Pythagorus' theorem, explain why the length of AC is 17 cm
Answer:
see below.
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]8^{2}[/tex] + [tex]15^{2}[/tex] = [tex]c^{2}[/tex]
64 + 225 = [tex]c^{2}[/tex]
289 = [tex]c^{2}[/tex]
[tex]\sqrt{289}[/tex] = [tex]\sqrt{c^{2} }[/tex]
17 = c
HELP ME PLEASE!!!!!!!!!!!!!!!!!
The figure shows three quadrilaterals on a coordinate grid: A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled A is shown on ordered pair 1, 1 and 3, 1 and 3, 2 and 1, 2. Another image of a rectangle labeled B is shown on ordered pair 2, 2 and 6, 2 and 6, 4 and 2, 4. Another image of a rectangle labeled C is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3 , 2 and negative 3, 1. Which of the following statements is true about the three quadrilaterals? (5 points) A and B are similar but not congruent. A and C are similar but not congruent. A and B are similar and also congruent. B and C are similar and also congruent.
Answer:
(a) A and B are similar but not congruent
Step-by-step explanation:
All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.
find the value of 3x-2 when x=4
find the value of 5x+6 when x=-2
Answer:
3(4) - 2 is 10 the value is 10
5(2) + 6 is 16 the value is 16
I hope this helps have a good day or night!
ABCD with vertices B (2,1), C (2,5), and D (6,1) has its orthocenter at which point?
A. (0,0)
B. (2,1)
C. (2,5)
D. (6,1)
Step-by-step explanation:
d is the answer as far as I can tell from a little experience
which of the following are examples of performance measures that should be considered when designing a queue? (there might be more than one correct answer) a. probability that the waiting time exceeds t minutes (e.g. t can be 10 minutes) b. probability that servers are busy more than t minutes (e.g. t can be 10 minutes) c. average
All of the following are examples of performance measures that should be considered when designing a queue.
There are several performance measures that should be considered when designing a queue, including:
a. Probability that the waiting time exceeds t minutes (e.g. t can be 10 minutes): This measure can be used to assess the likelihood that customers will have to wait longer than a certain amount of time before being served. A high probability of long waiting times may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.
b. Probability that servers are busy more than t minutes (e.g. t can be 10 minutes): This measure can be used to assess the likelihood that servers will be occupied for longer than a certain amount of time. A high probability of busy servers may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.
c. Average waiting time: This measure can be used to assess the average amount of time that customers spend waiting in the queue before being served. A high average waiting time may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.
Other performance measures that may be considered when designing a queue include the average number of customers in the queue, the average time that servers spend serving customers, and the probability that customers will leave the queue without being served.
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(COMBINING LIKE TERMS)
Classrooms on one side of the drama building are all numbered with consecutive odd integers. If the first room, the room with the smallest classroom number, on this side of the building is numbered x, write an expression in x for the sum of the first seven classroom numbers in a row. Then simplify this expression.
7k+42 is the result of adding the first five classroom numbers in a row.
What are consecutive integers?These integers that follow one another in a predictable counting pattern are referred to as consecutive integers. Due to the fact that no numbers are skipped while listing consecutive integers in a sequence, the distance between them is always fixed.
The smallest classroom number on the building's side is k, and there are two spaces between each succeeding odd number.
The first classroom is K.
The second classroom is k + 2.
The third classroom is k + 4.
The third classroom is k + 6.
The fifth classroom is k + 8.
The sixth classroom is k+10.
The seventh classroom is k+12.
The seven classrooms are added together as follows: k + (k + 2) + (k + 4) + (k + 6) + (k + 8)+(k+10)+(k+12)
When we combine terms that are similar,
we obtain,
k + k + k + k + k+ 2 + 4 + 6 + 8+10+12 = 7k+42.
Therefore, 7k+42 is the result of adding the first five classroom numbers in a row.
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A triangle has vertices (0,0), (2,4), and (5,1). What are the coordinates of the circumcenter?
I need steps pls
For the given triangle the coordinate of circumcenter is obtained as (1/3, 7/3).
What is circumcenter of a triangle?The circumcenter for a triangle is defined as the center of the circle that touches all the vertices of the triangle. It is also found as the point of intersection of all of the perpendicular bisectors of the sides of triangle. All the vertices of the triangle are equidistant from the circumcenter.
Suppose the coordinate of the circumcenter be (x, y).
Now, all the vertices of the triangle should be equidistant from the circumcenter.
The equation can be written using distance formula as follows,
(x - 0)² + (y - 0)² = (x - 2)² + (y - 4)²
⇒ 4x + 8y = 20
⇒ x + 2y = 5 (1)
And, (x - 0)² + (y - 0)² = (x - 5)² + (y - 1)²
⇒ 10x + 2y = 26
⇒ 5x + y = 13 (2)
Multiply equation (2) by 2 nd then subtract equation (1) to get,
2(5x + y) - (x + 2y) = 13 × 2 - 5
⇒ 9y = 21
⇒ y = 7/3
Substitute y = 7/3 in equation (1) to get,
x + 2 × 7/3 = 5
⇒ x = 5 - 14/3
⇒ x = 1/3
Hence, the coordinate of the circumcenter is given as (1/3, 7/3).
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Write the simplest polynomial function with the given root: -5, square root of 2, and -3i.
The needed 3rd-degree polynomial function with real coefficients matching the specified constraints will be y=-5x³+10x²-45x+90.
What is polynomial?A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial.
Here,
y=-5(x-2)(x-3i)(x+3i)
y=-5(x-2)(x²+9)
y=-5(x³-2x²+9x-18)
y=-5x³+10x²-45x+90
The required 3rd-degree polynomial function with real coefficients satisfying the given conditions will be y=-5x³+10x²-45x+90.
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A customer paid a total of $6.00 for 68 copies at a print shop. Some copies were black and white copies, the rest were color copies.
• each black and white copy cost $0.08
• each color copy cost $0.15
Which system of equations can be used to find b, the number of black and white copies and c, the number of color copies that the customer paid for at the print shop?
Answer:
D. b + c = 68
0.08b + 0.15c = 6.00
Step-by-step explanation:
The total cost is $6.00
The total amount of copies is 68
To find the total cost, we multiply the amount of copies by the individual price. So we get
0.08b + 0.15c = 6.00
We add the amount of copies bought to get a total of 68, so we get this equation:
b + 6 = 68
1.You have one full pizza, out of which your friend eat one-hundredths six
times from it. There is some part of the pizza left for you. How much you will
get to eat?
Answer:
there will be only 1 more slice to eat
Four integers have a mean of 8, a median of 6, a mode of 6 and a range of 14
Find the four integers
Answer:
Step-by-step explanation:
Let's call the four integers x, y, z, and w. We know that the mean of these four integers is 8, so:
x + y + z + w = 8 * 4 = 32
We also know that the median of these four integers is 6, which means that two of the integers are less than 6 and two are greater than 6. The mode of 6 means that one of the integers is 6.
Let's assume that x and y are the two integers that are less than 6. This means that z and w are the two integers that are greater than 6. We can then set up the following system of equations to represent this information:
x + y + z + w = 32
x + y < 12
z + w > 12
We also know that the range of these four integers is 14, which is the difference between the largest and smallest integers. Since z and w are the two largest integers, the range is equal to w - x. We can set up another equation to represent this information:
w - x = 14
We can solve this system of equations using substitution. First, we can solve the second equation for x:
x = 12 - y
We can then substitute this expression for x in the third equation to get:
w - (12 - y) = 14
w = 14 + y
Finally, we can substitute this expression for w in the first equation to get:
x + y + z + (14 + y) = 32
x + 2y + z = 18
We can then substitute the expression for x in the third equation to get:
(12 - y) + 2y + z = 18
-y + 2y + z = 18
z = 18 - y
We can then substitute this expression for z in the third equation to get:
w = 14 + y = 14 + (18 - z) = 14 + 18 - y = 32 - y
Substituting this expression for w in the first equation gives us:
x + y + z + (32 - y) = 32
x + 2y + z = 32
We can then substitute the expressions for x and z in the third equation to get:
(12 - y) + 2y + (18 - y) = 32
-y + 2y + 18 - y = 32
18 = 32
This equation is clearly not true, so the original assumptions we made about which integers were less than 6 and which were greater than 6 must be incorrect.
However, we can use a similar process to solve for the other possibility: that x and z are the two integers that are less than 6, and y and w are the two integers that are greater than 6.
In this case, we can set up the following system of equations:
x + y + z + w = 32
x + z < 12
y + w > 12
w - x = 14
Solving this system of equations using substitution gives us the solution x = 4, y = 10, z = 6, and w = 8.
Therefore, the four integers are 4, 6, 8, and 10.
equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven
Answer:
management accountant prepared a decision model which solve sell at split off or process
further decision problem. Which function did he provided?
A. Scorekeeping function C) Problem solving function
B. Attention directing function. D) Record keeping function E) None
the sum of the measures of the interior angles of a convex polygon is eight times the sum of the measures of its exterior angles. find the number of sides of the polygon
Interior angle-
All interior angles of a regular polygon are equal. The formula for calculating the magnitude of the interior angle is:
Interior angle of polygon = sum of interior angles ÷ number of sides. The sum of the exterior angles of a polygon is 360°.
Exterior angle-
An exterior angle is an angle that is parallel to, but outside, the interior angle of a polygon. The exterior angle measurement is equal to the sum of the two opposite interior angles.
according to the question,
given data
interior angle=8 exterior angle
we know that,
interior angle+ exterior angle=180
let us consider ,
exterior angle=x
so we can say that,
8 exterior angle + exterior angle =180
8x+x=180
9x=180
x=20
we know that ,
the number of sides=360/x
=360/20
=36/2
=18
the number of sides of the polygon is 18
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Anton mows two lawns. The first lawn is 8 feet long and 5 feet wide. The second lawn has the same length, and width that is 4 times the first one. What is the total area of the two lawns?
The total area of the two lawns is 200 ft²
What is Area?Area is the region occupied by an object.
What is the total area of the two lawns?Since Anton mows two lawns. The first lawn is 8 feet long and 5 feet wide. The second lawn has the same length, and width that is 4 times the first one, since the lawns are rectangles, their area is the area of a rectangle.
What is the area of a rectangle?The area of a rectangle is given by
A = LW where
L = length of rectangle and W = width of rectangle.Given that for the first lawn it is 8 feet long and 5 feet wide, we have that
L = 8 ft and W = 5 ftSo, its area A = LW
= 8 ft × 5 ft
= 40 ft²
Also, for the second lawn, the same length, and width that is 4 times the first one. So, we have that
L' = 8 ft and W' = 4W = 4 × 5 ft = 20 ftSo, its area A' = L'W'
= 8 ft × 20 ft
= 160 ft²
So, the total area of the two lawns is A" = A + A'
= 40 ft² + 160 ft²
= 200 ft²
So, the total area is 200 ft²
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Divide. 1585 ÷ 24 Write your answer as a mixed number.
Answer: 66 1/24
Step-by-step explanation:
SOS 50 PTS!
Use a coordinate proof to show that the diagonals of a rectangle are congruent
The diagonals of rectangle are congruent.
How to show congruent diagonals?
We should know that a rectangle is a plane shape with four sides, four vertices and four angles.
Using a rectangle with the lettering ABCD
The diagonal AC divide the rectangle into two right angled triangles
<ADC = 90⁰
In the rectangle, AD=BC and AB=CD
Also, The same diagonal AC has another right angled triangle ABC with <ABC=90⁰
Similarly, diagonal BD divides the rectangle into two right angled triangles of ΔBAD and ΔBCD with a common hypothenuse of BD
Hence AB=CD and AD= BC
Therefore, the two diagonals are congruent
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What is the simplified form of this expression? 15 – 10 (92 – 8 ×5 4) – 6
-8x < 32
Do what on both sides and change or keep the inequality sign?
See picture please
The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4
The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.
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Mr. Frankel bought 5 tickets to a puppet show and spent $28. He bought a combination of child tickets for $2 each and adult tickets for $8 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?
PLEASE HELP ASAP ASAP ASAP
Answer: He bought three adult tickets and two child tickets
Step-by-step explanation:
The answer is 28$
2+2= 4
8+8= 16
16 + 4= 20
20 + 8 =28
He bought two child tickets and three adult tickets
PLS HELP ME I NEED IT I PUT A PICTURE
Answer: <D, < E, <C
Step-by-step explanation:
Print Prince is a printing company that charges a $14.95 set-up fee and $0.03 per copy to print brochures. Emilio is charged $32.20 to print brochures that will be distributed to promote the annual science fair. Write an equation then solve
Hello,
I hope you and your family are doing well!
To solve this problem, we can use the formula:
total cost = set-up fee + (cost per copy * number of copies)
In this case, we know the total cost and the set-up fee, and we want to find the number of copies. We can substitute these values into the formula and solve for the number of copies:
$32.20 = $14.95 + ($0.03/copy * number of copies)
Subtracting the set-up fee from both sides of the equation gives:
$17.25 = $0.03/copy * number of copies
Dividing both sides of the equation by the cost per copy gives:
number of copies = $17.25 / $0.03/copy = 575 copies
So Emilio was charged $32.20 to print 575 copies of the brochures.
