AB and DC are parallel to each other and both are perpendicular to AD. So the quadrilateral is a right angled trapezoid. Hope this helps! :)
Final answer:
The given quadrilateral cannot be classified into a specific type.
Explanation:
The given quadrilateral has vertices with coordinates (-3,1), (0,3), (5,2), and (-1,-2). To determine the type of quadrilateral, we can find the slopes of the opposite sides. If the slopes are equal, the quadrilateral is a parallelogram. If the slopes are perpendicular, the quadrilateral is a rectangle. If both conditions are satisfied (equal slopes and perpendicular slopes), then the quadrilateral is a square.
Using the formula for slope between two points, we find:
Slope of the first side: (-3,1) to (0,3) -> m1 = (3 - 1) / (0 - (-3)) = 2/3
Slope of the second side: (-1,-2) to (-3,1) -> m2 = (1 - (-2)) / (-3 - (-1)) = 3/2
Slope of the third side: (-3,1) to (5,2) -> m3 = (2 - 1) / (5 - (-3)) = 1/8
Slope of the fourth side: (0,3) to (5,2) -> m4 = (2 - 3) / (5 - 0) = -1/5
Since the slopes of opposite sides are neither equal nor perpendicular, the given quadrilateral is neither a parallelogram, rectangle, nor a square. Therefore, the type of quadrilateral cannot be determined.
Use a half-angle identity to find the exact solution of cos 3 pi / 8
Answer:
-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
Step-by-step explanation:
The cosine half-angle formula is
[tex]cos\frac{\pi }{2}[/tex]=±[tex]\sqrt{\frac{1+cosx}{2} }[/tex]
we can write
[tex]cos \frac{3\pi }{8}[/tex]
as
[tex]cos\frac{\frac{3\pi }{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1+cos\frac{3\pi}{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}[/tex]
=-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
(cosine is negative is in second quadrant)
Using the half angle identity, the exact value of cos 3 pi / 8 is (√2 - 1) / 2√2.
Given a trigonometric expression,
cos 3π/8
We have to find the exact value of this using the half angle identity.
The half angle identity in terms of cosine function is,
cos (x/2) = ± √[(1 + cos x) / 2]
Here the angle is 3π/8.
This can be written as,
3π/8 = 3π/4 / 2
Substituting to the formula,
cos (3π/4/2) = √[(1 + cos 3π/4) / 2]
Now,
cos 3π/4 = cos (π - π/4)
= -cos(π/4)
= - 1/√2
Substituting to the formula,
cos (3π/4/2) = √[(1 - 1/√2) / 2]
= (√2 - 1) / 2√2
Hence the value is (√2 - 1) / 2√2.
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At Madison High School each student studies exactly one foreign language. Three-fifths of the students take Spanish, and one-fourth of the remaining students take German. If all of the others take French, what percent of the students take French?
PLEASE HELP
A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%. The percent of the students who took French is 30%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that Three-fifths of the students take Spanish, and one-fourth of the remaining students take German. Therefore, the number of students who took french is,
Number of students who took french = 1 - 3/5 - (2/5 × 1/4)
= 1 -0.6 -0.1
= 0.3
= 30%
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How much hot dogs was sold on Wednesday? musiclover10045, This is a question you need to answer...
Answer:
32-28=4
Step-by-step explanation:
See the attachment :)
Answer:
4
Step-by-step explanation:
he started with 32 the he had 28 and 32-28 is 4
a direct variation includes the points (4,20) and (1,n). find n
The constant of variation in a direct variation is found by dividing the y-coordinate by the x-coordinate. Using this constant, we can determine the y-value of a point given the x-value. In this case, n = 5.
Explanation:In a direct variation, the ratio of the two variables is constant. This means that the product of the two corresponding coordinates of any two points is always the same.
Given a point (4,20), we can find the constant of variation by dividing the y-coordinate by the x-coordinate, which yields 20/4 = 5. So, the constant of variation (k) is 5.
For the point (1, n), the product of the two coordinates should also yield the same constant of variation. Therefore, 1 * n = 5. Solving for n, we find that n = 5.
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write an expression that is equal to 10 using only four 2s and any number of math symbols
[tex](4 \times 2) + 2[/tex]
2x2x2+2=10. According to PEMDAS. You would multiply before you add so 2x2x2 equals 8 and then you add 2 more and you have 10
Simplify the expression using the distributive property. –4(–3x + 11) 1. Distribute the –4 through the parentheses: -4(–3x) + (-4)(11) 2. Find each product: x -44
The value of x is 11/3 for expression –4(–3x + 11)
What is Expression?An expression is combination of variables, numbers and operators.
Given expression is –4(–3x + 11)
Let us apply distributive property
–4(–3x + 11)
Minus four times of minus three x plus eleven
-4(-3x)-4(11)
Minus four times of minus three x minus four times of eleven
12x-44
12x=44
Divide both sides by 12
x=44/12
x=11/3
Hence, the value of x is 11/3.
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A plane intersecting a cube can create a cross section that is a decagon? True or false
Answer: False
Step-by-step explanation:
Elliot rides his bike at an average speed of 14 miles per hour.how many miles will he ride in 2 1/2 hours ?
Answer:
35 miles
Step-by-step explanation:
Given: Elliot rides his bike at an average speed of 14 miles per hour.
If he rides his bike at 14 miles every hour, and he was riding for 2.5 hours, all we need to do is take 14 and multiply it by 2:
[tex]2(14)=28[/tex]
We just found out how many miles he went in two hours. To find the remaining half, all we need to do is take his speed, divide it by two, and add it to the rest:
[tex]\frac{14}{2}=7[/tex]
[tex]28+7=35[/tex]
Elliot went 35 miles in 2.5 hours.
He will ride 35 miles in 2 1/2 hours.
Hope this helps.
Round your answers to one decimal place, if necessary.
Find the mean and median of these data: 2, 7, 12, 14, 19, 21.
Answer:
Mean=12.5
Median=13
Step-by-step explanation:
What you do for the mean is you add all the numbers together to get 75.
You will then divide it by 6 because there are 6 numbers to get 12.5 as your answer.
The median all you do is find the middle number. The middle numbers are 12 and 14. You will take 12 and 14 and add them together to get 26.
You will then divide it by 2 to get 13 as your answer.
The Mean of the data is 12.5 and the Median of the data is 13.
What are the mean and median?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data. The mean is calculated by adding all the data and dividing it by the number of the data.
The Median is the middle value of the data set when all the data is arranged in ascending order.
Given data is 2, 7, 12, 14, 19, 21. The mean of the data will be calculated as below:-
Mean = ( 2 + 7 + 12 + 14 + 19 + 21 ) / 6
Mean = 75 / 6 = 12.5
The Median will be calculated as below:-
Median = ( 12 + 14 ) / 2
Median = 26 / 2 = 13
Therefore, the Mean of the data is 12.5 and the Median of the data is 13.
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Without graphing classify each system as independent dependent or inconsistent -x -y=7
5x-5y=5
Answer:
Is a consistent independent system
Step-by-step explanation:
we have
[tex]-x-y=7[/tex] -----> isolate the variable y
[tex]y=-x-7[/tex] ----> equation A
[tex]5x-5y=5[/tex] -----> isolate the variable y
[tex]y=x-5[/tex] ---> equation B
Compare equation A and equation B
We can affirm that
The slopes are not equal ( so the lines are not parallel)
The lines are different
The product of their slopes is equal to -1 (the lines are perpendicular)
so
The system of equations has only one solution
therefore
Is a consistent independent system
By analyzing the given equations and rewriting them to compare coefficients, it is clear that the system of equations is independent because they have different slopes and will intersect at exactly one point.
To classify the system of equations as independent, dependent, or inconsistent without graphing, we have to analyze the equations and solve for their relation to each other. The given equations are:
-x - y = 7
5x - 5y = 5
We can start by putting the equations in the same form to compare the coefficients:
Equation 1 can be rewritten as: x + y = -7 (multiply by -1)
Equation 2 can be simplified: x - y = 1 (divide by 5)
The slopes of the lines represented by the two equations are different (they are not multiples of each other) which suggests that the lines will intersect at exactly one point. This means the system of equations is independent.
Which inequality represents the statement A final grade of at least 90? A. x < 90 B. x > 90 C. x ≤ 90 D. x ≥ 90
Answer:
D
Step-by-step explanation:
Since it is at least 90, it literally means that the lowest possible value is 90. Therefore the number can only be greater than or equal to 90. So, the answer is D.
Answer:
C. X is less than or equal to 90
Step-by-step explanation:
because as you can see that the last sentence it says. A final grade of at LEAST 90?
The Cotton family purchases a glass sculpture in the shape of a rectangler pyrimad.The base measures 7 1/2 inches by 5 inches.If the volume of the sculpture is 75 cubic inches, what isthe height of the pyrimad, in inches?
Answer Choices:
A) 15in
B) 6in
C) 2in
D) 37.5in
Answer:
6
Step-by-step explanation:
see attachment
Answer:
The answer is B. 6in.
Hope it helps!!!!!!!
The expression 2(l + w) is used to calculate the perimeter of a rectangle, where l is length and w is width. If the length is Fraction 2 over 7 unit and the width is Fraction 3 over 7 unit, what is the perimeter of the rectangle in units? (3 points)
LENGTH=2/7
WIDTH= 3/7
Perimeter is 2l+2w
Length= 2/7+ 2/7 is 4/7
Width= 3/7 + 3/7 is 6/7
Answer is 4/7+ 6/7 is 10/7
Answer= 10/7 = 1 3/7
Answer:
1 3/7
Step-by-step explanation:
Write the following coordinates where they belong in the line segments below. (5 1/2, -4 1/4) _______ (3 3/4, -1 1/4)
ANSWER
[tex](4 \frac{5}{8} , - 2\frac{3}{4} )[/tex]
EXPLANATION
The end points of the segment are:
[tex](5 \frac{1}{2} ,-4 \frac{1}{4} )[/tex]
and
[tex](3 \frac{3}{4} ,-1 \frac{1}{4} )[/tex]
The box represents the midpoint of the two points.
Using the midpoint formula;
[tex]( \frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
We substitute the end points of the line segment to obtain,
[tex]( \frac{5 \frac{1}{2} +3 \frac{3}{4} }{2} , \frac{ - 4 \frac{1}{?} + - 1 \frac{1}{4} }{2} )[/tex]
This simplifies to:
[tex]( \frac{37}{8} , - \frac{11}{4} )[/tex]
We convert back to mixed numbers to get,
[tex](4 \frac{5}{8} , - 2\frac{3}{4} )[/tex]
The correct choice is B
Camden gets paid every 2 weeks. Federal withholding is 15.6% of his gross pay, Social Security is 6.2% of his gross pay, and Medicare is 1.45%. Find Camden net pay after 2 weeks. Show your work.
Step-by-step explanation:
F=0.156g
S=0.062g
M=0.0145g
N=g-(F+S+M)
N=g-(0.156g+0.062g+0.0145g)
N=g-0.2325g
N=0.7675g
Camden's net pay is 76.75% of his gross pay
Alternative:
100%-15.6%-6.2%-1.45%=76.75%
Final answer:
To calculate Camden's net pay, you subtract federal withholding, Social Security, and Medicare deductions from his gross pay based on provided percentages. By applying these calculations to an example, Camden's net pay from a $2,000 gross salary over two weeks would be $1,535, after deductions totaling $465.
Explanation:
The calculation of Camden's net pay involves subtracting federal withholding, Social Security, and Medicare deductions from his gross pay. Assuming Camden's gross pay is a certain amount, we'll illustrate how to find the net pay. Let's not forget to account for the percentages provided for each deduction category: 15.6% for federal withholding, 6.2% for Social Security, and 1.45% for Medicare.
Calculate Federal Withholding: Gross Pay * 15.6%.
Calculate Social Security Deduction: Gross Pay * 6.2%.
Calculate Medicare Deduction: Gross Pay * 1.45%.
Add all deductions together: Federal Withholding + Social Security + Medicare.
Subtract the total deductions from the Gross Pay to get the Net Pay.
For example, if Camden's gross pay is $2,000 for two weeks, his deductions would be:
Federal Withholding: $2,000 * 15.6% = $312
Social Security: $2,000 * 6.2% = $124
Medicare: $2,000 * 1.45% = $29
Total Deductions: $312 + $124 + $29 = $465
Net Pay: $2,000 - $465 = $1,535
What is 19.55 rounded off to the nearest whole number
Answer:
20
Step-by-step explanation:
19.55 can be either 19 and 20, but it is closer to 20!
Answer: The answer is 20.
Step-by-step explanation: So anytime you are rounded if the number is 5 or over 5 it will round up. If it is under 5 it will round down and in this case it is over half or 5 so it would round up to 20 since 20 is a whole number.
What is the distance between the points (6, −3) and (6, 5)?
The distance between the points (6, −3) and (6, 5) is 8 units.
How to calculate the distance between two points ?The distance between two points, (x1,y1) and (x2,y2) is calculated by using the distance formula in coordinate geometry.
According to distance formula,
Distance = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex] units.
How to find the distance between two points in the question ?Given points are (6,-3) and (6,5).
Using the distance formula for calculating the distance -
Distance = [tex]\sqrt{(6 - 6)^{2} + (-3 - 5)^{2} }[/tex] units = [tex]\sqrt{8^{2} }[/tex] units = [tex]8[/tex] units
Therefore, the distance between the points (6, −3) and (6, 5) is 8 units.
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Final answer:
To find the distance between the points (6, -3) and (6, 5), calculate the absolute value of the difference between the y-coordinates, resulting in a distance of 8 units.
Explanation:
The distance between the points (6, −3) and (6, 5) can be found using the distance formula, which is derived from the Pythagorean Theorem. In this particular case, since the x-coordinates of both points are the same, the distance is simply the absolute value of the difference in the y-coordinates.
To calculate the distance (d):
d = |y2 − y1|
d = |5 − (−3)|
d = |5 + 3|
d = |8|
d = 8
Therefore, the distance between the points (6, −3) and (6, 5) is 8 units.
The company Digit Tech designs a new
SmartPhone. The packaging includes an
open box made out of cardboard. The
dimensions of the box
are 12 cm long, 9 cm wide, and 9 cm high.
Digit Tech expects to sell 1500 phones and
package each phone individually in a box.
In square centimeters, what is the minimum
amount of cardboard Digit Tech needs to
package all 1500 new SmartPhones?
Answer:
The amount of cardboard Digit Tech needs to
package all 1500 new Smart Phones = 891000 square cm
Step-by-step explanation:
Points to remember:-
Surface area of cuboid
Surface area = 2(lb + bh + lh)
Where, l - Length of cuboid
b - Breadth of cuboid and
h - Height of cuboid
It is given dimensions of cardboard box
12 cm long, 9 cm wide, and 9 cm high.
To find the surface area of box
Here l = 12 cm, b = 9 cm and h = 9 cm
Surface area = 2(lb + bh + lh) = 2[(9*12) + (9*9) + (12 * 9)]
= 2(108 + 81 + 108) = 2 * 297 = 594 square cm
To find the cardboard required for 1500 box
Total cardboard = 1500 * 594 = 891000 square cm
Four hours on an analog clock would be what amount of degrees?
Answer:
120 Degrees
Step-by-step explanation:
4/12 * 360
Answer:
I think the answer is 120 degrees.
Step-by-step explanation:
Lila makes bags of stickers that are exactly the same for 5 friends. She uses a total of 45 stickers. Each bag has 2 butterfly stickers and the rest are flower stickers. How many flowers stickers are in each bag? Write a first step question and answer. Then solve the problem.
Answer:
Step-by-step explanation:each bag has 7 flower stickers........I think
we multiplicate 9*5 that is 45
9-2 is seven ,seven flower stickers
How long does it take to get to space
Answer:
At 3,500 MPH, the shuttle is traveling approximately one mile per second. That means it only takes 32 seconds more to reach an altitude of 62 miles. If you want to take acceleration into account, it is a few seconds less. So it takes approximately 150 seconds for the shuttle to get out of earth's atmosphere.
Step-by-step explanation:
Answer:
That means it only takes 32 seconds more to reach an altitude of 62 miles. If you want to take acceleration into account, it is a few seconds less. So it takes approximately 150 seconds for the shuttle to get out of earth's atmosphere.
Which even number comes right before 29?
Answer:
28
Step-by-step explanation:
0, 2, 4, 6, 8, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 are even numbers.
mark as brainsliest♡
Answer:
28
Step-by-step explanation:
29, 28, 27
28 is before 29 and its even fam
2/3x - 2= 7 how do I solve it as a mixed number can someone help me please.
Answer:
13 1/2
Step-by-step explanation:
solve for x by simplifying both sides of the equation then isolating the variable.
you get 13 1/2
Answer:
The answer is 13 1/2
Step-by-step explanation:
Start by adding 2 to both sides.
2/3x - 2 = 7
2/3x = 9
Now multiply both sides by 3/2
2/3x = 9
x = 27/2
Now divide 27 by 2 which is 13 with a 1 remainder. We express that 1 over the 2 as the fraction.
13 1/2
what is the general form of the equation of a circle with its Center at -2 1 and passing through -4 one
Answer:
x² + y² + 4x - 2y + 1 = 0
Step-by-step explanation:
The equation of a circle is given by the general equation;
(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius.
In this case; the center is (-2,1)
We can get radius using the formula for magnitude; √((x2-x1)² + (y2-y1)²)
Radius = √((-4- (-2))² + (1-1)²)
= 2
Therefore;
The equation of the circle will be;
(x+2)² + (y-1)² = 2²
(x+2)² + (y-1)² = 4
Expanding the equation;
x² + 4x + 4 + y² -2y + 1 = 4 subtracting 4 from both sides;
x² + 4x + y² - 2y + 4 + 1 -4 = 0
= x² + y² + 4x - 2y + 1 = 0
Answer:
[tex]\large\boxed{x^2+y^2+4x-2y+1=0}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
The general form of an equation of a circle:
[tex]x^2+y^2+Dx+Ey+F=0[/tex]
We have the center (-2, 1). Substitute to the equation in the standard form:
[tex](x-(-2))^2+(y-1)^2=r^2\\\\(x+2)^2+(y-1)^2=r^2[/tex]
Put thr coordinates of the point (-4, 1) to the equation and calculate a radius:
[tex](-4+2)^2+(1-1)^2=r^2\\\\r^2=(-2)^2+0^2\\\\r^2=4[/tex]
Therefore we have the equation:
[tex](x+2)^2+(y-1)^2=4[/tex]
Convert to the general form.
Use [tex](a\pm b)^2=a^2\pm 2ab+b^2[/tex]
[tex](x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\qquad\text{subtract 4 from both sides}\\\\x^2+y^2+4x-2y+1=0[/tex]
if the following segment is reflected across the y-axis what are the new coordinates of the new endpoints? A.)(1,6) and (3,2) B.) (-6,1) and (-2,3) C.) (-1,-6) and (-3,-2) D.) (6,-1) and (2,-3)
Answer:
A.) (1, 6) and (3, 2)Step-by-step explanation:
Look at the picture.
[tex]\begin{array}{c|c|}&(x,\ y)\\S_{OX}&(x,\ -y)\\S_{OY}&(-x,\ y)\\S_{(0,0)}&(-x,\ -y)\end{array}[/tex]
PLEASE HELP!!!!!!!
Jacob makes the following statement:
"I have a 60% chance of being selected as the captain of the baseball team and a 20% chance of being elected student body president."
What is the probability that Jacob will be selected as the captain of the baseball team and will be elected student body president? (5 points)
a
80%
b
40%
c
12%
d
8%
Calculate the circumference of the following circles correct to one decimal place
Answer:
47.1 cm
Step-by-step explanation:
For this problem, I'll use an approximation of [tex]\pi \approx 3.14[/tex], which is good enough for the level of accuracy we need. The definition of π itself is given by the equation
[tex]\pi =\frac{c}{d}[/tex]
where c is the circumference of a circle and d is its diameter. If we want to find the circumference, we can simply multiply both sides of that equation by d to get the formula
[tex]c=\pi d\approx3.14d[/tex]
Here, we're given d = 15 cm, so plugging that in, we find our circumference to be
[tex]c\approx3.14(15)=47.1[/tex]
So the circumference of this circle is approximately 47.1 cm.
what is the distance?
5^2+6^2 = x^2
25+36 = x^2
61 = x^2 | sqrt
sqrt(61) = x^2
x ~ 7.81
The distance is 7.81
Step-by-step explanation:See the image
what is the range of the function f(x)=3/4 |x|-3
All real numbers
All real numbers less then or equal to 3
All real numbers less than or equal to -3
All real numbers greater than or equal to -3
The answer is the forth one.
The range of the given function is:
All real numbers greater than or equal to -3 Step-by-step explanation:We are given a modulus function f(x) by:
[tex]f(x)=\dfrac{3}{4}|x|-3[/tex]
From the graph of the function we may see that the graph continuously decreases from x= ∞ to x=0 and at x=0 the function attains the values ,
f(0)= -3
and then it again increases continuously and goes to infinity.
Hence, the function covers all the real values between -3 to ∞
i.e. The range of the function in interval form is: [-3,∞)
Hence, the answer is:
All real numbers greater than or equal to -3
What is the value of n in the equation below?
Answer:
The value of n is equal to 9
Step-by-step explanation:
12^(n) / 12^(5) = 12^4
12^(n-5) = 12^(4)
Which means
n - 5 = 4
n = 4 + 5
n = 9
We can chek this by dividing
12 ^ 9 = 5159780352
12 ^ 5 = 248832
5159780352 / 248832 = 20736
12^4 = 20736