Answers
Answer:
[tex] x = 18 [/tex]
Step-by-step explanation:
Given:
Angle ABC = 2x
Angle CDE = 8x
Required:
Value of x
SOLUTION:
Line AB is parallel to line CD, therefore, angle ABC and angle BCD are alternate interior angles. Alternate interior angles are equal. Thus:
Angle ABC = Angle BCD = 2x
Since, line BC is parallel to line DE, angle BCD and angle CDE are consecutive interior angles.
Consecutive interior angles are supplementary, therefore:
Angle BCD + Angle CDE = 180°
[tex] 2x + 8x = 180 [/tex]
Use this equation to solve for x
[tex] 10x = 180 [/tex]
Divide both sides by 10
[tex] \frac{10x}{10} = \frac{180}{10} [/tex]
[tex] x = 18 [/tex]
Related Questions
Compute the difference: -115-(-115) *
Answers
Answer:
0
Step-by-step explanation:
-115-(-115)
Subtracting a negative is like adding
-115 + 115
0
The answer is 0
Because they subtract each other
Witch are examples of unit rates
Answers
Answer:
30 miles in 2 hours
Step-by-step explanation:
Answer:
A unit rate is a rate where the second quantity is one unit , such as $34 per pound, 25 miles per hour, 15 Indian Rupees per Brazilian Real, etc. Example 1: A motorcycle travels 230 miles on 4 gallons of gasoline. Find the average mileage per gallon.
Step-by-step explanation:
Helene wrote a report. It took her 4 hours to write 24 pages.
What was her unit rate in pages per hour?
A.
1 득
page per hour
B.
page per hour
C. 6 pages per hour
D. 7 pages per hour
Answers
Answer:
C
Step-by-step explanation:
24÷6= 6 Hope this helps.
A ternary digit is either 0, 1, or 2. How many sequences of 6 ternary digits containing a single 1 and a single 2 are there?
Answers
Answer:
30sequences
Step-by-step explanation:
Using nx (n-1)
And
n is the number of ternary digits in the number.
So For 6 digits n is 6 so the number of numbers that have exactly one 1 AND exactly one 2 is 30.
That is 6(6-1)= 30
choose all expressions that are equal to 28.3. A. 27 + 0.91 + 0.39 B. 0.01 + 28.02 C. 9.9 + 9.8 + 9.6 D. 0.02 + 28 + 0.28 E. 27.3 + 1
Answers
Answer:
i think... a d and e?
Step-by-step explanation:
8
Answers
Answer:
8
Step-by-step explanation:
8 is the digit after 7 and previous to 9
The sum of two numbers is 24. One is 6 less than twice the other. Find the two numbers.
(apply polya's problem solving method)
Answers
Answer:
[tex]\huge\boxed{\sf x = 14 , y = 10}[/tex]
Step-by-step explanation:
Let the two numbers be x and y
Condition # 1:
x + y = 24 ---------------------(1)Condition # 2:
x = 2y - 6 ----------------------(2)[tex]\rule[225]{225}{2}[/tex]
Putting Equation # 2 in Equation # 1
2y - 6 + y = 24
3y - 6 = 24
Adding 6 to both sides
3y = 24 + 6
3y = 30
Dividing both sides by 3
y = 10
[tex]\rule[225]{225}{2}[/tex]
Putting y = 10 in Equation # 2
x = 2y - 6
x = 2(10) - 6
x = 20 - 6
x = 14
[tex]\rule[225]{225}{2}[/tex]
The two numbers are 10 and 14.
The sum of 2 numbers is 24.
let the number be x and y . Therefore,
x + y = 24
One is 6 less than twice the other. therefore,
2x - y = 6
Combine the equations
x + y = 24
2x - y = 6
3x = 30
x = 30 / 3
x = 10
x + y = 24
10 + y = 24
y = 24 - 10
y = 14
The 2 numbers are 10 and 14 .
learn more: https://brainly.com/question/2927457?referrer=searchResults
Find the extraneous solution of the equation |2x−12|=−4x.
Answers
Answer:
X=2
Step-by-step explanation:
|2x -12| = -4x
2x-12 = -4x
2x - (-4x) = 12
2x +4x =6x
6x=12
x=12/6
x=2
Help me plz ASAP explain why
Answers
Answer:
a. -2
b. 3
c. 3
d. -3
e. x=-2
Step-by-step explanation:
When a question asks for f(x), it is basically just asking for what the y-value is at the given point of x. So for example, to solve the first one: f(-4), we see that the x-value is -4. This means it is asking for the y-value at x=-4. As we can see from the graph, where x = -4, the y-value is -2 (along the bottom flat line) therefore f(-4) = -2.
This is the same for the other three, f(0) = 3 because the line at x=0 is crossing at y=3. etc.
Finally e is difference because it is instead asking for the x-value when y=6. To solve this we just need to find a point on the graph where the line is at y=6. This, as we can see is at the top of the highest point and occurs where x=-2.
Hope this helped!
Determine the simple interest. The rate is an annual rate. Assume 360 days in a year. p = $502.45,r=5.3%,t = 53days The simple interest is $ (Do not round until the final answer. Then round to the nearest cent as needed.)
Answers
r = R/100 = 5.3%/100 = 0.053 per year.
Putting time into years for simplicity,
53 days / 360 days/year = 0.147222 years.
Solving our equation:
A = 502.45(1 + (0.053 × 0.147222)) = 506.3704997767
A = $506.37
The total amount accrued, principal plus interest, from simple interest on a principal of $502.45 at a rate of 5.3% per year for 0.147222 years (53 days) is $506.37.
20 POINTS!!!!! A cartographer is making a city map. Line m represents Murphy Street. The cartographer translates points on line m along the vector angleleft1, −3angleright to draw Nolan Street. Draw the line for Nolan Street on the coordinate plane and complete its equation. What is the image of (0, 3) in this situation?
Answers
Answer:
[tex]y=2x-2[/tex] and image of (0,3) is (1,0).
Step-by-step explanation:
From the given graph it is clear that the line of Nolan Street passes through the points (0,-2) and (1,0).
So, the equation of Nolan Street is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{0-(-2)}{1-0}(x-0)[/tex]
[tex]y+2=2x[/tex]
[tex]y=2x-2[/tex]
So, the equation of the Nolan Street is [tex]y=2x-2[/tex].
It is given that the cartographer translates points on line m along the vector <1, −3> to draw Nolan Street. So, the rule of translation is
[tex](x,y)\to (x+1,y-3)[/tex]
The image of (0, 3) in this situation.
[tex](0,3)\to (0+1,3-3)=(1,0)[/tex]
The image of (0,3) is (1,0).
Simplify the given expression below: (4+2i)-(1–7i)
Answers
Answer:
3 + 9i
Step-by-step explanation:
(4 + 2i) - (1 - 7i)
distribute the (-)
(4 + 2i) - 1 + 7i
combine like terms
3 + 9i
If 3x = y - 5 and x = -4, then y =*
Answers
Answer:
y = -7
Step-by-step explanation:
3(-4) = y - 5
-12 = y - 5
y = -12 + 5
y = -7
240 students to 12 teachers as ratio
Answers
Answer:
1 : 20 20 students for every 1 teacher
Step-by-step explanation:
divide both sides by 12
help me I don't understand
Answers
Answer: the answer should be A
if this helps the equation format is y= mx + b your replace the with the slop and the b with the y intercept
the way to find the slope is rise over run
Step-by-step explanation:
PLEASE HELPPPPP I WILL MARK YOU BRAINLIEST Akai was eating a pizza over the course of the weekend. On Saturday night, he ate 3/4 of the pizza. On Sunday morning he ate 1/6 of the pizza, and on Sunday night he ate the rest of the pizza. What portion of the pizza did he eat on Sunday night?*
Answers
Answer:
50%
Step-by-step explanation:
34+16=50% he or she ate half of the pizza
Maria has an 8 sided die that is numbered 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8?
Answers
Answer:
12 times.
Step-by-step explanation:
96÷8=12
Select the correct graph for the function ƒ(x) = –x – 7.
Answers
Step-by-step explanation:
The second graph is the right one
Answer:
see below
Step-by-step explanation:
f(x) = -x-7 is of the form
y = mx+b where m is the slope and b is the y intercept
The line has a y intercept of (0,-7) and a slope of -1
A slope of -1 means the line goes down from left to right ( down 1 and to the right 1)
If A=[xy5−8] determine the values of x and y for which A2=A.
Answers
Answer:
x = 9, y = -72/5Step-by-step explanation:
Given the 2 by 2 matrix [tex]A = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right][/tex] , we are to find the value of x and y for the expression A² = A to be true.
First we need to find A² by multiplying the same matrix together
[tex]A^2 = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right] \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\\\ \ we \ normally \ multiply \ the \ rows \ of \ the \ first \ matrix \ with \ the \ column \ of \ the \ second \\\\A^2 = \left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right]\\\\Since \ A^2 = A,\ hence;\\\\\left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right] = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\[/tex]
Equating the first row and second column of both matrices together, we will have;
5x-40 = 5
add 40 to both sides of the equation
5x-40+40 = 5+40
5x = 45
x = 45/5
x = 9
Similarly, we will equate the second row and second column of both matrices to have;
5y+64 = -8
Subtract 64 from both sdies
5y+64-64 = -8-64
5y = -72
y = -72/5
Hence the value of x is 9 and y is -72/5
Matrices are used to represent data in rows and columns
The values of x and y are 9 and -14.4 respectively.
Matrix A is represented as:
[tex]\mathbf{A = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]
Calculate [tex]\mathbf{A^2}[/tex]
[tex]\mathbf{A^2 = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] \times \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]
Recall that [tex]\mathbf{A^2 = A}[/tex]
This means that:
[tex]\mathbf{\left[\begin{array}{ccc}x^2++5y&5x-40\\xy-8y&5y+64\end{array}\right] = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]
So, by comparison
[tex]\mathbf{5x - 40 = 5}[/tex]
[tex]\mathbf{5x = 40 + 5}[/tex]
[tex]\mathbf{5x = 45}[/tex]
[tex]\mathbf{x = 9}[/tex]
Similarly
[tex]\mathbf{5y + 64 = -8}[/tex]
[tex]\mathbf{5y =-64 -8}[/tex]
[tex]\mathbf{5y =-72}[/tex]
[tex]\mathbf{y =-14.4}[/tex]
Hence, the values of x and y are 9 and -14.4 respectively.
Read more about matrices at:
https://brainly.com/question/24810141
5000000 divided by what equals 400
Answers
The dimensions of a right rectangular prism are 1.5 cm, 0.5 cm and 2. 25 cm.
What is the volume of the prism?
A. 0.75 cm
B. 1.6875 cm
C. 3.375 cm
D. 4.25 cm
Answers
The volume of the right rectangular prism having dimensions 1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]
What is Volume?Volume is defined as the space covered by any object in the three dimensions having coordinates in all three sides is called as volume.
We know that the volume of the Rectangular prism is given as:
[tex]\rm V=L\times W\times D\\\\\\V=1.5\times 0.5\times 2.25\\\\\\V=1.6875\ \ \ cm^3[/tex]
Hence the volume of the right rectangular prism having dimensions 1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]
To know more about volume follow
https://brainly.com/question/1972490
#SPJ2
Need an answer quickly. Left my book at my friends house.
Answers
Answer:
A. 3
B. 3/4
C. 1/4
Step-by-step explanation:
1/4 of 12 is 3
3 plus 6 is 9 and 9 is 3/4 of 12
12 minus nine is also three leaving the tank still a 1/4 tank empty
Find the decimal equivalent to 4/15
Answers
To find a decimal that is equavalent to 4/15, all we need to do is divide.
4 / 15 = 0.26666...
Best of Luck!
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17. How much paper of each shade has been used in it?
Answers
Answer:
15.6 is the right answer
Step-by-step explanation:
Is the value of the first 5 ten times as great as the value of the second 5 in 5,045
Answers
Answer:
No
Step-by-step explanation:
Its 1000
Madison's breakfast was a bagel and juice. She spent a total of $4.30.
Madeline spent $6.00 on 2 bagels. How much did Madison pay for her
juice? *
Answers
Answer:
$1.30 for juice
Step-by-step explanation:
If madeline bought 2 bagels for $6 then one bagel must be $3. Madison spent $4.30 so $3 was the bagel and $1.30 was the juice.
At 11:00 p.m. , the temperature in Alaska was -5 degrees. Four hours earlier, the temperature was 40 degrees warmer. What was the temperature at 7:00 p.m. ?
Answers
Answer:
35°
Step-by-step explanation:
-5° + 40° = 35°
So the ansWer is 35°
Explain how to find the y-intercept of a linear equation.
Answers
Answer: simply
Step-by-step explanation: Example: 15y= -5x+0 First move -5 to other side of equal sign. So 15y+5x=0 Then simply by dividing by 5. So 5y+x=0
One number is eight less than a second number. Four times the first is 4 more than 5 times the second. Find the numbers
Answers
Question 958954: One number is five less than a second number. Five times the first is eight more than two times the second. Find the numbers.
hope this helps!
1. Is -2.75 a whole number rational number or a integer ?
Answers
Answer:
its an integer
Step-by-step explanation:
Because it has a negative sign