Answer:
D. exponential function
As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.
Explanation:
From the table of values:
x-values
[tex]\begin{gathered} 0-(-2)=2 \\ 2-0=2 \\ 4-2=2 \end{gathered}[/tex]The x-values increase by a constant amount, 2.
y-values
[tex]\begin{gathered} \frac{12}{4}=3 \\ \frac{36}{12}=3 \\ \frac{108}{36}=3 \end{gathered}[/tex]The y-values are multiplied by a constant amount, 3.
From these, we conclude that the set of ordered pairs represents an exponential function.
As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.
The correct option is D.
Determine the center and radius of the following circle equation:2² + y² – 2x – 6y – 54 = 0Center:13Radius:Submit Answer
Answer:
Centre = (1, 3)
radius = 8units
Explanation:
The standard equaton of a circle is expressed as;
[tex]x^2+y^2+2gx+2fy+C\text{ = 0}[/tex]The radius of the circle is expressed as;
[tex]r=\sqrt[]{g^2+f^2-C^{}}[/tex]The centre is at C(-g, -f)
Given the expression;
[tex]x^2+y^2-2x-6y-54=0[/tex]Get the centre of the circle.
Compare both equations
[tex]\begin{gathered} 2gx=-2x \\ g\text{ = -1} \end{gathered}[/tex]similarly;
[tex]\begin{gathered} 2fy=-6y \\ 2f=-6 \\ f=-\frac{6}{2} \\ f=-3 \end{gathered}[/tex]The centre will be located at C(-(-1), -(-3)) = C(1, 3)
Next is to get the radius
Recall;
[tex]\begin{gathered} r=\sqrt[]{g^2+f^2-C} \\ r=\sqrt[]{(-1)^2+(-3)^2-(-54)} \\ r=\sqrt[]{1+9+54} \\ r=\sqrt[]{64} \\ r=8\text{units} \end{gathered}[/tex]Hence the radius is 8units
Match each side length and angle to the correct answer. Simplify anyradicals.a= b=measure of angle C =measure of angle A=measure of angle B=c=
Given data:
The given figure of the triangle.
The measure of the side a is,
a=4 units.
The measure of the side b is,
b= 4 units.
The measure of the angle C is 90 degrees.
As the side a is equal to side b, it means the given triangle is isosceles right angle triangle.
The measure of the angle B is equal to the measure of the angle A which is 45 degrees.
The side c can be calculated as,
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=4^2+4^2 \\ c^2=32 \\ c=4\sqrt[]{2} \end{gathered}[/tex]Thus, a= 4 units, b=4 units, c=4√2, ∠C=90 degrees, ∠A= 45 degrees, and ∠B=45 degrees.
Bob's Car Wash had to close 26 days last year because of bad weather. If last year had 365 days, what is the ratio of days closed to days open for Bob's Car Wash?OA. 26 to 339OB. 26 to 365OC. 365 to 26OD. 339 to 26
Days closed = 26
Days open = Total days - days closed = 365 -26 = 339
Days closed to days open:
26 to 339
A car's rear windshield wiper rotates 135°. The total length of the wiper mechanism is 21 inches and the length of the wiper blade is 12 inches. Find the area wiped by the wiper blade. (Round your answer to one decimal place.)
The area wiped by the wiper blade is 424.08 in².
How to find the area?Using this formula to find the area
A= 1/2r² Ф
Where:
A = Area
r = Radius
Let plug in the formula
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (21 -12)² × 135° ×π /180 ]
A = [1/2 × (21)² × 135° ×π /180 ] - [1/2 × (9)² × 135° ×π /180 ]
A = [1/2 × (441) × 135° ×π /180 ] - [1/2 × (81) × 135° ×π /180 ]
A = 519.54 - 95.43
A = 424.08 in²
Therefore the area is 424.08 in².
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-9 is to the _____ of -3 on a number line so -9 is _____ than -3.right left more less
Answer:
-9 is to the left of -3
-9 is less than -3
Explanation:
If we're to write -9 and -3 on a number line from right to left, we'll see that -3 is going to come before -9, which means that -9 is to the left of -3.
On a number line, any number to the left of another number is less than the other number.
Since -9 is to the left of -3, so -9 is less than -3
Lana owns an office supply shop. At the beginning of each school year, she chooses two or three products to donate to the local middle school.
The table shows the school supplies that Lana has in her shop and how many of each kind she has in stock. Lana is considering different options of supplies to donate. For each option, determine the greatest number of identical boxes she could pack and the number of each supply item she could put in the boxes.
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
A option 1: pencils and erasers: ____boxes with ____ pencils and ____ erasers
B option 2: notebooks and folders: ____ boxes with ____notebooks and ____ folders in each box.
C option 3: erasers, markers, and folders: ____ boxes with ____ erasers ____ markers and ____ folders in each box.
Option-1: 221 boxes with 78 pencils and 143 erasers.
Option-2: 525 boxes with 195 notebooks and 330 folders in each box.
Option-3: 583 boxes with 143 erasers 110 markers and 330 folders in each box.
Given that,
Owning an office supplies store is Lana. Each school year, she selects two or three items to give to the neighborhood middle school.
We have to find the correct answer for the given options.
The table is
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
Option1:
Pencils and erases:
78+143=221
221 boxes with 78 pencils and 143 erasers.
Option 2:
Notebooks and folders:
195+330=525
525 boxes with 195 notebooks and 330 folders in each box.
Option 3:
Erasers, markers, and folders:
143+110+330= 583
583 boxes with 143 erasers 110 markers and 330 folders in each box.
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1. On a number line, graph the solution to the inequality -5(x + 1) > 7x +31? Also, write thesolution in interval notation.
We have the following:
[tex]\begin{gathered} -5\cdot\left(x+1\right)>7x+31 \\ -5x-5>7x+31 \\ -5x-5+5>7x+31+5 \\ -5x-7x>7x+36-7x \\ -12x>36 \\ x>\frac{36}{-12} \\ x<-3 \end{gathered}[/tex]interval notation:
[tex](-\infty,-3)[/tex]graph:
Determine the interest rate capitalized once in a year which can triple any amount in 6 years
ANSWER
interest rate = 20%
EXPLANATION
let P = x, A = 3x, t = 6 and R = ?
[tex]A\text{ = P}\ast(1+R)^t[/tex][tex]\begin{gathered} 3x=x(1+R)^6 \\ 3=(1+R)^6 \\ 1+R=3^{\frac{1}{6}} \\ 1+R\text{ = 1.2} \\ R\text{ = 1.2 - 1} \\ R\text{ = 0.2} \\ R\text{ = 20\%} \end{gathered}[/tex]The volume of dis rectangular prism is zero. Seven to a cubic yards. What is the value of C in yards?
To get the volume of a prims, we do the products of the base times its height.
Being a rectangular prims, the area of its base is the product of its dimesions, so the volume of a rectangular prism is simply the product of its three dimensions:
[tex]V=l\cdot w\cdot h=1.3\cdot1.4\cdot c=1.82c[/tex]Since the volume is equal to 0.728 yd³, we have:
[tex]\begin{gathered} 0.728=1.82c \\ c=\frac{0.728}{1.82}=0.4 \end{gathered}[/tex]So, the measure of c is 0.4 yards.
Evaluate the following expression.C(8,3)C=combinations
The formula for combination is
nCr = n!/(n - r)!r!
C represents the number of combinations
n represents the total number of objects to choose from
r represents the number of items selscted from n
From the information given,
n = 8 and r = 3
8C3 = 8!/(8 - 3)!3!
= 8! /5!3!
= 8 * 7 * 6 * 5 * 4 * 3!/5 * 4 * 3 * 2 * 1 * 3!
The 3! cancels out. It becomes
8 * 7 * 6 * 5 * 4 /5 * 4 * 3 * 2 * 1
= 6720/120
= 56
The answer is 56
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Kelly and nadir both had maths tests last week, Kelly scored 47/68 and nadir scored 35/52. Who got the higher percentage score
Answer:
Kelly got a higher percentage score.
Step-by-step explanation:
35 / 52 = 0.673
47 / 68 = 0.691
Suppose your final grade in this class is based on the following system:Class participation 10% homework 20%test average 30% final exam 25%quiz average 15%Given the grades listed below, what would your final grade in the class be?test grades(78, 87, 93, 75) quiz average (85)Class participation (95) homework(75)final exam(63)choices:A. 83B. 70C. 88D. 78
to find a percentage we multiply by the number and divide by 100
class participation
[tex]\begin{gathered} 95\times\frac{10}{100} \\ =9.5 \end{gathered}[/tex]homework
[tex]\begin{gathered} 75\times\frac{20}{100} \\ =15 \end{gathered}[/tex]test average
first find the average
[tex]\begin{gathered} \frac{78+87+93+75}{4} \\ =83.25 \end{gathered}[/tex]then the percentage
[tex]\begin{gathered} 83.25\times\frac{30}{100} \\ =24.975 \end{gathered}[/tex]Final Exam
[tex]\begin{gathered} 63\times\frac{25}{100} \\ =15.75 \end{gathered}[/tex]Quiz average
[tex]\begin{gathered} 85\times\frac{15}{100} \\ =12.75 \end{gathered}[/tex]finally we add to get the final grade
[tex]\begin{gathered} 9.5+15+24.975+15.75+12.75 \\ =77.97 \end{gathered}[/tex]the final grade is 78
Sasha owes a total of $1,845.00 on revolving credit accounts that have total limits of $4,500.00. Calculate the amount she needs to pay on her debt to reduce her revolving credit accounts to reach a 25% debt-to-credit ratio. $705.00$720.00$988.00$1,125.00
Sashas total debt is 1845
Total limit on the credit card account is 4500
25 × 4500 / 100 = 1125
25% of 4500 is 1125
So in order to reach a 25% debt to credit ratio Sasha needs to payback 720 of her debt.
1845 - 1125 = 720
Option B is the answer
jessica needs to bake 50 muffins her baking pan holds 12 muffins how many rounds of baking will she need to do
Let x be the number of rounds of baking. Jessica's baking pan holds 12 muffins. Total 50 muffins is to be made. Hence, we can write,
[tex]\begin{gathered} 12x=50 \\ x=\frac{50}{12}=\frac{25}{6}=4\frac{1}{6} \end{gathered}[/tex]So, we obtained that x is equal to 4 1/6. The number of rounds cannot be a fraction. Here, the number of rounds is equal to the sum of 4 and a fraction 1/6. So, we can say that 5 rounds is needed to make 50 muffins.
In the diagram, line AB is parallel to DE. Also, line DE is drawn such that the length of line DE is half the length of line AB. If sin A=0.5, then what is sin E?
By alternate interior angle theorem. Angle A is congruent with Angle E.
This makes ΔAFB similar to ΔEFD.
IF sin A = 0.5, then sin E is also equal to 0.5.
REWRITE EACH PROBLEM AS A MULTIPLICATION QUESTION!!!Students were surveyed about their favorite colors. 1/4 of the students preffered red, 1/8 of the students blue, and 3/5 of the remaining students preffered green. If 15 students preffered green, how many student were surveyed?
Let there are x total student surveyed, the 1/4x students prefer red, 1/8x prefer blue.
Determine the remaining students.
[tex]\begin{gathered} S=x-\frac{x}{4}-\frac{x}{8} \\ =\frac{8x-2x-x}{8} \\ =\frac{5}{8}x \end{gathered}[/tex]Determine the students that prefer green.
[tex]\frac{3}{5}\cdot\frac{5}{8}x=\frac{3x}{8}[/tex]The students who preferred green is 15. So equation for x is,
[tex]\begin{gathered} \frac{3x}{8}=15 \\ x=\frac{15\cdot8}{3} \\ =40 \end{gathered}[/tex]So total students that were surveyed is equal to 40.
On your first day of work at the Vanity Fur Grooming Shop, you groomed 3 dogs between 7:45 a.m. and 2:30 p.m., taking breaks that totaled 45 minutes. Your supervisor advises that you will be scheduling your own appointments when customers call to have their pets groomed. If you continue to work at the same rate, how much time should you allow for each grooming appointment?
Answer:
2 hours
Explanation:
First, calculate the length of time between 7:45 a.m. and 2:30 p.m.
[tex]\begin{gathered} \; \; 2\colon30P.M\text{.} \\ -7\colon45A.M\text{.} \\ _{----------} \\ 6\colon45 \end{gathered}[/tex]If the break totaled 45 minutes, the time spent grooming the 3 dogs = 6 hours.
Therefore, if you continue to work at the same rate, the time that should be allocated for each grooming appointment:
[tex]\begin{gathered} =\frac{6}{3} \\ =2\text{ hours} \end{gathered}[/tex]Select the correct answer from each drop-down menu.Phyllis bought 21 feet of wood to frame a window. If she makes a triangular window, what is the greatest area the window can have?For a given perimeter, the triangle with the largest perimeter isv triangle. Using this type of triangle, the sides wouldmeasureSo, the greatest area the window could be is aboutsquare feet
Equilateral Triangles
An equilateral triangle has all of its three sides of the same measure. Suppose the side length of an equilateral triangle is L.
The perimeter of such a triangle is:
P = 3L
Phyllis bought 21 feet of wood to frame a triangular window. This corresponds to the perimeter of the triangle, so we can calculate the side length:
L = P/3
L = 21 feet / 3
L = 7 feet.
Now we know the length of the side of the triangle, we calculate the area by using the formula:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]Substituting L = 7 feet:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(7ft)^2 \\ A=\frac{\sqrt[]{3}}{4}49ft^2 \\ \text{Calculating:} \\ A\approx21.22ft^2 \end{gathered}[/tex]when plqying a math game in class you drew 5 cards and had to find the sum of the numbers. your numbers were -9 3 2 - 5 4. what was the sum of your hand
We are required to sum up the numbers obtained. Our approach is to add the negative numbers separately and the positive numbers separately and then add up both.
[tex]\begin{gathered} (-9)+3+2+(-5)+4=3+2+4+(-9)+(-5) \\ 3+2+4=9 \\ -(9+5)=-14 \\ \text{Adding both} \\ 9+(-14)=9-14=-5 \end{gathered}[/tex]-5 is our answer.
Find a recursive formula for the following sequence:4, 11, 25, 53, 109, ...
Notice the following pattern in the given sequence:
[tex]\begin{gathered} 11=4\cdot2\text{ +3,} \\ 25=11\cdot2+3, \\ 53=25\cdot2+3, \\ 109=53\cdot2+3. \end{gathered}[/tex]Therefore, the n-term of the sequence has the following form:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]Answer:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]A( graph the system (Let t be represented by the hot axis and p be represented by the vertical axis B) find the solution to the system (t p)
I) p = 3.5t + 5
II) p = 7t/2 - 5
A) For equation I, if we replace t with 0 we find p = 5 and if we replace t with 2 we find p = 3.5*2 + 5 = 12. Therefore, to graph the line represented by this equation, we just need to draw a line passing through the points (0,5) and (2,12)
For equation II, if we replace t with 0 we find p = -5 and if we replace t with 2 we find p = (7/2)*2 - 5 = 2. Therefore, to graph the line represented by this equation, we just need to draw a line passing through the points (0,-5) and (2,2).
Here is the system represented by a graph:
B) By the graph, we can see that the lines are parallel and never intercept each other. This happens because they have the same slope (3.5 = 7/2). Therefore, this system has no solution.
1,1,2,6,24,_,_,_,_A) explain and complete the sequenceB) write an explicit and recursive formula for the sequence
As you can notice, this sequence is detailed as follows:
[tex]\begin{gathered} 1\cdot1=1 \\ 1\cdot2=2 \\ 2\cdot3=6 \\ 6\cdot4=24 \end{gathered}[/tex]Now, let's find the next four terms:
[tex]\begin{gathered} 24\cdot5=120 \\ 120\cdot6=720 \\ 720\cdot7=5040 \\ 5040\cdot8=40320 \end{gathered}[/tex]A possible formula could be:
[tex]a_n=n\cdot a_{n-1}[/tex]Where "n" is the number of the term given and it starts from 1. (a0 is 1) This is:
[tex]\begin{gathered} a_1=1.a_{1-1}=1\cdot a_0=1_{} \\ a_2=2\cdot a_{2-1}=2\cdot a_1=2 \\ a_3=3\cdot a_{3-1}=3\cdot a_2=6 \\ \text{and so on } \end{gathered}[/tex]Calculate the percent error. Darwin’s coach recorded that he had bowled points out of in a bowling tournament.
Given:
The recorded value is 250 points.
The true value is 300 points.
To find the percent error:
Using the formula,
[tex]P\text{ercent error}=\frac{|recorded\text{ value}-\text{true value|}}{\text{True value}}\times100\text{ \%}[/tex]On substitution we get,
[tex]\begin{gathered} =\frac{|250-300|}{300}\times100 \\ =\frac{50}{300}\times100 \\ =16.67\text{ \%} \end{gathered}[/tex]Hence, the percent error is 16.67 %.
Do You Know How? In 3-8, estimate each product using rounding or compatible numbers. 4. 104 x 0.33 3. 0.87 x 112 0.90x110=99 6. 0.54 x 24 5. 9.02 x 80 9x80=720 7. 33.05 x 200 a. 0,79 x 51
Estimating Products
Some operations can be estimated and its results approximated by using rounding and number that are easier to calculate.
For example the product 0.87*112 can be estimated by using 0.9 (a very close rounded number) and 110 instead of 112. One of the factors was rounded up and the other was rounded down. The product should be very close to the real exact product.
Now for 104*0.33. 104 can be rounded to 100 and it can be easily multiplied by 0.33. 100*0.33 = 33
0.54*24 can be estimated as 0.5*26=13 or as 0.6*30=18
33.05*200 is approximated as 33*200 = 6600
0.79*51 is estimated as 0.8*50 = 400
Some of the estimations above can be challenged and some people can propose better combinations for more accurate results. It's a subjective task.
what is the correct trigonometric ratio for the tangent of A?
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the figure,
opposite =8 and adjacent= 15
[tex]\tan A=\frac{8}{15}[/tex]V8 Splash $2.28 64 oz Walmart 0.04 cents per ozV8 Splash $ 2.49 64 oz Kroger 3.89 cents per ozWhich is the better deal?
Given:
V8 Splash $2.28 64 oz Walmart 0.04 cents per oz
V8 Splash $ 2.49 64 oz Kroger 3.89 cents per oz.
Best deal is
V8 Splash $2.28 64 oz Walmart 0.04 cents per oz
1.Given the Graph Circle One: Arithmetic, Geometric, or Neither Circle One: Common Ratio or Common difference: recursive formula-explicit formula-find the 5th term-
We can see in the graph that for every increment in x, the y-value is halved (that is, multiplied by 1/2).
Since the y-values are being multiplied for every increment of x, we have a geometric sequence or function.
Also, the function has a common ratio, which is the value 1/2 that multiplies y for every increment of x.
Last, we have a recursive formula: each value of y is half of the previous value of y (a_n = (1/2) * a_(n-1))
In order to find the explicit formula, since we have an exponential function, we can use the model y = a*b^x.
Using the points (1, 32) and (2, 16), we have:
[tex]\begin{gathered} 32=a\cdot b^1\to a=\frac{32}{b} \\ 16=a\cdot b^2\to b^2=\frac{16}{a}=\frac{16b}{32}\to b=\frac{1}{2} \\ 32=a\cdot\frac{1}{2}\to a=64 \end{gathered}[/tex]So the explicit function is y = 64 * (1/2)^x.
Looking at the graph, the 5th term of the sequence (x = 5) is found by halving the value y = 8 two times, so the 5th term is 2.
.converge or diverge? If it converges, to what value does it converge?
Given the series;
[tex]\sum ^{\infty}_{n\mathop=0}3(\frac{1}{5})^{n-1}[/tex]To obtain the sum of the series above and decide if it converges or diverges, we will
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}0}3(\frac{1}{5})^{n-1}=\sum ^{\infty}_{n\mathop{=}0}3(5)^{-(n-1)} \\ =\sum ^{\infty}_{n\mathop{=}0}3(5)^{(1-n)} \\ =\sum ^{\infty}_{n\mathop{=}0}15\times5^{-n} \\ =15\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n \end{gathered}[/tex]Simplify the resulting geometric series and decide if it converge or diverge
[tex]\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n\Rightarrow is\text{ an infinite geometric series, with first term a= 1 and common ratio r=}\frac{1}{5}[/tex]Solve for the sum to infinity of the geometric series
[tex]S_{\infty}=\frac{a}{1-r}=\frac{1}{1-\frac{1}{5}}=\frac{1}{\frac{4}{5}}=\frac{5}{4}[/tex]The sum of the series wil be
[tex]15\sum ^{\infty}_{n\mathop{=}0}(\frac{1}{5})^n\Rightarrow15\times\frac{5}{4}=\frac{75}{4}[/tex]Hence,
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}0}3(\frac{1}{5})^{n-1}=\frac{75}{4} \\ \text{The series converges} \end{gathered}[/tex]If Guillermo deposits $5000 into an account paying 6% annual interest compounded monthly, how long until there is $8000 in the account?
We have the following:
The formula in this case is the following:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]solving for t:
replacing
A is 8000, P is 5000, n is 12 and r is 6% (0.06)
[tex]\begin{gathered} 8000=5000(1+\frac{0.06}{12})^{12t} \\ \frac{8000}{5000}=1.005^{12t} \\ \ln (\frac{8}{5})=12\cdot t\ln (1.005)_{} \\ t=\frac{\ln (\frac{8}{5})}{12\ln (1.005)} \\ t=7.85 \end{gathered}[/tex]therefore, the answer is 7.9 years