Answer:
a² - b² = 1
Step-by-step explanation:
The given parameters are;
sec 50° = a
cot 40° = b
We note that sec(θ) = 1/cos(θ) and cot(θ) = 1/tan(θ)
a² - b² = sec²50° - cot²40°
Given that sec(90 - θ) = cosec(θ) where; cosec(θ) = 1/sin(θ), we have;
sec²50° - cot²40° = sec²(90° - 50°) - cot²40° = sec²(40°) - cot²40°
sec²(40°) - cot²40° = cosec²(40°) - cot²40°
Also we have;
cosoc²(θ) = 1 + cot²(θ)
Therefore, we have;
cosoc²(40°) - cot²40° = 1 + cot²(40°) - cot²40° = 1
Therefore, where sec(50°) = a and cot(40°) = b, the value of a² - b² is 1.
blake bought two iced coffees at dutch bros. He originally had $13.50 and now has $9 Write and solve an equation to find out how much each iced coffee cost
if he had $13.50 and now he has $9 all you have to do is minus $13.50 by 9 like this 13.50-9=4.50 the ice coffee costs $4.50 simple.
If you still have a question and don't understand this please ask again thank you.
Can someone please assist me...thank you
Answer:
x=10, y=24
[tex]\left(34-y\right)^2+y^2=676[/tex]
Step-by-step explanation:
Answer:
x = 10 and y = 24
Step-by-step explanation:
Perimeter of triangle = sum of the 3 sides of the triangle
:. x + y + 26 = 60
x + y = 60 - 26
x + y = 34 ---- (1)
From Pythagoras theorem,
x² + y² = 26²
x² + y² = 676 ---- (2)
From equation (1): y = 34 - x
:. x² + (34 - x)² = 676
x² + 1,156 - 68x + x² = 676
x² + x² - 68x + 1,156 - 676 = 0
2x² - 68x + 480 = 0
x² - 34x + 240 = 0
(x² - 24x) - (10x + 240) = 0
x(x - 24) -10(x - 24) = 0
(x - 24)(x - 10) = 0
x = 24 or 10
y = 34 - x
y = 34 - 10 = 24
:. x = 10 and y = 24
Given the function g(x) = x2 + 10x + 18, determine the average rate of change of
the function over the interval -11 < x < -1.
Answer:
-2.
Step-by-step explanation:
Average rate of change of the function = [ f(-1) - f(-11)] / [(-1 - (-11)]
= [(-1)^2 + 10*-1 + 18 - ((-11)^2 + 10*-11 + 18)] / 10
= (1 - 10 + 18 - (121 - 110 + 18) / 10
= (9 - (29) /10
= -20/10
= -2.
Answer:
Step-by-step explanation:
The answer is +2 or 2.
Find the graph of the inequality y<-1/5X+1.
Answer:
Please refer to attached image for the graph of inequality.
Step-by-step explanation:
Given the inequality:
[tex]y<-\dfrac{1}{5}x+1[/tex]
To graph this, first let us convert it to corresponding equality.
[tex]y=-\dfrac{1}{5}x+1[/tex]
As we can see that the above equation is a linear equation in two variables so it will be a straight line.
Now, let us find at least two points on the above equation so that we can plot them and then extend it to get the complete graph.
Two points that can be easily found, are:
1st put [tex]x = 0[/tex] , [tex]y=-\frac{1}{5}\times 0+1 =1[/tex]
So one point is (0, 1 )
Now, put y = 0,
[tex]0=-\frac{1}{5}\times x+1\\\Rightarrow 1=\frac{1}{5}\times x\\\Rightarrow x = 5[/tex]
Second point is (5, 0)
Let us plot the points on the graph and extend the straight line.
Now, we know that it is an inequality, the are will be shaded.
As there is no equal to sign in the inequality, so the line will be dashed.
Let us consider one point and check whether that satisfies the inequality or not.
If the point is satisfied in the inequality, we will shade that area towards the point.
Let us consider the point (0, 0).
0 < 0 +1
Point is satisfied.
Please refer to the attached image for the graph of given inequality.
During summer vacation, Wesley read, on average, 20 pages per night. Now that he has returned to school, he is averaging 65% fewer. How many pages per night is Wesley averaging now?
Answer:
He is currently reading 7 pages per night
Step-by-step explanation:
We can simply the question a little by finding what percent of the original Wesley is currently reading. Instead of saying 65% fewer, we can say he is reading 35% of what he used to read
Now we need to set up a proportion to solve the problem.
35% of 20
35/100=x/20
Cross multiply
35x20=700
700/100=7
He is currently reading 7 pages per night
What is the area of the following figure: A) 30 cm 2 B) 36 cm 2 C) 18 cm 2 D) 15 cm 2
Answer:
15 cm^2
Step-by-step explanation:
The area of the triangle is
A = 1/2 bh
A = 1/2 ( 10) * 3
= 1/2 (30)
= 15
Answer:
D) 15cm^2
Step-by-step explanation:
The area of the triangle is
A = 1/2 bh
A = 1/2 ( 10) * 3
= 1/2 (30)
= 15
ys is the perpendicular bisector of xz. What is the length of Xs if xz is 18 inches long?
Answer:
XS is 9 inches long.
Step-by-step explanation:
Given that
YS is the perpendicular bisector of XZ.
Length of XZ = 18 inches
To find:
Length of XS = ?
Solution:
First of all, let us learn about the perpendicular bisector.
Perpendicular bisector of a line AB is a line PQ, which divides the line AB in two equal parts and is at an angle of [tex]90^\circ[/tex] with the line AB.
If B is on the line PQ, then [tex]BP = BQ = \frac{PQ}{2}[/tex] and
[tex]\angle ABP = \angle ABQ = 90^\circ[/tex]
Applying the above property in our given question.
Kindly refer to the attached image for the given dimensions.
S is on the line XZ.
[tex]XS = SZ = \frac{XY}{2} = \dfrac{18}{2} \\\Rightarrow \bold{XS = 9\ inches}[/tex]
So, the answer is XS is 9 inches long.
What is the slope and the y-intercept of the line on the graph below? On a coordinate plane, a line goes through points (0, 1) and (4, 0).
The slope is the change in Y over the change in x:
Slope = (0-1) / 4-0) = -1/4
Slope = -1/4
Y intercept is the Y value when x is equal to 0. In the point (0,1) x is 0 and y is 1, so the y-intercept is 1
inscribed angles. need answers asap , thank u!
Answer:
40°
Step-by-step explanation:
The circumference of a circle is equal to 360°
The arc AB is 180°, the arc AC is given as 100° so the arc CB is 80° and since <A is an inscribed angle it is equal to the half of the arc it sees
80 ÷ 2 = 40
Simplify:
[tex] \sqrt[4]{6 ^{4} } [/tex]
Answer:
6
Step-by-step explanation:
Doing the fourth root of something is the equivalent of doing said number to the power of 1/4. So in this case I will convert the fourth root into an exponent and simplify:
6^(4*1/4) = 6^1 = 6
Hope this helps!
Problem Solve for t.
2(t+1) = 10
t=4
explanation
2(t+1)=10
2t+2=10
2t=8
t=4
Solve 18n - 7p-15n = 5p for n.
A n = 1
B. n=2p
C. n = 1/2
D. n=4p
Answer:
The answer is option DStep-by-step explanation:
18n - 7p-15n = 5p
To solve for n first make n the subject
Group like terms
That's
18n - 15n = 5p + 7p
Simplify
3n = 12p
Divide both sides by 3 to make n stand alone
That's
3n/3 = 12p/3
We have the final answer as
n = 4pHope this helps you
Answer:
D) n = 4p
Step-by-step explanation:
18n - 7p - 15n = 5p
18n - 15n = 5p + 7p
Add like terms
3n = 12p
Divide both sides by 3
3n/3 = 12p/3
n = 4p
If the length of a rectangle is 5y-7 and the width is 3y,represent the area of the rectangle
Answer:
15y^2 - 21y
Step-by-step explanation:
A = LW
A = (5y - 7)(3y)
A = 15y^2 - 21y
Answer:
A = 15y² - 21y
Step-by-step explanation:
3y(5y - 7)
15y² - 21y
Let u = , v = . Find u + v. (1 point)
Answer:
i couldnt find a solution to the equation all i could get is u +v
Step-by-step explanation:
what were you trying to say when you said "let u="
Answer:
4.8
Step-by-step explanation:
(-3,4) + (8,2) = 4.8
what are the squares from one to twenty
Answer:
1,4,9,16
Step-by-step explanation:
those are the squares
1 = 1²
4 = 2²
9 = 3²
16 = 4²
Step-by-step explanation:
[tex] {1}^{2} = 1 \times 1 = 1 \\ {2}^{2} = 2 \times 2 = 4 \\ {3}^{2} = 3 \times 3 = 9 \\ {4}^{2} = 4 \times 4 = 16 \\[/tex]
[tex] {5}^{2} = 5 \times 5 = 25 \\ [/tex]
[tex] {10}^{2} = 10 \times 10 = 100[/tex]
[tex] {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49 \\ {8}^{2} = 8 \times 8 = 64 \\ {9}^{2} = 9 \times 9 = 81 \\ [/tex]
[tex] {11}^{2} = 11 \times 11 = 121 \\ {12}^{2} = 12 \times 12 = 144 \\ {13}^{2} = 13 \times 13 = 169 \\ {14}^{2} = 14 \times 14 = 196 \\ [/tex]
[tex] {15}^{2} = 15 \times 15 = 225 \\ {16}^{2} = 16 \times 16 = 256 \\ {17}^{2} = 17\times 17 = 289 \\ {18}^{2} = 18 \times 18 = 324[/tex]
[tex] {19}^{2} = 19 \times 19 = 361 \\ {20}^{2} = 20 \times 20 = 400[/tex]
What is the smallest positive integer $n$ such that $\frac{n}{n+101}$ is equal to a terminating decimal?
Answer:
n = 24
Step-by-step explanation:
Given the fraction:
[tex]$\frac{n}{n+101}$[/tex]
To find:
Smallest positive integer [tex]$n$[/tex] such that the fraction is equal to a terminating decimal.
Solution:
The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.
i.e. Denominator must look like [tex]2^m\times 5^n[/tex], only then the fraction will be equal to a terminating decimal.
Now, let us have a look at the denominator, [tex]n+101[/tex]
Let us use hit and trial method to find the value of [tex]n[/tex] as positive integer.
n = 1, denominator becomes 102 = [tex]2 \times 3 \times 17[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 4, denominator becomes 105 = [tex]5 \times 3 \times 7[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 9, denominator becomes 110 = [tex]2 \times 5 \times 11[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 14, denominator becomes 115 = [tex]5 \times 23[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 19, denominator becomes 120 = [tex]5 \times 3 \times 2^3[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 24, denominator becomes 125 = [tex]2^0 \times 5 ^3[/tex] It is of the form [tex]2^m\times 5^n[/tex].
So, the answer is n = 24
How many planes exist that pass through points A, B,
and C?
O
1
2
3
Answer: 1
Step-by-step explanation:
Given : A, B, c are three points.
We know that a plane exist that pass through three points.
So 1 plane exist that pass through points A, B, and C.
A point (gives location) , a line(gives length) and a plane(2 dimensional flat surface) are 3 undefined terms.
We need two points two make a line and three points to make a plane.
Answer:
Step-by-step explanation:
The answer is 1
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
Question 9 (5 points)
3
6
9
--
What's the approximate measure of one interior angle of the regular polygon shown?
12
A) 1,620°
>
15
B) 220°
C) 2.7°
18
D) 147.3°
Answer:
147.3
Step-by-step explanation:
this is an hendecagon there is 11 sides the total interior measure is 1,620 if you divide that by each side which would be 11 you get 147.272727 which would ultimately round up to be 147.3
If a person invests $190 at 8% annual interest, find the
approximate value of the investment at the end of 10 years.
Answer:
$410
Answer From Gauth Math
Step-by-step explanation:
This the problem of compound interest
If any amount P is invested at rate of r% per year then its value after n years is given by
amount =
______________________________
Given
p = $190
r =8%
n = 10 year then
Find the area of each polygon
Answer:
1. 66 ft²
2. 102 cm²
3. 35 in.²
4. 7.36 in.²
5. 60 in.²
6. 91 m²
7. 48 m²
5. 567 mm²
9. 255 m²
10. The side length of the square is 9 cm
The area of the square is 81 cm²
Step-by-step explanation:
1. The area of the parallelogram = 11 × 6 = 66 ft²
2. The area of the triangle = 1/2×12×17 = 102 cm²
3. The area of the trapezium = 1/2×(5 + 9)×5 = 35 in.²
4. The area of the triangle = 1/2×4.6×3.2 = 7.36 in.²
5. The area of the parallelogram = 10 × 6 = 60 in.²
6. The area of the trapezium = 1/2×(15 + 11)×7 = 91 m²
7. The area of the parallelogram = 8 × 6 = 48 m²
5. The area of the trapezium = 1/2×(27 + 36)×18 = 567 mm²
9. The height of the wall = 17 m - 8 m = 15 m
The area = 17 × 15 = 255 m²
10. The dimensions of a square with perimeter = 36 cm are;
Side length = 36/4 = 9 cm
The area of the square = 9 × 9 = 81 cm².
which expression is equivalent to (3x-6)(4x+1)
Answer:
12x^2 -21x -6
Step-by-step explanation:
(3x-6)(4x+1)
FOIL
first 3x*4x= 12x^2
outer 3x*1 = 3x
inner -6*4x = -24x
last -6*1 = -6
Add them together
12x^2 +3x -24x -6
Combine like terms
12x^2 -21x -6
What is the answer when you evaluate n + m -2(m-m) when m = 3 and n = 2?
