vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
Midpoint :
The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
x= x1+x2/2
y=y1+y2/2
Now ,
D(7,3) is the midpoint of AB.
D (x',y') = (7,3)
vertex of A = (x1,y1)
vertex of B = (x2,y2)
x' = x1+x2/2
7 = x1+x2/2
14 = x1+x2 ...1
y' = y1+y2/2
3= y1+y2/2
6= y1+y2 .....2
E (x'',y'') = (10,4)
vertex of c = (x3,y3)
vertex of B = (x2,y2)
x''= x3+x2/2
y''=y3+y2/2
20= x3+x2 ....3
8 =y3+y2.......4
F (x''',y''') = (5,5)
vertex of c = (x3,y3)
vertex of A = (x1,y1)
10= x1 +x3 ...5
10 =y1+y3 .....6
For 1 & 3 & 5
14 = x1+x2 ...1
20= x3+x2 ....3
10= x1 +x3 ...5
Add all 1 & 3 & 5
44 = 2(x1+x2+x3)
22 = (x1+x2+x3) .....7
For 1 & 7
x3 = 8
For 3 & 7
x1 = 2
For 5&7
x2 = 12
For 2 , 4 & 6
6= y1+y2 .....2
8 =y3+y2.......4
10 =y1+y3 .....6
Add all 2 & 4 & 6
24 = 2 (y1+y2+y3)
For 2 & 8
y3 = 6
For 4 & 8
y1 = 4
For 6 & 8
y2 = 2
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
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D
Do you agree or disagree? Explain your thinking.
The 5th graders set up 20 rows of chairs with 25 chairs in
each row for the assembly. Mrs. Lord asked if they'd set
up enough chairs for all 552 students. Kamil said he could
skip-count to find out how many chairs there were in all,
and then they'd know if they had enough.
Answer:
Step-by-step explanation:
Bill Murray has 16 3/4 days of vacation per year. To date, he has taken 1 3/4 days in January, 4 2/3 days in February, and 2 1/6 days in March. How much more vacation time is Bill entitled to?
Step-by-step explanation:
16 3/4 days in total.
that are (16×4 + 3)/4 = 67/4 days.
he has taken
1 3/4 = (1×4 + 3)/4 = 7/4 days
4 2/3 = (4×3 + 2)/3 = 14/3 days
2 1/6 = (2×6 + 1) = 13/6 days
to be able to add abd subtract them directly, we need to bring all fractions to the same denominator.
we have 3, 4, 6 : the smallest common multiple is 12 (can be divided without remainder by 3, 4 and 6).
we need to multiply each fraction by a fitting n/n factor to bring the denominators to 12 and keep the overall value of the fraction unchanged.
67/4 = 67/4 × 3/3 = 201/12
7/4 = 7/4 × 3/3 = 21/12
14/3 = 14/3 × 4/4 = 56/12
13/6 = 13/6 × 2/2 = 26/12
the remaining vacation time is
201/12 - 21/12 - 56/12 - 26/12 = 98/12 = 49/6
49/6 = 8 and remainder 1 = (8×6 + 1)/6 = 8 1/6 days
log_(4)9x^(2)=log_(2)(5x-8). Solve for x
The value of x in the logarithm equation log₄(9x²) = log₂(5x - 8) is x = 4
How to solve for x in the equation?The equation is given as
log₄(9x²) = log₂(5x - 8)
Apply the change of base law of logarithm
So, we have
log(9x²)/log(4) = log₂(5x - 8)
Express 4 s 2^2 and 9 as 3^2
So, we have
log(3x)²/log(2²) = log₂(5x - 8)
Apply the power law of logarithm
So, we have
2log(3x)/2log(2) = log₂(5x - 8)
Evaluate the quotient
So, we have
log(3x)/log(2) = log₂(5x - 8)
Apply the change of base law of logarithm
So, we have
log₂(3x) = log₂(5x - 8)
Cancel out the common base
So, we have
3x = 5x - 8
Collect the like terms
So, we have
3x - 5x = - 8
Evaluate the like terms
So, we have
-2x = - 8
Divide both sides by -2
So, we have
x = 4
Hence, the value of x in the logarithm equation log₄(9x²) = log₂(5x - 8) is x = 4
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lots of points pls answer
The correct answer is D. the x- intercept of the given graph is (-1.75,0) and y - intercept is (0,3)
What is x - intercept and y - intercepts?
The x-intercept is the location where a line's graph crosses the x-axis.
The y-intercept is the location where a line's graph crosses the y-axis.
The shapes of these points are (x,0) and (0,y), respectively.
