The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3
What is function?
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
According to the question,
The given function is
[tex]f(x) = -5|x + 1| + 3[/tex]
Here f(x) = -12
Substitute f(x) and solve for x
[tex]- 12 = -5|x + 1| + 3[/tex]
By subtracting 3 on both sides
[tex]- 12 - 3 = -5|x + 1| + 3 - 3[/tex]
[tex]- 15 = -5|x + 1|[/tex]
By dividing -5 on both sides
[tex]3 = |x + 1|[/tex]
We get absolute values for the function.
[tex]x + 1 = 3 , x + 1 = -3[/tex]
By subtracting 1 on both sides
[tex]x + 1 - 1 = 3 - 1 = 2\\\\x + 1 - 1 = - 3 - 1 = -4\\\\x = 2 , x = - 4[/tex]
Therefore, the values of x are 2 and - 4 of the given function f (x) =-5|x+1| +3
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Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.
Answer:
Or if you don't want any rounding it will be 115.38461538461
28.6% of city employees ride the bus to work. Last year, 29.7% of city employees rode the bus to work. What is the relative change from last year to this year?
(Express your answer rounded correctly to the nearest tenth of a percent!)
A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.
Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,
Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%
Hence, the relative change from last year to this year is 3.7%.
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.0. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Answer:
1,887,436,800
Step-by-step explanation:
f(t) = a·b^t
f (t) = number of cases at year t
a = starting value = 1800 in 1983
b = growth factor = 2
t = years since 1983 = 2003 - 1983 = 20
f(t) = 1800·(2)^20 =
1,887,436,800
wyzant
philip p
urgent question is below
i doooooooont knoooooooooooooooow iiiittttttttttttttttttttttt
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. u2+65u
Answer:
(u + [tex]\frac{65}{2}[/tex] )²
Step-by-step explanation:
u² + 65u
to complete the square
add ( half the coefficient of the u- term )²
= u² + 2([tex]\frac{65}{2}[/tex] )u + [tex]\frac{4225}{4}[/tex]
= (u + [tex]\frac{65}{2}[/tex] )²
f(x)=x^2. which of these is g(x)?
Answer:
According to the graph, g(x) is stretched by what seems to be 5, so g(x) is (x^2) / 25. (Square the stretching/compressing factor so 5^2 became 25). We also divide x^2 by this because it is being stretched. You multiply if it's being compressed.
You can check this by plugging 5 for x and trying to get 1.
g(x) = x^2 / 25
g(5) = 5^2 / 25 --> 25/25
g(5) = 1
g(x) = (x^2)/25
Find the probability that a person is male given that the person prefers hiking near lakes and streams. Let M= male and L= prefers lakes and streams.
This is a conditional probability. What word signals that it is a conditional?
Regarding conditional probabilities, the keyword is always given, as a previous event is considered to have happened.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.The previous event having happened is represented by keyword given.
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The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to
the equation Ix - 72.5 = 4. What are the minimum and maximum temperatures in the house?
Answer:
he.....a red cap.(wants/want)
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5, 5),A(5,5),A, left parenthesis, 5, comma, 5, right parenthesis, comma B(7,5)B(7,5)B, left parenthesis, 7, comma, 5, right parenthesis, C(7,-1)C(7,−1)C, left parenthesis, 7, comma, minus, 1, right parenthesis, and D(5,-1)D(5,−1)D, left parenthesis, 5, comma, minus, 1, right parenthesis.
Given these coordinates, what is the length of side BCBCB, C of this rectangle?
Answer:
The length of the side BC is 6 units.
Step-by-step explanation:
Distance formula: This works for any two points in 2D space with coordinates (x₁, y₁) for the first point and (x₂, y₂) for the second pointIt is the length of the line segment joining two pointsd = [tex]\sqrt{(x_{2} {-} x_{1})^{2} +(y_{2} {-} y_{1})^{2}}[/tex]For the given question:Rectangle ABCD
Coordinates of Point A,B,C,D
[tex]A = ( 5 , 5)B = (7, 5)C = (7 , -1)D = (5 , -1)[/tex]
As we are asked to find the length of side BC, we'll apply the Distance formula on side BC
BC = [tex]\sqrt{(7_ {-} 7)^{2} +(-1 {-} 5)^{2}}[/tex]
= [tex]\sqrt{(0)^{2} +(-6)^{2}}[/tex]
= [tex]\sqrt{ 36}[/tex]
= [tex]6[/tex]
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What is the current yield on a 3 year bond with 10% annual coupons, a par value of 100, and a current price of 107.87?
Based on the annual coupons on the bond and the current price, the current yield will be 9.27%.
What is the bond's current yield?This can be found as:
= Annual coupon amount / Bond price
Annual coupon:
= 10% x 100
= $10
The current yield is:
= 10 / 107.87
= 9.27%
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HELP PLSSS I NEED THIS ASAP
Four students are simplifying the expression 5x(-3-7x).
Which student's work is correct?
O5x(-3-7x)
(5x)(-3) - 7x
-15x-7x
O 5x(-3-7x)
(5x)(-3) - (5x)(7x)
-15-35x
O5x(-3-7x)
-3 + 5x-7x
-3-2x
O5x(-3-7x)
(5x)(-3)+(5x)(-7x)
-15x-35x²
Multiplying the linear expressions, the correct sequence is given as follows:
5x(-3 -7x)(5x)(-3) + (5x)(-7x)-15x - 35x²How are linear expressions multiplied?They are multiplied applying the distributive property, in which all the terms are multiplied and the like terms are combined.
Hence:
5x(-3 -7x)
(5x)(-3) + (5x)(-7x)
-15x - 35x²
Hence the last option is correct.
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Next
Pretest: Coordinate Geometry
7
Select the correct answer from each drop-down menu.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
The
✓of their slopes is
so the lines are
I
Because both lines have the same slope but different y-intercepts, we conclude that the lines are parallel.
What can we conclude about the two given lines?
Here we have the two lines:
6x - 2y = -2
y = 3x + 12
If we write both of these in the slope-intercept form, we get:
y = (-2 - 6x)/-2 = 3x + 1
y = 3x + 12
So, as you can see, both lines have the same slope but different y-intercepts. That means that the two lines are parallel, so they never do intercept.
Then we can conclude that the correct option is parallel.
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Suppose your favorite coffee machine offers 13 ounce cups of coffee. The actual amount of coffee put in the cup by the machine varies according to a normal distribution, with mean equal to 14 ounces and standard deviation equal to 0.56 ounces.
Answer:
2
Step-by-step explanation:
5. There are 2 boys and 3 girls in the class. The
ratio of boys to girls in the class is equal to all
of the following except
Answer:
9:12
Step-by-step explanation:
since the others are multiples of 2:3
but 9:12 is not a multiple
A 6-sided die is loaded in such a way where odd outcomes occur 2/9 of the time, and even outcomes happen the other
1/9 of the time. What is this die's expected value?
A. 3.25
B. 4
C. 3.5
D. 3.33
Answer:
3.33, or 3 1/3
Step-by-step explanation:
Expected value:
[tex](9 \times \frac{2}{9} ) + (12 \times \frac{1}{9} ) = 2 + \frac{4}{3} = 2 + 1 \frac{1}{3} = 3 \frac{1}{3} [/tex]
[tex](a + b) {}^{2} [/tex]
Expand this expression.
Answer:
[tex] {a}^{2} + 2ab + {b}^{2} [/tex]
Step-by-step explanation:
[tex](a + b) {}^{2} = (a + b)(a + b) = {a}^{2} + ab + ab + {b}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
Hi!
___________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
a^2+2ab+b^2
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
Remember the rule for expanding a binomial squared.
[tex]\twoheadrightarrow\sf (a+b)^2=a^2+2ab+b^2[/tex]
So we square the first term, then multiply the product of the two terms times 2.
[tex]\twoheadrightarrow\sf a^2+2ab+b^2[/tex]
This is our answer.
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
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What is the y - cordanate of the point that divides the directed line segment from j to k into a ratio of 2:3
The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).
Let's call the point that divides the line segment point P.
Point P divides the line segment into a ratio of 2:3
What is the ratio of 2:3?The ratio of 2:3 means we are dividing the line segment into 2+3=5 equal parts.
The horizontal distance between the two coordinates is 5.
The vertical distance between the two coordinates is 10.
Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2.
Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.
The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).
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Solve for x in the inequality |2x + 5| ≤ 11. (If this is an "and" inequality, give your answer as a single compound inequality. If this is an "or" inequality, separate your answers using a comma.) Solve for x in the inequality | 2x + 5 | ≤ 11. ( If this is an " and " inequality , give your answer as a single compound inequality . If this is an " or " inequality , separate your answers using a comma . )
|2x + 5| ≤ 11
x = 3
2(3) + 5
6 + 5
11 ≤ 11
The solution for the x in the inequality |2x + 5| ≤ 11 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3}
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
|2x + 5| ≤ 11
To find the solution for the x, solve the inequality,
|2x + 5| ≤ 11
-11 ≤ 2x + 5 ≤ 11
Subtract 5 from whole the expression,
-11 - 5 ≤ 2x + 5 - 5 ≤ 11 - 5
-16 ≤ 2x ≤ 6
-8 ≤ x ≤ 3
The value of x for the given inequality varies from -8 to 3.
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The Super 20 Hotel currently contracts out its cleaning service to Great Maids cleaners who charge $50 a room. They also charge an additional $185 no matter how many rooms they clean. Which equation could be used to determine the cost C of the Great Maids cleaning n rooms?
Answer:
a computer is an electronic device,which input data/instruction,store and processes it and produces output in the desired from
When eighteen is reduced by two-thirds of a number, the result is 14. Find the number.
The number is
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!NO LINKS!! Please help me with this problem
Answer:
23.1 years (nearest tenth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $1200P = $600r = 3% = 0.03n = 12 (as compounded monthly)t = yearsSubstitute the given values into the formula and solve for t:
[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]
[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]
Take natural logs:
[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]
[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]
[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]
[tex]\implies t=23.13377513...[/tex]
[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]
The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.
Used formula
[tex]\boxed{\sf A=P(1+\dfrac{r}{n})^{nt}}[/tex]
[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]
Apply natural logarithm on both sides[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]
[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]
[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]
[tex]\\ \implies t=23.1years[/tex]
4(n+3)=24 solve for n
the height of a plant in centimeters is modeled as a function of time, in days. consider this graph of the function enter the average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20
The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.
What is average height?The average height is the ratio of change in height of the plant and the time taken taken for that change.
Given is the height of a plant in centimeters is modeled as a function of time, in days.
For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is
height per day = 42 - 18/ 20 -0
height per day = 1.2 cm/day
Thus, the average height of plant is 1.2 cm/day.
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Kmele had paid his credit card on time for three years, but last month he missed the due date. He then noticed that the amount owed increased by $35. This most likely happened because he was charged.
A. a late fee
B. a higher interest rate
C. a minimum-payment fee
D. an overdraft-fee
Answer:
It's most likely he was charged a late fee
Match each value on the left with the number on the right that includes that value.
Kerry has a job that pays $1,954 biweekly. How much is withheld annually for Social Security?
$82.07
$41.03
$2,113.77
$88.91
$177.81
Answer:
hi
Step-by-step explanation:
no
Given A(-2, 5) and B(13, -7), find the midpoint of AB.
Answer:
The mid-point is (9,-9/2)
Step-by-step explanation:
You would use the mid-point formula for this
[tex](\frac{x_{2} +x_{1} }{2} , \frac{y_{2}+y_{1} }{2} )[/tex]
if you plug that in it is ([tex]\frac{13-2}{2}, \frac{-7+5}{2}[/tex])
resulting in (11/2,-2/2) = (11/2,-1)
Solve the following inequality: ALGEBRA 1
Answer:
[tex]m > 5[/tex]
Step-by-step explanation:
[tex] \frac{m + 4}{3} > 3 \\ \frac{m + 4}{3} \times 3 > 3 \times 3 \\ m + 4 > 9 \\ m + 4 - 4 > 9 - 4 \\ m > 5[/tex]
y=x^2-4x-1 in vertex form
How is the two point formula used to find the equation of a line when 2 points are known? a. taking the change in y over the change in x c. dividing the first y by the first x b. taking the change in x over the change in y d. dividing the first x by the first y Please select the best answer from the choices provided A B C D
Taking the change in y over the change in x. Then the correct option is A.
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]
The equation of the line can be determined by the two known points.
Taking the change in y over the change in x.
Then the correct option is A.
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