5) In the segment below, segment DC = 29,
lengths AB, BC, AC, rounded to the nearest tenth, and angle measures for
Answers
Applying the trigonometric ratios and the triangle sum theorem, the missing lengths and angles are:
AB = 27.2 units
BC = 33.5 units
AC = 50.4 units.
m∠A = 38°
m∠ABC = 112°
What are the Trigonometric Ratios?The trigonometric ratios, SOHCAHTOA, are used to find the sides or angles of a right triangle.
Find BD using TOA:
tan ∅ = opp/adj
tan 30 = BD/29
BD = tan 30 × 29
BD = 16.7 units
Find AD using TOA:
tan ∅ = opp/adj
tan 52 = AD/16.7
AD = (tan 52)(16.7)
AD = 21.4 units
Find AB using SOH:
sin 52 = 21.4/AB
AB = 21.4/sin 52
AB = 27.2 units
Find BC using CAH:
cos 30 = 29/BC
BC = 29/cos 30
BC = 33.5 units
Find AC:
AC = AD + DC
AC = 21.4 + 29
AC = 50.4 units.
m∠A = 180 - 52 - 90 = 38° (triangle sum theorem)
m∠ABC = 180 - m∠A - m∠C (triangle sum theorem)
m∠ABC = 180 - 38 - 30
m∠ABC = 112°
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Related Questions
what is the approximate value of x in the exponential 4^x=14?
Answers
We know 4² = 16 , 4¹= 4
In this case we have :-
[tex] {4}^{x} = 14[/tex]
and we have to find the value of x
14 is less than 16 so x will be less than 2
14 is greater than 4 so x will be greater than 1
we can find the value of
[tex] {4}^{1.5} = {4}^{ \frac{3}{2} } \\ { (\sqrt{4}) }^{3} = {2}^{3} = 8[/tex]
so we can say 14 is much larger than 8 which means x will be much larger than 1.5
so according to above ideas we can say our answer is 2nd option which is 1.9037 is our answer
[tex]x \approx1.9037[/tex]
[tex]~~~~~~~4^x = 14 \\\\\implies \ln 4^x = \ln 14\\\\\implies x \ln 4 = \ln 14\\ \\\implies x = \dfrac{\ln 14}{ \ln 4}\\\\\implies x \approx 1.9037[/tex]
Complete the long division problem on your own sheet of paper. Then, fill in the digits.
Answers
Answer:
52
Step-by-step explanation:
5 goes in the top left under the 4 & 1 is 40 bring the 1 down drop the 6 next to the 1 write 16 under the 16 and you get 2 and at the very bottom write 0
Determine the equation of the line passing through the points (−1,1) and (1,7).
Write the line in standard form Ax+By=C.
Answers
Answer:
[tex]3x - y = -4[/tex]
Step-by-step explanation:
To make things easier, let's first find the equation in slope-intercept form ([tex]y = mx + b[/tex] where m is the slope and b is the y-intercept.
1. Find the slope:
[tex]\frac{7 - 1}{1 - (-1)} = \frac{6}{2} = 3[/tex]
2. Find the y-intercept by plugging in (-1,1) into the equation [tex]y = 3x + b[/tex]
[tex]1 = 3(-1) + b[/tex]
so [tex]b[/tex] = 4
3. Therefore the equation of the line in slope-intercept form is [tex]y = 3x + 4[/tex]
4. To convert slope-intercept form into standard form, let's move the 3x over to the other side and divide by -1 to get rid of the negative.
Our result is [tex]3x - y = -4[/tex].
Hope this helps :)
A group of friends were working on a student film. They spent all their budget on equipment and props. They spent $712 on equipment, and 11% of the total budget on props. What was the total budget for their student film?
Answers
Answer:
800 dollars
Step-by-step explanation:
The amount spent on equipment is 89% of the total
712÷89 = 8 x 100 = $800
the graph of y = (x) is shown below
Answers
Answer:
Step-by-step explanation:
Solution
The question is a bit obscure. The best choice I think, would be A. F(x) could equal something like y = x - 3. When y = 0, x = 3 or put the other way, when x = 3 y= 0.
What is the median of the data represented by the box plot?
Answers
Answer: 20
Step-by-step explanation:
Box plots give us the median just by looking at them. See attached.
can someone answer this question- I will give brainily if it is correct.
Answers
Answer:
A
Step-by-step explanation:
since decimals are 10ths and 100ths places, you can translate such into fractions
hope this helps:)
Find the Mean Absolute Deviation (MAD) of the following test scores.
Remember, the Mean is just the first step.
Scores:
{ 48, 61, 73, 76, 76, 74 }
Answers
Based on the calculation below, the Mean Absolute Deviation (MAD) of the test scores is 0.
How to calculate Mean Absolute Deviation (MAD)The mean of the 6 test scores is first calculated as follows:
Mean = Sum of the test scores / Number of test scores = (48 + 61 + 73 + 76 + 76 + 74) / 6 = 68
We can now calculate the MAD of the test scores as follows:
MAD = Sum of deviations of all the test scores from the Mean / Number of test scores = ((48 - 68) + (61 – 68) + (73 – 68) + (76 – 68) + (76 – 68) + (74 – 68)) / 6 = 0 / 6 = 0
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Vito has a fair 20-sided die with the faces
numbered 1 through 20. Vito will roll the die
100 times. About how many times will he
likely roll a 1, 4, or 5?
A 10
B 25
C 15
D 50
Answers
Answer:
15, C
Step-by-step explanation:
Any number is equally likely to appear. Therefore, we have 3/20 * 100 = 15. This is C.
Hope this helped!
~clouddragon
A telescope company needs to choose a cardboard box to ship its product across the country. Use the information to answer each question below. Brainlest to whoever answers with work.
Answers
Please help me answer this question please...
Answers
answer is here about stem and leaf
PLEASE HELP ASAP *URGENT* 20 POINTS!!!!
Answers
Answer:
a5 = 122
Explanation:
Given:
a1 = 2an = -3aₙ₋₁ + 2Solve:
a1 = 2
a2 = -3a1+2 = -3(2)+2 = -4
a3 = -3a2 + 2 = -3(-4)+2 = 14
a4 = -3a3 + 2 = -3(14) + 2 = -40
a5 = -3a4 + 2 = -3(-40) + 2 = 122
Answer:
a₅ = 122
Step-by-step explanation:
What is a₅ for the sequence defined by:
[tex]\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_{n-1}+2\\\end{array}\right\\\\\\\hrule[/tex]
Letting n=2:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{2-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{1}+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4[/tex]
Letting n=3:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{3-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{2}+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14[/tex]
Letting n=4:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{4-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{3}+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40[/tex]
Letting n=5:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{5-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{4}+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}[/tex]
STATISTICS MATH PLS HELP - In a study of the accuracy of fast food drive through orders, McDonald’s had 33 orders that were not accurate among 362 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%.
Answers
Answer:
See below for all information
Step-by-step explanation:
Given Information
Observed Sample Proportion: [tex]p=\frac{33}{362}\approx0.0912[/tex]Hypothesized Population Proportion: [tex]p_0=0.10[/tex]Sample Size: [tex]n=362[/tex]Significance Level: [tex]\alpha=0.05[/tex]We should conduct a two-tailed one-proportion z-test (remember to double the p-value to consider both tails!)Assume conditions are metNull and Alternate Hypotheses
Null: [tex]H_0:p=0.10[/tex] (this tells us that the actual proportion of inaccurate orders of 10% is equal to the observed proportion of inaccurate orders)Alternate: [tex]H_1:p\neq0.10[/tex] (this tells us that the actual proportion of inaccurate orders of 10% is NOT equal to the observed proportion of inaccurate orders)Determine z-statistic
[tex]\displaystyle Z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{\frac{33}{362}-0.10 }{\sqrt{\frac{0.10(1-0.10)}{362}}}\approx-0.5606[/tex]
Determine p-value from z-statistic
[tex]2\cdot P(Z < -0.5606)=2\cdot\text{normalcdf}(-1E99,-0.5606)\approx2\cdot0.28753\approx0.5751[/tex]
Draw conclusion of p-value based on given significance level
Since [tex]p > 0.05[/tex], we fail to reject the null hypothesis. This means that we do have sufficient evidence to say that the observed rate of inaccurate orders is equal to 10%, making it extremely likely that the null hypothesis is true.
What’s a good estimate for 2,745 x 6.9? Show how you got you estimate.
Answers
Answer:
21000
Step-by-step explanation:
2745 -> 3000
6.9 -> 7
3000 x 7 =
21000
Convert: 92 ounces = _____ pounds _____ ounces
9 pounds 2 ounces
5 pounds 2 ounces
1,472 pounds 0 ounces
5 pounds 12 ounces
Answers
Answer:
5 pounds and 12 ounces.
Step-by-step explanation:
Divide it all by 16, and you should get 5 with a remainder of 12 (which is the remaining ounces). Hope it helps ! ^_^
Answer:
5 pounds 12 ounces
Step-by-step explanation:
I copied the other answer
The probability of guessing on four true and false questions and getting all four questions correct
Answers
Answer:
50-50
Step-by-step explanation:
If yoiu have 4 and divide it b
10. What mass of carbon dioxide is produced when 6.2
moles of propane, C3Hg is burned in oxygen?
C3H2 + ___ O2 →
O2 → _ CO2 + _ H2O
-
-
Answers
4>-x-5 how do I solve for x? With the greater sign
Answers
Answer:
x>-9
Step-by-step explanation:
1. bring x over to the other side to make it a positive (4+x>-5)
2. bring 4 to the other side (x>-5-4)
3. simplify (x>-9)
Determine the intercepts of the line. Do not round your answers. y-6=4(x+5)y−6=4(x+5)
Answers
y-intercept=26
Three quarters of the sum of two numbers is 6 and half the difference of the two numbers is 1
Answers
Answer:
1 number= 4.5
2 number= 3.5
Step-by-step explanation:
simplify. 5ab/15a+10a²
Answers
What is the area of this shape?
Answers
The area of the figure presented in the image, which is formed by one right triangle and three rectangles is equal to an amount of 157 square kilometers.
How to determine the area of a compound shape
In this question we understand that the area of the compound shape is the sum of the area of small rectangles and triangles:
[tex]A = \sum \limits^{n}_{i = 1} A_{i}[/tex] (1)
Now we proceed to calculate the area of the compound shape:
A = 0.5 · (4 km) · (3 km) + (10 km) · (2 km) + (17 km) · (7 km) + (2 km) · (6 km)
A = 157 km²
The area of the figure presented in the image, which is formed by one right triangle and three rectangles is equal to an amount of 157 square kilometers.
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Jared wants to paint his room. The dimensions of the room are 12 feet by 15 feet, and the walls are 9 feet tall. There are two windows, each with dimensions 6 feet by 5 feet. There are two doors, each with dimensions 30 inches by 6 feet. If a gallon of paint covers about 350 square feet, how many gallons of paint will he need to put two coats of paint on the wall? List the steps to solve the problem and solve.
Answers
Answer:
1 ft = 12 in
1 in = (1/12) ft
30 in = (30/12) ft
30 in = 5/6 ft
The area of the surface that Jared needs to paint is:
2(12*9 + 15*9) - 2(5*6 + (5/6)*6) = 416 ft^2
Step-by-step explanation:
Answer:
3 gallons of paint
Step-by-step explanation:
Steps you have to take,
identifying the area of the 4 walls subtracting the windows and doors from the area.finding out how many gallons of paint it will take to cover the total area twiceFormula:
[tex](A = lw)(2) + (A = lw)(2) - (A = lw)(2) - (A = lw)(2)[/tex]
[tex](wall 1)(2) + (wall 3)(2) - (window)(2) - (door)(2)[/tex] ↑
door = 30in by 6ft
30in to feet = 2.5 feet
Lets start solving.[tex](A = 12(9))2 + (A = 15(9))2 - (A = 6(5))2 - (A =2.5(6))2[/tex]
[tex](A = 108)2 + (A = 135)2 - (A = 30)2 - (A = 15)2[/tex]
[tex](A = 216) + (A = 270) - (A = 60) - (A = 30)[/tex]
[tex]combine\\(A = 486) - (A= 90)\\(A = 396)[/tex]
two coats = A(2)396(2) =
792sq ft
We know that one gallon covers 350sq ft
792/350 =
2.26 gallons
(can't have .26 of a gallon so we round up)
it takes 3 gallons of paint Jared's roomKevin invest $2,000 at 4.6% compounded continuously. How long will it take him to have $3,700
Answers
Answer:
t=In(37/20)/0.046
Step-by-step explanation:
p=2000
r=0.046
A=3700
t=?
3700=2000e^0.046t
switch sides
2000e^0.046t=3700
Divide both sides by 2000
$2000e^0.046t/2000=$3700/2000
Simplify
e^0.046=37/20
Apply exponent rules
0.046=37/20
Solve 0.046t = ln(37/20)
t=In(37/20)/0.046
Find the sale price regular price $ 12.88 discount %15
Answers
Answer:
$ 1.932
Step-by-step explanation:
Need help please thanks
Answers
Answer: There is no zeros for this equation.
Step-by-step explanation: First, we use the quadratic formula and plug in values. -2 plus or minus the square root of 2^2 - 4*5*8.
The square root will be -39 (negative 39.) This is impossible without using complex numbers (you cannot use complex numbers to get a zero.) Negative square roots are not real. Thus, this equation has no real solution.
Which three-dimensional figure has nine edges?
rectangular prism
rectangular pyramid
triangular prism
triangular pyramid
Answers
Answer:
Triangular PrismStep-by-step explanation:
A geometrical shape that has 6 vertices and 9 edges is a triangular prism. A triangular prism is a three-dimensional object with two congruent...
Answer:
Triangular Prism
Step-by-step explanation:
Edge2022 :)
What is the 16th term in the following geometric sequence?
5, −10, 20, −40, 80,...
Answers
Explanation:
The formula to find the nth term for a geometric sequence is
(a1)(r)^n-1
So by plugging in the terms you get
(5)(-2)^16-1 = -163840
Step-by-Step Explanation:
As we can see, starting from the first term, every term is repeatedly multiplied by (-2) in order to form this sequence.
1) 5
2) 5 * -2 = -10
3) -10 * -2 = 20
4) 20 * -2 = -40
5) -40 * -2 = 80
6) 80 * -2 = -160
7) -160 * -2 = 320
8) 320 * -2 = -640
9) -640 * -2 = 1280
10) 1280 * -2 = -2560
11) -2560 * -2 = 5120
12) 5120 * -2 = -10240
13) -10240 * -2 = 20480
14) 20480 * -2 = -40960
15) -40960 * -2 = 81920
16) 81920 * -2 = -163840
17) -163840 * -2 =327680
Therefore, 16th Term = -163840
The rectangular prism below has a base area of 44 units2 and a height of 6 units. Find
its volume.
Answers
The volume of the rectangular prism given its base area and its height is 264 units³.
What is the volume?A rectangular prism is a three-dimensional object that has six faces, 12 sides and 6 vertices.
Volume = length x width x height
base area x height
44 x 6 = 264 units³
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Write a part -to part ratio that compares the girls to boy . Write this in 3 different forms
Answers
The ratio of girls to boys is 4:5.
For every four girls that are in the camp, there are five boys.
The ratio of girls to boys is 4/5.
The ratio of boys to girls is 5:4.
The ratio of boys to girls is 5/4.
The ratio of boys to girls is 1 1/4.
What are the ratios?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign used to denote ratios is :.
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