Find the length of side x in simplest radical form with a rational denominator.30°х60°12
Answers
Ok, to find the lenght of side x we are going to use the sine function:
[tex]\sin (30)=\frac{12}{x}[/tex]Clearing x:
[tex]x=\frac{12}{\sin (30)}=\frac{12}{1/2}=24[/tex]Finally we get that x is equal to 24.
Related Questions
Find the volume of a cube if an edge has length 2r st units.Volume =cubic unitsQuestion Help: Message instructorCheck Answer
Answers
You have a cube with side 2 rst units.
In order to calculate the volume of the given cube, you use the following formula:
V = a³
where a is the length of cube sides.
By replacing the value of a into V formula you obtain:
V = (2 srt)³ units³
V = 8 r³s³t³
where you have used tha fact 2³=8 and that variables r,s and t power to 3 are equal to r³s³t³.
Hence, the volume of the given cube is V = 8 r³s³t³ units³
Look at this diagram:If CE and FH are parallel lines and m
Answers
If CE and FH are parallel lines and angle EDG is 42 degree, then angle CDB is also 42 degree
If CE and FH are parallel lines and the line BI is the transversal
angle EDG = angle DGF (interior alternate angles)
(when two lines are parallel and is cut by a transversal, the interior alternate angles are equal)
So. angle DGF = 42 degree
angle CDB = angle DGF (corresponding angles)
(when two lines are parallel and is cut by a transversal, the corresponding angles are equal)
angle CDB = 42 degree
Therefore, if CE and FH are parallel lines and angle EDG is 42 degree, then angle CDB is also 42 degree
To learn more about parallel lines refer here
https://brainly.com/question/24607467
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Analyze the diagram below and complete the instructions that follow./Find the value of x.A.4B.5C.6D.9Please select the best answer from the choices providedABCD
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ANSWER
EXPLANATION;
Apply Pythagora's rule to find the value of x
[tex]\begin{gathered} \text{ Pythagora's rule} \\ \text{ Hypotenuse}^2\text{ = opposite}^2\text{ + adjacent}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Hypotenuse = }\sqrt{117} \\ \text{ Opposite = x} \\ \text{ Adjacent = \lparen x + 3\rparen} \end{gathered}[/tex][tex][/tex]20. Find the volume of the following figure.a. 448.4 cm3b. 149.5 cmC. 896.7 cm3d. 21.4 cm3
Answers
Volume of an hexagonal prism (v ): (3√3/2)a^2h
Where:
a = side base = 7cm
h= height = 7 cm
Replacing:
V = (3√3/2)7^2(7) = 891.14 cm3
Jeremy is given the choice between two chocoletes,chocolates, and Y. Which..........
Answers
To determine which option is correct, we first need to find the volume of both chocolate.
The volume of X:
The shape is a square-based pyramid. The volume is given by
[tex]\begin{gathered} V_x=\frac{1}{3}\times base\text{ area }\times height \\ V_x=\frac{1}{3}\times l\times b\times h \end{gathered}[/tex]From the diagram,
l = 5 cm
b = 6 cm
h = 10 cm
Substituting,
[tex]\begin{gathered} V_x=\frac{1}{3}\times5\times6\times10 \\ V_x=100\operatorname{cm}^3 \end{gathered}[/tex]The volume of Y:
The shape is a triangular-based pyramid. The volume is given by
[tex]\begin{gathered} V_y=\frac{1}{3}\times base\text{ area }\times height \\ V_y=\frac{1}{3}\times\frac{1}{2}\times b\times l\times h \end{gathered}[/tex]From the diagram,
l = 8 cm
b = 7.5 cm
h = 10 cm
[tex]\begin{gathered} V_y=\frac{1}{3}\times\frac{1}{2}\times7.5\times8\times10 \\ V_y=100\operatorname{cm}^3 \end{gathered}[/tex]From here, the volumes of both chocolates are the same.
Therefore, the chocolate he picks does not matter as both volumes are equivalent.
The SECOND OPTION is correct.
A nurse measured The blood pressure of each person who visit a hair clinic and created a relative frequency histogram for the systolic blood pressure readings approximately what percentage of the people had a systolic blood pressure Reading between 110 and 139 inclusive
Answers
Given a relative frequency histogram for the systolic blood pressure readings.
We will find the percentage of the people who had a systolic blood pressure reading between 110 and 139
As shown:
The percentage of people who had a systolic blood pressure reading between 110 and 119 = 0.35
The percentage of people who had a systolic blood pressure reading between 120 and 129 = 0.25
The percentage of people who had a systolic blood pressure reading between 130 and 139 = 0.15
So, the answer will be = 0.35 + 0.25 + 0.15 = 0.75
So, the answer will be option 3) 75%
What is the greatest common factor of the polynomial: 35y + 5y + 157 "
Answers
The greatest common factor of the expression is:
[tex]5y^3[/tex]This comes from the fact that 5 is the greatest common factor of the constants, whereas y^3 is the greatest common factor of the variable.
Find and simplify the difference quotient for the following function
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Therefore:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-8xh-h^2+7x+7h+4-(-4x^2+7x+4)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{7h-8xh-h^2}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(7-8x-h)}{h} \\ \frac{f(x+h)-f(x)}{h}=7-8x-h \end{gathered}[/tex]11> _ <49 how do I solve this?
Answers
The question is asking for a number less or equal than 11 and less or equal to 49, then by the options we have, the number would be:
[tex]11\ge8\leq49[/tex]31/32 - > Identify the ordered pairs in the graph. Then identify the domain and range. Is this a function? 7) 8) Domain: Domain: Range: that Range: Function? Function? O Type here to search gi 3
Answers
7)
The ordered pairs are:
(-4, -2), (-2, 1), (0, -1), (-3, 0), and (-3,2)
Domain = {-4, -3, -2, 0}
Range = {-2, -1, 0, 1, 2}
A function must map every element of the domain to a unique number in the range
But here -3 is mapped to 0 and 2.
Hence it is not a function
8)
The ordered pairs are:
(-2, 3), (-1,-1), (0,-1), (1,-3), (3, 1)
Domain = {-2, -1, 0, 1, 3}
Range = {-3, -1, 1, 3}
In this case, every element of the domain is mapped to a unique
ut -The ordered pairs are:
For the following figure, complete the statement for the specified points.RPoints R, S, and Tareneither collinear nor coplanarboth collinear and coplanarcollinearcoplanar
Answers
First we need to define what collinear and coplaner means.
It is said that 3 or more points are collinear if they all lie on the same line.
From the diagram, point R, S, T do not lie on the same line.
Hence point R, S and T are not collinear
For a point or line to be coplaner, it must line in the same plane
Also looking at the diagram, points R, S, T do not lie in the same plane.
Hence
Solve the equation. |k + 6| = 3
Question 7 options:
{–3, 9}
{–3, 3}
{–9, –3}
{all real numbers greater than or equal to –9 and less than or equal to –3}
Answers
Step-by-step explanation:
k= {-3,-9}
Because || always gets positive numbers.
For example |-5|=5, and |5|=5.
so |-9+6|=|-3| which is |-3|=3
and |-3+6|=|3| which is equal to 3.
Answer:
c) k = {-9,-3}
Step-by-step explanation:
Given equation,
→ |k + 6| = 3
Now the value of k will be,
→ |k + 6| = 3
→ k + 6 = 3 || → -(k + 6) = 3
→ k = 3 - 6 || → -k = 3 + 6
→ [ k = -3 ] || → [ k = -9 ]
Hence, value of k is -3 & -9.
Use the distributive property of multiplication to find 6x14.
Answers
Answer
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Explanation
Distributive property is used to open brackets. For example, the expression
a (b + c) can be solved using the distributive property to multiply into the bracket.
a (b + c) = ab + ac
So,
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Hope this Helps!!!
6. You deposit $1000 a year into an account. This account earns 8% interest compounded yearly,(20 points)a) how much will you have after 10 years?b) How much total money did you put in the account.c) How much total interest did you earn?
Answers
Compound interest formuae :
A = P ( 1+r/100)^ n or A = P( 1+i)^n or A = P ((1 + i )^n -1 )/i
we will use the highlighted formular due to compounded yearly statement on the question:
where A = Accumulated amount;
P = original amount invested/ (borrowed )
n = number of years
r = interest rate as a percentage
i = r/100
Answer to (a )
A = P ((1 + i )^n -1 )/i
where n = 10; i = 8/100 =0.08 ; P = 1000
A = 1000 ( 1 + (8/100))^10 -1)/ 0. 08
A =1000 ( 14.48)
A =$14486.56
b. 1000 X 10 = $12000
c. you earned interest of $14486 - $12000 = $2486
What expression represents the sum of ages of Hugo and his two siblings?
Answers
The correct option is D
The sum of their ages is 3x + 8
Explanation:Given that Hugo's age = x
Jasmine's age = x + 3
Manny's age = (x + 3) + 2 = x + 5
The sum of their ages is:
x + (x + 3) + (x + 5)
= x + x + x + 3 + 5
= 3x + 8
Heather dropped a water balloon over the side of her school a height of 80 feet. The approximate height of the balloon at any point during it's fall can be represented by the following quadratic equation: h=-16t^2+80. About how long did it take for the balloon to hit the ground.A.1.73B.2.24C.2.45D.2.83
Answers
h = - 16t^ 2 + 80
[tex]h=-16t^2\text{ + 80}[/tex]The balloon will hit the ground when the height = 0
[tex]\begin{gathered} 0=-16t^2\text{ + 80} \\ \text{collect like terms} \\ \\ 16t^2\text{ = 80} \\ \text{Divide both sides by 16} \\ t^2\text{ = }\frac{80}{16} \\ t^2\text{ = 5} \\ t\text{ =}\sqrt[]{5} \\ t\text{ = 2.236} \\ t\text{ = 2.24} \end{gathered}[/tex]The correct option is B = 2.24
The following summarizes the number of fiction read last summers by a sample of 28 students.
Answers
SOLUTION:
The mean is given by the formula;
[tex]\frac{\sum_^fx}{\sum_^x}[/tex]We calculate this as;
[tex]\frac{2(3)+3(10)+4(15)}{3+10+15}=3.4[/tex]Therefore, the mean is 3.4
Venus' orbital speed is approximately 210 kilometers in 6 seconds. Earth's orbital speed is approximately 270 kilometers in 9 seconds. Which planet travels at a faster speed per second?
Answers
We know that
• Venus' orbital speed is 210 kilometers in 6 seconds.
,• Earth's orbital speed is 270 kilometers in 9 seconds.
First, we have to divide the numbers to find the ratio
[tex]\begin{gathered} \frac{210}{6}=35 \\ \frac{270}{9}=30 \end{gathered}[/tex]As you can observe, Venus has greater speed because it's 35 kilometers per second.
Hence, the answer is Venus.x-5=11;x=5Determine if the value of x is a solution to the equation
Answers
Given data:
The given expression is x-5=11.
Substitute 5 for x in the above expression.
5-5=11
0=11
As LHS is not equal to RHS so x=5 is not the solution of the given exprression.
Thus, x=5 is not the solution.
The boxplot below shows salaries for Construction workers and Teachers.
Answers
First, let's identify each element in a box plot:
Looking at the first box plot (Construction, Jennie), the first quartile is 30, and looking at the second box plot (Teacher, Markos), the first quartile is 25.
Since the first quartile represents the salary, that means Jennie makes more money, and the amount she does more is $5000.
(The graph shows the money in thousands)
3/4 + 7/10Write your answer as a fraction in simplest form.
Answers
action
Given
[tex]\frac{3}{4}+\frac{7}{10}[/tex]Solution
First, find the LCM which is 20 and write as common denominator
[tex]\frac{15}{20}+\frac{14}{20}[/tex]Add the fraction
[tex]\frac{15}{20}+\frac{14}{20}=\frac{29}{20}[/tex]Now to the simplest form
[tex]\frac{29}{20}=1\frac{9}{20}[/tex]The final answer
[tex]1\frac{9}{20}[/tex]consider the equation -4x+3y=7. Assume that y is a function of x. rewrite the equation using function notation F(x)
Answers
y=(7+4x)/3
y=F(x)
Answer: F(x)=(7+4x)/3
Which of the following is equivalent to 10^4 x 10^3? A 10^7 B 20^12 C 20^7 D 10^12
Answers
Explanation
Let's remember some properties for the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ \frac{a^m}{a^n}=a^{m-n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]hence
let's calculate the product
[tex]\begin{gathered} 10^4\cdot10^3 \\ 10^4\cdot10^3=10^{4+3}=10^7 \\ 10^4\cdot10^3=10^7 \end{gathered}[/tex]therefore, the answer is
[tex]A)10^7[/tex]I hope this helps you
using demos find the line of best fit to compare fat (x) and the calories(y) from the table pictured. round to the nearest hundredth (2 decimal places if needed
Answers
Find line of aproximation to data
the regression data line gives as result
y = ax + b
a= 11.73
b= 193.85
Each ticket to a matinee movie costs $8. Part A: Complete this table relating the number of movie tickets bought, m, to the total cost, c, of the tickets. m C 4 6 9 Part B: Write an equation that models this situation, using the variables m and c. Answer: Brandy thinks the number of movie tickets bought depends on the total cost of the movie tickets. Brandy's brother thinks the total cost of the movie tickets depends on the number of movie tickets bought Part C: Whose thinking is correct, Brandy's, her brother's, or both? Explain how you know.
Answers
Part A
Since each ticket costs $8, we need to add $8 for each plus ticket one buys:
[tex]\begin{gathered} 1\text{ ticket: \$}8 \\ 2\text{ tickets: \$}8+\text{ \$}8=\text{ \$}16 \\ 3\text{ tickets: \$}16+\text{ \$}8=\text{ \$}24 \\ 4\text{ tickets: \$}24+\text{ \$}8=\text{ \$}32 \\ 6\text{ tickets: \$}32+\text{ \$}16=\text{ \$}48 \\ 9\text{ tickets: \$}48+\text{ \$}24=\text{ \$}72 \end{gathered}[/tex]Therefore, we have:
Part B
Notice that, instead of summing (8+8+8+...) we can multiply $8 by the number of tickets bought m to obtain the total cost c.
Thus, we have:
[tex]c=m\times\text{ \$}8[/tex]Part C
The equation above (c = m x $8) shows that the total cost c depends on the number of tickets bought.
However, we write that relation in another way:
[tex]m=c\div\text{ \$}8[/tex]Thus, if we know the total cost, we can divide it by $8 to find the number of tickets bought. Then, we can say that the number of tickets boght m depends on the total cost c.
Therefore, both thoughts are correct.
f(x) = 2x - 1 g(x) = 3x h(x) = x^2 + 1Find f(g(x))
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Given the following functions:
f(x) = 2x - 1
g(x) = 3x
h(x) = x2 + 1
f(g(x)) means that we will be substituting the function of g(x) as x of the f(x) function.
We get,
[tex]f\mleft(g\mleft(x\mright)\mright)\text{ }\rightarrow\text{ f(x) = 2x - 1 }\rightarrow\text{ }f(g(x))=\text{ 2(3x) - 1}[/tex][tex]f(g(x))=\text{ 6x - 1}[/tex]34. A school admissions office accepts 2 out of every 7 applicants. Given that the school accepted 630 students, how many applicants were NOT accepted? F. 140 180 490 J. 1,260 K. 1,575
Answers
We were told that the school admissions office accepts 2 out of every 7 applicants. Thus, the probability that the school accepts an applicant is 2/7
There are only two outcomes. It is either the school accepts an applicant or it doesn't. If the school accepts 630 students, It means that 2/7 of the total number of applicants were accepted
Assuming the totla number of applicants is x, it means that
2/7 * x = 630
2x = 630 * 7 = 4410
x = 4410/2
x = 2205
The total number of applicants is 2205
The number of applicants that were not accepted is
2205 - 630 = 1575
1575 applicants were not accepted
This Venn diagram shows sports played by 10 students.PLAYSBASKETBALLMaiPLAYSSOCCERMickeyMarcusFranEllalanKarlJadaGabbyJuanLet event A = The student plays basketball.Let event B = The student plays soccer.What is PAB)?O A.A. «0.17B. 1=0.1010
Answers
ANSWER
[tex]P(A|B)=\frac{1}{3}\approx0.333[/tex]EXPLANATION
We want to find the probability P(A|B).
This is a conditional probability and its formula is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where P(A n B) is the probability that the student plays basketball and soccer and P(B) is the probability that the student plays soccer.
We have that:
[tex]P(A\cap B)=\frac{1}{10}[/tex]and
[tex]P(B)=\frac{3}{10}[/tex]Therefore, we have that:
[tex]\begin{gathered} P(A|B)=\frac{1}{10}\div\frac{3}{10} \\ P(A|B)=\frac{1}{10}\cdot\frac{10}{3} \\ P(A|B)=\frac{1}{3}\approx0.333 \end{gathered}[/tex]That is the answer.
Using the graph, determine the coordinates of the x-intercepts of the parabola.10984-10-98-7 -6-5-427 8 9103 410-8-10
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The x-intercepts are the points where the parabola crosses the x-axis,
Also, the y coordinate is always zero,
By looking at the graph we can see that the parabola crosses the x-axis at x = 4 and x= 6
X-intercepts = (4,0) and (6,0)
If you randomly select a letter from the phrase "Ichiro Suzuki is at the top of the lineup," what is theprobability that you select a consonant? (Your answer must be in the form of a reduced fraction.)Submit Question
Answers
Given the phrase "Ichiro Suzuki is at the top of the lineup", you can identify that:
- The total number of letters the phrase has is:
[tex]Total=33[/tex]- The number of consonants the phrase has is:
[tex]Consonants=18[/tex]Therefore, you can find the probability that you select a consonant by dividing the number of consonants in the phrase by the total number of letters:
[tex]P=\frac{18}{33}[/tex]You can reduce the fraction by dividing the numerator and the denominator by 3:
[tex]\begin{gathered} P=\frac{18\div3}{33\div3} \\ \\ P=\frac{6}{11} \end{gathered}[/tex]Hence, the answer is:
[tex]P=\frac{6}{11}[/tex]