Answers
Answer:
x = 75
y = 105
Step-by-step explanation:
Remark
You can find y in two different ways.
One
You can recall that y is the sum of the 2 interior angles not connected to it. Those angles are called the remote interior angles. Or
Two
You can add the three angles to 180 and solve for x. Then since x and y are supplementary, you can find y.
Solution
One
y = 60 + 45
y = 105 Answer
Two
x + 60 + 45 = 180 All triangles have 180 degrees. Solve for x.
x + 105 = 180 Subtract 105 from both sides
x = 180 - 105 Combine
x = 75 Find an equation that relates x and y
x + y = 180 x and y are supplementary they add to 180
75 + y = 180 Subtract 75 from both sides.
y = 180 - 75 Combine
y = 105
Related Questions
what is the equation of a line that has an undefined slope (vertical line) and an x-intercept of -2
Answers
The equation of a vertical line: x = a (a - any real number).
x-intercept = -2, therefore your answer is:
x = -2What is the common ratio for this geometric sequence? 64,16,4,1,...
Answers
Answer:
r = ¼
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
We can get the value for r by dividing aₙ by aₙ₋₁.
a₄/a₃ = ¼
r = ¼
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what is the 20th term of the arithmetic sequence 8,21,34,47,60,..
Answers
Well considering that
F (1) = 8
F (x) = f(x-1) + 13
(Meaning the previous term plus 13)
So
F (x) = 13x - 5
F (0) = -5
The 20th term of the given arithmetic sequence 8, 21, 34, 47, 60... is 255.
Explanation:In the field of mathematics, this type of problem is referred to as an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.
In your question, the arithmetic sequence provided is 8, 21, 34, 47, 60... Here, the common difference is 13 (i.e., every term after the first is 13 more than the preceding term).
To find any term (let's say the nth term) in an arithmetic sequence, you can use the formula:
nth term = first term + (n - 1) * common difference
Applying this formula to find the 20th term:
20th term = 8 + (20 - 1) * 13 = 8 + 247 = 255
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The ratio of yellow tulip bulb to red tulip in a package is 2 to 3. There are 100 tulip in the package. How many of each color bulbs is there.
Answers
Answer:
Yellow: 40Red: 60Step-by-step explanation:
You have to distinguish the difference between a ratio of yellow bulb to red bulb and red bulb to total and yellow bulb to total. The totals are where you start.
2 bulbs out of 5 are yellow
3 bulbs out of 5 are red
Yellow
Set up the proportion for yellow. You could start with red.
2/5 = x / 100 Cross multiply5x = 2 * 100 Combine the right.5x = 200 Divide by 55x/5 = 200/5 Simplifyx = 40 Answer 1. Yellow bulbsRed
3/5 = x / 100 Cross multiply 5x = 3*100 Simplify5x = 300 Divide by 55x/5 = 300/5 Simplifyx = 60 Answer 2. Red bulbs.Note: Yellow to red is 2/3
(7.02) classify each sequence as arithmetic, geometric, or neither.
4/9,4/3,4,12,36
0,1,2,3,4,5,6
-10,-6,-2,2,6,10
Answers
Answer:
geometric
arithmetic
arithmetic
Step-by-step explanation:
1.
4/9,4/3,4,12,36
Multiply each term by 3 to get the next term. There is a common ratio between terms, so it geometric.
2.
0,1,2,3,4,5,6
Add 1 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
3.
-10,-6,-2,2,6,10
Add 4 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
What type of graph is best to use to graph data about the favorite sport for seniors and juniors? A. Bar Graph B. Double Bar Graph C. Line Graph D. Double Line Graph
Answers
Answer:
Bar Graph
Step-by-step explanation:
A bar graph would be best.
B.Double Bar Graph
There are TWO types of people so it needs to be a two type Bar Graph as in double Bar Graph. A line graph is not right because it is changes over time.
Hi!! Please Help ASAP!!
Answers
Answer:
The answer is A or the first one
Answer:
it's (2,3)
because look at the intersection between 2 line, that's the solution, it said nearest, so (2,3) is the most accurate
Natasha was thinking of a number. Natasha subtracts 16 from it and gets an answer of 18.2. What was the original number?
