Given: (GH) is a midsegment of ∆DEF. Show all work.
a. Find the value of x and y.
b. What is the length of DF?
Answers
Applying the triangle midsegment theorem:
a. x = 17; y = 2
b. Length of DF = 20 units.
What is the Triangle Midsegment Theorem?The triangle midsegment theorem states that the midsegment of a triangle is always parallel to the third side, and has a length that is half the length of the third side of the triangle.
GH is said to be the midsegment of triangle DEF, therefore:
a. GH = 1/2(EF) [triangle midsegment theorem]
Substitute
x - 3 = 1/2(28)
2(x - 3) = 28
2x - 6 = 28
2x = 28 + 6
2x = 34
2x/2 = 34/2
x = 17
HF = x - 7
Plug in the value of x
HF = 17 - 7
HF = 10
HF = DH = 10
y + 8 = DH
y + 8 = 10
y = 10 - 8
y = 2
b. Length of DF = HF + DH
Length of DF = 10 + 10 = 20 units.
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Related Questions
The ratio of words missed to correct on Marcy’s test was 1:4 if she got 4 words wrong, how many were correct
Answers
Answer:
Marcy got 16 wrong.
Step-by-step explanation:
You simply multiply 1 ( from the missed side of the ratio ) by 4 ( how many Marcy got wrong ) which equals 4. Then you do the same to the other side. 4 ( from the "correct" side of the ratio ) by 4 ( how many Marcy got wrong ). 4 x 4 is 16. So, Marcy got 16 wrong.
Answer:
16
Step-by-step explanation:
The ratio is 1:4 means for 1 wrong word, she got 4 words correct. If she has 4 words wrong, multiply that with 4 and you got 16.
There are 69 different species of flashing fireflies, also known as Lightning bugs, in the US a museum is designing a rectangular display of these 69 species with the same number of fireflies in each row. How many displays are possible
Answers
The number of displays are possible is 3
Total number of species Lightning bugs = 69
We have to arrange the same number of Lightning bugs in each row
First find the factors of the number 69
The factors of 69 = 1, 3, 23, 69
First combination is (1 × 69)
Arrange 1 Lightning bug in each row, then the number of rows will be 69
(3 × 23)
Arrange 3 Lightning bugs in each rows, then the number or rows will be 23
(23 × 3)
Arrange 23 Lightning bugs in each rows, then the number of rows will be 3
Hence, the number of displays are possible is 3
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What is the remainder when the function, f(x)=x²-2x² -5x+16, is divided by (x+3)
O-32
O-14
O 10
022
Answers
Answer:
14/x+3
Step-by-step explanation:
a professor wants to estimate how many hours per week her students study. a simple random sample of 74 students had a mean of 20 hours of studying per week. construct a 99% confidence interval for the mean number of hours a student studies per week. assume that the population standard deviation is known to be 3.5 hours per week. round to two decimal places.
Answers
99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)
Given:
mean x = 20
standard deviation σ = 3.5
sample size n = 78
z score for 99% = 2.576
Interval = x±z*s/[tex]\sqrt{n}[/tex]
= 20±2.576*3.5/[tex]\sqrt{78}[/tex]
= 20±2.576*0.39629
= 20±1.0208
Interval = (21.0208,18.9792)
Therefore 99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).
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Algebra 2 with Trigonometry
Raul baked a loaf of pumpkin bread that is 9 inches long. Each day, he cuts off a half-inch slice of the bread to have as dessert. Raul claims that the remaining length of pumpkin bread varies inversely with the number of slices of pumpkin bread he cuts and eats.
Write an equation that gives the remaining length of pumpkin bread p (in inches) as a function of the number of slices s that he cuts and eats.
Enter the correct expression in the box.
p = ___
Note: I'm not sure about the answer, but it is not an inverse variation function.
Answers
Answer: p = 9 - 0.5s
Optionally you can replace 0.5 with the fraction 1/2
===================================================
Explanation:
s = number of slices
0.5s = total width of all of those slices mentioned
9-0.5s = amount left over.
For example, if he eats s = 4 slices then he has eaten 0.5s = 0.5*4 = 2 inches of bread, and there are 9-2 = 7 inches left.
Notice how 9-0.5s=9-0.5*4 = 9-2 = 7.
The equation p = 9 - 0.5s is not an inverse variation because it's not in the form p = k/s, where k is some constant.
a wire is to be cut into two pieces. one piece will be bent into a square, and the other piece will be bent into a circle. if the total area enclosed by the two pieces is to be 144 m2, what is the minimum length of wire that can be used?
Answers
A wire is cut into two pieces, one piece bent into square and other piece will be bent into circle. Therefore, the minimum length of wire that can be used is 43 m.
The relationships between the radius of a circle and its circumference and area are :
C = 2πr
A = πr²
The relationships between the side length of a square and its perimeter and area are :
P = 4s
A = s²
So, the length of wire will be
W= C + P
W = 2πr + 4s
Subject to the constraint that the sum of areas is 144 m²:
πr² + s² = 144
Using the method of Lagrange multipliers to find the extremes of wire length, we want to set the partial derivatives of the Lagrangian (L) to zero.
L = 2πr + 4s + λ(πr² +s² -144)
∂L/∂r = 0 = 2π +2πλr ------------------------------- (1)
∂L/∂s = 0 = 4 +2λs ------------------------------- (2)
∂L/∂λ = 0 = πr² +s² -144 -------------------------------- (3)
Solving for λ, we find,
1 +λr = 0 ---------------------------- (4)
⇒ λ = -1/r ----------------------------- (5)
Substituting into equation (2), we get,
4 + 2(-1/r)s = 4
⇒ s/r = 2 -------------------------------- (6)
This tells us the maximum wire length is that which makes the circle diameter equal to the side of the square.
Substituting the relation s=2r into the area constraint, we find,
πr² +(2r)² =144
⇒ r = √(144/(π+4))
⇒ r= 12/√(π+4) ≈ 2.068965 . . . m
∴ The minimum wire length will be required when the entire area is enclosed by the circle. In that case,
πr² = 144
⇒ r = √(144/π)
and, C = 2πr
= 2π√(144/π)
= 24√π ≈42.5388 . . m
rounding up the minimum value 42.5388... in 43.
∴ The minimum wire length will be required is 43 m
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when the british ship gaspee ran aground in rhode island, the local population: question 23 options: 1) burned it. 2) rescued its crew. 3) attacked it. 4) pillaged it. 5) claimed it.
Answers
Using theories of Rhode island ,we got that when the British ship Gaspee ran a ground in Rhode island, the local population 1) burned it.
On June 9, Gaspee gave chase to the packet ship Hannah, but the Gaspee ran aground in shallow water on the northwestern side of bay on what is now Gaspee Point. Her crew were unable to free her and the Dudingston decided to wait for the high tide, which would possibly set the vessel afloat. Before that could happen, however, the band of Providence men led by John Brown decided to act on a "opportunity offered of putting an end to the trouble and the vexation she daily caused." They rowed out to the ship and boarded at the break of dawn on June 10.
Hence, when the british ship gaspee ran aground in rhode island, the local population 1) burned it.
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Use matrices A and B. Compute B - A, if you can.
Answers
Answer:
Step-by-step explanation:
When adding or subtracting, the matrices must be the same size!
Therefore, B-A is not possible.
in a small pond there are eleven lily pads in a row labeled 0 through 10. a frog is sitting on pad 1. when the frog is on pad , , it will jump to pad with probability and to pad with probability . each jump is independent of the previous jumps. if the frog reaches pad 0 it will be eaten by a patiently waiting snake. if the frog reaches pad 10 it will exit the pond, never to return. what is the probability that the frog will escape without being eaten by the snake? in a small pond there are eleven lily pads in a row labeled 0 through 10. a frog is sitting on pad 1. when the frog is on pad , , it will jump to pad with probability and to pad with probability . each jump is independent of the previous jumps. if the frog reaches pad 0 it will be eaten by a patiently waiting snake. if the frog reaches pad 10 it will exit the pond, never to return. what is the probability that the frog will escape without being eaten by the snake?
Answers
The probability that the frog will escape without being eaten by the snake is [tex]\frac{63}{146}[/tex]
What is Markov Process?
A Markov chain or Markov process is a stochastic model that depicts a series of potential occurrences where each event's likelihood is solely determined by the state it reached in the preceding event.
First, take notice that the frog has a probability of 1/2 of finally being eaten by the snake once it is on pad 5, and a probability of 1/2 of eventually emerging from the pond unharmed. Therefore, all that needs to be determined is the probability that the frog on pad 1 will make it to pad 5 without being eaten.
Consider the frog’s jumps in pairs. The frog on pad 1 will advance to pad 3 with probability [tex]\frac{9}{10} \frac{8}{10}[/tex][tex]=\frac{72}{100}[/tex] will be back at pad 1 with probability [tex]\frac{9}{10} \frac{2}{10}[/tex][tex]=\frac{18\\}{100}[/tex]
s
[tex]\frac{72}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{36}{41}[/tex] and the probability that it ultimately makes it to pad 0 is [tex]\frac{10}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{5}{41}[/tex].Similarly, in a pair of jumps the frog will advance from pad 3 to pad 5 with probability [tex]\frac{7}{10} \frac{6}{10} =\frac{42}{100}[/tex], will be back at pad 3 with probability [tex]\frac{7}{10} \frac{4}{10} +\frac{3}{10} \frac{8}{10} =\frac{52}{100}[/tex].
Because the frog will ultimately make it to pad 5 or pad 1 from pad 3, the probability that it ultimately makes it to pad 5 is [tex]\frac{42}{100}[/tex] ÷ [tex]( \frac{42}{100} +\frac{6}{100} )=\frac{7}{8}[/tex] and the probability that it ultimately makes it to pad 1 is [tex]\frac{6}{100}[/tex] ÷ [tex](\frac{42}{100} +\frac{6}{100} )=\frac{1}{8}[/tex]
The series of steps that must be made in pairs for the frog to get to pad 5 without being eaten is
1 → 3 → 5, 1 → 3 → 1 → 3 → 5, 1 → 3 → 1 → 3 → 1 → 3 → 5 and so on.
The sum of the respective probabilities of reaching pad 5 is then
[tex]\frac{36}{41} \frac{7}{8} +\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+.....[/tex]
[tex]= \frac{63}{82} (1+\frac{9}{82} +(\frac{9}{82})^{2} +....)[/tex]
[tex]=\frac{63}{82}[/tex]÷[tex](1-\frac{9}{82} )[/tex]
[tex]= \frac{63}{73}[/tex]
Therefore the requested probability is [tex]\frac{1}{2}\frac{63}{73} = \frac{63}{146}[/tex]
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125% of what number is 52.5
Answers
Answer:
42
Step-by-step explanation:
1.25x = 52.5 Divide both sides by 1.25
x = 42
If f(x) = x - 6 and g(x) = -2x + 4, what is f(x) times g(x)?
A.) -2x^2 - 24x + 16
B.) -2x^2 + 16x - 24
C.) -2x^2 + 16x + 16
D.) -2x^2 + 14x - 24
Answers
The product of f(x) and g(x) is -2x² +16x -24.
What is a function?A function is a relation such that there is only one unique output for every input.
Given that, the functions, f(x) = x-6 and g(x) = -2x + 4.
The value of f(x) × g(x) is,
f(x) × g(x)
= (x-6)(-2x+4)
= -2x²+4x + 12x -24
= -2x² +16x -24
Hence, the product of f(x) and g(x) is -2x² +16x -24.
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The equation d=3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.
What does 3 represent?
Answers
If t=1, then d=3: In 1 minute, the snail traveled 3 inches.
If t=2, then d=6: In 2 minutes, the snail traveled 6 inches.
If t=3, then d=9: In 3 minute, the snail traveled 9 inches.
The snails speed is 3 inches per minute. That's what the 3 represents. The change in distance (inches) for each minute that passes.
Jai has a points card for a movie theater.
He receives 20 rewards points just for signing up.
He earns 11.5 points for each visit to the movie theater.
He needs 181 points for a free movie ticket.
Answers
Answer: B
Step-by-step explanation:
What is the slope of a line parallel to the line whose equation is 10x+6y=-96. Fully simplify your answer.
Answers
The slope of a line parallel to the line whose equation is 10x + 6y = -96 is;
m = - 5/3
Find the slope fully simplify my answer.
10x + 6y =-96
y = - 5/3 x – 16
y = - 5/3 x + (-16)
y = - 5/3 x + (-16), m = - 5/3
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Alisa can work at most 30 hours next week, but she needs to earn at least $240. Her lawn mowing job pays $9 an hour, and her coaching job pays $15 an hour. Identify the variables, and then write a system of equations to represent the constraints on Alisa's work time and income.
Answers
The system of equation for the following conditions contains equation the equations: x + y ≤ 30 and 9x + 15y 240.
What is system of equation?
A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
Let the hours Alisa work for lawn mowing job is "x" hours and for coaching job is "y" hours.
As given in the question, Alisa can work at most 30 hours.
So the total working hours should be equal or less that 30 hours.
Therefore, the first equation can be written as:
x + y ≤ 30
And it is also given that, she needs to earn at least $240, while Her lawn mowing job pays $9 an hour, and her coaching job pays $15 for an hour.
So, Total earning = per hour earning x total hour
lawn mowing job earning = 9(x)
coaching job earning = 15(y)
Therefore, the second equation can be written as:
9x + 15y 240
Hence, the system of equation is: x + y ≤ 30 and 9x + 15y 240
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-2f-3.7 < 2.3 find inequality
Answers
The inequality results to f > -3.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
-2f-3.7 < 2.3
Now, solving the inequality
Add 3.7 both side
-2f-3.7 + 3.7 < 2.3 + 3.7
-2f< 6
Divide both side by 2.
-f< 3
f> -3
Hence, the inequality results to f > -3.
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Question
A triangle is cut from a rectangle. The height of the triangle is half of the unknown side length s. The area of the shaded region is 84 square inches. Write an equation you can use to find the side length s.
Answers
The equation that can be used to find the side length of the shape is 14s - 7s/2 = 84
How to calculate the length?From the information, the two sides of the rectangle are 14 and s.
Area of a rectangle = length × width
The triangle is cut from the rectangle, the height is s/2 and the base is 14.
The area will be: = 1/2 × base × height
= 1/2 × 14 × s/2
= 7s/2
The area of shaded part will be;
= Area of rectangle - Area of triangle
= 14s - 7s/2
Since area is 84, the equation is 14s - 7s/2 = 84.
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Solve this problem:
√-9k=√16-k
k=
Answers
Find the least common denominator of 7/2 and 3/10
Answers
Answer: 10
Step-by-step explanation: it’s 10 because 2 is a multiple of 10 and 10 is 10 so no change required.
Answer:
LCD = 10
Step-by-step explanation:
7/2 = 35/10
3/10 = 3/10
a researcher was interested in the differences in the opinions about marriage between men and women. the researcher predicted that women would have different opinions about marriage from men. what would the null hypothesis suggest in this situation?
Answers
There is no null hypothesis in this situation there is no differences in the opinions about marriage between men and women
In the field of science, hypothesis testing is an effective method of determining whether or not there is a relationship between two or more variables. A null hypothesis is a default position or a general statement that no relationship or connection exists between the given variables.
The hypothesis is then tested, and based on the results of the tests, a conclusion is drawn either approving or rejecting the null hypothesis.
In the given situation, where the researcher predicted that women would have different opinions about marriage than men, the null hypothesis could be formulated because there is no difference in the opinions of men and women about marriage.
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Determine whether a linear relationship exists between x and y. If the relationship is linear, find the constant rate of change.
X 1 2 3 4
y 4.3 8.6 12.9 16.3
Write "linear" or "nonlinear" in the Show your work area. If linear, type the constant rate of change in the answer box. if not linear, briefly explain why in the answer box.
Answers
The values of x and y are not in a linear relationship.
Given,
x y
1 4.3
2 8.6
3 12.9
4 16.3
The linear relationship between x and y can be determined by using,
[tex]y=kx\\k=\frac{y}{x}[/tex]
Where, k=constant rate of change
If k is same for all values of x and y then the given data are said to be in linear relationship.
At first row,
[tex]k=\frac{4.3}{1} =4.3[/tex]
At second row,
[tex]k=\frac{8.6}{2}=4.3[/tex]
At third row,
[tex]k=\frac{12.9}{3}=4.3[/tex]
At fourth row,
[tex]k=\frac{16.3}{4} =4.075[/tex]
So, the k is not same for all values for x and y. Hence, the given data is non linear
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NEED HELP ASAP, EXPLANATION WOULD BE APPRECIATED THANKS
Answers
The value of variable x is 16.5 using the cross-multiplication method.
What is the cross-multiplication method?The denominator of the first term is multiplied by the numerator of the second term when utilizing the cross-multiplication method.
In mathematics, more specifically in elementary arithmetic and elementary algebra, one could cross-multiply an equation between two fractions or rational expressions to make the equation easier or to determine the value of a variable.
So, the value of x will be:
Use the cross-multiplication method as follows:
2x-7/4 = x+3/3
3(2x-7) = 4(x+3)
6x - 21 = 4x + 12
2x = 12 + 21
2x = 33
x = 33/2
x = 16.5
Therefore, the value of variable x is 16.5 using the cross-multiplication method.
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Correct question:
Obtain the value of x.
Vicky and John share some sweets in the ratio 2:7. If Vicky ends up with 12 sweets, how many will John have?
Answers
By using ratio, it is calculated that John have 42 sweets.
What is ratio?
Ratio between two quantity tells us how much bigger is one quantity as compared to the other quantity.
The first part of the ratio is called antecedent and the second part of the ratio is called consequent
Vicky and John share some sweets in the ratio 2:7
Let Vick shares 2x sweets and John shares 7x sweets
Vicky ends up with 12 sweets
By the problem,
[tex]2x = 12\\x = \frac{12}{2}\\x = 6[/tex]
Number of sweets John have = [tex]7 \times 6 = 42[/tex]
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In the Fig, O is the Center of the Circle
If ∠OPQ = 25° & ∠ORQ = 20°
Find: ∠PQR & ∠POR
Answers
The angles in the figure are:
∠PQR = 45°
∠POR = 90°
Given : O is the centre of circle, ∠OPQ = 25° and ∠ ORQ = 20°
To Find : values of ∠ POR and ∠ PQR.
OP = OQ = Radius
⇒ ∠OPQ = ∠OQP
⇒ ∠OQP = 25°
OR = OQ = Radius
⇒ ∠OQR = ∠ORQ
⇒ ∠OQR = 20°
∠PQR = ∠OQP + ∠OQR
⇒ ∠PQR = 25° + 20°
⇒ ∠PQR = 45°
∠POR = 2∠PQR
⇒ ∠POR = 2*45°
⇒ ∠POR = 90°
Hence we get the two angles as 45° and 90° respectively.
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4. Rewrite the expression 12x + 8 to find an
equivalent expression. Show three possible
expressions. What do the rewritten expressions
tell you about the relationships among the
quantities?
Answers
To rewrite the expression 12x+8 to find an equivalent expression.
The answer is
12 x + 8 is equivalent to 4(3x + 2) is equivalent to
3x + 3x+3x+3x + 2 +2+2+2 is equivalent to (x+x+x)+(x+x+x)+(x+x+x)+(x+x+x)+2+2+2+2
Therefore these are the possible expressions
Step: 1
Here given that,
Rewrite the expression 12x + 8 to find an equivalent expression. Show three possible expressions. What do the rewritten expressions tell you about the relationships among the quantities.
Step: 2
When you rewrite an expression, you are writing an equivalent expression.
12 x + 8 is equivalent to 4(3x + 2) is equivalent to
3x + 3x+3x+3x + 2 +2+2+2 is equivalent to
(x+x+x)+(x+x+x)+(x+x+x)+(x+x+x)+2+2+2+2
Therefore these are the possible expressions
Hence the answer is
12 x + 8 is equivalent to 4(3x + 2) is equivalent to
3x + 3x+3x+3x + 2 +2+2+2 is equivalent to
(x+x+x)+(x+x+x)+(x+x+x)+(x+x+x)+2+2+2+2
Therefore these are the possible expressions
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simplify the expression, leaving only positive exponents in your answer
-3x^2(6xy-2x^3y^2z)
Answers
Answer:
simplify - 3x^2xy-(-3x^2) x 2x ^3y^2^z: -3x^3y+6x^2+3y2z
help! ASAP!!!!!!! 4 points if you help!!!
Answers
Answer:
I believe it would be 300 dollars per week, I hope this was right :)
Step-by-step explanation:
.4x750=300
n is an integer 5
5<2n<20
write down all the possible values of n
Answers
If n is an integer , the possible values of n in the given inequality are n > 5/2 and n < 10 .
In the question ,
it is given that ,
the inequality is 5 < 2n < 20 , where n is an integer .
we need to find the all the possible values of n that satisfy the given inequalities .
to find the possible values of n , we solve both sides of the inequality separately ,
that is ,
5 < 2n
dividing both sides in the inequality by 2, we get
5/2 < n
n > 5/2
and
2n < 20
dividing both sides in the inequality by 2 , we get
n < 20/2
n < 10
Therefore , the possible values of n are n > 5/2 and n < 10 .
The given question is incomplete , the complete question is
Write down all the possible values of n for the inequality 5<2n<20 , where n is an integer ?
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QUESTION 4/10 HELP ASAPP
Answers
Answer:
Left bottom graph is the correct one.
Answer: The bottom left graph
Step-by-step explanation: The top two are decreasing, so you can rule those answers out. The bottom right one is increasing by more than 4, so that wouldn’t be the answer either. That leaves you with one option which fits the description of the graph.
The sum of 3 consecutive even numbers is 78.
What is the second number in this sequence?
Answers
Answer: 26
Step-by-step explanation:
1. Make an equation
n+n+2+n+4=78
(You have n+2 because to get to the next even number you'd have to add 2. For example, 2 is even, to get to the next even number, 4, you have you add 2.)
2. Combine like terms
3n+6=78
3. Solve for n
3n=72
n=24
4. Solve for the second number
(The second number would be n+2)\
n+2
24+2
26
ANSWER: 26