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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What are the coordinates of point F?
On a coordinate plane, point F is 4 units to the right and 2.5 units down.
(Negative 4, Negative 2 and one-half)
(Negative 4, 2 and one-half)
(4, negative 2 and one-half)
(4, 2 and one-half)
The coordinates of point F are 4 and negative 2.5. Option C is correct.
What is the best way to understand the Cartesian coordinate plane?A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.
It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.
The location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.
'c' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x.
The coordinates of point F are 4 and negative 2.5.
Hence, the Option C is correct.
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I don’t understand this question can someone please help
Answer:
the second option listed
(A = 53 degrees)
(a = 13.3)
(c = 16.6)
Step-by-step explanation:
SOH CAH TOA
(sin = opposite / hypotenuse)
(cos = adjacent / hypotenuse)
(tan = opposite / adjacent)
For this question, you are provided an angle (37), and its opposite (10)
so, we can solve for either sin or tan first.
tan = opposite / adjacent
tan 37 = 0.7535540501
0.7535540501 = 10/a [multiply by a]
0.7535540501a = 10 [divide by [0.7535540501]
a = 13.2704482163
rounded to the nearest tenth, a = 13.3
we know that the three angles shown here must add up to 180
so,
90 + 37 + A = 180
127 + A = 180
- 127 - 127
A = 53
--this is enough information to answer, but I will also solve side c to prove my answer
c = hypotenuse
a²+ b²=c²
[13.3]² + [10]² = c²
176.89 + 100 = c²
276.89 = c²
√276.89 = √c²
16.6400120192 = c
c = 16.6 (rounded to the nearest tenth)
**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer
Mrs. Juergen's class is building a model city from craft sticks. each house requires 267 sticks. the class will build 93 houses. About how many sticks will be needed?
2 Simplify.
a
e
√72+√162
√50-√8
2√28+√√28
[tex] \sqrt{72} + \sqrt{162} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 3 \times 3 \times 3 \times 3} \\ \\ 2 \times 3 \sqrt{2} + 3 \times 3 \sqrt{2} \\ \\ 6 \sqrt{2} + 9 \sqrt{2} \\ \\ (6 + 9) \sqrt{2} \\ \\ 15\times1.4 \\ \\ 21[/tex]
--------------------------[tex] \sqrt{50} - \sqrt{8} \\ \\ \sqrt{2 \times 5 \times 5} - \sqrt{2 \times 2 \times 2} \\ \\ 5 \sqrt{2} - 2\sqrt{2} \\ \\ (5 - 2) \sqrt{2} \\ \\ 3 \sqrt{2} \\ \\ 1.7 \times 2 \\ \\ 3.4[/tex]
--------------------------[tex]2 \sqrt{28} + \sqrt{28} \\ \\ 2 \sqrt{2 \times 7 \times 7} + \sqrt{2 \times 7 \times 7} \\ \\ 2 \times 7 \sqrt{2} + 7 \sqrt{2} \\ \\ 14 \sqrt{2} + 7 \sqrt{2} \\ \\ (14 + 7) \sqrt{2} \\ \\ 21 \times 1.4 \\ \\ 29.4[/tex]
Given that log 2= 0.30103 and log 3= 0.47712. Evaluate log 12
Answer:
log12=log(2.2.3)
=log2+log2+log3
=0.30103+0.30103+0.47712
=0.60206+0.47712
=1.07918
Let −5, 3 be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.
The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have (−5, 3) be a point on the terminal side of θ.
Perpendicular = -5
Base = 3
From Pythagoras' theorem:
Hypotenuse² = (3)² + (-5)²
Hypotenuse = √34
cosθ = 3/√34
cscθ = -√34/5
tanθ = -5/3
Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
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Can somebody help me
Step-by-step explanation:
first function, f(x) = 5x-3 goes with option B
2nd function, 4- 4x goes with option A
3rd function goes with option D
4th goes with option C
If the cost, C, for manufacturing x units of a certain product is given by C= x² + 10x + 65, find the number of units manufactured at a cost of $7265
Answer:
80
Step-by-step explanation:
when you do the math you get two answers, -90 and 80
we dont use -90 because -90 units cannot be manufactured
A farmer raises only cows and Sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. He spends birr 5 to raise a cow and Br 2 to raise a sheep. He has Br 50 available for this purpose. Cows sell birr 100 and sheep birr 50. Required: How many of each animal should he raise to maximize profit? What is the maximum profit?
