a) We need to evaluate when x = 1
f(1): this means we will replace x with 1 in the given function
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f\mleft(1\mright)=3(1)^2+9(1)-4 \\ f(1)\text{ = 3(1) + 9 - 4 = 3 + 9 - 4} \\ f(1)\text{ = 8} \end{gathered}[/tex]b) We need to evaluate the function when x = x + h
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f(x\text{ + h): we will replace x with x + h in the given function} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]Expanding:
[tex]\begin{gathered} f(x\text{ + h) }=3(x^2+2xh+h^2)\text{ + 9(x + h) - 4} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \text{Since there are no like terms we can simplify, we can leave it in expanded form:} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \\ or\text{ the non expanded form:} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]what would be the most appropriate domain for this function? Number 7
Explanation:
This function is C(n) which means it's a function of n. It is said that n is the number of observed vehicles in a specified time interval. It cannot be negative and it has to be an integer. Therefore the domain is all integers greater or equal than zero.
Answer:
4) {0, 1, 2, 3...}
Use a unit multiplier to convert 90 meters per minute to meters per second.
Hello there. To solve this question, we'll have to remember some properties about unit conversions.
We want to convert 90 meters per minute to meters per second.
Remember 1 minute is equal to 60 seconds, therefore we can write
90 meters per 60 seconds
Simplify it by a factor of 30
3 meters per 2 seconds
Which is the same as
1.5 meters per second
The unit multiplier was divide the number by 60, in order to get minutes to seconds and, therefore, find the value in m/s.
identify the maximum from the tabletype your answer as an ordered pair (x,y)
We want to know the maximum value for f(x). In this case, we have that when f(x) = 10, x =6. Then, the ordered pair (6,10) represents the maximum from the table
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p-10.1=6.5p-4-0.01p? Select two options
Given:
Given the equation
[tex]2.3p-10.1=6.5p-4-0.01p[/tex]Required: Rewrite the given equation.
Explanation:
Take the common coefficients of p and add the constants.
[tex]\begin{gathered} 2.3p-10.1-6.5p+4+0.01p=0 \\ (2.3-6.5+0.01)p+(4-10.1)=0 \\ -4.19p-6.1=0 \\ 4.19p+6.1=0 \end{gathered}[/tex]Final Answer: The given equation can be rewritten as 4.19p+6.1 = 0
solve by substitution x+2y-z = 4 3x – y +z = 5 2x + 3y + 2z = 7
You have the following system of equations:
I find an awesome pair of red Jimmy Choo ‘Romy 100’ heels for 35% off. If the sale price is $812.50, what was the original price before the markdown?
812.50 ------------------------ 65%
x ----------------------- 100%
x = (100 x 812.50) / 65
x = 81250 / 65
x = $1250
The original price was $1250.00
what degree are vertical angles?
Vertical angles are opposite angles that also are congruent angles.
Then, due to the given figure, you can conclude that the vertical angles are:
angle FGD and angle of 15° are vertical, then
Frustratingly this is the third time I’m asking this question that two tutors got wrong. Please help?
To answer this question, we need to translate each of the expressions into algebraic form. Then we have:
1. We have that one number is 2 less than a second number.
In this case, let x be one of the numbers, and y the second number. Now, we can write the expression as follows:
[tex]x=y-2[/tex]2. We also have that twice the second number is 2 less than 3 times the first:
[tex]2y=3x-2[/tex]3. And now, we have the following system of equations:
[tex]\begin{cases}x=y-2 \\ 2y=3x-2\end{cases}[/tex]4. And we can solve by substitution as follows:
[tex]\begin{gathered} x=y-2\text{ then we have:} \\ \\ 2y=3(y-2)-2 \\ \\ 2y=3(y)+(3)(-2)-2 \\ \\ 2y=3y-6-2 \\ \\ 2y=3y-8 \end{gathered}[/tex]5. To solve this equation, we can subtract 2y from both sides, and add 8 from both sides too:
[tex]\begin{gathered} 2y-2y=3y-2y-8 \\ 0=y-8 \\ 8=y-8+8 \\ 8=y \\ y=8 \end{gathered}[/tex]6. Since y = 8, then we can use one of the original equations to find x as follows:
[tex]\begin{gathered} x=y-2\Rightarrow y=8 \\ x=8-2 \\ x=6 \end{gathered}[/tex]Therefore, we have that both numbers are x = 6, and y = 8.
In summary, we have that:
• The smaller number is 6.
,• The larger number is 8.
Find the equation of a line perpendicular to y + 1 =-1/2xthat passesthrough the point (-8, 7).
step 1
Find out the slope of the given line
we have
y+1=-(1/2)x
The slope is m=-1/2
Remember that
If two lines are perpendicular
then
their slopes are negative reciprocal
so
The slope of the perpendicular line is
m=2
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=2
point (-8,7)
substitute and solve for b
7=2(-8)+b
7=-16+b
b=23
therefore
the equation of the line is
y=2x+23I have to find the least common denominator and the domain, but i’m lost
Explanation:
[tex]\frac{2x\text{ - 3}}{x^2+6x+8}\text{ + }\frac{10}{x^2+x\text{ - 12}}[/tex]Finding the LCM:
[tex]\begin{gathered} =\frac{(2x-3)(x^2+x-12)+10(x^2+6x+8)}{(x^2+6x+8)(x^2+x-12)} \\ =\frac{(2x)(x^2+x-12)-3(x^2+x-12)+10(x^2+6x+8)}{(x^2+6x+8)(x^2+x-12)} \\ =\frac{(2x^3+2x^2-24x)-3x^2-3x+36+10x^2+60x+80}{(x^2+6x+8)(x^2+x-12)} \end{gathered}[/tex][tex]undefined[/tex]A text book store sold a combined total of 347 history and physics textbooks in a week. The number of history textbooks sold was 79 more than the number of physics textbooks sold. How many textbooks of each type were sold?
Let the number of history textbooks be h and the number of physics textbooks be p.
It was given that the bookstore sells a combined total of 347 books. Thus we have:
[tex]h+p=347[/tex]It is also given that the number of history textbooks sold was 79 more than the number of physics textbooks. This gives:
[tex]h=p+79[/tex]We can substitute for h into the first equation:
[tex]p+79+p=347[/tex]Solving, we have:
[tex]\begin{gathered} 2p+79=347 \\ 2p=347-79 \\ 2p=268 \\ p=\frac{268}{2} \\ p=134 \end{gathered}[/tex]Substitute for p in the second equation, we have:
[tex]\begin{gathered} h=p+79 \\ h=134+79 \\ h=213 \end{gathered}[/tex]Therefore, there were 134 physics textbooks and 213 history textbooks.
Can you please help me out with a question
The function c(x) = 50x represents the number of words c(x) you can type in x minutes. How many words can you type in 6.5 minutes? PLEASE HELP!
Given the function c(x) = 50x where c (x) is the number of words. In 6.5 minutes, the number of words that can be typed is
= 50 * 6.5
= 325 words
What value of x makes this equation true?3 - 2x = 8 - 13
First we have to solve the substraction on the right side of the equation:
[tex]3-2x=-5[/tex]Now we add 2x on both sides:
[tex]\begin{gathered} 3-2x+2x=-5+2x \\ 3=-5+2x \end{gathered}[/tex]Now add 5 on both sides:
[tex]\begin{gathered} 3+5=-5+5+2x \\ 8=2x \end{gathered}[/tex]And divide both sides by 2:
[tex]\begin{gathered} \frac{8}{2}=\frac{2x}{2} \\ 4=x \end{gathered}[/tex]The value of x that makes the equation true is 4
determine whether or not each equation is a linear equation in two variables. if so, identify a b and c a. 2x =5 + yb. y = 5x + 3
Given:
Linear equation in x and y:
An equation of the form y = mx + c or ax + by +c =0 is a linear equation as the degree of both variables x and y is one.
(a) 2x = 5 + y:
The equation can be written as:
[tex]y=2x-5\text{ or 2x-y-5=0}[/tex]This is of the form of ax+by+c=0 so it is linear.
Here, a=2, b= 1, c= - 5
(b) y = 5x + 3:
[tex]y=5x+3\text{ or 5x-y+3=0}[/tex]This is already in the form of ax + by+ c=0 so it also linear.
Here, a= 5 , b = - 1, c= 3
(r^2/s)^3 Simplify this exponential expression
Reason:
When we cube the (r^2) in the numerator, we're multiplying it by itself 3 times
(r^2)^3 = (r^2)*(r^2)*(r^2) = r^(2+2+2) = r^6
or a shortcut is to say
(r^2)^3 = r^(2*3) = r^6
That explains how we get r^6 in the numerator of the final answer.
The s^3 in the denominator is simply the result of cubing the 's' in the original expression.
Answer:
r2x3 / s1x3
Step-by-step explanation:
Raise both the numerator and denominator to the third power. Multiply by the exponents in the numerator (2x3). Multiply the exponents in the denominator (1x3). PF.
Which of these equations has infinitely many solutions? 3(1-2x + 1) = -6x + 2. 4 + 2(x - 5) = 1/2 {(4x - 12) (5x + 15) 3x - 5 = 5= 1/(5x () which statement explains a way you can tell the equation has infinitely many solutions? It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign. It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign. It is equivalent to an equation that has different variable terms on either side of the equation.
Answer
The equation with infinite solutions is Option B
4 + 2 (x - 5) = ½ (4x - 12)
The key way to know if an equation has infinite solutions is shown in Option B
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
Explanation
The key way to know if an equation has infinite solutions is when
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
So, we will check each of the equations to know which one satisfies that condition.
2x + 1 = -6x + 2
2x + 6x = 2 - 1
8x = 1
Divide both sides by 8
(8x/8) = (1/8)
x = (1/8)
This is not the equation with infinite solutions.
4 + 2 (x - 5) = ½ (4x - 12)
4 + 2x - 10 = 2x - 6
2x - 6 = 2x - 6
2x - 2x = 6 - 6
0 = 0
This is the equation with infinite solutions.
3x - 5 = (1/5) (5x + 15)
3x - 5 = x + 3
3x - x = 3 + 5
2x = 8
Divide both sides by 2
(2x/2) = (8/2)
x = 4
This is not the equation with infinite solutions.
Hope this Helps!!!
2. Does the data describe a positive or negative correlation? (1/2 point)3. Find the equation of your line of fit. (1 point)+4. What predicted vehicle weight would indicate a vehicle whose gas mileage is 30 miles per gallon?(1 point)5. Suppose you have a vehicle that weighs 1500 pounds. Use the model to determine the expected city MPGof the vehicle. (1 point)
Given the values shown in the table, let be "x" the Vehicle weight (in hundreds of lbs.) and "y" the City MPG (Miles per gallon).
1. Given the points:
[tex](27,25),(35,19),(39,16),(32,21),(40,15),(23,29),(18,31),(37,15),(17,46),(23,26),(37,17),(30,26),(23,29),(32,19),(20,33),(30,21)[/tex]You can plot them on a Coordinate Plane:
2. Notice the following line:
Notice that the points are closed to the red line that has a negative slope. Therefore, you can identify that when one of the variables increases, the other variable decreases. Hence, you can conclude that the data describes a negative correlation.
3. You need to follow these steps to find the equation of the line of best fit:
- You need to find the average of the x-values by adding them and dividing the Sum by the number of x-values:
[tex]\bar{X}=\frac{27+35+39+32+40+23+18+37+17+23+37+30+23+32+20+30}{16}[/tex][tex]\bar{X}=28.9375[/tex]- Find the average of the y-values:
[tex]\bar{Y}=\frac{25+19+16+21+15+29+31+15+46+26+17+26+29+19+33+21}{16}[/tex][tex]\bar{Y}=24.25[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{X})[/tex]Where this represents each x-values in the data set:
[tex]x_i[/tex]You get:
[tex]\sum_{i=1}^n(x_i-\bar{X})=(27-28.9375)+(35-28.9375)+(39-28.9375)+(32-28.9375)+(40-28.9375)+(23-28.9375)+(18-28.9375)+(37-28.9375)+(17-28.9375)+(23-28.9375)+(37-28.9375)+(30-28.9375)+(23-28.9375)+(32-28.9375)+(20-28.9375)+(30-29.9375)[/tex][tex]\sum_{i=1}^n(x_i-\bar{X})=1.0625[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{Y})[/tex]You get:
[tex]\sum_{i=1}^n(x_i-\bar{Y})=(25-24.25)+(19-24.25)+(16-24.25)+(21-24.25)+(15-24.25)+(29-24.25)+(31-24.25)+(15-24.25)+(46-24.25)+(26-24.25)+(17-24.25)+(26-24.25)+(29-24.25)+(19-24.25)+(33-24.25)+(21-24.25)[/tex][tex]\sum_{i=1}^n(x_i-\bar{Y})=-3.25[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{X})(y_i-\bar{Y})[/tex]You get:
[tex]=-857.75[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{X})^2[/tex]You can find it by squaring each Difference of the x-values and the Mean. you get:
[tex]=862.9375[/tex]- Find the slope of the line
[tex]m=\frac{-857.75}{862.9375}\approx-0.994[/tex]- Find the y-intercept with this formula:
[tex]b=\bar{Y}-m\bar{X}[/tex][tex]b=24.25-(-0.994)(1.0625)[/tex][tex]b=53.0135[/tex]Therefore, the line in Slope-Intercept Form:
[tex]y=mx+b[/tex]is the following:
[tex]y=-0.9940x+53.0135[/tex]4. If:
[tex]y=30[/tex]You can predict the vehicle weight by substituting that value into the equation found in Part 3, and solving for "x":
[tex]30=-0.9940x+53.0135[/tex][tex]\frac{30-53.0135}{-0.9949}=x[/tex][tex]x\approx23.1524[/tex]5. If a vehicle weighs 1500 pounds, then:
[tex]x=1500[/tex]Then you can determine the expected city MPG of the vehicle by substituting this value into the equation and evaluating:
[tex]y=-0.9940(1500)+53.0135[/tex][tex]y\approx-1437.9865[/tex]Hence, the answers are:
1.
2. It describes a negative correlation.
3.
[tex]y=-0.9940x+53.0135[/tex]4.
[tex]x\approx23.1524\text{ \lparen in hundreds of pounds\rparen}[/tex]5.
[tex]y\approx-1437.9865\text{ \lparen In miles per gallon\rparen}[/tex]
The water trough shown in the figure to the right is constructed with semicircular ends. Calculate its volume in gallons if thediameter of the end is 19 in. and the length of the trough is 5 ft. (Hint: Be careful of units.)(Round to the nearest tenth as needed.)
Solution
For this case we can use the following formula:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]what is the distance between two points to the nearest hundredths place?
The formula for calculating the distance between two points is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, for thr given points,
[tex]\begin{gathered} d=\sqrt{(-2-1)^2+(4-3)^2} \\ \text{ = }\sqrt{3+1} \\ \text{ =}\sqrt{4} \\ \text{ =2} \end{gathered}[/tex]Find the missing sides of the following without using calculator
The missing sides are 3 and 3√3
Explanation:Let the opposite sides be represented by x, and the other missing side be y, then
[tex]\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]Using the above, we have:
[tex]\begin{gathered} \sin 60=\frac{x}{6} \\ \\ x=6\sin 60 \\ =6\times\frac{\sqrt[]{3}}{2} \\ \\ =3\sqrt[]{3} \end{gathered}[/tex]And
[tex]\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \\ \cos 60=\frac{y}{6} \\ \\ y=6\cos 60 \\ =6\times\frac{1}{2} \\ \\ =3 \end{gathered}[/tex]The missing sides are 3 and 3√3
5 1/8 divided by 10
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
If [tex]5\frac{1}{8}[/tex] is divided by 10, 41/80 is the quotient.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line.
The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
The given expressions are
[tex]5\frac{1}{8}[/tex] / 10
41/ 8 ÷10
= 41/8 × 1/10
= 41/80
This is the quotient.
To know more about fractions, visit:
brainly.com/question/10708469
#SPJ1
Using the figure, determine the length, in units, of LM
Given the coordinates of L and M
To get the length between the two coordinates, we will follow the steps below
Step 1: List out the coordinates of L and M
[tex]L(-4,-3)[/tex][tex]M(-4,4)[/tex]step 2: calculate the distance
Since they both have the same x coordinates, we can simply subtract the y-coordinate of L from M
[tex]M-L=4-(-3)=4+3=7[/tex]Therefore, the distance LM is 7 units
What is the value of xin the product of powers below? 6^9 * 6^x = 6^2 -11 -7 7 11
Given:
[tex]6^{9\text{ }}\ast6^x=6^2[/tex]To find the value of x, first apply exponential property which is:
[tex]a^m\text{ }\ast a^{n\text{ }}=a^{m+n}[/tex]Now we have:
[tex]6^{9+x\text{ }}=6^2[/tex]Since both bases are equal, let's remove both bases, take the exponent and find x:
[tex]9\text{ + x = 2}[/tex]Now subtract from both sides:
[tex]9\text{ - 9 + x = 2 - }9[/tex][tex]0\text{ + x }=\text{ -7}[/tex][tex]x\text{ = -7}[/tex]The value of x is -7
State the equations and use the graph to determine where the 2 points intersect
EXPLANATION:
We are given an exponential function as shown below;
[tex]f(x)=2^x[/tex]When shifted one unit right we have the following;
[tex]m(x)=2^{x-1}[/tex]We also are given the quadratic function;
[tex]g(x)=x^2[/tex]When shifted one unit right and one unit up, we would have;
[tex]n(x)=(x-1)^2+1[/tex]The equations for both functions after the transformations would be;
[tex]\begin{gathered} m(x)=2^{x-1} \\ n(x)=(x-1)^2+1 \end{gathered}[/tex]The graphs of both equations is now shown below;
The two points where m(x) and n(x) intersect are;
[tex](1,1)\text{ and }(2,2)[/tex]ANSWER:
[tex]\begin{gathered} (a)\text{ }m(x)=2^{x-1} \\ n(x)=(x-1)^2+1 \\ (b)\text{ }(1,1),(2,2) \end{gathered}[/tex]A sequence is generated by An= -2n - 4, find the 5 terms of the sequence
William, this is the solution:
An= -2n - 4
A1 = -2 * 1 - 4
A1 = -6
A2 = -2 * 2 - 4
A2 = -4 - 4
A2 = -8
A3 = -2 * 3 - 4
A3 = -6 - 4
A3 = -10
A4 = -2 * 4 - 4
A4 = -8 - 4
A4 = - 12
A5 = -2 * 5 - 4
A5 = -10 - 4
A5 = - 14
I need help with the calculus portion of my ACT prep guide
The first thing we have to do is find the pascal coefficients of the triangle for this we use the following image
From our exercise we know that
[tex]\begin{gathered} (2x^3-3y)^3\to(a+b)^3 \\ a=2x^3 \\ b=-3y \end{gathered}[/tex]Then our coefficients of Pascal's triangle are 1 - 3 - 3 - 1
Using the right triangle we get:
[tex]1a^3+3a^2b+3ab^2+1b^3[/tex]We substitute the values of a and b in our new expression to find our solution
[tex]1(2x^3)^3+3(2x^3)^2(-3y)+3(2x^3)(-3y)^2+1(-3y)^3[/tex][tex]\begin{gathered} 8x^9+3(4x^6)^{}(-3y)+3(2x^3)(9y^2)^{}-27y^3 \\ 8x^9-36x^6y+54x^3y^2-27y^3 \end{gathered}[/tex]So the solution is:
[tex]8x^9-36x^6y+54x^3y^2-27y^3[/tex]I got the top part of my homework right, I’m just not sure how to do the bottom one. Thank you!
The graph of a function and its inverse are always symmetrical across the line defined by:
[tex]y=x[/tex]This is true for any function and its inverse.
which is higher? -32 or 36?
36 is higher
positive numbers are higher than negative numbers
Hence 36 is higher than -32
A recipe has a ratio of 6 cups of flour to 2 cups ofwater. There is cups of water for each cup offlour.
Given:
A recipe has a ratio of 6 cups of flour to 2 cups of water.
We need to find the number of cups of water for each cups of flour
So, let the number of cups of water = x
We have the following ratio:
[tex]\begin{gathered} \frac{x\text{ cups of water}}{1\text{ cup of flour}}=\frac{2\text{ cups of water}}{6\text{ cups of flour}} \\ \end{gathered}[/tex]Solve for x:
[tex]x=\frac{2}{6}=\frac{1}{3}[/tex]so, the answer will be:
There are 1/3 cups of water for each cup of flour.