Answer:
y = -x(x - 1).
Step-by-step explanation:
y = a(x - b)(x - c) where a is a constant and b and c are the x-intercepts.
y = a(x - 0)( x - 1)
y = ax(x - 1).
When x = 2, y = -2 so:
-2 = a(2) (2 - 1)
2a = -2
a = -1.
So the equation is y = -x(x - 1).
Answer:
[tex]y=-x^2+x[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation:
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Given:
x-intercepts: 0 and 1Point on the curve: (2, -2)Substitute the given values into the formula and solve for a:
[tex]\begin{aligned}y&=a(x-p)(x-q)\\\\\implies -2&=a(2-0)(2-1)\\-2&=a(2)(1)\\-2&=2a\\\dfrac{2a}{2}&=\dfrac{-2}{2}\\\implies a&=-1\end{aligned}[/tex]
Substitute the given x-intercepts and the found value of a into the formula:
[tex]y=-1(x-0)(x-1)[/tex]
Expand to standard form:
[tex]\implies y=-1(x)(x-1)[/tex]
[tex]\implies y=-x(x-1)[/tex]
[tex]\implies y=-x^2+x[/tex]
(ii) Find p if 3^p =
3 square root 9/3
We must know the following exponent rules to help us solve this question:
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex][tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex][tex](a^m)^n=a^{mn}[/tex][tex]a^m=a^n, \therefore m=n[/tex]Solving the Question
[tex]3^p=\dfrac{\sqrt[3]{9}}{3}[/tex]
⇒ Rewrite [tex]\sqrt[3]{9}[/tex] as [tex]9^\frac{1}{3}[/tex]:
[tex]3^p=\dfrac{(3^2)^\frac{1}{3}}{3}[/tex]
⇒ Multiply:
[tex]3^p=\dfrac{3^\frac{2}{3}}{3}[/tex]
⇒ Subtract:
[tex]3^p=3^{\frac{2}{3}-1}[/tex]
[tex]p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}[/tex]
Answer[tex]p=-\dfrac{1}{3}[/tex]
how many solutions does the expression |x + 8| + 5 = 2 have??
Answer:
x= -11
It only has one solution.
Step-by-step explanation:
The point ( 3, -7 )is on a line with the slope . 2/3 Find another point on the line.
Answer: (6, -5)
Step-by-step explanation:
The slope 2/3 means that there is a positive change of 2 in the y-value ( + 2) and a positive change in the x-value of 3 (+ 3) for every new point. To find another point on the line, we can add 2 to the y-value and 3 to the x-value.
➜ Slope is written as y over x
➜ Coordinate points are written as (x, y)
(3, -7)
(3 + 3, -7 + 2)
(6, -5)
We can also find a point on the line by graphing. See attached.
The lateral surface area of a cylinder is given by the formula S = 2pirh . Solve the equation for r.
I need help with this math question. Can someone help me? Thanks!
Answer: Eiko
Step-by-step explanation:
Eiko has the shortest time.
Round 369 962 to the nearest hundred.
Answer:
369,962
Step-by-step explanation:
If the rounding digit is 0, 1, 2, 3, or 4, drop all the digits to the right of it
If the rounding digit is 5, 6, 7, 8, or 9, add one to the rounding digit and drop all digits to the right of it
Misty estimated the product of 99 and 2.4 to be 240. She used to estimate.
Answer:
Not 100% sure what it's asking but if it's asking what number she used to estimate the 240, she used 100 because it's one-off 99. The actual number would be 237.6
Step-by-step explanation:
it took 2/3 minute to fill a barrel 1/4 full of water. find the unit fate in barrels per minute
Answer:
3/8 barrels / minute.
Step-by-step explanation:
Rate = fraction of barrel filled / time
= 1/4 / 2/3
= 1/4 * 3/2
= 3/8.
Find the value of x
(A) x= 135
(B) x= 25
(C) x= 35
(D) x= 90
THE SUM OF THE INNER ANGLES IS 180°
[tex](x - 7) + (2x - 8) + 90 = 180 \\ x - 7 + 2x - 8 + 90 = 180 \\ x + 2x = 180 + 7 + 8 - 90 \\ 3x = 105 \\ \frac{3x}{3} = \frac{105}{3} \\ x = 35[/tex]
THEREFORE x=35°OPTION C IS THE RIGHT ANSWER.
A boat is heading towards a lighthouse, whose beacon-light is 144 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 9^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 14^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Using the slope concept, the distance from point AA to point BB ≅ 360 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change.
It's also the tangent of the angle of depression.
We can get, the vertical change is of 144 feet.
At point A, the angle is of 9º, while the horizontal position is of [tex]x_{A}[/tex] ,
Then, we can write,
tan 9º = [tex]\frac{144}{x_{A} }[/tex]
[tex]x_{A}[/tex] = 144/tan 9º
Hence, tan 9º = 0.15
[tex]x_{A} =[/tex] 144/0.15
[tex]x_{A}[/tex] = 960
At point A, the angle is of 14º, while the horizontal position is of [tex]x_{B}[/tex] ,
Then, we can write,
[tex]x_{B}[/tex] = 144/tan 14º
Hence, tan 14º = 0.24
[tex]x_{B}[/tex] = 144/0.24
[tex]x_{B}[/tex] = 600
So, the distance in feet is of:
d = [tex]x_{A} -x_{B}[/tex]
d = 960 - 600
d = 360
d ≅ 360
Therefore,
A boat is heading towards a lighthouse, then the distance from point AA to point BB ≅ 360 feet.
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Find the value of the object round to the nearest hundredth
Answer:
8,377.58 [tex]mi^{3}[/tex]
Step-by-step explanation:
To solve for the volume of a right circular cone like the one in the picture, you use [tex]\pi[/tex][tex]r^{2}[/tex][tex]\frac{h}{3}[/tex].
Plug in the radius and height to get [tex]\pi[/tex][tex]20^{2}[/tex][tex]\frac{20}{3}[/tex].
Then solve (and round to the nearest hundredth) and you should get 8,377.58.
What exponent is understood on the base "x" in the following expression?
xy^3
What is the exponent of "x"?
The exponent that is understood on the base x in the given expression is; 1
How to interpret Exponents?The exponent of a number tells us how many times to use the number in a multiplication. Exponents are also called Powers or Indices. For example in the exponent form ab^(x), we can say that;
The base is a and its' exponent is 1.
Applying the above to our question gives us;
If the exponent form is xy^3, then we can say that;
The base is x.
We can see that there is no exponent attached to x and as such we will use 1 as 1 will still give us the value of x.
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Consider the matrices.
A =
[-1 7 -2 -6 2 -3 -1 10]
B = [- 2 -3 1 2]
C = [-6 -8]
D = [0 0 0 0]
E = [[-8 -2 1 4 3 9 2 -7]
Operation is defined.
What operations are defined for these matrices?
Drag the operation to the boxes to correctly complete the table.
Operation is defined
Operation is not defined.
E-A
A+C
B+D
C-B
Find the value of x show your steps
Draw a graph that
a. Has no x-intercepts
b. Has one y-intercept of (0,-2)
c. Is continuous
d. Is not a function
Answer:the answer is b
Step-by-step explanation:
A line has equation y=-½x−3
Find the gradient.
Answer:
gradient is 1/2 = 0.5
Step-by-step explanation:
y= 1/2 x−3
Swap sides so that all variable terms are on the left hand side.
1/2 x−3=y
Add 3 to both sides.
1/2 x=y+3
Multiply both sides by 2.
1/2 x = 1/2 y+3
Dividing by 1/2 undoes the multiplication by 1/2
x= 1/2 y+3
Divide y+3 by 1/2 by multiplying y+3 by the reciprocal of 1/2
.
x=2y+6
Find the equation of the line.
Use exact numbers.
Answer:
y = 4x + - 9
Step-by-step explanation:
(3, 3), (4, 7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 7 - 3 4
m = ------------ = ------------ = ------- = 4
x₂ - x₁ 4 - 3 1
y - y₁ = m(x - x₁)
y - 3 = 4(x - 3)
y - 3 = 4x - 12
+3 +3
----------------------
y = 4x - 9
I hope this helps!
help meeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!
Answer:
[tex]\frac{h^6}{h^8}[/tex]
Step-by-step explanation:
1. For now, let's leave the [tex]g^{-6}[/tex] to the side and just worry about the [tex]\frac{h^8}{h^2}[/tex].
2. When you apply the exponent rule you should have learned in class, we know that when you divide two bases with exponents, the exponents subtract. So, you can subtract 8 - 2, and then the greater digit's place in the fraction stays. So, since [tex]h^8\\[/tex] is the greater number (and it's in the numerator), you put the [tex]h^6[/tex] in the numerator as well.
1. Use the slope to find the speed of the object in the graph below.252015-distance (miles)105-150(1.39, 11.6)23time (hour)
Notice that the slope of the line is equal to the speed
[tex]\text{Slope (speed) = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{20\text{ -10}}{4\text{ - 2}}\text{ =}\frac{10}{2}=5\text{miles / hour}[/tex]hence, the speed = 5 miles / hour
Solve the following system of equations
5x-2y=4
8x+5y=-10
[tex]5x - 2y = 4 \\ 5x = 4 + 2y \\ \frac{5x}{5} = \frac{4 + 2y}{5} \\ x = \frac{4 + 2y}{5} ......(3)equation[/tex]
NOTE I AM SOLVING BY SUBSTITUTION
[tex]8( \frac{4 + 2y}{5} ) + 5y = - 10 \\ \frac{32 + 16y}{5 } + 5 y = - 10 \\ \frac{32 + 16y}{5} (5) + 5y(5) = - 10(5) \\ 32 + 16y + 25y = - 50 \\ 41y = - 50 - 32 \\ \\ \\ \\ 41y = - 82 \\ \frac{ - 41y}{41} = \frac{ - 82}{41} \\ y = - 2[/tex]
[tex]x = \frac{4 + 2( - 2)}{5} \\ x = \frac{4 - 4}{5} \\ x = \frac{0}{5} \\ x = 0[/tex]
ATTACHED IS THE SOLUTION
Answer: (0,-2)
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{5x-2y=4\ \ \ \ \ (1)} \atop {8x+5y=-10\ \ (2)}} \right.[/tex]
Multiply equation (1) by 5, and equation (2) by 2:
[tex]\displaystyle\\\left \{ {{25x-10y=20\ \ \ \ (3)} \atop {16x+10y=-20\ \ (4)}} \right.[/tex]
Add equations (3) and (4):
[tex]41x=0[/tex]
Divide both parts of the equation by 41:
[tex]x=0[/tex]
Let's substitute the value of x into equation (2):
[tex]8(0)+5y=-10\\0+5y=-10\\5y=-10[/tex]
Divide both parts of the equation by 5:
[tex]y=-2[/tex]
Thus, (0,-2)
What fraction is equal to 50% from 1 over 6
Rewrite 50% as 1/2
We need a fraction that is equal to 1/2 of 1/6.
-> That fraction equals to 1/2 x 1/6 = 1/12 (or 1/6 : 2)
Answer:
1/12
Step-by-step explanation:
1/6*100/50=1/12.
A rental car company charges $40 per day to rent a car and $0.08 for every mile driven. Justin wants to rent a car, knowing that:
He plans to drive 125 miles.
He has at most $170 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Justin can afford to rent while staying within his budget.
Answer:
He will only afford to rent the car for 4 days, he will spend 160 dolars to just have the car for 4 days. Since he plan to drive 125 miles, the cost for the miles will be 10 dolars. So if we add 160 (4 days with the car) plus 10 (for the miles) it would give 170.
Step-by-step explanation:
Probability involving one die or choosing from n distinct objects
The probability of picking an odd number ball in fraction form is; 6/11
What is the probability of selection?
We are told that a bag contains eleven balls labelled 1 through 11. These numbers are;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. This is a total of 11 numbers.
The even numbers are a total of 5 while the odd numbers are a total of 6.
Now, the probability of selecting an odd number will be;
P(selecting odd number) = Number of possible odd numbers/Number of Total Numbers
Plugging in the relevant numbers gives;
P(selecting odd number) = 6/11
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Write an equation that represents the line.
Use exact numbers.
Answer:
y = (3/2)x + 3
Step-by-step explanation:
Point 1: (0, 3) Point: (2, 6)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 6 - 3 3
m = ------------ = ------------ = --------
x₂ - x₁ 2 - 0 2
y - y₁ = m(x - x₁)
y - 3 = (3/2)(x - 0)
y - 3 = (3/2)x
+3 +3
------------------------
y = (3/2)x + 3
I hope this helps!
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1. A train travels at 80 miles per hour. What equation that compares the time (t) with the distance (d)?
d = 80t
t = 80d
t = d + 80
d = t + 80
the answer is T becouse T is the time which is what you get when distance is divided by 80 mph
ndustry standards suggest that 10% of new vehicles require warranty service within the first year. jones nissan in sumter, south carolina, sold 12 nissans yesterday. (round your mean answer to 1 decimal place and the other answers to 4 decimal places.)
The probability that none of these vehicles requires warranty service is 0.2824
The probability exactly one of these vehicles requires warranty service is
0.3766
The probability that exactly two of these vehicles require warranty service is 0.2301
The mean of this probability distribution is 1.2
Given, n=12, and the probability is 0.1, we use the binomial distribution formula to solve the probabilities:
[tex]P(X=0)=C^{n}_{x} } P^{x} Q^{n-x}[/tex]
The probability that none of these vehicles requires warranty service
[tex]P(X=0)=C^{12}_{0} } (0.1)^{0} (0.9)^{(12-0)}[/tex]
=0.2824
The probability exactly one of these vehicles requires warranty service
[tex]P(X=1)=C^{12}_{1} } (0.1)^{1} (0.9)^{(12-1)}[/tex]
=0.3766
The probability that exactly two of these vehicles require warranty service.
[tex]P(X=2)=C^{12}_{2} } (0.1)^{2} (0.9)^{(12-2)}[/tex]
=0.2301
Compute the mean of this probability distribution
Mean = n*P, where n = 12, P=0.1
=12*0.1
=1.2
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What is the value of the expression -38-16-(-23)?
O-31
O-45
O-54
O-77
Answer:
-31
Step-by-step explanation:
[tex]-38-16-(-23) \\ \\ =-38-16+23 \\ \\ =-54+23 \\ \\ =-31[/tex]
Help me please I’ll give lots of points
Equivalent equations (acceptable moves)
(1)
4(x+3)=32
x+3 = 8
(2)
[tex]\frac{(9x+4)}{2} =5\\\\9x+4=10[/tex]
(3)
x- 7+ 3x=25
4x-7=25
Not equivalent (unacceptable moves)
(1)
2(x+5) = 10
2x+5 = 5( 20 is wrong)
(2)
2x+4=22
2x= 22-4= 18 (26 is wrong)
(3)
[tex]\frac{(6x-1)}{3} =27\\\\6x-1=81[/tex] (9 is wrong)
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please please please help me I’m going to die
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{x}{13}~~ = ~~\cfrac{11}{x}\implies x^2=(13)(11)\implies x^2=143\implies x=\sqrt{143}[/tex]