Answer:
7
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [4, 6 ]
f(b) = f(6) = 6² - 3(6) - 10 = 36 - 18 - 10 = 8
f(a) = f(4) = 4² - 3(4) - 10 = 16 - 12 - 10 = - 6
Hence
average rate of change = [tex]\frac{8-(-6)}{6-4}[/tex] = [tex]\frac{14}{2}[/tex] = 7
Write an equation of the graph:
y = |x| translated half a unit upward
Answer: y = I x l + 1/2
Step-by-step explanation:
The answer is y= IxI+1 bc you moved it up by 1 so that makes it plus 1
Maximum number of possible solutions x^2+4y^2=64 x+y=5
Answer:
2
Step-by-step explanation:
We don't need to "solve" this to figure out the answer.
We need to recognize that the first equation given is that of an ellipse and the second equation given is that of a line.
A line and an ellipse in a coordinate system can have these outcomes:
1. They can intersect (touch) at 1 point
2. They can intersect at 2 points
3. Can't intersect at all
Thinking will make sense. So, the maximum number of possible solutions is 2.
Note: The number of points of intersection are the solutions as well
what is the solution to this equation -13x =25
Answer:
-1 12⁄13
Step-by-step explanation:
-13x = 25 [Divide by -13]
x = -1 12⁄13
13 is your divisor, which will be your denominator, and the numerator is your remainder. Since 13 goes into 25 ONCE, 1 gets multiplied by 13 to get 13, then deduct that from 25 to get your remainder of 12. This is where you start putting the pieces together as a mixed number. Then attach the negative because whenever you divide a positive by a negative, you get a negative:
-25⁄13 = -1 12⁄13
I am joyous to assist you anytime.
Trigonometry how to do this
I’m not sure either, but lets keep in touch because I do Acellus too, and Trigonometry. Give me a thanks so we can message
Trigonometry involves the study of angles and sides of triangles, where sine, cosine, and tangent are fundamental ratios used to solve problems. The Law of Sines and the Law of Cosines help calculate unknown lengths and angles in various types of triangles.
Explanation:Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right-angled triangles. Key concepts such as trigonometric ratios including sine, cosine, and tangent are fundamental in solving problems in trigonometry. When provided with a diagram like Figure 4.17 or Figure 5.27, one can determine the magnitudes of various components by applying these trigonometric principles.
For instance, if we know the angle and a side length adjacent to it, we can find the lengths of the unknown sides using functions such as cosine for the adjacent side or sine for the opposite side relative to the given angle. The Law of Sines and the Law of Cosines are also substantial tools in trigonometry, allowing us to calculate unknown lengths and angles in non-right triangles. Practicing these calculations with a calculator, as mentioned, helps familiarize oneself with the trigonometric functions and their inverses.
what is the solution to every system of equation
By graphing is the solution to every equation
A gold coin appreciated in value from $200.00 to $475.00 in 6 years. Find the yearly rate of appreciation. Show or explain all work.
Answer:
16%
Step-by-step explanation:
To solve this we are using the standard growth equation:
[tex]y=a(1+b)^x[/tex]
Were
[tex]y[/tex] is the final value after [tex]x[/tex] years
[tex]a[/tex] is the initial value
[tex]b[/tex] is the growth factor (yearly rate of appreciation in our case) in decimal form
[tex]x[/tex] is the time in years
We know from our problem that gold coin appreciated in value from $200.00 to $475.00 in 6 years, so [tex]y=475[/tex], [tex]a=200[/tex], and [tex]x=6[/tex].
Let's replace the values in our equation and solve for [tex]b[/tex]:
[tex]y=a(1+b)^x[/tex]
[tex]475=200(1+b)^6[/tex]
[tex]\frac{475}{200} =(1+b)^6[/tex]
[tex]2.375=(1+b)^6[/tex]
[tex]\sqrt[6]{2.375} =\sqrt[6]{(1+b)^6}[/tex]
[tex]1+b=\sqrt[6]{2.375}[/tex]
[tex]b=\sqrt[6]{2.375}-1[/tex]
[tex]b=0.155[/tex]
which rounds to
[tex]b=0.16[/tex]
Since our appreciation rate is in decimal form, we need to multiply it by 100% to express it as percentage:
0.16*100% = 16%
We can conclude that the yearly appreciation rate of our gold coin is approximately 16%
What is 23.014 written in expanded form?
A (2 x 100) + (3 x 10) + (0 x 10)+(1 x 100) + (4 x 7,000)
B (2 x 10) + (3 * 1) + (0 x 1b) + (1 100) +(4x 1,000)
C (2 x 10) + (3 * 1) + (0 x 1,000) + (1x 100 +(4 x to
D (2 x 10) + (3 x 1) + (0 x 1\1) + (1 x 1) + (4 x 100)
Please help
b(2 ×10)+(3*1)+(0×1b)+(1×100)+(4×1000)
Final answer:
The number 23.014 in expanded form is (2 x 10) + (3 x 1) + (0 x 0.1) + (1 x 0.01) + (4 x 0.001), illustrating the value of each digit according to its place value.
Explanation:
Writing the number 23.014 in expanded form means expressing each digit according to its place value. Expanded form represents a number by showing the value of each digit. For the decimal number 23.014, we look at the place value of each digit: the digit in the tens place, the ones place, the tenths place (one place after the decimal), the hundredths place (two places after the decimal), and so on.
The correct expanded form for 23.014 is:
<(2 x 10) + (3 x 1) + (0 x 0.1) + (1 x 0.01) + (4 x 0.001)
This means:
The '2' is in the tens place, so it represents 2 x 10, or 20.
The '3' is in the ones place, so it represents 3 x 1, or 3.
The '0' is in the tenths place, but since it's 0, it adds no value (0 x 0.1 = 0).
The '1' is in the hundredths place, so it represents 1 x 0.01, or 0.01.
Finally, the '4' is in the thousandths place, so it represents 4 x 0.001, or 0.004.
Therefore, 23.014 written in expanded form is (2 x 10) + (3 x 1) + (0 x 0.1) + (1 x 0.01) + (4 x 0.001).
if a sequence is defined recursively by (0)=3 and (n+1)=-f(n)+5 for n≥0, Then f(2) is equal to
Answer:
f(2) = 3
Step-by-step explanation:
We are given:
f(0) = 3
and
f(n+1) = -f(n) + 5
We have to find the value of f(2). In order to find f(2) we first have to find f(1)
f(n + 1) = - f(n) + 5
Using n = 0, we get:
f(0 + 1) = - f(0) + 5
f(1) = -f(0) + 5 Using the value of f(0), we get
f(1) = -3 + 5 = 2
Now using n = 1 in the function, we get:
f(1 + 1) = - f(1) + 5 Using the value of f(1), we get
f(2) = -2+ 5
f(2) = 3
Thus the value of f(2) will be 3
Which modified plot represents the data set?
10, 12, 2, 4, 24, 2, 7, 7, 9
P.S: Not actually asking just for those with the same question.
Box A is the plot that represents the data set hope this helps:)
Stefan sells Jin a bicycle for $173 and a helmet for $19. The total cost for Jin is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
a) $ 120
b) $ 53
Step-by-step explanation:
Cost of Bicycle paid by Jin = $173
Cost of Helmet = $ 19
Total amount paid by Jin = $173 + $19 = $192
This amount is 160% of what Stefan originally spent. Let the amount he originally spent was n, so we can write:
192 = 160% of n
192 = 1.6n
n = [tex]\frac{192}{1.6} = 120[/tex]
Thus, Stefan originally spent $120 for buying the bicycle and the helmet.
Profit which he made from this sale = $ 173 - $ 120 = $53
So he made $53 by selling Jin a bicycle and a helmet
To find the original cost Stefan spent, we calculate 160% of the original cost equal to the total selling price of $192. Divide $192 by 1.60 to find the original cost. Subtract this cost from $192 to find Stefan's profit.
Explanation:The student's question pertains to calculating the original cost and the profit made from a sale. To solve this, we can set up an equation where 160% of the original cost (which we will call 'x') is equal to the total selling price of the bike and helmet, which is $173 for the bicycle and $19 for the helmet, adding up to $192.
This equation can be represented as 1.60x = $192. To find the original cost (x), divide the total cost by 1.60: x = $192 / 1.60. Calculating this gives us the original cost that Stefan spent.
To find the profit, we subtract the original cost from the total selling price. If x represents the original cost, then the profit is $192 - x. The step-by-step explanation helps the student understand how to set up and solve equations involving percentages, a key concept in mathematics related to business and personal finance.
I need to know the output
of “n”
in a function table :)
Answer:
I believe the answer is (n-5)
Step-by-step explanation: If you look at the other inputs, you can see that you subtract 5 to get the output. For input 6, you would subtract 5 (6-5=1) and you would receive the output, 1. This is shown to be true for the other two inputs. I hope this helps you.
anyhow, notice the pattern, the output is always the input minus 5, thus n - 5.
what is the slope of a line that is perpendicular to the line that contains points (5,4) and (-7,9). explain please
Answer:
[tex]\frac{12}{5}[/tex]
Step-by-step explanation:
First find the slope of the line containing points (5,4) and (-7,9). To find the slope use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. Putting those values in, you have
[tex]\frac{9-4}{-7-5}[/tex]
Simplify
[tex]\frac{5}{-12}[/tex]
[tex]-\frac{5}{12}[/tex]
Then, to find the slope of the line perpendicular to that, find the negative reciprocal.
[tex]\frac{12}{5}[/tex]
what is the domain and range of the square root of x+3-1?
Answer:
[tex]\large\boxed{\text{The domain:}\ x\geq-3\to x\in[-3,\ \infty)}\\\boxed{\text{The range:}\ y\geq-1\to y\in[-1,\ \infty)}[/tex]
Step-by-step explanation:
[tex]y=\sqrt{x+3}-1\\\\The\ domain:\\\\x+3\geq0\qquad\text{subtract 3 from both sides}\\\\x\geq-3\to x\in[-3,\ \infty)\\\\The\ range:\\\\\sqrt{x+3}\geq0\qquad\text{subtract 1 from both sides}\\\\\sqrt{x+3}-1\geq-1\\\\y\geq-1\to y\in[-1,\ \infty)[/tex]
kelly just brought a new pair of shoes! she received a 30% discount, which saved $15 off of the original price. what was the original price of the pair of shoes
Set up an equation:
x * .30 = 15
Divide both sides by .30 in order to determine the value of x
x = 15/.30
x = 115.38
So, the original price of the pair of shoes is $115.38
What is the exact value for the expression the square root of 56. − the square root of 14. + the square root of 126.? Simplify if possible. the square root of 14. 4 the square root of 14. 2 the square root of 42. 8 the square root of 42.
[tex]\bf \sqrt{56}-\sqrt{14}+\sqrt{126}~~ \begin{cases} 56=&2\cdot 2\cdot 2\cdot 7\\ &2^2\cdot 14\\ 126=&2\cdot 3\cdot 3\cdot 7\\ &2\cdot 3^2\cdot 7\\ &3^2\cdot 14 \end{cases}\implies \sqrt{2^2\cdot 14}-\sqrt{14}+\sqrt{3^2\cdot 14} \\\\\\ \stackrel{\textit{let's add the like-terms}}{2\sqrt{14}-\sqrt{14}+3\sqrt{14}}\implies 4\sqrt{14}[/tex]
Answer:
Step-by-step explanation:
sqrt(56) = sqrt(4*14) = 2*sqrt(14)
sqrt(126)= sqrt(9*14) = 3*sqrt(14)
2*sqrt(14) - sqrt(14) + 3*sqrt(14)
5sqrt(14) - sqrt(14)
4*sqrt(14)
====================
The second one is not clear enough.
The volume of the cylinder with a hight of 1.5 cm and the diameter of 2 cm.
Answer:
4.71 ish centimeters
Step-by-step explanation:
The equation for a cylinder is [tex]\pi r^{2} h[/tex] , where h is the height and r is the radius. So plugging in the numbers you have Pi * (1)^2 *1.5.
4.71 centimeters is the answer
80x80divided by 8 ......
Answer:
800
Step-by-step explanation:
80*80=6400
6400/8=800
The answer is 800
800 hope this helps
Hope U get a A+
Measure the length to the nearest half inch
Maybe you should try using a ruler cause I can’t tell if it is combined the two above it or what to do
What is the value of the lower quartile?
0
8
6
2
the value of the lower quartile is 2 because that’s where the box ends
Select all the statements that are correct rational approximation of irrational numbers?
The answers would most likely be A,C,and B from my calculations
8^(2x+3)+8^(2×+1)-8^2×=519*2^2010
x=?
Answer:
x=335
Step-by-step explanation:
The given expression is
[tex]8^{2x+3}+8^{2x+1}-8^{2x}=519*2^{2010}[/tex]
Apply the reverse of the product rule: [tex]a^{m+n}=a^m\times a^n[/tex]
[tex]8^{2x}\times 8^3+8^{2x}\times 8^1-8^{2x}=519*2^{2010}[/tex]
Factor on the left
[tex](8^3+ 8^1-1})8^{2x}=519*2^{2010}[/tex]
Evaluate
[tex](512+ 8-1})8^{2x}=519*2^{2010}[/tex]
Simplify:
[tex]519*8^{2x}=519*2^{2010}[/tex]
Divide through by 519
[tex]8^{2x}=2^{2010}[/tex]
Write the the LHS as a power of 2.
[tex]2^{3*2x}=2^{2010}[/tex]
[tex]2^{6x}=2^{2010}[/tex]
Equate the exponent
[tex]6x=2010[/tex]
Divide by 6
x=335
4x-2y=4 6x-4y=6
Solve the systems of equations algebraically
Isolate “y” in one of the equations, then substitute it in the other equation. After you find x, put it in the isolated equation and you’ll find y value.
