Answer:
Step-by-step explanation:
If the sum of a pair of angles is 90, then they are complementary angles.
25 + 65 = 90
So, 25 and 65 are complementary angles
Answer:
25 and 65
Step-by-step explanation:
complementary angle= either of two angles whose sum is 90°
25 and 65, sum = 90°
yes31 and 71, sum = 102°
no60 and 40, sum = 100°
no145 and 35, sum = 180°
noIn ΔRST, the measure of ∠T=90°, ST = 44 feet, and TR = 84 feet. Find the measure of ∠R to the nearest tenth of a degree.
Answer:
[tex]27.6^\circ[/tex]
Step-by-step explanation:
Given:
A [tex]\triangle RST[/tex] with [tex]\angle T =90 ^\circ[/tex]
ST = 44 feet
TR = 84 feet
To find:
[tex]\angle R = ?[/tex]
Solution:
Please have a look at the attached figure for clear view of the given dimensions of the right angled triangle.
Here, we can use trigonometric formula to find out the [tex]\angle R[/tex].
We know that formula for tangent of angle [tex]\theta[/tex] is given as:
[tex]tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}[/tex]
Here, Perpendicular for [tex]\angle R[/tex] is side ST and
Base is side TR.
Putting the values in above tangent formula:
[tex]tan R = \dfrac{ST}{TR}\\\Rightarrow tan R = \dfrac{44}{84}\\\Rightarrow tan R = 0.523\\\Rightarrow \angle R = 27.6^\circ[/tex]
Hence, [tex]\angle R = 27.6^\circ[/tex] is the answer.
Answer:
66.1
Step-by-step explanation:
So I have to compute the following but i don't know what they mean any help?
Answer:
Step-by-step explanation:
This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr
i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.
I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.
Recall that
[tex]nCr=\frac{n!}{(r!)(n-r)!}[/tex]
Consider question a) we are given (5 1) or ₅C₁
we can see that n = 5 and r = 1
If we substitute this into the formula:
₅C₁ = (5!) / [ (1!)(5- 1)!]
= (5!) / [ (5- 1)!]
= (5!) / (4!)
= (5·4·3·2·1) / (4·3·2·1)
= 5
hence ₅C₁ = 5
Answer:
(a) 5
(b) 10
(c) 35
(d) 28
(e) 9
(f) 21
Step-by-step explanation:
[tex](\frac{n}{k} )=\frac{n!}{k!(n-k)!}[/tex]
(a)
[tex](\frac{5}{1} )=\frac{5!}{1!(5-1)!} \\\\(\frac{5}{1} )=\frac{5*4*3*2*1}{1*4!} \\\\(\frac{5}{1} )=\frac{120}{1*4*3*2*1} \\\\(\frac{5}{1} )=\frac{120}{24} \\\\(\frac{5}{1} )=5[/tex]
(b)
[tex](\frac{5}{3} )=\frac{5!}{3!(5-3)!} \\\\(\frac{5}{3} )=\frac{5*4*3*2*1}{3*2*1*2!} \\\\(\frac{5}{3} )=\frac{120}{3*2*1*2*1}\\\\(\frac{5}{3} )=\frac{120}{12} \\\\(\frac{5}{3} )=10[/tex]
(c)
[tex](\frac{7}{4} )=\frac{7!}{4!(7-4)!} \\\\(\frac{7}{4} )=\frac{7*6*5*4*3*2*1}{4*3*2*1*3!} \\\\(\frac{7}{4} )=\frac{5040}{4*3*2*1*3*2*1} \\\\(\frac{7}{4} )=\frac{5040}{144} \\\\(\frac{7}{4} )=35[/tex]
(d)
[tex](\frac{8}{2}) =\frac{8!}{2!(8-2)!} \\\\(\frac{8}{2}) =\frac{8*7*6*5*4*3*2*1}{2*1*6!} \\\\(\frac{8}{2}) =\frac{40320}{2*1*6*5*4*3*2*1}\\\\(\frac{8}{2}) =\frac{40320}{1440} \\\\(\frac{8}{2}) =28[/tex]
(e)
[tex](\frac{9}{8} )=\frac{9!}{8!(9-8)!} \\\\(\frac{9}{8} )=\frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1} \\\\(\frac{9}{8} )=\frac{362880}{40320} \\\\(\frac{9}{8} )=9[/tex]
(f)
[tex](\frac{10}{4} )=\frac{10!}{4!(10-4)!} \\\\(\frac{10}{4} )=\frac{10*9*8*7*6*5*4*3*2*1}{4*3*2*1*6!} \\\\(\frac{10}{4} )=\frac{3628800}{24*6*5*4*3*2*1} \\\\(\frac{10}{4} )=\frac{362880}{17280} \\\\(\frac{10}{4} )=21[/tex]
Find n so that C(n, 3) = P(n, 2).
Answer:
n = 19/6
Step-by-step explanation:
Formula for C(n,r) = n!/(r!(n-r)!)
C(n,3) = n! /( 3! * (n - 3)!)
Formula for P(n,r) = n!/(n-r)!
P(n,2)= n!/(n-2)!
C(n, 3) = P(n, 2)
n! /( 3! * (n - 3)!) = n!/(n-2)!
[tex]\frac{n!}{3!(n-3)!}= \frac{n!}{(n-2)!}[/tex] cross multiply
n!(n-2)! = n! 3! (n-3)!
(n-3)! = (n-3)(n-2)!
so n!(n-2)! = n! 3! (n-3)! becomes
n!(n-2)! = n! 3! (n-3)(n-2)! divide both sides by n!(n-2)!
1 =6(n-3)
1 =6n -18
19 = 6n
n = 19/6
if f(x)=1/2x-2 what is f(14)
Answer:
Hi there!
The correct answer is: 5
Step-by-step explanation:
Essentially they replace x with 14, so all you have to do is plug 14 into the equation. 14 multiplied by 1/2 is 7, because it's the same thing as 14 divided by 2. Then you minus 2 from 7, and you get 5.
A rectangle has a width that is 3cm less than its length. The perimeter of the rectangle is 22cm. What is the length and width of the rectangle? Please use problem solving algebraically and explain your answer so i can give you the brainliest. :)
Answer:
The length is 7 and the width is 4
Step-by-step explanation:
l = length
w = l-3
P =2( l+w)
22 = 2( l+ l-3)
Combine like terms
22 = 2(2l-3)
Divide each side by 2
22/2 = 2/2 (2l-3)
11 = 2l-3
Add 3 to each side
11+3 = 2l-3+3
14 = 2l
Divide each side by 2
14/2 =2l/2
7 = l
Now find w
w = l-3
w = 7-3 = 4
Answer: length = 7 cm
Width = 4 cm
Step-by-step explanation:
Perimeter = 2 (l + w)
22 = 2 ( l + l-3)
22=2 (2l - 3)
22=4l - 6
22+6 = 4l
4l = 28/4
l = 28/1 = 7 = length
Width = 7-3 = 4
Find the degree of each polynomial.
what is 18% of 39 equals what
Answer:
7.02
Step-by-step explanation:
[tex]\frac{18}{100}[/tex] x 39 = 7.02
First write 18% as a decimal by moving the
decimal point two places to the left to get .18.
Next, the word "of" tells us we need to multiply.
So we multiply (.18)(39) to get 7.02.
So 7.02 is 18% of 39.
Choose the highest common factor (HCF) of 6xy^3 and 9x^2y
A= x^2y^3
B= 3xy
C= 54x^3y^4
D=18x^2y^3
Answer:
B= 3xy
Step-by-step explanation:
6xy^3= 2ₓ3ₓ x ₓyₓyₓy
9x^2y= 3ₓ3ₓ x ₓ x ₓ y
common factors = 3, x , y
HCF: 3 ₓ x ₓ y
=3xy
if two angles are obtuse are they congruent
Answer:
No, obtuse simply means that the angle measures are > 90 and less than 360. Just because two angles are obtuse DOES NOT mean they are congruent.
Answer: No
Step-by-step explanation: Obtuse just means the angle is above 90 degrees and below 360, it doesn't mean its congruent.
Evaluate 4 - 2(a2 – b2)2 when a = 3 and b = 2.
Answer:
-46
Step-by-step explanation:
4 - 2(a^2 – b^2)^2 =
= 4 - 2(3^2 – 2^2)^2
= 4 - 2(9 - 4)^2
= 4 - 2(5)^2
= 4 - 2(25)
= 4 - 50
= -46
Answer:
= -46
Step-by-step explanation:
4 - 2(a² - b²)²
= 4 - 2(3² - 2²)²
= 4 - 2(9 - 4)²
= 4 - 2(5)²
= 4 - 2(25)
= 4 - 50
= -46
If 7+5x+9=−3x , then x=−2 . Drag and drop the reasons to correctly complete each box.
Answer:
Where are the reasons and boxes? Could you repost with more information or a picture please? Thank you!
Step-by-step explanation:
For questions 1 - 2, complete the given table of values. Then sketch a graph that shows two complete cycles. 1. Y=- cosx 2. Y = sin x+1
Answer:
See attachment.
Step-by-step explanation:
See attachments.
what is the solution to the system of equation below Y equals -1/3 X +6 and X equals -6
Answer:
y = 8
Step-by-step explanation:
y= [tex]\frac{1}{3} x[/tex] + 6
[tex]x[/tex] = -6
y=([tex]\frac{1}{3}[/tex] x 6) + 6
y= 2+6 = 8
Here is a circle touching a square. The area of the square is 36cm squared. Work out the area of the circle. Give your answer in terms of (Pi)
Answer:
see below
Step-by-step explanation:
Because the area of the square is 36 its side is 6 meaning the circle has a diameter of 6. This means that its radius is 3 so its area is 3² * π = 9π.
a can contains 15/16 pound of vegetables on serving these vegetables weighs 1/4 pound what is the total number of serving of vegetables in the can
Answer:
3 and 3/16 servings in the can.
Step-by-step explanation:
There are 3 1/4s in 15/16, and there are 3/16 left over.
What effect will replacing x with (x+7) have on the graph of the equation y=x2 y = x 2 ? A. slides the graph 7 units right B. slides the graph 7 units down C. slides the graph 7 units left D. shrinks the graph by a factor of 7
Answer:
C
Step-by-step explanation:
Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Thus y = (x + 7)²
represents a shift to the left of 7 units → C
The graph y = x² will slide the graph 7 units left by replacing x with (x+7) thus, the correct option is (C).
How to plot a graph?
In order to plot a graph, we have to substitute all the x's values into a function.
Find out the y's value corresponding to the x's and plot the graph in the coordinate geometry.
By the replacing x by (x + a) in the function y = f(x), the function is going to shift either left or right horizontaly.
1. If a is positive then the graph will slide left of the units.
2. If a is negative then the graph will slide right of the units.
Given that, y = x² is need to replace with y = (x+7)²
Since 7 is positive so the graph will slide 7 units left.
For more information about the graph
https://brainly.com/question/16608196
#SPJ2
HELP PLEASE. THIS IS ABOUT FUNCTIONS ! EXPLANATION NEEDED PLEASE
Answer:
B
Step-by-step explanation:
Looking at the graph we can see that the function is increasing -4<x<-2 and 0<x2
The graph is increasing when it is going upwards, or has a slope greater than 0
We can see that happening in two places in the function, which are the intervals of the x coordinate in B
Answer:
B
Step-by-step explanation:
The function is increasing - 4 < x < - 2 and 0 < x < 2 and has a slope greater than 0, and it's happening at 2 places on the graph, so it's B
Hope this helps!
What is the simplified expression in standard form
Answer:
[tex] \boxed{\sf - 2 {p}^{2} - 11p - 35} [/tex]
Step-by-step explanation:
[tex] \sf \implies - 2 {(p + 4)}^{2} - 3 + 5p \\ \\ \sf \implies - 2( {p}^{2} + 2(p)(4) + {4}^{2} ) - 3 + 5p \\ \\ \sf \implies - 2( {p}^{2} + 8p + 16) - 3 + 5p \\ \\ \sf \implies (( - 2) \times {p}^{2} ) + (( - 2) \times 8p) + ( ( - 2) \times 16) - 3 + 5p \\ \\ \sf \implies (- 2 {p}^{2} ) + ( - 16p ) + (- 32) - 3 + 5p \\ \\ \sf \implies - 2 {p}^{2} - 16p - 32 - 3 + 5p \\ \\ \sf \implies - 2 {p}^{2} + (- 16p + 5p) + ( - 32 - 3) \\ \\ \sf \implies - 2 {p}^{2} - 11p - 35[/tex]
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached the
spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
Answer:
[tex]s = \frac{3}{10}m[/tex]
I hope this helps!
Answer: s=3/10m
Step-by-step explanation:
I took the math test in Edgenuity.
Hope this helps!
solve the equation x square - 9+20=0
Answer:
[tex]\sqrt{11i}[/tex]
Step-by-step explanation:
x^2-9+20 = 0
x^2+11 = 0
x^2 = -11
x = [tex]\sqrt{-11} \\\sqrt{11i} \\[/tex]
Given f(x) = 4x3 − 12x2 + 40x + 12, find f(–2).
Hey there! :)
Answer:
f(-2) = -148.
Step-by-step explanation:
To calculate f(-2), simplify substitute -2 for x in the equation. Therefore:
f(x) = 4x³ -12x² + 40x + 12
Becomes:
f(-2) = 4(-2)³ - 12(-2)² + 40(-2) + 12
Simplify:
f(-2) = 4(-8) - 12(4) - 80 + 12
f(-2) = -32 - 48 -80 + 12
Finally, you get:
f(-2) = -148.
What is the range of the function f(x) = |x − 1| − 2? All real numbers all real numbers less than or equal to −2 all real numbers less than or equal to 1 all real numbers greater than or equal to −2
Answer:
B.)
Step-by-step explanation:
Took test
There are 41 students in 6th grade Group A of a junior high school,
and the number of boys is 3 more than the number of girls.
How many boys and girls are there in the class, respectively?
Answer:
23 boys 21 girls
Step-by-step explanation:
so what i would do is 41/2 =20.5 (we round up becaue its people) 21
so if there are 3 more boys then we have 23 boys and 21 -3(to make it equal in half) 18 girls
i might be wrong im not in this level of math yet
I want help! Please
Pocket allowance of 5 students respectively are:
125, 75, 150, 175, 200
Find out arithmetic mean.
Answer:
145
Step-by-step explanation:
125+75+150+175+200= 725
725÷5=145
Answer:
145
Step-by-step explanation:
(125+75+150+175+200)÷5
725÷5= 145
Nine subtracted from the product of 3 and a number is less than 23
Answer:
3n-9<23
You can use any variable you want for n
Answer:
32/3
Step-by-step explanation:
Nine subtracted from the product of 3 and a number is less than 23
-9 3n < 23
3n-9 < 23
3n < 23+9
3n < 32
n < 32/3
Don't forget to say THANKS
Please help! Correct answer only please! I need to finish this assignment by today.
You flip a coin.
What is P(not tails)?
Simplify your answer and write it as a fraction or whole number.
Answer:
1/2 or 0.5
Step-by-step explanation:
since there are two options, heads and tails, the probability of not flipping tails is 1/2, since the probability of flipping heads is 1/2
Answer:
1/2
Step-by-step explanation:
There are 2 sides of a coin.
Heads or Tails.
That means you have a 1/2 chance of getting tails. This also means you have 1/2 chance of not getting tails, in other words, getting heads.
Plzz give an example
how do you round to the nearest cubic
Answer:
I'm assuming that you mean "Cubic Unit". I will use inches in this example, but this will work with other units as well.
Let's say that the volume of a figure was 124.86 cubic inches.
Rounding to the nearest cubic inch is the same thing as rounding to the nearest whole number.
Locate the 'ones' place:
124.86
Check next door:
124.86
If the next door number is greater than or equal to 5, then we round up. If it's less than 5, we round down.
8 is greater then 5. Therefore, we would round up.
So, 124.86 cubic inches to the nearest cubic inch is 125 in³.
124.86in³ ≈ 125in³
What is the nth term in the sequence: 15, 22, 31, 42, 55
please answer asap the photo is below
Answer: 1; -5
Step-by-step explanation:
For this problem, we are asked to find the slope and y-intercept.
We see that this linear line goes through the y-axis at (0,-5). therefore, our y-intercept is -5.
To find the slope, we would use the formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. We can use the points (0,-5) and (5,0) since we can clearly see the line goes through these 2 points.
[tex]m=\frac{0-(-5)}{5-0} =\frac{5}{5} =1[/tex]
From our formula, we found that the slope is 1.
For the first box, you would fill in 1, the slope. The second box would be -5, the y-intercept.
Answer:
y = x - 5
Step-by-step explanation:
One can immediately read off the slope, m, from the graph: m = 5 / 5 = 1.
The y-intercept is (0, -5).
In slope-intercept form the equation of this graph is y = x - 5
help will mark brainliest
Answer:
no mistakes
Step-by-step explanation:
There are no mistakes in the derivation of the quadratic formula by completing the square
Step 1
Move c to the right hand side
Step 2 Get x^2 to have a coefficient of 1
Step 3 complete the square by adding ( b/2a) ^2 to each side
Step 4 Write in the completed square form ( x+ b/2x) ^2 = -c/a + ( b/2a) ^2
Step 5 take the square root of each side, remembering the plus and minus
Step 6 subtract (b/2a) from each side