please help me do this i think i’mdoing it right but i’m not sure The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.
Answers
Step 1
Write the parabola in vertex form eqaution
[tex](x-h)^2=-4a(y-k)[/tex]where
[tex]\begin{gathered} h=0=x-\text{coordinate of the vertex} \\ k=1=y-\text{coordinate of the vertex} \end{gathered}[/tex]Step 2
Find the required equation
The distance between the vertex and the focus = a
Therefore,
[tex]\begin{gathered} \text{The vertex=(0,1)} \\ \text{The focus= (0,-2)} \end{gathered}[/tex]Hence with the formula for the distance between two points we have
[tex]\begin{gathered} D=\sqrt[]{(0-0)^2+(-2-1)^2}^{}_{} \\ D=\sqrt[]{0^2+(-3)^2} \\ D=\sqrt[]{0+9} \\ D=\sqrt[]{9} \\ D=3 \\ a=D=3 \end{gathered}[/tex]Step 3
Get the required equation by substitution
[tex]\begin{gathered} (x-h)^2=-4(a)(y-k) \\ (x-0)^2=-4(3)(y-1) \\ x^2=-12(y-1) \end{gathered}[/tex]Hence in vertex form, the equation of the parabola will be
[tex]y=-\frac{1}{12}x^2+1[/tex]The answer is written as;
[tex]y=-\frac{1}{12}x^2+1[/tex]
Related Questions
Help mee pleasee!!
thank you <3
Answers
Answer:
never to leave the unknown shackspeare
Step-by-step explanation:
it never leaves
or never stays
and never comes back
My child ask for help on this I don’t know how to help
Them
Please see attached photo
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After 6 months he spents $228.5 on cable and for 10 months he could have cable service for $344.5
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given:
c(x)=29x+54.5
a) At x=6
c(6) = 29*6 + 54.5
c(6) = $ 228.5
b) c(x) = 344.5
344.5 = 29x+54.5
x = 10 months
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Choose the graph of the linear equation 24x + 64y = 384?
On a coordinate plane, a line goes through points (0, 6) and (16, 0).
On a coordinate plane, a line goes through points (0, 8) and (12, 0).
On a coordinate plane, a line goes through points (0, 16) and (6, 0).
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The graph that represents the linear equation, 24x + 64y = 384 is shown in the diagram.
How to Determine the Graph of a Linear Equation?A linear equation can be expressed as y = mx + b, which is the slope-intercept form where the slope is represented as m and the y-intercept is represented by b. This y-intercept is the point where the line intercepts the y-axis when x is equal to zero.
Given the linear equation, 24x + 64y = 384, rewrite in slope-intercept form to easily figure out the slope:
24x + 64y = 384
64y = -24x + 384
y = -24x/64 + 384/64
y = -6/16x + 6
This shows that the graph would have a y-coordinate, b = 6, while the slope is -6/16. The graph would be the one shown below in the diagram.
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Answer:
A
Step-by-step explanation:
Need x please?????????I’m looking to find x. The line inside is just to know where x is.Round to the nearest tenth.
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The triangle given in the exercise is a Right Triangle because the square inside it indicates that it has an angle that measures 90 degrees.
Then, you can use the following Trigonometric Function:
[tex]\sin \alpha=\frac{opposite}{hypotenuse}[/tex]In this case:
[tex]\begin{gathered} \alpha=31\degree_{} \\ opposite=11 \\ hypotenuse=x \end{gathered}[/tex]Then, by substituting values and solving for "x", you get:
[tex]\begin{gathered} \sin (31\degree)=\frac{11}{x} \\ \\ x\cdot\sin (31\degree)=11 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{11}{\sin (31\degree)} \\ \\ x\approx21.4 \end{gathered}[/tex]Therefore, the answer is:
[tex]x\approx21.4[/tex]Nixon will pay for his new car in 36 monthly payments. if his car loan is for 19,061, THEN HOW MUCH will pay each month
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Answer is 529.4 every month
I attached a picture of the graphIn which interval is the median age?Choose 1 answer:A.) 0 - 5B.) 5 - 10 C.) 10 - 15 D.) 15 - 20 E.) 20 - 25
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We have the following:
The median is the value of the half, therefore
[tex]M=\frac{25+0}{2}=12.5[/tex]Therefore the answer is C) 10 - 15
Answer:
dbxbdghdhdvddhbdhddu
Use the graph at the top of the page for 22 and 23. A) 8/3 B) 8 C) - 1/8 D) -3/8 22) Write the slope of the line that would be parallel to h(x)23) Write the slope of the line that would be perpendicular to h(x)
Answers
Given the line h(x), it can be observed that two points with coordinate below can be located
[tex]\begin{gathered} (-4,0),\text{point where h(x) cut the x-axis} \\ (4,-1),\text{point where h(x) and m(x) cross each other} \end{gathered}[/tex]The slope,s, of a line given coordinates of two points can be found using the formula below:
[tex]\begin{gathered} s=\frac{y_2-y_1}{x_2-x_1} \\ \text{points} \\ (x_1,y_1),(x_2,y_2) \end{gathered}[/tex]The slope of the line h(x) with the coordinates of the two points gotten can be gotten as shown below
[tex]\begin{gathered} (-4,0),(4,-1) \\ s_{h(x)}=\frac{-1-0}{4--4} \\ s_{h(x)}=\frac{-1}{4+4} \\ s_{h(x)}=-\frac{1}{8} \end{gathered}[/tex]It should be noted that two parallel lines have the same slope, while the slope of two perpendicular lines can be found to be negative inverse of their slopes
For example, if m1 is the slope of a line, the slope of its parallel line would be m1. But the slope of the perpendicular line would be -1/m1
The slope of the line that would be parallel to h(x) is the same as the slope of h(x)
The slope of the line that would be perpendicular to h(x) would be negative inverse of the slope of line h(x)
[tex]\begin{gathered} s_{\text{parallel}}=-\frac{1}{8} \\ s_{\text{perpendicular}}=\frac{-1}{-\frac{1}{8}}=-1\times\frac{-8}{1}=8 \end{gathered}[/tex]Hence, The slope of the line that would be parallel to h(x) is -1/8, while the slope of the line that would be perpendicular to h(x) is 8
Find 15.4% of 360°. (Round your answer to the nearest whole degree.)
Answers
We need to find 15.4% of 360º.
Notice that:
[tex]15.4\%=\frac{15.4}{100}=\frac{154}{1000}[/tex]Also, 15.4% of 360º corresponds to the product:
[tex]15.4\%\cdot360\degree[/tex]Thus, we have:
[tex]15.4\%\text{ of }360\degree=\frac{154}{1000}\cdot360\degree=\frac{154\cdot360}{1000}=\frac{154\cdot36}{100}=\frac{5544}{100}=55.44\degree[/tex]Since 0.44 < 0.50, rounding to the nearest whole degree, we obtain:
Answer
55º
the desnity of the conrete is 2400
what is mass
Answers
Answer:
360000
Step-by-step explanation:
Pls explain I have a test on this number 2
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Hello there. To solve this question, we have to remember some properties about equations of circles.
Given the following equation:
[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]It is called the equation of a circle with center at
[tex](x_0,\,y_0)[/tex]And radius R.
In the question, it gives us two equations that we might describe the shape of the equation, considering its key features (center, foci, asymptotes, semi-major and semi-minor axes, if applicable).
We have that
[tex](x+4)^2+(y-2)^2=16[/tex]Is the equation of a circle with center at (-4, 2) and radius equal to
[tex]R=\sqrt{16}=4[/tex]For the other equation
[tex](x-2)^2+(y-5)^2=64[/tex]Is also the equation of a circle, with center at (2, 5) and radius equal to
[tex]R=\sqrt{64}=8[/tex]Can someone please help me with this( there is a part two)
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Part A:
We will have that the inequality that represents the scenario is:
[tex]1.75x\le35[/tex]Where x is the number of horses.
Part B:
The solution of the inequality is:
[tex]x\le\frac{35}{1.75}\Rightarrow x\le20[/tex]This means that Sunshine Acre Farm can support at most 20 horses.
x(4b-a)² + y(4b - a)²
factor the binomial out of each polynomial.
please explain how you got the answer i am deeply confused.
Answers
Answer:
(4b - a)²(x + y)
Step-by-step explanation:
x(4b - a)² + y(4b - a)² ← factor out (4b - a)² from each term
= (4b - a)²(x + y)
Solve each expression by completing the square. x^2+6x=9
Answers
x^2+6x=9
To create a trinomial square on the left side of the equation, you have to find a value that is equal to the square of half of 9.
(9/2)^2=(3)^2
Then, add this therm to each side of the equation.
x^2+6x+(3)^2=9+(3)^2
Simplifying that equation:
x^2+6x+9=18
Factor the perfect trinomial square into (x+3)^2
(x+3)^2=18
To solve the equation for x, you have to take the square root of each side of the equation:
(x+3)^(2*1/2)=18^1/2
A. The graph of g(x) is horizontally compressed by a factor of 4.B. The graph of g(x) is shifted 4 units to the right.C. The graph of g(x) is horizontally stretched by a factor of 4.D. The graph of g(x) is vertically compressed by a factor of 4.
Answers
Give:
There are given the function:
[tex]f(x)=x^2,g(x)=(\frac{1}{4}x)\placeholder{⬚}^2[/tex]Now,
The transformation of the graph g(x) is shown below.
The,
Transformation is:
[tex][/tex]In an inverse variation, y = 1 when x = 4. Write an inverse variation equation that showsthe relationship between x and y.
Answers
In an inverse variation as one quantity increases the other decreases. For example, if x increases, y decreases
We can write it as:
x=k/y
where k is a constant.
or
x*y = k
replacing the values:
4*1=k
4=k
x*y=4
Use the rational zero thereom to help find the zeros
Answers
Answer
The zeros of the polynomial function using the rational zero theorem is
[tex]\frac{\pm p}{q}=\pm1,\pm\frac{1}{2},\pm\frac{1}{4},\pm2,\pm4[/tex]Explanation
The given polynomial function is
[tex]f(x)=4x^4+8x^3+21x^2+17x+4[/tex]What to find:
To find the zeros of the polynomial function the rational zero theorem.
Step-by-step solution:
The rational zero theorem: If a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Considering the given polynomial function
[tex]f(x)=4x^4+8x^3+21x^2+17x+4[/tex]The constant term, p = 4
The leading coefficient, q = 4
The factors of the constant p and the leading coefficient q are:
[tex]\begin{gathered} p=\pm1,\pm2,\pm4 \\ \\ q=\operatorname{\pm}1,\operatorname{\pm}2,\operatorname{\pm}4 \end{gathered}[/tex]Hence, the zeros of the polynomial function using the rational zero theorem will be
[tex]\begin{gathered} \frac{\pm p}{q}=\frac{\pm1,\pm2,\pm4}{\pm1,\pm2,\pm4} \\ \\ \frac{\operatorname{\pm}p}{q}=\operatorname{\pm}1,\operatorname{\pm}\frac{1}{2},\operatorname{\pm}\frac{1}{4},\operatorname{\pm}2,\operatorname{\pm}4 \end{gathered}[/tex]
4. Tyrell bought 4 pizzas and 5 subs and his bill was $56.25. Annabel bought 3 pizzas and 7 subs and her bill was $59.25. How much does each item cost?
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let p represent pizza
let s represent subs
when he bought 4 pizza and 5 subs bill is $56.25
[tex]4p\text{ + 5s = 56.25 --------1}[/tex]when he bought 3 pizzas and 7 subs his bill is $59.25
[tex]3p\text{ + 7s = 59.25}--------2[/tex]solving the two equations simultaneosly
[tex]\begin{gathered} 4p\text{ + 5s = 56.25 x 3 (multiply equation 1 by coefficient of p in equation 2 i.e 3)} \\ 3p\text{ + 7s = 59.25 x 4 ( multiply equation 2 by coefficient of p in eqaution 1 i.e 4)} \\ \text{these multiplications gives equation 3 and 4 below} \end{gathered}[/tex][tex]\begin{gathered} 12p\text{ + 15s = 168.75 -------3} \\ 12p\text{ + 28s = 237}--------4 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{subtracting equation 3 from 4, p is eliminated and the equation below is obtained} \\ 13s\text{ = 68.25} \\ (i\mathrm{}e\text{ 12p - 12p) + (28s-15s) = 237-168.75)} \end{gathered}[/tex]divide both side by 13
[tex]\begin{gathered} \frac{13s}{13}=\frac{68.25}{13} \\ s\text{ = 5.25} \end{gathered}[/tex]substitute s= 5.25 in equation 1
4p + 5(5.25) = 56.25
4p + 26.25 = 56.25
4p = 56.25 - 26.25
4p = 30
divide both side by 4
[tex]\begin{gathered} \frac{4p}{4}=\text{ }\frac{30}{4} \\ p=7.5 \end{gathered}[/tex]each pizza cost $7.5
each sub cost $5.25
suppose you spend 35% of your monthly budget on food and 14% on the bus fare food and bus fares total to 12.50/month what is your monthly budget 
Answers
Let the monthly budget be 100
35% of it was spent on food i.e 35/100×100= 35
14% of it was spent on bus fare i.e. 14/100×100= 14
Total 49% is spent on food and bus fare, when total budget is 100
∴ 1% is spent when budget is 100/49
12.5 is spent when budget = 100/49×12.5
=25.5
∵ The monthly budget is 25.5
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line g has an equation of y=-10x-2. Line h, which is perpendicular to line g, includes the point (4,1). what is the equation of line h?
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The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Given the equation of the line "g":
[tex]y=-10x-2[/tex]You can identify that:
[tex]\begin{gathered} m_g=-10 \\ b_g=-2 \end{gathered}[/tex]By definition the slopes of perpendicular lines are opposite reciprocals. Then, the slope of the line "h" is:
[tex]m_h=\frac{1}{10}[/tex]Knowing a point on the line "h" and its slope, you can substitute them into the equation
[tex]y=m_hx+b_h[/tex]And solve for the y-intercept:
[tex]\begin{gathered} 1=\frac{1}{10}(4)+b_h \\ \\ 1=\frac{2}{5}+b_h \\ \\ b_h=\frac{3}{5} \end{gathered}[/tex]Then, the equation of the line "h" is:
[tex]y=\frac{1}{10}x+\frac{3}{5}[/tex]Fourteen percent of the town's population is over the age of 65. If there are 322 residents over the age of 65, approximately what is the town's population?
Answers
If 14 percent of the town's population is over the age of 65 and there are 322 residents over the age of 65, then the population of the town is 2300
The percentage of people over the age of 65 = 14%
Number of residents over the age of 65 = 322
Consider the total population of the town as x
Then the equation will be
x × (14/100) = 322
From this equation we have to find the value of x, that is the population of the town.
x × (14/100) = 322
x × 0.14 = 322
x = 322/0.14
x = 2300
Hence, if 14 percent of the town's population is over the age of 65 and there are 322 residents over the age of 65, then the population of the town is 2300
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Consider this system of linear equations: y=4/5x-3 y=4/5×+1 a. Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning. Hint: answer should be 0, 1, or no solutions
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The solution of a system of linear equations is the point where the two lines meet. Note that for the given equations, both lines have the same slope (4/5). If two lines have the same slope, it means that those lines are parallel. Parallel lines do not meet at any point, they stay parallel to the infinite.
Therefore, since this two lines are parallel, they don't meet and the system has no solution.
Simplify square root of 540 Radical way
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help me please
thank you
Answers
The domain is (2,4,6,8,10,12,14) and range is (8,6,4,2,0,2,4).
What is domain and range?The domain of a function refers to the set of values that we are allowed to enter into our function.
The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values , the y values are these.
The range and domain must be understood to be all the values that the variable y can represent, respectively, and the x values.
Since the ordered pairs have the form (x,y), we can determine the values of x and y.
The x and y values of function are:
F(x,y) = (2,8), (4,6), (6,4), (8,2), (10,0), (12,2), (14,4)
Domain (x) = (2,4,6,8,10,12,14)
Range (y) = (8,6,4,2,0,2,4)
.
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Block of iron mass 40kg is sitting on an incline that has an angle of 28degrees above horizontal, what is the normal force of the block of iron
Answers
The normal force of the block of iron is mathematically given as
N=1412.64 N
This is further explained below.
What is normal force?Generally, the Mass of an iron block of m=40kg sitting on an incline
That has an angle of 28 degrees above horizontal
as-block is sitting on an incline hence Net force acting perpendicular to the incline will be zero
Then [tex]N-M g \cos 28^{\circ}=0[/tex]
N-Mgcos 28=0
[tex]$$\begin{aligned}&N=M g \cos 28^{\circ} \\&N=40 \times 40 \times 0.8829\\& \end{aligned}$$[/tex]
N=1412.64 N
In conclusion, the normal force on the block is N=86.6 Newton
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By using free body diagrams and trigonometric relations, the normal force of the block of iron has a magnitude of 352.579 newtons.
What is the normal force of the block of iron?
In accordance with the third Newton's law, normal forces (N), in newtons, are reactive forces as the result of the contact of the iron mass with the ground of the incline, that is to say, the normal force is the reaction of the weight of the iron mass (W), in newtons. If the iron mass is at rest, then we find the following free body diagram of the ground-mass system and its related geometric system.
Since the free body diagram represents a three force system, then the magnitude of the normal force is found by trigonometric relations:
N = W · cos 26°
N = (40 kg) · (9.807 m / s²) · cos 26°
N = 352.579 N
The normal force of the block of iron has a magnitude of 352.579 newtons.
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24.) In the figure below, Z1 is supplementary to z3 under which of the followingconditions?F Line a is parallel to line bG Line a is parallel to line c.H Line a is perpendicular to line c.J Line b is perpendicular to line c.the
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For this statement to be true, the only condition that is necessary is that Line a is parallel to Line b. The right answer is the first one.
Graph to find an ordered pair and where they intersect.y=-x+2y=-1/4x-1
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Given:
The equations are,
[tex]\begin{gathered} y=-x+2 \\ y=-\frac{1}{4}x-1 \end{gathered}[/tex]To draw the lines on the graph first find the points on the graph,
[tex]\begin{gathered} y=-x+2 \\ x=0,y=2 \\ x=1,y=-1+2=1 \\ x=2,y=-2+2=0 \\ x=-1,y=1+2=3 \end{gathered}[/tex]And,
[tex]\begin{gathered} y=-\frac{1}{4}x-1 \\ x=0,y=-1 \\ x=2,y=-\frac{1}{2}-1=-1.5 \\ x=-2,y=\frac{1}{2}-1=\frac{1}{2}=0.5 \\ x=1,y=-\frac{1}{4}-1=-1.25 \end{gathered}[/tex]Plot the points on the graph.
From the graph, the lines intersect at the point (4,-2).
There is a game where the outcome is a random integer from 1 to 50. If the outcome is odd, you wi $26. If the outcome is even, you win nothing. If you play the game, what is the expected payoff?
Answers
We have a game like the one described in the question and we have to calculate the expected payoff, which is equal to the sum of the possible outcomes weighted by the probability of that outcome.
In this case we have two outcomes:
1) We get an odd number and we win $26 (W=26).
2) We get an even number and we get $0 (W=0).
To calculate the probabilities of each oucome we have to know the proportion of odd an even numbers in the list of 1 to 50. We have a total of 50 numbers, rom which 25 are odd numbers and 25 are even numbers, so the probability of each outcome can be calculated as the relative frequency of each category:
[tex]\begin{gathered} P_1=\text{ number of odds / total numbers}=\frac{25}{50}=0.5 \\ P_2=\text{ number of evens / total numbers}=\frac{25}{50}=0.5 \end{gathered}[/tex]Then, we can calculate the expected payoff as:
[tex]E=\sum ^n_{i=1}p_iW_i=p_1W_1+p_2W_2=0.5\cdot26+0.5\cdot0=13+0=13[/tex]p_i: probability of outcome i.
W_i: prize when outcome i happens.
Then, the expected payoff for this game is $13.
Answer: the expected payoff for this game is $13.
Consider the followingA(-2.75,3)B(1, -2)Plot the given points on the graph.AnswerKeypadKeyboard ShortcutsTo plot a point on the graph, click on the appropriate position on the graph. To move a point, drag thepoint from its original position to its new position.Points can be moved by dragging or using the arrow keys.
Answers
Explanation
two important rules to plot a point in the cartesian plane are given
1.The first coordinate in the ordered pair (x) represents the left/right movement of a point from the origin.
2.The second coordinate in the ordered pair (y) represents the up/down movement of the point from the origin.
so
Step 1
let
[tex](x,y)\Rightarrow A(-2.75,3)[/tex]so
1) 2.75 to the left
2) 3 up
Step 2
B(1,-2)
I hope this helps you
17. John is making flower arrangements. He has 45 roses, 27 irises, and 18daisies. What is the GREATEST number of bouquets he can make using atleast one of each flower and each bouquet having the SAME arrangement?(He has to use ALL the flowers) *Options 452193
Answers
To find the greates number of bouques he can make, we need to find the greatest number that divdes the three numbers: 45, 27 and 18.
45 can be divided by the following numbers:
1,3,4,5,9,15,45
27 can be divided by the following numbers:
1,3,9,27
18 can be divided by the following numbers:
1,2,3,6,9,18
From the divisors of the three numbers we can see that the greatest number that divide the three of them is 9.
Thus, 9 is the greatest number of bouquets he can make using at leat 1 of each. Also those 9 bouquets would have all the same arrengement.
Answer: 9
George is putting trim around his rectangular deck, including the gate. He will need 50 feet of trim to do the entire deck. If the deck is 15 feet long, how wide is the deck?OA. 8 feetOB. 25 feetOC. 10 feetOD. 20 feet
Answers
George is putting trim around the rectangular deck, this means that he is surrounding the deck's perimeter with trim.
You know that he needs 50ft of trim to do the entire deck, this value represents the perimeter of the rectangular deck, and the length of the deck is 15ft.
Knowing the perimeter (P) and the length (l) of the rectangular deck, you can calculate the width (w) of the deck.
The formula for the perimeter of the rectangle is:
[tex]P=2l+2w[/tex]Write the formula for w:
[tex]\begin{gathered} P=2l+2w \\ P-2l=2l-2l+2w \\ P-2l=2w \\ \frac{P-2l}{2}=\frac{2w}{2} \\ w=\frac{P-2l}{2} \end{gathered}[/tex]Use P=50ft and l=15ft to calculate the width:
[tex]\begin{gathered} w=\frac{50-(2*15)}{2} \\ w=\frac{50-30}{2} \\ w=\frac{20}{2} \\ w=10ft \end{gathered}[/tex]The width of the deck is 10ft (option C)
