The measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.
We have been given the measure of each side of an equilateral triangle whose area is √3 cm².
Let the measure of each side would be "a"
We know that,
Area of an equilateral triangle = √3a² / 4
As per the question,
⇒ √3 cm²= √3a² / 4
⇒ √3a² = 4√3 / √3
⇒ a² = 4 = √4
⇒ a = 2 cm
Thus, the measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.
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Which number is a multiple of 4?
A.) 6
B.) 9
C.) 15
D.) 12
Answer:
D: 12
Step-by-step explanation:
multiples of 4: 4,8,12,16,20
12 is the only number that can be divided by 4 on the list
Hopes this helps please mark brainliest
Answer:
D. 12
Step-by-step explanation:
12 is a multiple of 4 because 4 goes into 12 (evenly, with no remainder).
That's what being a multiple means.
All the "answers" to 4 times table questions are multiples of 4. Here they are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...
Can't actually list them all because the list goes on forever.
NAME
DATE
Topic Representing Linear Relationships
PERIOD
4. A mountain road is 5 miles long and gains elevation at a constant rate.
After 2 miles, the elevation is 5,500 feet above sea level.
After 4 miles, the elevation is 6,200 feet above sea level. (Lesson 3-6)
a. Find the elevation of the road at the point where the road begins.
The elevation of the road is 4800 feet.
From the question, we have
y = mx + b
where m is the rate of change, b is the initial value of y and y, x are variables.
Let y represent the elevation of the road after x miles.
After 2 miles, the elevation is 5500 feet above sea level.
5500 = 2m + b (1)
After 4 miles, the elevation is 6200 feet above sea level.
6200 = 4m + b (2)
Solving equation 1 and 2, we get
m = 350, b = 4800
The elevation of the road 4800 feet.
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers. The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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(b) Write down the value of 12⁰
(c) Write down the value of 3-²
Answer:
b) 1 c) 0.1Step-by-step explanation:
b) The value of 12⁰ will be?
→ 12⁰ = ?
→ 12⁰ = 1
Hence, the solution is 1.
c) The value of (3)^(-2) will be?
→ (3)^(-2) = ?
→ (3)^(-2) = 0.1
Hence, the solution is 0.1.
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The maximum area that the material would cover is 640, 000 square yards
What is rate of change?A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then
rate of change = change in y / change in x
if 3200 yards was used for fencing, then 3200 yards is perimeter
and perimeter of a rectangle = 2( L + B)
so that,
2(L + B) = 3200
L + B = 1600
express L in terms of B
L = 1600 - B
Area(A) = L X B
A = L X B
substitute L = 1600 -B
A = (1600 - B) x B
multiply out
A = 1600B - [tex]B^{2}[/tex]
for maximum area,
[tex]\frac{dA}{dB}[/tex] = 0
But dA / dB = 1600 - 2B
1600 - 2B = 0
2B =1600
B = 1600/2
B = 800 yards
L = 1600 - B
L = 1600 - 800
L = 800 yards
Area = L X B
A = 800 x 800
A = 640,000 square yards
In conclusion, he maximum area is 640,000 square yards and the dimensions are 800 yards by 800 yards
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write the quotient as a power. a^21/a
the quotient as a power. a^21/a is a^20.
What is Power?
In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.
What is quotient?
The number we obtain when we divide one number by another is the quotient.
What is exponential function?
An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
Given that,
a^21/a
quotient as power = a^21/a
= a^(21-1)
= a^20
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,−1) and (8,7).
Answer: [tex]y=-\frac{1}{2}x+6[/tex]
Step-by-step explanation:
The slope of the line segment is [tex]\frac{-1-7}{4-8}=2[/tex].
So, the slope of the perpendicular bisector is -1/2.The midpoint of the line segment is [tex]\left(\frac{4+8}{2}, \frac{-1+7}{2} \right)=(6, 3)[/tex].
Thus, the equation is:
[tex]y-3=-\frac{1}{2}(x-6)\\\\y-3=-\frac{1}{2}x+3\\\\y=-\frac{1}{2}x+6[/tex]
Dolev shared his pretzels equally among 5 friends. If each friend received 7 pretzels, how many pretzels did Dolev have? Select all that apply. StartFraction p Over 5 EndFraction = 7 Divide by 5 on both sides of the equation. Multiply by 5 on both sides of the equation. 7 × 5 = 35. 7 ÷ 5 = 1.4. Dolev had 35 pretzels.
The correct options are that Multiply by 5 on both sides of the equation.
7 × 5 = 35. thus Dolev had 35 pretzels.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that Dolev has 5 friends and each friend got 7 pretzels, the equation that can be used to represent this will be;
p / 5 = 7
In order to determine the value of p, the following steps would be taken :
Now Multiply both sides of the equation by 5:
p = 7 x 5
Then Determine the product of the numbers :
7 x 5 = 35
The correct options are; that Multiply by 5 on both sides of the equation.
Dolev had 35 pretzels.
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Divide these numbers in the given ratios
36 in the ratio 4:5
8 The table shows number of bottles of water four
students drank. One bottle holds 335 milliliters. How
many more fluid ounces did Michael drink than
Lydia? (Hint: 1 fl oz ≈ 30 mL)
Kyle = 5 Bottles of Water
Lisa = 4 Bottles of Water
Lydia = 3 Bottles of Water
Michael = 6 Bottles of Water
Michael drinks 33.5 fl oz more fluid ounces than Lydia.
Given in question,
30 ml = 1 fl oz
1 ml = 1/30 fl oz
1 bottle = 335 milliliters
No. of bottles of water Michael drank = 6
= 6 * 335 milliliters
= 2010 milliliters
= 2010/30 fl oz
= 67 fl oz
No. of bottles of water Lydia drank = 3
= 3 * 335 milliliters
= 1005 milliliters
= 1005/30 fl oz
= 33.5 fl oz
Therefore, 67 - 33.5 = 33.5
Hence, Michael drinks 33.5 fl oz more fluid ounces than Lydia.
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so what is 9/4 divided by 6/5
Answer:
45/20
Step-by-step explanation:
Answer:
9/4 divided by 6/5 is 15/8
Step-by-step explanation:
9/4 ÷ 6/5 turns into 9/4 × 5/6 which is the reciprocal
9/4 × 5/6 = 45/24
Divide the numerator and denominator by 3 to get 15/8
15/8 is in its simplest form
f(x) = (1 + =)",
k, n EN,
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x),
(a) prove that n = 6k + 2.
Given also that the coefficients of x4 and x5 are equal and non-zero,
(b) form another equation in n and k and hence show that k = 2 and n = 14.
Using these values of k and n,
(c) expand f(x) in ascending powers of x, up to and including the term in x5.
Give each coefficient as an exact fraction in its lowest terms
n>2
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x)
(a) It is proved that n = 6k + 2
(b)k = 2 and n=14
(c) After expansion, the equation is
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
What is the binomial theorem?
The algebraic expansion of a binomial's powers is described by the binomial theorem (also known as binomial expansion) in elementary algebra.
The theorem states that the polynomial (x + y)n can be expanded into a sum including terms of the form axbyc, where the exponents b and c are nonnegative integers and b + c = n, and the coefficient an of each term is a particular positive integer dependent on n and b.
Solution Explained:
f(x)= (1+x/k)^n
Given that the coefficient of x^3 is twice the coefficient of x^2 in the binomial expansion of f(x)
a)
Coeff of x^3 = 1/6[n(n-1)(n-2)/k3]
Coeff of x^2 = 1/2[n(n-1)/k2]
1/6[n(n-1)(n-2)/k3] = 2* 1/2[n(n-1)/k2]
Canceling on both sides gives:
(n-2)/(6k) = 1
n = 6k+2 Hence proved
Given also that the coefficients of x^4 and x^5 are equal and non-zero,
b)
Coeff x^4 = 1/24 [n(n-1)(n-2)(n-3)/k4
Coeff x^5 = 1/120 [n(n-1)(n-2)(n-3)(n-4)/k5
1/120 [n(n-1)(n-2)(n-3)(n-4)/k5 = 1/24 [n(n-1)(n-2)(n-3)/k4
Canceling gives:
(n-4)/(120k) = 1/24
n = 5k+4
From previous:
n = 6k+2 = 5k+4
k = 2
n=14
Using these values of k and n,
c)
Give each coefficient as an exact fraction in its lowest terms
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
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How many times greater is 1.88 times 10^2 than then mass of 2.35 times 10^-1
1.88 × 10² greater than 2.35 × 10⁻¹ by 800 times which is found by using division.
The two numbers given are:
1.88 times 10²
= 1.88 × 10²
And
2.35 times 10⁻¹
= 2.35 × 10⁻¹
We need to find that how much time is 1.88 × 10² greater than 2.35 × 10⁻¹.
We will use division for the same.
So, we get that:
= 1.88 × 10² / 2.35 × 10⁻¹
Using the rules of exponents and simplify the expression, we get that:
= 0.8 × 10 ²⁺¹
= 0.8 × 10³
= 0.8 × 1000
= 800
Therefore, we get that, 1.88 × 10² greater than 2.35 × 10⁻¹ by 800 times which is found by using division.
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P. USE REPRESENTATIONS Sheila plans to invest $2000 or less in two different accounts. The low
risk account pays 3% annual simple interest, and the high risk account pays 12% annual simple
interest. Sheila wants to make at least $150 in interest this year.
a. Define the variables, then write and graph a system of inequalities to show how Sheila can
split her investment between the accounts.
Inconclusion the amount she invested in each account is $1,000 invested at interest rate 12% .
What is interest rate?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.Let x represent the amount invested at 3%.
. 12x +.03(2000-x)= 150
.09x+ 60 = 150
Collect like terms
.09x = 90
Divide both side by .09x
x = 90/.09
x=$1000
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HELP ME PLS IM STRUGGLING
1. If 1(-1) for the polynomial f(z) = 2z+z²-5 is-2, can you use the Factor Theorem to find the other factor?
No, because (x+1) is not a factor of the polynomial f(z) = 22 +2²-5,
Yes, because (x + 1) is a factor of all degree 4 polynomials.
No, because-2 is not an irrational number.
Yes, because-2 is the opposite of the leading coefficient of f(z) = 2x¹ +2²-5.
Answer: yes, because -2 is the opposite of the leading coefficient
Step-by-step explanation:
URGENT PLEASEEE!
What is an equation of the line that passes through the points (2, -8) and (-6, 0)
Answer:
It should be y=2x-1
Step-by-step explanation:
the robots are powered coffee alone. They use 2 bags of coffee each day. how long will 1/4 of a bag last them?
Answer:
3 hours
Step-by-step explanation:
The robots are powered coffee alone. They use 2 bags of coffee each day. how long will 1/4 of a bag last them?
1/4 = 0.25
0.25 / 2 = 1/8 or 0.125
0.125 * 24 hours = 3 hours
the owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. all measures are recorded in thousands of dollars. the summary output for the regression model is given below. anova df ss ms f significance f regression 6 19.4512364 3.24187273 18.10468324 1.2794e-05 residual 13 2.327814576 0.17906266 total 19 21.77905098 step 1 of 3 : what is the coefficient of determination for this model, r2? round your answer to four decimal places.
R square is the most appropriate compared to the adjusted r square value.
What is coefficient ?In mathematics, a coefficient is a multiplicative coefficient of some term in a polynomial, series, or expression. Usually numeric, but can be any expression. If the coefficients themselves are variables, they can also be called parameters.
CalculationIn this question, it is given that some of coils due to regression equal 16.75147827, likewise the samosta- is due to residual equals 5.751489304. So the total sum of squares. When we add this, both we will get 22.50296757. Likewise, it is given that the degrees of freedom for regression equals 110 degrees of freedom for residual equal 6, so the total degree of freedom is 7. So the first question is that we have to find the coefficient of determination for this data.We know that coefficient of determination, which is denoted by r square, equal s, s regression divided by the summa square for total, so this is equals 16.751 47827 divided by 22.50296757. So this is equals 0.744. 412 point. So we got the coefficient of determination that is r square. Next, we have to find the jester square. We know that jested r square equals 1 minus s s residual, divided by degrees of freedom, for residual, divided by s; s total divided by the degrees of freedom. For total, so this is equals 1 minus 5.751489304 divided by 6, divided by 22.50296757, divided by 7 point. So this is equals. 0.70. 1. 81. 4 point, so we got the adjusted r square value for this data. Also. The third question is that from these 2, which statistics is most appropriate for the pisareane order to determine the usefulness of the regression model and y, so we can say that r square is most appropriate, since the model has only 1 independent variable. So among the adjusted r square and r square, we can say that r square is the most appropriate compared to the adjusted r square valuelearn more about coefficient here :
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At the beginning of a chemistry experiment, the volume of liquid in a container was 3 milliliters. During the experiment, the volume dropped to
2.1 milliliters. Find the percent of decrease.
Answer:
30%
Step-by-step explanation:
To calculate the percent of change, you find the amount of change and divide that my the original amount
[tex]\frac{3-2.1}{3}[/tex] = [tex]\frac{.9}{3}[/tex] = .3 As a percent, this would be 30%
Write these numbers in standard form.
a) 200000
b) 80000
c) 900 000 000
d) 10 000 000 000
Answer:
a) 2.0 x 10^5
b) 8.0 x 10^4
c) 9 x 10^9
d) 1 x 10^10
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Robin's bank account has $1,876. Every month she withdraws $30 for her phone payment. Create an equation to describe how
much money she will have after a certain amount of months. Write the equation for this problem in function notation. Then
interpret how much money Robin will have after 6 months of payments. Make sure to define your variables and show all of your
work.
Answer: M = 1876 - 30n will give the amount of Money (M) remaining after n months of withdrawing exactly $30 per month, PROVIDED NOTHING ELSE IS EVER ADDED TO OR WITHDRAWN FROM THE ACCOUNT. (Not very realistic.)
Use n=6 to provide the balance after 6 months.
Step-by-step explanation:
in the simple linear regression equation , the term b0 represents: a. estimated or predicted response b. estimated intercept c. estimated slope d. explanatory variable
In the simple linear regression equation , the term b0 represents b) Estimated intercept
Define estimated intercept.The expected mean value of Y when all X=0 is the intercept, also referred to as the constant. Create a regression equation with X as the only predictor to begin. The expected mean value of Y at that value is the intercept in the event that X occasionally equals 0. When x is 0, the projected value for y—the intercept of the regression line—is simply 0. A line's slope and intercept can be expressed in terms of the equation y = slope x x + intercept. The Value of Interception The point where the function crosses the y-axis is known as the intercept and is frequently denoted as a constant. In some analyses, removing the intercept and reducing the regression line to Y = bX + error causes the regression model to only become significant.
Given,
In the simple linear regression equation , the term b0 represents:
b) Estimated intercept
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Which shape has exactly 4 lines of symmetry?
Answer:
Step-by-step explanation:
its a square so choose the yellow square.
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The equation of the parabola is f(x) = 7(x-3)^2+5.
Given:
The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.
If the parabola has same shape then its a values are same.
so f(x) = 7x^2
here a = 7
so the equation with vertex (3,5) also has a value is 7.
(h,k) = (3,5)
f(x) = a(x-h)^2+k
= 7(x-3)^2 + 5.
Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.
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Calculate the area of the square!
Answer:
The answer is 169
Step-by-step explanation:
im stumped please help
10p^2 - 20p - 34 = -4
Answer:
p = -1 ; p= 3
Step-by-step explanation:
10p^2 - 20p - 34 +4 = 0
10p^2 -20p - 30 = 0
10/10 p^2 - 20/10 p - 30/10 = 0
p^2 - 2p - 3 = 0
(p-3)(p+1) = 0
p = 3
p = -1
1. Why is identifying
the domain and range important when
defining a function?
Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.
Domain are represented by independent variable and are graphed on x coordinate of the axis.
Range are dependent values and are graphed on y axis of the graph.
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67,107 rounded to the nearest ten-thousand
Answer:
70,000
Step-by-step explanation:
Round up if the next digit is higher than or equal to 5.
edit: accidentally answered twice
Answer:
70,000
Step-by-step explanation:
Round up if the next digit is higher than or equal to 5.
if our circadian clocks are not reset each morning by exposure to light, they: a. tend to run a cycle that is a little longer than 24 hours b. tend to run a cycle that is a little shorter than 24 hours c. tend to run on a 12-hour cycle d. still run exactly on a 24-hour cycle
If our circadian clocks are not reset each morning by exposure to light, they a. tend to run a cycle that is a little longer than 24 hours.
Chronobiology, the study of the body's circadian rhythms, contends that our daily routine, including when we eat, exercise, go to bed, and are exposed to light, may have a significant impact on how our bodies function on a day-to-day basis.
According to the National Institute of General Medical Sciences, circadian rhythms are the normal physical, mental, and behavioral changes that take place in the body on a 24-hour cycle, typically in reaction to light and darkness. One illustration is resting at night and remaining awake during the day.
You might not be able to avoid daytime sleep and evening work if you work an overnight shift or other irregular hours. According to Wright, those people should pay extra close attention to making other healthy decisions a priority, such as getting enough exercise and quitting smoking.
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