Step-by-step explanation:
Let:-
[tex]p = {q}^{r}[/tex]be eqn.1
[tex]q = {r}^{p} [/tex]be eqn.2
[tex]r = {p}^{q} [/tex]be eqn.3
Susbstituting the value of p from eqn.1 to eqn.3 ,
[tex]r = {( {q}^{r} )}^{q} \: = {q}^{qr} [/tex]
Substituting the value of q from eqn.2 to eqn.3 ,
[tex]r = ( { {r}^{p} )}^{qr} = ( {r})^{pqr} [/tex]
[tex] = > {r}^{1} = {r}^{pqr} [/tex]
As bases are same in both the sides of this eqn.
[tex] = > pqr = 1[/tex]
We can easily prove the statement that if [tex]p=q^{r}[/tex], [tex]q = r^{p}[/tex] and [tex]r=p^{q}[/tex] , then pqr=1.
What is exponent?We know that a number's exponent indicates how many times it should be multiplied.
How to solve it?Given that
[tex]p=q^{r}[/tex]
[tex]q = r^{p}[/tex]
Now, [tex]r=p^{q}[/tex]
i.e. [tex]r=(q^{r})^{q}[/tex]
i.e. [tex]r=(q^{qr})[/tex]
i.e. [tex]r=(r^{p})^{rq}[/tex]
i.e. [tex]r=(r^{pqr})[/tex]
i.e. [tex]\frac{r}{r^{pqr}} =1[/tex]
i.e. [tex]r^{1-pqr} =r^{0}[/tex] [Since [tex]a^{0} = 1[/tex], a is any number]
i.e. 1 - pqr = 0
i.e. pqr = 1
We proved our statement that if [tex]p=q^{r}[/tex], [tex]q = r^{p}[/tex] and [tex]r=p^{q}[/tex], then pqr=1.
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write and evaluate an expression for the problem music lessons cost $20 per week. How much do 6 weeks of lessons cost?
The vertices of a triangle are p(3,7) Q(7,-6) R(-8,7). Name the vertices of the image reflected across the x axis
Answer:
P'(3,-7) Q'(7,6) R'(-8,-7).
Step-by-step explanation:
Reflection across the x-axis
Given a point P(x,y), its reflection across the x-axis will map to point P'(x,-y), i.e., the y-coordinate gets inverted.
We are given the vertices of a triangle P(3,7) Q(7,-6) R(-8,7). The vertices of the image reflected across the x-axis are:
P'(3,-7) Q'(7,6) R'(-8,-7).
The new triangle has vertices P'Q'R'.
I need help, please and thank you. I know that you have to multiply the diameter by 2 to find the radius, but with the 9 pi, it makes me unsure if I'm doing this correctly.
Answer:
r=6
Step-by-step explanation:
The area of a circle is given by πr². Note that this uses the radius, not the diameter.
Now, one quarter of this area (ABC) is given to be 9π.
So apparently:
[tex]\frac14 \pi r^2 = 9\pi[/tex]
If you solve this:
[tex]\frac14 r^2 = 9[/tex] (divide both sides by π)
[tex]r^2 = 9\cdot4[/tex] (multiply both sides by 4)
so
r = √36 = 6
so the radius is 6.
DESCRIBE IN WORDS THE TRANSLATION OF x represented by the translation rule <-6,8> (X) A. 6 units to the right and 8 units down B. 6 units to the left and 8 units up C. 8 units to the left and 6 units down D. 6 units to the right and 8 units up
Given:
Translation of x represented by the translation rule <-6,8>.
To find:
The correct statement for the given rule of translation.
Solution:
Rule of translation is <-6,8>.
Here, x-coordinate represents horizontal shift and y-coordinate represents vertical shift.
x-coordinate is -6, which is negative. So, the figure translated 6 units left.
y-coordinate is 8, which is positive. So, the figure translated 8 units up.
Thus, translation in words is defined as "6 units to the left and 8 units up".
Therefore, the correct option is B.
How do i explain this problem
-5 + (+4) =
Answer:
this question is essentially -5 + 4
You could say:
negative 5 plus 4
Just in case you need it, the answer to this problem is -1
May I have brainliest please? :)
What is the slope of the line through (3, 2) and (-3,4)?
Answer:
Choice A. -3
Step-by-step explanation:
Using the x1-x2/ y1-y2 u fill in. So it would be 3-(-3) (x-axis) and 2-4 (y-axis).
So when u do both of those you are left with 6/-2.
When u simplify 6/-2 you get -3.
Answer:
slope is -1/3
Step-by-step explanation:
slope is read rise over run so the line, in this case, fell down 1 and ran 3. Falling means negative so the slope is negative 1 over 3. To easily determine a negative slope, see if the line is moving from top left to bottom right. If so, then it's negative. The other way around is a positive slope.
(i don't do formulas well so I use the graph)
A digram of a swimming pool is shown what is the approximate circumference of the swimming pool use 3.14 as a estimate
Answer:
11 m
Step-by-step explanation:
Answer:
11 m
Step-by-step explanation:
I took the maps testing
f(x) = 10x + 1, g(x) = 10x + 4
Describe the transformation
Answer:
The function is translated 3 units up from its original position.
Step-by-step explanation:
If you look at the equations, nothing is changed besides the + 1 turning into a + 4. What does that mean? Well, if we find the difference between the 4 and the 1 by subtracting, that leaves us with 3. Since the number is positive, this indicates an upward vertical shift.
NEED HELP FAST PLEASE! Match each whole number with a rational, exponential expression.
Answer:
Step-by-step explanation:
1). [tex]((3^2)^{3} )^{\frac{1}{3} }[/tex] = 3² = 9
2). [tex](x^{3} )^{\frac{2}{3} }[/tex] = 4² = 16
3). [tex]((15^{3} )^{\frac{1}{3} } )^{2}[/tex] = 15² = 225
4). [tex]((21^{3} )^{\frac{1}{3} } )^{2}[/tex] = 14² = 196 (Sorry I made a mistake, the base should be 14)
5). [tex](5^{3} )^{\frac{2}{3} }[/tex] = 25
6). ( [tex](16^{3} )^{\frac{1}{3} }[/tex] )² = 256
Ann uses 3/4 cup pecans to make 2 dozen banana muffins. How many cups of pecans would she use to make 5 dozen muffins
Answer:
1[tex]\frac{7}{8}[/tex]cups
Step-by-step explanation:
2 dozen muffins = [tex]\frac{3}{4}[/tex]cups
5 dozen muffins = [tex]\frac{5}{2}[/tex] × [tex]\frac{3}{4}[/tex]cups
= [tex]\frac{15}{8}[/tex]cups
= 1[tex]\frac{7}{8}[/tex]cups
ASAP 30 POINTS PLEASE HELP
Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $17 to produce 2 widgets, $69 to produce 4 widgets, and $417 to produce 10 widgets. Here is the cost function used to represent this situation in terms of the number of widgets produced: c(x) = 4x2 + 2x - 3
Find the total cost of producing 6 widgets.
Answer:
the total cost of producing 6 widgets is $231
3(10)+5x=26
Answer this please!!
Answer:
=
4
-
5
Step-by-step explanation:
Is 700% of 5 less than 10 greater than 10 but less than 100 or greater than 100?
The Tigers’ second play went for +4 1/2 yards. Did the Tigers gain or lose yards on that play? How many yards did they gain or lose?
Answer:
They gained 4 1/2 yards
Step-by-step explanation:
It was a positive gain because they didn't go back.
Answer:
Since the number is positive number they gained 4 1/2 yards
Step-by-step explanation:
hope this helped have a good day :) :)
Bok Sanctuary in Lake Wales, FL, has a carillon tower that is 205 feet tall. Heather made a scale drawing of the tower using the scale 1 inch : 20 feet. In which proportion does h represent the height, in inches, of Heather's scale drawing?
Answer:
10.25 inches
Step-by-step explanation:
Given that:
Actual height of tower = 205 feets
Ratio of scale drawing = 1 inch : 20 feets
The proportion of the height of the scale drawing will be :
Actual height / 20 feets
205 feets / 20 feets
= 10.25 inches
h in inches of the scale drawing will be 10.25 inches
Matthew likes to buy movies from a DVD club. He pays $5 per month
plus $2 per movie. If he buys six movies in June, how much did he pay for the month of June?
Answer:
$17
Step-by-step explanation:
$5
6x$2=$12
$12+$5=$17
A baseball player had 4 hits in 8 games. At this rate, how many hits will the baseball player have in the next 28 games?
Answer: 14 hits
8 divided by 2 = 4 hits
So
28 divides by 2 = 14
Step-by-step explanation:
Answer:
14 hits
Step-by-step explanation:
find unit rate
4:8 = 2:1
2 hits in 1 game
divide 28/2
14
3) At a coffee shop, the price of a cup of coffee increased from $1.20 to $1.44. What is the change? Is it an increase or decrease?
Answer:
$0.22 increase
Step-by-step explanation:
Part A Consider the Similar triangles below :
B 4 6, A, 7, C
Q, 12 , P , R
Find the scale factor :
Part B :
Find the length of side PR
Answer:
scale factor = 2
length of PR = 14
Step-by-step explanation:
i hope this helps
If the graph of the parent function f(x) = x is shifted 7 units down, which of the following equations would the new graphed line represent?
Answer:
Option (2)
Step-by-step explanation:
If a function g(x) is shifted 'a' units downwards then the equation of the transformed function will be,
g(x) = f(x) - a
Similarly, when the parent function is shifted 'a' units upwards, equation of the transformed function will be,
g(x) = f(x) + a
If the parent function is f(x) = x
And the graph of this function is shifted 7 units downwards,
Transformed function will be,
f'(x) = x - 7
Option (2) will be the correct option.
6TH TIME POSTING....
Which algebraic rule describes the translation?
Wont let me copy and paste picture .-.
Cordinates: RUST: R= -4,-1 U= -4,-3 S= -1,-1 T= -1,-3
Cordinates: R'U'S'T': R'= 4,1 U'= 4,3 S'= 1,1 T'= 1,3
Answer:
I wanna say (x,y)→(-x,-y)
Step-by-step explanation:
.
Michael’s employer just switched to a new payroll system. He wants to make sure that his net pay has been computed correctly. His gross pay per pay period is $587.34. He has the following deductions: Social Security tax (6.2%), Medicare tax (1.45%), federal withholding tax $164.45, state withholding tax $76.34, retirement insurance contribution $50.00, disability insurance fee $8.00, medical insurance fee $23.00, and dental insurance fee $8.00. What should his net pay be for this pay period? Net pay = gross pay – deductions.
Answer:
Step-by-step explanation:
$587.34 x 6.2% = $36.42
$587.34 x 1.45% = $8.52
$36.42 + $8.53 + $164.45 + $76.34 + $50 + $8 + $23 + $8 = $374.73
$587.34 - $374.73 = $212.61
Michael's net pay for this pay period should be $212.63.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's calculate Michael's total deductions first:
Social Security tax = 6.2% of $587.34 = $36.40
Medicare tax = 1.45% of $587.34 = $8.52
Federal withholding tax = $164.45
State withholding tax = $76.34
Retirement insurance contribution = $50.00
Disability insurance fee = $8.00
Medical insurance fee = $23.00
Dental insurance fee = $8.00
Total deductions.
= $36.40 + $8.52 + $164.45 + $76.34 + $50.00 + $8.00 + $23.00 + $8.00
Total deductions = $374.71
Now we can calculate Michael's net pay:
Net pay = Gross pay - Total deductions
Net pay = $587.34 - $374.71
Net pay = $212.63
Therefore,
Michael's net pay for this pay period should be $212.63.
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please help im super behind :((
Answer: c = 3/10
Step-by-step explanation:
Answer:
c = 3/10
Step-by-step explanation:
Please get the correct answer for this, and you WILL recieve brainliest, I will know If this is the wrong answer.
Answer:
yes i think they are similar
Step-by-step explanation:
HELP ASAP WILL GIVE BRAINLEST
PLEASE HELP NOW ASAP
HELP
Answer:
x = 45°
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
since the whole angle is a right angle, we know its worth 90 degrees. since the line separates the 90 into two, with one part being 45, we can take 45 away from 90, and get our answer. 90-45=45. so the value of x=45
Help ASAP if you want brainliest, five stars, thanks, and friends list.
The two pics are the same question.
Answer:
Bro all of them are correct
Step-by-step explanation:
Suppose your family is taking a road trip of 120 miles to visit a family member how long would it take to make the trip if you go 40 miles per hour ?
Answer: 3 hours
Step-by-step explanation: 120 miles divided by 40 miles per hour is 3, 3 = how many hours it'll take to get to the destination
At Guevarra Clan Reunion, 4 1/2 kg of spaghetti was left.Lf there are 6 families,how much each family can take home equally.How much each family can take home equally?
Answer:
3/4 kg of sphagetti each
Step-by-step explanation:
The amount each family can take home, if the kg of sphagetti is divided equally is calculated as:
Kg of sphagetti left/Number of families
= 4 1/2kg/6
= 9/2 ÷ 6
= 9/2 × 1/6
= 9/12
= 3/4 kg
Hence, each family can take home 3/4 kg of sphagetti each.
Find the value of 3x 5(2)
Answer:
is it 30?
Step-by-step explanation:
can someone help me answer this? urgent‼️