Answer:
22.95 in = ~~ 23 inches
Step-by-step explanation:
16 + 9 = 25
9/16 = x/20 shows x = 11.25 in is height
diagonal ( via pyhtag theorem)
= sqrt ( 20^2 + 11.25^2 ) = 22.95 inches
Rationalise the denominator of 5/√(3-√5)
Pls send the answer by today
Answer:
[tex]\dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]
[tex]\textsf{or}\quad \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]
Step-by-step explanation:
[tex]\textsf{Given expression}:\dfrac{5}{\sqrt{3-\sqrt{5}}}[/tex]
Method 1
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}:[/tex]
[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}=\dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}[/tex]
Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{a} =a[/tex]:
[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})=3-\sqrt{5}[/tex]
Therefore:
[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}= \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}}[/tex]
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{3+\sqrt{5}}{3+\sqrt{5}}:[/tex]
[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}} \times \dfrac{3+\sqrt{5}}{3+\sqrt{5}}=\dfrac{5\sqrt{3-\sqrt{5}}(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}[/tex]
Simplify the denominator:
[tex]\implies (3-\sqrt{5})(3+\sqrt{5})=9+3\sqrt{5}-3\sqrt{5}-5=4[/tex]
Therefore:
[tex]\implies \dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]
Method 2
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}:[/tex]
[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}=\dfrac{5\sqrt{3+\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})}[/tex]
Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{b} =\sqrt{ab}[/tex]:
[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})=\sqrt{(3-\sqrt{5})(3+\sqrt{5})[/tex]
[tex]\implies\sqrt{(3-\sqrt{5})(3+\sqrt{5})}=\sqrt{9-5}=\sqrt{4}=2[/tex]
Therefore:
[tex]\implies \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]
[tex]\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}[/tex]
To rationalise:-
[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } [/tex]
There is a formula in math if there is root in denominator
for example
[tex] \frac{1}{ \sqrt{a - b} } [/tex]
we can say rationalize by multiplying √(a-b) in numerator and denominator both
[tex] \frac{1}{ \sqrt{a - b} } \times \frac{ \sqrt{a - b} }{ \sqrt{a - b} } \\ \frac{ \sqrt{a - b} }{a - b} [/tex]
In here
[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } \times \frac{ \sqrt{3 - \sqrt{5} } }{ \sqrt{3 - { \sqrt{5} } } } \\ \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } [/tex]
but still here is root to remove this we have to multiply
3 + √5 in numerator and denominator.
[tex] \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5} ) }{ {3}^{2} - { (\sqrt{5} )}^{2} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5}) }{9 - 5} \\ \frac{5( \sqrt{3 - \sqrt{5} } )(3 + \sqrt{5}) }{4} [/tex]
I’ve been struggling with these three for awhile I got everything else on the worksheet but these please help SOH CAH TOA
The distance between Casey and the base of the lighthouse is 49 ft.
What is the angle of elevation and depression?The angle of elevation refers to the angle formed by the straight horizontal line and an object. The crosshair of an observer is usually above the horizontal.
The angle of depression is the angle formed by the horizontal and a downward angle to an object. The crosshair of an observer is usually above below the horizontal.
1.The distance between Casey and the base of the lighthouse can be determined by using the tangent of trigonometry.
(TOA)
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan \ 58 = \dfrac{78}{x}}[/tex]
[tex]\mathbf{x= \dfrac{78}{1.6003}}[/tex]
x ≅ 49 ft
2.The height of the goal post can be determined by using the tangent of trigonometry.
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan 17 = \dfrac{x}{131}}[/tex]
x = (tan 17) × 131
x = 0.3057 × 131
x ≅ 40 ft
3.The horizontal distance between Zack and the water fountain is calculated by using the tangent of trigonometry.
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan \ 28 = \dfrac{75}{x}}[/tex]
[tex]\mathbf{x = \dfrac{75}{0.5317}}[/tex]
x = 141 ft
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Which function is modeled in this table
X
f(x)
1
1000
2
800
3
640
4
512
Answer:
[tex]f(x)=1250*(\frac{4}{5})^x[/tex]
Step-by-step explanation:
PLEASE HELP! WILL GIVE BRAINLIEST
Answer:
See below ~
Step-by-step explanation:
The equation which represents 1/12 :
1 ÷ 12 = ___The division equation which represents 1/14 :
1 ÷ 14 = ___Answer:
Question 3:
C) 1 divided by 12 _
Question 4:
A) 1 divided by 14 _
What is the square root of 144?
Answer:
12
Step-by-step explanation:
When you multiply 12 by itself its 144.
I hope it helps! Have a great day!
pan~
Answer:
12
Step-by-step explanation:
Divide 144 by 2 and it’s 12.
Or you could guess and check b dividing each number by itself until you get 144.
I hope it helps! Have a great day!
Muffin °-°
36x'ys
26 Which expression is equivalent to
(3xy)
for all values of x and y where the expression is
defined?
The expression (3xy) is an algebraic expression
The equivalent expressions of (3xy) are (6xy)/2 and (9xy)/3
How to determine the equivalent expression?The expression is given as:
(3xy)
Multiply by 2/2
(3xy) = (6xy)/2
Multiply by 3/3
(3xy) = (9xy)/3
The above products means that, we multiply the expression by 1 (i.e. n/n) to get an equivalent expression
Hence, the equivalent expressions of (3xy) are (6xy)/2 and (9xy)/3
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What is the base of this function?
f (x) = 3 In (2 - 4) 3 C 10
a. 3
b. e
c. 10
d. There is no base
Answer:
The base is 3.
Step-by-step explanation:
Find the surface area of the cylinder. Type an exact answer in terms of pi.
Answer:
~150.8
Step-by-step explanation:
surface area of a cylinder=2 pi r h + 2 pi r²
[tex]\large{\boxed{\mathfrak\pink{\fcolorbox{pink}{pink}{Answer:-}}}}[/tex]
→ POINTS TO BE NOTED
SURFACE AREA OF THE CYLINDER IS ALSO KNOWN AS TOTAL SURFACE AREA A solid figure bounded by a cylinder and two parallel planes intersecting the cylinder.nd, to find Surface area of cylinder there is one formula
[tex] \pink{ \boxed{ \sf2 \pi \: r(h + r)}}[/tex]
[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}} \orange{ \rule18mm{2.5pt}}[/tex]
★Here
r( RADIUS) = 3cmh(HEIGHT)= 5cm★ Let's solve:-
[tex] \sf \: ↦2 \pi \times 3(5 + 3) \\ \sf \:↦ 2\pi \times 15 + 9 \\ \sf \:↦ 2\pi \times 24 \\ \sf \: ↦48\pi\:cm²[/tex]
[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}}\orange{ \rule18mm{2.5pt}}[/tex]
Hence;
The surface area of the cylinder=48πcm²Calculate the perimeter of the shape below. Show ur work! TYSM!!
Answer:
1,001
Step-by-step explanation:
13ft X 11ft X 7ft = 1,001
Not sure if its correct but im glad to help atleast
Answer:
68 is the perimeter.
Step-by-step explanation:
You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.
:)
Mariam sells tires for $90 each and a service plan for $50. One customer
pays $410 for some tires and the service plan. Which equation represents
how many tires, t, the customer purchased?
A 410 = 50 + 90t
B 410 = 90 + 50t
© 410 = 50t + 90
D 410 = 90(4t) + 50
Answer:
the answer is A
Step-by-step explanation:
410 is the total amount paid
so 50 dollars was a base fee for the service charge
and 90 was per tire. Because we dont know how many tires she bought 90 x number of tires(t) = 90t
so 410 dollars = 50 dollars(service fee) + 90 dollars ( multilied by number of tires "t")
Cynthia is flying a kite in her back pasture. She let out 50 meters of kite string and the string makes an angle of elevation with the ground of 42. How high is the kite flying to the nearest tenth of a meter
The required kite is flying at a height of approximately 45.02 meters to the nearest tenth of a meter.
To find the height at which the kite is flying, we can use trigonometry, specifically the tangent function. The tangent of the angle of elevation (42 degrees) is the ratio of the height (h) of the kite to the distance from Cynthia to the kite (50 meters).
The formula for the tangent of an angle is:
[tex]tan(angle) = opposite/adjacent[/tex]
In this case, the angle is 42 degrees, the opposite side is the height of the kite (h), and the adjacent side is the length of the string (50 meters).
[tex]tan(42^o) = h / 50[/tex]
To find the height (h), we can rearrange the equation:
[tex]h = 50 * tan(42^o)[/tex]
Now, let's calculate the height:
[tex]h =50 * tan(42^o)[/tex]
h ≈ 50 meters * 0.9004
h ≈ 45.02 meters (rounded to two decimal places)
So, the kite is flying at a height of approximately 45.02 meters to the nearest tenth of a meter.
Learn more about trigonometry here:
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if a type of salami at the deli costs 1.59 per 100 g how much will you pay for 350 g? pls help and explain how to do it
Answer:
[tex]\huge\boxed{\sf 350\ g\ salami = 5.565}[/tex]
Step-by-step explanation:
From the question:
100 g salami = 1.59
Divide 100 to both sides
1 g salami = 1.59/100
1 g salami = 0.0159
Multiply both sides by 350
350 g salami = 0.0159 × 350
350 g salami = 5.565
[tex]\rule[225]{225}{2}[/tex]
PLEASE HELP! GRAPH THE FUNCTION
#8
y=4(x-0)²+0Vertex at (0,0)
#11
y=-6(x-0)²+0Same Vertex
#14
y=-(x-0)²+2Vertex (0,2)
Step-by-step explanation:
by order
the 1st one y = 4x^2
vetex (0,0) and upward
the 2nd one y = -6x^2
vertex (0,0) and downward
the 3rd one y = -x^2 + 2
vertex (0,2) and downward
Which of the following relations is a function?
a,
{(-2, -2),(-2, -1),(-2, 0),(-2, 1),(-2, 2)}
b.
{(1, 0),(-1, 0),(2, 1),(-2, 1),(3, 2),(-3, 2)}
c.
{(-2, 1),(-1, 2),(O, Q).(-1, 1),(2, -2)}
d.
((-3.3).(1, 3),(-3, 2),(1, 2),(-3, 1),(1, 1)}
Answer:
b
Step-by-step explanation:
please helpppppppppp
Answer:
THE ANSWER IS “your net worth”
Step-by-step explanation:
PLEASE HELP ASAP!!!! WILL GIVE BRAINIEST TO BEST ANSWER!
Answer:
63√6 cm
Explanation:
Perimeter is the total measure of all sides.
Solve:
15√6 + 12√54 + 6√24
factorize
15√6 + 12√6(9) + 6√6(4)
apply radical rule: √ab = √a √b
15√6 + 12√6 √9 + 6√6 √4
simplify
15√6 + 12(3)√6 + 6(2)√6
multiply
15√6 + 36√6 + 12√6
add similar terms
63√6
Answer:
63√6 cmStep-by-step explanation:
Perimeter : Sum of the sides
15√6 cm is already in simplest form6√24 = 6√(4 × 6) = 6 x 2 x √6 = 12√6 cm12√54 = 12√(9 x 6) = 12 x 3 x √6 = 36√6 cmPerimeter
15√6 + 12√6 + 36√627√6 + 36√663√6 cmWhat is the slope of a trend line that passes through the points (5, 80) and (7, 65)?
a.) -15/2
b.) -2/15
c.) 2/15
d.) 15/2
Answer:
65 - 80 = -15
7 - 5 = 2
which is -15/2
which is A
In the context of the least squares procedure, any data point that does not fall on the regression line is the result of
In the context of the least squares procedure, any data point that does not fall on the regression line is the result of multicollinearity.
What is least square regression?A least square regression simply shows the linear relationship that exist between two variables.
Here, in the context of the least squares procedure, any data point that does not fall on the regression line is the result of multicollinearity.
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What is 800divided by the a times the 9 3 times?
Answer:
21600/a
Step-by-step explanation:
800/a *9
7200/a
21600/a
First, times 800 divided by a by 9.
Then, we get 7200/a.
Lastly, times it by 3.
The answer is 21600/a
Sussy mcsuser
Poop noobs
Find the measure of arc STQ.
edit; found the wrong thing lol
Pls help I’m in a rush (find the pattern)
Answer:
y=x+12, add 12
Step-by-step explanation:
To get from each x to y you have to add 12
so the equation is:
y=x+12
Please help! Due in 10 minutes! I'll mark brianliest!
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Solve the system of equations below using elimination.
4x + 4y = -37
2x + 5y = -17
Part A: What is the x-value?
Part B: What is the y-value?
Part C: In one paragraph, using your own words, explain the work you did to find the answers to parts A and B.
Answer:
Step-by-step explanation:
4x + 4y = -37
2x + 5y = -17
we are told to use elimination , instead of substitution,
meaning get rid of the x or y in one of the equations.
Part C : let's multiply (2x + 5y = -17 ) * (-2) so we get
-4x - 10y = 34 , then add
4x + 4y = -37
0x -6y = -3 now we have only one variable , y
because both sides have a minus sign, we can just drop it
6y = 3 ( divide both sides by 6)
y = 3/6
Part B : y = 1/2 we now know y
plug in the y value into 1st equation.
4x + 4(1/2) = -37
now solve for x
4x + 2 = -37
4x = -39
Part A : x = - 39/4
A man invests $8 000 at 12% simple interest for 3 years. If he invests the same amount of money for the same time period at 12% compound interest, what is the difference between the two investments?
Answer:
$359.42
Step-by-step explanation:
The difference in the investment values can be computed by making use of the formulas for the account balance in each case.
compound interest: A = P(1 +r)^t . . . . interest at rate r compounded annually
simple interst: A = P(1 +rt) . . . . simple interest at rate r
__
The account earning simple interest will have a balance of ...
A = $8000(1 +0.12×3) = $10,880
The account earning compound interest will have a balance of ...
A = $8000(1 +0.12)^3 ≈ $11,239.42
The difference between the two investments is ...
$11,239.42 -10,880 = $359.42
can someone please help me with this!!!!
Which is the equation in slope-intercept form for the line that passes through (−1, 5) and is parallel to 3x + 2y = 4? y=−32x+72 y=23x+72 y=−23x+72 y=32x−72
Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?
y=32x+18
y=32x−12
y=23x+18
y=−32x+18
Which best describes the relationship between the lines?
2x – y = −1
4x – 2y = 6
parallel
same line
neither
perpendicular
1. The equation in slope-intercept form is: y = -3/2x + 7/2
2. y = -3/2x - 18
3. Both lines have the same slope, they are therefore parallel.
What is the Equation in Slope-intercept Form for Parallel Lines?Two lines that are parallel will have the same slope (m), and is represented by the equation in slope-intercept form as, y = mx + b.
1. Rewrite 3x + 2y = 4 in slope-intercept form:
2y = -3x + 4
y = -3x/2 + 4/2
y = -3/2x + 2
The slope is -3/2. Therefore, the slope (m) of the line that passes through (-1, 5) would be -3/2.
Substitute m = -3/2, and (a, b) = (-1, 5) into y - b = m(x - a):
y - 5 = -3/2(x - (-1))
y - 5 = -3/2(x + 1)
Rewrite in slope-intercept form:
2(y - 5) = -3(x + 1)
2y - 10 = -3x - 3
2y = -3x - 3 + 10
2y = -3x + 7
y = -3x/2 + 7/2
y = -3/2x + 7/2
2. The slopes of perpendicular lines are negative reciprocal to each other.
Rewrite 2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
The slope of the ine that passes (-2, 15) would be -3/2.
Substitute (a, b) = (-2, 15), and m = -3/2 into y - b = m(x - a):
y - 15 = -3/2(x - (-2))
y - 15 = -3/2x - 3
y = -3/2x - 3 - 15
y = -3/2x - 18
Therefore, the equation in slope-intercept form of the line that passes through (-2, 15) is: y = -3/2x - 18.
3. Given the equations, 2x – y = −1 and 4x – 2y = 6:
Rewrite in slope-intercept form and find their slope
2x - y = -1
-y = -2x - 1
y = 2x + 1 (slope if 2)
4x - 2y = 6
-2y = -4x + 6
y = -4x/-2 + 6/-2
y = 2x - 3 (slope is 2)
Both lines are therefore, parallel.
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please help ??????????
Helen bought 5 pounds of oranges. She sliced
2 pounds of oranges to bring to a party. How
many pounds of oranges does Helen have left?
Answer:
3 oranges
Step-by-step explanation:
Helen has 5 pounds of oranges
2 pounds of oranges are brought to a party, so they are gone
5-2 = 3
Helen will only have 3 oranges left.
What is the length of segment np? 1 unit 2 units 3 units 4 units
Answer:
2 units
Step-by-step explanation:
Answer:
The answer is 2 units
Step-by-step explanation:
10. Which of the following could be the perimeters of the three squares below?
A. 12 11 10 ft and 20 ft
B. 20 ft, 16 f1 and 24 ft
C. Both A and B
D. Neither A or B
Answer:
A, 12ft, 16ft, 20ft.
Step-by-step explanation:
3,4,5 Triangles are right triangles, Answer A on the Paper says 12:16:20 which is proportinate to said ratio, hence the answer is A
Please answer ASAP for 15 points pls
Answer: 125
Step-by-step explanation: