Answer: C & D
Step-by-step explanation: Ro 270, Ro -90
Set up a proportion to solve for x in the following similar triangles
Answer:
[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]
When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. which equation represents this situation? 6x2 5x - 4 = 0 6x2 5x 4 = 0 62x 5 x = 4 6 x2 5x = 4
Answer:
The answer would be 6x^2 + 5x - 4 = 0
Given the matrices A and B shown below, find -A + 1/3B
Step-by-step explanation:
1. first multiply -1 times all elements of matrix A
2. then multiply 1/3 by all elements of matrix B
3. then add each corresponding entries to get the result.
from step 1. matrix A will be
-4 -2. -1. -3
-2. 0. 1. -3
step 2. matrix B will be
3. -1. -2. -4
3. -10. 10. -1
add each corresponding elements to get
-1. -3. -3. -7
1. -10 11. -4
Type the correct answer in the box
Answer:
[tex]log\boxed{7}[/tex]
Step-by-step explanation:
[tex]log\frac{14}{3}+log\frac{11}{5}-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{14}{3}*\frac{11}{5}\bigg)-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{14*11}{3*5}\bigg)-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{154}{15}\bigg)-log\frac{22}{15}[/tex][tex]=log\bigg(\frac{154}{15}\div\frac{22}{15}\bigg)[/tex][tex]=log\bigg(\frac{154}{15}\times\frac{15}{22}\bigg)[/tex][tex]=log\bigg(\frac{154}{22}\bigg)[/tex][tex]=log\boxed{7}[/tex]AP Calculus AB Question from A, P .E* X
(Will give branliest if correct)
If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)
What is the domain of a function as a result of a binary operator
Binary operators are operators that involves two functions, there are four binary operators: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division. First, we determine the domains of the functions f(x) and g(x):
f(x):
Domain - [-3, 3]
g(x):
Domain - (- ∞, + ∞)
If we divide f(x) by g(x), then we must take g(x) = 0 into account, since it leads to indetermination. In this case, x = 1/3. Then, the domain of the resulting function:
(f/g)(x):
Domain - [-3, 1/3) ∪ (1/3, 3]
If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)
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A television has increased in price by 5%
the new price is £194.25. what was the original price?
Answer:
let the original price be X
now new price = original price + increment
increment = 5 % of X = X/20
new price = 194.25
now, 194.25 = X + X / 20 = 21X / 20
X = 194.25 * 20 / 21
X = 185
original price = 185
the graph of F(x) can be stretched vertically and flipped over the x axis to produce the graph of G(x) if F(x)=x^2 which of the following could be the equation of G(x)
A. G(x)=-1/5x^2
B. G(x)=-5x^2
C. G(x)=5x^2
D. G(x)=1/5x^2
Answer:
g(x) = -5x²
(option B)
Step-by-step explanation:
we know that our original graph, f(x) = x² is a parabola.
So, we can consider what happens when we adjust the function/equation of a parabola.
when we "vertically stretch" a parabola, we are increasing the value of x.
think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.
Let's say our x = 5
if f(x)=x²
f(5) = 25
> y value / steepness is 25
f(x) = 3x²
f(5) = 75
> y value / steepness is 75
So, we are looking for an equation with an increase in x present.
When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative
suppose that x = 1
if y = x² ; y = 1² = 1
if y = -(x²) ; y = -(1²) ; y = -1
So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)
This means that we are looking for a function with a negative x value.
So, we are looking for a negative x-value that is multiplied by a number >1
The graph that fits our requirements is g(x) = -5x²
hope this helps!!
What is the value of x?
Enter your answer in the box.
...°
What is the range of the relation in the table below?
The range of the relation is {0, 2, 4}
How to determine the range?The range of the relation are the y values
From the table, we have:
y values = 0, 2, 4, 2, 0
Remove the repetition
y values = 0, 2, 4
Hence, the range of the relation is {0, 2, 4}
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Why is it just as likely that the cube will show an even number as an odd number?
Graph of y = log(-x)?
Answer:
lklklkj
Step-by-step explanation:
67890-
One possible integer of x for which 1/4 < k/10 < 1/3 is true?
Answer:
[tex]\fbox {x = 3}[/tex]
Step-by-step explanation:
Decimal form of the lower and higher limits :
1/4 = 0.251/3 = 0.33...Hence, the best one which lies in the middle of the limits would be 0.3.
Now, equate the middle part :
x/10 = 0.3x = 3what is the value when 18times of the difference of 15 and 12 divided by 6
Need help with this ASAP if you could that would help!!
Answer:
the distance between DE is 2
The distance of EF is 5
The distance of FD is [tex]\sqrt{29}[/tex]
Perimeter is 7+[tex]\sqrt{29}[/tex]
Step-by-step explanation:
Distance of DE
[tex]\sqrt{(-3-(-3))^2+(3-1)^2}[/tex]
sqrt([tex](-3+3)^2+(2)^2[/tex])
sqrt([tex](0)^2+4[/tex])
[tex]\sqrt{4}[/tex]
=2
Distance of EF
[tex]\sqrt{(2-(-3))^2+(3-3)^2}[/tex]
Solve that like DE and it equals 5
Distance of FD
[tex]\sqrt{(2-(-3))^2+(3-1)^2}[/tex]
equals to [tex]\sqrt{29}[/tex]
P=DE+EF+FD
P=2+5+[tex]\sqrt{29}[/tex] = 7+[tex]\sqrt{29}[/tex]
PLEASE HURRY
Which of the following can be used to evaluate the series
e d g e
Answer:
1 55
2 455
3554
Step-by-step explanation:
nfn
consider an investment of $6000 that earns 4.5% interest.
How long would it take for the investment
to reach $15,000 if the interest is
compounded monthly? Round your
answer to the nearest tenth.
Answer:
20.4 years (nearest tenth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $15,000P = $6,000r = 4.5% = 0.045n = 12 (monthly)Substitute the given values into the formula and solve for t:
[tex]\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}[/tex]
[tex]\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}[/tex]
[tex]\implies \sf 2.5=\left(1.00375\right)^{12t}[/tex]
[tex]\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}[/tex]
[tex]\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)[/tex]
[tex]\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}[/tex]
[tex]\implies \sf t=20.40017123[/tex]
Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.
Please help! Consider the function y = 9-x^2, where x ≥ 3
What is the inverse of the function? What is the domain of the inverse? Show all of your work
(hint: swap x and y in the domain as well as the function)
Using it's concept, it is found that the inverse function is [tex]y = \sqrt{9 - x}[/tex], and the domain is [tex]x \leq 9[/tex].
How to find the inverse function?The inverse of a function y = f(x) is found exchanging x and y and isolating y. The domain of the inverse is the range of the original function f(x).
In this problem, the function is:
y = 9 - x²
Then, we exchange and isolate y, hence:
[tex]x = 9 - y^2[/tex]
[tex]y² = 9 - x[/tex]
[tex]y = \sqrt{9 - x}[/tex]
The domain is [tex]9 - x \geq 0 \rightarrow x \leq 9[/tex], as looking at the graph of y = 9 - x², the range is [tex]y \leq 9[/tex].
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Name a career that require data -analysis skills describe how data analysis skills describe how date analysis is used in this career be sepcific when typical values are given for salaries and housing prices the median is almost always given instead of mean.
A career as a Data Scientist would require data analysis skills.
What is the career for data analysis?1) A career as a Data Scientist would require data analysis skills.
2) The Data Scientist computes and analyzes large amounts of data from different sources and then uses the results for interpretations. The skills required by a data scientist are skills In Statistics, calculus, Probability, Programming, Excel, Visualization, Database management, and Machine Learning. He also needs a high level of accuracy when solving problems.
3) The median value is used when the data set contains values that occur repeatedly and which contains some extremely high values. The mean value would aggravate towards higher values while the Median value would give a salary value that is an average of the data set. That is why the median value is used in salaries and housing prices calculations.
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Marcia bought a car for £34500 and sold it for £29700. what was her percentage loss?
can i have an explanation please :)
Answer:
cost of car = 34500
selling price = 29700
amount of loss = 34500 - 29700 = 4800
loss percentage = (loss amount ÷ cost price ) * 100
= 13.913 ≈ 14% loss
Determine whether the given differential equation is exact. If it is exact, solve it. (tan(x)-sin(x)sin*y))dx+cos(x)cos(y)dy=0 g
The differential equation
[tex]M(x,y) \, dx + N(x,y) \, dy = 0[/tex]
is considered exact if [tex]M_y = N_x[/tex] (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function [tex]f(x,y)=C[/tex] such that [tex]f_x=M[/tex] and [tex]f_y=N[/tex].
We have
[tex]M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)[/tex]
[tex]N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)[/tex]
and [tex]M_y=N_x[/tex], so the equation is indeed exact.
Now, the solution [tex]f[/tex] satisfies
[tex]f_x = \tan(x) - \sin(x) \sin(y)[/tex]
Integrating with respect to [tex]x[/tex], we get
[tex]\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx[/tex]
[tex]\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)[/tex]
and differentiating with respect to [tex]y[/tex], we get
[tex]f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}[/tex]
[tex]\implies \dfrac{dg}{dy} = 0 \implies g(y) = C[/tex]
Then the general solution to the exact equation is
[tex]f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}[/tex]
3 *(x-7)*(x+7)-(x-1)*(3x+2)=13
The value of x will be 158. The value of x is obtained by simplifying the equation.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Identity used;
(x+a)(x-a) = x² - a²
Given expression;
3(x-7)(x+7) - (x-1)(3x+2) = 13
Solving the equation step by step;
[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]
Hence, the value of x will be 158.
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Cos(5 π/3)=___
A. √3/2
B. -√2/2
C. 1/2
D. √2/2
Answer:
i think the answer is C. 1/2
Price of an article is marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894. Find the cost price, marked price and profit percentage.
Step-by-step explanation:
here is your answer. where are you from
The cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
For example, if you say 678, we must also know the whole number, but if you say 80%, it becomes evident. The percentage is the same as the amount of that value but ranges from 1 to 100.
Let's say
Cost of article = c
Given,
Marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894
1.4c - 0.15×(1.4c) = 26894
c = Rs 22600
So,
Marked price = 1.40c = Rs 31640
Profit percentage = ( 26894 - 22600)22600 = 19%.
Hence cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.
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11. Find the amount of interest on $600, if a bank is paying 5.5% interest.
[A] $30 [B] $3.30
[C] $330
[D] $33
[E] $23
What is the additive inverse of x=-1317, and verify -(-x) = x ?
Answer:
1317 is the additive inverse of x = -1317.
Step-by-step explanation:
Additive inverse of a number which when added to the original number gives zero as the result.
Additive inverse of x = -1317
-1317 + 1317 = 0
1317 is the additive inverse of x = -1317.
Verification of -(-x) = x
L. H. S
-(-x) = -{-(-1317)}
= - 1317
R. H. S
x = -1317
Thus, L.H.S. = R.H.S
-(-x) = x
Verified
A hot air balloon is descending.
The height of the balloon n minutes after it starts to descend is hn
metres.
The height of the balloon (n +1) minutes after it starts to descend, hn + 1 metres, is given by
hn + 1 = K×hn
+ 20 where K is a constant.
The balloon starts to descend from a height of 1200 metres at 09 15
At 09 16 the height of the balloon is 1040 metres.
Work out the height of the balloon at 09 18
Answer:
The height of the balloon at 09 18 = 788.4 meters.
Step-by-step explanation:
As the hot air balloon is descending.
and the height of the balloon n minutes after it starts to descend is [tex]h_{n}[/tex]
meters.
The height of the balloon (n +1) minutes after it starts to descend, [tex]h_{n+1}[/tex]meters, is given by
[tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex] where K is a constant
Here the balloon starts to descend from a height of 1200 meters at 09 15
So [tex]h_{n}[/tex]=1200 meters
At 09 16 the height of the balloon is 1040 meters.
So [tex]h_{n+1}[/tex]= 1040 meters
the height of the balloon at 09 18 = [tex]h_{n+3}[/tex] meters
now [tex]h_{n+1}[/tex]= [tex]k *h_{n}+20\\[/tex]
k = [tex]\frac{h_{n+1 }-20 }{h_{n} }[/tex]
k= (1040 - 20) ÷ 1200
k = 0.85
Now [tex]h_{n+2}[/tex] = (0.85 × 1040) +20 =904 meters
Similarly [tex]h_{n+3}[/tex] = (0.85 × 904) +20 = 788.4 meters.
Therefore the height of the balloon at 09 18 = 788.4 meters.
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This is direct proportion .
I need help in question 2 only one of the questions then I can do the rest tysm
Il give
Answer:
(a) 2.5
Step-by-step explanation:
(a) Since y is directly proportional to x we can write y and x in terms of the following equation:
y = cx where c is a constant
and c = y/x ...(1)
or,
x = y/c ...(2)
For (a)
y = 8 when x = 2 ==> c = y/x = 8/2 =4 from (1)
From (2) we get x = 10/4 = 2.5
The other questions can be solved in a similar fashion
suppose a triangle has sides a, b, and c and the angle opposite the side of length a is acute what must be true?
A. b2+c2>a2
B. a2+b2
C. b2+c2
D. a2+b2=c2
The true statement about the triangle is (a) b^2 + c^2 > a^2
How to determine the true inequality?The sides are given as:
a, b and c
The angle opposite of side length a is an acute angle
The above means that:
The side a is the longest side of the triangle.
The Pythagoras theorem states that:
a^2 = b^2 + c^2
Since the triangle is not a right triangle, and the angle opposite a is acute.
Then it means that the square of a is less than the sum of squares of other sides.
This gives
a^2 < b^2 + c^2
Rewrite as:
b^2 + c^2 > a^2
Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2
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when 7 is subtracted from 3 times a certain number , the result is 28. What is the number
The number will be equal to 11.67.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expression will be formed from the given data. Let the number be x so the expression will be:-
3x - 7 = 28
3x = 35
x = 35 / 3
x = 11.67
Therefore the number will be equal to 11.67.
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How would i find the domain of this?
The domain of the graph is {x : x∈ R}
How to determine the domain?The domain of a function or graph is the set of input values the function can take.
This in other words represents the x values
From the graph, we can see that x values extend indefinitely on both axes.
This is indicated by the arrows at the ends of the curve
This means that the domain is the set of all real numbers
Hence, the domain of the graph is {x : x∈ R}
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