108° 4x+8° O alternate interior corresponding vertical linear pair same-side Interior alternate exterior degrees
Answers
Alternate Interior angles
x = 25
Explanations:By careful observation of the diagram, we would see that both angles are at the opposite sides of the transversal. At the same time, they are at the interior of the two parallel lines.
This means that <108 and <4x + 8 are alternate interior angles.
Since the two lines intersecting the transversal are parallel, the alternate interior angles are equal
That is,
4x + 8 = 108
4x = 108 - 8
4x = 100
x = 100/4
x = 25
Related Questions
Can two rays be congruent? Why or why not?
Answers
The line plot shows the ages at which a group of musicians started to play an instrument. Based on the data in the line plot, which statement is not true? X X х х X х х X X X X X X X + х х х X х х х х X х х х х х х Х + 4 5 6 7 8 9 10 11 12 Age of musician X X X The range of the ages shown is 8 years. There are 34 musicians included in the data. Fewer of the musicians started to play at age 12 than at age 5. Most of the musicians started to play at age 9 or older.
Answers
From the graph
Highest age of the musicians = 12
Loweat age = 4
Range = 12 - 4 = 8
Total number of people = 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 = 34
Age 4 = 2 people
Age 5 = 3
Age 6 = 4
Age 7 = 5
Age 8 = 6
Age 9 = 5
Age 10 = 4
Age 11 = 3
Age 12 = 2
Fewer of the musician play at the age of 12 than at the age of 5
Option D is not true. Number of musicians started to play at the age of 9 decrease downward.
consider the functions below. Match each with its simplified form.
Answers
We are given the following functions:
[tex]\begin{gathered} P(x)=\frac{2}{3x-1} \\ \\ Q(x)=\frac{6}{-3x+2} \end{gathered}[/tex]We are asked to determine:
[tex]P(x)\div Q(x)[/tex]This is equivalent to:
[tex]\frac{P(x)}{Q(x)}[/tex]Substituting the functions:
[tex]\frac{P(x)}{Q(x)}=\frac{\frac{2}{3x-1}}{\frac{6}{-3x+2}}[/tex]Now, we use the following property:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}*\frac{d}{c}[/tex]Applying the property we get:
[tex]\frac{P(x)}{Q(x)}=(\frac{2}{3x-1})(\frac{-3x+2}{6})[/tex]Solving the products:
[tex]\frac{P(x)}{Q(x)}=\frac{2(-3x+2)}{6(3x-1)}[/tex]Simplifying we get:
[tex]\frac{P(x)}{Q(x)}=\frac{-3x+2}{3(3x-1)}[/tex]And thus we get the desired expression.
Now, we are asked to determine:
[tex]P(x)*Q(x)[/tex]This is the product of the functions. Substituting we get:
[tex]P(x)*Q(x)=(\frac{2}{3x-1})(\frac{6}{-3x+2})[/tex]Solving the products:
[tex]P(x)*Q(x)=\frac{12}{(3x-1)(-3x+2)}[/tex]Since we can't simplify any further this is the final answer.
A rectangular garden has a length of 100 metres and a width of 50 metres. A
square swimming pool is to be constructed inside the garden. Find the length of
one side of the swimming pool if the remaining area (not occupied by the pool)
is equal to one half the area of the rectangular garden.
Answers
Answer:
50 by 50 meter pool
Step-by-step explanation:
since a 100 by 100 meter pool won’t fit the only option is a 50 by 50 meter pool
100x50=5000
5000/2=2500
50x50=2500
Hopes this helps please mark brainliest
Ellie took $200 to spend during summer vacation.She spent $32 a day for 5 days. Then she bought gelato for her and her three freinds for $6 each.How much did she have left at the end of the trip)
Answers
Ellie had $200 originally.
She spent $32 a day for 5 days. This means that she spends:
[tex]\Rightarrow32\times5=160[/tex]Therefore, she has left:
[tex]\Rightarrow200-160=40[/tex]She bought gelato for her and her three friends for $6 each. This means that she spent on gelato:
[tex]\Rightarrow6\times4=24[/tex]Subtracting this from the remaining balance, we have:
[tex]\Rightarrow40-24=16[/tex]At the end of the trip, Ellie has $16 left.
I have a question can you help me solve this. m-8=3
Answers
You have the following algebraic expression:
[tex]m-8=3[/tex]In order to solve the previous expression, you proceed s follow:
m - 8 = 3 First, you sum 8 both sides of the equation
m - 8 + 8 = 3 + 8 simplify (-8 + 8 cancel out, 3 + 8 is equal to 11)
m = 11
Hence, the solution to the equation is m = 11
Find the area of a triangle with legs that are: 15 mm, 10 mm, and 20 mm.A. 20.5 mm²B. 16.4 mm²C. 102.7 mm²D. 72.6 mm²
Answers
Answer:
D. 72.6 mm²
Explanation:
The area of the triangle can be calculated by Heron's Formula:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]Where a, b, and c, are the legs and s can be calculated as:
[tex]s=\frac{a+b+c}{2}[/tex]Therefore, replacing a, b, and c by 15, 10, and 20, we get that s is equal to:
[tex]\begin{gathered} s=\frac{15+10+20}{2} \\ s=\frac{45}{2} \\ s=22.5 \end{gathered}[/tex]Then, the area of the triangle will be equal to:
[tex]\begin{gathered} A=\sqrt[]{22.5(22.5-15)(22.5-10)(22.5-20)} \\ A=\sqrt[]{22.5(7.5)(12.5)(2.5)} \\ A=\sqrt[]{5273.44} \\ A=72.6mm^2 \end{gathered}[/tex]So, the answer is:
D. 72.6 mm²
6. Graph and solve the system. (1 point)3х +бу – 12 = 0X + 2y = 8-(3-3)(1,7)(-21)no solution
Answers
Solution
Given the equation
[tex]\begin{gathered} 3x+6y=12\text{ -----\lparen1\rparen} \\ \\ x+2y=8\text{ ------\lparen2\rparen} \end{gathered}[/tex]Dividing equation (1) by 3
[tex]x+2y=4\text{ ------\lparen3\rparen}[/tex]Now, Equation (2) - (3)
[tex]\begin{gathered} (x-x)+(2y-2y)=(8-4) \\ 0=4\text{ Absurd!} \end{gathered}[/tex]Hence, No Solution.
For each polynomial, identify its degree and say whether the polynomial is in standard forma. x^2 + x^4 - 3x^3 + 14x^2 -5Degree:Standard Form?Answer Yes or Nob. x^6 - x^7 + x^3 - 1Degree:Standard Form?Answer Yes or No
Answers
The first polynomial is-
[tex]x^2+x^4-3x^3+14x^2-5[/tex]Remember that the degree of a polynomial is defined by the greatest exponent. So, in this case, the degree is 4.
The standard form refers to the polynomial in the right order.
[tex]x^4-3x^3+15x^2-5[/tex]Therefore, the initial polynomial is not in standard form.
The second polynomial is
[tex]x^6-x^7+x^3-1[/tex]The degree of this polynomial is 7.
This polynomial is not in standard form since it's not in the right order.
a designer is making a banner, as shown in the diagram, of width 5x and height 3x, where x is in feet. one foot of material on each side is gray, as shown below
Answers
The function for the area of the rectangular white space is given as follows:
A = 15x² - 6x.
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is obtained by the multiplication of these dimensions, as follows:
A = lw.
For the white space in the rectangle shown by the image at the end of the answer, these dimensions are given as follows:
w = 5x - 2, as one feet is subtracted on each end of the base.l = 3x, as stated in the problem.The area is given by the multiplication of these dimensions, hence it is obtained as follows:
A = lw
A = (5x - 2)3x
A = 15x² - 6x.
Missing informationThe problem asks for the area of the rectangular white space given by the image at the end of the answer.
More can be learned about the area of a rectangle at https://brainly.com/question/10489198
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I will send you the question
Answers
Jack and Jill each scored 177 marks for their English and Maths exams. Both of their Maths marks add up to 153, what was the sum of their English marks?
