Answers
Step-by-step explanation:
2 things to remember for problems like this :
the sum of all angles in a triangle is always 180 degrees.
the law of sines :
a/sin(A) = b/sin(B) = c/sin(C) or upside-down (whatever fuss the situation better), with the sides being always opposite of the angles.
so, now for the given problems :
4.
x/sin(90) = 12/sin(29)
x/1 = x = 12/sin(29) = 24.75198408...
rounded x = 24.8
5.
the opposite angle of x is
180 - 90 - 16 = 74 degrees.
x/sin(74) = 37/sin(90) = 37
x = 37×sin(74) = 35.56668275...
rounded x = 35.6
6.
the opposite angle of x is
180 - 90 - 58 = 32 degrees.
x/sin(32) = 22/sin(58)
x = 22×sin(32)/sin(58) = 13.74712574...
rounded x = 13.7
7.
the opposite angle of 15 is
180 - 90 - 51 = 39 degrees.
x/sin(51) = 15/sin(39)
x = 15×sin(51)/sin(39) = 18.52345735...
rounded x = 18.5
Related Questions
Elizabeth invested $970 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 % compounded daily. Matthew invested $970 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 % compounded continuously. After 8 years, how much more money would Matthew have in his account than Elizabeth, to the nearest dollar?
Answers
Using continuous compounding and compound interest, it is found that Matthew would have $17 more than Elizabeth in his account.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
Continuous compounding:
[tex]A(t) = Pe^{rt}[/tex]
The parameters are:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For both of them:
Investment of $970, hence [tex]P = 970[/tex]Invested for 8 years, hence [tex]t = 8[/tex]Elizabeth:
Compounded daily, hence [tex]n = 365[/tex].Rate, as a percent, of [tex]6\frac{5}{8} = 6 + \frac{5}{8} = 6.625[/tex], hence [tex]r = 0.06625[/tex].Then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(8) = 970\left(1 + \frac{0.06625}{365}\right)^{365(8)}[/tex]
[tex]A(8) = 1648[/tex]
Matthew:
Rate, as a percent, of [tex]6\frac{3}{4} = 6 + \frac{3}{4} = 6.75[/tex], hence [tex]r = 0.0675[/tex].Then:
[tex]A(t) = Pe^{rt}[/tex]
[tex]A(8) = 970e^{0.0675(8)}[/tex]
[tex]A(8) = 1665[/tex]
The difference is:
1665 - 1648 = 17
Hence, Matthew would have $17 more than Elizabeth in his account.
A similar problem is given at https://brainly.com/question/24507395
Lee earns $17.00 per hour at her job. How much money will Lee earn if she works for 4 hours?
Answers
find 3 1/6 + (-4 1/3).
Answers
Answer:
-1 1/6
Step-by-step explanation:
[tex]3\frac{1}{6} + (-4\frac{1}{3} )[/tex]
Convert the mixed numbers into improper fractions
[tex]\frac{19}{6} + (-\frac{13}{3} )[/tex]
Apply the rule: a + (-b) = a - b
[tex]\frac{19}{6} + (-\frac{13}{3} ) = \frac{19}{6} - \frac{13}{3}[/tex]
The Least Common Multiplier of 6 and 3 is 6
Adjust the fractions on the LCM
[tex]\frac{19}{6} - \frac{26}{3}[/tex]
Apply the Fraction Rule: [tex]\frac{a}{c} -\frac{b}{c} = \frac{a - b}{c}[/tex]
[tex]\frac{19 - 26}{6}[/tex]
Subtract the numbers
[tex]\frac{-7}{6}[/tex]
Apply the Fraction Rule: [tex]\frac{-a}{b} = - \frac{a}{b}[/tex]
[tex]-\frac{7}{6}[/tex]
Convert improper fraction into a mixed number
[tex]-1\frac{1}{6}[/tex]
Hope this Helps :)
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] = 14
Answers
Answer:
This Inequality has no solution making it false.
Step-by-step explanation:
(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] = 14
5,069=322
False
Hope this helps :)
Answer:
Step-by-step explanation:
Line A is represented by the following equation: x + y = 2
What is most likely the equation for line B so the set of equations has no solution?
Answers
Answer:
[tex]ax+ay=k; a\ne0, k\ne2a[/tex]; line D in the options.
Step-by-step explanation:
The set of equations has no solutions if the two lines are parallel. A quick way to create a parallel line is to solve for y, put it in slope-intercept form. Else, as long as the cofficient of x and y are in the same ratio (in this case 1:1), the two lines are parallel, you just have to be careful not to pick the same line again!
The condition [tex]a\ne 0[/tex] makes sure you are still getting lines (else you would get rid of both x and y); the condition [tex]k\ne 2a[/tex] makes sure you're not picking line A again, just written in a different form.
Now that we have the options:
A and C have a different ratio for the coefficient of x and y (2:1 and 1:2) so are not good.
Choice B is just a more complicated way to write the same line, you can see by dividing both sides by 2 and get back x+y=2.
Line D is correct.
four more than the price ,p
Answers
Help me I really don’t understand this and I can’t fail please just please help I will mark brainliest
Answers
Answer:this question is confusing but it's probably the last one, must be the one passing through
x=1
y=-1
Marking Brainlest! 20pts. Thanks
The scatter plot shows the relationship between the average number of nightly customers and the number of months since a restaurant opened. The equation represents the linear model for this data.
y = 5x + 120
What does the number 5 in the equation mean in this context?
A. There were 5 customers per night when the restaurant opened.
B. The average number of customers per night decreased by 5 each month.
C. The restaurant has been open for 5 months.
D. The average number of customers per night increased by 5 each month.
Answers
Answer:
the answer is C trust me by
Your Fourthknight team is holding a fundraiser. The list shows all expenses for the fundraiser.
- A tablet that costs $250
- Soccer tickets that cost $150
- Gift cards totaling $425
- The cost of catering is $875
The members of the team will sell tickets at the fundraiser. The ticket cost is set so that 68 tickets will pay for the cost of prizes and food.
How much does each ticket cost?
Model the profit for the fundraiser using an equation:
Answers
Answer:
25
Step-by-step explanation:
Because when you add all the cost and divide by the amount of tickets you get 25
after working out for 45 minutes, Juanita heartbeat at 75 beats in 30 seconds what equation represent the relatship of b and m
Answers
Answer:
abcdefghijklmnopqrstuvwxyz
-8/9 - (2 1/3)
show all your work
Answers
Answer:
1 8/9 - 1 2/3 = 2/
9
≅ 0.2222222
Step-by-step explanation:
How do you solve fractions step by step?
Conversion a mixed number 1 8/
9
to a improper fraction: 1 8/9 = 1 8/
9
= 1 · 9 + 8/
9
= 9 + 8/
9
= 17/
9
To find a new numerator:
a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/
9
= 9/
9
b) Add the answer from previous step 9 to the numerator 8. New numerator is 9 + 8 = 17
c) Write a previous answer (new numerator 17) over the denominator 9.
One and eight ninths is seventeen ninths
Conversion a mixed number 1 2/
3
to a improper fraction: 1 2/3 = 1 2/
3
= 1 · 3 + 2/
3
= 3 + 2/
3
= 5/
3
To find a new numerator:
a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/
3
= 3/
3
b) Add the answer from previous step 3 to the numerator 2. New numerator is 3 + 2 = 5
c) Write a previous answer (new numerator 5) over the denominator 3.
One and two thirds is five thirds
Subtract: 17/
9
- 5/
3
= 17/
9
- 5 · 3/
3 · 3
= 17/
9
- 15/
9
= 17 - 15/
9
= 2/
9
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(9, 3) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 3 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - seventeen ninths minus five thirds = two ninths
The degree of polynomial is ?
Answers
the rate of change is _____ inches of growth per week
Answers
Answer:
4.5 inches per week
Step-by-step explanation:
Easy conversions
14. Find m
(9x + 2)
(15x -52)
Answers
Step-by-step explanation:
triangle BCD ~ triangle EFD so
angle BCD= angle EFD
9x+2=15x-52
6x=54
x=9
angle CBF =9x+2=83°
In the triangle ΔCBD, the angle measure of ∠CBF is 83°.
What are similar triangles?When the triangles have equal shape, but different sizes. It is called as similar triangles. The corresponding angles are congruent. And the sizes have the same proportionality rate.
Given:
The angle measures,
∠CBD = (9x + 2)°
∠EFD = (15x -52)°
From the diagram,
ΔCBD is similar to ΔEFD.
So, the corresponding angles are equal.
∠CBD = ∠EFD
(9x + 2)° = (15x -52)°
15x - 9x = 52 + 2
6x = 54
x = 9°
And ∠CBF = ∠CBD
So, ∠CBF = (9x + 2)°
Substituting the value of x,
∠CBF = (9(9) + 2)°
∠CBF = 83°
Therefore, the angle measure of ∠CBF is 83°.
To learn more about the similar triangles;
https://brainly.com/question/14926756
#SPJ2
May ALG 1A Unit 5 Modified Discussion
Answers
A pattern that increases or decreases at a constant rate is a linear function
Question 1 represents a linear functionQuestion 2 and 3 represent a nonlinear functionQuestion 1
From the table, we see that:
As x increases by 25, The value of y decreases by 1The rate of increment/decrement is constant for both variables.
Hence, question 1 represents a linear function
Question 2
From the table, we see that:
As x increases by 2, The value of y increases at different ratesThe rate of increment is not constant for variable y.
Hence, question 2 represents a nonlinear function
Question 2
From the table, we see that:
As the steps (i.e. x) increases by 1, The number of blocks (i.e. the value of y) increases at different ratesThe rate of increment is not constant for variable y.
The complete table is:
[tex]\mathbf{Step\to Blocks}[/tex]
[tex]\mathbf{1 \to 2}[/tex]
[tex]\mathbf{2 \to 6}[/tex]
[tex]\mathbf{3 \to 12}[/tex]
[tex]\mathbf{4 \to 20}[/tex]
Hence, question 3 represents a nonlinear function
Read more about patterns and rates at:
https://brainly.com/question/22386004
what is 6.30 divided by 18
Answers
Answer:
6.3/18 = 0.35
Step-by-step explanation:
0.35 is your answer
Write the equation of a line that
passes through the following points
:
Point 2: (0,-8)
Point 1: (-3,0)
Answers
Answer:
[tex]y = \frac{-8}{3}x - 8[/tex]
Step-by-step explanation:
Solving for the equation of the line with two points:
Let's remind ourself of the slope - intercept formula: [tex]y = mx + b[/tex]
We first have to find the slope of the line. This is found by using the formula :
[tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]
We have to find the change in y (Δy) and divide it by the change in x (Δx)
We then have to plug in a coordinate given to us, and use the point's x and y value to find the y - intercept
Step 1: SlopeLet's use the slope formula
[tex]\frac{0 - (-8)}{-3 - 0} = \frac{8}{-3}[/tex]
Slope = -8/3
Step 2: Y - InterceptTo find the y - intercept, we'll update our slope - intercept formula with the slope, and plugin a point. Let's use (-3,0)
[tex]y = \frac{-8}{3}x + b[/tex]
[tex]0 = \frac{-8}{3}(-3) + b[/tex]
[tex]0 = \frac{24}{3} + b[/tex]
[tex]0 = 8 + b[/tex]
[tex]b = -8[/tex]
Step 3: EquationLet's input our slope and y - intercept to the equation [tex]y = mx + b[/tex]
Slope = -8/3
Y - Intercept = -8
Equation: [tex]y = \frac{-8}{3}x - 8[/tex]
-Chetan K
4.99 for 13lb find the unit rate
Answers
Answer:
$0.38 per lb.
Step-by-step explanation:
unit rate formula; cost / quantity
4.99 / 13 = 0.3838461538461
round to the nearest hundredth
Miko filled two tanks with water. The ratio of the amount of water in Tank A to Tank B is 3 : 2. The total amount of water in both tanks is 210 ℓ. How much water must Miko pour from Tank A into Tank B so that both tanks have the same amount of water?
Answers
Step-by-step explanation:
answer is in the above picture
The Cougars, a football team, must gain 10 yards in the next four plays to keep possession of
the ball. The Cougars gain 5 yards, lose 12 yards, gain 14 yards, and finally lose 8 yards. Do
the Cougars keep possession of the ball?
Answers
Answer:
No
Step-by-step explanation:
Gain 5= 5 to go
Lose 12= 7 to go
Gain 14= 7 to go
Lose 8=15 to go
what is 29,032 to the nearest thousands
Answers
Answer:
29,000
Step-by-step explanation:
Answer:
30,000 i believe
Step-by-step explanation:
if that isnt the right answer then its just 29,000
Can someone pls help me
Solve for x
Please show your work
Answers
Answer:
Hence, the value of x is 9°
Step-by-step explanation:
7x + 14 = 9x - 4. [(Corres. ∠s]
⇛ 7x - 9x = -4 - 14
⇛-2x = -18
⇛x = -18÷-2
⇛x = 18/2
∴ x = 9
NOW,
7X + 14 = 7(9) + 14 = 63 + 14 = 77°.9X-4 = 9(9) - 4 = 81 - 4 = 78°.Read more:
Similar Question
find the measure of angle 1, given that AB || CD...
https://brainly.com/question/3983123?referrer
someone please help me asap
Answers
Answer:
I only can see that one of them are B i don't know for the rest
Step-by-step explanation:
What dp they mean 2 to the fourth equal 16.
Answers
Answer:
See Below
Step-by-step explanation:
I think you mean 2 the the fourth power, showing 2, with an exponent of 4.
To calculate this, you multiply your base, 2, by itself as many times as the exponent states. Like, 2x2x2x2 because you are multiplying it 4 times by 2.
2x2=4, then 4x2=8, then 8x2= 16.
Hope this helps!
Please help me with this question
I can't figure it out and please answer all of it
Answers
Step-by-step explanation:
1. False
2. True
3. True
4. False
Answer:
a. false
b. true
c. true
d. false
Step-by-step explanation:
hope this is right
(if not tell me in the comments and i will try to help you best i can)
the choices for the first one is either x values or y-values
Answers
Answer:
x values
division
Step-by-step explanation:
Vertical lines are all "rise" and no "run"
therefor the difference in x values is always 0
division by 0 is undefined
Answer: y- values
Step-by-step explanation:
.15 x (-0.6)
help me please
Answers
The answer is −0.09
It should be simple multiplication.
I hope this helps!
Ten times the sum of a number and 12 is 84.
Answers
Answer:
12×10 = 120
NOT 84
THE ANSWER IS 120
emma makes 21 laps during a 5 minute song how many laps per minute did emma make how do I show my work?
Answers
Answer:
4.2 laps per minute
Step-by-step explanation:
21laps/5min = 4.2laps/1min
write a linear function
Answers
Answer:
The equation of a linear function is expressed as: y = mx + b where m is the slope of the line or how steep it is, b represents the y-intercept or where the graph crosses the y-axis and x and y represent points on the graph.
Step-by-step explanation: