
An estimate of the real height of the lamp post is 9m.
What is the estimate of the real height?The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm
Scale = length of the lamp post / height of the car
10.8 / 1.8 = 6
Now, multiply the scale by the width of the car.
The real height of the lamp post = 6 x 1.5 = 9m
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WILL GIVE BRAINLIEST
Write an equation of the parabola that passes through the points (1, – 9), (0, – 8), and (2, -8).
Answer: y = x^2 - 2x - 8
Step-by-step explanation:
Reasonableness
Lexi subtracts 9,405 from 11,138.
Should her answer be greater than or less than 2,000?
Explain.
(Help meeee)
Answer:
I believe that it should be less than 2,000.
Step-by-step explanation:
11038 < 11405 = 9405 + 2000
11038 - 9405 < 2000
May you guys/girls please help me I have to submit this before mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
y =-0.25x + (-6)
Step-by-step explanation:
crosses y axis at -6 so that's your y-intercept
to find gradient use change in y / change in x
so make a triangle -1 / 4 = -0.25
PLEASE HELP ME ON THIS
A ball is thrown in the air the function h = 30t-5t^2 can be used to find the height (h) of the ball in meters after t seconds.
how long does it take the ball to reach a height of 45 meters?
This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t2 + 45.
How can one determine a function's maximum height?
The vertex, which is a maximum (or minimum) in a parabola, can be located by solving the square (yuck!) or by using the formula x = -b/2a. By re-entering the original equation with this x value as the vertex's x, we can determine the appropriate maximum height.
By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can get the height of the item of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 meters if theta is 50 degrees and D is 40 meters.
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Torrie has $430 and Sonia has $760. John has the same number of dollars more than Torrie as he has less than Sonia.How much money does John have?
John has $595 in his possession.
An algebraic expression is what?An expression that has been created utilizing integers, constants, variables, and algebraic operations is known as an algebraic expression.
For instance, [tex]x^{2} + 2x + 2[/tex]
2x + 3
etc
The answer to the query is
John has the same amount of more money over Torrie as he has under Sonia.
Let's suppose it is $x since John has the same amount of money more than Torrie as he has less than Sonia.
Case 1
Actual amount that John has is $430 plus $x.
Case 2
Actual amount that John has is $760 less $x.
⇒ $430 + $x = $760 - $x
⇒ $2x = $330
⇒ $x = $165
John currently possesses $595 ($760 - $x) or ($430 + $x) in his possession.
John therefore has $595 in his bank account.
The amount of money that john has is $595
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N
2.
Find the area of each sector. Round your answer to the nearest tenth.
1.
sector PQR
29
R
sector JKL
8 cm 135°
K
6m
P
90°
L
Area =
Area =
1 0.7
2 1.6
m²
cm²
3 28.7
4 75.4
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =135 \end{cases}\implies A=\cfrac{(135)\pi (8)^2}{360}\implies A=24\pi \implies A\approx 75.4[/tex]
40 push-ups in 5 days =
push-ups in 6 days
Answer:
48 push-ups
Step-by-step explanation:
40 to 5 = 48 to 6
prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called
Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.
What is extrapolation of data?In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.
One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.
In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.
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How do you reflect the image over the x-axis
The coordinates of the image of any point P(x, y), from any geometric locus, after being reflected over the x-axis.
How to reflect any geometric locus over the x-axis
Geometric loci are geometrical constructions formed by one or more points, these may represent a point or a figure formed by finite or infinite set of points.
Let P(x, y) = (x, y) a point of the geometric locus, which has to be modified by using reflection over the x-axis. This can done by adding the vector (- 2 · x, 0) to the vector P(x, y):
P'(x, y) = P(x, y) + (- 2 · x, 0)
P'(x, y) = (x, y) + (- 2 · x, 0)
P'(x, y) = (- x, y)
Where P'(x, y) is the image of point P, from any geometric locus, after making the reflection over the x-axis.
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1. The area of a rectangle is 45.5 square inches. The base of the rectangle is 7 inches. What is the height of the rectangle in inches?
2. A pharmacist put 4.536 ounces of vitamin pills into bottles in total. She put 0.043 ounces of vitamin pills into each bottle. How many bottles did the pharmacist use for these vitamin pills?
3. A baby weighed 7.25 lb at birth. At the end of 8 months, the baby weighed 2 3/4 times its birth weight. How many pounds did the baby weigh at the end of 8 months? Round your answer to the nearest tenth.
4. A recipe for cookies requires 2/3 cup of butter.
Rama wants to make 3/4 of the recipe. How many cups of butter should Rama use to make the cookies?
5. Ryan had a whole pizza. He ate 1/8 of the pizza for lunch and another 1/4 of the pizza for dinner. Write the fraction that represents how much of the pizza Ryan did not eat.
6. A sea turtle made 460 dives in 12 hours. At this rate, how many dives did the sea turtle make in 3 hours?
Also, can you help with the expression, solution, and work?
Using given area and base length of a rectangle we got that the height of the given rectangle is 6.5 inches.
What is the area of a rectangle?Rectangle is closed geometric figure that has four perpendicular sides with opposite sides equal.
The formula for the area of the rectangle :
Area of the rectangle = Length × Breadth
Given that the area of a rectangle is 45.5 square inches.
The base of the rectangle is given 7 inches
To find : Height of the rectangle
Let the base length is the length of the rectangle and height is the Breadth of the rectangle.
Then, Area of the rectangle = Length × Breadth
⇒ 45.5 = 7 × Height
⇒ 45.5 /7 = Height
⇒ 6.5 = Height of the rectangle
Therefore, the height of the rectangle is 6.5 inches.
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2w - 15w - 18 = -83 solve for w simplify as much as possible
Answer:
w = 5
Step-by-step explanation:
2w - 15w - 18 = -83
combine w on left side:
-13w - 18 = -83
add 18 to both sides:
-13w - 18 + 18 = -83 + 18
-13w = -65
divide both sides by -13:
-13w/-13 = -65/-13
w = 5
what is 12 times 12 i just need to know
Answer:
144
Step-by-step explanation:
12 * 12 = 144
Answer:
It's 144.
..............
5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7?
Answer:
Here is your answer So I did the Step for you and By the way I'm from South Africa
Answer: 7
Step-by-step explanation:
5*⁵(22-²9*¹2)-⁷2*⁶(3*³2+⁴4)+⁸7=7
1)9*2=18
2)22-18=4
3)3*2=6
4)6+4=10
5)5*4=20
6)2*10=20
7)20-20=0
8)0+7=7
What is the slope of the line?
Answer:
-7/4 seeing how the line touches -3,4 and 1, -3 only it goes down 7 and 3 to the right
Step-by-step explanation:
sub to imagine fn
How to solve? 14x(4x + y)
Answer:
| 56x² + 14xy
Step-by-step explanation:
14x(4x + y)
Apply the Distributive Property
14x x 4x + 14xy
Multiply the monomials
56x² + 14xy
Apply the distributive property on 4x + y, distributing 14x.
14x(4x + y)
(14x x 4x) + (14x x y)
56x + 14xy
Donnie writes an absolute value equation to determine the values that are 0.8 units from 3.5.
What equation does Donnie write and what values does he find?
Enter your answer in decimal form by filling in the boxes.
Absolute value equation |x- ___ | = ___
The values that are 0.8 units from 3.5 are ___ and ___
The absolute value equation which correctly represents the situation as described is; | x- 3.5 | = 0.8.
The values which are 0.8 units from 3.5 as given are therefore; 4.3 and 2.7.
What values are 0.8 units from 3.5 as described in the task content?It follows from the task content that the numbers which are 0.8 units away from 3.5 on the number line be determined.
On this note, the correct representation of the situation above involves an absolute value equation such that;
| x- 3.5 | = 0.8
Hence, to solve the equation; (x- 3.5) = 0.8 OR (x- 3.5) = -0.8.
x = 0.8 + 3.5. OR. x = -0.8 + 3.5
x = 4.3 OR x = 2.7.
Ultimately, the required values are; 4.3 and 2.7.
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