The area of the circle is given as:
[tex]A=\pi r^2[/tex]plugging the value given we have that:
[tex]\begin{gathered} 361\pi=\pi r^2 \\ r^2=361 \\ r=\sqrt[]{361} \\ r=19 \end{gathered}[/tex]Now, the circumference is given as:
[tex]C=\pi d[/tex]where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:
[tex]C=38\pi[/tex]Therefore the circumference is 38pi
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What is the slope of the line that passes through the points (9, -10) and (14, 5)?
Write your answer in simplest form.
What is the slope of the line that passes through the points (9 , -10 ) and (14 , 5)? Write your answer in simplest form.
From inspection on the given problem:
[tex] \sf{(x_1, y_1) = (9, -10)}[/tex][tex] \sf{(x_2, y_2) = (14, 5)}[/tex]To calculate the slope of the line passing through the given points, we must use the formula below:
[tex] \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}[/tex]Substitute the given values into the slope formula and solve for m:
[tex] \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - (-10)}{14 - 9} = \dfrac{15}{5} = \pmb{3}}[/tex]
Therefore, the slope of the line that passes through the given points is 3.
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Answer and explanation pls
Ray is a part of a line that has a fixed starting point but no endpoints.
There is no end point of any of those rays.
The point V labeled in the diagram is not on any of those rays.
What is a ray?Ray is a part of a line that has a fixed starting point but no endpoints.
We have,
Four rays:
SP, SQ, SU, and SW
A ray has a starting point but does not have an endpoint.
There is no end point of any of those rays.
There are seven points in the diagram.
P, Q, S, V, T, U, and W.
We see that point V does not lie on any of the four rays.
Thus,
There is no end point of any of those rays.
The point V labeled in the diagram is not on any of those rays.
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Given the graph above, what is the slope of this line?
Question 2 options:
1.m = -2
2. m = 3
3. m = 0
4. m = -3/2
Answer:
my answer would be m=-3/2
Step-by-step explanation:
given the coordinates
(0,0) - this is the origin and the first coordinate it will be treated as x1=0,y1=0
(-2,3)- this is the second given coordinate and will be treated as x2=-2,y2=3
To find the slope(m) we use the formula
m=y2-y1/x2-x1
m=3-0/-2-0
m=-(3/2)
m=-3/2
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In the diagram below, if < 2 = 123 °, what would be the measure of < 7?
Given:
[tex]\angle2=123^{\circ}[/tex]To find:
The angle 7.
Explanation:
We know that,
The sum of the exterior angles is supplementary.
So, we can write
[tex]\begin{gathered} \angle2+\angle7=180 \\ 123^{\circ}+\angle7=180 \\ \angle7=180-123 \\ \angle7=57^{\circ} \end{gathered}[/tex]Therefore, angle 7 is 57 degrees.
Final answer:
Angle 7 is 57 degrees.
what is the slope of a line that passes through (1,3) and (-7,-5)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. simplify using order of operations. Show all of your work and one operation at a time to receive all possible points. 90 divided by [10 plus (3^2-4)]
Please help!
the equation you summited is
90÷10+3²-4
Answer:
the answer to the question is 14
Step-by-step explanation:
90÷10+3²-4
Follow the PEMDAS order of operations
3²=9
90÷10+9-4
Multiply and divide from left to right
90÷10=9
9+9-4
Add and subtract from left to right
9+9=18
18-4=14
So the answer to your question is 14
The table below shows the population of the state of Washington for several decades starting in1900.Year1900191019201930194019501960Populationin millions0.521.151.371.571.742.392.86If the population is modeled by an exponential function of the form P(t) = a(b)^t, where t is yearssince 1900, which of the following would be a reasonable value for a?0.522.860.0351900
a represents the initial value of the function. Since the function starts at 1900, the associated population value for this year should be the answer. The answer is 0.52.
3. Compare the numbers 5/9 and 0.5^- Use the symbols <, >, or =.
So 5/9 is equal to 0.5- so the right answer is
[tex]\frac{5}{9}=0.\bar{5}[/tex]the little line on the top of the number means that this number will be repeated Infinitely is like 0.555555555...
Coupon A: $25 rebate on $96 shoes coupon B; 40% off of $96 shoes
Answer: Coupon B is more profitable
Here are two expressions whose product is a new expression, A: 1. What could we put in the boxes to make A be a polynomial?
We are given the following product:
[tex](-2x{}^3+B)(x^n+15)=A[/tex]For "A" to be a polynomial the value of the first box "B" must be a constant or a term of the form:
[tex]ax^n[/tex]We will use a constant. We will substitute the first box for "1":
[tex](-2x^3+1)(x^n+15)=A[/tex]For the second box, we need to use an exponent that is a positive whole number.
We will use 2:
[tex](-2x^3+1)(x^2+15)=A[/tex]With these values, the result of the product is a polynomial.
I need help on this question?
By definition, [tex](f \circ g)(x)=\boxed{f(g(x))}[/tex]. So, if [tex]g(2)=6[/tex] and [tex]f(6)=17[/tex], then [tex](f \circ g)(2)=f(g(2))=f(6)=\boxed{17}[/tex].
Juan rented a truck for one day. There was a base fee of $9.00, and there was an additional charge of 7 cents for each mile driven. The total cost, C (in dollars), for driving x miles is given by the following function.
C (x) = 9.00 + 0.07x
What is the total rental cost if Juan drove 30 miles?
Answer:
$11.10
Step-by-step explanation:
Ez
Can you help me ?
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
The cost of a school lunch is $2.50.
Complete the table to show the total cost of 1, 2, 3, and 4 lunches.
Lunches Bought 1 2 3 4
Total Cost ($)
Part B
Select the correct choices to complete the sentence.
The total cost is , 1 of 2.
Select Choice
to the number of lunches bought because the ratios between the quantities , 2 of 2.
Select Choice
the same unit rate.
The cost for the lunches will be:
1 lunch = $2.50
2 lunches = $5
3 lunches = $7.50
4 lunches = $10
How to calculate cost?From the information, the cost of a school lunch is $2.50. Therefore, the cost of 1 lunch will be:
= 1 × $2.50
= $2.50
The cost of 2 lunches will be:
= 2 × $2.50
= $5.00
The cost of 3 lunches will be:
= 3 × $2.50
= $7.50
The cost of 4 lunches will be:
= 4 × $2.50
= $10
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HELP PLS
Do anybody know answer to these problomes?
you can do this easily by BODMAS Frist open small bracket and slove it then open curly bracket and solve it at last open third bracket and open it then solve
Remember you should always open divide first then multiply then add and then subtract
Practice it is easy.
Step-by-step explanation:
[tex]28 \div (1 + 2 \times (19 - 16))[/tex]
[tex]28 \div (1 + 2 \times 3) [/tex]
[tex]28 \div (1 + 6)[/tex]
[tex]28 \div 7[/tex]
[tex]4[/tex]
LetW = the set of whole numbersF = the set of (non-negative) fractionsI = the set of integersN = the set of negative integersQ = the set of rational numbersSelect each set that is closed under addition.
Verify each set
W ---------> are closed under addition
F ------> are closed under addition
I ------> are closed under addition
N ----> are closed under addition
Q ----> are closed under addition
Specifically, I need the surface are which can be found by using this formula: S= Ph+2B
The surface area of a prism of heigh H and base of sides a, b, and c is:
A = PH + 2B
Where P = a + b + c is the perimeter of the base and B is its area.
We can see in the figure a prism of height H = 14 in, base sides of 10 in, 10 in, and 12 in. The height of the base is also given as h = 8 in.
Calculate the perimeter of the base:
P = 10 in + 10 in + 12 in = 32 in
The area of the base is:
[tex]B=\frac{12\text{ in }\cdot8\text{ in}}{2}=48\text{ }in^2[/tex]Calculate the surface area:
[tex]\begin{gathered} A=PH+2B \\ A=32\text{ in }\cdot\text{14 in}+2\cdot48\text{ }in^2 \\ A=448\text{ }in^2+96\text{ i}n^2 \\ A=544\text{ }in^2 \end{gathered}[/tex]The area is 544 square inches
Suppose line g is the line with equation y=x. Given A(8,−5), B(7,3), and C(−1,−7), what are the coordinates of the vertices of △A′B′C′ for the reflection?
The point (x,y) on the reflection about y = x axis changes to,
[tex]A(x,y)\rightarrow A^{\prime}(y,x)[/tex]Determine the coordinates of the vertices of triangle after reflection.
[tex](6,3)\rightarrow(3,6)[/tex][tex](8,-3)\rightarrow(-3,8)[/tex][tex](-2,-6)\rightarrow(-6,-2)[/tex]So vertices of triangle after reflection is,
(3,6), (-3,8) and (-6,-2)
Use a calculator to find the natural logarithm, base e. In 0.0746 In 0.0746
By using a calculator,
ln 0.0746 = - 2.596
Consider the matrix.[k q h][w p r]Which statement is true?A. The matrix has 2 rows and 2 columns.B. The matrix has 2 rows and 3 columns.C. The matrix has 3 rows and 2 columns.D. The matrix has 3 rows and 3 columns.
anyone know this one i was having troble
The zero of the linear function will be at (1, 0).
A linear function is the one which can be represented in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. The zero of a line is the point where the line crossed the x-axis which is also known as the x intercept. The equation of the line in slope intercept form is given as y = mx + c where m is the slope and c is the y intercept. The slope of line from points (0, 5) and (2, -5) can be found by m = -5 - 5/2 -0
m = -10/2
m = -5
Now, putting this and the point (0, 5) in y = mx + c we get
5 = -5×0 + c
=> c = 5
Now, equation of line is y = -5x + 5 and for x intercept we put y = 0
0 = -5x + 5
5x = 5
=> x = 1
=> (1, 0) which is the required point
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hello this is all 1 math problem together may I get help with the solve and check .
The given expression is,
[tex]7n+14=-21[/tex]So bringing "14" to the other side of the euals,
[tex]\begin{gathered} 7n=-21-14 \\ =-35 \end{gathered}[/tex]On division,
[tex]\begin{gathered} 7n=-35 \\ n=-\frac{35}{7}=-5 \end{gathered}[/tex]Now, let us substitute -5 for n,
[tex]7\times(-5)=-35[/tex]Hence checked.
The graph of a function g is shown below.
Find g (0)
Are there more buildings that have 10-19 bricks or buildings that have 50-59 bricks ?
We can see from the graph that there are 10 buildings that have 10-19 bricks and 2 buildings that have 50-59 bricks. So there are more buildings with 10-19 bricks in the neighborhood.
Answer: 10-19 bricks
10. A 300-room hotel collects $125 per occupied room and does not collect any money for vacantrooms. Which of the following functions best represents how many dollars, d, the hotel generates ifthere are v vacant rooms in the hotel?O d = 125(300 + V)O d = 300(75 - v)O d = 300(75+)O d = 125(300 - V)
If there are v vacant rooms, the number of occupied rooms is 300-v (in total there are 300 rooms).
As every occupied makes the hotel collect 125, the dollars the hotel generates are:
[tex]d=125(300-v)[/tex]It means that the correct answer is the last option.
what is the distance of (-23, -14 ) and ( -18,2)
From the given question,
There are given that two point, (-23, -14) and (-18, 2).
Now,
For finding the distance between two point,
Here use distance formula.
From the distance formula,
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]x_1=-23,y_1=-14,x_2=-18,y_2=2[/tex]Put the all values into the above formula,
Then,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-18_{}-(-23_{})^2+(2_{}-(-14)_{})^2} \\ d=\sqrt[]{(-18_{}+23_{})^2+(2_{}+14_{})^2} \end{gathered}[/tex]Then,
[tex]\begin{gathered} d=\sqrt[]{(-18_{}+23_{})^2+(2_{}+14_{})^2} \\ d=\sqrt[]{(5_{})^2+(16_{})^2} \\ d=\sqrt[]{25+256} \\ d=\sqrt[]{281} \end{gathered}[/tex]Hence, the distance of given
The midpoint of AB is (2,7) and point A is located at (5,-3).
What are the coordinates of point B?
The coordinates of point B =(5,10)
what is coordinates?
Coordinates are a set of values which helps to show the exact position of a point in the coordinates plane.
step - by - step explanation
5-2 = 3
2-3= -1 = the x coordinate of B
-7-3= -10
-7-10 = -13 = the y coordinate of B
(-1, -13) is the point B
A is 3 to the right of the midpoint ,so B is 5 to the left to the midpoint
A is 10 up from the midpoint so B is 10 down from the midpoint.
so the coordinates of point B is (5,10)
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49. Calculate the limit. Some of these limits are made easier by considering the logarithm of the limit first, and some are not.
lim x^lnx
x→0+
The limit of xlnx when x is tending towards zero is zero.
What is limit in mathematics?
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.
Given limit is:
[tex]\lim_{x \to 0} x lnX[/tex]
Considering f = x, and g = ln x
The limit of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the limit f/g equals it.
The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as
[tex]\frac{lnx}{1/x}[/tex]
We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as
The limits
[tex]\lim_{x \to 0^+} lnx= - \infty[/tex], and
[tex]\lim_{x \to 0^+} \frac{1}{x}[/tex]
The limits [tex]\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}[/tex] exists as:
[tex]\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0[/tex]
Hence the answer is 0.
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find the equation of a parabola with a focus of (0, -1) and directrix y = 1
Solution
For this case we see that the focus is (0,-1)
And the directrix is y=1
So then we have a parabola that open downwards:
The vertex is given by V= (h,k)
The focus is given by: F = (h, k+p)
And the directrix is given by: y= k-p
So then replacing we got:
1 = k-p (1)
h = 0
k+p = -1 (2)
Using equation (1) we got k:
k = p+1
Replacing into second equation we got:
p+1+p = -1
2p = -2
p= -1
k = -1 +1= 0
Then the vertex is given by: V= (0, 0)
And the formula is given by:
[tex](x-0)^2=4(-1)(y-0)[/tex]And thats equivalent to :
[tex]x^2=-4y[/tex]I really need help with this question!! How do you solve it?In 1985, they discovered a new sea creature. It was found to have an initial population of 832. Assuming the population was growing at a rate of 2.3% each year, when will the population exceed 1500?
Solution:
The growth rate is given below as
[tex]r=2.3\%[/tex]The initial population is
[tex]P_0=832[/tex]The exponential growth formula is given below as
[tex]\begin{gathered} P=P_0(1+r)^t \\ 832(1+\frac{2.3}{100})^t=1500 \\ 832(1.023)^t=1500 \\ (1.023)^t=\frac{1500}{832} \\ (1.023)^t=1.803 \\ take\text{ ln of both sides} \\ ln(1.023)^t=ln(1.803) \\ tln(1.023)=ln(1.803) \\ t=\frac{ln(1.803)}{ln(1.023)} \\ t=25.9years \\ \end{gathered}[/tex]Hence,
The final answer is
The population will exceed 1500 in approximately 26 years' time
No correlation means that as the x-values increase, the y-values O a have no effect Ob increase Ос decrease
we know that
If there is no correlation between x and y, that just means that there's no relationship, connection, or interdependence between the two variables
No correlation means that as the x-values increase, the y-values have no effect
the answer is the option A