Imagine a right triangle where a and b are the legs and c is the hypothenuse.
Pitagora: a²+b²=c²
Divide by c
(a/c)²+(b/c)²=1
But a/c=sin(B) and b/c=cos(B)
Thus sin² + cos² = 1
What is the slope of a line perpendicular to the line whose equation is y= 2x + 5?
slope = -1
Slope = -1/2
slope = -2
Answer:
The slope is -1/2 which is Option B
Step-by-step explanation:
A line that is perpendicular to another has the slope that has the sign reversed and is the reciprocal.
Example: Find the line perpendicular to y = 3x
First, you flip the sign which makes 3 into -3
Next, you make the reciprocal which makes -3 into -1/3
Problem: Find the line perpendicular to y= 2x + 5
First, you flip the sign which makes 2 into -2
Next, you make the reciprocal which makes -2 into -1/2
Answer: The slope is -1/2 which is Option B
The slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
Opposite → -2
Reciprocal → -1/2
Therefore, the answer is -1/2
Best of Luck!
Which expressions are equivalent to 7⋅7⋅7⋅7⋅7⋅7
SELECT 2 Answers
It's FROM KHAN academy
Answer:
7^6
and
7⋅7⋅7⋅7⋅7⋅7/1
Step-by-step explanation:
Hope this helps! It would be better for me to see the selections though.
Answer:
A - 7^8/7^2
C - (7^2)^3
Step-by-step explanation:
So there's a question exactly like this on khan, so here's the khan answer
Don't worry I tested it
please help me asap!!!!
Answer:
125
Step-by-step explanation:
5 × 5 × 5 = 125
Hope that helped.
Answer:
125
Step-by-step explanation:
5^3 is equivilent to 5*5*5
5*5=25
25*5=125
explanation needed tip by using chain rule
Answer:
1/(810pi) cm/s
Step-by-step explanation:
V = pi×r²×h = pi×90²×h = 8100pi×h
dh/dt = dh/dV × dV/dt
dV/dh = 8100pi
dV/dt = 10
dh/dt = (1/8100pi) × 10
= 1/(810pi) cm/s
what is the value of 4(3x + 5) when x = 11?
Answer:
152
Step-by-step explanation:
3(11)= 33
4(33+5)
4(33)=132
4(5)=20
132+20=152
The value of the expression 4(3x + 5) when x = 11 is 152. This was calculated by replacing x in the equation with 11, simplifying the resultant equation and finally calculating the product.
Explanation:The student has asked to compute the value of 4(3x + 5) when x = 11. This a problem in the field of Algebra, where 'x' is a variable and the equation 4(3x + 5) is an expression.
First, let's substitute x in the equation with 11. So the equation becomes 4(3*11 + 5). Let's simplify the equation. This gives us 4(33 + 5), which equals 4*38. Multiplying 4 by 38 gives us the final answer, 152.
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Solve the equation
−3(x + 8) − x = 2(2x − 7)
Answer:
-4x-24=4x-14 x is 1
Step-by-step explanation:
solved in my head. please give me brainliest!!!!!
If you are looking for x it would be 1
Two linear functions are combined with addition, and then the same two linear functions are combined by multiplication.
Which functions could be the result of the combinations? Select two options.
16x - 12
17x - 12
72x? - 96x
72x2 - 108
72x2 - 204x + 144
Adding two linear functions results in a linear function, which could be represented as '16 x - 12' or '17 x - 12'. Multiplying two linear functions results in a quadratic function, which could be represented as '72 x² - 204 x + 144'.
Explanation:In this scenario, when the two linear functions are being combined by addition and multiplication, it results in an expression that could be either linear or quadratic. When you add two linear functions together: f(x) = ax + b and g(x) = cx + d, the result is also a linear function: h(x) = (a+c)x + (b+d). Therefore, both 16 x - 12 and 17 x - 12 could be the result of an addition of two linear functions.
However, when you multiply two linear functions, you get a quadratic function: i(x) = (ax + b)(cx + d) = acx^2 + (ad+bc)x + bd. So 72 x² - 204 x + 144 could be the result of a multiplication of two linear functions.
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A painter estimates she can paint a house in 40 hours. She knows her assistant can do the same job is 60 hours. How long would it take them to paint the house working together?
24 hours
Step-by-step explanation:
1 hour
Painter1 1/40
Painter2 1/60
together 1/40+1/60=5/120=1/24
The time it would take them to paint a house working together is 24 hours.
How are number of people to time needed to complete a task related?(WORK DONE)More people to do a task means less time it will take.
Less people to do a task means more time it will take.
Thus, they are inversely related.
If x men take y time for a work,
We can define a constant as "Manpower" needed for doing that specific work.
Let we define:
Manpower needed for a work = y + y + y + .. + y = Time per man × count of men
Manpower needed for a work = xy
We are given that;
Time = 40hours
Time for her assistant= 60hours
Now,
First, let’s find their individual rates. The painter can paint 1/40 of a house per hour and the assistant can paint 1/60 of a house per hour. To find their combined rate, we add these fractions:
1/40 + 1/60 = 3/120 + 2/120 = 5/120
This means that together they can paint 5/120 of a house per hour. To find how long it would take them to paint one whole house (or 1/1), we use the formula:
Work done = Rate × Time 1/1 = (5/120) × Time Time
= (120/5) × (1/1) Time
= 24 hours
Therefore, by work and time the answer will be 24 hours.
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3. What is the correct factorization of x2 – 2x – 15?
Answer:
(x+3)(x−5)
Step-by-step explanation:
to factor, simply just think of what two numbers multiplied together would give you -15 but added together give you -2. since the produce is negative, you know one number is positive, and one is negative, and since the sum is also negative, you know that the larger root is negative
Hope this will help u..☝✌✌
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Volume of Prisms & Pyramids Practice
Find the volume of each figure. Be sure to include the units, and circle or box your answers.
1)
4 in
2)
12 m
10 m
2 in
2 in
2 in
2 in
3)
4 ft
4)
10 yd
8 yd
6 yd
8m
6m
9 yd
5 ft
12 ft
5)
11 m
6)
4 ft
12 ft
12 ft
4 ft
2 ft
10 m
4m
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Worksheet by Kuta Software LLC
7)
7 ft
8)
8 m
3m
4m
9)
12 in
9 in
9 in
10)
11 mi
8 ft
6 ft
5m
10 ft
12 in
12 in
11)
12)
6 mi 6 mi
8 mi
8 mi
10 in
10 in
3 in
7 in
5 mi
6 mi
3 in
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6 mi
Worksheet by Kuta Software LLC
Which is the equation of the function?
f(x) = 3|x| + 1
f(x) = 3|x – 1|
f(x) = |x| + 1
f(x) = |x – 1|
Answer:
the answer is d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Wendy already owns 4 necklaces, and additional necklaces are priced at 1 for a dollar. How
much money does Wendy need to spend on new necklaces in order to own a total of 26
necklaces?
Answer:
$22
Step-by-step explanation:
If she wants to own 26 necklaces. You take that number and subtract the four she already owns, leaving you with 22.
Answer:
She needs to spend $22.
Step-by-step explanation:
She has 4 necklaces. In order to have 26, she needs to buy more necklaces. How many does she need to buy?
We subtract 4 from 26.
26 - 4 = 22
She needs to buy 22 necklaces to have a total of 26 necklaces.
Each necklace costs $1.
22 necklaces cost 22 times $1.
22 * $1 = $22
Answer: She needs to spend $22.
8(4x + 6) what is the answer
Answer:
32x+48
Step-by-step explanation:
All that is needed to be done here is to multiply each digit inside the bracket by 8. We can even expand it to make it simpler to understand.
8(4x)+8(6)
8(4x)=32x
8(6)=48
We therefore have as our answer
32x+48
Can someone help me please
Answer:
q<5
Step-by-step explanation:
Since the line goes to the left of 5, q must be less than 5.
The open circle on 5 means that it cannot include 5.
Therefore, q is less than (<) five
Find the value of x to the nearest tenth! Help ASAP
The value of x is 10.
