Answer:
Basic Steps to Setting Up Equations
-Determine what the question is asking.
-Write down the relevant information in simple statements.
-Assign symbols to unknown values that need to be found.
-Determine how the statements relate to each other mathematically.
Solving Story Problems
Story problems can contain lots of information, including details that are not necessary to solve the problem. Additionally, the problem may assume general knowledge on the reader's part, and not explain all the information explicitly. Writing that information down in a streamlined form is an efficient way to solve problems.
Step-by-step explanation:
Change this radical to an algebraic expression with fractional exponents.
3√a
The fractional form of the expression [tex]\sqrt[3]a[/tex] is [tex]a^{\frac{1}{3}[/tex]
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, A radical expression [tex]\sqrt[3]a[/tex].
We know this describes the cube root of a or one-third root of a.
This can be written as a fractional exponent as [tex]a^{\frac{1}{3}[/tex].
Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
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I need help please!!!
On a hot day, a fan has a mark on the tip of one blade. The equation y
=20cos(x) + 25 represents the height of the mark, y centimeters, above the
table x seconds after the fan is turned on. What is the height of the mark
above the table when it is closest to the table?
===================================================
Explanation:
Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).
Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:
20*cos(x)+25
20*(-1) + 25
-20 + 25
5
The height of the fan tip is 5 cm when it is the closest to the table.
Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is [tex]5 \le y \le 45[/tex]
Maria flips a coin 20 times. The coin only lands on tails 9 times. According to theoretical
probability how many more times would Maria have expected the coin to land on tails?
Answer:
1
Step-by-step explanation:
A coin only has two outcomes. Meaning that she has a 50/50 chance of landing on each side. So, 50% of 20 is 10. According to the theoretical probabilty, the coin would have landed on heads 10 times and tails 10 times. So, for that to be true Maria would have had to land on tails one more time.
what is the coefficient of Q in the sum of
(2/3q - 3/4) and (-1/6q - 2)
please help me out
I need some help please.
Step-by-step explanation:
Answer: 2/4, 4,8, etc.
Step-by-step explanation:
Hello!
So basically, what I think this question is asking is for an equivalent fraction to 1/2. There are countless fractions that are the same as this and I listed a couple above!
Hope this helps! :D
Find the solution for x if |5x – 2| = 13.
Answer:
x=1 if that's 15 x
Step-by-step explanation:
Find the area of the rhombus.
Find the area. The figure is not drawn to scale.
Answer:
I don't know if this is right but I think it is 32m
Answer:
Hello! answer:
question 30: 128 m2
question 31: 1188 in2
Step-by-step explanation:
Hello just in advance I dont know if you need unuts or not but i believe those are correct if not Im sorry but the answers are 100% correct.
For the first one I found the area of a singular triangle then just multiplued by 4 cause all of those triangles are the same so... triangle area is... base × height ÷ 2 or base × height × 1/2
8 × 8 = 64 64 ÷ 2 = 32 32 × 4 = 128 therefore the area is 128 for the second I just did base × height therefore 36 × 33 = 1188 therefore thats the area hope that helps!
how long would it tak to go 75 miles if you can go 45 mph
How do logarithmic functions model real-world problems and their solutions? Give a specific example and explain.
The process of logarithmic functions in real-worlds problems is given below.
And an example of an application of logarithmic function is given.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
We know,
logarithmic function and exponential function are inverse of each other.
So, whenever we solve the exponential function,
we use the help of logarithmic functions.
To compute the number with bigger exponents,
we use the logarithms.
Because it reduces the size of the numbers.
Let the bacteria is growing exponentially,
b = 2ⁿ.
We know that the bacteria grows every hour.
We want to find time.
Here, we will use the inverse function to the exponential function.
How long will it take them to get 1000 bacteria?
1000 = 2ⁿ
Taking log on both sides,
log(1000) = n log2
n = log(1000)/log(2)
n = 9.96
n ≈ 10 hours.
Therefore, an application of logarithmic function is given above.
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Which graph represents the compound inequality?
-3
-5 -4 -3 -2 -1 0 1
2
3 4
5
-5 4 -3 -2 -1 0 1
2 3 4 5
-5 4 -3 -2 -1 0 1
2
3
4
5
OG
-5 4 -3 -2 -1 0 1 2 3 4 5
Answer:
4th option
Step-by-step explanation:
open circle means more than or less than
n is more than -3 but less than 1
FOR BRAINIEST PLEASE ANSWER ASAP
There are 24 students in a class, and three of them are named Madison. There are no other students in the class with the same name.
If the teacher calls on students randomly, which of the following BEST describes the probability of a Madison being chosen?
If you cannot see, zoom in on the photo.
Do not answer if you don’t know the answer.
Whoever answers correctly will get Brainliest!
Answer:
Mizuki is here to help! The answer is D!
Step-by-step explanation:
Ok... So there are 24 students in the class and no other students in the class has the same name right? So the fraction should be [tex]\frac{3}{24}[/tex] since there are three madisons, which will be 0.125!
Since three people have the same name, everyone else gets less probability of getting called so the answer would be D.
Answer:
Option D
Step-by-step explanation:
Total Students in a class: 24
Total Madisons in the class: 3
Denominator is always the total number of something so; [tex]\frac{3}{24}[/tex]
3/24 = 0.125
Any other student would have a probability of [tex]\frac{1}{24}[/tex] of being chosen which is less than [tex]\frac{3}{24}[/tex], therefore, Option D is the most sensible one.
Hope this helps!
In Figure 5.51 given to the right, m( <ABC) =
32°, m(<BHE) = 42° and m( <ADE) = 48°
Find m(<NAD).
Answer:
122
Step-by-step explanation:
<HEB=180-(42+32)
=180-74
=106
<DEA=180-106 (straight line)
=74
<NAD=48+74(exterior angle = sum of 2 interior opposite angles)
<NAD=122
Anybody who knows Pre Calc?? My last offer here
Solution PLS!
Answers:
true speed = 26.935546 knotstrue bearing = 102.265139 degreesThe values are approximate. Round them however you need to.
====================================================
Explanation:
The diagram you have drawn is correct if you're only considering one current. Specifically current #1 which has the bearing of 290 degrees moving at 25 knots.
The red angle is 290 degrees. The remaining portion that is needed to get a full 360 degrees is 360-290 = 70. This adds to the blue portion in quadrant 1, which is 90, and we get 70+90 = 160. So the blue angle is 160 degrees.
The vector for current #1 is <25*cos(160), 25*sin(160)>
This approximates to <-23.4923155, 8.5505036>
All of this is for current #1.
------------
Vector #2 is much more simple in terms that there aren't messy decimal approximations here. The direction is due north, which means that the vector is pointing straight up toward 90 degrees.
We can then say: <12*cos(90), 12*sin(90)> = <12*0, 12*1> = <0, 12>
Vector #2 is <0,12>
When you wrote <12,0>, you were on the right track, but you had the coordinates swapped in the wrong order.
----------
Then we have to account for a wind going 4 knots in the southwest direction. This is at the angle 225 degrees (we rotate 180 degrees plus another 45 to get 225). So,
vector #3 = <4*cos(225), 4*sin(225)> = <-2.8284271, -2.8284271>
This vector's coordinates are approximate
---------
To recap everything so far, vectors 1 through 3 are the following
p = <-23.4923155, 8.5505036>q = <0, 12>r = <-2.8284271, -2.8284271>I'm using variables to represent the vectors at this point, so we can then add them up to get...
s = p+q+r
s = <-23.4923155, 8.5505036> + <0,12> + <-2.8284271, -2.8284271>
s = <-23.4923155+0+(-2.8284271), 8.5505036+0+(-2.8284271)>
s = <-26.3207426, 5.7220765>
Vector s represents the sum of the three vectors p, q, and r. The two currents and the wind ultimately combine together to push the boat in the direction and along the length of vector s.
----------------------
Now that we know the coordinates of vector s, we use them to find the true speed and true bearing of the boat.
speed = sqrt(a^2 + b^2)
speed = sqrt( (-26.3207426)^2 + (5.7220765)^2 )
speed = 26.935546 knots, which is approximate
angle = arctan(b/a)
angle = arctan(5.7220765/(-26.3207426))
angle = -12.265139
Add 360 to this angle to find that we get to the coterminal angle of -12.265139+360 = 347.734861 degrees
This angle is in quadrant 4, which is the southeast quadrant. If we rotate another 360-347.734861 = 12.265139 degrees, going counterclockwise, then we'll face directly east. Then another 90 degree counterclockwise rotation has us face directly north.
In total, the true bearing is approximately 90+12.265139 = 102.265139 degrees
So we'll start aiming north, and then rotate roughly 102.265139 degrees toward the east to get to the true bearing.
An item on sale costs 80% of the original price. The original price was 33%
The sale price of the item is given by the equation A = $ 26.40
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the sale price of the item be represented as A
Now , the equation will be
The original price of the item = $ 33
An item on sale costs 80% of the original price
So , the sale price of the item A = 80 % x original price of the item
Substituting the values in the equation , we get
The sale price of the item A = ( 80 / 100 ) x 33
The sale price of the item A = 0.80 x 33
The sale price of the item A = $ 26.40
Therefore , the value of A is $ 26.40
Hence , the sale price is $ 26.40
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Samantha was driving down a road and after 4 hours she had traveled 70 miles. At this speed, how many hours would it take Samantha to drive 105 miles?
Answer:
It would take Samantha 6 hours to drive 105 miles.
Step-by-step explanation:
This question can be solved by proportions.
After 4 hours she had traveled 70 miles.
This means that she travels 70/4 = 17.5 miles per hour.
How many hours would it take Samantha to drive 105 miles?
17.5 miles per hour, so for 105 miles:
105/17.5 = 6
It would take Samantha 6 hours to drive 105 miles.
On a piece of paper graph f(x) = 3x if x<3 2x if x>3 then determine which answer choice matches the graph you drew
The graph of a piecewise function f(x) = 3x if x ≤ 3 and f(x) = 2x if x > 3 is shown in the picture.
What is a piecewise function?
The graph of a piecewise function contains numerous curve components. It signifies that it has a plethora of definitions based on the value of the input. In other words, a piecewise function behaves differently depending on the input.
We have:
f(x) = 3x if x ≤ 3
f(x) = 2x if x > 3
We can draw the piecewise function as shown in the attached picture.
At x = 3
f(3) = 3(3) = 9 because f(x) = 3x if x ≤ 3
Thus, the graph of a piecewise function f(x) = 3x if x ≤ 3 and f(x) = 2x if x > 3 is shown in the picture.
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hi!! ;; please help :) 20 points! no links or websites. please .
Answer: 22
Step-by-step explanation:
(1 × 3) + [2 × 3 [tex]\frac{1}{2}[/tex]] + [1 × 3 [tex]\frac{3}{4}[/tex] [1 × 4 [tex]\frac{1}{4}[/tex]] + [3 × [tex]\frac{3}{4}[/tex]] + [3 × 5 [tex]\frac{1}{4}[/tex]]
= 3 + [2 × [tex]\frac{3}{2}[/tex]] + [1 × [tex]\frac{9}{4}[/tex]] + [1 × [tex]\frac{4}{4}[/tex]] + [3 × [tex]\frac{12}{4}[/tex]] + [3 × [tex]\frac{5}{4}[/tex]]
= 3 + [tex]\frac{6}{2}[/tex] + [tex]\frac{9}{4}[/tex] + [tex]\frac{4}{4}[/tex] (equal to 1) + [tex]\frac{36}{4}[/tex] + [tex]\frac{15}{4}[/tex]
= 3 + 3 + [tex]\frac{9}{4}[/tex] + 1 + 9 + [tex]\frac{15}{4}[/tex]
= 16 + [tex]\frac{9+15}{4}[/tex]
= 16 + [tex]\frac{24}{4}[/tex]
= 16 + 6
= 22
Solve -3x + 2y = 5 for y
Answer:
y=4
Step-by-step explanation:
Answer:
y=2.5
Step-by-step explanation:
first you add -3x to both sides so you get 5-3x and then divide that by 2 to get Y by itself so now you have 5/2 - 3/2x and when you put in the equation y=5/2 - 3/2x in DESMOS, the answer is 2.5
The volume of
a refrigerator, in cubic centimeters, is given
by the function V(x) = (x)(x + 1)(x – 2). Write a
new function for the volume of the refrigerator
in cubic millimeters if x is in centimeters.
The newly rewritten function expression of V(x) is V(x) = (x)(x + 1)(x – 2)/1000
How to rewrite the function expression?From the question, we have the following parameters that can be used in our computation:
A function expression
The function expression is given as
V(x) = (x)(x + 1)(x – 2)
Where if x is in centimeters and V(x) is in cubic centimeters
The new function for the volume of the refrigerator is stated to be in cubic millimeters
Using the above as a guide, we have the following:
1 cubic centimeters = 1000 cubic millimeters
So, we have
V(x) = (x)(x + 1)(x – 2)
1 cubic centimeters = 1000 cubic millimeters
Cross multiply
V(x) * 1000 = 1* (x)(x + 1)(x – 2)
Divide both sides by 1000
V(x) = (x)(x + 1)(x – 2)/1000
Hence, the function is V(x) = (x)(x + 1)(x – 2)/1000
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How do I solve this system of equations using the elimination method
y=3x+13
2x=y-9
The value of x is -4 and the value of y is 1.
What is the value of x and y?In order to use the elimination method, rearrange the given linear equations.
y - 3x = 13 equation 1
y - 2x = 9 equation 2
Subtract equation 2 from equation 1:
-x = 4
x = -4
Substitute for x in equation 2
y - 2(-4) = 9
y + 8 = 9
y = 9 - 8
y = 1
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If k × k × k = 1; then k =
Answer: k^3=1
Step-by-step explanation:
Answer:k^3=1
Step-by-step explanation:
Find the missing length indicated. Leave your answer in simplest radical form.
Please help due today!!
Answer:
C) 25
Step-by-step explanation:
First, solve for the height (red dotted line) using the Pythagorean theorem 9²+b²=15²
81+b²=225
b²=225-81
b²=12
Then set up a ratio.
x/12=9/15
simplify
x/12=3/5
cross-multiply
3x=60
x=20
This gives us the base. Now we can solve for x using the Pythagorean theorem again.
20²+15²=x²
400+225=x²
625=x²
√x²=√625
x=25
7 x (n + 3) = (7 x 2) + (7 x 3)
Answer:
N = 2
Step-by-step explanation:
We must solve for N.
Solve inside the parenthesis if needed, otherwise open them
7n + 21 = (14) + (21)
Now solve, then simplify
7n + 21 = 35
7n = 35 - 21
7n = 14
N = 2
Three views of a solid are shown. What is this three-dimensional solid?
Answer:
pyramid
Step-by-step explanation:
Which box plot represents the data above?
W.
X.
Y.
Z.
A.
Z
B.
W
C.
X
D.
Y
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
Match each equation with the type of conic section it
represents.
Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.
Define equation.
Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.
Here,
are the definitions of each equation:
1. x^2 + y^2 - 4x + 6y - 5 = 0
The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.
2. x^2 - 6y = 0
The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.
3. 4x^2 + 9y^2 = 1
This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.
4. 7x^2 - 9y^2 = 343
A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.
Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.
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What's 6+89 .help me pls I'm going to kermit sewer side
Answer:
95
Step-by-step explanation:
Answer:
95
please don't
Help me plz I will give brainiest
Answer:
Side A = 11
Side B = 16
Side C = 25
I added an image that shows what I did in case you need it.