Answer:
all numbers greater than or equal to -1
Step-by-step explanation:
Let's find the vertex.
Since the function is in factored form, I'm going to find the zeros.
The average of the zeros will give me the x-coordinate of the vertex.
I can then find the y-coordinate of the vertex by using the equation
y=(x-4)(x-2).
Also the parabola is open up since the coefficient of x^2 is positive (or 1 in this case).
So the range has something to do with the y's. It is where the function exist for the y-values.
So the range for this one since the parabola is open up will be of the form
[y-coordinate of vertex , infinity).
So let's begin.
The zeros can found by solving (x-4)(x-2)=0.
This means we need to solve both x-4=0 and x-2=0.
x-4=0 gives us x=4
x-2=0 gives us x=2
Now the average of our x-intercepts (or zeros) is (4+2)/2=6/2=3.
So the x-coordinate of the vertex is 3. To find the y-coordinate of the vertex we are going to use y=(x-4)(x-2) where x=3.
Plug in: y=(3-4)(3-2)=(-1)(1)=-1.
So the range is [tex][-1,\infty)[/tex]
or all numbers greater than or equal to -1
Answer:
all real numbers greater then or equal to -1
Step-by-step explanation:
What is the absolute value of 9? -3?
Show your work
Answer:
|9| = 9|-3| = 3Step-by-step explanation:
The absolute value of number a:
|a| = a for a ≥ 0
|a| = -a for a < 0
|9| = 9
|-3| = -(-3) = 3
A: what is the discriminators for the quadratic equation?
B:based on the discriminant which statement about the number and type of solutions in the equation is correct?
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]
Answer:
0
Step-by-step explanation:
Descriminator is calculated by the following formula:
b*b - 4 * a * c, where a,b,c are the numbers in equitation.
Andy was playing a memory game with his sister. He turned over a tile to reveal a picture of the sun at the coordinates (5, 4). He looked under a tile that was 3 units to the left and 2 units down but revealed a picture of a tree. His sister knew that the other sun was 1 unit to the left and 1 unit up from the tree. What are the coordinates of the second sun? (JUSTIFY)
Answer:
(1, 3).
Step-by-step explanation:
The tree tiles coordinates are x = 5-3 = 2 and the y coordinate = 4 - 2 = 2
- that is (2, 2).
So the coordinates of the second sun are (2-1, 2 + 1)
= (1. 3).
A_____ is invested by Managers in a diversity of stocks bonds and other securities
Answer:
Step-by-step explanation:
A Mutual Fund is invested by Managers in a diversity of stocks bonds and other securities.
A mutual fund is a type of investment in which investors pool their money together to buy a portfolio of stocks, bonds or other securities in order to take advantage of diversification and professional portfolio management at a reasonable cost. It is operated by money managers, who invest the fund capital on the investors behalf. Investing in mutual funds enables those investing a modest amount of money to benefit from the same advantages enjoyed by large institutional investors....
There are 10 pennies, 14 nickels, and 6 dimes in a bag, and you remove three at random without replacing any. What is the probability that you will remove a penny, a nickel, and a dime in that order?
1. 1/29
2. 1/10
3. 1/30
4. 1/812
Answer:
1/30
Step-by-step explanation:
Find the first five terms of the sequence in which a(1) = –10 and a(n) = 4a(n) – 1 + 7, if n ≥ 2.
options:
A –33, –125, –493, –1965, –7853
B 11, 15, 19, 23, 27
C 47, –10, –33, –125, –493
D –10, –33, –125, –493, –1965
Answer:
hello : answer: A
Step-by-step explanation:
a(1) = –10 and a(n) = 4a(n– 1) + 7, if n ≥ 2.
n=2 : a(2)=4a(1)+7 a(2) =4(-10)+7 = -33
n=3 : a(2)=4a(2)+7 a(3) =4(-33)+7 = -125
n=4 : a(2)=4a(3)+7 a(4) =4(-125)+7 = -493
n=5 : a(2)=4a(4)+7 a(5) =4(-493)+7 = -1965
n=6 : a(2)=4a(5)+7 a(6) =4(-1965)+7 = -7853
Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be [tex]m = 2.[/tex]
[tex]y = 2x + b[/tex]
We substitute the given point to find b:
[tex]2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4[/tex]
Finally the line is:
[tex]y = 2x + 4[/tex]
Answer:
[tex]y = 2x + 4[/tex]
Answer:
y = 2x + 4.
Step-by-step explanation:
The slope = the slope of y = 2x - 3 which is 2.
Using the point-slope form:
y - y1 = 2(x - x1)
Using the point (-1, 2):
y - 2 = 2(x - -1)
y = 2x + 2 + 2
y = 2x + 4 is the answer.
Factor this trinomial completely.
2x2 + 8x + 6
Answer:
[tex]2 {x}^{2} + 8x + 6 \\ 2( {x}^{2} + 4x + 3) \\ = 2( {x}^{2} + x + 3x + 3) \\ = 2(x + 1)(x + 3)[/tex]
Answer:
the answer is correct, just backwards. thanks for your help!
Step-by-step explanation:
If g of x equals x squares minus 1, find g of 2
Answer:
g(2) = 3
Step-by-step explanation:
g(x) = x² - 1.
Substituting 2 for x in this formula, we get:
g(2) = 2² - 1, or g(2) = 3
Answer:
g(2) =3
Step-by-step explanation:
g(x) = x^2 -1
Let x=2
g(2) = 2^2 -1
=4-1
=3
If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. True or False?
Answer:
False
Step-by-step explanation:
This statement states that If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.
This is a false statement.
Lets recall the properties of a parallelogram to understand the concept. The definition says that a quadrilateral is said to be a parallelogram if its opposite angles are congruent and two consecutive angles are supplementary.
Therefore the statement is false....
Find the measure of a in the picture please
Answer:
a = 44 degrees
Step-by-step explanation:
Triangle AOB is an isosceles triangle.Angle A and B are same.All three angles of a triangle are equal to 180 degrees.angle 0 + angle a + angle b = 180 degrees
angle b = angle a
92 + a + b = 180 degrees
92 + 2a = 180 degrees
a = 44 degrees
!!
The figure shows the letter M and four of its transformed images—A, B, C, and D: Which of the four images was formed by a reflection of the letter M?
Answer:
Correct answer is figure D.
Step-by-step explanation:
According to the attached image Figure D is correct option.
In a reflection transformation, all the points of an object are reflected or flipped. It is a type of transformation where the new image is the mirror image of the original and x-coordinates and y-coordinates changes the place.
Figure A is rotation and translation and Figure B and C are translation
Thus the correct option is Figure D....
7. Select True or False for each statement.
A. The ordered pair (2, -5.2) is located in Quadrant IV.
B. Quadrant Il contains ordered pairs of the form
(positive number, negative number)
C. The point (-6, 0) is located on the y-axis
D. The origin is located in Quadrant |
E. To plot points in Quadrant III, move left and down
From the origin.
The answer addresses the true or false nature of five statements about the properties of coordinate pairs in a two-dimensional graph with respect to their quadrants, and the location of specific points on the coordinate plane.
The coordinates (x, y) indicate the position of a point on a two-dimensional graph in relation to the origin, which is at (0, 0). In a standard coordinate system, Quadrant I has both x and y as positive, Quadrant II has x as negative and y as positive, Quadrant III has both x and y as negative, and Quadrant IV has x as positive and y as negative.
A. False - The ordered pair (2, -5.2) is located in Quadrant IV, which is incorrect since Quadrant IV should have x as positive and y as negative, which is actually the case here, so the statement should be True.B. False - Quadrant II contains ordered pairs of the form (negative number, positive number), not positive x and negative y.C. True - The point (-6, 0) located on the x-axis, not the y-axis, since the y-coordinate is zero.D. False - The origin (0, 0) is not located in any quadrant as it is the point of intersection of all the quadrants.E. True - To plot points in Quadrant III, one indeed moves left (negative x direction) and down (negative y direction) from the origin.Elise picks 6 pounds of apples.She uses 1/2 pounds to make 1 container of apple sauce. How many containers of applesauce can Elise make with all apples?
Answer:
12
Step-by-step explanation:
Mass of apples = number of containers × mass in each container
6 lb = No of containers × ½ lb
No of containers = 6/½
To divide a whole number by a fraction, invert the fraction and change divide to multiply.
6/½ = 6 × 2/1
Multiply the numerator by the whole number.
6 × 2/1 = 12/1
Simplify the fraction.
12/1 = 12
Elise can make 12 containers of applesauce.
The legs of a right triangle measure 5 centimeters and 12 centimeters. What
is the length of the hypotenuse?
Answer:
13
Step-by-step explanation:
Using pythag the. , we see the rule a2+b2=c2 (Square)
so, a2=25, b2= 144,
25+144=c2
c2=169
sqrt=13
If two pyramids are similar and the ratio between the lengths of their edges is 3:4, what is the ratio of their volumes?
Answer:
The ratio of their volumes is 27/64
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
The scale factor is 3/4
step 2
Find the ratio of their volumes
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
[tex](\frac{3}{4})^{3}=\frac{27}{64}[/tex]
what is the sum of the polynomials (-x^2+9)+(3x^2-11x+4)
The answer is:
[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]
Why?To solve the problem, we must remember how to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.
For example:
[tex]2x+3x+x^{2}=x^{2}+(2x+3x)=x^{2}+5x[/tex]
We were able to add only the linear terms (terms that contains the variable x") because they were like terms: they share the same variable and the same exponent.
We need to perform the following operation between polynomials:
[tex](-x^{2}+9)+(3x^2-11x+4)[/tex]
So, calculating we have:
[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]
Have a nice day!
To bake one cake, Drew uses 18 ounces of flour. He has 850 ounces of flour. Let y represent the ounces of flour left and x represent the number of cakes he has baked. When the situation is modeled on a graph, what are the slope and the y-intercept of the line representing this situation?
A.
slope = 850 and y-intercept = 18
B.
slope = 18 and y-intercept = 850
C.
slope = -18 and y-intercept = 850
D.
slope = 850 and y-intercept = -18
Answer:
Choice C:
slope = -18x
y-intercept = 850
Step-by-step explanation:
Drew uses 18 ounces of flour
-18x represents the amount of flour used
850 ounces of flour
or (0,850) is the y-intercept and represents the total number of flour
Answer
slope = -18x
y-intercept = 850
Answer:
C
Step-by-step explanation:
C
Ms. Jackson has 32 students. She needs to order a set of books for her class.
Each box has 12 books. How many boxes must she order to make sure each
student gets a book?
Answer:
3
Step-by-step explanation:
12 times table= 12,24,36..
if we have 24 books then not everyone can get a book.
it's best to get the 3 boxes of 36 as everyone can get one. As my teacher always said, the more the better.
What is the rule for the reflection?
This image is being reflected over the y-axis. When reflecting over the y-axis the y-coordinate will stay the same, but the x-coordinate will have the opposite sign. Here is the rule for this reflection:
(-x, y)
Hope this helped!
~Just a girl in love with Shawn Mendes
List three decimals between 4.2 and 4.3
Answer:
4.21 and 4.22 (answers will vary)
Step-by-step explanation:
There are a lot of different numbers you can pick. It just has to be between 4.2 and 4.3. This means that 4.200000000000000000000000000001 can be an answer and 4.29999999999999999999999999 can be an answer.
A rectangular prism has a volume of 300 ft. If the base measures 5 ft by 8 ft, what is the height of the prism?
40 ft
13 ft
23.1 ft
7.5 ft
Answer:
7.5 ft
Step-by-step explanation:
Volume of a prism is V = L*W*H.
In this case, the volume is V = 300 ft^3 (not 300 ft). Therefore,
300 ft^3 = L*W*H = (8 ft)(5 ft)(height)
Solving for the height, H, we get:
300 ft^3
H = --------------- = 7.5 ft
40 ft^2
Answer:
7.5 ft
Step-by-step explanation:
Vole is the length time the width times the height
V = l*w*h
Substituting what we know
300 = 5*8*h
300 = 40h
Divide each side by 40
300/40 =40h/40
7.5 =h
What is the name of the property given below?
If a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.
Answer:
This is the zero product rule.
Step-by-step explanation:
a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.
This is the zero product rule.
It shows that for the product to be zero, at least one factor must be zero
If a*b= 0: It shows that one of the factor is zero or may be both the factors are zero that is why their resultant product is 0....
Each week your science teacher gives a fifteen-point quiz. Your current scores are shown in the table. What is your mean quiz score?
The answer is 12 points
I have the table so I added the numbers to get 108, and there are 9 numbers, so yu do 108/9 equaling to 12
Look at the figure. Find TW
Answer: NUMBER 9 I'm on gradpoint too
Step-by-step explanation:
Given the diagram below what is tan 60?
A. [tex]\sqrt{3}[/tex]
What is triangle and its properties?In the Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.
We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle
from we know that tangent represents the relation between opposite or adjacent of the right triangle.
[tex]tan = \frac{opposite}{adjacent}[/tex]
We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.
from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,
[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]
[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]
[tex]x=8[/tex]
Upon substituting these values on above formula we will get,
[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]
hence, the value of tan(60) is [tex]\sqrt{3}[/tex]and option B is the correct choice.
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What is the following product ^3sqrt16x^7*^3sqrt12x^9
Answer:
4x^5\sqrt[3]{3x}
Step-by-step explanation:
Given
[tex]\sqrt[3]{16x^7}\left(\sqrt[3]{12x^9}\right)\\\sqrt[3]{4^{2} x^7}\sqrt[3]{4(3)x^9}\\ 4^\frac{2}{3} . x^\frac{7}{3} . 4^\frac{1}{3} . 3^\frac{1}{3} . x^\frac{9}{3}\\ 4^\frac{2+1}{3} . 3^\frac{1}{3}. x^\frac{9+7}{3} \\4^\frac{3}{3} . 3^\frac{1}{3}. x^\frac{16}{3}\\ 4\sqrt[3]{3x^16}[/tex]
[tex]4\sqrt[3]{3} . x^\frac{16}{3} \\4\sqrt[3]{3} . x^\frac{15}{3} .x^\frac{1}{3} \\4\sqrt[3]{3} . x^5 .x^\frac{1}{3} \\4x^5\sqrt[3]{3x}[/tex] !
