Answer:
The equation f(x) = a(1 + r)x can also be used to compute exponential growth, where:
The function is represented by the word f(x).
The initial value of your data is represented by the a variable.
The growth rate is represented by the r variable.
Time is represented by the variable x.
Find the missing factor. x2 - 11x + 18 = (x - 2)( .) Enter the correct answer. 000 DONE Clear all DOO
we have the second degree polynomial
[tex]x^2-11x+18[/tex]we must find two numbers a,b such that
[tex]\begin{gathered} x^2-11x+18=(x+a)(x+b)\text{ and} \\ a+b=11 \\ ab=18 \end{gathered}[/tex]We can see that, a=-2 and b=-9 fulfill the above conditions. Therefore, we have
[tex]x^2-11x+18=(x-2)(x-9)\text{ }[/tex]Can someone help me with this geometry question?A.Triangular prismB.Hexagonal prismC.Triangular pyramidD.Hexagonal pyramid
B. Hexagonal Prism
1) One prism is defined, in terms of naming it by the base.
2) Counting the edges of the base in this net surface, we can tell that this is a Hexagonal Prism for the base is a hexagon.
Find the x-intercepts and y-intercept of the following
function.
f(x) = (x+7) (x + 1)(x − 2)
Write your answer in coordinate pairs of the form (x, y).
Provide your answer below:
x-intercept: ().(
]).() and
y-intercept:
Step-by-step explanation:
there are 3 x-intercepts (the x- values when y = 0). because y is only 0, when one of the 3 factors is 0.
and that is the case for
x = -7
x = -1
x = 2
so, formally, the x- intercepts are
(-7, 0), (-1, 0), (2, 0)
the y intercept is the y- value when x = 0.
(0 + 7)(0 + 1)(0 - 2) = 7×1×-2 = -14
the y-intercept is formally
(0, -14)
Three times a number decreased by 1 is 10 Three times the difference of a number is 1 is 10One less than three times a number is 10The quotient of a number and 3 is 10
Three times a number decreased by 1 is 10:
X is the number.
3x = three times a number.
3x - 1 = 10 (Three times a number decreased by 1 is 10)
3x = 10 + 1
3x = 11
x = 11/3
Need help asap please and thank you
Answer:
y=[tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
y=mx+b
m is the slope of the line, which you find by counting the rise over run between two points. In this case its up one, and right two, or [tex]\frac{1}{2}[/tex].
b is the y intercept, or where the line crosses the y axis
Will give brainliest thank you..!
Answer:
4
Step-by-step explanation:
4
4
4
4
What is 4x+10(2x) - 8x
4x+10(2x) - 8x
First, multiply to solve the parentheses:
4x+20x-8x
Add and subtract
16x
What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer
To find the inverse of the matrix, first let's find the determinant:
[tex]\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}[/tex]Then, we'll find the Adjunct of the matrix:
[tex]\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} In\text{verse of the matrix = }\frac{1}{|A|}\times\text{ adjunct} \\ A^{-1}\text{ = }\frac{1}{1}(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^{-1}\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}[/tex]Tiffany works at a lawnmower store.Part AA portion of Tiffany's monthly salary is based on commission. She earns 21% of everything she sells. This month she sold $27,000 worth of lawnmowers. Howmuch was her sales commission this month?Part BThe store purchased one riding lawn mower for $1,500 and sold it for $2025. What percentage was the markup for the mower?PartTiffany earns $15 per hour. The store offers her a raise-a 2% increase per hour. After the raise, how much will Tiffany make per hour?
1) Gathering the data
Part A
Tiffany's Commission: 21%
Sales Revenue: 27,000
2) In this case, we can figure out how much has she earned by doing this:
[tex]27,000\text{ }\times0.21=5,670[/tex]Part B)
$1,500
$ 2,025
We can solve it in 2 steps. Firstly let's find the equivalence of 2025 in percentage.
1500-------100%
2025- ----x
1500x = 202500
x=202500/1500
x =135%
Now we need to subtract from 100%. 135%-100%= 35%
So the percentage (markup) was 35%. That lawnmower was sold 35% above the price.
Part C)
$15 per hour
2% per hour (0.02)
In this, case we need a simple calculation multiplying that 15 by (1 +0.02)
15 x ( 1 +0.02)
15 x (1.02)
15.3
After the raise, Tiffany earns $15.30 per hour
Which of the following statements follows from (x - 3)2 = 7? ox2 +9=7 Ox-3=1 / OX-3 = +49 NEXT QUESTION O ASK FOR HELP
So, given the equation:
We could take the square root to both sides of the equation to obtain that:
So the correct option is B.
I need help figuring out how to write out this problem correctly.
Answer
[tex]\frac{\sqrt{10}}{11}[/tex]Step-by-step explanation
Given the expression:
[tex]\sqrt{\frac{10}{121}}[/tex]Distributing the square root over the division and evaluating the square root at the denominator:
[tex]\begin{gathered} \frac{\sqrt{10}}{\sqrt{121}} \\ \frac{\sqrt{10}}{11} \end{gathered}[/tex]reduce to lowest term.5p+5q/4p+4q
Explanation
[tex]\frac{5p+5q}{4p+4q}[/tex]Step 1
factorize
[tex]\begin{gathered} 5p+5q\rightarrow5\text{ is a common factor, so}\rightarrow5(p+q) \\ 4p+4q\rightarrow4\text{ is a common factor, so}\rightarrow4(p+q) \end{gathered}[/tex]hence, the expression would be
[tex]\begin{gathered} \frac{5p+5q}{4p+4q}=\frac{5(p+q)}{4(p+q)} \\ \frac{5(p+q)}{4(p+q)} \end{gathered}[/tex]Step 2
now, we can see there is the same factor in numerator and denominator (p+q), so it can be eliminated.
[tex]\begin{gathered} \frac{5(p+q)}{4(p+q)}=\frac{5}{4} \\ \frac{5}{4} \end{gathered}[/tex]therefore, the answer is
[tex]\frac{5}{4}[/tex]I hope this helps you
Solve the equation 7-(5t-13)=-25-15b+21+5b=-19
Let's solve the following expressions:
a.) 7 - (5t - 13) = -25
[tex]\text{ 7 - (5t - 13) = -25}[/tex][tex]\text{ 7 - 5t + 13 = -25}[/tex][tex]\text{ 20 - 5t = -25}[/tex][tex]\text{-5t = -25 - 20}[/tex][tex]\text{-5t = -4}5[/tex][tex]\frac{\text{-5t}}{-5}\text{ = }\frac{\text{-4}5}{-5}[/tex][tex]\text{ t = 9}[/tex]Therefore, t = 9
b.) -15b + 21 + 5b = -19
[tex]-15b+21+5b=-19[/tex][tex]-10b+21=-19[/tex][tex]-10b=-19\text{ - 21}[/tex][tex]-10b=-40[/tex][tex]\frac{-10b}{-10}=\frac{-40}{-10}[/tex][tex]\text{ b = 4}[/tex]Therefore, b = 4
I have a question about how to solve graphing a system of inequalities and about how to do the (0,0)
The given system of inequality is
[tex]\begin{gathered} 2x-3y>-12 \\ x+y\ge-2 \end{gathered}[/tex]At first, we must draw the lines to represent these inequalities
[tex]2x-3y=-12[/tex]Let x = 0, then find y
[tex]\begin{gathered} 2(0)-3(y)=-12 \\ 0-3y=-12 \\ -3y=-12 \\ \frac{-3y}{-3}=\frac{-12}{-3} \\ y=4 \end{gathered}[/tex]The first point is (0, 4)
Let y = 0
[tex]\begin{gathered} 2x-3(0)=-12 \\ 2x-0=-12 \\ 2x=-12 \\ \frac{2x}{2}=\frac{-12}{2} \\ x=-6 \end{gathered}[/tex]The second point is (-6, 0)
We will do the same with the second line
Let x = 0
[tex]\begin{gathered} 0+y=-2 \\ y=-2 \end{gathered}[/tex]The first point is (0, -2)
Let y = 0
[tex]\begin{gathered} x+0=-2 \\ x=-2 \end{gathered}[/tex]The second point is (-2, 0)
Since the sign of the first inequality is >, then the line will be dashed
Since the sign of the second inequality is >=, then the line will be solid
Let us substitute x, y by the origin point (0,0) in both inequalities to find the shaded part of each one
[tex]\begin{gathered} 2(0)-3(0)>-12 \\ 0-0>-12 \\ 0>-12 \end{gathered}[/tex]Since the inequality is true then the point (0, 0) lies on the shaded area
[tex]\begin{gathered} 0+0\ge-2 \\ 0\ge-2 \end{gathered}[/tex]Since the inequality is true, then point (0, 0) lies in the shaded area
Let us draw the graph
The red line represents the first inequality
The blue line represents the second inequality
The area of two colors is the area of the solution
Point (0, 0) lies in this area, then it is a solution for the given system of inequalities
Rewrite each equation in slope intercept form . Then determine whether the lines are perpendicular . Explain your answer .. y - 6 = - 5/2 (x + 4) 5y = 2x + 6
y - 6 = - 5/2 (x + 4)
To write in slope-intercept form means to write in the form;
y= mx + b
where m is the slope and b is the intercept
y - 6 = - 5/2 (x + 4)
open the parenthesis
y - 6 = -5/2 x - 10
add 6 to both-side of the equation
y = - 5/2 x - 10 + 6
y = -5/2 x - 4
[tex]y=-\frac{5}{2}x\text{ - 4}[/tex]Next is to check whether 5y = 2x + 6 is perpendicular to the above
To do that, we have to make the equation to be in the form y=mx+ b
5y = 2x + 6
Divid through by 5
y = 2/5 x + 6/5
[tex]y\text{ = }\frac{2}{5}x\text{ + }\frac{6}{5}[/tex]The slope of perpendicular equation, when multiply gives minus one (-1)
The slope of the first equation = -5/2
The slope of the second equation is 2/5
Multiplying the two slopes;
(-5/2) (2/5) = -1
Hence the lines are perpendicular
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 64 m wide. Find the area of the training field. Use the value 3.14 for n, and do not round your answer. Be sure to include the correct unit in your answer.
To find:
The area of the training field.
Solution:
The training field is made of two semicircles and a rectangle.
The length and width of the rectangle is 96 m and 64 m. So, the area of the rectangle is:
[tex]\begin{gathered} A=l\times w \\ =96\times64 \\ =6144\text{ m}^2 \end{gathered}[/tex]The diameter of the semicircle is 64 m. SO, the radius of the semicircle is 32 m.
The area of two semicircles is:
[tex]\begin{gathered} A=2\times\frac{1}{2}\pi r^2 \\ =3.14\times(32)^2 \\ =3.14\times1024 \\ =3215.36 \end{gathered}[/tex]So, the area of the training field is:
[tex]\begin{gathered} A=6144+3215.36 \\ =9359.36 \end{gathered}[/tex]Thus, the area of the training field is 9359.36 m^2.
Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,529.6 miles. The next time he fills up his Jeep, he pays for 10 gallons of gasoline he notes his odometer reading is 23,640.6 miles. How many miles per gallon did he get? (Round the answer to the nearest 10th if necessary.)
Answer:
11.1 miles per gallon
Explanation:
Given;
Odometer reading when the jeep is filled up with gasoline = 23,529.6 miles
Odometer reading when the jeep is filled up with 10 gallons of gasoline =23,640.6 miles
We can now go ahead and determine how many miles per gallon Harry got as seen below;
[tex]\begin{gathered} \frac{(Reading\text{ when j}eep\text{ is filled with 10 gallons }-Reading\text{ when j}eep\text{ is filled up)}}{\text{Gallo of gasoline}} \\ =\frac{23640.6-23529.6}{10}=\frac{111}{10}=11.1\text{miles per gallon} \end{gathered}[/tex]So Harry got 11.1 miles per gallon
karen recorded her walking pace in the table below. what equation best represents this relationship
Given Data:
The table given here shows time taken in the first column and the distance travelled in the second column.
First check the ration of distance /time to verify if the speed of the man is constant or not.
[tex]\begin{gathered} \frac{8.75\text{ m}}{2.5\text{ h}}=3.5\text{ m/h} \\ \frac{14\text{ m}}{4\text{ h}}=3.5\text{ m/h} \end{gathered}[/tex]As both ratios are same it means the speed of the man is constant and the distance travelled is directly proportional to the time taken and varies linealy with the time.
Now to determine the relationship between m and h we will use the same ratio of m and h which comes in the previous step.
[tex]\begin{gathered} \frac{m}{h}=3.5 \\ m=3.5h \end{gathered}[/tex]Thus, option (D) is the required solution.
in chess, the knight (the piece shaped like a horse) moves in an L pattern.
Answer:
That is true but still remember that playing the knight at the start can be very useful.
1 4 a) Is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
THe length of each cube is inreasing by 1. This means that the increment is in arithmetic sequence.
The formula for determining the nth term of an aritmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first tem of the sequence
Common difference, d represents the difference between consecutive terms
Given that a = 3, d = 1
Tn = 2 + (n - 1)1
Tn = 2 + n - 1
Tn = 1 + n
For the 18th term, n = 18
T18 = 1 + 18 = 19
The number of boxes in the square for the 19th term is
19 * 19 = 361
What two variables can you define to write an equation to match this scenario?x = number of minutes for fruit cans and y = number of minutes for vegetable cansx = total number of minutes and y = total number of cansx = number of minutes for fruit and y = total number of cansx = total number of minutes and y = number of minutes for vegetables
An equation to correctly match this scenario would have to include both separate products. The current order which is 384 cans of food, includes both fruits and vegetables, and therefore any expression that does not include them both would give a wrong answer and the order would not be properly met.
The correct scenario is;
[tex]\begin{gathered} x=Number\text{ of minutes for fruit cans} \\ y=\text{Number of minutes for vegetable cans} \end{gathered}[/tex]This way you can produce both at a maximum without overproducing one and underproducing the other.
Devon saw 19 adults wearing hats
Answer:
please add rest of question?
Step-by-step explanation:
complete the table of ordered pairs for the linear equation. 5x+8y=3
Given:
5x+8y=3
The objective is to fill the table using the given values of x otr y.
Let's take that, x=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5(0)+8y=3 \\ 0+8y=3 \\ y=\frac{3}{8} \end{gathered}[/tex]Hence, the the required solution will be (0,3/8).
Let's take that, y=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(0)=3 \\ 5x+0=3 \\ x=3-5 \\ x=-2 \end{gathered}[/tex]Hence, the the required solution will be (-2,0).
Let's take that, y=1 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(1)=3 \\ 5x+8=3 \\ 5x=3-8 \\ 5x=-5 \\ x=-\frac{5}{5} \\ x=-1 \end{gathered}[/tex]Hence, the the required solution will be (-1,1).
A straight line is 180 degrees. Find the value of X.
Given a straight line angle = 180
So, the angles (9x-100) and (40-x) are supplementary angles
So,
[tex](9x-100)+(40-x)=180[/tex]Solve for x:
[tex]\begin{gathered} (9x-x)+(40-100)=180 \\ 8x-60=180 \\ 8x=180+60 \\ 8x=240 \\ x=\frac{240}{8}=30 \end{gathered}[/tex]So, the answer will be x = 30
Can you help me solve the domain of this math word problem?
the domain refers to all possible values of x in the function.
since a negative time does not make sense, the smallest value of the domain is zero
on the other hand, the problem indicates that the model is considered accurate up to 100,000 years, therefore that would be the largest value of t
in conclusion, the domain of the function A(t) is
[tex]\lbrack0,100000\rbrack[/tex][ 0 , 100,000 ]
Given the function f(x)={4x+7 if x<0 6x+4 if x>0 _
Given:
[tex]f(x)=\begin{cases}4x+7ifx<0{} \\ 6x+4ifx\ge0{}\end{cases}[/tex]Required:
To find the value of f(-8), f(0), f(4), and f(-100)+f(100).
Explanation:
f(-8) :
Clearly -8<0,
So
[tex]\begin{gathered} f(x)=4x+7 \\ f(-8)=4(-8)+7 \\ =-32+7 \\ =-25 \end{gathered}[/tex]f(0) :
Clearly 0=0,
[tex]\begin{gathered} f(x)=6x+4 \\ =6(0)+4 \\ =4 \end{gathered}[/tex]f(4) :
Clearly 4>0,
[tex]\begin{gathered} f(x)=6x+4 \\ f(4)=6(4)+4 \\ =24+4 \\ =28 \end{gathered}[/tex]f(-100)+f(100) :
-100<0
[tex]\begin{gathered} f(x)=4x+7 \\ f(-100)=4(-100)+7 \\ =-400+7 \\ =-393 \end{gathered}[/tex]100>0
[tex]\begin{gathered} f(x)=6x+4 \\ f(100)=6(100)+4 \\ =600+4 \\ =604 \end{gathered}[/tex][tex]\begin{gathered} f(-100)+f(100)=-393+604 \\ \\ =211 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} f(-8)=-25 \\ \\ f(0)=4 \\ \\ f(4)=28 \\ \\ f(-100)+f(100)=211 \end{gathered}[/tex]The length of time (T) in seconds it takes the pendulum of a clock to swing through one compete cycle is givenby the formulaT= 2T✔️L/32 Where L is the length, in feet, of the pendulum, and is pie approximately 22/7. How long must the pendulum be of one complete cycle takes 2 seconds? Answer as a fraction or round to at least 2 decimal places.The pendulum must be__ feet.
we have the formula
[tex]T=2\pi\sqrt{\frac{L}{32}}[/tex]For T=2 seconds
substitute in the given formula
[tex]\begin{gathered} 2=2\pi\sqrt{\frac{L}{32}} \\ \\ 1=\frac{22}{7}\sqrt{\frac{L}{32}} \\ \\ squared\text{ both sides} \\ \\ (\frac{7}{22})^2=\frac{L}{32} \\ \\ L=\frac{7^2*32}{22^2} \\ \\ L=3.24\text{ ft} \end{gathered}[/tex]solve the equation for x. x/16=10
To solve further cross multiply both sides
so that
[tex]x\text{ }\times1\text{ = 16 }\times10[/tex]x = 160
Use the Distributive Property to solve the equation 2/3 (9a + 6) = 23.8
Distributive property tell us how to solve expressions in the form a(b+c), it says:
a(b+c)=ab+ac
Then,
[tex]\begin{gathered} \frac{2}{3}(9a+6)=23.8 \\ \frac{18a}{3}+\frac{12}{3}=23.8 \\ 6a+4=23.8 \\ 6a=23.8-4 \\ a=\frac{19.8}{6}=3.3 \end{gathered}[/tex]Write problem as a single radical using the smallest possible root. 20
Answer::
[tex]\sqrt[30]{r^{29}}[/tex]Explanation:
Given the expression:
[tex]\sqrt[5]{r^4}\sqrt[6]{r}[/tex]First, rewrite the expression using the fractional index law:
[tex]\begin{gathered} \sqrt[n]{x}=x^{\frac{1}{n}} \\ \implies\sqrt[5]{r^4}=r^{\frac{4}{5}};\text{ and} \\ \sqrt[6]{r}=r^{\frac{1}{6}} \end{gathered}[/tex]Therefore:
[tex]\sqrt[5]{r^4}\times\sqrt[6]{r}=r^{\frac{4}{5}}\times r^{\frac{1}{6}}[/tex]Use the multiplication law of exponents:
[tex]\begin{gathered} a^x\times a^y=a^{x+y} \\ \implies r^{\frac{4}{5}}\times r^{\frac{1}{6}}=r^{\frac{4}{5}+\frac{1}{6}} \\ \frac{4}{5}+\frac{1}{6}=\frac{24+5}{30}=\frac{29}{30} \\ \operatorname{\implies}r^{\frac{4}{5}}\times r^{\frac{1}{6}}=r^{\frac{4}{5}+\frac{1}{6}}=r^{\frac{29}{30}} \end{gathered}[/tex]The resulting expression can be rewrittem further:
[tex]\begin{gathered} r^{\frac{29}{30}}=(r^{29})^{\frac{1}{30}} \\ =\sqrt[30]{r^{29}} \end{gathered}[/tex]The single radical is:
[tex]\sqrt[30]{r^{29}}[/tex]