Answer:
2 & 4 :)
Step-by-step explanation:
Find the circumcenter of the triangle ABC.
A(-5,3), B(5, 8), C(-5.8).
The circumcenter is
(Type an ordered pair.)
The coordinates of the circumcenter of the triangle are (5,8).
Given, Three points of the circle,
A(-5,3), B(5, 8), C(-5.8).
Mid point of AB = (5-5 / 2, 8+3/2) = (0, 11/2)
Slope of AB = y2 - y2 / x2 - x1
= 8-3 / 5 + 5
= 5/10 = 1/2
Equation of AB = y - yo = m (x - xo)
y - 11/2 = 1/2 (x - 0)
2y - 11 = x .....(1)
Similarly finding the equation of AC and BC -
Mid points of BC = (0,8)
slope of BC = 0
equation of BC = y = 8 ....(2)
On solving (1) ans (2) simultaneously,
2y - 11 = x
y = 8
16 - 11 = x
x = 5
The coordinates of the circumcenter of the triangle are (5,8).
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7. The quiz scores for 6 students who studied together
in a math class are in the table.
a. What is the mean quiz score?
b. What is the median quiz score?
Score / Quiz Scores
3
4.5
6.5
00
8.5
10
The mean quiz score is 5.42.
The median quiz score is 5.5.
What is the mean and the median?
Mean is the average of a set of numbers. It is determined by adding the set of scores together and dividing it by the total scores in the dataset.
Mean = sum of the numbers / total number
Mean = (3 + 4.5 + 6.5 + 00 + 8.5 + 10) / 6 = 5.42
Median is the number at the center of the dataset when the scores are arranged in either an ascending or descending order.
The scores arranged in ascending order - 0, 3, 4.5, 6.5, 8.5, 10
Median = (4.5 + 6.5) / 2 = 5.5
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A baker used 1 5/8 teaspoons of baking powder to make 3 1/3 dozen cupcakes. What is the unit rate in teaspoons per dozen at which the baker uses baking powder to make dozens of cupcakes
The unit rate at which the baker uses baking powder to make dozens of cupcakes is 39/80 or 0.4875 teaspoons of baking powder per dozen cupcakes.
What is a unit rate?The unit rate refers to the comparison of two ratios that have 1 as their denominator. Unit rate is often used in calculations that compare two units. For instance kilometer/hour, meter/sec, and teaspoons/dozen as is the case in the above question.
To obtain the unit rate of the above question, we simply divide the teaspoons measurement by the quantity of cupcakes produced. This gives us:
13/8 ÷ 10/3
13/8 × 3/10
39/80 teaspoons per dozen cupcakes.
or 0.4875 teaspoons per dozen cupcakes in decimal form.
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Which of the following is not a proper fraction?
A.3/2​
B.4/3​
C.7/5
D.5/6
A. 3/2 is not a proper fraction because it is greater than 1.
A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). In the fraction 3/2, the numerator (3) is greater than the denominator (2), which means it is not a proper fraction. This can be expressed as a formula using inequality symbols:
Numerator < Denominator
3 < 2
Since 3 is not less than 2, 3/2 is not a proper fraction.
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Erwin Middle School has 350 boys. 66 2/3% of the students are girls. How many students go to this school?
By working with the given percentage, we will find that there are 1,050 students in the school.
How many students go to the school?
First, we know that (66 + 2/3)% = (66.66...%) of the students are girls.
Then the remaining 33.33% are boys.
And we know that there are 350 boys, so the 33.33...% of the students is equal to 350.
So we can write the equations for percentages:
350 = 33.33%
X = 100%
Where X is the total number of students, to find X, we can take the quotient between these two equations:
X/350 = 100%/33.33%
X = 350/0.333... = 1,050
So there are 1,050 students on that school.
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q16 ANSWER FOR 20 POINTS
Answer:
The first answer
Step-by-step explanation:
In this problem, i represents that number of items that Vance sells. Since he sold between 300 and 310 items, i can be any integer between those values. This immediately rules out the second option. Since you cannot sell only a part of an item, the third and fourth answer choices are also incorrect. Therefore, the first option is the correct answer.
hurry please and thank you #5
Considering the graph the true statements are
< CAB and < FDE are have the same measure because AB and DE are parallel
The length of AP is the difference between the x coordinates of the points A and F
Δ ABC and DEF are similar
What are correponding angles?When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal line
In the figure, < CAB and < FDE are corresponding angels.
the difference in the x axis between points A and F is the line AP. this is used in slope calculation
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You want to make more than $500 selling candles. You sell small candles for $10 each and you sell large candles for $25 each. Write a linear inequality to help so
the different amounts of candles you can buy.
You want to sell 25 or less candles. Write an inequality to determine the possible number of each size of candle to sell.
The inequality for different candles to buy.
10x + 25y > 500
The inequality for different candles to sell
x + y ≤ 25
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Small candles = x
Large candles = y
Cost of small candles = $10
Cost of large candles = $25
Now,
The inequality that makes more than $500.
10x + 25y > 500
Now,
The inequality to sell 25 or fewer candles.
x + y ≤ 25
Thus,
The inequalities are:
10x + 25y > 500
x + y ≤ 25
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2. When graphed, which equation pair will be parallel lines?
Oy=42-4 and y = -x +9
Oy=1-1 and y = x + 1
Oy=x and y = 2x + 2
Oy=-x-8 and y = x + 5
One of the options is c=d because matching angles are made and the same corners are congruent when a line joins two parallel lines.
How do parallel lines work?In geometry, parallel lines are coplanar, straight lines that don't intersect anywhere. Parallel planes are those in the same three-dimensional space that never cross one another. Curves do not touch or intersect when they are parallel to one another and keep a predetermined minimum distance between them. Lines in a plane are considered to be parallel if their spacing is constant. Objects cannot cross parallel lines. Perpendicular lines are those that intersect at a precise angle of 90 degrees.
Due to vertical angles, A = d is also a possible answer. The outcome is that b+d=180 since b+c=180 and c=d, and b+d=180 as a result. Therefore, the answer is B, C, E, where a=d, c=d, and b+d=180.
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How do you find the complex roots of a 6th degree polynomial?
You can find the complex roots of a 6th-degree polynomial by using approaches such as the rational root theorem.
The most common approach is to use the Rational Root Theorem, which can be used to determine the possible rational roots of the polynomial - these are the roots that can be expressed as a fraction with an integer numerator and an integer denominator.
Once you have identified these possible rational roots, you can then use the Synthetic Division algorithm to divide the polynomial with each of the rational roots to determine the actual roots of the equation.
Another approach is to use the Sturm’s Theorem, which can be used to determine the number of real and complex roots of the equation.
Finally, you can also use numerical methods, such as the Newton-Raphson method, to calculate the complex roots of the polynomial.
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9 x 4 divided 1 x 2 x 3 x 4
Answer:
864
Step-by-step explanation:
how large can δ be so that |x − 0.5| < δ guarantees that |cos(x) + 2 sin(3x) − l| < 0.5?
The largest possible value of δ that guarantees |cos(x) + 2 sin(3x) − 1| < 0.
What is trignomentry ?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of angles,sines, cosines and tangents and circles.
We can start by using the Triangle Inequality to find an upper bound on |cos(x) + 2 sin(3x) − 1| in terms of |x − 0.5|:
|cos(x) + 2 sin(3x) − 1| <= |cos(x) − 1| + 2 |sin(3x)|
We know that |cos(x) − 1| <= |x − 0.5| and |sin(3x)| <= |3x|, since |sin(x)| <= |x| for all x. So we have ,
|cos(x) + 2 sin(3x) − 1| <= |x − 0.5| + 2|3x|
Now we can set this inequality equal to 0.5 and solve for |x − 0.5|:
|x − 0.5| + 2|3x| <= 0.5
|x − 0.5| <= 0.5 − 2|3x|
To find the largest possible value of δ, we need to find the maximum value of the right side of the inequality,
δ = 0.5 - 2|3x|
The maximum value of the right side of the inequality occurs when |3x| is at its smallest. Since |3x| >=0 for all x, the maximum value of δ is 0.5.
So , the largest possible value of δ that guarantees |cos(x) + 2 sin(3x) − 1| < 0.
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How do you take the root of 6?
Answer:
6 times to equals what [tex]\sqrt{36}[/tex]
Step-by-step explanation:
To find Root 6 one can refer to the methods of simplifying square roots. To simplify a square root, the number should be made as small as possible while still keeping it as a whole number. Mathematically this can be written as:
√a.b = √a * √b
To write this equation for the square root of 6 simplification, we will get:
√6= √2 * √3
This can be further simplified by substituting the values of root 2 and 3 (rounded to three decimal numbers) as:
√6 = 1.414 * 1.732
√6 = 2.449
Thus, this is the simplified version of the square root of 6. Similarly, we can also find square roots of any other whole numbers and find out their factors. After finding the factors, we usually convert them into the lowest divisible number, as we have done above. Thus, we have found the value of root 6. This method is the most popularly used method for finding square roots of any number. Apart from this, if we use a calculator we can find the exact value of this as well. The exact value will always be a decimal number as it is nearly impossible to find a positive whole integer as a root for non-rational numbers.
Another simplistic example of how roots work with one another is by figuring out the Square root of 6 plus square root of 6, and this is an interesting problem with a simplistic solution. Let us see this problem and its solution mathematically,
Sqrt (6) + Sqrt (6) = √6 + √6
√6 + √6 = 2√6
Thus, by substituting the value of root 6, we can find the required answer. Keeping this in mind, we can add these roots together to find the solution to the problem while keeping the base root under the radical sign constant. Hence, in this method, we can find solutions to such problems.
Solve for n.
–
31–n>52
Answer:
n<-21
Step-by-step explanation:
31-n>52
-31 on both sides
-n>21
flip
n<-21
[tex]31-n > 52[/tex]
Simplify:
[tex]-n+31 > 52[/tex]
Subtract 31 from both sides:
[tex]-n+31-31 > 52-31[/tex]
[tex]-n > 21[/tex]
Divide both sides by -1:(to remove the negative from the variable)
[tex]\dfrac{-n}{-1} > \dfrac{21}{-1}[/tex]
Reverse the inequality sign since we are dividing by a negative number.
[tex]n < -21[/tex]
A pyramid with volume 40 cubic inches has a rectangular base. If the length of the base is doubled, the width tripled and the height increased by 50%, what is the volume of the new pyramid, in cubic inches
Answer:
[tex]26.666666667[/tex]
Step-by-step explanation:
To find the volume of a pyramid, you can use the formula:
Volume = (1/3) * base area * height
If the base is a rectangle, the base area is calculated by multiplying the length by the width.
Let's call the original length "L", the original width "W", and the original height "H".
The volume of the original pyramid is:
(1/3) * L * W * H = 40 cubic inches
If the length of the base is doubled, the new length is 2L.
The width is tripled, so the new width is 3W.
The height is increased by 50%, so the new height is 1.5H.
The volume of the new pyramid is:
(1/3) * (2L) * (3W) * (1.5H) = (2/3) * L * W * H = (2/3) * 40 cubic inches = 26.666666667 cubic inches.
So the volume of the new pyramid is approximately 26.666666667 cubic inches.
an arc of length 28cm subtend an angle of 24degree at the center of a circle in the same circle ,what angle does an arc of length 35cm subtend
By using the rule of 3 simple, we will see that the value of the angle of the arc is 30°.
How to get the angle for the arc of 35cm?
We know that an arc of 24 degrees has an arc length of 28cm, then we can write a relation:
24° = 28cm
(notice that it is just a relation so we can use the 3-simple-rule, that is not an equation, we only can do this because there is a linear relation between the angle and the length).
And for an angle x we have a length of 35cm, then we can write:
x = 35cm
Now we can take the quotient of these two equations to get:
x/24° = (35cm/28cm)
Solving for x:
x = (35cm/28cm)*24° = 30°
That is the angle of the arc.
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Buses and vans were hired during a field trip. Bowie HS hired 2 buses and 2 vans to accommodate 114 students while Duval HS hired a bus and 3 vans to accommodate 81 students. How many students can fit in each bus and each vans
The number of students that can fit in a bus and each van is 45 and 12 respectively
What is a simultaneous equation?You should know that when two equations are solved together in two variables, they are simultaneously solved.
The given parameters that can help us to get the number of students is
Bowie HS hired 2 buses and 2 vans to accommodate 114 studentsDuval HS hired a bus and 3 vans to accommodate 81 studentsThese can be expressed in equation form as follows
2x +2y = 114 .....................1
x + 3y = 81 .........................2
Making s the subject of the formular in equation 2
x=81-3y
substitute 81-3y in equation 1 to have
2(81-3y) + 2y = 114
162 -6y +2y = 114
-4y = 114-162
-4y = -48
Making y the subject of the relation we have
y = 48/4
y=12
= 12 vans
Recall that
x= 81-3y
Substitute 12 for y in the equation to have
x=81-3(12)
x=81-36
x=45
= 45 buses
In conclusion 45 buses and 12 vans will fit made available
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Which triangles could not be similar to triangle abc ? triangle a b c with right angle b. Side a b is 12 cm. Side b c is 5 cm. Side a c is 13 cm.
JKL triangles could not be similar to triangle abc if triangle a b c with right angle b. Side a b is 12 cm. Side b c is 5 cm. Side a c is 13 cm.
A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
This is because the lengths of each side JKL is a factor to ABC
respectively .
AB=12,JK=36
AC=13,JL=39
BC=5,KL=25
JKL triangles could not be similar to triangle abc if triangle a b c with right angle b. Side a b is 12 cm. Side b c is 5 cm. Side a c is 13 cm.
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Triangles that cannot be similar to triangle ABC are those that do not meet the necessary conditions for similarity, which are:
Corresponding angles are congruent
Corresponding side lengths are in proportion
Given the information provided, triangle ABC is a right triangle with a right angle at vertex B, and side lengths of 12 cm, 5 cm, and 13 cm.
A triangle with a right angle is already a special case of triangle, as the Pythagorean theorem must apply. Therefore any triangle that does not obey this theorem can not be similar.
So, any triangle that doesn't obey pythagorean theorem, not having the same angles or ratios of side lengths can't be similar to ABC triangle.
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Cambridge IGCSE Additional Mathematics O606 Paper 11 Q5,6.J
The normal to the curvey = x³ + 6x² -34x+44 at the point P(2, 8) cuts the x-axis at A and
the yaxis at B. Show that the mid-point of the line AB lies on the line 4y= x +9.
Cambridge IGCSE Additional Mathematics 0606 Paper 21 Q6 Nov 2012
[8]
SE CAMSTEUE
SITY PRESS
21
The midpoint of the line AB lies on the line 4y= x +9 is (-6, 248)
What are the coordinates of midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Let we've two endpoints of a line segment as A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2}\\y = \dfrac{q+n}{2}[/tex]
We are given that the normal to the curvey = x³ + 6x² -34x+44 at the point P(2, 8) cuts the x-axis at A and the yaxis at B.
y = x³ + 6x² -34x+44
dy/ dx = 3x² + 12x -34
Then the equation is
(y - 4) = -34(x - 0)
y + 34x = 44
So, -34x + 44 = x³ + 6x² -34x+44
x = 0
x = -6
Also, we d² y/ dx gives us 248
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What is the equivalent ratio to 3:8
Answer:
6 : 16, 12 : 32, 18 : 48 etc
Step-by-step explanation:
There are many equivalent ratios
3:8
3x2=6
8x2=16
so one ratio will be 6:16
Answer:
9:12
Step-by-step explanation:
...
A movie began at 3:12pm and ended at 5:10pm. Calculate the length of time the movie lasted (30 points
Melvin was given sh 1200 pocket money on openimg day. on the way to school she spent5/12 of the money. during a school outing she spent 1/4 of the remainder. on visiting day her father left her sh250. what fraction of the original pocket money did shehave after visiting day
Answer: 29/48
Step-by-step explanation:
If she spent 5/12 of 1200, she's left with 7/12 of 1200 which is 700. If she spends 1/4 of that, she has 3/4 of it left. 3/4 x 700 is 525. 525 + 250 is equal to 725. To simplify 725/1200, divide both sides by 25 to get 29/48.
How many is 7 sides?
A figure with 7 sides is a heptagon
A heptagon is a seven-sided shape. A heptagon is a closed object with straight lines and angles that is a type of polygon. (n-2) * 180 is the total number of angles in a heptagon, where n is the number of sides. There are 7-2 = 5 angles in a heptagon, each of which measures (180-2) = 128.57 degrees. Heptagons can be regular or irregular, with cyclic or dihedral symmetry groups.
It's also worth mentioning that the number of sides in a form is commonly referred to as its "order" in mathematics, hence a heptagon is often referred to as a "seven-gon."
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Find the area 11cm,14cm,9cm,20cm
Answer:
27720
Step-by-step explanation:
multiple all of them 11x14x9x20 = 27720
Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 8 inches, and the hole had side lengths of 5 inches, how much wood was left after the hole was cut out?
A diagram of cube shaped block of wood with a square shaped hole in the center.
Note: Figure is not drawn to scale.
A.
512 cubic inches
B.
387 cubic inches
C.
312 cubic inches
D.
39 cubic inches
Answer:
387 in³
Step-by-step explanation:
Volume of the solid 8" cube = 8³ = 512
The "empty space" volume of the 5" hole = 5³ = 125
Subtract the volume of the hole from the solid cube:
512 - 125 = 387 in³ (that's what is left)
Combining Like Terms to Simplify
Consider this
equation:x-9-2x+2=1
Which is an equivalent equation after combining like terms?
8
-11=1
8
-7=1
x-7=1
x-11=1
The equivalent equation after combining like terms is x-7=1. To solve this equation, simply add 7 to both sides of the equation and you will get x=8.
What is equivalent equation?An equivalent equation is an equation that is mathematically equal to another equation, meaning that both equations have the same solutions. For example, the equation "2x + 5 = 11" is equivalent to the equation "2x = 6". Both equations have the same solution, x = 3.
This is done by subtracting 2x from both sides, and then adding 9 to both sides. Doing so eliminates the -2x and -9 terms, leaving just x on one side, and 7 on the other. Combining like terms is a useful way to simplify equations, and it is important to understand how to do it in order to solve more complex equations.
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find the solution of the given initial value problem. y' − y = 3te2t, y(0) = 1
The solution to the initial value problem is y(t) = (3/2)te^(2t) + e^(-t) + 1.
To find the solution to the initial value problem, we need to first find the general solution to the differential equation. To do this, we can use the method of integrating factors. We can find the integrating factor is e^∫p(t)dt = e^t, multiplying both sides by it, we get e^ty' - e^ty = 3te^(t+1). Integrating both sides with respect to t, we get e^t*y = (3/2)te^(2t) + C. Solving for y, we get y(t) = (3/2)te^(2t) + Ce^(-t).
Next, we use the initial condition to find the value of C. We know that y(0) = 1, substitute this into the general solution, and we get 1 = (3/2)0e^(2*0) + Ce^(0) = C.
Therefore, the solution to the initial value problem is y(t) = (3/2)te^(2t) + e^(-t) + 1.
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what is the slope of y=14.25x
The equation you put is in slope-intercept form (y = mx + b).
m = slope, so 14.25 would be the slope.
Hope this helps.
Answer;
14.25
Step-by-step explanation;
Well take a look at what is right before x that is meant to tell you the slope when the equation is in y = mx+c form, which it is right here , y=14.25x is in y=mx+c form but c=0 .
hence m = 14.251 1/2 divided by 2 2/3
CAN SOMEONE PLEASE HELP ME
Answer : 9/16
so sorry if I’m wrong
if you are paid $27 per hour in your job how much will you get for working 6 hours per day for 15 days?