Identify the values of the variables. Give your answers in simplest radical form. Help PLEASE!!
Answers
Answer:
x = 5 sqrt(6)/3
y= 10 sqrt(6)/3
Step-by-step explanation:
We know sin 60 = opposite/hypotenuse
sin 60 = 5 sqrt(2) /y
Multiply each side by y
y sin 60 = 5 sqrt(2)
Divide each side by sin 60
y sin 60/ sin 60 = 5 sqrt(2)/ sin 60
y = 5 sqrt(2) / sin 60
y = 5 sqrt(2) / sqrt(3) /2)
y = 10 sqrt(2)/ sqrt(3)
You cannot leave a sqrt in the denominator
y= 10 sqrt(2)/ sqrt(3) * sqrt(3)/sqrt(3)
y= 10 sqrt(6)/3
tan 60 = oppositve/ adjacent
tan 60 = 5 sqrt(2)/ x
Multiply each side by x
x tan 60 = 5 sqrt(2)
Divide by tan 60
x = 5 sqrt(2)/tan 60
x =5 sqrt(2)/sqrt(3)
You cannot leave a sqrt in the denominator
x = 5 sqrt(2)/sqrt(3) * sqrt(3)/sqrt(3)
x = 5 sqrt(6)/3
Related Questions
Real estate values in a town are increasing at a rate of 14% per year.
Mrs. Knoxville purchased a building for $590,000 in 2012.
How much can she expect to sell the building for in 2020, assuming this trend continues?
Enter your answer in the box.
Round to the nearest whole dollar.
Answers
Answer:
$1,093,026
Step-by-step explanation:
We have been given that real estate values in a town are increasing at a rate of 14% per year. Mrs. Knoxville purchased a building for $590,000 in 2012.
We are told that real estate values are increasing at a rate of 14%, this means that values of real estates are increasing exponentially.
Since we know that an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r= growth rate in decimal form.
a= Initial value.
Let E(t) be value of real estates t years after 2012. Now let us substitute our given values in exponential function form.
Upon converting our increase rate to decimal form we will get,
[tex]14\text{ percent}=\frac{14}{100}=0.14[/tex]
[tex]E(t)=590,000*(1+0.14)^t[/tex]
[tex]E(t)=590,000*(1.14)^t[/tex]
Now let us substitute the value for building in 2020 by substituting t=8 as 2020-2012=8.
[tex]E(2020)=590,000*(1.14)^8[/tex]
[tex]E(2020)=590,000*2.8525864220672256[/tex]
[tex]E(2020)=1,683,025.989019663104\approx 1,683,026[/tex]
Now let us subtract 590,000 from 1683026 to find the amount that Mrs. Knoxville can get from selling the building.
1,683,026-590,000=1,093,026
Therefore, Mrs. Knoxville can get $1,093,026 from selling the building.
Find the cos(Θ) of an angle in standard position if the terminal side passes through the point (4, -8).
Note: Answer choices attached below
Answers
Look at the picture.
[tex]r=\sqrt{x^2+y^2}-\text{from the Pythagorean theorem}\\\\\sin\theta=\dfrac{y}{r}\\\\\cos\theta=\dfrac{x}{r}\\\\\tan\theta=\dfrac{y}{x}\\\\\cot\theta=\dfrac{x}{y}[/tex]
We have the point
[tex](4,\ -8)\to x=4,\ y=-8[/tex]
Calculate r:
[tex]r=\sqrt{4^2+(-8)^2}=\sqrt{16+64}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5[/tex]
Substitute:
[tex]\cos\theta=\dfrac{4}{4\sqrt5}=\dfrac{1}{\sqrt5}\to\boxed{C)}[/tex]
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(−8, 0) , B(−3, 5) ; 2 to 3
Answers
Answer:
Step-by-step explanation:
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-8,0)\qquad B(-3,5)\qquad \qquad \stackrel{\textit{ratio from 2 to 3}}{2:3} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-8,0)=2(-3,5)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\cfrac{(3\cdot -8)+(2\cdot -3)}{2+3}\quad ,\quad \cfrac{(3\cdot 0)+(2\cdot 5)}{2+3}\right) \\\\\\ P=\left(\cfrac{-24-6}{5}~,~\cfrac{0+10}{5} \right)\implies P=(-6~,~2)[/tex]
A triangle has sides measuring 5 inches and 8 inches. If x represent the length in inches of the third side , which inequality gives the range of possible values for x ?
Answers
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
1. x ≤ 5 ≤ 8 then x + 5 > 8 → x > 8 - 5 → x > 3 therefore 3 < x ≤ 5.
2. 5 ≤ x ≤ 8 then 5 + x > 8 → x > 3 therefore 5 ≤ x ≤ 8
3. 5 ≤ 8 ≤ x then 5 + 8 > x → 13 > x → x < 13 therefore 8 ≤ x < 13.
Answer: 3 < x < 13 → S = (3, 13)Answer:
3 < x < 13
Step-by-step explanation:
Since, a triangle is possible when the sum of any two sides is greater than the third side,
Given,
The sides of the triangle are 5 inches and 8 inches,
If x shows the third side,
Then, by the above statement,
x < 5 + 8 ⇒ x < 13
5 < x + 8 ⇒ -3 < x
8 < x + 5 ⇒ 3 < x
Hence, the required inequality gives the range of possible values for x is,
3 < x < 13
M∠A = 75 + 5x
m∠B = 111 − 6x
m∠C = 87 + 3x
m∠D = 39 + 6x
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are congruent. Prove that quadrilateral ABCD is a parallelogram by finding the measures of the opposite angle pairs?
A) 95°, 85°
B) 105°, 75°
C) 115°, 65°
D) 125°, 55°
Answers
Answer:
See below
Step-by-step explanation:
For a parallelogram m < A = m < C so:-
75 + 5x = 87 + 3x
2x = 12
x = 6
and m< A = 75 + 30 = 105
and m < C = 87 + 18 = 105
Now if the other 2 angles are = 75 degrees( that is the same side angles add up to 180 degrees) we have proved that it is a parallelogram.
m < B = m < D
111 - 6x = 39 + 6x
-12x = -72
x = 6
m < B = 111 - 36 = 75 and m < D = 39 + 36 = 75
So this has been proved.
To prove that quadrilateral ABCD is a parallelogram, solve for x to find the values that make the opposite angles congruent. Plug in the values of x to find the measures of the opposite angle pairs. None of the given answer choices are correct.
Explanation:To prove that quadrilateral ABCD is a parallelogram, we need to show that both pairs of opposite angles are congruent. We are given the measures of the angles using variable expressions. We can set the expressions for opposite angles equal to each other and solve for x to find the values of x that make the opposite angles congruent. Finally, we plug in the values of x to find the measures of the opposite angle pairs.
Step 1: Set the expressions for opposite angles equal to each other: 75 + 5x = 39 + 6x and 111 - 6x = 87 + 3xStep 2: Solve the equations for x. For the first equation, subtract 5x and 39 from both sides to get -64 = x. For the second equation, subtract 87 and 3x from both sides to get 24 = 9x. Divide both sides by 9 to get x = 8/3.Step 3: Plug in the values of x into the expressions for the opposite angles to find their measures. For angle A, substitute x = -64 into 75 + 5x to get 75 + 5(-64) = -205. For angle D, substitute x = -64 into 39 + 6x to get 39 + 6(-64) = -375. For angle B, substitute x = 8/3 into 111 - 6x to get 111 - 6(8/3) = 89. For angle C, substitute x = 8/3 into 87 + 3x to get 87 + 3(8/3) = 95.Step 4: Check if the opposite angles are congruent. Angle A and angle C have measures of -205 and 95, respectively, which are not congruent. Angle B and angle D have measures of 89 and -375, respectively, which are also not congruent.Since the opposite angles are not congruent, we cannot conclude that quadrilateral ABCD is a parallelogram. Therefore, none of the given answer choices (A) 95°, 85°, (B) 105°, 75°, (C) 115°, 65°, or (D) 125°, 55°, are correct.
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What number goes in the box so that \[x^2 + \boxed{\phantom{00}}x + 100\]is the square of a binomial? If you find more than one, give your answer as a list.
Answers
Since [tex]100=(\pm10)^2[/tex], the idea here is to find [tex]b[/tex] such that
[tex](x\pm10)^2=x^2+bx+100[/tex]
Expanding the left side completely, we find two possibilities:
[tex]x^2\pm20x+100[/tex]
so that [tex]b[/tex] can be either positive or negative 20.
The answer will be ±20
Let us consider a binomial (x ± a)
now squaring it we get [tex]x^{2}[/tex] ± 2ax + [tex]a^{2}[/tex]
If we compare it to the question we get [tex]a^{2} =[/tex] 100
⇒ a = ±10
According to the question we have to find the value of 2a
2a = 2×(±10) = ±20
Hence ±20 is the answer.
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You earn $1,166 gross taxable income every week, and have claimed no exemptions. Assuming that you have no other sources of income, what is the amount of income tax withheld each week? a. $323 b. $337 c. $340 d. $344Please select the best answer from the choices provided
Answers
Answer:
C
Step-by-step explanation:
Gross taxable Income = $ 1,166
Rate of Income tax = 30%
Amount of income tax = 30 % of 1,166
= [tex]\frac{30*1166}{100}[/tex]
=$339.6
≅$340
Answer:
$340
Step-by-step explanation:
A problem states: "There are 2 more horses than cows in a field. There are 16 animals in the field in all. How many horses are there in the field?"
Let h represent the number of horses.
Which equation represents the situation?
2h + 2 = 16
h + 2 = 16
2(h+2)=16
2h−2=16
Answers
Answer:
Correct choice is D
Step-by-step explanation:
Let h represent the number of horses. If there are 2 more horses than cows in a field, then (h-2) represent the number of cows. In total there are h+(h-2) animals. It is known that there are 16 animals in the field in all, then
h+h-2=16,
2h-2=16.
Given that [tex]2^x[/tex] = 7, find the value of [tex]4^x^-^1[/tex].
Answers
Answer:
[tex] \dfrac{49}{4} = 12.25 [/tex]
Step-by-step explanation:
[tex] 4^{x-1} = [/tex]
[tex] = (2^2)^{x - 1} [/tex]
[tex] = 2^{2(x - 1)} [/tex]
[tex] = 2^{2x - 2} [/tex]
[tex] = 2^{x + x - 2} [/tex]
[tex] = 2^x \times 2^x \times 2^{-2} [/tex]
[tex] = 7 \times 7 \times \dfrac{1}{2^2} [/tex]
[tex] = \dfrac{49}{4} = 12.25 [/tex]
WILL MARK BRAINLIEST!!! PLEASE HELP!!!! Triangle RDW below is a right triangle. Line RW is 26 units, Line WD is 24 units, and Line DR is 10 units. The measure of angle W is 50°. Find the sine W.
A. 5/10
B. 5/13
C. 13/5
D. 12/13
Answers
Answer:
5/13
Step-by-step explanation:
sine W = sine 50 degrees = opposite /hypotenuse
= 10/26
= 5/13
Final answer:
The sine of angle W in the right triangle is the ratio of the side opposite to angle W (24 units) to the hypotenuse (26 units). Therefore, the sine of angle W is 12/13(option D).
Explanation:
The problem describes a right triangle with sides of length 26 units, 24 units, and 10 units, and it asks for the sine of angle W, which is known to be 50 degrees. In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the angle over the length of the hypotenuse. Thus, to find the sine of angle W, we need the opposite side to angle W, which is WD measuring 24 units, and the hypotenuse RW, measuring 26 units.
The sine of angle W is calculated by the formula
sine of angle W = WD\RW
24\26
12\13
What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units
Answers
Answer:
the answer is C. 31 units
I just did the assignment
The length of segment AD be for the quadrilateral to be a parallelogram is 8 units. Therefore, option A is the correct answer.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
In quadrilateral ABCD, AD║BC.
Here, AD=BC
3x+7=5x-9
2x=16
x=8
Therefore, option A is the correct answer.
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The beginning balance of Zerina's savings account for the month of July was $1800 and it remained this way for the first 12 days of the month. On July 13, Zerina made a withdrawal of $400, so her balance changed, and it remained the same for a total of 8 days. On July 21, Zerina made a deposit of $1200, so her balance changed again, and it remained the same for 11 days to finish out the month. If Zerina's savings account has an APR of 7.3%, calculates interest daily, and pays interest at the end of the month, how much did Zernia earn in interest in the month of July?
Answers
^
2600×7.3
^
$18,980 total.
Answer:
Interest income in the month = $12.28
Final balance = 2612.28
Step-by-step explanation:
The initial amount of $1800 remains in the account for the first 12 days of July. Then:
Interest earned = [tex]\frac{1800 * 0.073 * 12}{365} = 4.32[/tex]
Withdrawal = 400
New balance = 1800 - 400 = 1400
The amount 1400 remains in the account for 8 days. Then:
Interest Earned = [tex]\frac{1400 * 0.073 * 8}{365} = 2.24[/tex]
Deposit = 1200
New balance = 1400 + 1200 = 2600
The amount 2600 remains in the account for 11 days. Then:
Interest Earned = [tex]\frac{2600 * 0.073 * 11}{365} = 5.72[/tex]
Balance = 2600 + 4.32 + 2.24 + 5.72 = 2612.28
Interest income in the month = 4.32 + 2.24 + 5.72 = $12.28
Given the literal equation for the area formula of a trapezoid: equation is in the photo attached. Only do the first one. PLEASE SHOW WORK :)
Answers
Answer:
2A/h - b1 = b2
Step-by-step explanation:
A = 1/2 h ( b1+b2)
We want to solve for b2
Multiply each side by 2
2A = 2* 1/2 h ( b1+b2)
2A = h ( b1+b2)
Divide each side by h
2A / h = h/h ( b1+b2)
2A / h = b1+b2
Subtract b1 from each side
2A/h - b1 = b1 + b2 -b1
2A/h - b1 = b2
For which function will both ordered pairs (2, 8) and (6, 12) be solutions?
y = 4x
y = 6 + x
y = 2x
y = 18 - x
Answers
Plug the numbers into the equations, for each ordered pair substitute the first number (2) for x and the second number (8) for y...
Do the same thing with (6, 12) and if the number on each side of the equals sign is the same for both ordered pairs then you have the solution.
Hope that helps!
Each unit costs 14p how much does942 cost?????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Answers
Answer:
13188
Step-by-step explanation:
PLEASE HELP The Brick Corporation pays its cumulative preferred stockholders $1.95 per share. There are 40,000 shares of preferred stock and 80,000 shares of common stock. In 2001, 2002, and 2003, Brick Corporation did not declare a dividend. In 2004, the Board of Directors declared a $600,000.00 dividend. What is the amount that the common shareholder will receive per share?
Answers
Answer:
$5.00
Step-by-step explanation:
Dividend Per Share = Total Dividends Paid / Shares Outstanding
How many shares outstanding?
Preferred stock + common stock
80,000+40000=120000
Dividend Per Share = $600,000.00 /120000
=$5.00
The preferred shareholder gets 1.95 per share plus dividends.
The common shareholder only gets dividends.
Answer:
$3.60
Step-by-step explanation:
Strep throat is caused by Streptococcus bacteria. The amount of bacteria multiplies at a rate of 10^13 per 10^2 hours. Part B What is the total amount of bacteria present after 10^3 hours? Show your work.
Answers
Answer:
10^14
Step-by-step explanation:
Number of bacteria For 10^2 hours = 10^13
Number of bacteria for 1 hour = 10^13/10^2 = 10^11
Number of bacteria for 10^3 hours = 10^11 x 10^3 = 10^ (11+3) = 10^14
Plz help
Which expression is equal to 228−−√−563−−√ ?
−377√
−7√
7√
−117√
Answers
Answer:
the correct answer is -11v7
Step-by-step explanation:
The correct expression that is equal to (2√28 - 5√63) is;
Option D; -11√7
The correct question is;
Which expression is equal to 2√28 - 5√63
The correct options are in the link at the end of this answer.
The given expression is in surd form. To solve it, we first have to break down the numbers inside the square roots into a product of two numbers with one of the numbers being a perfect square.
We know that;
28 can be expressed as 7 × 4 = 28
Also; 63 can be expressed as 7 × 9 = 63
Thus;
2√28 - 5√63 will be written as; 2√(7 × 4) - 5√(9 × 7)
From product law of surds, we know that;
√(a × b) = √a × √b
Thus, our expression is;
2(√4 × √7) - 5(√9 × √7)
⇒ 2(2√7) - 5(3√7)
⇒ 4√7 - 15√7
Factorize √7 out to get;
(4 - 15)√7
⇒ -11√7
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Give a real world example of two similar situations in which one is proportional relationship and the second one is non proportional
Answers
Real world examples of proportional and non-proportional relationships can be observed in the relationship between the distance a car travels and the fuel consumed (proportional), and in an employee's pay scale (non-proportional).
Explanation:In the real world, one can identify numerous examples related to proportional and non-proportional relationships. For instance, consider the relationship between distance and fuel consumption in a car. Here, a car maintains a set distance per gallon ratio, which is a proportional relationship - if distance doubles, fuel consumed also doubles.
Contrasting this, the pay scale in many workplaces may illustrate a non-proportional relationship. For instance, if an employee works overtime, he/she may earn a higher rate, different from their regular hourly wage. In this case, a doubling of hours worked does not necessarily equate to a doubling of the total salary.
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Alaina is selling wreaths and poinsettias for her chorus fundraiser. Wreaths cost $27 each poinsettia cost $20 each. If she sold 15 poinsettias and made $543, how many wreaths did she sell?
Answers
Answer:
The number of wreaths Alaina sells is 9 .
Step-by-step explanation:
As given
Alaina is selling wreaths and poinsettias for her chorus fundraiser.
Wreaths cost $27 each poinsettia cost $20 each.
If she sold 15 poinsettias and made $543.
Let us assume that the number of wreaths Alaina sells = x
As the number of poinsettias Alaina sells = 15
Than the equation becomes
27x + 15 × 20 = 543
27x + 300 = 543
27x = 543 - 300
27x = 243
[tex]x = \frac{243}{27}[/tex]
x = 9
Therefore the number of wreaths Alaina sells is 9 .
Alaina sold 9 wreaths. After calculating the revenue from poinsettias ($300), the remaining amount ($243) was divided by the cost of one wreath ($27) to find the number of wreaths sold.
To determine how many wreaths Alaina sold, we first need to calculate the total revenue from selling 15 poinsettias. Since each poinsettia costs $20, we multiply 15 by $20:
15 poinsettias x $20/poinsettia = $300Now, subtract the total revenue from poinsettias from the total amount made:
$543 total made - $300 from poinsettias = $243 remainingThis remaining amount must be from the sale of wreaths. Since each wreath costs $27, we divide $243 by the cost of one wreath:
$243 / $27 per wreath = 9 wreaths soldTherefore, Alaina sold 9 wreaths.
What is the greatest possible integer value of x for whichsquare root of x-5 is an imaginary number?
Answers
Answer: 4
Step-by-step explanation:
√x imaginary if and only if x < 0
√(x-5) imaginary ifi x-5 < 0
x<5
4 is the largest integer < 5.
Answer: It is 4
Step-by-step explanation: I got it correct on mines.
A square measures 8 inches on each side. What is its area rounded off to the nearest square centimeter? (Note: 1 inch ≈ 2.54 cm) a) 413 sq cm b) 512 in.² c) 64 cm² d) 32 in.²
Answers
Answer:
C.) 413 cm^2
Step-by-step explanation:
To figure out the area of a square, much like a rectangle we multiply length × width. In this case because the length and width are the same (definition of a square) then it's simply [tex]s^2[/tex] and 8 inches is 20.32 cm (8x2.54):
[tex]s^2=20.32^2=412.90 \approx 413[/tex]
a.) 413 cm^2
Answer:
41 sq cm is the answer
Step-by-step explanation:
A recipe that will make 3 pies calls for 7cups of flour. How many pies can you make with 28 cups of flour?
Answers
Matrix M shows the one-way fares for four commuter train routes. Suppose the rail service lowers all fares by 15%. Which formula shows how to find the matrix that would display the new fares?
A) 0.15M
B) 0.85M
C) 1.15M
D) M - 0.15
Answers
Answer:
B) 0.85M
Step-by-step explanation:
The new fare schedule is the current fare schedule reduced by 15% of current fares:
... M - 0.15M = 0.85M
I am redecorating my home. I am adding tile to the kitchen which is 18' long and 16' wide. I am also tiling the master bathroom. It is 12' wide and 15' long. I need to buy enough tile to cover both spaces. How many square feet of tile do I need for the kitchen? How many square feet of tile will I need for the bathroom? If the tile costs $2.50 per sq ft, how much money will I spend on tile?
Blank # 1
Blank # 2
Blank # 3
Answers
Answer:
The kitchen requires 288 sq. ft. of tile
The master bathroom requires 180 sq. ft. of tile
In total, we will spend $1170
Step-by-step explanation:
The area of the kitchen is length * width:
Area of Kitchen = [tex]18*16=288[/tex] sq. ft.
The area of the master bathroom is length * width:
Area of Master Bathroom = [tex]12*15=180[/tex] sq. ft.
Question 1: "How many square feet of tile do I need for the kitchen?"
The kitchen requires 288 sq. ft. of tile
Question 2: " How many square feet of tile will I need for the bathroom?"The master bathroom requires 180 sq. ft. of tile
Question 3: "If the tile costs $2.50 per sq ft, how much money will I spend on tile?"In total, we require [tex]288+180=468[/tex] sq. ft. of tiles. If $2.50 is charged per square feet, in total we will spend:
[tex]468*2.5=1170[/tex] dollars
You'll need 288 square feet of tile for the kitchen, 180 square feet for the bathroom, and the total cost for the tile will be $1170.
To calculate the amount of tile needed for the kitchen and the master bathroom, you first need to determine the area of each room. Area is calculated by multiplying the length by the width of the room.
For the kitchen:
Length = 18 feet
Width = 16 feet
Area = Length x Width = 18 ft x 16 ft = 288 square feet
For the master bathroom:
Length = 15 feet
Width = 12 feet
Area = Length x Width = 15 ft x 12 ft = 180 square feet
To calculate the total cost of the tile:
Cost per square foot = $2.50
Total area = Area of kitchen + Area of bathroom = 288 sq ft + 180 sq ft = 468 square feet
Total cost = Total area x Cost per square foot = 468 sq ft x $2.50 = $1170
When you want to change a cell color, which menu should you select?
A) Fill drop-down menu
B) Font size drop-down menu
C) AutoSum drop-down menu
D)Shapes drop-down menu
Answers
To change a cell color in a spreadsheet program, one should select the Fill drop-down menu, found in the Home tab, to choose and apply a new color to the cell.
Explanation:When you want to change a cell color in a spreadsheet program such as Microsoft Excel, you should select the A) Fill drop-down menu. This is the option that allows you to change the background color of a cell. You can typically find the Fill drop-down menu in the Home tab of the ribbon at the top of your spreadsheet application. To change a cell's color, you simply click on the cell you want to format, then go to the Home tab, click the Fill drop-down menu, and choose the color you wish to apply.
(15 points)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.
Given = 5√6
Answers
Answer:
Each of the legs of isosceles right triangle is 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Watch the attached figure for the isosceles right angled triangle
Looking at the figure we see that AB=5√6 and BC=CA
According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
1) Applying the Pythagorean theorem to the isosceles right triangle, we have
[tex]BC^{2} + CA^{2} = AB^{2}[/tex]
2) Let BC=a and CA=a as they both are equal
So,
[tex]a^{2} + a^{2} = (5\sqrt{6} )^{2}[/tex]
=> [tex]2a^{2} = (5\sqrt{6} )(5\sqrt{6} )[/tex]
=> [tex]2a^{2} = 5*5*\sqrt{6}*\sqrt{6}[/tex]
=> [tex]2a^{2} = 25*6[/tex] (since √6*√6 = (√6)²= 6)
=> [tex]2a^{2} = 150[/tex]
3) Dividing both sides by 2, we get
[tex]\frac{2a^{2} }{2} =\frac{150}{2}[/tex]
4) Cancelling out the 2's on the left, we get
[tex]a^{2}[/tex] = 75
5) Taking the square root on both sides, we have
[tex]\sqrt{a^{2}} = \sqrt{75}[/tex]
=> a = 5[tex]\sqrt{3}[/tex]
So,
Each of the legs of isosceles right triangle is 5[tex]\sqrt{3}[/tex]
Answer:
Hi :) if you're coming from heritage and/or your answer needs a 2 in it, it would be 6 sqrt 2
Step-by-step explanation:
For the members of a neighborhood meeting group, the probability of randomly selecting a member who likes to cook is 42%, the probability of randomly selecting a member who likes to sew is 23%, and the probability of randomly selecting a member who likes to both cook and sew is 7%.
What is the probability of randomly selecting a member who likes to cook or likes to sew?
Answers
Answer: Probability of randomly selecting a member who likes to cook or likes to sew = 58%
Step-by-step explanation:
Since we have given that
Probability of a randomly selecting a member who likes to cook=P(C) = 42%
Probability of a randomly selecting a member who likes to sew =P(S)= 23%
Probability of a randomly selecting a member who likes to both cook and sew
[tex]P(C\cap S)=7\%[/tex]
As we know the "Probability rules " :
[tex]P(C\cup S)=P(C)+P(S)-P(S\cap C)\\\\P(C\cup S)=42+23-7\\\\P(C\cup S)=58[/tex]
So, Probability of randomly selecting a member who likes to cook or likes to sew = 58%
Answer:
58%
Step-by-step explanation:
Trever and Marisa together have 28 t shirts to sell if marissa has 4 fewer t shirts than trevor find how many t shirt Trevor has
Answers
Answer:
Trevor has 16 number of shirts
Step-by-step explanation:
We have been given that Trevor and Marisa together have 28 t shirts to sell if Marissa has 4 fewer t shirts than Trevor
let the number of shirts Trevor have be x
And since, Marissa has 4 fewer than Trevor so number of shirts Marissa will have be x-4
Hence, according to question equation becomes:
x+x-4=28
We will solve for x to find the number of t shirts Trevor has
2x -4 =28
2x = 32
x =16
Hence, Trevor has 16 number of shirts
The height of a triangle is 2 less than 5 times its base. If the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?
A. 5x2 − 2x − 24 = 0
B. 5x2 − 2x − 6 = 0
C. 5x2 − 2x − 12 = 0
D. 25x2 − 10x − 24 = 0
Answers
Answer:
A. 5x^2 − 2x − 24 = 0
Step-by-step explanation:
height = 5b-2
b =x
We can rewrite the height as
h = 5x-2
We know the formula for area of a triangle
A = 1/2 bh
A =1/2 x * (5x-2)
Distributing the x
A= 1/2 (5x^2 - 2x)
We know A =12
12 = 1/2 (5x^2 - 2x)
Multiply each side by 2
12*2 = 2*1/2 (5x^2 - 2x)
24 = 5x^2 - 2x
Subtract 24 from each side
24-24 = 5x^2 - 2x-24
0 = 5x^2 - 2x-24
Answer:
C. 5x^2 − 2x − 24 = 0
Step-by-step explanation: