To simplify:
[tex]3x^3-12x\div3x^3+6x^2-24x[/tex]On division we get,
[tex]\begin{gathered} \frac{3x^3-12x}{3x^3+6x^2-24x}=\frac{3x(x^2-4)}{3x(x^2+2x-8)} \\ =\frac{(x^2-4)}{(x^2+2x-8)} \\ =\frac{(x+2)(x-2)}{(x-2)(x+4)_{}} \\ =\frac{x+2}{x+4} \end{gathered}[/tex]Hence, the simplest form is,
[tex]\frac{x+2}{x+4}[/tex]Which graph shows the transformation of the function f(x)=e^x where the function is translated four units to the right, vertically compressed by a factor of 1/3, and translated down five units then translated five units down?
The graph that shows the transformation of the function f(x) = e^x is option D.
Step - by - Step Explanation
What to find? The transformation of the function f(x)=e^x.
Given:
• f(x) = 4^x
,• Vertially compresses by a factor 1/3
,• Translated four units to the right.
,• Translated down five units.
Note that:
• If f(x) shifts up m- units, then we have f(x) + m.
,• If f(x) shifts down n-units then we have f(x) - n.
,• If f(x) shifts right p - units, then we have f(x - p).
,• If f(x) shifts left q - units, then we have f(x+q).
From the given question, f(x) is translated four units to the right., hence e^x becomes eˣ⁻⁴
f(x) is further compressed by a factor of 1/3, the function becomes 1/3 eˣ⁻⁴.
Finally, the function is translated down five units, hence, the function becomes:
[tex]f(x)=\frac{1}{3}e^{x-4}-5[/tex]The graph of the function after the translation is
Lynn has 54 pennies, 80 nickels, 22 dimes, 41 quaters, and 3 dollars. How much money does he have in total
He has 1999 cents that is equal to 20 dollars approximately as per money conversion theory that defines "The ratio between two currencies, which is known as a conversion rate and is most frequently used in foreign exchange markets, indicates how much of one currency must be exchanged for the value of another."
What is money?Any tangible object or verifiable record that is commonly accepted as payment for goods and services as well as the repayment of debts, such as taxes, in a specific nation or socioeconomic setting is referred to as money.
Here,
Lynn has 54 pennies, 80 nickels, 22 dimes, 41 quarters, and 3 dollars.
1 Penny=1 cent
1 Nickel=5 cents
1 Dime=10 cents
1 Quarter=25 cents
1 dollar=100 cents
by this,
54 pennies=54*1=54 cents
80 nickels=80*5=400 cents
22 dimes=22*10=220 cents
41 quarters=41*25=1025 cents
3 dollars=3*100=300 cents
The total money he has=54+400+220+1025+300
=1999 cents
100 cents make to 1 dollar.
so 1999 cents will make to 19.99 dollars.
According to the money conversion theory, which states that "the ratio between two currencies, which is known as a conversion rate and is most frequently used in foreign exchange markets, indicates how much of one currency must be exchanged for the value of another," he has 1999 cents, which is approximately equal to $20.
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Solve and graph on a number line x - 2 > -5 and x - 2 < 4
ANSWER
Interval notation: (-3, 6)
Inequality form: -3 < x < 6
Number Line Graph:
EXPLANATION
[tex]\begin{gathered} x\text{ - 2 > - 5 OR x - 2 < 4} \\ x\text{ > - 5 + 2 OR x < 4 + 2} \\ x\text{ > -3 OR x < 6} \\ \end{gathered}[/tex]Hence, -3 < x < 6
I need help to simplify 3x (x² - x - 2) + 2x (3 - x) - 7x. I've tried to solve the problem three times and have gotten 2x² - 2x - 6, then, x² - 1x - 6, then, 3x³ - 5x² - 13x, I can't figure out what I'm doing wrong.
Given the initial expression,
[tex]3x(x^2-x-2)+2x(3-x)-7x[/tex]Simplify it as shown below
[tex]\begin{gathered} =3x*x^2-3x*x-3x*2+2x*3-2x*x-7x \\ =3x^3-3x^2-6x+6x-2x^2-7x \end{gathered}[/tex][tex]\begin{gathered} =3x^3-3x^2-2x^2-7x \\ =3x^3-5x^2-7x \end{gathered}[/tex]Thus, the answer is 3x^3-5x^2-7xA trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
In this problem we have
p=kr
step 1
Find the value of k
k=p/r
we have the ordered pair (4,6)
substitute
k=6/4
k=1.5
therefore
the proportional equation is
p=1.5rI need help finding point slope form
We were given two points to find the equation of the line, these are (4,3) and (5,5).
We need to find the point-slope form, which can be writen as follow:
[tex]y-y_1=m\cdot(x-x_1)_{}[/tex]Where (y1,x1) is one point on the line and "m" is the slope of the line. We first need to find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (y1,x1) and (x2,y2) are the two known points. We can find the slope by applying the two points given to us:
[tex]m=\frac{5-3}{5-4}=2[/tex]We can know write the expression of the line:
[tex]y-5=2\cdot(x-5)[/tex]A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches. How many unit cubes with edge lengths of 0.5 inch can fit inside the prism?A)105 unit cubesB)210 unit cubes460 unit cubesD)840 unit cubes5)
Given
A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches.
To find how many unit cubes of edge length 0.5 inches can fit inside the prism.
Explanation:
It is given that, the volume of the rectangular prism is,
[tex]\begin{gathered} Volume=l\times b\times h \\ =10.5\times5\times2 \\ =105in^3 \end{gathered}[/tex]Since the edge length of 0.5inch.
Then,
[tex]\begin{gathered} Volume\text{ of rectangular prism}=n\times Volume\text{ of a cube} \\ 105=n\times(0.5)^3 \\ n=\frac{105}{0.125} \\ n=840 \end{gathered}[/tex]Hence, the number of cubes is 840 unit cubes.
Write an expression for the measure of the given angle
Solution:
Remember that the angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference. According to this, we can deduce the following expression for the measure of the given angle:
[tex]m\angle UXY=\frac{arc\text{ }UZW}{2}[/tex]What is the probability of a person who plays equation IQ being in grade 6? Enter the answer as a percentage, round to the nearest tenth place.
ANSWER
28.3%
EXPLANATION
The total number of people that play Equation IQ is 300 - we can know this by adding either the more right column or the lowest row of the table.
From those people, 85 are in grade 6. The probability of a person that plays Equation IQ being in grade 6 is:
[tex]P(\text{grade 6})=\frac{\#\text{ people in grade 6}}{\#\text{ total number of players}}=\frac{85}{300}\approx0.2833\ldots[/tex]To write it as a percentage we just have to multiply it by 100:
[tex]0.283\times100=28.3\text{ \%}[/tex]I know the first part but having trouble on the second part
Take into account that the standard deviation of a probability distribution table is given by:
[tex]\sigma=\sqrt[\placeholder{⬚}]{\Sigma\left(x-\mu\right)^2P\left(x\right)}[/tex]where x is each element of the first column of the table, μ is the mean and P(x) is the corresponding values of P(x) for each value of x in the second column.
By replacing the values of the table you obtain:
[tex]\begin{gathered} \sigma=\sqrt[\placeholder{⬚}]{\left(0-3.79\right)^2\lparen0.04)+\left(1-3.79\right)^2\left(0.23\right)+\left(3-3.79\right)^2\left(0.35\right)+\left(6-3.79\right)^2\left(0.15\right)+\left(7-3.79\right)^2\left(0.23\right)} \\ \sigma=\sqrt[\placeholder{⬚}]{5.6859} \\ \sigma\approx2.38 \end{gathered}[/tex]Hence, the standard deviation of the given data is approximately 2.38
Which graph fits this line? O y= 2x + 1 O A O D. B. x / X E. # Oc. *
Answer: Option A
Given the above equation
y = 2x + 1
Firstly, we need to find the y and x - intercepts
To find y - intercept, make x = 0
y = 2(0) + 1
y = 0 + 1
y = 1
To find x - intercept, put y = 0
0 = 2x + 1
Collect the like terms
0 - 1 = 2x
-1 = 2x
Divide both sides by 2
2x = -1
2x/2 = -1/2
x = -1/2
Therefore, x = -1/2 and y = 1
(-1/2, 1)
Step 2: Graph the point
Debra has ridden 6 miles of a bike course. The course is 15miles long. What percentage of the course has Debra ridden so far
From the question
Miles covered for bike course = 6 miles
Total miles of course = 15 miles
In percentage, this becomes
Let z = percentage of miles covered
Hence
[tex]z=\frac{\text{miles covered}}{Total\text{ miles}}\times100\text{\%}[/tex]Substitute in the values to get
[tex]z=\frac{6}{15}\times100\text{\%}[/tex]Simplify:
[tex]\begin{gathered} z=\frac{2}{5}\times100\text{\%} \\ z=2\times20\text{\%} \\ z=40\text{\%} \end{gathered}[/tex]Therefore, the percentage of the course Debra has ridden so far is 40%
what digit is in the
SOLUTION
Given the question in the image, the following are steps to solve the question.
Step 1: Write out the given function to be plotted on the graph.
[tex]x=6[/tex]Step 2: Plot the function on the graph. Please note that x=6 means that the line on the graph will pass through the point where x-axis is equal to 6. This can be better explained on the graph below.
The red line passing through x-axis at point 6 indicates x=6.
Given parallelogram ROCK and m R =159, find m 20.
Answer:
m∠C = 159
Explanation:
In parallelograms, opposite angles have the measure. Since angle C is opposite to angle R, we can write the following expression:
m∠C = m∠R
m∠R is equal to 159, so m∠C is equal to:
m∠C = 159
So, the answer is m∠C = 159
find the slope of the line. 5x-2y=7
Thus 5/2 is the slo
How many radians are equal to 180 degrees 2piPi 1 2
Given: An angle of 180 degrees.
Required: To find the measure of the given angle in radians.
Explanation: The degree and radians measure of an angle is related by the following relation
[tex][/tex]Please help me I don’t know how to solve this :(
You have already found the slope, which is 2
m =( y2-y1)/(x2-x1)
= (9200-9000)/(225-125)
= 200/100
= 2
The question tells us that it is a linear function
y = mx +b is the slope intercept form of a linear function
m is the slope and b is the initial value
c(n) = mn+b
c(n) = 2n+b
Using one of the points in the table we can find b
(125,9000)
9000 = 2(125) +b
9000 = 250+b
9000-250 = b
8750 = b
The initial value is 8750
This is also the estimate of c(0) because the initial value is when n=0
We can write the equation
c(n) = fixed cost + unit cost * number of units
The fixed cost is the initial value
the unit cost is the slope or m
c(n) = 8750 + 2n
write in slope intercept form and identity the slope and y intercept. a. x/3 + y/2 = 1b. 4x -3y + 2 =0c. x - y = 5(x - y)
Consider that the slope-intercept form of the straight line with slope (m) and y-intercept (c) is given by,
[tex]y=mx+c[/tex]a.
Modify the given equation as,
[tex]\begin{gathered} \frac{x}{3}+\frac{y}{2}=1 \\ \frac{y}{2}=-\frac{x}{3}+1 \\ y=-\frac{2}{3}x+2 \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=-\frac{2}{3}x+2[/tex]b.
Modify the given equation as,
[tex]\begin{gathered} 4x-3y+2=0 \\ 3y=4x+2 \\ y=\frac{4}{3}x+\frac{2}{3} \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=\frac{4}{3}x+\frac{2}{3}[/tex]c.
Modify the given equation as,
[tex]\begin{gathered} x-y=5(x-y) \\ x-y=5x-5y \\ 5y-y=5x-x \\ 4y=4x \\ y=x \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=x[/tex]Two buses leave town 1404 kilometers apart at the same time and travel toward each other. one bus travels 12 km/h faster than the other. if they meet in 6 hours, what is the rate of each bus?rate of faster bus: km/hrate of slower bus: km/h
Let rate of faster bus be x km/h and rate of slower bus be y km /hr.
The relation between rate of slower and faster bus is,
[tex]x=y+12[/tex]Two bus are travelling in opposite direction so relative speed is,
[tex]x+y[/tex]Two buses meet in 6 hours so,
[tex]\begin{gathered} (x+y)\cdot6=1404 \\ x+y=234 \end{gathered}[/tex]Substitute y + 12 for x in the equation to obtain the value of y.
[tex]\begin{gathered} y+12+y=234 \\ 2y=234-12 \\ y=\frac{222}{2} \\ =111 \end{gathered}[/tex]Determine the value of x.
[tex]\begin{gathered} x=111+12 \\ =123 \end{gathered}[/tex]So answer is,
Rate of faster bus is 123 km/hr
Rate of slower bus is 111 km/hr.
The triangle ABC shown on the coordinate plane below,is dilated from the origin by scale factor= 1/2. what is the location of triangle A'B'C'?
Explanation:
With a dialation about the origin of a scale factor of 1/2 every point of the dialated figure is now one half of the points from the original figure:
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]We have this points:
• A: (3, 4)
,• B: (-7, 2)
,• C: (2, 2)
The new coordinates of these points will be:
Answer:
• A': (1.5, 2)
,• B': (-3.5, 1)
,• C': (1, 1)
Brady wants to purchase a skateboard that costs $245. So far, he has saved $98 and plans to savean additional $25 per week.Part A:If w represents the number of weeks, write the inequality that represents how many weeks it willtake Brady to save at least $245.
number of weeks: w
cost of the skateboard: 245
Amount saved: 98
Additional per week: 25
98+25w ≥ 245
Since he have to save at least 245, the expression must be equal or greater to 245
17% of 800 is what number?
We want to obtain ;
[tex]17\text{ \% of 800}[/tex]That number would be
[tex]\begin{gathered} \frac{17}{100}\times800=\text{ }\frac{17\times800}{100} \\ =136 \end{gathered}[/tex]Therefore, 17% of 800 is 136.
someone help me
please and thank you
Answer: Answer C
Step-by-step explanation:
Because it is a reflection of the Y-axis, the X-coordinates would remain the same but the Y-coordinates would change.
f(x) = 2x^3+4x^2+2x+1g(x) = x^3 –x^2+7x+9Find (f+g)(x):
Let's rewrite the functions:
[tex]\begin{gathered} f(x)=2x^3+4x^2+2x+1 \\ g(x)=x^3-x^2+7x+9 \end{gathered}[/tex]To get (f+g)(x), we just add them together:
[tex](f+g)(x)=f(x)+g(x)=2x^3+4x^2+2x+1+x^3-x^2+7x+9[/tex]We can simplify be pairing the terms with the same order:
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x)=2x^3+x^3+4x^2-x^2+2x+7x+1+9= \\ =(2+1)x^3+(4-1)x^2+(2+7)x+10=3x^3+3x^2+9x+10 \end{gathered}[/tex]So:
[tex](f+g)(x)=3x^3+3x^2+9x+10[/tex]I need help with my math
we have
8.13x10^5
convert to standard form
10^5=100,000
substitute
8.13x10^5=8.13*(100,000)=813,000
therefore
answer is
813,0002 and the probability that event A occurs given 2 In an experiment, the probability that event B occurs is 3 6 that event B occurs is 7 What is the probability that events A and B both occur? Simplify any fractions.
In order to find the probability that events A and B both occurs, we can use the following formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]So we have that:
[tex]\begin{gathered} \frac{6}{7}=\frac{P(A\cap B)}{\frac{2}{3}} \\ 7\cdot P(A\cap B)=6\cdot\frac{2}{3} \\ 7\cdot P(A\cap B)=4 \\ P(A\cap B)=\frac{4}{7} \end{gathered}[/tex]What is the average value of -2/5, 7/10, 1/2, -1/5
The average of numbers is equal to sum of values to number of values.
Determine the average value of observations.
[tex]\begin{gathered} a=\frac{-\frac{2}{5}+\frac{7}{10}+\frac{1}{2}-\frac{1}{5}}{4} \\ =\frac{\frac{-4+7+5-2}{10}}{4} \\ =\frac{\frac{6}{10}}{4} \\ =\frac{3}{20} \end{gathered}[/tex]So average value of the numbers is 3/20.
6.Subtraction Solve: 4t+5=k t=6
We have the following:
[tex]\begin{gathered} 4t+5=k \\ t=6 \end{gathered}[/tex]replacing and solving:
[tex]\begin{gathered} 4\cdot6+5=k \\ k=24+5 \\ k=29 \end{gathered}[/tex]The value of k is 29
Find the measure of Zx in the triangle.
21°
The measure of Zx is
(Simplify your answer. Type an integer or a decimal.)
...
The third angle of the triangle is 87°.
The Pythagorean Theorem is used for finding the length of the hypotenuse of a right triangle.
Pythagoras was a Greek mathematician who discovered that on a triangle abc, with side c being the hypotenuse of a right triangle (the opposite side to the right angle), that: a² + b² = c².Formula for the Base of an Isosceles Triangle
If you know the side length and height of an isosceles triangle, you can find the base of the triangle using this formula: b = 2√a² - h²Equate the sum of all the angle which is equal to 180°.
Sum of triangle = 180°
∠A + ∠B + ∠C =180°
21° + 72° + x = 180°
93° + x = 180°
x = 180° - 93°
x = 87°
Hence, the third angle of the triangle is 87°.
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Solve for X using cosine law along with with written explanation.
Given:
The two sides and angle of triangle are
[tex]\begin{gathered} a=19m \\ b=25m \\ \angle C=65\degree \end{gathered}[/tex]Required:
To find the value of X.
Explanation:
By cosine rule
[tex]\begin{gathered} X=\sqrt{a^2+b^2-2ab\cos C} \\ \\ =\sqrt{19^2+25^2-2\times19\times25\cos65} \\ \\ =24.17m \end{gathered}[/tex]Final Answer:
The value of X is
[tex]X=24.17m[/tex]