John compares the graph of two functions.• The first function was y=3x +4.• The second function fits the values in the table below.22What is the distance between the y-intercepts of the two functions?O A. 5 unitsO B. 6 unitsO C. 4 unitsOD. 3 units
Answers
the y-intercept of a parabola is the y coordinate of the point where does the graph intersect the y-axis.
so from the figure, we can see that the parabola is intersecting the y-axis at (0, -6)
and it is intersecting the x-axis at (3,0)
thus. y-intercept is (0, -6) and x-intercept is (3,0)
that is option D
Related Questions
What is the missing reason for The third step in the proof below
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Solution
The image below contain the solution
The midpoint of AB is M(5,1). If the coordinates of A are (3,6), what are thecoordinates of B?
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We have a segment AB of which we know the coordinates of A(3,6) and the midpoint M(5,1).
We have to find the coordinates of B.
We know that the coordinates of the midpoint M are the average of the coordinates of the endpoints A and B, so we can write:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ 2\cdot x_M=x_A+x_B \\ x_B=2x_M-x_A \end{gathered}[/tex]Now we have the x-coordinate of B in function of the x-coordinates of A and M.
The same can be calculated for the y-coordinate:
[tex]y_B=2y_M-y_A[/tex]Then, we can replace and calculate:
[tex]\begin{gathered} x_B=2x_M-x_A \\ x_B=2\cdot5-3 \\ x_B=10-3 \\ x_B=7 \end{gathered}[/tex][tex]\begin{gathered} y_B=2y_M-y_A \\ y_B=2\cdot1-6 \\ y_B=2-6 \\ y_B=-4 \end{gathered}[/tex]Then, the coordinates of B are (7,-4).
Answer: B = (7,-4)
Find the X-Intercept and the y-intercept of 4x- 5y = 15X-Intercept:???Y-intercept: ???help
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The y-intercept is (0,-3) while the x-intercept is (18.75,0)
Here, we want to find the x and y-intercepts of the given line
Firstly, we have to rewrite the equation of the line in the standard form
We have this as;
[tex]\text{y = mx + b}[/tex]m is the slope and b is the y-intercept
Rewriting the given equation, we have this as;
[tex]\begin{gathered} 5y\text{ = 4x-15} \\ y\text{ =}\frac{4}{5}x-\frac{15}{5} \\ \\ y\text{ = }\frac{4}{5}x\text{ - 3} \end{gathered}[/tex]We have the y-intercept as -3
In the coordinate form, this is (0,-3)
To get the x-intercept, we set the y value to zero
We have this as;
[tex]\begin{gathered} 0\text{ = }\frac{4}{5}x-15 \\ 15\text{ = }\frac{4x}{5} \\ \\ 4x\text{ = (15}\times5) \\ 4x\text{ = 75} \\ x\text{ = }\frac{75}{4} \\ x\text{ = 18.75} \end{gathered}[/tex]The x-intercept is 18.75 which in the coordinate form is (18.75,0)
the line L3 is perpendicular to 3x-y+2=0 .find the gradient of L3
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Answer:
[tex]-\frac{1}{3}[/tex]Explanation:
Here, we want to get the gradient of the line L3
The equation of a straight line can be expressed as:
[tex]y\text{ = mx + b}[/tex]where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)
Now,let us write the equation of the first line in the slope-intercept form
Mathematically, we have this as:
[tex]\begin{gathered} 3x-y\text{ + 2 = 0} \\ y\text{ = 3x + 2} \end{gathered}[/tex]The gradient of the first line is 3
Now,let us get the gradient of the second line L3
Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1
Thus, we have it that:
[tex]\begin{gathered} m_1\text{ }\times m_2\text{ = -1} \\ 3\text{ }\times m_2\text{ = -1} \\ m_2\text{ = -}\frac{1}{3} \end{gathered}[/tex]the first drop down answers are 18,10,7,14the second drop down box options are 16.5,30.5,44.5the third options are 2.5, 1.5, 1,3 the fourth options are 14n, 18n, 7n, 10nthe fifth options are each movie tickets cost the same amount, there is a service fee for buying tickets online, the cost increase as tge number of tickets increase, the leaste amount of tickets you cab buy is 1
Answers
Answer:
Recursive formula:
a_n = a_n-1 + 14,
a_1 = 16.5
Explicit formula: a_n = 14(n - 1) + 16.5
Each movie costs the same amount.
Explanation:
Looking at the numbers we see that each next term a_n is 14 added to the previous term, a_n-1 and the first term a_1 is 16.5; therefore, we can say
[tex]\begin{gathered} a_n=a_{n-1}+14, \\ a_1=16.5 \end{gathered}[/tex]
Use the value of x to find the measure of Angle 1.x=25 5x-5 2x+10
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Given:
• x = 25
,• ∠1 = 5x - 5
,• ∠2 = 2x + 10
Let's find the measure of angle 1.
To find the measure of angle 1, substitute 25 for x in (5x - 5) and evaluate.
We have:
m∠1 = 5x - 5
m∠1 = 5(25) - 5
m∠1 = 125 - 5
m∠1 = 120
Therefore, the measure of angle 1 is 120 degrees.
ANSWER:
∠1 = 120°
A committee must be made up of two students from grades 9, 10, or 11, and another two students from grade 12. How many different committees can be made? Explain and show all of your work.
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to make the committee
according to a census, there were 66 people per square mile (population density) in a certain country in 1980. By 2000, the # of people per square mile had grown to 76. This information was used to develop a linear equation in slope intercept form, given below, where x is the time in years and y is the population density. Think of 1980 as year zero. what is the population density expected to be in 2018? y = 1/2x + 66
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Determine the value of x for taking 1980 as 0.
[tex]\begin{gathered} x=2018-1980 \\ =38 \end{gathered}[/tex]The equation is y = 1/2x + 66.
Substitute the value of x in the equation to determine the population density in 2018.
[tex]\begin{gathered} y=\frac{1}{2}\cdot38+66 \\ =19+66 \\ =85 \end{gathered}[/tex]So population density in year 2018 is 85.
Answer: 85
If Rosa is at most 27 years old. What symbol does at most refer to less than greater than less than or equal to greater than or equal to
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The correct answer is less than or equal to because at most 27 years means that Rosa's highest age is 27.
Hello, I need help writing a recursive formula for these I’m struggling bad
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1) Notice that:
[tex]\begin{gathered} 3=\frac{30}{10}, \\ \frac{3}{10}=\frac{3}{10}, \\ \frac{3}{100}=\frac{\frac{3}{10}}{10}. \end{gathered}[/tex]Therefore the recursive formula for the first sequence is:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]2) Notice that:
[tex]\begin{gathered} 11=14-3, \\ 8=11-3, \\ 5=11-3. \end{gathered}[/tex]Therefore the recursive formula for the second sequence is:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]Answer:
Left sequence:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]Right sequence:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]
Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which number line represents all of the possible weights, in pounds, of apples Patricia can keep in her store?
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Given:
The bins can hold no more than w(b) < 200 pounds.
The crate can hold no more than w(c) < 50 pounds.
The number of bins is n(b) = 3.
The number of crates is n(c) = 2.
The objective is to find the correct number line for the graph.
Explanation:
The maximum quantity of bins can be calculated as,
[tex]\begin{gathered} Q(b)The maximum quantity of crate can be calculated as,[tex]\begin{gathered} Q(c)To find the maximum store capacity:The maximum store capacity can be calculated as,
[tex]undefined[/tex]3.What are the coordinates of the center and the length of the radius of the circle whose equation is(x + 1)^2 + (-5)^2 = 16?
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The general equation of circle with centre (h.k) and radius r is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Simplify the equation to obtain the centre and radius of circle.
[tex]\begin{gathered} (x+1)^2+(y-5)^2=16 \\ (x-(-1))^2+(y-5)^2=(4)^2 \end{gathered}[/tex]So center of circle is (-1,5) and radius 4.
1/ (gg^2 e^5)^2 Write your answer with only positive exponents
Answers
ANSWER
[tex]\frac{1}{g^6e^{10}}[/tex]EXPLANATION
In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,
[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]Now, we also have the power of a product. The exponents can be distributed into the multiplication,
[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,
[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]Hence, the simplified expression is,
[tex]\frac{1}{g^6e^{10}}[/tex]solve the equation. check your solution 1/3 (2b+9) =2/3 (b+9/2)
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The equation to solve is:
[tex]\frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2})[/tex]We use distributive property [a(b+c)=ab+ac], simplify and solve for b:
[tex]\begin{gathered} \frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2}) \\ \frac{2}{3}b+3=\frac{2}{3}b+3 \end{gathered}[/tex]From here, we can't solve.