Answers
Answer:
34.2
Step-by-step explanation:
V/-6 +2=-1
what does v equal
Answers
-2=-2
V/-6=-3
×-6=-6
V=18
Evaluate for x=4 and y = -3
Answers
2y/x^2
Replace x and y with the given values:
2(-3) / 4^2
2*-3 = -6
4^2 = 16
Now you have -6/16. which can be simplifies to -3/8
The area of a trapezoid is given by the formula A = 1 2 h(B + b). Solved for b, this formula becomes b =
Answers
Answer:b = (2A - hB)/h
Step-by-step explanation:
See , we know area of a trapezoid is equal to 1/2*(sum of parallel sides)* perpendicular distance between parallel sides.
Here B and b are parallel sides which we know by comparing the equation.
And 'h' here is the perpendicular distance between parallel sides.
We have to write the equation in terms of one of the parallel sides 'b'
Our formula is A = 1/2*h*(B+b)
I.e. 2A = h*(B+b) (Multiplying both sides by 2)
I.e. 2A - hB = hb
I.e. b = (2A - hB)/h
Hope it helps!!!
Answer:
D) [tex]\frac{2A}{H} -b[/tex]
The height of the water in an a over ground pool is 3ft. As the number of water drains ,the rate of -1/2 inch per minute. Write and solve an equation to find how many minutes it will take to drain the pool
Answers
Answer:
36 - 1/2x = 0
72 minutes
Step-by-step explanation:
there is a total of 3 feet in the pool at the start, 1 ft = 12 in, and 3 ft = 36 in. the pool is losing water, so we have to subtract. it is losing water at a rate of -1/2 in per minute, and we don't know how many minutes it will take
we have to set it equal to 0 because we are trying to find out how long it will be until the pool is completely drained, which is when there will be no water left, so it will be 0
subtract 36 from both sides
-1/2x = -36
divide both sides by -1/2
x = 72
72 minutes
write the equation of the line that passes through the given points (0,-1) and (-5,-7) Simplify your answer
Answers
Answer:
y = 6/5 x-1 slope intercept form
6x-5y = 5 standard form
Step-by-step explanation:
We have the points (0,-1) and (-5,-7)
We can find the slope using
m = (y2-y1)/(x2-x1)
= (-7--1)/(-5-0)
= (-7+1)/(-5-0)
= -6/-5
= 6/5
We also have the y intercept ( when x=0) It is -1
We can use the slope intercept form of the equation y = mx+b
y = 6/5 x-1
Depending on what you mean when you say simplify your answer
We can put it in standard form ax+by = C
Multiply both sides by 5
5y =5* 6/5 x-1*5
5y = 6x-5
Subtract 6x from each side
-6x+5y = 6x-6x-5
-6x+5y = -5
Multiply by -1
6x-5y = 5
The lines below are perpendicular. If the slope of the green line is -3 what is the slope of the red line?
Answers
Answer:
1/3
Step-by-step explanation:
Given that two lines are perpendicular.
Slope of green line (one of the lines) is -3.
To find the slope of other perpendicular line red.
We know that angle between two lines with slopes m1 and m2 would be
[tex]tan^{-1} \frac{m1-m2}{1+m1m2}[/tex]
where m1 is the slope of I line and m2 slope of second line.
Here since two lines are perpendicular angle between them is 90 degrees and hence we get infinity as tan x
this implies denominator for [tex] \frac{m1-m2}{1+m1m2}[/tex]=0
i.e. 1+m1m2 = 0
Or m1m2 =-1
Since one of slope m1 = -3 we have
-3m2= (-1) or m2 = 1/3
Answer:
-3
Step-by-step explanation:
Apex~
Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Answers
Answer:
Option B is correct.
Reason:It is an argument
Step-by-step explanation:
Given: [tex]AB \cong BC[/tex] and [tex]BC \cong EF[/tex]
By transitive property: a = b and b = c then, a =c
⇒[tex]AB \cong EF[/tex]
AB = EF [def of [tex]\cong[/tex] segment]
By Segment Addition Postulate states that given two points A and C, and a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation
AB + BC = AC.
Since, the line segment EG , F lies on the line segment;
then, by segment addition postulates we have;
EG = EF + FG
By substitution AB=EF
⇒ EG = AB + FG hence proved!
Since, in the fourth statement reason is: It is an argument
Answer:
b
Step-by-step explanation:
there are a total of 124 students in the band and there are 12 more boys than girls the band. write a system of linear equations that represents this situation. how many boys and how many girls are in the band
Answers
will give you amount of girls
for boys add 12 so
g =56
b =68
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of boys is 68
The number of girls is 56
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation
2x + 4y = 6 is an equation.
We have,
Total number of students = 124
Number of boys = x + 12
Number of girls = x
Now,
x + 12 + x = 124
2x + 12 = 124
Subtract 12 on both sides
2x = 124 - 12
2x = 112
Divide 2 on both sides.
x = 56
The number of boys.
= x + 12
= 56 + 12
= 68
The number of girls.
= 56
Thus,
The number of boys is 68
The number of girls is 56
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I need the range and domain
Answers
Look at the picture.
The domain x ≥ 0 → x ∈ [0, ∞)The range y ≥ 0 → y ∈ [0, ∞)Which of the following is an irrational number
Answers
Answer:
A
Step-by-step explanation:
Pi is a never ending number.
The answer is B) because it is not a never ending number
Also, the question in the picture asks which is a rational number, not irrational
The range of f(x)=5x2^x is all positive real numbers true or false
Answers
Step by step-
A force of 250 N is applied to an object that accelerate at a rate of 5 m/s2 what is the mass of the object
Answers
Force=mass x acceleration
Plug in 250 N for the force and 5 m/s2 for the acceleration; solve for mass
250=5m
50kg=m
Hope this helps!!
Graph the equation by plotting three points -2y=-x+8
Answers
[tex]-2y=-x+8\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-4\\\\for\ x=0\to y=\dfrac{1}{2}(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=2\to y=\dfrac{1}{2}(2)-4=1-4=-3\to(2,\ -3)\\\\for\ x=4\to y=\dfrac{1}{2}(4)-4=2-4=-2\to(4,\ -2)[/tex]
(4.5,-1.75) and (8,0)
When 2x^2 - 20x + 49 = 19 is written in the form (x - p)^2 = q, what is the value of q? Show your work please.
Answers
Answer:
q = 10
Step-by-step explanation:
The desired form is a rearrangement of the given equation, divided by the leading coefficient.
Monic polynomialA monic polynomial is one with a leading coefficient of 1. The desired form requires that we start from that condition. In order to avoid fractions, we can begin by subtracting the constant term on the left.
2x^2 -20x +49 = 19 . . . . . . given
2x^2 -20x = -30 . . . . . . . . subtract 49
x^2 -10x = -15 . . . . . . . . . divide by 2
Completing the squareThe square of the binomial a+b is given by ...
(x +b)^2 = x^2 +2bx +b^2
That is the constant term on the right is the square of half the coefficient of x. To achieve this perfect square trinomial in our equation, we need to add the square of half of -10.
x^2 -10x +25 = -15 +25 . . . . . . add (-10/2)^2 = 25 to both sides
(x -5)^2 = 10 . . . . . . . . . . . write in the desired form
The value of q in the form ...
(x -p)^2 = q
is 10.
Write all factored equivalent expressions for 12z+36
Answers
The factored equivalent expression for 12z+36 is 12(z + 3) after factoring out the common factor of 12.
Explanation:When asked to write all factored equivalent expressions for 12z+36, we look for common factors. Both terms have a common factor of 12. Factoring out the 12, we get 12(z + 3). There are no other common factors, and the expression cannot be factored further as both terms within the parentheses are prime with respect to each other.
Jacob started that he solved the equation 2x+3=5 using addition and multiplication property of equality. Which statement is true?
A.Jacob added -3 to both sises and multiplied both sides by 1/2.
B.Jacob added -3 to both sises and multiplied both sides by 2.
C.acob added 3 to both sises and multiplied both sides by 1/2.
D.acob added 3 to both sises and multiplied both sides by 2.
Answers
Answer:
A. Jacob added -3 to both sides and multiplied both sides by 1/2.Step-by-step explanation:
To solve the equation, Jacob must add -3 to both sides, and multiply by 1/2 both of them, as it's shown below:
[tex]2x+3-3=5-3\\2x=2\\\frac{2x}{2}=\frac{2}{2}\\x=1[/tex]
So, you see, applying all operations like option A, we easily solve the equation.
Therefore, the right statement is the first one, A.Answer:
The correct option is A) Jacob added -3 to both sises and multiplied both sides by 1/2.
Step-by-step explanation:
Given :
[tex]2x+3=5[/tex] -------- (1)
Solution :
To find the value of x from equation (1) we have to first add both side -3 in equation (1), we get
[tex]2x = 2[/tex]
Now, multiply both the side of equation (1) by
[tex]\dfrac{1}{2}[/tex]
[tex]x= 1[/tex]
Therefore option A) is correct.
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which is better buy store a $12 for 3 pies or store b $10 for 2 pies
Answers
Answer:
Store A is the better buy
Step-by-step explanation:
Lets find out how much it will cost for a pie at each store
Store A
$12 /3 pies = $4 per pie
Store B
$10/2 pies = $ 5 per pie
Pink is shoe is 20.4 cm long Rajesh shoe is 7 mm longer than pinky shoe how long is Rajesh shoe in cm
Answers
To find the length of Rajesh's shoe, convert the additional length from millimeters to centimeters and add it to Pinky's shoe length. Rajesh's shoe is 21.1 cm long.
Explanation:The subject of this question is Mathematics and it is suitable for a Middle School student. To find the length of Rajesh's shoe, we need to add the length of Pinky's shoe to the additional length that Rajesh's shoe has. Pinky's shoe is 20.4 cm long, and Rajesh's shoe is 7 mm longer.
Firstly, we need to convert millimeters to centimeters since 1 cm equals 10 mm. Therefore, 7 mm is equivalent to 0.7 cm (since 7 divided by 10 equals 0.7).
Next, we add this length to Pinky's shoe length:
20.4 cm (Pinky's shoe length)+ 0.7 cm (additional length)Rajesh's shoe length equals 21.1 cm.
find the product of 10^3 * 10^6
Answers
When multiplying the same base with exponents, you keep the base the same and then you add the exponents, so for this question you do:
10^3 x 10^6
10^9
[tex] {10}^{3} \times {10}^{6} [/tex]
[tex] = {10}^{9} [/tex]
The answer is:
[tex] {10}^{9} [/tex]
This is because of the law of indices. When multiplying indices, you add the powers.
Which statement is true? The initial height of the coconut is 190 feet. The coconut will hit the ground between 4 and 5 seconds after it was dropped. The values of h(t) when t = 4 and 5 should be 0. The maximum height of the coconut was 1 second after it was dropped.
Answers
Answer: Based on the given data, the coconut has a height of 210 units and it hits the ground between 4 to 5 seconds where the height is less than zero or a negative number, this means that probably the coconut was buried in the ground at these times. The correct answers are:
The values of h(t) when t = 4 and 5 should be 0. This could also be without the assumption that the coconut is buried after falling.
Answer:
its C
Step-by-step explanation:
Compare the graph of g(x) =x^2 +6 with the graph of f(x)=x^2
Answers
Answer:
Step-by-step explanation:
If you know what g(x) looks like, you can find f(x). Every y point of g(x) is f(x) + 6.
The general point of g(x) is (x,f(x) + 6). That is the major difference. Just so you can see it visually, the both graphs are shown below.
red: f(x) = x^2
blue: f(x) = f(x) + 6 = x^2 + 6
green: x = 2 With the two points shown that intercept the two given functions.
Purple(?): x = - 2 with the two points shown that intercept the two given functions.
The graphs of both g(x) =x² +6 and f(x)=x² are parabolas. However, while the vertex of the graph of f(x) = x^2 is at the origin, the graph of g(x) = x² + 6 is shifted upwards by six units, with the vertex of g(x) at (0,6). The shape of the two graphs is identical.
Explanation:The graphs of g(x) =x² +6 and f(x)=x² are both parabolas, but their positions differ on the coordinate plane. The function f(x) = x² is a standard quadratic function with a vertex at the origin (0,0). On the other hand, g(x) = x² + 6 is a vertical translation of the graph of f(x) = x2 upwards by six units. So, the vertex of g(x) is at the position (0, 6). Furthermore, the shape of the two graphs will remain the same as they both have the same degree and leading coefficient.
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Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. Then find the area of the quadrilateral. A(2, -3), B(7, -3), C(9, 2), D(4, 2)
Answers
Answer: Parallelogram, Area = 25 units²
Step-by-step explanation:
Step 1: Find the lengths of all of the sides (use Pythagorean Theorem, distance formula, or count the spaces on the graph)
Step 2: Find the slopes of each line
Step 3: Evaluate the slopes to see if any are parallel (same slope) or perpendicular (opposite reciprocal slopes)
see attachment