Answer:
MP = 19
Step-by-step explanation:
MP = MN + NO + OP
we require to find OP and MN before we can evaluate MP
NO + OP = NP , that is
8 + OP = 15 ( subtract 8 from both sides )
OP = 7
and
MN + NO = M0 , that is
MN + 8 = 12 ( subtract 8 from both sides )
MN = 4
Then
MP = MN + NO + OP = 4 + 8 + 7 = 19
even if an independent variable has an effect on the dependent variable, it is still possible to obtain a sample mean that is very similar to the original population mean. what outcome is likely if this happens?
even if an independent variable has an effect on the dependent variable, it fail to reject the null hypothesis and make a type II error
Even if a treatment is effective in the real world (it has an effect), it is still possible to obtain a sample mean that is so similar to the population mean that the sample mean doesn't fall in the critical, or rejection, region. If this happens, you are likely to fail to reject the null hypothesis and make a type II error.
Since that sample mean is so similar to the population mean, the treatment effect may not be detected on analysis even though it is in fact significant, this will cause the research to erroneously concluded that the treatment effect is zero and accept the null hypothesis when it is actually not zero. This is a type II error. Type II error in statistics means the non-rejection of a false null hypothesis and type I error is the rejection of a correct null hypothesis.
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21. Higher Order Thinking The product
of a factor and 0.1 is 8.35. What is the
factor? What is the product of the factor
and 0.01?
The product of factor 83.5 with 0.01 will be 0.835
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, the given statement is :
The product of a factor and 0.1 is 8.35
Let the factor be a then :
a x 0.1 = 8.35
a = 8.35/0.1
a = 83.5
The factor is 83.5
Now, the product of this with 0.01 will be :
83.5 x 0.01 = 0.835
Therefore, The product of factor 83.5 with 0.01 will be 0.835
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It was hot at the boardwalk. The Real Scoop was doing very well. Russell had just
served up 55 cones, some single scoops, some double scoops, and some triple
scoops. If he served up a total of 103 scoops, how many of the cones were single
scoops, how many were double scoops, and how many were triple scoops?
NEED MORE THEN 2 ANSWERS!! PLEASE
Answer:
Image result for the government
The Federal Government is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.S. Constitution in the Congress, the President, and the Federal courts, respectively.
Step-by-step explanation:
James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. how much time did he have left after he finished cleaning?
James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. time left after he finished cleaning is 4 hour 36 minutes
James took 97 minutes to clean his house.
there were 12 rooms in the house,
and it took him the same amount of time to clean each room
how much time did he have left after he finished cleaning?
one room clean =97 minutes
12 room clean = 97*12 amount of minutes
= 1164 minutes
= 19hour 24 minutes
James took 19 hour 24 minutes to clean 12 room
amount of time left = 24 hour - 19 hour 24 minutes
= 4 hour 36 minutes
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Li Zhen, Kara and Rose were typing. Li Zhen typed 2 times as fast as Kara. The ratio
of the number of words Kara typed to the number of words Rose typed was 4 : 1.
a) What was the ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed?
Kara typed 48 words.
b) How many words did Li Zhen, Kara and Rose type altogether?
The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed = 8 : 4 : 1
Total numbers of words Li Zhen, Kara and Rose typed = 156 words
What is Ratio ?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Since, it's given that
the number of words Kara typed = 48
number of words Li Zhen typed = 2 x 48
=96words
a) The ratio of the number of words Kara typed to the number of words Rose typed = 4:1
Since, it's given that
the number of words Kara typed = 48
let, the number of words Rose typed = x
then, by equating them we get,
4/1 = 48/x
4x = 48
x = 48/4
x = 12
The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed :
= 96 : 48 : 12
= 8 : 4 : 1
b) Now we know that,
The number of words Li Zhen typed = 96words
The number of words Kara typed = 48words
The number of words Rose typed = 12words
Then, the total numbers of words Li Zhen, Kara and Rose type altogether
= 96 + 48 + 12
= 156 words
Hence, the total numbers of words Li Zhen, Kara and Rose type altogether is 156 words
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Solve y3 = 1.
y = −1
y = 1
y = ±1
y = 3
The value of the expression y³ = 1 is y = 1.
Expression:
An expression also known as algebraic expression consisting of variables, numbers and an arithmetic operation between them.
Given,
Here we have the expression y³ = 1.
Now, we need to find the value of y.
While we looking into the expression, when we have to find the value of y then we have to move the cube vale to the other side.
When we move the cube to the other side then it will be the cube root of the number.
While we simplify the cube root of the number then we get the result.
Therefore,
y³ = 1
Move the cube to the other side,
y = ∛1
We know that,
∛1 = 1
So, the value of y = 1.
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3. USE A MODEL To produce a handcrafted rocking chair, a woodworker needs to spend
30 hours on woodworking, and 3 additional hours on painting. The same woodworker
can make a simpler kitchen chair in 24 hours, and it takes an additional 3 hours of
painting. He has a maximum of 192 hours available for woodworking and 21 hours
available for painting in a month. The rocking chair sells for $550, and the kitchen chair
sells for $300. Write a system of inequalities to model this situation as well as a profit
equation, and find the number of rocking chairs and kitchen chairs the woodworker
should make to maximize his revenue for the month.
The woodworker should make atmost 4 rocking kitchen chair and 3 simple kitchen chair to maximize the profit under given conditions of 192 woodworking hours and 21 painting hours.
What is maximum profit?Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.
What is inequality?inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to etc.
Given,
Time needed to woodwork a rocking kitchen chair= 30 hours
Time needed to paint a rocking kitchen chair=3 hours
Time needed to woodwork a simple kitchen chair= 24 hours
Time needed to paint a simple kitchen chair=3 hours
Maximum time given by worker= 192 hours for woodwork and 21 hours to paint
Let x and y be the maximum number of chairs created by woodworker of both the types.
so the system of inequality would be,
30x+24y<192 ......(1)
3x+3y<21 ......(2)
To find x and y,
multiply the (2) by 10
30x+30y<210
subtract (1) from (2)
30x+24y-(30x+30y)<192-210
-6y<-18
y<3
3x+3y<21
3x+3*3<21
3x<12
x<4
By this, he can make maximum 4 rocking and 3 simple kitchen chair to earn the maximum profit.
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The equation below represents Function A and the graph represents Function B: Function A f(x) = x − 9 Function B graph of line going through ordered pairs negative 1, negative 3 and 2, 3 Which equation best compares the slopes of the two functions? (1 point) Slope of Function B = 2 x Slope of Function A. Slope of Function A = Slope of Function B Slope of Function A = 2 x Slope of Function B Slope of Function B = − Slope of Function A
We will see that the slope of function B is 2, and the slope of function A is 1. This means that the correct equation is:
Slope of function B = 2*Slope of Function A
Which equation compares the slopes?
First, a general linear equation is:
y = a*x + b
Where a is the slope and b the y-intercept.
Here the function A is:
f(x) = x - 9
Then the slope is equal to 1.
We know that function B is a line that passes through (-1, -3) and (2, 3)
Then the slope is:
s = (3 + 3)/(2 + 1) = 6/3 = 2
So the slope of function B is 2, and the slope of function A is 1. Then the equation is:
Slope of function B = 2*Slope of Function A
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give h(x)=-2x-3 find h(6)
Answer: h(x)=-15
Step-by-step explanation: First: We plug in h(6) for x. Gives us -2(6)-3. When we solve -12-3. -15.
Answer:
h(6) = 9
Step-by-step explanation:
h(x) = 2x – 3,
Let x = 6
h(6) = 2*6 -3
= 12 -3
= 9
Q2 - Word problems.
Solve the problems and write the answers
A trifle recipe requires 1½ cups of sugar. A chocolate cake recipe requires twice as much sugar. How many cups of sugar go into the cake?___
[tex] \frac{?}{?} [/tex]
Answer:
The answer is 3, but here’s how I got that answer.
Step-by-step explanation:
As we know the trifle recipe requires 1 ½ cups of sugar, and the chocolate cake requires double the amount of sugar.
You have two options.
Multiply 1½ by 2
1½ x 2 = 3
———————————
Or add 1½ + 1½
1½ + 1½ = 3
———————————-
Wasn’t sure what you were asking for with this this question, but hope it helped.
Answer: 3
Step-by-step explanation:
Since the trifle cake uses 1 ½ cups of sugar and the chocolate twice as much sugar as the trifle cake you should multiply 1 ½ x 2 which would equal 3. So, 3 cups of sugar should go into the cake. (This is my first answer to a question so I'm sorry if I'm confusing)
3x + 6x = 45 solve for x
Which of the following expressions is equivalent to x ⅔
Using the conversion of a fractional exponent to a rational expression, the equivalent expression to x^(2/3) is given by:
K. [tex]\sqrt[3]{x^2}[/tex]
How to convert a fractional exponent to a rational expression?A fractional exponent is converted to a rational expression applying the law of indices, in which the numerator, which is the top term of the fraction, will be the power of the base, while the denominator, which is the bottom term of the fraction, represents the root.
The law of indices is illustrated as follows:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
In the context of this problem, the expression is:
x^(2/3).
Hence the coefficients are n = 2 and m = 3, and thus the equivalent expression is:
[tex]x^{\frac{2}{3}} = \sqrt[3]{x^2}[/tex]
Meaning that option K is correct.
What is the missing information?The possible options for the question are missing, and are given by the image at the end of the answer.
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Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. the speed, s, is measured in miles per hour, and distance, y, is measured in yards. the line of fit is given by Å· = 3.98 53.59s. if the ball travels for a duration of 5 seconds, what is the predicted distance of the ball? 267.95 feet 271.93 feet 283.87 feet 287.85 feet
By evaluating the linear equation in t = 5 seconds, we will see that the distance traveled is 271.93 feet.
What is the predicted distance of the ball?
Here we know that the line that defines the distance traveled by the ball (y) as a function of time (t) is:
y = 3.98 + 53.59*t
Now we want to predict the distance traveled y the ball if it travels for 5 seconds, so we just need to evaluate the above linear equation in t = 5.
So we will get:
y = 3.98 + 53.59*5 = 271.93
So we conclude that the distance traveled in that time is 271.93 feet.
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Answer: 271.93 feet
Step-by-step explanation:
I took the test
what is 7+2b+7b+2 like terms where needed to be simplfied
Answer:
9+9b
Step-by-step explanation:
Answer:
9 +9b
Step-by-step explanation:
Simplify:Like terms are terms that have same variable with same power.
2b and 7b are like terms.
7 and 2 are like terms (constants).
7 + 2b + 7b + 2 = 7 + 2 + 2b +7b
= 9 + 9b
Determine the x- and y-intercepts of the graph of x−4y=8
Then plot the intercepts to graph the equation.
Show a picture, please.
The x-intercept of the equation is: (8, 0)
The y-intercept is of the equation is: (0, -2)
How to Find the X-intercept and the Y-intercept of a Line?The x-intercept is the point on the x-axis where the line cuts across the x-axis, while the y-intercept is the point on the y-axis that the graph intercepts.
The value of the x-intercept is the value of x when the value of y is equal to zero, while the y-intercept of a graph is the value of y when the value of x is zero.
Given the equation of the linear graph as, x - 4y = 8, to find the x-intercept, substitute y = 0 into the equation:
x - 4(0) = 8
Solve for x:
x - 0 = 8
x = 8
The x-intercept is: 8.
(8, 0)
To find the y-intercept, substitute x = 0 into the equation, x - 4y = 8 and solve for the value of y:
0 - 4y = 8
-4y = 8
-4y/-4 = 8/-4
y = -2
The y-intercept is: -2.
(0, -2)
The graph for x - 4y = 8 is shown in the attachment.
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2. Julian is cutting lengths of rope for a class project. Each rope length should be 10
inches long. The specifications allow for a difference of 0.5 inches. Which absolute
value inequality represents the difference between the rope lengths cut and the
specifications?
The absolute value inequality represents the difference between the rope lengths cut and the specifications are | x - 10 | ≤ 0.5.
What is the modulus value?Modulus value always outputs a positive value irrespective of the input value sign.
Julian needed to cut ropes for her school project and their length should be 10 inches long with a difference of 0.5 inches.
∴ The maximum allowable length of the rope should be (10 + 0.5) = 10.5 inches and the minimum allowable length of the rope should be
(10 -0.5) = 9.5 inches.
The absolute value of inequality that represents this condition is,
| x - 10 | ≤ 0.5.
x - 10 ≤ 0.5.
x ≤ 10.5, And
- ( x - 10) ≤ 0.5.
-x + 10 ≤ 0.5.
- x ≤ - 9.5. ( think of moving the terms on either side to make x positive).
x ≥ 9.5.
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3k-8=7
what is the value of k?
Answer:
[tex]\sf{k=5}[/tex]Step-by-step explanation:
[tex]\stackrel\ell{\boxed{\boxed{\begin{minipage}{7cm}\\\begin{aligned}\sf{3k-8=7}\\\downarrow\\\sf{3k=7+8}\\\downarrow\\\sf{3k=15}\\\downarrow\\\boxed{\boxed{\sf{k=5}}}\end{aligned}\end{minipage}}}}}[/tex]
I hope this helps!!
Answer:
5
step by step explaination
first side change -8=+8
7+8
now divide 15 by 3
Then
K=5
How are the entries of the matrix named by position?
⎡⎣⎢071−1−8236−35−4−5−2−98⎤⎦⎥
Drag an answer into each box to match the matrix entry with its position in the matrix.
The most appropriate choice for matrix will be given by-
The position number of all the matrix entries are
[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]
What is a matrix?
Any arrangement of numbers in the form of rows and columns are called matrix. The numbers inside a matrix is known as elements of the matrix.
The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.
We can do addition, subtraction, multiplication on matrix but two matrices cannot be divided.
Here,
The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.
The given matrix is
[tex]\left[\begin{array}{ccccc}0 & -1 & 3 & 5 & -2\\7&-8&6&-4&9\\1&2&-3&-5&8\end{array}\right][/tex]
The position numbers of all the matrix entries are given below
[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]
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Analyzing Exponential Functions
Compare the table values of f(x)
and g(x).
f(x) = 9x
g(x) = 9/1/2
The outputs of g(x) are the
of f(x).
Rising or growing steadily and quickly: a city in exponential expansion. noun. Mathematics the value of the constant e raised to the power of a given expression, represented as the exponential of 3x, e3x. something that is positive and raised in power.
Explain exponential functions?In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.
The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The values of f(x) and g(x) in the table for various values of f(x) = 9x + 7 and g(x) = 5x
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Exploration: More Conversions
The other day you worked with converting meters, centimeters, and millimeters. Here are
some more unit conversions.
1. Use the equation F = C + 32, where F represents degrees Fahrenheit and C
represents degrees Celsius, to complete the table.
temperature (C)
20
3.
4
175
2. Use the equation c = 2.54n, where c represents the length in centimeters and n
represents the length in inches, to complete the table.
length (in)
10
8
temperature (F)
3-—-/-
length (cm)
I
Are these proportional relationships? Explain why or why not.
They have not a proportional relationship.
What is Comparing Relationships with Equations?The equation that represents a proportional relationship, or a line, is y = k x , where is the constant of proportionality. Use k = y x from either a table or a graph to find k and create the equation. Proportional relationships can be represented by tables, graphs and equations.
From table 1.
temperature ( ∘ C) temperature ( ∘ F)
20 68
4 39.2
175 347
converted by using equation F=[tex]\frac{9}{5}[/tex]C+32
From table 2.
length (in) length (cm)
10 25.4
8 20.32
[tex]3\frac{1}{2}[/tex] 8.89
Converted by using equation c = 2.54n where c represent length (in cm) and n represent length in inches.
Now,
we will check the proportionality by [tex]\frac{c}{F}[/tex] if all the values of this ratio is same for the tables then they are showing proportionality .
From the table they are not showing proportionality.
Hence, They have not a proportional relationship
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Mimi earned a total of $38 by selling 19
cups of lemonade. How many cups of
lemonade does Mimi need to sell in all to earn
$44?
Answer:
22 cups in total
Step-by-step explanation:
In order to solve this problem we need to know how much money Mimi makes by just selling 1 cup of lemonade. We can find this by dividing
38/19 = 2
Now that we know how much money Mimi makes by just selling 1 cup of lemonade, we can use this to find how many cups she needs to sell in total to earn $44. We can use this equation
2x = 44 (x = cups of lemonade)
Now we solve for x
2x =44
/2 /2
x = 22
So Mimi needs to sell 22 cups in total to earn $44 dollars. Hope this helps :)
----------------------------------------------
Bonus: she need to sell 3 more cups lol incase you need to know
which situation is best modeled by an exponential distribution? suppose that, in a strand of dna, mutations occur randomly and independently of other mutations at an average rate of one mutation per 12,400 a. a geneticist is examining a strand of dna. what is the probability that she will observe a mutation within the next 15,000 a? suppose that defects in electrical wire occur randomly and independently of other defects. the average rate is 0.001 defects per cm of wire. what is the probability that a 100 m long spool of wire will contain fewer than two defects? suppose that a traffic light is green for 30 s, yellow for 4 s, and red for 56 s. if cars arrive at the intersection randomly, what is the probability a car will arrive when the light is yellow?
By probability , An average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .
Describe probability using an example?
By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are just two outcomes when you flip a coin: either it comes up heads or tails.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.Suppose that, in a strand f DNA ,mutations occur randomly and independently of other mutations .
at an average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .
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Tamika's car used 13 gallons to travel 572 miles. How far can she travel on 7 gallons?
Answer:
308
Step-by-step explanation:
Based on the given conditions, formulate: 7 x 572/13
Cross out the common factor: 7 x 44
Calculate the product or quotient: 308
Answer:
308
Step-by-step explanation:
572 divided by 13 is 44 which means there is 44 miles per gallon. So multiply 44 x 7 and you get 308 miles.
having trouble coming up with formula
Okay, here we have this:
Considering the provided information, we are going to calculate the speed at which he runs, so we obtain the following:
So we have the following equation:
Distance Traveled Walking + Distance Traveled Running = Total Distance
Distance Traveled Walking + Distance Traveled Running = 20 miles
And taking into account that speed is equal to distance over time, if we take speed to which runs as x we have:
((x/2) mi/h * 2h) + (x mi/h* 1.5h) = 20 miles
x mi+ 1.5x mi= 20 mi
2.5x mi=20mi
x = 20mi/2.5mi
x=8
Finally we obtain that he runs at 8 miles per hour.
The standard binet intelligence quotient iq measures intelligence. iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. what percentage of the population has an iq score between 70 and 115?
iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855% of the population has an iq score between 70 and 115
What is z-score?
The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.
Using z tables, you may calculate the proportion of the population that is either below or above the score.
Now, according to the question;
IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.
A z score is determined as follows:
z = (x - μ)/σ
μ = mean of the distribution
σ = standard distribution of the sampling.
Calculation for the z score for x = 70 and 115
z= (70-100)/15
= -30/15
=-2
and x=115
z = (115 - 100)/15
= 15/15
z = 1.0
Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,
P( -2 < z < 1)= P(z<1) - P(z< -2)
= 0.8413 - 0.02275
= 0.81855
Therefore, the percent of the population has an iq between 70and 115 is 81.855%.
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Write the equation of the line that passes through the points (-6,-1) and (-4,2). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}[/tex]
2. Three times one number minus a second is 8, and the sum of
the numbers is 12. Find the numbers.
Answer:
8
Step-by-step explanation:
Let the number be “X"
Solution:
4 + (X/2) = 8
(X/2) = 8-4
(X/2) = 4
X = 4×2
X = 8
THEREFORE THE ANSWER IS “8”
Answer:
This is a simultaneous equation.
Step-by-step explanation:
let the first number be x and second be y
Lets make an equation first:
3x-y = 8 .....(1)
x+y = 12........(2)
Solve by elimination.
Dass
3x+x= 8+12
4x=20
x=5
find y
x+y=12
5+y=12
y=12-5
y= 7
Therefore the two numbers are 5 and 7
Use the figure for #10-13. m/ABD = 127⁰
10. Find m/ABC =
A
II. Find m ZACB =
12. Find m/ ACD =
13. Find m/ CAB
B
D
Answer:
ABC =146.5
ACB=67
ACD=127
CAB=146.5
Step-by-step explanation:
ABD=127
ACD=127
BCD=60 ( Being equilateral triangle)
60+x=127
x=67
ACB=67
CAB=CBA=y (let)
y+y+ACB = 360 ( Sum of int angles of triangle)
2y+67=360
2y=293
y=146.5
CAB=146.5
ABC=146.5
Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles.
The angle pairs can be classified as follows
∠1 and ∠5 → Alternate exterior angles
∠2 and ∠10 → Corresponding angles
∠10 and ∠14 → Alternate interior angles
∠6 and ∠7 → Consecutive interior angles
∠5 and ∠12 → Consecutive interior angles
∠3 and ∠13 → Alternate exterior angles
Classifying angle pairsFrom the question, we are to classify each of the angle pairs as corresponding, alternate interior, alternate exterior, or consecutive interior angles.
Considering the given diagram, and applying the appropriate angle theorems, we can write that
∠1 and ∠5 are alternate exterior angles
∠2 and ∠10 are corresponding angles
∠10 and ∠14 are alternate interior angles
∠6 and ∠7 are consecutive interior angles
∠5 and ∠12 are consecutive interior angles
∠3 and ∠13 are alternate exterior angles
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adriel is younger than jevonte. There ages are consecutive odd integers. Find adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85
Answer:
Step-by-step explanation:
Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years
How to calculate the value?Let the ages be x and x + 2 since they're consecutive odd integers.
We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:
x² + 4(x + 2) = 85
x² + 4x + 8 = 85
Collect like terms
x² + 4x + 8 - 85
x² + 4x - 77 = 0
x² + 11x - 7x - 77 = 0
x(x + 12) - 7(x + 11) = 0
x - 7 = 0
x = 0 + 7
Therefore, the age is 7 years.
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