Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?
Shape 1 is congruent to shape 2, which can be shown using a sequence of dilations and translations.
Shape 1 is not congruent to shape 2 because the shapes do not have the same absolute coordinates.
Shape 1 is congruent to shape 2, which can be shown using a translation.
Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."
Answers
The "bulb" part of both shapes are congruent but because of their extensions they arent. Shapes dont have to be in same spot to be congruent. which is why second option isn't correct
Answer is last option
Solution:
As, you can see that shape 1 and shape 2 are not congruent nor the shape 1 is dilated by any factor to get the shape 2.
Both the shapes are concave polygon.
The base length of two shapes are equal .
→2 × AB = P Q →(approx)
→BC=QR
→2 × CD= RS→→→(approx)
If translation has taken place, all the vertices has been translated by same amount.
So, option (4) is true,which is Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."
Related Questions
I shall Upvote!
Suppose the population of a town is 8,200 and is growing 3% each year.
a. Write an equation to model the population growth.
b. Predict the population after 3 years.
A: y = 8,200 • 3^x ; about 221,400 people
B: y = 8,200 • 3^x ; about 8,960 people
C: y = 3 • 8,200^x ; about 73,800 people
D: y = 8,200 • 1.03^x ; about 8,960 people
Answers
Wait short time for answer a
half a pepperoni pizza plus three fourths a ham-and-pineapple pizza contains 765 calories. One fourth of a pepperoni pizza plus a whole ham-and-pineapple pizza contains 745 calories. How many calories are in each kind of pizza?
Answers
1. D (4,5)
2. C
3. D
4. A
5. C
6. D
7. B
8. C
9. A
10. B
OR
1. B (2,6)
2. A
3. A
4. C
5. D
6. A
7. A
8. B
9. C
10. A
Don't deny it, you came here for the answers ;)
Final answer:
A half pepperoni pizza contains 660 calories and a ham-and-pineapple pizza contains 580 calories.
Explanation:
Let's represent the number of calories in half a pepperoni pizza as x, and the number of calories in a ham-and-pineapple pizza as y. We can set up a system of equations to represent the given information:
0.5x + 0.75y = 765 -- Equation (1)
0.25x + y = 745 -- Equation (2)
We can solve this system of equations using the method of substitution:
From Equation (2), y = 745 - 0.25x
Substitute this value of y into Equation (1):
0.5x + 0.75(745 - 0.25x) = 765
Simplify and solve for x:
0.5x + 558.75 - 0.1875x = 765
0.3125x = 206.25
x = 660
Now substitute the value of x back into Equation (2) to find y:
0.25(660) + y = 745
Simplify and solve for y:
165 + y = 745
y = 580
Therefore, there are 660 calories in a half pepperoni pizza, and 580 calories in a ham-and-pineapple pizza.
4sin(x)−4=0
solve for x
Answers
4sin(x) - 4 = 0
4sin(x) = 4
sin(x) = 1
Now use the unit circle and you'll see that the only solution in the interval [0,2pi) is x = pi/2
If you want to ignore the restriction and consider all solutions, then x = (pi/2) + 2pi*n where n is any integer
A degree is larger than 30 arc minutes. ...?
true or false
Answers
Answer:
True
Step-by-step explanation:
Given : Statement - 'A degree is larger than 30 arc minutes'.
To find : True or False ?
Solution :
We know that,
1 degree is [tex]1^\circ=\frac{1}{360}[/tex] of a circle
1 arc minute is [tex]1^'=(\frac{1}{60})^\circ[/tex] of degree.
So, 30 arc minutes is [tex]30^'=(\frac{30}{60})^\circ[/tex] of degree.
30 arc minutes is [tex]30^'=(\frac{1}{2})^\circ[/tex] of degree.
Which clearly means,
[tex]1^\circ>(\frac{1}{2})^\circ[/tex]
[tex]1^\circ>30^'[/tex]
Therefore, The given statement is true.
'A degree is larger than 30 arc minutes'.
Nellie is buying bird seed to put in her bird feeders. She uses about 10 pounds of bird seed each week, but has room to store any extra that she purchases.The bird seed comes in 3 different sizes as given below: 3.5 pounds for $2.52 7.5 pounds for $5.40 11 pounds for $7.92 Nellie is trying to be a smart shopper and get the best deal on the bird seed. Which size bag of bird seed should Nellie buy?
Answers
All the bird seed bags Nellie is considering have the same cost per pound ($0.72). She should choose based on her weekly usage and storage preference. Any size will be cost-effective.
To determine the best deal on bird seed, Nellie needs to calculate the unit price for each option. The unit price is the price per pound of bird seed.
For the 3.5-pound bag:
[tex]\[ \text{Unit price} = \frac{\$2.52}{3.5 \text{ pounds}} \approx \$0.72/\text{pound} \]\\For the 7.5-pound bag:\[ \text{Unit price} = \frac{\$5.40}{7.5 \text{ pounds}} = \$0.72/\text{pound} \]For the 11-pound bag:\[ \text{Unit price} = \frac{\$7.92}{11 \text{ pounds}} \approx \$0.72/\text{pound} \][/tex]
Since all three options have the same unit price of approximately $0.72 per pound, Nellie should choose the size that offers her the most pounds of bird seed for the best value, as he has anyway room for storing extra purchase. Here, can choose to buy any of them.
10 POINTS!
Solve.
6 – 3x = 4(3 – x) – 6
A.
0
B.
–6
C.
all real numbers
D.
6
Answers
Please help! Numbers 16 & 17.. It will be much appreciated! :D
Answers
17. If the lion can run 15 miles in one hour, then in .25 hours or 1/4 of an hour the loin could be said to run 15/4 miles, or 3.75 miles.
Prove: the midpoint of the hypotenuse of a right triangle is equidistant from three vertices
Answers
From the picture attached,
Coordinates of point A → (0, 0)
Coordinates of point M → [tex](\frac{a}{2}, \frac{b}{2} )[/tex]
Coordinates of point A → (0, b)
Coordinates of point A → (a, 0)
Since, we have to prove that midpoint (M) of the hypotenuse BC is equidistant from all three vertices A, B and C,
AM = BM = CM
Use the expression for the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AM = [tex]\sqrt{(\frac{a}{2}-0 )^2+(\frac{b}{2}-0)^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2} )^2}[/tex]
BM = [tex]\sqrt{(a-\frac{a}{2} )^2+(\frac{b}{2})^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
CM = [tex]\sqrt{(0-\frac{a}{2} )^2+(b-\frac{b}{2})^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
Therefore, AM = BM = CM = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
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YES, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices -
AM = CM = BM.
We have a right - angled triangle → ΔABC.
We have to prove that midpoint of the hypotenuse of a right triangle is equidistant from three vertices.
What is Right Angled Triangle?A right angled triangle is a triangle with one of the angles as 90 degrees.
According to the question -
Consider the hypotenuse BC. The mid - point of BC has the coordinates as -
M([tex]\frac{a}{2} , \frac{b}{2}[/tex]).
Now -
Length AM →
AM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Length CM →
CM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2} - b) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Length BM →
BM = [tex]\sqrt{(\frac{a}{2} -a) ^{2} + (\frac{b}{2} ) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Therefore -
AM = CM = BM
Hence, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices.
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on a number line: What does a closed circle mean and what does an open circle mean?
Answers
An open circle is greater than or less than.
On a number line, closed circle on a point indicates that point is also included and the open circle indicates that point is not included.
What is a Number Line?Number lines are represented as straight lines drawn horizontally on which integers are written in equal intervals.
This line is extended to infinity on both sides.
Number line includes positive numbers, zero and negative numbers.
Closed circles and open circles are used in number line to represent linear inequalities in one variable.
Let 'n' be any number on the number line.
We use open circles on 'n' to denote inequalities like x < n and x > n.
We use closed circles on 'n' to denote inequalities like x ≤ n and x ≥ n.
Hence, open circles are used to numbers which are greater than or less than ( > or < ) and closed circles are used to numbers which are greater than or equal to and less than or equal to ( ≥ or ≤ ).
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The length of a rectangle is 5 inches less than 3 times the width. The perimeter of the rectangle is 14 inches. Find the length and width of the rectangle.
I did this: Length 3x-5; width 3x Then I did guess and check and came up with X=2 solving the problem with a perimeter of 14. But, the answer is supposed to be length 4inches, width 3inches.
Please explain what I did wrong. I know the answer but not how to get it.
Answers
A car Purchased for $18,500. After each year, the resale value decreases by 30%. What will the resale value be after 4 years
Answers
A = amount of money
P = Principle amount
r = annual rate of interest
t = number of years
The graph of y = x2 is shown below.
If graphed on the same grid, which of the following could be the graph of y = 0.4x2?
Answers
The answer is third graph (middle one)
Answer:
The answer is in the attachment.
Step-by-step explanation:
Coefficient in front of x^2 is 0.4. What that means is that for same increase of x now we will have less increse of y. If you picture that we can also say that graph would be wider. The graph will stay on positive side of y axis because x^2 is always positive and 0.4 times that is again always positive.
The answer is third graph (middle one)
Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.
Base 1 1/2 feet, altitude 6 inches.
Area = sq. ft. ...?
Answers
The area (A) of the parallelogram with altitude a and base b is:
A = a * b
We have:
A = ?
a = 6 in
Since 1 inch is 0.083 feett, then 6 inches is
a = 6 * 0.083 ft = 0.498 ft ≈ 0.5 ft = 1/2 ft
b = 1 1/2 ft = 1 + 1/2 ft = 2/2 + 1/2 ft = 3/2 ft
_______
A = a * b
a = 1/2 ft
b = 3/2 ft
A = 1/2 * 3/2 = 3/4 ft² = 0.75 ft²
Answer:
3/4 sq. ft.
Step-by-step explanation:
Hope it helps.
I really need help and no one will help..!
solve each system by substitution. explain step by step
r + s = -12
4r - 6s = 12
Answers
2r-3s=6
mltiply first equation by -2 and add to first
-2r-2s=24
2r-3s=6 +
0r-5s=30
-5s=30
divide by -5
s=-6
sub back
r+s=-12
r-6=-12
add 6
r=-6
r=-6
s=-6
How would 0.333333 be classified?
Answers
33%, 33/100.
If you want the name for the 0.3 occuring, it would be irrational.
Please make this answer the brainiest!
The given number 0.333333 is rational number and real number.
What is the decimal number?A decimal number is said to be irrational if it never repeats. For instance, since there is no repetition, the decimal representation of pi is an estimate. All rational numbers have decimal expansions that either come to an end (in which case all subsequent values are zero) or follow a pattern.
What is the ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What is the rational number?A rational number is defined as a number that can be represented as the ratio of two integers, where the denominator must not equal zero.
A rational number is any number that can be written as a ratio. Think of a ratio kind of like a fraction, functionally at least.
Given number, 0.333333 is a repeating decimal that comes from the ratio of 1 to 3, or 1/3. Thus, it is a rational number.
The number 0.333333 is also real number.
Hence, the number 0.333333 is rational number and real number.
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suppose sin u= x and u is between 0 and pi/2. what is sec u? ...?
Answers
a) sqrt(1-x^2)
b) x/sqrt(1-x^2)
c) sqrt(1-x^2)/x
D) 1/sqrt(1-x^2)
The answer should be c) sqrt(1-x^2)/x .
cos u = sqrt (1 - sin^2 u) = sqrt(1 - x^2), and cot u = cos u / sin u.
The required value will vary Between [1,∞)
What is Trigonometry?It is the branch of science that studies the relation between right-angled triangles.
How to solve?if sin u = x and u varies from 0 to [tex]\frac{\pi }{2}[/tex]
We know, Sec u = [tex]\frac{1}{cos u}[/tex]
Then, for sec u or sec u varying from 0 to [tex]\frac{\pi }{2}[/tex] value will be in between [1,∞)
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Simplify √550
A 5√22
B 10√55
C 5√11
D 25√5
Answers
Answer:
A) 5√22
Step-by-step explanation:
I took the K12 quiz and it was right
The simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The number in radical sign is 550 ie.
= √550
The factors of the 550 can be written as:
550 = 5x5x2x11
= √(5x5x2x11)
= 5√(2x11)
= 5√22
Thus, the simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.
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During World War I, the Germans had a gun
called Big Bertha that was used to shell Paris.
The shell had an initial speed of 2.41 km/s at
an initial inclination of 61.5 to the horizontal.
The acceleration of gravity is 9.8 m/s2 .
How far away did the shell hit?
Answer in units of km
How long was it in the air?
Answer in units of s
Answers
2.41 km/s = 2410m/s\
To solve the second part
First we have to find Vy Vy = 2410 m/s * sin 61.5 = 2410 m/s * 0.8788 =2117.908 m/s.
When the shell reaches it's maximum height the vertical velocity component will be zero
based on that theorem let's apply linear motion equation
V = u + at
0 = 2117.908 m/s - 9.8 m/S^2 * (t)
t = 216.1130 s
As the shell has to go upward and comes back to earth the shell will require a same amount of time in order to reach earth again so the total time that shell will spend on the air will be
2*t = 432.226 s
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
To find the distance the shell hit and the time it was in the air, we need to determine the total time it takes for the shell to hit the ground. The horizontal component of the shell's initial velocity remains constant, while the vertical component is affected by gravity. By solving for the time using the vertical component, we can then multiply it by the horizontal component to find the distance and convert it to kilometers.
Explanation:To find the distance that the shell hit, we need to determine the time it was in the air. We can do this by finding the total time it takes for the shell to hit the ground. The shell's initial velocity is given as 2.41 km/s at an angle of 61.5 degrees. We can break down the initial velocity into its horizontal and vertical components. The horizontal component remains constant, while the vertical component is affected by gravity. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the time it takes for the shell to reach the ground.
Find the horizontal component of the initial velocity using the equation horz_vel = init_vel * cos(angle).Find the vertical component of the initial velocity using the equation vert_vel = init_vel * sin(angle).Using the vertical component, solve for the time it takes for the shell to reach the ground using the equation -vert_vel = 0 + 0 * t - 0.5 * acceleration * t^2.The time calculated in step 3 will give us the total time the shell was in the air.Multiply the total time by the horizontal component of the initial velocity to get the distance that the shell hit.Convert the distance from meters to kilometers by dividing by 1000.So, the shell hit a distance of [distance] km away and was in the air for [time] s.
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1. A recipe calls for cups of flour, cup of white sugar, and cup of brown sugar. The recipe makes 6 servings.
(a) How many cups of flour are there per serving? Show your work.
(b) How many total cups of sugar (white and brown) are there per serving? Show your work.
(c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe? Show your work
Answers
So, 9÷1 1/2= 6 cups and 6÷ 1 1/2= 4 cups 6-4=2 cups . You would need two more cups of flour for the modified recipe than you would need for the original recipe.
Answer:
abc
Step-by-step explanation:
A=4 B= 26 C= 4 and 2
Which statement best explains whether y = 3x + 5 is a linear function or a nonlinear function?
1. It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 8), which are on a straight line.
2. It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 4), which are not on a straight line.
3. It is a nonlinear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.
4. It is a linear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.
Answers
A brownie recipe requires one and one third cups of sugar to one cup of chocolate chips. If four and two thirds cups of sugar is used, what quantity of chocolate chips will be needed, according to the recipe?
...?
Answers
Final answer:
To find the number of chocolate chips needed for four and two-thirds cups of sugar, we use the given ratio of 4/3 cups of sugar to 1 cup of chocolate chips and set up a proportion. Solving it gives us 3.5 cups of chocolate chips.
Explanation:
To determine the number of chocolate chips needed when using four and two-thirds cups of sugar according to the brownie recipe, we must first understand the ratio given in the recipe, which is one and one-third cups of sugar to one cup of chocolate chips. This ratio can be simplified to a fraction for easier calculation: 4/3 cups of sugar : 1 cup of chocolate chips.
With this ratio, we can set up a proportion to find the amount of chocolate chips needed for four and two-thirds cups of sugar:
(4/3 cups of sugar) / (1 cup of chocolate chips) = (14/3 cups of sugar) / (x cups of chocolate chips)To solve for x, we cross-multiply and solve the resulting equation:
(4/3) * x = (14/3) * 1x = (14/3) * (3/4)x = 14/4x = 3.5The quantity of chocolate chips needed is 3.5 cups when using four and two-thirds cups of sugar.
Complete y^2+15y+56=(y+7)(y+?) ...?
Answers
y² + 15y + 56 = (y + 7)(y + a)
y² + 15y + 56 = y² + (7 + a)y + 7a
We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.
15 = 7 + a; a = 8
OR
56 = 7a; a = 8
Second factor is (y + 8)
y² + 15y + 56 = (y + 7)(y + a)
y² + 15y + 56 = y² + (7 + a)y + 7a
We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.
15 = 7 + a; a = 8
OR
56 = 7a; a = 8
Second factor is (y + 8)
what is the largest perfect square of 45? ...?
Answers
So, the factors of 45 are 1, 3, 5, 9, 15, and 45.
As you can see, number 9 is the largest perfect square here.
The largest perfect square less than or equal to 45 is 36, which is the square of 6. Squaring numbers less than 7 shows that 36 is the perfect square closest to, but not exceeding 45.
Explanation:The largest perfect square that is less than or equal to 45 is the result of the greatest integer squared that does not exceed 45. To find this, you would look for the highest whole number whose square is less than or equal to 45. The numbers less than 45 are 1, 2, 3, ..., and so on. Squaring these: 12=1, 22=4, 32=9, 42=16, 52=25, 62=36. The next number, 7, squared is 49, which is greater than 45. Therefore, 62=36 is the largest perfect square less than or equal to 45. This concept is essential when simplifying square roots or in problems dealing with areas of squares.What is a soliloquy? ...?
Answers
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Suppose z=x^2*sin(y), x=2s^2−4t^2, y=4st.
A. Use the chain rule to find ∂z/∂s and ∂z/∂t as functions of x, y, s and t.
Answers
dz/dx = 2x sin(y)
dx/ds = 4s
dz/dy = x^2 cos(y)
dy/ds = 4t
∂z/∂s = 2x sin y * 4s + x^2 cos y * 4t = 8sx sin(y) + 4tx^2 cos(y)
∂z/∂t = dz/dx * dx/dt + dz/dy * dy/dt
dz/dx = 2x sin(y)
dx/dt = -8t
dz/dy = x^2 cos(y)
dy/dt = 4s
∂z/∂t = 2x sin y * -8t + x^2 cos y * 4s = -16tx sin(y) + 4sx^2 cos(y)
Use the chain rule of differentiation to calculate ∂z/∂s and ∂z/∂t. Start by differentiating the functions z with respect to x and y, then differentiate the functions x and y with respect to s and t. Finally, plug the derived values into the chain rule formula to get the expressions for ∂z/∂s and ∂z/∂t.
Explanation:To solve the problem, we will need to apply the chain rule in order to calculate ∂z/∂s and ∂z/∂t. The chain rule is used in calculus to differentiate a function that has other functions inside of it.
We will differentiate z which is the function of x and y, and x and y themselves are functions of s and t.
The steps are as follows:
Calculate ∂z/∂x and ∂z/∂y by differentiating z with respect to x and y. Calculate ∂x/∂s, ∂x/∂t, ∂y/∂s and ∂y/∂t by differentiating x and y with respect to s and t.Use these calculated values to calculate ∂z/∂s and ∂z/∂t by applying the chain rule formula.
The chain rule formula is:
∂z/∂s = ∂z/∂x * ∂x/∂s + ∂z/∂y * ∂y/∂s
and
∂z/∂t = ∂z/∂x * ∂x/∂t + ∂z/∂y * ∂y/∂t.
This will give you the final expressions for ∂z/∂s and ∂z/∂t as functions of x, y, s, t.
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in a carnival drawing,a green ticket wins $1,a yellow ticket wins $5,and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. in simplest form, what are the odds in favor of winning $5 or more?
Answers
The odds in favor of winning $5 or more at the carnival are 3 to 10.
To determine the odds in favor of winning $5 or more at the carnival, we need to consider the number of tickets that win $5 or more and the total number of tickets.
Identify the tickets that win $5 or more: Yellow tickets win $5 and Blue tickets win $10.
Count the number of these tickets:
Yellow tickets: 25
Blue tickets: 5
Total tickets that win $5 or more:
25 + 5 = 30
Total number of tickets:
100 + 25 + 5 = 130
Odds in favor of winning $5 or more is the ratio of favorable outcomes to unfavorable outcomes:
Winning tickets: 30
Non-winning tickets:
130 - 30 = 100
Simplified odds:
30 to 100 = 3 to 10
Therefore, the odds in favor of winning $5 or more are 3 to 10.
The odds in favor of winning $5 or more in a carnival drawing are 3 : 10. So, the correct option is (B).
To determine the odds in favor of winning $5 or more in a carnival drawing, observe the number of tickets for each prize and calculate the favorable outcomes.
Here are the ticket counts:
Green ticket ($1): 100 ticketsYellow ticket ($5): 25 ticketsBlue ticket ($10): 5 ticketsFirst, calculate the total number of tickets:⇒ 100 (green) + 25 (yellow) + 5 (blue) = 130 tickets
Next, calculate the number of tickets that win $5 or more:⇒ 25 (yellow) + 5 (blue) = 30 tickets
The remaining tickets are the losing tickets or those winning less than $5 (green):⇒ 130 (total) - 30 = 100 tickets
Therefore, the odds in favor of winning $5 or more are 30:100, which simplifies to 3:10. This converts to the following odds as a ratio:
So, the correct option is (B) 3:10.
Complete question:
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5 and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:1
B. 3:10
C. 2:1
D. 1:3
what is the area of a right triangle with side lengths 6, 8, and 10? a. 48 b. 40 c. 30 d. 24
Answers
The legs are 6 and 8, and the hypotenuse is 10 (the longest side).
Since 6 and 8 are the legs (i.e. the base and height),
area = 1/2 • base • height
= 1/2 • 6 • 8 = 24
In the diagram below, AB is parallel to CD. What is the value of x?
Answers
The correct answer is: Option (D) x = 72°
Explanation:
When two lines are crossed by another line, the angles in matching corners are called corresponding angles. When the two lines are parallel, the corresponding angles are equal.
Here in this case, the two lines are "AB" and "CD", and both are parallel and are crossed by the line; therefore, the corresponding angles will be the same.
Since the first corresponding angle is 72°, the second angle x will be 72° as well. The correct answer is: x = 72° Option (D).
In the diagram below, AB is parallel to CD. What is the value of x?
Answer: 72!
Find all solutions of the equation 2sin2x−cosx=1 in the interval [0,2π), what is x?
Find all solutions of the equation 2sin2x−cosx=1 in the interval [0,2π), what is x?
Answers
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2sin2x−cosx=1
4sinxcosx = 1 + cosx
16sin^2xcos^2x = 1 + 2cosx + cos^2x
16(1 - cos^2x)cos^2x = 1 + 2cosx + cos^2x
16cos^2x - 16cos^4x = 1 + 2cosx + cos^2x
16cos^4x - 15cos^2x + 2cosx + 1 = 0
let cosx = Y
16Y^4 - 15Y^2 + 2Y + 1 = 0
(Y + 1)(16Y^3 - 16Y^2 + Y + 1) = 0
there are four values for Y, -1, -0.2, 0.367, 0.836.
Then you solve for Y.
For example, Y = -1 means cosx = -1, x = π.
I will leave the rests to you. (Sorry, this seems to be an ugly way...)
a recipe calls for 2 1/2 cups of flour toake 2 dozen coockies.how many cups of flour would be required to bake 15 dozen cookies?