The linear function that represents the graph of that has the points on the table is: A. .f(x) = 32(3x - 1).
What are the Points of a Linear Function Graph?If a point is on a graph of a linear function, its coordinates will make the equation of the linear function true, if plugged into the equation.
Given the table that represents some of the points that are on a linear function graph, use one point, (1, 64), to check which of the functions represents the table.
Substitute x = 1 and .f(x) = 64 into each of the functions given to see which is true:
.f(x) = 32(3x - 1)
64 = 32(3(1) - 1)
64 = 32(3 - 1)
64 = 32(2)
64 = 64 [true]
.f(x) = -32(x - 3)
64 = -32(1 - 3)
64 = 64 [true], however, if we use another set of values, say (5, 448), this function will not be true.
.f(x) = -2(32x - 3)
6 = -2(32(1) - 3)
6 = -2(29)
64 = -58 [not true]
.f(x) = 16(2x - 1)
64 = 16(2(1) - 1)
64 = 16(1)
64 = 16 [not true]
Therefore, the function that represents the table is: A. .f(x) = 32(3x - 1).
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Can you guys work your mathical math ASAP
Answer:
216.025 I think
Answer: S=237.5 in
Step-by-step explanation:
S=2(5)(6,5)+2(6.5)(7.5)+2(5)(7.5)
S=6,5(10)+97.5+7.5(10)
S=65+97.5+75
S=237,5 in
A company offers premium cable for 39.96 pet month plus a one time set fee. The total cost for setup and 6 months I'd 264.70 wrote and solve a linear equation
The cost per month is 39.96, the setup fee is 24.94, and the equations are x = 39.96 and 6x + y = 264.70.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given data:
A company offers premium cable for 39.96 per month plus a one-time set fee,
The total cost for setup and 6 months I'd 264.70
Write the equation as shown below,
The number of months × price per month + one-time setup fee = total cost
Calculate the equations,
x = number of months, y = setup fees
1 × x + y = 39.96 ⇒ x = 39.96 (y = 0 for one month)
6 × x + y = 264.70 ⇒ 6x + y = 264.70
Solve the above equation by the elimination method
x = 39.96 and y = 24.94
Therefore, the cost per month is 39.96, the setup fee is 24.94, and the equations are x = 39.96 and 6x + y = 264.70.
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Help me please!! Ill rate 5/5 for whoever answers first
Answer:
7) d (21)
6) a (102)
Step-by-step explanation:
For the first question, we should start with what we know first:
When angles are complementary then, their angles add up to 90.
So here we have 69 + something = 90.
We find out that the missing angle (angle B) is 21.
For this second question, we know that a straight line has an angle of 180. Here we have a straight line, but only part of the angle in which we only have 78.
Since we know 78 + x = 180
Then we can figure out that x = 102.
suppose the population of the earth is doubling every 30 years. if the population of the earth is now 7 billion people, approximately how many people will be here when you are 95 years old?
Population after 95 years is more than 28 billion.
What is a growth rate?
The growth rate of a value (such as GDP, turnover, earnings, etc.) gauges how much it has changed over time (month, quarter, year). The percentage is a fairly universal way to communicate it.
Here, we have
The present size of the population is 7 billion.
Assuming that the population starts growing from the age of "0"
The number of people after 30 years is equal to two times the present population i.e 14 billion
The number of people after 60 years is equal to two times the population after 40 years i.e 28 billion
Hence, the population after 95 years is more than 28 billion.
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a bakery sells 5800 muffins in 2010. the bakery sells 7420 muffins in 2015. write a linear model that represents the number y of muffins that the bakery sells x years after 2010.
The required linear model is y = 5800 + 324x.
What is a linear equation?
Equations whose variables have a power of one are called linear equations.
Given, a bakery sells 5800 muffins in 2010
the bakery sells 7420 muffins in 2015
So, the number of muffins sold after 2010 through 2015:
7,420 - 5,800 = 1,620
Then, the sales per year:
1,620 muffins sold since 2010 / 5 years = 324 muffins per year.
Then our linear model will be:
y = 5800 + 324x
Hence, the required linear model is y = 5800 + 324x.
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How do you prove ABC isosceles?
Triangle ABC to be isosceles we need to prove that opposite pair of sides of triangle ABC are congruent to each other.
Explanation :
Let us consider a triangle ABC,
To prove : Triangle ABC is an isosceles triangle.
In triangle ABC draw perpendicular bisector through point A to BC at point D.In triangle ADC and triangle ADB,
m ∠CAD ≅ m ∠BAD ( AD bisect angle A )
AD = DA ( common side )
m ∠ADC ≅ m ∠ADB ( each 90° )
By Angle side angle (ASA ) theorem ,
ΔADC ≅ΔADB
By congruence parts congruent triangles :
AC ≅ AB
Therefore, by congruence parts congruent triangles side AC ≅ AB implies ABC is an isosceles triangle.
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Please help me! It’s so hard
The range of the data-set in this problem has a value given as follows:
7.7.
How to calculate the range of a data-set?The range of a data-set is calculated as the difference between the largest value of the data-set and the smallest value of the data-set.
The data-set in this problem is defined as follows:
{6.2, 9.1. 2.9, 1.6, 9.3, 5.5, 8.3}
Hence to obtain it's range we have to obtain the smallest and the highest values from these values between the brackets.
The smallest value of the data-set and the highest value of the data-set are defined as follows:
Smallest value: 1.6.Highest value: 9.3.Hence the range of the data-set is given by the difference of 9.3 and 1.6, as follows:
Range = 9.3 - 1.6 = 7.7.
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4. Jennifer has a lemonade stand. She charges $1.25 for a glass of lemonade. It costs her $0.60 to make each glass of lemonade plus $15 a day for other expenses. Write an equation (do not solve) to determine how many glasses of lemonade, 1, Jennifer needs to sell each day in order to break even?
In order to break even,
Total charge for x glasses = Per day cost
1.25x = 0.6x + 15
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the number of glasses of lemonade Jennifer needs to sell each day
Total charge for x glasses = 1.25x
It costs her $0.60 to make each glass of lemonade:
=> For x glasses, cost = 0.6x
Per day cost = 0.6x + 15
In order to break even,
Total charge for x glasses = Per day cost
1.25x = 0.6x + 15
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Please hurry and answer these questions, I don't have much time!
Max Points: 100,
I will also give brainliest.
Answer:
1. 20 minutes (segment A)
2. 40 minutes (segment B)
3. 10 minutes (segment C)
4. 10 minutes (Segment D minus Segment B)
5. Segments C & E (approaching x axis)
6. Segment A (greatest slope)
7. 115 minutes
a stop sign is a regular octagon, formed by cutting triangles off the corners of a square. if a stop sign measures 36 in. from top to bottom, what is the length of each side of the octagon?
The length of each side of the sign will be 14.81-inch approx.
It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.
[tex]s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1[/tex]
Also, it is a square. So, the measurement of length from side to side
[tex]2x+s=36....................Eq.2[/tex]
solving Eq.1 we get,
[tex]s=\sqrt{2} x[/tex]...putting this value in Eq.2,
[tex]s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }[/tex]
Putting this value of x in Eq.1,
s = 14.8
Hence, The length of each side of the sign will be 14.81-inch approx.
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7) The initial fee to have a website getup using a server is $48. It costs $44 per month to maintain the
website. Write an equation that gives the total cost of setting up and maintaining the website as a
function of the number of months it is maintained.
Find the total of setting up and maintaining the website for 6 months.
Answer:
a.) c(t)=44t+48
b.) the total initial cost of setting up a website and maintaining it for 6 months is $312
Step-by-step explanation:
h
A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 320 yards wide. What is the area of the actual park, in square yards?
PLEASE HELP!!!!! 20 POINTS
The area of the rectangular park is 143360 square yards.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 minute = 60 second
1 km = 1000 m
We have,
Scale drawing of a rectangular park:
Wide = 5 inches
Length = 7 inches
Actual rectangular park:
Wide = 320 yards
Length = 448 yards
Now,
5 inches = 320 yards
7 inches = 7/5 x 320 yards
7 inches = 7 x 64 yards
7 inches = 448 yards
Now,
The area of the actual park.
= Length x Wide
= 448 x 320
= 143360 square yards.
Thus,
143360 square yards is the area of the actual park.
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find the gradient of the line below
The gradient of the line in the given graph is 1/2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the graph, let us consider two points from where the line is passing.
(-2, 3) and (2, 5).
Gradient is nothing but slope of the line.
m=5-3/2-(-2)
=2/4
=1/2
Hence, the gradient of line in the given graph is 1/2.
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At the fisher farm, the weights of zucchini squash are normally distributed, with a mean of 5 ounces and a standard deviation of 0. 7 ounces. Which weight represents the top 10% of the zucchinis?.
Weight represents the top 10% of the zucchinis is 5.9
The formula for calculating a z-score is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
We're looking for:
Weight is 10% of zucchinis at the top.
Top 10% = 90% of the population
90th percentile Z score is 1.282.
Hence
1.282 = x - 5 / 0.7
1.282 × 0.7 = x - 5
0.8974 = x - 5
x = 5 + 0.8974
x = 5.8974
5.9 ounces, roughly.
The top 10% of the zucchinis have a weight of 5.9 ounces.
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The number of badgers in a forest increases
by 20% each year.
This year, there are 200 badgers in the forest.
Calculate the number of badgers that there will
be in the forest
a) after 1 year.
b) after 2 years.
By evaluating the exponential equation for the population:
P(x) = 200*(1.2)^x
We will get:
a) 240 badgers
b) 288 badgers
How to calculate the number of badgers after x years?We know that the number of badgers increases by 20% each year, that increase after x years is given by the exponential equation:
P(x) = A*(1 + 20%/100%)^x
P(x) = A*(1.2)^x
Where A is the initial amount.
Here we know that the initial population of badgers is 200, then we have:
P(x) = 200*(1.2)^x
a) To find the population after one year, we need to evaluate the exponential equation in x = 1, we will get:
P(1) = 200*1.2^1 =240
b) The population after 2 years is:
P(2) = 200*1.2^2 = 288
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Wade Boggs played professional baseball for three different teams in 18 years.
The table shows his total number of hits for each team.
the Red Sox had 2,098 hits, Yankees had 702 hits, and Devil Rays had 210 hits.
Suppose he made the same number of hits each of the 18 years. If t = total number of hits
and a = number of hits per year, which two equations can be used to determine the number
of hits he made each year? Drag these equations into the box.
The two equations that can be used to determine the number of hits that he had each year are given as follows:
t = 2098 + 702 + 210.a = t/18.How to obtain the equations?His hits by team are divided as follows:
Red Sox: 2098 hits.Yankees: 702 hits.Devil Rays: 210 hits.Then the total number of hits is obtained by the sum of the number of hits that he obtained with each of the three teams, as follows:
t = 2098 + 702 + 210 = 3010.
Then the amount of hits that he obtained each year is obtained applying the proportion, dividing t by 18, as follows:
a = t/18.
Hence the result is given as follows:
a = t/18 = 3010/18 = 167 hits per year.
Missing Information
The options are given by the image shown at the end of the answer.
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Find the zeros of the equation by factoring. x2 + 9x + 20 = 0 factors should have two whole numbers separated by a: + or - . Do not type parentheses and no spaces. Examples: x+7 x-8
x=
X=
Answer:
Step-by-step explanation:
(x+4)(x+5) = 0
x = -4
x = -5
Jude types 840 characters in 5 minutes. What is her typing rate in characters per minute?
From a hot-air balloon, Adriel measures a 22° angle of depression to a landmark
that's 743 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest hundredth of a foot if necessary.
The balloon's vertical distance above the ground is 300.19 feet.
What is angle of depression?
If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.
Given that a balloon make 22° angle with a fixed point. The horizontal distance of the balloon along the ground is 743 feet.
Here need to find the vertical distance.
To find the vertical distance, use tangent of 22°. The tangent of angle is the ratio of vertical distance to horizontal distance.
Therefore,
tan 22° = vertical distance/ horizontal distance
tan 22° = vertical distance/ 743
Multiply both sides by 743:
vertical distance = 743 × tan 22°
vertical distance = 300.191
vertical distance = 300.19 ( rounding to the nearest hundredth)
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How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.
Answer:
The right answer is C.
Step-by-step explanation:
The parent function is:
[tex]f(x)=x^3[/tex]
If something is subtracted from variable [tex]x[/tex] it means the graph shifted toward right and something is added to [tex]y[/tex] value then the graph is shifted up.
[tex]f(x)=(x-8)^3[/tex]
graph shifted toward right by [tex]8[/tex] units right
[tex]f(x)=(x-8)^3+3[/tex]
graph shifted toward right by [tex]3[/tex] units up
Thus the new function is:
[tex]g(x)=(x-8)^3+3[/tex]
DUE ASAP PLS HELP ME!!!!!!!
Answer:
A 5 and -5
Step-by-step explanation:
You take the root of both sides to solve.
For which of the following x-values is k(x) =80?
By reading the graph we can see that k(x) = 80 for x ∈ (5, 6]
For which value of x is k(x) = 80?Look at the graph and try to identify the line where y = 80, now move to the right until you hit the graph of k(x) (red graph).
Now, move downwards until you intercept the x-axis, that value in the x-axis is the input that gives k(x) = 80.
In this case, there is a set of values.
The open circle means taht the value does not belong to the set.
The closed circle means taht the value does belong to the set.
Then k(x) = 80 for all the values of x in the set:
(5, 6]
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The slope of line p q is (v – z) divided by . the slope of line p prime q prime is divided by (w a) – (x a). both lines have a slope that is divided by . therefore, the lines are .
The slope of Line P Q is (v - z) divided by (w - x). The slope of Line P prime Q prime is
(v + b) - (z +b) divided by (w + a) - (x + a). Both lines have a slope that is (v - z) divided by (w - x). Therefore, the lines are parallel.
Slope of line :
Line slope is a measure of the slope and direction of a line. Finding the slope of a line in the coordinate plane helps predict whether the line is parallel or perpendicular without actually using a compass. The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.
The formula for the slope is
m = (y₂ - y₁)/ (x₂ - x₁)
Where (x₁, y₁) and (x₂, y₂) are the points
We have given a line PQ passing through points (x,z ) and (w,v) then slope of line is
m = ( v- z)/(w-x) --(1)
that is line lie in XZ- plane .
The slope of line p prime and q prime
m' = (( v- b) - (z-b))/(w-a)- (x-a)
= (v -b -z + b) /(w-a -x + a)
= (v-z)/(w-x) --(2)
from (1) and (2) we get , m = m'
So, both lines are parallel lines .
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Complete question:
The slope of Line P Q is (v - z) divided by ________. The slope of Line P prime Q prime is _________ divided by (w + a) - (x + a). Both lines have a slope that is _______ divided by _______. Therefore, the lines are _______.
Answer: in the picture
Step-by-step explanation:
What are the next three terms in the sequences below?
(1). 2,5,7,12,__,__,__
(2). 9,11,20,31,__,__,__
(3). 2,5,10,50,__,__,__
(4). 1,3,3,9,__,__,__
△ABC has the verticies at A(4,5) B(-3,6) and C(-1,8)
the following transformations have been done to the triangle in that order...
rotated 90 degrees
reflected across the line y=0
then translated according to the rule (x+3,y-3)
The required coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3) are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].
To determine the coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3), we need to apply these transformations to the coordinates of the original vertices in the order given.
First, we rotate the triangle 90 degrees counterclockwise around the origin. This transformation can be represented by the matrix:[cos(90) -sin(90)][sin(90) cos(90)]
Applying this matrix to the coordinates of the vertices of △ABC, we get:A' = [-5, 4]B' = [6, -3]C' = [8, -1]
Next, we reflect the triangle across the line y=0.
This transformation can be represented by the matrix:[-1 0][0 1]
Applying this matrix to the coordinates of the vertices of △ABC', we get:A'' = [5, 4]B'' = [-6, -3]C'' = [-8, -1]
Finally, we translate the triangle according to the rule (x+3,y-3).
This transformation can be represented by the matrix:[1 0][0 1]
Applying this matrix to the coordinates of the vertices of △ABC'', we get:A''' = [8, 1]B''' = [-3, -6]C''' = [-5, -4]
Therefore, the coordinates of the vertices of △ABC after given transformations are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].
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Solve two and four-sevenths times two-thirds equals blank. one and fifteen twenty-firsts two and eight twenty-firsts two and twelve-fourteenths three and two-twelfths
After solving the given fraction, the resultant fraction is (A) 1 15/21.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
A fraction appears in the numerator or denominator of a complex fraction.
The numerator of a proper fraction is less than the denominator.
So, we have:
2 4/7 * 2/3
Now, solve the fraction as follows:
2 4/7 * 2/3
14+4/7 * 2/3
18/7 * 2/3
36/21
1 15/21
Therefore, after solving the given fraction, the resultant fraction is (A) 1 15/21.
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Answer now with steps and I will give brainliest. Use picture for reference.
The value of f(g(2)) is output of the function g(2) is in the input of f(x) which
is equal to 1.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.
In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
From the graphs f(x) = -x + 5 and g(x) = x².
Now, f(g(2)) is the output of g(2) is the input of f(x).
g(2) = (2)².
g(2) = 4.
Now, f(g(2)) = -(4) + 5.
f(g(2)) = 1.
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please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
6
Step-by-step explanation:
The y intercept is when x=0
At the beginning of spring, Allison planted a small sunflower in her backyard. When it was first planted, the sunflower was 15 inches tall. The sunflower then began to grow at a rate of 2 inches per week. How tall would the sunflower be after 9 weeks? How tall would the sunflower be after w weeks?
Answer:
Hope this helps you out
Step-by-step explanation:
After 9 weeks, the sunflower would be 39 inches tall.
After w weeks, the sunflower would be 15 + (2 * w) inches tall.
The area of the triangle formed by x and y intercepts of the parabola y=0. 5(x-3)(x+k).
The possible values of k are -0.56, -3.56, -2, and -1.
We have the equation of the parabola, y=0.5(x-3)(x+k)
When we Substitute x=0, we get that y=0.5*(-3) * k for instance y = -1.5k
So, the y-intercept is (0,-1.5k).
We will now substitute y=0, 0=0.5(x-3)(x+k) for instance 0=0.5(x-3)(x+k) x=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
We can see that 'k' cannot be 0 or -3 since height = 0 if k=0, which is not conceivable. If k = -3, the base is also 0, which is not feasible.
We know that area of a triangle is 1/2*base*height
when we substitute we will get
1.5=1/2*(3+k) *(1.5k)
3=4.5k+1.5k^2
k=-0.56 and k=-3.56
or
1.5=1/2*(-3-k) *(1.5k)
3=-4.5k-1.5k^2
k=-2 and k=-1
hence the possible values of k will be -0.56, -3.56, -2, and -1.
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Your question is incomplete, most probably the full question was:
The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all possible values of k.