[tex]\sin(66) = \frac{49}{x} \\ 0.913 = \frac{49}{x} \\ x = 53.6 \\ x = 54[/tex]
The missing side is 53.6 units for the given right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The right triangle is given in the question, as shown.
The ratio of the length of the side opposite the angle to the length of the hypotenuse of the triangle. The sine function is denoted by the symbol "sin" and is defined as follows:
sin(θ) = opposite / hypotenuse
Here, θ = 66°
Using the sine ratio in the given triangle, we get
sin 66° = perdenicular/hypertanuas
Substitute the known values in the above ratio,
sin 66° = 49/x
x = 49/sin 66°
x = 53.63717
Rounded to the nearest tenth,
x ≈ 53.6
Thus, the missing side is 53.6 units for the given right triangle.
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Mr. James asked his students that which of the following equations can be formed using the expression x = 5:
a)2 x + 3 = 13
b)3x + 2 = 13
c)x –5 =
1d)4x –9 = 21
Answer:
[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]
Ryan rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 74 cents for each mile driven. Ryan had to pay $133.17 when he returned the truck. For how many miles did he drive the truck?
Answer:
157 miles
Step-by-step explanation:
total cost = flat fee + cost per mile * miles
133.17 = 16.99 + .74 * m
Subtract 16.99 from each side
116.18 = .74m
Divide each side by .74
116.18 / .74 = .74m/.74
157 = m
You have 80$ panted cost 29$ And shirts cost 12$. Mom told you to buy one pair of pants and use the rest of the money to buy shirts. Use this information to write and solve and inequality how many shirts can you buy
Answer: 4 Shirts
Step-by-step explanation:
Given
Person has [tex]\$80[/tex]
Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]
Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts
Spent money must be equal or less than the total money. The inequality becomes
[tex]\Rightarrow 80\geq29x+12y[/tex]
For 1 pair of pants that is, 1 pants
[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]
That is maximum number of shirts that can be bought are 4.
I NEEDDDD D HELPPPPP!!!
Answer:
70 degrees
Step-by-step explanation:
there are multiple ways, as all the trigonometric functions are related.
let's try it this way :
consider the missing side to be the radius of a circle.
then 41 would be the cos value of the angle (multiplied by that radius, of course).
so, let's calculate the missing side per Pythagoras
c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450
c = 120.21
and now
41 = cos(?) × 120.21
cos(?) = 41/120.21 = 0.341...
? = 70.0576... ≈ 70 degrees
Answer:
70°
Step-by-step explanation:
tangent θ = (opposite side / adjacent side)
tangent θ = (113 / 41)
θ = arctan (113 / 41)
θ = 70.0576°
*Note: "arctan" is the same as "inverse tangent"
**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = 3/4x
h(x) = 1/4x
Answer:
Let the inverse of f(x) be h(x):
[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]
Draw a plane, showing the three (non-linear) points that define it.
Draw a plane, showing the three (non-linear) points that define it.[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
See this attachment
guys, please help i can't move on
Answer:
15
Step-by-step explanation:
32-19 = 13 that have both
70-57= 13 that have both again from that sample
total number of people that have both : 13 + 13 = 26
11 kids don't have either one, so :
26-11 = 15
Which is the correct form of the partial fraction decomposition for the expression StartFraction 4 x cubed + 3 x squared Over (x + 1) squared (x squared + 7) squared EndFraction?
Given:
The expression is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
To find:
The correct form of the partial fraction decomposition for the given expression.
Solution:
We have,
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]
By partial fraction decomposition, it can be written as:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex] ...(i)
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]
[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]
[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]
[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]
On comparing both sides, we get
[tex]A+C=4[/tex]
[tex]A+B+2C+D=3[/tex]
[tex]7A+C+2D=0[/tex]
[tex]7A+7B+D=0[/tex]
On solving these equations, we get
[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]
Substituting these values in (i), we get
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Therefore, the required partial fraction decomposition is:
[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]
Answer:
A on Edg
Step-by-step explanation:
got it right
On an electricity bill of $40.80, Mrs.
Miller pays only $38.76 because she pays
before a certain date. What percent
discount is Mrs. Miller allowed?
Answer:
100%_$40.80
? × _$38.76
Step-by-step explanation:
100%×$38.76÷$40.80=95%
Answer:
40.80
Step-by-step explanation:
Which numbers are integers? Check all that apply.
04
-15
-10
2.5
0-4
0.13
ILL GIVE BRAINLIEST
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 21% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 58 of the dragon eggs to incubate. Consider all the possible samples of 58 dragon eggs.
What is the usual number of yellow eggs in samples of 58 eggs? (Give answers as SENSIBLE whole numbers.)
minimum usual number of yellow eggs =
maximum usual number of yellow eggs
Answer:
usual number of yellow eggs = 12
Usual maximum = 21
Usual minimum = 3
Step-by-step explanation:
To solve this, we will use the expected value of a binomial probability.
The formula is;
E(X) = np
Where;
n is sample size
p is probability of success.
We are given;
n = 58
p = 21%
Thus;
usual number of yellow eggs in samples = np = 58 × 21% = 12.18 ≈ 12
From USL(Upper specification limit) and LSL(Lower specification limit) formula, we can find the maximum usual number and minimum usual number of eggs respectively.
Thus;
USL = n(p + 3√(p(1 - p)/n)
USL = 58(0.21 + 3√(0.21(1 - 0.21)/58)
USL = 21.48 ≈ 21
LSL = n(p - 3√(p(1 - p)/n)
LSL = 58(0.21 - 3√(0.21(1 - 0.21)/58)
LSL = 2.87 ≈ 3
A is 2 times older than B. Identify the appropriate expression.
Answer:
C. 2x
Step-by-step explanation:
Let
B's age = x years
A's age = 2 times older than B
= 2 * x
= 2x years
A's age = 2x years
For instance, if B's age is 17 years
Then,
A's age = 2x
= 2(17)
= 34 years old
Please help me with this
Answer:
A
Step-by-step explanation:
first answer gets marked brainliest!!!
Answer:
in neighbourhood q the total number of people in the nine families I higher than that in neighbourhood s because of we add up the number of people in the families in neighbourhood q we get a total of 35 yet we have a total of only 27 people in the nine families in neighbourhood s
hope that helps ❤
Travis makes and sells fishing lures. He
has 56 fishing lures that he is putting into
boxes. Each box can hold 5 fishing lures.
How many boxes can Travis fill
completely?
James is 8 years old. Last year, his father was 4 times as old as he was. In how many years' time will their combined age be 51?
Last year He was 7 years old.
His father is 4 times the age 7 x 4 = 28
Last year his dad was 28, so this year he is 29.
Combined age this year = 29 + 8 = 37
51 - 37 = 14 years
14/ 2 people = 7 years
8 + 7 = 15
29 + 7 = 36
15 + 36 = 51
It will take 7 years.
Solve the inequality 4 is greater than n over -4
Answer:
4 > [tex]-\frac{n}{4}[/tex]
-16 > n
Step-by-step explanation:
Greater than would mean that the "arrow" is not facing the number. It would mean it is larger than the other number. Also, you have to construct the other part of the inequality which would be [tex]-\frac{n}{4}[/tex].
4×4 > [tex]-\frac{n}{4}[/tex]×4
16 > -n
-16 > n
HELP!!!!!
If anyone knows the answer please tell me as soon as possible!!
PLEASE!!!!
How to find the area of this figure pls?
Kara Danvers (Supergirl) has always relied on her strength to win fights. But what happens when she meets an alien just as strong? Her sister is training her to be a more technical fighter so that Supergirl can meet any challenge. The data below record the significant strikes during randomly selected training sessions 6 months apart. Is Kara showing improvement in her fighting?
Strikes (pre): 29 32 44 34 19
Strikes (post): 51 45 68 92 64
Write the Hypotheses:
H_0:_______________, the mean difference in ___________ between ____________ and ______________ is _______________
H_a:_______________, the mean difference in ___________ between ____________ and ______________ is _______________
Answer:
H0 : The mean difference in strikes between pre and post strike is equal to 0
H1 : The mean difference in strikes between pre and post strike is not equal to 0
Step-by-step explanation:
The scenario described abibe meets the condition for a paired (dependent) sample t test as the same subject is involved in both the pre and post strike data. Therefore measurement from the strike(pre) must be paired with measurement from the strike(post) data.
For a paired test involving a single subject ; The mean difference in the two sample is 0 ; that is both are the same while the alternative negates the null by claiming that the mean difference is not equal to zero.
If $10,500 is borrowed for 5 years at an annual simple interest rate of 1.73%, how much interest will be paid if the entire loan is paid off at the end of the fifth year? Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Answer:
Step-by-step explanation:
So, yearly $2100 is paid, plus the 1.73% interest, so 1.73% interest is $2136.33every year interest stacks on itself so youll take 1.73% of the year 1 total with interest.
Year 1 total: $2136.33
Year 2 total:$2173.29
Year 3 total:$2210.89
Year 4 total:$2249.14
Year 5 total:$2288.05
Total Paid After 5 years:$11057.70
Year 1 total interest:$36.33
Year 2 total interest:$36.96Year 3 total interest:$37.60Year 4 total interest:$38.25Year 5 total interest:$38.91
Total Interest paid after 5 years:$188.05
Use the work shown below to find the simplified product
Given:
The expression is:
[tex]\dfrac{25x^2}{2x+6}\cdot \dfrac{2}{5x}[/tex]
To find:
The simple product.
Solution:
We have,
[tex]\dfrac{25x^2}{2x+6}\cdot \dfrac{2}{5x}[/tex]
It can be written as:
[tex]=\dfrac{5\times 5\times x\times x}{2(x+3)}\cdot \dfrac{2}{5x}[/tex]
Cancel out the common factors.
[tex]=\dfrac{5\times x}{x+3}[/tex]
[tex]=\dfrac{5x}{x+3}[/tex]
Therefore, the correct option is C.
PLS how to do this 3 sums
Answer:
Step-by-step explanation:
7) PQ // RS, RQ is transversal
x = 38 {Alternate interior angles are congruent}
In ΔPQR ,
x + y + ∠P = 180 {Angle sum property of triangle}
38 + 90 + y = 180
128 + y = 180
y = 180 - 128
y = 52
9) Construct XY // AB
XY // AB & AC is transversal
∠1 = ∠4 ---------(I) {alternate interior angles are equal}
XY // AB & BC is transversal
∠3 = ∠5 ---------(II) {alternate interior angles are equal}
∠1 + ∠2 + ∠3 = 180 {straight line angles}
∠4 + ∠2 + ∠5 = 180 {From (I) & (II) }
Sum of three angles of triangle is 180.Hence proved.
Point P is the incenter of DEF. Point P is the point of concurrency of the angle bisector. Find PV
Answer:
12
Step-by-step explanation:
because line FB divides triangle f v w into two equal halves therefore line WP is equal to line PV which is equal to 12
The required value of the PV is 12 in triangle DEF where p is the incenter.
Point P is the incenter of ΔDEF. Point P is the point of concurrency of the angle bisector. PV to be determined.
The incenter of a triangle is the intersection point of the internal angle bisectors of the triangle. In additional expressions, it can be clarified as the point where the internal angle bisectors of the triangle and perpendicular distance from this point to any of the sides of triangle is the same.
Since in triangle FGH, P is the incenter and PW, PV,PX is perpendicular distance to the sides HF, GF and GH respectively.
From image,
PW = 12
So by the property of incenter, perpendicular distance from this point to any of the sides of triangle is the same.
PW = PV
PV = 12
Thus, the required value of the PV is 12 in triangle DEF where p is the incenter.
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please help! see question below :)
Answer:
I have no clue sorry bro.
Jin bought a pair of pants that cost $47.83. The sale tax in her state is 7.43 % what is the total cost of the pants ?
(show your work)
Answer:
$51.38
Step-by-step explanation:
7.43% of 47.83=(rounded to the nearest hundredth) 3.55
7.43/100*x/47.83
x=3.55
because we are solving for x
we can also cross check by taking out the percentage
x/100*3.55/47.83
47.83x=355
x=7.42212000836
which is about 7.43%
47.83+3.55= 51.38
You just decided to open a savings account and went to the bank and made an initial deposit. You decide to save another set amount each month. Without any interest being paid, the equation =20+50
represents the amount of money,
y
, in your savings account after
m
months. Select what the slope and y-intercept represent in this problem.
(Choose 2)
Answer:
Options (1) and (4)
Step-by-step explanation:
Given equation for the deposit in the saving account is,
y = 20x + 50
Here, y = Amount of money in the account
20 = money added in the account every month
50 = Initial deposit
By comparing this equation with the slope-intercept form of the equation of a line,
y = mx + b
Here, slope m = money added in the account every month
And b = y-intercept
Therefore, Options (1) and (4) will be the answer.
What is the area of the triangle? A) 6 squared inches B) 7 1/2 square inches. C) 10 square inches. D) 12 square inches
Answer:
A) 6 square inches.
Step-by-step explanation:
A(Triangle) = 1/2bh
b = base length
h = height length
A(Triangle) = 1/2(4)(3) = 6
Therefore, the area of the triangle is 6 in².
Did I do this right?
Answer:
it must be yes!
Step-by-step explanation:
What is the answer I need help ASAP be truthful
Answer:
your closest number should be A
Answer:
A.√99
Step-by-step explanation:
10^2 = 100
Or vise versa √100 = 10
The closest number to 100 is 99
So √99 is closest to 10
