1. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.
2. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.
Answers
FD and DE are perpendicular, because D and F have the same x coordinate, and D and E the same y coordinate.
Let A(4, 1) be the midpoint of DE and B(1, 3) be the midpoint of FD.
Draw the perpendiculars from A and B. They meet at O(4, 3), since AO is parallel to DF and BO is parallel to DE.
the point where the perpendicular bisectors of the sides meet is the circumcenter, so the circumcenter is O(4, 3)
2.
Let the length of the second base be x.
the length of the midsegment is the sum of the ases divided by 2.
[tex]19= \frac{x+24}{2} [/tex]
19*2=x+24
38=x+24
x=38-24=14
Answers:
1) O(4, 3)
2) length of second base = 14 units
Related Questions
If there are x teams in a sports league, and all the teams play each other twice, a total of n(x) games are played, where n(x)equals
Answers
Consider a group of n objects. Assume we want to form groups of r, from these n objects.
There are in total [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex] many ways of doing so.
where, r! is "r factorial", calculated as 1*2*3*...*(r-1)*r
2.
C(x, 2) is the total number of pairs out of x objects, that we can form.
so let the x objects represent the x teams, and 2, represent a group of 2, which means a game.
The total number of games is:
n(x)=2*C(x, 2) = [tex]2* \frac{x!}{2!(x-2)!}= \frac{x!}{(x-2)!}= \frac{x(x-1)(x-2)!}{(x-2)!}=x(x-1)= x^{2} -x [/tex]
Remark, we multiplied by 2, since there will be 2 matches for each pair of teams.
Answer: [tex] x^{2} -x[/tex]
If your starting salary is 50000 and u earn a 4% increase annually, how much money will you earn over 16 years
Answers
it was 1091227 on APEX
If a=6 and b=5 what is the value of (A2-b2)2
Answers
(36-25)^2
11^2
121
a=6 and b=5
(6²-5²)²
pemdas, so simplify inside first
(36-25)²
(11)²
121
The ratio of the number of girls to the number of boys was 3 to 5 . of 2,520 were presented, how many were girls and how many were boys
Answers
3/8(2520) = 7560/8 = 945 girls <==
5/8(2520) = 12600/8 = 1575 boys <==
There were 945 girls and 1575 boys respectively.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or a/b
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. The numerator is the upper quantity in the fraction and the denominator is the lower quantity in the fraction). Remember that the ratio should always be taken of quantities with the same unit of measurement. Also, the ratio is a unitless(no units) quantity.
We have been given that the ratio of the number of girls to the number of boys was 3 to 5.
The ratio girls to boys;
3 to 5
The Total = 8
The number of boys was 3 to 5 . of 2,520, Then;
3/8(2520) = 7560/8
girls = 945
5/8(2520) = 12600/8
boys = 1575
Therefore, there were 945 girls and 1575 boys respectively.
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The function g(x) is defined as g(x) = 6x2 + 23x – 4. When does g(x) = 0?
a. x = –6 or x =
b. x = –4 or x =
c. x = or x = 6
d. x = or x = 4
ON EDUCATION2020 THE ANSWER IS (D)
Answers
Final answer:
To find when g(x) = 0 for the function g(x) = 6x² + 23x – 4, the quadratic formula is used, yielding the solutions x = 0.25 or x = −4.
Explanation:
The question asks for the values of x for which the quadratic function g(x) = 6x² + 23x – 4 equals zero. To find the values of x when g(x) = 0, one can use the quadratic formula, which is x = −(b ± √(b² ∔ 4ac)) / (2a) for a quadratic equation ax2 + bx + c = 0.
Here, a = 6, b = 23, and c = −4. Substituting these values into the quadratic formula gives:
x = −(23 ± √(23² ∔ 4 × 6 × (−4))) / (2 × 6)
After calculating the discriminant (√(b² ∔ 4ac)) and simplifying, we obtain the two solutions for x. Therefore, the correct answer is:
x = 0.25x = −4So, the correct answer, marked as (d) on Education 2020, corresponds to x = 0.25 or x = −4.
Which is a description of the graph that would represent the inequality below?
12 – 2x < 16
Answers
The graph of the inequality 12 - 2x < 16 is represented by an open circle at -2 on a number line, with shading to the right, indicating all values greater than -2.
To describe the graph representing the inequality 12 - 2x < 16, we first need to solve for x. Subtracting 12 from both sides of the inequality, we get -2x < 4. Dividing both sides by -2 (and remembering to flip the inequality symbol when dividing by a negative), we have x > -2.
Graphically, this is represented on a number line with an open circle at -2 and a shaded area to the right of -2, indicating that x can be any number greater than -2.
Suppose three out of every five people said they would prefer a television over a computer. If we surveyed 5,000 people, how many would prefer a television? A. 1,875 B. 5,000 C. 3,125 D. 3,000
Answers
60% of 5000 is equal to 0.6*5000=3000
Final answer: D
I'm studying for a test and i seriously can't figure this out. I took a screenshot. Please help and thanks. :) :P :D
Answers
What we are dealing with is called "Pythagorean Theorum", also known as the famous equation "A^2 + B^2 = C^2." The side length "A" is usually the side length opposite of the hypotenuse, which is the side length "C" that is directly across from the right angle of the triangle. The side length "B" is adjacent to the hypotenuse.
Let's apply this to our current triangle.
We have the side length "A", which is 12 in., and our side length "B", which is 6 in.
Now, let's plug in our numbers to our variables in order to solve for C.
A^2 + B^2 = C^2
Replace A with 12 and B with 6.
12^2 + 6^2 = C^2
Simplify the exponents.
144 + 36 = C^2
Simplify the left side.
180 = C^2.
Now, we must solve for C. As C is being squared, we must apply the opposite mathematical term, which is square rooting.
C^2 = 180.
Square root both sides to solve for C.
C = [tex] \sqrt{180} [/tex] in.
Your answer is (C).
I hope this helps!
ASAP WILL MARK BRAINIEST ANSWER FOR FIRST CORRECT ANSWER Find the image of A(4, -2) after it is reflected over the line y = 2, then reflected over the line x = 2. (-8, 6) (0, -2) (0, 6) (-8, -2)
Answers
Answer:
(0, 6)
Step-by-step explanation:
Since, when a points is reflected through the line y = 2,
Then, the rule will be,
[tex](x,y)\rightarrow (x, -(y-4))[/tex]
While, the points is reflected through the line x = 2,
Then, the rule will be,
[tex](x,y)\rightarrow (x-4, y)[/tex]
So, when (4,-2) is reflected over the line y = 2 is,
[tex](4,-2)\rightarrow (4, -(-2-4))[/tex]
Hence, the position of (4,-2) after reflection through line y = 2 is (4,6),
Now, when (4,6) is reflected over the line x=2 is,
[tex](4,6)\rightarrow (4-4, 6)[/tex]
Hence, the position of (4,6) after reflection through line x = 2 is (0,6),
Third option is correct.
Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo. Yesterday she had seven clients and earned $500. Let x represent only the clients that got a cut and y represent the clients that got a cut and color combo.
Which of the following equations could be used to represent this situation.
1. y=7-x
2. x + y= 500
3. 120x + 35y= 500
4. (35+120) (x + y)= 500
5. 35x + 120y= 500
Check all that apply
Answers
35x + 120y= 500
Always the last one! lol
Answer:
Option 5th is correct
[tex]35x+120y = 500[/tex]
Step-by-step explanation:
Here, x represents only the clients that got a cut and y represent the clients that got a cut and color combo.
As per the statement:
Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo.
" Charges $35 for a cut" translated to 35x
"$120 for a cut and color combo" translated to 120y
It is also given that yesterday she had seven clients and earned $500.
⇒[tex]35x+120y = 500[/tex]
therefore, an equations could be used to represent this situation is, [tex]35x+120y = 500[/tex]
In 1995, 57.5% of students at Gardiner University graduated in 4 or fewer years of study. In 2009 that number had fallen to 52.8%. What was the rate of change of percent of students graduating within 4 years from 1995 to 2009?
Answers
%change=100(52.8-57.5)/57.5
%change≈ -8.17%
Use the table below to answer this question:
x y
0 2
1 -1
2 -6
Find the average rate of change for the given function from x = 0 to x = 2.
Answers
(-6-2)/(2-0) = -4
You probably know that if the interval was pretty small, between 0 and 0.0001, it would take you to the concept of slope and derivatives, but average change is just ignoring anything in between x=0, and x=2 (it could go up/down million times, and still the answer would be -4)
hope it helps
Name a pair of complementary angles.
A. angle A E C and angle B E D
B. angle B E C and angle C E D
C. angle A E C and angle C E D
D. angle D E A and angle A E D
Answers
AEC and CED are complimentary
C. angle A E C and angle C E D
complementary angles: sum of angles = 90
There are 7 yellow, 5 green, and 3 blue party hats in a bag. you randomly choose a yellow party hat and put it on. then your friend randomly chooses a yellow party hat. what is the probability of both of you choosing a yellow party hat?
Answers
P(yellow party hat) = 7/15
do not replace
P(yellow hat) = 6/14
P(both) = 7/15 * 6/14 = 42/210 which reduces to 1/5 or 0.2 or 20%
The probability of choosing both yellow hats can be obtained as 1/5.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The number of yellow, green and blue hats are given as 7, 5 and 3.
Then, the total number of hats is 7 + 5 + 3 = 15.
Now, the probability for both hats to be yellow without replacement can be given as,
P(Both hats are yellow) = 7/15 × 6/14
⇒ P(Both hats are yellow) = 1/5.
Hence, the required value of probability is given as 1/5.
To know more about probability click on,
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Choose the answer that best represents the situation described below. Kurt is buying a new cell phone. He knows that the more features the cell phone has, the more expensive it will be. A. The cost of the cell phone is a function of the number of features. B. The size of the cell phone is a function of the number of features. C. The number of features is a function of the cell phone company Kurt chooses.
Answers
The cost of the cell phone is a function of the number of features.
Explanation:The answer that best represents the situation described is option A. The cost of the cell phone is a function of the number of features.
In this case, as Kurt is buying a new cell phone, he knows that the more features the cell phone has, the more expensive it will be. This implies that the cost of the cell phone is dependent on the number of features it has.
For example, if a cell phone with basic features costs $200, a cell phone with additional features like a better camera, more storage, and waterproof capabilities may cost $400 or more.
Which expression is equivalent to (2g^5)^3/(4h^2)^3
Answers
First option
Answer:
Step-by-step explanation:
It’s A
Solve the inequality. Check your solutions.
7−(2/b)<(5/b)
im not surehow to answer this, it's supposedly in a number form but I'mcompetely lost. Maybe a _
Answers
[tex]7- \frac{2}{b}\ \textless \ \frac{5}{b}[/tex]
write 7 as 7b/b to have all the expressions in common denominator:
[tex] \frac{7b}{b} - \frac{2}{b}\ \textless \ \frac{5}{b}[/tex]
[tex]\frac{7b-2}{b} \ \textless \ \frac{5}{b}[/tex]
[tex]\frac{7b-2}{b}- \frac{5}{b}\ \textless \ 0[/tex]
[tex]\frac{7b-2-5}{b}\ \textless \ 0[/tex]
[tex]\frac{7b-7}{b}\ \textless \ 0[/tex]
[tex]\frac{7(b-1)}{b}\ \textless \ 0[/tex]
here b=1 is a root and b=0 is not in the domain of the expression, but it still has an effect in the sign of the expression.
the sign table of [tex]\frac{7(b-1)}{b} [/tex] is :
+++++++[0] --------[1] +++++
this means that for values of b to the left of 0 and to the right of 1, the expression is positive, and for values of b in (0, 1), the expression is negative.
that is [tex]\frac{7(b-1)}{b}\ \textless \ 0 [/tex] for b∈(0, 1)
Answer: (0, 1)
ROUND 47342.6653106 TO 1 DECIMAL PLACE HELP!
Answers
HELP WILL GIVE BRAINLIEST (08.01)
Line Q is represented by the following equation: 2x + y = 11
Which equation completes the system that is satisfied by the solution (3, 5)?
x + 2y = 15
x + y = 15
x + y = 8
x − y = 2
Answers
3+2(5)=13 not 15
3+5=8 not 15
3-5 p=-2 not 2
The only logical answer is C
Answer:
C (1, 1) is the solution to line K but not to line J..
which of the following are not techniques used in geometric constructions with paper folding. Check all that apply
A. Creating arcs and circles work the compass
B. Drawing line segments
C. Measuring lengths of line segments by folding the paper and matching the endpoints
D. Folding the paper and aligning marks seen through the paper
Answers
There are two correct answers which are not techniques used in geometric constructions with paper folding and these are:
A. Creating arcs and circles work the compass
C. Measuring lengths of line segments by folding the paper and matching the endpoints
In geometric folding, a straight line becomes a crease or a fold. This is achieved by a person by folding a piece of paper and flattening the crease rather than drawing lines to make a guide. Therefore this means that shapes like arcs, curves, circles by using the compass, and measurement of line segments are not used. However, constructions using compass have a long history in Euclidean geometry.
The following are not techniques used in geometric constructions with paper folding:
A. Creating arcs and circles with the compass.
C. Measuring lengths.
What is a geometric construction?A geometric construction can be defined as a process that is used to draw angles, lines, and other geometric figures (shapes), especially through the use of only a compass and straightedge such as a ruler without measurements.
In Geometry, the techniques that should be used in geometric constructions with paper folding include the following:
Drawing line segments.Folding the paper and aligning marks that are seen through the paper.Read more on geometric construction here: https://brainly.com/question/7386615
There are five boys and five girls in a class. The teacher randomly selects three different students to answer questions. The first student is a girl, the second student is a boy, and the third student is a girl. Find the probability of this occuring.
Answers
Final answer:
The probability of selecting a girl, then a boy, and then another girl from a class with 5 girls and 5 boys is 10.42%.
Explanation:
The probability of a specific sequence of students being selected in a random draw can be calculated by multiplying the probabilities of each event occurring in succession. Since there are five boys and five girls in the class, the probability of drawing a girl first is 5/10, or 1/2. After drawing one girl, there are now four girls and five boys left, so the probability of drawing a boy second is 5/9. Finally, with one girl and one boy already picked, there are three girls and four boys left, making the probability of drawing a girl third 3/8.
To find the overall probability, we multiply these individual probabilities:
Probability = (First girl drawn) × (Second boy drawn) × (Third girl drawn)
Probability = (1/2) × (5/9) × (3/8)
Probability = (1 × 5 × 3) / (2 × 9 × 8)
Probability = 15 / 144
Probability = 0.1042 or about 10.42%
Final answer:
The probability of the teacher randomly selecting a girl, a boy, and another girl from a class of 5 boys and 5 girls is 5/6.
Explanation:
To find the probability of the teacher randomly selecting three different students, we need to consider the number of possible outcomes and the number of favorable outcomes. In this case, there are 10 students to choose from and the teacher needs to select one girl, one boy, and another girl. To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes.
The number of favorable outcomes is 5 for the first girl, 5 for the boy, and 4 for the second girl (since the first girl has already been selected). So the total number of favorable outcomes is 5 x 5 x 4 = 100.
The number of possible outcomes is the total number of ways to choose 3 students from the 10 available. This can be calculated using the combination formula: C(10, 3) = 10! / (3!(10-3)!) = 120.
Therefore, the probability of selecting a girl, a boy, and another girl is 100/120 = 5/6.
There are 10 pots exposed in the shop, 2 of which have hidden defects. the customer buys two pieces. what is the probability that at least one of them has a hidden bug ?
Answers
All the possible scenarios are:
1st.non defective, 2nd.non defective
1st.non defective, 2nd. defective
1st. defective, 2nd. non defective
1st. defective, 2nd. defective
consider the case 1st.non defective, 2nd.non defective
the probability that the first one is non defective is 8/10, since 8 out of 10 are non defective.
In this scenario, the second one is non defective as well. The probability for this to happen is 7/9, since now we have 7 non defective pots, and 9 in total.
This means that the probability of the first to be non defective, and the second non-defective is (8/10) * (7/9)=0.622
similarly we calculate the other cases, as shown in the picture.
P(at least one is defective)=
P(1st.non defective, 2nd. defective)+P(1st. defective, 2nd. non defective)+P(1st. defective, 2nd. defective)=
0.178+0.178+0.022=0.378
Answer: 0.378
If x and y are not both equal to zero 1/x+y = 1/x + 1/y
Look at the picture provided below
|
V
Answers
Answer:
True
Step-by-step explanation:
All work is shown and pictured
A rectangular room is 4 4 times as long as it is wide, and its perimeter is 60 60 meters. find the dimension of the room.
Answers
4w + w + w + 4w = 60
10w = 60
w = 6
4w = 24
L = 24
(just to check the answer, 24 + 24 + 6 + 6 = 60 :)
How do we do this ? is it c or a? 15 points!!!!
Answers
Assume that y varies inversely with x. If y=6.4when x=4.4, find y when x=3.2
Answers
y = k/x
where k = constant.
When x=4.4, y=6.4. Therefore
k/4.4 = 6.4
k = 6.4*4.4 = 28.16
The required relation is
y = 28.16/x
When x = 3.2, obtain
y = 28.16/3.2 = 8.8
Answer: 8.8
the answer is 8.8
that is the answer
Solve 3x2 + 13x = 10
a. x = two over three and x = −5
b. x = 3 and x = −3
c. x = −2 and x = five over three
d. x = −7 and x = 13
Answers
Write the equation as
3x² + 13x - 10 = 0
Use the quadratic formula to obtain
x = (1/6) [ -13 +/- √{13² - 4*3*(-10)} ]
= (1/6) [-13 +/- √289]
= (1/6) [-13 +/- 17]
x = -30/6 = -5
or
x = 4/6 = 2/3
The solution is x = 2/3 and -5.
Answer: a
Answer:
A. x = two over three and x = -5
The equation 3x^2 + 13x = 10 can be solved using the quadratic formula. The solutions are given by:
[tex]$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Substituting the values from the equation (where a = 3, b = 13, and c = -10), we get:
[tex]$$x = \frac{-13 \pm \sqrt{13^2 - 4*3*(-10)}}{2*3}$$[/tex]
This simplifies to:
[tex]$$x = \frac{-13 \pm \sqrt{289}}{6}$$[/tex]
So, the solutions are:
[tex]$$x = \frac{-13 + \sqrt{289}}{6} = \frac{2}{3}$$[/tex]
and
[tex]$$x = \frac{-13 - \sqrt{289}}{6} = -5$$[/tex]
So, the correct answer is A. x = two over three and x = −5.
5,200 g divided by 583.1 mL
Answers
there is 1 gram per 1 milliliter so just divide them
5200/583.1 = 8.91785
you don't say if it needs to be rounded to a certain amount
so since the mL has one decimal place
round to 8.9mL
Pretty sure this is super easy I'm just an idiot pls help!
Answers
7x + 3x - x
Combine like-terms first.
10x - x
9x
This is equivalent to 9x^1, or 9x to the degree of 1. This is known as a monomial.
A monomial is a number/product of numbers and variables with whole number exponents.
Some examples are as follows:
I hope this helps!
Given g(x) = 2x2 − 9x − 18 and f(x) = x − 6, identify (g/f)(x).
Answers
answer is 2x+3, x not equal to 6
see attached pic for steps
Answer:
2x + 3, x ≠ 6
Step-by-step explanation: