Given the function:
[tex]f(x)=\frac{4}{x}[/tex]We will find the following:
a) f(x+h)
So, we will substitute with x = x+h
[tex]f(x+h)=\frac{4}{x+h}[/tex]b) f(x+h) - f(x)
[tex]\begin{gathered} f(x+h)-f(x)=\frac{4}{x+h}-\frac{4}{x} \\ \\ f(x+h)-f(x)=\frac{4x-4(x+h)}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{4x-4x-4h}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{-4h}{x(x+h)} \end{gathered}[/tex]c) [f(x+h) - f(x)]/h
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h}{x(x+h)\cdot h} \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{-4}{x(x+h)} \end{gathered}[/tex]6 Find the height of the triangle pictured above, if the area is 12. Round your answer to the nearest tenth
We have that the area of a triangle is given by:
[tex]A=\frac{b\cdot h}{2}[/tex]We replace the values we know:
[tex]12=\frac{6\cdot h}{2}[/tex]Now, we solve for h:
[tex]\Rightarrow h=4[/tex]From this, we have that the height of the triangle is 4 units.
A bicycle has a listed price of $521.99 before tax. If the sales tax rate is 7.5%, find the total cost of the bicycle with sales tax included.Round your answer to the nearest cent, as necessary.
Total cost of the bicycle with sales tax included = $561.14
STEP - BY - STEP EXPLANATION
What to find?
The total cost of the bicycle with sales tax included.
Given:
Price of bicycle before tax = $521.99
Tax rate = 7.5%
To solve the given problrm, we will follow the steps below:
Step 1
Calculate the amount of the tax rate.
[tex]\text{amount of tax rate =}\frac{7.5}{100}\times521.99[/tex][tex]=\frac{3914.925}{100}[/tex][tex]=39.14925[/tex]Step 2
Add the amount of tax obtained in step 1 to the price of bicycle before tax.
[tex]\text{Total tax =price of bicycle before tax+tax}[/tex][tex]=521.99+39.14925[/tex][tex]\approx561.14[/tex]Therefore, the total cost of the bicycle with sales tax included is $561.14
(G.12, 1 point) Given: Circle P with center at (-6, 4) and a radius of v19. Identify the equation that could represent circle P. O A. (X+6)2 + (y + 4)2 = 19 o B. (X - 6)2 + (-4)2 = 19 C. (x + 6)2 + (y - 4)2 = 19 OD. (X-6)2 + (y + 4)2 = 19
In this case, we'll have to carry out several steps to find the solution.
Step 01:
center (-6, 4)
radius = √19
equation of the circle = ?
Step 02:
equation of a circle
(x - a)² + (y - b)² = r²
(x - (-6)) + (y - (4)) = (√19)²
(x + 6)² + (y - 4)² = 19
The answer is:
(x + 6)² + (y - 4)² = 19
The residents of a city voted on whenever to raise property taxes. The ratio of yes votes to no votes was 8 to 5. If there were 8463 total votes, how many no votes were there?
1) Gathering the data
The ratio of yes votes to no votes was 8 to 5.
8/5
8463 votes
2) Let's use the property of proportions, to write an expression to solve that problem:
[tex]\begin{gathered} \frac{8}{5}=\frac{8463-x}{x} \\ 8x\text{ = 5(8463-x)} \\ 8x=42315-5x \\ 13x=42315 \\ x=3255 \end{gathered}[/tex]So there were 3255 no votes.
What is the total amount of the monthly payments for a $5,300, 4-year
loan with an APR of 3% ? (Follow Example 2)
Do not use the $ sign in your answer and round to the nearest Cent
(100th):t
The principal amount given out as loan is 239447.08
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
Monthly payment = $5300Time = 4 yearsrate = 3%Principal = ?n = number of times compoundedThe formula is given as
[tex]m = P[\frac{r(1+r)^n}{(1+r)^n^-^1}[/tex]
Substituting the values and solving for the principal amount, this will cost 239,447.08.
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What change do you have to make to the graph?
EXPLANATION:
Given;
We are given the function below;
[tex]f(x)=3^x[/tex]Required;
We are required to describe what change would be made to graph the function;
[tex]g(x)=3^{x-7}[/tex]For a function given such as the one here, when the graph is shifted to the right, then the original function is affected as follows;
[tex]\begin{gathered} f(x)=x \\ \\ Shift\text{ }to\text{ }the\text{ }right: \\ f(x)+(x)=x \\ \\ Subtract\text{ }(x)\text{ }from\text{ }both\text{ }sides: \\ f(x)+(x)-(x)=x-(x) \\ \\ f(x)=x-(x) \end{gathered}[/tex]For a shift to the left, we would have a plus sign, that is, add x number of units the graph is being shifted.
Therefore, for a function that has changed such as the one given,
[tex]g(x)=3^{x-7}[/tex]What we have is shift the original graph 7 units to the right.
ANSWER:
[tex]Shift\text{ }the\text{ }graph\text{ }7\text{ }units\text{ }right[/tex]The first option is the correct answer.
3. Make Sense and Persevere In the equation 0.755s - 5/8= 44, how do you combine the like terms
The equation given is:
[tex]0.755s-\frac{5}{8}=44[/tex]"Like terms" are terms whose variables are the same. The coefficient (number in front of the variable) can be different. Also, constant (single numbers) are like terms with other constants.
In the equation given,
There is one term with the variable "s" and two "constant terms".
Thus, we combine the two constant terms and leave the "s" term as is because there isn't any other like term to combine it with.
So,
We have:
[tex]\begin{gathered} 0.755s-\frac{5}{8}=44 \\ 0.755s=44+\frac{5}{8} \\ 0.755s=44\frac{5}{8} \end{gathered}[/tex]Note that we added (5/8th) to the right hand side with "44". When we change sides, we change signs.
Use the following words to complete the sentences : 1) Run, 2) Positive , 3) Constant , 4) Linear , 5) Steepness ,6) Vertical 7) Horizontal ,8) Rise 9) Negative , 1) Slope is the ----- of a line. It is also know as the ------ rate of change. 2) If a line is slanting upwards we say it has a ------ slope. If a line is slanting downwards we say it has a ------ slope .3) A slope of zero means the line is ----- .4) An undefined slope means the line is ----- . 5) All straight line graphs are known as ------ relationships .6) To find the slope of a line we use the formula ----- over ------ .
1) Slope is the ----- of a line. It is also known as the ------ rate of change.
Slope means steepness and it is a constant rate of change meaning that it does not change.
2) If a line is slanting upwards we say it has a ------ slope.
Slanting upward means a positive slope, for example when you are moving uphill.
If a line is slanting downwards we say it has a ------ slope
Slanting downward means a negative slope, for example when you are moving downhill.
3) A slope of zero means the line is -----
a Slope of 0 means that the line is horizontal. for example when you are moving on a straight road.
4) An undefined slope means the line is -----
An undefined slope means that the line is vertical. for example when you are climbing a vertical wall.
5) All straight line graphs are known as ------ relationships.
They are known as linear relationships.
6) To find the slope of a line we use the formula ----- over ------
We use the slope formula that is rise over run.
Model Kara’s plan with a table,graph, and a explicit and recursive equation
We will write functions for the money that Kara and Kevin will receive each day.
1) The first day, Kara receives $3, and then she receives $1 more each day.
The money that she receives the n day is given by the following recursive function
[tex]f(n)=f(n-1)+1[/tex]where n is the nth day, and f(1) = 3. We can also write this function in the following form:
[tex]f(n)=3+(n-1)\cdot1[/tex]2) In the case of Kevin, he receives $0.25 the first day, and the next day he will receive the double.
So we can write the following recursive function:
[tex]g(n)=2\cdot g(n-1)[/tex]where n is the nth day, and g(0) = 0.25/2. We can also write this function in the following form:
[tex]undefined[/tex]Determine the angle measures of quadrilateral EFGH that would result in it's similarity to quadrilateral ABCD
Solution:
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1.
Similarity statement:
In geometry, it states that two sides are similar if they have the same side ratio and the same angles
From the image in the question,
The quadrilateral ABCD has the following angles
[tex]\begin{gathered} m\angle A=90^0 \\ m\angle B=132^0 \\ m\angle C=73^0 \\ m\angle D=65^0 \end{gathered}[/tex]From the similarity statement above,we can deduce that
[tex]undefined[/tex]I have a picture because it has a diagram
What represents the values of the range in the following graph?A.the range is represented by the average growth of the horse. B. The range is represented by cm/year.C. The range is represented by the height of the horse.D. The range is represented by the age.
The range is the set of possible output values, which are shown on the y-axis.
As shown in the graph, the range is represented by the average growth of the horse.
Therefore, the answer is letter A.
Answer:
A.the range is represented by the average growth of the horse.
Step-by-step explanation:
what is the product of 3/4 and -6/7. see attached
Solution
For this case we can do the following:
[tex]\frac{3}{4}\cdot(-\frac{6}{7})=-\frac{18}{28}=-\frac{9}{14}[/tex]Then the answer is:
-9/14
if a plane traveled 2100 miles in 210 minutes how many mph was it going?
First, let's convert 210 minutes to hours:
[tex]210\text{ minutes}=\frac{210}{60}\text{ hours}=3.5\text{ hours}[/tex]Now, to calculate the velocity in mph, let's divide the distance in miles by the time in hours:
[tex]velocity=\frac{2100}{3.5}=600\text{ mph}[/tex]Need to find circumference of the circle. Use 3.14 for the value of pi. m let diameter = 20 in
the circumference of the circle is 62.8 inches
Explanation
the circumference of a circle is given by:
[tex]\text{Circumference(C)}=\text{ Diameter(D)}\cdot\pi[/tex]Step 1
Let
[tex]\begin{gathered} \pi=3.14 \\ \text{Diameter}=\text{ 20 in} \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} \text{Circumference(C)}=\text{ Diameter(D)}\cdot\pi \\ C=\text{ 20in }\cdot3.14 \\ C=62.8\text{ inches} \end{gathered}[/tex]therefore, the circumference of the circle is 62.8 inches
I hope this helps you
this graph ( below ) shows how thr total number of pieces greta knows how to sing depends on the number of weeks she takes voice lessons . what is the rate of change .
The rate of change of the line is equal to its slope. To calculate the slope, choose two points on the line and write down their coordinates.
Take the points:
[tex]\begin{gathered} (0,4) \\ (5,6) \end{gathered}[/tex]Given two arbitrary points:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]The slope between them is given by the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]Substitute y_2=6, y_1=4, x_2=5 and x_1=0 into the formula for the slope to find the rate of change:
[tex]\begin{gathered} m=\frac{6-4}{5-0} \\ =\frac{2}{5} \end{gathered}[/tex]Therefore, the rate of change of the vocal pieces that Greta can sing over the weeks that she takes voice lessons, is 2/5.
simple interest of finance
The Simple Interest on the loan = $563.5
Explanations:Simple Interest is given by the formula:
[tex]I\text{ = }\frac{P\times R\times T}{100}[/tex]where I is the Simple Interest
P is the principal
R is the rate
T is the time in years
From the question:
P = $10500
R = 9.2%
T = 7 months = 7/12 years
Substituting the values of P, R, and T into the formula:
[tex]\begin{gathered} I\text{ = }\frac{10500\times9.2\times\frac{7}{12}}{100} \\ I\text{ = 105 }\times\text{ 9.2 }\times\text{ }\frac{7}{12} \\ I\text{ = }563.5 \end{gathered}[/tex]The Simple Interest on the loan = $563.5
Write the equation for each line in slope - intercept form:Y int: 4 and goes through (1,8)
Okay, here we have this:
Considering that the slope intercept form is the following:
y=mx+b
If we replace with the provided info we obtain the following:
8=m(1)+4
And here we can clear for the slope (m):
8=m(1)+4
8=m+4
m=8-4
m=4
With this slope we can replace in the slope intercept form and finally we obtain the following equation:
The daily dose for a man who weighs 175 pound is
Daily dosage of medicine for every 20 pounds of body weight = 70 mg
Daily dosage of medicine for every 1 pound of body weight = 70/20 mg
Daily dosage of medicine for every 1 pound of body weight = 3.5 mg
Daily dosage of medicine for every 175 pounds of body weight = 175 x 3.5
Daily dosage of medicine for every 175 pounds of body weight = 612.5 mg
Therefore, the daily dose for a man who weighs 175 pounds is 612.5 mg
If the man is to receive 900 mg in 8 hours
Dosage he will receive in 1 hour = 900/8
Dosage he will receivw in 1 hour = 112.5 mg
Dosage he will receive in 24 hours = 112.5 x 24
Dosage he will receive in 24 hours = 2700 mg
This means the man will take 2700 mg instead of the normal 612.5 mg. He is receiving the wrong dosage
Writing an equation in slope intercept form for the line passing through each pair of points. (0,3) (1,-2)
Calculating the slope of the line with points (0,3) (1,-2)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1}=\frac{-2-3}{1-0}=\frac{-5}{1}=-5 \\ m=-5 \end{gathered}[/tex]With the slope and one of the points we find the y-intercept with the equation y=mx +b.
y= mx + b (m: slope , b=y-intercept)
3=-5(0) + b (Replacing m=-5 and the point (0,3))
3= 0 + b (Multiplying)
3=b
The answer is y=-5x + 3.
Consider the right triangle with leg lengths of 5 and 12 units shown in the image below. One vertex of the triangle is located at (-6, 4).
Step 1
Define the equation of a circle
[tex]\text{The equation of a circle = (x-h)}^2+(y-k)^2=r^2[/tex]Step 2
Write down the parameters
r = radius = ?
h = -6
k = 4
Step 3
find the radius
Considering the triangle we can find the radius using the Pythagoras theorem
[tex]r^2=5^2+12^2[/tex][tex]\begin{gathered} r\text{ = }\sqrt[\square]{25\text{ + 144}} \\ r\text{ = }\sqrt[]{169} \\ r\text{ = 13} \end{gathered}[/tex]Step 3
Substitute the values into the equation and simplify
[tex]\begin{gathered} (x-(-6))^2+(y-4)^2=13^2 \\ (x+6)^2+(y-4)^2=13^2 \end{gathered}[/tex]Answer is option A
factor the equation 3x^2 +16x-12
(3x - 2)(x + 6)
Explanation:3x² +16x-12
a = 3, b = 16, c = - 12
a(c) = 3(-12) = -36
The factors of -36 whose sum will give +16 are -2 and 18
3x² + 18x - 2x - 12
3x(x + 6) -2(x + 6)
(3x - 2)(x + 6)
The factorisation: (3x - 2)(x + 6)
Containers R Us purchased 5 dozen work gloves for $73.80. How much did each pair of gloves cost?
In order to determine the price of each pair, just calculate the quotient in between the total price and the number of dozen works, which were 5:
73.80/5 = 14.76
Hence, each pair of dozen work costed $14.76
The midpoint of a segment can be found using the formulas for a directed line segment, x =C DaQ+bX2-X1) + X, and46]«y =aa + b-6/2 – Yı) + y1. When using these formulas to find a midpoint, which is true?O a = 1 and b= 2a = 2 and b = 1a = 1 and a + b = 2a = 2 and a + b = 2NextSubmitSave and ExitMark this and return
In general, the formula to find the midpoint of a line segment which ends have the coordinates (x₁,y₁) and (x₂,y₂) is given by
[tex]M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]Working with the formula we are given, for the x coordinate of the midpoint we have:
[tex]x=(\frac{a}{a+b})(x_2-x_1)+x_1=\frac{a(x_2-x_1)}{a+b}+\frac{(a+b)x_1}{a+b}[/tex]In order for this to be like the previous formula, we have the following equation:
[tex]\frac{a(x_2-x_1)}{a+b}+\frac{(a+b)x_1}{a+b}=\frac{x_2+x_1}{2}[/tex]From here, we see that a+b must be equal to 2, so:
[tex]\frac{a(x_2-x_1)}{2}+\frac{2x_1_{}}{2}=\frac{ax_2-ax_1}{2}+\frac{2x_1}{2}=\frac{ax_2-ax_1+2x_1}{2}=\frac{x_2+x_1}{2}[/tex]In order for this last equation to be true, a must equal 1:
[tex]\frac{x_2-x_1+2x_1}{2}=\frac{x_2+x_1}{2}[/tex]Let's verify this with the formula for the y coordinate of the midpoint:
[tex](\frac{1}{2})(y_2-y_1)+y_1=\frac{y_2-y_1}{2}+y_1=\frac{y_2-y_1}{2}+\frac{2y_1}{2}=\frac{y_2-y_1+2y_1}{2}=\frac{y_2+y_1}{2}[/tex]Since using our previous deduction leads us to the correct formula for the y coordinate of the midpoint as well, we can conclude that a=1 and a+b=2.
Mr. Nguyen bought a suit that was on sale for 40% off the original price. He paid 9% salea tax on the sake price. The original price of the suit was $260. How much did he pay for the suit, including tax, to the nearest dollar?
The original price of the suit was $260. If the sale price was 40% off the original price, it means that the amount of discount was
40/100 * 260 = 104
The sale price is 260 - 104 = $156
If he paid sales tax of 9% of the sale price, it means that the amount of tax is
9/100 * 156 = 14.04
Therefore, the amount that he paid including tax is
156 + 14.04 = $170.04
Rounding up to the nearest dollar, the amount is $170
what is the standard deviation of the following data set rounded to the nearest tenth
The general formula for the standard deviation is:
[tex]\sigma=\sqrt{\frac{\Sigma(x_i-\mu)^2}{N}}[/tex]in which, N is the number of data, and μ is the sample's mean.
Start by calculating the sample's mean
[tex]\begin{gathered} \mu=\frac{7.7+8.4+9+8+6.9}{5} \\ \mu=8 \end{gathered}[/tex]then, apply the standard deviation formula
[tex]\begin{gathered} \sigma=\sqrt{\frac{(7.7-8)^2+(8.4-8)^2+(9-8)^2+(8-8)^2+(6.9-8)^2}{5}} \\ \\ \sigma=\sqrt{\frac{(-0.3)^2+(0.4)^2+(1)^2+(0)^2+(-1.1)^2}{5}} \\ \\ \sigma=\sqrt{\frac{2.46}{5}} \\ \\ \sigma=\sqrt{0.492} \\ \sigma=0.701\approx0.7 \end{gathered}[/tex]Answer:
The standard deviation is 0.7
Two girls 21 miles apart. One going 3.5 mph one going 2.5 mph. How long until they meet up?
From the picture,
x + y = 21
From definition,
speed = distance/time
The girl whose speed is 3.5 mph, walks x miles in t hours, that is:
3.5 = x/t
or
x = 3.5t
Similarly,
y = 2.5t
(they walk for the same time)
Replacing into the first equation:
3.5t + 2.5t = 21
6t = 21
t = 21/6
t = 3.5
It will take 3.5 hours until they meet up
Illustrate each of the following diagram:TRY HARDERNeed rn asap :)
We will draw the Venn diagram to show the universal st U and the 3 sets A, B, C
Now we will start with the common elements of A and B
5 is the common element of A and B
1 is the common element between A and C
2, 4, and 6 are the common elements between B and C
3 is in A only
Now we can answer the question using the Venn diagram
1. A' means all the elements in U except A, then
[tex]A^{\prime}=\lbrace2,4,6\rbrace[/tex]2. B U C means all elements in B and C
[tex]B\cup C=\lbrace1,2,4,5,6\rbrace[/tex]3. A intersect C means common elements in A and C
[tex]A\cap C=\lbrace1\rbrace[/tex]4. B' all elements in U not in B
[tex]B^{\prime}=\lbrace1,3\rbrace[/tex]5. A U B all elements in A and B
[tex]A\cup B=\lbrace1,2,3,4,5,6\rbrace[/tex]a. (A U C}' means all elements in U except A and C
[tex](A\cup C)^{\prime}=\lbrace\rbrace=\Phi[/tex]Empty set because all elements are in A and C
b. A' intersects C'
[tex]\begin{gathered} A^{\prime}=\lbrace2,4,6),C^{\prime}=\lbrace3,5\rbrace \\ A^{\prime}\cap C^{\prime}=\lbrace\rbrace=\Phi \end{gathered}[/tex]No common elements between A' and C'
c. (A intersects B)' means all elements in U except the common elements between A and B
[tex]\begin{gathered} A\cap B=\lbrace5\rbrace \\ \\ (A\cap B)^{\prime}=\lbrace1,2,3,4,6\rbrace \end{gathered}[/tex]Find the odds in favor of getting an extra turnWhat is the probability of choosing a lemon-flavored piece
Given:
Probability of few cases is given
Required:
I would appreciate your feedback - you can provide it by rating the session.
Explanation:
(a)
[tex]\begin{gathered} the\text{ odds in favor of getting an extra turn=} \\ \\ =\frac{probability\text{ of chances to get an extra turn in 17 attempts}}{probability\text{ of chance to not get an extra turn in 17 attempts}} \\ \\ =\frac{6}{17-6}\text{ =}\frac{6}{11} \end{gathered}[/tex](b) Odds against is given by number of failures/number of successes
[tex]\begin{gathered} \frac{no\text{ of failures }}{no\text{ of success}}=\frac{9}{10} \\ \\ The\text{ total number of trials in failures+number of successes= 9+10=19} \\ \\ So\text{ getting a lamon-flavored piece is a success.} \\ \\ p(getting\text{ a lamon flavoured piece\rparen=}\frac{10}{19} \end{gathered}[/tex]Required answer:
[tex](a)\frac{6}{11}\text{ \lparen b\rparen}\frac{10}{19}[/tex]ethan buys vidio games for 39.99 sale on 20% how much ethan payed
The amount that Ethan pays for the video game is 47.988.
How to calculate the value?From the information illustrated, it should be noted that it was stated that Ethan buys video games for 39.99 sale on 20% tax.
In this case, the amount that he will pay will be:
= Original amount + Tax
= 39.99 + (20% × 39.99)
= 39.99 + 7.998
= 47.988
The amount is 47.988.
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Complete question
Ethan buys vidio games for 39.99 sale on 20% tax how much ethan payed