Answers
Answer:
x = 15
Angle ABC = 57°
Step-by-step explanation:
Hi there!
We're given:
⇒ ABD is a straight line
⇒ Angle ABC = 5x-18 degrees
⇒ Angle DBC = 8x+3 degrees
ABD is a straight line, meaning it measures an angle of 180 degrees.
Angles ABC and DBC create line ABD, so therefore, their sum is equal to 180 degrees:
[tex](5x-18)+(8x+3)=180[/tex]
Open the parentheses:
[tex]5x-18+8x+3=180[/tex]
Combine like terms:
[tex]13x-15=180\\13x=195[/tex]
Divide both sides by 13 to isolate x:
[tex]x=15[/tex]
Therefore, x = 15.
To find angle ABC, replace x with 15 in 5x-18:
[tex]5x-18\\=5(15)-18\\=75-18\\=57[/tex]
Therefore, the measure of angle ABC is 57 degrees.
I hope this helps!
Related Questions
Determine all values of the constant k for which the given set of vectors is linearly independent in R4.{(1,1,0,−1), (1,k,1,1),(5,1,k,1), (−1,1,1,k)}
Answers
If these vectors are to be linearly independent, then there exists some not-all-zero choice for scalars [tex]c_1,c_2,c_3,c_4[/tex] such that
[tex]c_1(1,1,0,-1) + c_2(1,k,1,1) + c_3(5,1,k,1) + c_4(-1,1,1,k) = (0,0,0,0)[/tex]
We can recast this as a system of linear equations,
[tex]\begin{bmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\\c_4\end{bmatrix} = \begin{bmatrix}0\\0\\0\\0\end{bmatrix}[/tex]
This system has a solution if the coefficient matrix on the left side is not singular. So we attempt to find k such that it *is* singular, i.e. the determinant is zero:
• A cofactor expansion along the first column gives
[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = \begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} - \begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} + \begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix}[/tex]
• Cofactor expansions along the first columns of the remaining 3x3 matrices give
[tex]\begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} = k \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}1&1\\1&k\end{vmatrix} + \begin{vmatrix}1&1\\k&1\end{vmatrix} = k^3-3k+2[/tex]
[tex]\begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} = \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}5&-1\\1&k\end{vmatrix} + \begin{vmatrix}5&-1\\k&1\end{vmatrix} = k^2-4k+3[/tex]
[tex]\begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix} = \begin{vmatrix}1&1\\k&1\end{vmatrix} - \begin{vmatrix}5&-1\\k&1\end{vmatrix} + \begin{vmatrix}5&-1\\1&1\end{vmatrix} = -k^2 - 6k + 7[/tex]
It follows that
[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = (k^3-3k+2) - (k^2-4k+3) + (-k^2 - 6k + 7) \\\\ \begin{vmatrix}\cdots\end{vmatrix} = k^3 - 2k^2 - 5k + 6 = (k-3)(k-1)(k+2)[/tex]
which makes the coefficient matrix singular if k = 3, k = 1, or k = -2.
Then the four vectors are linearly independent for
[tex]\left\{ k\in\mathbb R \mid k\not\in\{-2,1,3\}\right\}[/tex]
Show that the points (3,3) ,. (-2,3) are vertices of an isosceles triangle
Answers
Answer:
because the points are vertical and an isosceles has vertical sides
Solve the equation e2x dy/dx 1 given that y = 5 when x = 0
Answers
Answer:
The equation is
[tex]{ \underline{ \sf{y = - 2 {e}^{ - 2x} + 7 }}}[/tex]
Step-by-step explanation:
[tex]{ \sf{ {e}^{2x} \frac{dy}{dx} = 1}} \\ \\ { \sf{dy = {e}^{ - 2x} dx}}[/tex]
integrate:
[tex]{ \sf{ \int dy = \int { - e}^{2x} dx}} \\ { \sf{y = - 2 {e}^{ - 2x} + c}}[/tex]
c is a constant.
when y is 5, x is 0:
[tex]{ \sf{y = { - 2e}^{ - 2x} + c}} \\ { \sf{5 = - 2 {e}^{( - 2 \times 0)} + c }} \\ { \sf{5 = - 2 {e}^{0} + c }} \\ { \sf{5 = ( - 2 \times 1) + c}} \\ { \sf{5 = - 2 + c}} \\ { \sf{c = 7}}[/tex]
therefore, equation:
[tex]y = - 2 {e}^{ - 2x} + 7[/tex]
Customer are charged a late fee of 20% of their bill. This person is a week late on a bill of $200.00 What should we charge for the late fee?
Answers
Multiply the amount owed by 20% by changing the percent to a decimal.
20% = 0.20
200 x 0.20 = 40
The late fee is $40
The price of a sandwich decreases from $6 to $4. What is the percent decrease in the price of the sandwich?
Answers
Answer:
33.33%
Step-by-step explanation:
Decrease in price= Original price -- New price
= $6 - $4
= $2
Percentage decrease= $2÷$6 × 100
= 33.33%
-2/3-8=14 please help
Answers
Answer:
-33
Step-by-step explanation:
this math equation looks relatively simple so i assume the actual equation is -2/3x - 8 = 14
add 8
-2/3x =22
multiply by -3/2
answer is -33
If 18 drinks cost £54, how much will 7 drinks cost ?
Answers
Step-by-step explanation:
solution :
cost of 18 drinks (is)=52
Compare 7/2 and 10/8
Answers
Step-by-step explanation:
7/2
=3.5
10/8
=1.25
Hence, 3.5>1.25
Therefore, 7/2>10/8
In a survey of 60 students ,30 drink milk,25 drink curd and 10 students drink as well as curd then.Find the number of students who drink of them.draw a venn-diagram to illustrate the above information.
Answers
Simplify the complex fraction: 8/9 / -4
Answers
Step-by-step explanation:
[tex] \frac{ \frac{8}{9} }{ - 4} \\ \frac{8}{9} \times \frac{1}{ - 4} \\ \frac{8 \times 1}{9 \times - 4} \\ \frac{8}{ - 36} \\ \frac{2}{ - 9} \\ - 0.22[/tex]
Answer:
B. [tex] - \frac{2}{9} [/tex] (second option)
Step-by-step explanation:
[tex] \frac{ \frac{8}{9} }{ - 4} [/tex]
[tex] \frac{8}{9} \div 4 = \frac{8}{9} \times \frac{1}{4} [/tex]
[tex] \frac{8 \times 1}{9 \times 4} = \frac{8}{9 \times 4} [/tex]
[tex] - \frac{2}{9} [/tex] ✅
PLS HELP! WILL GIVE BRAINLIEST
Answers
Answer:
csc x sec x
Step-by-step explanation:
csc = 1/sin
1/sin^2 / cos/sin = 1 / sin^2 * sin/cos = 1 / sin cos = csc sec
6(a+2b+3c)=6, left parenthesis, a, plus, 2, b, plus, 3, c, right parenthesis, equals
Answers
1.
.? ESSENTIAL QUESTION
How are the
midpoint and length of a segment on the
coordinate plane determined?
Answers
Answer:
to find midpoint add both"X" coordinates and divide by 2
also add "Y" coordinates and divide by 2
then for line of segment use distance formula which is D=√[(x2-x1)²+(y2-y1)²]
Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
To determine the midpoint of two coordinates (x₁,y₁) and (x₂,y₂ )
Midpoint = [ (x₁ + x₂)/2 + (y₁ + y₂)/2 ]
The distance between two points (x₁,y₁) and (x₂,y₂ )
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
Hence "Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]".
For more about line segment,
https://brainly.com/question/25727583
#SPJ2
Tickets to a band concert cost 10 dollars each
Answers
Answer:
10
Step-by-step explanation:
It 10 bucks each ticket
Find the value of:
7- (1/2)3
Answers
Answer:
6.875
Step-by-step explanation:
7- (1/2)^3 = 7-1/8 = 6.875
If Marty spent $66 on movie tickets and one ticket costs $8.25 how many tickets did he buy
Answers
Answer:
8 tickets
Step-by-step explanation:
To find how many tickets he bought, we can divide.
66 / 8.25 = 8
Best of Luck!
Answer:
8
Step-by-step explanation:
66 divided by 8.25, bringing it to 8.
Find the area of this circle
Answers
Answer:
153.86 ft^2
Step-by-step explanation:
π=3.14
r=7ft
πr^2=3.14*7*7
=153.86 ft^2
Area of circle = π r²
Here , We have
π = 3.14r = diameter/2r = 14/2 r = 7 ft.Area of circle = 3.14 × (7)²
Area of circle = 3.14 × 49 ft²
Area of circle = 153.86 ft²
find the coordinates of the vertex
Answers
You can either transform this quadratic equation into a vertex form which would rather painful or use derivatives.
I'll use dervatives. We know that vertex of a quadratic function is either its maxima or its minima, since the leading coefficient [tex]-x^2[/tex] has a negative prefix that means we get a downward turned parabola with minima being the vertex.
First we take the derivative with respect to x,
[tex]\dfrac{d}{dx}-x^2-2x+3=-2x-2[/tex]
The derivative is esentially information what is the slope of a function at a particular x. When the slope is 0 we reached some sort of turning point, such as minima.
We therefore do,
[tex]-2x-2=0\implies x=-1[/tex]
So at [tex]x=-1[/tex] there appears to be a minima or x-coordinate of the vertex of the function.
Plug the coordinate into the function to get y,
[tex]y=f(-1)=-1+2+3=4[/tex]
So the vertex of the function is at [tex]\boxed{(-1,4)}[/tex].
Assuming you don't know derivatives, there is another way.
First compute the roots of the function,
[tex]-x^2-2x+3=0[/tex]
[tex]-(x-1)(x+3)=0[/tex]
[tex]x_1=1,x_2=-3[/tex]
In the middle between [tex]x_1,x_2[/tex] is an x coordinate of a vertex,
[tex]x=\dfrac{x_1+x_2}{2}=\dfrac{1-3}{2}=-1[/tex]
Just like we had before, we compute for y, [tex]h(-1)=4[/tex] and again the result is [tex]\boxed{(-1,4)}[/tex].
Hope this helps :)
Determine which of the following mappings are functions. If the relation is not a function, indicate why it is not.
Answers
Answer:
First mapping is a function because there is no more than one output for each input.Second mapping is not a function because there is more than one output for input B.Third mapping is a function because there is no more than one output for each input.Fourth mapping is a function because there is more than one output for each input.Step-by-step explanation:
A function can be defined as two variables (independent and dependent) which cannot have more than one output for each input.
Step-by-step explanation:
1. the first mapping is a function
2. the second mapping is not a function, because: B has 2 relations, C & E have no relations.
3. the third mapping is a function
4. the fourth mapping is not a function, because B has no relation.
-2/5 + 1/2 plz answer need help
Answers
Answer:
solution -2/5+1/2 =-2*2+1*5/5*2 =-4+5/10 =1/10
Write the interval notation represented by each description below:
1.
The set of all numbers less than negative ten.
2.
The set of all positive real numbers.
3.
The set of all numbers less than 4.242 and greater than 12.566.
4.
The set of all numbers that are greater than 15 and less than 50.
5.
The set of all numbers that are at most 5.
6.
The set of all numbers that are at least 18.
Thank you so much for your help!
Answers
Answer:
1. (-∞ , -10]
2. [0, ∞ )
3. [12.566, 4.242]
4. [15, 50]
5. (-∞ , 5]
6. [18, ∞)
Step-by-step explanation:
Answer:
1. The set of all numbers less than negative ten.
(- ∞, -10)2. The set of all positive real numbers.
(0, +∞)3. The set of all numbers less than 4.242 and greater than 12.566.
(-∞, 4.242 )∪ (12.566, +∞)4. The set of all numbers that are greater than 15 and less than 50.
(15, 50)5. The set of all numbers that are at most 5.
(-∞, 5]6. The set of all numbers that are at least 18.
[18, +∞)What is 12 divided by 2/5?
Answers
Answer:30
Step-by-step explanation:
expressions equal to 10^3
Answers
Answer:
1000
Step-by-step explanation:
10³
= 1000
Answer:
10 * 10 * 10
Step-by-step explanation:
Cubing a number just means you are multiplying that number 3 times to itself. Since we have 10^3, we multiply 10 to itself three times.
Best of Luck!
Enlargements I cannot do can someone help plz
Answers
Answers:
The coordinates of the vertices are
(6,2)(8,2)(8,6)(4,6)These coordinates are from the red points shown in the diagram below.
=============================================================
Explanation:
Because the center of dilation is at the origin, we'll multiply each coordinate of each point by the scale factor.
Specifically, we'll double the coordinate values since the scale factor is 2.
A point like (3,1) becomes (6,2)A point like (4,1) becomes (8,2)and so on
The diagram is shown below. The original preimage is in blue while the dilated enlarged image is in red. Your teacher only wants the location of the red corner points.
In a class of 25 students, 13 students wear glasses and 12 students do not wear glasses.
The ratio of glasses to non-glasses wearing students is 13:12.
Is this ratio part-to-part or part-to-whole?
Answers
the ratio of students do not wear glass to total students
[tex]\frac{12}{25}[/tex]
the ratio of students wear glass to total number of students is
[tex]\frac{13}{25}[/tex]
Given
In a class of 25 students, 13 students wear glasses and 12 students do not wear glasses
The ratio of glasses to non-glasses wearing students is 13:12.
Explanation :
we need to find the ratio students wear glasses to whole students
There are total of 25 students.
13 students wear glass
So the ratio of students wear glass to total number of students is
[tex]\frac{13}{25}[/tex]
Similarly , we can find the ratio of students do not wear glass to total students
[tex]\frac{12}{25}[/tex]
Learn more : brainly.com/question/17218035
___ minus 14 = 9 times 3
Answers
Answer: x=41
Step-by-step explanation:
Let x be the number missing
Given expression
x - 14 = 9 × 3
Simplify by multiplication
x - 14 = 27
Add 14 on both sides
x - 14 + 14 = 27 + 14
[tex]\boxed {x=41}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Step-by-step explanation:
[tex]x - 14 = 9 \times 3 \\ x - 14 = 27 \\ x = 27 + 14 \\ x = 41 \\ thank \: you[/tex]
Write the number in expanded form 68,020
Answers
Answer:
hope it is helpful
Step-by-step explanation:
68,020-
6= 60,000
8= 8,000
0=0
2= 20
0=0
what is
[tex] \frac{28}{141} [/tex]
as a percentage
Answers
Answer:
19,86%
Step-by-step explanation:
[tex] \frac{28}{141} = 0.198582[/tex]
➡️ [tex]0.1986[/tex]
➡️ [tex]0.1986 \times \frac{100}{100} [/tex]
➡️ [tex] \frac{0.1986 \times 100}{100} [/tex]
➡️ [tex] \frac{19.86}{100} [/tex]
➡️ [tex] = 19.86\%[/tex] ✅
Question 7 of 10
Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
A. None of these
B. What must be true
C. What may be false
D. What may be true
Answers
Answer:
what may be true
Step-by-step explanation:
i just took the test and got the answer correct, i hope this helps.
(-1,-6)(-1,-3)(-1,-2)(-4,-2)(-4,1)(-4,4) range
Answers
Answer:
range is the y part and domain is the x so the range is the y coordinates
-6,-3,-2,-2,1,4
Step-by-step explanation: