In ΔOPQ, the measure of ∠Q=90°, the measure of ∠O=26°, and QO = 4.9 feet. Find the length of PQ to the nearest tenth of a foot.
The length of PQ is ____ ft.
Answers
Given:
In ΔOPQ, m∠Q=90°, m∠O=26°, and QO = 4.9 feet.
To find:
The measure of side PQ.
Solution:
In ΔOPQ,
[tex]m\angle O+m\angle P+m\angle Q=180^\circ[/tex] [Angle sum property]
[tex]26^\circ+m\angle P+90^\circ=180^\circ[/tex]
[tex]m\angle P+116^\circ=180^\circ[/tex]
[tex]m\angle P=180^\circ -116^\circ[/tex]
[tex]m\angle P=64^\circ[/tex]
According to Law of Sines, we get
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Using the Law of Sines, we get
[tex]\dfrac{p}{\sin P}=\dfrac{o}{\sin O}[/tex]
[tex]\dfrac{QO}{\sin P}=\dfrac{PQ}{\sin O}[/tex]
Substituting the given values, we get
[tex]\dfrac{4.9}{\sin (64^\circ)}=\dfrac{PQ}{\sin (26^\circ)}[/tex]
[tex]\dfrac{4.9}{0.89879}=\dfrac{PQ}{0.43837}[/tex]
[tex]\dfrac{4.9}{0.89879}\times 0.43837=PQ[/tex]
[tex]2.38989=PQ[/tex]
Approximate the value to the nearest tenth of a foot.
[tex]PQ\approx 2.4[/tex]
Therefore, the length of PQ is 2.4 ft.
Related Questions
Need help anything would help at this point !!!? Extra points
Answers
Answer:
here,radius =2 in
now use formula pie (r)^2 where pie is 3.14
=pie *(r)^2
=3.14*(2in.)^2
=3.14*4in.^2
12.56in.^2
Step-by-step explanation:
will give brainliest and 50 points
Given the inequality -8 < 2, explain what happens when you multiply or divide both sides by 2 and what happens when you multiply or divide both sides by -2.
Answers
when you divide -8/2=-4 and 2/2=1
-4<1
when you divide by a negative number your sign changes
4>-1
When you multiply or divide each side by 2, the signs stay the same. −16 < 4 and −4 < 1. When you multiply or divide by −2, the inequality sign reverses. 16 > −4 and 4 > −1.
Answer:
see below
Step-by-step explanation:
When multiplying or dividing an inequality by a positive, the inequality remains the same direction
3x < 6
Divide by 3
3x/3 < 6/3
x <2
When multiplying or dividing an inequality by a negative, the inequality changes direction
-3x < 6
-3x/ -3 > 6/-3
x > -2
Due to budget cuts the Fire Department only has one ladder which is 35 feet long. While rescuing a damsel from a burning house the ladder must be 12 feet from the base of the house. How high up the house can the ladder reach?
a. Draw a diagram that models the situation. Be sure to label it.
b. Write an equation that models the situation and solve it.
Answers
Answer:
good luck always brings luck the answer is 12
Step-by-step explanation:
Question 9 (1 point) Evaluate the expression: For k=4 6k3 la 64 b 24. 384
Answers
What additional piece of information
would prove ALMK = ANMK by
Side-Angle-Side?
Answers
Answer:
MK bisects <LKN
Step-by-step explanation:
We can already say two sets of sides are equal; LK = NK because it is given and MK = MK because of reflexive property. In order to use Side-Angle-Side, we need to prove the angles between the sides are congruent. This means <LKM and <NKM. The only option that would help is with the is the lat option, MK bisects <LKN because, then we could say <LKM and NKM are congruent because MK would be an angle bisector. This is exactly what we want, so the answer is MK bisects <LKN.
There were 3 chihuahuas at the dog park last Saturday, along with 9 other dogs. Considering this data, how many of the next 20 dogs to arrive at the park next Saturday should you expect to be chihuahuas?
Answers
Answer:
5
Step-by-step explanation:
Since there are 3 chihuahuas out of 12 dogs IN TOTAL (which includes the 9 other dogs), the ratio is 1:4, or 1/4.
