A) The rate of change in this situation is -$100 per week.
B) She will have $300 left in her account after five weeks.
In the diagram below, point O is the center of the circle.
C
A
(2x+5)°
0
B
Use the given information in the diagram to determine the value of x.
The value of x for the angle C in the triangle ABC is equal to 42.5
What is a triangle formed by a circle diameterA triangle formed by the diameter of a circle is a right triangle, with one side being the diameter of the circle and the other two sides being radii of the circle. Since the diameter of a circle bisects the circle into two equal halves, it also bisects the right angle formed by the radii into two equal angles of 45 degrees each.
The angle C is equal to 90° and we shall solve for the value of x as follows:
2x + 5 = 90°
2x = 90° - 5 {subtract 5 from both sides}
2x = 85°
x = 85°/2 {divide through by 2}
x = 42.5
Therefore, the value of x for the angle C in the triangle ABC is equal to 42.5
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Complete the sentence below.
325 is a hundred times bigger than
Answer:
325 is a hundred times bigger than 32500
Step-by-step explanation:
if it is ten times bigger, add one 0 at the end
if it is one hundred times bigger, add two 0 at the end
Find the slope of the line on the graph. Reduce all fractional answers to lowest terms.
-1/3
-3
-1
The slope of the line on the graph is equal to: A. -1/3.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (-2, 4).
Points on y-axis = (2, 0).
Substituting the given data points into the slope formula, we have the following;
Slope, m = (0 - 2)/(4 + 2)
Slope, m = -2/6
Slope, m = -1/3.
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0
A
B
A"
C'
B'
2. What is the relationship among AC, A'C', and A"C"?
B"
Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides
What is Graph?a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.
The scale factors is the factor in which each linear measure of the figure is multiplied.
AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.
the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.
Hence, relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides
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Which of the following relations is a function?
Answer:
b
Step-by-step explanation:
make sure the y axis doesnt repeat
Without solving, determine the character of the solutions of the equation in the complex number system.
3x^2 + 7×=3.
(Simplify your answer.)
Answer:
Step-by-step explanation:
To determine the character of the solutions of the equation in the complex number system, we need to analyze the nature of the coefficients of the equation, specifically the discriminant, which is obtained by the equation: b^2 - 4ac, where a, b and c are the coefficients of the equation.
In this case, the equation is
3x^2 + 7x - 3 = 0
So, the coefficients are a = 3, b = 7, and c = -3.
We can now calculate the discriminant as follows:
b^2 - 4ac = 7^2 - 4 * 3 * -3 = 49 + 36 = 85
Since the discriminant is positive, we know that the equation has two distinct real solutions. The exact solutions can be obtained using the quadratic formula, but that's not required to determine the character of the solutions.
Therefore, the equation has two real solutions.
What is the frequency of the function given? f(x)=9cos(4πX)+10
Answer:
Step-by-step explanation:
The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).
The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.
For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.
So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.
Find the number of subsets of {1, 2, 3, 4, 5, 6, 7 that are subsets of neithe{1, 2, 3, 4, 5}nor{4, 5, 6, 7, 8}.
If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9
Let the sets be
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
B = {1, 2, 3, 4, 5}
C = {4, 5, 6, 7, 8, 9}
Then
B ∩ C = {4, 5}
Subsets of B ∩ C = {4}, {5}, {4,5}, {}
If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}
No. of elements in A = 9
No. of subsets of A = [tex]2^9[/tex]
No. of elements in B = 5
No. of subsets of B = [tex]2^5[/tex]
No. of elements in C = 6
No. of subsets of C = [tex]2^6[/tex]
If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C
But the null set will be subtracted twice
Also as the subsets of B ∩ C excluding null set will be subtracted twice
Therefore, total number of subsets of A not the subsets of B or C
[tex]k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414[/tex]
The sum of the digits of k=9
The complete question is-
If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.
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6. Application Juanita, who is 1.82 meters tall, wants to
find the height of a tree in her backyard. From the
tree's base, she walks 12.20 meters along the tree's
shadow to a position where the end of her shadow
exactly overlaps the end of the tree's shadow. She is
now 6.10 meters from the end of the shadows. How
tall is the tree?
The height of tree is 9.9372.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
ΔABC ~ ΔDEF only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.
Given;
Juanita is 1.82 meters tall
From the tree's base, she walks 12.20 meters along the tree's shadow to a position where the end of her shadow.
She is now 6.10 meters from the end of the shadows.
Now,
Let, h be the height of the tree;
Here, ΔABC ~ ΔADE,
So, DE/BC = AD/AB
h/1.82 = (6.10 + 12.20)/6.10
h/1.82= 18.30/6.10
h=33.306/6.10
h=5.46
h = 1.82*5.46
= 9.9372
Therefore, by congruency of triangle the answer will be 9.9372.
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Siri has decided to examine his checking account statements. Last month‘s account balance was $100 this month is 42. What is the percent of decrease in Pere’s account balance
Answer:
58% decrease
Step-by-step explanation:
Please I just need help so badly asap Please
Answer:
- It is a parallelogram
Step-by-step explanation:
- The interior angle sum of a quadrilateral is 360°
Considering the four angles;
[tex]{ \tt{m \angle A + m \angle B + m \angle C + m \angle D = 360 \degree}} \\ \\ { \tt{(x + 12) + \{2(x + 3) \} + ( \frac{3}{2} x - 15) + ( \frac{7}{3} x - 12) = 360}} \\ \\ { \tt{(x + 2x + \frac{3}{2}x + \frac{7}{3}x) + (12 + 6 - 15 - 12) = 360 }} \\ \\ { \tt{ \frac{41}{6} x - 9 = 360}} \\ \\ { \tt{ \frac{41}{6}x = 369 }} \\ \\ { \tt{41x = 2214}} \\ \\ { \tt{x = 54}}[/tex]
- Therefore, substitute in x and find the angles.
[tex] { \tt{m \angle A = (x + 12) = (54 + 12) = 66 \degree}} \\ \\ { \tt{m \angle B = 2(x + 3) = 2(54 + 3) = 114 \degree}} \\ \\ { \tt{m \angle C = ( \frac{3}{2}x - 15) = \{( \frac{3}{2} \times 54) - 15 \} = 66 \degree }} \\ \\ { \tt{m \angle D = ( \frac{7}{3}x - 12) = \{( \frac{7}{3} \times 54) - 12 \} = 114 \degree }}[/tex]
HELP ASAP!!! WILL MARK BRAINIEST
The value of the network density is 0.9
How to determine network density?
Since the potential connections (PC) formula is n(n-1)/2 and number of nodes is 5 (i.e. n = 5). We have:
PC = n(n-1)/2
PC = 5(5-1)/2
PC = (5*4)/2
PC = 20/2
PC = 10
Actual connection (AC) = 9
Network Density = AC/PC
Network Density = 9/10
Network Density = 0.9
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Chris buys a new car for $24000, if he pays $1200 in taxes, what is the effective tax rate?
Answer:
Step-by-step explanation:
The effective tax rate is the amount of tax paid as a percentage of the total purchase price. To calculate the effective tax rate, you can divide the amount of tax by the total purchase price and multiply the result by 100 to get the answer as a percentage.
In this case, the effective tax rate would be:
(1200 / 24000) * 100 = 5%
So Chris's effective tax rate on the purchase of his car is 5%.
The velocity v, in meters per second, of a certain type of wave is given by v(h) = 3√h, where h is the depth, in
meters, of the water through which the wave moves. What is the rate of change, in meters per second per meter, of
the velocity of the wave with respect to the depth of the water, when the depth is 2 meters?
Answer:
The rate of change of the velocity of the wave with respect to the depth of the water is 3/2 meters per second per meter when the depth is 2 meters. This can be found by taking the derivative of v(h) with respect to h, which is 3/2√h. When h is 2, the rate of change is 3/2√2, which is equal to 3/2 meters per second per meter.
If you toss 10 fair coins, in how many ways can you obtain at least one head and one tail?
Answer:1/2 head and 1/2 tails
Step-by-step explanation: no.of experiments for heads = 5
total no of experiments=10
probability=5/10=1/2
no.of experiments for = 5
total no of experiments=10
probability=5/10=1/2
PLEASE HELP WITH CHART:
You can fill in the rest of the table as shown below.
How to fill in the rest of the table?The derivative of a function is a concept from calculus that measures the rate of change of a function at a specific point. It provides information about how the value of the function changes as its input changes.
Use the following differentiation rules to fill the table:
d/dx(f(x)·g(x)) = f(x)·g'(x) + f'(x)·g(x) (product rule)
d/dx(f(x)/g(x)) = [ g(x)·f'(x) - f(x)·g'(x) ] / [(g(x))²] (Quotient rule)
d/dx(g(x)/f(x)) = [ f(x)·g'(x) - g(x)·f'(x) ] / [(f(x))²] (Quotient rule)
x f(x) f'(x) g(x) g'(x) d/dx(f(x)·g(x)) d/dx(f(x)/g(x)) d/dx(g(x)/f(x))
0 3 -2 -4 3 17 -1/16 1/9
1 2 -1 1 0 -1 -1 1/4
2 4 2 3 1 10 2/9 -1/8
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Given one form of a sequence, write the other form an= an-1 -4
In the algebra on of the form of sequence is arithmetic progression or sequence which is described below.
What is an arithmetic sequence?In the arithmetic sequence the common difference between any two consecutive terms remains constant .
In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any nth term in AP,
T = a + nd
d = T₂-T₁
Where, a is first term , n is nth term and d is common difference
If aₙ = aₙ₋₁ -4
where aₙ is a nth term and aₙ₋₁ is a (n-1)th term
Now,
a + nd = a + (n-1-1)d - 4
nd = (n - 2)d - 4
nd = nd -2d - 4
2d = -4
d = -2
So, aₙ = a -2n
aₙ₋₁ = a -2(n - 2)
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Select the correct answer.
A right triangle C B A with lengths of sides as follows: C B is the wall of length equals 12 feet; A C is the ladder of length equals 13 feet. Right angle is at B.
According to the diagram, a 13-foot ladder leans against a 12-foot wall. The distance from the base of the ladder to the base of the wall is 5 feet. Based on this information, which trigonometric ratio has the value
?
A.
tan C
B.
cos C
C.
tan A
D.
sin A
Reset Next
Trigonometric Ratios: Mastery Test
©
Answer:
Option A
Step-by-step explanation:
A = opposite/hypotenuse = 12/5
I don't really have anymore explanation I could give you because that just what I could think of!
Answer: I think D. Sin A…..
Step-by-step explanation: hope this helps:)
Identify the number types that describe .
O A. Rational, integer
OB. Real, rational
O C. Real, integer
OD. Real, irrational
The type of number types that are being described are A. Rational, integer.
What is a Rational Number?A rational number in mathematics is one that can be stated as the quotient or fraction of two integers, p and q, with p being the numerator and q being the denominator, respectively.
Therefore, whole numbers are the numbers 0, 1, 2, 3, 4 and so on and negative numbers are not considered whole numbers.
natural numbers are called the counting numbers that are the numbers 1, 2, 3, 4, and so on. they are positive numbers and zero is not considered a natural number as you can see.
integers are all the whole numbers and their opposite (negative) but negative numbers are NOT whole or natural numbers. fractions and decimals are not integers.
irrational numbers are an infinite number of digits to the right of the decimal point, without repeating.
Thus, option A is the answer
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Classify the real number. (Choose all that apply). –9 A.) Rational B.) Whole C.) Irrational D.) Natural E.) Integer
Data analysts pay attention to sample size in order to achieve what goals? select all that apply.
The practise of extracting information from data to guide better business decisions is known as data analysis. Five iterative phases typically comprise the data analysis process:
Choose the data you want to examine.
gather the data
Clean up the data before analysis.
Study the information
Interpret the analysis' findings
It is common knowledge that data analysts focus on the sample size in order to
To prevent a few outlier responses from distorting the results
ensuring that the data reflects a variety of viewpoints
to prevent making erroneous conclusions due to a tiny sample size
An analyst of data is who?
An individual involved in the handling of data is referred to by this phrase.
Such a person aids in the analysis, retrieval, and drawing of conclusions from the information at hand.
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.. who. staple. food of the Vedic Aryan was ?
A) Barley and rice. B) MMilk
Answer: b
Step-by-step explanation: ias chinadu
B because that's the VA which would be intellectually specialist.
Someone tell me that if you have 5 apples and the next day you got 10 times as many apples you had. Use the Property "Distributive Property of Multiplication"
Answer:
10x = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
Step-by-step explanation:
Distributive property of multiplication says every element within every pair of elements is added and multiplied to each other. So the value of 10 times that of 5 is 50.
A child is allowed to pick three candy treats from a bin of 15 different candies. How many ways can the child select 3 treats?
The number of ways for the child to select 3 treats is given as follows:
455 ways.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The order in which the treats are chosen is not relevant, hence the combination formula is used to solve this question.
Three treats are chosen from a set of 15, hence the number of ways is given as follows:
C(15,3) = 15!/(3! x 12!) = 455 ways.
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Find the Nth term sequence
Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
7 - 1 = 13 - 7 = 19 - 13 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 6 , then
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
Solve for v.
k = mv²
2
Ov=±m√2km
Ov=±2k√m
V = + √2km
±
v
m
0₂₁v = ±
√km
4
The equation for v is ±√k/m
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is k=mv²
k equal to m times of v square.
Where k is a formula of kinetic energy.
We need to solve for v
To do this we have to isolate the variable v
To isolate the variable v we have to Divide both sides by m
v²=k/m
v square equal to k by m.
Square root on both sides.
v=±√k/m
v equal to plus or minus square root of k by m.
Hence, the equation for v is ±√k/m
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A boat has a top speed of 26 knots and a displacement of approximately 93,000 tons. Express the top speed in miles per hour and the displacement in metric tons
The boat's displacement is approximately 84,016.8 metric tons.
How to convert from knots to miles?To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:
26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)
Therefore, the boat's top speed is approximately 29.86 miles per hour.
To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:
93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)
Therefore, the boat's displacement is approximately 84,016.8 metric tons.
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or problems 2-7, find the slope of the line.
1.
1.
-10
-10
2 PRACTICE
y
y
10
10
3.
y
10
H
5.
-10-
y
10
2
+
10
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The slope of the line in graph 2 is equal to 1.
The slope of the line in graph 3 is equal to 1/2.
The slope of the line in graph 4 is equal to 3/4.
The slope of the line in graph 5 is equal to 3.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (7 - 2)/(7 - 2)
Slope, m = 5/5
Slope, m = 1.
For the line in graph 3 with the given data points, we have:
Slope, m = (3 + 2)/(6 + 4)
Slope, m = 5/10
Slope, m = 1/2.
For the line in graph 4 with the given data points, we have:
Slope, m = (6 - 0)/(8 - 0)
Slope, m = 6/8
Slope, m = 3/4.
For the line in graph 5 with the given data points, we have:
Slope, m = (6 - 0)/(2 - 0)
Slope, m = 6/2
Slope, m = 3.
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What are the coordinates of (-5,6) after a dilation of 2 centered at the origin
Answer:
(-10, 12).
Step-by-step explanation:
A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).
So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).
So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).
Simplify the given trigonometric expression (sin (30° + x)+sin (30° - x))
The simplified expression is cos(x) of trigonometric expression (sin (30° + x)+sin (30° - x))
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We can simplify this expression using the sum-to-product formula for sine:
sin(a + b) + sin(a - b) = 2 sin(a) cos(b)
Let's use this formula by setting a = 30° and b = x:
sin(30° + x) + sin(30° - x) = 2 sin(30°) cos(x)
We know that sin(30°) = 1/2, so we can substitute:
sin(30° + x) + sin(30° - x) = 2(1/2) cos(x)
sin(30° + x) + sin(30° - x) = cos(x)
Therefore, the simplified expression is cos(x).
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Can anybody help me with question 20 please?
Answer:
N?A
Step-by-step explanation:
