The f(x) of the linear function is:
f(x) = -4x - 7
How to f(x) of a linear function?Since f is a linear function. The general form of a linear function is:
y = mx + b
where y = f(x), m is the slope and b is the y-intercept
Since f (−3) = 5, we have:
x = -3 and y = 5
Substitute into y = mx + b:
y = mx + b
5 = -3m + b ---- (1)
Also, f(5) = −27, we have:
x = 5 and y = -27
Substitute into y = mx + b:
y = mx + b
-27 = 5m + b ---- (2)
Solving (1) and (2) simultaneously by elimination method:
-3m + b = 5
5m + b = -27
-8m = 32
m = 32/(-8)
m = -4
Put m = -4 in (1) and solve for b:
-3x + b = 5
-3(-4) + b = 5
12 + b = 5
b = 5 - 12
b = -7
Put m and b into f(x) = mx + b to get f(x). That is:
f(x) = mx + b
f(x) = -4x - 7
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The federal government has developed the body mass index (bmi) to determine ideal weights. a person's bmi is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (a bmi of 19 to 25 corresponds to a healthy weight.) a 6-foot-tall person weighing 177 lb has bmi 24. find the bmi (to the nearest whole number) of a person whose weight is 176 lb and whose height is 77 in.
The BMI of a person whose weight is 176 lb and whose height is 77 inches is 21.
First, let's use the given information to find the constant of proportionality in the BMI formula:
BMI = k × (weight in pounds) / (height in inches)²
When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:
24 = k ₓ 177 / (72²)
k = 24 ₓ (72²) / 177
k ≈ 9.94
Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:
BMI ≈ 21
BMI = 9.94 ₓ 176 / (77²)
Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.
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Which statement best reflects how the cultural setting influences
Sigismondo's attitude in the excerpt from "The City Lost in the Snow"?
A
B
C
D
The competition between snow shovelers makes Sigismondo
excited to prove himself to Marcovaldo.
The fast-paced urban environment explains why workers like
Sigismondo must keep the city moving.
The scarcity of jobs makes Sigismondo appreciate the temporary
employment the snow provides.
The industrialization of the city leads Sigismondo to feel ambitious
about his future opportunities.
In the excerpt from "The City Lost in the Snow," the statement that best reflects how the cultural setting influences Sigismondo's attitude is: C.
The scarcity of jobs makes Sigismondo appreciate the temporary employment the snow provides. T
his statement reflects the importance of the cultural setting, as it shows that Sigismondo values the opportunity to work and earn money, even if it's temporary, due to the scarcity of jobs in the city.
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Screenshot, I WILL GIVE 20 POINTS AND BRAINLIST!!!!
Answer:
0.7 = 0.70, so 0.17 < 0.70
Calculate the area of the shape below
Answer:
Step-by-step explanation:
Area of rectangle+area of triangle
hope the picture helps
Write 4 as a logarithm with a base 4
Answer: Algebra Examples
Logarithm base 4 of 4 is 1.
Step-by-step explanation:
unity
The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.
1
Type here to search
day
How many more points did Zara score than John?
i
C
Number of Points
Points Scored in Basketball Game
25
20
15
10
5
0
e g
Read and Interpret Scaled Bar Graphs - Quiz - Level C
Mateo
Zara
Player
John
Mila
DONE
7
4
1
2
0
5
points
8
9
6
3
76°F Mostly cloudy
X
Th
Answer:
yes
Step-by-step explanation:
john has 34 marbles
Quadrilateral ABCD is translated 5 units up. What are the coordinates of
quadrilateral A'B'C'D?
A
D
A(-5, 5)
D(-5, 1)
B' Y
G
C₁
8(-1,5)
C(1, 2)
OA. A'(-5, 0), B'(-1,0), C'(-1, -3),
D'(-5,-4)
OB. A'(-5, 10), B'(-1, 10), C'(-1,7),
D'(-5, 6)
C. A'(-10, 10), B'(-6, 10), C'(-6, 7),
D'(-10, 6)
D. A'(-10, 5), B'(-6, 5), C'(-6, 2),
D'(-10, 1)
Answer:
it should be B but I could be wrong
Step-by-step explanation:
B
Solve the equation for y in terms of x, and replace y with function notation f(x). Then find f(2).
y+3x^2=5
f(x)=?
f(2)=?
Answer:
[tex]f(x)=-3x^2+5[/tex]
[tex]f(2) = -7[/tex]
Step-by-step explanation:
Given equation:
[tex]y+3x^2=5[/tex]
To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:
[tex]\implies y+3x^2-3x^2=5-3x^2[/tex]
[tex]\implies y=-3x^2+5[/tex]
Replace y with the function notation f(x):
[tex]f(x)=-3x^2+5[/tex]
Finally, to find the value of f(2), substitute x = 2 into the function:
[tex]\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}[/tex]
Answer:
[tex]f(2) = - 7[/tex][tex] f(x) = 5 - 3x^2[/tex]Step-by-step explanation:
To find:-
The value of [tex]f(2)[/tex]Answer:-
We are here a given a equation, with some steps to follow, in order to find out the value of [tex]f(2)[/tex].
Step 1 :- Solve the equation in terms of y ,
The given equation to us is,
[tex]\longrightarrow y + 3x^2 = 5\\[/tex]
To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .
[tex]\longrightarrow y = 5 - 3x^2 \\[/tex]
Step 2 :- Replace y with function notation [tex]f(x)[/tex]
Just simply replace y here with f(x) as ,
[tex]\longrightarrow f(x) = 5 - 3x^2\\[/tex]
Step 3 :- Find f(2) .
To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,
[tex]\longrightarrow f(2) = 5 - 3(2)^2\\[/tex]
Simplify,
[tex]\longrightarrow f(2) = 5 - 3(4)\\[/tex]
[tex]\longrightarrow f(2) = 5 - 12\\[/tex]
[tex]\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\[/tex]
Hence the required answer is -7 .
x^2-6x-16 when factored is
Answer: (x+2)(x-8)
Step-by-step explanation:
x^2-6x-16
x^2-8x+2x-16
x(x-8)+2(x-8)
(x+2)(x-8)
Please help meeee
describe an incident that shows how you were doing "selection" during the process of perception. Then, give your own example about a stereotype that you do.
The description of the incident is shown below
Describing the incidentOne incident that shows how selection works in the process of perception is when you are at a party and you hear your name being mentioned in a conversation across the room. In this situation, your attention is immediately drawn to the conversation, and you focus on it while filtering out other sounds and distractions around you.
This is an example of selective attention, where you choose to focus on a particular stimulus and ignore others.
As for an example of a stereotype that I have, it is that all people who live in a certain region or country behave in a particular way.
For instance, I may have the stereotype that people from a particular country are loud and aggressive.
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8a = -12 + 2a me need helpppppppppppppp
Answer: a = -2
Step-by-step explanation:
8a = -12 + 2a
8a - 2a = -12
6a = -12
a = -12/6
a = -2
Tom has $160,000 in his retirement account. It is earning an APR of 4.57%. What would be the monthly yield on the account for a 30-year period?
The monthly interest yield on Tom's retirement account for a 30-year period would be $637.71.
Assuming that the interest is compounded monthly, the monthly yield on Tom's retirement account with an APR of 4.57% for a 30-year period can be calculated using the formula:
Monthly Yield = (Principal × Monthly Interest Rate) ÷ (1 - (1 + Monthly Interest Rate[tex])^{(-Number of Months)}[/tex]
Here, Principal = $160,000
APR = 4.57%,
Number of Months = 30 years ÷ 12 months/year = 360 months.
First, we need to convert the APR to a monthly interest rate by dividing it by 12:
Monthly Interest Rate = 4.57% × 12
Monthly Interest Rate = 0.3808%
Monthly Yield = (160000 × 0.3808%) ÷ (1 - (1 + 0.3808%[tex])^{-360}[/tex]
Monthly Yield = $637.71
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Solve the problem in the picture please!
The answer choices are
A) 5
B) 2
C) 200
D) 100
1/5 of a large wall was covered in red paint, 1/10 in blue paint, and 1/4 in green paint. What
percentage of the whole wall is covered in paint (of any colour)?
19%
32%
55%
50%
68%
Answer:
55% of the whole wall is covered in paint of any color.
Step-by-step explanation:
To determine what percentage of the wall is covered in paint, we need to add the fractions of the wall covered by each color of paint and then convert the result into a percentage.
Red paint: 1/5
Blue paint: 1/10
Green paint: 1/4
First, we need to find a common denominator, which is the least common multiple (LCM) of the denominators 5, 10, and 4. The LCM of 5, 10, and 4 is 20. Now, we can convert the fractions to equivalent fractions with a denominator of 20:
Red paint: (1/5) * (4/4) = 4/20
Blue paint: (1/10) * (2/2) = 2/20
Green paint: (1/4) * (5/5) = 5/20
Now, add the fractions:
Total paint coverage = 4/20 + 2/20 + 5/20 = (4 + 2 + 5)/20 = 11/20
To convert this fraction to a percentage, we can divide 11 by 20 and multiply the result by 100:
(11/20) * 100 = 0.55 * 100 = 55%
Thus, 55% of the whole wall is covered in paint of any color.
Solve the systems by elimination.
x -y = 11
5x + 6y = -44
Answer: (6,-5)
Step-by-step explanation:
Here is another riddle:
-The sum of two numbers is less than 2
-If we subtract the second number from the first, the difference is greater than 1
The riddle can be represented by a system of inequalities. Write a inequality for each statement.
Name a possible (ordered pair) solution to the riddle.
Identify the shapes that make up the figure at the left. Then find the perimeter and area of the figure to the nearest hundredth.
Rectangle, semi circle, semi circle
Perimeter: 60.8
Area: 64.2
What is perimeter and area?In mathematics, the two key characteristics of two-dimensional forms are area and perimeter. The difference between area and perimeter is how much room each type of shape takes up.
Mathematical concepts like area and perimeter are crucial because they are applied to daily living. Any size and form, whether regular or irregular, can use this. Each design has a unique area and perimeter calculation. Forms like triangles, squares, rectangles, circles, spheres, etc. should be known to you. Here, the boundaries and surfaces of all forms are explained.
perimeter= 60.8
each of the three shapes' perimeters separately, then sum them all up to get 60.8.
area= 64.2
Calculate the area of each of the three shapes separately, then sum them all up to get 64.2.
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The complete question attached below,
The required size and perimeter of the Area are respectively 27.42 and 64.26 square units.
What is Perimeter of the shape?A shape's perimeter is its circumference. How are perimeters determined? By adding the lengths of each side of a shape, the border may be obtained.
A shape comprised of two circles and a rectangle has been provided.
the size of a circle = 12 - 6 = 6
then radius = 3 units
Perimeter = 3+3+3+3+3+3+π(3)
= 18 + 3.14(3)
= 18 + 9.42
= 27.42 units
and
Area = area of rectangle + area of two half circles
= 12(3) + π(3)²
= 36 + 28.26
= 64.26 sq units.
Therefore, the shape's needed area and perimeter are respectively 27.42 and 64.26 square units.
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how will the product change if one number is increase by a factor of 12 and the other is decreased by a factor of 4
Using factors, we can conclude that the new product will be 48 time more than the old product.
Define factors?In mathematics, the factor of a number is a divisor of the inputted integer that entirely divides it, leaving no residue. We can use a variety of techniques, including the division method and the multiplication method, to identify a number's components.
Let the product be P.
Let the numbers be a and b.
Now,
P = a × b
According to the question.
Let a is increased by a factor of 12 and b by 4:
P = 12a × 4b
P = 48 × a × b
Hence, we can conclude that the product will increase by a factor of 48.
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Describe the transformations that would map the graph
of f(x) = x^2 + 1 to the graph of g(x) = (x − 3)^2 − 2.
The graph of [tex]g(x)[/tex] is the result of taking the graph of [tex]f(x)\\[/tex], shifting it right three units and down two units.
What is the solution to x^3+4x^2 >x+4?
Answer:
Step-by-step explanation:
it’s equals 0 I think
PLS HELP :))
The property taxes on a house were $1265
. What was the tax rate if the house was valued at $115,000
? Follow the problem-solving process and round your answer to the nearest hundredth of a percent, if necessary.
The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.
What is property tax?The property tax is the levy imposed on the assessed value of the property of an individual or corporation.
Property tax is usually levied as a percentage of the assessed value.
Data and Calculations:Property tax = $1265
House value - $115,000
Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]
Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.
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Triangle ABC aid dilated by a scale factor of 3. Which is an algebraic representation of the dilation?
Answer:
[tex](3x, 3y)[/tex]
Step-by-step explanation:
The scale factor is 3 so you multiply 3 by the (x,y) to get (3x,3y) as the scale factor
Nathan rolls a number cube and records the result of each roll in the table.
Number Cube
Number Rolled
Frequency
1
11
2
16
3
14
4
20
5
12
6
17
Which statements below represent the situation? Select three options.
The correct three options are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
Nathan rolled the number cube a total of 90 times.
The number 4 was rolled more frequently than any other number.
The number 2 was rolled the least frequently of all the numbers.
The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.
The correct statements are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
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4 1/5 -5/3 subtract
how do i do this eqation
Answer:
38/15
Step-by-step explanation:
4 1/5 - 5/3
4 1/5 = 21/5
21/5 - 5/3 = 63/15 - 25/15 = 38/15
So, the answer is 38/15
5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4
[tex] \angle3 \: and \: \angle4 [/tex] are complementary.
What is Complementary angle?
If sum of two angles is 90° then we can say that those angles are complementary.
For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.
Here are some examples of complementary angles:
30 degrees and 60 degrees45 degrees and 45 degrees20 degrees and 70 degrees15 degrees and 75 degrees10 degrees and 80 degrees35 degrees and 55 degrees25 degrees and 65 degrees40 degrees and 50 degrees5 degrees and 85 degrees12 degrees and 78 degrees.Here given,
[tex] \angle1 \: and \angle2[/tex] are complimentary.
So,
[tex] \angle1 + \angle2 = {90}^{o} [/tex]
It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.
So, we can write,
[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]
Here sum of angle 3 and angle 4 is 90°.
According to definition angle 3 and angle 4 are complimentary angles.
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Given RP = 22, RA = 6, and PQ is tangent to .R at Q, find PQ.
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{PQ} \end{cases} \\\\\\ PQ=\sqrt{ 22^2 - 6^2}\implies PQ=\sqrt{ 484 - 36 } \implies PQ=\sqrt{ 448 }\implies PQ\approx 21.17[/tex]
PLS HELP ASP!!!
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
Answer: 98 cm²
Step-by-step explanation:
When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.
Original dimensions of Colorado on the map:
Length: 4 cm
Width: 2 cm
Enlarged dimensions using the scale factor of 3.5:
Length: 4 cm × 3.5 = 14 cm
Width: 2 cm × 3.5 = 7 cm
To find the area of the enlarged map, multiply the enlarged length and width:
Area = Length × Width
Area = 14 cm × 7 cm
Area = 98 cm²
The area of the enlarged map is 98 cm².
6+r=2r+3 how to solve this
Answer:
soln
6+r =2r+3
6-3=2r-r
3=r
ans r=3find the answer to 9/16 in decimal form
Answer:
0.5625
Step-by-step explanation:
x^3-6x^+2x-4 divided by x+2
Answer:
Step-by-step explanation: