Answers
y=4-2x and 4x+2y = 5 can be rewritten as:
y = -2x + 4
2y = -4x + 5
Multiply all 3 terms of the first eq'n by 2: 2y = -4x + 8
Note that 2y = -4x shows up in both equations. This is enuf info on which to conclude that the 2 lines have the same slope.
Related Questions
how do you solve for x and y
Answers
⇒ Ratio of the smaller triangle : larger triangle = 1 : 2
x = 34 x 2 = 68 units
Angles in a triangle sum up to 180:
y = 180 - 76 - 41 = 63°
Answer : x = 68 units, y = 63°
An event is three times as likely as its complement. What is the probability of the event?
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C = complement of event E
Since the events are complementary, this means P(E)+P(C) = 1
We know that P(E) = 3*P(C) since "an event is three times as likely as its complement"
So we can replace P(E) with 3*P(C) and then isolate P(C)
P(E) + P(C) = 1
3*P(C) + P(C) = 1
4*P(C) = 1
P(C) = 1/4
The probability of the complementary event is 1/4
So the probability of the original event is 3/4 (three times 1/4)
Answer: 3/4
note: in decimal form, 3/4 = 0.75
Dadas las funciones f(x) = x + 3, g(x)= x(cuadrada)+ 5x + 6,r(x) = x+2, s(x) = x(cuadrada) - 3x - 10
Determina (g(x)) (s(x))
Answers
a model car has been made using a scale factor if 1.5 inches:3 feet. If the actual car is 13.75 feet long, what is the length of the model?
Answers
To find the length of the model car, set up a proportion and cross multiply.
Explanation:To find the length of the model car, we need to use the scale factor given. The scale factor is 1.5 inches:3 feet. This means that for every 1.5 inches in the model, there are 3 feet in the actual car.
Given that the actual car is 13.75 feet long, we can set up a proportion:
1.5 inches / 3 feet = X inches / 13.75 feet
Cross multiplying, we get:
1.5 inches * 13.75 feet = 3 feet * X inches
Simplifying, we find that the length of the model car is approximately 6.88 inches.
factor 1/5 out of 1/5x+29/5
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we have 1/5 x+ 29/5= 1/5 x+ 1/5 x29= 1/5(x+29)
And we have done
Have a good day
To factor 1/5 out of the algebraic expression 1/5x + 29/5, we remove the common term 1/5. This leaves us with 1/5 * (x + 29), not altering the value of the original expression.
Explanation:To factor 1/5 out of 1/5x+29/5, we first need to understand what factoring entails. Factoring is basically expressing an algebraic equation as a product of its factors.
Step 1: Look at the expression '1/5x + 29/5'. We can see that '1/5' is common in both terms.
Step 2: Factor out the common term, which in this case is '1/5'.
So the expression '1/5x + 29/5' factored out would be '1/5 * (x + 29)'. Throughout this process, we have not changed the value of the original expression, only rewritten it in a different form.
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A store charges $280 for coat. This price is 40 percent more than the amount it cost the store to buy. At the end-of-season sale, store employees may purchase any remaining coats at 30 percent off the store’s cost. How much would it cost an employee to purchase the coat at the sale?
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it would cost an employee $140 to purchase the coat at the sale.
Let's break down the problem step by step:
1. The store charges $280 for the coat, which is 40% more than the amount it cost the store to buy. This means that the store's cost (let's call it ( C )) can be found by first determining what 100% of the cost is (since $280 is 140% of the cost, as 100% + 40% = 140%). We can set up the equation:
[tex]\[ 140\% \text{ of } C = $280 \]\[ 1.4C = $280 \]\[ C = \frac{$280}{1.4} \]\[ C = $200 \][/tex]
So, the store's cost for the coat is $200.
2. At the end-of-season sale, store employees can purchase any remaining coats at 30% off the store’s cost. This means they pay 70% of the store's cost. We can calculate this as:
[tex]\[ 70\% \text{ of } $200 = 0.7 \times $200 = $140 \][/tex]
Therefore, it would cost an employee $140 to purchase the coat at the sale.
Find the nonpermissable replacement for x in this expression x^2/-4x-8
Answers
The explanation is shown below:
1. You have the following expresssion given in the problem above:
x²/-4x-8
2. By definition, the nonpermissible replacement for x in this expression, is the value of x that makes the denominator equal to zero.
3. Keeping this on mind, you have:
-4x-8=0
-4x=8
x=8/-4
x=-2
x²/-4x-8= (-2)²/(-4)(-2)-8= 4/8-8= 4/0
Therefore, as you can see, the answer is x=-2.
what is the equivalent equation 2x-10/25-x^2
Answers
A miner descended 1200 feet into a mine. While in the mine, he then rose 450 feet and then descended 150 feet. What was the miner's net gain or loss in altitude? 1500 ft 600 ft –1500 ft –900 ft
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If he rose 450:
1200 + 450 = 1650
If he descended 150:
1650-150 = 1500
1500 feet, his net gain is -300 feet, his loss is 300 feet
Tshonda is buying a laptop computer. she will pay 8% sales tax on the price before any rebates. where will she get a better buy?
XYZ-Tronic
price - $629
mail-in rebate $150
TEC-U-COMP
price - $649
discount 25% off
Answers
The above me is clearly wrong. However, the reason I'm not going to post an actual answer is because this post is over 2 years old and there is a good chance the they aren't even in school anymore.
A rectangle has a perimeter of 34 cm in an area of 52 cm squared it's length is 5 more than twice its width write and solve the system of equations to find the dimensions of the rectangle
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Let [tex] l [/tex] be the length and [tex] w [/tex] be the width of the rectangle.
Given perimeter of the rectangle
[tex] 2(l+w)=34 \; l+w=17[/tex]
Area of the rectangle is
[tex] lw=52 [/tex]
Also length is 5 more than twice its width,
[tex] l=2w+5 [/tex]
From the above equations
[tex] (l-w)^2=(l+w)^2-4lw=17^2-4*52=81\\
l-w=9,\; since \; l>w [/tex]
Now [tex] 2l=9+17=26\;,l=13,w=4 [/tex]
The dimensions of the rectangle are length [tex] l=13 [/tex], and width [tex] w=4 [/tex].
y + 2.3 = 0.45x
–2y = 4.2x – 7.8
(2.4, –1.2)
(–1, 2.5)
no solution
infinitely many solutions
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2y + 4.6 = 0.90x
2y - 0.90x = -4.6
second equation is
-2y - 4.2x = -7.8
Adding:-
-5.1x = -12.4
x = 2.4
-2y = -7.8 + 4.2(2.4) = 2.3
x = -1.2
Answer x = 2.4 and y = -1.2
Its choice A
Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular VIP section. What is the maximum area that they can fence off? A) 3,200 square feet B) 6,400 square feet C) 12,800 square feet D) 24,000 square feet
Answers
l+w= 160
l=160-w
lw=A
160w-w²= A
w²-160w+A=0
w max= -b/(2a)= 160/2= 80 ft
Max A = 160(80)-(80)²= 6400 ft²
So B is correct
Answer:
B
Step-by-step explanation:
A ladder is leaning on a fence and it reaches up a wall 20 feet high. The fence is 10 feet from the wall and the base of the ladder is 12 feet from the fence. How tall is the fence, in feet?
Answers
Answer:
10.9 feetStep-by-step explanation:
The wall, fence and ladder form similar right triangles as pictured
Use the ratio of corresponding sides to solve for x, the fence height
x/12 = 20/(10+12)x/12=20/22x/12 = 10/11x = 12*10/11x = 10.9 feetThe fence is 10.9 feet tall
Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is , and the probability that he goes 3 days is .
Answers
For a probability distribution the expected value is the summation of product of probabilities with their respective data values. Let x be the probability that Jackson goes gym for 2 days and y be the probability that he goes gym for 3 days.
For the given case we have following values and their probabilities:
0 : 0.1
2 : x
3 : y
So the expected value will be = 0(0.1) + 2(x) + 3(y)
Expected value is given to be 2.05. So we can write the equation as:
2x + 3y = 2.05 (Equation 1)
Also for a probability distribution, the sum of probabilities must always equal to 1. So we can set up the second equation as:
0.1 + x + y = 1
x + y = 0.9 (Equation 2)
From Equation 2 we can write the value of x to be x = 0.9 - y. Using this value in equation 1, we get:
2(0.9 - y) + 3y = 2.05
1.8 - 2y + 3y = 2.05
1.8 + y = 2.05
y = 0.25
Using the value of y in equation 2 we get value of x to be 0.65
Therefore we can conclude that:
The probability that Jackson goes to gym for 2 days is 0.65 and the probability that he goes to gym for 3 days is 0.25
He goes to the gym 0, 2, or 3 days per week.
Let's assume P(0 days)=p, P(2 days)=q, and P(3 days) = r.
So, p+q+r = 1
E(X)= E(x=0)*P(0 days) + E(x=2)*P(2 days) + E(x=3)*P(3 days)
E(X) = 0*p + 2*q + 3*r = 2q + 3r
Given is the value of P(0 days) = p = 0.1
Given is the expected value of number of days is E(X) = 2.05
Therefore, we have 0.1 + q + r = 1 and 2q + 3r = 2.05
Or, q + r = 0.9 and 2q + 3r = 2.05
Solving the two equations :-
(2q+3r)-2*(q+r) = 2.05-2(0.9)
r = 0.25
q = 0.65
Therefore, P(2 days) = 0.65 and P(3 days) = 0.25
What is the length of the diagonal of rectangle abcd ?
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Three times the sum of a number and six
Answers
Answer:
3(x+6)
Step-by-step explanation:
3+45456688888876777888888
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Hope this helps! :)
Sarah bought a 16 ounce jar of strawberry jam for $3.20. What is the unit price
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3.20/16=0.2, so the unit price is $0.20.
I hope this helps!
-Raiden
For several months, a restaurant manager collected data on the number of people at a table (p) and the total bill, in dollars (d). She found that there is a positive linear association between p and d that is best modeled by the equation
d = 15.7p + 2.0.
What statement is true?
The model predicts that the average total bill for a table is $15.70.
The model predicts that for each additional 2 people at a table, the total bill increases by $15.70.
The model predicts that the average bill for any table with 2 people is $15.70.
The model predicts that for each additional person at a table, the total bill increases by $15.70.
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help please 38 points
Answers
A map has a scale of 1/2 inch to 4 miles. The shortest distance between two cities on the map measures 8 inches. If d represents the shortest distance between the two cities, what is d?
A. 16 mi.
B. 32 mi.
C. 64 mi.
D. 72 mi.
Answers
D = 64 mi.
Answer:
C
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Alice paid $17.00 for 2 beads for her bracelet. Then she paid $42.50 for 5 more of the same kind of beads for her bracelet. Which is the price of one bead?
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Answer:
Step-by-step explanation:
DF bisects EDG find the value of x
Answers
so EF = FG
5x + 24 = 9x
4x = 24
x = 6
answer
D. last one
6
PLEASE HELP ASAP!!!!!
Answers
What is QR to the nearest tenth
Answers
Finding the median in a data set?
Answers
Find the number in the middle.
If there are two numbers in the middle, find the mean of those two numbers.
How is the degree of the product of two polynomials p(x) and q(x) related to the degrees of p(x) and q(x)?
Answers
The degree of the product of two polynomials p(x) and q(x) is equal to the sum of the degrees of p(x) and q(x).
Explanation:The degree of the product of two polynomials p(x) and q(x) is related to the degrees of p(x) and q(x) by the following rule:
The degree of the product is equal to the sum of the degrees of the two polynomials.
For example, if p(x) is a polynomial of degree m and q(x) is a polynomial of degree n, then the product p(x)q(x) will be a polynomial of degree m+n.
9. Find the constant of variation, k, for y= –8 when x = 12.
show your work
Answers
Since you have not provided the relation between the two variables, I will provide the answer in both cases.
1- In case x was directly proportional to y:
This means that as x increases, y increases and vice-versa.
Translating this into an equation, we would get the following:
y = kx
where k is the constant of proportionality.
Now, we are given that:
y = -8 at x = 12
Substitute with these givens in the above equation to get k as follows:
-8 = k * 12
k = -8/12
k = -2/3
2- In case x was inversely proportional to y:
This means that as x increases, y decreases and vice-versa.
Translating this into an equation, we would get the following:
y = k / x
where k is the constant of proportionality.
Now, we are given that:
y = -8 at x = 12
Substitute with these givens in the above equation to get k as follows:
-8 = k / 12
k = -8*12
k = -96
Hope this helps :)
A consult needs to make at least $600 this week she earns $120 for each new piece and $60 for each review which of the following inequalities represents the possible combinations of reviews and new written pieces that she must complete
Answers
You are also told that each new piece = $120 and each review = $60. Let's use variables n = new piece and r = review. (You might be given different variables for your answer choices). That means the total money made from a combination of new pieces and reviews is:
120n (money made from each new piece times n number of new pieces) + 60r (money made from each review times r number of reviews).
Put that all together to get your inequality:
120n + 60r ≥ 600
-----
Answer: 120n + 60r ≥ 600
The possible combinations of reviews and new written pieces can be represented by the inequality 60r + 120n ≥ 600.
Explanation:To represent the possible combinations of reviews and new written pieces, we can use the variables r for reviews and n for new pieces.
The total earnings can be calculated by multiplying the number of reviews by $60 and the number of new pieces by $120, and this must be greater than or equal to $600.
Therefore, the inequality that represents the possible combinations is 60r + 120n ≥ 600.
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