The graph of F(x), shown below, resembles the graph of G(x)=x^2, but it has been changed somewhat.which of the following could be the equation of F(x)?
Answers
Answer:
Choice A. [tex]F(x) = -(x - 4)^{2} -3[/tex].
Step-by-step explanation:
Both F(x) and G(x) are quadratic equations. The graphs of the two functions are known as parabolas. All four choices for the equation of F(x) are written in their vertex form. That is:
[tex]y = a(x - h)^{2} + k[/tex], [tex]a \ne 0[/tex]
where
The point [tex](h, k)[/tex] is the vertex of the parabola, andThe value of [tex]a[/tex] determines the width and the direction of the opening of the parabola. [tex]a >0[/tex] means that the parabola opens upward. [tex]a <0[/tex] means that the parabola opens downwards. The opening becomes narrower if the value of [tex]a[/tex] increases.For the parabola G(x),
the vertex is at the point [tex](4, -3)[/tex], andthe parabola opens downwards.In other words,
[tex]h = 4[/tex],[tex]k = -3[/tex], and[tex]a \le 0[/tex].Hence choice A. [tex]F(x) = -(x - 4)^{2} -3[/tex].
The only equation that correctly represents the graph of F(x) as a vertically stretched and reflected version of the graph of G(x), shifted to the right by 4 units.
Option A. [tex]F(x)=-(x-4)^{2}-3[/tex] is correct.
To answer this question, we can consider the following transformations of the graph of [tex]G(x)=x^2$:[/tex]
Vertical stretch: [tex]$F(x)=kx^2$[/tex] for some positive constant k.
This will stretch the graph of G(x) vertically by a factor of k.
Vertical shift: [tex]$F(x)=x^2+h$[/tex] for some constant $h$.
This will shift the graph of G(x) up or down by $h$ units.
* **Horizontal shift: [tex]F(x)=(x+h)^2[/tex] for some constant $h$. This will shift the graph of G(x) to the left or right by h units.
* **Reflection: [tex]F(x)=-x^2[/tex]. This will reflect the graph of G(x) across the x-axis.
The graph of F(x) in the image appears to be a vertically stretched and reflected version of the graph of G(x), shifted to the right by 4 units. This suggests that the equation of F(x) could be of the form:
F(x)=-k(x-h)^2 for some positive constant k and some constant h.
To find the values of k and h, we can use the fact that the graph of F(x) passes through the points (-2,3) and (4,-3).
Substituting x=-2 and y=3 into the equation above, we get:
[tex]3=-k(-2-h)^2[/tex]
and substituting x=4 and y=-3 into the equation above, we get:
[tex]-3=-k(4-h)^2[/tex]
Dividing the second equation by the first equation, we get:
[tex]\frac{1}{3}=\frac{(-2-h)^2}{(4-h)^2}[/tex]
Taking the square root of both sides, we get:
[tex]\pm \frac{1}{\sqrt{3}}=\frac{-2-h}{4-h}[/tex]
Solving for $h$, we get:
[tex]h=4\pm \frac{4}{\sqrt{3}}[/tex]
Substituting this value of h into either of the original equations, we can solve for k.
For example, substituting [tex]$h=4+\frac{4}{\sqrt{3}}$[/tex] into the first equation, we get:
[tex]3=-k\left(-2-4+\frac{4}{\sqrt{3}}\right)^2[/tex]
Solving for $k$, we get:
[tex]k=3\cdot \left(-6+\frac{4}{\sqrt{3}}\right)^2[/tex]
Therefore, one possible equation for $F(x)$ is:
[tex]F(x)=-3\left(x-4+\frac{4}{\sqrt{3}}\right)^2[/tex]
Another possible equation for $F(x)$ is:
[tex]F(x)=-3\left(x-4-\frac{4}{\sqrt{3}}\right)^2[/tex]
These two equations are equivalent, since they both represent the same reflected and vertically stretched version of the graph of G(x), shifted to the right by 4 units.
Therefore, the answer to the question is:
[tex]A. F(x)=-(x-4)^{2}-3[/tex]
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Related Questions
Which unit would you most likely use to represent the time it takes to fly from
New York, New York to Portland, Oregon which is 2,442 miles away?
A. Minutes
B. Seconds
C. Hours
D. Days
Answers
Answer:
C. Hours
Step-by-step explanation:
It wouldn't take minutes or seconds to travel 2,442 miles so A and B don't make sense.
Also, it wouldn't take days to travel in the same country, it might a day but not days.
So the only answer that would make sense would be C. Hours
Hope This Helps!!
Isabel wanted her box of candy to last 6 days. If the box weighs one- half of pound、how much should she eat each day.
Answers
Answer:
i think she should eat
I think ??????
Step-by-step explanation:
Examine the following system of inequalities.
{y > −x + 4 and y ≤−(1/2)^x + 6
Which graph shows the solution to the system?
Dotted linear inequality shaded below passes through (negative 4, 0) and (0, 4). Solid exponential inequality shaded above passes through (negative 1, 8) & (0, 7).
Dotted linear inequality shaded below passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5).
Dotted linear inequality shaded above passes through (negative 4, 0) and (0, 4). Solid exponential inequality shaded below passes through (negative 1, 8) & (0, 7).
Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5).
Answers
Answer:
Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)
Step-by-step explanation:
we have
[tex]y > -x+4[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dotted line [tex]y=-x+4[/tex]
The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)
and
[tex]y \leq -(1/2)^{x} +6[/tex] -----> inequality B
The solution of the inequality B is the shaded area above the solid line [tex]y=-(1/2)^{x} +6[/tex]
The solid line passes through the points (0,5) and (-2,2)
therefore
The solution of the system of inequalities is the shaded area between the dotted line and the solid line
see the attached figure
Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)
Answer:
A i think
Step-by-step explanation:
Given f(x), find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely x.
f(x)=2/5x-1
Answers
Answer:
Please look at the different answers. I wasn't 100% sure what your expression was.
Step-by-step explanation:
If you mean 2/(5x-1) then g(x) will take the fraction into account with a constant 2 for the numerator and a variable for the denominator since that is where our variable is so g(x)=2/x.
Now h(x)=5x-1 since if you plug in 5x-1 into 2/x where x is you will get our original expression.
Now if you did mean (2/5)x-1 I would take notice of where the variable is which is in (2/5)x so g(x)=x-1 where h(x)=(2/5)x since if you plug (2/5)x in place of the x in x-1 you will get the original.
Please let me know if I didn't interpret your expression correctly.
The required functions which satisfy the condition [tex]\ h (x) = g (f (x))[/tex] are,
[tex]h (x) = \dfrac{2}{5} x[/tex] and [tex]g (x) = x - 1[/tex].
Used the concept of composition which states that,
The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that;
[tex]\ h (x) = g (f (x))[/tex]
Consider the given function as
[tex]f (x) = \dfrac{2}{5} x - 1[/tex]
It is given that [tex]\ f (x) = g (h (x))[/tex] and neither [tex]g (x)[/tex] nor [tex]h (x)[/tex] is solely x.
Let us assume that,
The function h (x) is defined as,
[tex]h (x) = \dfrac{2}{5} x[/tex]
Then we get;
[tex]\ f (x) = g (h (x))[/tex]
= [tex]h (x) - 1[/tex]
Substitute [tex]h (x) = x[/tex] in the above function for the value of function g (x),
[tex]g (x) = x - 1[/tex]
Therefore, the required functions are [tex]h (x) = \dfrac{2}{5} x[/tex] and [tex]g (x) = x - 1[/tex].
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evaluate -7(x-4y) when x=-4 and y= -6
Answers
Answer:
-140
Step-by-step explanation:
Plug in -4 for x, and -6 for y, in the expression:
-7(x - 4y) = -7((-4) - 4(-6))
Simplify. First, solve the terms within the parenthesis. Multiply:
-7((-4) (-4 * -6))
-7((-4) (+24))
-7(-4 + 24)
Solve the parenthesis. Add:
-7(20)
Fully simplify.
-7 * 20 = -140
-140 is your answer.
~
Assume a normal distribution and that the average phone call in a certain town lasted 9 min, with a standard deviation of 1 min. What percentage of the calls lasted less than 8 min?
Answers
Answer:
The percentage of the calls lasted less than 8 min is 16%
Step-by-step explanation:
* Lets explain how to solve the problem
- To find the percentage of the calls lasted less than 8 min, find the
z-score for the calls lasted
∵ The rule of z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- The average phone call in a certain town lasted is 9 min
∴ The mean (μ) = 9
- The standard deviation is 1 min
∴ σ = 1
- The calls lasted less than 8 min
∴ x = 8
∵ z = (x - μ)/σ
∴ z = (8 - 9)/1 = -1/1 = -1
∴ P(z < 8) = -1
- Use z-table to find the percentage of x < 8
∴ P(x < 8) = 0.15866 × 100% = 15.87% ≅ 16%
* The percentage of the calls lasted less than 8 min is 16%
Answer:
The percentage of the calls lasted less than 8 min is 16%.
Step-by-step explanation:
We are dealing with a normal distribution with an average phone call of 9 min and a standard deviation of 1 min. Below we can observe the empirical rule applied with a mean of 9 and a standard deviation of 1. The number 8 represents one standard deviation below the mean, so, the percentage of observations below 8 is 16%. Therefore the percentage of the calls lasted less than 8 min is 16%.
Select the correct answer
Which expression represents the series 1 + 5 + 25 + 125 + 6252
Answers
Answer:
The expression is 5⁵-1 (=3124)
Step-by-step explanation:
PLEASE HELP ME ON THIS!!
Answers
Answer:
-6
Step-by-step explanation:
This means what value can I plug into -3x-8 so that I get output 10.
g(x)=-3x-8
g(a)=-3a-8
So we are going to solve g(a)=10 for a.
g(a)=10
-3a-8=10
Add 8 on both sides:
-3a =18
Divide both sides by -3:
a =-6
Check it!
g(-6)=-3(-6)-8=18-8=10 and it's good! :)
What is the slope of the line that contains the points (-1, 2) and (3, 3)?
A -4
B 4
C 1/4
D -1/4
Answers
Answer:
[tex]\Huge \boxed{\frac{1}{4}}[/tex]
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle \frac{3-2}{3-(-1)}=\frac{1}{4}[/tex]
Therefore, the slope is 1/4, and the correct answer is 1/4.
Answer:
C 1/4
Step-by-step explanation:
To find the slope of the line given two points, we use the formula
m = (y2-y1)/(x2-x1)
= (3-2)/(3--1)
= (3-2)/(3+1)
= 1/4
Explain the steps you would take to find the area of the following composite shape.
Answers
What composite shape? Where is the shape?
Which sentence uses capitalization correctly?
(A)The book is about a japanese prince.
(B)Have you ever read Murasaki Shikibu’s book?
(C)His book is called The tale of genji.
Answers
Answer:
The answer Is B.
Step-by-step explanation:
In "A" I believe japanese should be capatalized and in "C" "genji" should be capitalized but In "B" Murasaki Shikibu’s is a name so it should be capitalized.
A point is one-dimensional.
A.true
B.false
Answers
Answer:
False
Step-by-step explanation:
A point has zero dimension, once two pints are connected then you get one dimension which is a line
B. False
A point is a fundamental concept in geometry and represents a location in space. It is considered zero-dimensional because it has no length, width, or height.
A point is often represented by a dot or a small symbol and is described by its coordinates in a coordinate system.
In a one-dimensional context, you would have a line segment or a line that consists of multiple points.
However, a single point on its own is considered to have no dimension and is therefore not classified as one-dimensional.
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Find an equation of a line that is parallel to 5x - 3y = 6 and passes through the point
(6, –2).
Answers
To find a line that is parallel to another line and passes through a specific point, you first find the slope of the original line. Then, you use the point-slope form of a line equation to find the equation of the new line. The final equation is y = 5/3x - 10.
Explanation:In order to find the equation of a line that is parallel to another and passes through a specific point, you first need to find the slope of the original line. The line given in the question is 5x - 3y = 6, which can be rearranged into slope-intercept form (y = mx + b) to become y = 5/3x - 2. The slope (m) of this line is 5/3. Parallel lines share the same slope, so the slope of the line we are trying to find is also 5/3.
Next, we use the point-slope form of a line equation, which is y - y1 = m(x - x1). The point given in the question is (6, -2), so x1 = 6 and y1 = -2. Substituting these into the equation, we find the equation of the line to be y + 2 = 5/3(x - 6).
Simplify this to y = 5/3x - 10, which is the equation of the line parallel to the given line and passing through the point (6, -2).
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To find an equation of a line parallel to a given line that passes through a specific point, you can use the point-slope form of a line. Find the slope of the given line, and use the slope and the given point to determine the equation of the parallel line.
Explanation:We can find the equation of a line parallel to the given line by using the fact that parallel lines have the same slope. To find the slope of the given line, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope:
5x - 3y = 6 → -3y = -5x + 6 → y = (5/3)x - 2
So, the slope of the given line is 5/3. Thus, any line parallel to this must also have a slope of 5/3.
Since we now have the slope and a point that the line passes through (6, -2), we can use the point-slope form of a line to find the equation:
y - y₁ = m(x - x₁) where (x₁, y₁) is the point given and m is the slope. Substituting the values in, we get:
y - (-2) = (5/3)(x - 6) → y + 2 = (5/3)(x - 6)
Simplifying this equation gives the final answer:
y = (5/3)x - 22/3
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Solve for x in the equation X2 - 12x+36-90
X = 6+3/10
X=6+2V7
X= 12+3 22
x= 12+3/10
Answers
Answer:
x = 6 + 3√10
Step-by-step explanation:
Since this is an unfactorable expression, we need to apply the Quadratic Formula, -b ± √b² - 4ac\2a [radical wrapped around b² - 4ac]. Evaluate, then you will end up with the answer above.
I am joyous to assist you anytime.
[WILL GIVE BRAINLIEST ANSWER TO ANYONE WHO SOLVES FIRST]
Answers
Answer:
it is 4x=-9
Step-by-step explanation:
An object is thrown upward at a speed of 152 feet per second by a machine from a height of 9 feet off the ground. The height h of the object after t seconds can be found using the equation h=−16t^2+152t+9
When will the height be 231 feet?
When will the object reach the ground?
Answers
Answer:
First part:
Set h(t) = 231and solve for t.
-16t²+ 152t + 9= 231
-16t² + 152t - 222= 0
Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.
Second part:
Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.
70% of all us households have vcrs. In a random sample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12, inclusive?
Answers
Answer:
Therefore the probability of 10 - 12 inclusive = 0.20613 + 0.21862 + 0.17004
= 0.59479
+ 59.5% to one place of decimals
Step-by-step explanation:
P(exactly 10) = 15C10 * (0.70)^10 * (0.30)^5
=15! / (10! * 5!) * (0.70)^10 * (0.30)^5
= (15*14*13*12*11) /(5*4*3*2*1) * (0.70)^10 * (0.30)^5
= 0.20613
P(exactly 11) = 15C11 * (0.70)^11 * (0.30)^4
= (15*14*13*12)/(4*3*2*1) *(0.70)^11 *(0.30)^4
= 0.21862
P(exactly 12) = 15C12 * (0.70)^12 * (0.30)^3
= (15*14*13)/(3*2*1) * (0.70)^12 * (0.30)^3
= 0.17004
Fathi has $1.10 , in his printing account. Each sheet of paper he uses reduces his printing account balance by $0.25. Fathi wants to print out a PDF document that is 47 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet.
After Fathi prints, what will be the balance in his printing account?
Answers
Answer:
-$1.9
Step-by-step explanation:
There are 47 pages.
Printing on both sides would divide the number of pages into half.
47/2 = 23.5
2 pages on each side would mean 4 pages on one sheet. Therefore, the number of pages will be further divided by 2.
23.5/2 = 11.75
There cannot be 11.75 pages so we will round it up to 12 pages.
Each page costs $0.25 so 12 pages will cost:
12 x 0.25 = $3
Faithi has $1.1 so new account balance will be:
1.1 - 3 = $-1.9
Therefore, Fathi's balance in his printing account would be negative $1.9.
!!
When Fathi prints a 47-page document using both sides of pages and printing 2 pages on each side, at a cost of $0.25 per sheet, his printing account balance will be -$1.90.
Explanation:The question asks what will Fathi's balance be in his printing account after printing a document that is 47 pages long, with specific printing constraints. To solve this, we first need to figure out the number of pages he will print per sheet. Given that Fathi prints two pages on each side of a sheet, he will print 4 pages per sheet. As the document is 47 pages, he will need a total of 12 sheets (47 divided by 4 and rounded up to the nearest whole number).
Next, we need to calculate the cost of printing those sheets. As each sheet reduces his printing account by $0.25, and he's using 12 sheets, the cost will be $3.00 (12 multiplied by $0.25).
Finally, to find the balance in his printing account, we subtract the cost of printing from his initial balance. Fathi started with $1.10 in his printing account, so after deducting the cost of printing 12 sheets, his final balance will be $-1.90 (which means he owes this amount to replenish his account back to zero).
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short cut method to mulitply 12 by 50
Answers
Answer:
12 * 50 = 600
Step-by-step explanation:
We have to multiply 12 by 50
Short cut method for multiplying a number by 50
Step 1: Take the half of the given number
Step 2: Multiply the result by 100
To find the short cut method to multiply 12 by 50
Here the number is 12
Step 1: divide the number by 2
12/2 = 6
Step 2: Multiply 6 by 100 we get 600
Therefore 12 * 50 = 600
Answer:
12 x 50= 600
Step-by-step explanation:
One way you can do is long and short. But the best way is to do it long because than you will get a better score and get the answer still.
Please help :) idk what the answer is
Answers
Answer:
[tex]\large\boxed{\dfrac{4}{3}}[/tex]
Step-by-step explanation:
Look at the picture.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have two points (0, -4) and (3, 0).
Substitute:
[tex]m=\dfrac{0-(-4)}{3-0}=\dfrac{4}{3}[/tex]
ind an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
Answers
Answer:
[tex]a_n=42n-621[/tex]
Step-by-step explanation:
This is arithmetic sequence so you should go to linear equations in your head.
Think of the question asking you to find the equation of line going through the points:
(14,-33) and (15,9).
First, let's find the slope.
You need to compute y's change over x's change.
The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.
Like this:
( 15 , 9)
-( 14 , -33)
------------------
1 42
So the slope is 42/1=42.
(The slope is our common difference.)
Now point slope form is:
y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.
So we have m=42 and (x1,y1)=(15,9). (You could have chose the other point.)
y-9=42(x-15)
I'm going to put in slope-intercept form. Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
y-9=42(x-15)
Solve for y by adding 9 on both sides:
y=42(x-15)+9
Distribute 42 to terms in the ( ) :
y=42x-42(15)+9
y=42x-630+9
y=42x-621
So we can which back to n now:
[tex]a_n=42n-621[/tex]
A 10-foot board is to be cut into 3 pieces. Two of the pieces will be the same length and one piece will be 2 feet longer than the other two.
Answers
Answer:
Step-by-step explanation:
According to the given statement two pieces are of same length:
If the length of one piece is x,
Then the length of other piece is also x.
And one piece is 2 feet longer than the other two = x+2
Total length of a board = 10 foot
Now make the equation from these terms:
x+x+x+2= 10
This is the equation of the given question.
You can further solve this equation:
x+x+x+2=10
3x+2=10
Now combine the constants:
3x=10-2
3x=8
x=8/3
x=2.67
It means that the length of two pieces of same length is 2.67
And the length of one piece which is longer than the other two = x+2 = 2.67+2 = 4.67 ....
Final answer:
To cut a 10-foot board into three pieces where two are the same length and one is 2 feet longer, denote the shorter length as 'x', create the equation 2x + (x + 2) = 10, and solve for 'x'. The two shorter pieces will each be approximately 2.67 feet and the longer one will be approximately 4.67 feet.
Explanation:
The question involves dividing a 10-foot board into three pieces with one piece being 2 feet longer than the other two equal pieces. To solve this, let's denote the length of the shorter pieces as 'x'. Since there are two of these, we have '2x', and the longer piece would be 'x + 2' feet long. The sum of the lengths of all three pieces is equal to the length of the board, so:
2x + (x + 2) = 10
This simplifies to:
3x + 2 = 10
Subtracting 2 from both sides gives:
3x = 8
Dividing both sides by 3 gives:
x = 8/3 or approximately 2.67 feet.
Therefore, the two shorter pieces are each approximately 2.67 feet long and the longer piece is 2.67 + 2, which is approximately 4.67 feet long.
Elsa sold 37 pairs of earrings for $20 each at the craft fair. She is going to use 1/4 of the money to buy new CDs and is going to put the rest of the money in her savings account. How much money will she put into her savings account?
Let s stand for the amount of money saved.
How much money did she spend on CDs?
How much money did she put in her savings account?
Show your work.
Answers
Answer:
37*20 = 740/4 = 185 -> Spent on new CD's
740 - 185 = $ 555 -> Savings Account
Step-by-step explanation:
Answer:
Amount of money she spend on CDs: $185
Amount of money she is going to be in her savings account: $555
Step-by-step explanation:
She sold 37 pairs of earrings with each of them costing 20 dollars.
That means she made 20(37)=740 dollars.
She is going to use 1/4 of 740 dollars to buy new CDS. This means she is going to use 740/4 =185 dollars on CDs.
So what money is left from 740 dollars after spending 185 dollars?
740-185=555 dollars
She is going to put 555 dollars into savings.
What is the equation of the parabola?
Answers
Answer:
D
Step-by-step explanation:
From any point (x, y ) on the parabola the focus and directrix are equidistant
Here the focus = (- 6, 0) and the directrix is x = 6
Using the distance formula
[tex]\sqrt{(x+6)^2+(y-0)^2}[/tex] = | x - 6 |, that is
[tex]\sqrt{(x+6)^2+y^2}[/tex] = | x - 6 |
Squaring both sides
(x + 6)² + y² = (x - 6)² ← distribute factors on both sides
x² + 12x + 36 + y² = x² - 12x + 36
Subtract x² - 12x + 36 from both sides
24x + y² = 0 ( subtract y² from both sides )
24x = - y² ( divide both sides by 24 )
x = - [tex]\frac{1}{24}[/tex] y² → D
PLEASE HURRY
BRAINLIEST TO THE FIRST ONE TO ANSWER
Answers
Answer:
[tex]cos^{-1}[\frac{6.3}{9.8}][/tex]
[tex]sin^{-1}[\frac{7.5}{9.8}][/tex]
Step-by-step explanation:
step 1
Find the measure of angle ABC using the function cosine
we know that
The function cosine of angle ABC is equal to divide the adjacent side to angle ABC by the hypotenuse of the right triangle
cos(∠ABC)=BC/AB
substitute
cos(∠ABC)=6.3/9.8
[tex]ABC=cos^{-1}[\frac{6.3}{9.8}][/tex]
step 2
Find the measure of angle ABC using the function sine
we know that
The function sine of angle ABC is equal to divide the opposite side to angle ABC by the hypotenuse of the right triangle
sin(∠ABC)=AC/AB
substitute
sin(∠ABC)=7.5/9.8
[tex]ABC=sin^{-1}[\frac{7.5}{9.8}][/tex]
Let f(x) = -4x - 2 and g(x) = 5x - 6. Find f⋅g and state its domain.
Answers
Answer:
-20x^2 +14x+12
The domain of f*g is all real numbers
Step-by-step explanation:
f(x) = -4x - 2
g(x) = 5x - 6.
f*g = (-4x-2) * (5x-6)
FOIL
first -4x*5x = -20x^2
outer -4x*-6 = 24x
inner -2*5x = -10x
last -2 *-6 = 12
Add them together
-20x^2 +24x-10x+12 = -20x^2 +14x+12
The domain of f is all real numbers, the domain of g is all real numbers
The domain of f*g is all real numbers
Answer:
[tex](f*g)(x)=-20x^2+14x+12[/tex]
Domain: All Real Numbers.
Step-by-step explanation:
Given the function f(x):
[tex]f(x) = -4x - 2[/tex]
And the function g(x):
[tex]g(x) = 5x - 6[/tex]
You need to multiply them. Then:
[tex](f*g)(x)=( -4x - 2)( 5x - 6)\\\\(f*g)(x)=-20x^2+24x-10x+12\\\\(f*g)(x)=-20x^2+14x+12[/tex]
Since we know that the domain is the set of all real values of the variable "x" that will give real values for the variable "y", the domain of [tex](f*g)(x)=-20x^2+14x+12[/tex] is ALL REAL NUMBERS.
Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?
5x + 13y = 232
12x + 7y = 218
A.The first equation can be multiplied by –13 and the second equation by 7 to eliminate y.
B.The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
C.The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
D.The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.
Answers
Answer:
C
Step-by-step explanation:
So the system is:
5x+13y=232
12x+7y=218
------------------
Let's look at the options to see which will work:
A) Multiply first equation by -13: -65x-169y=-3016
& second equation by 7 : 84x+49y=1526
There are no opposites in the either one of the variable columns so not this option.
B) Multiply first equation by 7: 35x+91y=1624
& second equation by 13 : 156x+91y=2834
There are no opposites in the either one of the variable columns so this is not option unless we were asked to subtract the equations.
C) Multiply first equation by -12: -60x-156y=-2784
& second equation by 5 : 60x+35y=1090
There is a column that contains opposites here so when you add the equations the x-variable will get eliminated.
Answer:
3rd one
Step-by-step explanation:
A fair number cube is rolled. What is the probability that a number greater than 2 is rolled
Answers
Answer:
2/3
Step-by-step explanation:
Ah, I see. A 1-6 die.
Probability of one number = 1/6
2 numbers? = 2/6
6/6-2/6=4/6
4/6=2/3
[tex]\huge{\boxed{\frac{2}{3}}}[/tex]
There are [tex]4[/tex] numbers on a number cube that are greater than [tex]2[/tex]. They are [tex]3, 4, 5, 6[/tex].
Write this as a fraction. [tex]\frac{\text{4 favorable outcomes}}{\text{6 total outcomes}}[/tex]
Divide both the numerator and denominator by [tex]2[/tex] to simplify. [tex]\boxed{\frac{2}{3}}[/tex]
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Answers
Answer:
16 mph
Step-by-step explanation:
You should first form equations related to this information
Given,Tamara can go 4 mph faster than her sister, Samantha
Lets take speed to ride a bike for Samantha to be= x mph
The speed to ride a bike for Tamara will be= x+4 mph
To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara
Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour
Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence
Time taken by Samantha
[tex]=\frac{80}{x}[/tex]
Time taken by Tamara
[tex]=\frac{80}{4+x}[/tex]
Equation for difference in time
[tex]=\frac{80}{x} -\frac{80}{4+x} =1[/tex]
Solve the equation for difference in time to get value of x which is samantha speed
[tex]=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0[/tex]
Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320
x=(-b±√b²-4ac)÷2a
x=(-4±√4²-4×1×-320)÷2×1
[tex]x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16[/tex]
Samantha speed is 16 mph
Which is the area of triangle BCD
Answers
Answer:
6 squared cm
Step-by-step explanation:
The height of a triangle is length of the segment that is perpendicular to the base. So that length is 2cm here.
The base and the height of the triangle should be perpendicular. So the base is 6cm
The area of a triangle is 1/2 * b * h.
1/2 * b * h
1/2 *6 * 2
3 * 2
6
The answer is 6 squared cm
Answer:
A. 6 square centimetersStep-by-step explanation:
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
In ΔBCD we have b = 6cm, and h = 2cm.
Substitute:
[tex]A_{\triangle BCD}=\dfrac{(6)(2)}{2}=\dfrac{12}{2}=6\ cm^2[/tex]