Answer:
a=210ft²
The area of the triangle is 210 square feet.
Step-by-step explanation:
This is a right triangle, as shown by the Pythagorean theorem:
[tex]20^{2} +21^{2} =29^{2} \\400+441=841\\841=841[/tex]
The 2 perpendicular legs of a right triangle are also the base and height of a rectangle of the same size. A right triangle is exactly half of that rectangle, and therefore the area of a right triangle is exactly half of the area of that rectangle.
The area of that rectangle is:
[tex]a=b*h\\a=20*21\\a=420[/tex]
And then the area of the triangle is:
[tex]a=\frac{420}{2}\\a=210[/tex]
The percent of Ivy Tech students receiving financial aid in 2018 was 82%, this was a 9.8% relative increase from 2017. What would the percent of students receiving aid in 2017 have been?
find the derivative of (Cosx/1+sinx)^5
Use the Chain Rule:
[tex]\frac{d}{dx} [f(g(x))] = f'(g(x)) * g'(x)[/tex]
Given Information:
[tex]f(x) = x^5\\ g(x) = \frac{cos(x)}{1} +sin(x)\\ f(g(x)) = ( \frac{cos(x)}{1} +sin(x))^5\\ \\ f'(x)=5x^4\\ g'(x)=\frac{-sin(x)}{1} + cos(x)\\f'(g(x))*g'(x)=5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]
The answer is:
[tex]5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]
Solve the Quadratic
Solve for x. Write in simplified radical form.
2x^2 + 3x – 20 = 0
Solution 1:
Solution 2:
~quadratic equation
======================
2x² + 3x - 20 = 0
= a + b = 3
= ab = 2(-20) = -40
= a = -5
= b = 8
= (2x² - 5x) + (8x - 20)
= x(2x - 5) + 4(2x - 5)
= (2x - 5) (x + 4)
= Solution 1 : x = 5/2 ✔️
Solution 2 : x = -4 ✔️
~ nice to help you ^^
[tex]2x^2 +3x -20 =0\\\\\\\implies x = \dfrac{-3 \pm \sqrt{(-3)^2 - 4 \cdot 2 \cdot (-20)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{-3 \pm \sqrt{169}}{4}\\\\\\\implies x = \dfrac{-3\pm 13} 4 \\\\\\\text{Hence} \\\\x = \dfrac{-3+ 13}{4} = \dfrac{10} 4 = \dfrac{5}2\\\\\text{Or}\\\\x= \dfrac{-3-13}4 = -\dfrac{16}4 =-4[/tex]
Identify which graph below contains the coordinate points (–3, 4),(–2, 0), and (0, –8). Select all that apply.
Answer:
A, C, D
Step-by-step explanation:
All of the plot curves contain (0, -8) and (-2, 0)
B doe NOT contain (-3, 4), though the plot lines seem kind of fuzzy and other curves may miss, but not by much.
Answer:
Graph A , B, and D
Step by-step explanation:
All the points are one these three graphs.
An eight-sided dice numbered from 1 to 8 is rolled 80 times to determine whether it is fair, a If the dice is fair, how many of each number would you expect to get?
Answer:
10 times for each number
Step-by-step explanation:
:)
Answer:
10
Step-by-step explanation:
if the dice is fair, the sides will land one time every 8, so if its rolled 80 time, and it was equal 10 would be your answer.
Question 1 of 10
f (2) = y + 10. Find the inverse of f(x).
O A f-'(x) = (x + 10)
O B. f-1(x) = 73 + 10
O C. f-1(x) = (x – 10)3
O D. f-'(x) = x3 – 10
Option D
step by step explanation:
[tex] \sf f(x) = \sqrt[3]{x + 10} \\ \sf y = \sqrt[3]{x + 10} \\ \sf y = \sqrt[3]{y + 10} \\ \sf y = {x}^{3} - 10 \\ \sf {f}^{ - 1} (x) = {x}^{3} - 10[/tex]
The inverse of the given function is represented as f' ( x ) = x³ - 10
What is Function Rule?A function is a mathematical object that takes an input (or several inputs) and produces an output. The rule of a function describes how the input is transformed to produce the output. It can be written using mathematical notation, words, or a combination of both.
Functions are used in many areas of mathematics, science, engineering, and other fields to model relationships between variables, make predictions, and solve problems.
Given data ,
Let the function be represented as A
Now , the value of A is
Now , the function is depicted as f ( x ) = ∛( x + 10 )
Simplifying results in
The function's inverse is obtained by swapping the x and y variables.
So ,
y = ∛( x + 10 )
x = ∛( y + 10 )
On solving for y , we get
y = x³ - 10
And , the inverse is f' ( x ) = x³ - 10
The function is therefore f' (x) = x³ - 10.
Go here to read more about the function rule.
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The zeros of the quadratic function described by the graph below is
7. The zeros of the quadratic function described by the graph below is
1
A. 2,1
B. -2,1
C. 2,-1
D. -2,-1
Answer :CWhich number should be multiplied by 45 so that it will have 3 nct prime factors?
Answer:
2
Step-by-step explanation:
Please help me and give explanation on how you got your answer if not that’s fine
(5x-7)^2-1=8 solve for x
Answer:
[tex]x = \frac{70 + \sqrt{900} }{50}\\[/tex] or [tex]x = 2[/tex]
Or:
[tex]x = \frac{70 - \sqrt{900} }{50}\\[/tex] or [tex]x = \frac{4}{5}[/tex]
Step-by-step explanation:
Step 1 - Simplify by expanding the brackets:
[tex](5x - 7)^2\\(5x - 7)(5x - 7)\\25x^2 - 35x - 35x + 49\\25x^2 - 70x + 49 - 1\\25x^2 - 70x + 48 = 8[/tex]
Step 2 - Subtract 8 from both sides so the equation equals 0:
[tex]25x^2 - 70x + 48 - 8 = 8 - 8\\25x^2 - 70x + 40 = 0[/tex]
Step 3 - Use the quadratic formula:
[tex]x = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\a = 25\\b = -70\\c = 40[/tex]
Plug variables in:
[tex]\frac{-(-70) +- \sqrt{(-70)^2 - (4 * 25 * 40)} }{2 * 25}[/tex]
[tex]\frac{70 +- \sqrt{4900 - 4000} }{50}\\\\\frac{70 +- \sqrt{900} }{50}\\[/tex]
So x is either:
[tex]x = \frac{70 + \sqrt{900} }{50}\\[/tex]
[tex]x = 2[/tex]
Or:
[tex]x = \frac{70 - \sqrt{900} }{50}\\[/tex]
[tex]x = \frac{4}{5}[/tex]
Hope this helps!
What is the temperature change between the greatest value and the least value?
-25°F, 5°F, 60°F, -45°F, -10°F, 90°F
WILL BR MARKED BEST
What would you do if you found out that you wrote a cheque of $78 but it was recorded as $98 in check register?
Answer:
I will cryy because I only want to write 78 why it recorded as 98
Determine whether the points p1 (6,9,7), p2(9,2,0), and p3(12,-5,-6) lie on the same line
Answer:
They are not.
Step-by-step explanation:
Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.
[tex]\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>[/tex]
At this point we have at least three options:
Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.
Calculate the cross product between the two, if it's non-zero the three point are not in a line.
Try to determine the plane passing for the 3 points: if we find one they are not in a line.
Option 1:
The vector form of the lne between the firs two points is [tex]<6+3t;9-7t;7-7t>[/tex]. Let's check the coordinates of the third point:
[tex]x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2[/tex]
So the three points are not in a line.
Option 2:
Let's calculate the cross product of the two vectors we found at the beginning.
[tex]\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0[/tex]
Since the result is not the null vector, the three points are not in a line.
Option 3:
Let's write the plane (in the [tex]z= ax+by+c[/tex] form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.
[tex]P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c[/tex]
Since you can determine a, b and c ( I ended up with [tex]a=-\frac {10}3; b=-\frac18; c= \frac{123}8[/tex] but I probably messed something in there) the thre points are not in a line
i need help asap plss
Answer:
12
Step-by-step explanation:
20% is 20/100 = 0.2
60% is 60/100 = 0.6
So 20% of 60%= 0.2*0.6=0.12
0.12 in % = 0.12*100 = 12%
Yes i know… Math sucks
Anyways have a great day and if its correct please give brainliest
Stay Safe And Healthy
Thank you
dont sound so smart doing it she will know
Jeremy is incorrect because a negative plus a negative will always be a negative.
Which expression is equivalent to 4w (-6w)
0 -2w3
O-202
0-24w3
0-24w2
Step-by-step explanation:
4w(-6w)
= (4*6)(w.-w)
= 24 * -w²
= -24w²
Select the correct answer
Consider the given solids with the dimensions shown. Which solids are similar?
Aonly figure 1 and figure 2
B.only figure 2 and figure 3
c.only figure 1 and figure 3
D. all three figures
E none of the figures
only figure 1 and figure 3 are similar.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
In figure 1, two of the sides (16 and 9 ) are perfect square and third is not.
If we take the ratio of three side as
16:9:12
(4)²:(3)²:(2√3)²
Similarly, In figure 3 two of the sides (64 and 36 ) are perfect square and third is not.
