In right triangle ABC, B = 51° and AB = 14.
BC = _____
8.8
10.8
11.3
Answers
Given: the triangle is a right triangle, find a.
(The side opposite angle A.)
Answer:
a = 8.8104 ≈ 8.8
Step-by-step explanation:
∠A = ?, ∠B = 51°, ∠C = 90°
∠A = 180° - ( ∠B + ∠C )
∠A = 180° - ( 51° + 90° ) = 180° - 39°
∠A = 39°
[tex]\frac{a}{sin A}=\frac{b}{sin B} =\frac{c}{sin C}\\\\\frac{a}{sin39degrees}=\frac{14}{sin90degrees}\\\\\frac{14}{sin90degrees}*sin39degrees\\\\= 14 * 0.629\\= 8.8104[/tex]
So side a or BC = 8.8
Related Questions
What is the simplified form of the expression? -(4)^-2
Answers
Answer:
The given expression [tex]-\left(4\right)^{-2}[/tex] becomes [tex]-\frac{1}{16}[/tex]
Step-by-step explanation:
Given : Expression [tex]-\left(4\right)^{-2}[/tex]
We have to write the simplified form of the given expression [tex]-\left(4\right)^{-2}[/tex]
Consider the given expression [tex]-\left(4\right)^{-2}[/tex]
Apply exponent rule , [tex]\:a^{-b}=\frac{1}{a^b}[/tex]
[tex]4^{-2}=\quad \frac{1}{4^2}[/tex]
[tex]\frac{1}{4^2} =\frac{1}{16}[/tex]
Thus, The given expression [tex]-\left(4\right)^{-2}[/tex] becomes [tex]-\frac{1}{16}[/tex]
The length of a rectangle is 2 in. more than twice its width. if the perimeter of the rectangle is 28 in., find the dimensions of the rectangle.
Answers
Width = w
Perimeter = 2length + 2width
28 = 2(2+w) + 2(w)
28= 4+ 2w + 2w
24= 4w
6 =w
width =6
length = 8
Evaluate each expression below.
Click on "Undefined" as needed.
0/9=
3÷0 =
Answers
The value of 0 divided by 9 is 0, while the value of 3 divided by 0 is undefined because division by zero does not result in a finite number in mathematics.
Explanation:The expressions presented here involve division, a basic operation in mathematics. Let's evaluate each one respectively.
0/9 = 0: This is because zero divided by any number equals zero. 3 ÷ 0 = Undefined: Division by zero is undefined in mathematics because there is no number that you can multiply by 0 to get a non-zero number. Learn more about Division in Mathematics here:
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If y=x+2 were changed to y=x-1 how would the graph of the new function compare with the first one
Answers
Answer: C shifted down :)
Answer:
it would be shifted down
Patricia donated 1 pint of blood to the blood bank.The lab assistant divided patricia's blood equally into 3 bags.How much blood was in each bag?
Answers
Each bag contained [tex]\(\frac{1}{3}\)[/tex] pint of blood.
To solve the problem, we need to divide the total amount of blood donated by Patricia equally into 3 bags. Patricia donated 1 pint of blood.
Since there are 3 bags, we divide 1 pint by 3 to find out how much blood is in each bag. The division is straightforward:
[tex]\[ \frac{1 \text{ pint}}{3 \text{ bags}} = \frac{1}{3} \text{ pint per bag} \][/tex]
Therefore, each bag contains [tex]\(\frac{1}{3}\)[/tex] pint of blood. This is the simplest form of the fraction, and there is no need to convert it to a different unit or simplify it further. The answer is [tex]\(\frac{1}{3}\)[/tex] pint per bag.
Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, what is g(x) − f(x)?
g(x) − f(x) = 5x − 8 − 3x
g(x) − f(x) = 5x − 12 − 3x<--------------------
g(x) − f(x) = 3x − 8 − 5x
g(x) − f(x) = 3x + 12 − 5x
Points earned on this question: 2
Answers
(PROOF)
f(x) = 3x + 2
g(x) = 5x - 10
g(x) - f(x) = (5x - 10) - (3x + 2)
g(x) - f(x) = (5x - 3x) + (-10 - 2)
g(x) - f(x) = 2x - 12
Answer:
Option B. g(x) - f(x) = 5x - 3x - 12
Step-by-step explanation:
In this question the given functions are
f(x) = 3x + 2
g(x) = 5x - 10
Now we have to calculate the value of g(x) - f(x)
g(x) - f(x) = (5x - 10) - (3x +2)
= 5x - 10 - 3x - 2
= (5x - 3x) - (10 + 2)
= 5x - 3x - 12
Option B. (5x - 3x - 12) is the answer.
A gardener charges an initial fee of $37.50 plus a rate of $44.90 per hour. Write a function that shows the total fees for H hours of work
Answers
44.9 = slope/rate
In problems like these, just use y = initial rate + rate(variable)
In this case, the answer would be y = 37.5 + 44.9h
here you go the brainless
Answers
Subtract the x-coordinates in the same order: 1 - 1 = 0
slope = (difference in y)/(difference in x) = 5/0
Since the slope ends up as division by zero, and division by zero is undefined, the slope of this line is undefined.
Hint for future:
Vertical line: undefined slope
Horizontal line: zero slope
Line tilts up to the right: positive slope
Line tilts down to the right: negative slope
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
Answers
Answer: divide by -4
Step-by-step explanation:
A coach needs both small and large cones to set up an obstacle course. The coach knows that there are fewer than 30 cones in the storage room. The coach needs at least a dozen large cones.
Let x represent the number of small cones and y represent the number of large cones.
Which inequalities model the situation? Select each correct answer.
x+y≤30
x>0
x+y<30
y≥12
y>12
Answers
He needs AT LEAST a dozen (12), so that means that 12 will work or more than 12:
[tex]y \geqslant 12[/tex]
Answer: The correct options are,
x+y < 30
y ≥ 12
Step-by-step explanation:
Here, x represent the number of small cones and y represent the number of large cones.
∵ Large cones are at least 12,
⇒ y ≥ 12,
Now, total cones = x + y
∵ There are fewer than 30 cones,
I.e. x + y < 30,
Now, number of cones can not be negative,
⇒ x, y ≥ 0
Use multiplying by 1 to find an expression equivalent to 18/19 with a denominator of 76b.
Answers
so we multiply by 4b/4b ( = 1) :-
18 * 4b 72b
---------- = ----- <------ Answer
19 * 4b 76b
What is the coefficient of x7 in the expansion of (1 + x)11?
Answers
11C(something)(1)(x)⁷ ----> This gives the coefficient of x⁷
11C7(1)⁴(x)⁷ ----> You know that pascal's triangle is equal on both sides
11C7×1⁴ = coefficient of x⁷ (just ignore x⁷)
330x1⁴=330
This means that the coefficient of x⁷ is 330. You can double check by expanding the equation. If you do not understand what I did there, you can ask me how I got to the solution.
Hope I helped :)
Final answer:
Using the binomial theorem, the coefficient of x⁷ in the expansion of (1 + x)¹¹ is found by calculating '11 choose 7', which is 330.
Explanation:
The coefficient of x⁷ in the expansion of (1 + x)¹¹ can be found using the binomial theorem. To find the coefficient of x⁷, we look for the term that comes from choosing x seven times in the expansion. This corresponds to the 8th term, because the terms are indexed from 0, where the binomial coefficient is found by calculating "11 choose 7" or C(11, 7).
To calculate "11 choose 7", use the formula:
C(n, k) = n! / [k!(n-k)!], which gives us:
C(11, 7) = 11! / [7!(11-7)!] = 11! / (7!4!) = (11×10×9×8) / (4×3×2×1) = 330
Therefore, the coefficient of x⁷ in the expansion of (1 + x)¹¹ is 330.
Two pounds is equivalent to approximately how many kilograms
Answers
what number should the fraction 7/8 be multiplied by in order to equal 1
Answers
(7/8) * (8/7) = 1
The solution is 8/7
The number which should by multiplied with 7/8 to get 1 is 8/7 or the reciprocal of the number
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as = N
The value of n is given by
The number ( 7 / 8 ) x N = 1
On simplifying the equation , we get
( 7/8 ) x N = 1
Multiply by 8 on both sides of the equation , we get
7N = 8
Divide by 7 on both sides of the equation , we get
N = 8/7
Therefore , the number N is 8/7
Hence , the number is 8/7 or reciprocal of 7/8
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In the last year a total of 2783 earthquakes occurred in the country. Of these, 85.8% were minor tremors w/ magnitudes of 3.9 or less on the richer scale. How many minor earthquakes occurred in the country last year? Round to nearest whole number.
Answers
In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 17 prospective jurors?
Answers
Explanation:
The 12 jurors from 17 prospective can be chosen in C17,12 ways.
That is: 17! / [12! (17 - 12)! ] = (17*16*15*14*13) / (5*4*3*2*1) = 6188 ways
The 2 alternates are chosen from a group of 17 - 12 = 5. Thas is C5,2
C5,2 = 5! / (2! 3!) = 5*4 / 2 = 10
So, the total number of ways is 6188 * 10 = 61880 ways.
Answer: 61880.
Final answer:
To find the different ways of choosing a panel of 12 jurors and 2 alternates from 17 prospective jurors, calculate the combinations separately (C(17, 12) for jurors and C(5, 2) for alternates) and multiply them, yielding a total of 61,880 different ways.
Explanation:
The question asks in how many different ways a panel of 12 jurors and 2 alternates can be chosen from a group of 17 prospective jurors. To solve this, we use the concept of combinations in mathematics. Since the order in which we select the jurors and alternates does not matter, we are dealing with combinations, not permutations.
First, we choose the 12 jurors from the 17, which is the combination of 17 taken 12 at a time. This can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n - k)!),
where 'n' is the total number of items, 'k' is the number of items to choose from, and '!' denotes factorial.
For the 12 jurors, we compute C(17, 12) which equals 17! / (12! * (17 - 12)!) = 17! / (12! * 5!) = 6188.
Next, we need to choose 2 alternates from the remaining 5 jurors. The calculation is C(5, 2) which equals 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = 10.
Since choosing jurors and alternates are independent events, we multiply the two combinations to get the total number of different ways to choose the panel:
6188 (ways to choose jurors) * 10 (ways to choose alternates) = 61,880 different ways.
solve the system
x+3y=5
x+4y=6
A) (2,1)
B) (1,5)
C) (8,-1)
D (11,-2)
Answers
x + 4y = 6
x + 3y = 5
Subtract the two equations.
You get y = 1.
The only answer with a value of y = 1 is A
A is your answer.
Have a nice day! :)
Answer:
A(2,1)
Step-by-step explanation:
We are given that system of equation
[tex]x+3y=5[/tex]
[tex]x+4y=6[/tex]
We have to solve the system
Subtract equation first from equation second
Then, we get
[tex]y=1[/tex]
Substitute the value of y in equation I
Then, we get
[tex]x+3(1)=5[/tex]
[tex]x=5-3=2[/tex]
Hence, the option A is true.
Answer:A(2,1)
Which situation CANNOT be represented by this equation? -13x+15=9
A-The water level in a tank measures 1515 inches and is decreasing every 1313 of a minute. At what rate, xx, does the water level need to decrease per minute to reach a depth of 99 feet?
B-The water level in a tank measures 99 inches and is rising 1313 of an inch every minute. How many minutes, xx, will it take for the water level to measure 1515 inches deep?
C-The water level in a tank measures 1515 inches and is decreasing 1313 of an inch every minute. How many minutes, xx, will it take for the water level to measure 99 inches deep?
Answers
THE ANSWER IS: PLEASE MARK AS BRAINLIST
The water level in a tank measures 9 inches and is rising 13 of an inch every minute.
How many minutes, x, will it take for the water level to measure 15 inches deep?
if a job pays $45,000 per year, you live in a state where your total tax burden is 22%, and you receive a weekly paycheck, what is your take-home pay from each paycheck?
Answers
Answer:
$190.38 per week
Step-by-step explanation:
45,000 x .22 (the tax) is 9,900
9,900 / 52 (weeks in a year) is 190.384
Rounded, your answer is $190.38 per week
Maya made $252 for 12 hours of work. at the same rate, how many hours would she have to work to make $168 ?
Answers
She makes $21 per hour
168÷21=8 hours
She needs to work for 8 hours.
Answer:
8
Step-by-step explanation:
252/12 = 21
168/ 21 = 8
David gained 16 pounds over the winter. he went on a diet and lost 25 pounds. then he regained 4 pounds and weighed 177 pounds. how much did he weigh originally?
Answers
x+16-25+4 = 177
x-5=177
x= 177+5= 182 pound
David's original weight was 182 pounds, as we determined by retracing his weight changes in reverse order.
Explanation:To find out how much David originally weighed, we need to work backwards from his ending weight, taking his weight changes into account. Currently David weighs 177 pounds. However, before gaining the last 4 pounds, he would have weighed 177 - 4 = 173 pounds.
Going back further, before losing 25 pounds, he would have weighed 173 + 25 = 198 pounds. Finally, before David gained 16 pounds over the winter, his original weight would have been 198 - 16 = 182 pounds.
So, David's original weight was 182 pounds.
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Which equation has the steepest graph
Answers
sorry if its wrong, then its c
Answer:
b
Step-by-step explanation:
Chris's uncle has a model car. the model is 6 inches long and 3 inches wide. the actual car is 75 inches long. what is the car's actual width, if we assume the model's proportions are accurate? if necessary, round to the nearest tenth of an inch.
Answers
I believe the right answer would be 37.5
Tyrell does sit-ups every day. On Monday, he did 4 sit-ups. On Tuesday, he did 8 sit-ups, and on Wednesday, he did 12 sit-ups. Based on the pattern, make a conjecture about the number of sit-ups he will do on Friday.
Answers
Answer: 20 sit ups.
Step-by-step explanation: if tyrell does situps everyday on monday he does 4 sit ups and tuesday 8 situps wendsday 12 situps thursday 16 situps friday 20 situps all u do to solve is add 4 every day.
your welcome.
Select all that justify the following statement.10 + x • 12 = 12x + 10
Answers
10 + x*12 = 12x+10
since the left side can be re-written as 12x+10 this does equal the right side
so any real number ( any value of x ) will work
Solve for the width in the formula for the area of a rectangle.
formulas
1. w = A - L
2. w = AL
3. w = L/A
4. w = A/L
Use the rewritten formula to find the width of a rectangle with an area of 42 square inches and a length of 16.8 inches.
1. 2.5 inches
2. 4.2 inches
3. 12.6 inches
4. 25.2 inches
Answers
A / L = W <==
when A = 42 and W = 16.8
A / L = W
42/16.8 = W
2.5 = W <=== width = 2.5 inches
W=A/L................
2.5 inches...........
A ship leaves port at 1:00 p.m. and travels s35°e at the rate of 26 mi/hr. another ship leaves the same port at 1:30 p.m. and travels s20°w at 20 mi/hr. approximately how far apart are the ships at 3:00 p.m.?
Answers
Triangle ABC is shown below.
What is the length of line segment AC?
7
9
14
18
Answers
Answer:
Option C. AC = 14 units
Step-by-step explanation:
In the given triangle ABC shown in the figure ∠ABC = ∠ACB
Since angles are equal so opposite sides of equal angles will be equal.
Now mAB = mAC
By putting values in terms of x
2x = 3x - 7
x = 7
Now mAC = 3x - 7
By putting value of x = 7
mAC = 3×7 - 7 = 21 - 7 = 14
Therefore length of line segment AC is 14 units.
is 2xy = -8 a function
Answers
You can find a value of x and a value for y that would make that true, so YES it is a function.
Example:
2(2)(-2) = -8
The equation 2xy = -8 is a rectangular hyperbola which is an example of the function.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
When the transverse and conjugate axes of a hyperbola are both the same length, the diagnosis and appropriate are said to be rectangular.
The equation is given below.
2xy = -8
Separate the variable 'y', then we have
2xy = -8
xy = -4
y = -4/x
The equation 2xy = -8 is a rectangular hyperbola which is an example of the function.
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Hour hand of a watch rotates 30 degrees every hour, how many rotations makes in 6 days