Answers
The value of [x] in the figure given is 54.
What are Alternate interior angles?
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
Given are two parallel lines.
The two lines are parallel and are intersected by a transversal. Assume
that -
∠1 = (x +3)°
∠2 = (2x - 61)°
Now, the angle at the vertically opposite position with respect to ∠2 will have same measurements. Let's call this ∠3 = (2x - 61)°.
Now, ∠3 and ∠1 are alternate interior angles and their measures will be equal. So, we can write -
∠1 = ∠3
x + 3 = 2x - 61
3 + 61 = 2x - x
x = 64
The value of [x] is 54
Therefore, the value of [x] in the figure given is 54.
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Related Questions
Next questionA man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $27,000 for 3 years with a sirinterest rate of 1.5%. Determine the amount of money the man must repay after 3 years.The man must repay
Answers
Simple interest formula (not compound interest formula) is used here, as much as i know.
the formula is:
f = p * (1 + r * n).
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
Given
[tex]\begin{gathered} P=27000 \\ r=1.5\%=\frac{1.5}{100}=0.015 \\ n=3years \end{gathered}[/tex]Therefore, we have
[tex]f=27000(1+0.015\times3)=\text{ \$}28215[/tex]Hence, the answer is
[tex]\begin{equation*} \text{\$}28215 \end{equation*}[/tex]5. an elevator in a building starts with five passengers and stops at 7 floors. if each passenger is equally likely to get off at any floor and all the passengers leave independently of each other, what is the probability that no two passengers will get off at the same floor?
Answers
The probability that no two passengers gets off at the same floor will be 0.15.
As per the question statement, an elevator in a building starts with five passengers and stops at 7 floors where each passenger is equally likely to get off at any floor and all the passengers leave independently of each other.
We are required to calculate the probability that no two passengers gets off at the same floor.
Here, since repetition is not allowed,
That is, the total number of ways for 5 passengers are to be assigned to seven floors but no two passengers on the same floor
= 7P5 = [(7!)/(7 - 2)!] = [(7!)/(2!)] = (7 * 6 * 5 * 4 * 3) = 2520
And, the total number of ways to assign 5 passengers to 7 floors, with repetition being allowed will be
= (7)⁵ = 16807.
Therefore, the probability that no two passengers gets off at the same floor will be = (2520/16807) = 0.14993 ≈ 0.15
Probability: It is that branch of Mathematics which deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.
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Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to-end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. IS THE RELATIONSHIP PROPORTIONAL
THIS IS DUE TODAY
Answers
Reason is because a rectangle has 4 sides at here for he can only put 4 chairs per table
Guys i need helps is this right?
Answers
What is the length of side BC to one decimal place?
Answers
Answer:
BC ≈ 9.0
Step-by-step explanation:
using the tangent ratio in the right triangle
tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{10}[/tex] ( multiply both sides by 10 )
10 × tan42° = BC , then
BC ≈ 9.0 ( to 1 dec. place )
simplify:
4(6+7)
O 13
O 17
O 24
O 52
Answers
Answer:
52
Step-by-step explanation:
[tex](4 \times 6) + (4 \times 7) \\ 24 + 28 = 52[/tex]
Answer:
4th answer is correct
Step-by-step explanation:
We have to solve this sum according to the BODMAS theorem.
That is:
B - Brackets
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction
Let us solve it now.
4 ( 6 + 7 )
4 × 13
52
3
1
1. How many groups of 1/8 are in 3?
8
2. Evaluate.
5
groups
|||
Answers
Answer:
answer to question 1: 24
Explanation: (btw sorry i couldn't answer question 2) multiply 8 times 3 and you get the answer
The required group of number is 24 of 1/8 in 3.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given numbers are 1/8 and 3.
Let there are n number of groups of 1/8 in 3.
To find the value of number of groups n,
Use equation form,
1/8 n = 3
n = 3 x 8
n = 24.
There are 24 groups of 1/8 in 3.
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for any two real numbers a and b where b ≠0 and for all integers is this true
Answers
Given:-
[tex]64^{\frac{1}{4}},256^{\frac{1}{8}},125^{\frac{1}{3}}[/tex]To find:-
The simplified value.
So now we have,
[tex]\begin{gathered} 64=2\times2\times2\times2\times2\times2 \\ 256=2\times2\times2\times2\times2\times2\times2\times2 \\ 125=5\times5\times5 \end{gathered}[/tex]So we have,
[tex]64=2^6,256=2^8,125=5^3[/tex]So now,
[tex]\begin{gathered} 64^{\frac{1}{4}}=(2^6)^{\frac{1}{4}},256=(2^8)^{\frac{1}{8}},125=(5^3)^{\frac{1}{3}} \\ 64=4,256=2,125=5 \end{gathered}[/tex]So the value is,
[tex]4,6,5[/tex]If you leave $2500 in an
account earning 9% interest, compounded daily, how
much money will be in the account after 4 years?
Answers
The amount of money that will be in the account after 4 years is $3,583.16
How many times is interest compounded annually?
The fact that the interest rate of 9% in this scenario is compounded daily means that the interest is compounded every day of the year, 365 days in a year, hence, our future value formula needs an adjustment for daily compounding as shown below:
FV=PV*(1+r/m)^(n*m)
FV=the accumulated balance in the account after 4 years=unknown
PV=amount invested or deposited initially=$2500
r=annual interest=9%
m=number of times in a year that interest is compounded=365
n=number of years=4
FV=$2500*(1+9%/365)^(4*365)
FV=$3,583.16
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how much more is 6.302 than 6.002 ?
Answers
Answer:
Step-by-step explanation:
0.3
Answer:
It is 0.3 more or 0.300 more
Step-by-step explanation:
6.002 + 0.3 or 0.300 = 6.302
6.302- 0.300 or 0.3 = 6.002
Hope I helped
determine whether the function has a minimum or maximum f(x)=-2/3x+5 if x<0 -x if 0 4 -x^2+4x+4 if x>4
Answers
The function has no minimum or maximum
How to determine the minimum or the maximum of the functionThe function is given as
f(x) = -2/3x + 5 if x < 0
f(x) = -x^2 + 4x + 5 if x > 4
The above function is a piecewise function
And the type of functions in the piecewise function are
Linear functionQuadratic functionA linear function does not have a minimum or a maximum
This means that the function would have no minimum or maximum
Hence, the minimum or the maximum value of the function does not exist
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what is the justification for step 3 in the solution process?
0.8a-0.1a=a-2.5
Step 1: 0.7a=a-2.5
Step 2: -0.3a=-2.5
Step 3: a=8.3
Answers
In step 3 each side of the equation is divided by - 0.3 to obtain the value of a = 8.3.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Consider the expression,
0.8a - 0.1a = a - 2.5
Step 1,
Subtracting similar terms,
a( 0.8 - 0.1 ) = a - 2.5
0.7a = a - 2.5
Step 2: Subtracting the term a from each side of the equation.
0.7a - a = a - 2.5 - a
- 0.3a = - 2.5
Step 3: Multiplying each side of the equation by - 1.
- 0.3a × - 1 = - 2.5 × - 1
0.3a = 2.5
Dividing each side of the equation by 0.3.
a = 2.5/0.3
a = 8.3
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Calculate the volume of liquid that would fill the bowl of the glass. SHOW ALL WORK!!
Answers
Answer:
49.7 cm³Step-by-step explanation:
We need to find the volume of the cone with:
Diameter = 5 cm andSlant height = 8 cmFirst, find the height, using Pythagorean, where hypotenuse of the triangle is 8 cm and base is the radius = 5 cm/2 = 2.5 cm:
[tex]h = \sqrt{8^2-2.5^2} =\sqrt{57.75} =7.6[/tex] (rounded)Find the volume of the cone:
[tex]V=\pi r^2h/3=3.14*2.5^2*7.6/3 = 49.7[/tex] (rounded)Jason is testing two fertilizers, grow well and green grow, so he went to a nursery and bought 50 tomato plants of the same variety. He planted all 50 plants In an identical environment. He then administered grow well to 25 of the tomato plants and green grow to the remaining 25 tomato plants
Answers
The true statements is:
(A) The number of tomato plants treated with Green Grow that are over 18 inches tall is more than the number of tomato plants treated with Grow Well that are over 18 inches tall.
Jason is testing with two fertilizers namely, grow well and green grow.
Jason brought 50 tomato plants of the same variety and planted them in an identical environment.
Jason administered grow well to 25 and green grow to the remaining 25.
The values and recorded data from the above histograms are:
Grow Well
height numbers of plants
12 - 14 14
15 - 17 6
18 - 20 3
21 - 23 2
Green Grow
height numbers of plants
12 - 14 4
15 - 17 3
18 - 20 6
21 - 23 12
From the table,
(A) The number of tomato plants over the height of 18 inches, when treated with green grow is, GG = 6 + 12 = 18
The number of tomato plants over the height of 18 inches, when treated with grow well is, GW = 3 + 2 = 5
Therefore, GG > GW
Hence, the statement is true.
(B) As statement A is true, this statement is false.
(C) The tomato plants over 18 inches when administered with green grow, GG = 6 + 12 = 18
The tomato plants over 18 inches when administered with grow well, GW = 3 + 2 = 5.
As GG ≠ GW, the statement is false.
(D) As the number of tomato plants over 18 inches when treated with green grow is greater than when treated with grow well. Hence, the statement is false.
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The complete question is mentioned below:
Jason is testing two fertilizers, Grow Well and Green Grow, so he went to a nursery and bought 50 tomato plants of the same variety. He planted all 50 plants in an identical environment. He then administered Grow Well to 25 of the tomato plants and Green Grow to the remaining 25 tomato plants. After four weeks, Jason measured the heights of the tomato plants to the nearest inch and recorded their heights in the following histograms.
Grow Well
height numbers of plants
12 - 14 14
15 - 17 6
18 - 20 3
21 - 23 2
Green Grow
height numbers of plants
12 - 14 4
15 - 17 3
18 - 20 6
21 - 23 12
Which of the following statements is true for the data sets above?
A. The number of tomato plants treated with Green Grow over the height of 18 inches is more than the number of tomato plants treated with Grow Well over the height of 18 inches.
B. All of the statements are false for the given data sets.
C. The number of tomato plants treated with Green Grow over 18 inches equals the number of plants treated with Grow Well over 18 inches.
D. The number of tomato plants treated with Green Grow over the height of 18 inches is to the number of tomato plants treated with Grow Well over the height of 18 inches.
please help this worth half ny grade
Answers
Answer:
see image
Step-by-step explanation:
See attached image
NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?
Answers
Answer:
Total moving cost = $2,053.84
Step-by-step explanation:
Let's write down Jay's requirements and costs associated
9 hours of loading/unloading at $95 per hour = 95 x 9 = $855
7 hours of packing/unpacking at $80 per hour = 80 x 7 = $560
200 miles of transportation at $2.50 per mile = 2.50 x 200 = $500
Total before-tax cost of moving = $855 + $560 + $500 = $1, 915
Sales Tax is additional at 7.25%
Sales Tax amount = 1915 x 7.25%
= 1915 x 7.25/100 = 138.8375 = $138.84
Total cost including sales tax = 1915.00 + 138.84 = $2,053.84
which expression is equivalent to 4/5-1/2
4/10-1/10
6/5-5/7
4/7-1/7
8/10-5/10
Answers
Which expressions represent the volume of the cube? Select all that apply.
A cube with side length 3-fourths foot.
3343ft3
(34)3ft3
2716ft3
2764ft3
916ft2
(34)2ft2
Answers
The volume of cube with side length 3/4 of a foot is (27/64) square feet which is the fourth option.
We know that the formula for the volume of a cube is given by:-
Volume of cube = (side)*(side)*(side) = [tex]side^3[/tex]
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
We have,
side = (3/4) foot
Hence, we can write,
Volume of cube = (3/4)*(3/4)*(3/4) = (27/64) square feet.
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Is the function y=x^2-x linear or not?
Answers
Answer:
NOT linear
Step-by-step explanation:
Your equation is:
y = x^2 - x
Since the y has no exponent, (which is a power of 1) and the x has an exponent of 2, this function is a parabola. It is not linear. (Linear functions have a graph that is a line)
Functions that are NOT linear have exponents greater than 1, or variables in the denominator, or, variables inside a radical.
What is the function g(x) that results when translating the function
f(x)=|x|
to the left 12 units and reflecting it over the x-axis?
g(x) =
Answers
The image of the function after the translation is g(x) = -|x - 12|
How to determine the equation of g(x) after the transformation?From the question, the given parameters are:
f(x) = |x|
The transformation is given as
Translate the function to the left 12 units and reflect it over the x-axis
Mathematically, this transformation can be represented as
(x, y) = (x - 12, -y)
When represented as a function, we have
g(x) = -f(x - 12)
So, we have
g(x) = -|x - 12|
So, we have the following equation
f'(x) = -|x - 12|
Hence, the equation of g(x) is g(x) = -|x - 12|
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I need help on this question
Answers
F(x) = -(x-4)^2 +9
(Negative slope, and vertex is point (4,9))
I need help finding the measurements of the numbered angles Question 1 and 2
Answers
In figure one the value of ∠2 = 65 ° ∠1 = 115° .
In figure two the value of ∠2 = 74° ∠1 = 106°.
What are corresponding angles in parallels lines?In the case of parallel lines, corresponding angles are congruent. Corresponding pairs are all angles that are situated in the same location with respect to the parallel and transversal lines. According to the definition of corresponding angles, when three parallel lines intersect two of them, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles. Alternate angles, co-Interior angles, and matching angles are three facts regarding angles in parallel lines that we use to do this. When a transversal crosses two parallel lines, alternate and matching angle pairs coincide. Only when a transversal crosses two parallel lines perpendicularly are consecutive angles congruent. When a transversal intersects two parallel lines, however, subsequent angles are not necessary.
Figure 1
Given angle = 65°
= ∠2
Cause they are corresponding angles.
∠1 + ∠2 = 180°
∠1 = 115
Figure 2
Given angle = 74 °
= ∠ 2
Cause they are corresponding angles.
∠1 + ∠2 = 180°
∠1 = 106°
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What’s the answer plss I need help asp
Answers
Answer:
I am 80% positive that it is DE but there is still that other 20% so keep in mind I am not entirely sure
Theatre tickets cost either $30 or $42. One evening twice as many $30 tickets are sold as $42 tickets and the total money taken is $18564. Find the total number of tickets that are sold.
Answers
1 + 2 = 3
18564 / 3 = 6188
6188 x 2 = 12376
Ratio = 6188:12376
6188 / 42 = 148 tickets
12376 / 30 = 413 tickets
413 + 148 = 561 tickets
Did anybody see my question for 24 I really need help
Answers
Answer:
48
hope its right sorryyyy
Standard Form & Scientific Notation• 3 examples of converting from standard form to scientific notation• 3 examples of converting from scientific notation to standard form
Answers
Required:
We need to convert from standard form to scientific notation and also scientific notation to standard form.
Explanation:
a) Convert from standard form to scientific notation:
1) Consider the number 4,520,000.
The given number can be written as follows.
[tex]4,520,000=452\times10000[/tex][tex]=452\times10^4[/tex][tex]=452\times10^4\times\frac{10^2}{10^2}[/tex][tex]=452\times\frac{10^4\times10^2}{10^2}[/tex][tex]=\frac{452}{100}\times10^6[/tex][tex]=4.52\times10^6[/tex]The scientific notation of s
[tex]4.52\times10^6[/tex]2) Consider the number
[tex]35.98\times10^3[/tex]Multiply and divide by 10.
[tex]35.98\times10^3=35.98\times10^3\times\frac{10}{10}[/tex][tex]=\frac{35.98}{10}\times10^3\times10[/tex][tex]=3.598\times10^4[/tex]The scientific notation is
[tex]3.598\times10^4[/tex]3) Consider the number.
[tex]600.89\times10^{-8}[/tex]Multiply and divide by 100.
[tex]600.89\times10^{-8}=600.89\times10^{-8}\times\frac{100}{100}[/tex][tex]=\frac{600.89}{100}\times10^{-8}\times10^2[/tex][tex]=6.0089\times10^{-6}[/tex]The scientific notation is
[tex]6.0089\times10^{-6}[/tex]b) convert from scientific notation to standard form:
1)
Consider the notation:
[tex]6.285\times10^{-5}[/tex][tex]Use\text{ }10^{-5}=\frac{1}{100000}.[/tex][tex]6.285\times10^{-5}=\frac{6.285}{100000}[/tex][tex]=0.00006285[/tex]The standard form is 0.00006285.
2) Consider the notation.
[tex]7.9\times10^4[/tex][tex]Use\text{ }10^4=10000.[/tex][tex]7.9\times10^4=7.9\times10000[/tex][tex]=79000[/tex]The standard form is 79,000.
3) Consider the notation.
[tex]9.008\times10^5[/tex][tex]Use\text{ }10^5=100000.[/tex][tex]9.008\times10^5=9.008\times100000[/tex][tex]9.008\times10^5=900800[/tex]The standard form is 900,800.
The northern hemisphere of planet earth has an inner core that is made up of iron and nickel. This iron nickel core is 30% of the volume of the northern hemisphere. If the diameter of the earth is 8,000 miles, what is the volume of iron-nickel core?
Answers
It turns out that the dynamo effect depends on the presence of up to 20% nickel in the Earth's core, a metal that behaves very differently from iron under extreme temperatures. Unlike the northern hemisphere mineral-rich crust and mantle, the core is made almost entirely of metal—specifically, iron and nickel. The shorthand used for the core's iron-nickel alloys is simply the elements' chemical symbols—NiFe. Elements that dissolve in iron, called siderophiles, are also found in the core.
Explain about the volume of iron nickel core?The core is almost entirely comprised of metal, notably iron and nickel, in contrast to the crust and mantle, which are rich in minerals. Iron-nickel alloys found in the core are denoted by their chemical symbols, NiFe. The core also contains siderophiles, or substances that dissolve in iron.volume calculation for the earth. Since the Earth is nearly spherical, its volume (V) may be determined using the formula V = 4/3 pi x r3, where r is its radius.The core of the earth is made up of iron, nickel, and other heavy metals like gold since they are the heaviest of all the metals and gravitated into the center of the planet.To learn more about iron nickel core refer to:
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Name a principal and interest rate where the amount of simple interest earned in 10 years would be $200. Justify your answer.
Answers
The relation between a principal and interest rate is;
⇒ P = $20 / r
Where, P is the principal amount and r is the interest rate.
What is Simple interest?
The simple interest is defined as;
Simple interest = P r t
Where, P is principal amount.
r is rate and t is time period.
Given that;
Simple interest = $200
Time period = 10 years.
Let principal amount = P
And, The interest rate = r
So, We get;
Simple interest = P r t
Substitute all the values, we get;
Simple interest = P r t
$200 = P × r × 10
Pr = $20
P = $20 / r
Thus, We get the relation between a principal and interest rate is;
⇒ P = $20 / r
Where, P is the principal amount and r is the interest rate.
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please help and show steps am failing class
Answers
answer:
D. y = 3x + 9
perpendicular means negative reciprocal of the number next to x
so if its 5x perpendicular would be -1/5x
make the equation look like y = ...
2x + 6y = 6
6y = -2x + 6
y = (-2x + 6)/6
y = -2x/6 + 6/6
y = -1/3x + 1
perpendicular line would be a negative reciprocal so
-1/3x would have a perpendicular that would be 3x
D. is the only one that has 3x
Question 3(Multiple Choice Worth 5 points)(05.01)A picture is 5 inches wide and 8 inches tall: A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged?40 in2250 in2100 in281.9 in2
Answers
Find the new dimentions of the enlarged picture multiplying the length of each side by the scale factor of 2.5:
[tex]\begin{gathered} 5in\times2.5=12.5in \\ 8in\times2.5=20in \end{gathered}[/tex]Now, multiply width times height to find the area of the picture (assuming that it has a rectangular shape):
[tex]12.5in\times20in=250in^2[/tex]Therefore, the area of the enlarged picture will be 250 squared inches.
