find the value of x in the figure below Assume that the lines are parallel
Answers
The value of x is 30.
We are given that lines l and m are parallel. We are asked to find the value of x.
Since we are given that l and m are parallel, we can use the property of alternate exterior angles.
This property states that when two lines are cut by a transversal, the alternate exterior angles are congruent.
In the diagram, we see that ∠A and 2x+15 ∘ are alternate exterior angles. Therefore, we have:
∠A=2x+15 ∘
We are also given that ∠A=75 ∘ .
Substituting this value into the equation above, we get:
75 ∘ =2x+15 ∘
Solving for x, we get:
2x=75 −15 ∘
2x=60 ∘
x= 60/2 ∘
x=30∘
Therefore, the value of x is 30 ∘ .
Related Questions
Gabriela has dinner at a cafe and the cost of her meal is \$45.00$45.00. Because of the service, she wants to leave a 15\%15% tip.
What is her total bill including tip?
Answers
Answer: Her total bill including tip is $51.75
Step-by-step explanation:
Hi, first, we have to multiply the cost of the meal by the tip percentage in decimal form (percentage divided by 100).
Mathematically speaking:
45 x (15/100) = 45 x 0.15 = 6.75 tip amount
Finally, add the amount of the tip to the meal's cost.
45 +6.75 = $51.75
Her total bill including tip is $51.75
Feel free to ask for more if needed or if you did not understand something.
A dozen eggs cost 3.84. At this rate how much wood 50 eggs cost
Answers
Answer:
$16
Step-by-step explanation:
A dozen is equal to 12 eggs. In order to find the amount for 50 eggs, we need to find the unit rate. In this problem, we can assume that each of the eggs cost the same amount. Therefore, we can divide 3.84 by 12 to get the amount of one egg.
3.84/12= 0.32
Now that we have found the unit rate, we simply have to multiply it by 50 to get the cost. To explain why we do this, I will set it up as a proportion.
3.84/1 = ?/50
In order to get the equivalent amount you must multiply by 50.
0.32 x 50= 16
Therefore, the answer is $16
The cost of 50 eggs is $16.
Given that, a dozen eggs cost $3.84.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, the cost of one egg = 3.84/12
= $0.32
Now, the cost of 50 eggs
= 50 × 0.32
= 16
Therefore, the cost of 50 eggs is $16.
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find f(x).g(x) if f(x) = 3x+11 and g(x)= -2x+7
Answers
Answer:
f(x)·g(x) = -6x² -x +77
Step-by-step explanation:
Given:
f(x) = 3x + 11
g(x) = -2x+7
f(x) * g(x) = (3x+11)*(-2x+7)
= -6x²+21x-22x+77
= -6x² -x +77
Provide the first six terms of the following sequence: t1=81 tn=13tn-1n ≥ 2
Answers
Answer: 81, 27, 9, 3, 1, 1/3
There are six terms listed. The first five are whole numbers and the sixth term is a fraction.
==============================================
Explanation:
The equation t1 = 81 means that the first term "t" is 81. The second term is t2 = 27 because we multiply 1/3 by 81, or divide 81 over 3, and we end up with 81/3 = 27 as the second term.
We know to multiply by 1/3 because of the equation tn = (1/3)*t_(n-1) where the "n-1" portion is smaller than 't'. We can write it like this[tex]t_n = \frac{1}{3}*t_{n-1}[/tex]
To get the next term, we multiply by 1/3 again: 27*(1/3) = 27/3 = 9 giving us the third term
And repeat until we have six terms
9*(1/3) = 9/3 = 3 is the fourth term
3*(1/3) = 3/3 = 1 is the fifth term
1*(1/3) = 1/3 is the sixth term
So that is how I got the first six terms to be 81, 27, 9, 3, 1, 1/3
Lia finds a second dress that was originally $72.00 and now was marked 15% off. How much did she pay for the second dress?
Answers
Answer:
The answer is $61.20
Step-by-step explanation:
First you multiply 72 by .15 (which is 15% converted to a decimal), which gives you 10.8. You then subtract 10.8 from 72.
The two rectangles shown have equal areas. Find the value of x
Answers
Answer:
x=18
Step-by-step explanation:
We need to find the areas of the rectangles
1st rectangle
A= l*w
A = (2x+4)*9
= 18x+36
2nd rectangle
A = l*w
= 15*(3x-30)
= 45x-450
Since the area of the rectangles are equal, we set these two equations equal
18x+36 = 45x-450
Subtract 18x from each side
18x-18x+36 = 45x-18x-450
36 = 27x-450
Add 450 to each side
36+450 =27x
486 = 27x
Divide by 27 on each side
486/27 = 27x/27
18=x
what is the solution to the system of equations y=x+3, y=3x+1
Answers
Substitution method
y = x + 3 (*)
y = 3x + 1 (**)
Substitute (*) to (**):
3x + 1 = x + 3 subtract 1 from both sides
3x = x + 2 subtract x from both sides
2x = 2 divide both sides by 2
x = 1Put the value of x to (*):
y = 1 + 3
y = 4Answer: x = 1 and y = 4 → (1, 4).A=1+Prt solve for p
Answers
[tex]A=1+Prt\\\\Prt=A-1\\\\P=\dfrac{A-1}{rt}[/tex]
Change each improper fraction into an equal mixed number.
a. 15⁄4
b. 41⁄9
c. 67⁄8
d. 135⁄11
e. 107⁄20
f. 493⁄174
Answers
Answer:
A. 3 3/4
B. 4 5/9
C. 8 3/8
D. 12 3/11
E. 5 7/20
F. 2 145/174
Hope That Helps!
Please help me with this and dont get any wrong!!!!!
Answers
1. The answer is A.
Based on the line plot, we can see that Sandy drank 12 juice boxes on October 12th. Each X on the plot represents 2 juice boxes, and there are 6 of them, meaning she drank 12. October 2nd has 1 X, meaning she drank 2 that day.
2. The answer is A.
On a graph, the point (1, 3) would mean that 1 is on the x-axis, and 3 is on the y-axis. Therefore, point B is correct because it is 1 space to the right, and 3 spaces up from the origin.
3. The answer is C.
If the coordinate we're looking for is (4, 0) then on a graph you would move 4 spaces to the right, and 0 spaces up or down. Therefore, point B is the correct choice.
A marketing company surveys 100 males and 100 females between the ages of 55 and 70 to determine how many times they text each day. The mean for males is 6 with a range of 4. The mean for the females is 8 with a range of 4. According to the statistics, which statement is TRUE?
A)
On average, females text more than males.
B)
On average, females text less than males.
C)
On average, females and males text about the same .
D)
On average, both males and females text 4 times each day.
Answers
Answer: I believe that A is the correct answer.
Answer:
It's A
Step-by-step explanation:
I just did this question
Triangle ABC is reflected over the y-axis. The coordinates of Point A are (–3, –1). What are the coordinates of Point A', the reflected image, using an algebraic representation?
Answers
Answer:
A'(3, - 1)
Step-by-step explanation:
Under a reflection in the y-axis
a point (x, y) → (- x, y), hence
A (- 3, - 1) → A'(3, - 1)
The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.
Given here: The coordinate of a Triangle A as (-3,-1)
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Thus The vertex of the triangle (-3,-1) it changes to (3,-1)
The algebraic representation for the transformation is given by '
(x,y)⇒(-1×x,1×y)
⇒(-x, y)
Hence, The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
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Mother has purchased 75 yards of green fabric and 125 yards of white fabric to make green and white curtains. What is the largest number of curtains she can make if she wants all the curtains to be exactly the same length, and to have no fabric left over? How many yards of each kind of fabric would be used for each curtain?
Answers
The mother can make 3 green curtains and 5 white curtains, using the greatest common divisor of 75 and 125 yards which is 25. Each curtain would thus be 25 yards.
Explanation:This question can be solved using the concept of Greatest Common Divisor (GCD), which finds the largest possible length that can divide two given lengths without leaving any remainder. In this case, the lengths are 75 yards and 125 yards, which are the quantities of green and white fabric respectively. The GCD of 75 and 125 is 25.
Therefore, the largest number of curtains that can be made is based on this length, which means the mother can make 75/25=3 green curtains and 125/25=5 white curtains. Each curtain would be 25 yards.
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Simplify completely 12x+36/x^2-4x-21 and find the restrictions on the variable
Answers
Answer:
[tex]\dfrac{12}{x-7},[/tex]
[tex]x\neq 7,\ x\neq -3.[/tex]
Step-by-step explanation:
Consider the expression
[tex]\dfrac{12x+36}{x^2-4x-21}.[/tex]
1. The numerator can be factored as
[tex]12x+36=12(x+3).[/tex]
2. The denominator [tex]x^2-4x-21[/tex] has the discriminant
[tex]D=(-4)^2-4\cdot (-21)\cdot 1=16+84=100.[/tex]
Then
[tex]x_{1,2}=\dfrac{-(-4)\pm \sqrt{100}}{2\cdot 1}=\dfrac{4\pm 10}{2}=7,\ -3.[/tex]
Then
[tex]x^2-4x-21=(x-7)(x+3).[/tex]
Note that restrictions on the variable x are [tex]x\neq 7,\ x\neq -3.[/tex]
3. Simplify the fraction:
[tex]\dfrac{12x+36}{x^2-4x-21}=\dfrac{12(x+3)}{(x-7)(x+3)}=\dfrac{12}{x-7}.[/tex]
a Panda eats about 20 kg of bamboo per day. About how many pounds of bamboo will the panda eat in 6 weeks?
Answers
Answer:
840 kg of bamboo in 6 weeks
Step-by-step explanation:
if a panda eats 20 kg of bamboo per day he eats 140 kg of bamboo every week. multiply the amount he eats per week (140) by the amount of weeks (6) and you get 840 kg of bamboo
Answer:
1,848
Step-by-step explanation:
The panda eats 20kg of bamboo per day, and 1 L = 2.2 Ib, so multiplying 20 x 2.2 = 44, and there is 42 days in 6 weeks, so you multiply 44 x 22 = 1,848. I hope this is the correct answer, you're welcome!
what is seven decreased by 3 times some number
Answers
the answer to the question is 7-3x.
Answer:
7 - 3x
Step-by-step explanation:
let "some number" = x
"3 times x" = 3(x)
"seven decreased by" 7 -
Put together the phrases.
"seven decreased by 3 times x" is 7 - 3x
7 - 3x is your answer
~
Please answer number 3.
Answers
I can't exactly SHOW you where to put the numbers, but I can teach you the process of how you'd do it.
First off, label your number line from 0-15, as it is the simplest. (You'd be counting by 1 per each line). Then, follow this process:
1) Look at the first digit of your value. Place your number according to your first digit. (So, you'd put 0.365 at the 0 line and 3.521 at the 3 line)
2) Look at the second digit of your value. Imagine that between the two main lines (0-1 and 3-4) that there is 10 smaller lines. Then, you can place your number according to your second digit. (So, you'd put 0.365 at the 0.3 line and 3.521 at the 3.5 line).
3) Look at the third digit of your value. Imagine that between the two smaller lines (0.3-0.4 and 3.5-3.6) that there is 10 smaller lines. Then, you can place your number according to your third digit. (So, you'd put 0.365 at the 0.36 line and 3.521 at the 3.52 line).
4) Look at the fourth digit of your value. Imagine that between the two even smaller lines (0.36-0.37 and 3.52-3.53) that there is 10 smaller lines. Then, you can place your number according to your fourth digit. (So you'd place 0.365 at the 0.365 line and 3.521 at the 3.521 line)
what is the value of B
Answers
Answer:
B = 2
Step-by-step explanation:
using the rule of exponents
• [tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
consider [tex]83^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{83^{2} }[/tex]
⇒ B = 2
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Find the measures of all angles formed by line a parallel to line b with transversal m, if one angle is 25° bigger than another
Answers
Answer:
Measures of all angles is either 77.5° or 102.5°
Step-by-step explanation:
See the attached figure.
As shown:
line a parallel to line b with transversal m
So, all the angles are either congruent or supplementary.
Let the supplementary angles x and y and y > x
x + y = 180° ⇒ (1)
one angle is 25° bigger than another
y - x = 25° ⇒ (2)
solving (1) and (2)
∴ x = 77.5° and y = 102.5°
what is i + 6i? You have to simplify
Answers
[tex]i=1i\\\\i+6i=1i+6i=(1+6)i=\boxed{7i}[/tex]
find the slope of the line through each pair of points.
Answers
You've baked 26 cookies, which is two-thirds of all the cookies you planned to bake. How many cookies did you plan to make?
Equation:
Solution:
Answers
Answer,
(26/2) * 3
= 39
Explanation,
26 cookies is only 2/3 of 3/3. So, we divide 26 by 2 to see how many cookies are in 1/3. We then can find out that when you make 1/3 of the cookies there are 13. Since that is only 1/3 and we want to find out 3/3. We multiply 13 by 3 and get 39 which is all the cookies she planned to make.
Hope this helps :-)
Mrs.Maxwell is buying pencils for her students. She has 3 classes of 28 students each. For Valentine’s Day, she wants to give each of her students 4 pencils. She can purchase packs of 18 pencils for $2.52. How many packs of pencils will Mrs. Maxwell need to purchase? Justify your answer.
Answers
Answer:
the answer might be 336 sorry if i am not right
Step-by-step explanation:
Answer:
I think the answer is approximately 5 packs of pencils.Hooe this helps :)
Step-by-step explanation: what I did was I multiplied 3 and 28 then divide that number by 12 and rounded my answer up.
In Phoenix, Arizona, the average n umber of sunny days is 211 per year. About what percent of the year is Phoenix sunny?
Answers
Answer:
21100%
Step-by-step explanation:
Move the decimal point two places to the right.
The exression below represents Julia's annual salary after t years.
25,000(1.04)t
Interpret the meaning of the expression.
Answers
Julie's salary started at $25,000. t is the number of years since her original $25,000 salary started. Each year she gets a 4% raise. The expression gives her salary at year t.
Answer:
b.
Step-by-step explanation:
Interpret the meaning of the expression.
A.
Julia's initial salary is $4,000, and the growth rate is 25% per year.
B.
Julia's initial salary is $25,000, and the growth rate is 4% per year.
C.
Julia's initial salary is $4,000, and the growth rate is 2.5% per year.
D.
Julia's initial salary is $25,000, and the growth rate is 40% per year.
Anu bought an air cooler as shown below. Its water tank is in the shape of a cuboid and can take 40 litres of water. Its dimensions are 50cmx 20cm. What will be the length of the water tank?
Answers
Answer:
40 cm
Step-by-step explanation:
Using the conversion
1 litre = 1000 cm³, then
40 litres = 40 × 1000 = 40000 cm³
The volume ( V) of a cuboid is
V = lbh ( divide both sides by bh )
l = [tex]\frac{V}{bh}[/tex] = [tex]\frac{40000}{50(20)}[/tex] = [tex]\frac{40000}{1000}[/tex] = 40 cm
Length of water tank is 40 cm
Given that;
Capacity of tank = 40 liters
Dimensions of tank = 50cm × 20cm
Find:
Length of water tank
Computation:
Capacity of tank = 40 liters
Capacity of tank = 40 × 1000
Capacity of tank = 40,000 cm³
Length of water tank = 40,000 / [50cm × 20cm]
Length of water tank = 40,000 / 1,000
Length of water tank = 40 cm
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Which characteristics describe the scatterplot? Check all that apply.
1.Negative Correlation
2.Positive Correlation
3.Strong Correlation
4.Weak Correlation
5.Linear
6.Nonlinear
Answers
A. Negative Association
C. Strong Association
E. Linear
Answer:
1. Negative Correlation
3. Strong Correlation
5. Linear
Step-by-step explanation:
We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.
Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.
We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.
We can also see that the slope of the line connecting all data points is approximately [tex]-1[/tex], which represents a strong negative correlation, therefore, 3rd option is correct as well.
If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.
4m of timber costs £33.60 what is the cost of 9m?
Answers
Answer:
£ 75.60
Step-by-step explanation:
4 m ↔ £ 33.60
1 m ↔ £ 8.40
9 m ↔ £ 75.60
The cost of one meter of timber is £8.40, calculated by dividing £33.60 by 4. To find the cost of 9 meters, multiply £8.40 by 9, resulting in a total cost of £75.60.
To determine the cost of 9 meters of timber when we know that 4 meters cost £33.60, we can use a unit rate approach. First, we need to calculate the cost of one meter of timber by dividing the total cost by the number of meters. Then, we multiply the cost per meter by 9 to find the cost of 9 meters of timber.
Find the cost per meter: £33.60 / 4 meters = £8.40 per meter.Calculate the cost for 9 meters: £8.40 per meter * 9 meters = £75.60.Therefore, the cost of 9 meters of timber would be £75.60.
You want to use square tiles to cover the top of a stepping stone you're making. The top is 24 inches by 20 inches. What is the side measure of the largest-sized square tile you can use to cover the stepping stone without any overlap or cutting?
Answers
The side measure of the largest-sized square tile will be 4 in.
What is the greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Given that, The top of a stepping stone is 24 inches by 20 inches.
GCF of 24 and 20 = 4
Hence, The side measure of the largest-sized square tile will be 4 in.
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what would the identity be?
[tex] \frac{2}{3} ( \frac{3}{2} ) = 1[/tex]
Answers
Answer:
Since both sides equal, there are infinitely many solutions
Step-by-step explanation:
Simplify brackets
2/3×3/1=1
Use this rule: a/b×c/d=ac/bd
Simplify 2×3 to 6
6/3×2=1
Simplify 3×2 to 6
6/6=1
cancel 6
1=1
Since both sides equal, there are infinitely many solutions