Considering the angle relations when two parallel lines are cut by a transversal, the measures of the angles are given as follows:
18. <4 = 56º.
19. <3 = 132º.
20. <2 = 55º.
21. <8 = 120º.
22. <6 = 129.5º.
23. <2 = 61.3º.
Parallel lines cut by transversalWhen two parallel lines are cut by a transversal, there are multiple relations among the angles, which are going to be used to solve this question.
In item 18, the angles 1 and 4 are consecutive interior angles, hence they are supplementary angles, meaning that the measure of angle 4 is found as follows:
<4 + <1 = 180º
<4 + 124º = 180º
<4 = 56º.
In item 19, angles 2 and 3 are also consecutive interior angles, hence:
<2 + <3 = 180º
48º + <3 = 180º
<3 = 132º.
For item 20, angles 2 and 4 are alternate interior angles, hence they are congruent and their measures are given by:
<2 = <4 = <55º.
For item 21, angles 6 and 8 are alternate exterior angles, also being congruent, hence their measures are given as follows:
<6 = <8 = 120º.
For item 22, angles 7 and 6 are same side exterior angles, meaning that they are supplementary, hence:
<6 + <7 = 180º
<6 + 50.5º = 180º
<6 = 129.5º.
For item 23, the relation is the same as item 19, hence:
<3 + <2 = 180º
<2 = 180 - 118.7
<2 = 61.3º.
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the value of the expression (-3.69)⁰?
The correct answer solved by indices and the value of the expression (-3.69)⁰ is: 1
What is indices based expression?
In mathematics, the indices expression are those whose base values are either same or constant can be solved with this method. This property states that the when the power is zero for any value or variable, then the output is 1.
According to the question, the given data states that the value of the expression (-3.69)⁰ can be calculated with the concept of indices:
As per indices property: any value or variable whose power is zero, can be consider as 1 in the answer.
Therefore, the value of the expression (a)⁰ = (-3.69)⁰ = 1.
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Two opposite numbers are 10 units away from each other. What are the numbers?
Answer:
-5 and 5
Step-by-step explanation:
5 + 5 = 10 and 5 and -5 are 10 spaces away from each other, hope this helps! :)
Answer:
5, -5
Step-by-step explanation:
5 = 5 units away from 0
-5 = 5 units away from zero
5 units + 5 units = 10 units
-5 to 5 = 10 units apart 5 and -5 are opposites of each other because positive is the opposite of negative and vice versa
hope this helped :) ^^
Need some help can anyone offer a hand?
∠SQU ≅ ∠VQT by the Vertical angles theorem.
From the figure, lines UV and WZ are parallel.
We need to arrive at the conclusion that angle VQT is congruent to angle WRS. i.e., ∠WRS ≅ ∠VQT.
So first we have the angles ∠SQU and ∠VQT. Both are vertical angles or opposite angles at Q.
The Vertical Angles Theorem states that two vertical angles are congruent to each other.
Thus, ∠SQU ≅ ∠VQT by the Vertical angles theorem.
Then we have the angles ∠SQU and ∠WRS. They are corresponding angles from the figure.
The Corresponding Angles Theorem states that two corresponding angles are congruent to each other.
Thus, ∠SQU ≅ ∠WRS by The Corresponding Angles Theorem.
Finally, ∠VQT ≅ ∠WRS by the Transitive property of Equality .
The transitivity property can be defined as if a ≅ b and b ≅ c, then a ≅ c.
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Help Please
Which of the following is equivalent to −4(2x + 3y) − 6(3q + 7p)?
A. −8x + 12y − 18q + 42p
B. −8x − 12y − 18q − 42p
C. −8x + 3y − 18q + 7p
D. −24(2x + 3y − 3q + 7p)
Answer: B. −8x − 12y − 18q − 42p
5. At the annual fall festival, Laney sets up a booth and sells wreaths and flower bouquets She has already received some requests,
so she knows she will need to make at least 8 houquets. Due to a shortage of evergreen branches, she cannot make more than
10 wreaths. In the month leading up to the festival, Laney will have time to put together at most 25 arrangements (either wreaths
or bouquets).
a. Write a system of inequalities for the scenario describing b bouquets and u wreaths
Answer:
Step-by-step explanation:
Let x and y stand for the numbers of Wreath and Flower bouquets, respectively.
We are told that:
x + y [tex]\geq[/tex] 8
and that:
x [tex]\leq[/tex] 10
plus:
x + y [tex]\leq[/tex] 25
-----------------
We can plot these inequalities to define the combinations of x and y that meet the requirements they set forth. See the attached image.
Any combination of wreath and flower bouquets found within the marked trapezoid are valid combinations of bouquets. The sample point (5,10) means that 5 wreath and 10 flower bouquets is a possible solution that meets all the requirements set forth above.
==============
Is (5,10) a valid combination?
x + y [tex]\geq[/tex] 8 5+10≥ 8? YES
x [tex]\leq[/tex] 10 5 [tex]\leq[/tex] 10? YES
x + y [tex]\leq[/tex] 25 5 + 10 [tex]\leq[/tex] 25? YES
Many other combinations are also possible. We need additional information to determine anythng more specific.
What is the equation in slope-intercept form of the line that passes through the point (6, 3) and is parallel to the graph of y = −2 3 - 2 3 x + 12?
The line passing through the coordinates (6, 3) and parallel to the y=-23-23x+12 graph. The equation of the slope intercept form of the line is 23x+y-141=0.
Given that,
We have to find what is the slope-intercept equation for the line passing through the coordinates (6, 3) and parallel to the y = -2 3 - 2 3 x + 12 graph.
The coordinates are (6,3).
y=-23-23x+12
y=-23x-11
The above equation is in the form of equation of the line that is y=mx+b
m value is -23.
Now,
The formula for the equation of line's slope intercept is
y-y₁=m(x-x₁)
y-3=-23(x-6)
y-3=-23x+138
23x+y-3-138=0
23x+y-141=0
Therefore, the equation of the slope intercept form of the line is
23x+y-141=0.
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4. Which value for x makes the sentence true?
3x - 8 = 16
x=
Answer: x = 8
Step-by-step explanation:
This is a very, very, very simple algebra problem. I assume you know the basics of algebra.
First, move 8 to the other side:
3x = 24
divide by 3 on both sides
x = 8
There! Would it kill you to give me a quartic question to spice my life up?
solve this equation
9+7n=-2+2(n-7)
(7) Write the equation of a line that has a slope of -5 and passes through the point (2, -137
In order to find the equation of the line, take into account that the general form of the expression of the line can be written as follow:
y - yo = m(x - xo)
where m is the slope and (xo,yo) is a point of the line.
in this case you have m = -5 and (xo,yo) = (2,-137). Replace the previous values into the general expression of the line and solve for y:
y - (-137) = -5(x - 2)
y + 137 = -5x + 10
y = -5x + 10 - 137
y = -5x - 127
Hence, the equation of the line is y = -5x - 127
a certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint. a.how many cups of red paint should be added. write your answer in terms of a fraction using a "/" for the fraction bar and no spaces. the answer to the question is
Hence 3/7 cup of Red paint should be added to white paint to create a certain pink shade.
Given :
Three cups of red paint and seven cups of white paint are mixed to produce a particular hue of pink.
To determine how many cups of red paint to add to one cup of white paint.
What is the proportionality constant?
Red ∝ White
Red = K ( White)
=> 3 = K ( 7)
=> k = 3/7
Hence constant of proportionality is 3/7
Red = (3/7) White
1 Cup of white
=> Red = 3/7
Hence 3/7 cup of Red to be added.
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Gabriel is deigning a rectangular planter box for their garden.It needs to cover an area of 15 1/2 m2 . Gabriel wants it to be 7 3/4 m long. How wide does the planter box need to be?
The width of the planter box will be 2 meter.
What is mean by Rectangle?
A quadrilateral with four right angles is called a Rectangle.
The area of a rectangle is defined as length times width.
Given that;
The area of a rectangular planter box = [tex]15\frac{1}{2}[/tex] m²
The length of cover to cover a rectangular garden = [tex]7 \frac{3}{4}[/tex] meter
Since, The area of a rectangle = Length x Width
Let the width of planter box = x meter.
Then, We can substitute all the values we get;
The area of a rectangular planter box = Length x Width
⇒ [tex]15 \frac{1}{2} = 7 \frac{3}{4} * x[/tex]
Change into improper fraction as;
⇒ 31/2 = 31/4 × x
Solve for x as;
⇒ 31/2 = 31/4 × x
Divide by 31/4;
⇒ x = 31/2 × 4/31
⇒ x = 4/2
⇒ x = 2 meter
Thus, The width of the planter box will be 2 meter.
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1 to the power of 2 + 2 to the power of 3 + 3 to the power of 4
Answer: 90
Step-by-step explanation:
desribe a sequence of trransformations that take isoceles trapezoid 7 degrees to its image
From T to T', there is a 90 degree counterclockwise transformation.
Transformation entails shifting a shape's location.
A figure is transformed when it is moved from its original location to another.
Angle of Rotation: The extent of the angle at which a figure is rotated. The common rotational angles are 45°, 90°, and 180°. A transformation that does not alter the size of a figure is called an isometric transformation.
There is a right angle between the isosceles trapezoid T and its image T' (i.e. 90 degrees)
To the right of T is Figure T'.
This implies:
Trapezoid T will reach T' if a 90 degree counterclockwise turn is made through point D.
Therefore, a 90 degree counterclockwise transformation through point D is necessary.
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Arianys broke a cell sample into 99 batches, each weighing 6.6\times 10^{-6}6.6×10 −6 grams. How much did the original sample weigh? Use scientific notation to express your answer.
Arianys broke a cell sample into 99 batches each weighing 6.6 x 10⁻⁶, the weight of the original cell sample is 653.4 x 10⁻⁶ grams which when expressed in scientific notation is 6.534 x 10⁻⁴ grams
Arianys broke a cell sample into 99 batches each weighing 6.6 x 10⁻⁶
If the weight of each batch of the original cell sample is 6.6 x 10⁻⁶
The weight of 99 batches = 6.6 x 10⁻⁶ x 99 grams
The weight of 99 batches = 653.4 x 10⁻⁶ grams
The weight of the original cell sample is 653.4 x 10⁻⁶ grams
Scientific notation is a way of expressing numbers in decimal form that are too large or too small. The absolute value of the coefficient of any number is greater than or equal to 1 but it should be less than 10
As per scientific notation it can be written as 6.534 x 10⁻⁴ grams
Therefore, if Arianys broke a cell sample into 99 batches each weighing 6.6 x 10⁻⁶, the weight of the original cell sample is 653.4 x 10⁻⁶ grams which when expressed in scientific notation is 6.534 x 10⁻⁴ grams
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7% turned into a fraction?
Percentages can be expressed as decimals.
7% = 1 x 0.07
Decimals can be expressed as fractions.
7% = 1 x 7/100
7% = 7/100
Answer:
7/100
Step-by-step explanation:
Percentage is out of 100 - Denominator
7% of 100 7-Numerator
7/100
There are c green notebooks on Sasha's desk. The number of red notebooks on her desk is 6 less than the number of green notebooks. How many notebooks are on Sasha's desk if all of them are either green or red
The formed equation for the green or red notebooks on the Sasha's desk is: 2c - 6
What is equation?
In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.
According to the question, the given parameters to form the equation for the given statement are as follows:
Green notebook on Sasha's desk: 'c'
Number of red notebooks: c - 6
Now, to calculate as well as form the equation for the number of notebooks on the Sasha's desk:
c + c - 6 = 2c - 6
Total number of notebooks on the desk is: 2c - 6
Hence, the formed equation for the green or red notebooks on the Sasha's desk is: 2c - 6
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jose bought 2 hammers and “y” number of tarps. The total cost was $87. How many tarps did he buy
Answer: He bought y tarps
Step-by-step explanation: this confusing
the average score of 100 students taking a statistics final was 72 with a stanndard deviation of 7. assuming a normal distribution, what is the probability that a student scored greater than 52
The probability of a student scoring higher than 52 is 0.0021.
When the data are normally distributed and the mean and standard deviation are known. Calculate the percentage of data that is greater than or less than a certain number. The standard normal distribution and the Z-score or the standard normal distribution for this.
In the question, the mean and standard deviation are provided as μ = 72 and σ = 7
It has also been said that the data is typically dispersed.
Determine the proportion or percentage of data that is greater than 52. The Z-Score, also known as the standard normal variate, is defined as:
Z = (x - μ) ÷ σ
Calculate the requisite Z-score by substituting the values of μ, σ, and x:
Z = (72 - 52) ÷ 7
Z = 2.857
The area under the curve is approximately 0.0021 on the right side of the Z value.
As a result, the probability of a student scoring more than 52 is 0.0021.
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Tell whether each statement about 20 and 30 is true or false the greatest common factor is 5 true or false 10 is a common multiple true or false the least common multiple is 60. 2 is a common factor true or false
The true statements are:
The greatest common factor of 20 and 30 is 10.
The least common multiple of 20 and 30 is 60.
The common factor is 2.
Consider the numbers 20 and 30,
The factors of 20 are 1, 2, 3, 4, 5, 10, and 20.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The common factors are 1, 2, 3, 5, 6, 10 and hence the greatest common factors are 10.
And, 2 is a common factor.
The multiples of 20 are 20, 40, 60, 80, 100, ....
The multiples of 30 are 30, 60, 90, 120, ...
Therefore, the least common multiple is 60.
The GCF and LCM of 20 and 30 are 10 and 60 respectively. The common factor is 2.
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Consider the function f(x)=3(2)−1.5x . What is the value of f(2)
The value of function f(2) is f(2) = 3
How to determine the value of the function?The equation of the function is given as
f(x) = 3(2) - 1.5x
Also, we have the function to be f(2)
This means that the value of x is 2
i.e we calculate f(x) when x = 2
Substitute 2 for x in the equation f(x) = 3(2) - 1.5x
So, we have
f(2) = 3(2) - 1.5 x 2
Evaluate the product
f(2) = 6 - 3
Evaluate the difference
f(2) = 3
Hence, the value of the function is 3
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2.83 in expanded form
Answer:
2+0.8+0.03
Step-by-step explanation:
Which number is prime?
77?
57?
63?
59?
i need help with this
In the expression in order to least to greatest is,
[tex](\frac{1}{6} )^{6}[/tex] < [tex]6^{-3}[/tex] < [tex]\frac{6^{6} }{6^{2} }[/tex] < [tex]\frac{6^{12} }{6^{6} }[/tex] by using [tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex] formula.
Based on the given condition,
⇒ [tex]\frac{6^{12} }{6^{6} }[/tex] [tex]\frac{6^{6} }{6^{2} }[/tex] [tex]6^{-3}[/tex] [tex](\frac{1}{6})^{6}[/tex]
Negative numbers grow as they get closer to 0 and positive numbers grow as they distance from 0
First classify numbers as positive and negative
We can use formula,
[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]
We can write,
⇒ [tex]\frac{6^{12} }{6^{6} }[/tex] = [tex]6^{12-6}[/tex]
[tex]\frac{6^{12} }{6^{6} }[/tex] = [tex]6^{6}[/tex]
⇒ [tex]\frac{6^{6} }{6^{2} }[/tex]= [tex]6^{6-2}[/tex]
[tex]\frac{6^{6} }{6^{2} }[/tex] = [tex]6^{4}[/tex]
⇒ [tex]6^{-3}[/tex] = [tex]6^{-3}[/tex]
⇒ [tex](\frac{1}{6} )^{6}[/tex] = [tex]\frac{1}{6^{6} }[/tex] = [tex]6^{-6}[/tex]
So,
[tex]\frac{6^{12} }{6^{6} }[/tex] = [tex]6^{6}[/tex]
[tex]\frac{6^{6} }{6^{2} }[/tex] = [tex]6^{4}[/tex]
[tex]6^{-3}[/tex] = [tex]6^{-3}[/tex]
[tex](\frac{1}{6} )^{6}[/tex] = [tex]6^{-6}[/tex]
We can write,
[tex]6^{-6}[/tex] < [tex]6^{-3}[/tex] < [tex]6^{4}[/tex] < [tex]6^{6}[/tex]
Then,
[tex](\frac{1}{6} )^{6}[/tex] < [tex]6^{-3}[/tex] < [tex]\frac{6^{6} }{6^{2} }[/tex] < [tex]\frac{6^{12} }{6^{6} }[/tex]
Therefore,
In the expression in order to least to greatest is,
[tex](\frac{1}{6} )^{6}[/tex] < [tex]6^{-3}[/tex] < [tex]\frac{6^{6} }{6^{2} }[/tex] < [tex]\frac{6^{12} }{6^{6} }[/tex] by using [tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex] formula.
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Simply then factor the expression 10W-2(3W+4)+4
Answer:
6(w +2)
Step-by-step explanation:
Factorize the expression:
Multiply each term of (3w + 4) by 4. Then add the constants.
2(3w + 4) + 4 = 2*3w + 2*4 + 4
= 6w + 8 + 4
= 6w + 12
Now, GCF (greatest common factor) of 6w and 12 is 6.
= 6*w + 6*2
= 6(w + 2)
What is the constant of variation for the quadratic variation?
7y = 0.28x²
A. 0.04
B. 0.28
C. 0.98
D. 7
Answer:
A.004
Step-by-step explanation:
I been Doing this for some Years And I knw it cuz I go on it EvenyDay
Solve this system of linear equations using substitution.
{(3x+2y=10),(2x+y=1):}
A (-8,17)
B(-4,17)
C(-8,6)
D (8,17)
[tex]y = 1 - 2x.....(3) \\ \\ 3x + 2(1 - 2x) = 10 \\ 3x + 2 - 4x = 10 \\ 3x - 4x = 10 - 2 \\ - x = 8 \\ \frac{ - x}{ - 1} = \frac{8}{ - 1} \\ x = - 8 \\ \\ \\ y = 1 - 2( - 8) \\ y = 1 + 16 \\ y = 17[/tex]
NOTE I FIRST DERIVED THE THIRD EQUATION FROM THE SECOND EQUATION BY MAKING Y THE SUBJECT OF THE EQUATION AND SUBSTITUTED THE DERIVED EQUATION TO THE FIRST EQUATION BY PLUGGING IN 1-2x IN THE PLACE OF Y AND SOLVED SO ON.
(-8,17)
OPTION A IS THE ANSWER.
GOODLUCK
Answer:
A
Step-by-step explanation:
3x + 2y = 10 → (1)
2x + y = 1 ( subtract 2x from both sides )
y = 1 - 2x → (2)
substitute y = 1 - 2x into (1)
3x + 2(1 - 2x) = 10
3x + 2 - 4x = 10
- x + 2 = 10 ( subtract 2 from both sides )
- x = 8 ( multiply both sides by - 1 )
x = - 8
substitute y = - 8 into (2)
y = 1 - 2(- 8) = 1 + 16 = 17
solution is (- 8, 17 )
Lisa is saving for college. The account is modeled by the function:
, when x represents how many years she has saved.
Xavier is also saving college. His account is modeled by this table:
x 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
The amount Lisa has in the account after 3 years is; 488.28.
The amount Xavier has in the account after 3 years is; 492.08.
The positive difference in their account after 3 years is; 4.20.
What is the positive difference in their account after 3 years?It follows from the task content that Lisa savings as described is modelled by the function;
F (x) = 250(1.25)^x
1. It therefore follows that the amount Lisa would have in the account after 3 years would be;
F(3) = 250 (1.25)³
F(3) = 250 × 1.953125
F(3) = 488.28125.
Hence, when rounded to the nearest hundredth; we have; F(3) = 488.28.
2. Also, the amount Xavier has after 3 years can be determined from the table as; 492.08.
3. The positive difference can therefore be determined as; | 492.08 - 488.28 | = 4.20.
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Answer and if you can put an explanation that would ben nice.
Explanation not necessary
The answer is b
In this image is the explanation, just click on it
M measures 12°
(a) Find the supplement of M.
(b) Find the complement of M.
168° is the supplementary angle of 12°.
The complement of the initial angle, which is 12 degrees, is 90 – 12 degrees, or 78 degrees.
What is an example of a supplementary angle?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
Two angles are said to be supplementary angles if they add up to 180 degrees. For example, if ∠A + ∠B = 180°, then ∠A and ∠B are called supplementary angles. Supplementary angles always form a straight angle (180 degrees) when they are put together.
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If the original angle is 12 degrees, then 90-12 = 78 degrees is the complement of that angle. Therefore, the angles of 12 degrees and 78 degrees are complimentary.
What is supplemetary and complementary angles?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.
complementary angles have a sum of 180 degrees. Supplementary and complementary angles can share a vertex or side but are not need to be near to one another.
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Derek is 70 and his granddaughter
Vanessa is 5.
In how many years will Vanessa be ¹/6 Derek's
age?