What is the solution to the system of linear equations?
6x+7y=59
4x+5y=41 how do you do it
Answer:
The correct answer is 4, 5 :)
Step-by-step explanation:
A system of linear equations can be solved by elimination, substitution or using graphs.
The values of x and y for [tex]6x + 7y= 59[/tex] and [tex]4x + 5y =41[/tex] are 4 and 5, respectively.
Given
[tex]6x + 7y= 59[/tex]
[tex]4x + 5y =41[/tex]
Make x the subject in [tex]4x + 5y =41[/tex]
[tex]4x = 41 - 5y[/tex]
Divide by 4
[tex]x = \frac 14(41 - 5y)[/tex]
Substitute [tex]x = \frac 14(41 - 5y)[/tex] in [tex]6x + 7y= 59[/tex]
[tex]6 \times \frac 14(41 - 5y)+ 7y = 59[/tex]
[tex]\frac 32(41 - 5y)+ 7y = 59[/tex]
Multiply through by 2
[tex]2 \times \frac 32(41 - 5y)+ 2 \times 7y = 2 \times 59[/tex]
[tex]3(41 - 5y)+ 14y = 118[/tex]
Open brackets
[tex]123 - 15y+ 14y = 118[/tex]
Collect like terms
[tex]- 15y+ 14y = 118 - 123[/tex]
[tex]-y = -5[/tex]
[tex]y = 5[/tex]
Substitute [tex]y = 5[/tex] in [tex]x = \frac 14(41 - 5y)[/tex]
[tex]x = \frac 14(41 - 5 \times 5)[/tex]
[tex]x = \frac 14(41 - 25)[/tex]
[tex]x = \frac 14(16)[/tex]
[tex]x = 4[/tex]
Hence, the solution to the system of linear equations is:
[tex]x = 4[/tex]
[tex]y = 5[/tex]
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The Ye Ol' Sandwich Shop sells 4 different sandwiches, 6 different drinks, and 3 different desserts. How many different orders could you place if you decided to buy a sandwich and a drink?
A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?
5
12
13
Answer:
r = 13
Step-by-step explanation:
The radius of a circle that its center at the origin, and passes through point (5, -12) is 13 units
How to determine the length of the radius?The given parameters are:
Center, (a,b) = (0,0)Point, (x,y) = (5,-12)The length of the radius is calculated using:
[tex]r = \sqrt{(x - a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(5 - 0)^2 + (-12 - 0)^2}[/tex]
Evaluate
[tex]r = \sqrt{169}[/tex]
Solve the square root
r = 13
Hence, the radius is 13 units long
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A rectangle of area 350 square feet is 14 times as wide as it is long. Find its length and width
if x and y are both negative when is x-y positive
Simplify. −64x6y9−−−−−−−√3 assume all variables are nonnegative.
Answer:
[tex]-4x^2y^3[/tex]
Step-by-step explanation:
We have been given an expression [tex]\sqrt[3]{-64x^6y^9}[/tex]. We are asked to simplify our given expression.
Applying radical rule [tex]\sqrt[n]{-a}=-\sqrt[n]{a}[/tex], when n is odd, we will get:
[tex]-\sqrt[3]{64x^6y^9}[/tex]
We can rewrite terms of our given expression as:
[tex]-\sqrt[3]{(4)^3(x^2)^3(y^3)^3}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]-4x^2y^3[/tex]
Therefore, simplified form of our given expression is [tex]-4x^2y^3[/tex].
1. If x-1 is a factor of p(x)=x^3-7x^2+15x-9, which of the following represents the complete factorization for p(x)?
A. (x-3)(x+4)(x+1)
B. (x-3)(x-3)(x-1)
C. (x-3)(x+3)(x-1)
D. (x-3)(x+3)(x+1)
2. The point (1,0) lies on the graph of p(x)=x^4-2x^3-x+2
True or false
Answer:
1. Option B is the correct answer.
2. The point (1,0) lies on the graph of p(x)=x⁴-2x³-x+2.
Step-by-step explanation:
1. Dividing x³-7x²+15x-9 with (x-1).
[tex]\frac{x^3-7x^2+15x-9}{x-1}=x^2-6x+9[/tex]
Factorizing x²-6x+9 we will get
x²-6x+9 = (x - 3)(x-3)
x³-7x²+15x-9 = (x-1)(x - 3)(x-3)
Option B is the correct answer.
2. We have p(x)=x⁴-2x³-x+2
That is y = x⁴-2x³-x+2
We have coordinates (1,0), substituting
y = 1⁴-2 x 1³-1+2 = 0
So when we are substituting x value as 1 we are getting y as zero, so the point lies in curve.
How many terms are in the algebraic expression 11;; +3 ?
.help me with this please. thank you
find the quotient.
-7 ÷ 14/3.
a. -2/3
b. -98/3
c. -1/2
d. -3/2
To find the quotient of -7 ÷ 14/3, simplify the fraction 14/3 to 42/3 and then divide -7 by 42/3. The quotient is -1/2.
Explanation:To find the quotient of -7 ÷ 14/3, we can simplify the fraction 14/3 to an improper fraction or a mixed number. Let's convert it to an improper fraction. We multiply the denominator (3) by the whole number (14) and add the numerator (0) to get the new numerator. This gives us 42/3. Next, we divide -7 by 42/3. When dividing by a fraction, we multiply by its reciprocal. So, -7 ÷ 42/3 is the same as -7 × 3/42. This simplifies to -21/42 which reduces to -1/2.
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Solve each problem and write your answer in scientific notation
The sides of ABC are 30 units, 40 units, and 60 units in length. If the corresponding sides of XYZ are r times as long as the sides of ABC, which expression gives the perimeter of XYZ? 130r 3 x 130r
John paid $100 for renting a canoe for 5 hours. Which graph shows the relationship between the cost of renting a canoe for different hours?
Answer:
The first one :)
Step-by-step explanation:
subtract 6/8 - 1/4 enter your answer in the box below as a fraction in lowest terms using the slash ( / ) as the fraction bar
The difference of the given fractions is 1/2.
Given that, 6/8 - 1/4.
Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.
Here, 6/8 - 1/4
= 6/8 - 2/8
= (6-2)/8
= 4/8
= 1/2
Therefore, the difference of the given fractions is 1/2.
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what is the converse of the linear pairs theorem
Simplify 3(3y + 2) + 8y. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
23y
–17y + 2
17y + 6
–17y + 6
PLEASE HELP on these problems! I really need the help and these are due in a few hours. Very urgent. I would really appreciate the help, so please help!!!
1. If f(x) = a(r)^x is an example of exponential decay, what must be the value of a and r?
2. The population of Greenfield was 52,500 at the beginning of 1980. Its population steadily decreased by 2.5% per year from 1980 through 1990. What is the population of Greenfield at the end of 1990?
3. If g(x) is the inverse of f(x) - 2x + 1, find a point on g(x) for which both coordinates are positive integers less than 10.
The length is 5 units more than the width. The perimeter is 9 times the width. Find the length and width of the rectangle. Can you also include the steps thanks!
The length, width, and perimeter of the rectangle are 7 units, 2 units, and 18 units.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
Let the width of the rectangle be represented by x. The length is 5 units more than the width. The perimeter is 9 times the width. Therefore, we can write,
Width = x
Length = 5 + x
Perimeter = 9x
Now, the length, width, and perimeter of the rectangle together can be written as,
Perimeter = 2(Length + Width)
9x = 2[(5+x) + x]
9x = 2(5 + x + x)
9x = 2(5 + 2x)
9x = 10 + 4x
9x - 4x = 10
5x = 10
x = 10/5
x = 2
Further, the dimensions can be written as,
Width = x = 2 units
Length = 5 + x = 2 + 5 = 7 units
Perimeter = 9x = 9(2) = 18 units
Hence, the length, width, and perimeter of the rectangle are 7 units, 2 units, and 18 units.
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what are three ways to name a line with 5 points?
Solve the equation n times 50 equals 5000 explain your solution
What is the length of TW¯¯¯¯¯¯ ?
segment T W with point U between T and W. segment T U is marked congruent to segment U W. segment T U is labeled as 16 units long.
Enter your answer in the box.
The length of TW of the given Line segment is; 32
How to find the length of a Line segment?From the given line segment with partition, we can see that;
Segment TU = 16
From the partition, we see that;
Segment TU is equal to Segment UW. Thus;
TU = UW = 16
Thus;
TW = TU + UW
TW = 16 + 16
TW = 32
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−65y+19<−2y+41 solve for Y please
Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. Apply the product rule and isolate dy/dx by moving terms.
Explanation:To find dy/dx by implicit differentiation, we'll differentiate both sides of the equation with respect to x. Let's start by differentiating y cos x = 5x2 + 3y2:
Using the product rule, we have: dy/dx * cos x + y * (-sin x) = 10x + 6y * dy/dx
Next, isolate dy/dx by moving terms:
dy/dx * cos x - 6y * dy/dx = 10x - y * (-sin x)
dy/dx * (cos x - 6y) = 10x + y * sin x
dy/dx = (10x + y * sin x) / (cos x - 6y)
What will the equation be if mowing need help. I need my lawn mowed every week from June through the middle of July. I will pay 35 dollars for each mowing for 7 weeks
the water level of a pond drops an inch every 7 days without rain how many days will it take the ponds water level to drop by 12 inches
1 inch in 7 days
multiply 7 by 12
7 *12 = 84 days
Which logical form represents this statement?
Either it is not cold today or I am wearing woolen coat.
p : It is cold today. q : I am wearing woolen coat.
~p ∧ ~q
~p ∧ q
~p ∨ q
~(p ∨ q)
2v+46=8(v-1)
I got -54/10 which I know is wrong. Please help.
What is the measure of ∠B?
Ken is making gift bags for a party. He has 64 colored penes and wants to put the same number in each bag. How many bags will ken make if he puts 4 in each bag?
Use the drop-down menus to identify the values of the parabola.
Vertex = ____
Domain = {x| ____ }
Range = {y| y ≤ ____ }
The answer is
Vertex: 0,4
Domain: x is a real number
Range: 4
:D
Answer:
Vertex - (0,4)
Domain - [tex]D=[x|x\in\mathbb{R}][/tex]
Range - [tex]R=[y|y\leq 4][/tex]
Step-by-step explanation:
Given : The graph of a parabola
To find : The values of the parabola - Vertex ,Domain and Range
Solution :
To identify the vertex the given parabola given by equation
[tex]y=-x^2+4[/tex]
Vertex is given by [tex]y=a(x-h)^2+k[/tex]
where (h,k) are the vertex.
Comparing with equation,
Vertex is (h,k)=(0,4)
Domain is the set of value where function is defined.
The domain of given function is all real numbers.
[tex]D=[x|x\in\mathbb{R}][/tex]
Range is the set of value that corresponds to the domain.
[tex]R=[y|y\leq 4][/tex]