Answer:
See explanation section
Step-by-step explanation:
Requirement A)
According to the graph, whenever Sarah purchased one comic book, she lost $5 from her allowance. Now the allowance remain after purchasing one comic book = ($100 - 5) = $95
Whenever she purchased three comic books, she lost $5 × 3 = $15 from her allowance. Now the allowance remain after purchasing three comic books = ($100 - 15) = $85. In that way, she lost her $50 after purchasing 10 comic books from her allowance. Therefore, the rate of change is $5.
Requirement B)
It represents that she spent $5 on her each comic book. It also represents that her each book decreases her allowance by $5.
Answer:
a) -5
Step-by-step explanation:
a) slope = (90-100)/(2-0) = -5
b) rate of change represents the deduction in amount left when one more book is purchased.. which is the cost of one book
Which expression is equivalent to (5g^4+5g^3-17g^2+6g)-(3g^4+6g^3-7g^2-12)/g+2
Option C:
[tex]2 g^{3}-5 g^{2}+6[/tex]
Solution:
Given expression:
[tex]$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}[/tex]
To find which expression is equal to the given expression.
[tex]$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}[/tex]
Expand the term [tex]-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right):-3 g^{4}-6 g^{3}+7 g^{2}+12[/tex]
[tex]$=\frac{5 g^{4}+5 g^{3}-17 g^{2}+6 g- 3 g^{4}-6 g^{3}+7 g^{2}+12}{g+2}[/tex]
Arrange the like terms together.
[tex]$=\frac{5 g^{4}- 3 g^{4}+5 g^{3}-6 g^{3}-17 g^{2}+7 g^{2}+6 g+12}{g+2}[/tex]
[tex]$=\frac{2 g^{4}- g^{3}-10 g^{2}+6 g+12}{g+2}[/tex]
Factor the numerator [tex]2 g^{4}-g^{3}-10 g^{2}+6 g+12=(g+2)\left(2 g^{3}-5 g^{2}+6\right)[/tex]
[tex]$=\frac{(g+2)\left(2 g^{3}-5 g^{2}+6\right)}{g+2}[/tex]
Cancel the common factor g + 2, we get
[tex]=2 g^{3}-5 g^{2}+6[/tex]
Hence option C is the correct answer.
Answer:
C.
Step-by-step explanation:
which of the following statements is true? A. 15-0=0 B. 0÷15=0 C. 15+0=0 D. 15÷0=0
Answer:
B) 0:15=0
Step-by-step explanation:
What do you multiply -2 by to get -24
Answer:
The answer is 12
Step-by-step explanation:
Step 1: Convert words into an equation
What do you is you multiply -2 by something to get -24
-2 * something = -24
We can represent something with a variable called x.
-2 * x = -24
-2x = -24
Step 2: Solve for x by dividing both sides by -2
-2x / -2 = -24 / -2
x = 12
Answer: The number we can multiply -2 by to get -24 is 12
Lets write this into an expression.
-2x = -24
Now, lets solve for x.
~Divide -2 to both sides
-2x/-2 = -24/-2
~Simplify
x = 12
Best of Luck!
Find Volume of Cylinders
1. The radius of a cylinder is 49 feet, and the height is 180 feet.
Find the volume of the cylinder.
Answer:
V ≈ 143.91938 ft
Step-by-step explanation:
V = π r² h
V = π r² h = π · 49² · 180
V ≈ 1.35773 × 10⁶
V ≈ 143.91938 ft
volume of the cylinder is 13577335.51 cubic feet
What is a cylinder?A 3-dimensional solid geometric figure with straight parallel sides and a circular or oval cross section is called a cylinder.
How to find the volume of the cylinder?The volume of the cylinder can be found with the help of the formula,V = πr²h
where, V = volume of the cylinder
r= the radius of base
h = height of the cylinder
According to the problem, volume of the cylinder = π(49)²( 180)
=13577335.51 cubic feet
∴ volume of the cylinder is 13577335.51 cubic feet
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hi! i could really use some help....
Answer:
with what
Step-by-step explanation:
Use the Distributive Property to express
24 + 36
Answer:
12(2 + 3)
Step-by-step explanation:
To use the distributive property, we must find a common factor between the two numbers. The greatest common factor or 24 and 36 is 12. Let's just use that. We get:
[tex]12(2+3) = 24+36[/tex]
That's our answer!
Answer:
12 ( 2 + 3 )= + 36
Step-by-step explanation: GCF between 24 and 36 by prime factorization should be:
24 = 2 * 2 * 2 * 3
36 = 2 * 2 * 3 * 3. what they both have in common between the prime factorization of both of the numbers are 2*2*3 which is GCF and equivlent to 12.
