Answers
The side length RQ of the triangle QRT that is 'x' will be 4 units.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
In triangle ΔRST, the side RT is given by the sine of angle 60°. Then we have
sin 60° = (2√3) / RT
(√3)/(2) = (2√3) / RT
RT = 2 x 2(√3) / (√3)
RT = 4
In triangle ΔQRT, the side QR is given by the tangent of angle 45°. Then we have
tan 45° = RQ / RT
1 = x / 4
x = 4
The side length RQ of the triangle QRT that is 'x' will be 4 units.
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Related Questions
For what value of x is line m parallel to line n?
Answers
Answer: x=-2
Step-by-step explanation:
they’re corresponding angles meaning they’re congruent or equal to each other then solve like any other problem
24 - 10x = 9 (ignore---------------------------------------------------------------------------------------------------------------)
Answers
[tex]\fbox{x=$\dfrac{3}{2}$}[/tex] or [tex]\fbox{x=1.5}[/tex]
Simplify Equation:
[tex]24-10x=9[/tex]
[tex]-10x+24=9[/tex]
Subtract 24 from both sides:
[tex]-10x+24-24=9-24[/tex]
[tex]-10x=-15[/tex]
Divide both sides by -10:
[tex]\dfrac{-10x}{-10} =\dfrac{-15}{-10}[/tex]
[tex]x=\dfrac{3}{2}[/tex] or [tex]x=1.5[/tex]
Who would win the race, (Camila or gabriela) Please help, on edge of failing ngl. !!
Answers
Answer:
Camilla will win.
Step-by-step explanation:
Camilla's rate = 12
Gabriella's rate = 10
The ratio x:y is equal to is 2 : 5, and y is 80% of z. Write an equation to represent the proportional relationship between x and z.
Answers
Answer:
z = 3.125 * x
Step-by-step explanation:
since y is 80 percent of z, we can represent it in the form of a ratio as 80:100.
Simplify it down: 80:100 = 8:10 = 4:5
therefore x:y = 2:5
and y:z = 4:5
"y" is common in both of these ratios. Therefore we now have to make the value of Y same in both of the ratios. Therefore we find the least common multiple of both the y values which is 5 and 4. It is 20.
Now we make the value of y in both the ratios 20. So we need to multiply 5 in 2:5 by 4. Since we multiplied one of the values by 4 we have to multiply the other one as well (2*4). Now our new ratio for x:y is 8:20. Do the same for the other ratio. the other ratio is 4:5. the y value here is 4. 4 needs to be multiplied by 5 to become 20. Therefore multiply 4 by 5 and multiply 5 by 4. our new ratio for y:z is 20:25
As you can see both the y values are similar now.
x:y = 8:20
y:x = 20:25
therefore we can now write x:y:z as 8:20:25
that also means that x:z is now 8:25.
Now we know that when x is 8 z is 25. in this case. 8 and 25 are directly proportional.
therefore we can write an equation as
25 = k*8
k = 25/8
k = 3.125
therefore z = 3.125 * x
Solve the following equations
25x²-4=0
Answers
Answer: x= (2)/5 & x= (-2)/5
Step-by-step explanation:
Factor Form:
1. Use the sum product patturn
25x^2-4=0 → 25x^2+10-10-4=0
2. Common factors from each pair
25x^2+10-10-4=0 → 5x(5x+2)-2(5x+2)=0
3. Rewrite the factored form
5x(5x+2)-2(5x+2)=0 → (5x+2)(5x-2)=0
4. Create separate equations
(5x+2)(5x-2)=0 → 5x+2=0 5x-2=0
5. Solve
5x+2=0 5x-2=0 → x=(2)/5 x=(-2)/5
The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.
Answers
Assuming this is what you were looking for.
We know points (6,33) (15,15) are on the line, we can use them to find slope using slope formula y2 - y1 over x2 - x1
15 - 33 over 15 - 6 = -18/9 or -2 slope
Using slope and the y intercept of 45 (where the line crosses the y axis) we can find the equation.
y = mx + b
y = -2x + 45
If we take one set of points and substitute them into our equation we can prove our equation.
15 = -2(15) + 45
15 = -30 + 45
15 = 15 they agree so problem solved!
NO LINKS!! Fredrico's Bank will you decide how often your interest will be computed, but with certain restrictions. Read the following options. What is the best deal after one year? Justify your answer.
Answers
Compounded quarterly; annual interest rate is 7.875%
========================================================
Explanation:
Let's say we are depositing P = 100 dollars, and we leave it in the account for a timespan of t = 1 year.
This will apply for options A through E.
-------------------
If we go with option A, then we would have n = 1 and r = 0.08
Use the compound interest formula to get the following:
A = P*(1+r/n)^(n*t)
A = 100*(1+0.08/1)^(1*1)
A = 108
We'll have $108 dollars in the account at the end of 1 year if we go with option A. The amount of interest only is A-P = 108-100 = 8 dollars.
-------------------
For option B, we have: n = 4 and r = 0.07875
A = P*(1+r/n)^(n*t)
A = 100*(1+0.07875/4)^(4*1)
A = 108.110625948487
A = 108.11
So far option B is slightly better since you've earned an extra $0.11, aka 11 cents.
-------------------
For option C, we have: n = 4 and r = 0.07875
A = P*(1+r/n)^(n*t)
A = 100*(1+0.0775/12)^(12*1)
A = 108.031299777277
A = 108.03
This amount is less compared to the $108.11 with option B. Therefore, option B is still the best so far.
-------------------
For option D, we have: n = 52 and r = 0.07625
A = P*(1+r/n)^(n*t)
A = 100*(1+0.07625/52)^(52*1)
A = 107.917207523206
A = 107.92
This is worse compared to option C.
Option B is still the best so far.
-------------------
For option E, we have: n = 365 and r = 0.075
A = P*(1+r/n)^(n*t)
A = 100*(1+0.075/365)^(365*1)
A = 107.787584644
A = 107.79
---------------------
Here's a table comparing the balance after 1 year for options A through E. Those balances all have a starting point of $100 as the deposit.
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Option} & \text{Balance after 1 year}\\\cline{1-2}A & \$108\\\cline{1-2}\boldsymbol{B} & \boldsymbol{\$108.11}\\\cline{1-2}C & \$108.03\\\cline{1-2}D & \$107.92\\\cline{1-2}E & \$107.79\\\cline{1-2}\end{array}[/tex]
Option B is the best choice earning the most ($108.11) if you deposit $100.
There's nothing special about the $100, so feel free to change it to something else to try other starting deposits. You'll find that option B will still provide the highest return.
Answer:
B
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedUse the Compound Interest Formula with the given values for each option to calculate a final equation where A equals a multiple of P.
The option with the greatest coefficient of P is the account which yields the highest interest after one year, and is therefore the best deal.
Option AGiven:
r = 8% = 0.08n = 1 (annually)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.08}{1}\right)^1[/tex]
[tex]\implies \sf A=1.08P[/tex]
Option BGiven:
r = 7.875% = 0.07875n = 4 (quarterly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.07875}{4}\right)^{4 \cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.0196875)^4[/tex]
[tex]\implies \sf A=1.081106259P[/tex]
Option CGiven:
r = 7.75% = 0.0775n = 12 (monthly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.0775}{12}\right)^{12\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.006458333\right)^{12}[/tex]
[tex]\implies \sf A=1.080312998P[/tex]
Option DGiven:
r = 7.625% = 0.07625n = 52 (weekly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.0765}{52}\right)^{52\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.001471154\right)^{52}[/tex]
[tex]\implies \sf A=1.079441506P[/tex]
Option EGiven:
r = 7.5% = 0.075n = 365 (daily)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.075}{365}\right)^{365\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.000205479\right)^{365}[/tex]
[tex]\implies \sf A=1.077875846P[/tex]
Summary[tex]\begin{array}{|c|l|}\cline{1-2} \sf Answer\;Option & \sf Coefficient\;of\;P\\\cline{1-2} A & 1.08\\\cline{1-2} B & 1.081106259\\\cline{1-2} C & 1.080312998\\\cline{1-2} D & 1.079441506\\\cline{1-2} E & 1.077875846\\\cline{1-2} \end{array}[/tex]
Therefore, the option with the greatest coefficient of P and therefore the best deal is option B.
49. $10,000 is invested at an APR of 4% for 10
years.
50. $10,000 is invested at an APR of 5% for 20 years.
51. $15,000 is invested at an APR of 3.2% for 25 years.
52. $3000 is invested at an APR of 4% for 12 years.
53. $5000 is invested at an APR of 3.1% for 12 years.
54. $40,000 is invested at an APR of 8.5% for 30 years.
Answers
The total amount, if $10,000 is invested at an APR of 4% for 10 years is $14000.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
$10,000 is invested at an APR of 4% for 10 years.
Calculate the total amount at the end as shown below:
[tex]A = p + p\times r\times t / 100[/tex]
A = 10000 + 10000 × 4 × 10 / 100
A = 10000 + 4000
A = 14000
Similarly, solve all the questions using this formula.
Therefore, the total amount, if $10,000 is invested at an APR of 4% for 10 years is $14000.
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The complete question is:
$10,000 is invested at an APR of 4% for 10 years. Find the total amount after 10 years.
Course Grade You were 6 points shy of a B in yo
394. How many points were possible in the course?
mathematics course. Your point total for the course was
(Assume that you needed 80% of the course total for a B.)
Answers
The point total possible for the given course is equal to 500.
What is a Percent?
A ratio whose second term is 100 is known as a percent. Parts per hundred are used in percentages. The mathematical representation of percent is %.The percent formula is given as, [tex]x=p \times b[/tex], where b is the base number, x is the number being compared to b, and p is the percent in decimal form.In the question, it is given that you were 6 points shy of a B and the current total points you have is 394.
So, the total number of points you require for a B is calculated as,
[tex]394+6=400[/tex]
So, the value of x is 400.
It is given that you need 80% of the course total for a B.
[tex]\implies p=\frac{80}{100}\\ \implies p=0.8[/tex]
Here, we have to find the base number (b).
We have, x = 80% of b
[tex]\implies x=0.8 \times b\\\implies 400= 0.8 \times b\\\implies x=\frac{400}{0.8}[/tex]
Simplifying, we get
[tex]x=500[/tex]
Therefore, 500 points were possible in the course.
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4. Which of the triangles below is not a right triangle?
3 cm, 4 cm, 5 cm
27 cm, 36 cm, 45 cm
6 ft, 8 ft, 12 ft
√6in, √10in, √4in
Answers
Answer:
3cm,4cm,5cm
Step-by-step explanation:
5 is the longest side ( the hypotenuse)
and by Pythagoras theorem x=√(3²+4²)
= √(9+16)
=√(25)
= 5
so 3cm,4cm,5cm is a right angle triangle.
x=√(27²+36²)
=√(729+ 1296)
=√2025
=45
so 27cm,36cm,45cm is a right angle triangle
to find out if a triangle is a right angle triangle try applying the law of Pythagoras theorem to see if it matches, and if it matches then it is a right angle triangle but if it doesn't then it's not a right angled triangle Try for the last two and put it down the comments I'll try to checkverify that (sin x -cos x)^2 =1-2 sin x cos x is an identity
Answers
By trigonometric formulas and algebra properties, the equivalence between the trigonometric expression (sin x - cos x)² and the trigonometric expression 1 - 2 · sin x · cos x.
How to prove the equivalence between two trigonometric expressions
In this problem we need to prove if the trigonometric expression (sin x - cos x)² is equivalent to the trigonometric expression 1 - 2 · sin x · cos x, this can be proved by trigonometric formulas and algebra properties. First, write the initial expression:
(sin x - cos x)²
Second, expand the binomial:
sin² x - 2 · sin x · cos x + cos² x
Third, use the fundamental trigonometric expression:
1 - 2 · sin x · cos x
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two more than a certian number is 15 less than the product of 7/8 and the number
Answers
The number is -136.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Let the number be x.
Given that, two more than the number, x, is 15 less than the product of 7/8 and the number, therefore:
x + 2 = (7/8)x - 15
x - (7/8)x = -15 -2
x/8 = -17
x = -136
Hence, the number is -136.
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Can someone help me with this problem?
Answers
Answer:
$33
Step-by-step explanation:
l=prt = 30 × 0.05 × 2=3
total save = 30+ 3= 33
What is the ratio of shaded to unshaded squares in the grid below?
Group of answer choices
3/5
5/8
1/3
Answers
Answer:
1/3
Step-by-step explanation:
shaded is 10 and unshaded is 15
so the answer is 1/3 because
5 can be multiplied both sides
5 times 3 is 15
5 times 1 is 5
So both sides can be multiplied by 5
Answer: alt account
Step-by-step explanation:
what is the reciprocal of 8?
Answers
Answer:1/8
Step-by-step explanation:
The reciprocal of a number is what you multiply by a number to give 1. Therefore
8x = 1
x = 1/8
Find log0.81 rounded to the nearest tenth.
Answers
The value of the logarithm of 0.81 for logarithm properties is equal to - 0.1.
How to determine the value of a logarithm
Herein we must use logarithm properties to simplify a given logarithm and solve the resulting expression. The properties to be used in this question are described below:
㏒ (a / b) = ㏒ a - ㏒ b
㏒ aᵇ = b · ㏒ a
First, write the logarithmic equation:
㏒ 0.81
㏒ 81 / 100
Second, use the logarithmic property for a division:
㏒ 81 - ㏒ 100
Third, use the logarithmic property for a power:
㏒ 3⁴ - ㏒ 10²
4 · ㏒ 3 - 2 · ㏒ 10
4 · ㏒ 3 - 2
4 · 0.477 - 2
- 0.092
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Help please i need to find what mHJ is
Answers
Answer: 72 for HJ.
Step-by-step explanation:
HELP!! 30 POINTS!!
What is the correlation of the data shown?
0
1
-0.5
-1
Answers
The correlation of the data shown on the graph is 0
How to determine the correlation?In this question, the graph represents the given parameter
From the graph, we have the following observations
The x values is on the horizontal axisThe y values is on the vertical axisAs the x values increase, the y values do not follow a patternWhen the change (increase) in the x values causes a random change (increment) in the y values, then the correlation is 0
From the list of options, we have
-1, -0.5 and 1 are not zero i.e. 0
This means that the correlation is (a) 0
Hence, the correlation of the data is 1
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[tex]y= 4\\y = \frac{8}{3} x - 4\\[/tex]
Answers
Answer: x=3
Step-by-step explanation:
Assuming you want to solve the system,
You are already given y = 4, so plug 4 in for the other y in the other equation.
[tex]y=\frac{8}{3} x-4\\\\4=\frac{8}{3} x-4\\4+4=\frac{8}{3} x-4+4\\\frac{3}{8}\times 8=\frac{3}{8} \times\frac{8}{3}x\\\\x=3[/tex]
Anna works at an electronics
store as a salesperson. Anna earns a 5% commission a
the total dollar amount of all
phone sales she makes, and earns a 7% commission Or
all computer sales. Anna made a total of $2100 in sales
and earned $119 in
commission. Write a system of equations that could be used to determine the dollar
amount of phone sales Anna made and the dollar amount of computer sales she
made. Define the variables that you use to write the system.
Let
Answers
Let p be the amount of sales (in dollars) of phones.
Let c be the amount of sales (in dollars) of computers.
Equation 1: sales
p + c = 2100
the amount of all sales is 2100
Equation 2: commission
0.05p + 0.07c = 119
5% commission on phones plus 7% commission on computers totals to 119
Given the function y = -5x +4, what is the range of the function if the domain is {-2, 0,5}
Answers
Answer:
range is { - 21, 4 , 14 }
Step-by-step explanation:
the domain gives the value of x , the input
the range is the corresponding values of y, the output
substitute values of x from the domain into the function
x = - 2 : y = - 5(- 2) + 4 = 10 + 4 = 14
x = 0 : y = - 5(0) + 4 = 0 + 4 = 4
x = 5 : y = - 5(5) + 4 = - 25 + 4 = - 21
then range is { - 21, 4 , 14 }
Whats the answer please help its worth 10 points!
Answers
This is the correct answer. Hope it helps :)
Please help! The answer is the slope and it needs to be rounded to 3 decimal places.
Answers
The slope is 0.003
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
the coordinates are (12000, 20) and (18000, 2)
so, slope= 18 / 6000
= 0.003
The 3 in the thousandths place rounds down to 3, or stays the same, because the digit to the right in the ten thousandths place is 0.003.
Hence, the slope is 0.003.
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"2. Compare and contrast the two major sects of Islam, Sunni and Shia, by filling out the table below. (10 points)
Similarities in the sects Differences between the sects"
Answers
The similarity is that Sunni and Shia Muslims agree on the fundamental tenets of Islam, such as worshiping Allah as God, acknowledging Muhammad (Peace Be Upon Him) as the Prophet, and adhering to the Quran's teachings.
The difference is that Shia place a greater emphasis on Muhammad's family ancestry through a succession of Imams than Sunnis do on imitating the Prophet and his example.
What is the Similarities and difference between the difference Islamic sect?All Shia and Sunni Muslims recognize the importance of the Quran; contrary to popular belief, Shi'a does not use a corrupted version of the Quran.
Shi'a and Sunni Muslims both use the Hadith, though they often prefer different collections of sayings.
They have different perspectives on imams. Imams are considered saints in Sunni Islam and must have a strong commitment to the Quran and Sunnah in order to be nominated. In Shia Islam, however, only God has the authority to name an imam. Only imams in Shia Islam have the authority to translate the Quran.
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What is Four divided by 1 8. It’s a faction the one and eight
Answers
Answer: 32
Step-by-step explanation:
4 ÷ 1/8
You can reduce the expression by cancelling out common factors;
4/1 ÷ 1/8
Cross cancel the ones, and then multiply 4 and 8
4 x 8 = 32
The frame of a bicycle weighs 16 pounds. Each tire weighs 9 ounces. The seat weighs 12 ounces. The handlebars weigh 24 ounces. How many pounds does the bicycle weigh?
Answers
The weight of the bicycle is 19.375 pounds.
Define weight.In physics and engineering, the weight of an object refers to the gravitational force that pulls on it. Weight is frequently described as a scalar quantity that measures the gravitational force's strength.
The weight of the frame of the bicycle= 16 pounds
1 pound= 16 ounces
Therefore, 16 pounds= 16 x 16 = 256 ounces
The weight of one tire= 9 ounces
Therefore, the weight of two tires= 9 x 2 = 18 ounces
The weight of the seat= 12 ounces
The weight of handlebars= 24 ounces
Therefore, the total weight of the bicycle = 256 + 18 + 12 + 24
= 310 ounces
Therefore, the bicycle weighs 310 ounces
That is 310/ 16 = 19.375 pounds
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What is the distance between Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles what is the difference between them I need it in scientific notation
Answers
The distance between Texas and Rhode Island will be;
⇒ 2.59 × 10⁵ square miles
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles.
Now,
Since, Texas 2.6* 10 to the 5th power square miles and Rhode Island 1.21 * 10 to the 3rd power square miles.
Hence, The distance between Texas and Rhode Island will be find as;
⇒ 2.6 × 10⁵ - 1.21 × 10³
⇒ 260 × 10³ - 1.21 × 10³
⇒ (260 - 1.21) × 10³
⇒ 258.79 × 10³
⇒ 2.59 × 10⁵ square miles
Thus, The distance between Texas and Rhode Island will be;
⇒ 2.59 × 10⁵ square miles
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Solve for a. √a-b+c=3 A. a=3+√b-√c B. a=9+b-c C.a=9+√b-√c D. a=3+b-c
Answers
Answer:
a=9+b−c
Step-by-step explanation:
how much would it cost to replace all the windows on all the buildings in the united states?
Answers
[(1 1/4 - 3/4) · (- 2/3) ³] ÷ (-4)
What is the value of the expression
Answers
Answer:
Step-by-step explanation:
1 1/4-3/4=5/4-3/4=(5-3)/4=2/4=1/2
(-2/3)3=-8/27