If we take the ratio of three side as
64:36:48
(8)²:(6)²:(4√3)²
Comparing the ratios of both figure, the figure 3 has twice the measurement of figure 1 sides.
Hence, only figure 1 and 3 are similar.
Learn more about this concept here:
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This morning, Megan and her dad had smoothies for breakfast. Megan made her smoothie with 1 cup of mango and 3 cups of strawberries. Her dad made a giant smoothie with 2 cups of mango and 6 cups of strawberries. Did the smoothies have the same ratio of mango to strawberries?
Answer:
Yes.
Step-by-step explanation:
A rectangular field is six times as long as it is wide. If the perimeter of the field is 1190 feet, what are the dimensions of the field?
A) Write an equation you can use to answer the given question. Let w be the width of the field. Do not solve the equation yet. The equation is _______
(Make sure you use the correct variable.)
B) Use your equation to find the dimensions of the field.
The width of the field is ____________ feet.
The length of the field is ____________ feet.
ATQ
[tex]\\ \tt\longmapsto 2(x+6x)=1190[/tex]
[tex]\\ \tt\longmapsto 2(7x)=1190[/tex]
[tex]\\ \tt\longmapsto 7x=595[/tex]
[tex]\\ \tt\longmapsto x=595/7[/tex]
[tex]\\ \tt\longmapsto x=85[/tex]
Length=6(85)=510ftWidth=85ftQuestion
Given that the market basket for gardening was $\$131.17$ last year and $\$131.96$ this year, what was the inflation rate?
(Round your answer to the nearest hundredth of a percent.)
Answer:
0.006%
Step-by-step explanation:
minused old price from the new one and then divided the answer by the old price
A waiter carried 6 baskets with 5 dinner rolls in each
basket. How many dinner rolls did he carry? Show
your work.
Answer:
30 dinner rolls
Step-by-step explanation:
There are 5 dinner rolls per basket and there are 6 baskets
So there are 6 groups of 5:
5 + 5 + 5 + 5 + 5 + 5
In other words, multiply 5 and 6
5 dinner rolls x 6 = 30 dinner rolls
Pls help this is timed and I don’t understand
Answer:
178
Step-by-step explanation:
All right!!
Line l is parellel to line m.
So if r is 91 then we can infer that s helps it make a 180 degree angle/straight line.
So 180 - 91 = 89
s = 89
If the two lines are parallel then s = u because of inner angles/outer angles stuff.
If s=u then u = 89 as well.
And because of vertical angles, t =u so t = 89.
Now the question asks to find t + u, so t + u = 89 + 89 = 178
Hope that helps!!
plz answer this with complete process plzzz I will give you brainlist ..........
Answer:
Step-by-step explanation:
Needs a picture to be solved, please put one.
Answer:
i know
Step-by-step explanation:
I know have a amazing day
7. Karen opened a savings account with $500. The money earns 0.2% interest per month. If she does not make any withdraws or any more deposits, approximately how much money will Karen have in the account after two years?
(North Carolina Math 2)
A. $502 B. $512 C. $515 D. $525
Answer:
The answer is A
Step-by-step explanation:
0.2% of 500 is 1 so in two year she would have 502$
Write the equation of the line in slope intercept form
Slope =−1/5 Y-Intercept =−3
Answer:
y = mx + c ......( general form)
y = -1/5X - 3
can somebody help me plssssss
Answer:
They are equal, so =
Step-by-step explanation:
We know that one-half is .50. 3/2 is an improper fraction and when we solve to a decimal, we get 1.5.
Consider the set {7,8,9; the elements of this set include?
a. 7,8,9
b. 9, 10, 11
c. none of these
Answer:
The correct answer is "Option A".
Step-by-step explanation:
Hope this helps :)
An unopened bag of gummy bears weighs 2 1/3 ounces. Drayven has 3/4 of a bag of gummy bears and Akila has 2/3 of a bag. Who has more? If they put their bags together, would they have more than one bag? Explain your answer.
Answer:
Drayven has more
Step-by-step explanation:
If you look at the fractions through a drawing you would see that my claim is correct.
How do I do this math !
Answer:
The equation of a straight line is always
[tex]y=mx+b[/tex]
The constant m always refers to the slope, and the constant b always refers to the y-intercept.
Simply substitute the numbers in:
[tex]y=-\frac{1}{2}x+3[/tex]
There's your equation!
An adult elephant eats about 300 pounds of food each day. Write an
expression to represent the number of pounds of food a herd of
12 elephants eat in/5 days.
Answer:
18000
Step-by-step explanation:
you multiply 12 by 300 which is 3600 then you would multiply by 5 and its 18000.