The slope of the line passing through the points (2, 1) and (6, 6) will be;
⇒ m = 5 / 4
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) is;
⇒ y - y₁ = m (x - x₁).
Given that;
The points on the line are (2, 1) and (6, 6).
Now,
Since, The slope of the line passing through the two points (x₁, y₁) and (x₂, y₂) will be;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Hence, The slope of the line passing through the points (2, 1) and (6, 6) will be calculated as;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (6 - 1) / (6 - 2)
⇒ m = 5 / 4
Therefore, The slope of the line passing through the points (2, 1) and
(6, 6) will be;
⇒ m = 5 / 4
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Find the missing exponent show work if u can
Answer: pretty sure its 5 to the power of 7
Answer:
7
Step-by-step explanation:
Exponents:[tex]\sf \boxed{\dfrac{a^m}{a^n}=a^{m-n}}[/tex]
In exponent division, if bases are same, subtract the exponents.
Let ? be 'x'.
[tex]\sf \dfrac{^{11}}{^x}=^4\\\\5^{11-x}=5^4[/tex]
As bases are same, compare the exponents.
11 - x = 4
-x = 4 -11
-x = -7
x = -7 ÷ (-1)
x = 7
There are 32 students in Ms. Bryant's class. 1/4 of those students use social media. How many students are allowed to use social media?
The most appropriate choice for fraction will be given by -
8 children are allowed to use social media.
What is fraction?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
Here,
Total number of children in class of Ms Bryant = 32
Fraction of students who use social media = [tex]\frac{1}{4}[/tex]
Number of children who use social media = [tex]\frac{1}{4} \times 32[/tex]
= 8
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A pail contains seven red, six green, three orange, and four black marbles. One marble is to be drawn at random. What is the probability that the marble is orange?
Answer:
[tex]\frac{3}{20}[/tex] or [tex]0.15[/tex]
Step-by-step explanation:
What is probability and how do we calculate it?
Probability, or the chances of a certain event happening at random, can be calculated with the following formula:
[tex]\bf P=\frac{\text{\bf number of successful outcomes}}{\text{\bf number of total outcomes}}[/tex]
In the formula written above, the number of successful outcomes refers to how many times the desired event is achieved (in this case, how many ways an orange marble could be picked), and the number of total outcomes refers to how many events were possible (how many ways a marble could be picked). (Note that the term "events" can be thought of as similar to "ways" - 3 events in which an orange marble is picked simply means that there are 3 ways for orange marbles to be picked.)
How do we calculate probability in this scenario?
In this scenario, we have 3 orange marbles out of a total of 7 + 6 + 3 + 4 = 20 marbles in the pail, and we want to find the probability, or chances, that one randomly picked marble out of the total will be orange. Thus, the number of successful outcomes is how many different events will result in an orange marble being picked. This is equal to how many orange marbles there are, which is 3. Similarly, the number of total outcomes is equal to how many different events there can possibly be when picking. This is equal to the number of marbles (not necessarily orange) there are in the pail, which is 20.
From the above observations, we can conclude that the probability of a randomly drawn marble being orange is [tex]\bf \frac{3}{20}[/tex] or [tex]\bf 0.15[/tex].
Analyze Nikia says that 3/2 divided by 1/4 equals 3/8. Draw a model and use words to
explain why Nikia's statement is not reasonable.
what is 3/2 divided by 1/4
Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal.
Nikia says that 3/2 divided by 1/4 equals 3/8.
Nikia's statement is wrong .
3/2 divided by 1/4 = [tex]\frac{3}{2} X \frac{4}{1}[/tex] = 6.
How do you divide two fractions with different denominators?To divide fractions with unlike denominators, first convert the division problem to a multiplication problem by multiplying the numerator of the division problem by the reciprocal of the denominator of the division problem, and then simplify.Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in dividing fractions is to find the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators. Then multiply the two denominators together.Here,
3/2 divided by 1/4 = [tex]\frac{3}{2} X \frac{4}{1}[/tex] = 6.
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on thursday, a local hamburger shop sold a combined total of hamburgers and cheeseburgers. the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold on thursday?
The number of hamburgers sold on Thursday is 106
Finding unknown quantity from Linear equation:
The Linear equation is a mathematical statement that is used to find an unknown quantity in a problem. Here to represent the Unknow qualities we use variables like x, y, z, etc.
Here we have,
On Thursday, a local hamburger shop sold a combined total of 424 hamburgers and cheeseburgers.
Since we don't know the number of hamburgers and cheeseburgers.
Represent them with variables x and y
Let x be the number of hamburgers
and y be the number of cheeseburgers
=> x + y = 424 ----(1)
Given that,
The number of cheeseburgers sold was three times the number of hamburgers sold
=> y = 3x -----(2)
From (1) and (2)
=> x + 3x = 424
=> 4x = 424
=> x = 106
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The complete question is
On Thursday, a local hamburger shop sold a combined total of 424 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Thursday?
The graph shows g(x), which is a translation of f(x)=x^2. Write the function for g(x)
The function after the transformation of f(x) is g(x) = (x - 2)^2
How to determine the transformation of the graph?The equation of the graph is given as
f(x) = x^2
The above equation a parent equation of a quadratic equation
Using the graph as a guide, we can see that
The function f(x) is translated to the right by 2 units to get g(x)
This means that
g(x) = f(x - 2)
So, we have
g(x) = (x - 2)^2
Hence, the equation of g(x) is g(x) = (x - 2)^2
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Nadine wants to cover a wall of her dining room with glass tiles. The wall is 8 feet by 8 feet, and the tiles are 16 inches by
16 inches. How many tiles will she need?
Nadine will need 36 tiles.
This question form linear equation.
What is linear equation ?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
We know, 1 feet = 12 inches
The wall is 8 feet by 8 feet
so convert it into inches we get, 96 inches by 96 inches.
It's given the tiles are 16 inches by 16 inches.
so, let x = tile she needs
x(16 * 16) = 96 * 96
now, find x
x = (96 * 96) / (16 *16)
x = 36
so, she needs 36 tiles
Therefore, Nadine will need 36 tiles.
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Line p has an equation of y=–5/6x–5. Line q includes the point (9,–4) and is parallel to line p. What is the equation of line q?
If line q is parallel to line p.The equation of line q will be y =-5/6 x + 3.5
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m =(y₂-y₁)/(x₂-x₁)
It is given that, Line p has an equation of y=–5/6x–5. Line q includes the point (9,–4) and is parallel to line p.
The slope of line p is -5/6.
If two lines are parallel the slope of the equation will be the same.
As a result, the slope of line q is -5/6.
The line passes through the point (9,–4) with slope -5/6 is,
y - y₁ = m (x -x₁)
y - (-4) = -5/6(x-9)
6(y+4) =-5(x-9)
6y+24 = -5x + 45
6y = -5x + 45 -24
6y = -5x +21
y =-5/6 x + 3.5
Thus, if line q is parallel to line p. The equation of line q will be y =-5/6 x + 3.5
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Sam had $26 when he went to the fair. He had a hot dog for $2.50, a drink for $1.75, and fried dough for $4.80. Then he bought a hat for $12.88. How much did he have left?
Answer:
4.07
Step-by-step explanation:
2.50+1.75+4.80+12.88=4.07 EZ
Obiri uses his bicyde to travel x km from his house to work He then uses 2½hours at a rate of 5km/h to his place of work If the distance from his house to work is 15 km. fond x
Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance traveled. Speed is inversely correlated with time and directly correlated with distance.
What are time, distance, and speed?
Speed tells us how swiftly or slowly an object is moving. While distance, as the name suggests, relates to the amount of space between two sites, time refers to the period of time separating two events. Speed is calculated as Distance x Time.
Time is calculated as Time = Distance Speed.
Distance is calculated as Distance = Speed x Time.
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A football team receives the ball on their own 50-yard line. They lose of 20 yards on the first play. What yard line is the ball on? (Please helppp!!)
If they give up 20 yards on the opening play, they're out. The ball is on the 30-yard line.
The starting line is the 50-yard line.
The new yard line following the first play Equals (The yard line following the first play) - (The number of yards lost)
As the football team lost 20 yards after the first play.
After the second play, the new yard line is 50 - 20 = 30 yards.
After the second play, the new yard line is 30.
The ball was on the 30-yard line at the end of the second play.
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………………helppppppppppp
Answer:
B.
Step-by-step explanation:
What is 44 laps in 4 days = ? Laps in 3 days
The graph of y=f(x) is shown on the grid. The graph G is a translation of the graph y=f(x)
The translated function is:
G(x) = f(x) - 1
b) The maximum of y = 2*f(x) is the point (0, 8).
How to write the equation of the translated function?
We know that G(x) is a translation of f(x), and the graph of G(x) is the pink one.
We can see that it is 1 unit below f(x), then we have a translation of one unit downwards, so we can write:
G(x) = f(x) - 1
This is the rule for G(x).
b) If the maximum of f(x) is (0, 4), then:
f(0) = 4
The maximum of 2*f(x) is also at x = 0, we will get:
2*f(0) = 2*4 = 8
So the maximum here is (0, 8).
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A line with a slope of 8 passes through the point (1, 8). What is its equation in
slope-intercept form?
The equation in slope-intercept form for the line with slope of 8 and passing through (1,8) is y = 8x
What is slope intercept form ?One of the most widely used forms for expressing a line's equation is the slope intercept form of a straight line. If you know the slope of the straight line and the y-intercept, you can use the slope intercept formula to determine the equation of the line ( the y-coordinate of the point where the line intersects the y-axis). Every point along a line must satisfy its equation in order for it to exist.
y=mx + b is the equation in slope intercept form
x=1, y=8
y=8x+ b
8 = 8 + b
b= 0
The equation in slope-intercept form for the line with slope of 8 and passing through (1,8) is y = 8x
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Given f(x) = 3x³ + kx- 10, and x - 2 is a factor of f(x), then what is the value of k?
Using factors, K has a value of -7.
Describe Factor.A divisor of an integer n, also known as a factor of n, is an integer m that may be multiplied by another integer to create n. In this case, it is also possible to assert that n is a multiple of m.
Given,
f(x) = 3x³ + kx- 10
Given factor of the equation is (x - 2)
Let us assume:
x - 2 = 0
x = 2
Since, x-2 is a factor of f(x)
∴ By factor theorem
f(2) = 0
3(2)³ + k(2) - 10 = 0
3(8) + 2k - 10 = 0
24 + 2k - 10 = 0
14 + 2k = 0
2k = -14
k = -14/2
k = -7
Hence, The value of k is -7
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Least to greatest PLEASE HELP ASAP!!!
Answer: d a c b
Step-by-step explanation:
b) suppose that pearson’s test of goodness of fit will be used to evaluate the claim that half of restaurants go out of business every three years, with a significance level of 0.01.(approximately) what will the chance of a type i error for this test be?
The Pearson's test of goodness fit can be used to check the significance of 0.01 but there would not be any type 1 error.
A statistical test that measures how well sample data matches a distribution from a population with a normal distribution is referred to as goodness-of-fit. Simply put, it hypothesizes if a sample is skewed or represents the data found in the actual population.
The goodness-of-fit test determines the difference between the actual and predicted values of the model in the case of a normal distribution. The chi-square is one of the approaches for determining goodness-of-fit.
Goodness-of-fit testing is a statistical technique used to draw inferences about observed values.
For example, check to see if a sampling group truly represents the entire population. That is, they establish the relationship between measured and predicted values in a model. When used in a decision-making process, goodness-of-fit tests allow you to foresee future trends and patterns.
Hence we can conclude that there would not be any error to the problem with a significance of 0.01 .
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the rectangular garden has an area 8x^2+14x-15 square meters.if the length measures (2x+5)meters.find the width.
The area of a rectangle can be calculated with this formula:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width of the rectangle.
In this case, you know that the area of the rectangle (in square meters) is represented with this expression:
[tex]8x^2+14x-15[/tex]And the length (in meters) is represented with the expression:
[tex]2x+5[/tex]Then, you can substitute the expressions into the formula:
[tex]\begin{gathered} A=lw \\ (8x^2+14x-15)=\mleft(2x+5\mright)w \end{gathered}[/tex]Now you need to solve for "w":
[tex]\begin{gathered} \frac{8x^2+14x-15}{2x+5}=w \\ \\ w=\frac{8x^2+14x-15}{2x+5} \end{gathered}[/tex]To simplify the expression, you can follow this procedure:
1. Factor the numerator as follows:
- Identify the coefficients:
[tex]\begin{gathered} a=8 \\ b=14 \\ c=-15 \end{gathered}[/tex]- Rewrite the middle term as a sum of two terms that makes that:
[tex]\begin{gathered} a\cdot c=(8)(-15)=-120 \\ \end{gathered}[/tex]And whose sum is:
[tex]b=14[/tex]Then, this is:
[tex]8x^2+14x-15=8x^2+(-6x+20x)-15=8x^2-6x+20x-15[/tex]Because:
[tex]\begin{gathered} -6+20=14 \\ \\ (-6)(20)=-120 \end{gathered}[/tex]- Make two groups of two terms:
[tex]=(8x^2-6x)+(20x-15)[/tex]- Factor out the Greatest Common Factor from each group of terms. Notice that the Greatest Common Factor of the first group is:
[tex]GCF=2x[/tex]And the Greatest Common Factor of the second group is:
[tex]GCF=5[/tex]Then:
[tex]=2x(4x-3)+5(4x-3)[/tex]- Factoring out this Greatest Common Factor:
[tex](4x-3)[/tex]You get:
[tex]=(4x-3)(2x+5)[/tex]2. Substitute the factored numerator into the equation:
[tex]w=\frac{(4x-3)(2x+5)}{2x+5}[/tex]3. Since:
[tex]\frac{(2x+5)}{(2x+5)}=1[/tex]You get:
[tex]\begin{gathered} w=(4x-3)(1) \\ w=4x-3 \end{gathered}[/tex]Therefore, you can determine that the answer is:
[tex]4x-3[/tex]NEED HELP! 76% of 250 and how do I show my work?
Answer:
Step-by-step explanation:
76/100 of 250
cancel out the zeroes
multiply and divide
76*250/100
=190
Answer:
190
Step-by-step explanation:
76%=76/100
so 76% of 250 can be written as :
76/100 * 250/1 =19000/100
you can simplify that and you get the answer 190
Help me out!! Click the pic to see the question
You have to plug 30 in for x
13.00 + 0.10(30)
13 + 3
$16
1. Is 8.6 x 107written in scientific notation?
Justify your response.
4) Which one of these pictures is not like the others? Use ratios to explain your reasoning. (From Unit 2, Lesson 1) co ΝΗ e M
We are shown three pictures and asked to identify which one of them is not like others.
Let us find the ratio of width and length of each inscribed cricle.
Picture L:
Width = 3 units
Length = 4 units
Ratio = 3/4 = 0.75
Picture M:
Width = 4 units
Length = 8 units
Ratio = 4/8 = 0.50
Picture N:
Width = 9 units
Length = 12 units
Ratio = 9/12 = 0.75
As you can see, picture L and N has the same ratio of width and length that is 0.75 but the picture M has a different ratio of width and length that is 0.50
Therefore, we can conclude that picture M is not like others.
Q(x)=-3x graph the linear function with points
The graph of the linear function passes through (0,0) , (1,-3) and (-2,6) and the graph is attached below.
A polynomial of degree one or even less, including the zero polynomial, is referred to as a linear function in calculus, analytic geometry, and related fields (the latter not being considered to have degree zero).
If a function's graph (in Cartesian coordinates) is a quasi-line in the plane, calculus and other related mathematical disciplines will refer to it as a linear function from the rational data to the real numbers. When the input vector is changed, the output frequently changes in a way that is proportional to the change in the input variable. When drawn using a different type of coordinate system, a straight line can represent a number of distinct functions.The graph of the function will be represented by the equation:
Q(x) = - 3x
at x=0 , Q(x) = 0
at x = 1 , Q(x) = -3
at x = -2 , Q(x) = 6
Therefore the graph will pass through the points (0,0) , (1,-3) and (-2,6).
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What is the value of |238| + |−28| − |−14|?
A 224
B 196
C 280
D 252
Answer:
D
Step-by-step explanation:
av= absolute value
av of 238 = 238
av of -28 = 28
av of -14 = 14
238 (+) 28 (-) 14 = 252
238 + 28 = 266
266 - 14 = 252
therefore 252 is the correct answer
hope this helped ^^
My brain stopped working so i need help
Answer:
-1.94
Step-by-step explanation:
Equation: [tex]\frac{c}{-1} + 0.56 = 2.5[/tex]
-
Solving the equation:
[tex]c + 0.56 = 2.5 * 1\\c + 0.56 = 2.5\\c = 2.5 - 0.56\\c = -1.94[/tex]
The volume of the rectangular prism is defined by V = lwh, find the volume of the
rectangular prism shown below.
Volume of the rectangular prism is 6x³ + 20x² - 2x - 24
How to find volume ?
The formula of volume of rectangular prism is v = lwh
l = length
w = width
h = height
so we have length = 3x+4 , width= x+3 & height = 2x - 2
apply to formula :
volume = lwh
v =(3x+4)*(x+3)*(2x -2)
finally we get ,
v =6x³ + 20x² - 2x - 24
Volume of the rectangular prism is 6x³ + 20x² - 2x - 24
volume :
Volume is a measure of occupied three-dimensional space.It is often quantified numerically using SI derived units or by various imperial units.The definition of length is interrelated with volume.To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.The formula for the volume of a prism is V=Bh. where B is the base area and h is the height. Liquid volume is a way to measure an amount of liquid by describing it how much 3-D space it occupies .To learn more about volume refer :
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A band expects to put songs on their next CD. The band writes and records % more songs than they expect to put on the CD. During the editing process, % of the songs are removed. How many songs will there be on the final CD?
The number of songs that will be found on the final CD is 3
How to determine the valueFrom the information given, we have the following deductions;
The number of songs that were put in the next CD is 12 songsThe percentage of extra songs that were added is 25%80% of the songs were removed after the final recordingWe have to determine the number of songs on the final CD,
For the recorded CD,
The percentage given is 25%
Then, we get;
12 + (25/100 × 12)
Divide through
12 + (0.25 × 12)
12 + 3
Add the values
15 songs
For the number of removed songs, the percentage given is 80%
Then, we get;
15 - (80/100 × 15)
Divide through
15 - (0.8 × 15)
Multiply the values
15 - 12
3
Hence, the value is 3
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What’s the middle point of -24 and 36
The middle point of the given numbers are 6 .
What does middle value mean?The median or the middle value is the number in the middle {2, 3, 11, 13, 26, 34, 47}, which in this instance is 13 since there are three numbers on either side.
To find the median value in a list with an even amount of numbers, one must determine the middle pair, add them, and divide by two.
The middle point of two numbers usually refers to the average of them .
thus the given numbers are - 24 and 36
This can be calculated by :
=> - 24 + 36 / 2
=> 12 / 2
=> 6
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In the first week of July, a record 1,040 people went to the local swimming pool. In the second week, 105 fewer people went to the pool than in the first week. In the third week, 140 more people went to the pool than in the second week. In the fourth week, 347 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
If In the first week of July, a record 1,040 people went to the local swimming pool, in the second week, 105 fewer people went to the pool compared to the first week, in the third week, 140 more people went to the pool than in the second week and 347 fewer people went to the pool in the fourth week than in the third week, the overall percentage decrease in the number of pool-goers over these four weeks, i.e., from the first week to the fourth week is 30%.
As per the question statement, 1,040 people went to the local swimming pool, in the second week, 105 fewer people went to the pool compared to the first week, in the third week, 140 more people went to the pool than in the second week and 347 fewer people went to the pool the fourth week than in the third week.
We are required to calculate the overall percentage decrease in the number of pool-goers over these four weeks.
To solve this question, we simply need to calculate the exact number people who went to pool in the fourth week, and then, calculate the percentage decrease in the number of pool goes, with respect to the record of the first week.
(1040 - 105 + 140 - 347) = [(1040 + 140) - (347 + 105)] = (1180 - 452) = 728,
That is, 728 people attended the pool in the fourth week.
Therefore, the decrease in the number of pool-goers from the first week till the fourth week = 312
Therefore, the overall percentage decrease in the number of pool-goers over these four weeks, i.e., from the first week to the fourth week will be,
[(312/1040) * 100]
= [{312/(104 * 10)} * 100]
= [(312/104) * (100/10)]
= (3 * 10)
=30%
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