In ADEF, e = 9.8 inches, f = 5.6 inches and ZD=149º. Find ZF, to the nearest 10th of
degree.
an
Answers
The angle measure of ∠F is approximately 66.9º.
What is an angle?
To find ∠F, we can use the Law of Cosines:
c² = a² + b² - 2ab cos(C)
Where c is the side opposite to the angle we want to find (in this case, side EF), a and b are the other two sides, and C is the angle opposite to side c (in this case, ∠F).
First, we need to find the length of side EF:
EF² = DE² + DF² - 2DE * DF cos(∠D)
EF² = (9.8)² + (5.6)² - 2(9.8)(5.6)cos(149º)
EF² ≈ 95.415
EF ≈ 9.769
Now, we can use the Law of Cosines again to find ∠F:
EF² = DE² + DF² - 2DE * DF cos(∠F)
cos(∠F) = (DE² + DF² - EF²) / 2DE * DF
cos(∠F) = ((9.8)² + (5.6)² - (9.769)²) / (2 * 9.8 * 5.6)
cos(∠F) ≈ 0.4035
∠F ≈ [tex]cos^{-1(0.4035)}[/tex]
∠F ≈ 66.9º (rounded to the nearest 10th)
Therefore, the measure of ∠F is approximately 66.9º.
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Complete question is: In ADEF, e = 9.8 inches, f = 5.6 inches and ZD=149º, the measure of ∠F is approximately 66.9º.
Related Questions
Find the difference:
16 16
Answers
Answer:
3 3/6 or 3 1/2 or 3.5
Step-by-step explanation:
Use the graph of the function,
f(x)=x-1/x^2+5x+6
to identify the function's
vertical asymptotes.
a. x=-1, x= 6
b. x=1, x=-6
c. x=-2, x=-3
d. X= 2, x= 3
Answers
Answer:
c. x = -2 or x = -3
Step-by-step explanation:
The vertical asymptotes occur where the denominator = 0. That happens when the f(x) is undefined. So,
x^2 + 5x + 6 = 0
(x + 2)(x + 3) = 0
x = -2 or x = -3
What type of sequence is this: an = 4 * 3(n-1)
Answers
Answer:
geometric sequence.
Step-by-step explanation:
Given the sequence an = 4 * 3(n-1)
The type of sequence written in this form is a geometric sequence. It is expressed Mathematically as;
an = ar^n-1
On comparison, we can see that;
a = 4
r = 3
a is the first term]
r is the common ratio
Factor the expression y^2+8x+12
Answers
Answer: y^2+8x+12
Step-by-step explanation:
Which statement about f(x) = 2x2 – 3x - 5 is true?
Answers
Answer:
-1, 5/2 ; f(x) = (x+1)(2x-5)
Step-by-step explanation:
2x² - 3x - 5 = 0
2x² - 5x + 2x - 5 = 0
x(2x - 5) +1(2x - 5) = 0
Factors are :
(2x - 5) = 0 ; (x + 1) = 0
2x - 5 = 0
2x = 5
x = 5/2
(x + 1) = 0
x = - 1
Zeros are ; x = 5/2 and x = - 1
help me with this question
Answers
b) set ^ this equation equal to the one on the paper, move the variable to one side, and the rest should be easy from there
c) he loses profits
Please help I was sick and missed out on class thank you.
Answers
Answer: slope=-5 and y-intercept=1
Step-by-step explanation:
The equation given is in slope-intercept form. Slope-intercept for is y=mx+b, where m is slope and b is y-intercept.
This gives m=-5 and b=1.
What is the first step in solving this equation ? y + 7 = 18
Answers
Answer:
subtract 7
Step-by-step explanation:
y+7=18
You need to get the y by itself, so you subtract 7 to cancel it out.
y+7=18
-7 -7
y=11
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hope it helps
1: What number must be multiplied by (5x + 6) to result in the expression 20x + 24?
2: On the first day of a road trip, you drive x miles.
On Day 2, you drive 10 more than twice the miles driven on Day 1.
On Day 3, you drive 100 miles less than Day 1.
Write an expression to represent the miles driven on each day of the road trip, then write a final simplified expression representing the total miles driven in three days.
a) Day 1:
b) Day 2:
c) Day 3:
d) Final simplified expression to represent total miles driven in three days:
e) Look at your expression for c) Day 3: "100 miles less than Day 1." Describe a real-word situation to explain why order matters when writing this expression.
Answers
1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.
2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:
a) Day 1: x
b) Day 2: 2x + 10
c) Day 3: x - 100
d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.
e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.
What is a mathematical expression?A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).
Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.
1) Multiplication:
(20x + 24) ÷ (5x + 6) = 4
Check:
4(5x + 6) = 20x + 24
2) Road Trip Expressions:
Day one driving distance = x miles
Day two driving distance = 2x + 10
Day three driving distance = x - 100
Total distance = x + 2x + 10 + x - 100
= 4x + 10 - 100
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In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year, 32 of the 44 online courses at this particular community college were taught by full-time faculty.
Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question.
Answers
Answer:
The p-value of the test is 0.5028>0.05, which means that there is sufficient evidence to determine that 68% represents the state in question.
Step-by-step explanation:
Test if 68% represents the state in question.
This means that at the null hypothesis, we test if the proportion is 68%, that is:
[tex]H_0: p = 0.68[/tex]
At the alternate hypothesis, we test if the proportion is different of 68%, that is:
[tex]H_a: p \neq 0.68[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.68 is tested at the null hypothesis:
This means that [tex]\mu = 0.68, \sigma = \sqrt{0.68*0.32}[/tex]
32 of the 44 online courses at this particular community college were taught by full-time faculty.
This means that [tex]n = 44, X = \frac{32}{44} = 0.7273[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.7273 - 0.68}{\frac{\sqrt{0.68*0.32}}{\sqrt{44}}}[/tex]
[tex]z = 0.67[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion differing by the population proportion by at least 0.7273 - 0.68 = 0.0473, which is P(|z| > 0.67), which is 2 multiplied by the p-value of z = -0.67.
Looking at the z-table, z = -0.67 has a p-value of 0.2514
2*0.2514 = 0.5028
The p-value of the test is 0.5028>0.05, which means that there is sufficient evidence to determine that 68% represents the state in question.
To find the next number in the sequence: 7, 10, 13, 16, ____ you would need to do which of the following?
Answers
Answer:
19. Add
Step-by-step explanation:
10 - 7 =
13 - 10 =
16 - 13 =
16 + 3 =
What is the value of x?
sin49°=cosx
Answers
Equations of Exponential Functions
Given the following equations of an exponential function
R = 10.5(0.535)t
determine the decay rate.
a. 0.535%
b. 10.5%
c. 50%
d. 46.5%
Please select the best answer from the choices provided
Answers
Answer:
D. 46.5%
Step-by-step explanation:
I calculated it logically
A pizza shop sold 18 medium pizzas. The number of large pizzas sold was 3 times as many as the number of medium pizzas sold. How many pizzas did the pizza shop sell altogether?
Answers
Answer:
18 × 3 = 54
18 + 54 = 72
Therefore, the answer is 72.
brainliest
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Answers
Jason spends no more than 20% of the money he earns at his job each week. He earns $80 each week for 4 weeks. Write an inequality that describes the total amount that Jason spends during this 4-week period.
Answers
9514 1404 393
Answer:
s ≤ 4(0.20×80)
Step-by-step explanation:
The maximum Jason spends each week is 0.20 × $80. Then the amount (s) he spends in 4 weeks will be less than or equal to 4 times this product.
s ≤ 4(0.20×80)
Sam has 6 choices of shirts, 4 choices of pants, 5 choices of socks, and 6 choices of shoes for his working dress. In how many ways Sam can select his outfit?
Answers
looooovvvvveeee these kinds of questions :D
anyways, there are 6 × 4 × 5 × 6=720 outfits
Lisette wrote the following algebraic expression to represent “4 times as large as the product of w and 11.”
Answers
The translation of the sentence "4 times as large as the product of w and 11" to an expression is 44w
How to translate the algebraic sentence to an expressionFrom the question, we have the following parameters that can be used in our computation:
“4 times as large as the product of w and 11.”
The number is represented with w
So, the statement remains unchanged as follows
“4 times as large as the product of w and 11.”
4 times as large means 4 *
So, we have the following representation
4 times as large as the product of w and 11 ⇒ 4 * the product of w and 11.
the product of means that we multiply
4 times as large as the product of w and 11 ⇒ 4 * w * 11
Evaluate the products
This gives
4 times as large as the product of w and 11 ⇒ 44w
Hence, the expression is 44w
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40% of an hour is what
Answers
Answer:
24 minutes
Step-by-step explanation:
100% = 60 minutes is 100%
So that means that 40% = 24 minutes.
Jose has a points card for a movie theater.
• He receives 50 rewards points just for signing up.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 85 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Jose can make to earn his first free movie ticket.