Answer:
1050 max profit
Step-by-step explanation:
cow 5brr 30br 600 × 6 cows 570
sheep 2brr 20br 500 ×10 sheeps 480
sheep&cows = 1050 max profit
In the last three years Frederic’s basketball team win 40 more games than they lost
Answer:
Wht is the total matches they played?
Your Uncle Malcolm has a honeybee colony that consists of a single queen, hundreds of male drones and roughly 60,000 female worker bees. His beehive produced 200
pounds of honey last year. If Uncle Malcolm continues beekeeping with the same
number of bees, how many pounds of honey will his hive produce after 10 years? Write
your answer in scientific notation.
In scientific Notation , After 10 years he will have in total 2 x 10 ³ pounds.
What is Scientific Notation ?Scientific Notation is a way of writing very large or small quantities.
It is written in the form of x 10ˣ
It is given that
The colony of bees has a single queen, hundreds of male drones and roughly 60,000 female worker bees.
The quantity of honey produced is 200 pounds.
After 10 years he will have in total
200 * 10 = 2000 pounds
In scientific Notation it will be written as
2 x 10 ³ pounds.
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evaluate -5+(-3)^2+2
Answer:6
Step-by-step explanation:at first calculate (-3)^2=9
then 9+2=11
finally the answer is 11-5=6
Answer:
6
Step-by-step explanation:
Given Problem:
[tex]-5+(-3)^2+2[/tex]
Using the PEMDAS order of operation:
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Thus, Solving in parentheses first.
[tex]-5+(-3)^2+2[/tex]
[tex](-3)^2=9[/tex]
[tex]-5+9+2=[/tex]
[tex]-5+11=[/tex]
[tex]6[/tex]
Hence, the answer to [tex]-5+(-3)^2+2=6[/tex]
RevyBreeze
Which of these correctly explains the solution of the system of equations shown below?
2 x + 3 y = 6
x + 3 y = 12
using elimination method
2x + 3y = 6 -----(1)
-
x + 3y = 12-------(2)
———————
x = 12
substitute x as 12 into equation (1) or (2), let's choose equation (1)
2(12) + 3y = 6
24 + 3y = 6
collect like terms
3y = 6 - 24
3y = 18
divide both sides by 3 ( to make y the subject of formula )
3y = 18
— —
3 3
y = 6
therefore X = 12 and y = 6
Hope this helps eh
Good luck ✅.
what is golden ratio, and explain it's history
Answer:
The golden ratio is a proper term in the field of mathematics, but it finally covers more than the research in the field of mathematics. According to the current literature discussion, we can say that the discovery of the Golden ratio and how it evolved is still a mystery. But studies have shown that the Pythagorean school of ancient Greece in the 6th century BC studied the formation of regular 5-sided and regular 10-sided plots, leading modern mathematicians to conclude that the Pythagorean school had touched on and even mastered some of the rules of the golden ratio and also discovered irrational numbers. It focuses on the relationship from mathematics, to explore the principle of beauty and that beauty is harmony and proportion, according to the proportional relationship can form beautiful patterns, this is actually a digital proportional relations, the line is divided into two parts, a long and a short period of the ratio of the equal to the ratio of length to a long, their proportion is around 1.618:1, This mathematical principle is also embodied in the famous Frederikian sequence, in which everything in this proportion shows the harmony and balance of its internal relations.
In the 4th century BC, the Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion. Around 300 BC, Euclid absorbed the research results of Eudoxus in writing The Elements of Geometry and further systematically discussed the Golden Section, which became the earliest treatise on the golden Section (i.e. the middle and the end ratio) [5].
After the Middle Ages, the golden ratio was shrouded in mystery. Italian mathematician Luca Pacioli called the middle and the end of the ratio sacred and wrote a book about it. The German astronomer Johannes Kepler called the divine ratio the Golden Ratio. Golden in the 19th century the name only gradually, and the evidence is that German mathematician Martin Ohm (English: Martin Ohm) wrote the second edition of the basic pure mathematics annotation wrote about the interpretation of the golden ratio: "people used to put any straight line along the way will be divided into two parts, the method of known as the golden mean". And in the ninth edition of the Encyclopaedia Britannica, published in 1875, Sully notes: "The interesting, experimental and strong idea put forward by Frederick... proclaimed the supposed superiority of the 'golden Section' in visual proportion." So the Golden Section was already popular. In the 20th century, American mathematician Mark Barr gave it the name Phi. The Golden Section has many interesting properties and has been widely used by humans to make it famous today. The most famous example is the golden ratio or 0.618 method in optimization, which is first proposed in 1953 by Jack Kiefer (English: Jack Kiefer), an American mathematician, and is promoted in China in 1970s.
Help me with this question please!!!
Answer: 98.5
Step-by-step explanation:
There were 942 people in total, 928 of which recognized Exxon.
So, the probability is 928/942, which is about 98.5%
The probability of random consumers knowing of exon will be 98.5%.
What is probability?Probability helps us to know the chances of an event occurring.
[tex]P =\dfrac{Desired \ Outcomes}{Possible outcomes}[/tex]
Given that:-
928 consumers knew exon and 14 did not.The probability will be calculated as:-
Total consumers are 942 out of which 928 knew exon and 14 did not.
P = 928 / 942
P = 0.985
P = 98.5%
Therefore the probability of random consumers knowing of exon will be 98.5%.
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2
What is the equation of the line that is perpendicular to y=x+4 and that passes through (5,-4)?
--5v-20
K
Perpendicular lines have slopes that are negative reciprocals of each other, so since the slope of the given line is 1, the slope of the line we want to find is -1.
Substituting into point-slope form,
[tex]y+4=-1(x-5)\\\\y+4=-x+5\\\\\boxed{y=-x+1}[/tex]
The graph of (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of (in red).
The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation h(x) = -1/2(x -3)² + 4
Translation of coordinates and functionThe given graph is a quadratic graph. Given the function of the blue parabola expressed as:
f(x) = -1/2x²
The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation
h(x) = -1/2(x -3)² + 4
Note that the upward translation will be positive while the horizontal shift to the right will be negative
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Urgent
find the values of x and y 8x+5y=-5 7x-3y=3
Answer:
x= 0, y= -1
Step-by-step explanation:
To obtain the values of x and y from a system of equations, start by labelling the given equations.
8x +5y= -5 -----(1)
7x -3y= 3 -----(2)
Let's solve by elimination.
Here, I will be working to eliminate the y term. This is done by ensuring both equations have the same numerical value in the coefficient of y.
(1) ×3:
24x +15y= -15 -----(3)
(2) ×5:
35x -15y= 15 -----(4)
Add the two equations together since the coefficient of y has opposite signs.
(3) +(4):
24x +15y +35x -15y= -15 +15
59x= 0
Divide both sides by 59:
x= 0
Now, substitute the value of x into any equations to find the value of y.
Substitute x= 0 into (1):
8(0) +5y= -5
5y= -5
Divide both sides by 5:
y= -5 ÷5
y= -1
Additional:
For similar questions on system of equations, do check out the following!
https://brainly.com/question/4346392HELP TO ASAP Compare the graph of f(x) with the graph of k(x) = 5(x-6)².
OA. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units right.
OB. The graph of k(x) is vertically stretched by a factor of 5 and shifted
6 units right.
OC. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units left.
Parent function
y=x²Now look the transformations
y=(x-6)²x is changed and shifted 6 units right
Then
y=5(x-6)²Horizontally Streched with a factor of 5
Answer:
B) The graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Given functions:
[tex]f(x) = x^2[/tex]
[tex]k(x) = 5(x - 6)^2[/tex]
Parent function: [tex]f(x) = x^2[/tex]
Translated 6 units right: [tex]f(x-6)=(x-6)^2[/tex]
Then stretched vertically by a factor of 5: [tex]5f(x-6)=5(x-6)^2[/tex]
[tex]\implies 5f(x-6)=5(x-6)^2=k(x)[/tex]
Therefore, the graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
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Consider the two savings plans below. Compare the balances in each year after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better?
Yolanda deposits $250 per month in an account with an APR of 4%, while Zach deposits $3000 at the end of each year in an account with an APR of 4%
The balance in Yolanda's saving plan after 14 years is; $9,455.36
How to calculate future value?We want to find the balance in Yolanda's saving plan after 14 years.
For Yolanda;
PV = 0
PMT = 250
i% = 4%/12 = 0.33%
N = 14 yrs * 12 = 168
FV = ?
For Zach:
PV = 0
PMT = $3300
i% = 4%
N = 14 yrs
FV = ?
From online future value calculator, we have;
Yolanda FV = $9,455.36
Zach FV = $47,204.19
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The surface area of a square pyramid is 189 square inches. The side length of the base is 7. What is the value of the height?
The value of the height of the prism is 8.68 inches
Surface of a square pyramidThe surface area is the sum of the area of the faces.
The formula for calculating the surface area of the pyramid is;
TSA = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]
where
a is the side length. = 7in
h is the height
Substitute
[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]
Square both sides to have
100 = 49/2 + h²
h² = 100 - 49/2
h² = 151/2
h² = 75.5
h = 8.68in
Hence the value of the height of the prism is 8.68 inches
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If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answer: 20
Step-by-step explanation:
f(-4) = -4² - (-4)
f(-4) = 16 + 4
f(-4) = 20
What are the values for y when x is 1, 3, and 5?
y = 3x + 10
Answer:
13, 19, 25.
Step-by-step explanation:
y=3x+10
-------------
x=1, y=3(1)+10=3+10=13
x=3, y=3(3)+10=9+10=19
x=5, y=3(5)+10=15+10=25
What is the value of this expression when c = -4 and d = 10?
A.
2
B.
9
C.
21
D.
41
The complete question is
"What is the value of this expression when c= -4 and d= 10?
1/4 (c^3+d²)
A.2
B.9
C.21
D.41"
The value of this expression when c = -4 and d = 10 will be option B 9.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]
Hence, the value of this expression when c = -4 and d = 10 will be option B 9.
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4x² + 24x + 20
common factor =
Sum, difference, and product..help!
The sum of the function will be (r – s)(x) = –2x² + x – 3, The difference of the function will be (r – s)(x) = –2x² + x – 3, and The product of the function will be (r × s)(x) = 2x³ – 6x².
The complete question is attached below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The functions are given below.
r(x) = x – 3
s(x) = 2x²
The sum of the function will be
(r + s)(x) = x – 3 + 2x²
(r + s)(x) = 2x² + x – 3
The difference of the function will be
(r – s)(x) = (x – 3) – 2x²
(r – s)(x) = –2x² + x – 3
The product of the function will be
(r × s)(x) = (x – 3) (2x²)
(r × s)(x) = 2x³ – 6x²
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Help me with this question please!! :)
Answer: 13/69
Step-by-step explanation:
13 students are female and got a B out of a total of 69 students, so the probability is 13/69
Find a polynomial f(x) of degree 3 that has the following zeros.
4, 0, -3
Leave your answer in factored form.
Answer:
f(x) = x(x - 4)(x + 3)
Step-by-step explanation:
given f(x) with zeros x = a and x = b then the corresponding factors are
(x - a) and (x - b)
f(x) is then the product of these factors
Given zeros are x = 4, x = 0, x = - 3 then the factors are
(x - 4) , (x - 0), (x - (- 3)) , that is
(x - 4) , x , (x + 3)
f(x) = x(x - 4)(x + 3)
PLS HELP ME ASAP!! TEN POINTS!!! Select each correct answer.
Answer:
It's 3
Step-by-step explanation:
if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.
Can anyone please help me with this question?
Karl receives his first mark of the year in his law course. He scores 94th percentile. What is his mark!?
Answer:
Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.
So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.
