The equation which represents the situation is 13 = 2x − 5 while Bernadette ran 9 miles so option (A) will be correct.
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.
Given that,
Andrew ran 5 miles less than two times the number of miles Bernadette ran.
If Bernadette ran x miles then,
13 = 2x - 5 is the correct representation.
Now,
2x - 5 = 13
2x = 18
x = 9 miles.
Hence " The number of miles that Bernadette ran is 9 miles while the equation of constraint is 13 = 2x − 5".
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d(A−N)=Q
solve for A
Answer:
A= Q/d +N
Step-by-step explanation:
First you want to move the d term over by dividing both sides
Next you can move the N over by adding it to both sides.
Step-by-step explanation:
adventures
Q
d and d will cancel and
it let d= A-N
Q
Name the property of real numbers illustrated by each equation.
(2√7) . √3 = 2(√7 . √3)
Associative Property Of Addition illustrated by each equation.
(2√7) . √3 = 2(√7 . √3)
What is Associative Property Of Addition?The total of three or more integers is constant according to the associative property of addition, regardless of how the numbers are arranged.The grouping of numbers does not alter their sum, according to the associative characteristic of addition. For instance, 75 + (81 + 34) = 75 + 115 = 190; and 75 + (81 + 34) = 75 + (81 + 34) = 156 + 34 = 190.According to the associative property, no matter how the addends are grouped, the total or product of adding or multiplying three or more integers will always be the same (or the multiplicands).This law essentially asserts that you can rearrange the numbers in a problem without changing the solution when adding or multiplying them.To know more about Associative Property Of Addition, refer to the following link:
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please help me witht this math problum.
Answer: 1/3
Step-by-step explanation:
what is a vonoroi diagram in SIMPLE terms please help!
Answer:
Image result for what is a voronoi diagram in SIMPLE terms please help!
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators)
Step-by-step explanation:yes
Identify a pattern and find the next three numbers in the pattern.
3,6,10,15, . . .
The pattern exists described as a sequence of repeating objects, shapes, or numbers. Patterns can also occasionally be referred to as a series.
The pattern follows the rule = Σn+(n+1)
The next three numbers in the pattern be 3, 6, 10, 15, 21, 28, 36.
What is meant by pattern?A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Let the numbers in the pattern be 3,6,10,15, . . .
t1 = 1 + 2 = 3
t2 = 3 + 3 = 6
t3 = 6 + 4 = 10
t4 = 10 + 5 = 15
t5 = 15 + 6 = 21
t6 = 21 + 7 = 28
t7 = 28 + 8 = 36
The pattern follows the rule = Σn+(n+1)
Therefore, the next three numbers is 21, 28, 36.
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Solve each system by elimination or substitution.
2 = 4y - 3x , 5x = 2y - 3
Using elimination method, the solution of the given system of equations is (-4/7, 1/14)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
2 = 4y - 3x ............ (1)
5x = 2y - 3 .............. (2)
Re-arrange the equations so that all variables are on the left sides:
2 = 4y - 3x
⇔ -3x + 4y = 2 ....... (3)
5x = 2y - 3
⇔ 5x - 2y = -3 ....... (4)
Choose one variable to eliminate. Let us choose y. Multiply equation (4) by 2, we get:
10x - 4y = -6 ....... (5)
Add equation (3) and (5)
-3x + 4y = 2
10x - 4y = -6 +
7x = -4
x = -4/7
Substitute back x = -4/7 into equation (3):
-3x + 4y = 2
-3.(-4/7) + 4y = 2
12/7 + 4y = 14/7
4y = 2/7
y = 2/28 = 1/14
Hence, the solution is (-4/7, 1/14)
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Find the center and the radius of each circle. x²+2 x+1+y²=4
The center and radius of the circle given by the equation x^2 + 2x + 1 + y^2 = 4 is (-1 , 0) and 2, respectively.
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + 2x + 1 + y^2 = 4, then the coefficients are:
D = 2
E = 0
F = 1 - 4 = -3
If D = -2h and D = 2, then
2 = -2h
h = -1
If E = -2k and E = 0, then
0 = -2k
k = 0
If F = h^2 + k^2 -r^2 and F = -3, then
-3 = (-1)^2 + 0^2 - r^2
r^2 = 1 + 0 + 3
r^2 = 4
r = 2
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How does the First Amendment to the Constitution affect American society?
The right to bear arms means many Americans own guns for protection.
The right to bear arms means many Americans own guns for protection.
The right to due process gives Americans a strong sense of ownership of their personal property.
The right to due process gives Americans a strong sense of ownership of their personal property.
The right to a jury trial has created a strong sense of fairness in the criminal justice system among Americans.
The right to a jury trial has created a strong sense of fairness in the criminal justice system among Americans.
The right to a free press allows Americans to have access to many independent sources of news and information.
The First Amendment to the Constitution affect American society as D. The right to a free press allows Americans to have access to many independent sources of news and information.
What is Constitution?It should be noted that Constitution simply refers to the rules and laws that guide a group of people especially a country.
In this case, the First Amendment to the Constitution affect American society as The right to a free press allows Americans to have access to many independent sources of news and information.
In conclusion, the correct option is D.
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The correct answer is "The right to a free press allows Americans" to have access to many independent sources of news and info
Explanation:
The First Amendment to the constitution was ratified in 1791, in this it was established government could not interfere in the right to exercise religion or assemble as well as the rights of freedom of speech and freedom of the press. This last aspect implies the government cannot interfere in the circulation of information, according to this, citizens have the right to create sources of news and information to report news or express opinions. Thus, the First Amendment affects American society because "the right to a free press allows Americans to have access to many independent sources of news and info".
Please Help with problem 24, algebra 1, In the attachment.
The measure of the given angle is 10 degrees.
what are supplementary and complimentary angles?Supplementary angles are those angles that sum up to 180 degrees.
Complimentary angles are those angles that sum up to 90 degrees
The supplement of the angle is 10° more than twice it's complement.
Therefore,
180 - x = 2(90 - x) + 10
open the brackets
180 - x = 2(90 - x) + 10
180 - x = 180 - 2x + 10
180 - 180 - 10 = -2x + x
-10 = -x
divide both sides by - 1
x = -10 / -1
x = 10
Therefore, the measure of the given angle is 10 degrees.
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Answer:
Step-by-step explanation:
you did that correctly but it will equal 90
List the angles and sides of ΔWXY in order from smallest to largest.
The order of the sides from smallest to largest is: WX, XY, YW
How to order of the angles from smallest to largest?Given: [tex]\angle[/tex] X = 90° (right angle) and [tex]\angle[/tex] W = 51°
The sum of the interior angles of any triangle is 180°, then
[tex]\angle[/tex] W + [tex]\angle[/tex] X + [tex]\angle[/tex] Y = 180°
Replacing the given values then we get
51° + 90°+ [tex]\angle[/tex] Y = 180°
141° + [tex]\angle[/tex] Y = 180°
Solving for [tex]\angle[/tex] Y
Subtracting 141° both sides of the equation:
141° + [tex]\angle[/tex] Y - 141°=180° - 141°
[tex]\angle[/tex] Y = 39°
The order of the angles from smallest to largest is:
[tex]\angle[/tex] Y = 39°, [tex]\angle[/tex] W = 51°, [tex]\angle[/tex] X = 90°
The opposite sides to these angles must be ordered in the same way:
Opposite side to [tex]\angle[/tex] Y: WX
Opposite side to [tex]\angle[/tex] W: XY
Opposite side to [tex]\angle[/tex] X: YW
The order of the sides from smallest to largest is: WX, XY, YW
Therefore, the correct answer is option C. WX, XY, YW
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Simplify 2(b-a)+5(b-a) and justify each step in your simplification.
The Simplified value of the expression 2(b-a)+5(b-a) is 7b-7a .
Distributive property for real numbers "a", "b" and "c" is defined as
a(b-c)=a*b-a*c.
In the given question
=2(b-a)+5(b-a)
Applying Distributive Property
=2*b-2*a+5*b-5*a
=2b-2a+5b-5a
Combining the like terms together
=2b+5b-2a-5a
=7b-7a (adding the like terms )
Therefore , the Simplified value of the expression 2(b-a)+5(b-a) is 7b-7a .
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Can somebody please Help me please!!!and thank you!!!!!!!
Answer:
17.25 < 17.252
Step-by-step explanation:
17.25 means 17.250. So, 17.250 is less than 17.253, which is correct. The other answer choices are incorrect because the sign is pointed the wrong way. 29.60 is not greater than 29.65, so that's incorrect. 21.51 is greater than 21.49. That is not an answer choice though, so that answer choice is incorrect. 7.602 is not greater than 7.612, so that is incorrect.
Hope this helps! :)
help please do the work
Answer:
16.97
Step-by-step explanation:
[tex]BF=\sqrt{(-2-0)^2 + (1-3)^2}=2\sqrt{2} \\ \\ BC=\sqrt{(0-4)^2 + (3-(-1))^2}=4\sqrt{2}[/tex]
So, the perimeter is
[tex]2(4\sqrt{2}+2\sqrt{2})=12\sqrt{2} \approx 16.97[/tex]
Determine whether following set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
10,16,18
The following set of numbers, 10, 16, and 18, can be the measures of the sides of an acute triangle.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 10, b = 16, and c = 18
a + b > c 10 + 16 > 18 26 > 18 True
a + c > b 10 + 18 > 21 28 > 16 True
b + c > a 16 + 18 > 21 34 > 10 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
10^2 + 16^2 = 356
2. Compare it to the square of the largest side.
18^2 = 324
324 < 356
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 10, 16, and 18 can be the measure of the sides of an acute triangle.
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2
If x²- y² = 20 and x+y = 10, then find x
Answer:
x = 6
Step-by-step explanation:
x² - y² is a difference of squares and factors as (x + y)(x - y)
given
x² - y² = 20 , then
(x + y)(x - y) = 20 ← substitute x + y = 10
10(x - y) = 20 ( divide both sides by 10 )
x - y = 2 → (1)
x + y = 10 → (2)
add (1) and (2) term by term to eliminate y
2x + 0 = 12
2x = 12 ( divide both sides by 2 )
x = 6
A rectangular mural measures 234 inches by 245 inches. rhianon creates a new mural that is 33 inches longer. what is the perimeter of rhianon's new mural?
The new mural created by Rhianon, which is 33 inches longer, has a perimeter of 1024 inches.
Perimeter refers to the total distance around a two-dimensional figure. The perimeter of a rectangle is the sum of all its 4 sides and is given by the formula
P = 2l + 2w
where l = length
w = width
If a rectangular mural measures 234 inches by 245 inches, length is usually longer than the width, and Rhianon creates a new mural that is 33 inches longer, then the length of Rhianon's mural is:
l = 245 inches + 33 inches
l = 278 inches
If the new mural is the same as the width of the rectangular mural and its length is 278 inches, then the perimeter can be solved using the formula for the perimeter of a rectangle.
P = 2l + 2w
P = 2(278 inches) + 2(234 inches)
P = 556 inches + 468 inches
P = 1024 inches
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what is 109 x 3= the answer is
327
Answer:
109 x 3 = 327
Step-by-step explanation:
Sketch the solid that results when the region enclosed by the given equations is revolved about the x -axis.
y = x²
y = 2x
y = x² , y = 2 x are the region enclosed by the given equations is revolved about the y -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers.Use enclose, encloses, and enclosing rather than inclose for other words that are similar to enclosed.The graph is attached in equation y = x² , y = 2 x
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Y=35x1 where x is distance and y is height
The average rate of change of the equation is 35
How to determine the average rate of change?The equation is given as
y = 35x^1
Evaluate the quotient x^1
So, we have
y = 35x
The above equation is a proportional linear equation
A proportional linear equation is represented as
y = mx
Where
m represents the average rate of change
By comparison, we have
m = 35
Hence, the average rate of change of the equation is 35
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Complete question
Given the equation y = 35x^1 where x is distance and y is height, calculate the average rate of change
On a coordinate graph, your house is located at the origin (0,0) You leave your house and walk 6 blocks north. Then you turn and walk 22 blocks west. Since it is getting late, you decide to walk straight back home. How many blocks is it to walk straight back to your house? Round your answer to the nearest tenth
Answer:
22.8 blocks
Step-by-step explanation:
We can think of your path as traveling on a coordinate plane. You start by walking 6 units in the positive y direction, then 22 units in the negative x direction, then walking from this point (-22, 6) back to (0, 0)
This path draws a right triangle. The shorter leg is 6 units long, and the longer end is 22 units long. You want to find the hypotenuse of this triangle.
The hypotenuse is found using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
A and B represent the sides of the triangle, and c represents the hypotenuse!
Before plugging in the functions, isolate c, since that's the answer we're looking for:
[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]
Now, plug in the side lengths of the triangle:
[tex]c=\sqrt{6^2+22^2}[/tex]
Now simplify!
[tex]c=\sqrt{36+484} \\x=\sqrt{520} x=22.8[/tex]
It is 22.8 blocks back to your house! Hope this helps!
Help me Pleaseee this has to be turned in by tomorrow I am a 7th grader for tips to get an accurate answer
Answer:
Parallelogram S: b = 7, h = 6
Parallelogram T: b = 3, h = 6
Area of Parallelogram S = 42
Area of Parallelogram T = 18
Step-by-step explanation:
The bases and heights of each parallelogram are given by the arrows, just count the number of boxes you see.
Area = base × height, so you just multiply these numbers. Area of parallelograms is found the same way as area for squares/rectangles.
7 × 6 = 42 and 3 × 6 = 18
Somebody help me ASAP
Answer:
⬤ = 8
⬛ = 6
Step-by-step explanation:
⬤ = x
⬛ = y
x + y = 14
x - y = 2
add the numbers on top of each other together:
add x to x = 2x , y + -y = 0 , 14 + 2 = 16
2x = 16
divide both sides by 2
x = 8, plug this back into the equation
8 + y = 14
8 - y = 14
y = 6
Summarize the possible relationships for the y -intercepts, slopes, and number of solutions in a system of two linear equations in two variables.
A consistent system of equations has at least one solution.
A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.
A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.
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A building in a city has a rectangular base. The length of the base measures 75 ft less than twice the width. The perimeter of this base is 840 ft. What are the dimensions of the base?
The dimensions of the base are 180 feet in length and 165 feet in width.
Let the width of the base be "x".The length of the base is 75 less than twice the width.The length of the base is 2x-75.The perimeter of the base is given to be 840 feet.The perimeter of a rectangular base is twice the sum of its length and its width.The perimeter of a rectangular base is 2[tex]\times[/tex][(2x-75) + x].840 = 2[tex]\times[/tex](3x-75)420 = 3x-753x = 495x = 165Thus, the width is 165 feet.The length is equal to 2(165-75) = 2[tex]\times[/tex]90 = 180 feet.The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.
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Given:
C is the midpoint of segment AE
C is the midpoint of segment BD
Segment AE is congruent to segment BD
Prove:
Segment AC is congruent to segment CD
Left column:
1. C is the midpoint of segment AE
C is the midpoint of segment BD
Segment AE is congruent to segment BD
2. AC=CD
BC=CD
3. AE=BD
4. AE=AC+CE
BD=BC+CD
5. AC+CE=BC+CD
6. AC+AC=CD+CD
7. 2AC=2CD
8. AC=CD
9. Segment AC is congruent to segment CD
Have to find right column.
The solving for the Segment CE is congruent to segment BC is bellow.
Congruent segments defines as:Congruent segments are those with the same length. Collinear points are those that are on the same line. A theorem is a mathematically proven proposition. A segment's midway is a point that divides one segment onto two congruent segments.
In Geometry, what are Congruent Lines?Congruent lines are two line segments that have the same length. For example, if we possess two 6 cm line segments AB as well as PQ, we may say AB PQ and so they are congruent.
According to the given data:Solving for the right column:
C is the midpoint of segment AE
C is the midpoint of segment BD
Segment AE is congruent to segment BD(given)
2. BC = EC
BC=CD
3. AE=BD
4. BD = BC + CD
AE=AC+CE
5. AC+CE=BC+CD
6. CE+CE=BC+BC
7. 2CE=2BC
8. CE=BC
9. Segment CE is congruent to segment BC.
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Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 7,24,25
Given set of numbers 7, 24, 25 represent a right triangle.
By the triangle inequality theorem , the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 7² + 24²
= 49 + 576
= 625
= 25²
Since the sum of the squares of the two smaller sides is equal to the square of the largest side, by Pythagoras theorem the triangle must be right triangle.
Therefore, given set of numbers 7, 24, 25 represent a right triangle.
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The amount of a commission is directly proportional to the amount of a sale. A realtor received a commission of 48,000 on the sale of an 800,000 house. How much would the commission be on a 650,000 house?
How much would the commission be on a 650,000 house? $39,000
Given:
Rate of the house 1= $8,00,000
Commission for the house 1=$48,000
Rate of the house 2= $6,50,000
Commission for the house 2=x
What is the commission for the house 2?
8,00,000 ⇒48,000
6,50,000 ⇒ x (directly proportional)
On cross multiplication,
[tex]8,00,000 *x= 48,000*6,50,000\\\\x=\frac{48,000*6,50,000}{8,00,000} =39,000[/tex]
Commission for the house 2 = $39,000
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10 = z/2 + 7 what is 10
Answer:
19
I first do plus 2and 7 and 10=z
If 35% of a number is 63 and 60% of the same number is 108, find 25% of that number.
Answer:22.05
hope it help
and have a good day
Answer:
45
Explanation
35% is 63
so 5% is 9
so 100% is 180 cuz 5 multiplied by 20 is 100
so 25 % is 25 divided by 100 is 0.25×180 which is 45
hope that helps
How do you find significant figures? Explain in detail with examples.