Answer:
The expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex]
Required
Products of both
To do this, we have to apply the laws of indices,
Follow the highlighted steps
Step 1: Multiply both parameters directly
Since they both have the same roots, they can be multiplied directly according to the law of indices
[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] becomes
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex]
Step 2: Apply the 1st law of indices
First law of indices states that
[tex]x^{a} * x^{b} = x^{a + b}[/tex]
So, [tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] becomes
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7} * x^{9} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7+9} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{16} }[/tex]
[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{192 * x^{16} }[/tex]
Step 3: Rewrite the expression
[tex]\sqrt[3]{192 * x^{16} }[/tex] = [tex]({192 * x^{16} })^{\frac{1}{3} }[/tex]
Step 4: Expand the Expression in bracket
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]({64 * 3* x^{15} * x^{1} })^{\frac{1}{3} }[/tex]
Break down into bits
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]64^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3}) ^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3*\frac{1}{3}}) * 3^\frac{1}{3} * (x^{15}*^\frac{1}{3}) * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 * 3^\frac{1}{3} * (x^{5}}) * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 (x^{5}})* 3^\frac{1}{3} * (x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3^\frac{1}{3} * x^{\frac{1}{3}})[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3x)^\frac{1}{3}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * \sqrt[3]{3x}[/tex]
[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Hence, the expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]
Solve by factoring or finding square roots
x^2-1=0
Answer:
{1,-1}
Step-by-step explanation:
Let's do both!
Factoring!
x^2-1 is a difference of squares.
The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So we want to solve the equation x^2-1=0 which is equivalent to solving
(x-1)(x+1)=0.
If you have A*B=0 then either A=0 or B=0.
So in our case we have x-1=0 or x+1=0.
Now we just solve the equations.
x-1=0 can be solved by adding 1 on both sides giving us x=1.
x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.
Square root!
When you want to use square roots, you have to have a perfect square containing the variables and a constant. We have that here.
We have x^2-1=0 which is equivalent to x^2=1. You could get this last equation by adding one on both sides of x^2-1=0.
Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]\sqrt{x^2}=\sqrt{1}[/tex]
[tex]x=\pm \sqrt{1}[/tex] It leads to two answers because [tex]\sqrt{x^2}=|x|[/tex].
[tex]x=\pm 1[/tex]
The solution to the equation x^2-1=0 is x = 1 or x = -1.
Explanation:To solve the equation x^2-1=0 by factoring or finding square roots, we can start by rearranging the equation to get x^2=1. This means that the square of x is equal to 1. To find the square root of both sides, we take the square root of 1, which gives us x=±1. So the solution to the equation is x = 1 or x = -1.
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Which statements about the hyperbola are true? Check all that apply.
The center is located at (0, 0).
There is a vertex at (–6, 0).
The transverse axis of the graph is vertical.
The foci are located within the rectangular reference box.
The directrices are vertical lines.
Answer:
True options: 1, 2 and 5
Step-by-step explanation:
From the given diagram, you can see that the center of the hyperbola is placed at the origin, so first option is true (see attached diagram for definition of center, vertices, foci, i.e.)
There are two vertices of the hyperbola, they are placed at (-6,0) and (6,0), so second option is true.
The transverse axis is the segment connecting vertices, this segment is horizontal, so option 3 is false.
The foci are not placed within the rectangular reference box, so this option is false.
The directrices are vertical lines with equations [tex]x=\pm \dfrac{a}{e}[/tex], so this option is true.
Answer:1 2 5
Step-by-step explanation:
What is the position of F on the number line below? write your answer as a fraction or mixed number
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
There are 4 steps to complete to go from 0 to 1. Hence each step is:
1 out of 4, or simply [tex]\frac{1}{4}[/tex]
F is located at the 3rd mark, which will be [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}[/tex]
Hence, F is located at [tex]\frac{3}{4}[/tex]
Answer:
F is on [tex]\frac{3}{4}[/tex] on the number line
Step-by-step explanation:
Notice in the image that between 0 and 1 there are 4 subdivisions.
Then divide.
[tex]\frac{1}{4} = 0.25[/tex].
Each subdivision is equal to 0.25 units.
Point F is in the third subdivision.
This means that the distance between 0 and F is:
[tex]\frac{1}{4}*3 = \frac{3}{4} = 0.75[/tex].
Finally F is on [tex]\frac{3}{4}[/tex] on the number line