Graph the linear function using the slope and the y-intercept.y = 2x + 3CORTUse the graphing tool to graph the linear equatium. Use the slope and y-intercept when drawing the line.Click toenlargegraph
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Answer:
Explanation:
If we have a linear equation of the form
[tex]y=mx+b[/tex]then m = slope and b = y-intercept.
Now in our case, we have
[tex]y=2x+3[/tex]which means that slope = 2 and y-intercept = 3
Therefore, we graph a line that has a slope of 2 and a y-intercept of 3.
A slope of 2 means that for every step you take to the right on a graph, you move 2 steps up to get to a point on the line.
The y-intercept of 3 means that the line passes through the point (0, 3).
Using these two facts about the line, we draw the following line.
From the above plot, we can clearly see that the line has a slope of 2 and a y-intercept of 3 - the same line described by y = 2x + 3.
Related Questions
G is the midpoint for FH what is the length of FG
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Since G is the midpoint of FH,
[tex]\begin{gathered} FG=GH \\ \Rightarrow11x-7=3x+9 \\ \Rightarrow11x-3x=9+7=16 \\ \Rightarrow8x=16 \\ \Rightarrow x=2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} FG=11x-7=11\cdot2-7=22-7=15 \\ \Rightarrow FG=15 \end{gathered}[/tex]The answer is 15, option a.
Find the distance between the points (-5,4) and (-2,-1)
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Answer
√34
Step-by-step explanation
Distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
• d: distance between two points
,• (x₁, y₁): coordinates of the first point
,• (x₂, y₂): coordinates of the second point
Substituting into the formula with the points (-5,4) and (-2,-1), we get:
[tex]\begin{gathered} d=\sqrt{(-2-(-5))^2+(-1-4)^2} \\ d=\sqrt{3^2+(-5)^2} \\ d=\sqrt{9+25} \\ d=\sqrt{34} \end{gathered}[/tex]8 / 1/3 and 2 / 1/9 what's the generalizations can make about the equations
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The generalization about the terms is that one is the cube root of the other
∛(8/9) = 2/3
What is generalizations in mathematics?Generalization can be viewed as a statement that holds true for a broad category of objects or numbers, as the method by which we arrive at a general statement, or as a means of transferring information from one context to another in the mathematics.
The equation represented as 8 / 1/3 and 2 / 1/9
is made an equated to each other and rearranged as follows
8 / 1/3 ⇔ 2 / 1/9
cross multiplying
8 * 1/9 ⇔ 2 * 1/3
8/9 ⇔ 2/3
the equation only holds true when the cube root sign is there then we have
∛(8/9) = 2/3
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Calculate the second and third derivative of y =9x-1/x
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y = 9x - 1/x
I like to rewrite 1/x as x^-1
y = 9x - x^-1
Taking the derivative
dy/dx = 9 - -1 x^-2
= 9 + 1/x^2
That is the first derivative
Now we do it again
dy^2/dx^2 = d/dx ( 9 + 1/x^2)
= d/dx( 9 + x^-2)
= 0 -2x^-3
=-2/x^3
The second derivative is -2 / x^3
Identify the equation without applying a rotation of axes.x squared +10xy+25y squared-2x-4y+10=0a. parabolab. ellipsec. hyperbolad. circle
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Solution
We are given the equation
[tex]x^2+10xy+25y^2-2x-4y+10=0[/tex]We will first simplify the equation
[tex]\begin{gathered} x^{2}+10xy+25y^{2}-2x-4y+10=0 \\ \left(x+5y\right)^2-2\left(x+y\right)+10=0 \\ (x+5y)^2=2(x+y)-10 \end{gathered}[/tex]We draw the graph
From the graph, one can see that this is a rotated parabola
Correct answer is a Parabola
Option A
you roll a six-sided number cube find theprobabilsty of rolling each of the followingP(1 or 6)
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When you roll a six-sided number cube you can get the next set of possible results:
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]You have a total of 6 possible results.
From the set of possible results you get the set of presults that are 1 or 6:
[tex]\lbrace1,6\rbrace[/tex]You have 2 results that are 1 or 6
The probability of rolling (1 or 6) is: The number of results that are 1 or 6 divided in the total number of possible results:
[tex]P(1or6)=\frac{2}{6}=\frac{1}{3}[/tex]Then, the probability of rolling (1 or 6) is 1/3If a student got 10 answers out of 15 what’s the percent?
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To calculate the percentage we have to write a simple fraction like this:
percentage = number of answers / total of questions
percentage = 10 / 15
percentage = 2 / 3
percentage = 0.667
Now, we have to multiply the result by 100:
percentage = 0.667 x 100
percentage = 66.7%
Answer: 66.7%
Anna rolls a die and then flips a coin. Identify the tree diagram which displays the outcomes correctly.
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Let:
1 = Get a 1
2 = Get a 2
3 = Get a 3
4 = Get a 4
5 = Get a 5
6 = Get a 6
H = Get heads
T = Get tails
The set of all possible outcomes of the experiment is:
[tex]\begin{gathered} S=\mleft\lbrace(1,H\mright),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),\ldots \\ \ldots(5,H),(5,T),(6,H),(6,T)\} \end{gathered}[/tex]Therefore, the only tree diagram which displays the outcomes correctly is the one in the option A.
please help me solve.I answered this 1808.64 but it is incorrect.
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Answer
Surface area = 2260.8 cm²
Explanation
The surface area of a normal sphere is given as
Surface area = 4πr²
where,
π = pi = 3.14
r = radius of the sphere = 12 cm
But this sphere has the middle of the sphere as part of the surface too
Surface area = 4πr² + πr² = 5πr²
Surface area = 5 (3.14) (12²)
Surface area = 2260.8 cm²
Hope this Helps!!!
Whats the other side?
Image attached
please show work
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The perimeter of the rectangle is 129.2×10⁵ if the area and one side of the rectangle is given.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is given that:
The area of the rectangle = 2.76×10¹² square cm
The length of the rectangle = 4.6×10⁵ cm
The other side measure = 2.76×10¹²/4.6×10⁵ = 0.6×10⁷ = 60×10⁵ cm
The perimeter of the rectangle = 2(4.6×10⁵ + 60×10⁵)
The perimeter of the rectangle = 129.2×10⁵
Thus, the perimeter of the rectangle is 129.2×10⁵ if the area and one side of the rectangle is given.
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Drag each label to the correct location on the flowchart.Given: Line l and line m intersectProve: Complete the proof. is supplementaryto is supplementaryto Line l and line mintersect
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Solution:
The question asked to prove that
[tex]\angle1\cong\angle3[/tex]The given statement is
Line l and line m intersect
Linear pair theorem:
In math, the linear pair postulate or linear pair theorem, says the same in mathematical terms. If two angles form a linear pair, then the measures of the angles add up to 180
Also,
Two angles are called supplementary when their measures add up to 180 degrees.
That is,
[tex]\begin{gathered} \angle2\text{ is supplementary to }\angle3 \\ \angle2+\angle3=180^0 \\ \angle3\text{ is supplementary to }\angle4 \\ \angle3+\angle4=180^0 \\ \angle1\text{ is supplementary to }\angle4 \\ \angle1+\angle4=180^0 \\ \angle2\text{ is supplementary to }\angle3 \\ \angle2+\angle3=180^0 \\ \angle1\text{ is supplementary to }\angle2 \\ \angle1+\angle2=180^0 \end{gathered}[/tex]Hence,
Linear pair theorem :
∠1 is supplementary to ∠2
∠2 is supplementary to ∠3
Congruent Supplements Theorem:
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.
Since angles 1 and 3 are supplements of the same angle 2
Therefore,
With the statement above we can conclude that
∠1 ≅ ∠3 (congruent supplements theorem)
The expression 12x+6 can be used to describe a sequence algebraically. Which of the following could be the first five numbers in this sequence?A. 18, 36, 54, 72, 90B. 6, 12, 18, 24, 30C. 18, 30, 42, 54, 66D. 6, 18, 24, 36, 42
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We need to find the first five numbers of a sequence determined by the expression:
[tex]12x+6[/tex]Notice that each time we increase the value of x by 1 unit, we add 12 to the previous result. Thus, subsequent terms in the sequnce differ by 12 units.
From the options, the only one with all the terms differing by 12 units is the beginning at x=1:
[tex]\begin{gathered} x=1:12(1)+6=18 \\ \\ x=2:12(2)+6=30 \\ \\ x=3:12(3)+6=42 \\ \\ x=4:12(4)+6=54 \\ \\ x=5:12(5)+6=66 \end{gathered}[/tex]Therefore, the answer is: C. 18, 30, 42, 54, 66
reshma is making a necklace using green beads and purple beads in a ratio represented on the following double number line fill in the missing values on the diagram and then answer the following question
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From the double number line, we can see that the corresponding number of Green and Purple beads needed in each case are stated.
[tex]\begin{gathered} 4\text{ Gre}en\text{ }\rightarrow5\text{ Purple} \\ 8\text{ Gr}een\text{ }\rightarrow10\text{ Purple} \\ \cdot \\ \cdot \\ 20\text{ Gre}en\text{ }\rightarrow\text{ 25 Purple} \end{gathered}[/tex]Therefore, for 20 Green beads she will need to use 25 Purple Beads.
[tex]25\text{ Purple Beads}[/tex]Circle B is a transformation of Circle A. Describe the transformations that show why Circle A is similar to Circle B. YA 12 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of . then translating the image 12 units down. 10 8 6 A А Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of then reflecting the image in the y-axis. 4 N -2 0 -2 2 4 6 8 10 12 x -4 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of, then translating the image 12 units down. -6 B -8 -10 -12 Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of then rotating the image 180°.
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The two circles, A and B have different diameters. The diiameter of circle A is 5 units while the diameter of circle B is 4 units. This means that circle B is smaller than circle A. This means that there is a dilation and it is a reduction. Thus, we can say that B is 4/5 * A
4/5 * 5 = 4
The image was then translated 12 units down. The correct option is the third one
Marked angle 3 different ways
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Answer:
where are question I don't understand this question
The famous mathematician Gauss is credited with deriving a formula for determining the the sum of the first n counting numbers. If the sum of the first 100 counting numbers is 5050, what is the difference between the sum of all of the even counting numbers and the odd counting numbers less than 101? Start by making the problem simpler and look for patterns. Describe how you came to your solution.
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Given:
The sum of the first 100 counting numbers is 5050.
To find:
The difference between the sum of all of the even counting numbers and the odd counting numbers less than 101.
Explanation:
Let us find the sum of all of the even counting numbers from 1 to 101.
The series is,
[tex]S_1=2+4+6+....+100[/tex]It can be written as,
[tex]S_1=2(1+2+3+.....+50)[/tex]Using the formula,
[tex]\begin{gathered} 1+2+3+.....+n=\frac{n(n+1)}{2} \\ S_1=2(1+2+3+....+50)=2[\frac{50(50+1)}{2}] \\ S_1=50(51) \\ S_1=2550........(1) \end{gathered}[/tex]Next, let us find the sum of all of the odd counting numbers.
[tex]\begin{gathered} S_2=Total-Sum\text{ of all even numebrs} \\ S_2=5050-2550 \\ S_2=2500.......(2) \end{gathered}[/tex]So, the difference between the sum of all of the even counting numbers and the odd counting numbers less than 101 is
[tex]\begin{gathered} S_1-S_2=2550-2500 \\ =50 \end{gathered}[/tex]Final answer:
The difference between the sum of all of the even counting numbers and the odd counting numbers less than 101 is 50.
A mattress with a list price of $2300 will be discounted 30% at the time of purchase. What is the sale price before taxes?
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So,
30% of $2300 is:
[tex]\frac{30\cdot2300}{100}=690[/tex]So that's the amount that will be discounted. Therefore, the sale price before taxes is $2300 - $690 = $1610
simplifying like terms and distributive property7b + 2(46 - 3)
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We will solve as follows:
[tex]7b+2(46-3)=7b+92-6[/tex][tex]=7b+86[/tex]So, the solution is 7b + 86.
Use Composition of FunctionsBOX OFFICE A movle theater charges $8.50 for each of the xtickets sold. The manager wants to determine how much the movietheater gets to keep of the ticket sales If they have to glve thestudlos 75% of the money earned on ticket sales t(x). If the amountthey keep of each ticket sale is k(x), which composition representsthe total amount of money the theater gets to keep?
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Given: The amout charged per ticket is $8.50
If x tickets are sold
Then the total revenue (amount made) will be =>
[tex]8.5\text{ x }x\text{ = \$8.50x}[/tex]If t(x) represents how much the studio collects
and k(x) represents how much is kept
Given: t(x) = 75% then
k(x)= (100 -75)%= 25 %
So that
The total amount that will be kept will be
25% of $8.50x
=>
[tex]\frac{25}{100}\text{ x (\$8.50x) }[/tex][tex]\frac{25\text{ x \$8.50x}}{100}\text{ = }\frac{212.5x}{100}=\text{ \$2.125x}[/tex]The amount that will be kept will be
= > $2.125x
Where x is the number of tickets
name a situation when a domain could not have a negative values
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The domain of a function is the set of numbers that can be used as an input. For every case when we are dealing with real world objects the domain can't have negative numbers. For example: If a function is modeling the revenue of a parking lot as a function of the number of cars that park there in a month, there is no negative car, therefore we can't have negative values as inputs. The worst case scenario would be a situation where no cars visited the parking lot for the whole month, which would be an input of 0.
What is the probability that the spinner lands on blue?
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Answer:
Concept:
The total number of angles in a circle is
[tex]\begin{gathered} =360^0 \\ =120^0+60^0+180^0=360^0 \end{gathered}[/tex]The angle of the sector that represents blue is
[tex]=60^0[/tex]To calculate the probability, we will use the formula below
[tex]\begin{gathered} P(\text{blue)}=\frac{n(\text{blue)}}{n(S)} \\ n(\text{blue)}=60^0,n(S)=360^0 \\ P(\text{blue)}=\frac{n(\text{blue)}}{n(S)}=\frac{60}{360} \\ P(\text{blue)}=\frac{1}{6} \end{gathered}[/tex]Hence,
The final answer is = 1/6
Find the circumference with a diameter of 10 feet long. I missed the notes for this section, so I don't know what I'm doing.
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We need to find the circumference using the diameter.
The equation for the circumference is given by:
[tex]C=\pi d[/tex]Where d represents the diameter.
Replace d=10 ft
[tex]\begin{gathered} C=\pi10ft \\ \text{Then, the circumference is:} \\ C=10\pi\text{ }ft \end{gathered}[/tex]someone help me
please and thank you
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Answer: Answer C
Step-by-step explanation:
Because it is a reflection of the Y-axis, the X-coordinates would remain the same but the Y-coordinates would change.
Please help with this question: I have attached the image A survey was done where males and females were asked if they would prefer to eat chicken or steak. The results of the survey are shown in the two-way frequency table. ChickenSteakMale0.2380.216Female0.3110.235What percent of the males surveyed prefer chicken?Enter your answer to the nearest tenth of a percent in the box. __%
Answers
23.8%
Explanation:
Since 0.238 represent the frequency of male who eats chicken
0.238 / 100 = 23.8%
Answer: 52.4%
Step-by-step explanation: I took the test and that was the correct answer.
function c is defined by the equation c(n)=50+4n. it gives the monthly cost in dollars of visitiing a gym as a function of the number of visits v. find the value of c (7). show your reasoning and explain what the value means in this situation
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The cost function is defined as
[tex]c(n)=50+4n[/tex]The value of c(7) can be determined by substituting 7 for n into the function.
Therefore, c(7) becomes;
[tex]\begin{gathered} c(7)=50+4(7) \\ c(7)=50+28 \\ c(7)=78 \end{gathered}[/tex]This means the cost of 7 visits to the gym is $78.
The cost function shows that there is an amount that doesnt change and that is 50. Then there is one that varies or changes with every visit, or n. That means as the value of n increases or decreases, the total amount also increases or decreases. When n equals zero, then the total cost becomes 50. This means when there is no visit to the gym, the cost still remains $50.
Therefore, n is a variable that can determine changes in the total cost.
Answer: c(7)=78
Step-by-step explanation:
C(n)=50+4n
c(7)=50+4(7)
=50+28
=78
C(7)=78
What are all of the answers for these questions? Use 3 for pi. Please do not use a file to answer, I cannot read it.Question 8.
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To calculate the area of the doughnut, we need to calculate the area of the larger circle and substract the area of the smaller circle.
The area of a circle can be calculated using its radius:
[tex]A=\pi r^2[/tex]The diameter of the larger circle is 6cm which meand that its radius is half as large, so the radius is 3 cm and the area of the larger circle is:
[tex]A_L=\pi3^2=9\pi[/tex]Area of 9π cm².
The smaller one have a diameter of 2 cm, so its radius is half as large, radius of 1 cm.
So, the area of the smaller circle is:
[tex]A_S=\pi1^2=\pi[/tex]Area of π cm².
The total shaded area is, then, the area of the larger minus the area of the smaller.
So, the shaded area is:
[tex]\begin{gathered} A=A_L-A_S \\ A=(9\pi-\pi)cm^2 \\ A=8\pi cm^2 \\ A\approx(9\cdot3)cm^2 \\ A\approx27cm^2 \end{gathered}[/tex]What is the exact solution of cos 2x? Thank you!
Answers
Answer:
119/169
Explanation:
We use the following trig identity
[tex]\cos2x=1-2\sin^2(x)[/tex]Now in our case, we know that
[tex]\sin x=-\frac{5}{13}[/tex]therefore, our formula gives
[tex]\cos2x=1-2*(\frac{5}{13})^2[/tex]which simplifies to give
[tex]\boxed{\cos2x=\frac{119}{169}.}[/tex]A and B are mutually exclusive events P(A) =0.60 and P(B)=0.30 what is P (A or B)
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We know that for any number of mutually exclusive events, we have the formula:
[tex]P(A_1\cup A_2\cup A_3\cup\ldots)=P(A_1)+P(A_2)+P(A_3)+\cdots[/tex]In this case, we have that P(A)=0.60 and P(B)=0.30, then:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)=0.60+0.30=0.90 \\ P(A\cup B)=0.90 \end{gathered}[/tex]Therefore, P(A or B) =0.90
A survey of 85 persons was conducted at TCC, and it was found that 54 persons carried a cell phone, 19 persons carried a tablet computer, and 16 carried both a cell phone and a tablet.How many people carried a cell phone or a tablet?How many people carried neither a cell phone nor a tablet?How many people carried a cell phone only?How many people carried a tablet but not a cell phone?
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Answer:
The universal set is given below as
[tex]\xi=85[/tex]The number of people with cell phone is
[tex]n(C)=54[/tex]The number of persons with tablet is
[tex]n(T)=19[/tex]The number of people who carry both cellphone and tablet
[tex]n(C\cap T)=16[/tex]Step 1:
To figure our the number of students that carry cellphone or tablets will be
[tex]\begin{gathered} =38+16+3 \\ =57\text{ }people \end{gathered}[/tex]Hence,
The number of people that carried cell phone or tablet
[tex]\Rightarrow57people[/tex]Step 2:
How many people carried neither a cell phone nor a tablet?
[tex]\begin{gathered} =85-(38+16+3) \\ =85-57 \\ =28 \end{gathered}[/tex]Hence,
The number of people that carried neither cell phone nor a tablet is
[tex]\Rightarrow28people[/tex]Step 3:
How many people carried a cell phone only?
Hence,
The number of people who carried cell-phone only is
[tex]\Rightarrow38people[/tex]Step 4:
How many people carried a tablet but not a cell phone?
Hence,
The number of people that carried a tablet but not a cell phone is
[tex]\Rightarrow3people[/tex]The base of a triangle is given by a number, x (metres). The height of the triangle is ten metres less than the product of two and the number. The area of the triangle is equal to the product of seven and the base length.
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According to the question the base of the triangle is x, the height is ten less than the product of two and x, this is 2x-10. The area of the triangle is the product of seven and the base, this is 7x.
The area of a triangle is given by:
[tex]A=\frac{b\cdot h}{2}[/tex]Replace each variable for the given expressions:
[tex]\begin{gathered} 7x=\frac{x\cdot(2x-10)}{2} \\ 7x=\frac{2x^2-10x}{2} \\ 7x=x^2-5x \\ 7=x-5 \\ x=7+5 \\ x=12 \end{gathered}[/tex]x has a value of 12.
