Answers
From the diagram given, we can see that line a is parallel to line b. This means that the position of each of the angle on line a is equal to the position of each of the angle in line b
From the figure <1 = <(7x+19)degree (corresponding angle). Also <5 = 7x+19 = <1 (corresponding angle as well)
From the above, we can say that <5 = <1 and since <5 and <6 lies on the same stright line, their sum will be 180.
Don't forget that <5 is now replaced as <1. Hence <1+<6 = 180 (supplementary angle).
From the expalnation above, the theorems that was used to prove the relationship between <1 and <6 are supplementary angle, corresponding angle and same side interior angle
Hence option D is correcct
Related Questions
Solve the equation involving simple interest Mike borrowed some money for 2 years at 2% simple interest. If he had to pay back a total of $3952, how much did he originally borrow?
Answers
Given that Mike borrowed an amount for 2 years at 2% simple interest, and paid back a total of $3952.
To Determine: The original money he borrowed
Solution:
The formula to find the amount for simple interest is
[tex]A=P(1+rt)[/tex]Where:
A is the Amount paid back
r is the rate
t is the time
Given that
[tex]\begin{gathered} A=3952 \\ r=\frac{2}{100}=0.02 \\ t=2 \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} A=P(1+rt) \\ 3952=P(1+0.02\times2) \\ 3952=P(1+0.04) \\ 3952=P(1.04) \\ 3952=1.04P \\ P=\frac{3952}{1.04} \\ P=3,800 \end{gathered}[/tex]Hence, the Mike originally borrow $3,800
How can I get the volume in cubic centimetres of one large cereal box? How do I calculate the total surface of a cereal box? How do I calculate the volume of the cereal box? If the height of a small box is 20cm, list two different Pairs of values which the company can use for the length and width of a small box?
Answers
The volume of the cereal box is 7200 cm³ and the surface area of the cereal box is 2776 cm².
The dimensions of the cereal box are given as:
Length = 25 cm
Width = 8 cm
Height = 36 cm
The volume of the cereal box is:
Volume = l × b × h
V = 25 cm × 8 cm × 36 cm
V = 7200 cm³
The surface area of the cereal box is:
Surface area = 2 l b + 2 b h + 2 h l
S = 2 (25) (8) + 2 (8) (36) + 2 (36) (25)
S = 400 + 576 + 1800
S = 2776 cm²
Therefore, we get that, the volume of the cereal box is 7200 cm³ and the surface area of the cereal box is 2776 cm².
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A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using thefollowing parametric equations. Rewrite the parametric equations by eliminating the parameter.
Answers
Solution
Given
[tex]\begin{gathered} x(t)=2t-1 \\ \\ y(t)=\sqrt{t}\Rightarrow y^2=t \\ \\ \Rightarrow x=2y^2-1 \end{gathered}[/tex]Hence, the correct option is D
A cubical tank with sides 6 feet is to be painted. It costs $2 per square feet to paint. Find the total cost to paint all the six sides.
Answers
We have that the surface area of a cube is given by
[tex]SA=6s^2[/tex]where s is the measure of the side
s= 6 ft
[tex]SA=6\cdot6^2=6\cdot36=216ft^2[/tex]If the square feet cost $2 the total cost will be
[tex]TC=216\cdot2=432[/tex]the total cost is $432
Lisa is saving $50 that she received from her grandmother. She earns $6 each time she walks her neighbor's dog, which she also saves. Which function can be used to find f, the amount of money Lisa will have saved after walking the neighbor's dog d times?
Answers
Let
f ------> the amount of money Lisa will have saved
d -----> number of times that she walking the neighbor's dog
so
Remember that
The linear equation in slope intercet form is equal to
f=md+b
where
m is the unit rate or slope
b is the y-intercept or initial value
in this problem we have
m=6
b=50
therefore
substitute
f=6d+50
answer is last one option
when I combine things to make zero it means l am adding zero
Answers
The combine things to make zero means we are combining same thing but off oppoite polarity or sign or direction.
The addition of zero to anything does not make anything to zero, it results in same quantity. So it is a false statement, as addition of zero does not chage anything, it results in original amount.
write the expression x^2 / x^-6 as a product of two factors and also as a negative exponent.
Answers
Writing the given expression as a product of two factors, we'll have;
[tex]\begin{gathered} \frac{x^2}{x^{-6}}=x^2\ast x^6=x^{2+6}=x^8 \\ \end{gathered}[/tex]Now, writing it as a negative exponent, we'll have;
Lin family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?A. 24.5 milesB. 50 milesC. 59.5 milesD. 200 miles
Answers
The given information is:
The family have traveled 35 miles and it represents the 70% of the trip.
To find how far is the trip we need to divide the 35 miles by the percentage that it represents:
[tex]35\text{miles}\cdot\frac{100\%}{75\%}=50miles[/tex]Thus, the trip is 50 miles.
Answer: B.
Question 8 of 10
If the Federal Reserve decreases the reserve rate from 10% to 8%, how does
this affect the amount of
money that would result because of fractional-
reserve banking from an initial deposit into a bank of $40,000?
C A. It increases the amount by $100,000.
•
B. It decreases the amount by $400,000.
•
C. It increases the amount by $400,000.
• D. It decreases the amount by $100,000.
Answers
The amount of money that would result because of fractional reserve banking from an initial deposit of $40,000 into a bank will increase by $100,000.
The initial reserve rate of the Federal Reserve was 10%. The final reserve rate of the Federal Reserve is 8%. Hence, the reserve rate decreased from 10% to 8%. We need to find the affect, due to this decrease, on the amount of money that would result because of fractional-reserve banking from an initial deposit of $40,000 into a bank.
The formula for the reserve is used here.
Reserve = (Deposit/Final Reserve rate) - (Deposit/Initial Reserve rate)
Reserve = ($40,000/0.08) - ($40,000/0.10)
Reserve = $500,000 - $400,000
Reserve = $100,000
Hence, the reserve amount is increased by $100,000.
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what is 14% of $3.40
Answers
In order to calculate the 14% of $3.40, you only calculate the multiplication of 14/100 and 3.40, just as follow:
14/100 x 3.40 = 0.14 x 3.40 = 0.476
Hence, the 14% of $3.40 is $0.476
The previous calculation can be summarized as follow:
- Divide the percentage between 100
14/100 = 0.14
- The previous result is multiplied by the quantity about you want to know what is the given percentage
0.14 x 3.40
Convert 7π/6 radians to degrees
Answers
ANSWER:
210°
STEP-BY-STEP EXPLANATION:
In order to convert from radians to degrees, we must take into account that π is equal to 180°, knowing this, let's do the conversion:
[tex]\begin{gathered} \pi=180\degree \\ \\ \text{ We replacing} \\ \\ 7\cdot\frac{180\degree}{6}=210\degree \end{gathered}[/tex]Therefore, 7π/6 radians is equal to 210°
Find the equation of the line that passes through the points (2,13) & (-1,-2)
Answers
The two endpoints of a line are given, and to find the equation we need to express it in the slope-intercept form written as follows;
y = mx + b, where m is the slope and b is the intercept of y.
To calculate the slope, we use the formular;
[tex]undefined[/tex]In the circle below, if arc AB = 48 °, and arc CD = 122 °, find the measure of < CPD.
Answers
SOLUTIONS
In the circle below, if arc AB = 48°, and arc CD = 122°, find the measure of < CPD.
[tex]\begin{gathered}Therefore the measure of angle CPD = 85 degree
Hence the correct answer = Option C
You would like to make Chili, Tacos and Grilled Cheese this week. The grocery store prices and ingredients for the meals are listed above. One of each item will be enough to cover all recipes, except you will need two packages of cheese to make all three recipes. How much will you spend on groceries?
Answers
Answer:
i dont get it
Step-by-step explanation:
Simplify: (2a-4)+2(a-5)-3(a+1)
Answers
Answer:
a-17 is the answer for this question
I’m not quite sure on why I’m not getting the correct solution. Please help!The questions are A) what is the initial value of Q, when t = 0? What is the continuous decay rate? B) Use the graph to estimate the value of t when Q = 2 C) Use logs to find the exact value of t when Q = 2
Answers
The given exponential function is
[tex]Q=11e^{-0.13t}[/tex]The form of the exponential continuous function is
[tex]y=ae^{rt}[/tex]a is the initial amount (value y at t = 0)
r is the rate of growth/decay in decimal
Compare the given function by the form
[tex]a=11[/tex][tex]\begin{gathered} r=0.13\rightarrow decay \\ r=0.13\times100\text{ \%} \\ r=13\text{ \%} \end{gathered}[/tex]a)
The value of Q at t = 0 is 11 and the decay rate is 13%
The initial value of Q is 11
The continuous decay rate is 13%
From the graph
To find the value of t when Q = 2
Look at the vertical axis Q and go to the scale of 2
Move horizontally from 2 until you cut the graph
Go down to read the value of t
The value of t is about 13
b)
At
Q = 2
t = 13
c)
Now, we will substitute Q in the function by 2
[tex]2=11e^{-0.13t}[/tex]Divide both sides by 11
[tex]\frac{2}{11}=e^{-0.13t}[/tex]Insert ln on both sides
[tex]ln(\frac{2}{11})=lne^{-0.13t}[/tex]Use the rule
[tex]lne^n=n[/tex][tex]lne^{-0.13t}=-0.13t[/tex]Substitute it in the equation
[tex]ln(\frac{2}{11})=-0.13t[/tex]Divide both sides by -0.13
[tex]\begin{gathered} \frac{ln(\frac{2}{11})}{-0.13}=t \\ \\ 13.11344686=t \end{gathered}[/tex]At
Q = 2
t = 13.11344686
I’m just starting writing these and I don’t understand it much
Answers
In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line, and plane, and are referred to as the "three undefined terms of geometry".
a. Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single endpoint. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.
b. Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the endpoint, and all points extending infinitely to one side of the endpoint.
1. (4x3.5x2 + 3) + (2x3 - 5x²)
Answers
Then
4x3.5x2 = 28
28 + 3 = 31
31 + 2x3= 37
and so answer is
=37 - 5x^2
Solve the right triangle ABC for all missing parts. Express all angles in decimal degrees. a= 306.5 km, c=591.3 km(Round to the nearest hundredth as needed)
Answers
Explanation
Step 1
we have a rigth triangle, then
let
[tex]\begin{gathered} side_1=306.5 \\ side_2=b \\ \text{hypotenuse}=591.3 \end{gathered}[/tex]to find the missing side we an use the Pythagorean theorem. it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} side^2+side^2=hypotenuse^2 \\ \text{replace} \\ 306.5^2+b^2=591.3^2 \\ \text{subtract }306.5^2i\text{n both sides} \\ 306.5^2+b^2-306.5^2=591.3^2-306.5^2 \\ b^2=591.3^2-306.5^2 \\ b=\sqrt[]{591.3^2-306.5^2} \\ b=\sqrt[]{255693.44} \\ b=505.66\text{ km} \end{gathered}[/tex]hence
b=505.66 km
Step 2
angles
a)A
[tex]\begin{gathered} \sin \text{ }\alpha=\frac{opposi\text{te side}}{\text{hypotenuse}} \\ \text{replace} \\ \sin \text{ A=}\frac{a}{c}=\frac{360.5\text{ }}{591.3} \\ A=\sin ^{-1}(\frac{360.5\text{ }}{591.3}) \\ A=37.56\~ \end{gathered}[/tex]and B
[tex]\begin{gathered} \sin \text{ B=}\frac{b}{c} \\ B=\sin ^{-1}(\frac{505.66}{591.3}) \\ B=58.77\text{ \degree} \end{gathered}[/tex]I hope this helps you
Write an equation in general form of the circle with the given properties. Ends of diameter at (5,7) and (-5,-7) ?
Answers
Write an equation in general form of the circle with the given properties.
Ends of diameter at (5,7) and (-5,-7)
we have that
the equation of the circle is
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and r is the radius
step 1
Find the center
Remember that
The center of the circle is the midpoint of diameter
so
[tex]\begin{gathered} (h,k)=(\frac{5-5}{2},\frac{7-7}{2}) \\ (h,k)=(0,0) \end{gathered}[/tex]the center is the origin
step 2
Find the radius
Find the diameter
calculate the distance between two points
[tex]\begin{gathered} d=\sqrt[\square]{(-7-7)^2+(-5-5)^2} \\ d=\sqrt[\square]{(-14)^2+(-10)^2} \\ d=\sqrt[\square]{296} \end{gathered}[/tex]simplify
[tex]D=\sqrt[\square]{296}=2\sqrt[\square]{74}[/tex]the radius is half the diameter
so
r=2√74/2=√74
step 3
the equation iof the circle is
x^2+y^2=(√74)^2
x^2+y^2=74Help Please, I don’t understand and it’s really confusing me
Answers
We have this expression:
[tex]\frac{15}{y}[/tex]Let's substitute y = 1/4 into this expression.
[tex]\frac{15}{\frac{1}{4}}[/tex]Multiply the top and bottom by 4/1 in order to get rid of the double fractions.
[tex]15(\frac{4}{1})=60[/tex]The answer to this problem is C) 60.
Jed bought a generator that will run for 2 hours on a liter of gas. The gas tank on the generator is a rectangular prism with dimensions 20 cm by 15 cm by 10 cm.If Jed fills the tank with gas, how long will the generator run? [1000 cm ^3 = 1 Liter]
Answers
Volume of the rectangular-shaped gas tank = Length x Width x Height
The fish population of a receding pond is 8,000. The population is expected to decrease at a rate of 8% each year.Which function represents the population of the fish in the pond after x years?
Answers
Answer: f(x) = 8000(0.92)^x
Explanation:
The formula for calculating exponential decay is expressed as
f(x) = P(1 - r)^x
where
f(x) is the population after a period of x
P is the initial population
r is the decay rate
x is the time
From the information given,
P = 8000
r = 8% = 8/100 = 0.08
By substituting r = 0.08 into the equation. We have
f(x) = 8000(1 - 0.08)^x
f(x) = 8000(0.92)^x
help i can’t understand this work and i need the answer
Answers
[tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]is equivalent expression of [tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is
[tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]
The power of whole term is multiplied with power of each term
[tex]x^{\frac{1}{2}} y^{\frac{3}{2}} xy^{8}[/tex]
When variables are same the powers will be added
[tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]
Hence, [tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]is equivalent expression of [tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]
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Um Im in fith grade and i need help with some of my math questions if your able to help me with five or 10 questions that will be great
Answers
Solution
For this case we can do the following:
Then the solution would be:
21 6/24 = 21 1/4
For this case we can do the following for 21 1/4
[tex]21\cdot\frac{1}{4}=\frac{21\cdot4+1}{4}=\frac{85}{4}[/tex]For the second part we can do this:
[tex]\frac{1}{3}\cdot5=\frac{5}{3}[/tex]Then the answer is 5/3
Please see attached photo for question
Answers
For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
Domain of a function is all possible input values for that function.
Here, the domain of g(x) is set of all integers numbers
The x intercept of g(x)
The x intercept is when the value of y is zero, analysing the graph the x intercept can be interpreted as -5 and 1
The y intercept is when the value of x is zero, analysing the graph the y intercept can be interpreted as 1
From the graph,
g(4) is 1
Therefore, For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
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please help this math seem hard 50 points anyone
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equivalent expression is
[tex]x^{3/2}y^{19/2}[/tex]
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
√(xy³) x ([tex]x^{1/2} y^4[/tex])²
This can be written as,
[ √ means 1/2, √a = [tex]a^{1/2}[/tex]]
√(xy³) = [tex]x^{1/2}y^{3/2}[/tex]
([tex]x^{1/2} y^4[/tex])² = x[tex]y^8[/tex]
Now,
√(xy³) x ([tex]x^{1/2} y^4[/tex])²
= [tex]x^{(1/2 + 1)}y^{(3/2 + 8)}[/tex]
= [tex]x^{3/2}y^{19/2}[/tex]
Thus,
The equivalent expression is
[tex]x^{3/2}y^{19/2}[/tex]
Option C is the correct answer.
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Functions > 1.02 Function families and transformations How do we shift the graph of y = f(x) to get the graph of y = f(x) + 2?
Answers
y = f(x)
to
y = f(x) + 2
Move up the graph by 2 units along the y- axis. (vertical translation)
solve each system of equations below by graphing, please use my graphy = -2x + 1 y = x - 5
Answers
In order to find the solution to the given system of equations, find x and y intercepts for each line, as follow:
y = -2x + 1
x-intercept:
0 = -2x + 1
2x = 1
x = 1/2
y-intercept:
y = -2(0) + 1
y = 1
Then, the points of intersection for the first line are (1/2 , 0) and (0 , 1)
y = x - 5
x-intercept:
0 = x- 5
x = 5
y-intercept:
y = 0 - 5
y = - 5
Then, the points of intersection of the second line are (5,0) and (0,-5)
Next, graph the two lines by using the previous points:
The solution of the system is the point of intersection between the two lines. As you ca notice, such a point is (2,-3)
Related to your system of coordinates, you have:
original price of shoes is $104.95 a discount of 30% tax 2%
Answers
Solving for the price of a $104.95 pair of shoes with 30% discount, after 2% taxes
First, we have to calculate the 70% of the original value (30% discount). Then, we calculate the 2% of that value (70% of $104.95) and add it up, as following:
[tex]\begin{gathered} 104.95\times\frac{70}{10}=73.47 \\ 73.47\times\frac{2}{100}=1.47 \\ 73.47+1.47=74.94 \end{gathered}[/tex]Thus, the retail price of the shoes, with 30% discount and after 2% taxes, would be 74.94