A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,
Vertical Shift by 4 units,
f(x)+4
Vertical stretch by a factor of 3
g(x) = 3(f(x) + 4)
g(x) = -3x + 12
Hence, the function g(x) can be written as g(x) = -3x + 12.
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Which of the following are solutions to the equation below?
4x^2 + 4x + 1 = 9
Check all that apply
Answer:
Option B and D
Step-by-step explanation:
Subtract 9 from both sides :
4x² + 4x - 8 = 0
Divide both sides by 4 :
x² + x - 2 = 0
Factorise using factorisation method :
x² - x + 2x -2 = 0
x(x - 1) +2(x-1) = 0
(x+2)(x-1) = 0
Solve for x
x +2 = 0 OR x - 1 = 0
x = -2 OR x = 1
Answer will be Option B and D
Hope this helped and have a good day
Answer:
option b. –2 and d. 1 are correct.
*For detailed explanation refer to the attachment
what does 5r-r-9=15 look like after combining like terms ?
and whats the answer for r?
The value of r from the expression is 6
Simplifying expressionGiven the expression below;
5r-r-9=15
Add 9 to both sides
5r - r - 9 + 9 = 15 + 9
4r = 15 + 9
4r = 24
After combining the like terms the expression will be 4r = 24
4r/4 = 24/4
r = 6
Hence the value of r from the expression is 6
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John is 1/8 meter shorter than Paul, and Paul is 0.25 meter taller than Andrew. John's height is 13/4 meters, what is Andrews height?
Answer:
About 2.13
Step-by-step explanation:
13/4 multiply by 7/8 to get 91/32, then multiply by 0.75(3/4), which is 273/128
Consider the systems of equations below. determine the number of real solutions for each system of equations. system a has real solutions. system b has real solutions. system c has real solutions.
System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.
Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.
For system A,
The two systems of equations are
x²+y²=17 ......(1)
y=-1÷2x ......(2)
Substitute the value of equation (2) into equation (1) as
x²+(-x÷2)²=17
x²+(x²÷4)=17
Simplify the above equation by taking L.C.M. as
(4x²+x²)÷4=17
5x²=68
x²=68÷5
x=±3.688
Find the value of y by substituting the value of x in equation (2).
When x=3.688 then y is
y=-(1÷2)×3.688
y=-1.844
And When x=-3.688 then y is
y=-(1÷2)×(-3.688)
y=1.844
Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)
So, the system of equations of A has 2 real solutions.
For system B,
The two systems of equations are
y=x²-7x+10 ......(3)
y=-6x+5 ......(4)
Substitute the value of equation (4) into equation (3) as
-6x+5=x²-7x+10
x²-7x+10+6x-5=0
x²-x+5=0
Simplify the above quadratic equation using the discriminant rule,
x=(-b±√(b²-4ac))÷(2a)
Here, a=1, b=-1 and c=5
Substitute the values in the discriminant rule as
x=(1±√(1-4\times 5\times 1))÷2
x=(1±√(-19))÷2
x=(1±√(19)i)÷2
Here, the value of x goes into the complex.
So, the system of equations of B has 0 real solutions.
For system C,
The two systems of equations are
y=-2x²+9 ......(5)
8x-y=-17 ......(6)
Substitute the value of equation (6) into equation (5) as
8x-(-2x²+9)=-17
8x+2x²-9+17=0
2x²+8x+8=0
Simplify the above quadratic equation using factorization method as
2x²+4x+4x+8=0
2x(x+2)+4(x+2)=0
(2x+4)(x+2)=0
x=-2,-2
Find the value of y by substituting the value of x in equation (5).
When x=-2 then y is
y=-2(-2)²+9
y=-8+9
y=1
Thus, the point where the equations of system C intersect each other is (-2,1)
So, the system of equations of C has 1 real solutions.
Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.
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What is another way to label KF? What is another point that is on Line AC? Are points A and D collinear? Are points E,D, and K coplanar? (Giving 40 points)
Coplanar points are those that are all in the same PLANE. The other point that lies on line AC is B.
What are Collinear Points and Coplanar points?Collinear Points: Points are collinear if they are all in the same straight line.
Coplanar points: Coplanar points are those that are all in the same PLANE.
A.) Another way to label KF is F K.
B.) The other point that lies on line AC is B.
C.) Yes, Any two points can form a line, thus, A and D are colinear.
D.) Coplanar points are those points that lie in the same place. Although D and K lie on the same plane,j; the point E does not lie on the same plane. Thus, points E, D, and K are not coplanar points.
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(02.07)
The equation below shows the relationship between the
temperature in degrees Celsius, C, and degrees Fahrenheit, F:
H
C
(F-32)
Which of the following formulas correctly solves for F? (1 point)
Answer:
[tex]\boxed {\frac{F -32}{9} = \frac{C }{5}}[/tex]
Step-by-step explanation:
The correct relation between degrees Celsius, °C, and degrees Fahrenheit, °F is :
[tex]\boxed {\frac{F -32}{9} = \frac{C }{5}}[/tex]
Inventory was taken on Day 1, Day 2, Day 5, Day 6, and Day 7. Norris wants to know roughly what the inventory was on Day 3.
What should he do to estimate the inventory on Day 3?
He should use the value for Day 2 because it is closest in value to Day 3.
He should randomly pick a point near the fitted line where x=3.
He should evaluate the function f(x)=−1/3 x+4 for y=3.
He should evaluate the function f(x)=−1/3 x+4 for x=3.
Answer:
A
Step-by-step explanation:
guessing
He should evaluate the function f(x)=−1/3 x+4 for x=3 , Option D is the correct answer.
What in Interpolation ?Interpolation is when the line of best fit is used to determine the value of a point that is within the range of plotted points.
It is given to find the value at Day 3 which lies in the range of the points used for plotting
The line for best fit is
f(x) = (-1/3)x +4
At x = 3
f(3) = (-1/3) * 3 +4
f(3) = -1+4 = 3
Therefore He should evaluate the function f(x)=−1/3 x+4 for x=3
Option D is the correct answer.
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Find the perimeter of this figure.
22 in.
17 in.
12 in.
12 in.
30 in.
40 in.
? ] = inches
Answer:
133 inches
Step-by-step explanation:
First, you need to do 22 + 17 which is 39
Next, you need to do 39 + 12 which is 51.
Next, you need to do 51 + 12 which is 63.
Next, you need to do 63 + 30 which is 93.
Lastly, you need to do 93 + 40 which is 133.
Remember This:
Perimeter is adding up all the side lengths to get your answer.
I Hope This Helped :D
Answer:
133
Step-by-step explanation:
Work out, giving your answer in its simplest form:
2/3 x 3 3/5
Answer: 12/5
Step-by-step explanation:
[tex]3 \frac{3}{5}=\frac{18}{5}\\\\\implies \frac{2}{3} \times 3 \frac{3}{5}=\frac{2}{3} \times \frac{18}{5}\\\\=\frac{36}{15}\\\\=\boxed{\frac{12}{5}}[/tex]
Ahman has a lawn care business. he charges $25 per lawn to mow the grass. if his monthly expenses are $100, how many lawns must he mow in order to make a profit of at least $250 per month?
Answer:
14
Step-by-step explanation:
you can write an equation to represent the situation:
let x represent the number of lawns he has to mow
then, the monthly profit would be 25x - 100.
in order to make $250, this equation has to be equal to 250:
[tex]25x-100=250[/tex]
now, solve this:
add 100 to both sides
[tex]25x = 350[/tex]
divide both sides by 25
[tex]x = 14[/tex]
he must mow 14 lawns
Find the value of X in the given
right triangle.
10
x= [?]°
Enter your answer as a decimal rounded to the
nearest tenth.
What is the volume in cubic inches of the cylinder, rounded to the nearest cubic inch? Do not use units or commas in your answer.
Answer: You didn't give any data about the cylinder
Step-by-step explanation:
The cylinder is just an extruded circle. To calculate the cylinder's volume you need to multiply its base circle by the cylinder's height.
To do that, get the circle's radius and square it. Multiply the squared radius by 3.14.
After that, multiply the result by the cylinder's height
8 1/2 - 3/8=?
pls answer fast
Answer:
65/8
Step-by-step explanation:
1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?
2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8
3) Can not simplify since there are no common factors between 65 and 8.
The temperature fell at a rate of 0.65 °C/h. The temperature was recorded at 37 °C
at 6 p.m. Which function can be used to represent this situation?
Of(x) = 37 -0.65x
Of(x) = 0.65x - 37
Of(x) = 37x + 0.65
Of(x) = 0.65x+37
The linear function that can be used to represent the temperature in x hours after 6 pm is given by:
f(x) = 37 - 0.65x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem:
The y-intercept is the initial temperature of 37ºC.The slope is the rate of change of -0.65ºC/h.Hence the function is:
f(x) = 37 - 0.65x.
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find the volume of this prism.
The volume of the prism as given with dimensions is; 840cm³.
What is the volume of the prism?The prism given in the task content can be further subdivided to be represented by two rectangular prisms as follows;
First prism = 10cm by 6cm by 8cm.
Second prism = 5cm by 12cm by 6cm
Hence, the volume of the prism is; (10×6×8) + (5×12×6) = 840cm³.
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Which expression can be used to find the difference of the polynomials? (10m – 6) – (7m – 4) [10m (–7m)] [(–6) 4] (10m 7m) [(–6) (–4)] [(–10m) (–7m)] (6 4) [10m (–7m)] [6 (–4)]
The expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]
Difference of polynomials
A polynomial is a function that has a leading degree of 3 and above.
Given the expression below
(10m – 6) – (7m – 4)
Expand
10m - 6 - 7m + 4
Collect the like terms
10m - 7m - 6 + 4
Simplify
3m -2
Hence the expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]
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Please solve! And explanation!
A fraction is a way to describe a part of a whole. The value of x is 6.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The value of x can be written as,
[tex]\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{x}}} = \dfrac{7}{13}\\\\\\\dfrac{1}{1+\dfrac{1}{\dfrac{x+1}{x}}} = \dfrac{7}{13}\\\\\\\dfrac{1}{1+\dfrac{x}{x+1}} = \dfrac{7}{13}\\\\\\\dfrac{1}{\dfrac{x+1+x}{x+1}}= \dfrac{7}{13}\\\\\\\dfrac{x+1}{x+1+x}= \dfrac{7}{13}\\\\[/tex]
13x + 13 = 7x + 7 + 7x
13x + 13 = 14x + 7
x = 6
Hence, the value of x is 6.
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Factor x² - 4x + 5.
A Prime
B (x + 5)(x - 1)
C (x - 5)(x - 1)
D (x + 5)(x + 1)
Answer:
[tex]\huge\boxed{\sf Option \ A}[/tex]
Step-by-step explanation:
Given expression:= x² - 4x + 5
We can not factor out this expression, because of we apply mid-term break to it, the factors -4x will break into are -5x + x the coefficients of which when multiplied give -5 and not +5 (side term). This is a known rule in the mid-term break formula.
So, the given expression is a prime expression.[tex]\rule[225]{225}{2}[/tex]
Please help! Consider the function y = 9-x^2, where x ≥ 3
What is the inverse of the function? What is the domain of the inverse? Show all of your work
(hint: swap x and y in the domain as well as the function)
Using it's concept, it is found that the inverse function is [tex]y = \sqrt{9 - x}[/tex], and the domain is [tex]x \leq 9[/tex].
How to find the inverse function?The inverse of a function y = f(x) is found exchanging x and y and isolating y. The domain of the inverse is the range of the original function f(x).
In this problem, the function is:
y = 9 - x²
Then, we exchange and isolate y, hence:
[tex]x = 9 - y^2[/tex]
[tex]y² = 9 - x[/tex]
[tex]y = \sqrt{9 - x}[/tex]
The domain is [tex]9 - x \geq 0 \rightarrow x \leq 9[/tex], as looking at the graph of y = 9 - x², the range is [tex]y \leq 9[/tex].
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Hi, please help me find the volume of this sphere :)
Answer: 8788
Step-by-step explanation:
Use the formula and use 3 for pi
13cm is the radius
[tex]13^{3\\[/tex] = 2197
2197 x 3 = 6591
6591 x 4/3 = 8788
Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
PLEASE HELP ILL MARK BRAINLEST
Help! Will mark the big B for correct answer!
Answer:
The answer is A
Step-by-step explanation:
They both have a maximum of 5!
Mr. Lopez fruit salad recipe requires 3/4 of a cup of fresh peaches for 1 serving. He uses 9 cups of fresh peaches to prepare the salad. How many servings of the fruit salad did he prepare?
Answer:
6.75 servings
Step-by-step explanation:
[tex] \frac{3}{4} \times 9 = \frac{27}{4} = 6 \frac{3}{4} = 6.75[/tex]
Answer:
9 servings
Step-by-step explanation:
feel free to ask where you don't understand.
sum of numbers 975,983,923,913 and 985 rounded upto hundredth place is
Answer:
4800
Step-by-step explanation:
If a question is asking for the "sum" of numbers, this just means we have to add them altogether.
975+983+923+913+985 = 4779
To find the hundredth place, we use our place value. 4 is in the thousands column, and 7 is in the hundreds. Once we find the hundreds, we need the number to the right of it (7).
7 > 5 so we round up. 7 becomes 8.
4800.
Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
To solve the problem substitute the value of n as 5 in each expression and then simplify to check if it equals to 16 or not.
A.) (25/n) + 7
= (25/5) + 7
= 12
This is not the required expression.
B.) 30 - 3n
= 30 - 3(5)
= 15
This is not the required expression.
C.) 7+ (45/n)
= 7 + (45/5)
= 7 + 9
= 16
This is the required expression.
D.) n² - 114
= (5)³ - 114
= 125 - 114
= 11
This is not the required expression.
Hence, the correct option is C.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
Using proportion, the equivalent units of the following units rounded to the nearest hundredth are as follows:
6km = 3.73 miles2.5 Litres = 0.66 gallons90 pounds = 40.82 kgHow to use proportion to find equivalent units?Using proportion,
1.60934 km = 1 miles
6 km = ?
cross multiply
distance(m) = 6 / 1.60934 = 3.7282364199 = 3.73 miles
1 litre = 0.264172 gallons
2.5 litres = ?
volume(gallons) = 2.5 × 0.264172 = 0.66 gallons
1 pounds = 0.453592 kg
90 pounds = ?
cross multiply
weight(kg) = 40.82328 = 40.82 kg
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Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let represent the number of students who bought a cup of orange juice and represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
+ 3 = 76
+ = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables.
In order to eliminate one of the variables, subtract one of the equation from the other equation.
How to eliminate one of the variables?Given these equations:
o + 3s = 76 equation 1
o + s = 36 equation 2
Where:
o = number of orange juice bought
s = number of sandwiches bought
In order to eliminate one of the variables, subtract equation 2 from equation 1. The result is :
2s = 40
s = 20
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The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds. Using the empirical rule, what is the probability that a cat will weigh less than 11 pounds?
If the value of the z-score is 1. Then the probability that a cat will weigh less than 11 pounds will be 0.84134.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds.
Then the probability that a cat will weigh less than 11 pounds will be
The value of z-score will be
z = (11 – 9) / 2
z = 1
Then the probability will be
P(x < 11) = P(z < 1)
P(x < 11) = 0.84134
Thus, the probability that a cat will weigh less than 11 pounds will be 0.84134.
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Select the correct answer.
Which value of n makes the equation true?
-1/2n=-8
OA. -16
OB. - -4
OC. 4
O D. 16
ответ: д
-1/2 * 16 = -8
или 16/(-2) = -8
Answer: by rewriting equation in the form, / 1\2 16 X 4X 4 f=~1_~) (Do-2)2=g=~
Step-by-step explanation: hope this helps
Laurie is trying to stay within 10 feet of her current diving depth of –30 feet (with regard to sea level) so that the light is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the minimum and maximum depths Laurie wants to stay between?
-30 - x = 10 and -30 - x = –10
-30 + x = 10 and -30 + x = –10
x + 10 = 30 and x + 10 = –30
x – 10 = 30 and x – 10 = –30
The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Diving is the art of going down to the depth of the ocean. Divers usually go deep down in the ocean to study the dynamics of ocean life.
The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30
Therefore the equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.
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