Answer: I just took the test and the answer is Student should show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.
Step-by-step explanation:
The solution for the given system of linear equations is (32/69, -10/23).
The given system of equations are 3x-6y=4 and 6x+11y=-2.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here,
3x-6y=4 ---------(I) and 6x+11y=-2 ---------(II)
Multiply equation (I) by 2, we get
6x-12y=8 ---------(III)
Subtract equation (III) from (II), we get
6x+11y-(6x-12y)=-2-8
⇒ 23y=-10
⇒ y=-10/23
Substitute y=-10/23 in (I), we get
3x-6(-10/23)=4
⇒ 3x+60/23=4
⇒ 3x=4-60/23
⇒ x=32/69
So, solution is (32/69, -10/23)
Therefore, the solution for the given system of linear equations is (32/69, -10/23).
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Write the equation x2+24x+60=0 in the form (x+p)2=q
Answer:
(x+12)^2=84
Step-by-step explanation:
x^2+24x+60=0
x^2+24x=-60
x^2+24x+(24/2)^2=-60+(24/2)^2
(x+24/2)^2=84
(x+12)^2=84 (ans)
14. Find the midpoint of the line segment with the endpoints located at (-3, 8) and (-8, 2).
A. (-13, -4)
B. (2.5, 3)
C. (2.5, -3)
D. (-5.5, 5)
the mid point of ab m(1,-1). if the coordinates of a are (7,-4) what are the coordinates of b
9514 1404 393
Answer:
b = (-5, 2)
Step-by-step explanation:
b = 2m - a = 2(1, -1) -(7, -4) = (2-7, -2+4)
b = (-5, 2)
__
About the formula
The midpoint is given by the formula ...
m = (a+b)/2
Solving for b gives ...
b = 2m -a . . . as above
A manufacturer produces 950 light bulbs per
day. Write an equation to find the number of
bulbs b the manufacturer makes in any
number of days d.
Answer:
b =950d
Step-by-step explanation:
The manufacturer makes 950 bulbs a day. So, you have to multiply the number of days by 950 to get the number of bulbs made. This can be written as an equation:
b = 950d
Hope this helps :)
An equation to find the number of bulbs b the manufacturer make in any number of days d will be written as b =950d.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a manufacturer produces 950 light bulbs per day.
The equation can be written as:-
b = 950d
The manufacturer makes 950 bulbs a day. So, you have to multiply the number of days by 950 to get the number of bulbs made. This can be written as an equation:
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How can real life problems involving one variable be modeled and solved?
Answer:
Writing an equation to model a real-world problem is often easier when you take the information given in the problem and express it in verbal form by using a few key words. This is very similar to translating verbal phrases into variable expressions. The difference is you will be translating a verbal sentence into an equation. Then, you can solve the equation using inverse operations.
Let’s look at an example.
Monica purchased a pair of tennis shoes that had this sticker on the bottom of the shoe.
$99.00$65.99
Use a verbal model to write and solve an equation to determine the amount of money Monica saved by purchasing the shoes on sale.
First, write a verbal model to represent the problem.
Verbal Model:
Sales Price+Amount Saved=Original Price
Next, name the variable.
Let ‘
s
’ represent the amount saved.
Next, solve the equation you have written. Remember an equation is like a balance scale. To keep the scale balanced, what you do to one side of the equation you must also do to the other side. When solving an equation your goal is to isolate the variable on one side of the equation and the numerical terms on the other side. This is done by performing inverse operations.
65.99+s=99.00
First, isolate the variable ‘
s
’ by subtracting 65.99 from both sides of the equation. Subtraction is the inverse of addition.
65.99−65.99+s=99.00−65.99
Next, simplify each side.
s=33.01
The answer is $33.01.
A variable can be any element that we can, in some way, change.
The general form of modeling and solving real life problems that involve one variable is:
Identify what the variable is and define it.Write the equation.Isolate the variable on one side of the equation.So for example, something that we can define with a variable is "How many of one type of item we can buy if we know its price"
For example, if we know that a shirt costs $10, then the price of x of these shirts is:
y = $10*x
Now, if you know how much money you have, you can use this equation to find how many shirts you can buy.
For example, you know that you have $20, then y = $20
$20 = $10*x
To solve this we need to isolate the variable on one side:
$20/$10 = x
2 = x
You can buy two shirts.
Now, the general form of modeling and solving real life problems that involve one variable is:
Identify what the variable is and define it.Write the equation.Isolate the variable on one side of the equation.If you want to learn more, you can read:
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Justin uses 2/3
of a gallon of paint to cover 1/12 of his bedroom wall.
How much paint is needed to cover the entire wall?
Answer
you would need 24/3 paint to cover the wall.
Step-by-step explanation:
and 24/3 simplified is 8/1.
so you will need 8/1 paint to cover the wall.
20000+8000000+4+3000+900
Answer:
80,023,904
Step-by-step explanation:
Just add all the numbers together.
Answer:
"8023904
Step-by-step explanation:
20 000 + 8 000 000=8020000
4+3000=3004
3004+900=3904
3904+ "8023904"
What is the volume of a cylinder with a height of 10 inches if the area of its base is 40 square inches?
400 in3
1,256 in3
4,000 in3
12,560 in3
Answer:
400 in³
Step-by-step explanation:
Height (h) = 10 in
Base Area [tex] \sf (A_B) [/tex] = 40 in²
Formula of Volume of Cylinder:
[tex] \boxed{ \bf{V = A_Bh}}[/tex]
By substituting values in the equation, we get:
[tex] \rm \longrightarrow V = 40 \times 10 \\ \\ \rm \longrightarrow V = 400 \: {in}^{3} [/tex]
Answer:
A
Step-by-step explanation:
What is the correct answer?
Step-by-step explanation:
id-8253381513
password-9999
Answer:
the correct answer is A. but dont trust me on this
Step-by-step explanation:
1/2,5/16,3/32,3/4,3/8 make it in least to greatest order plz
Answer:
3/32 , 5/16 , 3/8 , 1/2 , 3/4
Step-by-step explanation:
Multiply them to give them all a common denominator of 32
Answer:
3/32, 5/16, 3/8, 1/2, 3/4,
X+y=8 You can find more Solutions by replacing x with other values and then solving for Y. For example, let X = 6. What is y? ... the solutions of x+y=8 x is 5 and y is 3
Answer:
Step-by-step explanation:
x + y = 8 ⇔ y = - x + 8
If x = 6 , then y = - 6 + 8 = 2
( 6, 2 )
If x = 0 , then y = 0 + 8 = 8
(0, 8)
If x = 8 , then y = - 8 + 8 = 0
(8, 0)
find the mode of the following numbers:
7,4,3,5,6,3,3,2,4,3,4,3,4,3,3,3,3,2,2,4,3,5,4,3,4,3,4,3,1,2,3
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
3
I'll give brainliest please help
Answer:
x=15
Converse: If line x and y are parallel then angles on the same line are supplementary angles.
Step-by-step explanation:
Converse:
Let's start with the converse, so if line x and y are parallel then angles on the same line are supplementary angles. I'm not sure if that's the converse your teacher wants but my teacher taught me this.
Finding x:
Now we know that the angles are supplementary angles, that means if w add them together we get 180°. So our equation will be [tex]10x-22+3x+7=180[/tex]. Now we just solve it. We start by combining like terms, then adding the 15 to both sides, and lastly we divide the 13 to both sides and get...
[tex]10x-22+3x+7=180\\13x-15=180\\13x=195\\x=15[/tex]
x=15
can someone put
< or > for these questions pls
Answer:
2/3=6/9
5/24>1/6
Step-by-step explanation:
A food distributor conducts regular surveys of consumer spending on its products. The average weekly household spending (in dollars) on regular pasta and gluten-free pasta for each of 12 states was recorded. A scatterplot of spending on regular pasta versus gluten-free pasta is shown. Which of the following statements is true?
Graph shown below
A. Point (7.2, 10) is an outlier.
B. There is clear evidence of a negative association between spending on gluten-free pasta and regular pasta.
C. The equation of the least-squares regression line for this plot is approximately ŷ = 3.8 + two thirds times x.
D. The correlation for these data is r = 1.
E. The observation in the upper right corner of the plot is influential for the least-squares regression line.
Answer:
The equation of the least-squares regression line for this plot is approximately ŷ = 3.8 + two thirds times x.
Step-by-step explanation:
What is the equation of the line that passes through the point (6, 6) and has a slope
of o?
A line includes the points (-39,49) and (0,0). What is its equation in slope-intercept form?
Answer:
The equation in the slope-intercept form will be:
[tex]y=-\frac{49}{39}x+0[/tex]
Step-by-step explanation:
Given the points
(-39,49) (0,0)Finding the slope between the points using the formula
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-39,\:49\right),\:\left(x_2,\:y_2\right)=\left(0,\:0\right)[/tex]
[tex]m=\frac{0-49}{0-\left(-39\right)}[/tex]
[tex]m=-\frac{49}{39}[/tex]
We know that the point-slope of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting [tex]m=-\frac{49}{39}[/tex] and (-39,49) in the equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)[/tex]
Now writing the equation in slope-intercept form
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
[tex]y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)[/tex]
[tex]y-49=\frac{-49}{39}\left(x+39\right)[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]y-49=-\frac{49}{39}\left(x+39\right)[/tex]
[tex]\mathrm{Add\:}49\mathrm{\:to\:both\:sides}[/tex]
[tex]y-49+49=-\frac{49}{39}\left(x+39\right)+49[/tex]
[tex]y=-\frac{49}{39}x+0[/tex] ∵ [tex]y=mx+b[/tex]
Where
[tex]m=-\frac{49}{39}[/tex] and the y-intercept i.e. [tex]b=0[/tex]
Therefore, the equation in the slope-intercept form will be:
[tex]y=-\frac{49}{39}x+0[/tex]
Grade six math, Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool
This question is the same as yours and has a verified answer:
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I hope this helps!
Show work if possible, thanks!
help pls this is a missing assignment
Answer:#1 she didn't finish solving
#2 finish solving for a.
#3 it is similar to solving a two step equation because it is a two step equation just there are variables to go along with it.
Step-by-step explanation:
Simplify. Use the distributive property. 5(3x+1)
Answer:
15x+5
Step-by-step explanation:
First you distribute the 5 to the 3x ( 5 times 3x=15x)
Next you distribute the 5 to the 1 (5 times 1=5)
Finally you put the two answers together 15x+1
you cant simplify it anymore because you cannot add 15x to 1
[tex]\huge\boxed{Hello\:there!:)}[/tex]
The Distributive Property states that
a(b+c)=ab+ac (we multiply a by b and c)
Let's use this fantastic property to solve our problem:
5(3x+1)
15x+5
That's our final answer.
Remember, we can't add variables and numbers together.
[tex]\huge\boxed{\sf{Hope\:it\:helps!}}[/tex]
[tex]\huge\bf{Good\:luck!}[/tex]
[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]
When your gas tank is full, your car can drive 350 miles. If you’ve already driven 72 miles since the last time you filled up your gas tank, write an inequality representing the possible number of miles you can still drive in your car, then solve for the most amount of miles you can drive ?
Answer:
noentiendo. que preguntas?
Step-by-step explanation:
What is an equation of the line that passes through the points (0,8) and (-5,4)? Put your answer in fully reduced form.
A boat goes 3/4 hours with a speed of 8mph and 1/3 hours with a speed of 12mph. What distance did the boat cover in all this time?
Answer:
10 miles
Step-by-step explanation:
Distance d = v t
v - speed/velocity
t - time
d = [tex]\frac{3}{4}[/tex] (8) + [tex]\frac{1}{3}[/tex] (12) = 6 + 4 = 10 miles
can someone help? i dont understand it really well
4 1/2 x 2 2/3
ANSWER ASAPPPP TO BE BRAINLIEST
EXPLAIN HOW AND BE RIGHT
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
You turn the fractions improper, 9/2 x 8/3. Multiply the top numbers and then multiply the bottom. Simplify to get 12.
Emily typed 456 words in 8 minutes. Her friend Mary typed 32 fewer words in the
same time frame. At the same rate, how long would it take Mary to type 954 words?
PLEASEE HELPP WILL MARK BEAINLIEST
Write an equation in point-slope form of the line that passes through the two points given. Use the
first point to write the equation.
1.) (4,7) and (5,1)
2.) (9,-2) and (-3,2)
3.) (3,-8) and 7(-2)
Answer:
1. 9.8
2. 3.8
3. -19
Hope it helps :)
Solve the equation for all real values of x.
secʻx+ 2 secx = 0
Answer:
no solution for x in the real numbers
Answer:
A . 2pi/3+ 2nk.....
Step-by-step explanation:
The lager of two numbers is 15 more than three times the smaller.If the sum of the two numbers is 63,find the numbers
Answer:
The numbers are:
The smaller number = 12The larger number = 51Step-by-step explanation:
Let 'x' be the smaller number
As the lager of two numbers is 15 more than three times the smaller. so,
The larger number = 3x+15
As the sum of the two numbers is 63, so the equation becomes
[tex]x + 3x + 15 = 63[/tex]
[tex]x+3x=63-15[/tex]
[tex]4x=48[/tex]
Divide both sides of the equation by
[tex]\frac{4x}{4}=\frac{48}{4}[/tex]
[tex]x = 12[/tex]
Therefore,
The smaller number = x = 12
The larger number = 3x+15 = 3(12) + 15 = 36+15 = 51
Hence, the numbers are:
The smaller number = 12The larger number = 51