Answer:
y = -2x²
Step-by-step explanation:
The set of ordered pairs is:
(x₁, y₁) = (2, -8)
(x₂, y₂) = (3, -18)
(x₃, y₃) = (4, -32)
(x₄, y₄) = (5, -50)
First let's check if this is linear. For even increments of x, Δy is:
Δy₂₁ = y₂ − y₁ = -18 − -8 = -10
Δy₃₂ = y₃ − y₂ = -32 − -18 = -14
Δy₄₃ = y₄ − y₃ = -50 − -32 = -18
Δy isn't constant, so this isn't linear. However, the difference of the differences is constant:
Δy₃₂ − Δy₂₁ = -14 − -10 = -4
Δy₄₃ − Δy₃₂ = -18 − -14 = -4
So this is a quadratic.
y = ax² + bx + c
To find the coefficients of a, b, and c, we can either plug in three points from the set and solve the system of equations:
-8 = a(2)² + b(2) + c
-18 = a(3)² + b(3) + c
-32 = a(4)² + b(4) + c
Or, if it's simple, we can use a little trial and error.
-8 = -2 (2)²
-18 = -2 (3)²
-32 = -2 (4)²
So the function is:
y = -2x²
solve this problem in order of operations 4-[6(3x+2)-x]+4
[tex]4-(6(3x+2)-x)+4=-(18x+12-x)+8=-(17x+12)+8=-17x-12+8=-17x-4[/tex]
What is the reflection image of (5,-3) across the line y = -x?
If you apply the changes below to the absolute value parent function, f(x) =|x|
what is the equation of the new function?
• Shift 5 units right.
• Shift 7 units down,
Answer:
The new function is g(x) = Ix - 5I - 7 ⇒ answer C
Step-by-step explanation:
* Lets revise the translation of a function
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
∵ f(x) = IxI
∵ f(x) is shifted 5 units to the right
∵ If the function f(x) shifted to the right by h units
∴ g(x) = f(x - h)
- Change IxI to Ix - 5I ⇒ (1)
∵ f(x) is shifted 7 uints down
∵ If the function f(x) shifted down by k units
∴ g(x) = f(x) - k
- Change f(x) to f(x) - 7 ⇒ (2)
- From (1) and (2) the new function is:
g(x) = Ix - 5I - 7
* The new function is g(x) = Ix - 5I - 7
If the alternate hypothesis of an experiment is “The true mean height of the giraffes is more than 15 feet” what is the null hypothesis?
Answer: "The true mean height of the giraffes is less than or equal to 15 feet".
Step-by-step explanation:
A hypothesis in a statement that is made about a statistical parameter of a population.
A null hypothesis [tex]H_0[/tex] is usually the hypothesis that is tried to reject by an alternate hypothesis [tex]H_a[/tex]
In this case [tex]H_a[/tex] is:
"The true mean height of the giraffes is more than 15 feet".
Therefore, for this case, the null hypothesis must be:
"The true mean height of the giraffes is less than or equal to 15 feet".
Consider the graph of the equation y = 5. Which statements are true? Check all that apply.
The graph of y = 5 is a vertical line.
The graph of y = 5 is a horizontal line.
The graph of y = 5 is neither a vertical line nor a horizontal line,
The point (5,3) lies on the line.
The point (-4, 5) lies on the line.
Answer:
y=5 is horizontal
(-4,5) is on the line
Step-by-step explanation:
y= a number is always a horizontal line
x= b number is always a vertical line
So y=5 is horizontal and it includes every single ordered pair with a y-coordinate of 5. So it contain the ordered pair (-4,5).
So there are two statements.
The correct statements are :
The graph of y = 5 is a vertical line.
The point (-4, 5) lies on the line.
What are equations?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
How to know which statements are true?The equation y = 5 is a line parallel to the y axis .So, the line is vertical.The line also passes through all the points with ordinate 5
So the line passes through ( -4,5)
So options A and D are correct.
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The coordinates of points A and B (2, 3) and (-2,-4) respectively.what is the slope of the line that connects two points
Answer:
7/4
Step-by-step explanation:
The slope of the line going through (2,3) and (-2,-4) can be found by:
A) Lining up points
B) Subtracting the numbers vertically
C) Answer: Putting 2nd difference over 1st difference (yes a fraction)
Let's do it!
( 2 , 3)
-( -2 , -4)
--------------
4 7
So the slope is 7/4
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
We have as data the following points:
[tex](x1, y1) = (2,3)\\(x2, y2) = (- 2, -4)[/tex]
Substituting in the formula we have:
[tex]m = \frac {-4-3} {- 2-2}[/tex]
Equal signs are added and the same sign is placed:
[tex]m = \frac {-7} {- 4}\\m = \frac {7} {4}[/tex]
Answer:
[tex]m = \frac {7} {4}[/tex]
The presence of an angle bisector will result in what type of angles ?
Answer:
Congruent Angles
Reasoning:
An angle bisector bisects/splits an angle into two equal/congruent parts/angles.
Answer with explanation:
→ The Meaning of Angle bisector is that line or line segment which divide an Angle in two equal Parts.
→So, If a Line or line segment that is Angle bisector is bisecting an Angle , it will divide the angle into two equal Angles.
For example: Suppose an Angle has Measure of 60°, the Angle bisector will divide it into two congruent Angles each being equal to 30°.
⇒The presence of an angle bisector will result in Congruent type of angles
while you calculate the distance do you start from the bottom or the top?
Answer:
You start at the bottom
Distance, often assigned the variable d, is a measure of the space contained by a straight line between two points. Distance can refer to the space between two stationary points (for instance, a person's height is the distance from the bottom of his or her feet to the top of his or her head) or can refer to the space between the current position of a moving object and its starting location.
Using these integers 12345789 you put them in 2 groups of 4 coming up with the same summ
What is the solution to the linear equation?
4b + 6 = 2 – b + 4
Answer:
[tex]\large\boxed{b=0}[/tex]
Step-by-step explanation:
[tex]4b+6=2-b+4\qquad\text{combine like terms}\\\\4b+6=(2+4)-b\qquad\text{add}\ b\ \text{to both sides}\\\\5b+6=6\qquad\text{subtract 6 from both sides}\\\\5b=0\qquad\text{divide both sides by 5}\\\\b=0[/tex]
Hello!
Answer:
[tex]\boxed{b=0}\checkmark[/tex]
The answer should have a positive sign.
Step-by-step explanation:
First, switch sides and group like terms.
4b+6=-b+2+4
Then, add numbers from left/right.
2+4=6
4b+6=-b+6
Subtract by 6 both sides of an equation.
4b+6-6=-b+6-6
Simplify.
4b=-b
Next add b both sides of an equation.
4b+b=-b+b
Simplify.
5b=0
Therefore, you divide by 5 from both sides of an equation.
5b/5=0/5
Finally, you simplify and solve to find that answer is.
0/5=0
b=0 is the correct answer.
Hope this helps!
Have a nice day! :)
-Charlie
Thank you so much!
what is the quotient? 5/4c^2÷15/7c assume c is not equal to 0
Answer:
The quotient is [tex]\frac{7}{12c}[/tex]
Step-by-step explanation:
Given expression is: [tex]\frac{5}{4c^2}\div \frac{15}{7c}[/tex]
While dividing two fractions, first we need to change the division sign into multiplication and then flip the second fraction.
So, we will get.....
[tex]\frac{5}{4c^2}\div \frac{15}{7c}\\ \\ =\frac{5}{4c^2}\times \frac{7c}{15}\\ \\ =\frac{35c}{60c^2}\\ \\ = \frac{7}{12c} \ \ [Dividing\ both\ numerator\ and\ denominator\ by\ 5c][/tex]
So, the quotient is [tex]\frac{7}{12c}[/tex]
Answer:
the answer is B
Step-by-step explanation:
just did the assignment on edge
Nick found the quotient of 8.64 and 1.25....
Answer:
No, the power multiplied to 8.64 should havean exponent of zero.
HOPE THIS WILL HELP YOU
Answer:its the second one or b
Step-by-step explanation:
A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. The game operator designed a simulation using a random number generator to predict how many points would be earned for a turn.
Integer Value Points Frequency
0 - 5 50 55
6 - 8 75 32
9 150 13
10. What is game’s expected value of points earned for a turn?
(SHOW WORK)
Answer:
The game’s expected value of points earned for a turn is 71.
Step-by-step explanation:
Here we know that:
Points Frequency
50 55
75 32
150 13
Here points earned is a random variable.
We need to find its expected value,
Finding Expected value:
Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.
Total number of turns = sum of frequencies
= 55 + 32 + 14 = 100
Total points earned = 50(55) + 75(32) + 150(13)
= 7100
Expected value of points earned for a turn = Mean value of points
= Total points/no. of turns
= 7100/100
= 71
Write an expression to represent the perimeter of 12a, 6a+8, 10a-4, 6a+8
Answer:
34a + 12
Step-by-step explanation:
12a + 6a + 8 + 10a - 4 + 6a + 8
combine like terms
12a + 6a + 10a + 6a
and 8 + 8 - 4
34a + 12
Question 1 of 10
2 Points
The slope of the line below is – 3. Use the coordinates of the labeled point to
find a point-slope equation of the line.
(5.-7)
Answer:
[tex]\large\boxed{y+7=-3(x-5)}[/tex]
Step-by-step explanation:
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_2)-point\\\\\text{We have}\ m=-3\ \text{and}\ (5,\ -7).\\\text{Substitute:}\\\\y-(-7)=-3(x-5)\\y+7=-3(x-5)[/tex]
The _____ a0 of a segment divides the segment into two segments of equal length.
The Midpoint of a segment divides the segment into two segments of equal length.
Answer:
Midpoint
Step-by-step explanation:
The midpoint is the point on the segment halfway between the two endpoints. In some cases the midpoint of a segment can be found simply by counting.
For example in a straight line between (2,0) and (6,0) the midpoint would be located on the point (4,0).
Find the perimeter of the following shapes.
Answer:
4. (a) = 12 m
(b) = 27 cm
(c) = 24 mm
(d) = 18 km
(e) = 10 m
(f) = 36 cm
Step-by-step explanation:
Perimeter is sum the distance round a figure.
if a shape has those, they signify that the shape has two side that are equal
a) 4 + 4 + 2 + 2 = 12. The top part is equal to the bottom part signified by those two lines. And the left is equal to the right .
b) 10 + 10 + 7 = 27
c) 5 + 5 + 8 + 6 = 24
d) 3 + 3 + 6 + 6 = 18
e) 2.5 + 2.5 + 2.5 + 2.5 = 10
f) 12 + 7 + 7 + 5 + 5 = 36
If you need any clarification or more explanation pls do mention in the comment section. i would like to help more.
Hope this helps and if it does pls mark as branliest answer thx.
Tickets to see a movie cost $5 for children and $8 for adults. The equation 5x + 8y =
80 represents the number of children (x) and adults (y) who can see the movie with
$80. If no adults see the movie, how many children can see the movie with $80?
a) 13
b) 16
c) 6
d) 10
Answer:
16 chlildren
Step-by-step explanation:
5x+8y=80
y=0
5x=80
x=8-0/5=16
Answer:
Step-by-step explanation:
The answer is B.16
Since the equation is 5x+8y=80
There are no parents so it equation will turn into 5x+8(0)=80, AKA, 5x=80
Using algebra, 5x=80 will x=80/5
which is 16
Theo has $5 more than denise and denise has $11 more than rudy . Together , they have $45. How much money does denise have?
Answer:
Denise has $17
Step-by-step explanation:
T = Theo, D = Denise, and R = Rudy
T + D + R= 45
(D+ 5) +( D)+ (D - 11) = 45
3D -6 = 45
3D = 51
D = 17
What is the surface area of the figure?
Answer:
The surface area of the figure is [tex]SA=458\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the figure is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the L-shaped cross section
P is the perimeter of L-shaped cross section
H is the width of the figure
Find the area of the L-shaped cross section
[tex]B=12*7+5*5=109\ ft^{2}[/tex]
Find the perimeter P of L-shaped cross section
[tex]P=(12+7+7+5+5+12)=48\ ft[/tex]
[tex]H=5\ ft[/tex]
substitute
[tex]SA=2(109)+(48)(5)=458\ ft^{2}[/tex]
Answer:
Surface area = 458 square ft
Step-by-step explanation:
From the figure attached with this answer we can see figure.
To find the surface area of the figure
Surface area is sum of area of small rectangles
Surface area = 2(12 * 7 ) + 4(5 * 5) + 2(12 * 5) + 2(7 * 5)
= 2*84 + 4*25 + 2 *60 + 2*35
= 168 + 100 + 120 + 70
= 458
Therefore surface area of given figure = 458 square ft
Evaluate a + b for a = 2 and b = 3.
For this case we have the following expression:
[tex]a + b[/tex]
We must evaluate the expression to:
[tex]a = 2\\b = 3[/tex]
Substituting the values in the expression we have:
[tex]2 + 3[/tex]
Equal signs are added and the same sign is placed.
So:
[tex]2 + 3 = 5[/tex]
Finally, the value of the expression is 5.
Answer:
[tex]a + b = 5[/tex]for[tex]a = 2[/tex] and[tex]b = 3[/tex]
Enter the correct value so that each expression is a perfect-square trinomial.
x2 – 10x +
Answer:
[tex]x^2-10x+25[/tex]
Step-by-step explanation:
We have been given an expression [tex]x^2-10x+[/tex]. We are asked to convert our given expression into perfect-square trinomial.
We know that an equation in form [tex]x^2+bx+c[/tex] is a perfect square, if [tex]c=(\frac{b}{2})^2[/tex]
To convert our given expression into perfect-square trinomial, we need to add [tex](\frac{10}{2})^2[/tex] to our given expression.
[tex](\frac{10}{2})^2=5^2=25[/tex]
Therefore, our perfect square trianominal would be [tex]x^2-10x+25[/tex].
What is the slope of the line whose equation is 2x - 4y = 10?
Please I need this right away !
Answer:
1/2
or
0.5
Step-by-step explanation:
you need to get the line in the form of y = mx + b
2x - 4y = 10 Subtract 3x from both sides
-4y = - 2x + 10 3x on the left disappears. Divide by - 4
-4y/-4 =-2x/-4 +10/-4 Do the division
y = (2/4)x - 2.5
y = (1/2)x - 2.5
The slope is the number in front of the x
y = 0.5x - 2.5
Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?
Opions are:
A.
P(x) = 2x^2 + 74x + 644
B.
P(x) = 2x^2 + 28x - 414
C.
P(x) = 2x^2 + 102x + 1,288
D.
P(x) = 2x^2 + 110x + 1,472
Answer:
It's B.
Step-by-step explanation:
First is x + 23 and second is 2x - 18.
So the product is
(x + 23)(2x - 18)
= 2x^2 - 18x + 46x - 414
= 2x^2 + 28x - 414
There are three kids. The sum of individual squares of their body weights (2 + 2 + 2) is 100. The sum of the product of their weights taking two friends at a time i.e. + + is 150. What will the weighing machine read if all the three kids stand on it at the same time?
Answer:
20
Step-by-step explanation:
Givens
Let child one = x
Let child two = y
Let child three = z
Equations
x^2 + y^2 + z^2 = 100
xy + xz + yz = 150
Solution
There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).
(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
Take out 2 as a common factor from the last three terms.
(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )
Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150
(x + y + z)^2 = 100 + 2*150
(x + y + z)^2 = 100 + 300
(x + y + z)^2 = 400
Take the square root of both sides.
sqrt(x+y+z)^2 = sqrt(400)
x + y + z = 20
Note
This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.
i need help asap please
Answer:
C
Step-by-step explanation:
Given the inequality
(x - 3)(x + 5) ≤ 0
Find the zeros by equating to zero
(x - 3)(x + 5) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 5 = 0 ⇒ x = - 5
Thus the domain is split into 3 intervals
--------------------------------------------------------------
- ∞ < x ≤ - 5 → (1)
- 5 ≤ x ≤ 3 → (2)
3 ≤ x < + ∞ → (3)
Select a test point in each interval and check validity
x = - 10 → (- 13)(- 5) = 65 > 0 ← not valid
x = 0 → (- 3)(5) = - 15 < 0 ← valid
x = 10 → (7)(15) = 105 > 0 ← not valid
Solution is { x | - 5 ≤ x ≤ 3 }
the sum of the real numbers x and y is 25. their difference is 13. what is the value of xy?
The sum of the real numbers x and y is 25 and their difference is 13. To find the value of xy, we need to solve a system of equations. The value of xy is 114.
Explanation:To solve this problem, we need to set up a system of equations based on the given information. Let's denote x and y as the two real numbers. The sum of x and y is 25, so we can write the equation x + y = 25. The difference between x and y is 13, so the equation becomes x - y = 13. To find the value of xy, we need to solve this system of equations.
First, let's add the two equations together. (x + y) + (x - y) = 25 + 13. This simplifies to 2x = 38. Dividing both sides by 2, we find x = 19.
Now, we can substitute the value of x into one of the original equations (x + y = 25) to solve for y. 19 + y = 25. Subtracting 19 from both sides, we get y = 6.
Therefore, the value of xy is 19 * 6 = 114.
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Set m contains the values {-12, -7, 4, 11} and set n contains the values {-3,2,8}. What is the greatest possible difference of m^2 - n^2 ?
A. 76
B. 117
C. 140
D. 153
Answer:
C. 140
Step-by-step explanation:
We want m^2 to be the largest value it can be, so ignoring the sign of m the largest value of |m| is 12
(-12)^2 = 144 which is the largest value of m^2
We want n^2 to be the smallest it can be, so ignoring the sign of n the smallest value of |n| is 2
(2)^2 =4
m^2 -n^2
144-4 = 140
Simplify (5√2-1)^2
10 √2+51
-10 √2+51
41 √2
What is the period of f(x)=sin(x)?
-Pi/2
-Pi.
-3pi/2.
-2pi
Answer:
2pi
Step-by-step explanation:
period for sin is 2pi/b
its only x theres 1 before x so its 1x=b
2pi/1
= 2pi
The period of function f ( x ) = sin ( x ) is 2π.
The sine function ( sin ( x ) ) is a periodic function, which means it repeats its values in regular intervals. The period of sin(x) is the length of one complete cycle of the function before it starts repeating itself.
The period of the function f ( x ) = sin( x ) is 2π.
In the case of sin ( x ), it completes one full cycle ( from 0 to 2π ) every 2π units. Therefore, the period of f ( x ) = sin ( x ) is 2π.
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