Answer:
[tex]f(5)=3.5[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{3}{2}x-4\\f(5)=\frac{3}{2}(5)-4\\f(5)=7.5-4\\f(5)=3.5[/tex]
Hope this helped!! Have an amazing day :D
The required value of the linear function at x = 5 is 7 / 2.
Given that, a linear function f(x) = 3/2x-4 we have to determine the value of the function at x = 5 that is f(5).
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Liner function,
f(x) = 3/2x-4
Put x = 5 in above function,
f(5) = 3 * 5 / 2 - 4
f(5) = 15 / 2 - 4
f(5) = 15 - 8 / 2
f(5) = 7 / 2
Thus, the required value of the linear function at x = 5 is 7 / 2.
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Use the figure to find the measure of
the angle. Explain your reasoning.
1. ∠4
2. ∠5
3. ∠8
4. ∠6
Answer:
1. ∠4 = 152°
2. ∠5 = 152°
3. ∠8 = 152°
4. ∠6 = 28°
Step-by-step explanation:
1. ∠4 and 152° are vertical angles. Therefore, m∠4 = 152°.
2. ∠5 and 152° are corresponding angles. Therefore, m∠5 = 152°
3. ∠8 and 152° are alternate exterior angles, therefore, m∠8 = 152°
4. ∠6 and <8 are a linear pair. Therefore,
m∠6 + m∠8 = 180°
m∠6 = 180° - m∠8
m∠6 = 180° - 152°
m∠6 = 28°
Sue and Kim loved their skittles! Before throwing the bag away, Kim noticed that there were 160 calories for 40 grams of Skittles. Using the ratio table below.help Kim determine the number of calories for 80 grams of Slides
Answer:
320 calories
Step-by-step explanation:
Ratios.
let's say calories= c
grams = g
160c:40g
? :80g
So if you look at the grams, you see an increase by *2.
so the get: ?
you need to multiply 160 by 2.
57.8 divided by 81, estimate quotient
Answer:
0.71358024691 But really you can say .7
Complete the table of values for this equation:
y = 5x +20
Enter your answer by filling in the boxes.
x y
2
3
4
Answer:
X y
2 30
3 35
4 40
Step-by-step explanation:
Putting the value of x in equation u will get the value of y
The required table of values given that y = 5x + 20 will be given as
x y
2 30
3 35
4 40
Given the linear equation y =5x + 20
In order to fill the table, we will have to calculate the y-values for the corresponding x values given.
If x = 2
y = 5(2) + 20
y = 10 + 20
y = 30
If x = 3
y = 5(3) + 20
y = 15 + 20
y = 35
If x = 4
y = 5(4) + 20
y = 20 + 20
y = 40
Hence the required table of values will be given as
x y
2 30
3 35
4 40
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Which one one of the gradient of the line shown above ?
look at the graph help me !!!
9514 1404 393
Answer:
A 3/2
Step-by-step explanation:
The graph crosses the y-axis at (0, -3) and the x-axis at (2, 0). Using the slope formula, we can find the slope of the line to be ...
m = (y2 -y1)/(x2 -x1)
m = (0 -(-3))/(2 -0)
m = 3/2 . . . . matches choice A
Which property justifies drew first step ?
A.commutative property of multiplication
B.associative property of addition
C. subtraction property of equality
D. distributive property of multiplication over addition
hannah and jayna have disponsable camreas. The table and desprition shiw the number of shots left on thier cameras as a function of time.
Answer:
Okay, so what is the question?
Answer:
Tornado: clouds, strong wind, rain, hail.
Hurricane or cyclone: strong wind, heavy rain.
Blizzard: heavy snow, ice, cold temperatures.
Dust storm: strong winds, arid conditions.
Flood: heavy rainfall.
Hail storm: cold or warm temperatures, rain, ice.
Ice storm: freezing rain.Step-by-step explanation:
The total cost of production of spare parts of computer is given as C=4000x-100x²+x³ where x is the number of units of spare parts produced so that the average cost will be maximum?
Answer: 50
Step-by-step explanation:
Ok, we have the equation:
C=4000x-100x²+x³
Notice that the leading coefficient in this equation is positive, this means that as the value of x increases, also will the value of C.
Then we will not have a maximum, because as x →∞, C(x) →∞.
