Determine the interval(s) on which the given function is decreasing.
Polynomial going up from the left and passing through the point negative 1 comma 0 and going to a relative maximum at the point 0 comma 5 and then going down to a relative minimum at the point 1 comma 4 and then going up to the right
Answer Choices:
(–∞, –1) ∪ (1, ∞)
(–1, ∞)
(–∞, 0) ∪ (1, ∞)
(0, 1)
Analyzing the text, we find that the function is decreasing over the following intervals: (0, 1)
-------------------------
Polynomial going up from the left and passing through the point (-1,0), going to a relative maximum at the (0,5) and then going down to a relative minimum at the point (1,4).Going from maximum to minimum, meaning that between them the function decreases, thus, the first interval it is decreasing is between (0,1).
Going up to the right:Going up, increases.
-------------------------
Thus, the function decreases over the following interval: (0, 1)
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Jerry sold 320 tickets for the school play. He sold x adults tickets for $8 each and y child tickets for $5 each. He sold $1900 worth of tickets. Write a system of equations to model the situation.
What is the equation?
Answer:
x + y = 320
8x + 5y = 1900
Step-by-step explanation:
The equation x + y = 320 represents how 320 tickets were sold in total, from combining the adult and child tickets sold.
Since adult tickets are $8 each, the money from adult ticket sales can be represented by 8x.
The money from child ticket sales can be represented by 5y.
The equation 8x + 5y = 1900 represents how $1900 worth of tickets were sold.
So, the system of equations for the situation is:
x + y = 320
8x + 5y = 1900
Answer:
y = 220
x = 100
Step-by-step explanation:
x + y = 320
8x + 5y = 1900
x = 320 - y
8(320 - y) + 5y = 1900
2560 - 8y + 5y = 1900
2560 -3y = 1900
-2560 -2560
-------------------------
-3y = -660
----- -------
-3 -3
y = 220
x + 220 = 320
-220 -220
----------------------
x = 100
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
A. The slope of f(x) is greater than the slope of g(x).
B. The slope of f(x) is less than the slope of g(x).
C. The slope of f(x) is equal to the slope of g(x).
D. The slope of g(x) is undefined
Answer:
The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
a graph of a line labeled f of x passing through 0, negative 1 and 3, 1
x g(x)
0 2
3 4
6 6
Slope is defined as the change of the y axis to the z axis of a plane.
Slope = ∆y/∆x
Slope = y2-y1/x2-x1
For f(x) with coordinates (0, -1) and (3,1)
x1 = 0, y1 = -1, x2 = 3 and y2 = 1
Slope of f(x) = 1-(-1)/3-0
Slope = 1+1/3
Slope = 2/3
For g(x), we will choose any two of the coordinates from the table. Using the coordinates (3,4) and (6,6)
x1 = 3, y1 = 4, x2 = 6 and y2 = 6
Slope of g(x) = 6-4/6-3
Slope of g(x) = 2/3
It can be seen that the value of both slopes are equal. Hence, the slope of f(x) is equal to the slope of g(x) is the correct option.
Answer:
The answer is C. The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
Did the test.
write the equation for each word sentence and solve 2 problems.
problem one : 12 more than a number is 20
problem two: The sum of a number and eight equals the sum of four times the number and six.
Answer:
1. 12 + x = 20 2. x + 8 = 4x + 6
Step-by-step explanation:
problem 1 :
12 + x = 20
problem 2:
x + 8 = 4x + 6
what is the value of a in the functions equation?
Answer:
y= -2x^2 + 12x -14
Step-by-step explanation:
when I put the points into a graphing calculator this is what I got so I think the answer is -2
Answer:
Step-by-step explanation:
It is -2
What is the y-intercept of the line passing through the point (9,-7) with a slope of -1/8 ?
Answer:
-47/8.
Step-by-step explanation:
If the line has a slope of -1/8, that means the equation y = mx + b will be y = -1/8x + b.
In this case, we are given a point: (9, -7). That means that x = 9 and y = -7.
-7 = (-1/8)(9) + b
b - 9/8 = -7
b = -56/8 + 9/8
b = -47/8 = -5.875 = -5 and 7/8, which is your y-intercept!
