Answers
Check the picture below.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. So let's use proportions to get x,y and z.
[tex]\cfrac{x}{30}~~ = ~~\cfrac{30}{24}\implies \cfrac{x}{30}~~ = ~~\cfrac{5}{4}\implies x=\cfrac{150}{4}\implies \boxed{x=\cfrac{75}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{24}~~ = ~~\cfrac{x-24}{y}\implies \cfrac{y}{24}~~ = ~~\cfrac{\frac{75}{2}-24}{y}\implies \cfrac{y}{24}~~ = ~~\cfrac{~~ \frac{27}{2}~~}{y}\implies \cfrac{y^2}{24}=\cfrac{27}{2} \\\\\\ y^2=\cfrac{(24)(27)}{2}\implies y=\sqrt{\cfrac{(24)(27)}{2}}\implies \boxed{y=18} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{z}{y}~~ = ~~\cfrac{30}{24}\implies \cfrac{z}{18}~~ = ~~\cfrac{5}{4}\implies z=\cfrac{(18)(5)}{4}\implies \boxed{z=\cfrac{45}{2}}[/tex]
Related Questions
How do you explain a math equation?
Answers
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
[tex]\sf \sin A=\boxed{\dfrac{5}{13}}\quad\cos A=\boxed{\dfrac{12}{13}}\quad\tan A=\boxed{\dfrac{5}{12}}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuseGiven:
[tex]\theta[/tex] = AO = BC = 5A = AC = 12H = AB = 13[tex]\implies \sf \sin A=\dfrac{5}{13}\quad\cos A=\dfrac{12}{13}\quad\tan A=\dfrac{5}{12}[/tex]
What is the following sum?
3 b squared (RootIndex 3 StartRoot 54 a EndRoot) + 3 (RootIndex 3 StartRoot 2 a b Superscript 6 Baseline EndRoot)
6 b squared (RootIndex 3 StartRoot 2 a EndRoot)
12 b squared (RootIndex 3 StartRoot 2 a EndRoot
6 b squared (RootIndex 6 StartRoot 2 a EndRoot)
12 b squared (RootIndex 6 StartRoot 2 a EndRoot)
Answers
[tex]12b^2\sqrt[3]{2a}[/tex]
In word form, this is 12 b squared (RootIndex 3 StartRoot 2 a EndRoot
Or you could say 12b^2 times the cube root of 2a
========================================================
Work Shown:
[tex]3b^2\sqrt[3]{54a}+3\sqrt[3]{2ab^6}\\\\3b^2\sqrt[3]{27*2a}+3\sqrt[3]{b^6*2a}\\\\3b^2\sqrt[3]{(3)^3*2a}+3\sqrt[3]{(b^2)^3*2a}\\\\3b^2\sqrt[3]{(3)^3}*\sqrt[3]{2a}+3\sqrt[3]{(b^2)^3}*\sqrt[3]{2a}\\\\3b^2*3*\sqrt[3]{2a}+3*b^2*\sqrt[3]{2a}\\\\9b^2\sqrt[3]{2a}+3b^2\sqrt[3]{2a}\\\\(9b^2+3b^2)\sqrt[3]{2a}\\\\\boldsymbol{12b^2\sqrt[3]{2a}}\\\\[/tex]
The idea here is that we break the cube roots into smaller pieces, so we pull out perfect cubes when factoring.
The sum of the expression is 12 b squared (Root Index 6 Start Root 2 a End Root) or 12b²∛(2a).
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
We have the expression,
3 b squared (Root Index 3 Start Root 54 a End Root) + 3 (Root Index 3 Start Root 2 a b Superscript 6 Baseline End Root).
In numerical form,
3b²∛(54a) + 3∛(2ab⁶)
To find the sum of the above expression:
we simplify the expression,
3b²∛(54a) + 3∛(2ab⁶)
= 3b²∛3³(2a) + 3∛(2a)(b²)³
= 9b²∛(2a) + 3b²∛(2a)
= 12b²∛(2a)
Therefore, the sum is 12b²∛(2a).
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can someone help me ? need help asap
Answers
Answer:
The answer is 1/2. You are correct the slope is 1/2
Step-by-step explanation:
Gas prices are projected to increase by 125% Over the next several years. If a gallon of gas currently costs $3.60. What is the projected cost of a gallon of gas?
Answers
Answer:
$ 8.10
Step-by-step explanation:
3.60 * 2.25 =
Please help!! Can somebody give me a step by step answer for 3m = 531. I’ve been wanting to know how to do the questions but I don’t know how to solve them.
Answers
[tex]3m = 531 \\ divide \: both \: sides \: by \: 3 \\ \frac{3m}{3} = \frac{531}{3} \\ m = 177[/tex]
suppose f(x) =x . Find the graph of f(x)-4
Answers
Answer:
you just need two points to graph it.
x=0, you get y=0; which is the origin.
x=1, y=4.
you should get something like this:
Step-by-step explanation:
Bashir bought snacks for his team's practice. He bought a bag of apples for $2.91 and a 6-pack of juice bottles. The total cost before tax was $15.69. Write and solve an equation which can be used to determine j j, how much each bottle of juice costs.
Answers
An equation that can be used to determine j j, each bottle of juice costs 15.69 = 6j + 2.91
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Bashir bought snacks for his team's practice. He bought a bag of apples for $2.91 and a 6-pack of juice bottles.
The total cost before tax was $15.69.
An equation that can be used to determine j j, is how much each bottle of juice costs.
15.69 = 6j + 2.91
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The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 1 mg. What was the initial mass (in mg) of the sample?
Answers
A = A0(1/2)^(t/4)
A is given to us as 1, t is 24 and we are trying to find A0.
1 = A0(0.5)^6
1 = A0(0.015625)
A0 = 64g
Question 14 of 25 The image shows the location of ladders around a circular pool. 10 C 8 2 0 2 B (6y-2 85 -12 -10 0 2 Cody walks clockwise around the pool from point D to point E. How many degrees of arc does he walk? If your answer is a decimal, express your answer to the nearest hundredth.
Answers
The degrees of arc which Cody he walks clockwise around the pool from point D to point E is 105 degrees.
What is inscribed polygon in circle?The inscribed polygon in a circle is the polygon of which each corner point is on the circle.
The image shows the location of ladders around a circular pool. Cody walks clockwise around the pool from point D to point E. In the given image the value of x i,
[tex]2x+8=86\\2x=86-8\\x=\dfrac{78}{2}\\x=39^o[/tex]
Thus, the angle C and angle B are the supplementary angle. Thus,
[tex]m\angle C=m\angle D\\7y-4=360-(3y-6)\\7y+3y=360+6+4\\10y=370\\y=37[/tex]
3y-6 is the inscribed angle which intercept the arc DE. Thus,
[tex]\text {arc } DE= 3y-6\\\text {arc } DE= 3(37)-6\\\text {arc } DE= 105[/tex]
Thus, the degrees of arc which Cody he walks clockwise around the pool from point D to point E is 105 degrees.
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The perimeter of an equilateral triangle is 1/8 unit. What is the length, in units, of each side of the triangle
Answers
Answer:
[tex] {\longrightarrow \pmb{\sf {\qquad \frac{1}{24} }}} \\ \\[/tex]
[tex] \: [/tex]
Step-by-step explanation:
It is given that the perimeter of an equilateral triangle is 1/8 unit and we have to find the length of each side of the triangle.
So, we know that,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad 3a = Perimeter_{(Equilateral triangle) }}}} \\ \\[/tex]
Now, substituting the given values in the formula :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad 3a = \frac{1}{8} }}} \\ \\[/tex]
By doing cross multiplication we get :
[tex]{\longrightarrow \pmb{\sf {\qquad 3a(8) = 1(1) }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 24a = 1 }}} \\ \\[/tex]
Dividing both sides by 24 we get :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad \frac{24a}{24} = \frac{1}{24} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad a = \frac{1}{24} }}} \\ \\[/tex]
Therefore,
The length of each side of the triangle is 1/24 unitsWhat’s 12 3/4+17/2+5 4/6
Answers
The chart below describes the speed of four runners. Which runner is the fastest?
Runner A ran 1 mile in 8 minutes
Runner B ran 2 miles in 10 minutes
Runner C ran 3 miles in 20 minutes
Runner D ran 5 miles in 30 minutes
Answers
Answer:
Runner B
Step-by-step explanation:
speed = distance ÷ time
Runner A: 1 ÷ 8 = 0.125m/ms
Runner B: 2 ÷ 10 = 0.2m/ms
Runner C: 3 ÷ 20 = 0.15m/ms
Runner D: 5 ÷ 30 = 0.17m/ms
Runner B has the highest speed so he is the fastest runner.
(PLEASE HURRY)
Milan borrowed money from a credit union for 6 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $3780. How much money did he borrow?
Answers
Answer:
$54000
Step-by-step explanation: 3780 divided by the number of years he paid interest for, (6) gives you 630. If he pays 7% interest, you calculate what number 630 is 7% of (9000.) Therefore he takes out 9000 dollars a year. Meaning that in total, he borrowed 54,000 dollars. (9000 x 6)
How do you solve for this?
Answers
x = 9
[tex]\bold{EXPLANATIONS:}[/tex]
Which of the following is an example of theoretical probability? OA. Elena called 5 friends, and 3 of them were at home. The probability Elena's friends are at home is 3/5 B. A spinner has 8 equal sections numbered 1 ? 8. The probability of spinning the number 3 is 1/8 C. A coin was flipped 100 times, and the results were 53 heads and 47 tails. The probability of heads is 53/ 100 D. Greg turned over 10 playing cards, and 3 of them were aces. The probability of turning over an ace is 3/10
Answers
An example of theoretical probability from the considered option is given by: Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8
What is experimental probability?Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]
where, [tex]P_e(E)[/tex]is denoting experimental probability of occurrence of E.
What is theoretical probability?Probability which is derived theoretically, irrespective of what outcome comes, is called theoretical probability. Probabiltiy which is based on the outcomes of experiments performed is called experimental probability.
Suppose we want to find the probability of an event E.
Then, its theoretical probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Checking all the options to see which one gives theoretical probability:
Option 1: Elena called 5 friends, and 3 of them were at home. The probability that Elena's friend are at home is 3/5This option uses what was observed from one result. Thus, 3/5 is experimental probability here, as there is no evidence of it being theoretical probability but enough support towards being experimental probability.
Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8No experiment is done here, just the description of the setup of the random experiment.
Now, E = event of getting 3 on the spinner.
All spinner's parts are assumingly equally likely, we have:
Number of ways E can occur = 1
Number of ways spinner's outcome can come = 8
Thus, we get P(E) = 1/3
Thus, this option is demonstrating theoretical probability.
Option 3: A coin was flipped 100 times, out of which 53 heads and 47 tails. The probability of heads is 53/100This is using experimental results to get the estimated probability.
Actually, assuming coin being fair, both the tail and heads being equally probable, if we take:
E = event of getting head, then as there are two results possible being Tail or Head (assuming only 2 results), and there is one way of getting head in one toss, so we get:
P(E) = 1/2 = 0.5
Thus, this option is demonstrating experimental probability instead of theoretical one.
Option 4: Greg turned over 10 playing cards, and 3 of them were aces. The probability of turning over an ace is 3/10It is using the data from one experiment. So its experimental probability. Sometimes we can get experimental probability = theoretical probability value, but still, there'd be difference of how you calculated it from the start. Usually, if calculated from experiment, then its experimental probability, and if calculated virtually and based on theories, it is theoretical probability.
Thus, an example of theoretical probability from the considered option is given by: Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8
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Factorise 14e-16
Please explain
Answers
The expression 14e - 16 is an algebraic expression, and the factored expression is 2(7e - 8)
How to factor the expression 14e - 16?The expression is given as:
14e - 16
Express both terms as a product of 2
14e - 16 = 2 * 7e - 2 * 8
Factor out 2 in the expression
14e - 16 = 2 * (7e - 8)
Remove the product sign
14e - 16 = 2(7e - 8)
Hence, the factored expression of 14e - 16 is 2(7e - 8)
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What is the circumference of a circle with a radius of 11 cm? (Use = 3.14.)
A.
103.62 cm
B.
69.08 cm
C.
34.54 cm
D.
379.94 cm
Answers
First, we need to follow the circumference of a circle formula, which is [tex]C = 2 \pi r[/tex]. Since we know the radius, we can plug 11 for the radius and 3.14 for pi.
The equation should now look like this: [tex]C = 2 * 3.14 *11[/tex]. Then, we multiply. After solving, the circumference of the circle is 69.08 centimeters.
If i subtract my number, then square the result, I get the same answer as if i square my number, then subtract 20 from the result
Answers
The Algebraic equations (x - 20)² and x² - 20 have an equal value My number is 6.
What is an Algebra equation?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
I think of a number, if I subtract 10 from my number, then square the result, I get the same answer as if I square my number, then subtract 20 from the result.
Let the number be x.
If I subtract 20 from my number that is x - 20 then square the result that is (x-20)².
And if I square my number that is x² then subtract 20 from the result that is x² - 20.
Both the result are the same then we have
(x - 20)² = x² - 20
x² - 20x + 100 = x² - 20
-20x + 100 = -20
x = 6
My number is 6
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Find the value of x to the nearest tenth.
1.9
3.5
–4.4
7.5
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Answer:
The correct answer is 7.5
Step-by-step explanation:
[tex] \tan(62) = \frac{x}{4} [/tex]
then you multiply by 4 and you get:
[tex] \tan(62) \times 4 = x[/tex]
Result:
[tex]x = 7.5[/tex]
A local daycare is updating its marketing material. The owner wants to include the average age of children who currently attend the daycare. The current breakdown of children by age is located in the table below. Use this information to calculate the average age of children attending the daycare. Round to the nearest tenth.
Answers
Answer: n2.4
Step-by-step explanation:
Average age=6⋅1+4⋅2+3⋅3+5⋅46+4+3+5=4318=2.38888...=2.4
The average age of a child attending this daycare is 2.4 years old.
Nancy found that x=1 is one solution to the quadratic equation (x+2)2=a. What is the value of a?
-9
-3
3
9
Answers
Answer:
the answer is a
Step-by-step explanation:
i literaly just tookthetest on edginuity
Answer:
a = 9
Step-by-step explanation:
First we substitute 1 into the quadratic equation :
(x+2)² = a
(1+2)² = a
(3)² = a
3×3 = a
a = 9
Hope you understood, hope this helped and brainliest please.
Mill rate is the tax rate that is applied to the assessed value of a real estate property by a municipality. Your tax is calculated by multiplying the mill rate by the assessed value of a property and dividing by 1,000. If your town's mill rate is 8 and your assessed home value is $188,000, how much will your town tax bill be?
Answers
If your town's mill rate is 8 and your assessed home value is $188,000, your town tax bill will be $1504.
What will be your town tax rate?Tax is a complusory amount levied by the government or an agency of the government on the sales of goods and services. It is a fomr of transfer of wealth to the government.
Town tax = (8 x $188,000) / 1000 = $1504
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What is the volume of this cone? Use 3.14 for pi and round your answer to the nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then explain how u calculated it
Answers
Answer:
33.5 in^3
Step-by-step explanation:
The formula for a cone is (pi)(r^2)(h/3)
Since we need to use 3.14 for pi, we will plug in 3.14 for pi. It should look like this: (3.14)(r^2)(h/3)
The radius is 2 and the height is 8. Plug in the numbers:
(3.14)(2^2)(8/3)
Simplify:
(3.14)(4)(2.66...)
Multiply:
(12.56)(2.66...) -> 39.4933...
Finally, 39.4933... is rounded to the tenths place:
39.5
Hope this helps :)
How many days are in 19 lunar calendar new years with an extra month added in seven times?
Answers
There are 6939.56 days in 19 lunar calendar new years with an extra month added in seven times.
What is lunar year?"A lunar year is 12 lunar months, so 19 of these would be 228 lunar months. With the 7 extra months, the total period would be 235 lunar months of 29.530589 days each and is 6939.69 days.
We will notice that this is almost the same as 19 solar years of 365.24 days, which is 6939.56 days.
Now, you are referring to the Hebrew Calendar, a 19-year period that consists of 12 years of 12 months plus 7 years of 13 months,
Therefore, 19 years is the period after which the Hebrew and solar calendar dates will match up."
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The given box plot represents the number of pictures taken by tourists on the same group tour. Which five-number summary represents this
data set?
Photographs Taken by Tourists
00
8
10
12
18
26 28
30 32
14 16 20 22 24
Number of Photographs
OA. 8, 16, 23, 28, 32
OB. 10, 16, 23, 28, 32
Ос. 10, 16, 22, 28, 32
OD. 8, 10, 16, 28, 32
Answers
Answer: b: 10, 16, 23, 28, 32
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
its B !
P P,Q and R can finish a task in 8, 10 and 12 hours respectivly.They started working together but after 3 hours, P and R left. How long will Q take to finish the task now?
Detail it
Answers
Answer:
45 minutes
Step-by-step explanation:
Assume task completed in total x hours
[tex]\frac{x}{10} + \frac{3}{8} + \frac{3}{12} = 1 \\ 12x + 45 + 30 = 120 \\ 12x = 45 \\ x = \frac{15}{4} = 3 \frac{3}{4}[/tex]
So q will take 45 more minutes
How many 3-digit numbers contain at least one zero?
Answers
Answer:
171
Step-by-step explanation:
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I already wrote the ordered pair. Just write how the number pairs are related.
Answers
Answer:
it is related by 35 because you are adding 35.
Step-by-step explanation:
A college graduate invests $3,000 into an account that earns 6% annual interest compounded monthly. What is the value (in dollars) of
the investment after 5 years? (Round your answer to the nearest cent.)
Answers
Answer:
$4,014.68
Step-by-step explanation:
A = $4,014.68
A = P + I where
P (principal) = $3,000.00
I (interest) = $1,014.68
First, convert R as a percent to r as a decimal
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 3,000.00(1 + 0.06/1)^(1)(5)
A = 3,000.00(1 + 0.06)^(5)
A = $4,014.68