Answer:
c. (0, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}m+4n=8&(1)\\m=n-2&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\n-2+4n=8\qquad\text{add 2 to both sides}\\5n=10\qquad\text{divide both sides by 5}\\n=2\\\\\text{put the value of}\ n\ \text{to (2):}\\\\m=2-2\\m=0[/tex]
A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
Answer: is D
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
Work: 8+22=30 17+13=30 turn into a fraction then simplify to get answer;
22/30 simp= 73.0 (0.73)
13/30 simp= 43.0 (0.43)
8/30 simp= 26.667 (0.27)
17/30 simp= 56.667 (0.57)
Answer with Step-by-step explanation:
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Relative frequency of people above 40 years old who do not visit a dentist once a year
=Number of people above 40 years old who do not visit a dentist yearly/Number of people above 40
=13/(17+13)
=13/30
=0.43
Hence, Relative frequency of people above 40 years old who do not visit a dentist once a year is:
0.43
Use synthetic substitution to find g(3) and g(–5) for the function g(x) = x5 – 8x3 – 2x + 7.
Let's do the same thing to evaluate g(-5):
-5Answer:
Step-by-step explanation:
Never heard of "synthetic substitution." I think you meant "synthetic division," which is a great method of evaluating polynomials for given input values.
g(x) = x^5 – 8x^3 – 2x + 7 is missing two terms.
With all terms showing, it would read:
g(x) = x^5 – 0x^4 + 8x^3 – 0x^2 - 2x + 7. The coefficients are {1, 0, 8, 0, -2, 7}.
Let's evaluate g(3). Use 3 as divisor in synth. div.:
3 ) 1 0 8 0 -2 7
3 9 51 153 453
------------------------------
1 3 17 51 151 460 Since the remainder is 460, the value of g(3) is also 460.
-5 ) 1 9 8 0 -2 7
-5 -20 60 -300 1510
----------------------------------
1 4 -12 60 -302 1517
The remainder is 1517, and so g(-5) = 1517.
Answer:
28, -2,108
Step-by-step explanation:
match each function with its inverse function. use function composition to determine your answers.
QUESTION 1
[tex] \boxed {f(x) = 2x + 6 \to \: g(x) = \frac{1}{2}x - 3 } [/tex]
The reason is that:
[tex]g(f(x)) = 2( \frac{1}{2} x - 3) + 6[/tex]
Expand:
[tex]g(f(x)) = x - 6+ 6 [/tex]
[tex]g(f(x)) = x[/tex]
QUESTION 2
[tex]\boxed {f(x) =3 - 2x \to \: g(x) = - \frac{1}{2}(x - 3)} [/tex]
The reason that
[tex]g(f(x)) = - \frac{1}{2} (3 - 2x - 3)[/tex]
[tex]g(f(x)) = - \frac{1}{2} (- 2x )[/tex]
[tex]g(f(x)) =x[/tex]
QUESTION 3
[tex]\boxed {f(x) = \sqrt[3]{3x}+ 2 \to \: g(x) = \frac{ {(x - 3)}^{3} }{3} } [/tex]
The reason is that:
[tex]f(g(x)) = \sqrt[3]{ \frac{3 {(x - 2)}^{3} }{3} } + 2[/tex]
[tex]f(g(x)) = x-2 + 2[/tex]
[tex]f(g(x))=x[/tex]
QUESTION 4
[tex]\boxed {f(x)=3\sqrt[3]{x + 2} \to \: g(x) = \frac{1}{27} {x}^{3} - 2} [/tex]
The reason is that
[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} - 2 + 2} [/tex]
[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} } [/tex]
[tex]f(g(x)) = 3 \times \frac{1}{3} x[/tex]
[tex]f(g(x)) =x[/tex]
formula for area of polygon
Answer:
The formula for the area of a polygon is 1/2*a*p.
a = apothem, which is a line segment that is the shortest distance from the center to a side.
p = perimeter
Hope this helps. :)
Answer:
Step-by-step explanation:
There's no one formula for finding the area of any polygon.
There are specialized formulas for finding the area of a square, of a triangle, of a trapezoid, etc. Beyond these, you have to invent approaches, such as breaking up an octagon into 8 triangles, finding the area of 1 such triangle, and then multiplying that area by 8.
The data represents the number of traffic tickets written by two police officers in one day over the course of a week. Officer 1: 21, 11, 14, 16, 10, 18, 5 Officer 2: 16, 19, 20, 17, 6, 13, 23
(a) Draw a box and whiskers plot for each officer (b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?
Answer and Explanation :
Given : The data represents the number of traffic tickets written by two police officers in one day over the course of a week.
Officer 1: 21, 11, 14, 16, 10, 18, 5
Officer 2: 16, 19, 20, 17, 6, 13, 23
To find : (a) Draw a box and whiskers plot for each officer
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?
Solution :
a) We plot the box plot with the help of graphing calculator of both data.
Refer the attached figure below.
Figure 1 shows the data 1 with Median 14.
Figure 2 shows the data 2 with Median 17.
b) On comparing the median of both Officer's are different first officer has 14 median and second officer has 17 median.
You have 100 feet of fencing to build a circular sheet pen. what is the diameter of the largest pen you can build?
Answer:
The diameter of the largest pen you could build is [tex]\frac{100}{\pi }[/tex] or [tex]31.8309[/tex] ft
Step-by-step explanation:
As the equation for the circumference of a circle is
[tex]C=d\pi[/tex]
We can plug in the known value for C, which is 100 and solve for d
[tex]100=d\pi[/tex]
[tex]d=\frac{100}{\pi }[/tex]
ANSWER
The diameter of the largest pen you can build is 31.8 feet to the nearest tenth.
EXPLANATION
You have 100 feet of fencing to build a circular sheet pen.
The largest diameter you can get is when you use all the 100 feet of fencing to build the sheet pen.
The circumference of the circular sheet pen must then be 100 feet.
Then using the formula for circumference, we have:
C=πd
100=πd
[tex]d = \frac{100}{\pi} [/tex]
d=31.83 ft.
Which one show factor pairs of 16
Answer:
There is not enough information
Step-by-step explanation:
If you wanted to find all the factors, here’s a list.
1,2,4,8,16
Write these numbers in order from least to greatest
0.65, 2/3, 3/5 , 0.5
Answer:
0.5, 3/5, 0.65, 2/3Step-by-step explanation:
Convert the fractions to the decimals (you can use the calculator):
2/3 = 2 : 3 = 0.6666...
3/5 = 3 : 5 = 0/6
We have
0.65
0.666...
0.6
0.5
The order from least to greatest:
0.5
0.6
0.65
0.666..
[tex]\begin{array}{c|c|c|c|c}0&.&5\\0&.&6\\0&.&6&5\\0&.&6&6&6...\end{array}[/tex]
1 year, 27 weeks =
weeks
Answer:
Around 79.17 weeks
Step-by-step explanation:
Answer:
if you want to know how many weeks are in one year and 27 weeks, i can help out
Step-by-step explanation: 1 year has 365 days in it and one week has 7 days in it. Divide 365 by 7.
365/7= about 52 weeks.
52+27=79 weeks.
The exact amount of weeks is 79.177457
hope this helped!!
How do you find the length if you already know the perimeter? This is what I mean:
Morgan is ordering carpet for her bedroom. She measures the room and finds a width of 22 feet and a perimeter of 66 feet.
I know for sure that the first thing I need to do is find the length, but how do I do that with only knowing the width and perimeter?
You can find length by knowing the formula for perimeter: 2l+2w= p; where l= length, w= width, and p= perimeter. Substitute the things you know and solve.
In this case, the length would be 11 feet.
r(x)=x-3
s(x)= 4x²
write the expressions for (s+r)(x) and (s-r(x) and evaluate (s.r)(2)
What we are given:
r( x ) = x - 3
s( x ) = 4x²
We have to find:
( s + r )( x ) = ( x - 3 + 4x² )
→ 4x² + x - 3
( s - r )( x ) = ( x - 3 - 4x² )
→ -4x² + x - 3
For the last function, I am confused whether it is a multiplication or composite function, so I am going to do both.
Multiplication:
( x - 3 ( 4x² ))( 2 )
( 4x³ - 12x² )( 2 )
4(2)³ - 12(2)²
4(8) - 12(4)
32 - 48
→ -4
Composite function:
r(s(x))(2) = r(4x²) = 4x² - 3 = 4(2)² - 3 = 4(4) - 3 = 16 - 3
→13
Final answer:
The expressions for (s+r)(x) is 4x^2 + x - 3 and (s-r)(x) is 4x^2 - x + 3. The value of (s.r)(2) is 16.
Explanation:
To find the expression for (s+r)(x), we need to add the functions s(x) and r(x). Adding the two functions, we get (s+r)(x) = 4x^2 + (x-3). Simplifying this expression, (s+r)(x) = 4x^2 + x - 3.
To find the expression for (s-r)(x), we need to subtract the function r(x) from s(x). Subtracting the two functions, we get (s-r)(x) = 4x^2 - (x-3). Simplifying this expression, (s-r)(x) = 4x^2 - x + 3.
To evaluate (s.r)(2), we need to substitute 2 for x in the expression s(x) * r(x). Substituting 2 for x in the expression 4x^2, we get (s.r)(2) = 4(2)^2 = 16.
6,15,16,20,13,5,10,16 find the mean
Hello There!
To find the mean we have to add up all the numbers and divide by how many numbers there are.
6+15+16+20+13+5+10+16
Now, I will add 2 numbers at a time to make it easier for myself.
21+36+18+26
Once I add up these numbers, I will get a sum of 101
Finally, I divide 101 by 8 and get a quotient of 12.625
6 + 15 + 16 + 20 + 13 + 5 + 10 + 16 = 101/8 = 12.6
mean: 12.6
An inconsistent linear system has _ solutions
Answer:
zero im pretty sure
Step-by-step explanation:
Answer:
An inconsistent linear system has no solution(s).
Step-by-step explanation:
Just took the test.
there are some roses,lilies, and orchids in the vase. The number of roses is twice the number of lilies and the number of orchids is 5 more than the number of roses. if the total is 45, find the number of each type of flower
Answer:
Step-by-step explanation:
Let's say R is roses, L is lilies, and O is orchids.
R = 2L
O = R + 5
R + L + O = 45
Let's substitute the second equation into the third:
R + L + (R + 5) = 45
2R + L = 40
Now substitute the first equation:
2(2L) + L = 40
4L + L = 40
5L = 40
L = 8
Therefore:
R = 2L = 16
O = R + 5 = 21
There are 16 roses, 8 lilies, and 21 orchids.
Type an inequality statement using the < or > for the inequality symbols solve for x 6x-11-13x<7-5x
Answer:
-9 < x
Step-by-step explanation:
6x-11-13x<7-5x
Combine like terms
-11-7x<7-5x
Add 7x to each side
-11-7x+7x<7-5x+7x
-11 < 7+2x
Subtract 7 from each side
-11-7 < 7-7+2x
-18 < 2x
Divide by 2
-18/2 < 2x/2
-9 < x
If f(x)= 3/x+2-sqrt x-3, complete the following statement:
The domain for f(x) is all real numbers____ than or equal to 3.
Answer:
all real numbers greater than or equal to 3
Step-by-step explanation:
There's some ambiguity in your "3/x+2-sqrt x-3." I will assume that you meant:
3
---------- - sqrt(x - 3). Using parentheses often changes everything.
x + 2
Here we see that x cannot = -2, because x + 2 would be zero then. And x must be greater than or equal to 3, so that the input to the sqrt function will be 0 or greater. The domain for f(x) is all real numbers greater than or equal to 3. The prohibition against x = -2 has no bearing on the overall domain of this function.
Answer:
The domain for f(x) is all real numbers GREATER than or equal to 3
Step-by-step explanation:
3. What’s the answer to this question?
Answer:
Opt B. y=5-3x
Step-by-step explanation:
We need to write the given equation in slope-intercept form, so we can obtain the slope and the 'y' axis intercept point.
To do this, we need to isolate 'y' variable with a possitive sign, hence we perform the following operation:
Subtraction of -5 in both sides of equality sign.
-y=3x-5
Lets multiply by -1 the equation from above:
y= 5-3x.
From the above we can find the slope, is the coefficient of x. in this case -3
And the y-intercept point is 5.
what is 11/7 as a mixed number
Answer:
1 4/7
Step-by-step explanation:
11/7 As A Mixed Number Would Be 1 And 4/7
Write 1,000 as a power of 100
Answer:
10 or 100
Step-by-step explanation:
Answer:
100^1,000 if that's what you mean or 100 ^10 to make 1,000
Step-by-step explanation:
IF RIGHT PLZ MARK BRAINLIEST!! PLZZZ!!!!!!!!!!!!!
Which is the same as moving the decimal point 3 places to the right in a decimal number
Answer:
Multiplying the decimal number by 1000
Step-by-step explanation:
consider the number 12.2345.
For you to move the decimal point three places to the right, you have to multiply the number with 10³=1000
12.2345×1000= 12234.5
The decimal has moved from three places as it has skipped three places values to the right.
The choice which is the same as moving the decimal point 3 places to the right in a decimal number is; Multiplying the number by 1000.
Which is the same as moving the decimal point 3 places to the right in a decimal number?According to the task content;
We are required to determine which is the same as moving the decimal point 3 places to the right in a decimal number.Since, a decimal point movement one space to the right indicates a multiplication by 10, hence, it follows that the required multiplication is 1000.
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PLEASE HELP FAST In the diagram below, Xy and yz are tangent to o. What is the measure of
Xwz?
Answer:
240
Step-by-step explanation:
since that arc is 120 you subtract that form 360 and voila!
****BRAINLIEST The graph shows the solution for which inequalities?
y ≥ x + 2 and y ≤ 2x + 3
y ≥ x - 2 and y ≤ 2x - 3
y ≥ 3x - 2 and y ≤ x + 3
y ≤ 3x - 2 and y ≥ x + 3
Answer:
[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]
Step-by-step explanation:
Blue:
The inequality for the blue line is
[tex]y\geq 3x-2[/tex]
Yellow
The inequality for the yellow line is
[tex]y\leq \frac{1}{2} x+3[/tex]
This means that the correct answer is the third option,
[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]
The graph shows the solution for the inequalities y ≥ 3x - 2 and y ≤ x + 3.
How can find the inequalities?The inequalities can be found by substituting the coordinates of a point within the shaded area in both inequalities and seeing if they are satisfied.
We can find the inequalioties as follows:The options are given.
Let us take the options one by one:
Option A: y ≥ x + 2 and y ≤ 2x + 3Now, substitute (0,0) in the inequalities:
0 ≥ 2 and 0 ≤ 3
This is not true.
Option B: y ≥ x - 2 and y ≤ 2x - 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ - 3
This is not true.
Option C: y ≥ 3x - 2 and y ≤ x + 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ 3
This is true.
Option D: 0 ≤ - 2 and 0 ≥ 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ - 3
This is not true.
Therefore, we have found that the inequalities are y ≥ 3x - 2 and y ≤ x + 3. The correct answer is option C.
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A rectangular garden sits next to a house. Three sides of the garden are fenced, and the fourth side is the house. The length of the garden is 9 meters. A total of 21.5 meters of fencing is used. If w stands for the width of the garden in meters, which equation can be used to find its width?
A. 2w+9=21.5 C. 2w - 21.5 = 9
B. 2w + 18 = 21.5 D. 2w +21.5=18
the equation that can be used to find width is B
Answer:
It's a
Step-by-step explanation:
I did it
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?
To change the graph of f(x) = [tex]x^2[/tex] into g(x) = 4[tex]x^2[/tex] + 24x + 30, the transformations include a vertical stretch by a factor of 4 and a shift to the left by 3 units and up by 6 units. Completing the square helps identify these shifts.
Explanation:To transform the graph of f(x) = [tex]x^2[/tex] into the graph of g(x) = 4[tex]x^2[/tex] + 24x + 30, we can analyze the changes applied. First, the coefficient of x2 in g(x) is 4, which means the original parabola is vertically stretched by a factor of 4. Second, the term 24x indicates a horizontal transformation, specifically a shift, which is revealed when we complete the square.
To complete the square for the quadratic part of g(x), we rewrite the equation as 4([tex]x^2[/tex] + 6x) + 30 and add and subtract the square of half the coefficient of x inside the parentheses, giving us 4((x + 3)2 - 9) + 30. This simplifies to 4(x + 3)2 + 6, indicating that the graph of f(x) was also shifted to the left by 3 units and up by 6 units.
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The graph of y =
[tex] \sqrt[3]{x} [/tex]
is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?
ANSWER
See attachment.
EXPLANATION
The given parent function is:.
[tex]y = \sqrt[3]{x} [/tex]
If this graph is reflected over the x-axis and then translated down 2 units to form f(x), then the f(x) has equation
[tex]f(x) = - \sqrt[3]{x} - 2[/tex]
The graph of this function is shown in the attachment.
Answer:
the second graph
Step-by-step explanation:
the area of a square is 64 cm. what is the length of one side of the square?
Answer:
8cm
Step-by-step explanation:
Since the area of a square is Side X Side (s x s) it is also s². The s² is also equivalent = 64cm². To find the length of a side you do the √64cm² and you get 8cm for a side. Great Job!
2200 dollars is placed in an account with an annual interest rate of 7.25%. How much
will be in the account after 29 years, to the nearest cent?
Answer:
A = $2200(7.612) = $16,747.28
Step-by-step explanation:
You don't say whether this is simple interest or compound interest. I will assume you meant compound interest, for which the appropriate formula is
A = P(1 + r)^t, where P is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years. Then:
A = $2200(1 + 0.0725)^29, or
A = $2200(1.0725)^29, or
A = $2200(7.612) = $16,747.28
The amount in the account after 29 years will be approximately $8484.64.
Explanation:To calculate the amount of money that will be in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount ($2200 in this case), r is the annual interest rate (7.25% or 0.0725 as a decimal), n is the number of times interest is compounded per year (in this case, it's compounded annually, so n is 1), and t is the number of years (29 in this case). Plugging in the values, we get:
A = 2200(1 + 0.0725/1)^(1*29)
A = 2200(1.0725)^29
A ≈ $8484.64
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Solve x⁄6 = 20.
A. x = 14
B. x = 26
C. x = 120
D. x = 3
Answer:
120
Step-by-step explanation:
x/6=20
×=20×6
=120
PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)
Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
For the simple harmonic motion equation d=4sin(pi/8t) what is the maximum?
Answer:
Maximum value of the function is 4.
Step-by-step explanation:
Given function of simple harmonic motion is [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].
Now we need to find about what is the maximum value of [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].
We know that value of sine function varies from -1 to 1.
that means for any value of t, maximum value of sine function is 1.
[tex]\sin\left(\frac{\pi}{8}t\right) \leq 1[/tex]
[tex]4 \sin\left(\frac{\pi}{8}t\right) \leq 4[/tex]
[tex]d \leq 4[/tex]
Hence maximum value of the function is 4.