Hope this helps!
The value of x in this system of equations is 1. 3x + y = 9 y = –4x + 10 Substitute the value of y in the first equation: Combine like terms: Apply the subtraction property of equality: Apply the division property of equality:
Answer:
X = 1
Step-by-step explanation:
To solve the system of equation by susbtitution:
3x + y = 9
y = –4x + 10
We can follow the steps thus:
Substitute the value of y in the first equation:
As in the second equation y = -4x + 10 we can substitute in the first equation as follows:
3x + y = 9
3x + -4x + 10 = 9
Combine like terms:
3x + -4x + 10 = 9
Like therms are the therms with X (3x - 4x = -1x):
-1x + 10 = 9
Apply the subtraction property of equality:
-1x + 10 = 9
As 10 is suming, it passes to subtracting the 9:
-1x = 9 - 10
-1x = -1
Apply the division property of equality:
-1x = -1
Dividing in -1:
x = -1 / -1
X = 1Answer:
b
Step-by-step explanation:
The value of x in this system of equations is 1.
3x + y = 9
y = –4x + 10
Substitute the value of y in the first equation:
Combine like terms:
Apply the subtraction property of equality:
Apply the division property of equality:
3x + (–4x + 10) = 9
–x + 10 = 9
–x = –1
x = 1
What is the value of y?
y =
Please Help. Will Mark Brainliest Answer. A container of juice is taken from the refrigerator and poured into a pitcher. The temperature of the juice will warm to room temperature over time. The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator. Use the drop-down menus to complete the explanation of how the function models the juice warming over time. Dropdown possible answers: When t = 0, the temperature of the juice is -0.06, 0, 2.718, 32, 40, 72 degrees. As time increases, -32(2.718)^-0.06t gets close and closer to -0.06, 0, 2.718, 32, 40, 72. So, f(t) gets close and closer to -0.06, 0, 2.718, 32, 40, 72.
Answer:
When t= 0
f(t)= 40 degrees
The value of −32(2.718)^−0.06t approach 0 as t increases
If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72
Step-by-step explanation:
The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator.
f(t)=72−32(2.718)^−0.06t
When t= 0
f(t)=72−32(2.718)^−0.06(0)
f(t)=72−32(2.718)^(0)
f(t)=72−32(1)
f(t)=72−32
f(t)= 40 degrees
As t increases −32(2.718)^−0.06t
Let t= 1
=−32(2.718)^−0.06(1)
= −32(2.718)^−0.06
= -30.14
Let t = 2
=−32(2.718)^−0.06(2)
=−32(2.718)^−0.12
=−32(0.8869)
= -28.38
The value of −32(2.718)^−0.06t approach 0 as t increases
If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72
When t = 0, the temperature of the juice is 40°.
As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.
So, f(t) gets close to 72°
Function representing the temperature of of the juice at any time 't' is,
[tex]f(t)=72-32(2.718)^{-0.06t}[/tex]
1). If t = 0,
[tex]f(0)=72-32(2.718)^{-0.06\times 0}[/tex]
[tex]=72-32(1)[/tex]
[tex]=40[/tex] degrees
2). If [tex]t\rightarrow \infty[/tex],
[tex]-\frac{1}{32(2.718)^{0.06t}} \rightarrow 0[/tex]
[As denominator of the fraction becomes larger and larger with the increase in the value of t, value of fraction gets smaller and smaller]
3). if [tex]t\rightarrow \infty[/tex], [tex]f(t)\rightarrow 72[/tex]
Therefore, when t = 0, the temperature of the juice is 40°.
As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.
So, f(t) gets close to 72°.
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Sakura solved a fraction division problem using the rule "multiply by the reciprocal." Look at her work. 7 ÷ 2/ 5 1/ 7 × 2/ 5 = 2/35 Did she solve the problem correctly?
Answer:
D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Step-by-step explanation:
A. Yes. She solved the problem correctly.
B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.