It is the same equation.
No Solution.
what is 8q= 96 what is it?
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To find the value of q, divide both sides of the equation by 8:
[tex]\begin{gathered} 8q=96 \\ \Rightarrow\frac{8q}{8}=\frac{96}{8} \end{gathered}[/tex]Simplify both members of the equation:
[tex]\begin{gathered} \Rightarrow q=\frac{96}{8} \\ \Rightarrow q=12 \end{gathered}[/tex]Therefore:
[tex]q=12[/tex]evaluate the expression 0.03^3
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The given expression is,
[tex]0.03^3[/tex]So, expanding we have,
[tex]0.03^3=0.03\times0.03\times0.03=\text{0}.000027[/tex]Suppose the booster club is raising money to help offset the cost of a trip.You make $10 per door wreath sold and $2 per candy bar sold. The clubwants to raise at least $400.00. Write an inequality to represent thissituation.
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Let the number of door wreath sold is x.
Let the number of candy bar sold is y.
The inequality can be represented as,
[tex]10x+2y\ge400[/tex]Thus, the above inequation gives the required inequality.
Some roads in the Rocky Mountains have a rise of 7 feet for every 100 horizontal feet.What is the slope of such roads?
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Let's begin by listing out the information given to us:
The road rises by 7 feet every 100 horizontal feet
The equation becomes:
Slope (m) = Δy/Δx = 7/100 = 0.07
Slope (m) = 0.07
write an equation of the line that satisfies the given conditions. give the equation (a) in slope intercept form and (b) in standard form. m=-7/12 ,(-6,12)
Answers
Given the slope of the line:
[tex]m=-\frac{7}{12}[/tex]And this point on the line:
[tex](-6,12)[/tex](a) By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:
[tex]12=(-\frac{7}{12})(-6)+b[/tex][tex]12=\frac{42}{12}+b[/tex][tex]\begin{gathered} 12=\frac{42}{12}+b \\ \\ 12=\frac{7}{2}+b \end{gathered}[/tex][tex]\begin{gathered} 12-\frac{7}{2}=b \\ \\ b=\frac{17}{2} \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept Form is:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) The Standard Form of the equation of a line is:
[tex]Ax+By=C[/tex]Where A, B, and C are integers, and A is positive.
In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:
[tex]\frac{7}{12}x[/tex]Then, you get:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]Hence, the answers are:
(a) Slope-Intercept Form:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) Standard Form:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?
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If the line of the graph is vertical then the slope of the graph is zero. The coordinate of the y-value will never change on vertical lines.
What are vertical lines?The vertical line is a line that is parallel to the y-axis. A vertical line can be defined as a line on the coordinate plane where all the points on the line have the same x-coordinate. A form of test employed in relation is the vertical line test. Any kind of vertical line equation lacks a y-intercept. The vertical line test is used to determine whether or not the given relation is a function. The vertical line is another name for the vertical bar. A mathematical sign is an upright slash. Depending on the context, it may be used to represent a certain kind of logic or an operation. The vertical line is the line that runs along the y-axis.
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A freight train is carrying goods across the country. The distance it has traveled directly with the number of gallons of fuel it has used. See the graph below
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1) To find how many miles per gallon that freight train makes is to find a rate. We can find it in two ways, either by setting a proportion or by finding the slope.
2) Note that this direct variation depicted by the graph is proportional. Therefore, let's find the slope by picking two points:
[tex]\begin{gathered} (200,50),(400,100) \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{100-50}{400-200}=\frac{50}{200}=\frac{1}{4} \end{gathered}[/tex]3) Thus, the answers are:
3. If the mZLKI - 174º and KR bisects LLKI, then find the mLLKR.
R
E
K
87°
1740
0740
90°
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1:
[tex]undefined[/tex]Answer:
87°
Step-by-step explanation:
Angle bisector:Angle bisector is a ray that divides an angle into two congruent angles.
∠LKR = ∠LKJ ÷ 2
= 174° ÷ 2
= 87°
A gift box for a shirt has a length of 60 centimeters, a width of 30 centimeters, anda height of 10 centimeters. Find the surface area of the gift box.
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A rectangular box has six faces. The surface area is given by the sum of the area of those faces. Parallel faces have the same area, therefore, we just need to calculate the area of three of them and multiply by 2. The surface area of our gift box is:
[tex]\begin{gathered} S=2(60\times30+60\times10+30\times10) \\ =2(1800+600+300) \\ =2(2700) \\ =5400 \end{gathered}[/tex]The surface area of the box is 5400 cm².
solve equation 10 - 25x = 5 what is the value of x
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ANSWER
x = 1/5
EXPLANATION
We are given the equation:
10 - 25x = 5
To find the value of x, first we subtract 10 from both sides of the equation:
10 - 25x - 10 = 5 - 10
10 - 10 - 25x = 5 - 10
-25x = -5
Now, divide both sides by 5:
=> x = -5 / -25
x = 1/5
That is the value of x.
which portion must be true?
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The two figures are similar
Using the similarity theorem
The only true proportion is
[tex]\frac{8}{2}\text{ = }\frac{x}{y}[/tex]Translate this sentence into an equation.The product of 5 and Julie's height is 80.Use the variablej to represent Julie's height.
Answers
ANSWER:
5 x j = 80
STEP-BY-STEP EXPLANATION:
The sentence as an equation would be the multiplication of j and 5 equal to 80, just like this:
[tex]5\times j=80[/tex]find the shaded area to the nearest tenth, use 3.14 for pi. help pls due tmrw
Answers
The area of the shaded region inside the circle is 49.04cm².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the shaded area is:
We can easily tell that the diameter of the circle here is 12cm.
So, the radius will be 6cm.
Now, calculate the area of a circle as follows:
A = πr²
A = 3.14(6)²
A = 3.14(36)
A = 113.04cm²
Now, the area of the smaller square:
A = s²
A = 2²
A = 64²
Area of the shaded region:
113.04 - 64
49.04 cm²
Therefore, the area of the shaded region inside the circle is 49.04cm².
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5. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at P.IP = 3x, DP = 6x-2, NP = 3y, and YP = 7x - 2.
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Given the INDY
The diagonals has intersected at the point P
IP = 3x, DP = 6x - 2
NP = 3y , YP = 7x - 2
So, IP = DP
[tex]6x-2=3x[/tex]Solve for x :
[tex]\begin{gathered} 6x-2=3x \\ 6x-3x=2 \\ 3x=2 \\ \\ x=\frac{2}{3} \end{gathered}[/tex]And : NP = YP
[tex]3y=7x-2[/tex]substitute with the value of x :
[tex]\begin{gathered} 3y=7\cdot\frac{2}{3}-2=\frac{23}{3}-2=\frac{17}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]So, the answer is :
[tex]\begin{gathered} x=\frac{2}{3} \\ \\ y=\frac{17}{9} \end{gathered}[/tex]How to solve this problem step by step in depth. I have no idea how to solve this
Answers
Answer
[tex]f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5}[/tex]Explanation
The given function is
[tex]f(x)=-5x-4[/tex]Let y = f(x), this implies
[tex]y=-5x-4[/tex]Now, make x the subject of the formula
[tex]\begin{gathered} y=-5x-4 \\ 5x=-y-4 \\ \text{To get x, we divide both sides by 5} \\ \frac{5x}{5}=\frac{-y-4}{5} \\ \\ x=\frac{-y-4}{5} \end{gathered}[/tex]Since f(x) = y, then x = f⁻¹(y)
[tex]\begin{gathered} f^{-}^{1}\mleft(y\mright)=\frac{-y-4}{5} \\ \therefore f^{-1}(x)=\frac{-x-4}{5} \end{gathered}[/tex]The above inverse function can be rewritten as follows
[tex]\begin{gathered} f^{-1}(x)=\frac{-x}{5}-\frac{4}{5} \\ f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5} \end{gathered}[/tex]. Compare: what is greater 5/3 or 9/16
Answers
hello
between 5/3 and 9/16, 5/3 is greater than 9/16
[tex]\frac{5}{3}>\frac{9}{16}[/tex]