The ordered pair (-1, -7) is the solution to the equation 7x - 5y = 28.
Define solutions of linear equations.The collection of variable values in linear equations that yields all feasible solutions is referred to as the solution of a linear equation. In order to describe real-world issues, linear equations contain unknown values in the form of one or more variables. The collection of values for each variable in a system of linear equations is referred to as the solution set.
Consider the equation,
7x - 5y = 28
Now put the values from options, the pair values at which LHS = RHS that will be the solution to the equation.
Put x = 77, y = 9 in the equation
7(7) -5(9)
= 49 - 45
= 4
This is not a solution.
Put x =4, y= 10
7(4) - 5(10)= 28 - 50
= -32
This is not a solution.
Put x= -1, y = -7
7(-1) - 5 (-7)
= -7 + 35
= 28
So, this is the solution to the equation as LHS = RHS
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Answer:
C. the ordered pair (1.5, 10)
Step-by-step explanation:
Simplify this equation please
48
Answer:
Please look at the attached image, thank you so much! Hope this helps! :D
Step-by-step explanation:
Answer:
6.92820323028, rounded would be 6.92. Even more rounded would be 7.
Step-by-step explanation:
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A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the following grouped frequency distribution. What is
the class width?
The class width is
The class width of the distribution is 4
What is class width?Class width is the difference between the Upper class limit and the Lower class limit of a class interval.
Class Width = Upper Class Limit − Lower Class Limit. For example: For a class interval, 163−175, Class Width =175−163=12.
Similarly for a class interval of 75-79, the class width is 79-75= 4.
The upper class limit is 79 and the lower class limit is 75.
The class limit for all the frequency distribution is constant.
Therefore the class width of the distribution is 4
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In your own words, tell me the difference between a geometric and an arithmetic sequence.
As several differences are there between them and is differentiated below.
What is Sequence?
A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.
Let a sequence's terms be a1, a2, a3,..., an,..., etc.
The term's position is indicated by the subscripts. That implies,
Initial phrase = a1
term two = a2
term three Equals a3
….
The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.
Geometric Sequence:
It is a sequence of numbers in which each new term is calculated by multiplying by a non-zero and fixed number.Multiplication or Division is done in every step.A common ratio between 2 successive terms is the common ratio.It is of the Exponential Form.Arithmetic Sequence:
It is a list of numbers, in which every new term alters from another preceding term by a definite quantity.Addition or Subtraction is done in every step.A common ratio between 2 successive terms.It is of the Linear Form,To learn more about Sequence, visit:
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 7 and 2
24 units is the area of the shaded region if the "frame" is 2 units wide.
What is Area of Rectangle?The area of Rectangle is length times of width
We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:
width = 7 units
length = 12 units
Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).
So the measures for the shaded rectangle are:
width = 7 units - 4 units = 3 units
length = 12 units - 4 units = 8 units.
And the area of a rectangle is given by the product between the width and length, then we have:
A = (3 units)*(8 units) = 24 square units.
Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.
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I’m certain year, there were 86 female officials in congress, which comprised of the House of Representatives and the senate. If there were 58 more female me members of the House of Representatives than female senators, find the number of females in each house of congress
Answer:
58 members of the House of Representatives, and 28 members of the senate.
Step-by-step explanation:
We can find the answer to this by simply subtracting:
86 - 58 = 28
So, there are 58 members of the House of Representatives, and 28 members of the senate.
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A canoe rental service charges a $20 transportation fee and $30 dollars an hour to
rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe
for x hours. What is the cost of renting a canoe for twelve hours?
The graph of the equation y = 30x + 20 is shown below.
It would cost $380 for 12 hours.
How to Write and Graph an Equation?The equation of a graph can be written as y = mx + b, if we know the slope of the graph (m) and the y-intercept (b) which is the point on the y-axis that the line will intercept.
Therefore:
Slope/unit rate (m) = $30 per hour
Rental service charges is the y-intercept (b) = $20
To write the equation, substitute m = 30 and b = 20 into y = mx + b:
y = 30x + 20
See the attachment below for the graph of the equation.
Substitute x = 12 into the equation y = 30x + 20 to find the cost of renting canoe for 12 hours:
y = 30(12) + 20
y = $380
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a group of four numbers has an average of 15. The first three numbers are 12,19 and 7. What is the other number
Answer:
22
Step-by-step explanation:
12 + 19 + 7 + _?_ = 15
38 + _?_ = 15
-38 -38
-----------------------
? = 23
12 + 19 + 7 + 23 = 61
-1
12 + 19 + 7 + 22 = 60
60 ÷ 4 = 15
I hope this helps!
Given the function f (x)= x2 −5x + 6 , evaluate
Actually 20 is the answer
In ARST, r = 71 cm, /T=48° and /R=37°. Find the length of t, to the nearest 10th of
a centimeter.
In the given triangle, the length of side t is 87.7 cm
Calculating the length of a side in a triangleFrom the question, we are to determine the length of t.
From the given information,
r = 71 cm
∠T = 48°
∠R = 37°
From the law of sines, we can write that
t / sin T = r / sin R
t / sin 48° = 71/sin 37°
t = (71 × sin 48°)/sin 37°
t = 87.6736
t ≈ 87.7 cm
Hence, the length of t is 87.7 cm
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Jaxon goes to a restaurant and the subtotal on the bill was x dollars. A tax of 8% is applied to the bill. Jaxon decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Jaxon paid.
Answer:
Step-by-step explanation:
If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.
Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.
Explain why the slope(m) of this line is
2/6
The slope is 2/6 because the rise is 2 while the run is 6
rise 2
------- = -------
run 6
The volume of a cube with side s is s3. Edna bought a cube-shaped jewelry box that has 7-inch sides. What is the volume of the jewelry box?
The volume of the jewelry box will be;
⇒ 343 inch³
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The volume of a cube with side s = s³
And, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Now,
Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Hence, The volume of the jewelry box = 7³
= 7 x 7 x 7
= 343 inch³
Thus, The volume of the jewelry box will be;
⇒ 343 inch³
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15 points!! Is the triangle a right triangle?
Answer: Yes.
Step-by-step explanation:
Answer:
yes, it is because the right side is the bigger side.
Step-by-step explanation:
See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.
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The solution is Option D.
The equation of the line is y = 28x
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the total distance traveled by the car y = 476 miles
Let the total amount of gasoline x = 17 gallons
So , the equation of line is given by
y = mx + c
where m is the slope
Slope m = y /x
Substituting the value for y and x in the equation , we get
Slope m = 476 / 17
= 28
Therefore , the equation of line is y = 28x and the graph is given below
Hence , The equation of the line is y = 28x
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Assume gas cost $3.70 a gallon. Write an equation representing the total amount you need to spend on the car for the trip, after paying for a one time tune-up of $100.
The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Also an equation is a set of variables that are constrained through a situation or case.
Given that the 1 gallon is $3.70
x gallons = $3.70x
So, C = 3.70x
This will be the cost of x gallons
Hence "The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x".
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If the variance of the data values in a sample is 289, what is the standard
deviation of the data values?
O A. 17
OB. 19
OC. 18
O D. 16
Answer:
17
Step-by-step explanation: ..
The length of a rectangle is 3ft longer than its width.
If the perimeter of the rectangle is,58ft find its length and width.
The length and width of the rectangle is 16 ft and 13 ft respectively.
What is the dimensions of the rectangle?The perimeter of a rectangle = 2(length + width)
Perimeter of the rectangle = 58 ftWidth of the rectangle = w ftLength of the rectangle = (w + 3) ftThe perimeter of a rectangle = 2(length + width)
58 = 2{(w + 3) + w}
58 = 2(w + 3 + w)
58 = 2(3 + 2w)
open parenthesis
58 = 6 + 4w
subtract 6 from both sides
58 - 6 = 4w
52 = 4w
divide both sides by 4
w = 52/4
w = 13
Hence,
Width of the rectangle = w ft
= 13 ft
Length of the rectangle = (w + 3) ft
= 13 + 3
= 16 ft
Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively
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what are steps to solving 30,002-28,596
Answer:
1,406
Step-by-step explanation:
Simplify Oa Ob Oc Od 10x² -32 4
Answer:
Step-by-step explanation:
Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 5x2 + 14x - 3 < 0 The solution set is O A. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) O B. The solution set is the empty set. Which number line below shows the graph of the solution set? O A. В. + -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 7 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4. 7 8 C. + + + + + + + D. + -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 5 7 8 E. F. + + + + -7 -6 -3 -2 -1 1 2 3 6 -8 -7 -6 -5 -4 -3 -2 -1 1 3 5 6 7 8 OG. →O H.
The power P (in W) generated by a particular windmill is given by P=0.015V where V is the velocity of the wind (in
mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.9 mph. Round
your answer to the nearest tenth.
OA. 0.3 W/mph
OB. 3.5 W/mph
OC. 1.6 W/mph
D. 6.2 W/mph
The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.
What is the rate of change function?
The pace at which one quantity changes in relation to another is known as the rate of change function.
Given, P = 0.015[tex]V^{3}[/tex]
Differentiating P with respect to V:
P′=(0.015)(3)[tex]V^{2}[/tex]
At V = 5.9 mph, then
P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph
Hence, the instantaneous rate of change of power is 1.6 W/mph.
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A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $54 . The total cost to rent 5 chairs and 3 tables is $36 . What is the cost to rent each chair and each table?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The cost of each chair is $2.25.
The cost of each table is $8.25.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 4 = 5 is an equation.
We have,
Cost of each chair = x
Cost of each table = y
Now,
2x + 6y = 54 _____(1)
5x + 3y = 36 ______(2)
From (1) we get,
2x = 54 - 6y
x = (54 - 6y)/2 ______(3)
Now,
Putting (3) in (2) we get,
5(54 - 6y)/2 + 3y = 36
270/2 - 30y/2 + 3y = 36
135 - 15y + 3y = 36
99 = 12y
y = 99/12
y = 8.25 ______(4)
Now,
Putting 4 in (3) we get,
x = (54 - 6 x 8.25) / 2
x = 4.5/2
x = 2.25
Thus,
The cost of each chair is $2.25.
The cost of each table is $8.25.
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A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built
The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet
How to find the dimensions of the rectangle for the most economical fence?Given: Area = 1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot
In order to calculate the dimension of the fence
Let L and W represent the length and width of the fence respectively
Thus, the area of the fence can be represented as:
A = L × W = 1250 ---- (1)
L = 1250/W
Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot
C = 6×(2W + L) + 18×L
C = 12W + 24L ---- (2)
Substituting the value of L from equation 1 into equation 2 we have:
C = 12W + 24×(1250/W)
To minimize the cost we differentiate both sides with respect to W and equate the result to zero:
C = 12W + 24×(1250/W)
dC/dW = d/dW (12W + 30000/W)
0 = 12 - 30000/W²
12W² = 30000
W² = 2500
W = 50 feet
Since L = 1250/W
L = 1250/50
L = 25 feet
Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet
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No
0.7
What’s the percentage
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
How is solving a real-world problem with a system of equations similar to solving a real-world problem with a single equation in one variable? How is the process different?
Answer:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
Step-by-step explanation:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
hope it helps
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A student is using colored beads to make a model of magnesium hydroxide, Mg(OH)2. Magnesium atoms are
represented by orange beads, oxygen atoms by green beads, and hydrogen atoms by blue beads.
Model bead color key.
Magnesium orange beads O (orange)
Oxygen green beads O (green)
Hydrogen blue beads O (blue)
What combination of beads should the student use for the model?
The combination of beads that the student will use to make a model of magnesium hydroxide, Mg(OH)₂ is
Magnesium orange beads - 1Oxygen green beads - 2Hydrogen blue beads - 2What is model of molecule?Molecule models depict the positions of the various atoms, roughly to scale, and typically with color coding, as well as how they are joined together.
These models are helpful tools for visualizing the structures and shapes of groupings of atoms, which is vital for understanding the behavior of molecules
Over the course of the development of contemporary atomic theory, models have been employed to represent atom configurations.
The model of magnesium hydroxide, Mg(OH)₂ will require the atoms in the ratio:
Magnesium : Oxygen : Hydrogen = 1 : 2 : 2
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what is the slope of a line that is parallel to the line connecting point O (-5,1) and point P (2,3)?
Answer:
2/7
Step-by-step explanation:
2 parallel lines have the same slope
we just need to find the slope of the line with the point’s connecting O and P
We use y2-y1/x2-x1 to find slope
3-1/2-(-5)
2/7
2/7 is the slope
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Your car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol. How much of 69% percent ethanol fuel should you use so
that your tank is 40 percent ethanol?
Answer: 7.5
Step-by-step explanation:
the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent
.69 divided by 15 is .046
.13 divided by 15 is .008
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
What is mixture?A mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.Given is that a car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol.
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -
{x} = 69% of 15 - {40% of 15}
{x} = (69/100 x 15) - (40/100 x 15)
{x} = 10.35 - 6
{x} = 4.35
Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
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Julie likes to make bead necklaces. She has 296 beads altogether, but has 32 more round beads than square beads. How much of each bead does she have?
Can somebody help me with this please?
Answer: -16.66
Reason: 10*-5/3=−16.66666667 or −50/3
two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?
Answer:
$33.25
1 package is $4.75
Step-by-step explanation:
9.5 divided by 2 is 4.75, that is how much one package costs.
4.75 times 7 is 33.25, that's seven packages worth.