Answer:
2
Step-by-step explanation:2x + 3 = 5x - 3
Move x to one side:
[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]
Remove the -3:
[tex]3x-3(+3)=(3+3)[/tex]
[tex]3x=6[/tex]
Remove the 6 to get x by itself:
[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]
The number 2 from the number set would solve the equation.
Checking the Answer:2(2) + 3 = 5(2) - 3
4 + 3 = 10 - 3
7 = 7
The statement is true.
An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be simplified as shown below,
2x + 3 = 5x - 3
Subtract 2x from both sides of the equation,
2x + 3 - 2x = 5x - 3 - 2x
3 = 5x - 3 - 2x
Add 3 on both sides of the equation,
3 + 3 = 5x - 3 - 2x + 3
6 = 3x
3x = 6
Divide both the sides of the equation by 3,
3x/3 = 6/3
x = 2
Hence, the number(s) from the set that will satisfy the given equation is 2.
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PLEASE HELP WILL GIVE BRAINLIEST! One fifth of the student a Riverview Elementary walk to school each day. There are 350 students in the school. How many students walk to school?
A.) 50
B.) 100
C.) 270
D.) 150
E.) 70
The right answer is Option E.
Step-by-step explanation:
Given,
Total number of students in school = 350
Students who walk to school = [tex]\frac{1}{5}\ of\ total\ students[/tex]
Number of students who walk to school = [tex]\frac{1}{5}*350[/tex]
Number of students who walk to school = 70
70 students walk to the school.
The right answer is Option E.
Keywords: fraction, division
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Final answer:
The calculation shows that 70 students at Riverview Elementary walk to school.
Explanation:
The question is asking us to calculate what fraction of the total number of students at Riverview Elementary walk to school each day.
Since one fifth of the students walk to school, we need to divide the total number of students by 5 to find the number of students who walk to school.
To find one fifth of 350 students, we calculate:
350 ÷ 5 = 70
Therefore, 70 students walk to school each day at Riverview Elementary.
PLEASE HELP ITS URGENT!!
Given: △ABC is isosceles; 1 ≅ 3
Prove: AB || CD
Answer:
AB ║ CD. (Proved)
Step-by-step explanation:
See the attached diagram of the triangle.
It is given that Δ ACD is an isosceles triangle.
Therefore, AC = AD and ∠ ACD = ∠ ADC, ⇒ ∠ 3 = ∠ 4 .......... (1)
Again, given that ∠ 1 = ∠ 3 ........... (2)
Now, from equations (1) and (2) we can write, ∠ 1 = ∠ 4
Now, AB and CD are two straight lines and AD is the transverse line and hence, ∠ 1 and ∠ 4 are alternate angles that are equal.
Therefore, AB and CD are parallel straight lines and AB ║ CD. (Proved)
I have a 100 question study guide it is worht 20 points in total how many points is it
Answer:
2000 points
Step-by-step explanation:
Given:
Number of questions in a study guide (Q) = 100
Number of points for 1 question (n) = 20
Now, total number of points is calculated using unitary method by multiplying number of questions and number of points in one question.
Therefore, the total number of points is given as:
Total points = [tex]n\times Q[/tex]
Total points = [tex]20\times 100[/tex]
Total points = [tex]2000[/tex]
Hence, the study guide is worth 2000 points.
Answer:
10
Step-by-step explanation:
d/5=4 A. d=20 B. d= 4/5 C. d=5/4
Answer:
The value of A = [tex]\dfrac{1}{16}[/tex]
The value of B = [tex]\dfrac{1}{16}[/tex]
The value of C = [tex]\dfrac{25}{16}[/tex]
The value of D = [tex]\dfrac{5}{4}[/tex]
Step-by-step explanation:
Given as :
The following relations are as
[tex]\dfrac{d}{5}[/tex] =4 A ...........1
d = 20 B ...........2
d = [tex]\dfrac{4}{5}[/tex] C ...........3
And d = [tex]\dfrac{5}{4}[/tex]
Now, From the above relations
Put the value of d in eq 1
∵ 4 A = [tex]\dfrac{d}{5}[/tex]
So, d = 5 × 4 A
Or, [tex]\dfrac{5}{4}[/tex] = 20 A
∴ A = [tex]\frac{\frac{5}{4}}{20}[/tex] = [tex]\dfrac{1}{16}[/tex]
I.e The value of A = [tex]\dfrac{1}{16}[/tex]
Again
From eq 2
∵ d = 20 B
Put the value of d
So, [tex]\dfrac{5}{4}[/tex] = 20 B
Or, B = [tex]\frac{\frac{5}{4}}{20}[/tex]
∴ B = [tex]\dfrac{1}{16}[/tex]
I.e The value of B = [tex]\dfrac{1}{16}[/tex]
Similarly
From eq 3
d = [tex]\dfrac{4}{5}[/tex] C
Put the value of d
So, [tex]\dfrac{5}{4}[/tex] = [tex]\dfrac{4}{5}[/tex] C
Or, C = [tex]\frac{5\times 5}{4\times 4}[/tex]
∴ C = [tex]\dfrac{25}{16}[/tex]
I.e The value of C = [tex]\dfrac{25}{16}[/tex]
Hence The value are
The value of A = [tex]\dfrac{1}{16}[/tex]
The value of B = [tex]\dfrac{1}{16}[/tex]
The value of C = [tex]\dfrac{25}{16}[/tex]
The value of D = [tex]\dfrac{5}{4}[/tex]
Answer
6. (08.02 MC)
Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490n. What is the percent change in volume between cylinders A and b
Answer:
The percentage change in volume between cylinder A and cylinder B is 50%
Step-by-step explanation:
The volume of a cylinder is given by the formula
V= πr^2h
For cylinder A, where r=7 and h= 5, π=22/7
V= π * 7^2 * 5
V= π * 49 * 5
V= 769.69 cubic inch
For cylinder B
V= 490π
V= 1539.3804 cubic inch
The percentage change in volume between cylinder A and cylinder B
=[ (VA- VB)/VB] *100
=( 1539.3804 - 769.69) / 1539.3804
= 0.5000 * 100
= 50%
The percentage change in the volume between cylinder A and cylinder B is 50%
What is a cylinder?
A cylinder is a three-dimensional object. It is a prism with a circular base.
volume of a cylinder = πr²h
π= 22/7
r = radius
h = height
Volume of cylinder A = π(7² x 5) = 245π
Percentage change in volume = (245 / 490) - 1 = 50%
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Find the equation of the line parallel to y = 2x + 8 and passes through (4, - 6)
Answer:
y=2x-14
Step-by-step explanation:
y=2x+8
y-y1=m(x-x1)
y-(-6)=2(x-4)
y+6=2x-8
y=2x-8-6
y=2x-14
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars? If bisects , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. If bisects , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent. If bisects , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. If bisects , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up.
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up.
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To prove that point D is equidistant from the jungle gym and monkey bars (points A and B), we would utilise the geometrical concept of congruent triangles. This involves drawing line segments from D to A and D to B, and if those segments are congruent, then point D is equidistant from points A and B. The process would encompass drawing a perpendicular bisector from point D to segment AB.
Explanation:To demonstrate that point D is equidistant from the jungle gym and the monkey bars, Beth would need to use specific concepts from geometry. First, she would need to identify points A and B as the jungle gym and monkey bars respectively. Point D is the location of the swings.
Next, she would draw line segments from D to A and D to B. If line segment DA is congruent to line segment DB, this means they have the same length, hence point D is an equal distance from both points A and B (the jungle gym and the monkey bars).
This can be proved through congruent triangles if a perpendicular bisector is drawn from point D to line segment AB. Such concept echoes that a point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment. The resulting triangles would be congruent, meaning every part, including the sides DA and DB, would be the same.
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Find the range of these numbers:
15,2,3,7,8,4,3,2,16,2,4
(04.01 LC)
Marneshia walked of a mile in of an hour. What equation can be used to calculate her unit rate in miles per hour? (1 point)
Question 2 options:
1)
= mile per hour
2)
= miles per hour
3)
= miles per hour
4)
= mile per hou
The answer is 1 mile an hour
A swimming pool is being drained so it can be cleaned. The amount of water in the pool is changing according to the función f(t)= 80,000 - 16,000t , where t = time in hours and f(t) = amount of water in liters. What is the domain of this function in this situation? Explain how you found your answer.
Answer:
0 ≤ t ≤ 5.
Step-by-step explanation:
In the function [tex]f(t)[/tex], [tex]t[/tex] is the independent variable. The domain of [tex]f[/tex] is the set of all values of [tex]t[/tex] that this function can accept.
In this case, [tex]f(t)[/tex] is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,
[tex]t \ge 0[/tex].[tex]f(t) \ge 0[/tex].The first condition is an inequality about [tex]t[/tex], which is indeed the independent variable.
However, the second condition is about [tex]f[/tex], the dependent variable of this function. It has to be rewritten as a condition about [tex]t[/tex].
[tex]\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}[/tex].
Hence, t ≤ 5.
Combine the two inequalities to obtain the domain:
0 ≤ t ≤ 5.
what is the volume of a square pyramid with base edges 24ft and slant height 20ft
The volume of the square pyramid is: 3072 ft³
What is the volume of the square pyramid?
The volume (V) of a square pyramid can be calculated using the formula:
V = ⅓ × base area × height
The base area of a square pyramid is given by the formula:
base area = base edge²
Given that the base edges (a) is 24 ft and the slant height (s) is 20 ft, we can calculate the height (h) of the pyramid using the Pythagorean theorem.
h = √(20² - (24/2)²)
h = √256
h = 16 ft
Thus:
Volume = ⅓ * 256 * 16
Volume = 3072 ft³
Last year 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. Find the percent of decrease.
Answer:
17.25%.
Step-by-step explanation:
We have been given that last ear 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. We are asked to find the percent of decrease.
We will use percent decrease formula to solve our given problem as:
[tex]\text{Percent decrease}=\frac{|\text{Final - Original}|}{\text{Original}}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{|211-255|}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{|-44|}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{44}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=0.1725490\times 100\%[/tex]
[tex]\text{Percent decrease}=17.25490\%[/tex]
[tex]\text{Percent decrease}\approx 17.25\%[/tex]
Therefore, percent decrease is approximately 17.25%.
Which of the following describes the placebo effect?
O
A. At least one block of subjects in an experiment receives only
placebos.
O
B. Subjects may respond to a treatment simply because they believe
it is affecting them.
C. Subjects receive inactive sugar pills instead of real medication.
O
D. An experiment is repeated many times with real drugs and
placebos
O
E. Subjects are prevented from knowing whether they are receiving
real drugs or placebos.
Answer:
b is the correct answer
The placebo effect describes how a person might show improvement simply because they believe a treatment is working, even if it's a dummy treatment. It's an essential aspect considered during clinical studies to distinguish between actual treatment effects and the impact of patients' expectations.
Explanation:The placebo effect is best described as the phenomenon in which a person experiences a perceived improvement in their condition or symptoms simply due to their belief in the efficacy of the treatment, even if the treatment is inactive or a 'dummy' treatment, such as a sugar pill. This is represented in the provided choices by option B. Subjects may respond to a treatment simply because they believe it is affecting them.
Notably, this effect is considered in the design of clinical trials and studies. This is typically done by using a control group that receives a placebo treatment, which allows researchers to separate the physiological effects of the treatment from psychological effects induced by expectations- a crucial aspect of medical and scientific research.
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Complete the steps in order to write the inverse of f(x) = x + 5
Answer:
[tex]f^{-1}[/tex](x) = x - 5
Step-by-step explanation:
Let y = f(x) and make x the subject
y = x + 5 ( subtract 5 from both sides )
y - 5 = x
Change y back into terms of x, thus
[tex]f^{-1}[/tex](x) = x - 5
Find the x- and y-intercepts of the equation -5x+y=30
Answer:
x-intercept: -6y-intercept: 30Step-by-step explanation:
You can put the equation into intercept form by dividing by 30:
-5x/30 + y/30 = 1
x/(-6) + y/30 = 1
Intercept form is ...
x/(x-intercept) +y/(y-intercept) = 1
This lets us recognize the x-intercept as -6 and the y-intercept as 30.
Mr. Martin and his son are planning a fishing trip to Alaska. The rates of two companies are shown.
Wild Fishing Inc.
Round Trip Flight $200 / Daily Rate $25
Fisherman's Service
Round Trip Flight $150 / Daily Rate $30
Part A : Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?
Part B : Which company would charge $700 for 6 days for both of them?
Part C : Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.
Answer:
Part A) Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$
Part B) Wild Fishing's Inc. would charge $700 for 6 days for both of them.
Part C) Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
w = 2(200) + 2n(25) = 400 + 50n
Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
f = 2(150) + 2n(30) = 300 + 60n
Step-by-step explanation:
Part (A) Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?
The rate offered by Wild Fishing Inc:Round Trip Flight $200 / Daily Rate $25
The rate offered by Fisherman's Service:Round Trip Flight $150 / Daily Rate $30
Analyzing Wild Fishing Inc. Offer for a three day trip
As Mr. Martin and his son are planning a fishing trip to Alaska.Expenses cost for Mr. Martin and his son if they chose Wild Fishing Inc
The formula to calculate Mr Martin expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal:
Net expense faced by Mr. Martin and his son: 275 + 275 = 550$
So, Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.
Analyzing Fisherman's Service Offer for a three day trip
As Mr. Martin and his son are planning a fishing trip to Alaska.
Expenses cost for Mr. Martin and his son if they chose Fisherman's Service
The formula to calculate Mr Martin expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal:
Net expense faced by Mr. Martin and his son: 240 + 240 = 480$
So, Fisherman's Service will cost 480$ to both Mr. Martin and his son.
Choosing the right company that offers a better 3 days deal:
As we have determined that
Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.Fisherman's Service will cost 480$ to both Mr. Martin and his son.Therefore, Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$.
Part (B) Which company would charge $700 for 6 days for both of them?
Checking Wild Fishing Inc. expenses for 6 days trip:
The formula to calculate Mr Martin expenses for 6 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal for 6 days:
Net expense faced by Mr. Martin and his son: $350 + $350 = 700$
Checking Fisherman's expenses for 6 days trip:
The formula to calculate Mr Martin expenses for 6 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[A]
The formula to calculate Mr Martin's son expenses for 3 day trip:
Round trip Cost + 6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[B]
Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal for 6 days:
Net expense faced by Mr. Martin and his son: $330 + $330 = 680$
So, Wild Fishing's Inc. would charge $700 for 6 days for both of them.
Part (C) Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.
Expression for Wild Inc.
Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
w = 2 (Round trip Cost) + 2n (Daily rate)
As Round trip costs $200 and $25 is the daily rate for Wild Fishing Inc.
So, w can be written as:
w = 2(200) + 2n(25) = 400 + 50n
Expression for Wild Inc.
Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.
f = 2 (Round trip Cost) + 2n (Daily rate)
As Round trip costs $150 and $30 is the daily rate for Fisherma''s Service.
So, w can be written as:
f = 2(150) + 2n(30) = 300 + 60n
Keywords: cost, expenses, deal
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Celia uses 4 ounces of yogurt for each smoothie she makes.she makes.she has 1 quart of yogurt.how many smoothies can she make with the yogurt? explain your thinking
You can use the fact that 1 quart is equal to 32 ounces.
Next, you can use the division fact, 32 divided by 4 equals 8.
And so, Celia can make 8 smoothies.
Evaluate: (4 + 6 ⋅
3) + 3
16
66
33
25
Answer:
25
Step-by-step explanation:
Do multiplication first 6*3 is 18 18+4 is 22 22+3 is 25
PLEASE HELP WITH THIS QUESTION
Answer:
angle bisector
Step-by-step explanation:
Definitions:
median: line that meets the middle of VX
angle bisector: line that cuts angle Y in half
altitude: line that meets VX at 90°
perpendicular bisector: line that meets VX at 90° and the middle of VX
YW does not meet VX at 90° and does not meet it in the middle. Without measurements or symbols, angle Y seems to be cut in half.
The table represents a linear equation. A two column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 6, 10. The second column, y, has the entries, negative 11, negative 6, 14, 24. Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form? y – 6 = y minus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2) y – 6 = negative StartFraction 2 Over 5 EndFraction. (x – 2) y + 6 = y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2) y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)
Answer:
[tex]y+6=\frac{5}{2}(x+2)[/tex]
y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.
Step-by-step explanation:
we have the ordered pairs
[tex](-4,-11),(-2,-6),(6,14),(10,24)[/tex]
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
[tex](-4,-11),(-2,-6)[/tex]
substitute the given values
[tex]m=\frac{-6+11}{-2+4}[/tex]
[tex]m=\frac{5}{2}[/tex]
step 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{5}{2}[/tex]
[tex](x1,y1)=(-2,-6)[/tex]
substitute in the equation
[tex]y-(-6)=\frac{5}{2}(x-(-2))[/tex]
[tex]y+6=\frac{5}{2}(x+2)[/tex]
In a square or rectangle. How do you find the distance from the top left corner to the bottom right corner diagonally
Answer:
You use the Pythagorean theorem.
Step-by-step explanation:
https://math.stackexchange.com/questions/33549/calculating-the-distance-from-top-left-corner-to-bottom-right-corner-on-a-rectan
Which values of a, b , and c correctly represent the answer in the simplest form?
Answer:
a=1 b=5 c=9
Step-by-step explanation:
Answer: answer is A
Step-by-step explanation:
The graphs of y=x2- 3 and y = 3x -4 intersect at
approximately
1) (0.38,-2.85), only
2) (2.62,3.85), only
3) (0.38, -2.85) and (2.62,3.85)
4) (0.38, -2.85) and (3.85,2.62)
Answer:
Option 3) (0.38, -2.85) and (2.62,3.85)
Step-by-step explanation:
we have
[tex]y=x^{2}-3[/tex] ----> equation A
[tex]y=3x-4[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations is the intersection point both graphs
using a graphing tool
The intersection points are (0.38,-2.85) and (2.62,3.85)
see the attached figure
therefore
The graphs intersect approximately at (0.38,-2.85) and (2.62,3.85)
Simplify: 6(3 + 5)
48
65
47
15
Answer:
48
Step-by-step explanation:
Step #1, Use PEMDAS,(Purple,Eyed,Monster,Drinks,A,Soda
Step #2, Add (3+5)
(8)
Step #3, Multiply 8×6
Step #4, No You
Answer:
48
Step-by-step explanation:
50 PINTS！！！！！！！！ PLEASE HELP QUICK!!!!!!!!!!! What is the slope of the line shown in the graph? (4 points) A coordinate plane is shown with points graphed at 2 comma 2 and 0 comma 1. The points are joined by a line. −2 −1 −1 over 2 1 over 2
We are given, [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] where [tex]P_1(2,2),P_2(0,1)[/tex].
Using slope formula we obtain
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{0-2}=\dfrac{-1}{-2}=\boxed{\dfrac{1}{2}}[/tex]
Hope this helps.
Answer:
1/2
Step-by-step explanation:
I took the test :)
Given that (4,7) is on the graph of f(x), find the
corresponding point for the function
f(x-2)
If [tex]P(4,7)\in G_f[/tex] where [tex]G_f=\{(x,f(x):\forall x\in\mathbb{R}\wedge f(x)\in\mathbb{R}\}[/tex] then [tex]f(x-2)[/tex] will shift the original function by 2 in the right resulting with new point [tex]P'(6,9)[/tex].
Hope this helps.
Nick has to build a brick wall. Each row of the wall requires 6^2 bricks. There a
the wall?
10²x6
10^6
6^10
10×6^2
Answer:
D. [tex]10\times 6^2[/tex]
Step-by-step explanation:
Please consider the complete question.
Nick has to build a brick wall. Each row of the wall requires [tex]6^2[/tex] bricks. There are 10 rows in the wall. How many bricks will Nick require to build the wall?
To find the number of total bricks required to make the wall, we will divide bricks used to make one row [tex](6^2)[/tex] by total number of rows that is 10.
[tex]\text{Number of total bricks required}=10\times 6^2[/tex]
Therefore, Nick will require [tex]10\times 6^2[/tex] bricks to make the wall and option D is the correct choice.
A 2-liter bottle of soda (67.6 ounces) costs $1.89. A case of twelve 12 ounce
cans of the same soda costs $2.99. Calculate the unit price (price/ounce) of each
item and determine which is the better bargain.
Answer:
The better bargain is the case of twelve 12 ounce cans.
Step-by-step explanation:
2-liter bottle of soda:
67.6 ounces cost $1.89, then
1 ounce costs
[tex]\$1.89\div 67.6\approx \$0.028[/tex]
A case of twelve 12 ounce cans:
[tex]12\times 12=144[/tex] ounces of the same soda cost $2.99, then
1 ounce costs
[tex]\$2.99\div 144\approx \$0.021[/tex]
The better bargain is the second choice, the case of twelve 12 ounce cans.
The probability that a truck will be going over the speed limit on I-80 between Cheyenne and Rock Springs is 75%. Suppose a random sample of 5 trucks is observed on this stretch of I-80.
a) What is the probability that exactly 2 trucks are going over the speed limits?
Answer:
The probability that exactly 2 trucks are going over the speed limit is 56.3% (rounding to the next tenth)
Step-by-step explanation:
1. Let's check all the information provided to us to answer the question correctly:
Probability that a truck will be going over the speed limit on I-80 between Cheyenne and Rock Springs = 75%.
Number of trucks in the random sample = 5
2. What is the probability that exactly 2 trucks are going over the speed limit?
Let's recall that two events are independent if the result of the second event is not affected by the result of the 1st event. If a first truck goes over the speed limit and a second truck does the same are independent events, the probability of both events occurring is the product of the probabilities of the individual events.
P (T₁ and T₂) = P (T₁) * P (T₂)
P (T₁ and T₂ ) = 0.75 * 0.75 = 0.5625
The probability that exactly 2 trucks are going over the speed limit is 56.3% (rounding to the next tenth)
The ratio of girls to boys at a movie is 7:3 if there are 9 boys how many girls are at the movie
Work is provided in the image attached.
Final answer:
Using the ratio of 7 girls to 3 boys and knowing that there are 9 boys, we find that there are 21 girls at the movie by setting up a proportion and solving for the number of girls.
Explanation:
To find out the number of girls at the movie, we need to use the ratio given, which is 7 girls to 3 boys or 7:3. Since there are 9 boys, we can set up a proportion to solve for the number of girls (G):
7 girls : 3 boys = G girls : 9 boys
Now we cross multiply and solve for G:
7 * 9 = 3 * G
63 = 3 * G
Divide both sides by 3 to find the number of girls:
G = 63 / 3
G = 21
Therefore, there are 21 girls at the movie.