By doing an online search i found this same question, but with the change that we want to find x such that the average cost is minimum (this makes more sense).
Then let's do that:
The total cost for making x pieces is:
C(x) = 4000x-100x²+x³
Then the average cost, or the cost per piece, will be:
F(x) = C(x)/x = 4000 - 100*x + x^2
Notice that F(x) is a quadratic function with a positive leading coefficient, then the arms of the quadratic function will open upwards, this means that the minimum will be at the vertex.
To find the minimum, we must look at the zeros of the first derivation of F(x):
F'(x) = dF(x)/dx = -100 + 2*x
The zero is when:
F'(x) = 0 = -100 + 2*x
100/2 = x
50 = x
Then the number of x that minimizes the average cost is x = 50.
Which inequality is represented by this graph?
5+
(0,1)
(3,0)
A. ys-3x+1
B. y>-*x+1
C. 72-3x+1
D. y< -1x+1
The inequality is represented by the given graph is y ≤ -x/3+1.
The correct option is B.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
We have,
A graph of an inequality, passing by (0, 1) and (3, 0).
A and D are eliminated since the line is solid.
C is disregarded because the line is shaded below as well.
Then, the inequality will be y ≤ -x/3+1
Hence, the inequality is represented by the given graph is y ≤ -x/3+1.
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Given that for an arithmetic sequence, the first term is q and the second term is qz.
(a) Find the common difference d the general term Tn and the sum of the first n terms. Answer must
be in terms of q and z.
(b) Hence, find the sum of the first 10 terms in terms of q and z.
Answer:
[tex]d = q(z-1)[/tex]
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
[tex]S_{10} = 5q(9z -7)[/tex]
Step-by-step explanation:
Given
[tex]T_1 = q[/tex]
[tex]T_2 = qz[/tex]
Solving (a1): The common difference (d)
d is calculated as
[tex]d = T_2 - T_1[/tex]
This gives:
[tex]d = qz - q[/tex]
Factorize:
[tex]d = q(z-1)[/tex]
Solving (a2): Sum of n terms
This is calculated using:
[tex]S_n = \frac{n}{2}(2*T_1 + (n-1)d)[/tex]
Substitute values for T1 and d
[tex]S_n = \frac{n}{2}(2*q + (n-1)q(z-1))[/tex]
[tex]S_n = \frac{n}{2}(2q + q(n-1)(z-1))[/tex]
Factorize:
[tex]S_n = \frac{n}{2}(q(2 + (n-1)(z-1)))[/tex]
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
Solving (b): Sum of first 10.
In this case, n = 10
So:
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
becomes
[tex]S_{10} = \frac{10 * q}{2}(2 + (10-1)(z-1))[/tex]
[tex]S_{10} = 5 * q(2 + 9(z-1))[/tex]
[tex]S_{10} = 5q(2 + 9(z-1))[/tex]
[tex]S_{10} = 5q(2 + 9z-9)[/tex]
[tex]S_{10} = 5q(2 -9+ 9z)[/tex]
[tex]S_{10} = 5q(-7+ 9z)[/tex]
[tex]S_{10} = 5q(9z -7)[/tex]
Given that the first term and the second term of an arithmetic sequence is q and qz respectively, therefore:
a. Common difference (d) = [tex]\mathbf{d = q(z - 1)}[/tex]
Sum of the first n terms is: [tex]\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. [tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
Recall:
The common difference (d) of an arithmetic sequence = difference between the next term and the previous termSum of n terms, [tex]S_n[/tex] of arithmetic sequence = [tex]\frac{n}{2}[2a + (n - 1)d][/tex]Given:
First term, [tex]T_1 = q[/tex] (this is also "a")Second term, [tex]\\\\T_2 = qz[/tex]a. Common difference (d) = [tex]T_2 - T_1[/tex]
Substitute[tex]d = qz - q\\\\\mathbf{d = q(z - 1)}[/tex]
Sum of n terms:
[tex]T_n = \frac{n}{2}[2a + (n - 1)d][/tex]
Substitute by plugging in the value of d and a[tex]S_n = \frac{n}{2}[2(q) + (n - 1)q(z - 1)]\\\\S_n = \frac{n}{2}[2q + q(n - 1)(z - 1)]\\\\S_n = \frac{qn}{2}[2 + 1(n - 1)(z - 1)]\\\\\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. Sum of the first 10 terms:
Substitute n = 10 into [tex]S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)][/tex][tex]S_{10} = \frac{q(10)}{2}[2 + (10 - 1)(z - 1)][/tex]
Simplify[tex]S_{10} = 5q[2 + (9)(z - 1)]\\\\S_{10} = 5q(2 + 9z - 9)\\\\[/tex]
Add like terms[tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
In summary, given that the first term and the second term of an arithmetic sequence is q and qz respectively, therefore:
a. Common difference (d) = [tex]\mathbf{d = q(z - 1)}[/tex]
Sum of the first n terms is: [tex]\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. [tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
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I NEED HELP PLEASE HELP ME
Answer:
Step-by-step explanation:
the rock has changed color due to weathering.
just by looking at it, you cant tell for sure making it an inference.
Answer:
4. the rock has changed colour due to weathering
Step-by-step explanation:
the rock's colour has changed as a result of interference
PLEASE HELP!
x=3 is a factor of x^3+3x^2-7x+19.
A. Never
B. Always
C. Sometimes
Answer:
I think it is
C. Sometimes
4.) What is the area of this shape?
Answer:
212
Step-by-step explanation:
What is the difference between the maximum and minimum of the quantity x2y287, where x and y are two nonnegative numbers such that x+y=6?
Answer:
27/29
Step-by-step explanation:
What is the solution to the equation below?
1.5 (2x+ 5) +2.5 = 1.5 (-2x + 7)= 0.5
The equation -2y = 5x + 8 represents a line.
What are the slopes of lines that are parallel and perpendicular to the given line?
Drag the correct numbers into the boxes to complete the sentence.
Answer:
Lines parallel to the given equation will have a slope of -⁵/2 and lines perpendicular to the given line will have a slope of ⅖.
Step-by-step explanation:
Given the equation of a line, -2y = 5x + 8, first rewrite the equation in the slope-intercept form, before determining the slope of the lines that will be parallel to it, and slope of lines that will be perpendicular to it.
-2y = 5x + 8
Divide both sides by -2
y = 5x/-2 + 8/2
y = -⁵/2x + 4
The slope of the line of this equation is -⁵/2.
Linea that will be parallel to the given equation will have the same slope, while all lines that will be perpendicular to it will be a negative reciprocal of the slope of the equation.
Therefore:
Lines parallel to the given equation will have a slope of -⁵/2 and lines perpendicular to the given line will have a slope of ⅖.
Answer:
Lines parallel to the given equation will have a slope of -5/2 and lines perpendicular to the given equation will have a slope of 2/5.
Step-by-step explanation:
I took the test.
can you please help me with this question
Answer: I think it would be A
Step-by-step explanation: If you do the first equation it would equal -0.1 then if you do equation A -6.7 plus -0.1 = -6.8 plus 6.8 = 0
Answer:
A
Step-by-step explanation:
It's letter A
Pythagoras was born about 582 BC. Isaac Newton was born in 1643
AD. How many years apart were they born.?
Answer:
2225
Step-by-step explanation:
1643 A.D. years plus 582 B.C. years in between the births
Turner took a total of 8 quizzes over the course of 4 weeks. How many weeks of school will Turner have to attend this quarter before he will have taken a total of 16 quizzes? Assume the relationship is directly proportional. plz just put the answer
Answer:
8 wks
Step-by-step explanation:
It's 8 weeks
It's literally 8 weeks
Y’ALL PLEASE HELP ME ON MY TEST PLEASE I’VE BEEN STRUGGLING TO UNDERSTAND THE CLASSES AND MY TEACHER WONT EVEN EXPLAIN ANYTHING JUST SAY “I don’t know what you want me to do.” LIKE EXPLAIN PLEASE. SOMEONE PLEASE JUST HELP ME ON MY TEST
Answer:
1. 4320
2. 248
3. -180
4. 1/8
Clare ran 4 miles on Monday. Then for the next six days, she ran the same distance each day. She ran a total of 22 miles during the week. Which tape diagram represents this situation?
Answer:
In a week we have 7 days.
On the first day, Clare runs 4 miles.
On the other six days, she runs the same distance, let's call it D.
In total, she runs 22 miles.
Then:
4mi + 6*D = 22 mi
6*D = 22mi - 4mi = 18mi
D = 18mi/6 = 3mi.
Then the other 6 days, Clare runs 3 miles, then the tape diagram would look something like:
[tex]\left[\begin{array}{cccccc}Monday&-&-&-&-\\Tuesday&-&-&-\\Wednesday&-&-&-\\Thursday&-&-&-\\Friday&-&-&-\\Saturday&-&-&-\\Sunday&-&-&-\end{array}\right][/tex]
Where each "-" represents one mile.
Answer:
3 miles
Step-by-step explanation:
(6*3 Square root ÷9=
#7 Write an equation in slope-intercept form to represent the line perpendicular to 3x + 2y = -7 passing through the point (1, 1). O y=-3x + 4 O y = -3/2x + 1/3 y = 2/3x + 1/3 O y = 3x + 1
Answer:
y = 2/3 x + 1/3
Step-by-step explanation:
First find the slope of the given line by solving for "y":
3 x + 2 y = -7
2 y = - 3 x - 7
y = - 3/2 x - 7/2
which shows a slope of "- (3/2)"
Then, the slope of a line perpendicular to it must be "the opposite of the reciprocal" of this slope, that is: "2/3"
We use this info and the requested point (1, 1) to find the complete equation of the perpendicular line:
y = 2/3 x + b
1 = 2/3 (1) + b
1 - 2/3 = b
b = 1/3
Then the equation of the line is:
y = 2/3 x + 1/3
which agrees with the third answer shown in the list of options.
The points A (-3, -2), B (-3, 3) and C (5, 3) are 3 points.
What type of triangle is ABC?
Answer:
It's a right angle triangle
Step-by-step explanation:
in 2005 a company spent 493,749,335 on advertising. round the advertising figure to the nearest hundred thousand.
Answer: 493,700,000
Step-by-step explanation:
2/3-×+3/×+3=6x/x2-9
hi there! if you're asking us to simplify this equation, here is my answer for you...
Answer:
x = 2.09716754…
hope this helped. have a good one!
josie walks 3/4 miles in 1/5 hour. what is josie’s speed in miles per hour
Answer:
3 miles per hour
Step-by-step explanation:
3 times 5 is 15 15 divided by 4 is 3
Josie's speed will be 15/4 miles per hour.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Josie walks 3/4 miles in 1/5 hour.
Now,
The distance = 3/4 miles
The time = 1/5 hour
Since, We know that;
Speed = Distance / Time
Substitute all the values, we get;
Speed = 3/4 miles / 1/5 hour
= 3 x 5 / 4
= 15/4 miles per hour
Thus, Josie's speed will be 15/4 miles per hour.
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round 803 to the nearest ten. Enter your answer in the box below.
Answer:
800
Step-by-step explanation:
Answer:
Hey buddy, here is your answer. Hope it helps you
Step-by-step explanation:
It will round off to 800 as it is below 5. Above 5 it will round off to 810.
How long will it take an investment to double in value if the interest rate is 6% compounded continuously
Answer:
11.55 years
Step-by-step explanation:
Formula to calculate the final value when the money is compounded continuously is,
Final value = [tex]\text{(Present value)}.e^{rt}[/tex]
Here 'r' = rate of interest
t = duration for the investment
Let the money invested = $x
We have to find the duration in which the present value gets doubled.
Final value = $2x
Rate of interest = 6% per year ≈ 0.06
By substituting these values in the formula,
[tex]2x=x.e^{0.06t}[/tex]
[tex]2=e^{0.06t}[/tex]
ln(2) = [tex]\text{ln}e^{0.06t}[/tex]
0.693147 = 0.06t
t = 11.55 years
Therefore, invested amount will be doubled in 11.55 years.
What are the coordinates of its image, J'K'L, if this
triangle is dilated by a factor of 5 with respect to the
origin?
J'(2,7),K (8,7), and L'(5, 1)
O J'(-5, 2), K (5,2), and L'(0, -5)
J'(-3, 2), K (8, 2), and L'(0, -9)
J'(-15, 10), K (15, 10), and L'(0, -20)
Its the last one. I just took the quiz on edge.
Step-by-step explanation: The scale factor is 5. You mutiply 5 with the coordinates. J is (-3,2) so multiply 5 and -3 which is -15 then do the same thing with 2 which equals 10. J'=(-15,10)