h = 7 is the solution to the equation 1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
The equation given that,
1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)
The least common multiple of the denominators is:
h² - 25 = (h - 5) (h + 5)
We multiply through with the LCM to obtain:
= [(h - 5) × (h + 5)] × [1 / (h - 5)] + [(h - 5) × (h + 5)] × [2 / (h - 5)]
= 16 / (h² - 25) × [(h - 5) × (h + 5)]
We cancel out common factors to obtain:
= 1 (h + 5) + 2 (h - 5)
= 16
We expand the brackets to obtain
= h + 5 +2h - 10
We group like terms to get:
h + 2h = 16 - 5 + 10
This simplifies to:
3h = 21
We now divide through by 3 to obtain:
h = 7
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The vertices of a convex pentagon are $(-1, -1), (-3, 4), (1, 7), (6, 5)$ and $(3, -1)$. What is the area of the pentagon
On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit
what is a pentagon?A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.
vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).
Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]
Area = 1/2| 60 |
Area of pentagon = 30 sq unit
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Samuel walked in the Labor Day parade. He walked 3 1/8 miles along the parade route and 2 5/6 miles home. For numbers 3a-3c, fill in each blank.
3a. Rounded to the closest benchmark, Samuel walked about. Miles on the parade route.
3b. Rounded to the closest benchmark, Samuel walked about. Miles home.
3c. Samuel walked about. Miles in all
3a) Rounded to the closest benchmark, Samuel walked about 3 Miles on the parade route.
3b) Rounded to the closest benchmark, Samuel walked about 2 Miles home
3c) Samuel walked about 5 Miles in all
We know that when rounding a fraction to the closest benchmark:
1) if the numerator is much smaller than the denominator, round a fraction to 0
2) if the numerator is about half the denominator, round a fraction to 1/2
3) if the numerator is nearly equal to the denominator, round a fraction to 1
Samuel walked 3 1/8 miles along the parade route.
Rounding to the closest benchmark a fraction 3 1/8 woule be
3 1/8
= 3
This means, he walked about 3 Miles on the parade route.
Samuel walked 2 5/6 miles home.
Rounding to the closest benchmark a mixed fraction 2 5/6 woule be
2 5/6
= 2
This means, he walked about 2 Miles homes.
The total distance would be,
d = 3 + 2
d = 5 miles
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Suppose that ƒ(−1)=10 and ƒ'(x)≥−3 for all values of x. What is the least possible value of ƒ(3)?
Using the mean value theorem, the least possible value of f(3) is - 2
What is the mean value theorem?The mean value theorem states that for a function f(x) on the interval (a, b), there exists a value c such that
f'(c) = f(b) - f(a)/(b - a)
How to find the least possible value for f(3)?Since ƒ(−1) = 10 and ƒ'(x) ≥−3 for all values of x, we require the least possible value of f(3).
Using the mean value theorem where
b = 3, a = -1 and f'(c) ≥ 3.We choose f'(c) = 3 since f'(x) = 3 is the minimum value of f'(x).
So, substituting the values of the variables into the equation, we have that
f'(c) = f(b) - f(a)/(b - a)
f'(x) = f(3) - f(-1)/(3 - (-1))
f'(x) = f(3) - f(-1)/(3 + 1)
f'(x) = f(3) - f(-1)/4
So, making f(3) subject of the formula, we have that
f(3) = f(-1) + 4f'(x)
Since
f'(x) = 3 and f(-1) = 10,Substituting the values of the variables into the equation, we have that
f(3) = f(-1) + 4f'(x)
f(3) = 10 + 4(-3)
f(3) = 10 - 12
f(3) = - 2
So, the least possible value is - 2
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HELP ASAP, LINKS AND ABSURD ANSWERS WILL BE REPORTED! I WILL MARK BRAINLIEST!!
Answer:
3/4
Step-by-step explanation:
brainliest please
Answer:
(x so long as x is less than or equal to .7 and x is grater than 0.) I think, The number line is hard to interpret. if it's asking where the line stops then it is 7/10. but the answer in parentheses makes the most sense to me.
Step-by-step explanation:
Good Luck
Have a nice day
A meteor crashed onto a planet and caused a crater that was 15,219.88 in deep. Round your answer to the nearest tenth.
Answer:
15,219.90
Step-by-step explanation:
.88 rounded to the nearest tenth would be 90. 8 is closer to 10 than 0 therfore you round up to .90
9. Calculate the volume of the sphere
8 cm
A. 2144 66 cm
B. 64 cm
C. 200.96 cm
D. 448.12 cm
—PLEASE HELP QUESTION IS IN PIC—
Answer:
ur answer is A
Step-by-step explanation:
I just did the problem
Help ASAP.. WILL MARK BRAINLIEST
Answer: 14
Step-by-step explanation: 3 x 4 = 12, 12 - 2 =10, so, the bottom line is 10, and the cd line is slightly longer than the bottom one, thus, the answer is 14.
Answer:
Okie the correct answer is 5
Step-by-step explanation:
I just took the test for that and I had the same answers.
I hope that helps
a question that can be answered by collecting data that will vary. "On average, how old are the people who live in my building?" is an example.
A. Mean
B. Mode
C. statistical question
find the measure of angle 2
Answer:
52°
Hope this helps!
32% of the students in the class forgot to charge their computer. If there are 25 total
students in the class, how many forgot to charge their computer?
Find the volume of this
Answer:
37.8 yd^3
Step-by-step explanation:
base area = (4.5 x 2.8)/2 = 6.3 yd^2
Volume = 6.3 x 6 = 37.8 yd^3
the perimeter of a right triangle is 24 ft, and one of its legs measures 6 ft. Find the length of the other leg and the hypotenuse.
a) 6 ft, 12ft
b) 5 ft, 13 ft
c) 8 ft, 10 ft
d) 7 ft, 11 ft
Answer:
Step-by-step explanation:
We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).
By pythagoras we know that
[tex]h^2= a^2+b^2.[/tex]
and the perimeter is [tex]P=h+a+b[/tex].
Since P=24 and a=6 we have these equations:
[tex]h^2=36+b^2\\24=h+6+b[/tex]
From the last equation we have [tex]h=18-b[/tex]. Replace h in the first equation we get that
[tex](18-b)^2=36+b^2[/tex]
[tex]18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8[/tex]
and h=18-8=10
How do you check whether 7 3x is a factor of 3x3 7x?
7 + 3x is not a factor of expression 3x^3 + 7x
Consider given expression 3x^3 + 7x
Let f(x) = 3x^3 + 7x
Assume that 7 + 3x is a factor of 3x^3 + 7x
This means, 7 + 3x = 0 would be the root.
x = -7/3
If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0
We find the value of given polynomial for x = -7/3
f(x) = 3x^3 + 7x
f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)
f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)
f(-7/3) = [(-343) - 147] / 9
f(-7/3) = -490 / 9
f(-7/3) ≠ 0
Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial f(x) = 3x^3 + 7x
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NO WEBSITES/ fake links or your getting reported! Help me with ALL the problems!
1) we need to find the common denominator so we can multiply the denominators with each other.
[tex]\frac{6*4}{10*4}[/tex][tex]+\frac{3*10}{4*10}[/tex][tex]=\frac{24}{40} +\frac{30}{40}[/tex][tex]=\frac{54}{40}=1\frac{14}{40}[/tex]
2) make first fraction into improper fraction
[tex]\frac{20}{12} -\frac{2}{3} =\frac{20}{12} -\frac{2*4}{3*4} =\frac{20}{12} -\frac{8}{12}=\frac{12}{12} =1[/tex]
3) turn into improper fraction[tex]\frac{3}{4}+\frac{12}{5} +\frac{3}{4} =\frac{3*5}{4*5}+\frac{12*4}{5*4} +\frac{3*5}{4*5}=\frac{15}{20}+\frac{48}{20}+\frac{15}{20}=\frac{78}{20}[/tex]
4) turn into improper fraction
[tex]\frac{38}{8} +\frac{14}{5} =\frac{38*5}{8*5} +\frac{14*8}{5*8}=\frac{190}{40} + \frac{112}{40}=\frac{302}{40}[/tex]
then we minus 2 3/4
[tex]\frac{302}{40} - \frac{11}{4} = \frac{302}{40} - \frac{11*10}{4*10}=\frac{302}{40} - \frac{110}{40}=\frac{192}{40}[/tex]
5) 7/3= 2.33333333333 or [tex]2 \frac{1}{3}[/tex]
Please help, I’m having trouble answering this question
Answer:
13+5+7+5+5
Its because if you calculate it mean and media. will be 7 and obviously mode is 5
Hope you're helped!
For each set of values for a and b evaluate the given expressions and record your answers in the table. ( I only need this one).
A = -1/2 B =6
A divided by -b
PLEASE HELP
Answer:
Set1 = 1/12
Set2 = 1/12
Set3 = -12
Step-by-step explanation:
Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.
Also to multiply fractions, multiply
top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.
see image.
55 pecans put them in 2 buckets where one has 15 more than the other
The number of pecans in each bucket will be 20 and 35.
How to illustrate the expression?From the information, there are 55 pecans are put in 2 buckets where one has 15 more than the other. An expression show the relationship between the variables.
In this case, 55 pecans put them in 2 buckets where one has 15 more than the other.
This will be:
x + x + 15 = 55
2x + 15 = 55.
Collect the like terms
2x = 55 - 15
2x = 40
Divide
x = 20
The other number will be:
x + 15.
= 20 + 15
= 35
The numbers are 20 and 35.
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55 pecans are put in 2 buckets where one has 15 more than the other. What is the amount in each bucket.
PLEASE HELP
Explain what the unit rate means in the context of the problem.
Answer in at least two complete sentences.
Answer:
Step-by-step explanation:
A unit rate means a rate for one of something. You should write it as a ratio with a denominator of one.
For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate
IT's 0.80 per serving i think
5. Emmanuel makes 82,000 as a software designer. Use the follow tax chart to find what he will pay in taxes this year.
A. 4925
B. 5456
C. 1245
D. 3426
The list shows the score of each game completed at a bowling alley during a one-hour period.
90, 96, 120, 124, 130, 135, 138, 140, 145, 148, 290, 290
How would the data graphed on a horizontal number line appear to be clustered or skewed? Explain your answer,
Answer:
it would be clustered because the scores are all close together :)
It would be clustered because the scores are all close together.
We have given that,
The list shows the score of each game completed at a bowling alley during a one-hour period.
90, 96, 120, 124, 130, 135, 138, 140, 145, 148, 290, 290.
What is clustered or skewed?Grouping similar objects into common groups, also known as clustering, is an important problem of unsupervised machine learning.
We have to determine the data graphed on a horizontal number line appear to be clustered or skewed.
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What is the solution of 2x² 3x 2 0?
The equation 2x² + 3x - 2 = 0 has the solutions or roots 1 and -2. The quadratic equation is 2x² + 3x - 2 = 0
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.
given
Below is the quadratic equation.
2x² + 3x - 2 = 0
When you factor the equation, you get
2x² + 3x - 2 = 0
2x² + 4x - x - 2 = 0
2x(x + 2) - 1(x + 2) = 0
(x - 1)(x + 2)
x = 1, -2
The equation 2x2 + 3x - 2 = 0 has the solutions or roots 1 and -2
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Whats is two fifths divided by one sixth
Answer:
2 2/5
Step-by-step explanation:
please help you will get brainliest!
click the image for the question someone pls help i suck at algebra ill love u forever <3‼️
Answer:
$ 30,000
Step-by-step explanation:
c = 300 ³√n²
= 300× ³√1000²
= 300× 100
= 30,000
Answer: $30000
Step-by-step explanation:
[tex]300\sqrt[3]{n^2}[/tex]
[tex]300\sqrt[3]{1000^2}[/tex]
[tex]300\sqrt[3]{1000000}[/tex]
300 × 100 = 30000
A service station tracks the number of cars they service per day. Construct a histogram for the data and describe the shape of the distribution
Answer:
See attachment for histogram
The histogram is left skewed
Step-by-step explanation:
Given
[tex]40, 47, 37, 42, 46, 31, 50, 41, 17[/tex]
[tex]43, 46, 45, 21, 43, 45, 23, 49, 50[/tex]
[tex]48, 26, 42, 46, 35, 52, 27, 51, 31[/tex]
[tex]44, 35, 27, 46, 39, 33, 50, 45, 50[/tex]
Solving (a): Construct a histogram
First, we construct a frequency table
Calculate Range
[tex]Range = Highest - Least[/tex]
[tex]Range = 52 - 17[/tex]
[tex]Range = 35[/tex]
Using a class width of 5, we have the following classes:
[tex]17 - 22; 23 - 28; 29 - 34; 35 - 40; 41 - 46; 47 - 52[/tex]
So, the frequency table is:
[tex]\begin{array}{ccccccc}{Class} & {17-22} & {23-28} & {29-34} & {35-40} & {41-46} & {47-52} \ \\ {Count} & {2} & {4} & {3} & {5} & {13} & {9} \ \end{array}[/tex]
See attachment for histogram
From the attached histogram, we can see that the height of the bars of the histogram tend to increase towards the left.
Hence, the shape of the histogram is left skewed
Suppose the diameter of a circle is 4units. What is its circumference?
Answer:
C = 12.6 (rounded to the nearest tenth)
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr
R = radius
The radius is the half of a diameter, so 4/2 is 2.
C = 2π(2)
C = 12.56637061
HELP ME PLZ I NEED HELP
Answer:
A
Step-by-step explanation:
[tex]\frac{12}{a} = \frac{9}{b} => 12b = 9a[/tex]
[tex]12 * 1.5 = 9 * 2[/tex]
[tex]18 = 18[/tex]
This option works
I don’t know this question
help me
The number of groups of like terms is 3
What is an algebraic expression?An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.
These algebraic expressions are also composed of mathematical operations, such as;
AdditionSubtractionDivisionBracketParenthesesMultiplication, etcA term can be described a single variable, number or numbers and variables that are multiplied together.
From the information given, we have the terms;
3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰
The similar terms are;
3x¹³, 3x¹⁰, 3¹³
Hence, the number is 3
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Can someone help me with this? I've asked my teachers and I'm still lost
Answer:
Click the link?
Step-by-step explanation:
Answer:
so well go to the guide and check the q. Then either create an doc or slide when done click file then download then pdf. k. then click add file then add the pdf file.
Step-by-step explanation: