The table shows values for a linear function, f(x). What is an equation for f(x)?
Answers
Given a table that shows values for a linear function, f(x). we are asked to determine the equation of f(x).
Table:
x f(x)
-1 -8
3 -5
7 2
11 1
First, let us consider the lines of the equation as:
f(x) = ax + b
When x = -1 f(x) = -8
f(-1) = a(-1) + b
-8 = -a + b ------------------ eqn I
When x = 3 f(x) = 5
f(3) = a(3) + b
-5 = 3a + b ------------------- eqn II
subtract eqn I from eqn II:
-5 - (-8) = (3a + b) - (-a + b)
-5 + 8 = 3a + b + a - b
3 = 4a (-b and +b cancels out).
divide both sides by 4:
a = 3/4
Let's put the value of a = 3/4 into equation I
-8 = -a + b
-8 = -3/4 + b
make b the subject of formula:
b = -3/4 + 8
b = -32 + 3
4
b = -29/4
Let's now place the values of a an b into the lines equation:
recall the lines equation is :
f(x) = ax + b
f(x) = 3/4 x - 29/4.
Related Questions
Find the sum of all multiples of 7 between 1 to 200, inclusive.
Answers
Answer:
2842
Explanation:
The first multiple of 7 =7
The last multiple of 7 before 200 = 196
This problem forms an arithmetic sequence where:
• The first term, a= 7
,• The last term, l = 196
To determine the sum, we find first the number of multiples of 7 between 7 and 196.
[tex]\begin{gathered} \text{Number of multiples=}\frac{196}{7} \\ =28 \end{gathered}[/tex]For a sequence with first and last terms, its sum is:
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ =\frac{28}{2}(7+196) \\ =14\times203 \\ =2842 \end{gathered}[/tex]The sum of all multiples of 7 between 1 to 200 is 2842.
•
I WILL GIVE BRAINLIEST. NO LINKSA cliff is 80 feet above the sea. From the cliff the angle of depression to a boat is 35 degrees. How far is the boat from the base of the cliff? Round your answer to one decimal place.
Answers
Solution
For this case we can create the following diagram:
For this case we want to find the value of x and we can use the following property:
[tex]\tan 35=\frac{80}{x}[/tex]And solving we got:
[tex]x=\frac{80}{\tan 35}=114.25[/tex]
By visual inspection, determine the best-fitting regression model for thescatterplot.
Answers
From visual inspection it is clear that the best fitting regression model for this scatterplot is linear.
In the graph we can clearly see that the points form an almost straight line with a negative slope.
Now we know that a straight line has an equation of y = mx + c
The regression equation will be Y = aX + b which is a linear equation.
The mathematical figure known as a scatter plot, also known as a scatter graph, scatter chart, scattergram, a scatter diagram, uses Cartesian coordinates to display values in typically two variables for a set of data.
One more variable can be shown if a points are color, shape, and size coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable, and its position on the vertical axis by the value of the other variable.
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12. A bag of peanuts could be divided among 6 children, 9 children, or 10 children with each bag getting the same number, of peanuts. What is the smallest number of peanuts that could be in the bag?A.72 B.90 C.108 D.120
Answers
the numbers of children we have
6 children group , 9 children group or 10 children group
for equal quantity of peanuts among these groups will be LCM of these groups
so LCM of 6 , 9 , 10 is
6 = 2 x3
9 = 3 x 3
10 = 2 x 5
so, the LCM is 2 x 3 x 3 x 5 = 90
so smallest number of the peanuts will be 90
Solve for y:6y -4 = 3y +2
Answers
1) Solving for y, the following expression
6y -4 = 3y +2 Add 4 to both sides
6y = 3y +2+4
6y = 3y +6 Subtract 3y from both sides
6y -3y = 6
3y = 6 Divide both sides by 3
y= 2
S={2}
2) So the solution for this is y=2
a bakery must pay the 8% sales tax on this week total sales of $2,050. How much sales tax will the bakery pay to the state for this week?
Answers
It must pay 8% of $2050 which is $2050*8% = $164
Write the expression without a negative exponent.1/a^-4
Answers
Explanation
We are given the expression below:
[tex]\frac{1}{a^{-4}}[/tex]We are required to rewrite the expression without a negative exponent.
This can be achieved thus:
[tex]\begin{gathered} \frac{1}{a^{-4}} \\ We\text{ }know\text{ }from\text{ }indices\text{ }that\text{ }a^{-x}=\frac{1}{a^x} \\ \therefore\frac{1}{a^{-4}}=1\div a^{-4}=1\div\frac{1}{a^4} \\ =1\times\frac{a^4}{1}=a^4 \end{gathered}[/tex]Hence, the answer is a⁴.
Paul is planning to sell bottled water at the local carnival. Paul's profit (in dollars) from selling b bottles of water is given by the formula P=1.05b-151.
Answers
Explanation :
• The standard linear function takes the form of y = mx +c
• Since the Pauls profit is given by the formula ,P = 1.05b -151,, The curve of this profit is in line with the slope ,m = 1.05, as comparing with the standard linear fuction.
,• Therefore, Paul profit is increasing at a rate of 1.05 dollar per bottle.,
10. In July, Ariel recorded the height of a pine tree and how quickly it was expected to grow in thenext several monthsQ. Write an equation for the table.Height ofTree (inches)b. What does theторе represent608c. What does the y-intercept represent?
Answers
Using the table to find the equation:
Let x is the number of months, and y is the height of the tree
The general form of the line y = mx + c
where m is the slope and c is the y-intercept
So, at the beginning at x = 0 , y = 600
So,
600 = m * 0 + c
c = 600
When x = 3 , y = 602
so,
602 = 3m + 600
solve to find m
602 - 600 = 3m
3m = 2
m = 2/3
So,
[tex]y=\frac{2}{3}x+600[/tex]b. What does the slope represent?
The slope represents the rate of growth each month
which mean the tree grow (2/3) inches per month
c. What does the y-intercept represent?
y-intercept represents the first height of the tree
I need help on prime factorization just describe how to do it for me
Answers
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself.
For example, if we take the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.
Let us take another example and solve for its prime factorization
Prime factorization of 72
Hence, the prime factorization of 72 = 2³×3².
Finally,
Simplify the expression showed question … which is the correct answer
Answers
Okay, here we have this:
We need to simplify the following expression:
[tex]\begin{gathered} (5^{-4}(25)^4)^2 \\ =(5^{-4}(5^2)^4)^2 \\ =(5^{-4}\cdot5^8)^2 \\ =(5^{-4+8})^2 \\ =(5^4)^2 \\ =5^8 \end{gathered}[/tex]Finally we obtain that the correct answer is the option B.
Find each of the following products by first using division and then multiplication each will be a while number answer
Answers
so
[tex]\begin{gathered} \frac{11}{4}\text{ x 8=11 x 2=22 by multiplication} \\ \end{gathered}[/tex]now by division, we can write
[tex]\frac{11}{4}\text{ }\div\frac{1}{8}=22\text{ }[/tex]when we divide by a fraction, we multiply by its reciprocal
The area of this rectangle is 15ft^2. Write and equation and solve it to find y
Answers
The Area of a rectangle can be calculated by using the formula:
[tex]A=L\times W[/tex]Where A is the area, L is the length and W is the width.
By replacing the given values, your equation will be:
[tex]15ft^2=y\times3ft[/tex]Do the next steps to find the value of y:
[tex]\begin{gathered} \text{Divide both sides by 3 ft} \\ \frac{15ft^2}{3ft}=y\times\frac{3ft}{3ft}\text{ } \\ \text{Simplify and reorder terms} \\ 5ft=y \\ y=5ft \end{gathered}[/tex]Thus, the value of y is 5 ft.
Convert 1 in^3 into cm^3 using the measurement conversion 1 inch= 2.54 cm. Round yo two decimals.
Answers
A cubic inch is the same an inch to the third power.
[tex]in^3=in\times in\times in[/tex]If we use our measurement conversion
[tex]1in=2.54\operatorname{cm}[/tex]In our previous equation, we have
[tex]in\times in\times in=2.54\operatorname{cm}\times2.54\operatorname{cm}\times2.54\operatorname{cm}[/tex]Solving this product, we have
[tex]2.54\operatorname{cm}\times2.54\operatorname{cm}\times2.54\operatorname{cm}=16.387064cm^3[/tex]Then, this is our answer.
[tex]1in^3=16.387064cm^3[/tex]The equation of the line parallel to y = 3x + 8 that passes through the point (4, 5) is
Answers
To answer this question, we need to remember that a line is parallel to another one if its slopes are the same. A line parallel to y = 3x + 8 must has a slope, m = 3.
Now, to find the parallel line, we can use the point-slope form of the line equation as follows:
1. The point for which the line passes through is (4, 5):
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
(4, 5) ---> x1 = 4, y1 = 5
m = 3
[tex]y-5=3(x-4)\Rightarrow y-5=3x-12[/tex]Then
[tex]y=3x-12+5\Rightarrow y=3x-7[/tex]Therefore, the equation of the line parallel to y = 3x + 8 that passes through the point (4, 5) is y = 3x - 7.
find the absolute extrema for the function on the given internal
Answers
Given the function;
[tex]f(x)=-3x^2-24x+3[/tex]The first derivative of the function is;
[tex]f^{\prime}(x)=-6x-24[/tex]At critical points;
[tex]\begin{gathered} -6x-24=0 \\ -6x=24 \\ x=\frac{24}{-6} \\ x=-4 \end{gathered}[/tex]Thus, the f(x) at x=-4 is;
[tex]\begin{gathered} f(-4)=-3(-4)^2-24(-4)+3 \\ f(-4)=-48+96+3 \\ f(-4)=51 \end{gathered}[/tex]Thus, the absolute maxima on the given point is;
[tex](-4,51)[/tex]The absolute minima on the given points is;
[tex](4,-141)[/tex]YOU BE THE TEACHER Your friend solves the equation 9x2 = 36. Is your friend correct? 9x2 = 36 x = 4 x= 14 x= +2 O yes O no Explain your reasoning.
Answers
ANSWER
Yes
EXPLANATION
Your friend is correct.
First he divided both sides by 9: 36 divided by 9 is 4
Then he did the square root, which has two results: one positive and one negative. This gives +2 and -2.
Another way to check the result is to replace it into the equation. If the equation is true, then the result is correct:
[tex]\begin{gathered} 9(2)^2=36 \\ 9\cdot4=36 \\ 36=36\text{ }\rightarrow\text{ true} \\ \\ 9(-2)^2=36 \\ 9\cdot4=36 \\ 36=36\text{ }\rightarrow\text{ true} \end{gathered}[/tex]A chicken soup recipe calls for 15 cups of chicken stock. How much is this in quarts?Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer
Answers
Recall the conversion
1 quarts = 4 cup
Given that there is 15 cups, multiply it by the ratior of quarts to cup, making sure that the cup is in the denominator
[tex]\begin{gathered} 15\text{ cups}\times\frac{1\text{ quarts}}{4\text{ cups}} \\ =15\cancel{\text{cups}}\times\frac{1\text{ quarts}}{4\cancel{\text{cups}}} \\ =\frac{15\times1\text{ quarts}}{4} \\ =\frac{15\text{ quarts}}{4} \\ =3\text{ }\frac{3}{4}\text{ quarts} \end{gathered}[/tex]Therefore, 15 cups is equivalent to 3 and 3/4 quarts.
please help ASAP!!!!!
Answers
The first question
[tex]\frac{5x^2-28x-12}{x-6}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
The 2nd question
[tex]\frac{x^2+11x+28}{x+4}=\frac{(x+7)(x+4)}{x+4}=x+7[/tex]so, it can be solved by inspection.
The 3rd question
[tex]\frac{6x^2+2x+7}{3x-2}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
Finally, 4th question
[tex]\frac{x^2-x-35}{x-6}[/tex]can be rewritten by polynomial division.
You want to walk from home to a grocery store that is 1/2 miles away. You stop for a rest after 1/4 miles. How much farther do you have to walk? Write your answer as a fraction in simplest form.
Answers
Answer: 1/4
Step-by-step explanation:
1/2-1/4=1/4 because 1/4x2=2/4 and 2/4=1/2
Answer: 1/4 mile
Step-by-step explanation: so 1/2 = 2/4. You stop after 1/4, so subtract. You get 1/4, meaning you have to walk 1/4 mile. Also, r u sure you're in college, cuz this problem is pretty easy.
In the circle below, if AD is a diameter, and the chord BC = 48, find the length of the segment BP.
Answers
Solution
- The length BP is the half of length BC.
- The Diameter is AD and it divides the chord into two equal parts.
- Thus, BP is half of BC. This means that
[tex]\begin{gathered} BP=\frac{BC}{2} \\ \\ BP=\frac{48}{2}=24 \end{gathered}[/tex]Final Answer
BP = 24
Lottery: I buy one of 5000 raffle tickets for $1. The sponsors then randomly select one grand prize worth $500, two second prizes worth $200 each, and three third prizes at $100 each. Create the probability distribution for this raffle and calculate my expected value. Enter each row of your table as a separate line, but don't worry too much about formatting. Tables should look similar to those given in questions 1 and 3. Don't forget to give your expected value.
Answers
To give the probability distribution, we need to calculate the probability of each possible outcome and the value of this outcome.
We have 5000 raffle, 1 will win the first prize, 2 will win the second prize, 3 will win the third prize and the rest 4994 will win no prize.
The first prize is $500, but the raffle cost $1, so the outcome is actually $499.
The second prizes are $200 each, minus the cost we have an outcome of $199.
The third prizes are $100 each, minus the cost we have an outcome of $99.
The others will not receive prizes, but they will still have the cost of $1, so the outcome is -$1.
The first prize is 1 in 5000, so the probability is 1/5000
The second prizes are 2 in 500, so the probability is 2/5000
The third prizes are 3 in 5000, so the probability is 3/5000
The lost is the rest of the 4994 in 500, so the probability is 4994/5000
So, the table for the probability distributions is:
Value gained | P(x)
$499 | 1/5000
$199 | 2/5000
$99 | 3/5000
-$1 | 4994/5000
To calculate the expected value, we multiply the value by its probability and add them:
[tex]\begin{gathered} E(x)=499\cdot\frac{1}{5000}+199\cdot\frac{2}{5000}+99\cdot\frac{3}{5000}-1\cdot\frac{4994}{5000}_{} \\ E(x)=\frac{499}{5000}+\frac{398}{5000}+\frac{297}{5000}-\frac{4994}{5000} \\ E(x)=\frac{499+398+297-4994}{5000} \\ E(x)=-\frac{3800}{5000} \\ E(x)=-0.76 \end{gathered}[/tex]So, the expected value if -$0.76.
Find two values of angle A between 2pi where sin A = [tex] \frac{ - \sqrt{2 } }{2} [/tex]
Answers
Answer:
Explanation:
First of all, we know that
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]And knowing the unit circle, we know that the sine takes negative values in 3rd and 4th quadrants. Therefore, from the above value of the angle, If we go π radians counterclockwise, we encounter negative values of sine; hence,
[tex]\sin \lbrack\frac{\pi}{4}+\pi\rbrack=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{5\pi}{4}=\frac{-\sqrt[]{2}}{2}[/tex]The second value of the angle that yields the above value for sine is found by adding π/2 radians to the angle above (we are now in the 4th quadrant)
[tex]\sin \frac{5\pi}{4}+\frac{\pi}{2}=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{7\pi}{4}=-\frac{\sqrt[]{2}}{2}[/tex]Hence, the two values of angles between 0 and 2π are 5π/4 and 7π/4.
Given:• PQRS is a rectangle.• mZ1 = 50°PeNSRWhat is mZ2?130°85°70°65°
Answers
We can start answering this having that a rectangle is a parallelogram. The diagonals of a parallelogram bisect each other. Therefore, we have that the sides Q to the point where the diagonals intersect each other of the rectangle is congruent to R to this point. Then, we have two congruent sides.
The angles opposite to these sides are congruent too. They have the same measure. Since we have a triangle, and the sum of the internal angles of a triangle is equal to 180, we can say that:
[tex]m\angle1+2\cdot m\angle2=180[/tex]Then, we have:
[tex]50+2\cdot m\angle2=180[/tex]Subtracting 50 from both sides of the equation, and then dividing this equation by 2, we have:
[tex]50-50+2\cdot m\angle2_{}=180-50\Rightarrow2\cdot m\angle2=130[/tex][tex]2\cdot\frac{m\angle2}{2}=\frac{130}{2}\Rightarrow m\angle2=65[/tex]Therefore, the measure of angle 2 (m<2) is equal to 65 (degrees) (last option).
Samant coria 5 awz D X 3y + 2x25 26-27 +32=8 -2xtily - 29-12 267-37 +32-21 x+4y + 3xl 5x+7-28=-34 -X134+32=2
Answers
Given data:
The first given equation is x-3y+2z=5.
The second given equation is 2x-4y+3z=8.
Third equation is -2x+4y-2z =-12.
Add second and third equations.
[tex]\begin{gathered} (2x-4y+3z)+(-2x+4y-2z)=8-12 \\ z=-4 \end{gathered}[/tex]Substitute -4 for z in first and second equations.
[tex]\begin{gathered} x-3y=13 \\ x=13+3y \\ 2x-4y=20 \\ 2(13+3y)-4y=20 \\ 26+2y=20 \\ 2y=-6 \\ y=-3 \end{gathered}[/tex]The value of x is,
[tex]\begin{gathered} x-3(-3)+2(-4)=5 \\ x=4 \end{gathered}[/tex]Thus, the value of x is 4, the value of y is -3, and the value of z is -4.
8. Find the center of the circle that can be circumscribed about the triangle.y-4-262-224
Answers
The labelled triangle is shown below
The required center is the point where the perpendicular bisectors meet. It is called the circumcenter. We would find it by applying the midpoint method. The midpoint formula is expressed as
midpoint, M(x, y) = (x1 + x2)/2, (y1 + y2)/2
For AB,
x1 = - 4, y1 = 0
x2 = 4, y2 = 0
Midpoint = (- 4 + 4)/2, (0 + 0)/2 = (0, 0)
For AC,
x1 = - 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (- 4 + 0)/2, (0 + 4)/2 = (- 2, 2)
For BC,
x1 = 4, y1 = 0
x2 = 0, y2 = 4
Midpoint = (4 + 0)/2, (0 + 4)/2 = (2, 2)
We woulf find the slope of AC
Slope, m = (y2 - y1)/(x2 - x1) = (4 - 0)/(0 - - 4) = 4/(0 + 4) = 4/4
m = 1
Slope of the line per
A plater holds 24 strawbers,2 aplles,16 oranges.What fraction of all the fruits are strawberiias?Fracion of apples?Fraction of oranges?
Answers
The fraction for strawberries, apples, and oranges is 12/21, 1/21, and 8/21 respectively.
What are fractions?A fraction depicts a portion of an entire. This entire could be a location or a group of things. The Latin word "fraction," which means "to break," is where the word "fraction" comes from. In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. The numerator displays how many pieces the whole has been divided into. It is positioned at the top of the fraction, beneath the fractional bar is the denominator.
Given,
Number of strawberries = 24
Number of apples = 2
Number of oranges = 16
So, the total number of fruits is given as
= 24 + 2 + 16
= 42
The fraction for strawberries = 24/42
=12/21
The fraction for apples = 2/42
= 1/21
The fraction for oranges = 16/42
=8/21
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What is the approximate length of the radius of a circle with a circumference of 63 inches?A. 4 inchesB. 8 inchesC.10 inchesD. 20 inches
Answers
The formula for the circumference of a circle given it's radius is :
C = 2πr
Reversely, the formula for the radius given it's circumference is :
r = C/2π
From the given problem, the circumference is 63 inches,
Solve for the radius using π = 3.14
r = 63/(2 x 3.14)
r = 10.03 inches
So the answer is Choice C. 10 inches
I believed I solved correctly but want a double check pls
Answers
We have the original price P and it will increase a rate r%, we can express is as
[tex]P+P\cdot r[/tex]As we can see, P is the original price and P*r is what's going to be added to the original price, we can even simplify it to
[tex]P(1+r)[/tex]That's a generic expression to find it, so here we have P = 153 and r = 19% = 0.19, then
[tex]\begin{gathered} P(1+r)=153(1+0.19) \\ \\ 153(1+0.19)=153\cdot1.19 \\ \\ 153\cdot1.19=182.07 \end{gathered}[/tex]The price will be $182.07
Scale the rectangle by finding 3A. What are the vertices of the scaled rectangle
Answers
Given A, the matrix that contains the vertices of a rectangle on the plane, calculate 3A as shown below
[tex]3A=3\begin{bmatrix}{1} & {6} & {6} & {1} \\ {1} & {1} & {5} & {5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3*1} & {3*6} & {3*6} & {3*1} \\ {3*1} & {3*1} & {3*5} & {3*5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3} & {18} & {18} & {3} \\ {3} & {3} & {15} & {15} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Where each column of the 4x2 matrix above represents a vertex of the new rectangle; therefore, the 4 vertices are
(3,3), (18,3), (18,15), (3,15). The second option.