The possible values of angles A and C are;
60° and 70° or 55° and 75°
How to find the angles in a triangle?
An acute triangle is a triangle that has all the measures of its angles to be less than 90°. This means that none of the angles is greater than 90°
Since sum of the angles in a triangle is equal to 180°, then it means that;
∠A + ∠B + ∠C = 180°
We are given that;
∠B = 50°
Thus;
50° + ∠A + ∠C = 180°
∠A + ∠C = 180° - 50°
∠A + ∠C = 130°
It should be noted that all the angles of the acute triangle are also different.
Thus, the possible values of A and C are 60° and 70° or 55° and 75° because their sum must be equal to 130°
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A corner shelf is of a circle and has a radius of 10.5 inches.
10.5 in
10.5 in
Enter the area of the shelf, in square inches. Round your answer to the nearest hundredth
Answer: 346.19
Step-by-step explanation:
So we know that the radius of the corner shelf is 10.5 inches. So first you write down the formula for finding the area of a circle. The formula for finding the area of a circle is:
A= pi x r squared
A= 3.14 x 10.5 squared
A= 3.14 x 110.25
A= 346.185 or 346.19
Hope that helps
Solve this equation. Enter your ans
-4(x-26) = -200
Solve the following radical equations.
2√x =√(x+1)
The solution for the radical equation 2√x =√(x+1) is x=1/3
The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
Eliminate the radical on the both sides by squaring on both sides-
Both sides must be raised to the second power
(2√x)²=(√x+1)²
After squaring we get 4x=x+1
Solving the equation-
We get rearranged equation as 4x=x+1
3x=1 x=1/3
Check if the solution is correct by putting it in original equation-putting x=1/3 in the equation 2√x =√(x+1)
2×√1/3=√1/3+1
4/3=4/3
Therefore, the solution for the radical equation 2√x =√(x+1) is x=1/3.
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Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₃ 8
Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 8}{log \\3}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
[tex]log_38[/tex]
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
[tex]log_38[/tex] = [tex]\frac{log \ 8}{log \ 3}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 8}{log \\3}[/tex]
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Simplify each number. 64²/₃ 64²/₃
The result of simplifying each number 64²/₃ 64²/₃ using the exponent rules is 256
To solve this exercise we have to resolve algebraic operations following the exponent rules.
64²/₃ * 64²/₃
Base= 64Exponent = 2/3The base number 64 is the same that: 4³, then we get:
(4)³ ⁽²/₃⁾ * (4)³ ⁽²/₃⁾
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
4⁽³*²/³⁾ * 4⁽³*²/³⁾
4⁽⁶/³⁾ * 4⁽⁶/³⁾
(4)² * (4)²
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
4⁽²⁺²⁾
4⁴
4*4*4*4
256
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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According to the box-and-whisker plot shown above, identify the following:
5) The 25th quartile
6) The 75th quartile
7) The range
According to the box-and-whisker plot,
5)The 25th quartile = 60
6)The 75th quartile = 100
7)The range = 40
Box-and-whisker plot allows us to determine the mean, the largest or the lowest number in the data set as well as the quartiles in the data.
In this case, from the given figure,
Median is equal to = 80,
The range is equal to = 110-40
We can subtract the value,
So we can write,
The range is equal to = 70.
The 25th quartile is equal to = 60
The 75th quartile is equal to = 100.
The range is equal to = 100-60
We can subtract the value,
So we can write,
The range is equal to = 40.
So,
Then,
The median=80
The range=70
Therefore,
According to the box-and-whisker plot,
5)The 25th quartile = 60
6)The 75th quartile = 100
7)The range = 40.
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( 4, -3 ) ( 8 , -3 ) slope
The perimeter of a rectangle is equal to two times the length plus twice the width
The expression of the mathematical statement given as "The perimeter of a rectangle is equal to two times the length plus twice the width" is P = 2l + 2w
How to rewrite the statement as an expression?The mathematical statement is given as
The perimeter of a rectangle is equal to two times the length plus twice the width
Represent the perimeter with P
So, we have
P is equal to two times the length plus twice the width
Represent the length and the width with l and w
So, we have
P is equal to two times l plus twice w
So, we have
P = 2l + 2w
Hence, the expression of the mathematical statement given as "The perimeter of a rectangle is equal to two times the length plus twice the width" is P = 2l + 2w
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Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd-numbered page. What page is Josiah reading?
The two pages the boys are reading are pages 31, and 30. I'm not sure which is which. (would depend on who is reading the odd number page).
Josiah is reading page 31. The page he is reading is an odd-numbered page is 31 by factorizing number.
Step 1: Determine the factors of 930.
The factors of 930 are 1, 2, 3, 5, 6, 10, 15, 31, 62, 93, 155, 186, 310, 465, and 930.
Step 2: Identify the factors that correspond to odd-numbered pages in the book.
Since Josiah is reading an odd-numbered page, eliminate the even factors.
This leaves with the odd factors:
1, 3, 5, 15, 31, 93, 155, and 465.
Step 3: Determine which odd factor corresponds to a page number within the range of the book.
Since the book has 50 pages, eliminate the odd factors greater than 50. This leaves us with the odd factors: 1, 3, 5, 15, and 31.
Step 4: Identify the odd factor that, when multiplied by its complement, equals 930, that is:
31 × 30 = 930,
so Josiah is reading page 31.
Therefore, Josiah is reading page 31 of the book.
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Can someone help me with this one
Answer:
#9 has 8 vertices
# 10 has 5 vertices
Step-by-step explanation:
A vertex is is a point where two or more curves, lines, or edges meet. The word "vertices" is the plural of the word "vertex."
Evaluate each logarithm.
log₂2⁵
After evaluating the logarithm log₂ 2⁵, we get the result as 5.
The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.
For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output. The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.
For example, the natural logarithm of 78 is written as ln 78. The natural logarithm determines how much we need to multiply "e" to get the required output.
We need to evaluate log₂ 2⁵Using the property logₐ (mⁿ) = n logₐ m log₂ 2⁵ can be written as
log₂ 2⁵ = 5 log₂ 2
We know that logₐ a = 15 log₂ 2= 5
Therefore, after evaluating the logarithm log₂ 2⁵, we get the result as 5.
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Doctors recommend us to eat between 3 to 8 percent of our bodyweight each day. If one
day someone eats 7.2 pounds, calculate the biggest weight the person can be by writing
an inequality to model this situation.
The biggest weight the person can be based on the recommendation by the doctor is 90 pounds.
How to calculate the value?From the information, it was stated that doctors recommend us to eat between 3 to 8 percent of our bodyweight each day and that one day someone eats 7.2 pounds.
It should be noted that based on the information given, the highest percentage which is 8% will be used for the calculation.
Therefore, the biggest weight the person can be will be:
8% of x <= 7.2
0.08x <= 7.2
x <= 7.2/0.08
x <= 90 pounds
Therefore, the biggest weight the person can be based on the recommendation by the doctor is 90 pounds.
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If f(x) = x-5, evaluate each of the following. Type a numerical answer in the space provided.
f(-1)=
f(0) =
f(1) =
f(2)=
f(5) =
f(8) =
Answer:
see explanation
Step-by-step explanation:
substitute the values of x, situated inside the parenthesis into f(x)
f(- 1) = - 1 - 5 = - 6
f(0) = 0 - 5 = - 5
f(1) = 1 - 5 = - 4
f(2) = 2 - 5 = - 3
f(5) = 5 - 5 = 0
f(8) = 8 - 5 = 3
1) Substitute x = -1 into f(x) = x - 5
f(x) = x - 5f(-1) = (-1) - 5f(-1) = - 1 - 5f(-1) = -62) Substitute x = 0 into f(x) = x - 5
f(x) = x - 5f(0) = (0) - 5f(0) = 0 - 5f(0) = -53) Substitute x = 1 into f(x) = x - 5
f(x) = x - 5f(1) = (1) - 5f(1) = 1 - 5f(1) = -44) Substitute x = 2 into f(x) = x - 5
f(x) = x - 5f(2) = (2) - 5f(2) = 2 - 5f(2) = -35) Substitute x = 5 into f(x) = x - 5
f(x) = x - 5f(5) = (5) - 5f(5) = 5 - 5f(5) = 06) Substitute x = 8 into f(x) = x - 5
f(x) = x - 5f(8) = (8) - 5f(8) = 8 - 5f(8) = 3Evan charged Jill $32 for parts and $15 per hour to repair her bicycle. If he spent 4 hours repairing
her bike, how much does Jill owe him?
Answer:
$92
Step-by-step explanation:
32+4x where x is 15
32+(4*15)=?
32+60=92
what is the range of the data set: 7, 12, 15, 4, 23, 15, 25, 9
Answer: 21
Step-by-step explanation:
When it comes to finding the range, you must take the biggest number and subtract it from the smaller number, therefore in your question the answer is
25 - 4 = 21
Hope it helped :D
3(2x-2)=6(x-1)
How do you do this
[tex]\large\bf\implies{infinitely \:many\: solutions}[/tex]
Alternate forms :
[tex] \large \bf \implies{x \in ( - \infty \: , \infty)}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow{3(2x - 2) = 6(x - 1)}[/tex]
Apply the Distributive Property[tex] \bf \longrightarrow{6x - 6 = 6x - 6}[/tex]
Rearrange variables to the left side of the equation[tex] \bf \longrightarrow{6x - 6x = - 6 + 6}[/tex]
Apply the inverse property of addition[tex] \bf \longrightarrow{0 = 0}[/tex]
Bases on the given conditions, the (system of) equation(s) has[tex]\bf \longrightarrow{infinitely \:many\: solutions}[/tex]
Juan and his children went into a restaurant where they sell drinks for $2 each and
tacos for $4 each. Juan has $40 to spend and must buy a minimum of 11 drinks and
tacos altogether. If a represents the number of drinks purchased and y represents
the number of tacos purchased, write and solve a system of inequalities graphically
and determine one possible solution.
The number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.
How to generate Inequality Graph?We are given that;
a represents the number of drinks purchased.
y represents the number of tacos purchased
He must buy a minimum of 11 drinks and tacos altogether. Thus, the inequality that describes this is;
2a + 4y ≤ 40
a + y ≥ 11
The inequality graph that represent the given system of inequalities is as shown in the atatched file.
From the given inequality graph, we can tell that one possible solution is; (a, y) = (2, 9)
Thus, the number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.
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How do you model a situation in which a function behaves differently over different parts of its domain?
Enter your answer.
The situation in which a function behaves differently over different parts of its domain is modeled by considering it to be a piecewise function.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable
Such a situation can be explained through an example:
f(x) = { x, for x > 0
{ 1, for x = 0
{ -x, for x < 0
now, when we take x value less than 0, say x= -1
thus, f(x)= f(-1)= -(-1) = 1 , here we used f(x) given x<0
now, when we take x value more than 0, say x= 1
thus, f(x)= f(1)= (1) = 1, here we used f(x) given x>0
now, when we take x = 0,
thus, f(x)= f(0)= 1, here we used f(x) given x=0
this is how we model piecewise function, we use f(x) as per the value of x. Following image shows plotted answer for this example.
Since inequalities given are exclusive of 0, we leave the dot at the origin unfilled. Now, for x = 0. Since the value is constant at f(x) =1, we pointed a point at (0,1)
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What is it? Do y’all know
Answer: I believe it is ZERO
Step-by-step explanation:
Answer:
No Solution
Source: cymath.com
Step-by-step explanation:
Yuan read 15 books from the library each month for y months in a row. Write an expression to show how many books Yuan read in all. Then evaluate the expression for y = 9. (if you see this question pls answer!) tysm
15y; 135 books
15/y; 135 books
15 + y; 24 books
15 − y; 24 books
The expression for y months is 15y and the number of books is 135
How to write an expression to show how many books Yuan read in all?The rate is given as
Rate = 15 books in a month
The number of month is given as
Months = y
The total number of books is
Total = Rate * Months
So, we have
Total = 15 * y
Evaluate
Total = 15y
When y = 9, we have
Total = 15 * 9
Evaluate
Total = 135
Hence, the expression for y months is 15y and the number of books is 135
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what is the distance of (-3, 7) and (77, -11)
Answer: Option D is correct.
Step-by-step explanation:
Given: 7 and 11
We need to find the geometric mean of 7 and 11.
Geometric series whose common ratio is equal.
The geometric mean of two numbers is the square root of the product of two numbers.
If a, b and c are in GP then the geometric mean is b
The geometric mean of any two numbers a and b is
The given numbers are 7 and 11
Geometric mean is [tex]\sqrt 7x11\\[/tex]
Geometric mean: [tex]\sqrt{x} 77[/tex]
Question 4 of 10
If you subtract 13 from an even number, the answer will be odd.
A. True
OB. False
SUBM
I know the answer this is the see what you know.
Think of a number 3-8
Multiply
If you can’t then add it 5 times
Tell me what you got
Answer:
I think about 5
5+5+5+5+5
25.
1. The regular price of a sweater is $80. It is on sale for 25% off. Find the final price
including 13% tax.
No links
Answer:
Step-by-step explanation:
hi
A student wants to save $ 8000 for college in five years. How much should be put into an account that pays 5.2% annual interest compounded continuously?
- What information do you know?
The amount that should be put into account is $6171.88
The formula for the compounded continuously is
[tex]A = P(1 + {r}/{n})^{tn}[/tex] (1)
where , A = future amount or the final amount
P = principal amount to be invested
r = annual interest rate
t = time
n = number of compounding in a year
According to the question we have been given that
A = $8000
r = 0.052
t = 5
n = 12
putting the required values in equation (1) we get
8000 = P(1 + 0.052/12)^(5*12)
8000 = P (1.004)^60
8000 = P*1.27
P = 8000/1.27
P = $6171.88
Thus the amount that should be put into account is $6171.88
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4x10^6 is larger than 2x10^3 by what number
Write each logarithmic expression as a single logarithm. log₂4+3 log₂9
The solution for the given logarithmic expression log₂4+3 log₂9 as a single logarithm is log₂ (2916).
What are the logarithmic expression?A logarithmic equation is one that includes a logarithm in the variable x.
An exponential formula is one where the variable is represented by an exponent. To answer exponential equations, first determine whether both sides of the equation can be written as powers of the exact number. If you can't, take the common logarithm from both of the equation's sides and use property 7 to solve the problem.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿNow, as per the stated condition in question;
The expressed equation is;
= log₂4+3 log₂9
Using the Power Rule in the second term.
= log₂4+log₂9³
= log₂4+log₂729
As, the base of each log term is 2. We can use product rule to simplify the equation.
= log₂(4×729)
= log₂ (2916) [As a single log function]
Therefore, the simplification of the given logarithmic expression as the single logarithm is log₂ (2916).
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Hello please can you help me for this i am new i will give all my points
Solve each equation. Check your answers.
2 log (x+1)=5
2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: 2 log (x + 1) = 5
=> log (x + 1) = [tex]\frac{5}{2}[/tex]
Raising both sides by 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(x+1)} = 10^{2.5}[/tex]
=> x + 1 = 316.22 ( as [tex]a^{log_a(x)} = x[/tex])
=> x = 315.22
Hence, 2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.
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4(x-8)= 4x + 2
what is x
Answer:
undefined
Step-by-step explanation:
4x-32=4x+2
-4x
-32=2
undefined