The actual distance between Dallas and Austin in miles is 180 miles.
What is Unit conversion?Conversion of units means to convert between different units of measurement for the same quantity. Example of units are - m, cm, litre.
Given is the distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles.
The maps use scale in order to depict large distances with very small length measurements. As mentioned in the question - 1 cm represents 20 miles. This scale shrinks 20 miles of distance into 1 cm
Distance between Dallas and Austin on a map - 9 cm
On map - 1 cm = 20 miles
Therefore, 9 cm will be equivalent to (9 x 20) or 180 miles.
Hence, the actual distance between Dallas and Austin in miles is 180 miles.
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there are 3 sides to a triangle 1 measures 115 and the other 2 are x what is x. write and solve an equation
If one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each, then the equation to be solved to obtain the value of "x" is [(115 + 2x) = 180] and the value of "x" will be 32.5°.
As per the question statement, one angle of a 3-sided triangle measures 115° and the other two angles measure "x" degrees each.
We are required to determine a Linear equation of singular value that can describe our concerned situation, and solving which, we will be able to obtain our desired value of "x".
To solve this question, we need to know about one basic yet very important property of a triangle, that is, the sum of all the three interior angles of a triangle is equal to 180 degrees.
Here, the three angles measure 115°, x° and x°.
Therefore, our required equation will [(115 + x + x)° = 180°]
or, [(115 + 2x)° = 180°]
Now solving the above mentioned equation to obtain the value of "x", we get, [(115 + 2x)° = 180°]
Or, [2x = (180 - 115)°]
Or, (2x = 65°)
Or, x = (65/2)°
or, x = 32.5°
Equations: In Mathematics, an equation is a statement that expresses the relation of equation between two separate expressions (of numbers and/or variables) connected by an "equal to" sign.To learn more about Equations, click on the link below.
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Need help with this pls
Answer:
Step-by-step explanation:
Gabriella enlarged the size of a painting to a width of 78 cm. What is the new height if it was originally 6 cm wide and 19 cm
tall?
After using substitution method - The new height of the painting will be 247cm.
What is the substitution method?
To solve many simultaneous linear equations, use the substitution method in algebra. As implied by the name, this strategy involves replacing a variable's value from one equation with another.
we are given the original width of the painting to be 6cm and the original height to be 19cm.
after enlarging the size of the painting the new and enlarged width becomes 78cm
and we assume the new and enlarged height of the painting to be xcm.
we now the ratios
original height : original width = enlarged height : enlarged width ,
will remain equal,
Hence substituting the numerical values in the ratios we get
19/6 = x/78
19 * 78 = 6x
1482/6 = x
247cm =x
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What is the domain of the relation(x,y):y=x(x-3) / (x+4)(x-7) ?
{ x : x = R, x -4, x 7}
{ x : x R, x = -4, x 7}
{ x : x R, x -4, x 7}
{ x : x R, x -4, x 7}
The domain of the relation as given in the task content; (x,y): y = x(x-3) / (x+4)(x-7) is the set of all real number values except; -4 and 7 and hence is represented as; { x : x R, x ≠ -4, x ≠ 7}.
What is the domain of the relation given; { x : x R, x -4, x 7}?It follows from the task content that the domain of the relation given in the task content be determined.
On this note, since the domain of a relation or function simply refers to the set of all possible input values of such function.
Since the relation in this scenario is a rational function, it follows that the domain is the set of all real number values except that which renders the relation undefined.
Therefore, since the values which render the relation undefined, render the denominator equal to 0; we have;
(x+4)(x-7) = 0.
x = -4 OR x = 7.
Ultimately, the domain of the relation is the set of all real numbers except; x = -4 and x = 7.
Therefore, when represented by set builder notation; we have; { x : x R, x ≠ -4, x ≠ 7}.
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Which statement best defines an angle?
A.
two lines that share a common line segment called the vertex
B.
two rays that share a common endpoint called the vertex
C.
two line segments that intersect at a point called the vertex
D.
two lines that intersect at a point called the vertex
Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.
We need to define the angle.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
Parts of an Angle
There are two main parts related to an angle - the arms and the vertex.
Arms of the Angle
The two rays which join at a common point to form the angle are called the arms of the angle.
Vertex of the angle
Vertex is a common endpoint that is shared by the two rays.
Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.
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Jaime, Ralph, Marvin and Victor decided to put up a small business. Their initial investment is in the ratio of 8:3:12:2 respectively and Marvin's had invested Php 240,000. In terms of the profit they have decided to split them base on the ratio of their investment. In the first three months of their company made a total of Php 150,000 profit. Based on Marvin's initial deposit. How much did Victor invested?
Proportionately, based on Marvin's initial deposit, Victor invested Php 40,000 in the partnership.
What is a proportion?Proportion is like a ratio that shows a numerical relationship between two variables.
Proportions equate one ratio to a value.
For instance, we can equate Marvin's investment ratio to his investment.
This equation helps us to calculate the total investment made by the four partners in the small business.
Jamie Ralph Marvin Victor Sum of Ratio
Investment ratio 8: 3: 12: 2 25
Investment amount ? ? Php 240,000 ? ?
Marvin investment = Php 240,000 = 12/25
Total investment by the partners = Php 500,000 (Php 240,000/12 x 25)
Victor's investment = Php 40,000 (Php 500,000 x 2/25)
Profit for the year = Php 150,000
Thus, based on proportional contributions of Marvin, Victor's investment is Php 40,000.
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Which could not be the number of snowballs Penn has?
From the question, we have:
P(n) = P(n - 1) + n²
P1 = Po + 1² = 0 + 1 = 1
P2 = P1 + 2² = 1 + 4 = 5 (This is option C)
P3 = P2 + 3² = 5 + 9 = 14 (This is option B)
P4 = P3 + 4² = 14 + 16 = 30 (This is option D)
Therefore the number of snowballs cannot be 25.
So, the correct option is A, which is 25.
How do you solve this?
The value of x are 4 and 2.4 after simplifying and applying the quadratic formula.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The equation is:
4/(x - 2) + 3/(x - 3) = 5
4(x - 3) + 3(x - 2) = 5(x -2)(x - 3)
4x - 12 + 3x - 6 = 5x² - 25x + 30
5x² - 32x + 48 = 0
After solving the above quadratic equation by the formula:
[tex]\rm x = \dfrac{-(-32) \pm\sqrt{(-32)^2-4(5)(48)}}{2(5)}[/tex]
x = 4
x = 2.4
Thus, the value of x are 4 and 2.4 after simplifying and applying the quadratic formula.
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Find an equation of the line that passes through the given point and is parallel and perpendicular to the given lines. Point: (-2,3) Line: 3x-6y=3
The equation of the line parallel to 3x-6y=3 and passes through (-2, 3) is y = 1 / 2 x + 4
How to find equation of a line?The equation of the line passes through (-2, 3) and it is parallel to the equation 3x - 6y = 3.
Therefore, the equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptParallel lines have the same slope.
Hence,
3x - 6y = 3
3x - 3 = 6y
y = 1 / 2 x - 1 / 2
Therefore, the slope of the equation is 1 / 2.
Let's find the y-intercept using (-2, 3).
3 = 1 / 2 (-2) + b
3 + 1 = b
b = 4
Therefore, the equation is y = 1 / 2 x + 4
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4x^3 - 10 = 2x^3 + 6
Answer:
⚠️⚠️⚠️⚠️⚠️⚠️♀️
Step-by-step explanation:
⚠️⚠️⚠️♀️
I just need a brief explanation with the answer and I just need answers to the last two
The sum of the internal angles of a triangle is 180°
Since AD is parallel to BC and DC is parallel to AB, the angle ADC must be equal to the angle ABC, which is 123°
Then, the angle CAB is 180° - 24° - 123° = 33°
The function $y=-\frac{1}{40}\left(x-25\right)^2+15$ models the path of a football kicked by a player, where $x$ is the horizontal distance (in yards) and $y$ is the height (in yards). the player kicks the ball a second time so that it travels the same horizontal distance but reaches a maximum height that is 5 yards less than the maximum height of the first kick. write a function that models the path of the second kick.
The quadratic function that models the path of the second kick is given by:
y = -2/125(x - 25)² + 10.
What is the equation of a parabola of vertex (h,k)?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which the coefficients are explained as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.For the first kick, the equation is:
y = -1/40(x - 25)² + 15.
Meaning that the ball reached a maximum height of yards after an horizontal distance of 25 yards.
For the second kick, the horizontal distance is the same, but the maximum height if 5 yards less, that is, of 10 yards, hence the vertex is:
(h,k) = (25, 10).
Hence the equation is:
y = a(x - 25)² + 10.
After 50 yards, the ball hits the ground, hence the leading coefficient a is found as follows:
0 = a(50 - 25)² + 10
625a = -10
a = -10/625
a = -2/125
Hence:
y = -2/125(x - 25)² + 10.
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23. What is the mode of the following numbers, and what word can be used to describe the
distribution of the data set?
5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
We can conclude that the mode of the following data are 4 and 5.
What is the mode?A set of data values' mode is the value that appears the most frequently. The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable. In other words, it is the value that will be sampled most frequently.As the given data set is:
5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7Mode is calculated when in the given data set the number appears most often.
So, count each number as we get the result:
4 appears 3 times, also5 appears 3 timesHaving two modes is called "bimodal".Therefore, the modes are 4 and 5.
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-2 3/8 as an improper fraction
please help asap thank u so much
Answer: -19/8
What is an improper fraction?
An improper fraction is where the numerator is greater than the denominator. To turn -2 3/8 into an improper fraction, we will "combine" -2 and 3/8.
First, we will find what -2 becomes. -2 is the same as two wholes:
-2 * 8 = -16
Next, we will subtract this into the numerator of the fraction:
-16 - 3 = -19
Lastly, we will put this new numerator over the denominator:
-2 3/8 = -19/8
a recycling bin 3kg of plastic and 500g of paper whats the ratio of plastic to paper in the bin give answer in simpliest form
Based on the weight of the plastic to the weight of the paper, the ratio of plastic to paper in the simplest form is 6 : 1
How to find the ratio?To find the ratio of plastic to paper, there is a need to convert the weights such that they have the same units.
Assuming we convert the plastics to grams, the number of grams of plastic would be:
= 3 kg x 1,000 grams per kg
= 3,000 grams
The ratio then would be:
3,000 grams of plastic : 500 grams of paper
To get to the simplest form, divide both sides by 500:
3,000 / 500 : 500 / 500
6 : 1
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Write a sentence as an equation. Use x to represent "a number." twice a number gives 108
Answer:
2x=108
Step-by-step explanation: This is the equation because when it says twice a number, you are multiplying a number two times. In this case, the number is not given, so x is the variable being multiplied two times. If the number was 8, it would look like this: 2(8)=108. Of course this isn't true, but to find the actual answer you would divide two on both sides of the equation. This is so that both of the two's cancel out on the left side of the equation. and the variable is left on that side. Our goal is to isolate the variable. In these types of equations, our goal is to isolate the variable and find what the variable is worth. If we do 108 divided by 2 that gives us 54. Since there was x left on the left side of the equation and there is 108 left on the right side we have our equation. x=54
Number explanation below
2x=108
2x/2=108/2
x=54
Mason and Daisy are building towers. Each one of Masons blocks is 6cm tall. Each one of Daisys blocks is 8cm tall. They both build towers that are exactly the same height. What is the smallest height that their towers could be?Give your answer in cm
Reason:
GCF = greatest common factor
LCM = lowest common multiple
GCF of 6 and 8 = 2
LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24
We can list out the multiples of each to confirm this
multiples of 6 are: 6, 12, 18, 24, 30, ...multiples of 8 are: 8, 16, 24, 32, ...If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.
The smallest height that their towers could be 24 cm.
What is the lowest common factor?The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). The least Common Multiple and Least Common Divisor are other names for it (LCD). For instance, 12 is the least frequent multiple of 4 and 6.
GCF = greatest common factor
LCM = lowest common multiple
GCF of 6 and 8 = 2
LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24
We can list out the multiples of each to confirm this
multiples of 6 are 6, 12, 18, 24, 30, ...
multiples of 8 are: 8, 16, 24, 32, ...
If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.
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Look at this graph.
What is the equation of the line in slope-intercept form?
Answer:
y = 4x -80
Step-by-step explanation:
We need the slope and the y intercept.
The y intercept is -80. This is where the line crosses the y axis.
The slope is the change in y over the change in x.
Let's go from point (0,-80) the y intercept the the point that cross the x axis (20,0) Start at -80, how many units to you go up until you are at the same level as point (20,0)? 80 units. Now, from (0,0) how many units do you go right to get to (20,0)? 20.
We end up go 80 unit up and 20 units right, this would be written [tex]\frac{80}{20}[/tex] Which simplifies to 4. This is our slope.
Slope (m) = 4
y intercept (b)= -80 Plug those into
y = mx + b
y = 4x -80
7) A certain store's sales increased by 175% compared to the previous year. How many squares
would be shaded on 10 x 10 grids to represent 175%?
squares
The given percentage cannot be represented on the grid.
What is percentage?
A percentage (from Latin: per centum, "by a hundred") is a quantity or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is commonly used, however the abbreviations "pct.", "pct," and sometimes "pc" are also used. A % is a non - dimensional (pure) quantity; it does not have a unit of measurement. In the context of sports statistics, the term "%" is frequently used incorrectly since the referred figure is stated as a decimal proportion, not a percentage. Similarly, a team's winning percentage, or the fraction of matches won, is commonly reported as a decimal proportion; a team with a.500 winning percentage has won 50% of its matches.
The given percentage cannot be represented on the grid.
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Please help asap, I will give brainliest
Answer:
the answer is A
Step-by-step explanation:
To check your answer, move 4 units to the right and 3 units up
Write an equation of the line that passes through the points. (2,8), (-2,10)
Explanation.
The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)
To do this, we can use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]In our case, we have
[tex]\begin{gathered} x_1=2 \\ y_1=8 \\ x_2=-2 \\ y_2=10 \end{gathered}[/tex]We will simply put all the values above into the formula to get the equation of the line
[tex]\frac{10-8}{-2-2}=\frac{y-8}{x-2}[/tex]Simplifying further
[tex]\begin{gathered} \frac{2}{-4}=\frac{y-8}{x-2} \\ \\ -\frac{1}{2}=\frac{y-8}{x-2} \end{gathered}[/tex]Cross multiplying
[tex]\begin{gathered} y-8=-\frac{1}{2}\left(x-2\right) \\ y-8=-\frac{1}{2}x+1 \\ y=-\frac{1}{2}x+1+8 \\ y=-\frac{1}{2}x+9 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=-\frac{1}{2}x+9[/tex]Mitchell bought 3 postcards for $3.14. At this rate, how much would 12 postcards cost?
Answer:
12.56$
Step-by-step explanation:
12 / 3=4
4 × 3.14 = 12.56
If there is no solution to a compound inequality, does the compound inequality involve OR or AND? Explain.
If there is no solution to a compound inequality, it can involve AND.
A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the equal validity of both statements in the compound sentence. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true.
The term "OR" can help us find more solutions, whereas the phrase "AND" can help us find less solutions. As a result, we can create a compound inequality with no solution by using "AND."
Therefore, if there is no solution in compound inequality, it may involve AND.
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The function f(t)=16t2 represents the distance (in feet) a dropped object falls in t seconds. The function g(t)=s0 represents the initial height (in feet) of the object. A necklace is dropped from a height of 64 feet. After how many seconds does the necklace hit the ground?
By solving a quadratic equation, we will see that the necklace hits the ground 2 seconds after it is dropped.
After how many seconds the necklace hits the ground?We know that the function:
f(t) = 16*t^2
Represents the distance that an object falls down in t seconds.
If the necklace is dropped from a height of 64 feet, the necklace will hit the ground when the distance that an object falls down in t seconds is equal to 64 feet, so we just need to solve the quadratic equation:
f(t) = 64
16*t^2 = 64
t^2 = 64/16 = 4
t = √4 = 2
The necklace will hit the ground after 2 seconds.
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Find g(x), where g(x) is the translation 2 units right of f(x)=x.
Write your answer in the form mx+b, where m and b are integers.
The image of the function f(x) = x , after the translation is g(x) = x -2 .
In the question
it is given that
the function f(x) = x ,
and f(x) has to be translated 2 units to the right means subtract 2 from the function .
which means g(x) = f(x) - 2
substituting f(x) = x , we get
g(x) = x - 2
the answer in the form of mx+b is g(x) = x - 2
(can refer to the graph given below)
Therefore , The image of the function f(x) = x , after the translation is g(x) = x - 2 .
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Determine the distance between the points (−4, −7) and (−8, −13). square root of 10 units square root of 82 units square root of 544 units square root of 52 units
Question Should look like
determine the distance between (-4,-7) and (-8,-13)
A. [tex]\sqrt{10}[/tex]
B. [tex]\sqrt{82}[/tex]
C. [tex]\sqrt{544}[/tex]
D. [tex]\sqrt{52}[/tex]
Answer: D. [tex]\sqrt{52}[/tex]
Step-by-step explanation:
[tex]a^{2}+b^{2}= c^{2}[/tex]
a =(8-4)... b=(13-7)
a=4, b=6
therefore...
[tex]a^{2}+b^{2}= c^{2}\\4^{2}+6^{2}=c^{2}\\16+36=c^{2}\\52=c^{2}\\c=\sqrt{52}[/tex]
Help me please! (And sorry for my english)
Factorize the expression: 7abcd-21bcde+14cdef
Answer:
7cd(ab-3be+2ef)
Step-by-step explanation:
they all have the number 7 In common so you take that out and you take out whatever letters they have in common
Answer:
7cd(ab - 3be + 2ef
Step-by-step explanation:
Simplify:
7abcd = 7 * a * b* c * d
21bcde = 7 * 3 * b * c * d * e
14cdef = 7 * 2 * c * d * e * f
GCF = 7 cd
7abcd - 21bcde + 14cdef = 7cd*( ab - 3be + 2ef)
Find the x- and y-intercepts of the graph of x+y=18. State each answer as an integer or an improper fraction in simplest form
The x- and y-intercepts of the graph of x + y = 18 both have the values of 18
What is the x-intercept of the function?The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0
How to determine the x- and y-intercepts of the graph?The equation of the graph is given as
x + y = 18
To calculate the x-intercept, we set the value of y to 0
This is represented as
y = 0
So, we have the following equation
x + 0 = 18
Evaluate the like terms
x = 18
To calculate the y-intercept, we set the value of x to 0
This is represented as
x = 0
So, we have the following equation
0 + y = 18
Evaluate the like terms
y = 18
This means that the x-intercept has a value of 18 and the y-intercept has a value of 18
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Mrs. Rollins raises prize chickens. Each chicken eats the same amount of food. Mrs. Rollins bought 100 pounds of chicken food last week. How much food did each chicken eat?
10 pounds of food each chicken eat last week.
This is a problem from an algebraic equation. We can solve this problem by following a few steps.
Each chicken eats the same amount of food, as per the question. Let's assume there is x number of chickens.
Therefore, if each chicken eats the same amount of food then the total food required for all chickens is, (x × x) = x² pound.
Again, Mrs. Rollins bought 100 pounds of chicken food.
Hence x² is equivalent to 100 pounds. We can generate an equation from this. Which is,
x² = 100
Or, √x² = √100 [ root both sides ]
Or, x = 10
Now, we can conclude that there are 10 chickens and each chicken eats 10 pounds of food in a week.
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If angle DEF is a straight angle, angle DEG = (23x - 3) , and angle GEF = (12x + 8) , find each measure.
x=
mmm
The measure of x, m∠DEG, m∠GEF and m∠DEF will be 5,112°,68°and 180° respectively.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle."
It is given that,
m∠DEG = (23x-3)°
m∠GEF = (12x+8)°
As m∠DEF is a straight angle its angle measurement is 180
As a result,
m∠DEF=m∠DEG+m∠GEF
180°=m∠DEG+m∠GEF
Put the given values
180°=(23x-3)°+(12x+8)°
180=35x+5
35x=180-5
35x=175
x=5
Substitute the value of x to obtain all the angles as
m∠DEG=(23x-3)°
m∠DEG=(23(5)-3)°
m∠DEG=112°
For m∠GEF,
m∠GEF=(12x+8)°
substitute the value of x
m∠GEF=(12(5)+8)°
m∠GEF=68°
Thus, the measure of x, m∠DEG, m∠GEF and m∠DEF will be 5,112°,68°and 180° respectively.
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