Answer:
x = {x: -1, 5}
Step-by-step explanation:
[tex]{ \rm{f(m) = (x + 1)(x - 5)}}[/tex]
- To find the values of function f(m), we consider its zero or its root by letting f(m) = 0
[tex]{ \rm{f(m) = 0 = (x + 1)(x - 5)}} \\ { \rm{(x + 1)(x - 5) = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
- Either (x + 1) or (x - 5) is equated to zero
For (x + 1);[tex]{ \rm{x + 1 = 0}} \\ { \rm{x = - 1}}[/tex]
For (x - 5);[tex]{ \rm{x - 5 = 0}} \\ { \rm{x = 5}}[/tex]
Therefore, x is -1 and 5
[tex]{ \bold{ \boxed{ \red{ \delta}}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]
Cylinder a r=4 h = 7 7 b. h= 14.3, r = 8.5
To calculate the volume of a cylinder you have to multiply the area of the circle by the height of the cylinder.
[tex]\begin{gathered} V=A\cdot h \\ V=\pi r^2\cdot h \end{gathered}[/tex]We know that the radius of the circle is r=4 and the height of the cylinder is h=7, replace both values on the formula to determine the volume:
[tex]\begin{gathered} V=\pi(4^2)\cdot7 \\ V=\pi\cdot16\cdot7 \\ V=112\pi \\ V\approx351.86 \end{gathered}[/tex]The volume of the cylinder is approximately 351.86 cubic units.
I solved this and think the range is: y>=3.Did I solve correctly?
Notice that
[tex]\begin{gathered} x^2\ge0,x\in\Re \\ \Rightarrow x^2+3\ge3,x\in\Re \\ \Rightarrow f(x)\ge3,x\in\Re \end{gathered}[/tex]Therefore, the range of the function is f(x)>=3, or [3,infinite)
Finding the Slope of a LineVy10What is the slope of a line that contains the points (1,9) and (4, 3)?The slope of the line is<88642N2x624.8
Given the points: (1, 9) and (4, 3)
To find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{3-9}{4-1}[/tex]m = -2
Write in simplest form 0.875:1/4
Hey there!
[tex]0.875:1/4\/\\\textmd{To Simplest form}[/tex]
[tex]0.875[/tex] ÷ [tex]\frac{1}{4}[/tex]
[tex]=3.5[/tex]
Your final answer would be 3.5.
Hope this helps!
If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).
(f . g)(x)= ____
(Simplify your answer.)
The value of the functions are;
(f. g)(x) = 9x² + 5
(g . f)(x) = 3x² + 15
What is a function?A function can be defined as a law, rule or expression showing the elaborate relationship between two variables in an expression or equation.
The variables are;
The dependent variableThe independent variableGiven the functions;
f(x)=x²+5g(x)=3xTo determine (f .g)(x), we substitute the value of g(x) as x in the function, we have;
(g)(x) = (3x)² + 5
expand the bracket
(g)(x) = 9x² + 5
To determine (g . f )(x), substitute the value of x as fx)
(g . f)(x) = 3(x² + 5)
expand the bracket
(g . f)(x)= 3x² + 15
Hence, the functions are 9x² + 5 and 3x² + 15
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Marlene decided to buy 2 bags of apples weighing 3 14 pounds each, instead of 3 bags weighing 2 25 pounds each. Did she end up with more apples or fewer apples by buying the bigger bags?To find the total weight of 2 bags of apples weighing 3 14 pounds, multiply. 2 × 3 14 = To find the total weight of 3 bags weighing 2 25 pounds, multiply. 3 × 2 25 = She ended up purchasing apples by buying the bigger bags.
Answer:
She ended up with fewer apples by buying the bigger bags.
Explanation:
The total weight of 2 bags of apples weighing 314 pounds each is equal to:
2 x 314 = 628 pounds
At the same way, the total weight of 3 bags weighing 223 pounds each is:
3 x 225 = 675 pounds
Since 628 pounds is less than 675 pounds, Marlene ended up with fewer apples by buying the bigger bags
Solve this system of equations byusing the elimination method.x - 5y = 164x – 2y = -8([?],
Given:
There are given two equations:
[tex]\begin{gathered} x-5y=16...(1) \\ 4x-2y=-8...(2) \end{gathered}[/tex]Explanation:
To find the value by using the elimination method, we need to multiply by 4 into the equation (1) and 1 into the multiply by (2):
Then,
From the equation (1):
[tex]\begin{gathered} 4(x-5y=16) \\ 4x-20y=64...(3) \end{gathered}[/tex]And,
From the equation (2):
[tex]\begin{gathered} 1(4x-2y=-8) \\ 4x-2y=-8...(4) \end{gathered}[/tex]Now,
From the equation (3) and equation (4):
[tex]4x-20y-64=4x-2y+8[/tex]Then,
[tex]\begin{gathered} 4x-20y-64-4x+2y-8=0 \\ -20y-64+2y-8=0 \\ -18y-72=0 \\ -18y=72 \\ y=-4 \end{gathered}[/tex]Now,
Put the value of y into the equation (3):
[tex]\begin{gathered} \begin{equation*} 4x-20y=64 \end{equation*} \\ 4x-20(-4)=64 \\ 4x+80=64 \\ 4x=64-80 \\ 4x=-16 \\ x=-4 \end{gathered}[/tex]Final answer:
Hence, the value of x and y is shown below:
[tex](-4,-4)[/tex]As the value of cosx approaches 1 and the value of sinx approaches 0, the value of cotx approaches infinity. True or false?
Recall that:
[tex]\cot \text{ x=}\frac{\cos x}{\sin x}[/tex]Therefore as sin x approaches 0 and cos x approaches 1, the value of cot x approaches infinity.
Answer: True.
f(x) = x² + 9x from x1 = 4 to x2 = 8.
is the rate of change 21?
The average rate of change of f(x) on the interval [4, 8] is 21.
How to find the rate of change?
For a function f(x), the rate of change on an interval [a, b] is given by:
R = ( f(b) - f(a))/(b - a)
In this case the function is:
f(x) = x² + 9x
And the interval is [4, 8]
Then the rate of change is
R = ( f(8) - f(4))/(8 - 4)
we will get:
f(8) = 8² + 9*8 = 136
f(4) = 4² + 9*4 + 16 + 36 = 52
Replacing that we get:
R = (136 - 52)/4 = 21
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If a costume designer takes 20 hours to make 16 costumes, at what rate per hour are costumes being made?
Answer:it takes 1 hor 25 minutes to make a costume
Step-by-step explanation:
20 divided by 16 =1.25
The half-life of radium is 1690 years. If 50 grams are present now, how much will be present in 800 years?
In order to determine the amount of radium after 800 years, use the following formula:
[tex]N=N_oe^{-\lambda t}[/tex]where,
N: amount of radium after t years = ?
No: initial amount of radium = 50g
λ: decay constant
t = 800
The decay constant is calculated by using the following expression:
[tex]\lambda=\frac{ln2}{t\frac{_1}{2}}=\frac{ln2}{1960}\approx3.5*10^{-4}[/tex]where t1/2 = 1960 is the half-life.
Now, by replacing λ, No and t = 800 you obtain:
[tex]N=50e^{-(3.5*10-4)(800)}\approx37.68g[/tex]Hence, after 800 years there are approximately 37.68g of uranium
The standard trampoline has a diameter of 14 feet. What is its circumference?
The circumference, C, of a circle is computed as follows:
[tex]C=\pi D[/tex]where D is the diameter of the circle. Substituting with D = 14 ft, we get:
[tex]\begin{gathered} C=\pi\cdot14 \\ C\approx44\text{ ft} \end{gathered}[/tex]The circumference of the trampoline is approximately 44 feet
Lucy bought a plant and planted it in a pot near a window in her house. The initial height of the plant was 12 inches and it grew at a rate of 2 inches per month. Make a table of values and then write an equation for H, in terms of t, representing the height, in inches, of the plant tt months after Lucy bought the plant.
I need the equations
The equation for H, in terns of t, representing the height , in inches, of the plant tt months after Lucy bought the plant is :
H=12+2t
Given, A plant that Lucy had purchased was placed in a pot next to a window in her home. The plant initially stood 12 inches tall and grew at a rate of 2 inches per month.
from the given information, the equation can be framed as:
H = 12 +2t
where the initial height of the plant is increased at a rate of two inches every month.
from the table substitute the value of months in t, to find the height of the plant in that particular month.
t = 0
H=12+2(0)
H=12
hence when t=0 then H=12
t=1
H=12+2(1)
H=12+2
H=14
after a month the height of the plant changes to 14 inches.
t=2
H=12+2(2)
H=12+4
H=16
after two months the height changes to 16 inches.
t=3
H=12+2(3)
H=12+6
H=18
after three months the height changes to 18 months.
t=4
H=12+2(4)
H=12+8
H=20
finally after four months the height of the plant changes to 20 months.
hence we get the required equation as H=12+2t
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Lydia is at a coffee shop and knows
she can spend no more than $65
before tax. She sees this price list in
the coffee shop.
Item
Dark Roast Coffee
Pumpkin Spice Coffee
Breakfast Tea
Price per pound
$7.50
$10.50
$23.50
Part A
Write a number in each blank to complete an inequality Lydia can use to find how
many pounds of Pumpkin Spice coffee, p, she can buy along with 2 pounds of
Dark Roast coffee.
Answer:
10.50p+15≤65
p≤ 100/21
Step-by-step explanation:
Let p represent pounds of Pumpkin Spice coffee.
We have been given that Lydia is at a coffee shop and knows she can spend no more than $65 before tax. She sees this price list in the coffee shop.
Item Price per pound
Dark Roast Coffee
$7.50
Pumpkin Spice Coffee
$10.50
Breakfast Tea
$23.50
Lydia wants to buy 2 pounds of Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be $7.50×2=$15 .
We are told that cost of each pound of Pumpkin Spice coffee is 10.50,socostof′ p'
pounds of Pumpkin Spice coffee would be 10.50
Since Lydia can spend no more than $65 before tax, so the cost of 2 pounds of Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.
We can represent this information in an inequality as:
10.50p+15≤65
Therefore, our required inequality would be 10.50p+15≤65
10.50+15-15≤65-75
10.50≤50
Divide both sides by 10.50:
10.50p/10.50 ≤ 50/10.50
P ≤ 50*2/10.50*2
P ≤ 100/21
P ≤ 4.76190
Therefore, Lydia can buy less than or equal to 100/21 pounds of Pumpkin Spice coffee.
The length of a rectangle is (5x+1) inches. The width is (x). Express the area of the
checkerboard in terms of the variable x. Use the formula: A = L-W
14.
Answer: A = 7x
Step-by-step explanation:
Area = Length x Width
A = L * W
L = 5x + 1 W = x
Plug the length and width into the equation for area.
A = (5x + 1) * x
A = 6x + x
A = 7x
Using the graphs what are the solutions to the following systems
The solution to the system is the intersection of the graphs.
From the problem, the intersection is at (-3, 2)
The answer is (-3, 2)
Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).Question 19 options:A) y = 3(x + 2)2B) y = (x – 2)2C) y = (x + 2)2D) y = 3(x – 2)2
SOLUTION
Equation of a parabola is given by the equation
[tex]y=a(x-h)^2+k[/tex]Where (h, h) are the coordinates of the vertex.
From the question given, the vertex is (2, 0)
So, h = 2, k = 0.
The y-intercept is given as (0, 12).
So, this means that x = 0 and y = 12
Substituting the values for h, k, x and y into the equation we have
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 12=a(0-2)^2+0 \\ \\ 12=a\times-2^2+0 \\ \\ 12=4a \\ \\ a=\frac{12}{4} \\ \\ a=3 \end{gathered}[/tex]Now, let's substitute the value of a into the equation to get equation for the parabola.
This becomes
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ y=3(x-2)^2+0 \\ \\ y=3(x-2)^2 \\ \\ \end{gathered}[/tex]Write two decimals that are equivalent to the given decimal 3,200
The two equivalent expression of the decimal 3.200 is 3200/1000 and 3.2
What is defined as the decimals?A decimal is a number with a whole as well as a fractional part. Decimal numbers are between integers as well as represent numeric values for whole plus some fraction of a whole. When we divide a whole in to the smaller parts, we get decimals. A decimal number has two parts: a whole number component and a fractional component. The decimal place value system is identical to the whole number value system for the entire part of a decimal number. However, as we move to the right after the decimal point, we get the fractional part of a decimal number.For the given question, the stated decimal is;
3.200
Removing point will be;
3200/1000 is the equivalent expression.
Divide numerator an denominator by 100 .
32/10 = 3.2 is also the equivalent expression of 3.200.
Thus, the two equivalent expression of the decimal 3.200 is 3200/1000 and 3.2.
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The correct question is-
Write two decimals that are equivalent to the given decimal 3.200
Blue and yellow dye are mixed in an 8: 3 ratio to make 44 litres of a green-coloured dye. A further 8 litres of yellow dye are added to the mixture. What is the new ratio of blue to yellow dye in its simplest form?
Answer: The new ratio of blue to yellow dye in its simplest form is 8/5.
Step-by-step explanation:
Blue and yellow dyes are mixed in an 8: 3 ratio to make 44 liters of a green-colored dye. A further 8 liters of yellow dye are added to the mixture. What is the new ratio of blue to yellow dye in its simplest form?
What is the Ratio?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Calculating the fraction of blue and yellow in the green dye,
Blue dye = 8/(3+8) * 44
Blue dye = 8/11 * 44
Blue dye = 32 liters
Similarly,
yellow dye = 3/11*44
yellow dye = 12
Now
Blue dye + yellow dye = 32+12 = 44
Now yellow dye is increased by 8 liters
the new volume fraction of yellow dye = 12+8
= 20
a fraction of blue dye remains the same,
the ratio of blue dye to new yellow dye in teal color.
= 32/20
=8/5
Thus, the new ratio of blue to yellow dye in its simplest form is 8/5.
Answer:
8/5
Step-by-step explanation:
The Outsiders
Movie vs. Book Comparison Project
If you use 15 fl oz of milk how much flour shold be used
Is it true that Weight is a function of Height?
Answer:
Yes
Step-by-step explanation:
The number of height is also the number of wegt
The diameter of a circle is 18 cm. Find its circumference in terms of T. Answer: C = om Submit Answer
The circumference of a circle is given by the formula:
[tex]C\text{ = 2 }\pi\text{ r}[/tex]The diameter of the circle, d = 18cm
Radius = diameter / 2
r = d/2
r = 18/2
r = 9 cm
[tex]\begin{gathered} C\text{ = 2}\pi(9) \\ C\text{ = 18}\pi \end{gathered}[/tex]Could someone please help me with this?
Answer:
1. f(4) = 4
2. g(2) = -4
3. f(-5) = -14
4. g(-3) = 21
5. f(0) = -4
6. g(0) = 0
7. f(3) - 1 = 1
8. f(1/4) = -3.5 or -7/2
9. g(1/4) = -0.9375 or -15/16
10. f(a^2) = 2a^2 - 4
11. f(k+1) = 2k - 2
12. g(2n) = 2n^2 - 8n
13. f(3x) = 6x - 4
14. f(2) + 3 = 3
15. g(-4) = 32
Step-by-step explanation:
here’s a pic of my work:
You pick a card at random, put it back, and then pick another card at random. 3 4 5 6 7 What is the probability of picking a divisor of 6 and then picking a number less than 5? Simplify your answer and write it as a fraction or whole number.
Probability = required outcome /all possible outcome
You have 5 cards on the deck. The exercise has reposition, i.e. you put the card back into the deck before picking the next one, so the total number of cards is always 5.
all possible outcome = 5
Divisor of 6 = 3, 6
Probability of picking a divisor of 6 = 2/5
Number less than 5 are : 3 and 4 = 2/5
The intersection between both events is equal to the product of both probabilities since the events are independent.
The probability of picking a divisor of 6 and then picking a number less than 5 is:
P(divisor of 6) and P(no.less than 5) = 2/5 * 2/5 = 4/25
If I was asked to think of a number and multiply it by 2, I could write this algebraically as 2x. Write the following algebraically, using x as your unknown. "I think of a number, multiply it by 3, add 4 and square the result."
Answer: (3x + 4)^2
Step-by-step explanation:
I think of a number => x
Multiply it by 3 => 3x
Add 4 => 3x + 4
Square the result => (3x + 4)^2
please i need help. can someone please help me
Hello can someone help I dont really think I'm correct.
According to the given number line A is on -7, X is on -2 and E is on 8.
As you can observe in the image below, X is 5 units away from A. At the same time, X is 10 units away from E.
Therefore, point X is double distant from E as far as it is from A.The ratio of this relation would be 2:1 from E to A.
K 370 45° Which equation can be used to find the value of k? 37° - K +45º = 180° 37° + k +45º = 180° 37" + k = 45° 180° 37° -45° - 180°
The sum of angle on a straight line is always 180 degree.
Determine the equation for the angle.
[tex]k+37+45=180[/tex]Which graph represents the following function?
f(x) = |x|.
The graph of the function f (x) = |x| is shown in attached figure.
Hence, Option A is true.
What is mean by Modulus function?
The modulus function is the magnitude or absolute value of a positive or negative number. It is defined as y = |x| or f (x) = |x|
Where, f : R → R and x ∈ R.
This is also called the absolute value function.
Given that;
The modulus function is,
⇒ y = |x|
Now, The modulus function is,
⇒ y = |x|
Since, The function y = |x| is not differentiable at x = 0.
So, It break at point x = 0, and have all positive values of y.
Which is shown in image A.
Thus, The graph of function y = |x| is shown in attached figure.
Therefore, In the images;
⇒ Option A is true.
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