The figures have corresponding sides that are proportional, therefore, they are similar figures.
What are Similar Figures?When two figures are similar to each other, the corresponding sides are proportional to each other.
The two figures given have two opposite sides that are parallel and congruent to each other. Therefore:
DA/VS = 21/7 = 3
AB/ST = 15/5 = 3
Thus, we can conclude that since their corresponding sides are proportional, therefore, they are similar to each other.
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Can someone please help me out Question 1 of 10
f(x) = x². What is g(x)?
-5
g(x)
y
f(x)
(2, 2)
O A. g(x)=x²
9(x)-(²x)*
O c. g(x)=x²
OD. g(x) = 2x²
OB. g(x)=
X
Answer:
C
Step-by-step explanation:
let f(x)=y and g(x)=x
so y=x²
if y-2=(x-2)
y=x
500 soldiers in a fort had enough food for 30 days if 125 more soldiers joined them then for how many days will the food last
Answer:
500+125=625625÷30=21 daysIsla is dividing 3x3 + x2 – 12x – 4 by x + 2 using a division table.
Quotient
Divisor
3x2
– 5x
– 2
x
3x3
–5x2
–2x
+ 2
6x2
A
B
What are the missing values in the table?
The value of A and B are -10x and -4 respectively.
Division involves gathering a number of expressions into smaller forms.
The quotient is represented by the expression
Quotient= Dividend /Divisor
We have the value of the Dividend from the division table given in the question
Dividend of the Operation= A
Divisor of the Operation=2
Quotient of the Operation= -5x
As we know Quotient= Dividend /Divisor
So, -5x= A/2
multiplying 2 on both sides
⇒(-5x)2= A/2*2
⇒ A= -10x
Similarly, We have the value of the Dividend from the division table given in the question
Dividend of the Operation= B
Divisor of the Operation=2
Quotient of the Operation = -2
As we know Quotient= Dividend /Divisor
So, -2= B/2
multiplying 2 on both sides
⇒(-2)2= AB2*2
⇒ B= -4
Therefore the value of A and B are -10x and -4 respectively.
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what are the rates of the cyclists?
Answer:
24 km/h and 17 km/h
Step-by-step explanation:
We know that when two cyclists are traveling together, they will meet in the same time as if one cyclist with the combined speed of the two cyclists travelled the whole length. We don't know the speeds of the cyclists, so let's assign the one with the slower speed "x", and the one with the faster speed "x+7" the combined speeds is "2x+7"
Since the speed = distance / time, we can plug in the values
2x+7=205/5
2x+7=41
2x=34
x=17
We substitute x into the equation for the speed of the cyclists
Cyclist 1's speed: x, so their speed is 17 km/h
Cyclist 2's speed: x+7, so their speed is 17 + 7, or 24 km/h
NOTE: Angles not necessarily drawn to scale.
Answer: 60°
Step-by-step explanation:
- the two angles created by CD and EF are vertical angles so they are equal
- one angle is 30° so the other one is 30° and it splits an existing 90° angle so 90-30 = 60 so x is 60°
hope this helps :)
Answer:
∠x=60°
Step-by-step explanation:
Add 90° and 30° then subtract by 180 to find ∠x.
How I got 30 degrees is because of the vertical angle. Vertical angles are always equal.
I got the 90 degrees from the left top side.
180 degrees is the degrees of a straight angle.
90+30=120
180-120=60
Hope this helps!
If not, I am sorry.
Solve the problems. Write the complete proof.
ONLY HAVE TO PROVE HOW BD IS PERPENDICULAR TO AC!
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. An isosceles triangle is one with two equal-length sides.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
In ΔBAD and ΔBDC,
m∠ADB = m∠CDB {Given}
BD = BD {Common side in two triangles}
AD ≅ DC {Given}
Using the ASA postulate the two triangles are congruent. Therefore,
m∠BAD= m∠BCD.........equation 1
m∠ABD= m∠CBD
In ΔADC, AD ≅ DC {Given}, therefore, the triangle is an isosceles triangle. Thus,
m∠DAE = m∠DCE.......equation 2
Adding two of the equation 1 and 2,
m∠BAD + m∠DAE = m∠DCE + m∠BCD
∠BAC = ∠BCA
Since in ΔABC, ∠BAC = ∠BCA therefore, the triangle is an isosceles triangle, thus, AB = BC,
BE is the common side between ΔAEB and ΔCEB
Also, m∠ABD= m∠CBD
Therefore, ΔAEB ≅ ΔCEB
Now as ΔAEB ≅ ΔCEB, therefore, AE=EC,
Thus, BE is the median of the isosceles triangle ABC, and for an isosceles triangle, the median opposite to the non-common sides is the perpendicular bisector to the opposite side.
Hence, BD⊥AC.
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PLS HELP ME ASAP FIRST CORECT ANSWER GETS BRAINLEIST
Answer:
The area of the shape is 68 cm².
Step-by-step explanation:
We have to calculate the areas of the rectangle and triangle separately, and then add them together.
• Area of rectangle = length × breadth
= 30 cm × 2 cm
= 60 cm²
• Area of triangle = [tex]\frac{1}{2}[/tex] × base × perpendicular height
= [tex]\frac{1}{2}[/tex] × 2 cm × 8 cm
= 8 cm²
Adding the areas together = 60 cm² + 8 cm²
= 68 cm²
Ms sullivan bought some pens at the school supply store, including 5 red pens. 25% of all the pens she brought were red.
Answer:
20 pensStep-by-step explanation:
Note : I am assuming that the question is asking for all no. of total pens.
If 5 red pens were 25% of the total quantity, we can say that 1/4th of the pens were red.
If 5 pens = 1/4, we multiply 5 * 4 to find the total quantity. 5*4 = 20
So, Ms. Sullivan bought 20 pens.
Hope this helps!
Please help!!! A phone company offers two long-distance plans. The first charges a flat value of $5.00 per month plus $0.99 for each minute used, and the second charges $10.00 a month plus $0.79 for each minute used.
If x represents the number of minutes used each month, which system of equations represents the total amount of money, y, you would spend for each long-distance plan?
Answer:
C
Step-by-step explanation:
Given y = amount of money spend for the long distance plan per month
and x = minutes used each month
Note these 2 plans are in per month basis.
Plan A: Flat $5 + $0.99 Per min used (variable cost)
transform into an equation:
y = 0.99x + 5
Plan B: Flat $10 + $0.79 per min used (variable cost)
transform into equation:
y = 0.79x + 10
Put these 2 equations together, will give you the answer as C.
RATING BRAINLIEST Which of the following demonstrates the Distributive Property?
4(2a + 3) = 8a + 3
4(2a + 3) = 2a + 12
4(2a + 3) = 6a + 7
4(2a + 3) = 8a + 12
Answer:
D: 4(2a+3)=8a+3
Step-by-step explanation:
4x2a = 8a and 4x3 = 12
Answer:
just saying this so other can get brainliest
Step-by-step explanation:
d
I NEED HELP ASAP!!!!!!!!!!!!!!!!!!!! PLS COME QUICK! Question 4 (Essay Worth 10 points)
(01.07 MC)
The dimensions of a rectangular prism are shown below:
Length: 2 and 1 over 4 feet
Width: 1 foot
Height: 1 and 1 over 4 feet
The lengths of the sides of a small cube are 1 over 4 foot each.
Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)
Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)
The number of cube that can be packed in the rectangular prism is 30 cubes
Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³
How to find the volume of rectangular prism and cube?volume of rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
volume of rectangular prism = 3 / 2 × 1 × 5 / 2 = 15 / 4 ft³
volume of cube = 1 / 2 × 1 / 2 × 1 / 2 = 1 / 8 ft³
number of cube that can be packed in the rectangular prism = 15 / 4 × 8 = 30 cubes
Volume of the rectangular prism in terms of small cube and unit cube = 30(1 / 8) ft³
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pls help asap.............
The First graph does not have an initial Value
The second graph's solution is (3, -4)
What is Quadratic graph?A quadratic graph is a pictorial representation of quadratic functions.
It shows the relationship between a variable on the x-axis and a variable on the y-axis.
Analysis:
The First graph did not either start from the x or y-axis so it does not have an initial value.
The second graph each mark is 0.5 on both axes so the point of intersection of the two graphs is the solution of the graphs which the x- value is 3 and the y-value is -4.
Therefore (3, -4) is the solution of the graph.
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For the data in the table, tell whether y varies directly with x . If it does, write an equation for the direct variation.
x y
2 -6.6
3 -9.9
4 -13.2
5 -16.5
yes; y = x – 3.3
no
yes;
yes; y = –3.3x
Answer:
yes , y = - 3.3x
Step-by-step explanation:
if y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation , then
k = [tex]\frac{y}{x}[/tex]
checking k for each ordered pair in the table
[tex]\frac{-6.6}{2}[/tex] = - 3.3
[tex]\frac{-9.9}{3}[/tex] = - 3.3
[tex]\frac{-13.2}{4}[/tex] = - 3.3
[tex]\frac{-16.5}{5}[/tex] = - 3.3
thus k = - 3.3
so y varies directly with x and the equation of direct variation is
y = - 3.3x
Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:
Number of years
1
2
3
Car 1 (value in dollars) 17,390 16,346.60 15,365.80
Car 2 (value in dollars) 17,500 16,500 15,500
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years?
Explain your answer, and show the value of each car after nine years. (4 points)
There is a significant value in the difference in the value of the car after nine years
The type of function (linear or exponential)?The table of values is given as:
Years 1 2 3
Car 1 17,390 16,346.60 15,365.80
Car 2 17,500 16,500 15,500
The values of car 1 have a common ratio of 0.94; this is calculated by dividing the terms of the function
The common ratio implies that the function of car 1 is a geometric function.
The values of car 2 have a common difference of -1000.
The common difference implies that the function of car 2 is a linear function.
The function of each car typeCar 1
In (a), we have:
Common ratio, r = 0.94
The initial value is given as:
a = 18,500
So, the function of car 1 is
f(x) = 18500 * 0.94^x
Car 2
In (a), we have:
Common difference, d = -1000
The initial value is given as:
a = 18,500
So, the function of car 2 is
f(x) = 18500 - 1000x
The car with the greatest value after 9 yearsThis means that
x = 9
So, we have:
Car 1
f(9) = 18500 * 0.94^9
f(9) = 10600
Car 2
f(9) = 18500 - 1000 *9
f(9) = 9500
10600 is greater than 9500
Hence, there is a significant value in the difference in the value of the car after nine years
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Multiply (6 - 5)².
OA) 11+ 60i
B) 36 +25i
OC) 11-60i
OD) 36-25i
Answer:
[tex]\textsf{C)} \quad 11-60i[/tex]
Step-by-step explanation:
[tex]\textsf{Multiply }\: (6-5i)^2[/tex]
[tex]\implies (6-5i)(6-5i)[/tex]
[tex]\implies 6(6-5i)-5i(6-5i)[/tex]
[tex]\implies 36-30i-30i+25i^2[/tex]
[tex]\implies 36-60i+25i^2[/tex]
[tex]\textsf{Remember that }i^2=-1:[/tex]
[tex]\implies 36-60i+25(-1)[/tex]
[tex]\implies 36-60i-25[/tex]
[tex]\implies 36-25-60i[/tex]
[tex]\implies 11-60i[/tex]
Compute the following without using a calculator. You must show your work to receive full credit.
50,001^2 - 49,999^2
Answer: 50,001²-49,999²=0,2.
Step-by-step explanation:
[tex]50,001^2-49,999^2=(50,001+49,999)*(50,001-49,999)=100*0,002=0,2.[/tex]
VERBAL
3. Explain how to interpret the initial value in a word problem that uses a linear function.
Answer:
The initial value in the word problem is the output value when input value is set to zero.
Step-by-step explanation:
In the question, it is given that a problem uses a linear function.It is required to explain how to interpret the initial value in a word problem.In order to find the initial value in a world problem, find the output value when input value is set to zero.If the initial value is marked as b for a linear function f(x), find it as follow,b = f (x=0)I need help please!!!
Based on the number of coins in the jar, the probability that Nina would not pick a penny or dime is a. 0.36.
The cost of the entire trip to the Cross family should they use the two cars is c. $107.07.
What is the probability to Nina?This can be found as:
= Number of quarters, and nickels) / (Number of quarters, nickels, dimes, and pennies)
= (13 + 18) / (13 + 25 + 18 + 30)
= 0.36
What is the cost of gasoline to the Cross family?= Cost of gas to first car + Cost of gas to second car
= (450/18 x 2.49) + (450 / 25 x 2.49)
= 62.25 + 44.82
= $107.07
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. Suppose that the times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit will take at least 43 minutes
The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.
Given: The times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes.
It can be deduced that the probability that a randomly selected cable repair visit will take at least 43 minutes will be calculated thus:
= 1 - [(43 - 40)/(65 - 40)
= 1 - 0.12
= 0.88
Hence, The probability that a randomly selected cable repair visit will take at least 43 minutes will be 88%.
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In the formula V = s²h, if s is doubled and
h tripled, then V multiplied by
This shows that if s is doubled and h tripled, then V multiplied by 12
Volume of a cuboidGiven the formula below expressed as:
V = s²h
If s is doubled and h tripled, the new volume will ne:
V1 = (2s)² * 3h
V2 = 4s² * 3h
V2 = 12s²h
V2 = 12V
This shows that if s is doubled and h tripled, then V multiplied by 12
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Can you guys please help? The image is attached.
See below for the description of changes when the dependent and the independent variables are switched
How to determine the changes?The table of values
When the dependent and the independent variables are switched, the values also become switched on the table.
This means that the table becomes an inverse table of the function
The scatter plot
Switching the variables implies that the original function is being reflected across the line y = x
The description in words
This description is an inverse relation of the original function
The equation
This description is an inverse equation of the original function.
If the initial equation is y = ax + c, the new equation becomes x = ay + c
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Question 4 of 10; can someone help me.
HELP HELP HELP
If your an expert please help me do these 5 quick algebra 1 questions for 50 points!
Only answer if you know the answers to all of the questions please! ;)
Answer:
Step-by-step explanation:
2. Given a point with integral coordinates (a, b):
Vertical line that contains (a, b):
So here it's not to hard, all you have to understand, is what a vertical line is. If you were to draw a vertical line, you would notice that the x-values remain constant, and the only thing that changes is the y-value. So you're going to have an equation as such: x=a, where a is some constant value, and y is literally anything. So in this case b doesn't matter. The only thing that matters is that x=a. Which is the equation. As long as x is equal to a, it should pass through (a, b)
Horizontal line that contains (a, b):
So this is very similar to the vertical line, as one of the values is constant, although the variable that's constant is different. If you were to draw a horizontal line, you would notice the x is changing, but the y-value isn't. This means the y is going to equal to constant value, which may look something like: y=b, which is the equation in this case, since as long as y=b, then the x should at some point equal a on the horizontal line
Why is it impossible to write the equation of a vertical line in slope-intercept form:
As mentioned before, in a vertical line, the only thing that varies is the y-value, so if you wrote a vertical line as such: y=mx+b, then the x-value would have to vary. But if we were to put restrictions on the equation so that x can only equal some constant value, that means y would only be one point, but if you draw a vertical line, you would know that the y-value is all real numbers (unless of course you put some range restriction), but even then it's going to be more than one number. The other thing is to write an equation in slope-intercept form, you need to know the slope. which is defined as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. and by definition a vertical line only varies in y-values and not x. The value of x is defined in the constant equation: x=a. So the slope would be defined as: [tex]\frac{y_2-y_1}{a-a} = \frac{y_2-y_1}{0} = \text{undeefined}[/tex] ("I typed undefined wrong intentionally since it won't let me type it for some reason"). anyways the point is you can divide by 0. So main takeaways: the x-value can't vary, the formula has to output all real numbers for the y-value (unless some range restriction), the slope will have 0 as the denominator since x doesn't vary meaning x_2 - x_1 will = 0, because x_2 = x_1 (because x doesn't vary)
Given an equation in point slope form, explain how to determine the coordinate of the y-intercept:
There are two ways to do this. The point slope form is expressed as such: y-a = m(x-b). But the m can be distributed so the equation becomes y-a = mx-mb and then add "a" to both equations to get y=mx -mb+a, in this case (0, -mb+a) will be the y-intercept, because if you plug in x as 0, mx will become 0 and it will leave these two values. You could also just of course plug in 0 as x in the point slope intercept form: y-a = m(x-b) and then solve for y. This gives the same result as it simplified to y-a = m(-b) which becomes y-a=-mb which then becomes y=-mb+a.
If nicolai earns an 8 percent after tax rate of return, 9,500 today would be worth how much to nicolai in five years?
Nicolai would get worth of 13958.62 in five years for an 8% rate of return.
What is the rate of return?The net gain or loss of an investment over a given period stated as a percentage of the investment's starting cost is known as a rate of return (RoR).
Any type of investment instrument, including real estate, bonds, equities, and fine art, can be subject to a rate of return.
You determine the percentage change from the start of the period to the end when computing the rate of return.
Initial amount=9500
Rate of return=8%
Amount after 5 years=[tex]9500*(1+\frac{8}{100}) ^{5}[/tex]
[tex]=9500*(\frac{108}{100} )^{5}[/tex]
[tex]\\=13958.62[/tex]
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Find the decay factor from the equation y = 453(0.87)^4
The decay factor of the equation given in the task content is; 0.87.
What is the decay factor from the equation?According to the task content; the equation given is; y = 453(0.87)^4.
By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.
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Someone please help me out with this one. If LM=XY, then LM-GH=
LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.
How to illustrate the information?It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.
In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.
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Multiply a Polynomial by a Monomial
In the following exercises, multiply.
236. (8b − 1)b
Answer:
The given expression is (8b − 1)b.We have to multiply the given expression.Distribute the expression then simplify to determine the answer.(8b − 1)b = 8b*b - 1*b
= 8b2 - b
Step-by-step explanation:
Hence the expression (8b − 1)b=8b2 - b.
F (x) = -6 x + 1/2 : find the inverse
The inverse of the given function is y = (12-x)/6
Inverse of a functionGiven the following function expressed as:
f(x) = -6x +1/2
Replace y with x
x = -6y + 1/2
Make y the subject of the formula
6y = -x + 12
y = (12-x)/6
Hence the inverse of the given function is y = (12-x)/6
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(05.02)The area of the parallelogram below is ___ square meters
Numerical Answers Expected!
Answer for Blank
Step-by-step explanation:
the area of a parallelogram is
baseline × height
which is in our case
9 × 7 = 63 m²
Answer:
ayo give the other guy brainilest
Step-by-step explanation:
write a quadratic function F whose zeros are 12 and 1
Answer:
[tex]f(x) = (x-12)(x-1)[/tex]
Step-by-step explanation:
So when you have a quadratic equation it can usually be expressed as: [tex]a(x-b)(x-c)[/tex] where b and x are the roots of the equation. Since it's just asking for a function whose zeroes are 12 and 1, I'm assuming it doesn't care about the stretch/compression (value of a determines that), so I'll just assume a=1. if 12 and 1 are zeroes, that means it makes one of the factors equal to 0 because is x-b = 0 then no matter the value of x-c the value of y is 0 because 0 * (x-c) will be 0. So the equation becomes [tex]f(x) = (x-12)(x-1)[/tex] plugging in 12 or 1 as x will make one of the factors 0 thus making f(x) equal to 0