Answers
Answer:
x ≥ 10
Step-by-step explanation:
Total Points = 50 + 3.5x
Total Points ≥ 85
50 + 3.5x ≥ 85
3.5x ≥ 35
then divide both sides by 3.5
x ≥ 10
Explain the cyclin-dependent regulation
cell cycle
Answers
Cyclins drive the events of the cell cycle by partnering with a family of enzymes called the cyclin-dependent kinases (Cdks). A lone Cdk is inactive, but the binding of a cyclin activates it, making it a functional enzyme and allowing it to modify target proteins.
hope this helps!
Answer:
Cyclins drive the events of the cell cycle by partnering with a family of enzymes called the cyclin-dependent kinases (Cdks). A lone Cdk is inactive, but the binding of a cyclin activates it, making it a functional enzyme and allowing it to modify target proteins.
Step-by-step explanation:
Locating Fractions on a Number Line
A B
Hot
-2
-1
Intro
C
D
+++++
0 1 2
Use the drop-down menus to label the points on the
number line.
Point A is at
Point B is at
Point C is at
Point D is at
<
Done
Answers
On solving the provided question we cans ay that - order when writing it on the number line: = -1.25, -0.75, 0.25, 1.5, 2
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
The numbers on the number line must be
[tex]6/3 = 2\\-3/4 = -0.75\\1.5 = 1.5\\0.25 = 0.25\\-5.4 = -1.25\\[/tex]
In ascending order, t
[tex]-1.25 = -5/4\\-0.75 = -3/4\\0.25\\1.5\\2 = 6/3[/tex]
order when writing it on the number line:
-1.25, -0.75, 0.25, 1.5, 2
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BC is the diameter of the semicircle. The area of rectangle ABCD is 20 and the length of line AB is 5.What is the area of the semicircle?
Answers
Answer:
2[tex]\pi[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
BC is equal to 4 because 5*4=20.
The radius is 2. The equation for the area of a circle is [tex]\pi r^2[/tex].
Therefore, if we plug in 2 we will get [tex]4\pi[/tex].
But then we divide by 2 to get 2[tex]\pi[/tex] [tex]units^{2}[/tex] as our answer.
Hope this helped! :)
Solve this inequality for x.
Answers
Answer:
A. x ≥ 21[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
81 - 1[tex]\frac{1}{5}[/tex] x ≤ 55
-1[tex]\frac{1}{5}[/tex] x ≤ 55-81
-[tex]\frac{6}{5 }[/tex] x ≤ -26
x ≥ -26(-[tex]\frac{5}{6}[/tex]) **flip the inequality when you divide by a negative number
x ≥ 21[tex]\frac{2}{3}[/tex]
Which of the statements below is true for the following set of numbers? 20, 15, 50, 85, 75, 60
The range is 70 and the midrange 50 is .
The range and the midrange are equal.
The range is 85 and the midrange is 55.
The range is 70 and the midrange is 55.
Answers
Can someone help me with my last question for my hw plz
Answers
answer:
-4
explanation:
when reflected the a will be at -2 in the third quadrant, when moved 2 units to the left you get the y coordinate of -4
hope this helped!
this isn’t a question but i just wanted to tell everyone you all are doing great. this year has been hard and everyone is working as hard as they mentally can. i’m so proud of all of you. don’t forget to take breaks and rest.
Answers
Thank you so much friend.
I think a advantage of this will be that we will be able to tell our grandchildren about how we survived the pandemic, just like our grandparents talk about World War. Lol.
factorise y^6 - 64 as possible
Answers
Answer:
Step-by-step explanation:
Observe that [tex]y^6-64=y^6-2^6.[/tex]
And you factor out using this expression:
[tex](a^6-b^6)=(a-b)(a^5+a^4b+a^3b^2+a^2b^3+ab^4+b^5)[/tex]
Take a=y and b=2.
Answer:
(y - 2)(y + 2)([tex]y^{4}[/tex] + 4y + 16)
Step-by-step explanation:
[tex]y^{6}[/tex] - 64 ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
[tex]y^{6}[/tex] - 64
= (y² )³ - 4³
= (y² - 4)([tex]y^{4}[/tex] + 4y + 16) ← note y² - 4 is a difference of squares
= (y - 2)(y + 2)([tex]y^{4}[/tex] + 4y + 16)
Evaluate -3x³-4x for x = -1.
A)-1
B)7
C)1
Answers
Answer:
B) 7
Step-by-step explanation:
-3x³-4x =
-3(-1)³-4(-1) =
-3(-1)+4=
3+4 =7
Population Growth
Using the graph, find the value of 7 when x = 7.
a. = 7 c. y = 2.71
b. y = 6.1 d. y = 4.42
Please select the best answer from the choices provided
Answers
Answer:
D. y = 4.42
Step-by-step explanation:
I calculated it logically