The standard equation is: y = (-2)x² + 8x + 5
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0, with a ≠ 0 .
We know,
y = ax² + bx + c
For (-1, -5)
-5 = a - b + c..................(1)
For (0, 5)
5 = c
For (1, 11)
11 = a + b + c.....................(2)
From (1) and (2), we get
a=-2
and b= 8
Hence, the standard equation is:
y = (-2)x² + 8x + 5
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4. What is the slope of the line that passes through the points (2, 7) and (6, 21)? Answer may be in decimal
point. Someone please please help I would really appreciate it
Answer:
About 3.5
Step-by-step explanation:
To get slope, you essentially need to find the rise (the y values) over run (the x values). You'll most likely see the formula for slope written like this:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Thankfully, you have the values you need to solve the problem!
x1 = 2
x2 = 6
y1 = 7
y2 = 21
So plugging these numbers in, we get:
[tex] \frac{(21) - (7)}{(6) - (2)} \\ \\ \frac{14}{4} \\ \\ 3.5 [/tex]
[EDIT: I misread 6 as 5. Answer has been updated!]
A test is worth of 150 points and contains 70 questions. Some questions are worth 2 points, and some are worth 4 points
2x + 4y = 150
Answer:
65 2 point questions, 5 4 point questions
Step-by-step explanation:
write a system of equations:
let x be the number of 2 point questions and y be the number of 4 point questions
2x + 4y = 150
x + y = 70 (since there are 70 total questions)
x + y = 70
subtract x from both sides
y = -x + 70
substitute y = -x + 70 into 2x + 4y = 150
2x + 4(-x + 70) = 150
2x - 4x + 280 = 150
-2x = -130
x = 65
substitute x = 65 into x + y = 70
65 + y = 70
subtract 65 from both sides
y = 5
2
A B
-10-9-8
5
Point A
Point B
Point C
Point D
6
ch point on the number line represents the product (-4)(-2)(-1)?
8
012
9
10
C D
5 6 7 8 9 10
59:3
We can actually deduce here that the point on the number line that represents the product (-4)(-2)(-1): -8.
What is number line?Number line is actually known to be a horizontal or vertical line that is graduated with both negative and positive numbers. A number line is known to have both negative and positive numbers.
We see here that if we multiply out the brackets, (-4)(-2)(-1) = (8)(-1) = -8.
Thus, the answer is -8.
See attached image.
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What is the result of adding the system of equations? Equation 1: 2x + y = 4 Equation 2: 3x - y = 6 A) 5x = 10 B) x = 5 C) x = 10
An equation is formed of two equal expressions. The correct option is A, the sum will be equal to 5x = 10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two systems of equations Equation1: 2x+y=4 and Equation 2: 3x-y=6. Now if the two of the given equations are added the result will be,
2x + y + 3x - y = 4 + 6
5x = 10
Hence, the correct option is A, the sum will be equal to 5x = 10.
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Translate the following statements into algebraic expressions.
One-half of the sum of 8 and x.
Answer:
1/2(8 + x)
Step-by-step explanation:
In this statement, it tells us to add 8 and x and then multiply that with 1/2.
5. In an arithmetic sequence, the fifth term is 44 and the ninth term is 80.(a) Find the common difference. (b) Find the first term. (c) Find the sum of the first 50 terms of the sequence.
Step-by-step explanation:
first you should do is that find the common difference which is 9
g(t)=2.0.4^t for t = -2
Answer:
2(0.4)^-2 = 12.5
Step-by-step explanation:
do math noob
Mason can type 210 words in 6 minutes. find the unit rate ( words per mintute )
Answer:
Step-by-step explanation:
words type per minute =210/6
=35
find the value of a from the following 1. tan3a=cot2a
The value of a is 14.
What is Trigonometry?
The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
tan3a=cot2a
tan 3a= tan (90- 2a)
On comparing
3a= 90- 2a
5a= 90
a= 14
Hence, the value of a is 14.
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Solve the following please:
Answer:
most likely b
Step-by-step explanation:
the more than symbol tells me that it is going to move past 10.
Find the value of x.
Answer:
x = 20°
Step-by-step explanation:
(4x-10)+x=90
4x-10+x=90
4x+x-10=90
5x-10=90
5x=100
x=20
Answer:
20
Step-by-step explanation:
Straight line angles:
Angles on a straight line add up to 180°.
90 + 4x - 10 + x = 180
90 - 10 + 4x + x = 180
Combine like terms.
80 + 5x = 180
Subtract 80 from both sides,
5x = 180 - 80
5x = 100
Divide both sides by 5
x = 100 ÷ 5
[tex]\sf \boxed{x = 20^\circ}[/tex]
Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74000 miles and a standard deviation of miles. these tires come with a -mile warranty. the manufacturer of the tires can adjust during the production process, but the adjustment of is quite costly. the manufacturer wants to set once and for all so that only of the tires will fail before warranty expires. find the standard deviation to be set. carry your intermediate computations to at least four decimal places. round your answer to at least one decimal place.
The standard deviation will be 6816.9645.
How to compute the standard deviation?From the information given, the mean is 74000 and X is given as 60000.
P[(Z < (-60000 - 74000)/SD] = 0.02
Note that 0.02 will be -2.0537 under the normal distribution table.
-14000/SD = -2.0537
SD = -14000/-2.0537
SD = 6816.9645
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The sum of 8 and a number is less than 15. Which of the following
inequalities expresses the solution?
The inequality which expresses the solution to the task is; x < 7.
Which inequality expresses the solution to the graph?According to the task content; The sum of 8 and a number is less than 15. Therefore, it follows that;
let
The unknown number = x
sum of 8 and a number:
8 + x
sum of 8 and a number is less than 15:
8 + x < 15
x < 15 -8
x < 7.
Ultimately, the required inequality is; x < 7.
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It is known that 10 workers take 30 days to complete a project. They start working and the next day one quits. the next another, the third day another, and so on until the sixth day when they are left alone 5 workers. How many days will it take those 5 workers to finish the job?
Answer:
5 workers finish this work in 60 daysStep by step explanation:
The problem tells us that at the end of the day, there are only 5 workers left, which we must find how many days it takes to finish said work.
We start by finding the type of proportionality we have.
In this case, we have that the more workers there are, they will finish that work in less time, and the fewer workers there are, the longer it will take to finish the work. This is the inverse proportionality, to more less, to less more.
We have only 5 workers left.
In the first case there are 10 workers, and in the second case there are 5 workers left. We find the relationship between the workers in the second case among the workers in the first case.
Ratio = 5 workers / 10 workers = 1/2We see that the time is found by dividing the number of days in which the 10 workers finish the work, by 1/2.
As we know, dividing two fractions is the SAME as multiplying by the inverse fraction.
[tex]\rm 30 * 2/1 \: = 60 \: days[/tex]
By so
5 workers finish this work in 60 daysDrag a statement or reason to each box to complete this proof.
If −3(x+8)=−21, then x=−1.
(Please refer to attached image for more info.)
Answer:
1. -3(x+8) = -21
2. Division property of equality
3. x + 8 = 7
4. Subtraction Property of Equality
(Not quite sure whether #2 is division or distributive, but i'm 90% sure it's division).
The jet stream is traveling nearly due south from Wyoming to Colorado at 110 knots. If the plane’s speed is 400 knots, what will be its ground speed if it travels from Wyoming to Colorado?
Considering the direction of the wind, it is found that the ground speed needs to be of 510 knots.
What is the ground speed?The ground speed, considering that the wind is flowing from Wyoming to Colorado, and the same direction as the trip, is given by:
G = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 400 knots.Wind: 110 knots.Hence the ground speed is given by:
G = 400 + 110 = 510 knots.
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Which of the equations have only 1 solution -5x+12=5x-5
Answer:
in the pic...
Step-by-step explanation:
Hope it Helps!!!
Please help! Evaluate the following expression:
4+ (8x √9) ÷ (2+4)
A. 6
B. 28/6
C. 8
D. 15/6
Answer:
the answer to the question is C) 8
Assuming no air resistance, how long would it
take a skydiver to fall 180 feet? (Estimate
your answer to one decimal place. Hint: Use the
equation d = 16+²)
Using the given equation, the time it would take for the skydiver to fall 180 feet is of 3.35 seconds.
What is the height considering no air resistance?The height in feet that a person has fallen after t seconds is given by:
d = 16t².
In this problem, we want the time for a fall of 180 feet, hence.
[tex]16t^2 = 180[/tex]
[tex]t = \sqrt{\frac{180}{16}}[/tex]
t = 3.35
The time it would take for the skydiver to fall 180 feet is of 3.35 seconds.
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Construct a regular hexagon inscribed in a circle. Please help.
Answer:
no lo sd
Step-by-step explanation:
solo se que is really
In what? desmos, drawing?
What is the quotient in scientific notation?
The function h(x) is a transformation of the square root parent function,
f(x)=√x. What function is h(x)?
-5
5
-5-
h(x)
f(x)
K
I
5
The function h(x) is a transformation of the square root parent function,
f(x)=√x. The function is h(x) A: √x+5.
What is Transformations?Transformations come in the form;
y =√(x-h) +k,
where h is responsible for left-right movements, and k is responsible for up-down movements.
From the graph, we can see that f(x) is simply the parent square root function, √x.
To translate a function right by p units and up by q units, the function becomes
g(x) = f(x -p) +q
(p, q) = (5, 0)
To get h(x), there is a translation of 5 units to the left, which can be represented by a value of h = -5.
h(x) = f(x + 5) +0
h(x) = √(x+ 5)
Hence, The function h(x) is a transformation of the square root parent function, f(x)=√x. The function is h(x) A: √x+5.
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square
for the following equation? 4x^2+64x+467=15
The intermediate step in the following equation is (4x + 16)² = - 196
What is an Equation ?An Equation is the mathematical statement formed when two algebraic expressions are equated using an equal sign.
The given equation is
4x² +64x+467 = 15
4x² + 2 * 2x *16 + 256 -256 +467 = 15
(4x + 16)² +211 = 15
(4x + 16)² = - 196
Therefore the intermediate step in the following equation is
(4x + 16)² = - 196
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HEEEEEEEELLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
6
Step-by-step explanation:
This problem centers on recognizing the relationship between fractions and repeating decimals.
Note the following:
[tex]\frac{1}{3}=0.33333333333333333333333333333333333333333333333...[/tex]
or more simply [tex]\frac{1}{3}=0.\bar{3}[/tex]
This means that [tex]2\frac{1}{3}=2.\bar{3}[/tex]
Going back to the original expression, [tex]3\frac{2}{3}+2.\bar{3}[/tex] simplifies to [tex]3\frac{2}{3}+2\frac{1}{3}[/tex]
Next, adding mixed numbers. For adding mixed numbers, whole number parts and fractional parts can be added separately (this is because of the associative and commutative properties of addition)... because
[tex]3\frac{2}{3}+2\frac{1}{3}[/tex] means the same thing as
[tex](3+\frac{2}{3})+(2+\frac{1}{3})[/tex]
Changing the order, we can write it as
[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]
Adding the whole number parts, 3+2 is 5.
Next, adding the fraction parts:
For adding fractions, one must have a common denominator (the bottom part of the fraction must be the same). Once they are the same, the denominator just sort of "hangs out" until the end without changing, and the numerators (the tops) are added together.
Fortunately, the denominators are already the same. So, add the numerators, and the denominator will stay as a 3.
[tex]\frac{2}{3}+\frac{1}{3}[/tex]
[tex]\frac{1+2}{3}[/tex]
[tex]\frac{3}{3}[/tex]
It is important to recognize that any fraction* where the number on the top matches the number on the bottom, the fraction is equivalent to 1.
*(except if the number we're talking about is zero)
So, the fraction parts added together, are equivalent to 1, and the whole number parts added were equal to 5. Returning to our expression...
[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]
[tex]5+\frac{3}{3}[/tex]
[tex]5+1[/tex]
[tex]6[/tex]
A _______ random variable has infinitely many values associated with measurements.
Answer:
continuous random variable
The boarding platform of a Ferris wheel is 4 meters above the ground and the Ferris wheel is 24 meters in diameter and spins once every 7 minutes. How many minutes of the ride are spent higher than 22 meters above the ground
The number of minutes of the ride that are spent higher than 22 meters above the ground is; 2.64 minutes
How to find the number of revolutions?We are given;
bottom of the Ferris Wheel is 4 meters off the ground.
Radius = diameter/2 = 24/2; r = 12 meters.
Thus, the center of the Ferris Wheel is 4 + 12 = 16 meters off the ground.
A horizontal line through the center of the Ferris Wheel is 16 meters off the ground, and therefore the lower half of the Ferris Wheel is always below 22meters.
The distance from the horizontal to 22 meters is 22 - 16 = 6 meters.
The angle between the horizontal and a radius to 22 meters is;
sin(θ) = 6/16
θ = sin⁻¹(6/16)
θ = 22.02°.
This angle height is on both sides of the Ferris Wheel and as such;
180° + (2 * 22.02) = 224.04° is always under 16 meters.
Thus, what is above 16 meters is 360° - 224.04° = 135.96°
Since it takes 7 minutes for 1 revolution, then the amount of time the Ferris Wheel is above 16 meters is;
(135.96/360) * 7 min ≈ 2.64 minutes
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How to rationalise 1000/3
Answer:
Step-by-step explanation:
there is no root in denominator so I think it is rationalised
The table above shows some values of the linear function F. Which of the following defines F? A) f(n) = n-3 B) f(n) = 2n-4 C) f(n) = 3n-5 D) f(n) = 4n-6
Answer:
3n - 5
Step-by-step explanation:
f(n) = 3n - 5. Works for all of them
Given circle with radius of 5cm.
Find out
(a) diameter
(b) perimeter
(c) area
Answer:
(1) 10
(2) 10π
(3) 25π
Step-by-step explanation:
We are given the radius of the circle which is halfway through a circle. The radius of this circle is 5.
We are required to find the diameter, perimeter, and area using the given data we have been provided with.
Let's start:
#1: Diameter
To find diameter [tex]d[/tex] use formula:
[tex]d=2*r[/tex]
After substituting [tex]r=5[/tex] we have:
[tex]d=2*5\\d=10[/tex]
After calculating, we have found that the diameter of the circle is 10.
#2: Perimeter
The perimeter can also be known as the circumference of a circle as they both measure the outline.
To find circumference [tex]C[/tex] use formula:
[tex]C=2*r*\pi[/tex]
After substituting [tex]r=5[/tex] we have:
[tex]C=2*5*\pi[/tex]
[tex]C=10\pi[/tex]
Convert [tex]10\pi[/tex] to a decimal and round it to the nearest tenth and we have:
⇒ 31.4159265359
⇒ 31.4
After calculating, we have found that the perimeter (or circumference of the circle is 10π or 31.4 (Rounded to the nearest tenth in decimal form).
#3: Area
To find area [tex]A[/tex] use the formula:
[tex]A=r^2*\pi[/tex]
After substituting [tex]r=5[/tex] we have:
[tex]A=5^2*\pi \\A=25*\pi \\A=25\pi[/tex]
Convert [tex]25\pi[/tex] to a decimal and round it to the nearest tenth and we have:
⇒ 78.5398163397
⇒ 78.6
After calculating we have found that the area of the circle is either 25π or 78.6 (rounded to the nearest tenth).
After finding all the required information, we have now completed the answer.
Find the equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4)
The equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4) would be Y=-1/9(x^2-36).
What is the equation of the parabola that has zeros?Since the zeros are symmetrical to the y axis, the equation can be written as;
y = a(x-b)(x+b),
where a is a scale factor and b is x-intercept.
From the given zeroes
y = A(x-6)(x+6).
Now we can plug in the y-intercept (0,4)
4 = A(0-6)(0+6)
4 = A(-36)
-36A=4
A = -1/9
Therefore the equation would be
Y = -1/9(x-6)(x+6),
or Y=-1/9(x^2-36)
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