Lesson 13.3 Checkpoint
1. Use trigonometric ratios to find the unknown side lengths of each triangle.
I really need the help I’m almost finished with my work
Answers
Answer:
a. LK = 4√3, JL= 4√6
b. PQ = 10√3, RP = 5√3
Step-by-step explanation:
a. LK =4√3,
LK=KJ= 4√3
sin(45°) = opposite/hypotenuse
hypotenuse (JL)= opposite/sin 45° = 4√3/√2/2 = 8√3/√2 = 8√3√2/2 = 4√6
b.
cos 30° = adjacent/hypotenuse = QR/PQ = 15/PQ
cos 30° = 15/PQ
PQ = 15/cos 30° = 15/√3/2)= 30/√3 = 30√3/3 = 10√3
tan 30° = opposite/adjacent = RP/QR
√3/3 = RP/QR
√3/3 = RP/15
RP = √3*15/3 = 5√3
Related Questions
Which of these statements BEST describes the relationship between college and health and wellnes
professionals?
A. A more advanced degree usually mean a higher salary.
B. A more advanced degree usually mean a lower salary.
C. A less advanced degree usually mean a higher salary.
D. There is no relationship between college degree and salary.
Answers
Answer:
which of these statements BEST describes the relationship between college and health and wellness D There is no relationship between college degree and salary.
Rectangle A has a width of 3 inches and a length of 5 inches. Part A Rectangle A has the same perimeter as Rectangle B. If its width is 4 inches, what is its length? Enter your answer in the box. Rectangle B has a width of 4 inches and a length of inches
Answers
Answer:
Rectangle B has a length of 4 inches.
Step-by-step explanation:
Rectangle A has a width of 3 inches and a length of 5 inches.
Let us find its perimeter:
Perimeter = 2(L + W)
where L = length
W = width
Its perimeter is therefore:
P = 2(5 + 3)
P = 2 * 8 = 16 inches
Rectangle B has the same perimeter as Rectangle A. Let us find the length of B.
Its width is 4 inches, therefore, perimeter is:
P = 2(L + W)
16 = 2(L + 4)
16 = 2L + 8
16 - 8 = 2L
8 = 2L
=> L = 8 / 2 = 4 inches
Rectangle B has a length of 4 inches.
Trig With Picture ASAP
Answers
Answer:
18
Step-by-step explanation:
V=a^3
a=∛1000=10
volume=1000 cm^3=10*10*10
one side =10 cm
to find the measure of AB (the diagonal)=10√3 =17.32
the smallest dispenser has to be greater than 17.32
the smallest amount is 18
The population of a large city can be calculated using the function . What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10
Answers
Answer:
The rate of change will be the same for all years.
Step-by-step explanation:
As it is mentioned in the question, that the rate of change is 7%.
And as we know that
= I (1 + R)^T
where
I = Initial amount
R = Rate of growth,
And T = Time.
So in the given case, the rate is 0.07, or 7% while on the other hand the growth RATE remains constant and the growing amount would be increased each year.
Therefore the rate of change would be the same for all the year
What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y-4=‐2/3(x-6) and passes through the point (-2, -2)?
y=-x-10
y=-2x19
y=x-1
y=x+1
Answers
Answer:
y=3/2x+1
Step-by-step explanation:
y-4= -⅔(x-6)
y-4=-⅔x+4
y=-⅔x+4+4
(equation of line 1) y= -⅔x+8 gradient= -⅔
(line 2)gradient=3/2
note* the gradients of perpendicular lines multiplied result to -1
gradient=y²-y²
x²-x¹
3 =y+2
2. x+2
multiply both sides by 2(x+2)to remove the denominators
3(x+2)=2(y+2)
3x+6=2y+4
3x+6-4=2y
3x+2=2y
divide all sides by 2
3/2x+1=y
y=3/2x+1
The following polynomial has factors (x + 8) and (3x + 2). Determine the value of k. −6x^3-55x^2+kx−16
Answers
Answer:
k = - 58Step-by-step explanation:
Since (x + 8) and (3x + 2) are factors of the polynomial it means that if either one of them is equated to zero and substituted into the polynomial will give us zero
Using x + 8
We have
x + 8 = 0
x = - 8
Substitute the value of x into the polynomial
- 6x³ - 55x² + kx - 16
That's
- 6(-8)³ - 55(-8)² + k(-8) - 16 = 0
-6(-512) - 55(64) - 8k - 16 = 0
Expand
3072 - 3520 - 8k - 16 = 0
Simplify
- 464 - 8k = 0
8k = -464
Divide both sides by 8
k = - 58
Hope this helps you
The slope-intercept form of the equation of a line that passes through point (–3, 8) is y =- 2 /3x +8 . What is the point-slope form of the equation for this line? y – 3 = –2/3 (x + 8) y + 3 = -2/3 (x - 8) y + 8 = - 2/3 (x - 3) y - 8 = -2/3 (x + 3 )
Answers
Answer:
y - 8 = - [tex]\frac{2}{3}[/tex](x + 3)
Step-by-step explanation:
y = - [tex]\frac{2}{3}[/tex] x + 8 ← is in slope- intercept form with slope m = - [tex]\frac{2}{3}[/tex]
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - [tex]\frac{2}{3}[/tex] and (a, b) = (- 3, 8), thus
y - 8 = - [tex]\frac{2}{3}[/tex] (x - (- 3)), that is
y - 8 = - [tex]\frac{2}{3}[/tex] (x + 3)
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point.
Answers
Answer:
(2√5)/5
Explanation:
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION
From the question we can deduced that the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance, we can say that the y-coordinate, is twice of the horizontal, then let call the horizontal "y", the vertical would be 2y.
from the attachment the question on the unit circle is interpreted using a figure,then, hypotenuse was first calculated
Answer:
C, 2 sqrt 5 / 5
write the unit digit of denominator of (x+y)*z where x = -4/3 y =1/2 z= -7/5 plz help
Answers
Answer:
6
Step-by-step explanation:
(x+y)*z= (-4/3+1/2)*(-7/5)= -5/6* (-7/5)= 35/30=7/6
Denominator is 6.
A drawer contains a dozen each of red, blue, green, and white socks, all unmatched. Laura takes socks out at random in the dark. How many socks must Laura take out to be sure she has two pairs of white socks?
Answers
Answer:
8
Step-by-step explanation:
The probability of picking out a certain colour = 12/48 = 1/4
So, this means that every 4 socks you pick out you can be sure of having one of each colour. If you need to find a pair, then you pick out 8.
Hope this helps
8 plus w/4 when w = 16
Answers
Answer:12
Step-by-step explanation: first you replace w for 16 and divide that by 4 because of GEMDAS or PEMDAS.. Your left with 4 now add 4 plus 8 which is 12
8 Use prime factorization to find the LCM of 20 and 44,
O 64
0 220
880
Answers
Answer:
Th answer is 220
Step-by-step explanation:
In the picture down below
Answers
Work Shown:
The idea is that you replace f(x) with y, swap x and y, then solve for y to get the inverse.
[tex]f(x) = \frac{3x-2}{6}\\\\y = \frac{3x-2}{6}\\\\x = \frac{3y-2}{6}\\\\6x = 3y-2\\\\3y-2 = 6x\\\\3y = 6x+2\\\\y = \frac{6x+2}{3}\\\\f^{-1}(x) = \frac{6x+2}{3}\\\\[/tex]
15. An electric can opener is worth 38 dollars when it is new. After each year it is worth half what it was the
previous year. What will its worth be after 4 years? Round your answer to the nearest cent.
$4.19
$4.75
b. $1.19
d. $2.38
a.
c.
Answers
Answer: d. $2.38
Step-by-step explanation:
Exponential decay function: [tex]Ab^x[/tex], where A = initial value
x= Time mperiod
b = multiplicative decay rate
As per given, we have
A = 38 dollars
b= 0.5
Amount after x years : [tex]38(0.5)^x[/tex]
Then, at x= 4
Amount after 4 years : [tex]38(0.5)^4=38(0.0625)[/tex]
[tex]=2.375\approx2.38[/tex]
Hence, the worth of electric can opener after 4 years = $2.38.
So, correct option is d. $2.38
ILL MARK BRAINLIEST In independent random samples of 10 men and 10 women in a coed basketball league, the numbers of points scored per season are given by the back-to-back stemplot below:
Part A: Describe the shape of each data set.
Part B: Michaela analyzed the data and stated that the better measure of center for the women is the mean. Is Michaela correct? Explain your reasoning.
Part C: Michaela decided there are no outliers in the women's data set. Is she correct? Justify your answer mathematically.
Answers
Answer:
Step-by-step explanation:
Hello!
a)
To compare both datasets I've made a box plot for them.
The yellow one belongs to the points scored by the men and the green one is for the points scored by the women.
Women: The box seems symmetrical, the median and the mean (black square) are almost the same. The whiskers are almost the same length, you could say that in general the points scored by the women have a symmetrical distribution.
Men: The box looks a little skewed to the right, the median is closer to the 1st quantile and the mean is greater than the median. The whiskers are the same length, in general the distribution seems almost symmetrical.
b)
As you can see in the box plot the median and mean of the points scored by the women are almost the same. Using the data I've calculated both values:
Me= 24.50
X[bar]= 23.80
The median divides the sample in halves (50-50), it shows you where the middle of the distribution is.
The average shows you the value that centers the distribution, meaning, it is the value around which you'll find most of the data set. It summarizes best the sample information and therefore is a better measure of center.
c.
As you can see in the box plots, there are no outliers in both distributions.
An outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.
Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:
X < Q₁ - 1.5 IQR
X > Q₃ + 1.5 IQR
Or extreme outliers if:
X < Q₁ - 3 IQR
X > Q₃ + 3 IQR
For the women data set:
Q₁= 17; Q₃= 30; IQR= 30 - 17= 13
Lower outliers: X < Q₁ - 1.5 IQR= 17-1.5*13= -2.5 ⇒ The minimum value recorded is 03, so there are no outliers.
Upper outliers: X > Q₃ + 3 IQR= 30 + 1.5*13= 49.5 ⇒ The maximum value registered is 41, so there are no outliers.
I hope this helps!
The annual sales of romance novels follow the normal distribution. However, the mean and the standard deviation are unknown. Forty percent of the time, sales are more than 470,000, and 10% of the time, sales are more than 500,000. What are the mean and the standard deviation?
Answers
Answer:
Mean(m) = 462,536
sd = 29,268.29
Step-by-step explanation:
Given the following:
P(sales > 470,000) = 40% = 0.4
P(sales > 500,000) = 10% = 0.1
Using the z - table, we can locate the corresponding P values
Z = 1 - p = 1 - 0.4 = 0.6; 1 - 0.1 = 0.9
Locating the closest value to 0.6 on the z table ;
(0.25 + 0.26) / 2 = 0.255
Locating the closest value to 0.9 on the z table ;
Z = 1.28
Recall;
z =( x - m) / sd
Where m = mean ; sd = standard deviation
First condition:
0.255 = (470,000 - m) / sd
0.255 × sd = (470,000 - m) - - - - - (1)
1.28 = (500,000 - m) / sd
1.28 × sd = (500,000 - m) - - - - (2)
We can solve for one of the unknowns y subtracting equation (1) FROM 2
1.28sd - 0.255sd = (500,000 - m) - (470000 - m)
1.025sd =500,000 - m - 470000 + m
1.025sd = 30,000
sd = 29,268.29
Substituting the value od SD into (1) or (2)
1.28 × 29,268.29 = 500000 - m
37463.41 = 50000 - m
m = 50000 - 37463.41
Mean(m) = 462,536
Asap Help please THANK YOU!!
Answers
Answer:
≈451.37 cm³
Step-by-step explanation:
Since the diameter of the can is 6, the radius is 3.
Old can height: 12
Old can base radius: 3
Old can volume: 339.12 cm³
New can height: 12×1.1=13.2
New can base radius: 3×1.1=3.3
New can volume: 13.2×3.14×3.3²=13.2×3.14×10.89=451.36872 cm³
y
10,6)
(-a, 0)
(0,0)
(a 0)
(0-5)
What is the perimeter of the polygon in the diagram?
Answers
Answer:
I think its O-5 I am not sure
6.12)
Jennifer had some money in her
pocket. She spent $1.35, which left
her with $2.30. Which equation could
Jennifer use to find m, the original
amount of money she had in her
pocket?
A m + 2.30 = 1.35
B m - 1.35 = 2.30
C 2.30 = 1.35 – m
D m = 2.30 x 1.35
Answers
Answer:
B
Step-by-step explanation:
m-1.35=2.30
you would add -1.35 to the other side
so then you have
m=3.65
which is how much money she had to begin with
Answer:
B
Step-by-step explanation:
m - 1.35 = 2.30
The Marauders foosball team is improving with each game. The first game they scored no points, but the second game they scored some goals. In their third game they scored 8 more points than the second. Now in their last game they scored three times as many points as their third. Altogether they scored 117 points!!! How many points did the Marauders score in the third game?
Answers
Answer:
25 points.
Step-by-step explanation:
In the second game, you can say the Foosball team scored x points.
In their third game, they would have scored x points, plus 8.
In the last game, they would have scored x points, plus 8, then multiply the WHOLE THING by 3.
We would get the following equation...
x + (x + 8) + 3(x + 8) = 117
x + x + 3x + 8 + 24 = 117
5x + 32 = 117
5x = 85
x = 17
So, the Marauders scored 0 points in the first game. In the second game, they scored 17 points. In the third, they scored 17 + 8 = 25 points. In the last, they scored 25 * 3 = 75 points. Altogether, that's 117 points!!
Hope this helps!
Answer:
.
Step-by-step explanation:
what point lies on y-2=5(x-6)
Answers
Answer: (0, -28)
Step-by-step explanation:
Turn this equation into slope-intercept form.
y-2=5x-30
y=5x-28.
Because the y-intercept is -28, the point (0,-28) must be on the line.
Hope it helps <3
Increase £426 by 34% Give your answer rounded to 2 DP.
Answers
Answer:.£570.84
Step-by-step explanation:
426 x 1.34 = 570.84
Answer:
£426 * 1.34 = £570.84
Step-by-step explanation:
find 1st- 4th nTH term and then the 10TH term, rule is 12-n
Answers
Answer:
When n is 1
12-n
=12-1
=11
When n is 2
12-n
=12-2
=10
When n is 3
12-n
=12-3
=9
When n is 4
12-n
=12-4
=8
When n is 10
12-n
=12-10
2PLEASE HELP ME AND MY DAUGHTER
Answers
Answer:
0.85
Step-by-step explanation:
The interquartile range of any given data set is simply the difference between the Q3 and the Q1, i.e. Q3 - Q1.
Let's find the Q3 and the Q1 of the given data set: 30.8, 29.9, 30.0, 31.0, 30.1, 30.5, 30.7, 31.0
First, let's order the data given in increasing order from small to the largest value:
29.9, 30.0, 30.1, 30.5, 30.7, 30.8, 31.0, 31.0
Let's find the median:
Since the number of data set given is even number (8), our median would be the average of the 4th and 5th data value = (30.5+30.7) ÷ 2 = 30.6
Let's find Q3 and Q1
Q1 is the middle value from the median point to our left = (30.0+30.1) ÷ 2 = 30.05
Q3 is the middle value from the median point to our right = (30.8+31.0)÷2 = 30.9
Interquartile Range = 30.9 - 30.05 = 0.85
Lisa collects rainwater in a large barrel that weights 25 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 108.4 pounds. when there are 20 gallons of water, the total weight is 191.8 pounds. What equation and graph math this situation?
Answers
Step-by-step explanation:
Hello!Plzz refer attachment for your answer.
What is a lifetime cap?
O A. A limit on how many loans a person can acquire in his or her
lifetime
O B. A limit on how much an ARM's interest rate can change over the
life of a mortgage
O C. A limit on how many years a loan can be for
OD. A limit on a loan's initial interest rate
SUS
Answers
Answer:
B) A limit on how much an ARM'S interest rate can change over there
I tried my best
stay at home stay safe
and keep rocking
V2 is in between what two numbers??
Answers
Answer:
sqrt of 2 is between 1 and 2
The square root of 2 is in between the square of one and the square of 2.
que son los angulos adyacentes
Answers
Answer:Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.
Step-by-step explanation:
Donna brought 2 baseball caps to school on Monday. Each day during that week, she brought twice as many baseball caps as the day before. How many baseball caps did Donna bring to school on Friday? *
Answers
Answer:
32 baseball caps
Step-by-step explanation:
[tex]Monday: 2\\Tuesday: 2*2=2^2=4\\Wednesday: 2*2*2=2^3=8\\Thursday: 2*2*2*2=2^4=16\\Friday:2*2*2*2*2=2^5=32[/tex]
She brought 32 baseball caps on Friday.
Circle C is inscribed in triangle QSU. Circle C is inscribed in triangle Q S U. Points R, T, and V of the circle are on the sides of the triangle. Point R is on side Q S, point T is on side S U, and point V is on side Q U. The length of Q R is 10, the length of R S is 2 x, the length of S T is x + 3, and the length of T U is 4. What is the perimeter of triangle QSU? 3 units 16 units 30 units 40 units
Answers
Answer:
I can confirm the answer is:
D. 40 units
Step-by-step explanation:
I just took the test on edge and got it right!
The perimeter of the Δ QSU is given as 40 units. (Option D). See explanation below.
What is the perimeter of Δ QSU?We can derive the perimeter by stating:
2x = x + 3 ⇒ x = 3
This is because Δ RSC ≅ Δ TSC
RS = 2 x 3 = 6 = ST
This is because ΔQRC ≅ ΔQVC
TV = VU = 4; we know this because
ΔCVU ≅ Δ CTU
Thus
QR = QV = 10
CΔQSU = 10 + 6 + 10 +14
= 40 Units.
Learn more about perimeter of triangles at:
https://brainly.com/question/24382052
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