please help me :((((((
Answer:
Answer D
Step-by-step explanation:
It says to divide f(x)/g(x), which is displayed in D and if we find the domain it would be x is not equal to -1/4
You are given that cos(A)=−35, with A in Quadrant II, and cos(B)=817, with B in Quadrant I. Find cos(A−B). Give your answer as a fraction.
Expand cos(A - B) with the identity
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1 ⇒ sin(A) = + √(1 - (-3/5)²) = 4/5
cos²(B) + sin²(B) = 1 ⇒ sin(A) = + √(1 - (8/17)²) = 15/17
Then
cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85
cos (A - B) is 36/85
How to simply the identity
Expand cos(A - B) with the identity
You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
Since A is in quadrant II, so sin(A) > 0,
B is in quadrant I, so sin(B) > 0.
Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1
Make sin A the subject of formula
[tex]sin(A)^{2}[/tex] = ([tex]\sqrt{(1 - (-3/5}[/tex])²)
Find the square root of both sides, square root cancels square
[tex]sin A[/tex] = 4/5
Repeat the same for the second value
[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]
[tex]sin A[/tex] = 15/17
Substitute values into cos(A - B)
cos(A - B) = cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17
cos (A - B) = 36/85
Therefore, cos (A - B) is 36/85
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find the indicated side of the right triangle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 3\sqrt3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \tan(60) = \cfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{3} = \dfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: x = 3 \sqrt{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Which linear equation has a slope of 3 and a y-intercept of -2?
y = 3x + 2
y = 3x - 2
y = -2x + 3
y=-2x-3
Answer:
y = 3x - 2
Step-by-step explanation:
The number beside the x is the slope. The number at the end of the equation is the y-intercept.
All the answers are in this form:
y = mx + b
m is the slope.
b is the y-intercept.
With a 3 filled in for slope and -2 filled in for the y-intercept, you get:
y = 3x + -2
is the same as,
y = 3x - 2
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P ( X > 2 ) , n = 5 , p = 0.7
The value of the probability P(x > 2) is 0.8369
How to evaluate the probability?The given parameters are:
n = 5
p =0.7
The probability is calculated as:
[tex]P(x) = ^nC_x *p^x * (1 - p)^x[/tex]
Using the complement rule, we have:
P(x > 2) = 1 - P(0) - P(1) - P(2)
Where:
[tex]P(0) = ^5C_0 *0.7^0 * (1 - 0.7)^5[/tex]
P(0) = 1 *1 * (1 - 0.7)^5 = 0.00243
[tex]P(1) = ^5C_1 *0.7^1 * (1 - 0.7)^4[/tex]
P(1) = 5 *0.7^1 * (1 - 0.7)^4 = 0.02835
[tex]P(2) = ^5C_2 *0.7^2 * (1 - 0.7)^3[/tex]
P(2) = 10 *0.7^2 * (1 - 0.7)^3 = 0.1323
Recall that:
P(x > 2) = 1 - P(0) - P(1) - P(2)
So, we have:
P(x > 2) = 1 - 0.00243 - 0.02835 - 0.1323
Evaluate
P(x > 2) = 0.83692
Approximate
P(x > 2) = 0.8369
Hence, the value of the probability P(x > 2) is 0.8369
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.0. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Answer:
1,887,436,800
Step-by-step explanation:
f(t) = a·b^t
f (t) = number of cases at year t
a = starting value = 1800 in 1983
b = growth factor = 2
t = years since 1983 = 2003 - 1983 = 20
f(t) = 1800·(2)^20 =
1,887,436,800
wyzant
philip p
Which of the following could be the first step in solving the equation below 4+2log_(3)x=17
Answer:
subract 4 from both sides
Step-by-step explanation:
At the end of 2 years, P dollars invested at an interest rate r compounded annually increases to an amount, A dollars, given by the following formula. Upper A equals Upper P (1 plus r )squared Find the interest rate if $32 increased to $50 in 2 years. Write your answer as a percent.
The interest rate will be equal to 24% in 2 years.
What is compound interest?Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-
Given that:-
Find the interest rate if $32 increased to $50 in 2 years.The interest rate will be calculated by using the following formula:-
[tex]A = P[1+\dfrac{r}{n}]^{nt}[/tex]
[tex]50=32[1+\dfrac{r}{1}]^{2}[/tex]
[tex]\dfrac{50}{32}=(1+r)^2[/tex]
1.56 = ( 1 + r )²
√1.56 = ( 1 + r )
r = 1.24 - 1
r = 0.24
r = 24%
Therefore interest rate will be equal to 24% in 2 years.
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Find two functions defined
implicity by this equation:
(x − 5)² − 3(y + 2)² = 4
Answer:
[tex] \frac{dy}{dy} = \frac{x - 5}{3y + 6} [/tex]
Find the solution to the following system by substitution.
5x + y = 20
y = 5x
A. (2,10)
B. (4,0)
C. (0,20)
D. (4,20)
Answer:
A. (2,10)
Step-by-step explanation:
5x + y = 20
y = 5x
The second equation is already solved for y, so substitute 5x for y in the first equation to find x.
5x + 5x = 20
10x = 20
x = 2
Now substitute 2 for x in the second original equation to find y.
y = 5(2)
y = 10
Answer: (2, 10) which is A.
Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train
Answer:
Step-by-step explanation:
Solve the equation.
-x+8+3x = x-6
O x=-18
O x=-14
O x = 2
O x = 4
Answer:
x = -14
Step-by-step explanation:
- x + 8 + 3x = x - 6
- x + 8 + 3x - x + 6 = 0
x + 14 = 0
x = -14
Which of the following is NOT a rational expression?
The expression that is not rational is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
Which of the given expressions is not rational?A rational expression is something of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.
This means that we need to have the variable "x" on the denominator.
Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
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Answer: B
Step-by-step explanation:
I took the test and this was the correct answer
Which statements about the system are true? Select two options.
y=-x-4
3y-x = -7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The slope for both the line is m= 1/3 and they are parallel lines , Option B and C are correct two options
The first equation is
y = (1/3)x-4 and not y = -x-4
(if the equation is not corrected then it will not have two true statements)
What is a System of Equation ?A system of equation is a set of equation which have a common solution
The given system of equation is
y = (1/3)x-4
3y -x = -7
3y = x-7
As it can seen from the standard equation of a line that
y =mx+c
so slope for both the line is m= 1/3
Therefore they are parallel lines
Thus , Option B and C are correct two options
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What is the partial fraction decomposition of StartFraction 7 x squared + 14 Over (x squared + 3) squared EndFraction?
The final decomposition of the given partial fraction is; 7 + (-7/(x² + 3))
How to decompose partial fractions?We are given the polynomial fraction (7x² + 14)/(x² + 3) to decompose.
Now, due to the fact that the degree of the numerator is not less than the degree of the denominator, we will perform polynomial long division to get;
(7x² + 14)/(x² + 3) = 7 + (-7/(x² + 3))
Now, the second term (-7/(x² + 3)) cannot be decomposed further and as such, we say that our final decomposition of the given partial fraction is;
7 + (-7/(x² + 3))
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Step 2 of 2 : Suppose a sample of 782 suspected criminals is drawn. Of these people, 548 were not captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
What is confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given sample, n= 782
As, 548 were not captured.
x= 548
So, p= 548/ 782
p = 0.7007
q= 1- 0.7007 = 0.2993
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
Now,
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
For confidence level of 98% , z is 2.33
Now,
(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782
= (0.6625, 0.7388)
Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
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Graph the line passing through (6, 1) whose slope is m = 3.
Answer: [tex]y=3x-17[/tex]
Step-by-step explanation:
use point-slope form:
[tex]y_{1} -y=m(x_{1} -x)[/tex]
[tex]y-1=3(x-6)[/tex]
[tex]y-1=3x-18[/tex]
[tex]y=3x-17[/tex]
Answer:
equation: y = 3x - 17
[image attached]
Step-by-step explanation:
we know that the equation for a line is y = mx + b
we are given a point, (6, 1)
remember that a point is (x, y)
we can plug these sample x and y values into our equation, replacing x and y
y = mx + b
1 = m6 + b
we know that m = 3 [this was a given], so we can plug this into our equation
1 = (3)(6) + b
1 = (18) + b
1 = 18 + b [we can now solve for "b"]
1 = 18 + b
-18 - 18
-17 = b
so, we can re-write our equation so that we can graph it:
y = 3x - 17
we can now plug in x-values to graph this:
(you'll see these written in the table on the graph)
y = 3(0) - 17
y = -17
y= 3(1) - 17
y = 3 - 17
y = -14
y = 3(2) - 17
y = 6 - 17
y = -11
y = 3(3) - 17
y = 9 - 17
y = -8
y = 3(4) - 17
y = 12 - 17
y = -5
y = 3(-1) - 17
y = -3 - 17
y = -20
y = 3(-2) - 17
y = -6 - 17
y = -23
y = 3(-3) - 17
y = -9 - 17
y = -26
[there is an image attached of my graph]
hope this helps!! :)
Need help ASAP, will mark brainliest if you can check my answer:
According to the compound interest model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61
How to determined all the variables associated with compound interest
Compound interest describes the capital gain in term of deposited capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:
C' = C · (1 + r/100)ˣ (1)
Where:
C - Initial capitalC' - Current capital r - Interest rate, in percentage.t - Time, in yearsThe doubling time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):
x = (㏒ 2)/[㏒ (1 + r/100)] (2)
Now we proceed to calculate each missing variable:
Case I - Doubling time
x = (㏒ 2)/[㏒ (1 + 6.2/100)]
x ≈ 11.5
Case I - Current capital
C' = 75000 · (1 + 6.2/100)⁵
C' = 101317.36
Case II - Interest rate
[tex]r = 100\cdot \left(\sqrt [5] {\frac{7130.90}{5000} }-1\right)[/tex]
r ≈ 7.4
Case II - Doubling time
x = (㏒ 2)/[㏒ (1 + 7.3/100)]
x ≈ 9.8
Case III - Initial capital
C = 11414.71/(1 + 8.4/100)⁵
C = 7626.38
Case III - Doubling time
x = (㏒ 2)/[㏒ (1 + 8.4/100)]
x ≈ 8.6
Case IV - Interest rate
[tex]r = 100\cdot \left(\sqrt [11] {2 }-1\right)[/tex]
r ≈ 6.5
Case IV - Initial capital
C = 17539.32/(1 + 6.5/100)⁵
C = 12801.61
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Are the two triangles congruent?
Answer:
yes.......................
Step-by-step explanation:
Elian's credit card had a balance of $132.20 on April 1. On April 5, he charged $74.50. On April 18, he made a payment of $52. On April 22, hecharged $18.75 and did not use the credit card the rest of the month. What was his average daily balance? $166.76 $173.45 $206.70 $179.86
Answer:
I iitiriririrrifjjrjr idiocy jdkthink 179.86
What is one possible value of 2x
Answer:
really good
Step-by-step explanation:
thanks for your help you with that do not have a copy of the receipt for your time to help you with theWhat is the solution to t - 3 < 12
Answer:
[tex]\boxed {t < 15}[/tex]
Step-by-step explanation:
Given :
⇒ t - 3 < 12
Add 3 to each side :
⇒ t - 3 + 3 < 12 + 3
⇒ t < 15
Answer: t < 15
Step-by-step explanation:
rearrange the terms t - 3 < 12
calculate the sum or difference t < 12 + 3
answer t < 15
when finding the margin of error of the mean of a normally distributed population from a sample, what is the critical probability, assuming a confindence level of 58%
The critical probability, assuming a confindence level of 58% is 0.79.
How to calculate probability?From the information given, the confidence level is 58%. The alpha will be:
= 1 - (58/100)
= 1 - 0.58
= 0.42
The critical probability will be:
= 1 - (0.42/2)
= 1 - 0.21
= 0.79
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The price of 11 pizzas and 5 hamburgers is 40$. The price of 1
hamburger is 2.50$. What is the price of a hamburger?
Step-by-step explanation:
you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...
1 hamburger = $2.50
5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50
that leaves for the 11 pizzas (slices)
40 - 12.5 = $27.50
so, 1 pizza (slice) is
27.5 / 11 = $2.50
Answer:
One hamburger costs $2.50
One pizza also costs $2.50
Step-by-step explanation:
Let's say Nigel is the one purchasing lots of food for no reason.
Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)
We can write this algebraically:
11p + 5b = 40
We know that the price of 1 Hamburger is $2.50.
Now we can plug that into out equation and find the price of one pizza:
11p + 5(2.50) = 40
11p + 12.5 = 40
11p = 27.5
p = 2.5
Now, we have the price of one pizza, $2.50
Given: a || b, transversal k
Prove <3 = <6
By the property of corresponding angles ∠3 ≅ ∠5.
What is transversal line?In geometry, a transversal is any line that intersects two straight lines at distinct points.
If two parallel lines are cut by a transversal, then each pair of corresponding angles are equals.
That is, ∠3 = ∠5 and ∠4 = ∠6.
Therefore the given angles ∠3 and ∠5 are equal.
Hence ∠3 ≅ ∠5 .
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What is the value of x for the regular polygon shown below?
2x + 4
36
A shopkeeper buys 72 articles for $82.80. How much will he have to pay if he buys 150 such articles.
Answer: He have to pay $172.5 if he buys 150 such articles.
72 articles for --> $82.80
1 article for - - - > 82.80/72
150 articles for --> (82.80/72)*150
= $172.5
Answer:
$172.5
Step-by-step explanation:
Given:
Shopkeeper buys = 72 articles
Price = $ 82.8
To Find:
The amount he'll need to pay If he buys 150 articles.
Solution:
Amount if he buys 150 articles
[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]
[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]
[tex]= \$ (150* 1.15)[/tex]
[tex] = \$172.5[/tex]
So we can conclude that:
$172.5 he will have to pay if he buys 150 such articles.
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles faster than the other. If the two buses are 640 miles apart after 5 hours, what is the rate of each bus?
If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Two buses leave a station at the same time and travel in opposite directions.
One bus travels 14 miles faster than the other.
Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).
If the two buses are 640 miles apart after 5 hours.
Then the rate of each bus will be
Then the relative speed of the buses will be
S = x + x + 14
S = 2x + 14
Then the value of x will be
2x + 14 = 640 / 5
2x + 14 = 128
2x = 114
x = 57 miles per hour
Then the speed of the other bus will be
⇒ 57 + 14
⇒ 71 miles per hour
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Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition.
The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The associative property states that when adding or multiplying it can be represented by:
(a + b) + c = a + (b + c)
For multiplication:
a * (b * c) = (a * b) * c
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Which statements about the system are true? Select two options.
y=-x-4
3y - x = -7
O The system has one solution.
O The system consists of parallel lines.
O Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The system of equation has one solution
How to determine the true statements?The equations are given as:
y = -x - 4
3y -x = -7
Rewrite the first equation as:
y + x = -4
Add y + x = -4 to the second equation to eliminate x
4y = -11
Divide by 4
y = -11/4
Substitute y = -11/4 in y + x = -4
-11/4 + x = -4
Make x the subject
x = -4 + 11/4
Evaluate
x = -5/4
The above means that the system of equation has one solution
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Option A and B. The system has one solution and the system consists of parallel lines.
Slope of the linesThe slope of the lines is calculated as follows;
y = -x - 4
slope = - 1
3y - x = -7
3y = x - 7
y = x/3 - 7/3
slope = 1/3
Solution of the equationsy = -x - 4 ----(1)
3y - x = -7 ----(2)
solve (1) and (2)
3(-x - 4) - x = -7
-3x -12 - x = -7
-4x = 5
x = -5/4
y = -5/4 - 4
y = -5.25
Thus, the system has one solution and the system consists of parallel lines.
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