Answers
Answer:
First questionTo find ? we use sine
sin ∅ = opposite / hypotenuse
From the question
The hypotenuse is 50
The opposite is 25
So we have
sin ? = 25 / 50
sin ? = 1/2
? = sin-¹ 1/2
? = 30°Second questionTo find ? we use tan
tan ∅ = opposite / adjacent
From the question
the opposite is 8
the adjacent is 33
So we have
tan ? = 8/33
? = tan-¹ 8/33
? = 13.62
? = 14° to the nearest degreeHope this helps you
Related Questions
I need the answers to the questions highlighted with the black rectangles.
Answers
Answer:
b) P(more than 10) = 2/9
c) P(less than 7) = 2/9
Step-by-step explanation:
a) Yaniq spins both spinners and then adds up the results together.
The results are as follow:
5
7
9
6
8
10
7
9
10
These are a total of 9 outcomes.
b) What is the probability that Yaniq gets a total of more than 9?
The probability is given by
P = Number of favorable outcomes/Total number of outcomes
For this case, the favorable outcomes are all those outcomes where the total score is more than 9.
Count the number of times Yaniq got a score of more than 9.
Yes right!
2 times (10 and 10)
P(more than 10) = 2/9
c) What is the probability that Yaniq gets a total of less than 7?
For this case, the favorable outcomes are all those outcomes where the total score is less than 7.
Count the number of times Yaniq got a score of less than 7.
Yes right!
2 times (5 and 6)
P(less than 7) = 2/9
Multiply using distributive property.
(d+8)(d-4)
PLEASE HELP!!! ASAP!!!
Answers
Answer:
Step-by-step explanation:
Use F.O.I.L
F - First
O- Outside
I- Inside
L- Last
First multiply the ds from both to get [tex]d^{2}[/tex], next multiply the first d and the -4 and get -4d, then the 8 and the second d = 8d, and finally the 8 and -4 to get -32
you get [tex]d^{2}[/tex]-4d + 8d - 32
You then simplify and end up with [tex]d^{2}[/tex] + 4d -32Evaluate each expression for the given values of the variables: |a−b| − |c+d| , if a=−5; b=4; c=1; d=−3
Answers
Answer:
11
Step-by-step explanation:
|a−b| − |c+d|
Let = a=−5; b=4; c=1; d=−3
|-5−4| − |1+-3|
|-9| − |-2|
Absolute values means take the non-negative value
9 + 2
11
Answer:
7
Step-by-step explanation:
| a - b | - | c + d |
Plug in the values for the variables.
| -5 - 4 | - | 1 + -3 |
Evaluate.
| - 9 | - | -2 |
Apply rule : | -a | = a
9 - 2
Subtract the numbers.
= 7
PLEASEEEEE HELP MEEE
Answers
Answer:
4.16% is the hourly growth rate
Step-by-step explanation:
What we can do here is to first set up an exponential relationship that relates the present number of bacteria, the initial number of bacteria, the growth rate of the bacteria and the number of hours.
What we want to establish here has a resemblance with the compound interest formula in finance.
Let’s see the initial number of bacteria as the amount deposited, the present number of bacteria as the amount after some months, the growth rate as the monthly percentage while the number of hours works like the number of months.
Mathematically, what we have will be;
P = I(1 + r)^h
where P is the present bacteria number, I is the initial, r is the growth rate while h is the number of hours.
Thus, we have the following values from the question;
P = 1530
I = 1,300
r = ?
h = 4
Substituting these values, we have;
1530 = 1300(1 + r)^4
divide both sides by 1,300
1.177 = (1+r)^4
Find the fourth root of both sides
(1.177)^(1/4) = 1+ r
1.0416 = 1 + r
r = 1.0416-1
r = 0.0416
This in percentage is 4.16%
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Answers
Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35
Please help I will give out brainliest
Answers
Answer:
All the points change, there are no invariant points
Step-by-step explanation:
The given parameters are
To translate the square OABC by the vector [tex]\dbinom{1}{3}[/tex], we have;
The coordinates of the point O is (0, 0)
The coordinates of the point A is (3, 0)
The coordinates of the point B is (3, 3)
The coordinates of the point C is (0. 3)
The translation is by moving 1 step right and three steps up to give;
O' is (0+1, 0+3) which is (1, 3)
A' is (3+1, 0+3) which is (4, 3)
B' is (3+1, 3+3) which gives (4, 6)
C' is (0+1, 3+3) which gives (1, 6)
As all the points change, there are no invariant points and the number of invariant points is zero.
A car can go from rest to 90 km⁄h in 10 s. What is its acceleration?
Answers
Answer:
2.5 m/s^2
Step-by-step explanation:
Answer:
2.5 m/s²
Step-by-step explanation:
First, convert to SI units.
90 km/h × (1000 m/km) × (1 h / 3600 s) = 25 m/s
a = Δv / Δt
a = (25 m/s − 0 m/s) / 10 s
a = 2.5 m/s²
Chris purchased a tablet for $650. The tablet depreciates at a rate of $25 per month.
Write and simplify an equation that models the value V(m) of the tablet after m months.
Answers
Let d equal the final amount it depreciates.
Let m equal the number of months.
Since d is the final amount, we put this at the very end of the equation.
Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).
The final equation comes out too: d = 650 - 25m
Best of Luck!
Algebra 2 help needed!
Answers
Answer:
(g + f) (x) = (2^x + x – 3)^1/2
Step-by-step explanation:
The following data were obtained from the question:
f(x) = 2^x/2
g(x) = √(x – 3)
(g + f) (x) =..?
(g + f) (x) can be obtained as follow:
(g + f) (x) = √(x – 3) + 2^x/2
(g + f) (x) = (x – 3)^1/2 + 2^x/2
(g + f) (x) = (x – 3)^1/2 + (2^x)^1/2
(g + f) (x) = (x – 3 + 2^x)^1/2
Rearrange
(g + f) (x) = (2^x + x – 3)^1/2
the three-dimensional shape that this net represents is _______. The surface area of the figure is _____ square centimeters.
Answers
Answer:
Shape - Cube
Area= 864
Step-by-step explanation:
The shape folds to become a cube and all the edges are the same size.
Area of a cube is Length * Width * Height = Area
12*12*12= 864
Answer:
Shape - Cube
Area= 864
Step-by-step explanation:
The shape folds to become a cube and all the edges are the same size.
Area of a cube is Length * Width * Height = Area
12*12*12= 864
Simplify $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$
Answers
Let [tex]x=\sqrt[3]{3}[/tex] and [tex]x^2=\sqrt[3]{9}[/tex]. Then
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2x^2}{1+x+x^2}[/tex]
Multiply the numerator and denominator by [tex]1-x[/tex]. The motivation for this is the rule for factoring a difference of cubes:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Doing so gives
[tex]\dfrac{2x^2(1-x)}{(1+x+x^2)(1-x)}=\dfrac{2x^2(1-x)}{1-x^3}[/tex]
so that
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2\sqrt[3]{9}(1-\sqrt[3]{3})}{1-3}=\sqrt[3]{9}(\sqrt[3]{3}-1)=3-\sqrt[3]{9}[/tex]
what is the distance formula
Answers
Answer:
14.42 units
Step-by-step explanation:
Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:
AB² = AC² + BC²
AB² = 12² + 8²
AB = √(12² + 8²)
AB = 14.42 units
Please answer it now in two minutes
Answers
Answer:
[tex] C = 28.9 [/tex]
Step-by-step explanation:
Given the right angled triangle, ∆BCD, you are required to find the measure of angle C.
Apply the trigonometric ratio formula to find m < C.
Adjacent side = 7
Hypotenuse = 8
Trigonometric ratio formula to apply would be:
[tex] cos(C) = \frac{7}{8} [/tex]
[tex] cos(C) = 0.875 [/tex]
[tex] C = cos^{-1}(0.875) [/tex]
[tex] C = 28.9 [/tex]
(To nearest tenth)
factor the equation using zero product property. x2+7x=-6
Answers
Answer:
x = -6 x = -1
Step-by-step explanation:
We want to solve using the zero product property
x^2+7x=-6
Add 6 to each side
x^2 +7x +6 = 0
Factor
What 2 numbers multiply to 6 and add to 7
( x+6) (x+1) =0
Using the zero product property
x+6 =0 x+1 =0
x+6-6 =0-6 x+1-1 = 0-1
x = -6 x = -1
The final exam had three times as many points as the first test, plus a bonus question worth 25 points . The final exam was worth 160 points (including the bonus). How many points was the first test worth?
Answers
Answer:
45
Step-by-step explanation:
The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.
Answer:
45
Step-by-step explanation:
The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.
Which expression represents a factorization of 32m + 56mp?
A. 8(4m +7p)
B. 8(4 + 7)mp
C. 8p(4 + 7m)
D. 8m(4 + 7p)
Answers
Answer:
The answer is option D
Step-by-step explanation:
32m + 56mp
First factor out the HCF out
The HCF of 32and 56 is 8
So we have
8 ( 4m + 7mp)
next factor m out
We have the final answer as
8m( 4 + 7p)Hope this helps you
What is the slope of the line through the points (2,8) and (5,7)
Answers
Answer:
-1/3
Step-by-step explanation:
The slope of the line can be found by
m = (y2-y1)/(x2-x1)
= ( 7-8)/(5-2)
= -1/3
Answer:
-1/3.
Step-by-step explanation:
The slope can be found by doing the rise over the run.
In this case, the rise is 8 - 7 = 1.
The run is 2 - 5 = -3.
So, the slope is 1 / -3 = -1/3.
Hope this helps!
After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y). A student determined y to be –2. Evaluate the student's answer. A. The student is correct. B. The student incorrectly calculated the scale factor to be –2. C. The student incorrectly divided by the scale factor instead of multiplying by it. D. The student incorrectly added the scale factor instead of multiplying by it.
Answers
Answer:
B. The student incorrectly calculated the scale factor to be –2
Step-by-step explanation:
Given that :
After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).
The student determined y to be -2
If a figure dilated with a center of (0, 0) and scale factor k, then
(x , y) → (kx , ky)
(4, -6) → (12, y)
[tex]k = \dfrac{x'}{x}[/tex]
[tex]k = \dfrac{12}{4}[/tex]
k = 3
Thus; the scale factor is 3
Now; the y-coordinate can now be calculated as;
ky = (3 × -6)
ky = -18
Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.
The measure of each exterior angle of a regular polygon is 30 degrees. How many sides does the polygon have
Answers
Answer:
12 sides
Step-by-step explanation:
To find the number of sides, use a formula.
[tex]\frac{360}{\theta }=n[/tex]
θ is the measure of each exterior angle of the regular polygon.
n is the number of sides of the regular polygon.
[tex]\frac{360}{30} =12[/tex]
The area of a rectangle is 42 ft squared, and the length of the rectangle is 5 ft more than twice the width. Find the dimensions of the rectangle. length and width.
Answers
Answer:
Length = 12 ftWidth = [tex] \frac{7}{2} ft[/tex]
Step-by-step explanation:
Given,
Area of rectangle = [tex]42 \: {ft}^{2} [/tex]
Width = X
Length = 2x + 5
Now,
[tex]x(2x + 5) = 42[/tex]
[tex]2 {x}^{2} + 5x = 42[/tex]
[tex]2 {x}^{2} + 5x - 42 = 0[/tex]
[tex]2 {x}^{2} + 12x - 7x - 42 = 0[/tex]
[tex]2x(x + 6) - 7(x + 6) = 0[/tex]
[tex](2x - 7)(x + 6) = 0[/tex]
Either
[tex]2x - 7 = 0[/tex]
[tex]2x = 0 + 7[/tex]
[tex]2x = 7[/tex]
[tex]x = \frac{7}{2} [/tex]
Or,
[tex]x + 6 = 0[/tex]
[tex]x = 0 - 6[/tex]
[tex]x = - 6[/tex]
Negative value can't be taken.
So, width = [tex] \frac{7}{2} ft[/tex]
Again,
Finding the value of length,
Length = [tex]2x + 5[/tex]
[tex]2 \times \frac{7}{2} + 5[/tex]
[tex]7 + 5[/tex]
[tex]12[/tex]
Length = 12 ft
Answer:
length = 12 ft, width = 3.5 ft
Step-by-step explanation:
w = width
l = length = 2w + 5
A = wl = w(2w + 5) = 42
2w² + 5w - 42 = 0
(w + 6)(2w - 7) = 0
w + 6 = 0, w = -6 (dimension cannot be negative)
2w - 7 = 0, w = 3.5
l = 2(3.5) + 5 = 12
please solve this using quadratic formula :")
Answers
Answer:
Step-by-step explanation:
The given equation is expressed as
(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12
Simplifying the right hand side of the equation, it becomes
[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)
x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)
(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)
4x/(x - 1)(x + 1)
Therefore,
4x/(x - 1)(x + 1) = 7/12
Cross multiplying, it becomes
4x × 12 = 7(x - 1)(x + 1)
48x = 7(x² + x - x - 1)
48x = 7x² - 7
7x² - 48x - 7 = 0
Applying the quadratic formula,
x = - b ± √(b² - 4ac)]/2a
from our equation,
b = - 48
a = 7
c = - 7
Therefore
x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)
x = [48 ± √(2304 + 196]/14
x = (48 ± √2500)/14
x = (48 ± 50)/14
x = (48 + 50)/14 or x = (48 - 50)/14
x = 98/14 or x = - 2/14
x = 7 or x = - 1/7
Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7
Step-by-step explanation:
Please answer this question now
Answers
Answer:
This is simple! (Kind of)
Step-by-step explanation:
First, notice how HJ is tangent. HG is a radius intersecting HJ at H.
This means, (According to some theorem that I forgot the name of) that GHJ is a right angle.
Thus, we can use the 180* in a triangle theorem.
[tex]180=90+54+6x+6[/tex]
So, let's solve!
[tex]30=6x\\5=x[/tex]
So, there you go! Nice and simple!
Hope this helps!
Stay Safe!
Step-by-step explanation:
hope it helps yoy..........
If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be tru
Answers
Answer:
The leading coefficients of f(x) and g(x) are Opposites.Option A is the correct option.
Step-by-step explanation:
As the graph of ( f + g ) ( x ) is a line. So, ( f + g ) ( x ) is linear which means x² of f ( x ) and x² of g ( x ) get cancelled on adding . They must be equal and opposite in sign.
So, Option A is correct.
Hope this helps..
Best regards!!
Angles α and β are angles in standard position such that: α terminates in Quadrant III and sinα = - 5/13 β terminates in Quadrant II and tanβ = - 8/15
Find cos(α - β)
-220/221
-140/221
140/221
220/221
Answers
Answer:
140/221.
Step-by-step explanation:
For the triangle containing angle α:
The adjacent side is -√(13^2-5^2) = -12.
For the triangle containing angle β:
Hypotenuse = √(-8)^2 + (15)^2) = 17.
cos(α - β) = cos α cos β + sin α sin β
= ((-12/13) * (-15/17) + (-5/13)* (8/17)
= 180/221 + - 40/221
= 140/221.
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answers
Answer:
11.7
Step-by-step explanation:
Let H be the heipotenys of the big triangle:
sin68° = 26/H H= 26/sin68°H= 28.04
Let's calculate the third side using the pythagorian theorem:
H²= 26²+ d²(the third side)
d² = 28.04²-26²= 110.24
d= 10.49
let's calculate x now
tan42°= 10.49/xx= 10.49/tan42°x= 11.65 ≈ 11.7
I NEED HELP QUICK like very quick
Answers
Answer:
2.5 or 2 1/2
Step-by-step explanation:
i caculated do order of operations
PLEASE HELP
What is the y-intercept of the given graph? -4 3 4 None of these choices are correct.
Answers
Answer:
3
Step-by-step explanation:
the line crosses the y-axis at (0,3)
Answer:
3
Step-by-step explanation:
The y intercept is where the graph crosses the y axis ( where x =0)
The lines crosses at y=3
Y intercept is 3
Simplify the following expression. (m^2-m^3-4)-(4m^2+7m^3-3)
Answers
Answer:
2m
4
−2m
3
−26m
2
−23m+20
Step-by-step explanation:
find the hypo when the opposite is 36 and the adjacent is 27
Answers
Answer:
45
Step-by-step explanation:
Given the legs of the right triangle.
Then using Pythagoras' identity
The square oh the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is
h² = 36² + 27² = 1296 + 729 = 2025 ( take the square root of both sides )
h = [tex]\sqrt{2025}[/tex] = 45
Answer:
45
Step-by-step explanation:
When you are given the opposite and adjacent sides of a triangle, the easiest way to find the hypotenuse is through the Pythagorean theorem!
The formula is a^2 + b^2= c^2
Plugging in the values, your formula would now look like 36^2 + 27^2= c^2
Once you do square your values and add them up, the result would end up being 2025, but since that is squared, to find the actual value of c you have to take the square root of this number, this will result in 45.
if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6
Answers
Answer:
d. 20
Step-by-step explanation:
To answer the question given, we will follow the steps below:
we need to first find p(3)
p(x) = x+ 7/ x-1
we will replace all x by 3 in the equation above
p(3) = 3+7 / 3-1
p(3) = 10/2
p(3) = 5
Similarly to find q(2)
q (x) = x^2 + x - 2,
we will replace x by 2 in the equation above
q (2) = 2^2 + 2 - 2
q (2) = 4 + 0
q (2) = 4
The product of p(3) and q(2) = 5 × 4 = 20