Solution:
Given triangle is a right triangle.
θ = 50°, adjacent side = 6, hypotenuse = x
The value of cos 50° = 0.6
Using trigonometric ratio formulas,
[tex]$\cos \theta=\frac{\text { Adjacent side of } \theta}{\text { Hypotenuse }}[/tex]
[tex]$\cos50^\circ=\frac{6}{x}[/tex]
[tex]$0.6=\frac{6}{x}[/tex]
Do cross multiplication, we get
[tex]x\times 0.6=6[/tex]
Divide by 0.6 on both sides, we get
[tex]$\frac{x\times 0.6}{0.6}=\frac{6}{0.6}[/tex]
x = 10
The value of x is 10.
In a club there is 13 women and 8 men. A committee of 9 women and 4 men is to be chosen. How many different ways are there to select the committee?
A. 50,050 ways
B. 3,744 ways
C. 273 ways
D. 34 ways
Final answer:
To find the number of ways to form a committee of 9 women and 4 men from a group of 13 women and 8 men, calculate the combinations separately for women and men, and multiply them together. The answer is 50,050 ways. So the correct option is A.
Explanation:
The question involves calculating the number of ways to choose a committee consisting of 9 women from a group of 13 women, and 4 men from a group of 8 men. This is a problem that requires knowledge of combinations, a concept in probability and statistics.
Step-by-step solution:
Calculate the number of ways to choose 9 women out of 13, which is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial. For the women, C(13, 9) must be calculated.Calculate the number of ways to choose 4 men out of 8, using the same formula. This will be C(8, 4).Multiply the two results to get the total number of ways to form the committee, since the selections of women and men are independent events.Now, using the combination formula:
C(13, 9) = 13! / (9! × (13-9)!) = 13! / (9! × 4!)C(8, 4) = 8! / (4! × (8-4)!) = 8! / (4! × 4!)Therefore, the total number of ways to select the committee = C(13, 9) × C(8, 4).After calculating, we find that the number of ways to form the committee is 50,050, which corresponds to option (A).
Help with any please!
Answer:
1. A
2. 128°
3. 112°
4. 20°
5. 125°
6. 35°
7. 158°
8. 140°
9. B
10. C
The measure of 2 ACD is 147º and the measure of Z BAC is 29º. What is the measure of Z ABC?
(not drawn to scale)
Answer:
Answer is option c) 118 degrees
Step-by-step explanation:
[tex]the \: exterior \: angle \: is \: equal \: to \: the \: \\ sum \: of \: the \: opposite \: interior \: angles \\ by \: using \: this \: concept \: \: we \: find \: that \\ angle \: abc \: is \: 118 \: degrees.[/tex]
If you have any doubts see the image. or write in comments box.
HAVE A NICE DAY !
During halftime of a football game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 80 feet per second. The T-shirt is caught 35 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
It takes 2 seconds to reach a maximum height of 69 feet, and the range is [5, 69].
The equation is of the form
h(t) = -16t² + v₀t + h₀, where -16 is the gravitational constant, v₀ is the initial velocity, and h₀ is the initial height. Using the values from our problem, we have:
h(t) = -16t² + 64t + 5
To find the maximum height, we find the vertex. The first step in this is to find the axis of symmetry, which is given by -b/2a:
-64/2(-16) = -64/-32 = 2
This is our value for t, so it takes 2 seconds to reach the maximum. Substituting this into our function, we have
h(2) = -16(2²) + 64(2) + 5 = -64 + 128 + 5 = 64 + 5 = 69
This is the maximum height.
The range of heights goes from 5 to 69, inclusive, or [5, 69].
The T-Shirt reaches its maximum height of 104 feet at 2.5 seconds. The range of the height over time is from 4 feet to 104 feet.
To analyze the projectile motion of the T-Shirt, we'll use the kinematic equations. The height h(t) at any time t can be modeled by the equation:
h(t) = -16t2 + v0t + h0
where:
h(t) is the height at time tv0 is the initial velocity (80 ft/s)h0 is the initial height (4 ft)1. Time to reach maximum height:
To find the time to reach maximum height, we use the formula for the time at which the velocity becomes zero:
t = v0 / g
t = 80 ft/s / 32 ft/s2 = 2.5 s
2. Maximum height:
Now, substituting t = 2.5 s into the height equation, we get:
h(2.5) = -16(2.5)2 + 80(2.5) + 4
h(2.5) = -100 + 200 + 4 = 104 feet
3. Range of the height function:
The T-Shirt starts at 4 feet, reaches a maximum of 104 feet, and is caught at 35 feet. Hence, the range of the height function is [4, 104] feet.
Part B: If Taylor and Miley both
work for 2 weeks, how much more
will Taylor earn?
Answer: $661.50
Step-by-step explanation:
Taylor makes $771.25 per week and makes twice that much in two weeks.
2×771.25=2(700+70+1+0.25)=1400+140+2+0.50
So Taylor makes $1542.50 in two weeks.
Miley makes $440.50 per week and so will make $881 in two weeks. Since
1542.50−881=742.50−81=741.50−80=701.50−40=661.50
We know that Taylor will make $661.50 more than Miley in two weeks.
Hope this helps!
Solve t. Soving proportion 7-3=4-t t=
Answer:
t = 0
Step-by-step explanation:
Step 1: Solve for t
7 - 3 = 4 - t
4 - 4 = 4 - t - 4
0*-1 = -t*-1
0 = t
Answer: t = 0
4x−4<8 AND 9x+5>23 Solve for X.
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$300 invested at 12% compounded monthly after a period of 1.5 years
Answer: $358.8 to the nearest tenth
Step-by-step explanation:
Compound interest is calculated by Where: A = P(1 + r)t
Where P= 300, r= 12% = 0.12, t= 1.5 years
Slot in the figures
300 (1 + 0.12) 1.5
300 (1.12) 1.5
300x 1.12
336e1.12
A = $ 358.84
Find the slope of the line that passes through -2,5 and -1,1
Answer:
m= -4
Step-by-step explanation:
use the slope formula m=rise/run y2-y1/x2-x1
(24y + 2x)divide(1/4z
Answer:
96y/z + 8x/z
Step-by-step explanation:
hope this helped
Last month, the Nunez family spent $218.85 for 1,214 kilowatt hours of electricity. What is the unit rate per kilowatt hour?
Answer:
$.18 per kilowatt hour
Step-by-step explanation:
To find the rate per kilowatt hour
Take the price and divide by the kilowatt hours
218.85/1214
.180271829
Since this is money,we round to the nearest cent
$.18 per kilowatt hour
solve the system of equations -x-y=-4 and -2x+4y by combining the equation
Answer:
×=8/3 and y=4/3
Step-by-step explanation:
-x-y=-4
-2x+4y=0
-2x=-4y
x=2y
so -2y-y= -4 and x= 2•4/3
-3y=-4 x=8/3
y=4/3
A bake sale earns 80$ from selling 50 brownies. Each brownie cost the same amount. How much was 1 brownie?
Answer:
cost of one brownie is $1.60
Step-by-step explanation:
Cost of one brownie$80 from selling 50 brownies
we can create a ratio
80 : 50
x : 1
we can use cross multiplication to solve this:
80 = 50x
80/50 = x
x = $1.60
cost of one brownie is $1.60What ratio is equivalent to 2/8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{2}{8}=\dfrac{2\div2}{8\div2}=\boxed{\bf{\dfrac{1}{4}}}}}[/tex]
[tex]\mathsf{Rewrite\ \dfrac{1}{4}\ as\ ratio\ and\ that\ will\ be\ your\ answer!}[/tex]
[tex]\mathsf{\dfrac{1}{4}=\bf{1:4}}[/tex]
[tex]\boxed{\boxed{\bf{Your\ answer: \boxed{\huge\text{\bf{1:4}}}}}}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
2. The 120 sixth graders are going on a
field trip to the museum. The museum
requests a ratio of students to adult
chaperones of 8:1. How many adult
chaperones will be needed?
Answer:
15 chaperones
Step-by-step explanation: