The line which is parallel to 2x-2y=-4 that passes through the
point (3,9) is x-y = -6.
Given that, 2x-2y = -4 passes through the point (3,9) then we have to find the equation of a line which is parallel to the given equation of line.
Let's proceed to find the equation of the line.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
Using the slope-intercept formula, the equation of the line is:
y = mx + b
where,
m = the slope of the line
b = y-intercept of the line
(x, y) represent every point on the line
x and y have to be kept as the variables while applying the above formula.
2x-2y = -4
-2y = -4-2x
y = -4/-2 - 2x/-2
y = 2+x
y = x+2
On comparing with y = mx+b
m = 1 and b = 2
As the lines are parallel then the slope of other line will also be same i.e., m = 1
The point from which it is passes is (3,9)
⇒ x₁ = 3 and y₁ = 9
y-y₁ = m(x-x₁)
⇒ y-9 = 1(x-3)
⇒ y-9 = x-3
⇒ y = x-3+9
⇒ y = x+6
⇒ x-y = -6
Therefore, the line which is parallel to 2x-2y=-4 that passes through the
point (3,9) is x-y = -6.
Hence, x-y = -6 is the required answer.
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Which relation is a function?
For the triangle shown, find the length AD. (Assume u = 17, v = 17, ∠x = 25°, and ∠y = 25°
Using the law of Sines, the length of side AD, |AD|, is 7.44
Calculating lengthFrom the question, we are to determine the length of side AD
From the given information, we have that
u = 17 and v = 17
Then,
ΔBCD is an isosceles triangle
∴ m ∠DBC = m ∠ BCD
m ∠DBC = x = 25°
∴ m ∠BCD = 25°
Also,
m ∠BCA = ∠y + m ∠BCD
m ∠BCA = 25° + 25°
m ∠BCA = 50°
Now, we will determine the measure of ∠CAD.
m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)
m ∠CAD + 25° + 50° = 180°
m ∠CAD = 180° - 25° - 50°
m ∠CAD = 105°
Now,
From law of Sines, we can write that
|AD| / sin DCA = |DC| / sin CAD
|AD| / sin y = u / sin CAD
|AD| / sin 25° = 17 / sin 105°
|AD| = (17 × sin 25°) / sin 105°
|AD| = 7.43795
|AD| ≈ 7.44
Thus,
Length AD is 7.44
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Simplify: (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
7r³ + 11r²s -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
How to simplify equation?The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.
Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.
Let's review some of the crucial words used during expression simplification:
In an algebraic expression, a variable is a letter with an undetermined value.
A coefficient is a number that is used with a variable.A term with a fixed value is called a constant.Variables with the same letter and power are known as like terms. Sometimes, similar terms will have different coefficients.We have been asked to simplify the expression
(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
Let's simplify
⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
⇒ 7r³ + 10r²s −3rs² − 8s + r²s -6rs²
⇒ 7r³ + 11r²s -9rs² - 8s³
Thus, 7r³ + 11r²s -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
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Similarities and differences between AAS and ASA Congruence Postulates
Answer:
Similarity: Both are geometry terms, used in proofs.
Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.
Step-by-step explanation:
ASA: Angle, Side, Angle
AAS: Angle, Angle, Side
Similarity: Both are geometry terms, used in proofs.
Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.
I am going to use the drawer to show the differences:
Can you help me solve this question?
SOLUTION
Step1:
hence from the diagram above, the dimension of the rug is
[tex]\begin{gathered} 34-2x\text{ and } \\ 24-2x \end{gathered}[/tex]Since we have area of the rug,
then we have
[tex](34-2x)(24-2x)=704[/tex]We now solve the equation above quadratically
[tex]\begin{gathered} (34-2x)(24-2x)=704 \\ \text{expand the parenthesis } \\ 16-116x+4x^2=704 \\ \text{subtract 704 from both sides } \\ 816-116x+4x^2-704=704-704 \end{gathered}[/tex]Then we have
[tex]4x^2-116x+112=0[/tex]Solve using factor method we obtain
[tex]\begin{gathered} \text{Divide through by 4} \\ x^2-29x+28=0 \\ x^2-28x-x+28=0 \\ x(x-28)-1(x-28)=0 \\ (x-28)(x-1)=0 \end{gathered}[/tex]Equating each factor to zero we have
[tex]\begin{gathered} x-28=0,x-1=0 \\ x=28,1 \end{gathered}[/tex]Since x can not be 28, the value of x is 1
The Dimension of the rug becomes
[tex]\begin{gathered} 34-2x=34-2(1)=32 \\ \text{and } \\ 24-2x=24-2(1)=22 \end{gathered}[/tex]Hence the dimension of the rug is 32 ft by 22ft (22,32)
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Lauren had brochures printed for her new business venture. She originally ordered 4 boxes of black-and-white brochures and 4 boxes of color brochures, which cost a total of $148. After those ran out, she spent $125 on 4 boxes of black-and-white brochures and 3 boxes of color brochures. Given that the prices didn't change, what was the price of each type of brochure?
