Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
(1)
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values , firstly calculating ∠ B
[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]
[tex]\frac{a}{sin78}[/tex] = [tex]\frac{18}{sin53}[/tex] ( cross- multiply )
a sin53° = 18 sin78° ( divide both sides by sin53° )
a = [tex]\frac{18sin78}{sin53}[/tex] ≈ 22.0 ( to the nearest tenth )
(3)
[tex]\frac{c}{sinC}[/tex] = [tex]\frac{a}{sinA}[/tex] , substitute values
[tex]\frac{35}{sinC}[/tex] = [tex]\frac{45}{sin134}[/tex] ( cross- multiply )
45 sinC = 35 sin134° ( divide both sides by 35 )
sinC = [tex]\frac{35sin134}{45}[/tex] , then
∠ C = [tex]sin^{-1}[/tex] ( [tex]\frac{35sin134}{45}[/tex] ) ≈ 34.0° ( to the nearest tenth )
(5)
Calculate the measure of ∠ B
∠ B = 180° - (38 + 92)° = 180° - 130° = 50°
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{BC}{sin38}[/tex] = [tex]\frac{10}{sin50}[/tex] ( cross- multiply )
BC sin50° = 10 sin38° ( divide both sides by sin50° )
BC = [tex]\frac{10sin38}{sin50}[/tex] ≈ 8.0 ( to the nearest tenth )
Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for $5dollar each. If she buys 10 raffle tickets, then she would spend a total of $135 at the fundraiser.
The number S of dollars Camille spends at the fundraiser is a function of r, the number of raffle tickets she buys.
Write the function's formula.
Answer:
50r + a = 135
Admission cost was $85
Step-by-step explanation:
We are missing a crucial amount of information here. It is how much she spent on her admission. We can create an equation symbolizing this problem.
5r + a = 135
We know that she purchases 10 tickets so we can substitute that in r and solve for a.
50 + a = 135
a = 85
Best of Luck!
What represents the inverse of the function f(x) = 4x
Answer:
[tex]f { - 1}^{ } = \frac{x}{4} [/tex]
Step-by-step explanation:
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I need help with this
Answer: 13.5 Okay! Here's the method count the legs of the right triangle
The formula we'll use will be
A^2 + B^2 = C^2
In this case we're counting by twos
The base is 11 so we times it by itself =110
The leg is 8.5 so we going to times itself to make 72.25 add those together so 110+ 72.25 = 182.25 then we \|-----
182.25
Then you have got ur answer of 13.5
Step-by-step explanation:
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Step-by-step explanation:
You want to buy a house that has a purchase price of $180,000 you plan to make a down payment of 10% of the purchase price and then while the rest what is the dollar value of the down payment?
Step-by-step explanation:
=10% of $180000
= 10*$180000/100
=$180
please answer quickly!! and no links please!
Step-by-step explanation:
here are the answers for your problems
Select the correct answer.
The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake,
M= log (I/I)
.Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?
Answer:
[tex]M = \log(10000)[/tex]
Step-by-step explanation:
Given
[tex]M = \log(\frac{I}{I_o})[/tex]
[tex]I = 10000I_o[/tex] ---- intensity is 10000 times reference earthquake
Required
The resulting equation
We have:
[tex]M = \log(\frac{I}{I_o})[/tex]
Substitute the right values
[tex]M = \log(\frac{10000I_o}{I_o})[/tex]
[tex]M = \log(10000)[/tex]
The equation that calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake is A. M = ㏒10000
Since the magnitude of an earthquake on the Richter sscale is M = ㏒(I/I₀) where
I = intensity of eartquake and I₀ = reference earthquake intensity.Since we require the magnitude when the intensity is 10,000 times the reference intensity, we have that I = 10000I₀.
Magnitude of earthquakeSo, substituting these into the equation for M, we have
M = ㏒(I/I₀)
M = ㏒(10000I₀./I₀)
M = ㏒10000
So, the equation that calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake is A. M = ㏒10000
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Devaughn is 10 years older than Sydney. The sum of their ages is 104. What is Sydney's age?
I
Answer:
Sydney's age = 42
Step-by-step explanation:
104 divided by 2 = 52
52 - 10 = 42
I am sorry if this is wrong. But this is what I learned at my school.
Please help. I don't understand how to solve for number 17, 19, and 21. Please show how you solved each problem
(17) From the plot, you see that
Pr[$15,500 ≤ x ≤ $18,500] = 99.7%
We can split up the probability on the left at the mean, so that
Pr[$15,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $18,500] = 99.7%
Any normal distribution is symmetric about its mean, so the two probabilities here are the same. The one on the left is what you want to compute. So you have
2 × Pr[$15,500 ≤ x ≤ $17,000] = 99.7%
==> Pr[$15,500 ≤ x ≤ $17,000] = 49.85%
(19) The mean of a normal distribution is also the median, so half the distribution lies to either side of the mean. Mathematically, we write
Pr[x ≥ $17,000] = 50%
The plot shows that
Pr[$16,500 ≤ x ≤ $17,500] = 68%
and by using the same reasoning as in (17), we have
Pr[$16,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $17,500] = 68%
2 × Pr[$17,000 ≤ x ≤ $17,500] = 68%
Pr[$17,000 ≤ x ≤ $17,500] = 34%
Now
Pr[x ≥ $17,000] = 50%
Pr[$17,000 ≤ x ≤ $17,500] + Pr[x ≥ $17,500] = 50%
34% + Pr[x ≥ $17,500] = 50%
==> Pr[x ≥ $17,500] = 16%
(21) From the plot,
Pr[$16,000 ≤ x ≤ $18,000] = 95%
This means (by definition of complement) that
Pr[x ≤ $16,000 or x ≥ $18,000] = 100% - 95% = 5%
and by symmetry,
Pr[x ≤ $16,000 or x ≥ $18,000] = 5%
Pr[x ≤ $16,000] + Pr[x ≥ $18,000] = 5%
2 × Pr[x ≤ $16,000] = 5%
==> Pr[x ≤ $16,000] = 2.5%
Can someone help me
Answer: Around 38.2°
Step-by-step explanation:
Set ∠A = x & a = 15Set ∠B = 27° & b = 11Substitute them into the formula for the law of sines:
[tex]\frac{sinA}{a} =\frac{sinB}{b} \\\\\frac{sinx}{15}=\frac{sin27}{11} \\[/tex]
Cross-multiply:
[tex]11sinx=15sin27[/tex]
Solve for x:
[tex]sinx=\frac{15sin27}{11} \\\\x=sin^{-1} (\frac{15sin27}{11})\\\\=38.2488[/tex]
What are the coordinates A’ after 90 counterclockwise rotation about the origin.
Answer:
the above is the answer
hope this is helpful
Absolute Value Equations
Answer:
4 is E, 5 is A
Step-by-step explanation:
4) Divide both sides by 5 to get |2x + 1| = 11, then solve for x to get 5 and -6.
5) Add 7 to both sides to get ½|4x - 8| = 10. Multiply both sides by 2 to get |4x - 8| = 20, then solve for x to get 7 and -3.
Please answer this question. Will give brainiest fast
Answer: The answer is C the one you chose
Obtain all other zeros of 2 x power 4 - 6 x cube + 3 X square + 3 x minus 2 if two of its zeros are 1\ square root 2 and -1\square root 2
What would you do to isolate the variable in the equation below, using only one
step?
X + 9 = - 12
O Subtract 9 from both sides of the equation.
O Add 9 to both sides of the equation.
का
O Subtract 12 from both sides of the equation.
O Add 12 to both sides of the equation.
Answer:
O Subtract 9 from both sides of the equation.
Step-by-step explanation:
Notice that on the left hand side of the equation, you have two parts: X and 9. The variable is X, so we must do something to the 9 to remove it. Remember that we can cancel things by adding the negative of it. For example, 47+(-47)=0. Therefore, the opposite of 9 is -9. That essentially means subtracting 9.
1. What kind of special angle pair do the 2
angles make? (corresponding,
supplementary, or vertical)
Answer:
supplementary angle is whose is mesure is 180
Hari earns Rs 4300 per month. He spends 80% from his income. How much does he save in a year? please give answer in step by step explaination
Saving percentage=100-80=20%
Saving amount:-
[tex]\\ \sf\longmapsto 4300\times 20\%[/tex]
[tex]\\ \sf\longmapsto 4300\times \dfrac{20}{100}[/tex]
[tex]\\ \sf\longmapsto 43\times 20[/tex]
[tex]\\ \sf\longmapsto 860[/tex]
saving per year=Saving per month×12[tex]\\ \sf\longmapsto 12\times 860[/tex]
[tex]\\ \sf\longmapsto Rs10320[/tex]
Step-by-step explanation:
i think this will be help you
Which table has a constant of proportionality between y and x equal to 0.3?
Answer:
C
Step-by-step explanation:
you can divide y/x
1.2/4= 0.3
2.4/8= 0.3
3.9/13= 0.3
-Ba+9=Q²a solve for a
Answer:
[tex]a= \frac{9}{B+Q^2}[/tex]
Step-by-step explanation:
Given;
-Ba+9=Q²a
To solve for "a", make "a" the subject of the formula.
First, collect similar terms together;
-Ba - Q²a = -9
multiply through by "-1" to remove the negative sign;
Ba + Q²a = 9
factor out a;
a(B + Q²) = 9
divide both sides of the equation by "(B + Q²) ";
[tex]\frac{a(B+Q^2)}{B+Q^2} = \frac{9}{B+Q^2} \\\\a = \frac{9}{B+Q^2}[/tex]
Therefore, the value of "a" in the given expression is [tex]\frac{9}{B+Q^2}[/tex]
Solve the following formula for the specified variable:
C = 1/2 e * p for e
Given:
The formula is:
[tex]C=\dfrac{1}{2}e\cdot p[/tex]
To find:
The formula for e.
Solution:
We have,
[tex]C=\dfrac{1}{2}e\cdot p[/tex]
Multiply both sides by 2.
[tex]2C=e\cdot p[/tex]
Divide both sides by p.
[tex]\dfrac{2C}{p}=\dfrac{e\cdot p}{p}[/tex]
[tex]\dfrac{2C}{p}=e[/tex]
Interchange the sides.
[tex]e=\dfrac{2C}{p}[/tex]
Therefore, the required formula for e is [tex]e=\dfrac{2C}{p}[/tex].
Q is equidistant from the sides of TSR. Find the value of x.
T
(2x + 240°
30°
S
R
Lets do
[tex]\\ \sf\longmapsto 2x + 24 = 30 \\ \\ \sf\longmapsto 2x = 30 - 24 \\ \\ \sf\longmapsto 2x = 6 \\ \\ \sf\longmapsto x = \frac{6}{2} \\ \\ \sf\longmapsto x = 3[/tex]
Determine the type of quadrilateral given the following coordinates. Show and explain all steps to prove your answer. A(2, 3) B(-1, 4) C(0, 2) D(-3, 3)
Answer:
The quadrilateral is a parallelogram
Step-by-step explanation:
If you plot the points on the graph it resembles the shape of a parallelogram. It prove this you need to check if the lengths are correct. The slope between point A and point B is 1/3 and the slope between point C and point D is also 1.3. The slope between point B and D is 1/2 and the slope between point A and point C is also 1/2
hope this helps
The quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
What is a parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.
For the given situation,
The coordinates are A(2, 3) B(-1, 4) C(0, 2) D(-3, 3).
The graph below shows these points on the coordinates and the points ABDC forms the parallelogram.
This can be proved by finding the distance between these points.
The formula of distance between two points is
[tex]AB=\sqrt{(x2-x1)^{2}+ (y2-y1)^{2}}[/tex]
Distance AB is
⇒ [tex]AB=\sqrt{(-1-2)^{2}+ (4-3)^{2}}[/tex]
⇒ [tex]AB=\sqrt{(-3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]AB=\sqrt{9+ 1}[/tex]
⇒ [tex]AB=\sqrt{10}[/tex]
Distance BD is
⇒ [tex]BD=\sqrt{(-3+1)^{2}+ (3-4)^{2}}[/tex]
⇒ [tex]BD=\sqrt{(-2)^{2}+ (-1)^{2}}[/tex]
⇒ [tex]BD=\sqrt{4+ 1}[/tex]
⇒ [tex]BD=\sqrt{5}[/tex]
Distance DC is
⇒ [tex]DC=\sqrt{(0+3)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]DC=\sqrt{(3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]DC=\sqrt{9+ 1}[/tex]
⇒ [tex]DC=\sqrt{10}[/tex]
Distance CA is
⇒ [tex]CA=\sqrt{(2-0)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]CA=\sqrt{(2)^{2}+ (1)^{2}}[/tex]
⇒ [tex]CA=\sqrt{4+ 1}[/tex]
⇒ [tex]CA=\sqrt{5}[/tex]
Thus the lengths of the opposite sides are equal, the given points forms the parallelogram.
Hence we can conclude that the quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
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According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
PLS HELP IM TIMED
Answer:
Option (1)
Step-by-step explanation:
Fundamental theorem of Algebra states degree of the polynomial defines the number of roots of the polynomial.
8 roots means degree of the polynomial = 8
Option (1)
f(x) = (3x² - 4x - 5)(2x⁶- 5)
When we multiply (3x²) and (2x⁶),
(3x²)(2x⁶) = 6x⁸
Therefore, degree of the polynomial = 8
And number of roots = 8
Option (2)
f(x) = (3x⁴ + 2x)⁴
By solving the expression,
Leading term of the polynomial = (3x⁴)⁴
= 81x¹⁶
Therefore, degree of the polynomial = 16
And number of roots = 16
Option (3)
f(x) = (4x² - 7)³
Leading term of the polynomial = (4x²)³
= 64x⁶
Degree of the polynomial = 6
Number of roots = 6
Option (4)
f(x) = (6x⁸ - 4x⁵ - 1)(3x² - 4)
By simplifying the expression,
Leading term of the polynomial = (6x⁸)(3x²)
= 18x¹⁰
Degree of the polynomial = 10
Therefore, number of roots = 10
Refer to the picture above
Answer:
3.14
Step-by-step explanation:
First find the circumference of the circle:
[tex]2\pi r[/tex] = Circumference.
[tex]2 * \pi * 6[/tex] = [tex]12\pi[/tex]
Find the ratio of the angle in relation to the entire circle:
[tex]30^o[/tex] is what we have. So:
[tex]\frac{30^o}{360^o} = \frac{1}{12}[/tex]
Use the ratio and multiply the circumference to find the length:
[tex]12\pi * \frac{1}{12}[/tex] = [tex]\pi[/tex]
Round answer to the hundredth:
[tex]\pi = 3.14[/tex]
HELP FAST PLEASE!!!!!! Name the marked angle in 2 different ways.
Answer:
you forgot to add an image I dont know what angles your talking about
The duration of shoppers' time in Browse Wrld's new retail outlets is normally distributed with a mean of 27.8 minutes and a standard deviation of 11.4 minutes. How long must a visit be to put a shopper in the longest 10 percent
Answer:
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 27.8 minutes and a standard deviation of 11.4 minutes.
This means that [tex]\mu = 27.8, \sigma = 11.4[/tex]
How long must a visit be to put a shopper in the longest 10 percent?
The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 27.8}{11.4}[/tex]
[tex]X - 27.8 = 1.28*11.4[/tex]
[tex]X = 42.39[/tex]
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
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Answer:
yes
Step-by-step explanation:
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The gradient of a straight line passes through points (6,0) and (0,q) is -3/2. Find the value of q
Answer:
Step-by-step explanation:
gradient is essentially the slope of a straight line.
Use (y2-y1)/(x2-x1):
(q-0)/(0-6) = -3/2
q = 9
The expected value of X, E(X) must never be less than zero. True or False.
Answer:
I think true
Step-by-step explanation:
like and mark brainlist
Which of these is a factor in this expression?
7z4 – 5 + 10 (y3 + 2)
A. -5 + 10 (y + 2)
B. (y3 + 2)
C. 7z4 – 5
D. 10 (y3 + 2)
Answer:
A
Step-by-step explanation:
-5+10(y+2) is a factor
The factor in the expression is (y³ + 2)
How to determine the factor in the expression?The expression is given as:
7z⁴ - 5 + 10 (y³ + 2)
The terms of the expressions are:
7z⁴ , -5 and 10 (y³ + 2)
The factors are
7 and z⁴10 and (y³ + 2)Hence, the factor in the expression is (y³ + 2)
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