Answers
Given that
There are two points and we have to find the slope of the line passing through these points.
Explanation -
The given two points are (19/2, -8/3) and (-7/2, -1/15)
The general formula to find the slope through two points is given as
[tex]\begin{gathered} If\text{ points are \lparen x}_1,y_1)\text{ and \lparen y}_1,y_2) \\ Then \\ slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]So on substituting the values we have
[tex]\begin{gathered} Slope=m=\frac{-\frac{1}{15}-(-\frac{8}{3})}{-\frac{7}{2}-\frac{19}{2}}=\frac{-\frac{1}{15}+\frac{8}{3}}{-\frac{7}{2}-\frac{19}{2}} \\ \\ m=\frac{\frac{-1\times1+5\times8}{15}}{\frac{-7-19}{2}}=\frac{\frac{-1+40}{15}}{\frac{-26}{2}}=\frac{\frac{39}{15}}{-\frac{13}{1}} \\ \\ m=\frac{39}{15}\times\frac{-1}{13}=-\frac{3}{15}=-\frac{1}{5} \end{gathered}[/tex]So the required slope passing through the given two points is -1/5.
Final answer -
Therefore the final answer is -1/5.Related Questions
The total cost of a jacket and shirt was $75.08 if the price of the jacket was $5.32 less than the shirt what was the price of the jacket
Answers
Let 'j' be the cost of the jacket and let 's' be the cost of the shirt. Then, if they cost $75.08, then we have the following expression:
[tex]j+s=75.08[/tex]since the price of the jacket was 5.32 less than the shirt, then, we have:
[tex]j=s-5.32[/tex]using this equation on the first equation, we get the following:
[tex]\begin{gathered} s-5.32+s=75.08 \\ \Rightarrow2s=75.08+5.32=80.40 \\ \Rightarrow s=\frac{80.40}{2}=40.20\rbrack \\ s=40.20 \end{gathered}[/tex]now that we have that the shirt costs $40.20, we can find the price of the jacket:]
[tex]j=40.20-5.32=34.88[/tex]therefore, the price of the jacket is $34.88 and the price of the shirt costs $40.20
Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Hello my child needs help with this question could someone help
Answers
Solution
We want to get why
[tex]\frac{3}{\text{ \lparen1/5\rparen}}\text{ is different from }\frac{\text{ \lparen1/5\rparen}}{3}[/tex]Reason 1: Commutation Law Does Not Hold For Division (or quotient)
Generally,
[tex]\frac{a}{b}\ne\frac{b}{a}[/tex]Reason 2: Actual Computation
First
[tex]\begin{gathered} \frac{3}{\text{ \lparen1/5\rparen}}=3\div\frac{1}{5} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=3\times\frac{5}{1} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=15 \end{gathered}[/tex]Secondly
[tex]\begin{gathered} \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\div3 \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\times\frac{1}{3} \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{15} \end{gathered}[/tex]It is now obvious that
[tex]\frac{3}{\text{ \lparen1/5\rparen}}\ne\frac{\text{ \lparen1/5\rparen}}{3}[/tex]at the rate shown in the table how many books were sold in 3 weeks
Answers
210 books were sold in 3 weeks
Explanation
Step 1
you can easily solve this by using a rule of three
number of weeks=1
sold books=70
then, the rate is
[tex]\text{rate}=\frac{70\text{ books}}{1\text{ we}ek}=70\text{ book}s\text{ per w}eek[/tex]Step 2
Let
x represents the number of books sold in 3 weeks,then the rate is
[tex]\text{rate}=\frac{x}{3\text{ w}eeks}[/tex]as the rates are equal
[tex]\begin{gathered} 70=\frac{x}{3} \\ Multiply\text{ both sides by 3} \\ 70\cdot3=\frac{x}{3}\cdot3 \\ x=210 \end{gathered}[/tex]I hope this helps you
Part BNow you’ll attempt to copy your original triangle using two of its angles:Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment, DE¯, parallel to the line segment you located on ∆ABC. You can draw DE¯ of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC.From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC.Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.Take a screenshot of your results, save it, and insert the image in the space below.
Answers
Step 1)
We used angles alpha and betta from the original triangle
Step 2)
Then,
Step 3)
Notice that the two triangles are similar due to the AAA postulate. (The length of DE is different than that of AB)
Simply this expression 4(1-3x)+7x-8
Answers
Answer:
-5x-4
Step-by-step explanation:
4(1-3x)+7x-8
Distribute the 4
4(1)+4(-3x)+7x-8
4-12x+7x-8
Combine like terms
-12x+7x+4-8
-5x-4
hopes this helps please mark brainliest
Can’t figure this fraction equation. 5/6 is the fraction getting divided by 2. Answer must be in the simplest form
Answers
Solution:
5/6 divided by 2, i.e.
[tex]\frac{5}{6}\div2[/tex]Applying the fraction rule
[tex]\begin{gathered} \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c} \\ =\frac{5\times\:1}{6\times\:2} \\ =\frac{5}{6\times\:2} \\ =\frac{5}{12} \end{gathered}[/tex]Hence, the answer is 5/12
During a hurricane evacuation from the east coast of Georgia, a family traveled 200 miles west. For part of the trip, they averaged 60 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time ct travel was 6 hours, how many miles did they drive at the reduced speed?
Answers
Given:
Total distanced traveled is 200 miles.
speed is 60 mph, but as the congestion got bad, they had to slow to 10 mph.
Time = 6 hours.
Let, x be the travel time at 60 mph
The equation is,
[tex]\begin{gathered} 60x+10(6-x)=200 \\ 60x+60-10x=200 \\ 50x=200-60 \\ 50x=140 \\ x=\frac{140}{50} \\ x=2.8 \end{gathered}[/tex]It mean at the speed of 60 mph, the distance traveled is,
[tex]60x=60(2.8)=168\text{ miles}[/tex]So, the distance traveled for the speed of 10 mph is,
[tex]200-168=32\text{ miles.}[/tex]Answer: The family traveled 32 miles at reduced speed.
write an express to 4× + 12 by coming like terms
Answers
the initial expression is:
[tex]4x+12[/tex]We can see that they have in common a factor of 4 so we can rewrite it like:
[tex]4(x+3)[/tex]Printer Paper Store normally sells laser paper for 89,99 per ream, It has a special, 1
ream free with the purchase of 2. If you buy 2 reams and get 1 free, what is your (a)
cost per ream, and (b) markdown per ream?
Answers
The required (a) cost per ream becomes 59.99 and (b) the markdown per ream is 30.
Given that,
Printer Paper Store normally sells laser paper for 89,99 per ream, It has a special, 1 ream free with the purchase of 2. If you buy 2 reams and get 1 free.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Cost of the 1 ream = 89,99
Cost of the 2 reams = 179.98
According to the question,
Cost of the 3 reams = 179.98
Cost of the one ream among the 3 reams = 179.88/3 = 59.99
markdown per ream = 89.99 - 59.99 = 30
Thus, the required (a) cost per ream becomes 59.99 and (b) the markdown per ream is 30.
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Latex paint sales for $25 per gallon and will cost you $175 to paint your room if each gallon will cover 330 ft.² how many square feet of wall space do you have in your room
Answers
The square feet of wall space in your room if paint cost $25 per gallon and will cost you $175 to paint the room is 2,310 square feet
What is the square feet of wall space in your room?Cost of latex paint per gallon = $25Total cost of paint = $175Square feet covered by each gallon = 330 ft.²Number of latex paint need to paint your room = Total cost of paint / Cost of latex paint per gallon
= $175 / $25
= 7 gallons
Number of square feet of wall space in your room = Number of latex paint need to paint your room × Square feet covered by each gallon
= 7 × 330
= 2,310 square feet
In conclusion, the square feet of wall space in your room is 2,310 square feet
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ХI went to the bank 4 times last week and withdrew a total of $160. What was theaverage amount withdrew each time? Write and solve an expression to find theanswer
Answers
Consider the equation 14 x 10^0.5w= 100.Solve the equation for w. Express the solution as a logarithm in base-10.W = _____ Approximate the value of w. Round your answer to the nearest thousandth.w ≈ _____
Answers
Solution:
Given;
[tex]14\cdot10^{0.5w}=100[/tex]Divide both sides by 14, we have;
[tex]\begin{gathered} \frac{14\cdot10^{0.5w}}{14}=\frac{100}{14} \\ \\ 10^{0.5w}=\frac{50}{7} \end{gathered}[/tex]Take the logarithm of both sides; we have;
[tex]\log_{10}(10)^{0.5w}=\log_{10}(\frac{50}{7})[/tex]Applying logarithmic laws;
[tex]0.5w=\log_{10}(\frac{50}{7})[/tex]Divide both sides by 0.5;
[tex]\begin{gathered} \frac{0.5w}{0.5}=\frac{\log_{10}(\frac{50}{7})}{0.5} \\ \\ w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \end{gathered}[/tex](b)
[tex]\begin{gathered} w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \\ \\ w\approx1.708 \end{gathered}[/tex]Stats, Practice Test 5-6 ) There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?
Answers
Step 1: Problem
There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?
Step 2: Concept
Find the principal P that corresponds to the future value F= $1,300 under r = 4% interest compounded daily for t = 3 years. Round your final answer to two decimal places.
Answers
The formula to find the principal is:
[tex]FV=P(1+i)^n[/tex]Where
FV is future value
P is principal
i is the rate of interest
n is the time frame
Given,
FV = 1300
i = r = 4%, or 4/100 = 0.04
n = t = 3
Plugging into formula and solving gives us:
[tex]\begin{gathered} FV=P(1+i)^n \\ 1300=P(1+0.04)^3 \\ 1300=P(1.04)^3 \\ P=\frac{1300}{1.04^3} \\ P=1155.695 \end{gathered}[/tex]Rounding to 2 decimal places:
$1155.70
Pythagorean Theorem Task Card #1 A pool table is 9 feet long and 5 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket? Round to the nearest tenth.
Answers
A right triangle is made where the two legs are 9 ft (a) and 5 ft (b), and we have to find the hypotenuse (c). Using Pythagorean Theorem:
c² = a² + b²
c² = 9² + 5²
c² = 81 + 25
c = √106
c ≈ 10.3 ft
A construction crew built 1/2 miles of road in 1/6 days. What is the unit rate in simplest form.
Answers
For this problem, we are given the distance a construction crew built a road and the time in days it took to build it. We need to determine the unit rate for this problem, which is achieved by dividing the distance and time. We have:
[tex]\text{ unit rate}=\frac{\frac{1}{2}}{\frac{1}{6}}=\frac{1}{2}\cdot\frac{6}{1}=\frac{6}{2}=3\text{ miles per day}[/tex]The unit rate is 3 miles per day.
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 4
percentage points with 95% confidence if
(a) he uses a previous estimate of 38%?
(b) he does not use any prior estimates?
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) n =
(b) n=
(Round up to the nearest integer.)
(Round up to the nearest integer.)
Answers
The required sample sizes for the confidence intervals are given as follows:
a) Estimate of 38%: 566.
b) No estimate: 601.
How to obtain the required sample sizes?The margin of error for a confidence interval of proportions, using the z-distribution, is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The parameters of the equation are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The desired margin of error in this problem is of:
M = 0.04.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For item a, the estimate is of [tex]\pi = 0.38[/tex], hence the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.38(0.62)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.38(0.62)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.38(0.62)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.38(0.62)}}{0.04}\right)^2[/tex]
n = 566.
For item b, when there is no estimate, we use [tex]\pi = 0.5[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
n = 601.
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the product of 8 and a number increased by 17
Answers
You have the following stament:
The product of 8 and a number increased by 17
In order to write the previous statment in an algebraic way, you take into account that "the product of 8 and a number" means the multiplication of 8 and a variable, which is "increased" by 17. That is, number 8 is multiplying the sum of a variable and 17.
Thus, you have:
The product of 8 and a number increased by 17:
8(x + 17)
The function f(x) = -x2 - 4x + 5 is shown on the graph. What is the domain and range of this function?
Answers
Step 1
The domain includes all the x-values that fall within the function
Hence, the domain of this function is [ All real values of x]
Step 2
Find the range
The range includes all values of y that fall within the function
Hence the range of the function is [-∞, 9]
m/cour16121/quizzes/2919544/take22A totem pole casts a shadow 45 feet long at the same time that a 6-foot-tallmancasts a shadow that is 3 feet long. Find the height of the totem pole.Height of the totemfeetHint: set a proportion like this oneshadow totemshadow manactual height totem actual height manucation
Answers
The totem pole with its shadow form a right triangle, and the same happens with the man and its shadow. Since it happens at the same time of the day, the "inclination" of the sunlight is the same for both, and those two triangles are similar, which means that their corresponding ratiso betweens sides are the same.
Using the hint given on the problem, we can estabilish the following equation for the height of the totem(let's call it h).
[tex]\frac{45}{h}=\frac{3}{6}[/tex]Now, we just need to solve for h.
[tex]\begin{gathered} \frac{45}{h}=\frac{3}{6} \\ \frac{45}{h}=\frac{1}{2} \\ \frac{h}{45}=2 \\ h=2\cdot45 \\ h=90 \end{gathered}[/tex]The height of the totem pole is 90 ft.
Consider the following function.f(x) = |x − 9|Find the derivative from the left at x = 9. If it does not exist, enter NONE.Find the derivative from the right at x = 9. If it does not exist, enter NONE.
Answers
The form of the derivative of the absolute equation is
[tex]\begin{gathered} f(x)=\lvert x-a\rvert \\ \frac{dx}{dy}=\frac{\lvert x-a\rvert}{x-a} \\ \frac{dy}{dx}=\frac{x-a}{\lvert x-a\rvert} \end{gathered}[/tex]For the given function
[tex]f(x)=\lvert x-9\rvert[/tex]We will find the derivative from the left at x = 9
[tex]\frac{dy}{dx}=\frac{x-9}{\lvert x-9\rvert}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dy}{dx}=\frac{9-9}{\lvert9-9\rvert} \\ \frac{dy}{dx}=\frac{0}{0} \end{gathered}[/tex]Then dy/dx does not exist (None)
The derivative from right at x = 9
[tex]\frac{dx}{dy}=\frac{\lvert x-9\rvert}{x-9}[/tex]Substitute x by 9
[tex]\begin{gathered} \frac{dx}{dy}=\frac{\lvert9-9\rvert}{9-9} \\ \frac{dx}{dy}=\frac{0}{0} \end{gathered}[/tex]Then dx/dy does not exist (None)
Kyra is participating in a fundraiser walk-a-thon. She walks 3 miles in 45 minutes. If she continues to walk at the same rate, determine how many minutes it will take her to walk 7 miles. Show how you found your answer.
Answers
3 milles ---> 45 minutes
7 miles ---> x minutes
then
[tex]\begin{gathered} 3\times x=7\times45 \\ 3x=315 \\ \frac{3x}{3}=\frac{315}{3} \\ x=105 \end{gathered}[/tex]answer: 105 minutes for walk 7 miles
The table gives a set of outcomes and their probabilities. Let A be the event "the outcom less than or equal to 2". Let B be the event "the outcome is a divisor of 3". Find P(AB). Outcome Probability 1 0.2 2 0.6 3 0.2
Answers
Given the table:
Outcome Probability
1 0.2
2 0.6
3 0.2
Let A be the event "the outcome less than or equal to 2.
Let B be the event "the outcome is a divisor of 3.
Let's find P(A ∩ B).
To find P(A ∩ B) let's first find P(A) and P(B).
Numbers less than or equal to 2 = 2 and 1
Outcomes less than or equal to 2 = P(2) or P(1)
Probability the outcome is less than or equal to 2 = P(A) = 0.2 + 0.6 = 0.8
Divisor of 3 = 1 and 3
Outcome is a divisor of 3 = P(1) and P(3)
Probability the outcome is a divisor of 3 = P(B) = 0.2 x 0.2 = 0.04
To find P(A ∩ B), we have:
P(A ∩ B) = P(A) x P(B) = 0.04 x 0.8 = 0.032
ANSWER:
0.032
I need help with my math
Answers
Given the question
4 (3x -6) + 2x + 18
To simplify the above expression, we will observe the following steps
Step 1: Expand the parenthesis (bracket)
[tex]\begin{gathered} 4(3x-6)+2x+18 \\ \Rightarrow4\times3x-\text{ 4x6 + 2x+18} \\ \Rightarrow12x\text{ -24+2x +18} \end{gathered}[/tex]Step 2: Simplify the expression by collecting like terms
[tex]\Rightarrow\text{ 12x +2x -24+18}[/tex][tex]14x\text{ -6}[/tex]Answer = 14x - 6
If triangle ABC is reflected across the y-axis, what are the coordinates of C?O A. (5,-3)O B. (-5, 3)O C. (3,-5)O D. (-3, -5)
Answers
B) (-5,3)
1) We need to locate the vertex location since the point here is to find the coordinates of C'. So, let's do it before applying the required transformation.
C(5,3)
2) Since we want to know the coordinates of C', and there was a reflection across the y-axis, we can write the following:
C(5,3) Rule (x,y) --> (-x,y) C'(-5,3)
3) Thus, the answer is (-5,3)
what type from f x to g x on the graph ?
Answers
When looking at the graph, we can discard two of the options, rotation (as they don't have any intersection, there are no possibilities of having a rotation axis) and reflection. It occured a translation. To know which of the options is correct, we can see the y intercepts of both lines. The y intercept of f(x) is 0 and the y intercept of g(x) is -4, which means that the line was translated down 4 units.
It means the right answer is D. Vertical Translation down 4 units.
If Vegetable Oil costs $3.47 for 48 ounces, what is the cost of 1 tablespoon of vegetable oil?
A) 7 cents, B) 70 cents C) 4 cents D) $1.40 E) 25 cents
Answers
If Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.
1 tablespoon has alomst 0.5 ounce
If Vegetable Oil costs $3.47 for 48 ounces
Cost of 48 ounces of vegetable oil = $3.47
cost of 1 ounce of vegetable oil = $ 3.47 / 48 = $0.0722
cost of 0.5 ounce of vegetable oil = $0.0722/2 = $0.0361
cost of 0.5 ounce of vegetable oil is $0.0361
1 dollar = 100 cents
0.0361 dollar = 0.0361 x 100 cents
0.0361 dollar = 3.6 cents = 4 cents (approx)
Therefore, if Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.
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The table lists recommended amounts of food to order for 25 party guests. Amanda and Syndey are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should Amanda and Syndey order for a graduation party with 45 drop-in guests?
Answers
Amanda and Sydney are hosting a graduation party for 40 guests.
Also, they have 45 drop-in guests (each of these will count as half a guest).
Then, the total number of guests is:
[tex]40+\frac{45}{2}=\frac{40\times2+1\times45}{1\times2}=\frac{80+45}{2}=\frac{125}{2}[/tex]The table shows the recommended amounts of food for 25 party guests:
Fried Chicken: 24 pieces
Deli meats: 4 1/3 pounds
Lasagna: 10 3/4 pounds.
Let's find the proportion for 125/2 guests:
a. Fried chicken:
[tex]\begin{gathered} \frac{24\text{ pieces}}{25\text{ guests}}=\frac{x\text{ pieces}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ 24\times\frac{125}{2}=x\times25 \\ \frac{24\times125}{2}=x\times25 \\ 1500=x\times25 \\ \text{Divide both sides by 25} \\ \frac{1500}{25}=\frac{x\times25}{25} \\ \text{Simplify} \\ 60=x \end{gathered}[/tex]Then, they'll need to order 60 units of fried chicken for the party.
b. Deli meats:
Start by converting the mixed number 4 1/3 into a fraction:
[tex]4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{12+1}{3}=\frac{13}{3}[/tex]Now, apply proportions:
[tex]\begin{gathered} \frac{13/3\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{13}{3}\times\frac{125}{2} \\ x\times25=\frac{13\times125}{3\times2} \\ x\times25=\frac{1625}{6} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{1625}{6\times25}=\frac{1625}{150}=\frac{65}{6} \\ \text{Simplify} \\ x=\frac{65}{6} \end{gathered}[/tex]You also can convert this fraction into a mixed number:
[tex]\begin{gathered} \text{When you divide 65/6 you obtain a quotient of 10 and remainder 5.} \\ \text{Then the whole part is 10 and the fraction is 5/6} \\ \frac{65}{6}=10\frac{5}{6} \end{gathered}[/tex]Then, they'll need to order 10 5/6 pounds of deli meats for the party.
c. Lasagna
Convert the mixed number to fraction:
[tex]10\frac{3}{4}=\frac{10\times4+3}{4}=\frac{40+3}{4}=\frac{43}{4}[/tex]Apply proportions:
[tex]\begin{gathered} \frac{43/4\text{ pounds}}{25\text{ guests}}=\frac{x\text{ pounds}}{125/2\text{ guests}} \\ \text{Set the product of the diagonals equal to each other:} \\ x\times25=\frac{43}{4}\times\frac{125}{2} \\ x\times25=\frac{43\times125}{4\times2} \\ x\times25=\frac{5375}{8} \\ \text{Divide both sides by 25} \\ \frac{x\times25}{25}=\frac{5375}{8\times25}=\frac{5375}{200}=\frac{215}{8} \\ \text{Simplify} \\ x=\frac{215}{8} \end{gathered}[/tex]You also can convert this fraction into a mixed number:
[tex]\begin{gathered} \text{When you divide 215/8 you obtain a quotient of 26 and remainder 7.} \\ \text{Then the whole part is 26 and the fraction is 7/}8 \\ \frac{215}{8}=26\frac{7}{8} \end{gathered}[/tex]Then, they'll need to order 26 7/8 pounds of lasagna for the party.
Parallelogram ABCD was translated to parallelogram AB'C'D'.How many units and in which direction were the x-coordinates of parallelogram ABCD moved?
Answers
Number of units: 7
Direction: left of the x coordinate
Explanation:Given:
Parallelogram ABCD was translated to parallelogram AB'C'D'
To find:
the number of units and in which direction were the x-coordinates of parallelogram ABCD moved
To determine the number of units, we will use the diagram below:
From A to A', B to B', C to C' and D to D', the number of units for the movement in the x coordinate is 7. The vertical position didn't change. This means to movement in the coordinate.
The parallelogram ABCD was moved to the left of the x axis to get parallelogram A'B'C'D'
Number of units: 7
Direction: left of the x coordinate
7 units to the left
What is the value of u? H 88 U +64 I K к 88 50 J U =
Answers
HK = KJ
So:
u+64 = 5u
Solve for u
Combine like terms:
64 = 5u-u
64= 4u
Divide both sides by 4
64/4 =4u/4
16 = u