Assuming this ratio is consistent, (1/4)*20 is 5.
In conclusion, you can expect there to be 5 chihuahuas out of the next 20 dogs to arrive at the park.
Hope it helped, and have a beautiful day/night! <3
The area of the region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.
(a, b) can't equal
Answers
The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units. So, all the options satisfy the value of a and b except (7, -9).
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.
Then summing all those pieces' area gives us the area of the main big region.
The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.
f(x) is a linear function, the area under the curve on the interval [0,4] is a trapezoid with a height of 4 and bases of lengths f(0) and f(4).
The area of a trapezoid is the height times the average of the bases.
a. f(x)=-2x+8 f(0)=8, f(4)=0;
area = 4(8/2) = 16
b. f(x)=x+2; f(0)=2, f(4)=6;
area = 4(8/2) = 16
c. f(x)=3x-2; f(0)=-2, f(4)=10;
area = 4(8/2) = 16
d. f(x)=5x-6; f(0)=-6, f(4)=14;
area = 4(8/2) = 16
e. f(x)=7x-9; f(0)=-9, f(4)=19;
area = 4(10/2) = 20
Thus, The area is NOT 16 for choice e.
Learn more about Area here:
https://brainly.com/question/13056790
#SPJ2
50 points!!!!! need answer ASAP
Answers
Answer:
the first option
Step-by-step explanation:
i believe
A gallon of gas costs $3.05 per gallon. Joey's car gets 35 miles per gallon on the highway and 27 miles per gallon in the city. Using the
highway, Joey drives at an average speed of 54 miles per hour, and it takes him 0.5 hours to get to work. The highway has one $1.25 toll.
Using a city street route, Joey drives at an average speed of 36 miles per hour, and it takes him 1 hour to get to work.
Which quantities would be used to determine the total cost for Joey to drive to work using the highway? Choose all that apply. A. 0.5 hours B. 1 hour C. $1.25 per car D. $3.05 per gallon E. 27 miles per gallon F. 35 miles per gallon G. 36 miles per hour H. 54 miles per hour
Answers
Answer:
The quantities that would be used to determine the total cost for Joey to derive to work using the highway are:
A. 0.5 hours
C. $1.25 per car
D. $3.05 per gallon
F. 35 miles per gallon
H. 54 miles per hour
Step-by-step explanation:
Cost of a gallon of gas = $3.05
Distance travelled per gallon on the highway = 35 miles
Distance travelled per gallon in the city = 27 miles
Joey's average speed using the highway = 54 miles per hour
Number of hours to get to work using the highway = 0.5 hours
Toll on the highway = $1.25
Joey's average speed using the city street route = 36 miles per hour
Number of hours to get to work using the city street route = 1 hour
Relevant data for highway driving total costs:
Cost of a gallon of gas = $3.05
Distance travelled per gallon on the highway = 35 miles
Joey's average speed using the highway = 54 miles per hour
Number of hours to get to work using the highway = 0.5 hours
Toll on the highway = $1.25
Total costs for using the highway = $1.25 + ($3.05/35 * 54 * 0.5) = $3.60
Answer:
A, B, D, F, H
Step-by-step explanation:
A pinwheel's four blades are all congruent right trapezoids.
4 in
2 in
2 in
What is the combined area of the four blades, in square inches?
Answers
Answer:
[tex]Area = 24\ in^2[/tex]
Step-by-step explanation:
Given
Let
[tex]a, b \to[/tex] opposite sides of each trapezoid
[tex]h \to[/tex] height
[tex]a = 2; \ \ \ b = 4 \ \ \ \ h = 2[/tex]
See attachment for trapezoids
Required
The combined area of the 4
First, we calculate the area of 1
[tex]Area = \frac{1}{2}(a + b) * h[/tex]
So:
[tex]A_1 = \frac{1}{2}(2 + 4) * 2[/tex]
[tex]A_1 = \frac{1}{2}*6 * 2[/tex]
Using a calculator
[tex]A_1 = 6[/tex]
The combined area is:
[tex]Area =n * A_1[/tex]
Where
[tex]n = 4[/tex] --- 4 blades
So:
[tex]Area = 4 * 6[/tex]
[tex]Area = 24\ in^2[/tex]
I am a 3-digit number divisible by 7, but not 2. The sum of my digits is 4. Hint it is not 121
Answers
Answer:
301
Step-by-step explanation:
3 + 0 + 1 = 4
301 / 7 = 43
301 / 2 = 105.5
Answer:
301
Step-by-step explanation:
301 divided by 7 = 43
301 is not divisible by 2
3 + 1 + 0 = 4
Hope this helps :)
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.
3 7 8 9 10 10 10 9 9 9 9 8 5
6 7 7 9 8 10 9 8 7 6 8 7 9
5 3 9 10 10 9 9 8 9 8 6 10 8
4 7 3 10 8 9 8 10 10 8 8
Develop a 95% confidence interval estimate of the population mean rating for Miami (to 2 decimals).
Answers
Answer:
The 95% confidence interval estimate of the population mean is (7.38, 8.46).
Step-by-step explanation:
Before building the confidence interval, we need to find the mean and standard deviation of the sample.
In this sample, there are 50 values.
Mean of the sample:
Sum of all values divided by the number of values.
With the help of a calculator, the mean is of 7.92.
Standard deviation:
Square root of the division of the sum of the difference squared between each value and the mean by the number of the values.
With the help of a calculator, the standard deviation is of 1.8958.
Confidence interval:
We have the confidence interval for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.01
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.01\frac{1.8958}{\sqrt{50}} = 0.54[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.92 - 0.54 = 7.38
The upper end of the interval is the sample mean added to M. So it is 7.92 + 0.54 = 8.46
The 95% confidence interval estimate of the population mean is (7.38, 8.46).
What is the mean of the data set below? Round to the nearest tenth when necessary. 96, 98, 56, 88
Answers
search up mean calculator
Which value is a solution of 7/4x^2-2=-0.5+4?
Answers
Answer:
x=√154 over 7 , −√154 over 7
Step-by-step explanation:
Answer:
the answer is that x=positive or negative square root of 22 over square root of 7
Step-by-step explanation:
la
You spend some time in the kitchen making sure the recipe is just right for
the cooking show. You spend 2 3/4 hours baking and half of an hour
cleaning up the kitchen. How much time were you in the kitchen?
Answers
Answer: 3¼ hours
Step-by-step explanation:
Number of hours used in baking = 2¾ hours
Number of hours used in cleaning up the kitchen = ½ hour
Therefore, the time used in the kitchen will be the addition of the time used in baking plus the time used in cleaning the kitchen which will be:
= 2¾ + ½
= 2 3/4 + 2/4
= 2 5/4
= 2 + 1¼
= 3¼ hours
Therefore, 3¼ hours was used in the kitchen.
7m + 3mn
when m = 3 and n = -4
Answers
Answer:
-15
Step-by-step explanation:
When m=3 and n=-4
So, put the values
7(3)+3(3)(-4)
-> -15
Answer:
-15
Step-by-step explanation:
= 7(3) + 3(3)(-4)
= 21 + 3(3×-4)
= 21 + 3(-12)
= 21 + -36
= 21-36
= -15
PLS HELPPPP ! I need itttt
Answers
Answer:
x = 10
Step-by-step explanation:
find the area of the figure
area: units2
Answers
Answer:
Area of the figure = 25 square units
Step-by-step explanation:
Area of the given figure = Area of ΔCDE + Area of rectangle BCEI + Area of ΔABH + Area of GIF
Area of ΔCDE = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(CE)(DK)[/tex]
= [tex]\frac{1}{2}(8)(4)[/tex]
= 16 units²
Area of rectangle BCEI = Length × Width
= CE × EI
= 8 × 1
= 8 units²
Area of ΔABH = Area of ΔGIF = [tex]\frac{1}{2}(1)(1)[/tex]
= [tex]\frac{1}{2}[/tex] units²
Area of the complete figure = 16 + 8 + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex]
= 25 units²
what is the answer (x + 3)2 – 5 = 0
Answers
x= -1/2 is the answer to your question. Mark as brainliest!!!!
Find the measure of angle QZT.
Answers
========================================================
Explanation:
Minor arc QV is 80 degrees because it adds to minor arc VU = 100 to get 80+100 = 180. Note how angle QPU = 180, since it's a straight line and QU is a diameter of the circle.
Add up the minor arcs
TUUVVQto get: 44+100+80 = 224
This means arc TUQ is 224 degrees. Inscribed angle QZT subtends arc TUQ. Use the inscribed angle theorem to say that the inscribed angle is half of the arc it cuts off.
angle QZT = (arc TUQ)/2
angle QZT = 224/2
angle QZT = 112 degrees
3. What is the missing term in the sequence 10, 12, 16, 24,
, 72?
A. 32
B. 40
C. 48
D. 64
4. What rule is being used in this sequence 25, 28, 26, 29, 27?
A. Add 3.
B. Add 3, subtract 2...
C. Subtract 3, add 2...
D. Multiply by 3, subtract 2...
5. What is the value of kin 6k - 19 = 23?
A. 14
B. 11
C. 7
D. 5
Answer pls. ASAP Need it now
Answers
Answer:
3. B
4. B
5. C
Step-by-step explanation:
J.UIV1.2.2 DUN 2 formative Jackson, Braddyn OO 10 1 Abox, shaped like a rectangular prism, is shown below. 2 in. 8 in. 10 in. What is the surface area of the box? 232 square inches 160 square inches 116 square inches O 96 square inches ?
Answers
Answer:m
Step-by-step explanation:
guys please help its my final either i pass or not
Answers
Answer:
Step-by-step explanation:
1 yes 2 no 3 no 4 yes 5 no
Answer:
1. yes
2. yes
3. no
4. yes
5. no
Step-by-step explanation:
go to mathwa* and type in the same equation and click to see if function or not.
gl on the final
this guy above me is wrong for #2
Y-intercept = -4
• Slope = -1
2
y
10
9
8
2
6
5
4
3
2
-10
-9
-8
-7
-6
-5
- 4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
2
-3
-4
-5
-6
-7
-8
-9
-10
Answers
Answer:
First point: -4 on y axis.
Second point: (2, -5)
Step-by-step explanation:
When graphing, we always set the equation as y=mx+b where m = slope and b = y intercept
y = mx + b
y = [tex]-\frac{1}{2}x-4[/tex]
Then we plot by starting with the y intercept going four units down, one unit below and two units to the right.
Which expression is equivalent to 1/3b - 7
Answers
Answer:
The answer Is 1/3(b-21)
Step-by-step explanation:
A soccer ball is kicked from the top of a 64 ft building into the air at an initial speed of 48 ft/sec. Its flight as a functions of time can be modeled by: h(t)=−16t2+48t+64. After how many seconds, will the soccer ball hit the ground (h=0)?
Answers
Answer:
t = 4 seconds
Step-by-step explanation:
The height of a soccer ball as a function of time is given by :
[tex]h(t)=-16t^2+48t+64[/tex]
We need to find the time when the ball hit the ground i.e. h = 0
Put h = 0 in above equation. So,
[tex]-16t^2+48t+64=0\\\\16(-t^2+3t+4)=0\\\\-t^2+3t+4=0[/tex]
It is a quadratic equation such that,
t = -1 s and t = 4 s
Neglecting -1 s, the ball will hit the ground after 4 seconds.
Help ur homie out pls
Answers
I'm still doing the rest but number 1 is D
HELP! Will give branliest!
Answers
Answer:
angle 1 is 99
angle 2 is 81
Step-by-step explanation:
3x+x+48=180
4x+48=180
4x=132
x=33
Que sucede cuando dividimos un numero entre si mismo
Answers
Answer:
no pasa nada
Step-by-step explanation:
espero que eso te ayude:)
Answer:
Cualquier número dividido entre si mismo da como resultado 1
A recipe book has 24 appetizer recipes
and 37 dessert recipes. There are 10
more dinner recipes as appetizer and
dessert recipes combined. How many
recipes are in the book in all?