Answer:
The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem
Step-by-step explanation:
1. The function must be continuous.
Trigonometric functions are continuous.
2. It must be true that f(a) = f(b) = 0
For this case sin(pi) = sin(3pi) = 0
3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0
For this case f(x) = cos(x)
And cos(x) = 0 at x = 3(pi)/2,5(pi)/2
Find the area of Parallelogram ABCD given M< A=30° AB=10in AD=6in A=
Answer:
30 in²
Step-by-step explanation:
Parallelogram height is,
6/2 (since it's a 30°-60°-90° triangle)
= 3
Area = base × height
= 10×3 in²
= 30 in²
Answered by GAUTHMATH
6. Circle all the expressions that are equivalent to this expression: 6p+ 7.
You will lose a point for every wrong expression that you circle.
1.p+2+52 +5
2. 42p
3. 7p +6
4. 3p + 2p + P +7
5. 13P
6. p+p+p+p+p+p+5+1+1
Answer:
6
Step-by-step explanation:
because the equation above says p+p+p+p+p+p+5+1+1
so if we add up the p's it will give us 6p and if we add up the nos it will give us 6p+7
HELP PLEASE!!!!
The median age for a first marriage in the United States for women was 25.9 in 2009 and 26.1 in 2010. Use an exponential model to predict the median age for women in 2019, where x is the number of years since 2009.
A) 23.9
B) 28.3
C) 28.0
D) 24.0
Answer:
29.1 Is the answer for 2009
Step-by-step explanation:
build and sketch 2x2+7x+6)
Answer:
Step-by-step explanation:
HELP !
Find the measure it the given angle.
Answer:
it's 90
Step-by-step explanation:
inscribed angle intercepts a semicircle is always 90
Solve this equation for x. Round your answer to the nearest hundredth.
8 = In(x + 3)
Answer:
2977.96 =x
Step-by-step explanation:
8 = In(x + 3)
Raise each side to the base of e
e^8 = e^ ln(x+3)
e^8 = x+3
Subtract 3 from each side
e^8 -3 = x+3-3
e^8 -3= x
2977.95798 = x
Rounding to the nearest hundredth
2977.96 =x
Answer:
[tex]\displaystyle x = 2977.96[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural logarithms ln and Euler's number eStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 8 = ln(x + 3)[/tex]
Step 2: Solve for x
[Equality Properties] e both sides: [tex]\displaystyle e^8 = e^{ln(x + 3)}[/tex]Simplify: [tex]\displaystyle x + 3 = e^8[/tex][Equality Property] Subtract 3 on both sides: [tex]\displaystyle x = e^8 - 3[/tex]Evaluate: [tex]\displaystyle x = 2977.96[/tex]Find the length of AC on this triangle
Answer:
A
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan12° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{44}[/tex] ( multiply both sides by 44 )
44 × tan12° = AC , then
AC ≈ 9.35 ( to 2 dec. places )
Joey's strategy for his first marathon (26.2 miles)was to run 2 miles, walk 1 mile, run 2 miles, walk 1 mile, and continue this pattern until he completed the race. Joey's average running pace is 8 minutes per mile, and his average walking pace is 16 minutes per mile. How many minutes will it take Joey to complete the marathon
========================================================
Explanation:
We have this sequence
(2+1)+(2+1)+(2+1)...
Effectively, we're repeating "2+1" over and over.
We can see that
2+1 = 3(2+1)+(2+1) = 3+3 = 6(2+1)+(2+1)+(2+1) = 3+3+3 = 9Each time we add on another copy of (2+1), we're adding on 3
Dividing 26.2 over 3 gets us (26.2)/3 = 8.733 approximately
If we had 8 copies of (2+1) added together, then we would get
8*(2+1) = 8*3 = 24
This is 26.2-24 = 2.2 miles short of his goal.
He'll need to run 2 more miles, plus walk another 0.2 of a mile
----------------------------------------------------
In summary so far, Joey will run 8+1 = 9 sections (two miles each) and walk 8 sections that are 1 mile each. At the very end, he'll walk 0.2 miles to finish the race. Each running and walking section is alternated of course.
Since he runs 9 sections, each 2 miles, that accounts for 9*2 = 18 miles.
His running pace is 8 minutes per mile, so this means he has run for 8*18 = 144 minutes. This is just the running part and not the walking part.
Let A = 144 so we can use it later.
----------------------------------------------------
He walks 8 sections of 1 mile each. His walking pace is 16 minutes per mile. This must mean he spends 8*16 = 128 minutes on this walking portion.
Then for the last 0.2 mile section he walks, we can solve the proportion below
(1 mile)/(16 min) = (0.2 miles)/(x min)
1/16 = 0.2/x
1*x = 16*0.2
x = 3.2
He spends 3.2 minutes walking the remaining 0.2 of a mile at the end.
So his total walking time is 128+3.2 = 131.2 minutes.
Let B = 131.2
-----------------------------------------------------
To wrap things up, we'll add up the results of each of the previous two sections.
A = total running time = 144 min
B = total walking time = 131.2 min
C = total marathon time
C = A+B
C = 144+131.2
C = 275.2 minutes
This converts to 275 min, 12 sec.
This is also equivalent to 4 hrs, 35 min, 12 sec.
Homework:Assignment 3 Question 20 Score: 0 of 1 point A vending machine dispenses coffee into -ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of ounce. You can allow the cup to overfill % of the time. What amount should you set as the mean amount of coffee to be dispensed?
Answer:
19.92
Step-by-step explanation:
To overfill 5% of the time ;
The Zscore (value) to the left of (1 - 0.05) = 0.95 is 1.645
Using this Zscore value with the Zscore formula :
Zscore = (x - μ) / σ
σ = 0.05 ; x = 20 ounce
Substituting into the Zscore formula :
1.645 = (20 - μ) / 0.05
1.645*0.05 = 20 - μ
0.08225 = 20 - μ
μ = 20 - 0.08225
μ = 19.91775
μ = 19.92
Calculate the volume pyramid whose height de Priangular by of a 20cm, and has base of 8cm by 12cm by 150mm
Answer:
see it
Step-by-step explanation:
What is the x-coordinate of the point of intersection for the two lines below?
-6 + 8y = -6
7x -10y = 9
Answer choices
1.) -6
2.) -3
3.) 3
4.) 7
Answer:
c.
Step-by-step explanation:
Given the mean for six numbers is 24. If three numbers which are x, (x + 2) and (x - 2) are added into the data set, the value of mean changed to 30. Calculate the value of x.
Answer:
42
Step-by-step explanation:
We know that the mean of 6 numbers is 24. This means that
[tex] \frac{x}{6} = 24[/tex]
Solve for x.
[tex]x = 144[/tex]
If we add, x, (x+2), and (x-2). We will have 9 terms. The value of mean will change to 30. This also means that
[tex] \frac{270}{9} = 30[/tex]
[tex]144 + x + (x + 2) + (x - 2) = 270[/tex]
[tex]3x + 144 = 270[/tex]
[tex]3x = 126[/tex]
[tex]x = 42[/tex]
PLEASE HELP ASAP!!!!!
Step-by-step explanation:
Area ABC=1/2ab×sin C
=1/2 ×20×10 ×Sin C
Sin C =100
Find the value of the variable y that results in congruent triangles
Answer:
y = 5
Step-by-step explanation:
[tex]7y-10=25\\7y=35\\y=5[/tex]
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
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Answer:
(b) 7x + 2y = 1
Step-by-step explanation:
You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)
7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does
The equation is ...
7x +2y = 1
__
Additional comment
The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.
Answer:
b
Step-by-step explanation:
The manager at a smoothie stand keeps track of the number of protein smoothies and berry smoothies sold each day and the total money received. On Saturday, a total of 43 smoothies were sold, and the money collected was $314. If protein smoothies are sold for $10 and berry smoothies are sold for $6, how many protein smoothies and berry smoothies were sold?
Answer:
Protein smoothie =14
Berry Smoothie= 29
Step-by-step explanation:
Let number of protein smoothie be X
Let number of berry smoothie be Y
1. X+Y=43
Y=43-X
2. 10X+6Y=314
5X+3Y= 157
5x+3(43-x)=157 (substitute)
5x+129-3x=157
2x=157-129
x=14
X+Y=43
Y=43-14
Y=29
Brainliest please~
Solve for the value of x
Answer:
Step-by-step explanation:
This is the Law of Cosines. Use the following formula:
[tex]5.1^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x)[/tex] and simplify to
26.01 = 10.89 + 10.89 - 21.78cos(x) and a bit more to
4.23 = -21.78cos(x) and finally to
-.194214876 = cos(x) and use the 2nd button along with the cos button to find that the missing angle is 101.2 degrees
Help please 6x + 3 > a if the inequality above is true for the constant a which of the following. coupd be a vakue of z
Answer:
[tex]\frac{a+3}{6}[/tex]
Step-by-step explanation:
Treat it like any other math problem with a equals sign:
6x + 3 = a
subtract 3 from both sides: 6x = a + 3
divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]
swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]
the only time the sign flips is if you divide by a negative
(b) Express the prime number 43 as the difference of two squares? 43 =
Find the shortest distance from
A to B in the diagram below.
Shortest distance = Displacement
And please provide the diagram
Must click thanks and mark brainliest
HELP PLEASE! INEEED HELPPP RIGHT NOW The graph of y=x−2−−−−√ is is transformed to become y=x+3−−−−√−2. Which of the following statements best describes the effect this transformation has on the graph of y=x−−√?
Answer:
I think it's D but I don't know how to do this, but I ask my Friend and he gave me this graph I hope it helps.
Option (C) the graph is translated 5 units left and 2 units down is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The function is [tex]y=\sqrt{x-2}[/tex]
This function is transformed to become the function as [tex]y=\sqrt{x+3}-2[/tex]
Now compare this transformation with the function [tex]y=\sqrt{x}[/tex].
These functions are plotted in the graph below.
On comparing this transformation,
The graph is translated 5 units left and 2 units down.
Hence we can conclude that option (C) the graph is translated 5 units left and 2 units down is the correct answer.
Learn more about graph of a function here
https://brainly.com/question/2275360
#SPJ2
a display order of numbers are called
Answer:
I think
A display order of numbers are called sequences.
Instructions: Given the vertex of a quadratic function, find the axis
of symmetry.
Vertex: (5,7)
Taking into account the definition of axis of simmetry and vertexn the axis of symmetry is x = 5.
So, first of all, you must know what a quadratic function is. Every quadratic function can be expressed as follows:
f(x) = a*x² + b*x + c
where a, b and c are real numbers.
Axis of symetryThe graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry.
That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are equal of each other.
In other words, the axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves and always passes through the vertex of the parabola.
VertexThe point of intersection of the axis of symmetry with the parabola is called the vertex.
The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
SummaryBeing the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.
Learn more with this examples:
https://brainly.com/question/2799442?referrer=searchResultshttps://brainly.com/question/20862832?referrer=searchResultshttps://brainly.com/question/15266651?referrer=searchResultsfind the exact value of tan(165°) using a difference of two angles
Answer: [tex]-2+\sqrt{3}[/tex]
=========================================================
Work Shown:
Apply the following trig identity
[tex]\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\[/tex]
Now let's rationalize the denominator
[tex]\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\[/tex]
----------------------
As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.
Or you can note how
[tex]\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949[/tex]
which helps us see that they are the same thing.
Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as [tex]\sqrt{3}-2[/tex] but it's the same as above.
