Answer:
y = -1
Step-by-step explanation:
You want the solution to -12 = 12y^97.
SolutionThe one real solution is can be found by ...
-1 = y^97 . . . . divide by 12
y = (-1)^(1/97) = -1
The value of y is -1.
__
Additional comment
There are 96 complex solutions to this equation as well.
They are y = cos(nπ/97) +i·sin(nπ/97) . . . . for integer n = 0 .. 96.
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4.5x + 5 = (if x = 4)
Answer:
23
Step-by-step explanation:
A file that is 273 megabytes is being downloaded. If the download is 15.6% complete, how many megabytes have been downloaded? round your answer to the nearest tenth.
1750 megabytes has been downloaded.
What do you mean by percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'.Percentages have no dimension. Hence it is called a dimensionless number.
It is given that 273 megabytes has been downloaded and it is 15.6% of complete.
Let x be the complete storage
15.6% of x = (15.6/100) × x
(15.6/100) × x = 273
x = (273/15.6) × 100 = 2730/15.6 = 1750
Therefore, 1750 megabytes has been downloaded.
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GG is considering two websites for downloading music. The costs are detailed here.
Website 1: a yearly fee of $15 and $5 for each download
Website 2: $7 for each download
Select the equation for Website 1.
Responses
y=15x+5
y=5x+15
y=−7x
y=7x
The equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
GG is considering two websites for downloading music.
Website 1: a yearly fee of $15 and $5 for each download
Let x be the number of downloads
Equation for the website 1:
Total cost is y
y = 15 + 5x
Thus, the equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
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Nate's age is six years more than twice Connor's age. If the sum of their ages is 24 find each age
Answer:
12
Step-by-step explanation:
nate's age=6
connor's age =6+6=12
Nate's age +connor's age =24
Nate's age=24÷3=8
connor's age=8+8=16
the sum of thier ages =24
ow 3. Hto What is the surface area of this triangular prism? 15 in. 12 in. 7 21 in 18 in. A. 846 in. B. 909 in. C. 1,062 in. D. 1,224 in. 2
To obtain the surface area of a triangular prism, the formula to employ is:
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ \text{where A}_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where s=}\frac{a+b+c}{2} \\ a,b\text{ and c are sides of the triangular prism and h is the height} \end{gathered}[/tex]From the image, a=18in, b=21in, c =15in and h=12in
We have to obtain the value of 's' first, from the equation:
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{18+21+15}{2} \\ s=\frac{54}{2} \\ s=27in \end{gathered}[/tex][tex]\begin{gathered} \text{Then, we obtain the value of A}_B \\ A_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A_B=\sqrt[]{27(27-18)(27-21)(27-15)} \\ A_B=\sqrt[]{27(9)(6)(12)} \\ A_B=\sqrt[]{17496} \\ A_B=132.27in^2 \end{gathered}[/tex]The final step is to obtain the area of the triangular, having gotten the values needed to be inputted in the formula;
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ A_{triangular\text{ prism}}=(2\times132.27)+(18+21+15)12 \\ A_{triangular\text{ prism}}=264.54+(54)12 \\ A_{triangular\text{ prism}}=264.54+648 \\ A_{triangular\text{ prism}}=912.54in^2 \end{gathered}[/tex]Hence, the surface area of the triangular prism is 912.54 square inches
There is a population of 205 tigers in a national park. They are being illegally poached at the rate of 7tigers per year.Assume the population is otherwise unchanging, write a linear model using "P" for population and "t" fortime.What does the t-intercept signify?NOTE: This answer will NOT be automatically graded and will appear as a 0 until the instructor hasgraded it.Question Help: Message instructorSubmit Question
Solution.
Initial population = 205
After 1 year, population = 205 - 7 = 198
After 2 years , population = 198 - 7 = 191
After 3 years , population = 191 - 7 = 184
We can generate a table of value for the changes
[tex]\begin{gathered} Slope\text{ of the line, m = }\frac{198-205}{1-0} \\ m=-\frac{7}{1} \\ m=-7 \end{gathered}[/tex]One point on the line = (0, 205)
[tex]\begin{gathered} The\text{ equation of the linear model can be gotten using the formula} \\ y-y_1=m(x-x_1) \\ y-205=-7(x-0) \\ y-205=-7x \\ y=-7x+205 \\ Replacing\text{ y with P and x with t} \\ The\text{ linear model is P = -7t + 205} \end{gathered}[/tex]The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park
Answer:
Step-by-step explanation:
bbbbbbbbbbb
I NEED HELP WITH THIS
Answer:
see explanation
Step-by-step explanation:
given that W varies jointly with l and d² then the equation relating them is
W = kld² ← k is the constant of variation
(a)
to find k use the condition W = 6 when l = 6 and d = 3 , then
6 = k × 6 × 3² = 6k × 9 = 54k ( divide both sides by 54 )
[tex]\frac{6}{54}[/tex] = k , then
k = [tex]\frac{1}{9}[/tex]
W = [tex]\frac{1}{9}[/tex]ld² ← equation of variation
(b)
when W = 10 and d = 2 , then
10 = [tex]\frac{1}{9}[/tex] × l × 2² ( multiply both sides by 9 to clear the fraction )
90 = 4l ( divide both sides by 4 )
22.5 = l
(c)
when d = 6 and l = 1.4 , then
W = [tex]\frac{1}{9}[/tex] × 1.4 × 6² = [tex]\frac{1}{9}[/tex] × 1.4 × 36 = 1.4 × 4 = 5.6
George shot the basketball 20 times in his game on Saturday. Of those 20 shots, he made 15.
What percentage of the shots did George make?
George made 75 percent of the shots.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
We are given the following:
George shot the basketball 20 times in his game on Saturday.
Of those 20 shots, he made 15.
We need to find the percentage of the shots George made.
The percentage of shots George made is given by:
Percentage = 15 / 20 * 100 = 15 * 5 = 75 %
So, 75 % of the shots did George make.
Thus, George made 75 percent of the shots.
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Given AABC with vertices A(7, 7) B(-5, 3) and C(3,-5),
1) If BE is a median, then point E is located at what coordinate?
2) If AL is a median, at what coordinate would L be located?
3) If LP is a perpendicular bisector, what would be the slope of LP?
4) An altitude is always.
to the side of the triangle.
ABC's vertices are points A, B, and C. ABC's sides are made up of the AB, BC, and CA segments.
How to calculate vertices of ABC?Determine the length of the median across vertex A of triangle ABC, which has vertices A (7,3), B (5,3), and C.
Assume M(x,y) represents the ABC median from A to BC.
M will be the point at which BC splits in half.
x 1 =5, y1 =3
x 2 =3,y2 =−1
Using the midpoint formula, x=(x 1 + x 2)/2
∴x=(5+3)/2=8/2=4
Using the midpoint formula, y=(y 1 + y 2 )/2
∴y=(3+(−2))/2=2/2=1
Consequently, M's coordinates are (4,1).
The distance formula reads d(AM)=
By distance formula, d(AM)= √[(x2 - x1)² + (y2 -y1)²]
x1 = 7,y1 = -3
x2 = 4,y2 = 1
∴d(AM) = √[(4- 7)² + (1 - (-3)²]
∴d(AM) = √(-3)² + (4)² = √9 + 16
∴d(AM) = √25 = 5
As a result, the median AM is 5 units long.
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can someone help and explain how to do this. Ive been stuck in this lesson for days. This is so confusing and hard.
Divide f(x) = x^3 - x^2 - 2x + 8 by (x-1) then find f(1)
Division of f(x) = x³ - x² - 2x + 8 by (x-1) will have a quotient of x² - 2 and a remainder of 6.
What is the remainder theoremThe remainder theorem states that if f(x) is divides by x - a, the remainder is f(a).
We shall divide the f(x) = x³ - x² - 2x + 8 by x - 1 as follows;
x³ divided by x equals x²
x - 1 multiplied by x² equals x³ - x²
subtract x³ - x² from x³ - x² - 2x + 8 will result to -2x + 8.
-2x² divided by x equals -2
x - 1 multiplied by -2 equals -2x + 2
subtract -2x + 2 from -2x + 8 will result to a remainder of 6, and a quotient of x² - 2.
f(1) = (1)³ - (1)² - 2(1) + 8
f(1) = 1 - 1 - 2 + 8
f(1) = 6
Therefore, f(1) is a remainder of as x - 1 divides f(x) = x³ - x² - 2x + 8 resulting to a quotient of x² - 2 and a remainder of 6
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Joe borrowed $9,000 from the bank at a rate of 7% simple interest pa year. How much interest did he pay in 5 years? In 5 years, Joe pays ? In Interest
Principal = 9000
Interest rate = 7% = 0.07
Time = 5 years
Simple interest formula:
A = P(1 + rt)
In this case:
A = 9000(1 + 0.07*5) = 9000(1 + 0.35) = 9000(1.35) = 12150
Interest = A - P = 12150 - 9000 = 3
two cards are drawn without replacement from a standard deck of 52 playing cards what is the probability of choosing a club and then without replacement a spade
occurringGiven a total of 52 playing cards, comprising of Club, Spade, Heart, and Spade.
[tex]\begin{gathered} n(\text{club) = 13} \\ n(\text{spade) =13} \\ n(\text{Heart) = 13} \\ n(Diamond)=\text{ 13} \\ \text{Total = 52} \end{gathered}[/tex]Probability of an event is given as
[tex]Pr=\frac{Number\text{ of }desirable\text{ outcome}}{Number\text{ of total outcome}}[/tex]Probability of choosing a club is evaluated as
[tex]\begin{gathered} Pr(\text{club) = }\frac{Number\text{ of club cards}}{Total\text{ number of playing cards}} \\ Pr(\text{club)}=\frac{13}{52}=\frac{1}{4} \\ \Rightarrow Pr(\text{club) = }\frac{1}{4} \end{gathered}[/tex]Probability of choosing a spade, without replacement
[tex]\begin{gathered} Pr(\text{spade without replacement})\text{ = }\frac{Number\text{ of spade cards}}{Total\text{ number of playing cards - 1}} \\ =\frac{13}{51} \\ \Rightarrow Pr(\text{spade without replacement})=\frac{13}{51} \end{gathered}[/tex]Thus, the probability of both events occuring (choosing a club, and then without replacement a spade) is given as
[tex]\begin{gathered} Pr(\text{club) }\times\text{ }Pr(\text{spade without replacement}) \\ =\frac{1}{4}\text{ }\times\text{ }\frac{13}{51} \\ =\frac{13}{204} \end{gathered}[/tex]Hence, the probability of choosing a club, and then without replacement a spade is
[tex]\frac{13}{204}[/tex]Logarithm 6) If log 5 = A and log 3 = B, find the following in terms of A and B:
Given the following parameters:
log 5 = A
log 3 = B
According to the law of product and quotient of logarithm as shown:
[tex]\begin{gathered} \log AB=\log A+\log B \\ \log (\frac{A}{B})=\log A-\log B \\ \log A^b=b\log A \end{gathered}[/tex]Applying the laws of logarithm in solving the given logarithm
[tex]\begin{gathered} a)\log 15 \\ =\log (5\times3) \\ =\log 5+\log 3 \\ =A+B \end{gathered}[/tex]For the expression log(25/3)
[tex]\begin{gathered} b)\log (\frac{25}{3}) \\ =\log (\frac{5^2}{3}) \\ =\log 5^2-\log 3 \\ =2\log 5-\log 3 \\ =2A-B \end{gathered}[/tex]For the expression log135
[tex]\begin{gathered} \log (135) \\ =\log (5\times27) \\ =\log (5^{}\times3^3) \\ =\log 5^{}+\log 3^3 \\ =\log 5+3\log 3 \\ =A+3B \end{gathered}[/tex]For the expression log₅27
[tex]\begin{gathered} \log _527 \\ =\frac{\log 27}{\log 5} \\ =\frac{\log 3^3}{\log 5} \\ =\frac{3\log 3}{\log 5} \\ =\frac{3B}{A} \end{gathered}[/tex]For the expression log₉625
[tex]\begin{gathered} \log _9625 \\ =\frac{\log 625}{\log 9} \\ =\frac{\log 5^4}{\log 3^2} \\ =\frac{4\log 5}{2\log 3} \\ =\frac{\cancel{4}^2A}{\cancel{2}B} \\ =\frac{2A}{B} \end{gathered}[/tex]For the value of 15, this can be expressed as shown. Since:
[tex]\begin{gathered} \log 5=A;10^A=5 \\ \log 3=B;10^B=3^{} \end{gathered}[/tex]Since 15 = 5 × 3, writing it in terms of A and B will be expressed as:
[tex]\begin{gathered} 15=5\times3 \\ 15=10^A\times10^B \\ 15=10^{A+B} \end{gathered}[/tex]Please help quickly
The equation of the function in standard form is y = 3x -12.
How to write the equation of a function in a standard form when two points are given?
1. First find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁)
2. Find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
3. Write the equation using the slope and y-intercept.
Here, we have
Points (2,-6) and (5, 3)
First we find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁), we get
m = (3 + 6) / (5 - 2)
m = 3
then, we find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
we get,
-6 = 3*2 + b
-6 - 6 = b
b = 12
Now, we write the equation using the slope and y-intercept
we get,
y = mx + b
y = 3x - 12
Hence, the equation of the function in standard form is y = 3x -12.
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Kyle can wash the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
Step-by-step explanation:
Kyle can do in 1 minute 1/30 of the work.
Michael can do in 1 minute 1/40 of the work.
the whole work is 1.
how much can they do together in 16 minutes ?
16×1/30 + 16×1/40 = 8/15 + 2/5 = 8/15 + 3/3 × 2/5 =
= 8/15 + 6/15 = 14/15
which is less than 1 = 15/15.
so, as they cannot even do the whole work in 16 minutes, they cannot do it in less than 16 minutes either.
Isabelle read a total of 20 books over 2 months. If Isabelle has read 30 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
Answer: she has been in book club for 3 months
Step-by-step explanation:
The reason is that she can read 10 books in one months than you would multiply it by three.
Answer:
3 months
Step-by-step explanation:
20:2/2=
10:1
10:1 x 3 = 30:3
30 books= 3 months.
How do you do it further problems.1. Find the Unit Rate2. Find the scale factor.3. Use the scale factor to get your answer.Find an equation of the line that satisfies the conditionPasses through (-1,-3) and (4,2)
The points given are:
(-1, -3) and (4, 2)
Coordinates are:
x₁ =-1 y₁=-3 x₂ = 4 y₂ = 2
First, let's find the slope(m) of the equation using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{2+3}{4+1}=\frac{5}{5}=1[/tex]Next, find the inetercept of the equation by substituting x =-1 y=-3 m = 1 into y=mx+ b
-3 = 1(-1) + b
-4 = -1 + b
Add 1 to bothside
-4+1 = b
-3 = b
b = -3
We can now form the equation of the line by simply substituting the value of m and b into y=mx+ b
y = x - 3
Therefore, the equation of the line that satisfies the condition is y = x - 3
Select the correct difference.-325 - (-725)4 z4 25-10 25-45
Given:
-325 - (-725)
We know that negative negative equals positive
(- -) = +
Therefore, we have:
-325 - (-725)
= -325 - -725
= -325 + 725 = 400
ANSWER:
400
PLEASE HELP WILL GIVE BRAINLIEST URGENTTTTT. AM I RIGHT?
Answer 3rd one
Step-by-step explanation:
For the expression, which of the following is the coefficient of the term involving the variable x. x^3/2 + 4y + 5z²1. 3/22. 23. 34. 1/2
Given the expression:
[tex]\text{ }\frac{x^3}{2}+4y+5z^2[/tex]The term that involves the variable x is x^3/2.
Let's determine its coefficient:
[tex]\text{ }\frac{x^3}{2}\text{ = }\frac{1}{2}x^3[/tex]Therefore, the coefficient of the term that involves the variable x is 1/2.
Which of the following lines is not perpendicular to y = –1.5x + 11?A. y =2/3x + 5B. 3y = 2x – 9C. 2y = 3x + 10D. –2x + 3y = 7
B. 3y = 2x – 9
is not perpendicular to the given line.
Explanation:The slopes of perpendicular lines are negative reciprocals
Given the line
y = -1.5x + 11
The slope is -1.5 or -3/2
Any line perpendicular to the one above must have its slope as 2/3
A. The slope is 2/3 . CORRECT
B. The slope is 2/3. CORRECT
C. The slope is 3/2. WRONG
D. The slope is 2/3. CORRECT
Factorise 49n^3 -- 25m^3
Factorization of 49n^3 -- 25m^3 is (5m + 7n) × (5m - 7n)
A difference of two perfect squares, A2 - B2 can be factored into (A+B×(A-B)
(A+B) • (A-B)
= A2 - AB + BA - B2
= A2 - AB + AB - B2
= A2 - B2
AB = BA is the commutative property of multiplication.
- AB + AB equals zero and is therefore eliminated from the expression.
⇒ 25 is the square of 5
⇒ 49 is the square of 7
⇒ m2 is the square of m1
⇒ n2 is the square of n1
Hence, The Factorization is (5m + 7n) × (5m - 7n)
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Determine the range of the following graph:
Answer:
R: {y | -11 ≤ y < 11}
Step-by-step explanation:
Range is going to include the possible output values in regards to the Y-axis on the graph. As far as when to use equal to and not, the open circle means it does NOT include that number, since the circle is not colored in on that number, while the full circle DOES include that number, and that is when you would introduce the equal than.
Hope this helps.
Radiation machines used to treat tumors produce an intensity of radiation that variesinversely as the square of the distance from the machine. At 3 meters, the radiationintensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.6 meters?The intensity is(Round to the nearest tenth as needed.)
Answer: Intenisy = 83.2 milliroentgens per hour
Let the intensity from the radiation = I
Let the distance = d
The intensity is inversely proportional to the square of its distance
[tex]\begin{gathered} I\text{ }\propto\text{ }\frac{1}{d^2} \\ \text{Introducing a proportionality constant} \\ I\text{ = }\frac{k\text{ x 1}}{d^2} \\ I\text{ = }\frac{k}{d^2} \\ \text{When I = 62.5 , d = 3} \\ \text{From the above equation} \\ K=I\cdot d^2 \\ K\text{ = 62.5 }\cdot(3)^2 \\ K\text{ = 62.5 x 9} \\ K\text{ = 562.5 } \\ \text{ Find the intensity wen D = 2.6 meters} \\ I\text{ = }\frac{k}{d^2} \\ I\text{ = }\frac{562.5}{(2.6)^2} \\ I\text{ = }\frac{562.5}{6.76} \\ I\text{ = 83. 2 milliroentgens per our} \end{gathered}[/tex]Directions: Find the missing number in each question, then identify the property used.4. 10* ( 2 + 6 )= ( 10 * 2 ) + ( 10 * x )
Answer:
The missing number: 6
The property used: Distributive Property of Multiplication
Explanation:
Given the below;
[tex]10\cdot(2+6)=(10\cdot2)+(10\cdot x)[/tex]The below shows an example of the distributive property of multiplication;
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Applying the distributive property in the given equation, we can see that;
[tex]x=6[/tex]So the missing number is 6 and the equation can be written as;
[tex]10*(2+6)=(10\cdot2)+(10\cdot6)[/tex]calculate the average speed of a lion that runs 45 m in 5 seconds
Answer:
9 m /s
Step-by-step explanation:
To find the speed, take the distance and divide by the time
45 m/ 5 s
9 m /s
Answer:
[tex] \sf9ms ^{ - 1} [/tex]
Step-by-step explanation:
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time}[/tex]
Let us find the average speed now.
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time} \\ \sf \: Average \: speed = \frac{ 45m }{5s} \\ \sf \: Average \: speed = 9ms ^{ - 1} [/tex]
Write the equation in standard form for the circle passing through (-7,7) centered at theorigin.
Step 1
State the equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h= -7
k= 7
Step 2
Find r
r is the distance between the origin and (-7,7)
Distance between 2 points is
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}}[/tex][tex]\begin{gathered} \text{where} \\ x_2=0 \\ x_1=-7 \\ y_2=0 \\ y_1=7 \end{gathered}[/tex]Hence the distance is given as
[tex]\begin{gathered} d=\sqrt[]{(0-(-7))^2+(0-7)^2} \\ d\text{ =}\sqrt[]{49+49} \\ d=\sqrt[]{98} \\ d=7\sqrt[]{2} \end{gathered}[/tex]Hence r =7√2
Step 3
Write the equation in standard form after substitution.
[tex]\begin{gathered} (x-(-7))^2+(y-7)^2=(7\sqrt[]{2})^2 \\ (x+7)^2+(y-7)^2=(7\sqrt[]{2})^2 \end{gathered}[/tex](A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?
To solve this problem, we have to use the combination formula
[tex]C^r_n=\frac{n!}{r!(n-r)!}[/tex]Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have
[tex]C^2_8=\frac{8!}{2!(8-2)!}=\frac{8!}{2!(6)!}[/tex]Remember that factorials are solved by multiplying the number in a reversal way, as follows
[tex]C^2_8=\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(2\cdot1)(6\cdot5\cdot4\cdot3\cdot2\cdot1)}=\frac{40,320}{2(720)}=\frac{40,320}{1,440}=28[/tex]Therefore, there are 28 ways to form a 2-person subcommittee from a committee of 8.Math To Do, -ReadyHome Jefferson County School X+/student/dashboard/homeWhich unit would you most likely use to measure the capacity of a mug?
Although both fluid ounces and quarts are measurements for volume, the mug would be a very small fraction of a quart.
Thereby, the most likely unit of measurement used for the capacity of a mug would be fluid ounces.