Answer/Step-by-step explanation:
y = mx + b
Slope = m
y₂ - y₁
---------- = m
x₂ - x₁
----------------------------------------------------------------------------------------------------------
y - intercept = b
y - y₁ = m(x - x₁)
If there's an equation I can solve it, but I hope this helps!
When looking at a graph of a line, there are two things you should look for straight off the bat. First, the y-intercept. And second, the slope.
The equation of a line is y = mx + b, where m is the slope, b is the y-intercept, and x is the input.
What is slope?
Slope is a number that determines how the line changes. It is often referred to as the "rate of change" because it represents how much the y-value of the line changes when the input (x) changes. The formula for slope is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Breakdown: This formula represents the change in the line, typically left to right. It shows the change in x-value over the change in corresponding y-value. This is also known as "rise over run," because the y-value is how much the line changes vertically, while the x-value is how much it changes horizontally.
Example: Let's say our line has a slope of 4, or m = 4/1. This means the y-value will change 4 units when the x-value changes by 1.
What is y-intercept?
Y-intercept is a value that determines the location of the line. When x = 0, the value of b will be the y-value. Essentially, when the line crosses the y-axis, that will be the y-value of the line.
Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Congruent Shapes
Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),
All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.
The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.
Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is
xm = (-6+4)/2 = -1
Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:
xm = (-8+6)/2 = -1
For the points R(-4,-6) and D(2,-6):
xm = (-4+2)/2 = -1
For the points Q(-9,-4) and D(8,-4):
xm = (-9+8)/2 = -0.5
Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent
For both shapes to be congruent, the coordinates of Q should have been (-10,-4)
Instructions: Find the missing length indicated.BII1600900X
From the diagram given in the question, we are asked to find the missing length indicated.
We can see from the diagram that the right triangles are similar, so the ratio of hypotenuse to short leg is the same for all.
So,
x/900 = (1600 + 900)/x
Let's cross multiply:
x² = 900(2500)
let's take square of both sides:
x = √(900) * √(2500)
x = 30(50)
x = 30 * 50
x = 1500
Therefore, the missing length is 1500
Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]Write the equation of the line that passes through the points (12, 4) and (22,9).
Given the following points that pass through the line:
Point A : 12,4
Point B : 22,9
Step 1: Let's determine the slope of the line (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{9\text{ - 4}}{22\text{ - 12}}[/tex][tex]\text{ m = }\frac{5}{10}\text{ = }\frac{1}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 12,4 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 4 = (}\frac{1}{2})(12)\text{ + b }\rightarrow\text{ 4 = }\frac{12}{2}\text{ + b}[/tex][tex]\text{ 4 = 6 + b}[/tex][tex]4\text{ - 6 = b}[/tex][tex]\text{ -2 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1/2 and b = -2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (}\frac{1}{2})x\text{ + (-2)}[/tex][tex]\text{ y = }\frac{1}{2}x\text{ - 2}[/tex]Therefore, the equation of the line is y = 1/2x - 2.
I'm not sure how to do this. This is a long one that's why.
We have the following:
For the area surface:
[tex]As=2\pi rh[/tex]repacing:
r = 1.5 in
h = 7 in
[tex]\begin{gathered} As=2\cdot3.14\cdot1.5^{}\cdot7 \\ As=65.94 \end{gathered}[/tex]The answer is 65.9 in^2
For volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=3.14\cdot1.5^2\cdot7 \\ V=49.455 \end{gathered}[/tex]The answer is 49.5 in^3
Which expression has a negative value
Answer:
bottom one
Step-by-step explanation:
True or False: A power has two parts, a base and an exponent. True False
The said statement is true.
A power has two parts, a base and an exponent.
Example
[tex]2^3[/tex]The answer is TRUE
shirts are 15% off. The original price of one shirt is $20. What is the total cost, in dollars, of a shirt, at the sales price, including a 10% sales tax?
The original price of the shirt is , 20 dollar.
It is given that the shirts are 15% off.
Therefore, the price of the shirt is ,
[tex]20-20\times\frac{15}{100}=17.[/tex]The price of the shirt is, 17 dollar after 15% off.
It is also given that there are 10% sales tax.
The total cost of the shirt is determined by including the sales tax in the price of the shirt after 15% off.
[tex]17+(17\times\frac{10}{100})=18.7[/tex]Thus, The total cost of shirt is calculated as, 18.7 dollar.
On the Richter Scale, the magnitude R of an earthquake of intensity I is given by the equation in the image, where I0 = 1 is the minimum intensity used for comparison. (The intensity of an earthquake is a measure of its wave energy). Find the intensity per unit of area I for the Anchorage Earthquake of 1989, R = 9.2.
we have the formula
[tex]R=\log _{10}\frac{I}{I_0}[/tex]we have
R=9.2
I0=1
substitute in the given equation
[tex]\begin{gathered} 9.2=\log _{10}\frac{I}{1} \\ 9.2=\log _{10}I \\ I=10^{(9.2)} \\ \end{gathered}[/tex]I=1,584,893,192.46
45% of 240 is what number?
We are asked to determine the 45% of 240. To do that we need to multiply 240 by 45/100, that is:
[tex]240\times\frac{45}{100}=108[/tex]therefore, 45 percent of 240 is 108
Answer the statistical measures and create a box and whiskers plot for the following set of data.
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]The coordinates of triangle LMN are shown.YL(-1,4)XN (4, -1)M(-1, -3)What is the length of LM? Enter the answer in the box.unit(s)
Given data:
The given coordinate of L is (-1,4).
The given coordinate of M is(-1, -3).
The expression for LM length is,
[tex]\begin{gathered} LM=\sqrt[]{(-1-(-1))^2+(-3-4)^2} \\ =\sqrt[]{0+49} \\ =7 \end{gathered}[/tex]Thus, the LM length is 7 units.
how do i evaluate 8!4!/7!2!
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
4. Adam had $200. He spent $75 on clothes and $55 on a video game. Then his Momgave him $20 more dollars. How much money does Adam have now?
Adam had $200
He spent $75 on clothes and $55 on video game
The total money spent by Adam is
[tex]=75+55=\text{ \$130}[/tex]The amount left with Adam is
[tex]=200-130=\text{ \$70}[/tex]Then his mom gave him $20
The total amount of money Adam have now is
[tex]=70+20=\text{ \$90}[/tex]Hence, the answer is $90
factor bofe problems using synthetic division and list All zeros
Given:
[tex]f(x)=x^3-7x^2+2x+40;\text{ x -5}[/tex]Let's factor using synthetic division.
Equate the divisor to zero:
x - 5 = 0
x = 5
List all terms of the polynomial: 1, -7, 2, 40
Palce the numbers representing the divisor and dividend into a long division-like configuration
To factor using synthetic division, we have:
Therefore, the factored expression is:
[tex]\begin{gathered} 1x^2-2x-8 \\ \\ =x^2-2x-8 \\ \\ =(x-4)(x+2) \end{gathered}[/tex]The zeros are also the roots of the polynomial.
The zeros of a polynomial are all the x-values that makes the polynomial equal to zero,
To find the zeros, equate each afctor to zero:
(x - 4) = 0
x = 4
(x + 2) = 0
x = -2
Thus, the zeros are:
x = 4, -2
ANSWER:
[tex]\begin{gathered} (x-4)(x+2) \\ \\ \text{Zeros: 4, and -2} \end{gathered}[/tex]Jackson started a savings account using the bonus he received from work of $3,500. Theaccount is compounded weekly with an interest rate of 1.75% How much interest did theaccount earned in 18 years?O $1,295.65O $1,102.500 $4,795.65o $1,290
The amount compounded is given by the formula ;
[tex]A=P\lbrack1+\frac{r}{100n}\rbrack^{nt}[/tex]Here, P = $3500, r = 1.75%, n = 52 , t = 18 years.
[tex]\begin{gathered} A=3500\lbrack1+\frac{1.75}{100\times52}\rbrack^{52\times18} \\ A=4795.65 \end{gathered}[/tex]Therefore, the interest the account will earn is 4795.65-3500 = $1295.65, Option A
98) Cost to store: $145Markup: _?Selling price:$319.
Answer: Mark up is 220%
Cost to store : $145
selling price = $319
let x = mark up
Using the below equation
[tex]\begin{gathered} \text{Part = whole x percentage} \\ \text{part = selling price} \\ \cos t\text{ to store = whole} \\ \text{Mark up = percentage} \\ 319\text{ = 145 }\cdot\text{ x\%} \\ \text{ x\% = }\frac{319}{145}\text{ x 100\%} \\ x\text{ = 2.2 x 100\%} \\ x\text{ = 220\%} \\ \text{Therefore, the mark up is 220\%} \end{gathered}[/tex]I am studying for the big test tomorrow and just need someone to go through this sheet I made with me.Sorry
SOLUTION
Let us solve the simultaneous equation
[tex]\begin{gathered} -2x-y=0 \\ x-y=3 \end{gathered}[/tex]using elimination
To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.
So to make the y's different, I will multiply the second equation by a -1. This becomes
[tex]\begin{gathered} -2x-y=0 \\ (-1)x-y=3 \\ -2x-y=0 \\ -x+y=-3 \end{gathered}[/tex]So, now we can eliminate y, doing this we have
[tex]\begin{gathered} -2x-x=-3x \\ -y+y=0 \\ 0-3=-3 \\ \text{This becomes } \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2-y=0 \\ \text{moving -y to the other side } \\ y=-2 \end{gathered}[/tex]So, x = 1 and y = -2
Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,
[tex]\begin{gathered} x-y=3 \\ \text{making y the subject we have } \\ y=x-3 \end{gathered}[/tex]Now, we will put y = x - 3 into the other equation, which is equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2x-(x-3)=0 \\ -2x-x+3=0 \\ -2x-1x+3=0 \\ -3x+3=0 \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]So, substituting x for 1 into equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2\times1-y=0 \\ -2-y=0 \\ y=-2 \end{gathered}[/tex]Substituting x for 1 into equation 2, we have
[tex]\begin{gathered} x-y=3 \\ 1-y=3 \\ y=1-3 \\ y=-2 \end{gathered}[/tex]Now, for graphing,
Which description is paired with its correct expression?
O seven less than the quotient of two and a number squared, increased by six;
Onine times the difference of a number cubed and three, 9(n²-3)
7-+8
O eight more than the quotient of a number squared and four, decreased by seven;
Otwice the difference of a number cubed and eight, 27³-8
8+/-7
Answer:
seven less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
nine times the difference of a number cubed and three; 9(n³-3)
eight more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
twice the difference of a number cubed and eight; 2 n³- 8
Step-by-step explanation:
A person chooses a number in a set containing the first 5 cubic numbers. Find the set representing the event E of choosing a number that can be evenly divided by 2. Give your answer as a set, e.g. {1,2,3}, using the cubed number (not the base number) and do not include E= in your answer.
The first 5 cubic numbers are:
[tex]\lbrace1,8,27,64,125\rbrace[/tex]To find the set that represents event E we have to choose the numbers from the set above that are evenly divided by 2; this means that we have to choose the numbers that are multiple of 2. We notice that this numbers are 8 and 64, therefore the set that represents event E is:
[tex]\lbrace8,64\rbrace[/tex]Ethan found the spinner shownbelow and planned to use it for agame.2332453235After studying the spinner beforeusing it, Ethan correctly concludedthat the spinner was-A least likely to land on 2B least likely to land on 5C most likely to land on 3D most likely to land on 2
we have that
the number 3 appears 4 times
so
answer is
option C most likely to land on 3
inserted a picture of the question, can you just answer the question and not ask a lot of questions yes i’m following
Step-by-step explanation:
A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,
so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.
[tex]\frac{360}{9}=40[/tex]Therefore the degrees will a nonagon have rotational symmetry
Hene the correct answer is Option B
2. Write a story that can be represented by the equation y = x + 1/4 x.Question 2 On a hot day a football team drank an entire 50-gallon cooler of water and half as much again. How much water did they drink? Create an equation to represent this situation.
y= x+ 1/4 x
Y = dependent variable
x= independent variable
Jenny has a bank account. In the first month, she deposits a certain amount of money (x), and in the month after she deposits 1/4 of that amount.
Find the total amount of money deposited (y).
distributive property 3x(7x+6)
By distributive property, we distribute 3x, and multiply it to each term inside the binomial (7x+6) accounting for the sign.
[tex]\begin{gathered} 3x(7x+6) \\ \Rightarrow3x(7x)+3x(6) \\ \Rightarrow21x^2+18x \\ \\ \text{Therefore, }3x(7x+6)=21x^2+18x \end{gathered}[/tex]Find F as a function of x and evaluate it at x = 2, x = 5 and x = 8.
Given:
[tex]F(x)=\int_2^x(t^3+6t-4)dt[/tex]Find-:
[tex]F(x),F(2),F(5),F(8)[/tex]Sol:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ \end{gathered}[/tex]Use integration then:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ F(x)=[\frac{t^4}{4}+\frac{6t^2}{2}-4t]_2^x^ \\ \\ \\ F(x)=\frac{x^4}{4}+3x^2-4x-\frac{2^4}{4}-3(2)^2+4(2) \\ \\ F(x)=\frac{x}{4}^4+3x^2-4x-8 \end{gathered}[/tex]The function value at x = 2 is:
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(2)=\frac{2^4}{4}+3(2)^2-4(2)-8 \\ \\ F(2)=4+12-8-8 \\ \\ F(2)=16-16 \\ \\ F(2)=0 \end{gathered}[/tex]The function value at x = 5
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(5)=\frac{5^4}{4}+3(5)^2-4(5)-8 \\ \\ F(5)=156.25+75-20-8 \\ \\ F(5)=203.25 \end{gathered}[/tex]Function value at x = 8
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(8)=\frac{8^4}{4}+3(8)^2-4(8)-8 \\ \\ F(8)=1024+192-32-8 \\ \\ F(8)=1216-40 \\ \\ F(8)=1176 \end{gathered}[/tex]fill in the table using the function rule y= 6x-3
Answer:
-9,-3,3,27
Step-by-step explanation:
Just multiply x by 6 and subtract 3 to that
Question 8 of 10What is the slope of the line described by the equation below?y=-x+ 8A. 8B. 1OOOC. -8O D.-1SUBMIT
We have the following equation
y = -x + 8
this equation is writen in slope intercept form
y = mx + b
where m is the slope
From the above, we can see that the slope is m = -1
Solve the system of two linear inequalities graphically,4x + 6y < 24(x22Step 1 of 3 : Graph the solution set of the first linear inequality.AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (--)Enter two points on the boundary line:10-5Select the region you wish to be shaded:
Answer:
To solve the system of two linear inequalities graphically,
[tex]\begin{gathered} 4x+6y<24 \\ x\ge2 \end{gathered}[/tex]For step 1,
Draw a line 4x+6y=24
Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.
Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,
Similarly for the inequality,
[tex]x\ge2[/tex]It covers the region right side of the line x=2,
we get the siolution region as the intersecting region of both inequality which defined in the graph as,
Dark blue shaded region is the required solution set for the given inequalities.
Given sin(x)=.4 and cot(x) >0 what is cos(x)?
The cotangent is given by the cosine over the sine.
If the cotangent is positive and the sine is positive, that means the cosine is also positive.
Now, in order to find the value of cos(x), we can use the following property:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (0.4)^2+\cos ^2(x)=1 \\ 0.16+\cos ^2(x)=1 \\ \cos ^2(x)=1-0.16 \\ \cos ^2(x)=0.84 \\ \cos (x)=0.917 \end{gathered}[/tex]