Select all that are asymptotes of the
tangent graph.
x = pi/4
x=pi/2
x=pi
x=3pi/2
x=3pi
Answer:
[tex]x = \frac{\pi}{2} [/tex]
[tex]x = \frac{3\pi}{2} [/tex]
Step-by-step explanation:
The tangent function is
[tex]y = \tan(x) [/tex]
We can rewrite it as:
[tex]y = \frac{ \sin(x) }{ \cos(x) } [/tex]
This graph has vertical asymptotes at where the denominator is zero.
[tex] \cos(x) = 0 \\ \implies \: x = \frac{\pi}{2} \: or \: \frac{3\pi}{2} [/tex]
The correct options are : (b) [tex]\( x = \frac{\pi}{2} \)[/tex] and (d) [tex]\( x = \frac{3\pi}{2} \)[/tex]
The asymptotes of the tangent graph are the vertical lines where the tangent function is undefined. The tangent function, [tex]\(\tan(x)\)[/tex], is undefined where the cosine function is zero, which happens at:
[tex]\[ x = \frac{\pi}{2} + k\pi \quad \text{for integer values of } k \][/tex]
So, let's check each given value to see if it fits this form.
1. [tex]\( x = \frac{\pi}{4} \)[/tex]
[tex]\[ \frac{\pi}{4} \neq \frac{\pi}{2} + k\pi \][/tex]
This is not an asymptote.
2. [tex]\( x = \frac{\pi}{2} \)[/tex]
[tex]\[ \frac{\pi}{2} = \frac{\pi}{2} + 0 \times \pi \][/tex]
This is an asymptote.
3.[tex]\( x = \pi \)[/tex]
[tex]\[ \pi \neq \frac{\pi}{2} + k\pi \][/tex]
This is not an asymptote.
4. [tex]\( x = \frac{3\pi}{2} \)[/tex]
[tex]\[ \frac{3\pi}{2} = \frac{\pi}{2} + \pi \][/tex]
This is an asymptote.
5.[tex]\( x = 3\pi \)[/tex]
[tex]\[ 3\pi \neq \frac{\pi}{2} + k\pi \][/tex]
This is not an asymptote.
The asymptotes of the tangent graph from the given options are:
[tex]\( x = \frac{\pi}{2} \)[/tex]
[tex]\( x = \frac{3\pi}{2} \)[/tex]
The complete Question is
Select all that are asymptotes of the
tangent graph.
a. x = pi/4
b. x=pi/2
c. x=pi
d. x=3pi/2
e. x=3pi
how do you evaluate (-8) to the 4th power?
Answer:
4096
Step-by-step explanation:
You want to evaluate (-8)⁴.
ExponentThe exponent of 4 signifies the base (-8) is a factor 4 times in the product:
(-8)⁴ = (-8)×(-8)×(-8)×(-8)
The multiplication is accomplished in the usual way. There are an even number of minus signs, so the product will be positive. The value is ...
(-8)×(-8)×(-8)×(-8) = 8·8·8·8 = 64·8·8 = 512·8 = 4096
(-8)⁴ = 4096
__
Additional comment
It can be faster to decompose the exponent into powers of 2. This makes it possible to use squaring to reduce the number of operations required.
(-8)⁴ = (8²)² = 64·64 = 4096
Quincy has a piece of pipe that is 2/3 yard long - he uses 3/4 to repair a sink. What length of the pipe will he use for the sink?
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Answer:
Step-by-step explanation
Length of pipe =2/3yard
3/4 of pipe = 3/4 × 2/3
= 2/4 = 1/2 yard
V(r)=c((r^3)-72.25r) solve for c
Answer:
c = V/((r^3)-72.25r)
Step-by-step explanation:
V is proportional to c, so you can simply divide by the coefficient of c.
c = V/((r^3)-72.25r)
What is the value of y?
A. y = -1
B. y = 0
C. y = 1
D. y = 3
Step-by-step explanation:
The centroid divides the length of each median in 2:1 ratio.
The length of the part between the vertex and the centroid is twice the length between the centroid and the mid-point of the opposite side.
In case of median KM,
K is the vertex and M is the midpoint of the side JL
KT = 2× TM
5y+3 = 2(y+3)
5y+3= 2y +6
5y-2y= 6-3
3y = 3
y= 1
Choose the product. -7 p3 (4 p2 + 3 p - 1)
The product of -7p³ and the trinomial (4p² + 3p - 1) is obtained by multiplying -7p³ by each term of the trinomial and combining like terms, resulting in -28p⁵ - 21p⁴ + 7p³.
