Given:-
[tex]\frac{11}{12}[/tex]To find:-
Decompose the fraction in two ways.
Way one,
[tex]\frac{11}{12}=\frac{5}{12}+\frac{6}{12}[/tex]Way two,
[tex]\frac{11}{12}=\frac{10}{24}+\frac{12}{24}[/tex]in exponential growth functions the base of the exponent must be greater than 1.how would the function change if the base of the exponent were1? how would the function change if the base of the exponents were between 0 and 1
The height, in feet, of a particle from the ground is given by the function s(t) = 1.512 + 20r, where 0 ≤ ≤ 17.
Find the velocity of the particle at t = 4.
Answer
feet per second
The velocity is v= 30.6 ft/ sec.
What is a velocity?Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.
Given that,
We have given the height
s(t) = 0.2[tex]t^{3}[/tex] + 21t, where 0 ≤ [tex]x[/tex] ≤ 17.
To find the velocity we have to differentiate s(t) wrt to t.
s(t) = 0.2[tex]t^{3}[/tex] + 21t
= 0.6[tex]t^{2}[/tex]+21
velocity of the particle at t = 4
s(4) = 0.6*[tex]4^{2}[/tex]+21
= 9.6+21
= 30.6
v= 30.6 ft/ sec
Hence, The velocity is v= 30.6 ft/ sec.
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QuestionFind the equation of a line that contains the points (-6, 3) and (5,-8). Write the equation in slope-intercept form.
ANSWER
y = -x - 3
STEP BY STEP EXPLANATION
Step 1: The given points are:
(-6, 3) and (5, -8)
Step 2: The slope-intercept form is
[tex]y\text{ = mx + c}[/tex]where m is the slope and c is the intercept
Step 3: Find the slope m
[tex]\begin{gathered} \text{slope (m) = }\frac{y_2-y_1}{x_2-x_1} \\ \text{m = }\frac{-8_{}-\text{ 3}}{5\text{ - (-6)}} \\ m\text{ = }\frac{-11}{11}\text{ = -1} \end{gathered}[/tex]Step 4: Solve for intercept c using either of the points
[tex]\begin{gathered} y\text{ = mx + c} \\ c\text{ = y - mx} \\ c\text{ = 3 - (-1)(-6)} \\ c\text{ = 3 - 6} \\ c\text{ = -3} \end{gathered}[/tex]Step 5: Re-writing the slope-intercept form to include the values of m and c
[tex]\begin{gathered} y\text{ = mx + c} \\ y\text{ = -x - 3} \end{gathered}[/tex]Hence, the equation of the line in slope-intercept form is y = -x - 3
Janelle says that lines l and m are skew lines. Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal. Is Janelle correct? Yes, because the lines are not parallel. Yes, because the lines will intersect. No, because the lines are in the same plane. No, because the lines are perpendicular.
Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.
What is a line that is perpendicular?
Perpendicular lines are those that cross at a perfect right angle. Parallel lines are those that are always the same distance apart from one another.
The question is incomplete.
Please see the accompanying image for a comprehensive explanation of the question.
Line l and line m are the two lines that are depicted in the image.
The skew lines are in different planes and do not overlap, as far as we are aware.
Therefore,
Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.
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Find the equation for the line through points (-3,1) and (4,7) use y=Mx+b
A = (-3, 1) and B = (4,7)
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{7-1}{4-(-3)}=\frac{6}{7}[/tex][tex]y=\frac{6}{7}x+b[/tex]Now, for b, using point B
[tex](7)=\frac{6}{7}(4)+b[/tex][tex]b=7-\frac{6}{7}(4)\rightarrow b=\frac{25}{7}[/tex][tex]y=\frac{6}{7}x+\frac{25}{7}[/tex][tex]((1.25 \times {10}^{ - 15} ) \times (4.15 \times {10}^{25} )) \div ((2.75 \times {10}^{ - 9}) \times (3.4299 \times {10}^{8} ))[/tex]solve. final answer in scientific notation
done
[tex]\text{result = 5.4999 x 10}^{10}[/tex][tex]Inscientificnotation=5.4999x10^0[/tex]Calculate the slope of the given line using either the slope formula m = y 2 − y 1 x 2 − x 1 or by counting r i s e r u n . Simplify your answer. You can choose your method.
The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with the points (-8, 3) and (0,1) we get:
[tex]m=\frac{1-3}{0-_{}(-8)}=\frac{-2}{8}=-\frac{1}{4}[/tex]Pure acid is to be added to a 10% acid solution to obtain 90L of 81% solution. What amounts of each should be used?How many liters of 100% pure acid should be used to make the solution? 04
Let's use the variable x to represent the amount of pure acid and y to represent the amount of 10% acid.
Since the total amount wanted is 90 L, we can write the equation:
[tex]x+y=90[/tex]Also, the final solution is 81%, so we can write our second equation:
[tex]100\cdot x+10\cdot y=81\cdot(x+y)[/tex]From the first equation, we can solve for y and we will have y = 90 - x.
Using this value in the second equation, we have:
[tex]100x+10(90-x)=81(x+90-x)[/tex]Solving for x, we have:
[tex]\begin{gathered} 100x+900-10x=81\cdot90 \\ 90x+900=7290 \\ 90x=7290-900 \\ 90x=6390 \\ x=\frac{6390}{90} \\ x=71 \end{gathered}[/tex]Therefore the amount of pure acid to be used is 71 L and the amount of 10% acid is 19 L.
Perform the indicated operation of multiplication or division on the rational expression and simply.
The rational expression is given as,
[tex]\frac{15x}{2y^3}\cdot\frac{12y^2}{5x}[/tex]Performing the division and multiplication in the given rational expression,
[tex]\frac{15x}{2y^3}\cdot\frac{12y^2}{5x}=\frac{3\times6\times y^3}{y^2}[/tex][tex]\frac{3\times6\times y^3}{y^2}=\frac{18}{y}[/tex]The rational expression after using the indicated operation we get,
[tex]\frac{18}{y}\text{.}[/tex]I got stuck and I need help on this I would appreciate the help:0
1) In this problem, we can see that this is an isosceles right triangle.
2) So, one way of solving it is to make use of the Pythagorean theorem. Note that an isosceles triangle has two congruent sides, so we can write out:
[tex]\begin{gathered} a^2=b^2+c^2 \\ b=c \\ 9^2=x^2+x^2 \\ 81=2x^2 \\ 2x^2=81 \\ \frac{2x^2}{2}=\frac{81}{2} \\ x^2=\frac{81}{2} \\ \sqrt[]{x^2}=\sqrt[]{\frac{81}{2}} \\ x=\frac{9}{\sqrt[]{2}} \end{gathered}[/tex]Usually, we rationalize it. But since the question requests the denominator to be a rational one, so this is the answer.
I need help ASAP
Jeannette is participating in a hot-dog-eating contest. She has already eaten 18 hot dogs but needs to eat more than 35 hot dogs to win. Jeannette is eating 2.6 hot dogs per minute. Which of the following inequalities could be used to solve for x, the number of minutes Jeannette needs to continue eating hot dogs to win the contest
A.
2.6x > 35
B.
2.6x - 18 > 35
C.
2.6x > 18
D.
2.6x + 18 > 35
Answer:
I may be wrong but I think it's D.
Step-by-step explanation:
I made an educated guess.
Does the following table show a proportional relationship? 8 h 3 9 6 36 9 81 O Yes No
Proportional relationships are relationships between two variables where their ratios are equivalent.
From the table given;
g:h are respectively;
[tex]\begin{gathered} 3\colon9=1\colon3 \\ 6\colon36=1\colon6 \\ 9\colon81=1\colon2 \end{gathered}[/tex]Since the ratios above are not equivalent, their relationship is not proportional.
Hence, the correct option is B
A deep-dish pizza is cut into twelve equal slices. If you eat four slices, how manydegrees of pizza do you eat?240°120°45°90°
The shape of the pizza is circular. This means that the total angle possible is 360 degrees.
Since the pizza have 12 equal slices
Then each slice will represent
[tex]\frac{360}{12}=30^0[/tex]Therefore, If you decide to eat 4 four slices, then
you will eat
[tex]4\times30^0=120^0[/tex]Answer = 120 degrees
1. (10 pts) The formula for calculating the distance, d, in miles that one can see to the horizon on aclear day is approximated by d = 1.22√x, where x, is the elevation in feet of a person's eyes.a. Approximate how far in miles can a person whose eyes are 5' 6" from the ground see tothe horizon when they are at sea-level. (Hint: Height is often measured with two units,feet and inches, but this formula does not allow for two units.) Figure out if you need toconvert to feet or inches and then do the conversion out as a multiplication problembefore you answer the question Round to the nearest hundredth if necessary.b. How far does the same person see when they are standing on top of an 8,000 footmountain? (Hint: Consider where are their eyes if the mountain is the given height)Round to the nearest hundredth if necessary.
1) We need to use one single unit to express the elevation of a person's eyes.
a)
[tex]5^{\prime}6"=5\:feet+6\:inches=66"=5.5^{\prime}[/tex]Remember that 1 foot is equal to 12 inches. And dividing 66" by 12 yields 5.5'
Now, let's plug into the formula we've been given:
[tex]d=1.22\sqrt{5.5}\Rightarrow d=2.86\:miles[/tex]b) Now, let's bear in mind that this same person has reached the top of a mountain, and now he's at 8,000 feet high:
[tex]d=1.22\sqrt{8000}\Rightarrow d=109.12\:miles[/tex]Note that x, is always given in feet, as well as, d is in miles.
Solve: 5|4x+5|−2≤33 Give your answer as an interval. If no solutions exists - enter No solutions.
The expression given is,
[tex]5|x-3|+3>7[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 5|x-3|+3-3>7-3 \\ 5|x-3|>4 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5|x-3|}{5}>\frac{4}{5} \\ |x-3|>\frac{4}{5} \end{gathered}[/tex]Apply absolute rule:
[tex]\begin{gathered} x-3<-\frac{4}{5}\text{ or x-3>}\frac{4}{5} \\ \end{gathered}[/tex]Add 3 to both sides
[tex]\begin{gathered} x-3+3<-\frac{4}{5}+3\text{ or x-3+3>}\frac{4}{5}+3 \\ x<\frac{11}{5}\text{ or x>}\frac{19}{5} \end{gathered}[/tex]Therefore, the answer has the form:
[tex](-\infty,A)\cup(B,\infty)[/tex]Hence, the solution using interval notation is
[tex](-\infty,\frac{11}{5})\cup(\frac{19}{5},\infty)[/tex]solve for x in the parallelogram below
A number from 1-40 is chosen at random. Find each probability.1. Pleven | at least 12)2. P(perfect square | odd)3. P(less than 25 | prime)4. P(multiple of 3 | greater than 15)
Given:
Numbers from 1 - 40
Let's find the probability of:
Pleven | at least 12)
Where:
Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 20 numbers
Even numbers that are at least 12 = 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 15 numbers.
Numbers that are at least 12 = 29 numbers
Therefore, to find the probability, we have:
[tex]P(even|atleast12)=\frac{P(even\text{ and at least 12\rparen}}{P(at\text{ least 12\rparen}}[/tex]Where:
[tex]\begin{gathered} P(even\text{ and at least 12\rparen = }\frac{15}{40}=0.375 \\ \\ P(at\text{ least 12\rparen= }\frac{29}{40}=0.725 \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} P(even|atleast12)=\frac{0.375}{0.725} \\ \\ P(even|atleast12)=0.52 \end{gathered}[/tex]Therefore, the probability that a number chosen at random is even given that it is at least 12 is 0.52
ANSWER:
0.52
Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The correct option is negative 23 over 14 times j plus negative 1 over 15
Given,
The expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
The expression; -1/7j + 2/5 - 3/2j + 7/15
negative one seventh j = - 1/7j
two fifths = 2/5
three halves j = 3/2 j
seven fifteenths = 7/15
Now,
Substitute the values;
- 1/7j + 2/5 - 3/2j - 7/15
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Therefore,
The correct option is negative 23 over 14 times j plus negative 1 over 15
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which three statements are true about the line segment CBit's the radius of the circleit is the circumference of the circleit is a cordit is 6cm longit is diameter of the circle it is 7cm longit is 1.75cm long
Answer:
It is the diameter of the circle
it is 7 cm
it is a chord
Explanation:
First, we notice that the line segment CB passes through the centre of the circle and its endpoints touch the circumference - this tells us that CB is the diameter.
Furthermore, any line segment whose endpoints lie on the circumference of the circle is a chord (meaning that the diameter is the longest chord), and so we deduce that CB is also a chord.
Since CB is the diamter, its length is 2 times the radius. The raduis of the circle we know is DA = 3.5 cm; therefore, the dimater is CB = 2 DA = 2 * 3.5 = 7 cm.
Hence, the correct choices are:
It is the diameter of the circle
it is 7 cm
it is a chord
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
The length of BC is 29 units (solved using trigonometry and its applications).
What is trigonometry?
Trigonometry (from Ancient Greek v (trgnon) 'triangle' and (métron)'measure') is a field of mathematics that explores the correlations between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. The Greeks concentrated on chord computation, whereas Indian mathematicians established the first-known tables of values for trigonometric ratios (also known as trigonometric functions) such as sine. Trigonometry has been used throughout history in geodesy, surveying, celestial mechanics, and navigation. Trigonometry is well-known for its many identities. These trigonometric identities are frequently used to rewrite trigonometrical expressions with the goal of simplifying an expression, finding a more usable form of an expression, or solving an equation.
Let the point where AB is cut through line from C be D
This can be solved using trigonometry and its applications.
In triangle ACD,
tan 45° = CD/AD
or, CD = tan 45° x AD
= 1 x 20
= 20 units
In triangle CDB,
tan Ф = CD/BD
or, Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
or, BC = CD/sin 43.6°
= 20/0.689
= 29 units
The length of BC is 29 units.
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Answer:
29
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/SQRT2
What is f(2) - f(0) answer choices:A) 1B) 2C) 3D) 4
The points of the graph of a function f(x) have the form (x,f(x)). This means that the values of f(0) and f(2) are the y-values of the points in the graph that have 0 and 2 as their x-values. If you look at the graph you'll notice that the points (0,1) and (2,4) are part of the graph which implies that:
[tex]\begin{gathered} (0,f(0))=(0,1)\rightarrow f(0)=1 \\ (2,f(2))=(2,4)\rightarrow f(2)=4 \end{gathered}[/tex]Then we get:
[tex]f(2)-f(0)=4-1=3[/tex]AnswerThen the answer is option C.
Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }
The Solution:
The given expression is
[tex]\frac{8}{1-\sqrt[]{17}}[/tex]Rationalizing the expression with the conjugate of the denominator, we have
[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]This becomes
[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]Thus, the correct answer is
[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]There were 18 students in a class taking a test. 4 students did pass the test. What percent did not pass the test.
Answer
Percent of students who did not pass the test = 77.8%
Explanation
The percent of an event is given as
[tex]\begin{gathered} \text{Percent of an event} \\ =\frac{\text{Number of elements in the event}}{Total\text{ number of elements}}\times100 \end{gathered}[/tex]For this question,
Percent of the event = Percent who did not pass the test = ?
Number of elements in the event
= Number of students who did not pass the test
= (Total number of students) - (Number of students who passed the test)
= 18 - 4
= 14
Total number of elements = Total number of students in the class = 18
Percent of students who did not pass the test
= (14/18) × 100%
= 0.778 × 100%
= 77.8%
Hope this Helps!!!
I just need to know if You just have to tell me if the circles are open or closed.
Solution
- The solution is given below:
[tex]\begin{gathered} y-2<-5 \\ y-2>5 \\ \\ \text{ Add 2 to both sides} \\ \\ y<-5+2 \\ y<-3 \\ \\ y-2>5 \\ y>5+2 \\ y>7 \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} y<-3 \\ or \\ y>7 \end{gathered}[/tex]- Thus, the plot is:
This is lines, functions and systems. Graph the line with slope 2/3 passing through the point (2, 1).
Note that the slope is expressed as :
[tex]\text{slope}=\frac{\text{rise}}{\text{run}}[/tex]From the given, the slope is 2/3
[tex]\text{slope}=\frac{\text{rise}}{\text{run}}=\frac{2}{3}[/tex]So it means that from the point (2,1)
You need to rise 2 units upward and run 3 units to the right
It will be look like this :
Next step is to connect these two points by drawing a line.
That's it, the line is in blue line.
Use the substitution u = (2x - 2) to evaluate the integral x³e(^2x^4-2) dx
The substitution u = (2x - 2) to the integral x³e(^2x^4-2) dx is (2x – 2)/4 +c
What is meant by integral?In mathematics, an integral assigns numerical values to functions in order to describe concepts like displacement, area, volume, and other outcomes of the combination of infinitesimally small data. Integral discovery is a process that is referred to as integration. One of the fundamental, crucial operations of calculus, along with differentiation, is integration[a]. It can be used to solve issues in mathematics and physics involving, among other things, the volume of a solid, the length of a curve, and the area of an arbitrary shape. The integrals listed here are those that fall under the category of definite integrals, which can be thought of as the signed area of the region in the plane that is enclosed by the graph of a particular function between two points on the real line.Therefore,
Use the substitution
U = (2x -2)
to evaluate integral x³e(^2x^4-2) dx
let u = 2x -2
du = x dx or dx =du/2
u = 2x-2
du = d(2x – 2)
du = 2dx
dx = du/2
∫ (2x -2)dx = ∫u du/2
=1/2 ∫u du
= ½ u square /2 +c
= u square /4 +c
= (2x – 2)/4 +c
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PLEASE HELP I REALLY NEED AN ANSWER ALSO ONLY ANSWER IF YOUR GOING TO GIVE A STEP BY STEP SOLUTION
The answer of the given expression is 80.
Exponents
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
For example:-
[tex]5^4[/tex] can be written as 5*5*5*5.
Here 4 is the exponent or power and 5 is the base.
There are some laws of exponents which we use while calculating the answer to such expressions.
Given expression:-
[tex]\frac{12^7*30^5}{25^2*8^5*27^4}[/tex]
We have to simplify the given solution using the laws of exponents.
First we will divide them in their prime factors.
We know that,
[tex](x^a)^b=x^{ab}[/tex]
We can write,
[tex]12^7 = (2^2)^7*3^7=2^{14}*3^7[/tex]
[tex]30^5=2^5*3^5*5^5[/tex]
[tex]25^2=(5^2)^2=5^4[/tex]
[tex]8^5=(2^3)^5=2^{15}[/tex]
[tex]27^4=(3^3)^4=3^{12}[/tex]
Hence, we can write the given expression as follows,
[tex]\frac{2^{14}*3^7*2^5*3^5*5^5}{5^4*2^{15}*3^{12}}[/tex]
Also, we know that,
[tex]x^a*x^b=x^{a+b}\\x^a/x^b=x^{a-b}[/tex]
We can write,
[tex]{2^{(14+5-15)}*3^{(7+5-12)}*5^{(5-4)}}[/tex]
[tex]2^4*3^0*5^1[/tex] = 16*1*5 = 80
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The convex polygon below has 8 sides. Find the value of x.140°11801270153013401561170
Explanation
The formula for calculating the sum of interior angles in a polygon is ( n − 2 ) × 180 ∘ where is the number of sides.
[tex](n-2)\cdot180=\text{ Sum of internal angles}[/tex]Step 1
find the sum of the internal angles in the given polygon
Let
number of sides = 8
Now, replace
[tex]\begin{gathered} (n-2)\cdot180=\text{ Sum of internal angles} \\ (8-2)\cdot180=\text{ Sum of internal angles} \\ 6\cdot180=\text{Sum of internal angles} \\ 1080=\text{Sum of internal angles}\rightarrow equation(1) \end{gathered}[/tex]Step 2
now, we have the other angles, so
sum of internal angles is:
[tex]\text{angle}1+\text{angle}2+\text{angle}3+\text{angle}4+\text{angle}5+\text{angle}6+\text{angle}7+\text{angle}8=\text{ sum of the internal angles}[/tex]replace
[tex]\begin{gathered} 127+140+118+153+156+117+x+132=\text{ Sum of internal angles} \\ x+943=\text{Sum of internal angles}\rightarrow equation\text{ (2)} \end{gathered}[/tex]hence
[tex]x+945=1080[/tex]subtract 945 in both sides to solve for x
[tex]\begin{gathered} x+945=1080 \\ x+945-945=1080-945 \\ x=135 \end{gathered}[/tex]i hope this helps you
Simplify the expression -3n-8-7n + 17
We simplify by combining like terms
therefore
[tex]\begin{gathered} -3n-8-7n+17 \\ =-3n-7n-8+17 \\ =-10n+9 \end{gathered}[/tex]On July 31, Oscar Jacobs checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What is the total amount of his check, expressed in words?
On July 31, Oscar Jacobs checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What is the total amount of his check, expressed in words?
step 1
Multiply $76.90 by 4
76.90*4=$307.6
so
expressed in words is
three hundred seven and six tenths