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We are asked to prove that triangles AED and CFD are congruent. To do that we will prove that we can use the ASA (Angle Side Angle) rule of congruency.
First, we are given that D is a midpoint of segment AC, therefore:
[tex]\bar{AD}=\bar{AC}[/tex]Also, we are given that:
[tex]\bar{BA}=\bar{BC}[/tex]This means that triangle ABC is an isosceles triangle and therefore, its base angles are equal. This means that:
[tex]\angle BAC=\angle BCA[/tex]And, since we are given that angles EDA and FDC are equal, then by ASA we can conclude that:
[tex]\Delta AED\cong\Delta CFD[/tex]Related Questions
A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 9 ft from the side of the house. Find thelength of the ladder. If necessary, round your answer to the nearest tenth.х5?9ExplanationCheck
Answers
Given:
Distance of top of ladder to the ground = 10 ft
Distance of bottom of ladder from the side of the house = 9 ft
Let's find the length of the ladder.
Since the ladder forms a right triangle with the house, to find the length of the ladder apply Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]Where:
a = 10 ft
b = 9 ft
c = length of ladder
Thus, we have:
[tex]\begin{gathered} c^2=10^2+9^2 \\ \\ c^2=100+81 \\ \\ c^2=181 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{181} \\ \\ c=13.5 \end{gathered}[/tex]Therefore, the length of the ladder rounded to the nearest tenth is 13.5 ft
ANSWER:
13.5 ft
Based on the two data sets represented below, complete the following sentences.Options: "greater" or "less"
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We can check that the median of the dataset T is 14, and its mean is also close to 14, while the median of the dataset U is 17 and its mean is close also close to 17. We can also check that the range of the dataset T is 14 and the data is more concentrated at its center, while the range of the dataset U is 20 and the data is more dispersed.
Therefore, we can state that The center of Data Set T is less than the center of Data Set U, and the spread of Data Set T is less than the spread of Data Set U.
Rewrite the expression by factoring out (y+4).3(y + 4)+7y(y+4)
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Given-:
Function is:
[tex]3(y+4)+7y(y+4)[/tex]Find-:
Expression by factoring
Explanation-:
Factoring the function is:
[tex]\begin{gathered} =3(y+4)+7y(y+4) \\ \\ =(y+4)(3+7y) \end{gathered}[/tex]Factoring is:
[tex]=(y+4)(3+7y)[/tex]Subtract and simplify the answer. 8/9 - 1/3
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Solution
We want to simplify
[tex]\frac{8}{9}-\frac{1}{3}[/tex]Now
[tex]\begin{gathered} \frac{8}{9}-\frac{1}{3}=\frac{8}{9}-\frac{1\times3}{3\times3} \\ \frac{8}{9}-\frac{1}{3}=\frac{8}{9}-\frac{3}{9} \\ \frac{8}{9}-\frac{1}{3}=\frac{8-3}{9} \\ \frac{8}{9}-\frac{1}{3}=\frac{5}{9} \end{gathered}[/tex]Therefore, the answer is
[tex]\frac{5}{9}[/tex]You are trying to help a friend calculate their utilization rate for their study time. They can complete a maximum of 60 HW problems per hour. In the last hour, they were a little distracted but managed to complete 20 HW problems. What is their utilization rate (in %)? Calculate as a percentage (thus .05 would be entered as 5)
Answers
The utilization rate of friends' study time is 33%
In this question, we need to find the utilization rate for friends' study time.
They can complete a maximum of 60 HW problems per hour. In the last hour, they were a little distracted but managed to complete 20 HW problems.
We know that the formula for the utilization rate:
Utilization % = Actual Number of Hours Worked / the Total Available Hours.
So the utilization rate would be,
r = 20/60
r = 0.33
r = 0.33 × 100
r = 33%
Therefore, the utilization rate of friends' study time is 33%
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evaluate each limit. this is in the topic of jump discontinuities.
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we have
[tex]\begin{gathered} \lim _{x\to-2}-x^2-4x-5 \\ \lim _{x\to-2}-(-2)^2-4(-2)-5 \\ \lim _{x\to-2}-4^{}+8-5 \\ \lim _{x\to-2}--1 \end{gathered}[/tex][tex]\lim _{x\to-2}-1=-1[/tex]therefore
the answer is -1INT ALGEBRAL: 1. Write an equation that passes through (0,5) and is parallel to 3x+5y=6
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
Answers
The equation of the parallel line is y = -3/5x + 5
How to determine the line equation?The equation is given as
3x + 5y = 6
The point is also given as
Point = (0, 5)
The equation of a line can be represented as
y = mx + c
Where
Slope = m and c represents the y-intercept
So, we have
3x + 5y = 6
This gives
5y = -3x + 6
Divide
y = -3/5x + 6/5
By comparing the equations y = mx + c and y = -3/5x + 6/5, we have the following
m = -3/5
This means that the slope of y = -3/5x + 6/5 is -3/5
So, we have
m = -3/5
The slopes of parallel lines are equal
This means that the slope of the other line is -3/5
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -3/5
(x₁, y₁) = (0, 5)
So, we have
y = -3/5(x + 0) + 5
Open the brackets and evaluate
y = -3/5x + 5
Hence, the parallel line has an equation of y = -3/5x + 5
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Which of these shows the result of using the first equation to substitute for y?
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D) 9x=18
Explanationgiven
[tex]\begin{gathered} y=3x\Rightarrow equation(1) \\ 3x+2y=18\Rightarrow equation(2) \end{gathered}[/tex]Step 1
substitute the y value from equation (1) into equation(2)
so
[tex]\begin{gathered} 3x+2y=18\operatorname{\Rightarrow}equat\imaginaryI on(2) \\ replace \\ 3x+2(3x)=18 \\ 3x+6x=18 \\ add\text{ like terms } \\ 9x=18 \end{gathered}[/tex]therefore, the answer is
D) 9x=18
I hope this helps you
The oldest child in a family of four children is three times as old as the youngest. The two middle children are 19 and 23 years old. If the average age of the children is 28.5, how old is the youngest child?
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Answer:
18 years old
Solution:
Let x represent the age of the youngest child.
So the age of the oldest = 3x
If the ages of the two middle children are 19 and 23, and the average age of the four children is 28.5, let's go ahead and find x;
[tex]\begin{gathered} \frac{(x+19+23+3x)}{4}=28.5 \\ 4x+42=114 \end{gathered}[/tex]Let's go ahead and subtract 42 from both sides;
[tex]4x=72[/tex]Dividing both sides by 4, we'll have;
[tex]x=\frac{72}{4}=18[/tex]Therefore, the youngest is 18 years old.
There are 120 teachers. Select a sample of 40 teachers by using the systematic sampling technique.
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Given:
Total number of teachers = 120
To select a number of teachers = 40
Required:
To find a sample of 40 teachers by using the systematic sampling technique.
Explanation:
The probability formula is given as:
[tex]\begin{gathered} P=\frac{number\text{ of favourable outcomes}}{Total\text{ number of outcomes}} \\ P=\frac{40}{120} \\ P=\frac{1}{3} \end{gathered}[/tex]Final Answer:
[tex]undefined[/tex]Which of the following is the exact value of cot(pi/4)
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We have to select the correct value of cot (pi/4).
It is known that the value of cot (pi/4) is 1.
Thus, the correct option is B.
Evaluate the indicated function for f(x)=x^2-1 & g(x)=x-2 algebraically .
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Given:
[tex]f(x)=x^2-1\text{ ; g(x)=x-2 }[/tex][tex](\frac{f}{g})(t+2)=\frac{f(t+2)}{g(t+2)}[/tex][tex](\frac{f}{g})(t+2)=\frac{(t+2)^2-1}{(t+2)^{}-2}[/tex][tex](\frac{f}{g})(t+2)=\frac{t^2+4t+4-1}{t+2-2}[/tex][tex](\frac{f}{g})(t+2)=\frac{t^2+4t+3}{t}[/tex][tex](\frac{f}{g})(t+2)=\frac{(t+1)(t+3)}{t}[/tex]Subway wants to know how their customers feel about their food quality and service. When each customer pays for their food, the Subway employee hands them their receipt and tells them that they have a chance to win $500 if they go on line and answer a few questions about the restaurant. a) Experimentb) Observational Studyc) None of thesed) Survey
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From the question, we were told that a subway company decides to reward their customers if they go online and answer a few questions about the restaurant.
We are to determine what the process means.
The general view, examination, or description of something or someone in most cases for a reward is known as a survey.
So since subway wants its customers to go online and answer some question about the restaurant and get a reward, then it is a survey.
So, the process that was carried out is a survey.
Therefore, the correct option is D, which is survey.
Aaron took out a 30-year mortgage for $70,000. His monthly mortgage payment is $466. How much will he pay over 30 years? Interest rate = 7%
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Answer:
[tex]\text{ \$167,760}[/tex]Explanation:
Here, we want to get how much will be ppaid over the course of 30 years
From the question, we have it that he pays $466 monthly
Now, to get the amount he will pay over the course of the years, we have to understand that there are 12 months in a year
The total number of months for which he will be paying will be:
[tex]30\times\text{ 12 = 360}[/tex]He will be paying $466 per month for a total of 360 months
So, the total amount he is to pay is the product of this two
Mathematically, that would be:
[tex]360\times466\text{ = 167,760}[/tex]HELP I JUST WANT TO FINISH GET MY CREDIT AND GRADUATE 70 POINTS HELP ASAP What are the values of x and y in the matrix subtraction below? [[- 20, 16], [4, 0], [9, - 6]] - [[- 5, 1], [- 6, 7], [0, 11]] = [[x, y], [10, - 7], [9, - 17]]
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SOLUTION
We want to solve the question below
We can see that a matrix was subtracted from another. In Addition or subtraction of matrix, we just add or subtract the element. So
We have in the first row
[tex]\begin{gathered} -20-(-5)=x \\ -20+5=x_ \\ x=-15 \end{gathered}[/tex]And
[tex]\begin{gathered} 16-1=y \\ 15=y \\ y=15 \end{gathered}[/tex]Hence x = -15 and y = 15, the first option is correct
hey there ms or mr could you help me out with this problem please?
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Similar figures have corresponding sides that are proportional.
We can set up a ratio where we are putting corresponding sides of each triangle, cross mutliply, and solve for the unknow.
Looking at answer choices:
A)
if we have x and 24 to one side, we need corresponding pair from right hand side triangle, which should be 15 and 9. But the ratio is 9 over 15. So, this isn't right.
B)
If 24 is paired with 9 [corresponding side of each triangle], then we need same correspondence.
But we have 15 and x, which is opposite of what we want. So, this isn't right.
C)
32 goes with x and 12 goes with 15. They are indeed in correspondence to each other.
This ratio is correct.
We can say Option C is the correct answwer.
what is 2 3/24 simplified
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2 3/24
Multiply the denominator by the whole number and add the numerator to obtain the new numerator. the denominator stays the same.
(2x24)+3 /24 = 48+3 /24 = 51/24
simplify by 3
17/8
Find the perimeter of the square.
Width = 4x
Length = 36 – 5x
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Answer:
The perimeter of the square is 64 units===========================
GivenA square with dimensions:
Width = 4x,Length = 36 - 5x.To findThe perimeterSolutionSquare has all sides equal:
width = length4x = 36 - 5x4x + 5x = 369x = 36x = 4Each side is:
4*4 = 16 unitsPerimeter:
P = 4*16 = 64 unitsThe perimeter of the square is found as 64 units.
What is defined as the perimeter of the square?The perimeter of such a square is indeed the total length of all of its sides. As a result, we can calculate the perimeter of the a square besides adding its four sides.A square's sides are all equal. As a result, the perimeter of such a square is determined by multiplying the side of a square by four.For the given question,
The dimension of the square are given as;
Width = 4xLength = 36 – 5xFor square, as all sides are equal.
Then,
Width = Length
Put the values.
4x = 36 – 5x
9x = 36
x = 4
Put in dimensions.
Width = 4×4 = 16 unitsLength = 36 – 5×4 = 16 units.The perimeter of square is;
Perimeter = 4 × side
Perimeter = 4 × 16
Perimeter = 64 units.
Thus, the perimeter of the square is found as 64 units.
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Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
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The derivative of the function f(x) = -5x²+3x-2 is -10x+3.
Given the function is f(x) = -5x²+3x-2
Differentiate with respect to x.
d/dx -5x²+3x-2 = d/dx (-5x²) + d/dx(3x) - d/dx(2)
using the power rule d/dx [xⁿ] = nxⁿ⁻¹
⇒ d/dx -5x²+3x-2 = -5(2)x²⁻¹ + 3(1) - 0
⇒ d/dx -5x²+3x-2 = -10x+3
The power rule states that the derivative of xn is nx(n-1) for every x if n is a positive integer, regardless of whether you are thinking of derivatives at a point (numbers) or derivatives on an interval (functions).
Hence we get the derivative as -10x+3.
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Use the Distributive Property to rewrite each product below. Simplify your answer.
A.) 28 · 63
B.) 17 (59)
C.) 458 (15)
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As per the concept of distributive property, the values of
A.) 28 · 63 = 1768
B.) 17 (59) = 1003
C.) 458 (15) = 6870
Distributive property:
Distributive property states that, " multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together."
It can be written as expression like the following,
A( B + C) = AB + AC
Given,
Here we have the expressions,
A.) 28 · 63
B.) 17 (59)
C.) 458 (15)
Now, we have to find the solution for this by using the distributive property.
Now, we have to expand the given expressions by using the distributive property then we get,
A) 28. ( 60 + 3) = (28 x 63) + (28 x 3)
=> 1680 + 84
=> 1768
Similarly, we have simplify the next expression as,
B) 17 (59) = 17 x (50 + 9)
As per the distributive property,
17 x (50 + 9) = (17 x 50) + (17 x 9)
=> 850 + 153
=> 1003
Finally, applying the distributive law, we get,
C) 458 (15) = (450 + 8) x 15
=> (450 x 15) + (8 x 15)
=> 6750 + 120
=> 6870
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Please help. I've been trying to answer this question but I haven't been successful.
Answers
Equations
It's required to find the value of x that satisfies the conditions of the figure.
We have an equilateral triangle. We know it's equilateral because all of its interior angles have the same measure (look at the tick mark on each angle).
Recall the sum of the interior angles of any triangle is 180°.
If all the interior angles have the same measure, then each angle measures 180/3 = 60°.
One of the angles is assigned an expression of x. We can equate it to 60:
5x - 18 = 60
Adding 18:
5x = 78
Dividing by 5:
x = 78/5
x = 15.6
Answer: I do believe the answer is 15.6. Hope this helps! ^w^
5. Infer from the problem: What is the y-intercept of the line y=3x-5 ?
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the given expression is
y = 3x - 5
y +5 = 3x
y - (-5) = 3(x - 0)
so the y-intercept is -5.
Solve radical∛x²-8=4
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Let's determine the value of x on the given radical expression:
[tex]\text{ }\sqrt[3]{x^2-8}\text{ = 4}[/tex]f A and B are independent events with P(A)=0.3 and P(B)=0.7, find P(A AND B). Provide your answer below:
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If A and B are independent events with P(A) = 0.3 and P(B) = 0.7, then the value of P(A AND B) = 0.21
A and B are independent events
Independent events are events that does not depends on any other events.
Probability is the ratio of number of favorable outcomes to the total number of outcomes
The value of P(A) = 0.3
The value of P(B) = 0.7
If A and B are independent events, then P(A AND B) = P(A) × P(B)
Substitute the values in the equation
P(A AND B) = 0.3 × 0.7
= 0.21
Hence, if A and B are independent events with P(A) = 0.3 and P(B) = 0.7, then the value of P(A AND B) = 0.21
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Alicia borrow 15000 to buy a car she borrowed the money at 8% for 6 years how much will she have to pay the bank at the end of 6 years
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Answer:
Explanation:
First, we identify the main components:
• Principal = $15,000
,• Rate = 8% =0.08
,• Time = 6 years
[tex]undefined[/tex]find the function domain and range and the slope of the graph
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The line end points are (4,3) and (-5,-2).
The value of x coordinates give the domain and values of y coordinates give the range.
Since point (4,3) lies on the line and point (-5,-2) does not lie on ther line.
Domain is,
[tex](-5,4\rbrack[/tex]Range is,
[tex](-2,3\rbrack[/tex]Determine the slope of line.
[tex]\begin{gathered} m=\frac{3-(-2)}{4-(-5)} \\ =\frac{5}{9} \end{gathered}[/tex]So slope is 5/9.
Find the rate of change of the line represented by the table.
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Slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Replacing:
[tex]m=\text{ }\frac{4-6}{3-3}=-\frac{2}{0}=\text{ undefined}[/tex]since x is constant , it is a vertical line, with an undefined slope.
The coordinate pairs for triangle ABC are A(1,2), B(4,5), C(2,2). It undergoes a translation of 2 units right and 1 unit 1 up. Write down the coordinates of A'
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We will have the transformation rule (x, y) -> (x+2, y+1)
Then, for A' we will have:
A'(3, 3)
B'(6, 6)
C'(4, 3)
Solve the triangle with the given measures. More than one triangle may be possibletriangle ABCM
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then
[tex]undefined[/tex]Graph A) -f(x) B) f(x+2) -4Then find the domain and range of each
Answers
a. Graph -f(x):
By the transformations rules for functions, the graph of -f(x) is equal to a reflection over the x-axis, and a change of the y-coordinates:
[tex](x,y)\rightarrow(x,-y)[/tex]Then, given the function:
[tex]f(x)=\sqrt[]{x}[/tex]The graph of -f(x) is:is
The domain of the function is the set of all possible x-values, then it is:
[tex]\lbrack0,+\infty)[/tex]The range is the set of all possible values of the function, then it is:
[tex]\lbrack0,-\infty)[/tex]b. Graph f(x+2)-4:
The transformation f(x+2) is an horizontal translation left 2 units.
And the transformation f(x+2)-4 is a vertical translation down 4 units.
Then, the coordinates of this graph in comparison to the given graph are:
[tex](x,y)\rightarrow(x-2,y-4)[/tex]Then for the point (1,1) the new coordinates are (1-2,1-4)=(-1,-3).
For (4,2): the new coordinates (4-2,2-4)=(2,-2)
For (9,3): the new coordinates (9-2,3-4)=(7,-1)
The graph is:
The domain of this function is:
[tex]\lbrack-2,+\infty)[/tex]And the range is:
[tex]\lbrack-4,+\infty)[/tex]