Answers
Answer:
201
Step-by-step explanation:
177 times 2=354
354-153=201
What is x i need help plesae
Answers
Answer:
x = 82°
Step-by-step explanation:
Similar Triangles
Two triangles are similar if their corresponding sides are always in the same ratio.
In similar triangles, corresponding angles are always congruent.
From inspection of the given diagram, the two triangles are similar as their corresponding sides are in the same ratio. Therefore, their corresponding angles are equal:
⇒ 2x - 19° = x + 63°
⇒ 2x - 19° - x = x + 63° - x
⇒ x - 19° = 63°
⇒ x - 19° + 19°= 63° + 19°
⇒ x = 82°
A party man is made by adding nuts that sell for $2.50 per kg to a cereal mixture that sells for $1 per kg How much of each should be added to obtain 60 kg of a mix.that will sell for $1.90 per kg?
Answers
Given:
Nuts = $2.50
Cereal mixture = $1
Find -: How much each should be added.
Sol:
Obtain = 60 kg.
Let nuts = x kg
Cereal = y kg
To obtain 60 kg means:
[tex]\begin{gathered} x+y=60 \\ \\ y=60-x \end{gathered}[/tex]Pricing at $1.90 per kg means:
[tex]\begin{gathered} x(2.50)+y(1)=60(1.90) \\ \\ 2.5x+y=114 \end{gathered}[/tex]Put the value of "y" then:
[tex]\begin{gathered} 2.5x+60-x=114 \\ \\ 1.5x=114-60 \\ \\ 1.5x=54 \\ \\ x=\frac{54}{1.5} \\ \\ x=36 \end{gathered}[/tex]Then the value of "y" is:
[tex]\begin{gathered} y=60-x \\ \\ y=60-36 \\ \\ y=24 \end{gathered}[/tex]So,
In the mixture 36 kg of nuts and 24 kg of cereal.
Describe the mixed numbers that come between one and two on the number line. write a mixed number that comes between one and two on the number line
Answers
A mixed number is simply a whole number and a fraction written together.
The mixed numbers between 1 and 2 on the number line can be any range of fractions written along with 1 as the whole. It cannot include the number 2, because if that happens, then the number has crossed beyond 2 on the number line.
An example of a mixed number that comes between 1 and 2 on the number line is
[tex]1\frac{3}{4}[/tex]James has 42.00 he bought his sister a gift that cost x dollars. how much money does james have now, in terms of x
Answers
Given data:
The amount of money James have A=42.00 .
The amount of money left after gift purchased.
[tex]\begin{gathered} L=A-x \\ =42-x \end{gathered}[/tex]Thus, the amount of money left is 42-x.
solve for the value K: (4k-7)° (3k+6)°
Answers
Problem
Solution
For this case we can do the following :
3 k + 6= 90 - (4k-7)
And then we can solve for k on this way:
3k +6 = 90 -4k +7
3k +6 = 97 -4k
7k = 97-6
7k= 91
k= 91/7= 13
then the solution for this case would be K=13
Solve the following system by elimination. Show work and explain each step. [tex]3x + y = 13 \\ 4x - 3y = 13[/tex]
Answers
There are two equations given 3x + y = 13 and 4x - 3y = 13.
Multiply the first equation by 3 to get 9x + 3y = 39 and add it to second equation.
[tex]\begin{gathered} 9x+3y+4x-3y=39+13 \\ \Rightarrow13x=52 \\ \Rightarrow\frac{13x}{13}=\frac{52}{13} \\ \Rightarrow x=4 \end{gathered}[/tex]Substitute x = 4, in first equation to find y,
[tex]\begin{gathered} 3(4)+y=13 \\ \Rightarrow12+y=13 \\ \Rightarrow y=13-12 \\ \Rightarrow y=1 \end{gathered}[/tex]A baker has 1,382 chocolate chips. She uses 302 chocolate chips to make chocolate fondue and uses the rest to make chocolate chip cookies. She wants to put exactly 8 chocolate chips in each cookie. How many chocolate chip cookies can the baker make? Answer: _____________________
Answers
1080/8
135 cookies
Find the first term and the difference in an arithmetic sequence if the 100th term is 32 and the 200th term is 116.
Answers
Given
Arithmetic sequence
100th term is 32 and the 200th term is 116.
Find
a) Difference ,d
b) First term , a
Explanation
as we know that the nth term of an arithmrtic sequence is given by
[tex]a_n=a+(n-1)d[/tex]according to the question ,
[tex]\begin{gathered} a_{100}=a+99d=32 \\ a_{200}=a+199d=116 \end{gathered}[/tex]solve these two equation by elimination method .
subtract both equation to eliminate a ,
[tex]\begin{gathered} a+99d-a-199d=32-116 \\ -100d=84 \\ d=-0.84 \end{gathered}[/tex]now put value of d in one of the equation,
[tex]\begin{gathered} a+99(-0.84)=32 \\ a-83.16=32 \\ a=32+83.16 \\ a=115.16 \end{gathered}[/tex]Final Answer
therfore , the difference = -0.84 and first term = 115.16
A rectangular garden has a length of x + 8 units and a width of x - 4 units. Draw a diagram and label the dimensions. Find the area. Hint: Draw a picture.
Answers
The garden has a length of x + 8 units and a width of x - 4 units. This can be represented by:
Therefore, the area is given by:
[tex](x+8)(x-4)=x^2+8x-4x-32=x^2+4x-32[/tex]Show exact steps o solve! Solve using the distance formula!Answer #3
Answers
Given:
The triangle SUE is,
a) To prove the given triangle is right triagle,
Find the distance between each point and then use pythagoean thoerem to show the given traingle is right triangle.
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}} \\ d(SE)=\sqrt[]{(8-(-2))^2+(-9-(-4))^2} \\ =\sqrt[]{10^2+(-5)^2} \\ =\sqrt[]{125} \\ =5\sqrt[]{5} \end{gathered}[/tex][tex]\begin{gathered} d(SU)=\sqrt[]{(2-(-2))^2+(-1-(-4))^2} \\ =\sqrt[]{4^2+3^2} \\ =\sqrt[]{25} \\ =5 \end{gathered}[/tex][tex]\begin{gathered} d(UE)=\sqrt[]{(8-2)^2+(-9-(-1))^2} \\ =\sqrt[]{6^2+(-8)^2} \\ =\sqrt[]{100} \\ =10 \end{gathered}[/tex]So, the length of the sides of the triangle is,
[tex]\begin{gathered} SE=5\sqrt[]{5} \\ SU=5 \\ UE=10 \end{gathered}[/tex]It is obsereved that,
[tex]\begin{gathered} (SU)^2+(UE)^2=5^2+10^2 \\ =25+100 \\ =125 \\ (SE)^2=(5\sqrt[]{5})^2=25\times5=125 \\ \Rightarrow(SE)^2=(SU)^2+(UE)^2 \end{gathered}[/tex]Thus, the longer side is equivalent to other two sides.
Hence, the given triangle SUE is right triangle.
b) Isosceles triangle: the triangle that has two sides of equal length.
But in the given triangle does not have two equal sides.
So, the given traingle is not Isosceles rigth triangle.
William is building a gazebo and wants to brace each Corner replacing a 12 inch wooden bracket diagonally as shown how far below the corner should he fastened the bracket if he wants to distances from the corner to eat to the end of the bracket to be equal
Answers
Let the distance from the corner is x.
The length of diagonal -12 inch.
the fiure show a right angle triangle
Apply the pythagoras theorem to find the values of x
Pytahgoras theorem state as the square of the hypotenuse is equal to sum of the squre of perpendicular and the square of base of right angle triangle,
[tex]\text{Hypotenuse}^2=Perpendicular^2+base^2[/tex]In the given figure we have,
Hypotenuse=12
Base=x
Perpendicular=x
Substutute the value in the pythagoras theorem
[tex]\begin{gathered} 12^2=x^2+x^2 \\ 144=2x^2 \\ x^2=72 \\ x=8.485 \\ x=8.5\text{inch} \end{gathered}[/tex]The corner will be at a distance of 8.5 inch.
4 Solve for d. -10 = -2 + 3d O A. d=-24 O B. d=-16 O c. d = -6 OD d=-4 Reset
Answers
the expression is
[tex]-10=-2+\frac{1}{2}d[/tex][tex]\begin{gathered} -10+2=\frac{1}{2}d \\ -8=\frac{1}{2}d \\ d=-16 \end{gathered}[/tex]so the correct answer is d = -16
what is the quotient 36 divided by 487 and what is the remainder?
Answers
Given:
There are given the two numbers 36 and 487.
Explanation;
According to the question:
We need to find the quotient and remainder. when we divide 487 by 36.
So,
From the concept of quotient:
The quotient is defined for the final results when we divide one number from another number.
Then,
[tex]487\div36[/tex]Then,
[tex]\frac{487}{36}=13\frac{19}{36}[/tex]In the above expression:
[tex]\begin{gathered} 13\rightarrow Quotient \\ 19\rightarrow Remainder \end{gathered}[/tex]Final answer:
Hence, the values of quotient and remainder is shown below:
[tex]\begin{gathered} Quotient\rightarrow13 \\ Remainder\rightarrow19 \end{gathered}[/tex]A baker needs 2 2/3 cups of flour for her recipe, but she only had a 1/3 scoop. How many scoops will she need for the recipe?
Answers
Given a baker needs 2 2/3 cups of flour for her recipe.
[tex]2\frac{2}{3}=\frac{8}{3}[/tex]Now, she only had 1/3 scoops.
The number of scoops she needs for the recipe is
[tex]\begin{gathered} \frac{8}{3}\times\frac{1}{\frac{1}{3}}=\frac{8}{3}\times3 \\ =8 \end{gathered}[/tex]Thus, the given options c is correct.
If shown, AB and CD are straight lines. Find x in each case.\
PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
Step-by-step explanation:
Ok:
so Kl= 90 degrees and x+x+4x=
6x
Then:
360 degrees-90=
270/6x=
x= 45 degrees as answer
A vector starts at point ( 8, 7) and ends at point (5, 4) what is the magnitude of the vector, answer to two decimal places.
Answers
The points are given below,
[tex]\begin{gathered} A\rightarrow(x_1,y_1)\rightarrow(8,7) \\ B\rightarrow(x_2,y_2)\rightarrow(5,4) \end{gathered}[/tex]The formula for the magnitude of the vector AB is,
[tex]|\vec{AB}|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}}[/tex]Solving for the magnitude of the vector AB by substituting the values of x₁ = 8, x₂= 5, y₁ = 7, y₂ = 4.
[tex]|\vec{AB}|=\sqrt[]{(5-8)^2+(4-7)^2}[/tex]Therefore,
[tex]\begin{gathered} |\vec{AB}|=\sqrt[]{(-3)^2+(-3)^2_{}^{}} \\ |\vec{AB}|=\sqrt[]{9+9} \end{gathered}[/tex][tex]\begin{gathered} |\vec{AB}|=\sqrt[]{18}=4.242640687\approx4.24(nearest\text{ 2decimal places)} \\ |\vec{AB}|=4.24 \end{gathered}[/tex]Hence, the magnitude of the vector AB is 4.24.
Solve by completing the square and using square roots 6x^2-6=90
Answers
In this equation we can't complete the square (cause there's no linear term) but we can solve it, so let's do that:
[tex]\begin{gathered} 6x^2-6=90 \\ 6x^2=96 \\ x^2=\frac{96}{6} \\ x^2=16 \\ x=\pm\sqrt[]{16} \\ x=\pm4 \end{gathered}[/tex]Therefore x=4 or x=-4.
Solve -17 = x/-3 for x x =
Answers
Answer
x = 51
Explanation
We are asked to solve for x
[tex]\begin{gathered} -17=\frac{x}{-3} \\ \text{Cross multiply} \\ x=-17\times-3 \\ x=51 \end{gathered}[/tex]Hope this Helps!!!