If [tex]f(x)=3x-3[/tex], then [tex]f(1)[/tex] is saying that your x-value is 1. So you substitute 1 in for x and clean it up:
[tex]f(1)=3(1)-3[/tex]
[tex]= 3-3[/tex]
[tex]= 0[/tex]
Would the answer to this be 5 or did I do something wrong
Simplify the expression
[tex]\begin{gathered} \frac{(3^2+4^2)}{(2+3)}=\frac{9+16}{5} \\ =\frac{25}{5} \\ =5 \end{gathered}[/tex]Answer is 5.
Which set of numbers can represent the lengths of the sides of a triangle ?
It's important to know that the sum of two sides must be greater than the length of the third side, this rule defines triangles. So, we have to make sure that the correct answers meets the rule. For example, the first set of numbers represent a triangle because 3+5 > 7, 3+7 > 5, and 5+7 >3.
Therefore, the correct answer is A.The two legs of a right triangle are the same length. The hypotenuse is 3 meters long. Find the length of the legs, Express your answer insimplified radical form, or as a decimal rounded to four places.
Solution
To solve this question, we will apply Pythagoras theorem, which states that:
[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]- We are given that:
[tex]\begin{gathered} Hypotenuse=3 \\ Opposite=Adjacent=x \end{gathered}[/tex]- Thus, we can say:
[tex]\begin{gathered} 3^2=x^2+x^2 \\ 2x^2=9 \\ \text{ Divide both sides by 2} \\ x^2=\frac{9}{2} \\ \\ Take\text{ the square root of both sides} \\ x=\sqrt{\frac{9}{2}}=\frac{3}{\sqrt{2}} \\ \\ x=\frac{3}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\ \\ x=\frac{3}{2}\sqrt{2} \end{gathered}[/tex]Final Answer
The length of the legs are:
[tex]\frac{3}{2}\sqrt{2}[/tex]A.) (5,8)B.) (-7,-7)C.) (6,-3)D.) (4,4)Are the available options, thank you for the help.
We can find the point that is a solution to this system of linear equations by looking at the shaded region of the graph and determining which of the following points is included inside the shaded region.
By looking at the graph, we can determine that (5,8), (-7,-7), and (6,-3) are not part of the shaded region.
The point (4,4) is the only point that is included in the shaded region, inclusive on the red line.
Therefore, D) (4,4) is a solution to this system of linear inequalities.
Identify the function that relects f(x)=5x^3-3 across the x-axis and shifts it 2 units up.
To find the new function, follow the steps below.
Step 01: Reflect the function over the x-axis.
After reflecting the function f(x) over the x-axis, the new function is -f(x).
Then:
[tex]\begin{gathered} f(x)=5x^3-3 \\ -f(x)=-(5x^3-3) \\ -f(x)=-5x^3+3 \end{gathered}[/tex]Step 02: Shift the function 2 units up.
When the function is shifted n units up, the new function if f(x) + n.
The,
[tex]\begin{gathered} h(x)=-f(x)+2 \\ h(x)=-5x^3+3+2 \\ h(x)=-5x^3+5 \end{gathered}[/tex]Answer:
[tex]h(x)=-5x^3+5[/tex]
Describe the accumulated value a of the sum of money P the principal after two years at annual percent rich are in the decimal form compounded continuously complete the table for the saving account subject to continuous compounding.
In order to calculate the value of t, we can use the given formula with the values P = 6000, A = 2P and i = 11% = 0.11:
[tex]\begin{gathered} 2\cdot6000=6000\cdot e^{0.11t}\\ \\ 2=e^{0.11t}\\ \\ \ln2=\ln e^{0.11t}\\ \\ 0.693147=0.11t\\ \\ t=\frac{0.693147}{0.11}=6.3 \end{gathered}[/tex]Therefore the time needed is t = 6.3 years.
please help me on homework
let f(x) = y
y = 7/2 x + 5
put x = 0
y= 5
(0, 5)
put y = o
0 = 7/2 x + 5
7/2 x = -5
multiply both-side by 2/7
x = - 10/7
x = - 1.4
Divide. Give the quotient and remainder 503 ÷ 7
Given the expression 503 ÷ 7 , we are to look for the quotient and the remaninde when 500 is divided by 7.
This is as shown in the diagram below;
From the expression above, you can see that the quotient which is the answer is 71 and the remainder after the division is 6.
