We have the following:
[tex](5n+6)\cdot(5n-5)[/tex]we apply distribute property:
[tex]25n^2-25n+30n-30=25n^2+5n-30[/tex]Resultant of the distributive property is 25n² + 5n - 30 .
Given,
(5n+6)(5n-5)
Now,
Distributive property in multiplication : a x (b x c) = (axb) x c
Thus apply the property in the given expression,
(5n+6)(5n-5)
= 25n² - 25n + 30n - 30
Solve the terms with variable n,
= 25n² + 5n - 30
Final expression : 25n² + 5n - 30
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Find the measure of arc BC, the measure of angle A, and the measure of arc AB.
Explanation
If we have the question as
Then, we will have the measure of arc BC as 45 degrees (An arc measure is an angle the arc makes at the center of a circle)
For the measure of angle A
[tex]Measure\text{ of angle A=}\frac{1}{2}\times45^0=22.5^0(Angle\text{ at center is twice that at the center})[/tex]To get the measure of angle AB
we will have
So that
[tex]\begin{gathered} x+x+45=360 \\ 2x=360-45 \\ 2x=315 \\ x=\frac{315}{2} \\ \\ x=157.5^0 \end{gathered}[/tex]Therefore, the measure of the arc AB is 157.5 degree
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
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.
A person is running a distance rate at a constant rate. What time will they finish the race? What information would i need to be able to dolve this problem?
We know
[tex]D=RT[/tex]Where
D is the distance
R is the rate (or speed)
T is the time
We would need to know ANY 2 variables to solve for the 3rd variable.
Since, we want to know the time (T), we MUST somehow know R (rate/speed) and D (distance).
This way, we will be able to solve the problem.
Find the value of x in the picture below using the provided 4 answer choices.
The second choice is the correct answer
So, if you look at number 17 I need to know how to do the strategy so I can wright it down and study it for my test tomorrow! Will give 5 stars if you do an amazing explanation!
Question:
What is:
[tex]51+5^2.31+18^2-9.7[/tex]Solution:
Consider the following expression:
[tex]51+5^2.31+18^2-9.7[/tex]By precedence in arithmetic operations, we will first perform the powers:
[tex]51\text{ + (25)(31)+(324)-(9)(7)}[/tex]now, by precedence in arithmetic operations, we will perform the multiplications:
[tex]51\text{ +775+324-}63[/tex]now, by precedence in arithmetic operations, we will perform the sums:
[tex](51\text{ +775+324)-}63[/tex]that is:
[tex]1150-63[/tex]Finally, we perform the respective subtraction:
[tex]1083[/tex]so that, we can conclude that the correct answer is:
[tex]1083[/tex]
65091/4562Long division This this is to solve how many brownies Joshua has. Help please and thank you.
Given:
[tex]\frac{65091}{4562}[/tex]Number of Brownies= 14.27
Number of Brownies=14 (approximately)
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]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
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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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]The time, in years, that it takes an amount of money to double when invested at a simple interest rate can be approximated by dividing 0.72 by the interest rate expressed as a decimal. Approximately how many years would it take an investment of $1000 to be worth $2000 if the money were invested at a simple interest rate of 4%?
11)
The number of years for the investment to double = 0.72/interest
From the information given,
interest = 4% = 4/100 = 0.04
Therefore,
number of years for the investment to double = 0.72/0.04 = 18
Option 5 is correct
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
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.
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.
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
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.
which fraction is equivalent to 35/50a) 25/45b 18/20c) 7/9d) 28/40
EXPLANATION:
To know which of all is the equivalent fraction, we must try with the same number, that is, divide the numerator and denominator by the same number;
Also in the opposite case, we must multiply the numerator and denominator by the same number.
So we have the following:
first step, check each fraction:
[tex]\frac{35}{50}\text{ divide }5=\frac{7}{10}[/tex]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.
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
An angle has a cosine of 4/5. What will its cosecant be?
Recall that the cosine ratio is determined by adjacent side, divided by the hypotenuse of a right triangle.
Given that cosine is 4/5, the opposite side is
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2+(4)^2=(5)^2 \\ a^2+16=25 \\ a^2=25-16 \\ a^2=9 \\ \sqrt{a^2}=\sqrt{9} \\ a=3 \end{gathered}[/tex]Now that we have solved for the opposite side, recall that cosecant is determined by the equation
[tex]\csc\theta=\frac{\text{hypotenuse}}{\text{opposite}}[/tex]Substitute
hypotenuse = 5
opposite = 3
and we get
[tex]\csc\theta=\frac{5}{3}\text{ \lparen final answer\rparen}[/tex]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
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
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:
(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
I need help with a question
we must replace the value of D
A.-11
[tex]\begin{gathered} 2(-3(-11)-8)\le98 \\ 2(33-8)\le98 \\ 2(25)\le98 \\ 50\le98 \end{gathered}[/tex]the option is right
B. -36
[tex]\begin{gathered} 2(-3(-36)-8)\le98 \\ 2(108-8)\le98 \\ 2(100)\le98 \\ 200\le98 \end{gathered}[/tex]the option is wrong
C.-19
2()
D.-29
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]Consider the graph of f(x) = 5 ^ x + 1 1. Explain how to find the average rate of change between x = 0 and x = 4 . What is the average rate of change ?
1. To determine the average rate of change of a function "f(x)" between the points "x = a" and "x = b" we use the following formula:
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]2. In this case, we have the following function:
[tex]f(x)=5^x+1[/tex]And we have the points:
[tex]\begin{gathered} x=0 \\ x=4 \end{gathered}[/tex]Now we determine the value of f(b) by replacing x = 4 in the function:
[tex]\begin{gathered} f(4)=5^4+1 \\ f(4)=626 \end{gathered}[/tex]Now we determine f(0):
[tex]\begin{gathered} f(0)=5^0+1 \\ f(0)=1+1=2 \end{gathered}[/tex]Replacing in the formula for the average rate of change we get:
[tex]A=\frac{626-2}{4-0}[/tex]Solving the operations:
[tex]A=\frac{624}{4}=156[/tex]Therefore, the average rate of change is 156.
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)