Let the price of black and white brouchers be x
The price of color brochures be y.
A/q,
4x+4y=148.....(1)
4x+3y=125 .....(2)
The equation (1) becomes,
x+y=37
y=37-x.......(3)
Putting (3) in (2) we have,
4x+3(37-x)=125
4x+111-3x=125
x=14
Putting the value of x in (3) we have,
y=37-14=23
The price of black and white brouches is $14
The price of color brouchers is $23.
The city of St. Louis is creating a welcome sign on a billboard for visitors to see as they enter the city. The following picture needs to be enlarged so that 1/2 inch represents 7 feet on the actual billboard. Will it fit on a billboard that measures 14 feet in height if the height of the figure is 1 in?
The scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.
Now,
[tex]1\text{ in = }\frac{1}{2}in\text{ +}\frac{1}{2}in.[/tex]That means that 1 inch corresponds to 7ft +7ft= 14ft.
Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.
Answer: The scaled figure will fit in the billboard.
What is the equation of the following graph
Answer:
y = 1
The graph has no gradient and only intersects at the y-axis.
Find the perimeter of hexagon ABCDEF plotted below.
Use the Polygon tool to draw an image of the given polygon under a dilation with a scale factor of and center of dilation (0,0)
The dilated polygon image is attached below under a dilation with a scale factor of 3 and center of dilation (0,0)
What exactly is a polygon?In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.
What is transformation and dilation?Transformation is the movement of a point from one location to another. Transformations include rotation, reflection, translation, and dilation.
Dilation is the process of increasing or decreasing the size of a figure by a factor k. If a point A(x, y) is dilated about the origin by a factor k, the new point is A' (kx, ky).
Assume the polygon has vertices at A(0, 0), B(3, 3) and C. (-3, 3). If the polygon is dilated by a factor of three with the center of dilation at (0, 0), the new vertices are as follows:
A'(0,0), B'(1, 1) and C'(-1, 1)
Therefore, the polygon graph is attached in which the polygon is dilated by a factor of three with the center of dilation at (0, 0),
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highest common factor of 106 and 104
The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.
Given that,
The numbers 106 and 104.
We have to find the greatest common factor of 106 and 104.
The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)
The factors of 104 are 1,2,4,8,13,26,52,104;
The factors of 106 are 1,2,53,106.
Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.
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A retailer owes a wholesaler $300,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. Since the bill isn't due immediately, the retailer can invest the $300,000 in a certificate of deposit and make money on the interest. The retailer has two options: a 45-day certificate of deposit (CD) earning 6% per year simple interest or a 60-day certificate earning 7% per year simple interest.
A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.
What is simple interest ?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.
Simple interest=p*n*r
=300000*6/100*45/365
=2250
Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.
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Find a with the given information.
m=-6/7 (-10,0) and (a,-6)
Based on the slope formula for a line, the value of a is: a = -3.
How to Calculate the Slope of a Line?If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:
Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.
The given line has the following:
(-10, 0) = (x1, y1)
(a, -6) = (x2, y2)
Slope (m) of the line = -6/7.
Plug in the values into the slope formula for a line:
(-6 - 0) / (a - (-10)) = -6/7
-6/(a + 10) = -6/7
Cross multiply and solve to find the value of a in the equation:
-6(a + 10) = -6(7)
Apply the distributive property
-6a - 60 = -42
Add 60 to both sides
-6a - 60 + 60 = -42 + 60 [addition property of equality]
-6a = 18
Divide both sides by -6
-6a/-6 = 18/-6 [division property of equality]
a = -3
Therefore, the value of a is -3.
The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).
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f(x) = x + 3g(x) = 2x2 - 4Find (f ·g)(x)
SOLUTION
f(x) = x + 3
[tex]undefined[/tex]Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend. Write and evaluate an expression
Answer:
x + 15 - 30
x -15
Step-by-step explanation:
please help me out i’ll give you brainlist !
Answer:
In order, the answers are d, b, c, a
Step-by-step explanation:
[tex] \frac{ {x}^{7} }{ {x}^{4} } = {x}^{3} [/tex]
[tex] {x}^{ - 3} = \frac{1}{ {x}^{3} } [/tex]
[tex] {x}^{0} = 1[/tex]
[tex] \frac{ {x}^{4} }{ {x}^{3} } = x[/tex]
Match the following.
Matching the given mathematical operation equations to the specified choices, gives;
A•B = B•A ; Commutative Property of Multiplication
A + B = B + A ; Commutative Property of Addition
(A•B)•C = A•(B•C); Associative Property of Multiplication
A•0 = 0; Multiplicative Property of 0
(A + B) + C = A + (B + C); Associative Property of Addition
A•1 = A; Multiplicative Identity
A + 0 = A; Additive Identity
What are the properties of mathematical operations?The properties of mathematical operations includes; inverse, associative, distributive, associative and commutative properties
Commutative propertyCommutative property in mathematics is one in which for a binary operation, the result of an operation remains unchanged when the order in which the operands appears in the expression is changed.
Therefore;
Commutative property of multiplication is therefore; A•B = B•A
Commutative property of addition is; A+B = B+A
Associative propertyAssociative property relates with operations that have results which remains the same when the parentheses in the expressions are rearranged.
Therefore;
(A•B)•C = A•(B•C) represents the associative property of multiplication
The associative property of addition is represented by (A+B)+C = A+(B+C)
Multiplicative property of 0The multiplicative property of 0, which can be understood as the zero product property, states that the product of any number and 0 is 0
Therefore, the equation, A•0 = 0, represents the multiplicative property of 0
Multiplicative and additive identityThe multiplicative and additive identity states that an expression remains the same following the product of the expression with an identity element such as 1, or following the addition of the expression with an identity element such as 0
The multiplicative and additive identity are therefore represented by A•1 = A and A + 0 = A respectively
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Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(aza)0.4314, find a. Round to two decimal places.
The z-score of the given expression P(-a < z < a) = 0.4314 is; 0.55
How to Interpret Normal Distribution?We are told that P(-a < z < a) = 0.4314. Thus;
P(-a < z < a) = 0.4314 is represented by the area about mean. This means that; 0.4314/2 = 0.2157 is the area each on the left side and right side of mean.
Now, from online z-score calculator, we see that the z value corresponding to 0.2157 is 0.55.
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1, if P(-a < z < a) = 0.4314, then it means that the z score is 0.55.
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Complete question is;
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−a < z < a) = 0.4314, find d a. Round to two decimal places
Karen the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday therewere 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Karen trained her Monday clients fora total of 10 hours and her Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
ive n
lan A
Plan B
Monday: 3 clients - Plan A
5 clients - Plan B
Total 10 hours
Tuesday
6 clients - Plan A
2 clients - Plan B
Total 10 hours
rocedure
Let's define a system of linear equations that represents the above problem.
A: Number of hours of workout in plan A
B: Number of hours of workout in plan B
[tex]\begin{gathered} 3A+5B=10 \\ 6A+2B=10 \end{gathered}[/tex]The goal here is to solve
3A+5B=10 and
6A+2B=10 for the variables A and B.
The solutions to your equations are:
A = 5/4 hour
B = 5/4 hour
pls help i dont get it
Answer:
Step-by-step explanation:
Answer: You can add 5. The question is asking you what can you do to make both sides equal 8. I am not a professional but I hope that helped.
The mass, m kilograms, of a horse is 429 kg, correct to the nearest kilogram.
Complete this statement about the value of m.
Answer:
400 < m< 430 kg
Step-by-step explanation:
the mass of horse is 429 kg
estimated to the nearest hundred is 400 kg
estimated to the nearest tens is 430 kg
thus the value of m mass lies between 400 to 430
therefore
400 < m< 430 kg
The answer is 400 < m< 430 kg
When your spel of dice, there are several homes, showWhen rolling the dice, the outcome is expressed as a sum of the two dice. Forcrample, il after you rolled the dice, and one die was 33 and the other was 34 youwill have rolled aSelect all of the TRUE statements below There may be more than oneThe probabiliny troling the same digit with cach die is 1/4The odds in favour of roliga 10 is 1:13.The odds against rolling a nurther leathan 7 is 7:5.1$
The total possible outcome for the experiment is 36.
The ossible outcomes for same number on each dice is 6.
So probability for the same number on dice is,
[tex]\frac{6}{36}=\frac{1}{6}[/tex]So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.
find the surface area of the figure in square yards.
Answer:
578.0 yd^2
Explanation:
The formula for finding the surface area of a cylinder is given as;
[tex]A=2\pi r(h+r)[/tex]where A = surface area
pi = 3.14
r = radius of the base of the circle = diameter/2 = 8/2 = 4 yd
h = height = 19yd
Let's go ahead and substitute these values into our formula and solve for A;
[tex]\begin{gathered} A=2\ast3.14\ast4(19+4) \\ =25.12(23) \\ =577.76 \\ \therefore A=578.0yd^2 \end{gathered}[/tex]Use the following information to prepare a classified balance sheet for Alpha Co. at the end of Year 1. Accounts receivable $ 26,500 Accounts payable 12,200 Cash 20,500 Common stock 30,000 Land 10,000 Long-term notes payable 17,500 Merchandise inventory 26,300 Retained earnings 23,600
The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.
What is a classified balance sheet?A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.
It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.
The balance sheet is illustrated below:
Current Assets
Accounts Receivable 26500
Cash 20500
Merchandise Inventory 26300
Total Current Assets 73300
Property, Plant and Equipment
Land 10000
Total Property, Plant and Equipment 10000
Total Assets 83300
Current Liabilities
Accounts Payable 12200
Long Term Liabilities
Long-Term Notes Payable 17500
Stockholders' Equity
Common Stock 30000
Retained Earnings 23600
Total 53600
Total Liabilties 83300
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g(x) = 5x – 3g(-2) =?
Donna bought a desk on sale for $343. This price was 35% of the original price.
The original price for the desk is $980.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
Given:
Sale price = 343
price was 35% of the original price.
let the original price be x
35% of x = 343
35 / 100 * x = 343
x= 343 * 100/ 35
x=980
Hence, the original price of the desk was $980.
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Need help with the bottom ones.. which is part b please.
EXPLANATION:
Solution first(a) exercise part b:
All the internal angles of a right triangle must add up to 180, so to order the internal angles from least to greatest we must find the missing angle;
The exercise is as follows:
[tex]\begin{gathered} D=61\text{ degr}ees \\ E=48\text{ degre}es \\ F=X \\ D+E+F=180 \\ 61+48+F=180 \\ 61+48-180=F \\ 71=F \\ The\text{ thre}e\text{ angles }added\text{ }must\text{ give 180;} \\ (D+E+F)=180 \\ (61+48+71)=180 \\ \\ \end{gathered}[/tex]Now we must order them from lowest to highest, the order is as follows:
[tex]ANSWER\colon E=48;\text{ D=61, F=71}[/tex]f(x) = c f(-x) = c
Does f(x) = f(-x)?
Does f(-x) = f(x)?
+c does not equal -c
The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true
How to determine the true statements?The functions are given as
f(x) = c
Also, we have
f(-x) = c
In the above function definitions, we can see that
The functions f(x) and f(-x) have the same value
i.e. f(x) = f(-x) = c
This means that f(x) =f(-x)
By the symmetric property of an equation, the above can also be rewritten as
f(-x) = f(x)
Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true
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The right angled triangle has an area of 22.5 cm² X+1 X-3 help quick with no calcalator way or quadratic formula
Answer:
x = 8
Step-by-step explanation:
You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².
Triangle areaThe area of a triangle is given by the formula ...
A = 1/2bh
Then the area of this triangle is ...
22.5 = 1/2(x -3)(x +1)
45 = x² -2x -3
48 = x(x -2) . . . . . . . add 3 and factor out x
We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.
__
Additional comment
x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.
please its due tomorrow
1 Answer:
Evaluate the following expression when q = 13.
q-10
2 Answer:
Evaluate the following expression when x = 4.2.
34.5x
3 Answer:
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
1. The value of the expression when q = 13 in q - 10 is 3.
2. The value of the expression when x = 4.2.
34.5x is 144.9
3. The interest will be $5.25.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
1. The expression when q = 13 in q - 10 will be:
= q - 10
= 13 - 10
= 3
2. The value in the expression when x = 4.2 will be:
= 34.5x
= 34.5 × 4.2
= 144.9
3. Principal = $70
Rate = 3%
Time = 2.5 years
Interest = PRT / 100
= (70 × 3 × 2.5) / 100
= $5.25
The simple interest would you earn in 2.5 years is $5.25.
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