To solve the following equation we are going to use inverse operations to solve equations, that means addition and subtraction are inverse operations, multiplication and division too.
Then,
[tex]\begin{gathered} \frac{1}{2}x+7=12 \\ \frac{1}{2}x=12-7 \\ x=5\cdot2 \\ x=10 \end{gathered}[/tex]Complete the sentence about Pattern G and Pattern H. Use the table to help H O O 2 16 4 24 Each term in Pottern Gl. corresponding term in Pattern H. 2 times 4 times
We can see that the values of H can be found dividing each value of G by 4. So, the answer is:
Each term in Pattern G is 4 times the corresponding term in Pattern H.
A plant is already 48 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after
m months is given by the following.
H=48+m
What is the plant's height after 31 months?
Answer:79
Step-by-step explanation:
every month it grows 1centimeter so 1cm x 31 days =31 + 48 = 79
The digits of a two digit integer N are interchanged to form an integer K. Find all possibilities for N is odd and exceeds by more than 18
let t be the tens digit of N
let u be the units digit of N
10t + u = N
10u + t = K
N - K > 18
(10t + u) - (10u + t) > 18
10t + u - 10u - t > 18
9t - 9u > 18
t - u > 2
t > u + 2
Since t < 10, it must be that u < 7
since N is odd the unit digits u = 1 , 3 , 5 ,...
If u = 1, t > 3, then N = 41 , 51 , 61 , 71 , 81 , 91.
If u = 3, t > 5, so N = 63 , 73 , 83 , 93.
If u = 5, t > 7, so N = 85 , 95.
Jamie entered his sister into their town's Smelly Shoe Competition. Jamie observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes. Tennis shoes High heels 13 10 Under age 12 13 to 30 years old 31 to 50 years old 13 9 12 16 What is the probability that a randomly selected contestant is 13 to 30 years old and is no wearing tennis shoes? Simplify any fractions.
To find the probability of a randomly selected contestant to not be wearing tennis shoes we need to divide the number of contestans in that age range by the total number of contestants. This is shown below:
[tex]p=\frac{9}{13+10+13+9+12+16}=\frac{9}{73}[/tex]The probability is 9/73
Plsss help Identify each of the colas radius, diameter, or circumference
Radius, diameter, diameter, circumference, radius, diameter, circumference
See explanation below
Explanation:The length of the minute hand of a clock is referred to as the radius of the clock since it is circular
Radius = 5 in
The distance across a sink drain is 3.8cm.
This will mean the diameter is 3.8cm
The tires on a mining truck are ft tall. When the tire is upright, the height is represented as the diameter of the tire which is circular.
Diamter is 14ft
The fence around a circular pool is 75ft long. The fence will be the perimeter of the circular pool.
Hence, this is the circumference.
The distance from the tip of a slice of a pizza to the crust is 7in
The tip is from the middle of the pizza which is circular.
The distance betwen them is the radius.
Breaking a cookie in half create a straight side 10cm long.
A cookie is circular so breaking it half, you will get the diameter of the circle.
The length of the metal rim around a glass lens is 190mm.
The metal rim is circular. The length of the around it will be the perimter of the round rim.
This is the circumference
A new school building was recently built. the entire cost of the project was $18,000,000 the city has put the project on a 30 year loan with an APR of 2.7% there are 17,000 families that will be responsible for making payments towards the loan. determine the total amount that each family should be required to pay each year to cover the cost of the new school building.
We will have the following:
Assumin it is compounded once each year, we will first determine the total to be paid each year overall:
[tex]18000000=P(1+\frac{0.027}{1})^{1\cdot30}\Rightarrow P=\frac{18000000}{(1+0.027)^{30}}[/tex][tex]\Rightarrow P=8093925.398[/tex]Now, we simply divide by the total number of families and we determine the amount of money each family will pay:
[tex]=P_f=\frac{8093925.398}{17000}\Rightarrow P_f=476.1132587\ldots[/tex][tex]\Rightarrow P_f=476.1[/tex]So, each famiy will pay approximately $476.11 each year.
Describe the graph of y=3x+15 /x-2. Define the horizontal and vertical asymptotes and several points on either side.
SOLUTION
The given equation is:
[tex]y=\frac{3x+15}{x-2}[/tex]The graph of the function is shown:
The vertical asymptotes is x=2
The horizontal asymptote is y=3
19. Demonstrate that the points (-8, 0) and (6,0) do
not determine a unique parabola by writing the
equations of two different parabolas that pass
through these two points.
Step-by-step explanation:
equation: y-y1=m(x-x1)
Slope: Y2-Y1
------------
X1- X2
0-(-8). 8
-------- = ------
0-6. -6
when putting a point in a equation it needs to have an opposite signs. ex: point: (-8,0( point in equation (8,0)
y+8= 8/-6(x-0)
y-6= 8/-6(x-0)
Question attached Answer 1 A. B>1B. 01F 01B. 01F. 0
EXPLANATION:
Given;
We are given the general form of an exponential function and that is;
[tex]y=a\times b^x[/tex]Required;
We are required to determine when it represents a growth and when it represents a decay.
Step-by-step solution/explanation;
The exponential function in its expanded form is given as follows;
[tex]y=a(1+r)^x[/tex]Take note of the following variables;
[tex]\begin{gathered} a=initial\text{ }value \\ r=rate\text{ }of\text{ }growth \\ x=interval,\text{ }years,\text{ }days,\text{ }etc \end{gathered}[/tex]Hence, note also, that;
[tex](1+r)=growth\text{ }factor[/tex]Note also that;
[tex](1+r)=b[/tex]Therefore, if there is a growth, the formula would be;
[tex]y=a(1+r)^x[/tex]Which means;
[tex]\begin{gathered} (1+r)>1 \\ OR \\ b>1 \end{gathered}[/tex]And if there is a decay, the formula would be;
[tex]y=a(1-r)^x[/tex]Which means;
[tex]\begin{gathered} (1-r)<1 \\ OR \\ b<1 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]The\text{ }relation\text{ }represents\text{ }a\text{ }growth\text{ }when\text{ }B>1[/tex][tex]And\text{ }a\text{ }decay\text{ }when\text{ }0First is option ASecond is option B
Suppose a three dimensional container has a volume of 19845 cubic inches. Calculate the volume of the container in cubic yards and round your answer to two decimal places.
Answer:
0.43 cubic yards
Explanation:
We know that 1 cubic yard is equivalent to 46656 cubic inches. So, we can convert 19845 cubic inches into cubic yards as:
[tex]19845\text{ cubic inches }\times\frac{1\text{ cubic yard}}{46656\text{ cubic inches}}=0.43\text{ cubic yards}[/tex]Therefore, the answer is 0.43 cubic yards
You mix 1 1/4 quarts of juice with 3 1/3 quarts of ginger ale to make fruit punch. What is the ratio of the amount of juice to the amount of ginger ale in simplest form?
0.25 and 3.33
Step-by-step explanation:
Yusuf needs to order some new supplies for the restaurant where he works. The restaurant needs at least 568 knives. There are currently 307 knives. If each set on sale contains 20 knives, what is the minimum number of sets of knives Yusuf should buy?
Answer:
14
Step-by-step explanation:
This is because when we look at the total needed 568 and then subtract the amount we have 307 we are left with 261 and if each box contains 20 we can divided it and get 13.05 which means we have to order 14 boxes to get all of the knives needed.
x^2+y^2-2x+6y=-3.What are the coordinates of the center and the length of the radius of the circle?
Given:
[tex]x^2+y^2-2x+6y=-3[/tex]is given as the equation of circle.
Required:
The coordinates of the center and the length of the radius of the circle.
Explanation:
The general equation of circle is
[tex]x^2+y^2+2gx+2fy+c=o[/tex]where
[tex]\begin{gathered} center=(-g,-f) \\ and \\ radius=\sqrt[]{g^2+f^2-c} \end{gathered}[/tex]now by comparing the general and given equation we get
[tex]\begin{gathered} g=-1 \\ f=3 \\ c=3 \end{gathered}[/tex]now substitute in the formulas
[tex]center=(-g,-f)=(1,-3)[/tex][tex]radius=\sqrt[]{g^2+f^2-c}=\sqrt[]{7}=2.65[/tex]Final answer:
[tex]\begin{gathered} center=(1,-3) \\ and \\ radius=2.65 \end{gathered}[/tex]
Two lines are perpendicular if their slopes are the same.TrueFalse
ANSWER :
False
EXPLANATION :
Two lines are perpendicular if their slopes, m1 and m2, are the negative reciprocal of each other.
[tex]m_2=-\frac{1}{m_1}[/tex]Therefore, the given statement is False
What interest rate compounded semiannually will yield an effective interest rate of 6%?
Equate the formula for compound interest with the added interest rate
6% => 0.06
[tex]\begin{gathered} 1+0.06=(1+\frac{r}{n})^2 \\ 1.06=(1+\frac{r}{2})^2 \end{gathered}[/tex]Get the square root of both sides.
[tex]\begin{gathered} \sqrt[]{1.06}=\sqrt[]{(1+\frac{r}{n})^2} \\ \sqrt[]{1.06}=1+\frac{r}{2} \\ \sqrt[]{1.06}-1=\frac{r}{2} \\ r=2(\sqrt[]{1.06}-1) \\ r=0.0591260282 \end{gathered}[/tex]Converting the result to percentage, and rounding it off to the nearest tenth of a percent. The rate is 5.9%.
Determine whether the units are commensurable or incommensurable with grams. (2 pointsCommensurable IncommensurableAcresKilometersKilogramsHours
The grams are part of the fundamental unit mass, therefore:
Acres - It is a unit of length, incommensurable with grams
Kilometers - It is a unit of length, incommensurable with grams
Kilograms - It is a unit of mass, commensurable with grams
Hours - It is a unit of time, incommensurable with grams
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.A charitable organization in Livingston is hosting a black tie benefit. Yesterday, the organization sold 21 regular tickets and 38 VIP tickets, raising $5,228. Today, 44 regular tickets and 58 VIP tickets were sold, bringing in a total of $8,792. How much do the different ticket types cost?
Let's use the variable x to represent the price of a regular ticket and the variable y to represent the price of a VIP ticket.
If 21 regular tickets and 38 VIP tickets cost $5228, we can write the following equation:
[tex]21x+38y=5228[/tex]If 44 regular tickets and 58 VIP tickets cost $8792, we can write the following equation:
[tex]44x+58y=8792[/tex]Now, to solve this system of equations, let's solve the first equation for x and then use its value in the second equation:
[tex]\begin{gathered} 21x=5228-38y \\ x=\frac{5228-38y}{21} \\ \\ 44\cdot(\frac{5228-38y}{21})+58y=8792 \\ 10953.9-79.619y+58y=8792 \\ -21.619y=8792-10953.9 \\ -21.619y=-2161.9 \\ y=100 \\ \\ x=\frac{5228-3800}{21} \\ x=\frac{1428}{21} \\ x=68 \end{gathered}[/tex]Therefore the price of a regular ticket is $68 and the price of a VIP ticket is $100.
I need this answered please
Answer:
r = 2
Step-by-step explanation:
The equation in the point slope form of the line is
y +2 = [tex]\frac{-1}{4}[/tex](x -19) To change to the y intercept form of a line distribute the [tex]\frac{-1}{4}[/tex]
y + 2 = [tex]\frac{-1}{4}[/tex] x + [tex]\frac{19}{4}[/tex] Subtract 2 from both sides of the equation
y = [tex]\frac{-1}{4}[/tex]x + [tex]\frac{11}{4}[/tex] ( [tex]\frac{19}{4}[/tex] - [tex]\frac{8}{4}[/tex])
Now that we have the equation. The ask what is r when x is 3 (r is the y in the equation
y = [tex]\frac{-1}{4}[/tex] ([tex]\frac{3}{1}[/tex]) + [tex]\frac{11}{4}[/tex]
y = [tex]\frac{-3}{4}[/tex] + [tex]\frac{11}{4}[/tex]
y = [tex]\frac{8}{4}[/tex] = 2
Given line l is a perpendicular bisector of ⎯⎯⎯⎯⎯⎯⎯⎯CB¯ and CB = 6.8, find DB.
For this problem, we are given a triangle with a line that bisects its base BC on point D. We need to determine DB using the fact that CB is equal to 6.8.
A bisector divides a segment in two equal parts. Since the line I bisects the segment CB, then it divides this segment in two equal parts such as:
[tex]\begin{gathered} CB=CD+DB\\ \\ CB=x+x\\ \\ CB=2x \\ \end{gathered}[/tex]Since the value of CB is equal to 6.8, we have:
[tex]\begin{gathered} 6.8=2x\\ \\ 2x=6.8\\ \\ x=\frac{6.8}{2}=3.4 \end{gathered}[/tex]The value of DB is equal to 3.4 cm.
Select the correct description for the expression 8(x + 4).A. The quotient of a difference and a numberB. The product of a number and a sumC. The product of a number and a differenceD. The quotient of a sum and a number
The expression 8(x+4) is a product between 8 and (x+4), which is a number (8) and a sum.
Then, it correspond to Option B: The product of a number and a sum.
f(x)=(0.13x⁴+0.22x³)-0.88x²-0.25x-0.09for this polynomial use a graph and find the increasing and decreasing intervals and write them in interval notation
Let's take a look at the graph of the polynomial:
Now, notice that those three turning points tell us that the function changes from decreasing to increasing, or viceversa, right at that point.
This way, the decreasing intervals are:
[tex]\begin{gathered} (-\infty,-2.531) \\ (-0.136,1.398) \\ \end{gathered}[/tex]And the increasing intervals are:
[tex]\begin{gathered} (-2.531,-0.136) \\ (1.398,\infty) \end{gathered}[/tex]George was riding his bike downhill on a street in a Canadian town. The street- side speed sensor clocked him at 30 km per hour. His bike speedometer was set up in U.S. units of mph. What would the readout have been?b. A short-course meter pool is 25 meters long.
In order to find the readout in his bike speedometer, we need to know the approximate value for the conversion between miles and kilometers, then,
[tex]1\text{ }mi\Rightarrow1.609\text{ }km[/tex]then, use conversion factors with the street side sensor,
[tex]\frac{30km}{h}\ast\frac{1mi}{1.609km}\approx\frac{18.64mi}{h}[/tex]Answer:
The approximate value shown in his bike speedometer is 18.64 mph
select all the representations that are appropriate for comparing exam score to number of hours of sleep the night before exam.
The best way to compare exam score to the number of hours of sleep is by
Histogram, you can easily determine the score using the bars on the histogram at every hours of sleep.
Scatter
2x - 3y = 6 2x - 6y = 9
Rosie, this is the solution to the system of equations:
___________________________________________
2x - 3y = 6
2x - 6y = 9
___________
Step 1: Let's multiply by -1 the second equation, therefore we have:
2x - 3y = 6
-2x + 6y = -9
___________
Step 2: We eliminate x and solve for y, as follows:
-3y + 6y = 6 - 9
3y = -3
Dividing by 3 at both sides:
3y/3 = -3/3
y = -1
_______________________
Step 3: We substitute y and solve for x in the first equation, this way:
2x - 3 (-1) = 6
2x + 3 = 6
Subtracting 3 at both sides:
2x + 3 - 3 = 6 - 3
2x = 3
Dividing by 2 at both sides:
2x/2 = 3/2
x = 3/2
_________________________
Step 4: Now, let's prove x = 3/2 and y = -1 are right, replacing in the second equation, as follows:
2x - 6y = 9
2 (3/2) - 6 (-1) = 9
3 + 6 = 9
9 = 9
We proved that x = 3/2 and y = -1 are correct.
A rectangle whose base is twice it’s altitude is inscribed in a circle whose radius is 5mm. Find the area of the rectangle.
Answer and Explanation:
40 square mm
See the attached image.
Basically, the 5mm radius that is given is half the diagonal of the rectangle. So if we double the radius, it becomes the diagonal, which is the hypotenuse of the right triangle that can be constructed of half the rectangle. From there, we can use the Pythagorean theorem to solve for the rectangle's side length by substituting a for [tex]\ell[/tex] and b for [tex]2\ell[/tex]. Finally, we multiply [tex]\ell[/tex] and [tex]2\ell[/tex] to get the area of the rectangle:
[tex]A = \ell \cdot 2\ell[/tex]
[tex]A = 2\sqrt5 \cdot 2(2 \sqrt{5})[/tex]
[tex]A = 2^3 \cdot (\sqrt5)^2[/tex]
[tex]A = 8 \cdot 5[/tex]
[tex]A = 40 \, \textrm{mm}^2[/tex]
Question 1
O 38,617 kWh/month
O 2,601 kWh/month
O 115,853 kWh/month
quiz.
The Schmidt family checks their electric meter three months after the last time they checked it. The
old reading was 113,252 kilowatt-hours and the new reading was 115,853 kilowatt-hours. What
was the average electricity usage for the Schmidt family during the three months?
867 kWh/month
1 pts
The average electricity usage for the Schmidt family during the three months is 867 kWh/month.
Given,
The old reading of electric meter = 113,252 kWh
The meter reading after 3 months = 115,853 kWh
We have to find the average electricity usage for the Schmidt family during the three months.
That is,
Average use in 3 months = new reading - old reading / 3
Average use in 3 months = [115,853 - 113,252] / 3
Average use in 3 months = 2601/3
Average use in 3 months = 867 kWh/month
Therefore,
The average electricity usage for the Schmidt family during the three months is 867 kWh/month.
Learn more about average electricity usage here;
https://brainly.com/question/9993543
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can you just show me where to plot these ?
Use the given coordinates to classify the triangle and find its perimeter.S(1, - 6), A (6, – 6), U (3, - 2)
1) Firstly, we'll need to find the length of all legs. We'll use the distance formula derived from the Pythagorean Theorem
[tex]\begin{gathered} d_{SA}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_{SA}=\sqrt[]{(6-1)^2+(-6+6)^2}=5 \\ d_{AU}=\sqrt[]{(3-6)^2+(-2+6)^2}=5 \\ d_{SU}=\sqrt[]{(3-1)^2+(-2+6)^2}=2\sqrt[]{5} \end{gathered}[/tex]Since an isosceles triangle has at least 2 congruent sides then this is an Isosceles Triangle.
2) The Perimeter (2P) is the sum of all sides' length of a polygon. Hence
[tex]\begin{gathered} 2P\text{ =5+5+2}\sqrt[]{5} \\ 2P=10+2\sqrt[]{5} \end{gathered}[/tex]3) So the answer is Isosceles Triangle and 2P =10+2√5
Can someone thoroughly explain this and place the points for me please? Thank you.
f(2) = 8
f(3) = 14
f(4) = 20
Explanation:[tex]\begin{gathered} \text{From the table, we can deduce that:} \\ To\text{ find }nthterm, \\ f(n)\text{ = f(n - 1) + 6} \\ \\ \text{When n = 1 } \\ \text{We were given value for f(1)} \\ f(1)\text{ = 1st term = 2} \end{gathered}[/tex]
This is a recursive formula as we will have to find each of term in the table using preceding term:
[tex]\begin{gathered} \text{when n = 2} \\ f(2)\text{ = f(2-1) + 6} \\ f(2)\text{ = f(1) + 6} \\ f(1)\text{ = 2 (given)} \\ f(2)\text{ = 2 + 6 = 8} \\ \text{under f(n), type 8} \end{gathered}[/tex][tex]\begin{gathered} \text{when n =3} \\ f(3)\text{ = f(3-1) + 6} \\ f(3)\text{ = f(2) + 6} \\ f2)=\text{ 8} \\ f(3)\text{ = 8 + 6 = 14} \\ \text{under f(n), type 14} \end{gathered}[/tex][tex]\begin{gathered} \text{when n = 4} \\ f(4)\text{ = f(4-1) + 6} \\ f(4)\text{ = f(3) + 6} \\ f(3)\text{ = 14} \\ f(4)\text{ = 14 + 6 = 20} \\ under\text{ }f(n),\text{ type 20} \end{gathered}[/tex]is 7+25+33=(7+33)+25 true or false
Answer:
True
Step-by-step explanation:
7+25+33=(7+33)+25
Solve Parentheses
7+25+33=40+25
Combine Like Terms
65=65
Answer:
true
Step-by-step explanation:
7+25+33 =(7+33)+25
65=(40)+25
65 =65