The question involves multiplying a monomial by a trinomial in algebra, which is a process of using the distributive property. To multiply -7p³ by (4p² + 3p - 1), you distribute -7p³ across each term in the trinomial:
-7p³ x 4p² = -28p⁵-7p³ x 3p = -21p⁴-7p³ x (-1) = 7p³Combine the results to get the final product:
-28p⁵ - 21p⁴ + 7p³
Write the equation y=2/3x-4
in standard form.
Rectangular pyramid: volume 3800 area of the base 300
Answer:
4000
Step-by-step explanation:cause u add 3
7. The ratio of wins to losses for Loyola basketball was 4 to 1. If the team played 30 games, how
many wins and how many losses did they have? Show your work.
Answer:
24:6
Step-by-step explanation:
It is 4 to 1. The ratios added up is 5. So 30 divided by 5 is 6. So 1 (the ratio) is 6 games. 4x6=24. So the new ratio is 24 to 6. 24 wins and 6 losses.
The team won 24 games and lost 6, calculated by first solving for x in the equation 5x = 30 and then applying the 4:1 win-to-loss ratio.
If the ratio of wins to losses for Loyola basketball is 4 to 1, and they played 30 games, we want to find how many of those games were wins and how many were losses. Let's say the number of wins is 4x and the number of losses is x. According to the ratio, there are 4 wins for every loss, which makes the total number of games 4x + x = 5x.
Since we know 5x is 30 games, we can solve for x to find out the number of losses. Dividing 30 by 5, we get x = 6. That's the number of losses. To find the number of wins, we multiply 4 times the number of losses (4x), which gives us 4 * 6 = 24 wins.
One x-intercept for a parabola is at the point
(2,0). Use the quadratic formula to find the
other x-intercept for the parabola defined by
this equation:
y=x² – 3x + 2
Answer:
The other x-intercept is the point (1,0)
Step-by-step explanation:
we have
[tex]y=x^2-3x+2[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]y=x^2-3x+2[/tex]
equate to zero
[tex]x^2-3x+2=0[/tex]
so
[tex]a=1\\b=-3\\c=2[/tex]
substitute in the formula
[tex]x=\frac{-(-3)\pm\sqrt{-3^{2}-4(1)(2)}} {2(1)}[/tex]
[tex]x=\frac{3\pm\sqrt{1}} {2}[/tex]
[tex]x=\frac{3\pm1} {2}[/tex]
so
[tex]x=\frac{3+1} {2}=2[/tex]
[tex]x=\frac{3-1} {2}=1[/tex]
therefore
The other x-intercept is the point (1,0)
What is the sum of -8 and it’s opposite
Answer:0
Step-by-step explanation:
-8 + 8 (opposite)
=0
Answer:
0
Step-by-step explanation:
the oppisite of -8 is 8 the sum of 8+(-8)
is the same as 8-8
Given the equation 3x+9y=-8,write a second linear equation to create a system that has exactly one solution.
A second linear equation that forms a system with exactly one solution with 3x+9y=-8 could be y = -2x + 4, as it has a different slope and y-intercept, ensuring the lines intersect at one point.
Explanation:To create a system of equations with exactly one solution, you need to write a second linear equation that has a different slope than the first equation (3x+9y=-8) but does not share any points with it. The slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, will be used to construct our new equation.
Given the slope-intercept form y = 9 + 3x as an example, we see that the slope (m) is 3 and the y-intercept (b) is 9. To ensure our second equation has only one solution when paired with the first equation, we can select a different slope and y-intercept. For instance, an equation such as y = -2x + 4 would suffice, as it has a different slope (-2) and intercept (4), ensuring that the two lines will cross at exactly one point on the graph.
In summary, the original equation 3x+9y=-8 and the second equation y = -2x + 4 when graphed will intersect at exactly one point, forming a system of linear equations with one solution. This process involves selecting different values for the slope and y-intercept to make sure the lines are not parallel and do not coincide.
what are the y-intercept and the slope of the graph of the following equation? -2x + 4y = 8
Answer:
Slope=2/4 or 1/2
Y-Intercept=8
Step-by-step explanation:
-2x+4y=8
+2x both sides
4y=2x+8
/4
y=2/4x+8
Slope=2/4 or 1/2
Y-Intercept=8
The slope of the graph of the equation -2x + 4y = 8 is [tex]\frac{1}{2}[/tex] , and the
y-intercept is 2.
To calculate the y-intercept and slope of the graph of the equation -2x + 4y = 8, to change the given equation in the general form of line. The general form of the line is y = mx + b, where m is the slope of the line and b is the y-intercept of the line.
Find the value of y from the given equation of graph.
Calculate y as:
[tex]-2x + 4y = 8\\4y = 2x + 8\\y=\dfrac{2}{4}x+2\\ y=\dfrac{1}{2}x +2[/tex]
Here, the slop of the graph m is [tex]\dfrac{1}{2}[/tex] and y-intercept is 2
Therefore, the slope of the graph is 1/2, and the y-intercept is 2.
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Find the vertex and axis of symmetry for f(x)=2x^2-1
Solution:
Given is:
[tex]f(x) = 2x^2 - 1[/tex]
We have to find the vertex and axis of symmetry
The general equation is given as:
[tex]f(x) = ax^2 + bx + c[/tex]
Comparing with given equation,
a = 2
b = 0
c = -1
The axis of symmetry is given as:
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{0}{2(2)}\\\\x = 0[/tex]
Thus axis of symmetry is 0
The x coordinate of the vertex is the same
x coordinate of the vertex = 0
h = 0
The y coordinate of the vertex is:
k = f(h)
k = f(0)
[tex]f(0) = 2(0) - 1\\\\f(0) = 0 - 1\\\\f(0) = -1[/tex]
Thus, y coordinate of the vertex is -1
Therefore, vertex is (0, -1)
How many students are in Ms. Jackson’s class?
A. 10
B. 15
C. 23
D. 25
There are 15 students in Ms. Jackson’s class
How many students are in Ms. Jackson’s class?
From the question, we have the following parameters that can be used in our computation:
The Venn diagram
Where, we have
Both = 5
None = 2
Using the above as a guide, we have the following:
Total students = (10 -5) + 5 + (8 -5) + 2
Evaluate
Total students = 15
Hence. there are 15 students in Ms. Jackson’s class
Tell which quadrant each of the following points is located in: I, II, III, or IV.
11. (20, 10) -
10. (-9,17) -
9. (15, -12)
13. (30,-8)
12. (-6, -23)
14. (-5.-5)
16. (-14,-2)
17. (-8, 35)
15. (18, 10)
Can anyone help me I did not know how to do it
answer:
11.Quadrant 1 10.quadrant II 9. IV 13. IV 12. III 14. III 16: III 17: II 15 I
Step-by-step explanation:
this should help https://socratic.org/questions/what-is-the-order-of-quadrants-in-a-graph just look at the coordinates x and y if they correspond to which quadrant.
Each point is placed in a quadrant based on its x and y values. Quadrant I contains points where both values are positive, Quadrant II where x is negative and y is positive, Quadrant III where both are negative and Quadrant IV where x is positive and y is negative
Explanation:To determine which quadrant a point is located in, recognize that the x-y coordinate plane is divided into four sections called quadrants. The quadrants are numbered I through IV and progress counterclockwise, starting with quadrant I in the upper right corner.
Quadrant I: Both x and y are positive. Quadrant II: x is negative, y is positive. Quadrant III: Both x and y are negative. Quadrant IV: x is positive, y is negative.
With this in mind, let's carry out the following:
(20, 10) - this is in Quadrant I because both values are positive.(-9,17) - because x is negative and y is positive, this is in Quadrant II. (15, -12) - because x is positive and y is negative, this is in Quadrant IV. (30,-8) - for the same reason as before, this is in Quadrant IV.(-6, -23) - this is in Quadrant III because both x and y are negative.(-5,-5) - this is in Quadrant III for the same reason as above.(-14,-2) - this is in Quadrant III for the same reason as above.(-8, 35) - this is in Quadrant II because x is negative and y is positive.(18, 10) - this is in Quadrant I because both values are positive.Learn more about Coordinate Plane here:https://brainly.com/question/31180198
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Jill collected a total of 19 gallons of honey.if she distributes all of the honey equally between 9 jars,how much honey will be in each jar
Answer:
2.1 gaallons of honey
Step-by-step explanation:
If you have to istrubute things then its obvous you need to divide something. To get 19 equally into 9 containers you divide 19 by 9 an get 2.1
I hope this helped
Each jar will have approximately [tex]\( \boxd{2.111 \text{ gallons}} \)[/tex] of honey.
Step 1
To find out how much honey will be in each jar when Jill distributes all of the honey equally among 9 jars, we need to divide the total amount of honey by the number of jars.
Given:
Total amount of honey = 19 gallons
Number of jars = 9
So, to find out how much honey each jar will have, we divide the total amount of honey by the number of jars:
[tex]\[ \text{Amount of honey per jar} = \frac{\text{Total amount of honey}}{\text{Number of jars}} \]\[ \text{Amount of honey per jar} = \frac{19 \text{ gallons}}{9} \]\[ \text{Amount of honey per jar} = \frac{19}{9} \text{ gallons} \][/tex]
Step 2
Now, let's perform the division:
[tex]\[ \text{Amount of honey per jar} = 2.111111 \text{ gallons} \][/tex]
So, each jar will have approximately [tex]\( \boxd{2.111 \text{ gallons}} \)[/tex] of honey.
the length of a rectangle is four feet longer than the width. the area is 21. find the dimension
The dimensions of the rectangle are: Width = 3 feet, Length = 7 feet.
The formula for Area of rectangle
Area = length x width
Given:
Area of rectangle = 21 square feet.
Let the width of the rectangle is w feet.
According to the given information, the length of the rectangle is four feet longer than the width,
So, length = w + 4 feet.
So, Area of rectangle = length x width
21 = w (w+4)
[tex]\[21 = w^2 + 4w\][/tex]
[tex]\[w^2 + 4w - 21 = 0\][/tex]
Solve this quadratic equation, set it equal to zero:
w² + 7w -3w -21 =0
w(w+7)-3 (w+7)= 0
(w+7)(w-3) =0
Setting each factor equal to zero:
w+ 7 =0
w= -7
or, w - 3 =0
w = 3
So, the length of rectangle is
= 3+ 4
= 7 feet
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1. Which of the following expressions is equivalent to -3(x + 2) + (x – 3)x:
A. -5x – 6
B. -5x + 2
C. x2 - 6x – 6
D. x2 - 6x + 2
Answer:
C)x^2 - 6x-6
Step-by-step explanation:
-3(x + 2) + (x – 3)x=
-3x-6+x^2-3x=
x^2 - 6x-6
Answer:
C
Step-by-step explanation:
-3(x + 2) + (x – 3)x = -3*x + (-3)*2 +x*x - 3*x
= -3x - 6 +x² - 3x
= x² - 3x -3x - 6
= x² - 6x - 6
there are points (1,62) (2,123) (3,188) (4,228) (5,280) (6,344) on a graph
I need to find the slope in the form of y=Mx+b
Answer:
Step-by-step explanation:
Find the change in y over the change in x.
1. 123-62/2-1
2. Slope = 39x
A student timed his drive to work each day for the three days. The times are shown 15 minutes 16 minutes 20 minutes what was his mean time
Answer:
Step-by-step explanation:
first you add all the numbers together-
15+16+20=51
you add them up as shown-
=51
and the divide by 3, because you added up 3 numbers-
51/3=17
so your answer is 17
The price of an item has been by 95% the original was $35
is y = 2x + 4 a proportion relationship
Answer: No
Step-by-step explanation:
When graphing [tex]y=2x+4[/tex] it comes out not being a proportion relationship.
*(revised answer)
So the answer is no, a proportional relationship has to run through the origin, and y=2x+4 has a y-intercept of 4, meaning that even though x increases when y does, the y-intercept means that this equation is not a proportional relationship.
Hope this helps!
(Thx for helping)
Find the equation of straight line bisecting the segment joining the point (5,3) and (4,4) and the making of an angle of 45 degree with positive direction of x axis
Step-by-step explanation:
Let the required line bisects the segment joining the point (5,3) and (4,4) at point M (x, y).
Therefore, M is the mid point of segment joining the point (5,3) and (4,4).
Now by mid-point formula we have:
[tex]M = ( \frac{5 + 4}{2} \: \: \frac{3 + 4}{2} ) = ( \frac{9}{2} \: \: \frac{7}{2} ) \\ \\ \therefore \: M \: = ( 4.5 \: \: 3.5 ) = (x_1 \: \: y_1)\\ \\ \because \: Line \: makes \: 45 \degree \: angle \: with \: positive \: \\ \: \: \: \: \: direction \: of \: x - axis. \\ \\ \therefore \: Slope \: of \: line: \: \\ \: \: \: \: \: \: \: m = tan \: 45 \degree = 1 \\ \\ Equation \: of \: line \: in \: slope \: point \: form\\ \: is \: given \: as: \\ y-y_1 =m(x-x_1) \\ \therefore \: y - 3.5 = 1(x - 4.5) \\ \therefore \: y - 3.5 = x - 4.5 \\ \therefore \: y = x - 4.5 + 3.5 \\ \therefore \: y = x - 1\\ \huge \purple { \boxed{\therefore \: x - y - 1 = 0}} \\ [/tex]
is the equation of required line.