Angle two and angle six line up with one another. Angle three would consequently be consistent with angle six. Angles two and three are congruent because they both have vertical angles.
What are the alternate interior angles?Alternate internal angles are the pair of angles formed on the inner side of the parallel lines and on the opposing sides of the transversal when two parallel lines are intersected by a transversal. These angles are all equal. There is an alternative perspective on this. The parallelism or non-parallelism of the provided lines can be determined by the alternative inner angles. If these angles are equivalent, the given lines that a transversal crosses are said to as being parallel.
To see the many internal angles, look at the following diagram. Here, a transversal divides AB and CD, two parallel lines.
Alternate Interior Angles Theorem's opposite, then?The two lines are said to be parallel if a transversal intersects them such that their alternate interior angles are equal, according to the converse of the alternate interior angles theorem.
Let's examine the following diagram to better comprehend this: 1 = 5 (matching angles), 3 = 5 (vertically opposite angles). Thus, ∠1 = ∠3. The same goes for the demonstration of 2 = 4. This demonstrates that the two supplied lines are parallel to one another since their alternate inner angles are equal.
Example: Two lines are parallel to one another if the alternate interior angles created by the transversal line on two coplanar are congruent. As a result, we can write that 2 and 5 are corresponding angles.
Transformations would show that the accompanying exterior angles EBI and BCJ are congruent, proving that an is parallel to a pair of alternate exterior angles with measurements of 130° and 50°.
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Please look at picture! thank you!
Answer:
16
Step-by-step explanation:
write the equation for a3
a3 = a2 + 3(3) -> eq1
now find what is a2, write equation for a2
a2 = a1 + 3(2) -> eq2
you know a1=1, replace that into eq2
a2 = 1 + 3(2) = 1 + 6 = 7
replace a2 into eq1
a3 = 7 +3(3) = 7 + 9 = 16
Select the correct answer.
Eric traveled to two cities on a single highway. The total distance one way was 200 miles. The distance from his original location to the first city was 40
miles less than the distance from the first city to the second city. Suppose that x represents the distance from the original location to the first city and y
represents the distance from the first city to the second city. The following system of equations represents the given situation
x + y = 200
x = y - 40
Which pair of coordinates represents the solution (in miles) to this system of equations?
O A.
(70, 130)
(80, 120)
(160, 120)
(100, 100)
B.
O c.
D.
E. (140, 60)
In linear equation, The solution to this system is (80, 120)
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).The following system of equations represents the given situation
x + y = 200
x = y - 40; substituting x from this equation to the first:
y - 40 + y = 200
2y = 240
y = 120
Corresponding value of x:
x = 120 - 40
x = 80
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Please read in round your answer to the nearest whole number do not round any intermediate calculations
Solution
Total space
[tex]337+240+173+180=930[/tex]Probability
[tex]Probability\text{ =}\frac{Possible\text{ outcome}}{Total\text{ sample}}=\frac{337}{930}[/tex]Now for the next thin crust of 2000 pizza
[tex]\frac{337}{930}\times2000=724.7311[/tex]The final answer
[tex]725[/tex]Find the trigonometric form of the complex number. Hint: Graph the complex number first to give yourself a visual representation.
First, let's graph the complex number:
The trigonometric form will be given by:
[tex]-2-2i=r(\cos \theta+i\sin \theta)[/tex]The angle θ here is 225° (5π/4), the r-value will be
[tex]\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ \\ r=\sqrt[]{4+4} \\ \\ r=\sqrt[]{8}=2\, \sqrt[]{2} \end{gathered}[/tex]Now we have the trigonometric representation:
[tex]-2-2i=2\, \sqrt{2}\mleft(\cos \mleft(\frac{5\pi}{4}\mright)+i\sin \mleft(\frac{5\pi}{4}\mright)\mright)[/tex]Therefore the correct answer is the letter D.
May I please get help with this where I have tried multiple times but still cannot find the right answers for them
Given a point with coordinates (x, y), to rotate 90º counterclockwise, the rule is:
[tex](x,y)\Rightarrow(-y,x)[/tex]In thisc ase, we have the point:
[tex](2,-1)[/tex]Applying the rule:
[tex](2,-1)\Rightarrow(1,2)[/tex]Jason has three more than four times the amount of money Jeff has together they have $72 how much money does each person have
hello
determine the amount each of them have, let's write an equation to represent thier total amount
let x represent the amount Jason have
let y represent the amount Jeff has
now, we know that Jason has 3 more than 4 times the amount Jeff has
x = 4y + 3 .... equation 1
x + y = 72 .... equation 2
from equation 2,
make x the subject of formula
[tex]\begin{gathered} x+y=72 \\ x=72-y \end{gathered}[/tex]x = 72 - y .....equation 3
put equation 3 into equation 1
x = 4y + 3
72 - y = 4y + 3
solve for y
[tex]\begin{gathered} 72-y=4y+3 \\ \text{collect like terms} \\ 4y+y=72-3 \\ 5y=69 \\ y=\frac{69}{5} \\ y=13.8 \end{gathered}[/tex]we know y = 13.8
we can simply substitute the value into equation 2 and solve for x
[tex]\begin{gathered} x+y=72 \\ y=13.8 \\ x+13.8=72 \\ x=72-13.8 \\ x=58.2 \end{gathered}[/tex]therefore, Jason has $58.2 and Jeff has $13.8
A real estate licensee leased a building for 10 years at an annual rent of$48,000. she will receive a commission of 7.5 % for the first 5 years, 5% for the next there years and 3.5% for the final two years. what will her income be from this commission over the life of the lease?
We have the lease of a building is for 10 years with an annual rent of $48 000.
We first determine the 7.5% for the first 5 years, for that we add the cost of the rent for 5 years, that is:
[tex]5(48000)=240000[/tex]In 5 years the rent will be of $240 000, now we find the 7.5%:
[tex]c_5=\frac{240000\cdot7.5}{100}\Rightarrow c_5=18000[/tex]Her commision for the first 5 years is going to be of $18 000.
Now we determine the 5% for the next 3 years, for this we determine the rent for 3 years:
[tex]3(48000)=144000[/tex]The rent for 3 years adds $144 000, now we determine the 5%:
[tex]c_3=\frac{144000\cdot5}{100}\Rightarrow c_3=7200[/tex]From this we have that the commission for the next 3 years will be of $7200.
And finally, we determine the rent for the two remaining years:
[tex]2(48000)=96000[/tex]We have that the last two years the rent will be of $96000, now we determine the 3.5% of her commission during that time:
[tex]c_2=\frac{96000\cdot3.5}{100}\Rightarrow c_2=3360[/tex]From this we have her commission for the last two years will be of $3360.
Finally we add all of the values of the commissions she will get:
[tex]c_t=18000+7200+3360\Rightarrow c_t=28560[/tex]From this we have that the total commision money she will be getting during those 10 years will be $28 560.
Find the value of the smaller angle. (Hint find the value of x first)
The sum of both angles must be 180°, therefore:
(2x+24) + (4x+36) = 180°
6x + 60 = 180°
6x = 120°
x = 120/6 = 20°
Then, the smaller angle is 2*20 + 24 = 64
Name the coordinates of Q(6, -4) under a reflection in the x-axis.
The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4)
The coordinates of x will remain the same for reflection in the X axis, while y will change with the opposite sign.
From the question, we have
The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4).
Reflection:
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively. The coordinate system may be referred to by the reflection transformation (X and Y-axis).
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Choose the graph of this equation. y = 2.5x
Answer:
1
Step-by-step explanation:
estimate 6 and five ninths times sixty eight and 1 third
To estimate this, let's first translate to figures.
We have:
[tex]\begin{gathered} \text{Five ninths = }\frac{5}{9} \\ \\ Sixty\text{ eight = 68} \\ \\ 1\text{ third = }\frac{1}{3} \end{gathered}[/tex]Let's estimate, we have:
[tex]undefined[/tex]a stationary shop had an equal number of pens and notepads at first. after selling 1250 pens and 380 notepads, there were 4 times as many notepads as pens left. how many pens did the stationary shop have at first
The stationary shop had 90 pens with them initially.
Let,
The number of pens initially at the stationary shop=x
The number of pens and the number of notepads are said to be equal. Therefore, The number of notepads initially at the stationary shop=x
After selling,
The number of pens = x-1250
The number of notepads = x-380
The number of pens was four times the number of the number of notepads. Modelling the linear equation for the situation:
x-1250=4(x-380)
x-1250=4x-1520
x=4x-270
-3x=-270
x=90
The stationary shop had 90 pens initially.
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PLEASE HELP ASAP!!!!!!!! (NO BOTS OR LINKS- WILL BE REPORTED)
The minimum number of tiles will be 122 that Imane needs to cover the floor.
How to Convert Square Feet to Square Inches?Multiply the area by the conversion ratio to convert a square foot measurement to a square inch measurement. Because one square foot equals 144 square inches, you may use the following easy formula to convert:
square inches = square feet × 144
The area in square inches is equal to the square feet multiplied by 144.
The floor she wants to cover has an area of 216 square feet.
The required area in square inches is :
216 × 144 = 31,104 sq in
Each tile covers an area of 256 square inches.
The minimum number of tiles = 31,104 sq in / 256 sq in
The minimum number of tiles = 121.5 ≈ 122
Thus, the minimum number of tiles will be 122 that Imane needs to cover the floor.
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Find the nth term of this
quadratic sequence
2, 8, 18, 32, 50, ..
Answer:
The nth term is 2n^2.
Step-by-step explanation:
We see that each term is twice a square number. So it follows that
[tex]a(n )= 2 {n}^{2} [/tex]
for n = 1, 2, 3,.....
what is the answer to 3 1/8 ÷1 2/3
Answer: 3 1/8 ÷ 1 2/3 = 15/8. 15/8 as a simplified mixed number is 1 7/8
Step-by-step explanation: 15/8 is at it's simplist form and cannot be divided again that is why you convert it into a mixed number. I hope this helps!
The table shows our research activities of two students at an observatory how much does a student pay to use a telescope for 1 hour the supercomputer? for 1 hour?
Answer: Student 1 pays $23.5 to use a supercomputer and pays $14.1 to use a telescope
Step-by-step explanation:
Using cross multiply and divided method, we can find the unit rate or just dividing.
Student 1. 3 1
$70.5 x
70.5 x 1 = 70.5
70.5 ÷ 3 = $23.5
x = $23.5
5 1
70.5 x
70.5 x 1 =70.5
70.5 ÷ 5 = 14.1
x = $14.1
Student 1 pays $23.5 to use a supercomputer and pays $14.1 to use a telescope.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Using the cross multiply and divide method, we can find the unit rate or just divide.
Student 1. 3 1
$70.5 x
70.5 x 1 = 70.5
70.5 ÷ 3 = $23.5
x = $23.5
5 1
70.5 x
70.5 x 1 =70.5
70.5 ÷ 5 = 14.1
x = $14.1
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Elizabeth has
4 1/2 feet of material to make bookmarks. She will use 9 inches of material for each bookmark. How many bookmarks can Elizabeth make?
When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?
Step-by-step explanation:
When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?
Answer:
The sign flips.
≤ becomes ≥
and ≥ becomes ≤
Where can I calculate the shaded area of this diagram?
We are asked to find the area of the shaded region.
Notice that the overall figure is a rectangle and the missing area is a triangle.
The area of the rectangle is given by
[tex]A_{\text{rect}}=w\cdot l[/tex]Where w is the width and l is the length of the rectangle.
width = 7 m
length = 16 m
[tex]A_{\text{rect}}=w\cdot l=7\cdot16=112\; \; m^2[/tex]So, the area of the rectangle is 112 m²
The area of the triangle is given by
[tex]A_{\text{tri}}=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
base = 7 m
height = 8 m
[tex]A_{\text{tri}}=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot7\cdot8=28\; \; m^2[/tex]So, the area of the triangle is 28 m²
The area of the shaded region can be found by subtracting the area of the triangle from the area of the rectangle.
[tex]\begin{gathered} A=A_{\text{rect}}-A_{\text{tri}} \\ A=112-28 \\ A=84\; \; m^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 84 m²
Emma is scrapbooking. She has 9 inches of paper and needs to cut it into 2/5 inch strips of paper. How many whole strips will she be able to make?
*
1 point
The number of strips Emma will be able to make 22.5 i.e. 22.
What is strips?The set of points in the plane between two parallel lines in the plane. The x,y coordinates plane of the points in the stripe satisfy the inequality C1 < . Ax + By < C2, where A, B, C1, C2 are certain constants and both A and B cannot be zero. The strip number is typically used in preparing the data for matching (or as a matching transformation within the matching processor). For text data that has numbers in the data but that you know are irrelevant, removing the numbers before matching is useful. As an abstract topological space, the Mobius strip can be embedded in three-dimensional Euclidean space in various ways. The twist is greater than 1 or the centerline is knotted.According to question
Total paper = Total strips × size of one
9 = n × 2/5
n = 22.5
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Need help with 5 hurry I have to go somewhere in 5 minutes
Answer:
c. What is your favorite book?
Explanation:
A question is said to be biased when it is asked in such a way that it leads or skews people intentionally to a particular answer.
Looking at the given questions in the options, we can see that three of them have a particular person or thing mentioned in the question. These are examples of biased questions.
But the question, "What is your favorite book?" does not suggest a name of a particular book to the respondent which could influence their responses. This type of question is not biased.
Given below is a number written in factored form. Use this representation to determine the following. Factored Form 7.7.7.7.7.7 Enter the number in exponential form. Enter the number in standard form.
Given number in factored form 7.7.7.7.7.7 can be represented in the following way :
Exponential form : 7⁶
Standard form. : 11.7649 × 10⁴
As given in the question,
Given number in factored form is equal to 7.7.7.7.7.7
Represent the given factored form number into exponential form and standard form is written as :
Exponential form is given by :
7.7.7.7.7.7
= 7¹⁺¹⁺¹⁺¹⁺¹⁺¹
= 7⁶
Standard form is given by :
7.7.7.7.7.7
= 117649
= 11.7649 × 10⁴
Therefore, given number in factored form 7.7.7.7.7.7 can be represented in the following way :
Exponential form : 7⁶
Standard form. : 11.7649 × 10⁴
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10x−1= 7 x + 26 7x+26
Answer:
x = - 27/179
Step-by-step explanation:
10x - 1 = 7x + 182x + 26
10x - 1 = 189x + 26
10x - 189x = 26 + 1
- 179x = 27
x = - 27/179
3 to the power of 2 divided by 3
Answer:
3
Step-by-step explanation:
3 to the power of 2 is nine because 3 x 3 = 9
9 / 3 is 3
Answer:
3
Step-by-step explanation:
3²÷3¹
=3²-¹
=3¹
=3
or
3²÷3¹
=9÷3
=3
Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.5, 9, 13, 17, 21,
We can say that it's an arithmetic sequence since it has a common rate of change or common difference of 4.
Arithmetic sequences are represented by the following formula:
Recursive formula:
[tex]\begin{gathered} a_n=a_{n-1}+d \\ \text{Explicit formula:} \\ a_n=a_1+(n-1)d \\ \text{The next three numbers would be: }a_6,a_7,a_8 \end{gathered}[/tex]an= nth term
a1= 1st term
n= number of terms
d= common difference
[tex]\begin{gathered} a_6=5+(6-1)\cdot4 \\ a_6=25 \\ a_7=5+(7-1)\cdot4 \\ a_7=29_{} \\ a_8=5+(8-1)\cdot4_{} \\ a_8=33 \end{gathered}[/tex]The figure below shows a circle with center J, diameter LT, secant TO, andtangents EB and IP. Which of the angles must be right angles? Select all thatapply.
Answer:
Explanation:
The angles that are right angles are the ones that measure 90 degrees.
These are:
angles formed at L
angles formed at E
Answer:
Explanation:
The angles that are right angles are the ones that measure 90 degrees.
These are:
angles formed at L
angles formed at E
Suppose S and T are mutually exclusive events. Find P(S or T) if P(S)= 6/11 and P(T)= 1/10
A. 71/110
B. 3/55
C. 1/3
D. 71/21
The value of P(S or T) is 71/110.
What is mutually exclusive event?
If two events cannot happen simultaneously, they are mutually exclusive or discontinuous. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.
As given,
S and T are mutually exclusive events. P(S)= 6/11 , P(T)= 1/10.
By using,
P(S ∪ T) = P(S) + P(T) - P(S ∩ T)
= 6/11 + 1/10 - P(S ∩ T)
= 71/110 - P(A ∩ T)
But the events S and T are mutually exclusive events.
therefore, P(S ∩ T) = 0.
So,
P(S ∪ T) = 71/110
Therefore, value of P(S or T) is 71/110.
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Write an equation in point-slope form for the line that has a slope of 1/5 and contains the point (2,−9).
The equation is y+9=(1/5)(x-2).
What is a slope form?It is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The three major forms of linear equations are point-slope form, standard form, and slope-intercept form. The equation of the slope form is y-y₁ = m(x - x₁)
The formula for the point-slope is,
y-y₁ = m(x - x₁)
y₁ is the y-coordinate of the point in the line, x₁ is the x-coordinate of the point in the line and m is the slope.
y₁ = -9
m = 1/5
x₁ = 2
Substituting the above values in the above equation, we get
y-(-9) = (1/5)(x-2)
By simplifying the above equation, we get
y+9 = (1/5)(x-2)
Therefore, the equation is y + 9 = (1/5)(x-2).
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Jordan types at a constant rate of 40 words per minute. The number of words typed, y, is a function of the number of minutes spent typing Part A Which equation models this situation? 95 CV 40and how many words can he type in 7.5 minutes
To write the equation that represents the situatio, as y is in function of x, you multiply the rate by the number of minutes (x):
[tex]y=40x[/tex]In 7.5 minutes he can type:
[tex]y=40(7.5)=300[/tex]Perform the following food service calculation.
Meat served: chicken with a bone
Pounds of chicken available: 48 lbs.
How many guests can be served?
The number of guests that can be served is 12
How to determine the number of guests?From the question, we have the following parameters that can be used in our computation:
Meat served: 4 lbs chicken with a bone
Pounds of meat available: 48 lbs.
The number of guests needed is calculated using the following equation
Number of guests = Pounds of meat available/Meat served
Substitute the known values in the above equation, so, we have the following representation
Number of guests = 48/4
Evaluate the quotient
Number of guests = 12
Hence, 12 guests can be served with the available meat
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Possible question
Perform the following food service calculation.
Meat served: 4 lbs chicken with a bone
Pounds of meat available: 27 lbs.
How many guests can be served?