Answers
We can see here that simplifying, we have:
a. h²
b. h³
c. 1/(1 + h)
d. 3h
e. 3h/(64 + 4h)
f. h/(4h + 2h²)
What is simplification?Simplification is the process of reducing something to its most basic form or removing any unnecessary complexity.
In mathematics, simplification is often used to make equations or expressions easier to work with, solve, or understand. This can involve combining like terms, cancelling out common factors, or using rules of exponents and logarithms to simplify an expression.
We see here that the below gives us the workings:
a. (5 + h)³ - 125/ h = h³ + 5³ - 125/h = h²
b. [tex]\frac{(3 + h)^{4} - 81 }{h} =\frac{ 3^{4} + h^{4} - 81}{h} = \frac{ h^{4} + 81 - 81}{h} = h^{3}[/tex]
c. (1/1+h) - 1/h = 1/1+h - 1 ÷ h = 1/1+h
d. 3(1 + h)² -3/h = 3h² + 3 - 3/h = 3h²/h = 3h
e. [(3/4+h) - 3/4]/4 = (3/4+h - 3/4) ÷ 4 = 3h/64+4h
f. (-1 + 2 + h) + 1/2 ÷ h = h/4 + 2h × 1/h = h/4h + 2h²
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Related Questions
2. Sam spent $15 at an art store on paints, brushes, and paper. The paints cost $7.75 and the
brushes cost $3. Write and solve an equation you could use to find how much Sam spent on
paper.
Answers
15
-7.75
-3
=4.25
Find the number of ways to arrange the letters in HEDGEHOG.
There are blank ways to arrange the letters in HEDGEHOG.
Answers
Answer:
Step-by-step explanation:
The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.
The total number of arrangements of the eight letters is 8!:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
The number of arrangements of H's is 2!:
2! = 2 x 1 = 2
The number of arrangements of E's is 3!:
3! = 3 x 2 x 1 = 6
So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:
40320 / (2 x 6) = 40320 / 12 = 3360.
Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".
13. Interpret the IQR and median in the context of the data set.
Answers
The interquartile range is 4 and the median is 27.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. On a box plot, the interquartile range is the difference between the first line and the third line on the box.
Interquartile range = 28 - 24 =4
Median is the central value of a data set. On a box plot, the median is the second line on the box.
The median is 27.
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet of water weigh in pounds? In tons?
Answers
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
PLSSS HELP ME DUE TODAY!!!
Meg is heading back to her car after a hike to Misty Falls. The waterfall is at an elevation of 4,000 feet, and the trail descends an average of 500 feet for every 1 mile she hikes. You can use a function to approximate Meg's elevation after she hikes x miles.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.
Answers
Step-by-step explanation:
Since every single mile it descends the same amount (which is 500ft), that means it's linear, so we'll use that they gave us, the h(x) = mx+b
To find m, we use the following equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
to find b, we have to find out the starting point. luckily they gave it to us, which is 4,000ft. B = 4000
Now every 500 feet, we go down 1 mile
Which means at 1000 feet, we go down 2 miles
500 and 1000 can be our y1 and y2
1 and 2 can be our x1 and x2
[tex] \frac{1000 - 500}{2 - 1} = \frac{500}{1} = 500 = m[/tex]
Now that we have our m and b, we just put it together
[tex]h(x) = - 500x + 4000[/tex]
A negative was placed before the 500 because they are descending, not ascending.
In the diagram, RSTU~ ABCD. Find the ratio of their perimeters.
U
R
18 S
36
T
D
A
24
The ratio of their perimeters is
B
C
Answers
Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.
Since UR = 18 and DA = 24, k = 24/18 = 4/3.
So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.
Now that we have the lengths of all sides of ABCD, we can find its perimeter:
Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC
Perimeter of RSTU = 18 + 36 + 18 + 36 = 108
So the ratio of their perimeters is:
Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108
Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:
20/18 + BC/108 = 4/3
Solving for BC:
BC = (4/3 - 20/18) * 108 = 36
Step-by-step explanation:
Over the last 3 evenings, Laura received a total of 68 phone calls at the call center. The third evening, she received 2 times as many calls as the first evening. The first evening, she received 8 more calls than the second evening. How many phone calls did she receive each evening?
Answers
On first evening she receives 19 calls and on second evening she receives 11 calls while on 3rd evening she receives 38 calls.
What is equation?A mathematical equation is a fοrmula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences oοn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol, fοr instance, 2x – 4 = 2.
X, Y, and Z represents the 1st , 2nd, and 3rd evenings
X + Y + Z = 68
⇒ X = Y + 8
⇒ Z = 2(Y + 8)
⇒ Y + Y + 8 + 2(Y + 8) = 68
Y = 11 calls
And
X = (11)+ 8 = 19 calls
Z = 2((11) + 8) = 38 calls
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Jim takes a counter at random from a bag containing 10 counters, numbered
1, 2, ..., 10.
Lyn throws an ordinary dice.
ind the probability that
Jim and Lyn both get a 3
Answers
The probability both get a 3 is 1/60
How to determine the probability both get 3From the question, we have the following parameters that can be used in our computation:
Jim = 1 to 10
Lyn = 1 to 6
Using the above as a guide, we have the following:
P(Jim = 3) = 1/10
P(Lyn= 3) = 1/6
Using the above as a guide, we have the following:
Required probability = 1/10 * 1/6
Evaluate the product
Required probability = 1/60
Hence, the probabilty is 1/60
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Kara earns 9.75 per hour plus 15.50 in tips each night. If she works for 5 2/5 hours four nights this week how much money will she earn
Answers
Answer: $272.60
Step-by-step explanation:
9.75x5.4= 52.65
52.65+15.50=68.15
68.15x4=272.6
a toy manufacturer needs a piece of plastic in the shape of a right triangle with one leg 5 cm longer than the other and the hypotenuse 10 cm longer than the shorter leg. what is the perimeter of the triangle
Answers
The triangle's perimeter is roughly 25.29 cm.
In arithmetic, what is perimeter?The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.
Let's call the right triangle's shorter leg "x" for short.
The longer leg is then 5 cm longer than x, or x + 5, according to the situation.
The hypotenuse measures x + 10 cm longer than x.
By the Pythagorean theorem, we know that:
x² + (x+5)² = (x+10)²
Expanding and simplifying this equation gives:
2x² + 10x - 75 = 0
Dividing both sides by 2 gives:
x² + 5x - 37.5 = 0
We can find the value of x by using the quadratic formula:
x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2
x = (-5 ± sqrt(175)) / 2
x ≈ -8.68 or x ≈ 3.43
Since x represents a length, we must choose the positive solution x = 3.43 cm.
Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:
3.43 + 8.43 + 13.43 = 25.29 cm
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Write a story that could represent this math problem. (2 points)
Answers
If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?
I believe that is what type of story you needed, if wrong let me know.
Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6
Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.
for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.
The answer after multiplying it is 6/24 or 1/4.
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Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y2 = x, x = 3y; about the y-axis V=
Answers
The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.
We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of
y² = x, x = 3y.
=> x = 3y --(1)
=> y² = 3y
=> y² - 3y = 0
=> y( y - 3 ) = 0
=> y = 0 or y - 3 = 0
=> y = 0 , y = 3
from (1), x = 3y => x = 0, x = 9
Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is
[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]
where R = 3y , r = y²
[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]
[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]
[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]
[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]
[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]
Hence, the required volume is 162π/5 cubic units.
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Ramesh ran at a speed of 7 km/h for 3 h. He then 2 He took 6 h altogether to complete the whole journe (a) Find the total distance that Ramesh ran. (b) Find his average running speed for the whole j a mixed number in its simplest form.
Answers
Find the total distance that Ramesh ran is 23km. His average running speed for the whole journey is 3 5/6 km/h.
How to calculate Ramesh Total distance and average running speedTo find the average speed,
We find the total distance and divide it by the total time.
During the first part of the run, she ran 3 hours at a speed of 7 km/h.
To find the the distance she ran, multiply the speed times the time: 3 x 7 = 21 km.
From the second part of the run, she ran 2km.
So the total distance he ran is 21 + 2 = 23km.
The total time was 6 hours.
To find the the average speed;
Divide 23 by 6 to get the average speed, which comes to 3 5/6 km/h.
hence, the average speed is 3 5/6 km/h.
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I need the first one
Answers
Answer:
∠1 = ∠2 = 135
Step-by-step explanation:
We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180° = 3 x 180°= 540°. Hence, the sum of interior angles of a pentagon is 540°.
so ∠1 + ∠2 + 3(90°) = 540°
since ∠1 = ∠2
∠1 + ∠1 + 3(90) = 540
2∠1 + 270 = 540
2∠1 = 540 - 270
2∠1 = 270
∠1 = 270/2 = 135
Find the total area of the shaded region. Ay 1.5- 14 x=5y3 (5,1) * = 5y? 0.5- х 07 0 2.5 5 7.5 Find the area of the region enclosed by the curves x= x = 7y?, x=0, and y=1. The area of the region enclosed by the curves is (Type a simplified fraction.)
Answers
The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).
From the attached graph :
The area of the shaded region :
x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :
= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]
= [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]
Substitute the lower limit and upper limit we get,
= (5 /3 )( 1 )³ - 0 - ( 5 / 4 )( 1⁴) + 0
= ( 5 / 3 ) - ( 5 / 4 )
= ( 20 - 15 ) / 12
= 5 / 12
Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .
The given question is incomplete, I answer the question in general according to my knowledge:
Find the total area of the shaded region x = 5y³ , x = 5y² for the interval
( 5, 1 ).
Graph is attached.
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What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?
A number line goes from negative 5 to 10. Point D is at negative 4 and point F is at 9. A line is drawn from point D to point F.
Answers
The position of G in the given line segment is at point 1, which is between points F and D and the line segment between F and D in the ratio 8:5.
What is meant by line segment?
Two unique points on a line define the boundaries of a line segment. A line segment is a section of the path a line takes to join two locations. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given, the locations of D and F on the line segment.
D = -4
F = 9
Number of units between F and D = 9 - (-4) = 13
Point G partitions the line segment from F to D in the ratio 8:5.
So distance of G from F = [8/(8+5)] * 13 = 8
Distance of G from D = [5/(8+5)] * 13 = 5
So from F, it is 8 units behind F = 9 - 8 = 1
from D, it is 5 units in front of D = -4 + 5 = 1
Therefore the position of G in the given line segment is at point 1.
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A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in 4 years?
• $50,000
• $500
• $125
• $12,500
Answers
[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]
_____________
[tex] \: [/tex]
Given:-
[tex] \rm{Principal= \bold {5000}}[/tex][tex] \rm{Time= \bold 4}[/tex][tex] \rm{Intrest Rate= \bold { 2.5}}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]
[tex] \: [/tex]
Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI= \frac{50 \cancel{00}×4×2.5}{1 \cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=50×4×2.5}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \rm{ \red{SI= 500}}}}[/tex][tex] \: [/tex]
hope it helps!:)
Answer: the answer is c.$500 hope that helps !
Step-by-step explanation: I took the test
There are 15 students in an art class. Mr Popplewell has 300 colored pencils to distribute equally among the students. How many colored pencils will each student receive?
Answers
Answer:
Step-by-step explanation:
15 into 300 is 20
300÷ 15 = 20
Which of the following tables of x- and y-values represents a function?
Answers
The tables of x- and y-values that represents a function include the following: C. table C.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range) representing a given scenario or situation such as the following:
x 1 3 7 5 2 4
y 6 6 6 6 6 6
In conclusion, we can reasonably infer and logically deduce that only table C represent a function.
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need help looking for the anwser
Answers
Answer:
need help looking for the anwser here it's the 2.5
Convert 1,2kg to g to two decimal places where applicable
Answers
Answer: 1200g
Step-by-step explanation:
1 kilogram is equal to 1000 grams, so since you want 1.2, simply multiply by that quantity. So the answer is 1200 grams.
our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
Answers
As modeled, a movie is projected into a large outdoor screen. The bottom of the 60 foot-tall
Answers
Answer:
-
Step-by-step explanation:
the question isn't clear enough to answer it
Find x round to the nearest whole number
Answers
Answer:
Below
Step-by-step explanation:
Instead of x , I assume you want the angle For RIGHT triangles, remember
cos (angle ) = adjacent leg / hypotenuse
cos ( angle ) = 5 /12
angle = arccos( 5/12) = 65 °
You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.
Find the volume to each equation
(Directions listed above questions)
Answers
The volume of the cube is 444.19 in³
The volume of the rectangular prism is 661.2 ft³
The volume of the triangular prism is 30.04 yd³
The volume of the cylinder is 380.57 km³
How to find the volumeVolume of a cube is solved using the formula
= length³
= 7.63³
= 444.19 in³
Volume of a rectangular prism is solved using the formula
= Area of base * height
= 9.5 * 8.7 * 8
= 661.2 ft³
Volume of a triangular prism is solved using the formula
= 1/2 × base × height × length
= 1/2 * 5.84 * 3.08 * 3.34
= 30.04 yd³
Volume of a cylinder is solved using the formula
= π * radius² * height
= π * 3² * 13.46
= 380.57 km³
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Write the following comparison as a ratio reduced to lowest terms. 7 nickels to 47 dimes
Answers
7 nickels is 7/5, thus 7 nickels to 47 dime is 1.4 dime to 47 dime.
When both terms are multiplied by their biggest common factor, 1.4 dime, the ratio can be simplified to its simplest form: 47 dimes = 14: 470
What is the ratio?The ratio of quantity, amount, or size of two or more items is known as proportion. It is the indicated quotient of two mathematical expressions.
As a ratio, what is 1 to 2?"1 to 2" is the way to write the ratio 1: 2. Accordingly, of the total of 3, there is one component that is worth 1 and another part that is worth 2. Changing a part-to-part ratio to a fraction To get the whole, add the ratio terms. The denominator should be this.
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An account that earned 23% annual interest compounded quarterly for 3 years and currently has a balance of $6258.
Answers
The initial balance of the account was approximately $3541.83.
What is interest is compounded?This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
We can utilise the compound interest formula to find a solution to this issue:
A = P(1 + r/n)ⁿⁿ
In this case, we have P = the initial balance of the account, r = 0.23 (23% expressed as a decimal), n = 4 (since interest is compounded quarterly), t = 3 years, and A = $6258. We can solve for P by rearranging the formula:
P = A / (1 + r/n)ⁿⁿ
Substituting the values we know, we get:
P = 6258 / (1 + 0.23/4)⁴ˣ³
Simplifying this expression gives:
P = 6258 / 1.76757
P ≈ $3541.83
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Can someone help me with the step by step solutions to these? Thanks
Answers
Answer:
c. √2/30
f. 13√3/14
i. -11√10/24
Step-by-step explanation:
You want the sums of the fractions shown.
Sum of fractionsTwo fractions can be added like this:
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]
If the denominators have a common factor (k), then this can be reduced to ...
[tex]\dfrac{a}{bk}+\dfrac{c}{dk}=\dfrac{ad+bc}{bdk}[/tex]
The product bdk is the least common denominator when k is the greatest common factor.
Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.
c[tex]\dfrac{\sqrt{2}}{5}-\dfrac{\sqrt{2}}{6}=\sqrt{2}\left(\dfrac{1}{5}-\dfrac{1}{6}\right)=\sqrt{2}\cdot\dfrac{6-5}{5\cdot6}=\boxed{\dfrac{\sqrt{2}}{30}}[/tex]
f[tex]\dfrac{3\sqrt{3}}{7}+\dfrac{\sqrt{3}}{2}=\sqrt{3}\left(\dfrac{3}{7}+\dfrac{1}{2}\right)=\sqrt{3}\cdot\dfrac{3\cdot2+7}{7\cdot2}=\boxed{\dfrac{13\sqrt{3}}{14}}[/tex]
iThe denominators have a common factor of 2: 6=3·2, 8=4·2.
[tex]\dfrac{-5\sqrt{10}}{6}+\dfrac{3\sqrt{10}}{8}=\sqrt{10}\left(\dfrac{-5}{6}+\dfrac{3}{8}\right)=\sqrt{10}\cdot\dfrac{-5\cdot4+3\cdot3}{3\cdot4\cdot2}=\boxed{-\dfrac{11\sqrt{10}}{24}}[/tex]
Points B and D are on the perpendicular bisector of ^ABC. The measure of
Answers
The measure of angle ABC in the figure of triangle attached is
< ABC = 46 degreesWhat are perpendicular bisectors?In geometry, a perpendicular bisector is a line or line segment that divides another line segment into two equal parts and is perpendicular to it.
From the definition of perpendicular bisector, we have that
< A = < C
and using triangle ABD
< A + < ABD = 90
< A + 28 = 90
< A = 90 - 28
< A = 62
Using triangle ABC
< A + < ABC + < C = 180
62 + < ABC + 62 = 180
< ABC = 180 - 62 - 62
< ABC = 56
OR
< ABD = < DBC = 28 degrees
and < ABC = < ABD + < DBC adjacent angles
< ABC = < ABD + < DBC
< ABC = 28 + 28
< ABC = 56 degrees
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complete question
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees
Yang Bai is investing $10,000 and wants a portfolio that is 80% stocks and 20% bonds. She has decided to accomplish this using just 2 exchange-traded funds (ETFs): a stock ETF trading for $50 per share and a bond ETF trading for $100 for share. What should she do to meet her asset allocation goal?
