Answers
Answer:
A(-1,4) and B(2,0)
Step-by-step explanation:
The quadratic parabola equation is represented as;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':
[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]Hence, the equation for the parabola:
[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]Now, for the line since it is a horizontal line, the equation would be:
[tex]g(x)=5[/tex]Then, for (f+g)(x):
[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]Then, the graph for the composite function and the points that lie on the graph:
A(-1,4) and B(2,0)
Related Questions
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answers
Answer:
1/4
Step-by-step explanation:
you just look at rise over run from one point to another and simplify.
Joe has $6,500 to invest One option is to invest some of his money in an account that earns 3% simple interest and the rest in an account that earns 2% simple interest. Joe would like to make at least $200 in interest this year. The following system of equations can be used to help Joe determine how much of his money he should invest at each rate. x +y = 6500 0.03x + 0.02y ≥ 200 The mathematical solution to this system is x=7000. Explain what the solution means in terms of how much Joe should invest in each account.
Answers
Data:
[tex]\begin{gathered} x+y=6500 \\ \\ 0.03x+0,02y\ge200 \end{gathered}[/tex]In this case;
x is the amount of money Joe should invest in first account (with 3% simple interest)
y is the amount of monet Joe should invest in second account (with 2% simple interest)
Then, if the mathematical solution for the given system is x=7000 it means that in order to get at least $200 in interest this year Joe needs to invest a bigger amount of money that he has, in the fisrt account ($7000) and in the second account y Joe shoul take a loan of $500 with 2% simple interest
[tex]\begin{gathered} x=7000 \\ x+y=6500 \\ y=6500-x_{} \\ y=6500-7000=-500 \end{gathered}[/tex]Joe is painting his wooden fence post before putting them in his yard. They are each 8 feel tall and have a diameter of 1 foot. There are 12 fence post in all. How much Paint will Joe need to paint all the surfaces of the 12 fencepost? Use 3:14 for tt and round your final answer to the nearest number Total paint needed: _______
Answers
Given
The number of fence post is 12.
The dimension of each fence post is 8ft tall and 1ft diameter.
To find: How much paint is needed to paint all the surfaces of the 12 fenceposts.
Explanation:
It is given that,
The number of fence post is 12.
The dimension of each fence post is 8ft tall and 1ft diameter.
Therefore,
The fencepost is cylindrical in shape.
Then, the total surface area of the cylinder is,
[tex]\begin{gathered} TSA\text{ of cylinder}=2\pi r(h+r) \\ =2\times3.14\times\frac{1}{2}\times(8+\frac{1}{2}) \\ =3.14\times\frac{17}{2} \\ =26.69ft^2 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} Required\text{ }quantity\text{ }of\text{ }paint=12\times26.69 \\ =320.28 \\ =320ft^2 \end{gathered}[/tex]Hence, the required quantity of paint is 320ft^2.
find the length of the gray arc in terms of pi
Answers
Given
a: angle
a = 60
r: radius
r = 3
Procedure
The length of an arc depends on the radius of a circle and the central angle θ
[tex]\begin{gathered} s=\theta r \\ s=\frac{1}{3}\pi\cdot3 \\ s=\pi \end{gathered}[/tex]The answer would be s = pi
What is x in x/4=1.8/5
Answers
x/4 = 1.8/5
Multiply both sides by 4
x = 7.2/5
x = 1.44
Answer:
x = 1.44
Step-by-step explanation:
Multiply both sides by 4 to get rid of the denominator on the LHS(Left hand Side) of the equation and you get x
(x/4) x 4 = 1.8/5 x 4
x = 1.44
Use the deck of 52 standard playing cards to answer the question.
Answers
Given:
A deck of 52 playing cards is given.
Required:
Probability of selecting a number card, a red card and an ace.
Answer:
There are 40 number cards.
Therefore, probability of selecting a number card=
[tex]\frac{1}{40}[/tex]There are 26 red cards.
Therefore, probability of selecting a red card=
[tex]\frac{1}{26}[/tex]The probability of selecting an ace =
[tex]\frac{1}{52}[/tex]Final Answer:
The Probabilities of selecting a number card, a red card and an ace are,
[tex]\frac{1}{40},\frac{1}{26},\frac{1}{52}[/tex]respectively.
6. Oliver is playing a game in which he has to choose one of two numbers (2 or 7) and then one of five vowels (a, e, i, o, or u). How many possible outcomes are there? 2 7 There are possible outcomes.
Answers
Answer
Number of possible outcomes for everything = 240 ways
Explanation
The number of possible outcomes can be calculated by taking each of these two groups.
First group contains 2 elements
Number of possible ways to pick the elements = 2! = 2 × 1 = 2 ways
Second group contains 5 elements
Number of possible ways to pick the elements = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways
Number of possible outcomes for everything = 2! × 5! = 2 × 120 = 240 ways
Hope this Helps!!!
Me.Hoffman has a doorstop in his classroom shaped like a triangular prism shown
Answers
- To determine the perimeter of the base, consider that the length is 5 in and the width is the same as the width of the top face of the prism, that is, 2 in. Then, the perimeters is:
P = 2l + 2w
w = 2 in
l = 5 in
P = 2(5 in) + 2(2 in)
P = 10 in + 4 in
P = 14 in
- The height of the doorstop is 1.2 in
- The area of the base is:
A = wl
A = (2 in)(5 in)
A = 10 in²
Identify the vertex and axis of symmetry of the quadratic equation. Then, sketch the graph f(x) = (x + 2)² - 1
Answers
Answer
Vertex = (-2, -1)
Axis of symmetry: x = -2
The graph of the function is presented below
Explanation
The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.
The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.
To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.
(df/dx) = 0
f(x) = (x + 2)² - 1
f(x) = x² + 4x + 4 - 1
f(x) = x² + 4x + 3
At the vertex, (df/dx) = 0
(df/dx) = 2x + 4
2x + 4 = 0
2x = -4
Divide both sides by 2
(2x/2) = (-4/2)
x = -2
We can then obtain the corresponding y-coordinate of the vertex
f(x) = (x + 2)² - 1
f(-2) = (-2 + 2)² - 1
f(-2) = 0² - 1
f(-2) = -1
So, the vertex is given as
Vertex = (-2, -1)
Although, one can obtain the vertex from the form in which that equation is given, the general form is that
f(x) = (x - x₁)² + y₁
Comparing that with
f(x) = (x + 2)² - 1
we see that,
x₁ = -2, y₁ = -1
So, Vertex: (-2, -1)
Then, the axis of symmetry will be at the point of the vertex.
Axis of symmetry: x = -2
And for the graph, we just need to obtain a couple of points on the line to sketch that.
when x = 0
f(x) = (x + 2)² - 1
f(0) = (0 + 2)² - 1
f(0) = 4 - 1 = 3
(0, 3)
when y = 0
x = -3 and x = -1
So,
(-3, 0) and (-1, 0)
(-2, -1), (0, 3), (-3, 0) and (-1, 0)
So, with these points, we can sketch the graph.
The graph of this function is presented under answer above.
Hope this Helps!!!
Identify the quadrant or ask is that the following points lie on if the point lies on an axis specify which part positive or negative of which axis X or Y
Answers
ANSWER
Quadrant II
EXPLANATION
There are four (4) quadrants on the coordinate plane:
Let us now plot the point:
Therefore, the point (-1, 9) lies on quadrant II.
how long does it take the snail to crawl 86 inches enter answer in decimal number
Answers
To get the equation of the line graph, first, we have to find its slope. The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the picture, the line passes through the points (0,0) and (10, 1), then its slope is:
[tex]m=\frac{1-0}{10-0}=\frac{1}{10}_{}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
From the graph, the line intersects the y-axis at y = 0, this means that b = into
the equation. Therefore, the equation is:
y = 1/10x
where x is distance (in inches) and y is time (in minutes).
To find how long it takes the snail to crawl 86 inches, we have to replace x = 86 into te equation as follows:
[tex]\begin{gathered} y=\frac{1}{10}\cdot86 \\ y=8.6 \end{gathered}[/tex]The snail takes 8.6 minutes to crawl 86 inches
Ryan bought 3 1/2 boxes of paper clips. Allan bought 1 3/4 more boxes than Ryan.
Colin bought 1 1/2 times as many boxes as Allan How many boxes did Colin buy?
Answers
Answer:
Colin bought 7 7/8 boxes
Step-by-step explanation:
Let R represent the number of boxes bought by Ryan and A represent the number of boxes bought by Allan
R = 3 1/2
Convert to improper fraction:
3 1/2 = (3 x 2 + 1)/2 = 7/2
Allan bought 1 3/4 more boxes than Ryan
A = R + 1 3/4
Convert 1 3/4 to improper fraction:
1 3/4 7/4
So A = 7/2 + 7/4 = 14/4 + 7/4 = 21/4
Colin bought 1 1/2 times as many boxes as Allan
C = 1 1/2 x A
Convert 1 1/2 to improper fraction:
1 1/2 = 3/2
So C = 3/2 x 21/4
= 63/8 = 7 7/8 boxes
it says how many one eights are in the product of 9x7/8
Answers
Answer
63
Explanation
Given the product 9 * 7/8
We are to find the number of one eighths that are in the product
Finding the product;
= 9 * 7/8
= (9*7)/8
= 63/8
= 63 * 1/8
= 63 * one-eighth
This shows that there are 63 one eighth in the product
How many terms are included in the expression below?x² – 3x+7A. 2B. 7o oC. 1D. 3
Answers
Answer:
Choice D: 3 terms
Explanation:
The term of a expressions constant or a variable of an equation, The variable
find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point..y=x²+9
Answers
using the parabola formula:
y = a(x-h)² + k²
vertex = (h, k)
We are given a parebola equation of: y = x²+9
comparing both equations to get the vertex:
y = y
a = 1
(x-h)² = x²
x² = (x + 0)²
(x-h)² = (x + 0)²
h = 0
+k = +9
k = 9
The vertex of the parabola as (x, y): (0, 9)
I just need to know the answer quick because I have to go somewhere
Answers
From the given graph, it is seen that f(x) is not defined for x<-4. The function g(x) is not defined for x>2
But the function p(x) represents a straight line which is defined for all real x.
Hence, the function p(x) has all real numbers as its domain.
Thus, the correct option is (D)
Sort the sequences according to whether they are arithmetic, geometric, or neither. (98.3, 94.1, 89.9, 85.7,) (1, 0, -1, 0) (1.75, 3.5, 7, 14) (-12, -10.8, -9.6, -8.4) (-1, 1, -1, 1)
Answers
hello
to know what type of sequence they are, we need to test either for common difference of common ratio
first sequence
(98.3, 94.1, 89.9)
first term = 98.3
in this case there's a common difference here
we can find that by subtracting the second term from the first term or the third term from the second term
[tex]\text{common difference (d) = 94.1-98.3=-4.2}[/tex]first sequence is an arithmetic progression
second sequence
(1, 0, -1, 0)
first term = 1
common difference or common ratio does not exist here
third sequence
(1.75, 3.5, 7, 14)
first term = 1.75
in this case, there's no common difference but rather common ratio
common ratio (r) can be found by dividing the second term by the first term or the third term by the second term
[tex]\begin{gathered} \text{common ratio(r) = }\frac{3.5}{1.75}=2 \\ \frac{14}{7}=2 \end{gathered}[/tex]the common ratio here is 2 and this is a geometric progression
fourth sequence
(-12, -10.8, -9.8, -8.4)
first term = -12
in this sequence, there's no common difference or common ratio
fifth sequence
(-1, 1, -1, 1)
the fifth sequence is neither a geometric or artimethic progression because there no common difference or ratio
2) What is the sum of all the angles in the rectangle
Answers
the sum of all the angles in a rectangle is 360°
find the measures of GH and CH.
Answers
The length of the lines GH and CH are 16 units and 12 units.
What is a line?A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends. In geometry, lines are drawn with arrows at either end to indicate that they extend indefinitely. Two line points can be used to name a line (for example, AB) or just a letter, usually in lowercase (for example, line m ). The ends of a line segment are two.So, the measure of lines GH and CH:
We know that AC ⊥ GH hence cuts GH in two equal lines.
GB = BH GB is 8 units then BH is also 8 units.GB = BH = 8 units.But,
GH = GB + BHGH = 8 + 8GH = 16 unitsWe can observe that △GCH is an isosceles triangle.
GC = CHGC = CH = 12 unitsTherefore, the length of the lines GH and CH is 16 units and 12 units.
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A positive integer is 38 more than 27 times another their product is 5057. Find the two integers.
Answers
Answer:
13 and 389
Explanation:
Let the two positive integers be x and y
If a positive integer is 38 more than 27 times another, then;
x = 27y+ 38 ...1
If their product is 5057, then;
xy = 5057 .....2
Substitute equation 1 into 2
(27y + 38)y = 5057
Expand the bracket
27y^2 + 38y = 5057
27y^2 + 38y - 5057 = 0
Factorize
27y^2 -351y + 389y - 5057 = 0
27y(y-13) + 389(y-13) =0
(27y+389)(y−13) = 0
27y + 389 = 0 and y - 13 = 0
27y = -389 and y = 13
Since y is a positive integer, hence y = 13
Substiute y = 13 into equation 1;
x = 27y+ 38 ...1
x = 27(13)+ 38
x = 351 + 38
x= 389
Hencethe two positive integers are 13 and 389
Find P on line segment CD that is 3/4 the distance from C(0, 0) to D (0, 12).
Answers
We have two points C(0, 0) and D (0, 12).
P is on the line segment and 3/4 of the distance from C to D.
Third-degree, with zeros of -3, -2, and 1, and passes through the point (4, 10).
Answers
The required third degree expression is 1/7 (x³ + 2x² - 5x - 6)
Given,
Find a third degree expression f(x) that has zeros -3, -2, 1 and the equation y = f(x) passes through (4, 10). ,
If the roots/zeroes of a nth order expression are given as r₁, r₂, r₃....rₙ, the expression is given by f(x) = c(x - r₁) (x - r₂) (x - r₃)....(x - rₙ)
Since we know the three roots of the third degree expression, the function is;
f(x) = c(x - (-3)) (x - (-2)) (x - 1)
= c(x + 3) (x + 2) (x - 1)
= c (x³ + 2x² - 5x - 6)
Also y = f(x), passes through(4, 10) , so
10 = c(4³ + 2 x 4² - 5 x 4 - 6)
10 = c(64 + 32 - 20 - 6)
10 = 70c
c = 10/70 = 1/7
∴Required expression is 1/7 (x³ + 2x² - 5x - 6)
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Find the future value in dollars of an 18 month investment of $4900 into simple interest rate account that has an annual simple interest rate of 5.5%
Answers
Answer:
$5304.25.
Explanation:
The simple interest formula is given by
[tex]A=P(1+rt)[/tex]where
A = future value
P = princple amount
r = interest rate /100
t = time interval.
Now in our case
A = unknown
P = $4900
r = 5.5 / 100
t = 18 / 12 ( we are converting months to years. 18 months = 18 /12 years )
Putting the above values into the simple interest rate formula gives
[tex]A=4900\lbrack1+\frac{5.5}{100}\times(\frac{18}{12})\rbrack[/tex]which simplifies to give
[tex]\boxed{A=\$5304.25.}[/tex]Hence, the future value is $5304.25.
The distance from the earth to Pluto is 4.67x10^9 mi, If a new flying machine can travel 1.92x10^5 miles per year, how many years would it take to reach Pluto? Write your answer in standard form, rounded to the nearest year.
Answers
24333 years
Explanationto solve this we need to use the time formula ,it says
[tex]time=\frac{distance}{speed}[/tex]Step 1
a)given
[tex]\begin{gathered} distance=4.67*10^9\text{ miles} \\ speed=1.92*10^5\text{ }\frac{miles}{year} \end{gathered}[/tex]b) now, replace in the formula and calculate
[tex]\begin{gathered} time=\frac{distance}{speed} \\ time=\frac{4.67*10^9}{1.92*10^5}=2.43*10^{9-5}=2.43*10^4 \\ time=2.43*10^4\approx24333\text{ years} \end{gathered}[/tex]therefore, the answer is
24333 years
I hope this helps you
For the following scores:a. construct a frequency distribution table.b. sketch a histogram of the frequency distribution.5, 4, 3, 5, 4, 2, 4, 15, 4, 6, 1, 4, 5, 2, 3
Answers
Given the data set:
5, 4, 3, 5, 4, 2, 4, 1, 5, 4, 6, 1, 4, 5, 2, 3
Using the given data set, let's answer the following questions:
• (a). Construct a frequency distribution table.
Let's first arrange the terms in ascending order:
1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6
Here, we can have the following:
1 ==> Occurs twice
2 ==> Occurs twice
3 ==> Occurs twice
4 ==> Occurs 5 times
5 ==> Occurs 4 times
6 ==> Occurs once.
Therefore, for the frequency distribution table, we are to use the number of times each data occur (this is the frequency).
We have the table below:
• Part b.
Let's sketch a histogram of the frequency distribution.
• We have the histogram of the frequency distribution below:
Jeremy said I added 3/4+1/5 and got 4/9, does Jeremy’s answer make sense? Explain how you know without calculating the answer
Answers
If
[tex]\frac{3}{4}+\frac{1}{5}=\frac{4}{9}[/tex]That would imply that 9 is a common multiple of 4 and 5, which is false since 9=3^2.
Additionally, 3/4 is greater than 4/9; so 3/4+1/5 has to be greater than 4/9.
subtract 7 1/4 - 4 3/4 simplify the answer and write as a mixed number .122 1/21/43 1/2
Answers
Answer
The simplified fraction is 2 1/2
Step-by-step explanation:
[tex]\begin{gathered} \text{Substract 7}\frac{1}{4}\text{ - 4}\frac{3}{4} \\ \text{Step 1: convert the mixed fraction into an improper fraction} \\ 7\frac{1}{4}\text{ = }\frac{(7\text{ x 4) + 1}}{4} \\ 7\frac{1}{4}\text{ = }\frac{29}{4} \\ \\ 4\frac{3}{4}\text{ = }\frac{(4\cdot4)+3}{4} \\ 4\frac{3}{4}\text{ = }\frac{19}{4} \\ We\text{ have} \\ \frac{29}{4}\text{ - }\frac{19}{4} \\ \text{ Find the common denominator} \\ \text{The common denominator is 4} \\ \frac{29\text{ - 19}}{4} \\ =\text{ }\frac{10}{4} \\ =\text{ }\frac{5}{2} \\ =\text{ 2}\frac{1}{2} \\ \text{Hence, the answer is 2}\frac{1}{2} \end{gathered}[/tex]HELP PLEASE ANWER AS SOON AS POSSIBLE ALSO PLEASE GIVE A STEP BY STEP EXPLANATION PLEASE!!
Answers
Given that f(x)=x2-4/3, f(a)=7, and f(11)=b, a+b can only be a multiple of prime numbers is 5
This calculator for finding the prime factors and the factor tree of an integer is available for use.
How is a prime factor discovered?
The simplest method for determining a number's prime factors is to keep dividing the starting number by prime factors until the result equals 1. When we divide the number 30 by its prime factors, we obtain 30/2 = 15, 15/3 = 5, and 5/5 = 1. We received the balance, thus it cannot be factored any further.
Example: 36 can be written as the product of two prime factors, 22 and 32. The prime factorization of 36 is stated to equal the equation 22 32.
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Find the parabola with focus (2,7) and directrix y = -1.
Answers
A parabola with focus (a, b ) and directrix y = c has the equation
[tex](x-a)^2+b^2-c^2=2(b-c)y[/tex]In our case, (a, b) = (2, 7) and c = -1; therefore, the above becomes
[tex](x-2)^2+7^2-(-1)^2=2(7-(-1))y[/tex][tex](x-2)^2+48=16y[/tex][tex]\Rightarrow\textcolor{#FF7968}{(x-2)^2=16(y-3)}[/tex]which is our answer!
identify the terms ,coefficients constants in 5c2 + 7d
Answers
Algebraic expressions are compound by algebraic terms that are compound by a signed number or coefficient, one or more variables and one or more exponents.
In the given expression:
[tex]5c^2+7d[/tex]There are 2 terms which are 5c^2 and 7d, its coefficients are 5 and 7 respectively and there is not any constant, which are independent terms.