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Happy Holidays!
Point B has coordinates (5,2). The x-coordinate of point A is -3. The distance between point A and point B is 10 units. What are the possible coordinates of point A?
Answer:
The possible coordinates of point A are (-3, 8) and (-3, -4).
Step-by-step explanation:
We can find the possible coordinates of point A by using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2-x1)^2 + (y2-y1)^2. We know that the x-coordinate of point A is -3 and the distance between point A and point B is 10 units. We can use this information to solve for the y-coordinate of point A:
Copy code
d = sqrt((x2-x1)^2 + (y2-y1)^2)
d = sqrt((5-(-3))^2 + (2-y1)^2)
d = sqrt(8^2 + (2-y1)^2)
d = sqrt(64 + (2-y1)^2)
d = sqrt(64 + (y1-2)^2)
d = 10
sqrt(64 + (y1-2)^2) = 10
64 + (y1-2)^2 = 100
(y1-2)^2 = 36
y1-2 = +/- 6
y1 = 8 or -4
Therefore, the possible coordinates of point A are (-3, 8) and (-3, -4).
The following figure was drawn using a straightedge and a compass. Where was the point of the compass located in order to make the arcs?
1. points X and Y
2. point D
3. point C
4. points A and B
The point of the compass located in order to make the arcs is points X and Y.
Define arc.An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.
Given
The following figure was drawn using a straightedge and a compass.
The point of the compass located in order to make the arcs:
1. points X and Y
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Write an equation and use it to solve for x.
The value of the x would be 9.
Option (A) is correct.
What is a complementary angle?
A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.
Angle JKM and angle MKN are complementary angles
so
(3x + 2) + (6x + 7) = 90
9x + 9 = 90
9(x + 1) = 90
x + 1 = 10
x = 9
Hence, the value of the x would be 9.
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After solving the equation the value of the x would be 9. Therefore, the correct option is A.
What is a complementary angle?
A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.
Angle JKM and angle MKN are complementary angles
so (3x + 2) + (6x + 7) = 90
9x + 9 = 90
9(x + 1) = 90
x + 1 = 10
x = 9
Hence, the value of the x would be 9.
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bob has a total of 17 quarters and nickels. If the total value of the coins is $1.85, write the system of equations that could help him find the number of quarters
First, identify the variables:
n = amount of nickels
d = amount of dimes
Next, setup the equations based on what you know. The first equation is:
n + d = 28
For the second equation, we know that a dime is worth 10¢ and a nickel is 5¢, so it should be:
0.05n + 0.10d = 1.95
This a three-step answer:
In one formula (you can use any of them; most people use the simplest one), single out the variable on one side
Apply the first formula into the second formula, and solve it to get the value of one variable
Apply the answer from the second formula into the first formula, and solve it to get the value of the other variable
If f(x)=-x+6 and g(x)=-x^2-2x+8, the solutions to the equation f(x)=g(x) are x= and x=
The solution to the equation f(x)=g(x) are x=-2 and x=1.
What is solution to an equation?The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.
Now, f(x)=g(x)
-x+6=-x²-2x+8
⇒ x²+x-2=0
⇒ x²+2x-x-2=0 (Splitting middle term method)
⇒ x(x+2)-1(x+2)=0
⇒ (x+2)(x-1)=0
⇒ x+2=0 and x-1=0
⇒ x=-2 and x=1
Therefore, the solution for the obtained equation are x=-2 and x=1.
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2(2x-20)= -12
6x-20= -12
6x=8
X=8
_
6
Find the mistake
Answer:
The mistake was made when we rewrote the equation wrong after dividing 2 to both sides
Step-by-step explanation:
After we divide two on both sides the equation should have been rewriting as [tex]2x-20=-6[/tex] not [tex]6x-20=-12[/tex]
Help me !!??!!!????please
What is (x + 3)(x - 5) in generic rectangle
the area of the generic rectangle will be x²-2x-15.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.
Area of rectangle is A = a*b
(x + 3)(x - 5) in a generic rectangle
The product will give the area
x²-2x-15
hence the area of the generic rectangle will be x²-2x-15.
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The price of a pair of shoes after 8% sales tax was added was $77.76. Find the original price before sales tax
Answer: $71.53
Step-by-step explanation:
77.76 = 100%
