If PQ = 6x - q and PR = 15x - 29, then QR =?
1/3 (x + 5) + x = 4 ( x - 4) -9
Distributing and combining similar terms
[tex]\begin{gathered} \frac{1}{3}\cdot x+\frac{1}{3}\cdot5+x=4\cdot x-4\cdot4-9 \\ \frac{1}{3}x+x+\frac{5}{3}=4x-16-9 \\ \frac{4}{3}x+\frac{5}{3}=4x-25 \end{gathered}[/tex]Subtracting 4/3x at both sides
[tex]\begin{gathered} \frac{4}{3}x+\frac{5}{3}-\frac{4}{3}x=4x-25-\frac{4}{3}x \\ \frac{5}{3}=(4-\frac{4}{3})x-25 \\ \frac{5}{3}=(\frac{4\cdot3-4}{3})x-25 \\ \frac{5}{3}=\frac{8}{3}x-25 \end{gathered}[/tex]Adding 25 at both sides:
[tex]\begin{gathered} \frac{5}{3}+25=\frac{8}{3}x-25+25 \\ \frac{5+25\cdot3}{3}=\frac{8}{3}x \\ \frac{80}{3}=\frac{8}{3}x \end{gathered}[/tex]Multiplying by 3/8 at both sides
[tex]\begin{gathered} \frac{80}{3}\cdot\frac{3}{8}=\frac{8}{3}x\cdot\frac{3}{8} \\ \frac{80}{8}=x \\ 10=x \end{gathered}[/tex]Answer:
x=10 am not sure
Step-by-step explanation:
Find the greatest common factor for the list of terms.x4, x7, x9
To find the greatest common factor (GCM) for monomials, as you have in this case, you can write the complete factorization of each monomial and find the common factors. Then:
[tex]\begin{gathered} x^4=x\cdot x\cdot x\cdot x \\ x^7=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x \\ x^9=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x \end{gathered}[/tex]As you can see, all of these terms have x*x*x*x in common, and this is equal to x^4.
Thus, the GCF for this list of terms is:
[tex]x^4[/tex][20] A food label shows a total of 448 calories for 4 servings. How many
calories would that be per serving?
Answer:
112
Step-by-step explanation:
448/4=112
Angelo's kayak travels 10km/h in still water. If the river's current flows at a rate of 4km/h, How long will it take to travel 35km downstream? it'll take [____] hours.
Given that Angelo's kayak travels 10km/h in still water, and the river's current flows at a rate of 4km/h.
Travelling downstream means Angelo is travelling with the current, that is the current of the water will add to Angelo's speed.
Their combined speed will be;
[tex]\begin{gathered} v=10\text{ km/h + 4 km/h} \\ v=\text{ 14 km/h} \end{gathered}[/tex]To travel 35 km downstream;
[tex]\text{distance = 35km}[/tex]Recall that;
[tex]\begin{gathered} \text{speed = }\frac{\text{ distance}}{\text{time}} \\ \text{time = }\frac{\text{ distance}}{\text{ speed}} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} \text{time = }\frac{35\operatorname{km}}{14\text{ km/h}} \\ \text{time =2.5 hours} \end{gathered}[/tex]Therefore, it'll take 2.5 hours
[tex]undefined[/tex]The ratio of children to teachers at a preeschool is 14:5 .How many children are there at the preschool if there are 30 teachers
Answer:
84
Step-by-step explanation:
5*6=30
14*6=84
If you need further explanation just tell me!
Work Shown:
(14 children)/(5 teachers) = (x children)/(30 teachers)
14/5 = x/30
14*30 = 5*x
420 = 5x
5x = 420
x = 420/5
x = 84
Consider parallelogram VWXY below.Use the information given in the figure to find mZY, mZYVX, and x.म7503903xmZY - •mZYVX - _х$12
In a parallelogram, opposite angles are congruent, this means that,
[tex]\begin{gathered} m\angle Y=m\angle W \\ m\angle Y=75 \end{gathered}[/tex]Similarly, in a parallelogram, we have that angles in green are congruent because they are alternate interior angles:
This implies that
[tex]m\angle YVX=39[/tex]On the other hand, opposite sides are congruent, this implies that
[tex]3x=12[/tex]Then, by moving 3 to the right hand side, we get
[tex]\begin{gathered} x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, the answers are
[tex]\begin{gathered} m\angle Y=75 \\ m\angle YVX=39 \\ x=4 \end{gathered}[/tex]Arithmetic sequence is given by
and .
What is the sum of the first terms of that arithmetic sequence?
The sum of the first four terms of the arithmetic sequence is 24.
How to calculate the sequence?From the information illustrated, the arithmetic sequence is given by 2n + 1.
The first term will be:
= 2n + 1
= 2(1) + 1 = 3
The second term will be:
= 2n + 1
= 2(2) + 1 = 5
The third term will be:
= 2n + 1
= 2(3) + 1
= 7
The fourth term will be:
= 2n + 1
= 2(4) + 1
= 9
The sum of the first four terms will be:
= 3 + 5 + 7 + 9
= 24
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An arithmetic sequence is given by 2n + 1. What is the sum of the first 4 terms of that arithmetic sequence?
Solve the following equation:
4x - 3 = 12 + x
A x = 45
B x = 15
C x = 5
D x = 3
Answer:
C x = 5
Step-by-step explanation:
4x - 3 = 12 + x
Add 3 on both sides:
4x - 3 + 3 = 12 + 3 + x
4x = 15 + x
Subtract x from both sides:
4x - x = 15 + x - x
3x = 15
x = 15/3
or
x = 5
Answer:
[tex]4x - 3 = 12 + x \\ \\ ➪4x - x = 12 + 3 \\ \\ ➪3x = 15 \\ \\ ➪x = \frac{15}{3} = 5[/tex]
C] x = 5 Is ᴛʜᴇ ʀɪɢʜᴛ ᴀɴsᴡᴇʀ.
What is the slope of the line?
*2
*1/2
*-1/2
*-2
The answer is 2 m = -4 / -2 = -2 / -1 = 2
Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 4 cars will enter the car wash? Round your answer to four decimal places.
The probability that, in any hour, exactly 5 cars will enter the car wash is P(x = 5) = 0.0920.
This can be modeled as a Poisson random variable.
The mean rate is the parameter of the Poisson distribution:
λ = 4 cars/30 mins
λ = 8 cars/hr
The probability that exactly k cars will enter the car wash can be calculated as:
P(x = k) = ([tex]8^{k}[/tex] × [tex]e^{-8}[/tex]) ÷ k!
Then, the probability that exactly 5 cars will enter the car wash for k=5 is:
P(5) = ([tex]8^{5}[/tex] × [tex]e^{-8}[/tex]) ÷ 5!
P(5) = (32768 × 0.0003) ÷ 120
P(5) = 0.0920
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HELP PLEASE
thank youuu
Answer:
a/c
Step-by-step explanation:
Sine is always the side opposite the angle and the hypotenuse
Answer:
[tex]\large \text{Second Choice: $\dfrac{a}{c}$}[/tex]
Step-by-step explanation:
For any given triangle, the Law Of Sines states that the ratio of each side to the sine of the angle opposite that side is the same
So we have
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{\sin \angle 90} = \dfrac{b}{\sin \angle G} \\\\[/tex]
[tex]\sin \angle 90 = 1[/tex]
So we get from the first two ratio equality,
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{1} \\\\\\\dfrac{a}{\sin \angle F} = c\\\\\\\dfrac{a}{c} = sin \angle F\\\\[/tex]
Or, in other words,
[tex]\sin \angle F = \dfrac{a}{c}[/tex]
I need help with this!!
Answer:
Step-by-step explanation:
In the sale room at a store, every item is on sale for half the original price, plus 3 dollars.
Complete parts a through d.
(a) Write a function g(x) that finds half of x.
(b) Write a function f(x) that adds 3 to x.
(c) Write and simplify the function (f o g)(x).
(d) Use the function from part (c) to find the sale price of a shirt at the store that has the original
price $60
The solution to the questions are
g(x) = 1/2xf(x) = x + 3(f o g)(x) = 1/2x + 3The sales of shirt that originally costs $60 is $33How to find the equation of function g(x)?The given parameters are:
Every item is on sales for half the original price, plus 3 dollars.
In this case, the function g(x) is half the original price
Let the original price be x
So, we have the following equation
Price = 1/2x
Express as a function
g(x) = 1/2x
How to find the equation of function f(x)?The given parameters are:
Every item is on sales for half the original price, plus 3 dollars.
In this case, the function f(x) is the 3 dollars added
Let the original price be x
So, we have the following equation
Price = x + 3
Express as a function
f(x) = x + 3
The function (f o g)(x)In (A) and (B), we have
g(x) = 1/2x
f(x) = x + 3
The function (f o g)(x) is calculated as
(f o g)(x) = f(g(x))
So, we have
(f o g)(x) = g(x) + 3
Substitute g(x) = 1/2x
(f o g)(x) = 1/2x + 3
The sales of shirt that originally costs $60Here, we have
(f o g)(x) = 1/2x + 3
This means that x = 60
So, we have
(f o g)(60) = 1/2 x 60 + 3
Evaluate
(f o g)(60) = 33
Hence, the value of the shirt is $33
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What is the image of point (-3,-1) under a reflection in the origin?
(1) (3,1)
(3) (1,3)
(2) (-3,1)
(4) (-1,-3)
The image of point (-3,-1) under a reflection in the origin( 3 , 1 )
Point (x, y) is reflected over the line y = x, and the reflection is (y, x)
Find the point of a reflection on a point by what method?
The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x. The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x. Therefore, Point (x, y) is reflected over the line y = x, and the reflection is (y, x)
following a reflection, a 3-1 picture Reason: A(3,1) becomes A'(3,3+3(1)), or A', when it is reflected over y=3 (3,7)
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What is the equation of this line?
The equation of this line is y =4.
What is the Equation of line?The equation y = mx + c, where m is the gradient of the line (how steep the line is), and c is the y-intercept, is the universal equation of any straight line (the point in which the line crosses the y-axis).In the linear equation y = mx + c, the variables x and y correspond to points on the line.We get a result for y when we enter a value for x into the equation y = mx + c.In light of the fact that y depends on the value of x, x is an independent variable and y is a dependent variable.From the given graph we can infer that line A is a horizontal line
It can be expressed in the form y = constant
Hence the equation of this line is y = 4
Similarly, from the given graph we can infer that line B is a vertical line
It can be expressed in the form x = constant
Hence the equation of this line is x = 8
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I need help with geometry. Were learning similarity and i have a test soon but im really confused. I've been trying to figure it out for the past 2 hours but I really have no idea. I attached a photo of my assignment from today if anyone could help me with that.
Consider the upper triangle
if we want to find b side, consider the following trigonometric identity:
[tex]\cos \text{ (}\theta\text{) = }\frac{adjacent\text{ side}}{hypotenuse}[/tex]in this case, we have:
[tex]\cos \text{ (45) = }\frac{b}{20}[/tex]solve for b:
[tex]b\text{ = cos(45) x 20 = }\frac{\sqrt[]{2}}{2}\text{ x 20 = 10}\sqrt[]{2}[/tex]then, we can conclude that
[tex]b\text{ = 10}\sqrt[]{2}[/tex]Now, for a-side, consider the following trigonometric identity:
[tex]\sin \text{ (}\theta\text{) = }\frac{opposite\text{ side}}{hypotenuse}[/tex]in this case, we have:
[tex]\sin \text{ (}\theta\text{) = }\frac{a}{20}[/tex]solve for a:
[tex]a\text{ = }\sin \text{(45) x 20 = }\frac{\sqrt[]{2}}{2}\text{ x 20 = 10}\sqrt[]{2}[/tex]then, we can conclude that
[tex]a\text{ = 10}\sqrt[]{2}[/tex]Now, for the c-side, consider the greater triangle :
if we denote the hypotenuse by h, then by Pythagorean theorem we have:
[tex]h^2=20^2+15^2[/tex]but h = a + c, then, replacing this in the previous equation we have
[tex]h^2=(a+c)^2=20^2+15^2[/tex]but, we know that a is
[tex]a\text{ = 10}\sqrt[]{2}[/tex]then we have:
[tex](10\sqrt[]{2}+c)^2=20^2+15^2\text{ = 625}[/tex]now, taking the square root of both sides of the equation we obtain:
[tex]10\sqrt[]{2}+c^{}=\text{ 25}[/tex]solve for c:
[tex]c^{}=\text{ 25}-\text{ 10}\sqrt[]{2\text{ }}\text{ }\approx10.85[/tex]then we can conclude that :
[tex]a\text{ = 10}\sqrt[]{2}[/tex]
[tex]b\text{ = 10}\sqrt[]{2}[/tex]
and
[tex]c^{}=\text{ 25}-\text{ 10}\sqrt[]{2\text{ }}\text{ }\approx10.85[/tex]
Solve for xF(x)=2x+10
So:
f(x) = 2x + 10
To solve for x, we are going to subtract 10 on both sides of the equation:
f(x) - 10 = 2x + 10 - 10
f(x) - 10 = 2x
Then, dividing by 2, we get:
[tex]\begin{gathered} \frac{f(x)-10}{2}=\frac{2x}{2} \\ \frac{1}{2}f(x)-5=x \end{gathered}[/tex]Answer:
[tex]x=\frac{1}{2}f(x)-5[/tex]
PLEASE HELP! Sharel received a bank account statement report the recent changes to her account. The statement showed an overall increase in the account balance of $4,317.59. During the time shown on the statement, Sharel was paid three times and withdrew a total of $1,230.67 to cover all her bills and expenses. How much (x) is each of Sharel's paychecks? Write an equation to represent this situation.
Use the square root property to solve the equation.x² = 36Select one:O A. (18)O B. {16}O C. {±6i}O D. {6}
Given the equation
[tex]x^2=36[/tex][tex]x=\sqrt{36}[/tex][tex]x=\pm6[/tex]Then
The Correct answer is
Option D 6
what 3 factors were used to create this product game board with the numbers 4 6 9 14 49?
What product is missing?
By using 3 factors 2, 3, and 7, if we create a product game board with the numbers 4 6 9 14 49 then the missing product is 21.
To solve this problem we have to follow a few steps. First, we should know about factors.
What are the factors?
Factors of a number are such numbers as they can divide the whole number without remaining.
Example: The factors of 24 are 1, 2, 3, 4, 6, 8, and 12.
Now we have to analyze the given numbers,
4 = 2× 2
6 = 2× 3
9 = 3× 3
14 = 2× 7
49 = 7× 7
The factors are 2, 3, and 7. Therefore, the missing product is, 3× 7= 21
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Determine whether the values in the table
are best modeled by a linear or nonlinear
function. (Lesson 2-2)
X
-2
0
2
4
6
y
6555o
Answer: nonlinear function
Step-by-step explanation:
The rate at which y increases is not constant with respect to x.
how do you write 4.501795324E^-6 in simpler form
A test requires that you answer either part A or part B. Part A consists of 6 true-false questions, and part B consists of 6 multiple-choice questions with one correct answer out of six. How many different completed answer sheets are possible?
If a test requires that you answer either part A or part B. Part A consists of 6 true-false questions, and part B consists of 6 multiple-choice questions with one correct answer out of six. 46720 different completed answer sheets are possible.
What is Combination?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items.
A test requires that you answer either part A or part B.
Part A consists of 6 true-false questions.
i.e. there are 2 choices to answer each question
Now, the number of ways to answer Part A : 2⁶=64 (1)
Part B consists of 6 multiple-choice questions with one correct answer out of five.
i.e. there are 6 choices to answer each question.
Now, the number of ways to answer Part B : 6⁶=46656
Now, the number of different ways to completed answer sheets are possible= 46656+64
=46720
Hence 46720 different completed answer sheets are possible.
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Bharat types 20 words/min. How many words can he type in each length of time? a) 5 min b) 30 min c) 23 min
Bharat can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 12×2 = 24
Bharat types 20 words per minute which are given in the question.
To determine the number of words can he type in each length of time
We have to multiply the time by his typing speed.
The number of words that can be typed by Bharat in 5 minutes :
⇒ 20 × 5
⇒ 100
The number of words that can be typed by Bharat in 30 minutes :
⇒ 20 × 30
⇒ 600
The number of words that can be typed by Bharat in 23 minutes :
⇒ 20 × 23
⇒ 460
Therefore, He can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
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Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps.
The expression 26+8 as the product of the GCF and a sum will be; 2(13+4).
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that we have the expression as 26+8
We have to find the greatest common factor of the numbers 26 and 8.
26 = 2 × 13
8 = 2 × 2 × 2
Then Multiply all the prime factors, both numbers share in order to determine the GCF:
Therefore, GCF = 2
Now we can write the expression as;
26 + 8
=2(13 + 4)
=2×17
=34
Hence. the required expression will be; 2(13 + 4).
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A professor tells a student that he has a 90% chance of getting an A for the course that he score an 85 or better on the midterm exam. The student thinks he has only a 50% chance of getting 85 better. what is the probability that the student scores an 85 or better and he receive an A in the score?
The probability that the student scores an 85 or better and he receive an A in the score is 0.45.
In the question it is given that the professor tells that the student has 90% chance of getting A, if he gets 85 or better in mid term exam.
The student is 50% sure that he will get 85 or better in the examination.
To get the probability of the student scores an 85 or better and he receives an A grade, we use multiplication rule.
P( student getting A grade and 85 or better)= P(getting A) x P(getting 85 or better)
P(getting A)=0.9
P(getting 85 or better)=0.5
= 0.9x0.5
P( student getting A grade and 85 or better)=0.45
Therefore, probability that the student scores an 85 or better and getting A is 0.45.
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Reduce the vector shown to its (X) horizontal component. (Round your final answer to two decimal places.)
The horizontal component of the provided vector is 100cos35 or 8.19 after reducing.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is given that:
The vector is shown in the picture.
Let's draw an imaginary line from the tail of the vector and it makes the angle between the imaginary line and the vector 35 degrees.
The horizontal component of the vector:
H = 100cos35
The value of the cos35 is 0.819
H = 10(0.819)
H = 8.19
Thus, the horizontal component of the provided vector is 100cos35 or 8.19 after reducing.
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Circumference =96cm, find radius, diameter and area
The Radius is 15.27 cm and the the Diameter is 30.55 cm
Given
Circumference = 96cm
Circumference is the total arc length of a circle or it is simply the perimeter of a circle.
The formula for circumference is 2πr
where π = Ratio of circumference to the diameter of a circle
π = 3.14
r = Radius of the circle
Substituting the value in the formula we get
2πr = 96 cm
πr = 48 cm
r = 15.27 cm
Diameter (d) = 2 × r
hence d = 2 × 15.27 cm
d = 30.55 cm
Hence the radius = 15.7cm
Diameter = 30.55 cm
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- A fireworks show starts at 9:00 P.M.
Orange rockets burst every 1.5 minutes,
green rockets burst every 30 seconds,
and silver showers burst every minute. [
What time is it when all three burst at
the same time?
A. 9:03 P.M.
C. 9:10 P.M.
BLcatc21
B. 9:05 P.M.
D. 9:25 P.M.