Quotient = 71
Remainder = 6
what is 1/3 devided by 1/6
To perform the division of fractions, take the reciprocal of 1/6:
[tex]\frac{6}{1}[/tex]Rememer that to divide by a fraction is the same that to multiply by its reciprocal. Then:
[tex]\begin{gathered} \frac{1}{3}\div\frac{1}{6}=\frac{1}{3}\times\frac{6}{1} \\ =\frac{1\times6}{3\times1} \\ =\frac{6}{3} \\ =2 \end{gathered}[/tex]Therefore:
[tex]\frac{1}{3}\div\frac{1}{6}=2[/tex]Solve the following system of equations without graphing: 72 + 3y = 53 - 4x + 10y = 29 ) Write your solution as an ordered pair ( (Remember: you want to eliminate one of the variables)
1 72x + 3y= 53
2 -4x + 10y= 29
We are going to multiply our second equation by 18, in order to change the coefficient of x .
2 18*-4x + 18*10y= 29*18
2 -72x + 180y = 522
Then we add the last equation to the first equation
1 72x + 3y= 53
+
2 -72x + 180y = 522
----------------------------------
183 y = 575
y= 575/183
Solving for y we get y= 3.14
Then we replace y in the equation 2 to get x. but first we need to isolate x
2 -4x + 10y= 29
2 -4x = 29 - 10y
2 x = (29 - 10y)/-4
2 x = 0.605
The final answer must be ( 0.605 , 3.14 )
What are the coordinates for the center of the circle and the length of the radius
Given:
[tex]x^2+y^2+14x+2y+14=0[/tex]To find the center of the circle and the radius of the circle:
The given equation is of the form,
[tex]x^2+y^2+2gx+2fy+c=0[/tex]Comparing we get,
[tex]\begin{gathered} g=7 \\ f=1 \\ c=14 \end{gathered}[/tex]The center is,
[tex](-g,-f)=(-7,-1)[/tex]The radius is,
[tex]\begin{gathered} r=\sqrt[]{g^2+f^2-c} \\ =\sqrt[]{(7)^2+(1)^2-14} \\ =\sqrt[]{49+1-14} \\ =\sqrt[]{36} \\ =6\text{ units} \end{gathered}[/tex]Therefore, the center of the circle is (-7,-1) and the radius of the circle is 6 units.
The volume of cube is `1000cm^(3)`.Find its total surface area.
Given:
[tex]\text{Volume of a cube=1000cm}^3[/tex]Let the length of a side is 'a' cm.
[tex]\begin{gathered} \text{Volume of a cube=1000} \\ a^3=1000 \\ a^3=10^3 \\ a=10\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} \text{Total surface are of a cube=6}a^2 \\ \text{Total surface are of a cube=}6(10)^2_{} \\ \text{Total surface are of a cube=}6(100) \\ \text{Total surface are of a cube=}600cm^2 \end{gathered}[/tex]i dont understand conjecture 7:30 7:55 8:20 8:45
conjecture here is nothing but the addition of 25 minutes in the previous time to get next time slot.
[tex]\begin{gathered} \text{ So,} \\ 7\colon30+\text{ 25 =7:55} \\ 7\colon55\text{ +25 = 8:00+20 =8:20} \\ 8\colon20+\text{ 25 = 8:45} \\ 8\colon45+\text{ 25 =9:00+10 = 9:10} \\ 9\colon10\text{ + 25 = 9:35} \end{gathered}[/tex]solve the system of equations using substitutiony=7y=2x-5
we have
y=7 -----> equation A
y=2x-5 ------> equation B
substitute equation A in equation B
7=2x-5
solve for x
2x=7+5
2x=12
x=6
the solution is the point (6,7)A science class has a total of 37 students. The number of males is 5 more than the number of females. How many males and how many females are in the class?
Given:
The total number of students = 37.
The number of males is 5 more than the number of females.
Required:
We need to find the number of female and male students.
Explanation:
Let x be the number of female students.
More than 5 means adding 5 to the number.
The number of male students = x+5.
The sum of the number of female and male students = the total number of students.
[tex]x+x+5=37[/tex][tex]2x+5=37[/tex]Subtract 5 from both sides.
[tex]2x+5-5=37-5[/tex][tex]2x=32[/tex]Divide both sides by 2.
[tex]\frac{2x}{2}=\frac{32}{2}[/tex][tex]x=16[/tex]The number of female students =16.
The number of male students = x+5= 16+5 =21.
Final answer:
The number of female students =16 students.
The number of male students =21 students.
write the standard form of thr equation of the line through the pair of points (3,6) and (3,-7) simplify your answer
The standard form of the equation of a line is given in the form:
[tex]Ax+By=C[/tex]where A, B, and C are constant integers.
We can write the equation in the point-slope form first, before getting the standard form of the equation:
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope, calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the points, the slope will be:
[tex]m=\frac{-7-6}{3-3}=\frac{-13}{0}[/tex]The answer is undefined. Therefore, the line is a vertical line.
Given it is a vertical line, the equation will be in the form:
[tex]x=C[/tex]At the point (3, 6), we have that:
[tex]3=C[/tex]Therefore, the equation of the line will be:
[tex]x=3[/tex]A Man has four pairs of shoes three suits and four shirts if he picks a pair of shoes, a suit, and a shirt at random, what is the probability that he picks his favorite shoes, suit, and shirt? Enter the probability as a fraction
SOLUTION
The man has 4 pairs of shoes
3 suits and
4 shirts
Probability is given as
[tex]\text{Probability = }\frac{\exp ected\text{ outcome }}{\text{total outcome }}[/tex]If he is to pick his favorite pair of shoes, suit and shirts, it means he will pick 1 pair of shoe, 1 suit and 1 shirt.
Then the probability of picking
His favorite pair of shoes becomes
[tex]\frac{1}{4}[/tex]Then the probability of picking
His favorite suit becomes
[tex]\frac{1}{3}[/tex]And Then the probability of picking
His favorite shirt becomes
[tex]\frac{1}{4}[/tex]Hence the required probability is
[tex]\begin{gathered} \frac{1}{4}\times\frac{1}{3}\times\frac{1}{4} \\ =\frac{1}{48} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{48}[/tex]A cubical water tank has a height of 9.6 inches. How much water canthe tank hold?Round your answer to tenth place.
The volume of a cube is given by:
[tex]V=l^3[/tex]where l is the length of its edges. In this case the length is 9.6 inches, plugging these values we have:
[tex]\begin{gathered} V=(9.6)^3 \\ V=884.736 \end{gathered}[/tex]Therefore, the tank can hold 884.7 cubic inches of water.
Find the vertex, line of symmetry, y - intercept, strategic points
Given:
[tex]f(x)=-x^2+4x[/tex]Opens downward.
[tex]f(x)=-x^2+4x-4+4[/tex][tex]f(x)=-(x^2-4x+4)+4[/tex][tex]f(x)=-(x-2)^2+4[/tex]Vertex of the parabol is (2,4)
Line of symmetry:
[tex]x=2[/tex]Y-intercept:
[tex]f(0)=4[/tex]y=4 is the y intercept.
[tex]\Rightarrow(0,0)[/tex]Strategic points are :
[tex](2,4),(0,0),(4,0)[/tex]) From the example below, choose the Independent quantity and dependent quantity. An increase in cardio exercise results in a decrease in weight. independent quantity dependent quantity
In order to identiy which is the dependet quantity and independent quantity, you consider that an independent quanity is that quantity does not depend of any other. Insteas of that, dependent quantity depends of the values of other quantity.
In the given case, you have that an increase in cardio exercise results in a decrease in weight. In this case you can notice that the weight depends of the cardio exercide. Hence, cardio exercise is the independent quantity, and weitgh is the dependent quantity.
Matrix A is mapped onto matrix B by dilation, What is the value of x in the new matrix?
To find the value of x, we will have to follow the steps below:
step 1: find the scale factor (f) of the dilation between matrix A and B
This will be achieved by comparing similar members of both matrices.
we can observe that
[tex]\begin{gathered} f=\frac{B_{12}}{A_{12}}=\frac{6}{10}=\frac{3}{5} \\ f=\frac{B_{21}}{A_{11}}=\frac{8.4}{14}=\frac{3}{5} \end{gathered}[/tex]Thus, the scale factor is 3/5
Step 2: use the scale factor to find the value of x
[tex]\begin{gathered} \frac{B_{11}}{A_{11}}=\frac{x}{4.28}=f \\ \frac{x}{4.28}=\frac{3}{5} \end{gathered}[/tex]cross-multiply
[tex]x=\frac{3\times4.28}{5}=2.568[/tex]Hence, the value of x = 2.568
Find the average rate of change of g(x) = 7/x over the interval [3,6]
Given:
The function is,
[tex]g(x)=\frac{7}{x}\text{ over interval \lbrack{}3,6\rbrack}[/tex]The average rate of change is calcuated as,
[tex]\begin{gathered} \frac{f(b)-f(a)}{b-a} \\ \lbrack a,b\rbrack=\lbrack3,6\rbrack \\ \frac{f(6)-f(3)}{6-3}=\frac{\frac{7}{6}-\frac{7}{3}}{3}=\frac{\frac{21-42}{18}}{3}=\frac{-21}{18\times3}=-\frac{7}{18} \end{gathered}[/tex]Answer: avarage rate of change is -7/18.
Please help me with the question below (also please explain).
To find the surface area of the given figure identify all the faces on the figure, calculate the area of each face and then sum the areas:
Measures in red
Number of faces in green, total faces 9
Area of a triangle:
[tex]A=\frac{1}{2}bh[/tex]Area of a rectangle:
[tex]A=bh[/tex]Area of faces 1 and 2(rectangles):
[tex]\begin{gathered} A_1=A_2=20in*11in \\ A_1=A_2=220in^2 \end{gathered}[/tex]Area of faces 3 and 4 (triangles):
[tex]\begin{gathered} A_3=A_4=\frac{1}{2}(12in)(9in) \\ \\ A_3=A_4=54in^2 \end{gathered}[/tex]Area of faces 5 and 6 (rectangles):
[tex]\begin{gathered} A_5=A_6=12in*5in \\ A_5=A_6=60in^2 \end{gathered}[/tex]Area of faces 7 and 8 (rectangles):
[tex]\begin{gathered} A_7=A_8=20in*5in \\ A_7=A_8=100in^2 \end{gathered}[/tex]Are of face 9 (rectangle):
[tex]\begin{gathered} A_9=20in*12in \\ A_9=240in^2 \end{gathered}[/tex]Total surface area:
[tex]\begin{gathered} SA=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8+A_9 \\ \\ SA=220in^2+220in^2+54in^2+54in^2+60in^2+60in^2+100in^2+100in^2+240in^2 \\ \\ SA=1108in^2 \end{gathered}[/tex]Then, the surface area of the given figure is 1108 square inchesEach student in the Junior class was asked if they had to complete chores at home and if theyhad a curfew. The table represents the data.Yes choresNo choresTotalYes curfew513081Let:Event A Having a curfewWEvent B Having choresWNo curfew Total24 7512 4236117Which statement accurately describes this data?
SOLUTION
From the table, we can see that the event having a curfew and having chores are dependent events. So there are not independent events.
Also the probability of A given B is
[tex]P(A|B)=\frac{51}{75}[/tex]and Probability of A
[tex]P(A)=\frac{81}{117}[/tex]Hence the second op
Rome question and type your response in the box provided. Your response will be saved automatically,The wheels on a car has a diameter of 28 inches. Find the area and Circumfrence of the car tire. (YOU MUST FIND BOTH TO GET FULL CREIDT).B IV 112021 Illuminate Education Inc.
Circumference: 28π inches and Area: 196π in²
1) Considering that the diameter of each wheel is 28", then we can state that
D=2R ⇒ R = D/2 , R = 14
2) So to find out the circumference of the tire, we'll need to use the Circumference formula:
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\pi\cdot14 \\ C=28\pi \end{gathered}[/tex]And now let's find out the area of the tire, by making use of another formula:
Plugging into that the radius length:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=(14)^2\pi \\ A=196\pi \end{gathered}[/tex]3) Hence, the answers are:
Circumference: 28π inches and Area: 196π in²
Part BSales associates at an electronics store eam different commissionpercentages based on the items they sell. The table shows the totalsales and commission earnings for four sales associates at theelectronics store last month.Electronics Store Sales and CommissionsTotal SalesCommissionEarnings5673$22$1.298$37$3,277S101$5.180$150The table below shows the total sales of two sales associates at theelectronics store last month.Electronics Store SalesSales TotalAssociate SalesJon $2,881Tia $4,163Use the model you created in Part A to estimate how much moremoney, in dollars, Tia eamed in commission than Jon. Show orexplain your workEnter your answer and your work or explanation in the boxprovided
From the table shown:
we need to find the relationship between the commission earnings and the total sales
John's sales = $2881
Tia's sales = $4163
Note that:
$2881 falls between $1298 and $3277
Using the extrapolation formula:
[tex]\begin{gathered} Y(x)\text{ = Y(1) + }\frac{x-x(1)}{x(2)-x(1)}\times\text{ \lbrack{}Y(2)-Y(1)\rbrack} \\ 2881\text{ = 1298 + }\frac{x-37}{101-37}\times\lbrack3277-1298\rbrack \\ 51.2\text{ = x - 37} \\ x\text{ = 51.2 + 37} \\ x\text{ = 88.2} \end{gathered}[/tex]Jon's commission = $88.2
For Tia's commission:
What is the surface area of the cone to the nearest tenth? The figure is not drawn to scale.thank you ! :)
To calculate the surface area of a cone we can use the following formula:
[tex]S=\pi r^2+\pi Lr[/tex]where r represents the radius of the base and L represents the slant height.
The radius of our cone is 7cm and the slant height 19cm, using those values on the formula we have our answer:
[tex]S=\pi(7)^2+\pi(19)(7)=49\pi+133\pi=182\pi\approx571.8[/tex]The surface area of this cone is 571.8 cm².
I need help with this, it’s from my trig prep guide.It asks to answer (a) and (b) But please put these ^ separately so I know which is which
Part (a).
Sigma notation (or summation notation) of binomial expansion is the following:
[tex](w+z)^n=\sum ^n_{k\mathop=0}\binom{n}{k}w^{n-k}\cdot z^k[/tex]where
[tex]\binom{n}{k}[/tex]denotes the binomial coefficient.
In our case, n is 4 and
[tex]\begin{gathered} w=3x^5 \\ z=-\frac{1}{9}y^3 \end{gathered}[/tex]So by substituting these terms into the sigma expantion, we have
[tex](3x^5+(-\frac{1}{9}y^3))^4=\sum ^4_{k\mathop{=}0}\binom{4}{k}(3x^5)^{4-k}\cdot(-\frac{1}{9}y^3)^k[/tex]So, the sum in summation notation is:
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}\binom{4}{k}(3x^5)^{4-k}\cdot(-\frac{1}{9}y^3)^k[/tex]Part b.
By expanding the above sum, we have
[tex]\begin{gathered} (3x^5-\frac{1}{9}y^3)^4=\binom{4}{0}(3x^5)^4\cdot(-\frac{1}{9}y^3)^0+\binom{4}{1}(3x^5)^3\cdot(-\frac{1}{9}y^3)^1+\binom{4}{2}(3x^5)^2\cdot(-\frac{1}{9}y^3)^2+ \\ \binom{4}{3}(3x^5)^1\cdot(-\frac{1}{9}y^3)^3+\binom{4}{4}(3x^5)^0\cdot(-\frac{1}{9}y^3)^4 \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \binom{4}{0}=1 \\ \binom{4}{1}=4 \\ \binom{4}{2}=6 \\ \binom{4}{3}=4 \\ \binom{4}{4}=1 \end{gathered}[/tex]we have
[tex](3x^5-\frac{1}{9}y^3)^4=(3x^5)^4+4(3x^5)^3\cdot(-\frac{1}{9}y^3)^{}+6(3x^5)^2\cdot(-\frac{1}{9}y^3)^2+4(3x^5)^1\cdot(-\frac{1}{9}y^3)^3+(-\frac{1}{9}y^3)^4[/tex]which gives
[tex](3x^5-\frac{1}{9}y^3)^4=81x^{20}-12x^{15}\cdot y^3+\frac{6}{9}x^{10}\cdot y^6-\frac{12}{729}x^5\cdot y^9+\frac{1}{6561}y^{12}[/tex]Therefore, the simplified expansion is given by:
[tex](3x^5-\frac{1}{9}y^3)^4=81x^{20}-12x^{15}\cdot y^3+\frac{2}{3}x^{10}\cdot y^6-\frac{4}{243}x^5\cdot y^9+\frac{1}{6561}y^{12}[/tex]I just wanted to make sure that my answer is correct.I have to find the reference angle given the degree.
Answer:
[tex]\text{ 80}\degree[/tex]Explanation:
Here, we want to get the reference angle of the angle given
The reference angle is simply the acute angle that corresponds to the given angle
Since the angle is negative, we have to add multiples of 360 degrees until we get an acute angle
Mathematically, we have this as:
[tex]\text{ -13600 + 360(38) = 80}\degree\text{ }[/tex]Learning Diagnostic Analytics Recommendations Skill plans Math Level K HH.5 Trigonometric ratios: find an angle measure RSS You have prize Find mZH. I 8 G 4 H Write your answer as an integer or as a decimal rounded to the nearest tenth. mZHE
The Solution:
Given:
We are required to find the measure of angle H.
By applying the trigonometric ratio, we have that:
[tex]\begin{gathered} \tan\angle H=\frac{opposite}{adjacent} \\ \\ \tan\angle H=\frac{8}{4} \end{gathered}[/tex][tex]\begin{gathered} \tan\angle H=2 \\ \text{ Take the arctan of 2} \end{gathered}[/tex][tex]\angle H=\tan^{-1}(2)=63.4349\approx63.4^o[/tex]Therefore, the correct answer is 63.4 degrees.