Andre and Mai are discussing how to solve for side AB. Andrethinks he can use the equation tan(12) = 3 to solve for AB.Mai thinks she can use the equation tan(78) = to solve forAB. Do you agree with either of them? Show or explain yourreasoning.
Answers
Tangent ratio is the ratio between the opposite and the adjacent sides to given angle.
It depends on the given angle to stablish which is the adjacent and which is the opposite side.
For example, for the angle that measures 12°, the opposite side is the one that measures x and the adjacent is the one that measures 6, it means:
\(\tan 12=\frac{x}{6}\)For the other angle, the one that measures 78, the opposite side now is the one that measures 6 and the adjacent is the one that measures x, it means:
\(\tan 78=\frac{6}{x}\)It means that both Andre and Mai are correct.
Related Questions
Write an equivalent fraction for 15 over 20 by simplifying the fractions. Reduce the following to their lowest terms. Write an equivalent fraction for 33 over 88 by simplifying the fractions. Reduce the following to their lowest termsWrite an equivalent fraction for81 over 120 by simplifying the fractions. Reduce the following to their lowest terms
Answers
Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.
To get an equivalent fraction, the numerator and the denominator of one fraction are either multiplied or divided by the same constant number to produce the equivalent fraction.
Part A:
To reduce a fraction to its lowest term, we divide both the numerator and the denominator by a constant number.
Dividing both the numerator and denominator by 5
\(\begin{gathered} \frac{15}{20} \\ \frac{15}{20}=\frac{\frac{15}{5}}{\frac{20}{5}}=\frac{3}{4} \\ \frac{15}{20}=\frac{3}{4} \end{gathered}\)Therefore, an equivalent fraction in its lowest term for
\(\frac{15}{20}\text{ is }\frac{3}{4}\)Part B:
Dividing both the numerator and denominator by 11
\(\begin{gathered} \frac{33}{88} \\ \frac{33}{88}=\frac{\frac{33}{11}}{\frac{88}{11}}=\frac{3}{8} \\ \frac{33}{88}=\frac{3}{8} \end{gathered}\)Therefore, an equivalent fraction in its lowest term for
\(\frac{33}{88}\text{ is }\frac{3}{8}\)
Part C:
Dividing both the numerator and denominator by 3
\(\begin{gathered} \frac{81}{120} \\ \frac{81}{120}=\frac{\frac{81}{3}}{\frac{120}{3}}=\frac{27}{40} \\ \frac{81}{120}=\frac{27}{40} \end{gathered}\)Therefore, an equivalent fraction in its lowest term for
\(\frac{81}{120}\text{ is }\frac{27}{40}\)Given the vectors shown, find the sum (P+Q+R).
Answers
An employee started a new job and must enroll in a new family health insurance plan. One of the options involves prescription drug coverage. The employee estimates that the entire family will fill 6 prescriptions per month, totaling $850. The monthly premium for the plan is $48, with 90% coverage for the first $450 in prescription costs, then 80% coverage for all prescription costs over $450. What is the total out-of-pocket expense for one month?
$173
$125
$773
$677
Answers
The total out-of-pocket expense for one month is $677. The correct option is D.
The first step is to calculate the amount of the prescription costs that will be covered by the insurance plan.
Since the family will fill 6 prescriptions per month and the total cost is $850, the average cost per prescription is $850/6 = $141.67 per prescription.
The insurance plan covers 90% of the first $450 in prescription costs, which is $450 * 0.9 = $405.
The remaining $141.67 - $405 = -$263.33 of the first prescription is not covered, since it is below the $450 threshold. This means that the family will have to pay the full cost of the first prescription, and the insurance will not contribute anything to it.
For the remaining 5 prescriptions, the insurance will cover 80% of the cost, since they are over the $450 threshold. The remaining 20% will be the family's responsibility.
The cost of the remaining 5 prescriptions is $141.67 x 5 = $708.35.
The insurance will cover 80% of this amount, which is $708.35 x 0.8 = $566.68.
The family will be responsible for the remaining 20% of the cost, which is $708.35 x 0.2 = $141.67.
Adding up all the costs, the total out-of-pocket expense for one month is:
$405 (first prescription) + $141.67 (20% of remaining prescription costs) + $48 (monthly premium) = $594.67
Therefore, the correct answer is option D: $677.
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Help!!!!!!!!!!!!!!!!
Answers
Answer:
13.8
Step-by-step explanation:
We know that 1 inch is 9.2 miles. The houses are 1.5 inches away. We need to divide 9.2 by 2. We get 4.6. 9.2+4.6=13.8!
13.8
A researcher wanted to determine the number of televisions in households. He conducts a
survey of 40 randomly selected households and obtained the data to the right. Draw a dot plot of
the televisions per household.
Choose the correct dot plot below.
O A.
0 1 2 3 4 5
Numb of Televisions
OB.
H
0 1 2 3 4 5
Number of Televisions
Q
OC.
LL
0 1 2
3 4 5
Number of Televisions
LV
1
2
1
2
1
1
2
5 2 3
2
2
3
1
1
2 2
1
3 2
3
1
2
1
2 2
3₁
3
O D.
2
1
5
0
2
3
2
10
3
3
3
1
:
T
0 1 2 3 4 5
Number of Televisions
Q
Answers
Answer:The correct dot plot is:
Step-by-step explanation:
LV
1
2
1
2
1
1
2
5 2 3
2
2
3
1
1
2 2
1
3 2
3
1
2
1
2 2
3₁
3
In this dot plot, each dot represents one household, and its position on the vertical axis corresponds to the number of televisions in that household. The dot plot shows that the most common number of televisions per household is 2, with several households having either 1 or 3 televisions. There are also a few households with 5 televisions.
Orlando and Nancy are scuba diving. Orlando is at an elevation of -60 feet, and he is descending at a rate of 8 feet per minute. Nancy is at an elevation of -35 feet and she is descending at a rate of 12 feet each minute. The variable t represents the time in minutes. After how many minutes will Orlando and Nancy be at the same elevation? At what elevation will they be at that time?
Answers
Answer:
Orlando and Nancy will be at an elevation of -110 when they are at the same elevation.
Step-by-step explanation:
We can set up an equation to find the time it takes for Orlando and Nancy to be at the same elevation
We will use the variable T to represent the time in minutes
Orlando's elevation : -60 + 8t
Nancy's elevation : -35 + 12t
We will solve for t to see at what time the elevations were equal
-60 + 8t = -35 + 12t
-60 + 35 = 12t - 8t
-25 = 4t
4t = -25
t = -6.25
This means that both will be at the same elevation 6.25 minutes before Orlando goes down
To find the elevation they will be at that time, we will plug -6.25 into either expression.
-60 + 8t = -60 + 8(-6.25) = -110
Orlando and Nancy will be at an elevation of -110 when they are at the same elevation.
Graph this point on the coordinate plane.
(−412, −2)
Answers
The given coordinate point lies in third quadrant which shown in the graph below.
The given coordinate point is \((-4\frac{1}{2}, -2)\).
A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
In the given coordinate point both x-coordinate and y-coordinate are negative.
Hence, the given coordinate point lies in third quadrant which shown in the graph below.
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There are 78 students in the fourth grade 39 of them are girls
Answers
Answer:
This means that the answer is 39
Step-by-step explanation:
if u subtract 78 from 39 u get 39 just as if u add 39 + 39= 78.
Which of the following equations is equivalent to 7 = 2y + 9?
a.) -3 = 2y + 1
b.) 8 = 9y - 1
c.) -4 = 2y + 6
d.) -2 = y – 1
Answers
Answer:
d.) -2 = y – 1
Step-by-step explanation:
Solve using tangent and cosine
Answers
The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.
What are the sides of the triangle labelled x?The figures in the image are right triangles.
A)
angle D = 17 degree
Adjacent to angle D = 14 mm
Opposite to angle D = x
To solve for the missing side length x, we use the trigonometric ratio.
Note that: tangent = opposite / adjacent
Hence:
tan( 17 ) = x/14
x = tan( 17 ) × 14
x = 4.3mm
B)
angle Z = 82 degree
Adjacent to angle Z = 43.1 m
Hypotenuse = x
Using trigonometric ratio,
cosine = adjacent / hypotenuse
cos( 82 ) = 43.1 / x
x = 43.1 / cos( 82 )
x = 309.7 m
Therefore, the measure of x is 309.7 meters.
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x^(2)+y^(2)+14x+18y+114=0
i will give u brainliest and my eternal love
Answers
Answer:
(x+7)^2+(y+9)^2=16
Step-by-step explanation:
This is the equation written in standard form, I'm not sure if that's what you wanted.
2.1. Provide a general rule to describe the relationship between the dates of spread and number of people infected infected.
Answers
The relationship between the dates of spread and the number of people infected can vary depending on various factors such as the infectiousness of the disease, the effectiveness of containment measures, population density, and individual behaviors.
However, there is a general rule that can describe the relationship:As the dates of spread progress, the number of infected individuals tends to increase initially, reaching a peak, and then gradually decreasing over time.
This pattern is often referred to as the epidemic curve or the epidemiological curve. In the early stages of an outbreak, the number of cases may grow rapidly as the disease spreads through a susceptible population. This rapid increase is often influenced by factors such as the contagiousness of the disease, population density, and social interactions.
As containment measures, such as vaccination campaigns, public health interventions, and behavioral changes, are implemented, the rate of new infections may start to decline. This can lead to a peak in the number of cases, after which the curve gradually decreases as the disease is brought under control and fewer susceptible individuals remain.
It's important to note that the specific shape, duration, and magnitude of the epidemic curve can vary significantly depending on the disease and the effectiveness of the response measures implemented. Additionally, emerging variants, changes in behavior, and other factors can impact the trajectory of the epidemic curve.
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find the range of values of a for which 11- 2a>1 is ____
Answers
Answer:
a<5
Step-by-step explanation:
11-2a>1
-2a>1-11
-2a>-10
a<5
74 pages·4 MB
Please help me solve this! also this is proportions by parts
Answers
Answer:
dat easy
Step-by-step explanation:
The top of a kitchen table measures 160cm by 90cm. A beetle walks diagonally across the table from one corner to the other. Calculate how far the beetle walks.
Answers
Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."
So, applying the Pythagorean theorem, we have:
d^2 = 160^2 + 90^2
Simplifying:
d^2 = 25600 + 8100
d^2 = 33700
Taking the square root of both sides:
d ≈ √33700
d ≈ 183.54 cm
Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.
Jaylin Earned $36 for 3 hours of work and $60 for 5 hours of work. What is the Constant of Proportionality?
Answers
Explanation
36 divide by 3 = 12
60 divide by 5 = 12
So twelve is your answer
At a high school reunion of a class of 620 students, a quick poll wasconducted. There were two questions asked; Did you graduate fromcollege and do you have a family?242 people graduated from college• 58 of graduates said yes to both• 68 people answered no to both questionsCreate a Venn Diagram based on the information above. Label the circles.
Answers
We can graph in a Venn Diagram as follows:
Here GC represents "graduated from college", HF represents "Has family" and N represents "None to both questions".
So I have a grade of 100.6 (an A+) and I had this assignment that was due a while ago (that was 15 points) and now I’m not allowed to turn it in. What would be my grade now that I didn’t do that assignment?
Answers
Answer:
maybe an 80 or 90
Step-by-step explanation:
Which problem solving strategy would be best to solve this problem?
Brandon went to the store and spent $2.50 on pencils. He spent half of what he had left on a notebook and paper. When he got home he had $5.00 left. How much money did Brandon have before going to the store?
Answers
Answer: The best problem solving strategy to solve this problem with is a formula. Additionally Brandon had $12.50 before going to the store.
Step-by-step explanation: Formula and Solving it
He Spent $2.50 on pencils.
Amount left after buying a pencil = x - 2.50
Next, he spent half of the amount left in his pocket.
He spent (x - 2.50)/2 on notebook and paper.
So the total amount he spent = 2.50 + (x -2.50)/2
Amount left when he got home =$ 5.00
That means, x - Total amount spent = 5
=> x - (2.50 + (x -2.50)/2 ) = 5
=> x - 2.50 -x/2 + 2.50/2 = 5
=> x/2 - 2.50/2 = 5
=> x/2 = 5 + 2.50/2
=> x/2 = 6.25
=>x = $12.5
Cual es el suplemento del angulo de 134 grados
Answers
Answer:
El suplemento es 46°
Step-by-step explanation:
180° -134° = 46°
Answer:
46
Step-by-step explanation:
supplement = 180
180-134 = 46
PLEASE HELP THIS IS HARD
Answers
The Area of the shaded portion is: 72 square inches
What is the Area of the shaded region?The formula for the area of a triangle is given by the formula:
Area = ¹/₂ * base * height
Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.
Thus:
Area of larger triangle = ¹/₂ * 17 * 13 = 110.5 square inches
Area of smaller triangle = ¹/₂ * 11 * 7 = 38.5 square inches
Thus:
Area of shaded portion = 110.5 square inches - 38.5 square inches
Area of shaded portion = 72 square inches
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Use the original price and the markup to find the retail price.
Original price: $60; Markup: 20%
Answers
Answer:
$72 would be the retail price
Step-by-step explanation:
6:___=9:12
Find the missing number of ratio
Answers
Answer:
8Step-by-step explanation:
6:___=9:12
Find the missing number of ratio
6 : x = 9 : 12
x = 6 * 12 : 9
x = 8
----------------------------
check
6 : 8 = 9 : 12
0.75 = 0.75
the answer is good
Name:
Unit 7: Polygons & Quadrilaterals
Homework 5: Rhombi and Squares
Per:
Date:
(2.5
CD =
** This is a 2-page document! **
Directions: If each quadrilateral below is a rhombus, find the missing measures.
1. UV = 8 and WX = 5
무 7
2. BC = 28 and BD = 32
TU =
T
WU =_10
TX =
B
(284
FD=_16
EF=_16
EC= _32
8
TV =
112
E
V
28
D
28+32²=c?
784+1024=
1,808=1
U2,5
NK =
K
2
NL =_10
3. MK = 24, JL = 20, and mZMJL = 50°
12 ²+10²=c2
244=c²
20
15.GC
mZKNL =
mZKJL =
mZMLK =
ML =
w
JM = _15.6
mZJKM =
mZJML =
M
L
4. Find PQ.
5. Find mZHGI.
N
P
F
(7x-1)
5x + 16
S
(4x + 3) +
J
R
9x - 32
e
1
H
6. Find mZADB.
7. If mZXYZ = 136°, solve for x.
B
W
X
D
(9x + 4)
(13x - 16)° C
R
Z
(10x-8)
Y
Gina Wilson All Things Alan
Answers
Answer:
Step-by-step explanation:
1.
Tu=8
WU=10
Tx=5.65
Tv=11.3
1)TX=XV=√39
2)WX=XU=5
In the given rhombus TUVW
TW=8(Given)
WX=5(Given)
What is a rhombus?A rhombus is a quadrilateral whose four sides all have the same length.
As we know that diagonals of the rhombus intersect at a right angle
So, by Pythagoras' theorem
\(TW^2 = TX^2 + WX^2\\8^2=TX^2 + 5^2\\TX = \sqrt{39}\)
We know that the diagonals of a rhombus bisect each other
So XV =√39
Similarly, XU=WX =5.
Therefore, in the given rhombus TUVW
1)TX=XV=√39
2)WX=XU=5
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Points A and B are on opposite sides of a lake. Another point, C. is 94.4 meters from Angle A. The measure of Angle A is 72° and the measure of Angle C is 30°. Find the distance between A and B.
Answers
To find the distance between points A and B, we can use trigonometry and the given information.
Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.
Using trigonometry, we can use the tangent function to find the value of "d".
tan(72°) = d / 94.4
To solve for "d", we can rearrange the equation:
d = tan(72°) * 94.4
Using a calculator, we can evaluate the expression:
d ≈ 4.345 * 94.4
d ≈ 408.932
Therefore, the distance between points A and B is approximately 408.932 meters.
What is the slope of the line that contains the points (4, 3) and (2, 7)?
Answers
The slope for a linear line is rise/run. Rise would be the y coordinates and run would be the x coordinates.
7-3/2-4 becomes 4/-2 and reduces to -2
To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 9%. The first credit card compounds interest quarterly, while the second credit card compounds monthly. The homeowner plans to pay off the loan in 10 years.
Part A: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)
Part B: Determine the total value of the loan with the monthly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)
Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences. (2 points)
Please only responded if you know how to do it, will give the brainiest to however answers it correctly
Answers
The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.
Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the total value of the loan,
P is the principal amount (initial loan amount),
r is the interest rate (in decimal form),
n is the number of times interest is compounded per year,
and t is the number of years.
Given:
P = $20,000,
r = 9% or 0.09,
n = 4 (quarterly compounding),
t = 10 years.
Substituting the values into the formula, we have:
A = 20000(1 + 0.09/4)^(4*10).
Calculating this value, we find:
A ≈ $45,288.38.
Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.
Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:
n = 12 (monthly compounding).
Substituting the values into the formula, we have:
A = 20000(1 + 0.09/12)^(12*10).
Calculating this value, we find:
A ≈ $45,634.84.
Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.
Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.
For the loan with quarterly compounding:
Total interest = Total value - Principal
Total interest = $45,288.38 - $20,000
Total interest ≈ $25,288.38.
For the loan with monthly compounding:
Total interest = Total value - Principal
Total interest = $45,634.84 - $20,000
Total interest ≈ $25,634.84.
The difference between the total interest accrued on each loan is approximately $346.46.
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I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answers
To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:
y = 3 - 4
Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:
y = -1
Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.
Answer
\(\pink\sf{y=-1}\)
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
\(\sf{y=3-4}\)
And now we just simplify the last part:
\(\sf{y=-1}\)
∴ answer: y = -1
When solving quadratic equation, what do the X value stand for as it relates to plotting the graph of the equation?
Answers
Step-by-step explanation:
step 1. The x values refer to the domain of the function.
step 2. if you set y = 0 and solve the quadratic equation the x values refer to the point the graph crosses the x axis.
describe how a graph would look for the solution set for the inequality in problem 5. describe what the solution means and how the price of the balloons bought will affect the amount in the budget.
Answers
A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125
ii) solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.
C) See the description of the solution below.
What is the explanation for the above?
Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.
The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:
0.80b + 65 ≤ 125
Now we can solve for b:
0.80b + 65 ≤ 125
0.80b ≤ 125 - 65
0.80b ≤ 60
b ≤ 75
Therefore, the dance committee can buy up to 75 balloons to stay within their budget.
To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.
The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.
As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.
Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.
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Full Question:
Since the above question is incomplete, it appears you are referring to the question below.
The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.
A) Write and solve an inequality to show the number of balloons that the dance committee could buy.
B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.