How many times will the digit "3" appear if we write all whole numbers from 1-9999?
Answer:
4000
Step-by-step explanation:
from 1 - 1000 = 300
1's = 100
10's = 100
100's = 100
1000's = 0
300 * 10 = 3000
then add in all the 3000's (ie 3001,3002, etc ) that adds one more thousand
3000 + 1000 = 4000
Answer:
3000?
Step-by-step explanation:
I need help guys thanks so much
Answer:
A. 243
Step-by-step explanation:
[tex] 81^\frac{5}{4} = (3^4)^\frac{5}{4} = 3^{4 \times \frac{5}{4}} = 3^5 = 243 [/tex]
Answer: A
I just simplified it to 3^5, and that is also 243.
Al gave correct answers to 22 of the 25 questions on the driving test. What percent of the questions did he get correct?
A line passes through the point (-3, -3) and has a slope of 1/2 What is the equation of the line?
Answer:
y= 1/2x-3/2
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 1/2x+b
Using the point for x and y we can find b
-3 = 1/2(-3)+b
-3 = -3/2 +b
-6/2 = -3/2+b
Add 3/2 to each side
-6/2 +3/2 = b
-3/2 = b
y= 1/2x-3/2
Answer:
Step-by-step explanation:
y + 3 = 1/2(x + 3)
y + 3 = 1/2x + 3/2
y + 6/2 = 1/2x + 3/2
y = 1/2x - 3/2
Michelle ate a watermelon with 81 seeds. She picked out 1/9 of all the seeds to plant in her backyard. But her mother said there is no room for that many watermelon plants, so her mom only let her plant 1/3 of the seeds she had chosen. How many watermelon seeds was she allowed to plant in her backyard?
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Answer:
3
Step-by-step explanation:
1/3 of 1/9 of 81 is ...
81×1/9×1/3 = 9×1/3 = 3
Michelle was allowed to plant 3 seeds.
Help for number 2a) b) c)
Thank you!! Make u the brainliest
9514 1404 393
Answer:
a) 300 square units
b) 260 square units
c) 264 square units
Step-by-step explanation:
The total surface area of a triangular prism is the sum of the areas of its 5 faces. Two of those are triangles (the bases), and three are rectangles. The area of an individual triangle is A = 1/2bh, but the area of the two of them together will be simply A = bh.
The area of the three rectangular faces is the sum of the products of the height of the prism and the edge length of each face. Then the sum of these products can be computed as the product of the height and the perimeter of the base.
These repetitive calculations are nicely done by a spreadsheet loaded with the appropriate formulas. Areas are all in "square units." (For problem 3, the units are centimeters.)
Example: (2a)
Base area = 5×12 = 60 . . . . combined area of both bases
Lateral area = (5 +12 +13)(8) = 30×8 = 240
Total surface area = 60 + 240 = 300 . . . . square units
Answer:
2. a. 300 units²
b. 260 units²
c. 264 units²
Step-by-step explanation:
2. a. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 12
h = 5
s1 = 13
s2 = 12
s3 = 5
H = 8
Plug in the values into the formula
Surface area of triangular prism = 12*5 + (13 + 12 + 5)*8
= 60 + (30)*8
= 60 + 240
Surface area = 300 units²
b. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 11
h = 3
s1 = 11
s2 = 5
s3 = 6.7
H = 10
Plug in the values into the formula
Surface area of triangular prism = 11*3 + (11 + 5 + 6.7)*10
= 33 + (22.7)*10
= 33 + 227
Surface area = 260 units²
c. Surface area of triangular prism = bh + (s1 + s2 + s3)*H
Where,
b = 6
h = 8
s1 = 10
s2 = 6
s3 = 8
H = 9
Plug in the values into the formula
Surface area of triangular prism = 6*8 + (10 + 6 + 8)*9
= 48 + (24)*9
= 48 + 216
Surface area = 264 units²
