Answer:
0.47
Step-step explanation:
Add 8+7 which gives you 15. So 7/15. Then turn it into decimal form which is 0.47. Hope this helps!
Solve the following equation for x. 12^2 - 36x = 0
Let U be a matrix where u_ij = 0 if i > j, and L be a matrix where l_ij = 0 if i < j.
(a) U is called an upper triangular matrix and L is a lower tri-angular matrix. Explain why.
(b) Prove or disprove: The sum of two upper triangular matrices is an upper triangular matrix.
(c) Prove or disprove: The product of two upper triangular matrices is an upper triangular matrix.
Answer:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 )
B) sum of two upper triangular matrices = upper triangular matrix.
C) product of two upper triangular matrices = upper triangular matrix
Step-by-step explanation:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 ) since Lij = 0 if i < j
B) To prove that sum of two upper triangular matrices
attached below
C) Prove or disprove that product of two upper triangular matrices is an upper triangular matrix
attached below
CAN SOMEONE PLEASE HELP ME!!!!!!!
Answer:
30.2
Step-by-step explanation:
We know that quadrilateral KLMN is larger than quadrilateral GHIJ by a scale factor. In order to figure out that scale factor, we must divide a value of a side of KLMN by the value of the side that it corresponds to on GHIJ. One said side is NM, because we know it corresponds to JI on GHIJ. The value of NM is 56, and the value of JI is 13, so to figure out the scale factor, we must divide 56 by 13. We have the scale factor as 56/13, so to figure out the measure of side NM, we must find the side it corresponds to on GHIJ. The side it corresponds to is side JG, which has a value of 7. To get the value of NK, we must multiply the scale factor by 7, and the scale factor is 56/13. 56/13 times 7 is equal to 392/13. Rounding to the nearest tenth, we have the answer as 30.2
help with 1 b please. using ln.
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]
Step 2: Rewrite
[Function] Exponential Rule [Root Rewrite]: [tex]\displaystyle y = \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}}[/tex][Equality Property] ln both sides: [tex]\displaystyle lny = ln \bigg[ \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg)[/tex]Step 3: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg) \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \frac{dy}{dx} \bigg[ \frac{x}{2 - x} \bigg][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \bigg[ \frac{2}{(x - 2)^2} \bigg][/tex]Simplify: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{-1}{x(x - 2)}[/tex]Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-y}{x(x - 2)}[/tex]Substitute in y [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{-\sqrt{\frac{x}{2 - x}}}{x(x - 2)}[/tex]Rationalize: [tex]\displaystyle \frac{dy}{dx} = \frac{-\frac{x}{2 - x}}{x(x - 2)\sqrt{\frac{x}{2 - x}}}[/tex]Rewrite: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{x(x - 2)(2 - x)\sqrt{\frac{x}{2 - x}}}[/tex]Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{-x(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Using the following equation, find the center and radius: x2 −2x + y2 − 6y = 26 (5 points)
Answer:
Center: (1,3)
Radius: 6
Step-by-step explanation:
Hi there!
[tex]x^2-2x + y^2 - 6y = 26[/tex]
Typically, the equation of a circle would be in the form [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.
To get the given equation [tex]x^2-2x + y^2 - 6y = 26[/tex] into this form, we must complete the square for both x and y.
1) Complete the square for x
Let's take a look at this part of the equation:
[tex]x^2-2x[/tex]
To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:
[tex]x^2-2x+1[/tex]
Great! Now, let's add this to our original equation:
[tex]x^2-2x+1+y^2-6y = 26[/tex]
We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:
[tex]x^2-2x+1+y^2-6y = 26+1\\x^2-2x+1+y^2-6y = 27[/tex]
Complete the square:
[tex](x-1)^2+y^2-6y = 27[/tex]
2) Complete the square for y
Let's take a look at this part of the equation [tex](x-1)^2+y^2-6y = 27[/tex]:
[tex]y^2-6y[/tex]
To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:
[tex]y^2-6y+9[/tex]
Great! Now, back to our original equation:
[tex](x-1)^2+y^2-6y+9= 27[/tex]
Remember to add 9 on the other side as well:
[tex](x-1)^2+y^2-6y+9= 27+9\\(x-1)^2+y^2-6y+9= 36[/tex]
Complete the square:
[tex](x-1)^2+(y-3)^2= 36[/tex]
3) Determine the center and the radius
[tex](x-1)^2+(y-3)^2= 36[/tex]
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.
I hope this helps!
Answer:
[tex]\sqrt{g^2+f^2-c}[/tex]
[tex]g=-1,f=-3,c=-26[/tex]
so, the Center of the equation is [tex](1,3)[/tex]
Center → (1 , 3)[tex]\sqrt{(-1)^2+(-3)^2-(-26})[/tex]
[tex]=\sqrt{1+9+26}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
Radius → 6OAmalOHopeO
F(x)=-2x^2+4x+5
Find the critical numbers
Answer:
To find critical points, take the first derivative and set it equal to zero:
f(x) = -2x^2 + 4x + 5
f'(x) = -4x + 4
-4x+4 = 0
-4x = -4
x = 1
Critical point at x = 1
Alternatively, if you mean zeros, or where the x intersects, you can use the quadratic equation.
help what it is please help
9514 1404 393
Answer:
A. the mean
Step-by-step explanation:
The Greek letter μ is customarily used to represent the mean of a distribution or data set. Its location in this figure at the highest point and the line of symmetry is consistent with μ identifying the mean of this normal distribution.
The price of the cinemas meal deal has increased from £7.25 to £9.28.
What is the percentage change in price?
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Answer:
8.28% increase i believe
Step-by-step explanation:
formula: final amount - initial ÷ initial amount.
9.28-7.25= 2.03. now divide by the initial amount. 2.03÷7.25=8.28.
so, an 8.28% increase to the price
Kenneth needs $5,000 for university in 5 years. His parents plan to invest some money in an account paying interest at a rate of 7.2% per annum, compounded monthly. How much should they invest now to have $5,000 in 5 years.
Need help is this right or what is the right answer
Answer:
A
Step-by-step explanation:
the answer is A and not C. equation in form of y=mx+b
so start off by (0,2) and you can see the graph go by 1 x and 1 y.
C=n+2
Answer:
A
Step-by-step explanation:
its starting point is 2 up to +2 and it goes up at out by 1 so n also ik this was already answered but i want the brainly points
Correct
Suppose it takes John 27 minutes to run 3 miles. How long would it take him to run 4 kilometers? Round your answer to the nearest minute,
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Answer
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Answer:
Step-by-step explanation:
4km
[tex]\frac{3 }{27} \frac{miles}{minutes}[/tex] * [tex]\frac{60}{1} \frac{min}{hour}[/tex] * [tex]\frac{1}{.6213} \frac{km}{mile}[/tex]
4km ÷ 10.73 km/hr = .37 hr = 22.3 minutes
Help me solve the question in picture
9514 1404 393
Answer:
√5 +√6
Step-by-step explanation:
We know that the square of a binomial is ...
(a +b)^2 = a^2 +2ab +b^2
Then the square root of it is ...
a + b = √(a^2 +b^2 +2ab)
Using a=√x and b=√y, this is ...
√x +√y = √(x + y + 2√(xy))
__
For the given expression, we need to find x and y such that ...
xy = 30 and x+y = 11
Using x=5, y=6, we meet those requirements.
[tex]\displaystyle \sqrt{11+2\sqrt{30}}=\sqrt{5+6+2\sqrt{5\cdot6}}=\boxed{\sqrt{5}+\sqrt{6}}[/tex]
Answer:
√5+√6 ≈ 4.68555772
Step-by-step explanation:
I hope it's correct
Students apply for admission to different academic programs within a college. Because of space, each program can only accept a limited number of students. The table below shows the acceptance data for a selection of majors in the college.
Acceptance Status
Accepted Rejected Total
College Major Chemistry 72 18 90
Business 65 35 100
Spanish 45 15 60
Total 182 68 250
What is the probability that a student was accepted, given that the student applied to the business program?
26.0%
35.0%
35.7%
65.0%
I think the answer is (A). 26%. Can someone check?
Answer:
Your wrong, it's 65%.
Step-by-step explanation:
The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.
yw :)
The probability that a student was accepted is 5.0% since option b be the correct answer.
ProbabilityProbability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,
How to find probability?We have to find out the probability of the selection of a student applied for the business program.
We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events
So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.
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Heather has $20 in her purse she earn some money at work and add it to the money in her purse at the end of the day she has $95 in her purse use M as a variable
Answer:
M=$75
Step-by-step explanation:
I used M for money that Heather earned.
$20+M=$95
Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.
Answer:
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
Step-by-step explanation:
Given :
Groups:
x1 = 69 ; s1 = 19 ; n1 = 38
x2 = 32 ; s2 = 14 ; n2 = 37
1 - α = 1 - 0.95 = 0.05
Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :
The confidence interval obtained is :
(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between
(24.32 ; 39.68) .
Jasmine the Great Dane has a head 30 cm long. Her tall is equal to the size of her head plus one-half the size of her body. Her body is the size of her head phluss the tal. How long is Jasmine?
Answer:
240 cm
Step-by-step explanation:
Let x = tail y = body
x = 30 + 1/2y
y = 30 + x
Let's plug in the x equation at the bottom
y = 30 + 30 + 1/2y
y = 60 + 1/2y
Bring the like terms to one side
y = 60 + 1/2y
-1/2y -1/2y
1/2y = 60
Multiply both sides by 2 to get the length of the body
1/2y x 2 = 60 x 2
y = 120
Now we can plug in the new y into another equation, let's use the top one
x = 30 + 1/2(120)
x = 30 + 60
x = 90 = length of the tail
Add em all up
120 + 90 + 30 = 240
It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01.
a. Define the null and alternative hypotheses in mathematical terms as well as in words.
b. Identify the level of significance.
c. Include the test statistic and the P-value.
d. Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not?
Diameters data frame of the first sample (showing only the first five observations)
diameters
0 3.46
1 2.64
2 1.89
3 2.56
4 2.09
Diameters data frame of the second sample (showing only the first five observations)
diameters
0 3.10
1 2.04
2 2.18
3 2.60
4 2.76
test-statistic = 2.06
two tailed p-value = 0.0394
Data for all 50 samples cannot be obtained, however, the solution below uses the 10 samples below to show how the hypothesis can be tested.
Answer:
Step-by-step explanation:
Average diameter, μ = 2.30
H0 : Average diameter is equal to 2.30cm
H1 : Average diameter is greater than 2.30 cm
The hypothesis :
H0 : μ = 2.30
H1 : μ > 2.30
Using the readings from the data above :
3.46, 2.64, 1.89, 2.56, 2.09, 3.10, 2.04, 2.18, 2.60, 2.76
Sample size, n = 10
Mean, xbar = ΣX/ n = 25.32 / 10 = 2.532
Sample standard deviation, s = 0.4973 (from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.532 - 2.30) ÷ (0.4973/√(10))
T = 1.475
The Pvalue :
Degree of freedom, df = n - 1 ; 10 - 1 = 9
Pvalue(1.475, 9) = 0.087
Decision region :
Reject H0 ; If Pvalue < α;
Since 0.087 > 0.01 ; we fail to reject the Null and conclude that there is no evidence to suggest that the average diameter is greater than 2.30 cm
what fraction of 1 day is 48 minutes
Answer:
48 ÷ 60 = 4/5
Step-by-step explanation:
4/5 is the answer
Answer:
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:
We require the number of minutes in a day.
i hour = 60 minutes
24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )
Then
fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )
= [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )
= [tex]\frac{1}{30}[/tex]
Max has 3 fiction books and 6 nonfiction books to donate to the community center. He wants to package them so that there is an equal number of fiction and nonfiction books in each group. He also wants to have as many packages as possible. How many books are in each group?
Answer:
Each group has 1 fiction book and 2 nonfiction book(s).
A line passes through the point (-4, -6) and has a slop of 5. Write an equation for this line.
9.
How many years will it take to earn N8100
simple interest on N180000 at 9% per annum?what the answer?
9514 1404 393
Answer:
1/2 year
Step-by-step explanation:
Put the numbers into the interest formula and solve for t.
I = Prt
8100 = 180000(0.09)t
t = 8100/16200 = 1/2
It will take 1/2 year to earn N8100 in interest at 9%.
A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are considered affluent. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.08 to 0.34 0.08 to 0.16 0.24 to 0.34 0.16 to 0.24
Answer:
0.08 ; 0.16
Step-by-step explanation:
Given :
x = 32 ; n = 267 ; phat = x / n = 32 / 267 = 0.11985
The Zcritical at 95% = 1.96
The confidence interval for proportion :
C. I = Phat ± Z*√(phat(1-phat))/n
C. I = 0.11985 ± 1.96√(0.11985(1-0.11985))/267
C. I = 0.11985 ± 1.96(0.0198765)
C. I = 0.11985 ± 0.0389581
C. I = 0.08 ; 0.158
C. I = 0.08 ; 0.16
What is the volume of the
cylinder? Use 3.14 for a.
A 1200 cubic inches
B 1884 cubic inches
C 3768 cubic inches
D 28,260 cubic inches
Answer:
Step-by-step explanation:
area of top face = π15² = 225π in²
volume = 225π × 40 = 9000π ≅28,260 in³
At snack time, Ms. Rivera passes out 24 cookies to her class. She also passes out 1 glass of lemonade to each student. This equation correctly represents the total number of items distributed, where a is the number of students in the class.
a(2+1)=36
What is the value of a?
=======================================================
Explanation:
Let's solve the given equation for the variable 'a'
a(2+1) = 36
a*(3) = 36
3a = 36
a = 36/3
a = 12
There are 12 students in the class. This must mean there are 12 lemonades, because each person gets 1 lemonade.
Since there are 24 cookies, each student gets 24/12 = 2 cookies
Since each student gets 2 cookies and 1 lemonade, this is where the "2+1" comes from in the original equation. Each student gets 3 items total, which explains the notation 3a.
The value of 'a' from the given expression would be 13.
Given that;
At snack time, Ms. Rivera passes out 24 cookies to her class. She also passes out 1 glass of lemonade to each student.
Here, the equation is,
a(2+1)=36
Solve for a;
a × 3 = 36
3a = 36
Divide both sides by 3;
a = 36/3
a = 13
Thus, the value of a is 13.
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The graph is that of a fourth-degree polynomial function. Which of the following correctly shows three factors of the function? Image included, please help!
C.
Observe that the roots of polynomial are [tex]-3,2,5[/tex]
We have a polynomial in a factored form,
[tex](x+3)(x-2)(x-5)[/tex]
If you substitute x for any of [tex]-3,2,5[/tex] the product will always equal to zero that is these numbers are roots of polynomial.
Hope this helps :)
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden. She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
What is the sample mean of the heights of the plants in Susan's garden?
Answer:
3.5 inches
Step-by-step explanation:
Sample mean basically means that we need to find the average of the samples.
So the formula for finding average is
Number of observations/ Number of Occurrences
So when we add the values together we get
42.
So there are 12 numbers
So, 42/12 =
3.5 inches
The sample mean of the heights of the plants in Susan's garden is
3.5 inches.
Here,
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.
She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
We have to find the sample mean of the heights of the plants in Susan's garden.
What is Average?
Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.
Now,
The recorded data is;
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.
Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]
Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]
Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.
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356 miles in 5 days
is a:
Unit Rate
Unit Price
Ratio
Rate
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Answer:
Rate
Step-by-step explanation:
Since there are no currency units involved, it is not a price or unit price.
Since the denominator (days) is not 1, it is not a unit rate.
The usual wording for a ratio is "to" rather than "in", so we probably would not say this is a ratio. Though, the usual reason for expressing the numbers this way is to indicate we might be interested in their ratio.
There is time involved, so it is reasonable to call this a "rate," which is usually the ratio of some quantity to the time associated with that quantity.
Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.)
Round your answer to two places, where applicable.
Side AB 3 Side BC 4 Side AC ?
Answer:
side AC is 5
Step-by-step explanation:
by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.
AB =3 BC=4
9+16=25
25 square root is 5
makeing AC=5
Find hypotenuse,perpendicular and base
Answer:
Consider the angle Ф.
the line opposite to Ф is the perpendicular -> PQ = 5cm
The base is the line with whom the perpendicular has 90° angle -> PR = 12cm
Finally, hypotenuse is the line opposite to the 90° which is QR= 13cm
Answer:
hypotenuse = QR = 13 cm
Perpendicular = PQ = 5 cm
Base = PR = 12 cm
1/4 (2.6x+0.25)-5/8 (2.5-0.88x)
The given expression 1/4 (2.6x+0.25)-5/8 (2.5-0.88x) when simplified is 1.2x - 1.5.
To simplify the expression 1/4 (2.6x + 0.25) - 5/8 (2.5 - 0.88x), we'll apply the distributive property and combine like terms.
First, let's simplify the expression within the first set of parentheses:
2.6x + 0.25
Next, we multiply this expression by 1/4:
(1/4) * (2.6x + 0.25) = (2.6/4)x + (0.25/4) = 0.65x + 0.0625
Now, let's simplify the expression within the second set of parentheses:
2.5 - 0.88x
We'll multiply this expression by -5/8:
(-5/8) * (2.5 - 0.88x) = (-5/8)(2.5) - (-5/8)(0.88x) = -1.5625 + 0.55x
Finally, we can combine the simplified expressions:
0.65x + 0.0625 - 1.5625 + 0.55x = (0.65x + 0.55x) + (0.0625 - 1.5625) = 1.2x - 1.5
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Complete question is:
Simplify the expression 1/4 (2.6x+0.25)-5/8 (2.5-0.88x)