C. No. She multiplied the denominators instead of finding a common denominator.
D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Her workings
7 ÷ 2/ 5
=1/ 7 × 2/ 5
= 2/35
Dividend=7
Divisor=2/5
The correct working
7 ÷ 2/ 5
=7 × 5/2
=35/2
Answer:
D
Step-by-step explanation:
I got an 100% on the quiz I took with this question :)
Hope I could help good luck on passing!!
find the multiplicative inverse of 3 by 4 minus 5 by 7
Answer:
28
Step-by-step explanation:
[tex]\frac{3}{4}-\frac{5}{7}[/tex]
Least Common Denominator of 4 & 7 is 4 * 7 = 28
[tex]\frac{3}{4}-\frac{5}{7}=\frac{3*7}{4*7}-\frac{5*4}{7*4}\\\\\\=\frac{21}{28}-\frac{20}{28}\\\\\\=\frac{21-20}{28}\\\\\\=\frac{1}{28}[/tex]
Multiplicative inverse of [tex]\frac{1}{28}[/tex] is [tex]\frac{28}{1} = 28[/tex]
The tens digit is 2 less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
Answer:
68
Step-by-step explanation:
Hello, the number is 'ab' meaning that we can write it as 10a +b
For instance 42 = 10*4 + 2
So, a = b - 2
and 10a + b + 10b + a = 154
11(a+b)=154
a+b = 154/11 = 14
We replace a by b - 2
b+b-2 = 14
2b = 14 + 2 = 16
b = 8 and then a = 6
the original number is 68.
Thanks
Write an expression that represents an increase of 5% over the
original cost of $d as both a sum and product of d.
Answer:
Sum equation: [tex]d + 0.05d[/tex]
Product equation: [tex]1.05d[/tex]
Step-by-step explanation:
If we have an increase in 5% of d, that means that 5% of d ([tex]0.05\cdot d[/tex]) will be the total amount of money added to it.
However, we need to still count the original price of d, if we increase it by 5%!
So we add d to 0.05d.
[tex]d + 0.05d[/tex] is the sum equation.
Now, we can create the product equation for d by expanding the coefficients for the previous equation, [tex]d + 0.05d[/tex].
[tex]1d + 0.05d[/tex]
We can add like terms here: [tex]1 + 0.05 = 1.05[/tex]! So we can just multiply this by d for our product equation.
[tex]1.05d[/tex]
Hope this helped!
I need help with this question. PLZZ HELP!!!
Answer:
the 8 in the graph
Step-by-step explanation:
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART
Answer:
I have to agree
it's A.
but I'm also thinking it's D.
1 point 56. While riding a bicycle, a person travelled 5 blocks in 2 minutes. At this rate, how many blocks will the person travels in 16 minutes? Q
the person will travel 40 blocks in 16 minutes
complete by using the distributive property (y+3)(y+3)(y+3)
Answer:
y^3+9y^2+27y+27
Step-by-step explanation:
Step 1: Start by understanding FOIL. First. Outer. Inner. Last.
Step 2: In this case we have three sets of parenthesis not 2. So we have to do the same thing but multiply 2 (y+3) sets by y and 3 instead of only multiplying y and 3 by one set.
Step 3: So we get y^3+6y^2+9y+3y^2+18y+27.
This simplifies to y^3+9y^2+27y+27
5 and 6? i got 3 for both
Answer:
Hey there!
5. f(4) is 3. f(3) is 2. Thus, f[f(4)]=2
6. g(2) is 3. g(3) is 1. g[g(2)]=1
Hope this helps :)
The graph represents revenue in dollars as a function of greeting cards sold. A coordinate plane showing Greeting Card Revenue, Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. A line starts at (0. 0) and passes through (2, 8), (4, 16), and ends at (5, 20). Which equation represents the function shown on the graph? y = x y = x y = 2x y = 4x
Answer:
D
Step-by-step explanation:
Just did it
A function assigns the values. The equation that represents the function shown on the graph is y=4x.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the graph represents revenue in dollars as a function of greeting cards sold. Therefore, we can write the function as,
Revenue ∝ Number of cards sold
Since the Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. Therefore, we can write,
y ∝ x
Removing the proportionality, we will get,
y = k x
Now, substitute any point through which the graph of the function passes to get the value of k,
20 = k × 5
20/5 = k
k = 4
Thus, the function can be represented as,
y = kx
y = 4x
Hence, the equation that represents the function shown on the graph is y=4x.
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A dealer bought 3 gross buttons at $.38 a dozen. He sold the buttons at 5 cents each. How much was his profit per gross?(12 dozen equals one gross)
Answer:
$2.64
Step-by-step explanation:
Selling them at 5 cents each ($0.05), he could sell 1 dozen buttons for
12 * $0.05 = $0.60
As he bought them at $0.38 per dozen, the profit per dozen would be
$0.60 - $0.38 = $0.22
As 12 dozen is 1 gross, the profit per gross would be
12 * $0.22 = $2.64
3 x 12 = 36
.5 x 36 = 18.0
36 divided by .38 is about 94.7
18 - 94.7 = -76.7
ANSWER:
about -76.7
(I may have done this wrong
Is (3,-3)(3,−3)left parenthesis, 3, comma, minus, 3, right parenthesis a solution of the graphed system of inequalities?
Hi there!
»»————- ★ ————-««
I believe your answer is:
No.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
If we mark the point at (3, -3), the we can tell that the point does not lie in any shaded region. This means that it is NOT a solution to the system.See the graph attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
No, (3, -3) is not the solution to the graphed system of inequalities.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
From the graph,
The point of intersection is (2, 3).
This is the solution to the graphed system of inequalities.
But,
(3, -3) is given as the solution which is not true.
Thus,
(3, -3) is not the solution.
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What ratio of 25 dextrose and 10% dextrose should be mixed to make a 20% Dextrose? Comments for What Ratio of 25% Dextrose and 10% Dextrose to make 20% Dextrose? 10 parts 25% and 5 parts 10% solution equals 20% mixture.
Answer:
10:5 OR 2:1
Step-by-step explanation:
Let x be the parts of 25% dextrose and
y be the parts of 10% dextrose are mixed so that
20% dextrose mixture is obtained.
amount of dextrose in the mixture will be 20% of (x+y).
We have to find the value of [tex]\frac{x}y \ OR\ x:y[/tex]
Now, we can apply the concept that sum of amount of dextrose in the two liquids will be equal to the amount of dextrose in the mixture.
[tex]\Rightarrow x \times 25\% + y \times 10\%=(x+y)\times 20\%\\\Rightarrow x \times\dfrac{25}{100} + y \times \dfrac{10}{100}=(x+y)\times \dfrac{20}{100}\\\Rightarrow x \times25 + y \times 10=(x+y)\times 20\\\Rightarrow 25x + 10y=20x+20y\\\Rightarrow 25x -20x =20y-10y\\\Rightarrow 5x=10y\\\Rightarrow \dfrac{x}{y} = \dfrac{10}{5}\\\Rightarrow \bold{x:y=10:5\ OR\ 2:1}[/tex]
So, the answer is 10:5 or 2:1.
Answer:
4.90% is approximately the new Dextrose concentration.
Explanation:
Volume by Volume percent is given by ;
Volume percentage of dextrose solution = 5%
In 100 mL of solution 5 ml of dextrose is present.
Now, volume sterile water added was equal to the 40% of volume of dextrose volume.
So, volume of the sterile water added =
Total volume of the solution after addition of water = 100 mL + 1 mL = 102 mL
New concentration of dextrose will be;
4.90% is approximately the new Dextrose concentration.
Step-by-step explanation:
Find the first four terms in the sequence
an 15 + 6n
A. 21, 27, 33, 39
B. 18, 12, 6,0
C. 20, 26, 32, 38
D. 20, 14, 8, 2
Answer:
A. 21, 27, 33, 39
Step-by-step explanation:
an =15 + 6n
Let n=1
a1 = 15 +6(1) = 15+6 = 21
Let n=2
a2 = 15 +6(2) = 15+12 = 27
Let n=3
a3 = 15 +6(3) = 15+18 = 33
Let n=4
a4 = 15 +6(4) = 15+24 = 39
Answer:
A
Step-by-step explanation:
You do not know where n starts. Is it 1 or zero or something else. Raise your hand and complain.
I'll assume that n = 1 to start with
n = 1
15 + 6(1) = 21
n = 2
15 + 6(2) = 15 + 12 = 27
n = 3
15 + 6* 3 = 33
n = 4
15 + 6*4 = 39
Possible Points: 100 One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After si hours, what was the temperature?
f(x) = x2. What is g(x)?
Answer:
g(x)=3x(superscript)2
Answer:
g(x) = 3x².
Step-by-step explanation:
In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).
Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.
So, g(x) = 3x².
Hope this helps!
in the solution of the equation…
Answer:
add -5
Step-by-step explanation:
hope it helps!!!!!
Is 3.824 a rational number?
Answer:
NopE, can’t be made into a fraction
Answer:
Yes
Step-by-step explanation:
A number is rational if it can be expressed in the form p/q, where q is not zero.
3.824 can be expressed as 3824/1000.
So, it satisfies the criteria of a rational number.
Anyone know how to do this?
Please answer the question in the image below ASAP
Answer:
c
Step-by-step explanation:
diameter will be 36, radius 18 and the height is 6
SOMEONE PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
Let the quadratic equation of the function by the points in the given equation is,
f(x) = ax² + bx + c
If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),
For (0, 8),
f(0) = a(0)² + b(0) + c
8 = c
For a point (-3, -10),
f(-3) = a(-3)² + b(-3) + 8
-10 = 9a - 3b + 8
9a - 3b = -18
3a - b = -6 --------(1)
For (-4, -8),
f(-4) = a(-4)² + b(-4) + 8
-8 = 16a - 4b + 8
-16 = 16a - 4b
4a - b = -4 ------(2)
Subtract equation (1) from equation (2)
(4a - b) - (3a - b) = -4 + 6
a = 2
From equation (1),
6 - b = -6
b = 12
Function will be,
f(x) = 2x² + 12x + 8
= 2(x² + 6x) + 8
= 2(x² + 6x + 9 - 9) + 8
= 2(x² + 6x + 9) - 18 + 8
= 2(x + 3)² - 10
By comparing this function with the vertex form of the function,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the function 'f' will be (-3, -10)
And axis of symmetry will be,
x = -3
From the given graph, axis of the symmetry of the function 'g' is; x = -3
Therefore, both the functions will have the same axis of symmetry.
y-intercept of the function 'f' → y = 8 Or (0, 8)
y-intercept of the function 'g' → y = -2 Or (0, -2)
Therefore, y-intercept of 'f' is greater than 'g'
Average rate of change of function 'f' = [tex]\frac{f(b)-f(a)}{b-a}[/tex] in the interval [a, b]
= [tex]\frac{f(-3)-f(-6)}{-3+6}[/tex]
= [tex]\frac{-10-8}{3}[/tex]
= -6
Average rate of change of function 'g' = [tex]\frac{g(b)-g(a)}{b-a}[/tex]
= [tex]\frac{g(-3)-g(-6)}{-3+6}[/tex]
= [tex]\frac{7+2}{-3+6}[/tex]
= 3
Therefore, Average rate of change of function 'f' is less than 'g'.
A clerk at Agency Y has determined that at speeds of 25 pages per minute it is typical for 3 out of every 100 pages she photocopies to contain some type of printing error. How many pages with printing errors would she expect to find during a 4-hour photocopying session at 25 pages per minute
Answer:
180 pages
Step-by-step explanation:
Since her photocopy session is 25 pages per minute, the total number of pages photocopied in 4 hour session can be calculated as;
number of pages = time × speed
= (4 × 60) × 25
= 240 ×25
= 6000 pages
Thus, number of pages photocopied in 4 hours is 6000.
For every 100 pages, 3 would contain some type of printing error. The number of pages she expect with printing error during 4 hour session can be determined as;
= [tex]\frac{6000}{100}[/tex] × 3
= 60 × 3
= 180 pages
The expected number of pages with printing error during 4 hour photocopying session is 180 pages.