Remember that the domain is the data set of all possibles values of x and the range is the data set of all possibles values of y
so
Looking at the graph
Domain is the interval for x
[-5,8}
All real numbers greater than or equal to -5 and less than or equal to 8
Range is the interval for y
[-3,2]
All real numbers greater than or equal to -3 and less than or equal to 2
f(x) = 3x² +5
g(x) = 4x - 2
h(x) = x²-3x+1
Find f(x) + g(x) - h(x).
O 2x² + 7x + 2
O 2x² + x + 2
O 5x² + 4
O 7x² + x +4
Answer:
f(X)+g(X)-h(X)
3x²+5+4x+2-(x²-3x+1)
3x²+5+4x+2-x²+3x-1 [opened the brackets and changed the signs]
3x²-x²+4x+3x+5+2-1 [arranged the liked terms]
2x²+7x+7-1
2x²+7x+6
I don't see my answer in your options but trust me I have learned this and I am pretty sure that my answer is correct!!!!!!!
starting at 00 if you were to go up 7 units and left for you is what coordinates would you end up at what quadrant would you be in
The coordinate is starting from the origin
7 units up and 4 units to the left
My coordinate will be (4, 7)
This is because the up is positive y- axis and the left is postive x - axis as well
X = 4 and y = 7
Joining the two points together will end up in the first quadrant
The answer is (4, 7) and First quadrant
estimate the answer the amount of money rick spends on gasoline in a year if the average amount he spends per month is $140.87.chose the correct estimate below a: $16,800b:$168 c:2,520d: $1,680
Given data:
The given amount of money spend in a month is $140.87.
The expression for the given statement is,
[tex]1\text{ month =\$140.87}[/tex]Multiply the above expression by 12 on both sides.
[tex]\begin{gathered} 12(1\text{ month))=12(\$140.87)} \\ 1\text{ year=\$1690.44} \end{gathered}[/tex]Thus, the amount Rick spends in a year is $1690.44.
2. Find the measure of ZRST.(5x – 4):R(8x + 4)ºST
From the picture we notice that the angles R and Q are the same. Furthermore the interior angle S of the triangle is:
[tex]180-(8x+4)[/tex]Then we have the equation:
[tex]2(5x-4)+180-(8x+4)=180[/tex]Solving for x we have:
[tex]\begin{gathered} 10x-8-8x-4=0 \\ 2x-12=0 \\ x=6 \end{gathered}[/tex]Now we plug the value of x in the expression for the angle RST, then:
[tex]8(6)+4=52[/tex]Therefore the angle RST is 52°.
7.) Write the equations below in words m=2×7÷9
Given
[tex]m=2\cdot\frac{7}{9}[/tex]
Procedure
m is equal to the multiplication of 2 by 7 and then divided by 9.
2. Microsoft Corp. has made an offer to acquire 1.5 million shares of Apple$374 per share. They offered Apple 10 million shares of Microsoft worth $25 pershare, but they need to make up the difference with other shares. They have othershares worth $28 per share. How many of the $28 shares (to the nearest share) dothey also have to offer to make an even swap? Explain your work using words,numbers, and/or pictures
A standard deck of cards has 52 cards. Suppose you decide to play a game using only half of a standard deck. If you draw one card at a time from the half-deck, without replacement, how many different ways can you draw all of the cards? Remember that "without replacement" means that the cards are not returned to the deck after they are chosen. Write your answer in factorial notation.
We are asked to determine in how many ways we can draw all of the cards in half a deck. Since in a deck there are 52 cards, in half a deck there are:
[tex]n=\frac{52}{2}=26[/tex]The number of ways in which the cards can be drawn is equivalent to the number of permutations. And this is equivalent to:
[tex]P=n![/tex]Where "p" is the number of permutations and n! is the factorial of the number of cards in half a deck. Substituting the values we get:
[tex]P=26![/tex]Solving the operations:
[tex]P=403291461126605635584000000[/tex]Thus we determine the number of ways the cards can be drawn.
On a school trip, there are 9 boys, 10 girls and 4 adults. Write each as a ratio.Girls to Boys10:9Boys and Girls to Adults9:10:4Adults to Boys and Girls4:9:10
Given
Boys = 9
Girls = 10
Adults = 4
Find
ratio
Explanation
girls to boys
as girls are 10 and boys are 9 ,
so the ratio =
[tex]10\colon9[/tex]boys and girls to adults
boys and girls = 9 + 10 = 19
so the ratio =
[tex]19\colon4[/tex]adults to boys and girls
[tex]4\colon19[/tex]Final Answer
a) 10:9
b) 19:4
c) 4:19
in general the ____ of a linear model represents how the two types of data change in correlation of each other.1. trend line2. y-intercept3. slope4. x intercept5. correlation coefficient
How 2 tipes of data change
it could be two options
Trend line
Coefficient of correlation
Find F-1(x), the inverse of F(x), for 3 and 4
Solving for number 3:
Step 1. Define the function.
The original function we have is:
[tex]F(x)=x-10[/tex]Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:
[tex]y=x-10[/tex]Step 3. Now, we are going to interchange the letters x and y (swap x and y):
[tex]x=y-10[/tex]Step 4. Finally, the last step is to solve for y:
[tex]y=x+10[/tex]change y for F-1(x), and the inverse function is:
[tex]F^{-1}(x)=x+10^{}[/tex]Answer:
[tex]F^{-1}(x)=x+10[/tex]Answer:
Solving for number 3:
Step 1. Define the function.
The original function we have is:
Step 2. To find the inverse function, the first thing we need to do is to change F(x) for y:
Step 3. Now, we are going to interchange the letters x and y (swap x and y):
Step 4. Finally, the last step is to solve for y:
Change y for F-1(x), and the inverse function is:
Answer:
Step-by-step explanation:
Use the Remainder Theorem to explain whether or not (x − 2) is a factor of F(x) = x4 − 2x3 + 3x2 − ax+ 3
The remainder theorem states that when a polynomial P(x) is divided by (x - a), for some number a, the remainder r is equal to P(a). Also states that when P(a) = 0, then (x - a) is a factor of P(x).
Then, let us see the result of evaluating the given polynomial when x = 2.
[tex]\begin{gathered} x=2 \\ F\lparen x)=x^4−2x^3+3x^2−ax+3 \\ F(2)=2^4−2(2)^3+3(2)^2−a(2)+3 \end{gathered}[/tex]What is 32/3 as a proper fraction also I am gay if you don't agree don't help and my name is Oliver
A fraction can be proper or improper.
When a fraction is proper, the numerator is less than the denominator, and therefore, the fraction is less than unity. For example:
[tex]\frac{3}{4}=0.75<1[/tex]When a fraction is improper the numerator is greater than the denominator and therefore the fraction is greater than unity. For example:
[tex]\frac{9}{5}=1.8>1[/tex]So, in this case, you have
[tex]\frac{32}{3}=10.67>1[/tex]Then, as you can see 32/3 is an improper fraction.
To take it to a proper fraction, you can convert this fraction into a mixed number.
A mixed number is made up of an integer part and a proper fraction.
So, you have
[tex]\begin{gathered} \frac{32}{3}=\frac{10\cdot3+2}{3}=\frac{10\cdot3}{3}+\frac{2}{3}=10+\frac{2}{3}=10\frac{2}{3} \\ \text{ Then,} \\ \frac{32}{3}=10\frac{2}{3} \end{gathered}[/tex]Therefore, 32/2 as a proper fraction will be
[tex]10\frac{2}{3}[/tex]9Philip is saving money to buy a new computer. He saves the same amount ofmoney each week.After 2 weeks of saving, Philip still needs $520 to buy the computer.After 6 weeks of saving, Philip still needs $300 to buy the computer.How much does the computer cost?
First let's calculate how much money Philip saves each week.
In 4 weeks, he saved 520 - 300 = $220, so he saved 220/4 = $55 per week.
Then, we have that after 2 weeks of saving, he still needed $520, so before this saving, he needed:
[tex]\begin{gathered} 520+2\cdot55 \\ =520+110 \\ =630 \end{gathered}[/tex]So the computer costs $630.
Find an equation of the line that goes through the points (-10,13) and (-4,7). Write your answer in the formY=mx+b
1) In this problem, let's plug those points into the slope formula to get the slope, i.e. the measure of how steep is the line between those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-13}{-4-(-10)}=\frac{-6}{6}=-1[/tex]2) Now, let's find the y-intercept, a.k.a. the linear coefficient "b". To do that we need to plug into the Slope-Intercept Formula one of those points, the slope, and solve it for "b"
[tex]\begin{gathered} (-4,7),m=-1 \\ y=mx+b \\ 7=-4(-1)+b \\ 7=4+b \\ 7-4=b \\ b=3 \end{gathered}[/tex]3) Therefore, the equation of the line is:
[tex]y=-x+3[/tex]write a cubic function with the three open blue points as roots
Okay, here we have this:
Considering the provided points, we are going to write a cubic function with these points as roots, so we have this:
The factored function will be equal to the multiplication of three binomials, where the first term will be x and the second will be each root with an inverse sign. Then we have:
[tex]f(x)=\mleft(x+2\mright)\mleft(x-2\mright)\mleft(x-6\mright)[/tex]Now we are going to operate each term to obtain the expanded function:
[tex]\begin{gathered} f(x)=x^2x+x^2\mleft(-6\mright)-4x-4\mleft(-6\mright) \\ f(x)=x^3-6x^2-4x+24 \end{gathered}[/tex]The last one we write is the function we are looking for and satisfies the requested roots.
Write a compound inequality for the graph shown below.Use x for your variable.++-10-9-8-7 -6 -5 4-3-2-1002 3 4 5 6 7 8 9 10 xDand口口>DorOSONO?X
The question said we should write a compound inequality of the given graph.
We are also asked to use x as the variable.
From the graph, we can see that both end values are shaded dots, which means x is inclusive of those two values.
Since:
x ≥ -5
and
x ≤ 6
Therefore, the compound inequality of the given graph is:
-5 ≤ x ≤ 6.
If f(x) =(if necessary)?(x-76what is the value of f(3), to the nearest thousandth
The function we have is:
[tex]f(x)=\frac{\sqrt[]{x}-7}{6}[/tex]And we need to find the value of f(3).
To solve this problem and find f(x), we need to substitute x=3 into the given function.
• Substituting x=3 into f(x) to find f(3):
[tex]f(3)=\frac{\sqrt[]{3}-7}{6}[/tex]And now, we start solving the operations.
Since the square root of 3 is equal to 1.732:
[tex]f(3)=\frac{1.732-7}{6}[/tex]Substracting 7:
[tex]f(3)=\frac{-5.268}{6}[/tex]And finally, dividing by 6:
[tex]f(3)=-0.878[/tex]To round to the nearest thousandth we need to round to 3 decimal places, which in this case we already have, thus, the final answer is:
[tex]-0.878[/tex]A line passes through(1,-5) and (-3,7) write an equation for the line in point-slope form Rewrite the equation in slope-intercept form A. Y-5=1/3(x+1) ; y =1/3x + 16/3 B. Y+5=-3(x-1); y=-3x-2 C. Y-1=1/3(x+5);y=-1/3x+3/8 D. Y-5=3(x-1);y=3x+8
Step 1: Concept
Write the formula for the equation of a line in terms of point-slope form
and in slope-intercept form.
[tex]\begin{gathered} Pi\text{ont slope form is given below} \\ y-y_1=m(x-x_1) \\ \text{Slope}-\text{intercept form} \\ y\text{ = mx + c} \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Where
m = slope
c = intercept
Step 2: Represent the coordinates
[tex]\begin{gathered} (x_1,y_1\text{ ) = (1, -5)} \\ (x_2,y_2\text{ ) = ( -3, 7)} \end{gathered}[/tex]Step 3: Find the slope, using slope formula.
[tex]\begin{gathered} m\text{ = slope} \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{7\text{ -(-5)}}{-3\text{ -1}} \\ m\text{ = }\frac{7\text{ + 5}}{-4} \\ m\text{ = }\frac{12}{-4} \\ m\text{ = -3} \end{gathered}[/tex]Step 4: Write an equation for the line in point-slope form.
[tex]\begin{gathered} \text{y - y}_1=m(x-x_1) \\ y\text{ -(-5) = -3(x - 1)} \\ \text{y + 5 = -3(x - 1)} \end{gathered}[/tex]Step 5: Simplify the equation in 4 to write the equation in slope-intercept form.
y + 5 = -3(x - 1)
y + 5 = -3x + 3
y = -3x + 3 - 5
y = -3x - 2
Final answer
Option B
y + 5 = -3(x - 1)
y = -3x - 2
Explain the different ways a linear equation can be transformed. Then give an example and describe the transformation. (It's not a Test, I don't know how to explain that's why)
Answer: Translation, Rotation, or Reflection
Step-by-step explanation: The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y-intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = MX + b
Kim bought new shoes and used a 12% off coupon. The original cost of the shoe is represented as s. The total amount Kim paid for the shoes is represented as s-0.12s= s, which means that _______ of 12% is the same as ___
The difference s - 0.12s is equal to 0.88s. So, the first blank has to be 0.88.
The second blank is "decrease", and the last one is "multiplying by 0.88" because the difference is actually equivalent to 0.88s.
graph a right triangle with the two points forming the hypotenuse . using the sides find the distance between two points, to the nearest tenth.(-5,-3) and (4,-1)
graph a right triangle with the two points forming the hypotenuse . using the sides find the distance between two points, to the nearest tenth.(-5,-3) and (4,-1)
see the attached figure
Find out the distance, using the sides
Applying the Pythagorean Theorem
c^2=a^2+b^2
a=4-(-5)=4+5=9 units
b=-1-(-3)=-1+3=2 units
c^2=9^2+2^2
c^2=81+4
c^2=85
c=√85
c=9.2 unitsGiven a function f(x)=|7-4x| ,find the objects with an image 11
Given the function f(x) defined as:
[tex]f(x)=|7-4x|[/tex]If the image is 11, the corresponding objects (x-values) are:
[tex]\begin{gathered} |7-4x|=11 \\ 7-4x=11\ldots(1) \\ 7-4x=-11\ldots(2) \end{gathered}[/tex]Solving (1) to find the first object:
[tex]\begin{gathered} 7-4x=11 \\ 7-11=4x \\ -4=4x \\ x=-1 \end{gathered}[/tex]Now, we solve (2) to find the second object:
[tex]\begin{gathered} 7-4x=-11 \\ 7+11=4x \\ 18=4x \\ x=4.5 \end{gathered}[/tex]Answer: -1 and 4.5
10. Do the ratios -2:1,-4: 2 and - 6:3 represent a proportional relationship? O No, the ratios do not represent a proportional relationship because, when graphed, the line passes through the origin but is not straight. No, the ratios do not represent a proportional relationship because, when graphed, the line is not straight, and it does pass through the origin. Yes, the ratios represent a proportional relationship because, when graphed, the line passes through the origin and is a straight line. No, the ratios do not represent a proportional relationship because, when graphed, the line is straight, but it does not pass through the origin.
Solution
For this case we have the following proportions:
-2:1 = -2
-4:2 = -2
-6:3 = -2
If we plot the relationship we got something like this
And then we can conclude that the answer is:
Yes the ratios represent a proportional relationship because when graphed the line passes through the origin and is a straight line
Suppose that the demand and supply for artificial Christmas trees is given by the functions below where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price.p=109.70−0.10q (demand function)p=0.01q2+5.91 (supply function)
The equilibrium price is the price at which the demand function is equal to the supply function.
Hence it is given by:
[tex]\begin{gathered} 109.70-0.10q=0.01q^2+5.91 \\ 0.01q^2+0.10q-103.79=0 \end{gathered}[/tex]Solve the quadratic equation to get:
q=97,-107.
Now the quantity cannot be negative hence the value of q=97. Hence 97 hundred trees is the demand.
The equilibrium price is given by:
[tex]p=109.70-0.10q=100\text{ dollars}[/tex]Hence Option A is correct and the boxes to be filled is given by the statement given below:
The equilibrium price of $100 gives a demand that is equal to a supply of 97 hundred trees.
Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.
SOLUTION
The given expression is:
[tex](x-4)^5[/tex]Using binomial theorem, the function is expanded as follows:
[tex](x-4)^5=x^5+5(x)^4(-4)^+\frac{5(5-1)}{2!}x^3(-4)^2+\frac{5(5-1)(5-2)}{3!}x^2(-4)^3+\frac{5(5-1)(5-2)(5-3)}{4!}x^(-4)^4+(-4)^5[/tex]This gives:
[tex](x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024[/tex]The pascal triangle is shown:
Using pascal triangle the expansion is shown:
[tex]\begin{gathered} (x-4)^5=x^5+5x^4(-4)+10x^3(-4)^2+10x^2(-4)^3+5x(-4)^4+(-4)^5 \\ (x-4)^5=x^5-20x^4+160x^3-640x^2+1280x-1024 \end{gathered}[/tex]which graph represents the inequalities.2x+y>4. i attatched the graphs below.
Answer:
Explanations:
According to the given question, you are to find the graph that represents the inequality 2x+y>4.
First, we need to find the x and y-intercept of the line.
For x-intercept
x-intercept occurs at the point where y = 0.
[tex]\begin{gathered} 2x+y=4 \\ 2x+0=4 \\ 2x=4 \\ x=2 \end{gathered}[/tex]Hence the x-intercept occur at (2, 0)
For the y-intercept
y-intercept occurs at the point where x = 0
[tex]\begin{gathered} 2(0)+y=4 \\ y=4 \end{gathered}[/tex]Hence the y-intercept s at (0, 4)
To get the correct graph, we will look at the line that has an x-intercept at (2, 0) and y-inercept at (0, 4)
Which of the following equations is the translation 2 units down of the graph of y = Ixl?y = |x - 2|y = |x + 2|y = |xl - 2y = Ixl + 2
Answer:
y = | x | - 2
Explanation:
If we have a function g(x) = f(x) + c, we can say that g(x) is a translation of c units up or down of f(x)
If c is negative, the translation is c units down.
Therefore, the translation of 2 units down of the graph y = | x | is:
y = | x | - 2
There are 25 people who work in an office together. Five of these people are selectedto go together to the same conference in Orlando, Florida. How many ways can theychoose this team of five people to go to the conference?
ANSWER
53,130
EXPLANATION
There are 25 people and 5 have to be chosen from that group, with no specific order,
[tex]_{25}C_5=\frac{25!}{(25-5)!5!}=\frac{25\times24\times23\times22\times21\times20!}{20!\cdot5\times4\times3\times2\times1}=\frac{25\times24\times23\times22\times21}{5\times4\times3\times2\times1}=53,130[/tex]Hence, there are 53,130 ways to choose the five-people team.
Line I is parallel to line m. If the measure of >6 is 75^ what is the measure of <4?
The measure of <4 = 75°
Explanation:Note that:
• <4 and <6 are alternative interior angles
,• Alternative interior angles are equal
Therefore, based on the points given above:
m<4 = m<6 = 75° (Alternative interior angles are equal)
The measure of <4 = 75°
Use the inverse relationship between logarithmic and exponential functions to solve the equation for x. Simplify your answer using the rules of logarithms and the change of base formula.ln(x) = −2X=________
using the following property
[tex]e^{b\ln a}=a^b[/tex]We can rewrite our expression by exponentiating both sides:
[tex]\begin{gathered} e^{\ln x}=e^{-2} \\ x^1=e^{-2} \\ x=\frac{1}{e^2} \end{gathered}[/tex]