Im sorry I suck at math i have a learning disability a processing disorder and sever adhd
Answer:
5
Step-by-step explanation:
n + m -2(m-m)
Combine like terms
n+m+2(0)
n+m
Let m=3 and n=2
2+3
5
help on the circled problems, will mark brainliest :D
Answer:
see explanation
Step-by-step explanation:
(1)
x - (9x - 10) + 11 = 12x + 3(- 2x + [tex]\frac{1}{3}[/tex] ) ← distribute parenthesis on both sides
x - 9x + 10 + 11 = 12x - 6x + 1 ← collect like terms on both sides
- 8x + 21 = 6x + 1 ( subtract 6x from both sides )
- 14x + 21 = 1 ( subtract 21 from both sides )
- 14x = - 20 ( divide both sides by - 14 )
x = [tex]\frac{-20}{-14}[/tex] = [tex]\frac{10}{7}[/tex]
(3)
- 4x - 2(8x + 1) = - (- 2x - 10) ← distribute parenthesis on both sides
- 4x - 16x - 2 = 2x + 10
- 20x - 2 = 2x + 10 ( subtract 2x from both sides )
- 22x - 2 = 10 ( add 2 to both sides )
- 22x = 12 ( divide both sides by - 22 )
x = [tex]\frac{12}{-22}[/tex] = - [tex]\frac{6}{11}[/tex]
(7)
8(2x + 9) = 56 ( divide both sides by 8 )
2x + 9 = 7 ( subtract 9 from both sides )
2x = - 2 ( divide both sides by 2 )
x = - 1
Hi how do I solve this simultaneous equation
Answer:
M (-3, -5/2)
N (3, -1)
Step-by-step explanation:
Solve the first equation for x.
4y = x − 7
x = 4y + 7
Substitute into the second equation.
x² + xy = 4 + 2y²
(4y + 7)² + (4y + 7)y = 4 + 2y²
Simplify.
16y² + 56y + 49 + 4y² + 7y = 4 + 2y²
18y² + 63y + 45 = 0
2y² + 7y + 5 = 0
Factor.
(y + 1) (2y + 5) = 0
y = -1 or -5/2
Plug back into the first equation to find x.
x = 4(-1) + 7 = 3
x = 4(-5/2) + 7 = -3
M (-3, -5/2)
N (3, -1)
What is the surface area of the cylinder with height 7 in and radius 3 in? Round your
answer to the nearest thousandth.
Answer:
188.495
Step-by-step explanation:
Given that,
h=7
r=3
Surface area of a cylinder = 2πr(h + r)
=2π×3(7+3)
=18.8495559215 (10)
=188.495
How do u simplify each expression by combining like terms?
Answer:
1. 8y - 9y = -1y
( 8 - 9 = -1)
3. 8a - 6 +a - 1
( i have showed the like terms here)
8a - 1a= 7a
-6 - 1 = -7
7a - 7
5. -x - 2 + 15x
( i have showed the like terms here)
-x + 15x = 14x
(x = 1)
14x + 2
7. 8d - 4 - d - 2
( i have showed the like terms here)
8d - d = 7d
-4 -2 = -6
7d - 6
8. 9a + 8 - 2a - 3 - 5a
( i have showed the like terms here)
9a - 2a - 5a = 2a
8 - 3= 5
2a + 5
the area of square is 64cm square .find its length
Answer:
8 cm
Step-by-step explanation:
Because A=a*a
Area equals length times length
So, 8 is the length
64 divided by some number must equal the exact same number. Let me show what I am talking about.
Our length is a. We multiply a times itself (because that's the formula for the square's area)
Does this number exist?
Yes, it does.
And it's a whole number.
And we know from our times tables that 8*8=64
Hope it helped you
Answer:
8 cm
Step-by-step explanation:
please mark me as brainliest
please help me please
Answer:
14 cm
Step-by-step explanation:
Answer:
14 cm will be the answer
Please help solve this, I solved it on my own but I think my calculations are wrong. here is the problem,
b-(b+a×4c÷4); use; a=-6, b=1, and c=2?
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
Answer: 12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~First we need to substitute the value of the variable into the expression and simplify.
b-(b+a×4c÷4) = 1 - (1 + -6 × 4(2) ÷ 4).
Now we need to solve 1 - (1 + -6 × 4(2) ÷ 4).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1 - (1 + -6 × 4(2) ÷ 4)
|
| First, we cancel out 4 and 4.
\/
1 - (1 - 6 × 2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Next, we multiply -6 and 2 to get -12.
1 - (1 - 12)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Then we subtract 12 from 1 to get -11.
1 - (-11)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The opposite of -11 is 11.
1 + 11.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Add 1 and 11 to get, you guessed it, 12!Answer:
Answer: 12
Hope this helps