The value of x = 1 and y = 0.
How to solve the systems of equations algebraically?Consider the given system of equation
4x - 2y = 4 ........(1)
6x - 4y = 6 ........(2)
Solve the system algebraically,
By using the elimination method,
Multiply equation (1) by 2, and we get,
(1) ⇒ 8x - 4y = 8 ............(3)
Subtract equation (2) from (3), we get,
8x - 4y - (6x - 4y) = 8 - 6
Simplifying the above equation, we get
8x - 4y - 6x + 4y = 2
8x - 6x = 2
⇒ x = 1
Substitute x = 1 in (1) and solve for y, we get,
⇒ 4x - 2y = 4
⇒ 4 (1) - 2y = 4
⇒ 2y = 4 - 4
⇒ 2y = 0
⇒ y = 0
Therefore, the value of x = 1 and y = 0.
To learn more about algebraic expression
https://brainly.com/question/12111796
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how do you factor a polynomial by its greatest common monomial factor of 25y^2-35y
Answer: 5y(5y-7)
Step-by-step explanation: 25y^2 - 35 y
factor out 5y
5y(5y-7)
Answer:
[tex]\large\boxed{25y^2-35y=5y(5y-7)}[/tex]
Step-by-step explanation:
[tex]25y^2=(5y)(5y)\\\\35y=(5y)(7)\\\\25y^2-35y=(5y)(5y)-(5y)(7)=(5y)(5y-7)[/tex]
The sixth grade students are having an activity day at the end of the school year. There are a total number of 232 students in the grade level.
Write and solve an equation to determine S, The number of students that will be on team #4
If this helps please considering giving me brainliest as it helps me a lot.
232-(59+57+58) = S
232-174 = S
S = 58
Hope this helps!
PLS HELP I GIVE BRAINLIEST
Answer:
MNStep-by-step explanation:
If ΔLMN ≅ ΔXYZ, then corresponding angles and corresponding segments are congruent:
∠L ≅ ∠X
∠M ≅ ∠Y
∠N ≅ ∠Z
and
LM ≅ XY
MN ≅ YZ
LN ≅ XZ
Answer:
Line MN.
Step-by-step explanation:
As you can see, YZ is in fact the hypotenuse of the other triangle.
Using this information, YZ should be congruent to the other hypotenuse, which in this case is MN.
Therefore, YZ=MN.
Worth 30 points!
please help
Answer:
y,n,y,y
Step-by-step explanation:
1*15=15
2*15=30
3*15=45
Answer:
(1,15) = yes
(1,30) = no
(2,30) = yes
(3,45) = yes
Step-by-step explanation:
The points on the graph:
(0,0)
(1,15)
(2,30)
(3,45)
(4,60)
(5,75)
(6,90)
(7,105)
(8,120)
(9,135)
(10,150)
(Hope you understand!)
what is the domain of f(x)=5^x?
Answer:
[tex]x\in(-\infty,\infty)[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=5^x[/tex]
Domain is the set of x values for which the function is defined.
The function [tex]f(x)=5^x[/tex] is an exponential function and for any real values of x, the function f(x) will be defined.
Therefore, we can conclude that the domain of the function is all real numbers.
In interval notation, the domain of f(x) is
[tex]x\in(-\infty,\infty)[/tex]
The domain of the function f(x) = 5^x is all real numbers.
Explanation:The domain of the function f(x) = 5x is all real numbers. In exponential functions like this one, the domain is always the set of all real numbers. This means that there are no restrictions on the values that x can take. For example, you can plug in any real number into the function, such as 0, 1, -2, or 3.5, and the function will still output a valid value.
Learn more about Domain of exponential functions here:https://brainly.com/question/15352175
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In geometry, the word draw means the same as the word
Answer:
Construct
Step-by-step explanation:
"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.
the distance formula is required to find the length of a horizontal segment. true or false?
Answer:
To use the distance formula to find the length of a line
So you're answer would be false
Hope this Helps (:
You can use the Distance Formula to find the length of such a line. This formula is basically the Pythagorean Theorem, which you can see if you imagine the given line segment as the hypotenuse of a right triangle. By using a basic geometric formula, measuring lines on a coordinate path becomes a relatively easy task.
Answer:
True...
Let me know if that was right, but I'm almost a hundred percent sure it is...
The graph below represent a trip taken by bicycle. Use the graph to answer questions
11. During the trip the cyclist stops for a time. During which labeled section-A, B, C, or D- did he stop? ________
12. During which labeled section was he traveling the slowest? _______
13. During which labeled section was he traveling the fastest? ______
14 Calculate the speed of the cyclist during section D _______
15. How far away was the cyclist when he turned around and headed home? _______
I'm pretty sure that the answer to this question is B