The value of m∠2 will be equal to 40°.
Transversal may be defined as a line which cuts two different lines which lie on the same plane at two different points. Alternate interior angles may be defined as the angles which are formed when a transversal cut the two different lines. These angles lie on the interior of the parallel lines, but they are on the opposite side of the transversal. If two parallel lines are cut by a transversal, then their alternate interior angles are equal. Thus, m∠1 = m∠2
4(x + 2) = 2x + 24
4x + 8 = 2x + 24
2x = 16
=> x = 16/2
=> x = 8
Now, m∠2 = 2x + 24
m∠2 = 2×8 + 24
m∠2 = 40° which is the required answer.
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(b-2)x = 8In the given equation, b is a constant. If the equationhas no solution, what is the value of b ?A) 2B) 4C) 6D) 10
(b-2)x = 8
In the given equation, b is a constant. If the equation
has no solution, what is the value of b ?
Step 1
identify
b is a constant, so (b-2) is a constant too.
If the equation has no solution, it is, there is not a value of x to satisfy (b-2)x=8
Step 2
solve for x
[tex]\begin{gathered} \left(b-2\right)x=8 \\ x=\frac{8}{(b-2)} \\ \end{gathered}[/tex]This value becomes indeterminate when the denominator takes the value of zero,it is
[tex]\begin{gathered} b-2\text{ =0} \\ \text{isolating x} \\ b=2 \\ \end{gathered}[/tex]so , the value of b=2 makes the equation has no solution.
Answer
A) 2
)) Solve for r. 1= 2r - 1
Answer:
r=1
Step-by-step explanation:
1=2r-1
Add 1 on both sides
2=2r
Divide 2 on both sides
r=1
Enter the value for n for the equation 3^5 x 3^n = 3^8
Hope this will be helpful.
Given l || m
n, find the value of x.
m
The value of 'x' is highlighted in the box
Write the equation in standard form for the circle with center (-5,0) passing through (-5, 3/2)
The equation of the circle in standard form is (x + 5)² + (y)² = 9/4.
How to write the equation of the circle in standard formThe general representation of the equation is:
(x-h)² + (y-k)²= r²
Where (h,k) is the coordinates of the center of the circle and r is the radius. And x and y are the corresponding x and y values of the point the circle passes through
Since we have the coordinate of the center as (-5,0) and the circle passes through (-5, 3/2). Therefore:
h = -5, k = 0, x = -5 and y = 3/2
Let's put these values in the formula.
(x-h)² + (y-k)²= r²
(-5 - (-5) )² + (3/2 - 0)² = r²
(-5 + 5)² + (3/2)²= r²
(0)² + (3/2)²= r²
(3/2)² = r²
r = 3/2
Putting radius, r = 3/2, h = -5 and k = 0 back into the formula wiil give:
(x + 5)² + (y - 0)²= (3/2)²
(x + 5)² + (y)² = 9/4
Therefore,the standard form of the equation of the circle is (x + 5)² + (y)² = 9/4.
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3. A construction company uses the function (p), where P is the number of
people working on a project, to model the amount of money it spends to
complete a project. A reasonable domain for this function would be
(3)
positive integers
positive real numbers
(2) both positive and negative integers
(4) both positive and negative real numbers
The domain of the function would be a positive integer.
So option 1) positive integer is correct.
What is the domain of the function?Domain of a function is the set of values accepted by the function.
So in this question the value is always a integer.
Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function if it successfully allows the production of a single value y using another value for x.
And the model is made to determine the amount of money spend to complete the project.
We can't define money in negative term.
So it must be a positive integer.
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n open rectangular box is formed by cutting congruent squares from the corners of a piece of cardboard and folding the sides up. if the original piece of cardboard was 24 inches by 45 inches, what are the dimensions of the box with maximum volume?
1080 inches² are the dimensions of the box with maximum volume .
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.rectangular box length = 24 inches
width = 45 inches
maximum volume = 24 * 45
= 1080 inches²
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I need help with my math
Consider the formula,
[tex]x^m\cdot x^n=x^{m+n}[/tex]The expression is given as,
[tex](2.3\times10^4)(3\times10^5)[/tex]Solve the expression as,
[tex]\begin{gathered} =(2.3\times10^4)(3\times10^5) \\ =2.3\times10^4\times3\times10^5 \\ =2.3\times3\times10^4\times10^5 \\ =6.9\times10^{4+5} \\ =6.9\times10^9 \end{gathered}[/tex]Thus, the given expression is evaluated as,
[tex](2.3\times10^4)(3\times10^5)=6.9\times10^9[/tex]write 0.578 as a percent?
0.578 can be expressed as a percent if we can multiply the decimal by 100%
Step 1: Multiply 0.578 by 100
To multiply by 100, we simply have to shift the decimal point by the number of zeros (twice)
0.578 x 100 = 57.8%
Answer = 57.8%
How long is the hypotenuse?
The hypotenuse of the given right angle triangle is: 50 cm
What is hypotenuse?
In mathematics, the hypotenuse is the longest side of a right angle triangle. It is defined as the standard formula, which states that the square of the hypotenuse is equal to the square of their adjacent sides.
According to the question, to calculate the hypotenuse with the given parameters. First name all the three vertices.
AB = 30 cm; BC = 40 cm; AC = ?
Using standard hypotenuse formula, which states:
AB² + BC² = AC²
⇒ 30² + 40² = AC²
⇒ AC² = 900 + 1600 = 2500
⇒ AC = 50 cm
Hence, the hypotenuse of the given right angle triangle is: 50 cm
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Emerson pays $227. 25 for 3 new wundows. Write an equation that represents the cost. C for w windows. Show work
The equation which show the cost of windows:-
C = $75.75 * W
where W = no of windows
What is equation ?
A mathematical equation can be defined in a variety of ways.
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
$227.25 ÷ 3 = $75.75
The equation which show the cost of windows:-
C = $75.75 * W
where W = no of windows
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Check
Solve the equation 3x-7 = 2.
Bruno works for Poseidon Pool Service. He needs to drain a 38,000-gallon pool so that he can repair the cracked plaster. The Pool drains 12 gallons per minute.
Write an equation to represent the pool draining in slope-intercept form.
How long will it take for the pool to fully drain? Explain using numbers and words
Bruno needs to refill the pool now that the plaster is repaired. The Pool fills 16 gallons per minute.
Write an equation in slope intercept form to represent the pool filling back up.
*
How long will it take for the pool to fill back up? Explain using words and numbers..
*
We need to find the function in slope-intercept form. We thus need the y-intercept and slope. We know there are 38000 gallons in the pool already, so the y-intercept is 38000. The pool drains 12 per minute, so the slope is -12.
y = mx + b
y = -12x + 38000
To find the time it takes to drain the pool, we need to find x where y = 0, so we set the equation to 0 and solve for x.
0 = -12x + 38000
-38000 = -12x
-38000/-12 = -12x/-12
3167 = x
Now, to fill it back up, the y-intercept is 0. We know the slope is 16, so the equation is:
y = 16x
Finally, we need to find 16x = 38000. This is simple enough.
y = 16x
38000 = 16x
38000/16 = 16x/16
2375 = x
when analyzing research data, if the difference between group a and group b did not happen by chance and the data showed a real difference, the results are called:
When analyzing research data, if the difference between group a and group b did not happen by chance and the data showed a real difference, the results are called statistically significant.
Statistically significant results occur in a research data when the difference between two groups is not likely to occur on its own, without the benefit of the independent variable. Statistically significant findings suggest that the researchers' outcomes are unlikely to be a result of chance, and that there is a relationship between the variables under investigation in the larger population. In such cases, the research usually rejects the null hypothesis and accept the alternative hypothesis.
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(50 POINTS) and will give BRAINLIEST to BEST ANSWER!
200 divided by 5 x 32 + 12 -101=______?
Answer:
–87.75
Step-by-step explanation:
Write the equation:
200 ÷ 5 • 32 + 12 – 101 = ?
PEMDAS
200 ÷ (5 • 32) + 12 – 101 = ?
(200 ÷ 160) + 12 – 101 = ?
(1.25 + 12) – 101 = ?
(13.25 – 101) = ?
–87.75 = ?
–87.75
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The front of the tent pictured at the right is shaped like an isosceles
triangle. The angles that the sides of the tent make with the ground
are congruent. If m<1 = 40°, find m<2 and m<3.
The measure of the angles 2 and 3 are 70°
What is an angle?
An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles also were generated when plane cross. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.
Given, angle 1 = 40°
and, angle 2 = angle 3 = x
In a triangle, sum of angles = 180°
or, m∠1 + m∠2 + m∠3 = 180°
or, 2x = 180-40
or, 2x = 140
or, x = 140/2 = 70°
Hence, the measure of the angles 2 and 3 are 70°
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Which of the following whole numbers are perfect squares? (Please select ALL correct answers for full credit).
Answer:
81, 100, 25, 4
Step-by-step explanation:
The square root of each of these numbers is whole
Answer:
these are the perfect squares
Step-by-step explanation:
To receive an A in a course, John must have an average of 90 or above. If johns first four exam grades are 96,90,87, and 95, what is the minimum grade John can receive on the last exam to get an A in the course?
Answer: 72
Step-by-step explanation:
The average is 90.
To calculate the average, you add the grades and divide by the total amount of them. The number of grades is 5. We need to know what value of x satisfies the following equation:
[tex]90 = \frac{96+90+87+95+x}{5}[/tex]
To solve the equation, we first multiply each side by 5, netting:
450 = 96 + 90 + 87 + 95 + x.
Then we subtract each grade from each side.
450 - 378 = 378 - 378 + x
72 = x
Choose the slope and y intercept on the graph 50 points
When we want to find the slope of a line, we divide its increase on the [tex]y[/tex]-axis by its increase on the [tex]x[/tex]-axis. In other words, we look at its [tex]tan(a)[/tex]. As you can see in the photo, I chose two points that exactly intersect the axes and connected them in a right triangle. I then divided the increase in the [tex]y[/tex]-axis ([tex]3[/tex]) by the increase in the [tex]x[/tex]-axis ([tex]4[/tex]). Since the line slopes to the right, its sign will be positive. Also, this line intersects the [tex]y[/tex]-axis [tex](x=0)[/tex] at [tex]1[/tex].
A right-angled triangle is shown below.
10 cm
0
Write tan as a decimal.
45 cm
46.1 cm
Not drawn accurately
Values given are approximate
Answer:
tan θ = 4.5
Step-by-step explanation:
tan = opposite/adjacent
The opposite of θ is 45 cm long
The adjacent of θ is 10 cm long
tan θ = 45 / 10 = 4.5
The solution is: the value of tan is : tan θ = 4.5.
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
here, we have,
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Here, we have,
we know,
tan = opposite/adjacent
from the given diagram, we get,
given that,
The opposite of θ is 45 cm long
The adjacent of θ is 10 cm long
so, we get,
tan θ = 45 / 10
= 4.5
Hence, The solution is: the value of tan is : tan θ = 4.5.
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IONS: Find the value of
85°
45°
Answer:
x = 45, y = 85
Step-by-step explanation:
In this figure we can see a Z-angle, which tells us that x = 45
In a triangle, the sum of the angles is 180 degrees,
so the unknown angle in the triangle is 180 - 45 - 85 = 50
For a straight line, the total angle is 180 degrees,
, so y + x + unknown angle of triangle = 180
since x = 45, and unknown angle of triangle = 50,
y = 180 - 45 - 50 = 85
This can also be seen when you realise that the two parallel lines give an F-angle, which tells us that Y = 85
Find the 96th term of the arithmetic sequence 1, -12, -25,
The 96th term of the arithmetic sequence (1, -12, -25,.......) is 1234.
We are provided with the arithmetic sequence mentioned below;
1, -12, -25,...........
We know that, the rule to calculate the nth term in an arithmetic sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + ( n - 1 ) d equation 1
Here, d is the difference between two consecutive terms in the arithmetic sequence , [tex]a_{1}[/tex] is the first term, n is the number of terms and [tex]a_{n}[/tex] is the nth term.
We have,
n = 96
[tex]a_{1}[/tex] = 1
d = -12 -1 = -13
Now, substitute these values in equation 1 i.e, formula of arithmetic sequence and on substituting we will get
[tex]a_{96}[/tex] = 1 + ( 96 - 1 ) ( -13 )
[tex]a_{96}[/tex] = 1 - (95) (13)
[tex]a_{96}[/tex] = 1 - 1235
[tex]a_{96}[/tex] = 1234
So, we can conclude that the 96th term of the arithmetic sequence is 1234.
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2x- y=-4 x and y intercept
Answer:
y = 2x+4
Step-by-step explanation:
2x - y = -4
We add y on both sides:
2x - y + y = -4 + y
so 2x = -4 + y
We now add 4 on both sides:
2x + 4 = -4 + 4 + y,
so 2x+4 = y,
so y = 2x+4
So intercept for y = 2x+4
Nicole's getaway spa (ngs) has been so successful that nicole has decided to expand her spa by selling merchandise. she sells things such as nail polish, at-home spa kits, cosmetics, and aromatherapy items. nicole uses a perpetual inventory system and is starting to realize all of the work that is created when inventory is involved in a business. the following transactions were selected from among those completed by ngs in august.
The journal entry will be prepared thus:
Date General Journal Debit Credit
2-Aug
Cash $540
Unearned Service Revenue $378
Sales Revenue $162
2-Aug
Cost of goods sold $105
Inventory $105
3-Aug
Accounts receivable $550
Sales revenue $550
3-Aug
Cost of goods sold $450
Inventory $450
6-Aug
Sales return (550/5) $110
Accounts receivable $110
6-Aug
Inventory $90
Cost of goods sold (450/5) $90
10-Aug
Unearned service revenue $126
Service Revenue $126
(378/3 = 126 each)
20-Aug
Cash $350
Sales revenue $350
20-Aug
Cost of goods sold $121
Inventory $121
22-Aug
Cash $440
Accounts receivable $440
What is a journal entry?A journal entry is the act of recording any transaction, whether one that is economic or not.
An accounting diary that displays the debit and credit balances of a corporation lists transactions. Multiple recordings, each of which is either a debit or a credit, may be included in the journal entry.
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Aug.2 Sold a bundle of spa services with a merchandise basket. When sold separately, the spa service part of the bundle sells for $420 and the merchandise basket normally sells for $180. Together, the bundle was sold to Val Amy for cash at a selling price of $540 (total). Val booked a spa treatment for August 10, and she took the basket of goods with her. The goods had cost NGS $105.
Aug.3 Sold 5 identical items of merchandise to Cosmetics R Us on account at a selling price of $550 (total); terms n/30. The goods cost NGS $450.
Aug.6 Cosmetics R Us returned one of the five items purchased on August 3. The item could still be sold by NGS in the future and credit was given to the customer.
Aug.10 Val Amy used one of the three spa treatments she had purchased as part of the bundle sold to her on August 2.
Aug.20 Sold two at-home spa kits to Meghan Witzel for $350 cash. The goods cost NGS $121.
Aug.22 Cosmetics R Us paid its remaining account balance in full.
Prepare all journal entries
The probability that a health nurse will find a client at home on a particular day is 0.7. what is the probability that on two home visits made by the nurse in a day, she will find each client at home?
The probability that the nurse will find the two patients is P = 0.49.
How to find the probability?
We know that the probability that the nurse finds the client on a particular day is 0.7
So, each time that the nurse goes that a home, that probability is the same and is independent of what happened before.
So if the nurse goes to two houses, the probability that she will find the client on the first home is 0.7
And the probability that she will find the client on the second home is 0.7
Then the joint probability (the product of the two individual ones) is:
P = 0.7*0.7 = 0.49
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Joe has a piece of wood that is 8/9 of a foot long. He is going to cut it into 4 equally sized pieces. He is going to sell the 4 smaller pieces of wood for a total of 10 dollars. How large will each of the 4 smaller pieces be? How much is he going to charge for each of the 4 smaller pieces?
Answer:
Step-by-step explanation:
The wood is (8/9) foot long. If cut into 4 pieces, each piece would be (8/9)/4 foot long.
(8/9)/4
((8/9)(1/4)= 8/36 or 2/9 foot long for each piece.
If he sells all 4 pieces for a total of $10, he will charge $10/4) = $2.50 each.
What is the union of the two sets A = {1, 5, 8, 12, 17} and B = {5, 17}?
{1, 5, 8, 12, 17}
{5, 17}
{1, 5, 17}
{17}
The union of set A = {1, 5, 8, 12, 17} and B = {5, 17} is
AUB= {1, 5, 8, 12, 17}
This is further explained below.
What is the union of the two sets?Generally, The set that contains all of the elements that are part of both sets A and B, or all of the elements that are part of both sets combined, is referred to as the union of the two sets A and B. The symbol is used to represent the union of all the elements in the set.
In conclusion, The union of these sets sees the value of both sets represented
A = {1, 5, 8, 12, 17} and B = {5, 17}
AUB= {1, 5, 8, 12, 17}
Option A
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Answer:
Step-by-step explanation:
just like when you have 5+(17-8) you don't have to do all the work you can just do this 17-8 is 9 and that is when you add 5+9 is 14
6 (y - 5) = 18 - 2y
[tex]6(y) + 6( -5 ) = 18 - 2y \\ 6y - 30 = 18 - 2y \\ 6y + 2y = 18 + 30 \\ 8y = 48 \\ \frac{8y}{8} = \frac{48}{8} \\ y = 6[/tex]
ATTACHED IS THE SOLUTION
The probability distribution for a random variable x is given in the table.
x -10 -5 0 5 10 15 20
probability .20 .15 .05 .1 .25 .1 .15
Find the probability that x(=>)5
Probability that x greater than or equal to 5 is 0.6 i.e., Probability that x ≥ 5 = 0.6
The probability distribution for a random variable x is given in the table.
x | -10 -5 0 5 10 15 20
probability | 0.20 0.15 0.05 0.1 0.25 0.1 0.15
If a random variable x has values x₁, x₂, .. ,xₙ with their corresponding probabilities given for each of them P(xₐ), then probability that x ≥ xₐ, for some a = 1, 2, .. , n is,
P(x ≥ xₐ) = P(xₐ) + P(xₐ₊₁) +...+P(xₙ).
Here we need to find the probability that the random variable x is greater than equal to 5. So we need to add up the probabilities corresponding to the random variables x ≥ 5.
So here, probability that x ≥ 5 is
P(x ≥ 5) = P(5) +P(10) + P(15) + P(20)
= 0.1 + 0.25 + 0.1 + 0.15
= 0.6
Hence Probability that x ≥ 5 is 0.6.
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5 Circle the function types whose graphs consist only of lines. Choose all that apply.
Quadratic functions
Linear functions
Exponential functions
Constant functions
Linear absolute value functions
The functions whose graphs consist only of lines are-
Linear functionsConstant functionsLinear absolute value functionsWhat is termed as the functions?A function is a relationship between a set of inputs (referred to as the domain) and a set of permissible outputs (referred to as the codomain), in which each input is connected to exactly one output. A function on one variable is frequently denoted by f.
Linear functions: A straight line just on coordinate plane is represented by a linear function. For instance, y = 3x - 2 symbolizes a straight line on the a coordinate plane and thus a linear function.
Constant functions: A constant function is employed to portray a quantity that remains constant over time and is considered the simplest type of real-valued function.
Linear absolute value functions: The Absolute Value Function is a two-linear function piecewise defined function.
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