Utilize the fact that all x-intercepts have a y-value of zero and all y-intercepts have an x-value of zero to get the x- and y-intercepts algebraically. Set x=0 and find the equivalent y value to calculate the y -intercept. Set y=0 and then figure out the matching x value to discover the x -intercept.
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A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assuming a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 50 mg, calculate the margin of error for a 95% confidence interval assuming the previous study enrolled 600 individuals.
a. E = ± 4.19
b. E = ± 63.57
c. E = ± 4.00
d. E = ± 0.27
The margin of error for a 95% confidence interval assuming the previous study enrolled 600 individuals is C . E = ± 4.00
How to calculate the value?Based on the information, the following can be deduced:
n = 600
mean = 490.
standard deviation = 50.
At 95% confidence interval, z will be:
= 1 - 95%
= 0.05
Using the distribution table, the value will be Z(0.05/2) = Z value of 0.025 = 1.96
Therefore, the margin of error for a 95% confidence interval assuming the previous study enrolled 600 individuals will be:
= ± 1.96 × 50/✓n
= ± 4.00
In conclusion, the correct option is C.
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Which expression is equivalent to (18)2⋅(19)2
The expression that is equivalent to the given expression where the expression is given as (18)2⋅(19)2 is (18 * 19)^2
How to determine which expression is equivalent to the given expression?The expression is given as
(18)2⋅(19)2
Rewrite the above expression properly
So, we have
(18)^2 * (19)^2
The factors in the above expression have the same exponent.
So, the expression can be rewritten as
(18 * 19)^2
Hence, the expression that is equivalent to the given expression where the expression is given as (18)2⋅(19)2 is (18 * 19)^2
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Can you guys help me solve this
Step-by-step explanation:
so, first $300 must be paid without any ifs and whens.
for the rest of the amount the insurance will cover 70%.
the bills total to
700 + 930 = $1630
he must pay $300 of that directly.
that leaves 1630 - 300 = $1330 for the 70/30 split between insurance and patient.
the patient must pay 30% of these $1330.
100% = 1330
1% = 100%/100 = 1330/100 = $13.30
30% = 1% × 30 = 13.30 × 30 = $399
so, the patient pays
300 + 399 = $699
of the $1630 bill.
if the hypotenus of a right triangle is 6 m and one side is 4 m, what's the length of the other side
Answer:
[tex]\sqrt{20} \text{ or } 2\sqrt{5}[/tex]
Step-by-step explanation:
So in this question we want to use the Pythagorean Theorem which essentially gives us a relationship between the sides of a triangle and is as follows: [tex]a^2+b^2=c^2[/tex]
In this formula the "a" and "b" represent the base and the height and "c" represents the hypotenuse of the triangle
The order in which you assign "a" and "b" do not matter, so let's just say that: [tex]a=4\ \text{and}\ c=6[/tex]
Although it is important that you assign the hypotenuse to "c".
So plugging in known values we have the equation:
[tex]4^2 +b^2=6^2[/tex]
Square the values
[tex]16+b^2=36[/tex]
Subtract1 16 from both sides
[tex]b^2=20[/tex]
take the square root of both sides
[tex]b=\sqrt{20}[/tex]
This "b" represents our other side, which we did not initially know, so this is our answer :)
You can simplify this further by separating the radical into: [tex]\sqrt{20} = \sqrt{4} * \sqrt{5} = 2\sqrt{5}[/tex]
Having a spot of difficulty after re-watching the main video a few times. I followed his example but the answer I got was 2 (yay...). I would appreciate the help!
Using it's formula, the variance of the data-set is of 15 units squared.
What are the mean and the variance of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set.For this problem, the mean is given by:
Mean = (3 + 4 + 5 + 7 + 10 + 12 + 15)/7 = 8.
Hence the variance is given as follows:
Variance = 1/8 x [(3-8)² + (4-8)² + (5-8)² + (7-8)² + (10-8)² + (12-8)² + (15-8)²] = 15.
Hence the variance of the data-set is of 15 units squared.
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Determine ratio of A to B. Round as indicated.
A = 24.7% is the divorce rate in City A
B = 28.7% is the divorce rate in City B
(Round to the nearest hundredth when necessary.)
Select one:
O a. 0.09
O b. 8.61
OC. 0.86
O d. 1.16
Answer:
C
Step-by-step explanation:
The highest naturally occurring recorded temperature on earth is 134
degrees Fahrenheit. The lowest naturally occurring recorded temperature on
earth is 129 degrees Fahrenheit below zero. What is the difference between
these two temperatures?
Solve y+1/2-2y-1/3=4
Answer:
y=-23/6
Step-by-step explanation:
Answer:
y=-26
Step-by-step explanation:
multiply each side by 3
Y+1/2-2y-3=12
Multiply each side by 2
Y+1-2y-3=24
Add 3 to each side
Y+1-2y=27
Subtract each side by 1
Y-2y=26
-y=26
Multiply each side by -1
Y=-26
The side of the triangle are measured correct to the nearest cm. Work out the maximum possible perimeter of the triangle.
The maximum possible perimeter of the triangle 25cm.
What is perimeter of a triangle?
The length of all a triangle's sides added together yields the perimeter of a triangle.
How to calculate the perimeter of a triangle?
Add the lengths of the triangle's sides to determine its perimeter. For instance, the perimeter of a triangle with sides a, b, and c is P = a + b + c.
Given the lengths of sides of triangle are 7cm, 8cm, and 10cm.
The perimeter of the triangle is 7 + 8 + 10 = 25cm
Therefore, the maximum possible perimeter of the triangle 25cm.
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Two inequalities are graphed on the same coordinate plane. Which region represents the solution to the system of two inequalities?
The region that represents the solution to the system of two inequalities would be Region A.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Since x≥0 and y≥0 at every point in the shaded region in the first quadrant represent a solution of the given system of inequalities
Since, the system of two inequalities are strict then in graph lines drawn is dotted line as point on line does not includes in the inequality.
The region that represents the solution to the system of two inequalities would be Region A; because the shaded regions are not required.
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how do I write in slope-intercept form the points (-3, 0); slope=2/3
The equation of line can be written as, y = 2/3x + 2
Given,
The points, (x, y) = (-3, 0)
Slope = 2/3
Equation of a line, y = mx + c
Where, m is the slope and c is the y-intercept.
Here, m is 2/3.
The point at the x-intercept has co-ordinates : (-3, 0)
Where, x is -3 and y is 0.
So, substitute the values in equation:
y = mx + c
0 = 2/3 × (-3) + c
0 = -2 + c
c = 2
Therefore, the equation of line will be:
y = 2/3x + 2.
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Please help this has to be done tomorrow
The surface area of the right rectangular prism is 398 square meters
How to determine the surface area of the right rectangular prism?The net of the right rectangular prism is the given parameter
On the net of the right rectangular prism, we have the following values
Length, l = 11 m
Width, w = 9 m
Height, h = 5 m
The surface area of the right rectangular prism is calculated using
Surface area = 2 * (l * w + l * h + w * h)
So, we have
Surface area = 2 * (11 * 9 + 11 * 5 + 9 * 5)
Evaluate the sum of products
So, we have
Surface area = 2 * 199
Evaluate the products
So, we have
Surface area = 398
Hence, the surface area of the right rectangular prism is 398 square meters
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PLS HELP 50 POINTS!!!
A large downtown hotel consists of twenty-four levels. Any level above ground is referred to as a" floor". There are twenty-two floors and each floor corresponds to its number on the number line (2 is second floor, 3 is third floor, etc...) and two underground levels reserved for underground parking. The first level below ground level is Parking A, and the second level below ground level is labeled Parking B.
If each above ground level floor corresponds with its floor number on the number line, what number on the number line represents Parking A? [Type your answer as a number.]
Answer:
-1
Step-by-step explanation:
Assuming "ground level" is 0, then the one below it (parking level A) would be -1.
Line segment is reflected about the y-axis to form C’D’. Which is statement describes C’D’?
The statement that describes C’D’ is (d) C'D' and CD are equal in length.
How to determine the statement that describes C’D’?The complete question is added as an attachment
The statement is given as:
A reflection of CD about the y-axis to form C’D’
When a line is reflection, the line segment of the image and pre-image are congruent
This is so because the reflection transformation is a rigid transformation
Hence. the statement that describes C’D’ is (d) C'D' and CD are equal in length.
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Complete question
The line segment is reflected about the y-axis to form C'D'. Which statement describes C'D'?
C'D' is perpendicular to CD.
C'D' is half the length of CD.
C'D' is greater than twice the length of CD.
C'D' and CD are equal in length.
If the parent function f(x) = |x| is transformed to g(x) = |x + 5|, what transformation occurs from f(x) to g(x)?
The transformation that occurs from f(x) to g(x) is the graph of f(x) is shifted to the left to create g(x).
What transformation occurs from f(x) to g(x)?The equations of the functions are given as
f(x) = |x|
g(x) = |x + 3|
The above implies that
g(x) = f(x + 3)
When a function is shifted to the left by h units, it is represented as
g(x) = f(x + h)
This means that
h = 3
So, the transformation that occurs from f(x) to g(x) is the graph of f(x) is shifted to the left to create g(x).
Hence, the required transformation that occurs from f(x) to g(x) is the graph of f(x) is shifted to the left to create g(x).
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How many of mrs. Lynch’s students prefer cheese pizza?
Step-by-step explanation:
100 nsmzmsmsmsmsmsmsnsnnsnsbsnjsjjsjsjsj
The table shows pricing information for two pizzas. How many toppings would
number 13 only
The number of toppings where the cost of each pizza would be equal is 5.
How many toppings would make the pizza equal?The first step is to formulate an equation that represents the cost of each type of pizza.
Total cost = price of cheese pizza + (price per topping x number of toppings)
Cost of pizza A = $10 + $1.50t
Cost of pizza B = $12.50 + t
When the cost of both pizzas are equal, the above equations would be equal to each other.
$10 + $1.50t = $12.50 + t
To determine the value of t, take the following steps:
Combine similar terms: 1.50t - t = $12.50 - $10
Add similar terms = 0.50t = 2,50
Divide both sides by 0.50 = t = 2.50 / 0.50
t = 5
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For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
56,18
Answer:
74
Step-by-step explanation:
(74)-18=56
74 subtracted from 18 gives 56
4/9 divided by what makes 12
Un ganadero tiene tiempo suficiente para alimentar 220 vacas durante 45 días. ¿cuántos días podrá alimentar con la misma cantidad de tiempo a 450 vacas?
Answer:
112.5
Step-by-step explanation:
450(45/220) = 450/4 = 112.5
9 less than 18 times a number x
Answer: 18x- 9
Step-by-step explanation:
1.) Put the numbers in their correct lineup. 18 * x - 9
2. Add parentheses around 18 * x, secluding them away from the -9.
(18 * x) -9
3.) Remind yourself of PEMDAS (Parentheses, Exponents, Multiplication, Division, Add, and Subtract). In this equation, 18 * x are in parentheses().
(18 * x)
4.) Multiply 18 * x... Which equals 18x.
5. Equation should now look like : 18x - 9
6. You can't combine those two numbers because the coefficiant (The coefficiant is 18.) and the regular number (-9) are not equal.
8. Answer : 18x-9
Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
A furniture store has a sale offering 10% off of all furniture. If Amanda spent $459.99 on furniture before tax, what was the price of the furniture she purchased before the discount and before tax?
Answer:
0.9x=459.99, $511.10
Step-by-step explanation:
If the original cost was x, the cost after the discount is 0.9x.
[tex]0.9x=459.99 \\ \\ x=\frac{459.09}{0.9}=511.10[/tex]
Find the digit in each indicated place value in the number 6,048,230,157 .
The digit in each indicated place value in the number 6,048,230,157 are as follows:
6 = ones.0 = tens.4 = hundreds.8 = thousands.2 = tens of thousands.3 = hundred of thousands.0 = millions.1 = tens of millions.5 = hundreds of millions.7 = billions.What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.Read more on place value here: https://brainly.com/question/569339
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Neva writes the following in her math notebook.
A right rectangular prisum has 6 rectangular faces.
I disagree with Neva's conclusion about the rectangular prism
How to determine the true statement?The complete question is added as an attachment
From the question, we have the following statements:
The points where the faces of a rectangular prism meet are called the vertex
Truly, a rectangular prism has 6 faces.
However, the vertices in the rectangular prism is just 8
Hence, I disagree with Neva's conclusion about the rectangular prism
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f(x) =|x| y-axis 3 units right
Answer:
f(x)/y = |x - 3| y
Step-by-step explanation:
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=-5. The y-intercept is y=-6
Find the formula for p(x)
P(x)=
the formula for the polynomial is:
p(x) = (-3/10)*(x - 2)^2*(x + 5)
How to find the formula for p(x)?Here we have a polynomial with the following roots:
x = 2, with a multiplicity of 2.x = -5 with a multiplicity of 1.So, if we define A as the leading coefficient, we can write the polynomial as:
p(x) = A*(x - 2)^2*(x + 5)
We know that the y-intercept is -6, so evaluating in x = 0 we should get:
p(0) = -6 = A*(0 - 2)^2*(0 + 5) = A*4*5 = A*20
-6/20 = A = -3/10
Then the formula for the polynomial is:
p(x) = (-3/10)*(x - 2)^2*(x + 5).
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