To solve for h and r in the equation bh + hr = 25, isolate one variable, solve for h using division, and solve for r by expanding the equation. There is no unique solution for h and r in terms of each other.
Explanation:To solve for h and r in the equation bh + hr = 25, we need to isolate one variable on one side of the equation. Let's solve for h first:
bh + hr = 25
Factor out h from the left side of the equation:
h(b + r) = 25
Divide both sides by (b + r) to solve for h:
h = 25 / (b + r)
Now, let's solve for r. Replacing h in the original equation:
bh + hr = 25
b(25 / (b + r)) + r(25 / (b + r)) = 25
Multiply both sides by (b + r) to get rid of the denominators:
25b + 25r = 25(b + r)
Expand the equation:
25b + 25r = 25b + 25r
As we can see, the equation is an identity, meaning any value of r will satisfy it. Therefore, there is no unique solution for r in terms of h, and vice versa.
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Question 2
Find the next term in this arithmetic sequence: 2/3, 2, 3 1/3, ____
4 2/3
3 2/3
4
4 1/3
A large adult elephant weighs 24,000 pounds. A baby elephant, on the other hand, weighs only 260 pounds. How much more does the adult elephant weigh?
24,000 - 260 = 23,740
23,740 + 260 = 24,000
The adult elephant weighs 23,740 more pounds than the baby elephant.
If m∠TRK equal 32.5°, what is m∠TSK?
The measure of angle TSK is 130°, because it is an inscribed angle that intercepts the same arc as angle TRK, and angle TRK is half the measure of the central angle that intercepts the same arc.
The correct answer is option C.
The center of the circle is S, and the measure of angle TRK is 32.5°. We want to find the measure of angle TSK.
We can use the following theorem to solve this problem:
Inscribed Angle Theorem: An inscribed angle is half the measure of the central angle that intercepts the same arc.
In other words, if an angle is inscribed in a circle and intercepts a certain arc, then the measure of that angle is half the measure of the central angle that intercepts the same arc.
In this problem, angle TRK is an inscribed angle that intercepts arc KT. Therefore, the measure of angle TRK is half the measure of the central angle that intercepts arc KT.
Let's call the central angle that intercepts arc KT θ. Since angle TRK measures 32.5°, we know that θ measures 32.5° * 2 = 65°.
Now, we can use the Inscribed Angle Theorem again to find the measure of angle TSK.
Angle TSK is an inscribed angle that intercepts arc KT, and the measure of the central angle that intercepts arc KT is 65°. Therefore, the measure of angle TSK is half the measure of the central angle that intercepts the same arc, which is 65° * 2 = 130°.
The measure of angle TSK is 130° making option C the correct option.
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The question probable may be:
The center of the circle is S. Note: Figure not drawn to scale. If mangle TRK equal 32.5 ° , what is mangle TSK ? A. 32.5 ° B. 65 ° C. 130 ° D. 16.25 °
how do you do this system using the equal values method?
steve saved $2000. he saved $100 in june. what percent of the total amount did her save in june?
8 cakes cost £4.00 how much do three cakes cost
Consider the function y = x^2 − 18x. Enter the values for the variables to complete the inverse
Given the equation:
y = x^2 – 18x
Rewrite in vertex form:
y = x^2 – 18x + (18/2)^2 – (18/2)^2
y = (x – 9)^2 – 81
Swap x and y:
x = (y – 9)^2 – 81
Solve for y:
x + 81 = (y – 9)^2
y – 9 = sqrt (x + 81)
y = sqrt (x + 81) + 9
or
y = (x + 81)^(1/2) + 9
please help with math
Which Greek mathematician wrote the most definitive text on geometry, one that is still referred to today?
a.Thales
b.Pythagoras
c.Euclid
d.Archimedes
e.Hippocrates
Answer:
The correct answer is Euclid.
Step-by-step explanation:
Euclid was a Greek mathematician, who is referred as the father of geometry and founder of geometry.
One of Euclid's most notable work, in the form of 'The Elements' has the strongest fundamental texts on geometry.
Apart from geometry, Euclid also developed many mathematical theories.
Which values of x will make the absolute value equation true?
|x – 4| = 7
A.
{–3, 3}
B.
{–3, 11}
C.
{–11, 11}
D.
no solution
In the game Kazoo, teams lose one point each time they skip a turn. They earn one point each time their team guesses correctly. Maria's team skipped 888 turns. They guessed correctly 666 times.
One number is two less than three times another. if their sum is decreased by one, the result is nine. find the numbers.
Dimitri is paid 8 percent commission on his total sales every pay period. Last pay period, he sold $6,300 worth of items. After a state tax of 6 percent is deducted from his commission, how much is left to the nearest dollar?
Answer:
$ 474 is left.
Step-by-step explanation:
Given,
The amount at which the items are sold = $ 6,300,
Also, commission percentage = 8 %,
Thus, commission = 8% of 6300
[tex]=\frac{8\times 6300}{100}[/tex]
[tex]=\frac{50400}{100}[/tex]
[tex]=\$ 504[/tex]
Now, deducted tax percentage on commission = 6%,
Hence, the left amount of commission = commission - 6% of the commission
[tex]=504-\frac{6\times 504}{100}[/tex]
[tex]=504-\frac{3024}{100}[/tex]
[tex]=504-30.24[/tex]
[tex]=\$ 473.76[/tex]
[tex]\approx \$ 474[/tex]
Which line has a slope of 2?
Why does dividing by a fraction make a number bigger?
A number dividing by a proper fraction always make the number bigger.
What is Fraction?Fractions are a kind of real numbers where we express a number as a part of a whole.
Fractions are of the form p/q, where p is called the numerator and q is called the denominator.
Algebraically speaking when a number is divided by a fraction, then actually the number is getting multiplied by it's reciprocal.
For example [tex]\frac{5}{1/2}[/tex] = 5 × [tex]\frac{2}{1}[/tex] = 10
That is a number when get divided by a proper fraction, operation is changed into the multiplication of the reciprocal.
In other words, we have to find that 5 is divided into how many equal 1/2
parts or 0.5 equal parts. Now, 1/2 part is actually the half part of 1.
Since 1/2 is half part of 1, 1 can be divided into 2 equal 1/2 parts.
We know that 5 when divided into equal 1 parts, we will get 5 parts.
So 5 can be divided into 5 × 2 = 10 equal 1/2 parts.
Hence, dividing by a fraction make a number bigger.
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How do you write 7 to the fourth power in exponential form using exponents?
ou are cycling around Europe with friends.
A famous cycling race is taking part in the north of Spain. You want to travel there from France, but it will take too long by bike. You decide to catch the train.
You need to take 2 trains to get to Spain. On one website the first train will cost £64.98 and the second train will cost £32.88. There is also a £6.99 charge for cycle storage for the whole trip.
How much would the journey cost you?
She could tell of the Crows, who she had never seen, and of the Black Hills, where she had never been. I wanted to see in reality what she had seen more perfectly in the mind’s eye... Which tone is conveyed by the language in this excerpt? a sense of respect for Aho misgivings about the future spiritual longing for the past disinterest in the present
Answer:
A sense of respect for Aho.
Explanation:
In N. Scott Momaday's memoir "The Way To Rainy Mountain", he narrates how he embarked on rediscovering his Kiowa heritage and the importance of preserving one's cultural background. Momaday uses a semi- autobiographical form of writing in providing the history and migration of the Kiowa people from their initial residence in Montana to Oklahoma.
In the given passage, the narrator is talking about his grandmother Aho who perfectly remembers the "Crows, who gave them the culture and religion of the Plains". But she was never a part of those who traveled, but rather the stories told by her forefathers. Her ability to remember and preserve those memories as if she had personally experienced them impressed the narrator, who have a huge respect for her. Her memory of the "crows,.... and the Black Hills where she had never been" shows how she values the stories and tales of her own forefathers and the culture and heritage of the Kiowa people as a whole.
HELP PLEASE THANKS!!!!!
Solve the following inequality.
-2/3x>8
A) x < - 4
B) x > - 4
C) x > -12
D) x < -12
A color printer prints 9 pages in 3 minutes. how many minutes does it take per page
Final answer:
To calculate time per page, divide the total printing time by the number of pages. A printer that prints 9 pages in 3 minutes takes approximately 0.333 minutes (or 20 seconds) to print one page.
Explanation:
The question is asking us to calculate the time it takes for a color printer to print one single page. To find this, we need to divide the total time taken to print multiple pages by the number of pages printed. So, if a printer prints 9 pages in 3 minutes, we can calculate the time per page as follows:
First, identify the total time taken for printing multiple pages, which is 3 minutes for 9 pages.
Divide the total minutes by the number of pages to get the time per page. In this instance, it would be 3 minutes ÷ 9 pages.
Perform the division to find the time it takes to print one page. 3 minutes ÷ 9 pages = 0.333... minutes per page.
Therefore, it takes approximately 0.333 minutes (or 20 seconds) for the color printer to print one page.
Consider the equation 2y−5x=30 . Determine the x-intercept
2 ⋅
−5x=30
−5x=30
=30
x=
The x-intercept for the equation 2y - 5x = 30 is found when y is set to zero and the equation is solved, resulting in the x-intercept being -6.
Explanation:To find the x-intercept of a given equation, you need to set y equal to zero and solve for x. So, for the equation 2y - 5x = 30, you set y = 0 which leads to the adjusted equation of -5x = 30
To isolate x, you should divide both sides of the equation by -5, which gives x = -6. Therefore, the x-intercept of the equation 2y - 5x = 30 is -6.
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if y+1 is an even integer, what is the next consecutive even integer?
The next consecutive even integer will be y + 3
What is Arithmetic Progression?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.
The nth term of an AP is given be aₙ = a₁ + ( n - 1 ) d
where a₁ = first term
d = common difference between terms
Given data ,
y + 1 = even integer
The next consecutive even integer can be calculated by adding 2 because the difference between two consecutive even or odd integers is always two.
Therefore , y + 1 + 2 = y + 3
Hence , the next consecutive even integer will be y + 3
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The volume of a box with a square base can be written as V = s² x h where V is the volume, s is one side of the square base, and h is the height. Find the volume of a rectangular prism where s = 6 cm and h = 9 cm.
A.108 cm³
B.54 cm³
C.486 cm³
D.324 cm³
What is the inverse of the following statement? If at first you don’t succeed, try, try again. Select the best answer from the choices provided. If you try, try again, then you did not succeed at first. If at first you succeed, then do not try, try again. If you don’t try, try again, then you succeeded at first. Try, try again if at first you don’t succeed. NextReset
Answer:
Try, Try again if at first you dont
exceed
Step-by-step explanation:
Right triangle ABC is shown.
a to c is 3m
c to b is a
b to a is c and ab is 50 degrees
Which equation can be used to solve for c?
sin(50o) =
sin(50o) =
cos(50o) =
cos(50o) =
Answer:
The required equation which can be used to solve for the value of c is given by :
[tex]\bf\sin 50=\frac{3}{c}[/tex]
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
AC = 3 meter
CB = a meter
BA = c meter
m∠ABC = 50°
Now, to find the value of c.
In right angle triangle right angled at C, we need to find the length of hypotenuse, so using the sine rule in the ΔABC
[tex]\implies \sin\theta=\frac{Perpendicular}{Hypotenuse}\\\\\implies \sin 50=\frac{3}{c}[/tex]
Hence, the required equation which can be used to solve for the value of c is given by :
[tex]\bf\sin 50=\frac{3}{c}[/tex]
The product of 3 and a number subtracted from 16 is 7. Find the number.
Can you find the missing angle measurements
y=9x+4 is translated 4 units , what would be the equation on a graph?
Evi what to make to pottery she needs 3/5 pounds of clay for one piece and 7/10 Pound of clay for the other piece she has three bags of clay that wiegh 4/5 pound each.how many bags of clay will Eva need to make both pieces of pottery?How many pounds of clay will she have left over ?