determine whether the ordered pair is a solution of the given equation Remeber to use alphabetical order for substitution (-6,-2) a solution of the equation r-s=4 is (-6,-2) a solution of the equation r-s=4?
Answers
To check if an ordered pair is a solution to an equation, substitute the value for each coordinate into the equation.
Since the substitution has to be performed in alphabetical order, then the coordinates are given in the form:
[tex](r,s)[/tex]Substitute r=-6 and s=-2 into the given equation to check if (-6,-2) is a solution:
[tex]\begin{gathered} r-s=4 \\ \Rightarrow(-6)-(-2)=4 \\ \Rightarrow-6+2=4 \\ \Rightarrow-4=4 \end{gathered}[/tex]Since -4 is NOT equal to 4, then the point (-6,-2) is not a solution to the equation r-s=4.
Related Questions
One boat sails 30 miles west and 22 miles north. Another boat sails 55 miles west and 40 miles north. Which boat traveled in the direction closest to due north?
Answers
The boat that sailed in the direction closest to due north is the both that has lesser angle to the vertical ,which is the boat that that sailed 30 miles west and 22 miles north.
How to find the boat that traveled in the direction closest to due northGiven data
One boat sails 30 miles west and 22 miles north
Another boat sails 55 miles west and 40 miles north
Say boat A sail 30 miles west and 22 miles north while boat B sails 55 miles west and 40 miles north
Boat A
let the angle boat A made with the vertical be a. This is given as
tan a = 30 / 22
a = arc tan ( 30 / 22 )
a = 53.746 degrees
Boat B
let the angle boat B made with the vertical be b. This is given as
tan b = 55 / 40
b = arc tan ( 55 / 40 )
b = 53.973 degrees
Comparing angle a and angle b shows that angle a is lesser hence boat A is the boat that sailed in the direction closest to the north
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Write down equation of lines l and m
Answers
Step-by-step explanation:
I assume you need the slope-intercept form
y = ax + b
"a" is the slope of the line, "b" is the y- intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
for l we go from (5, 20) to (8, 80) and get
x changes by +3 (from 5 to 8)
y changes by +60 (from 20 to 80)
the slope is therefore
+60/+3 = 20/1 = 20 = a
so, we have
y = 20x + b
the y- intercept looks to be -80, but to be sure we use a point (e.g. 5, 20)
20 = 20×5 + b = 100 + b
b = -80
yes, the equation is
y = 20x - 80
for m we go from (5, 20) to (8, -40) and get
x changes by +3 (from 5 to 8)
y changes by -60 (from 20 to -40)
the slope is
-60/+3 = -20/1 = -20
we have therefore
y = -20x + b
we use the same trick for b as before
20 = -20×5 + b = -100 + b
b = 120
and our full equation is
y = -20x + 120
You ask a deli clerk for x pounds of ham and x pounds of cheese. You end up getting 4 extra ounces of ham and
3 fewer ounces of cheese. The ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice
as much on ham as you do on cheese. How much do you spend in total?
Answers
If the ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice as much on ham as you do on cheese. The amount spent in total is: $187.20.
Total costLet number of ham bought = x + 4
Let number of cheese bought = x - 3
Price of ham = $6.24
Price of cheese = $4.80
Hence,
Amount spent on ham = (x+4)×6.24
Amount spent on ham =6.24x + 24.96
Amount spent on cheese = (x−3)×4.80
Amount spent on cheese =4.80x−14.40
So,
6.24 x + 24.96 = 2 (4.80 x - 14.40)
6.24x + 24.96 = 9.60 x - 28.80
Combine like terms
24.96 + 28.80 = 9.60 x - 6.24 x
3.36 x = 53.76
Divide both side by 3.36x
x = 53.76/3.36
= 16x
Now let find the total money spent where x is 16
Total amount = 6.24(16) + 24.96+ 4.80(16) - 14.40
Total amount = $187.20
Therefore the amount of $187.20 was spent in total.
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The length of the shadow of a 4 ft stick can be found by comparing its shadow to the shadow of a 32 ft tall building. The building had a shadow 6 ft long. How long would the stick's shadow be at that time?
Answers
The shadow of the 4 feet stick is 3/4 feet or 0.75 feet.
It is a question of ratio and proportion.
It is given in the question that the 32 feet tall building had a shadow 6 feet long.
We have to find the length of the shadow of a 4 ft stick.
Let the length of the shadow of a 4 ft stick be x.
We know that length and shadow of a 4 feet stick and a 32 feet building will be in proportion.
Hence, we can write,
Length of building/Length of stick = shadow of building/shadow of stick
32/4 = 6/x
8 = 6/x
x = 6/8 feet = 3/4 feet = 0.75 feet
x = 0.75 feet.
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the value of 2 [3 (x^2 - 5) + 5y] when x = 9 and y = 3. A. 729.
Answers
[tex] = 2(3( {(9})^{2} - 5) + 5(3)) \\ = 2(3(81 - 5) + 15) \\ = 2( 3(76) + 15) \\ = 2(228 + 15) \\ = 2(243) \\ = 486[/tex]
ATTACHED IS THE SOLUTION
YOU DID NOT PROVIDE FULL OPTIONS THEREFORE I WON'T BE ABLE TO CHOOSE.
GOODLUCK .
Answer the following:
a) 3 x √25 =
b) √(2 x 50)
=???
Answers
After evaluating, we get
3 *√25 = 15√(2 * 50) = 10In the given question, we are given two expressions that include numerical in Roots. We have to calculate their values for each.
These are examples of Products. Product is when two numbers or terms are multiplied together.
The first expression is represented by:
=> 3 *√25, Calculating this expression we get
=> 3 * 5
=> 15
The second expression is represented by:
=> √(2 * 50), calculating this expression we get
=> √(100)
=> 10
Hence, after calculating both A. and B. expressions we get values 15, and 10 respectively
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You have 40 stickers. Twenty-four of the stickers glow in the dark. What fraction of stickers, in fifths, do not glow in the dark?of the stickers
Answers
If 24 out of our 40 stickers glow in the dark, we would have 16 that don't
As a fraction relative to our total 40 stickers, those 16 would be:
[tex]\frac{16}{40}[/tex]Simplifying,
[tex]\frac{16}{40}\rightarrow\frac{2}{5}[/tex]hereby, 2/5 of the sticketrs don't glow in the dark
Simplify 3.5p(4 − 0.3p).
14 − 1.05p2
14 − 0.3p2
14p − 1.05p2
14p − 0.3p2
Answers
The correct explanation for the expression 3.5p(4 − 0.3p) will be;
⇒ 14p - 1.05p²
Option C is true.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called the Mathematical expression.
Given that;
The mathematical expression is;
⇒ 3.5p(4 − 0.3p)
Now, Solve the expression as;
The mathematical expression is;
⇒ 3.5p(4 − 0.3p)
Hence,
⇒ 3.5p(4 − 0.3p) = 3.5 x 4p - 3.5p x 0.3p
= 14p - 1.05p²
Thus, After simplify we get;
⇒ 3.5p(4 − 0.3p) = 14p - 1.05p²
Therefore, The correct explanation for the expression 3.5p(4 − 0.3p) will be;
⇒ 14p - 1.05p²
Option C is true.
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may anyone help me please?
Answers
Answer: 20 is the answer hope you have a great day
!!!!!
Step-by-step explanation:
The population of City A is 8.59 x 104. The population of City B is 3.2 x 103. Select all of the values that show the difference in population of City A and City
B.
8.27 x 104
5.39 × 10¹
2.748 x 107
82,700
7.8 x 104 + 4.7 x 10³
Answers
The difference between the population in City A and City B is 8.27 x [tex]10^{4}[/tex] and 82,700.
What is the difference in the population?The numbers are written in scientific notation. Scientific notation is a method that is used in mathematics to compress large numbers. In order to write a number in scientific notation, the number is written as a decimal number between 1 and 10 and multiplied by a power of 10. For example, 3 x 10² is equivalent to 300
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers.
8.59 x [tex]10^{4}[/tex] - 3.2 x 10³
(0.859 x [tex]10^{4 - 1}[/tex]) - ( 3.2 x 10³)
(0.859 x 10³)- (3.2 x 10³)
0.827 x 10³
8.27 x [tex]10^{4}[/tex] = 82,700
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can someone please explain how to do this? it’s urgent!
Answers
The measure of the angle b is 61°.
In Euclidean geometry, an angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. The plane that contains the rays contains the angles created by two beams.
Vertical Angles (Vertically Opposite Angles): The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.
The figure describes two angles 61° and b.
Now, from the figure the angles 61° and b are vertically opposite angles.
Therefore, the angles are equal.
b = 61°
Hence, the measure of angle b is 61°.
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1. Solve the inequality.
6x2 – x<2
Please show your work using methods learned in unit 1:
1) Factor
2)Discover the interval or intervals as learned in this unit.
3) Use a number line to graph.
4)State your answer in interval notation.
Answers
The solution of the inequality expression in interval notation is;
-1/2 < x < 2/3 and the number line is attached
How to solve the Inequality?We are given the Inequality expression as;
6x² - x < 2
To express the function in quadratic form, we subtract 2 from both sides to get;
6x² - x - 2 < 0
We now factorize this expression to get;
(2x +1)(3x - 2) < 0
This means that we have two inequalities solution which are expressed as; (2x + 1) < 0 and (3x - 2) < 0
For (2x + 1) < 0, add 1 to both sides to get;
2x < 1
divide both sides by 2 to get;
x < 1/2
Similarly, for (3x - 2) < 0;
Add 2 to both sides and then divide by 3 to get;
x < 3/2
Thus, the solution to the inequality is x = -1/2 and x = 3/2
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solve the equation. (x + 4)^2 = 15 - 2x^2.
Quadratic Formula
Answers
The equation has two solutions [tex]x_{1}[/tex] = [-4 + 2√13]/3] and
[tex]x_{2}[/tex] = [-4 - 2√13]/3]
Given the question:
(x + 4)^2 = 15 - 2x^2.
To solve the above Equation by using Quadratic Formula:
Solving Steps of Equation:
[tex](x+4)^2 = 15 -2x^2[/tex]
Expand the expression
[tex]x^{2} +8x+16=15-2x^2[/tex]
Move the expression to the left
[tex]x^{2} +8x+16-15+2x^2[/tex] = 0
Collect like terms
[tex]3x^{2} +8x+1=0[/tex]
Use the Quadratic formula:
x = [-b ± √(b2 – 4ac)]/2a
x = [-8 ± √(8^2 – 4x3x1)]/2x 3
Multiply and evaluate :
x = [-8± √(64 – 12)]/6]
Calculate:
x = [-8± 2√13]/6]
Separate the solutions
[tex]x_{1}[/tex] = [-4 + 2√13]/3]
[tex]x_{2}[/tex] = [-4 - 2√13]/3]
Hence, The equation has two solutions [tex]x_{1}[/tex] = [-4 + 2√13]/3] and
[tex]x_{2}[/tex] = [-4 - 2√13]/3]
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PLEASE ANSWER QUICKLY
Answers
one forth of the villains nabbed by the Second-Rate Superheroes were jaywalkers. One-ninth of those were illegal double parkers. What fraction of the villains were both jay walkers and illegal double parkers.
Answers
Answer:
1/36
Step-by-step explanation:
You want the fraction of villains that are both jay walkers and double-parkers, given that 1/9 of jay walkers are double-parkers and 1/4 of villains are jay walkers.
Doubly-bad villainsThe fraction of villains that both jay walk and double park is 1/9 of 1/4 of all villains.
1/9 × 1/4 = 1/(9×4) = 1/36
1/36 of all villains are both jay walkers and double parkers.
What is -3/4 plus -1/6
Answers
Answer:
-11/12
Step-by-step explanation:
explanation: find common denominator r least common factor between the two. it is 12. 4 times 3 is 12 and 6 times 2 is 12, so multiply the numerators by this same number.
-3/4 -> -9/12 and -1/6 -> -2/12
which equals -11/12
I need help with this practice problem I will send an additional pic that goes along with this, it’s a graph, use the graph to answer
Answers
It is given that,
[tex]\begin{gathered} a^-=\langle-3,-5\rangle \\ b^-=\langle1,4\rangle \end{gathered}[/tex]By using parallelogram method,
[tex]a^-+b^-=\langle-2,-1\rangle[/tex]The graph is as shown below:
Use the following values to evaluate the expression (Will give 69 points)
w = 5, x = 9, y = 2
3. x + 20 - 1
A. 28
B. 19
C. 30
D. 32
(Conexus student)
Answers
The solution to the given expression (x + 20 - 1) when x = 9 is: A. 28.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to evaluate the given expression and determine its solution. Therefore, we would evaluate the given expression as follows:
x + 20 - 1
Substituting the value of x into the given expression, we have:
Expression = 9 + 20 - 1
Expression = 29 - 1
Expression = 28.
In conclusion, we can reasonably and logically deduce that 28 is the solution to this expression (x + 20 - 1).
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Answer:
a) 28
Step-by-step explanation:
Now we have to,
→ evaluate the expression.
The expression is,
→ x + 20 - 1
Solving the expression,
→ x + 20 - 1
→ 9 + 20 - 1
→ 9 + 19
→ 28
Hence, solution is 28.
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Five friends ate lunch and spent a total of $63.75. They each bought the same meal for $9.75, and they each bought the same dessert.
Write and solve an equation to determine the cost of the dessert, d.
5(9.75)d = 63.75; d = 1.31
5(9.75 + d) = 63.75; d = 3.00
5d + 9.75 = 63.75; d = 10.80
5(9.75) + d = 63.75; d = 15.00
Answers
The written and solved equation to determine the cost of the desserts, d is 5(9.75 + d) = 63.75; d = 3.00
How to write and solve equations?Five friends ate lunch and spent a total of $63.75.
They each bought the same meal for $9.75, and they each bought the same dessert.
The equation to determine the cost of the dessert, d can be represented as follows:
They are 5 friends,
Hence,
5 (9.75 + d) = 63.75
48.75 + 5d = 63.75
Therefore, let's use the equation to solve for d.
48.75 + 5d = 63.75
63.75 - 48.75 = 5d
15 = 5d
divide both sides by 5
15 / 5 = 5d / 5
d = 3
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Tell if each pair of triangles are either 1. Similar By SSS similarity 2.Similar by AA similarity3.Similar by SAS similarity 4.not similar Pls label the triangle also so it’s easy to tell which one you are talk about thank you
Answers
We have the following:
1. Similar By SSS similarity
4/2= 2
7.3.5 = 2
6/3 = 2
2. Similar by AA similarity, same angles, 90°, 70° and 50°
3. Similar by SAS similarity
, same angles and related sides.::
4/2 = 2
6/3 = 2
4. Similar by SAS similarity, same angles and related sides:
12/6 = 2
8/4 = 2
A submarine was situated 800800 feet below sea level.
If it ascends 275275 feet, what is its new position relative to the sea level?
Answers
If a submarine was situated 800 feet below sea level. If it ascends 275 feet, its new position relative to the sea level is: -525 feet.
New position relative to the sea levelGiven :
Initial position of the submarine = 800ft below sea level
Ascending =275ft.
Hence, the New position relative to the sea level is calculated as:
New position relative to the sea level = (-800+ 275)
New position relative to the sea level = - 525 feet
Therefore the new position is: -525 feet.
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0.0379 rounded to the nearest whole number ?
Answers
Answer: 0
Step-by-step explanation: We have to 2 answers to choose between, 0 and 1. 0.0379 is closer to 0 because if your decimal was more than 0.5 it would round to 1 as its nearest whole number. Hope this helps!
Suzanne is going to rent a car while she is out of town. The car rental company offers a flat rate of $35 plus $0.10 per mile. If she paid $105, then how many miles did she drive?
Answers
Answer: 700
Step-by-step explanation:
105-35=70
0.10Xx=70
x=700
700
Can someone please help I give lots of points...
Answers
Answer:
y=-x^2+16x-55
Step-by-step explanation:
Since two intercepts are given (the two x-intercepts in this case), we should probably use intercept form.
y=a(x-b)(x-c)
plug in the intercepts which are 5 and 11 in this case
y=a(x-5)(x-11)
to solve for a, use the remaining point and set x to 6 and y to 5. we can do this because (6,5) is given to us as a solution of one of the points on the graph.
5=a(6-5)(6-11)
5=a*(-5)
a=-1
so, the equation should be:
y= - (x-5)(x-11)
expand the parentheses to get:
y=-x^2+16x-55
(also 5 points isn't a lot of points...)
1=0.76r-9-0.36r[tex]1 = 0.76r - 9 - 0.36r[/tex]
Answers
Do you have a picture of your question?
Send it please
ok, ready
1 = 0.76r - 9 - 0.36r
1 + 9 = 0.76r - 0.36r
Simplify like terms
10 = 0.4r
Solve for r
r = 10/0.4
r = 25
Result
r = 25
b)
[tex]\begin{gathered} \text{ -5 = }\frac{1}{4}z\text{ - 20 + }\frac{1}{2}z \\ \text{ -5 + 20 = }\frac{1}{4}z\text{ + }\frac{1}{2}z \\ \text{ 15 = }\frac{1\text{ + 2}}{4}z \\ \text{ 15 = }\frac{3}{4}z \\ \text{ 15x4 = 3z} \\ \text{ 60 = 3z} \\ \text{ z = }\frac{60}{3} \\ \text{ z = 20} \end{gathered}[/tex]Result
z = 20
Add the polynomials?
Answers
Combine like terms and you will get your answer, -4p^2 +1
An individual wants to bring multiple copies of two comic books to a convention this week. There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. The individual can only fit 40 oz. of comics in a bag. If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz. Calculate how much each comic (S) weighs.2.3 oz.2.25 oz.2.1 oz.
Answers
Let x represent the weight of the comic book to be sold
Let y represent the weight of the appraised book to be appraised
There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. It means that
15x + 8y = 49.9 equation 1
If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz, it means that
10x + 4y = 30.2 equation 2
Multiplying equation 2 by 2, it becomes
20x + 8y = 60.4 equation 3
Subtracting equation 3 from equation 1, it becomes
20x - 15x + 8y - 8y = 60.4 - 49.9
5x = 10.5
x = 10.5/5
x = 2.1
Substituting x = 2.1 into equation 2, it becomes
10(2.1) + 4y = 30.2
21 + 4y = 30.2
4y = 30.2 - 21 = 9.2
y = 9.2/4
y = 2.3
Weight of the comic(S) to be sold = 2.1 oz
Find the volume of composite solid.
Answers
The volume of the given cylinder is 37.68ft³.
What is a cylinder?The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers. Real-world examples of cylinders include toilet paper rolls and cold beverage cans.So, according to the given image, the given solid is a cylinder.
The formula for the volume of cylinders is V = πr²hHeight is 3ft and D is 4ft so r will be 2 ft.Now, insert values in the formula as follows:
V = πr²hV = π2²3V = π4(3)V = 12πV = 37.68 (Let, π be 3.14)Therefore, the volume of the given cylinder is 37.68ft³.
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The store manager put 7 belts in sale. The belts were originally $16. The manager marked down the price of the belts by 40% how much money did the store receive for selling all 7 belts
Answers
Original price: $16
Discount: 40%
First, multiply the original price by the percentage discount in decimal form (divided by 100)
16 x 40/100 = 16 x 0.4 = $6.4 ( discount amount)
Subtract the discount amount to the original price
16-6.4 = $9.6 new price
multiply by 7 :
9.6 x 7 = $67.2
Which of these is the best approximation for square root 7?172.63.012.2