The length of the vine is 21 ft
what is the circumference of a circle?
the circumference is the perimeter of a circle
the perimeter of the circle = 2πr = 3 ft
the vine is 7 times the perimeter
length of vine = 7×3= 21 ft
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If the tree is 20 feet tall with circumference 3 feet then the length of vince is around 21 feet.
Given the height of tree is 20 feet and the circumference of tree is 3 feet.
We have to find the length of vine.
Circumference is the perimeter of a circular object. Because the trunk of a tree is in shape of circle so the perimeter of the trunk is 2πr.
We have been given the circumference of tree be 3 feet.
Circumference=2πr
Because vine is 7 times the circumference so the length of vine being:
Length of vine=7*3
=21 feet.
Hence if the tree is 20 feet tall with circumference 3 feet then the vince is around 21 feet long.
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1. In the process of solving the radical equation, x − 5 =radical 3x −11 , you will need to solve which of the following quadratic equations?
a) x2 −7x+16=0
b) x2 −3x−14=0
c) x2 +13x−36=0
d) x2 −13x + 36 = 0 e)
none of these
In the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0
Solving radical equationsRadical equations are expression that are under the square root. For instance √x is a radical expression.
Given the equation expressed as:
x − 5 = √3x −11
Square both sides to have;
(x-5)² = (√3x −11 )²
This can be further expressed as:
(x-5)² =3x −11
Expand
x² -10x + 25 = 3x - 11
Equate to zero
x² -10x + 25 - 3x +11 = 0
x² -10x - 3x +36 = 0
x² - 13x + 36 =0
Hence in the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0
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Tami earned $20.64 in simple interest by investing a principal of $400 in a Treasury bill.
If the interest rate was 1.72%/a, for how many years did she have her investment?
The number of years she had her investment is after 3 years
How to determine the years of investment?From the question, the given parameters are:
Principal Amount, P = $400Interest Rate, r = 1.72%Simple Interest, I = $20.64The number of years (T) is calculated from the following simple interest formula
I = PRT
Substitute the given parameters in the above equation
20.64 = 400 * 1.72% * t
Express 1.72% as decimal without percentage
20.64 = 400 * 0.0172 * t
Evaluate the product
20.64 = 6.88 * t
Divide both sides by 6.88
20.64/6.88 = 6.88/6.88 * t
Evaluate the quotient
3 = t
Rewrite the equation as
t = 3
This means that she had her investment after 3 years
Hence, the number of years she had her investment is after 3 years
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PLEASE EXPLAIN!!
The ratio of my sister's age to my age is 10: 9.
The ratio of my brother's age to my age is 29 : 27.
I am over 40 years old but under 70 years old.
What is my age?
Sis : you : bro
10 : 9 : ?
? ? : 27 : 29
We can get the 9 at the top to 27, by multiplying the whole row by 3 to get:
30 : 27 :?
? : 27 : 29
Your age matches (in the ratios or relation to your sis & bro) now 27 yrs in both ratio. Creating a single ratio, whereby multiplying the top row by 3 to get you to 27 & bottom row by 1 to get you to 27. Knowing when you're 27 in both cases, you know how old your sis & bro is
So, replace the ? with the number above or below it, creating a single ratio, where you are in common with both, by being 27 in both cases.
The ratio of sis : you : bro is now -
The ratio of sis : you : bro is now - 30: 27 : 29
To find what your age is we need to increase the ratio in the same amount to find your maximum age under 70.
So, if we were to double your age to 54, by multiplying your previous age of 27 by 2. We've got to do the same for your sis & bro too, they're aging with you.
We get :
We get :60 : 54 : 58
(30 x 2) : (27 x2) : (29 x2)
Keep increasing the ratio, to the point you're not above 70 years. Now, I'll multiply all ages by 3.
30: 27 : 29
(30 x 3) : ( 27 x 3) : (29 x 3)
We get:
We get:90 : 81 : 87
Right now, you're above the age of 70.
Thus, your maximum age must be 54, where you're under 70 years, but over 40 years.
Answer : 54 years
Hope this helps!
WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
ACCOUNT IN HER NAME AT A SAVINGS AND LOAN ASSOCIATION (S&L). AT THE TIME,
THE S&L PAID 6% INTEREST COMPOUNDED SEMI-ANNUALLY. AFTER 10 YEARS, THE
S&L CHANGED TO A RATE OF 6% COMPOUNDED QUARTERLY. WHAT WAS THE
VALUE OF THE ACCOUNT AFTER 18 YEARS WHEN THE MONEY WAS WITHDRAWN TO
HELP PAY FOR HER COLLEGE EXPENSES
The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.
How are the future values determined?The future values of the savings account are calculated in two installments.
The first installment is for 10 years when the account earns 6% compounded semiannually.
Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.
Future values can be determined using the future value formula or an online finance calculator, as follows:
Data and Calculations:Investment of $2,000 for 10 years:N (# of periods) = 20 (10 years x 2)
I/Y (Interest per year) = 6%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $3,612.22
Total Interest $1,612.22
Investment of $3,612.22 for 8 years:N (# of periods) = 32 (8 years x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)
PMT (Periodic Payment) = $0
Results:
FV = $5,816.85
Total Interest $2,204.63
Thus, the value of the account after 18 years was $5,816.85.
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Simplify: 9x + 2(x - 3) - 2x + 10
Answer: 9x+4
Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.
Answer:
9x + 4
Step-by-step explanation:
9x + 2x - 6 - 2x + 10
Rearranging,
=> 9x + 2x - 2x + 10 - 6
=> 9x + 4
The rat population in a major metropolitan city is given by the formula
n
(
t
)
=
24
e
0.015
t
where
t
is measured in years since 2004 and
n
(
t
)
is measured in millions.
What was the rat population in 2004 ?
rats
What does the model predict the rat population was in the year 2012 ?
rats
The rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.
How to determine the populationGiven the function of the population to be;
n (t) = 24 e^0. 015t
Where;
t is measured in years since 2004n(t) is measured in millionsIn 2004, t = 1
Substitute into the formula;
n(1) = 24 e^0. 015t
n(1) = 24 e^(0.015 × 1)
n(1) = 24 e^0. 015
n(1) = 24. 8 millions
In year 2012, t = 8
n(8) = 24 e^(0. 015 × 8)
n(8) = 24e^0. 12
n(8) = 31. 6 millions
Thus, the rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.
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the width of a large butterfly is about 0.08. What is the width when it is written in scientific notation
Answer: 8 x 10^2
Step-by-step explanation:
scientific notation has to be greater than 1, less than 10
therefore:
0.08 = 8 x 10^2
Apply the rule (-x, y - 2) to the following point, what is the result?
(-3,5)
O (-5,-5)
O (3, 3)
O (-5,3)
O (-3,7)
Answer:
[tex] - 3 \times - 1 = 3 \\ \\ 5 - 2 = 3[/tex]
Step-by-step explanation:
3,3
Answer: Second Choice. (3, 3)
Step-by-step explanation:
Given point
(x, y) = (-3, 5)
Given the rule for application
(-x, y - 2)
Determine the new x-value
x = -3
-x = - (-3) = 3
Determine the new y-value
y = 5
y - 2 = (5) - 2 = 3
Therefore, the result is [tex]\Large\boxed{(3,~3)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A pitaya, or dragon fruit, is a tropical fruit with pink skin and pulp filled with tiny black
seeds. The weight of a pitaya seed is 1 x 107 ounce. What is the weight of the pitaya
seed in standard form?
Type the number in the box.
oz
The standard form the weight of a pitaya seed is 1 x 10⁷ ounces.
What is a standard form?Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 x 10⁸.
Given that a pitaya, or dragon fruit, is a tropical fruit with pink skin and pulp filled with tiny black seeds. The weight of a pitaya seed is 1 x 10⁷ ounces.
The standard form can be written as:-
Weight = 10000000 ounces
Weight = 1 x 10⁷ ounces.
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A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was 15.1 eggs. Let μ = the true mean number of eggs the chickens lay each day. Under the assumption that the true mean number of eggs is 16, 100 simulated means for samples of size 10 are shown in the dotplot. A dotplot titled mean number of eggs. A number line labeled simulated means of samples, n = 10, goes from 15.0 to 17.2. A sample mean of eggs of 15.1 or less only occurred twice. Using the dotplot, is there evidence that the chickens are laying fewer than 16 eggs? Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16. Yes, since a sample mean number of eggs of 15.1 is less than the mean number of eggs of 16, there is evidence to prove that the true mean number of eggs is less than 16. No, since a sample mean number of eggs of 15.1 is only 0.9 eggs less than a mean number of eggs of 16, there is insufficient evidence that the true mean number of eggs is less than 16. No, since a sample mean number of eggs of 15.1 never occurred in the dotplot, it is not possible that a random sample of 10 eggs will have a mean number of eggs of 15.1. Therefore, there is insufficient evidence that the true mean number of eggs is less than 16.
Given the above information, it is correct to say Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16. (Option A)
What is the explanation for the above?
Recall that the mean (statistically speaking) is a measure of central tendency of a probability distribution along median and mode.
You could also state that it is an expected value. Given that samples of actual value taken from the
Hence, since from 100 samples taken, the number of eggs of 15.1 or less occurred, then the true mean or actual mean is less than 16.
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- Describe the slope of each line. Then find the slope.
Using the quote, "Those of us on the margins wonder if our stories matter" what is the significance of the quoted text?
The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.
What is a quote?Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.
Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.
You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.
In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.
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thank you for helping
Answer: TRS is congruent to CSE
Step-by-step explanation:
You can find congruent angles by locating the ones with the same number of lines. You want to start with the angles in the order of TRS.
Angle T has 1 line, so is congruent to C, which also has 1 line.
Angle R has 2 lines, so is congruent to S, which also has 2 lines.
Angle S has 3 lines, so is congruent to E, which also has 3 lines.
You want to keep these in the same order, so TRS, in the order of 1-2-3 lines, is congruent to CSE, also in the order of 1-2-3 lines (aka congruency markings).
What is the solution to the system of equations graft below
Answer:
( 2,-3)
Step-by-step explanation:
The solution to the system of equations is where the two graphs intersect
The two graphs intersect at x = 2 and y = -3
( 2,-3)
How do I write the following number in scientific notation?
788,000
Find the coordinates of the point on the curve y = 2x² - x - 1 at which the gradient is 7
Answer:
See below
Step-by-step explanation:
The derivative of the function is the slope
2x^2 - x -1 take derivative ( f ' )
4x -1 equate to 7
7 = 4x -1
x = 2 sub into the original equation to find y = 5
f(x) = 2x^2 - x -10
What are the x-intercepts of the graph of f(x)? Show your work
Answer:
[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=2x^2-x-10[/tex]
The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.
To find these points, factor the quadratic equation, set it to zero, then solve for x.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=2 \cdot -10 = -20[/tex]
[tex]\implies b=-1[/tex]
Therefore, the two numbers are -5 and 4.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 2x^2-5x+4x-10[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x-5)+2(2x-5)[/tex]
Factor out the common term (2x - 5):
[tex]\implies (x+2)(2x-5)[/tex]
Set the factored function to zero:
[tex]\implies (x+2)(2x-5)=0[/tex]
Apply the zero-product property:
[tex]\implies (x+2)=0 \implies x=-2[/tex]
[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]
Therefore, the x-intercepts of the graph are:
[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]
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when a fraction of 17 is taken away from 17 what remains exceeds one third of seventeen by six Using symbolic language
Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. So that the required symbolic language required in the question is: 17 - [tex]\frac{x}{17}[/tex] = [tex]\frac{17}{3}[/tex] + 6
Thus the value of x is 90[tex]\frac{2}{3}[/tex].
Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. Some types of fractions are mixed fractions, proper fractions, and improper fractions.
Thus to express the given question in a symbolic language, let the fraction of 17 taken away be represented by x.
So that;
i. a fraction of 17 is taken away from 17 can be expressed as 17 - [tex]\frac{x}{17}[/tex].
ii. remains exceeds one-third of seventeen by six can be expressed as [tex]\frac{17}{3}[/tex] + 6
Therefore the required symbolic language to the question is:
17 - [tex]\frac{x}{17}[/tex] = [tex]\frac{17}{3}[/tex] + 6
So that,
[tex]\frac{289 - x}{17}[/tex] = [tex]\frac{17 + 18}{3}[/tex]
cross multiply to have
3(289 - x) = 17(17 + 180)
867 - 3x = 595
3x = 867 - 595
=272
x = [tex]\frac{272}{3}[/tex]
= 90[tex]\frac{2}{3}[/tex]
x = 90[tex]\frac{2}{3}[/tex]
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11. Use the following information for problems a-b. The table shows the results of a school lunch survey. In the
survey, students were asked whether they have chores and a curfew
Using it's concept, the probabilities are given as follows:
a) C. 7/20.
b) D. 15/22.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For item a, we have that there are 60 students with no curfew, and of those, 21 have no chores, hence the probability is given by:
p = 21/60 = 7/20
Which means that option C is correct.
For item b, we have that there are 66 students with no shores, and of those, 45 have a curfew, hence the probability is given by:
p = 45/66 = 15/22
Which means that option D is correct.
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Find the length of UX
Answer:
[tex]\dfrac{8}{\sin(6^\circ)} \approx 76.53[/tex]
Step-by-step explanation:
[tex]UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}[/tex]
Can anyone help me with this question!
Answer:
94. 25 in³Step-by-step explanation:
The radius of the base is the distance between the center of the circle and the edge of the base, therefore in this case it is equal to 3 in.
The volume of a cone is given by:
V = π * r² * h / 3
V = π * (3)² * 10 / 3
V = 94. 25 in³
Therefore, The volume of is 94. 25 in³.
Step-by-step explanation:
6.25 points
Find the GCF for the list.
10m4, 40m⁹
10m5
40m4
10m4
6.25 points
list
Determine the slope of the line passing through the two points in the graph below.
The slope of the points on the graph is 4/3
How to determine the slope?The points on the graph are
(x, y) = (4,3) and (1, -1)
Slope is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (-1 - 3)/(1 - 4)
Evaluate
m = 4/3
Hence, the slope of the points on the graph is 4/3
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Problem What is the volume of this rectangular prism?
Answer:
[tex] \frac{27}{8} cm {}^{3} [/tex]
Is the volume of this right rectangular prism.
Step-by-step explanation:
Rectangular prism volume formula is:-
[tex]v = l \times w \times h \\ v = \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}apply \: fraction \: rule \\ v = \frac{27}{8} .... \frac{a}{b} \times \frac{c}{d} = \frac{a \times b}{c \times d} [/tex]Answer:
[tex]V=\frac{27}{8}\: cm^3[/tex]
Step-by-step explanation:
The formula to find the volume of a rectangular prism is:
V = length × height × width
Let us find now.
[tex]V = length \:* height \:* width\\\\V =\frac{3}{2} *\frac{3}{2} *\frac{3}{2} \\\\V=\frac{9}{4}*\frac{3}{2} \\\\ V=\frac{27}{8}\: cm^3[/tex]
The question is below
The events E1 and E2 are not independent events.
How to determine if the events are independent?The two events are given as:
E1 and E2 such that
P(E1) = 0.27, P(E2) = 0.40 and P(E1 U E2) = 0.58.
The two events E1 and E2 are independent if the following equation is true
P(E1 and E2) = P(E1) * P(E2)
Where
P(E1 and E2) = P(E1) + P(E2) - P(E1 U E2)
Substitute the known values in the above equation
P(E1 and E2) = 0.27 + 0.40 - 0.58
Evaluate the sum in the above equation
P(E1 and E2) = 0.67 - 0.58
Evaluate the difference in the above equation
P(E1 and E2) = 0.09
Substitute P(E1 and E2) = 0.09 in P(E1 and E2) = P(E1) * P(E2)
P(E1) * P(E2) = 0.09
Substitute P(E1) = 0.27 and P(E2) = 0.40 in the above equation
0.27 * 0.40 = 0.09
Evaluate the product
0.108 = 0.09
The above is false because 0.108 and 0.09 are not equal
Hence, the events E1 and E2 are not independent events.
Independent Events A and BHow to solve for x
We have:
P(A) = x
P(B) = x + 0.2
P(A n B) = 0.15
For independent events, we have:
P(A) * P(B) = P(A n B)
So, we have:
x * (x + 0.2) = 0.15
Expand
x^2 + 0.2x - 0.15 = 0
Using a graphing calculator, we have:
x = 0.3
Hence, the value of x is 0.3
The value of P(A U B)
This is calculated using
P(A U B) = P(A) + P(B) - P(A n B)
Substitute the known values in the above equation
P(A U B) = x + x + 0.2 - 0.15
Evaluate the like terms
P(A U B) = 2x + 0.05
Substitute 0.3 for x
P(A U B) = 2 * 0.3 + 0.05
Evaluate
P(A U B) = 0.65
Hence, the value of P(A U B) is 0.65
The value of P(A' U B')
This is calculated using
P(A' U B') = P(A') + P(B') - P(A' n B')
Where
P(A') = 1 - x
P(B') = 1 - x - 0.2 = 0.8 - x
P(A' n B') = P(A') * P(B')
P(A' n B') = (1 - x) * (0.8 - x)
Substitute the known values in the equation P(A' U B') = P(A') + P(B') - P(A' n B')
P(A' U B') = (1 - x) + (0.8 - x) - (1 - x) * (0.8 - x)
Substitute 0.3 for x
P(A' U B') = (1 - 0.3) + (0.8 - 0.3) - (1 - 0.3) * (0.8 - 0.3)
Evaluate
P(A' U B') = 0.85
Hence, the value of P(A' U B') is 0.85
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NO LINKS!! Please help me with this problem
Answer:
[tex]x^2+y^2=64[/tex]
Step-by-step explanation:
So the first important thing in solving this problem, is identifying what the major and minor axis are. The major axis is the bigger one, and we want to find on which axis it is.
So by simply looking at the eclipse, you can see that it's larger on the horizontal axis, so the major axis is on the horizontal axis, and the minor axis is on the vertical axis.
This means the equation will be expressed as:
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1[/tex]
In this equation the major axis, has a length of 2a, and the minor axis has a length of 2b. It's also important to note that (h, k) is the middle of the eclipse, but in the equation you provided, there is no subtraction, so it's just 0, meaning the center is at the origin (0, 0)
So now let's solve for a, and b. I'll look at each individual fraction separately.
[tex]\frac{x^2}{64}[/tex]
The denominator is equal to the value of a^2, so we simply take the square root of this to get the equation: a=8
[tex]\frac{y^2}{36}[/tex]
The denominator is equal to the value of b^2, so we simply take the square root of this to get the equation: b=6
So by just looking at the graph the larger circle appears to have a denominator that is equal to the length of the major axis. The major axis is equal to 2a, and since we know the value of a (8), we simply multiply this by 2 to get a length of 16. This was a bit redundant to do, since in the equation of a circle we need the radius, and the radius is just half the diameter, so now we divide this 16 by 2 to get a radius of 8.
The circle also appears to be centered at the origin so the equation will have (x-0)^2 and (y-0)^2 which is just x^2 and y^2
Plugging in all the values we get the equation:
[tex]x^2+y^2=64[/tex]
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The ellipse shown here is a horizontal ellipse that has major axis parallel to x - axis and minor axis parallel to y - axis. Length of major axis = 2a, and that of minor axis = 2b.
And it has it's centre on origin, it's equation can be written as :
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
so, let's equate given equation with the standard equation ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]
so we get :
a² = 64 ; a = 8b² = 36 ; b = 6As we know, length of major axis is : 2a = 2 × 8 = 16 units
and, the larger circle has diameter = 2a = 16 units
so, it's radius = 8 units ~
Now, let's write the equation of circle with origin as centre and radius = 8 units
[tex]\qquad \sf \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
[ h = 0, k = 0, since circle has centre at origin ]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + {y}^{2} = 64[/tex]
Distance between -11 and 4 on a number line?
Answer:
Distance = 15
Step-by-step explanation:
4 - (-11) = 4 + 11 = 15
Use five different colors to paint the four rectangles A, B, C and D shown in the figure. No two rectangles sharing an edge can be the same color. How many ways are there to color the rectangles?
There are 120 ways to color the 4 rectangles
How to determine the number of ways?The given parameters are:
Paints, n = 5
Rectangles, = 4
The number of ways to color the rectangles is
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^5P_4[/tex]
Apply the permutation formula
[tex]Ways = \frac{5!}{1!}[/tex]
Evaluate the expression
Ways = 120
Hence, there are 120 ways to color the 4 rectangles
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write and solve an inequality that means a number plus four than or equal to twelve.
The correct answer for the solution of inequality is [tex]x\geq 8[/tex].
Let the unknown number be "[tex]x[/tex]."
The statement "a number plus four" can be written as "[tex]x+4[/tex]."
The phrase "is greater than or equal to twelve" can be expressed as "[tex]\geq 12.[/tex]
Put these together, the inequality becomes:
[tex]x + 4\geq 12[/tex]
solve for "[tex]x[/tex]," isolate the variable on one side of the inequality:
Subtract -[tex]4[/tex] from both side of the expression:
[tex]x + 4 - 4 \geq 12 - 4[/tex]
[tex]x\geq 8[/tex]
The correct expression for the inequality is [tex]x\geq 8[/tex]
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07* Calculate the limits
(a) lim x→∞ (3x^7/2+7x^-1/2) / (x²-x^1/2)
infinity
-infinity
3
1
The limit is
[tex]\displaystyle \lim_{x\to\infty} \frac{3x^{7/2} + 7x^{-1/2}}{x^2 - x^{1/2}} = \lim_{x\to\infty} \frac{3x^{3/2} + 7x^{-5/2}}{1 - x^{-3/2}} = \boxed{\infty}[/tex]
since the degree of the numerator exceeds the degree of the denominator.
an angle exceeds three times its complement by 10 find it. please explain properly i will mark as brilliant
Answer:
It's supplementary angle I think
Answer:
one angle is 20° and the other is 70°
Step-by-step explanation:
Complementary angles add up to 90°.
Here it is given that an angle exceeds 3 times its complement by 10. So, we are taking the complement as x. Since it exceeds its complement 3 times, we are multiplying the complement 3 times. so we get [tex]3x[/tex].
Now we also need to add 10, so we get the final equation [tex]3x+10[/tex], which is the second angle.
As of now, first angle = x and second angle = 3x+10.
Since they are complementary angles, both angles add up to 90°
⇒ 1st angle + 2nd angle = 90°
∴ [tex]x+3x+10 = 90[/tex] [since 3x and x are like expressions, we should add 3x + x = 4x]
⇒ [tex]4x = 90 - 10[/tex] [by transposing 10 from LHS to RHS]
⇒ [tex]4x = 80[/tex]
⇒ [tex]x = \frac{80}{4}[/tex] [by transposing 4 from LHS to RHS]
⇒ [tex]x = 20[/tex]
∴The complementary angle is 20° and the given angle is [(3 × 20) + 10)] = 70°