We can rewrite the linear equation as:
y = -x + 3
There we can see that the slope is -1.
What is the slope of the linear equation?A linear equation written in the slope-intercept form is:
y = a*x + b
Where a is the slope.
Here the linear equation is written kinda weird, I guess that the line is:
y - 3 = -(x - 2) - 2
Let's isolate y and simpify the equation, we will get:
y - 3 = -(x - 2) - 2
y = -(x - 2) - 2 + 3
y = -(x - 2) + 1
Now we can apply the rule of signs in the right side:
y = -x + 2 + 1
y = -x + 3
y = -1*x + 3
So the slope of the linear equation is -1.
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Use the first five terms of the trigonometric series to approximate the value of sin 4pi/5 to four decimal places. Then
compare the approximation to the actual value.
The first five terms of the given trigonometric series are (C) 0.5884, 0.5878.
What is a trigonometric series?
A mathematical series where the sines and cosines of integral multiples of a variable angle are used to connect the components.
Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent are the six trigonometric functions.
Below is a graph of the first five terms in the trigonometric series of sin:
sinx = x - x³/3! + x⁵/5! - x⁷/7! + x⁹/9! .......
Insert x = 4π/5
sin4π/5 = 4π/5 - (4π/5)³/3! + (4π/5)⁵/5! - (4π/5)⁷/7! + (4π/5)⁹/9! .......
Upon resolution, we determine an approximate value of:
sin4π/5 = 0.5884
Find the true value now:
sin4π/5 = 0.5878
Therefore, the first five terms of the given trigonometric series are (C) 0.5884, 0.5878.
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Complete question:
Use the first five terms of the trigonometric series to approximate the value of sin to four decimal places. Then compare
the approximation to the actual value.
a. -0.9568, -0.9659
b. -0.9649, -0.9659
C. 0.5884, 0.5878
d. -0.9609, -0.9659
an inequality shows the Relationship between numbers
The answer to this Question is YES. Inequalities do show the relation between Numbers.
What are Inequalities?
Inequalities are the operators the we want to compare the data when equality is not valid
Solution:
The Inequalities shows nice relation between numbers like when we say for example 2 and 4 we know that 2 is not equal to 4 but we know that
2 is less than 4 in this case inequalities help us to develop relations between numbers that are not equal
Inequalities are also used in inequations where they represents large set of data .
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Duncan begins to hike a trail that is at an elevation of 1000 feet. As he hikes, his elevation increases 2000 feet each hour that he hikes. Determine the y-intercept.
The y-intercept in Duncan's hike situation as described in the task content is; 1000 feet.
What is the y-intercept in Duncan's hike scenario as described?It follows from the task content that the y-intercept of Duncan's hike scenario is to be determined.
In context, the y-intercept is otherwise termed; the starting value.
According to the task content; Duncan begins to hike a trail that is at an elevation of 1000 feet.
On this note, Duncan's starting elevation is; 1000 feet and consequently, the y-intercept in this scenario is; 1000 feet.
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• Solve for x.
• Show all of your work to earn full credit.
•
Use the "mountain" icon to upload a piucture of your handwritten work.
→
-1 + 14x
12x + 17
If you do this for me you have to show me your work ;)
The value of 'x' for the given (alternate exterior angles) is found as 9.
Explain the term alternate exterior angles?The pair of angles the outside of the two parallel lines but on the opposing side of the transversal are known as alternate exterior angles.A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (total four angles) of alternate outside angles since they are situated "outside" the pair of parallel lines but on different sides of the transversal.For the stated question.
-1 + 14x = 12x + 17 (alternate exterior angles)
Simplifying,
14x - 12x = 17 + 1
2x = 18
x = 9
Thus, the value of 'x' for the given (alternate exterior angles) is found as 9.
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2. sophia is considering buying a dress and a necklace. the probability she will buy a red dress is 0.2, and similarly, it is 0.4 for a blue dress. there is a 10% chance she will buy a necklace. she wants to buy at most one dress, and buying a necklace is independent of buying a dress find the probability she buys at least one of the previous items. assume event a: she buys a red dress; event b: she buys a blue dress; event c: she buys a necklace.
Therefore the probability that she buys at least one of the previous items is 0.1333
What is probability ?The area of mathematics known as probability deals with numerical descriptions of the likelihood that an event will occur or that a statement is true .A number between 0 and 1 is the likelihood of an event, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes its certainty.
Given:
event A: she buys red dress.
event B: she buys a blue dress.
event C: she buys a necklace.
the probability she will buy a red dress is 0.2,
the probability she will buy a blue dress is 0.4
there is 10% chance she will buy a necklace =0.10
The probability she wants to buy at most one dress,
P(A or B or C) =0.2 +0.4 +0.1 -(0.08 -0.04 -0.02 +0.08)
P(A or B or C) =0.568
the probability she buys at least one of the previous items is
[tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex] = [tex]\frac{0.2 * 0.1 * 0.4}{(0.2 * 0.1)+(0.1 *0.4)}[/tex]
[tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex]= 2/15 =0.133
Therefore the probability that she buys at least one of the previous items is 0.1333
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How to turn 33.3 into a decimal and a fraction
Turn 33.3 into a fraction:
Write down 33.3 like this:
[tex]\dfrac{33.3}{1}[/tex]
Multiply the numerator and denominator by 10(since there is 1 digit after the decimal):
[tex]\dfrac{33.3\times10}{1\times10} \rightarrow\dfrac{333}{10}[/tex]
[tex]\dfrac{333}{10}[/tex] would be the fraction form of [tex]33.3[/tex].
To turn [tex]\dfrac{333}{10}[/tex] into a decimal, divide the numerator by the denominator:
[tex]333\div10=33.3[/tex]
Hope this helps!
x^2+6x+1=0
solve using quadratic formula
The values of the x of the given equation [tex]x^{2} + 6x + 1 = 0[/tex] using quadratic formula is -10 and -2.
What is quadratic formula of a equation ?
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula:
(-b±√(b²-4ac))/(2a)
Given equation;
[tex]x^{2} + 6x + 1 = 0[/tex]
Using quadratic formula
x = [tex]-b[/tex] ± [tex]\frac{\sqrt{(b^{2} - 4 (ac) } }{4a}[/tex]
Substitute the values a = 1, b = 6, c = 1, we get;
x = [tex]-6[/tex] ± [tex]\frac{\sqrt{( (6) ^{2} - 4. 1.1)} }{2*1}[/tex]
x = -6 ± 4
x = -6 - 4 & x = -6 + 4
= -10 = -2
x = -10, -2
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If m<1=55, then find the value of m<3
The measure of angle 3 is given as follows:
m < 3 = 55º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles in this problem are listed as follows:
1 and 3.2 and 4.The measure of angle 1 is given as follows:
m < 1 = 55º.
Angle 1 and angle 3 are vertical angles, hence the measure of angle 3 is obtained as follows:
m < 3 = 55º.
As angle 3 is congruent to angle 1.
Angles 2 and 4 are also supplementary to angles 1 and 3, meaning that the sum of their measures is of 180º, hence m<2 = m<4 = 125º.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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Determine if you have enough information to find the missing lengths. If so, find them. If not, explain why.
DE is parallel to AC . Find the lengths of AC and AD.
The lengths of AC and AD using the concept of similar triangles are; AC = 12.5 and AD = 3
How to solve similar triangles?We are given that;
∆BDE is a similar triangle to ∆BAC.
This means that their sides are proportional. Thus, we can say that;
BD/BA = BE/BC
Thus;
2/BA = 4/(6 + 4)
BA = 2 × 10/4
BA = 5
Similarly;
BE/BC = DE/AC
4/10 = 5/AC
AC = 5 × 10/4
AC = 25/2
Finally,
AC = 25/2 = 12.5.
Thus;
AD = BA - BD = 5 - 2 = 3.
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Use synthetic division to find the result when 2x^3-14x^2+15x-18 is divided by x-6.
The Answer:
2x^2−2x+3
The result of the expression (2x³ - 14x² + 15x - 18) ÷ (x - 6) on dividing will be (2x² - 2x + 3).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (2x³ - 14x² + 15x - 18) ÷ (x - 6)
The factor of the expression (2x³ - 14x² + 15x - 18) is given as,
⇒ (2x³ - 14x² + 15x - 18)
⇒ 2x³ - 12x² - 2x² + 12x + 3x - 18
⇒ 2x²(x - 6) - 2x (x - 6) + 3(x - 6)
⇒ (x - 6)(2x² - 2x + 3)
Then the expression is written as,
⇒ (2x³ - 14x² + 15x - 18) ÷ (x - 6)
⇒ [(x - 6)(2x² - 2x + 3)] / (x - 6)
⇒ (2x² - 2x + 3)
The final solution of the expression (2x³ - 14x² + 15x - 18) ÷ (x - 6) on dividing will be (2x² - 2x + 3).
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Selena and Luis are building a model bridge out of balsa wood. To make a strong bridge, they create each post by laying out two long wooden poles horizontally, as shown in the diagram, and connecting them with smaller strips of balsa wood laid diagonally in a triangle pattern. The triangle pattern is continued down the entire length of the wooden poles.
The poles are 12 centimeters apart, and each small strip of balsa wood is 13 centimeters long.
If the two poles are each 100 centimeters long, how many small strips of balsa wood will they need to connect them?
If the two poles are each 100 centimeters long, The number of small strips of balsa wood they will need to connect them is: C. 20.
How to find the number of small strips?Using Pythagorean theorem formula to find triangle side a.
a=√b²+c²
a = √ 13² - 12²
a = √ 169 - 144
a = √ 25
a = 5
Hence, the number of small strips of balsa wood they need to connect them is:
100 / (2a)× 2
100 / ( 2×5) ×2
100/ 10 ×2
10 × 2
=20
Therefore the correct option is C.
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Someone please answer this my question is in the picture I will give you brainliest and your getting 50 points no fraud answers.
Step-by-step explanation:
I will help you sir.
Given
Opposite Sides are Congruent
Reflexive
SSS
CPCTC
In 2014, 100 trees were planted by the people in Cherry Hill. The table below shows the number of trees planted of each type.
Trees Planted
Tree Number of Trees
Oak 45
Maple 17
Palm 28
Pine 10
Which circle graph correctly shows the information from the table?
Answer:
where is your circle graph
Step-by-step explanation:
i need the graph in order to solve this
Question included in file
please help I need an answer quick
The midpoint of the line AN is (3(1/2) , -1).
What is midpoint?
The midpoint is located halfway between the two end points. Its x and y values are in the middle of the two x and y values.Add both "x" coordinates, divide by 2, and add both "y" coordinates, divide by 2 to calculate it.Midpoint of the line(x , y) = (x₁ + x₂ / 2) , (y₁ + y₂ / 2)
x₁ = 2, x₂ = 5
y₁ = -3, y₂ = 1
So,
Midpoint of the line(x , y) = (2+5/2) , ((-3)+1 / 2)
= (7/2 , -2/2)
= (7/2, -1)
We can write 7/2 as 3(1/2)
Hence, the midpoint of the line AN is (3(1/2) , -1)
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The trinomial x² - 14x + 49 can be expressed as
(1) (x-7)²
(2) (x + 7)²
(3) (x-7)(x + 7)
(4)) (x-7)(x + 2)
Answer:
(1)
Step-by-step explanation:
This is because (x-7)²=(x-7)(x-7), which when expanded using the FOIL method, is equal to x²-7x-7x+49=x²-14x+49.
if kenneth has 11 dimes and nickels in his pocket, and they have a combined value of 80 cents, how many of each coin does he have?
Answer: let d=# of dimes
let n= # of nickels
n+d=11
5n+10d=80
5d+25
5 dimes and 6 nickels
Jerry bulit a table with a square top. the perimeter of the tabletop is 18 feet. He knows that the side lentgh of the table is 3, 3 1/4 4 or 4 1/2 use the equation 18 = 4s where s is the side length of the table to determine the side length explain how you found your answer
Answer:
4 1/2 ft
Step-by-step explanation:
18 = 4s
Divide both sides by 4.
18/4 = 4s/4
9/2 = s
4 1/2 = s
The side of the table is 4 1/2 ft.
There are 3 fewer yellow beads than red beads. There are twice as many green beads as yellow beads. Write expressions for the number of red, green, and yellow beads.
Answer:
yellow = red - 3 and green = yellow x 2 and red = yellow + 3
or
green= (red-3) x 2
Step-by-step explanation:
Three fewer yellow than read is the same as saying red -3
twice as many green as yellow is the same as yellow x 2
if green is yellow x 2 you can substitute yellow for the equation to find yellow
you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3
i need help, i don’t understand
Answer:
x = 2; y = 10
Step-by-step explanation:
y = 5x
2x + 3y = 34
You have a system of equations. Since the first equation is already solved for y, we can easily use the substitution method. Substitute 5x for y in the second equation.
2x + 3y = 34
2x + 3(5x) = 34
2x + 15x = 34
17x = 34
x = 2
Now substitute 2 for x in the first equation.
y = 5x
y = 5(2)
y = 10
Solution: x = 2; y = 10
Points A, B, and C are collinear. Point B is between A and C. Find the value of x.
AC = 24
AB = 2x + 1
BC = 3x − 2
Responses
A 55
B 33
C 99
D 7
Therefore, the value of the given equation of x comes out to be x =5.
What kinds of equations are there?Equations can be classified as either identities or conditioned equations. For each amount of the variables, an identity is true. Only specific values of the variables make a conditional equation legitimate. The equality sign ("="), which separate the two expressions, is a symbol for an equation.
Here,
Given data: A, B, and C are parallel, B is located between A and C, AC equals 24, AB equals 2x+1, and BC equals 3x-2.
In the event where A, B, and C are collinear and B is positioned between A and C, we obtain
Replace the given equation with AC = 24, AB = 2x+1, and BC = 3x-2.
AB plus BC equals AC
=> AC= AB + BC
On combining like terms we get
=> 2x+1 + 3x-2 = 24
=> 5x -1 =24
=>5x =25
=>x =5
Therefore, the value of x comes out to be x =5.
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The expression 10x – x2
can be written in the form p – (x – q)2
for all values of x.
a) Find the values of p and q.
b) The expression 10x – x2
has a maximum value.
(i) Find the maximum value of 10x – x2
.
(ii) State the value of x for which this maximum value occurs.
The values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
Expression 10x – x²
The expression can be written as
10x – x² = p – (x – q)²
10x – x² = p - x² - q² + 2xq
10x – x² = - x² + 2xq + p - q²
Compare the quantities on both sides,
10x = 2xq and 0 = p - q², p = q²
q = 10x / 2x = 5
p = 5² = 25
Therefore, the values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.
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Xander was in the lead for 75% of the laps during PE. If the race lasted 12 laps, how many laps did Xander lead?
Answer:
9 laps
Step-by-step explanation:
75% of something is the same as three-fourths, or multiplying by 0.75
12 x 0.75 = 9
or you can divide by 4 and then multiply by three if you know what to separate the original number into
12/4 = 3 3 x 3 = 9
Choose the correct statements (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.) A random variable is a quantitative outcome of a chance experiment. A probability distribution includes the likelihood of each possible outcome. A probability distribution is the outcome of an experiment. A random variable represents the likelihood of an outcome.
A random variable is a quantitative outcome of a chance experiment.
A probability distribution includes the likelihood of each possible outcome.
A random variable is a variable whose value is determined by chance or randomness. It is often used to represent a numerical outcome of a chance experiment, such as the result of a coin toss, the roll of a die, or the outcome of a survey. Random variables can take on any numerical value, but it is often useful to assign probabilities to each possible value. This probability, known as a probability distribution or probability density function, describes the likelihood that a given value of the random variable will occur.
A normal distribution is a type of probability distribution that is symmetrical and bell-shaped, with the mean, median, and mode all equal. The values of the distribution are spread out around the mean, with the majority of the values within one standard deviation of the mean. A normal distribution is also known as a Gaussian distribution, as it was discovered by Carl Friedrich Gauss in the early 19th century.
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Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour. How many pages can Shawn type in one hour? A. B. C. D.
Answer:
5 1/7 pages in one hour. And what does "A.B.C.D." Mean?
Step-by-step explanation:
LOT OF POINTS!!
PLEASE NEED ANSWERS QUICKLY!!
By using the properties of angle,
The proof of ∠1 ≅ ∠3 has been given below
What is angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle
1. ∠2 ≅ ∠4 [Given]
2. m∠2= m∠4 [Angle Congruence Postulate]
3. ∠2 and ∠3 are supplementary [Given]
4. m∠2+m∠3 = 180° [Definition of Supplementary angles]
5. ∠1 and ∠4 are supplementary [Angle on a straight line]
6. m∠1+m∠4 = 180° [Definition of supplementary angles]
7. m∠1+m∠4 = m∠2+ m∠3 [ Substitution from 4 and 6]
8. m∠1+m∠4 = m∠4+m∠3 [Substitution from 2]
9. m∠1=m∠3 [Cancellation property]
10. ∠1 ≅ ∠3 [Converse of angle congruence theorem]
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the mayor of a town has proposed a plan for the annexation of a new community. a political study took a sample of 800 voters in the town and found that 63% of the residents favored annexation. using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 60%. testing at the 0.02 level, is there enough evidence to support the strategist's claim? step 4 of 7 : determine the p-value of the test statistic. round your answer to four decimal places.
As per the concept of hypothesis testing, the p-value of the test static is 0.0837
Hypothesis testing:
In statistics, when the alternative hypothesis is of the "greater than or greater than or equal to" type, the p-value can be calculated by calculating the probability of the z statistic being greater than the test statistic value.
Given,
Here we have the mayor of a town has proposed a plan for the annexation of a new community. and the political study took a sample of 800 voters in the town and found that 63% of the residents favored annexation. using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 60%. testing at the 0.02 level.
Here we need to find the p-value of the test statistic.
While we looking into the given question we have identified the following hypothesis,
=> H0 : p <=0.6
=> H1: p > 0.6
And the value of alpha=0.02 p{reject H0 | H0 true} test statistic is a z from a 1 way 1 proportion test
So, the z value is z> 7.1286
Then the z value is calculated as,
=> 0.03/sqrt(0.6*0.63/800)
=> z = 1.3801
Therefore, the reject H0, the true proportion is greater than 60% and the p-value is 0.0837
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help me find the slope please
answer needs to be correct or i will report and ban you.
thank you
-lazyuser30
#35
On the real number line, what is the midpoint of
-3 and 11?
A. -5
B. 0
C. 4
D. 7
E. 14
Answer:
C. 4
Step-by-step explanation:
You want the midpoint between -3 and 11 on the number line.
MidpointThe midpoint is the average of the end point coordinates:
(-3 +11)/2 = 8/2 = 4
The midpoint is 4.
In his free time, Gary spends 9 hours per week on the Internet and 12 hours per week playing video games. If Gary has five hours of free time per day, what percent of his free time is spent on the Internet and playing video games
Answer: 11.64%
Step-by-step explanation:
Write the sum using summation notation. There may be multiple representations. Use i as the index of
summation.
1/3 - 1/9 + 1/27 - 1/81 + 1/243 - 1/729
The summation notation of the sum is given as follows:
[tex]\sum_{i = 1}^{6} \frac{(-1)^{i-1}}{3^i}[/tex]
How to write the summation notation?The summation notation of the sum is written considering the patterns of the terms that compose the terms.
First we look at the fact that the sum has six terms, and the first term is considered as having index 1, hence:
[tex]\sum_{i = 1}^{6}[/tex]
Then we consider that the signal is alternating, with the terms with odd indices being positive and those with even indices being negative, hence the numerator is of:
[tex](-1)^{i - 1}[/tex]
(any of -1 or +1 would work here).
Then we considering that the denominator is composed by the powers of 3, hence it is given by:
[tex]3^i[/tex]
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