Answer:
From sin²θ + cos²θ = 1, we have;
sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ
Step-by-step explanation:
The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ
We have;
(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;
(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1
Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ = 1
From which we can get;
(sin²θ + cos²θ)·(sin²θ + cos²θ) = 1
Given that sin²θ + cos²θ = 1
Therefore;
1 × 1 = 1
To get to the initial equation in the question, we have;
sin²θ + cos²θ = 1
(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1
(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1
∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ = 1 - 2·sin²θ·cos²θ
Therefore;
sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.
? Question
Type the correct answer in each box. Round your answers to one decimal place.
Use the function g(x) = 4(0.6)¥ to complete the table and find the y-intercept.
Answer:
-10=661.5
-1=6.7
0=4.0
1=2.4
2=1.4
8=0.1
(0,4)
Step-by-step explanation:
The y intercept is (0,4)
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is g(x) = 4 (0.6)ˣ
The table shows the value of x
The value of g(x) at different value of x is
At x = -10
g(x) = 661.5
At x = -1
g(x) = 6.7
At x = 0
g(x) = 4
At x = 1
g(x) = 2.4
At x = 2
g(x) = 1.4
At x = 8
g(x) = 0.1
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Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
x = 60°
Step-by-step explanation:
let the missing angle be = x
Cos x = 8/16
x = Cos-¹ 0.5
x = 60°
Find the missing lengths of the sides.
What is the unit price of a quart of juice for $0.79?
A. $3.16/gallon
B. 3 half-gallons for $5.40
C. $3.16/1b
D. 7 pints for $4.20
Answer:
a
Step-by-step explanation:
there are 4 quarts in a gallon.
4 times $0.79 =$3.16
Provide an appropriate response. At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a random sample of 12 of the freshmen, a random sample of 9 of the sophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example.
Answer: Stratified Sampling
Step-by-step explanation: Stratified Sampling involves creating subdivisions of the population such that each subdivisions is seen as a subgroup or smaller chunk of the population which is split based on certain criteria or attribute. The stratified random sampling may be employed in delineating certain characteristics or to investigate further how a feature or characteristics vary between one subdivision to the other.
In the scenario above, the researcher made use of the stratified sampling by performing a random sampling selection of its subjects based on the different subdivisions of students available in the college
In a local town, 54,000 families have incomes less than $25,000 per year. This number of families is 60% of the families that had this income level 12 years ago. What was the number of families who had incomes less than 25,000 per year 12 years ago
Answer: 90,000
Step-by-step explanation:
From the question, we are informed that in a local town, 54,000 families have incomes less than $25,000 per year. We are further told that this number of families is 60% of the families that had this income level 12 years ago.
To calculate the number of families who had incomes less than 25,000 per year 12 years ago goes thus:
Let the the number of families who had incomes less than 25,000 per year 12 years ago be represented by x.
Since we are told that this number of families is 60% of the families that had this income level 12 years ago. This means that:
60% of x = 54,000
60/100 × x = 54,000
0.6 × x = 54,000
0.6x = 54,000
Divide by 0.6
0.6x/0.6 = 54000/0.6
x = 90,000
The number of families who had incomes less than 25,000 per year 12 years ago was 90,000.
1. Arjun puts £750 into his savings account. The account earns 5% simple interest per annum. After 4 years, how much money will Arjun have in his savings account? £ 1. Connor invests £1500 of his money for 2 years at a simple interest rate of 10%. How much money will he get back in interest?
Answer:
1. 900
2. 350
Step-by-step explanation:
the formula,
A= P(1+rt)
A= final amount
P= starting amount
r= intrest rate
t= time
1. A=750(1+.05*4)
A=750(1.2)
A=900
2. A=1500(1+.1*2)
A=1500(1.1)
A=1650
But theyre
asking for how much intrest will they get back, so you subtract the new amount by the starting amount to find how much intrest was earned
1650-1500=350
Please help I’m being timed!!! A country commits to decreasing spending for infrastructure in various ways at a rate of 30% per year. At the time of the announcement, the country is spending $12 billion per year. Which graph models the amount of infrastructure spending for future years?
Answer:
It would be the graph that has point (0,12) and is decreasing to the right.
Which is the best estimate of A.2 B.6 C.12 D.24
Answer:
24
Step-by-step explanation:
90/7 ÷ 1 3/4
Change to an improper fraction
90/7 ÷ ( 4*1 +3 ) /4
90/7 ÷ 7/4
Copy dot flip
90/7 * 7/4
90/4
22.5
Best estimate is 24
Answer:
A:2
Step-by-step explanation:
A is the answer because 90 divided by 7 is 12.8 which would be 13, and the 1 and 3/4 would be 7. 13 divided by 7 would equal 1.85. When rounded your answer would be 2.
Please help, thanks :) (Question is attached below)
Answer:
Solution : Graph 4
Step-by-step explanation:
Let's break down this function,
{ y = 5 if x ≤ - 2, y = 0 if x = 3, y = - 1 if x > 3 }
As you can see, graph 4 is the only one that represents this.
• When y = 5, x ≤ - 2. This is represented by a ray with a colored hole, indicating that x = - 2. At the same time this ray extends infinitely in the negative direction, indicating that x < - 2.
• When y = 0, x = 3. This is represented as the point ( 3, 0 ).
• And when y = - 1, x > 3. At y = - 1 another respective ray, that has a non - filled hole, indicates that x ≠ 3. The ray extends infinitely in the positive direction, meeting the criteria that x > 3.
Complete the table for the given rule.
1
Rule: y =-
4
y
13
4
2
Answer:
x y
1/4 0
13/4 3
2 7/4
Step-by-step explanation:
To complete the table we just need to replace the value of x and get y as:
for x = 1/4
[tex]y=\frac{1}{4}-\frac{1}{4}=0\\[/tex]
for x=13/4
[tex]y=\frac{13}{4}-\frac{1}{4}=\frac{12}{4}=3[/tex]
for x=2
[tex]y=2-\frac{1}{4}=\frac{7}{4}[/tex]
So, the complete table is:
x y
1/4 0
13/4 3
2 7/4
the scale on the map is 1 cm represents 40 km . the actual straight line distance between 2 cities is about 320 km what is the map distance between these 2 cities
Answer:
8cm
Step-by-step explanation:
the ratio of cm to km is 1 cm on the map equals 40 km. or 1/40 so you have to find what is x/320 using the ratio of 1/40 you gt that x equals 8
Which was one of the goals for some advocates of the Progressive movement?
A: conservation
B: laissez-faire economy
C: welfare
D: establishment of a national bank
Answer:
d
Step-by-step explanation:
Eric has a bag of 100 marbles. The bag contains 27 red marbles and 42 green marbles, and the rest are blue
marbles.
Eric is interested in the following events.
A: drawing a blue marble
B drawing a red marble
if Eric randomly draws two marbles, without replacing the first one, what is P(AB)?
Enter your answer as a fraction in simplest form. For example. If your answer is which reduces to enter it like
this: 3/4
Answer:
P(AB) = 837/9100
Step-by-step explanation:
The given parameters are;
The number of marbles in the bag = 100 marbles
The number of red marbles = 27
The number of green marbles = 42
The number of blue marbles = 100 - 27 - 42 = 31
The probability, A of drawing a blue marble = 31/100
The probability,B of drawing a red marble after a blue marble has been taken without replacement = 27/91
The probability P(AB) = 31/100× 27/91 = 837/9100
The probability that Eric randomly draws two marbles without replacing the first one where the first one is a blue marble and the second marble is a red marble is 837/9100.
Rectangle EFGH is the image of rectangle ABCD after a sequence of transformations. Which statement describes the transformation that occurred?
A. Rectangle ABCD was rotated 90 counterclockwise about the origin followed by dilation with center (0, 0) and a scale factor of 3/4.
B. Rectangle ABCD was translated right 3 units and down 11 units followed by a dilation with center (0, 0) and a scale factor of 1/2.
C. Rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.
Answer:
C. Rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.
Step-by-step explanation:
See figure for intermediate steps.
The transformed rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the rectangle be represented as ABCD
Now , the coordinates of the rectangle are
A ( 1 , 9 ) , B ( 1 , 6 ) , C ( 7 , 6 ) and D ( 7 , 9 )
Now , the rectangle is dilated with scale factor of 1/2 , we get
A ( 0.5 , 4.5 ) , B ( 0.5 , 3 ) , C ( 3.5 , 3 ) and D ( 3.5 , 4.5 )
And , the rectangle is translated right 3.5 units and down 8 units.
So , the new coordinates of the rectangle is
E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )
Hence , the transformed rectangle is E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )
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Triangle T U V is shown. Side T U has a length of 5 units, side U V has a length of 8 units, and side T V has a length of 11 units. Which statement is true regarding triangle TUV? Angle T is the smallest angle. Angle V is the smallest angle. Angles U and V must be equal. Angles U and T must be equal.
Answer:
b
Step-by-step explanation:
edg 2020
The smallest measure of angle is angle ∠ V due to opposite angle of smallest side which is correct option(B).
What is a Triangle?A triangle is defined as simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol of Δ and consists of three connected vertices. Triangles can be categorized into a number of different varieties according on their sides and angles.
A triangle has three sides, three vertices, and three interior angles.
The angle sum property of a triangle states that the sum of the three interior angles of a triangle is always 180°
In ΔTUV,
Length of Side TU = 5 units
Length of Side UV = 8 units
Length of Side TV = 11 units
Side TU is opposite of angle ∠ V
Side UV is opposite of angle ∠ T
Side TV is opposite of angle ∠ U
The sides in order from longest to shortest : Side TV > Side UV = Side TU
The longest side is always opposite of the largest angle, and the smallest side is always opposite of the smallest angle.
Hence, the angle in order from longest to shortest : angle ∠ U > angle ∠ T > angle ∠ V
Thus, the smallest measure of angle is angle ∠ V.
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3) The Buendorf family has agreed to let their children get some animals. The kids said they
want chickens and goats, so the parents told them the number of chickens could be four
times that of the number of goats. They are allowed to have no more than 30 total animals.
What are the possible number of chickens and goats?
Answer:
The possible number of goats is 6 and the possible number of chicken is 24
Step-by-step explanation:
Let
chicken=c
Goat=g
the number of chickens could be four times the number of goats
c=4g
Total number of animals=30
c+g=30
Recall, c=4g
So,
c+g=30
4g+g=30
5g=30
Divide both sides by 5
5g/5=30/5
g=6
Recall,
c+g=30
c+6=30
c=30-6
=24
c=24
The possible number of goats is 6 and the possible number of chicken is 24 making a total of 30 animals
A garden has an area of 264ft^2. Its length is 10 ft more than its width. What are the dimensions of the garden?
Answer:
Length = 22 ftWidth = 12 ftStep-by-step explanation:
Let length of the garden be ' x + 10 '
Let breath of the garden be ' x '
Area of the garden = 264 ft²
Now, let's find the breath of the garden 'x'
[tex]x(x + 10) = 264[/tex]
Distribute X through the parentheses
[tex] {x}^{2} + 10x = 264[/tex]
Move constant to left and change its sign
[tex] {x}^{2} + 10x - 264 = 0[/tex]
Write 10x as a difference
[tex] {x}^{2} + 22x - 12x - 264 = 0[/tex]
Factor out X from the expression
[tex]x(x + 22) - 12x - 264 = 0[/tex]
Factor out -12 from the expression
[tex]x(x + 22) - 12(x + 22) = 0[/tex]
Factor out X +22 from the expression
[tex](x + 22)(x - 12) = 0[/tex]
When the products of factors equals to 0 , at least one factor is 0
[tex]x + 22 = 0[/tex]
[tex]x - 12 = 0[/tex]
Solve for X
[tex]x + 22 = 0[/tex]
[tex]x = 0 - 22[/tex]
[tex]x = - 22[/tex]
Again,
[tex]x - 12 = 0[/tex]
[tex]x = 0 + 12[/tex]
[tex]x = 12[/tex]
(The dimensions can't be negative. )
So, width = 12 ft
Now, let's find the length of the garden ' X + 10 '
[tex]x + 10[/tex]
Plug the value of X
[tex]12 + 10[/tex]
Calculate the sum
[tex] = 22 \: ft[/tex]
Therefore,
Length = 22 ftWidth = 12 ftHope this helps..
Best regards!
factor 16x to the 5th power subtract x to the third power
Answer:
X ^3 (4x+1) (4x-1)
Step-by-step explanation:
Factor x3 out of 16x5−x3
Rewrite 16x2 as (4x)2
Rewrite 1 as 1^2
Factor
x^3 (4x+1) (4x-1)
I hope I helped
The co ordinates of the point where lines ax = by and ay=6x intersects are
Answer: (0, 0)
Step-by-step explanation:
ax = by ay = 6x
[tex]\dfrac{ax}{b}=y\qquad \quad y=\dfrac{6x}{a}[/tex]
Use substitution:
[tex]\dfrac{ax}{b}=\dfrac{6x}{a}\\\\\\\text{Cross Multiply:}\\a^2x=6bx\\\\\\\text{Solve for x:}\\a^2x-6bx=0\\x(a^2-6b)=0\\x=\dfrac{0}{a^2-6b}\\\large\boxed{x=0}[/tex]
Substitute x = 0 to solve for y:
[tex]\dfrac{ax}{b}=y \\\\\dfrac{a(0)}{b}=y\\\\\large\boxed{0=y}[/tex]
if sade can be 12 years and his mother senior him with 24 years and his dad senior him with 30 yearshow old is the sum of the both parents
Answer:
88
Step-by-step explanation:
mother's age = 12+24
= 36
father's age = 12+40
=52
add the parent age= 36+52
= 88
The length of the second side of a triangle is 2 inches less than the length of the first side.The length of the third side is 12 inches more than the length of the first side.the perimeter of the triangle is 73 inches.Find the length of each side of the triangle.
Answer:
The lenght of the tree sides of the triangle are:
first side: 21 inches
second side: 19 inches
third side: 33 inches
Step-by-step explanation:
a + b + c = 73
b = a - 2
c = a + 12
a = leght of the first side of the triangle
b = lenght of the second side of the triangle
c = lenght of the third side of the triangle
then:
a + (a-2) + (a+12) = 73
3a - 2 + 12 = 73
3a + 10 = 73
3a = 73 - 10
3a = 63
a = 63/3
a = 21 inches
b = a - 2
b = 21 - 2
b = 19 inches
c = a + 12
c = 21 + 12
c = 33 inches
Check:
21 + 19 + 33 = 73
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The length of the sides of the triangle are:
first side: 21 inchessecond side: 19 inchesthird side: 33 inchesWhat is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the sides of triangles be x, y, z.
As, perimeter of the triangle is 73 inches.
x+ y+ z= 73................(1)
and, length of the second side of a triangle is 2 inches less than the length of the first side.
y= x- 2
and, length of the third side is 12 inches more than the length of the first side.
z= x + 12
Substitute the values of y and z in equation (1)
x+ x-2 + x+ 12= 73
3x + 10 =73
3x= 63
x= 21
Then, First side= 21 inch
second side = 21 - 2 = 19 inch
third side= 21+ 12 = 33 inch
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Valerie had a jug that contained 128 fl oz of salsa to put into bowls at a restaurant. She filled each bowl with 6 fl oz of salsa until there was not enough salsa left in the jug to completely fill another bowl. How many fluid ounces of salsa were left in the jug?
Answer: 2 fl oz
Step-by-step explanation:
Division with remainders
128/6=21.33333..
[tex]21\cdot 6=126[/tex]
128-126=2
2 fl oz was left in the jug
the legnth of rectangular sheet decreases by 34.5 cm its width decreases proportionally that is by the same percentage. if the sheets original width was half of the legnth and the new (smaller) area was 1.2 m^2 what was original sheet's width
Answer:
The original width was 94.71 cm
Step-by-step explanation:
Given:
new smaller area = 1.2m^2
Decrease in length of the rectangular sheet = 34.5cm
Therefore:
1. the final width of the sheet is given as
2X^2 = 1.2 m^2
X^2 - 0.6 m^2
X^2 = 10000 * 0.6 cm
X = 77.46 cm (this is the width)
2. The length of the sheet
= 2 * 77.46
= 154.92 cm.
3. Initial length of the sheet
= 154.92 + 34.5
= 189.42 cm.
4. Initial width of the sheet ( original ).
= 189.42 / 2
= 94.71 cm.
5. Initial area of the sheet
= 94.71 * 189.92
= 17939.9 cm^2
New area of the sheet
= 79.46 * 154.92
= 12000.1 cm^2
Difference between the initial and new area
= 17939.9 - 12000.1
= 5939.86 cm^2
Percentage of area decrease
= 5939.86 ' 17939.9
= 33.1%
38. Convert 85 to a number in base eight.
O 95 (base eight)
O 105 (hase eight)
O 115 (base eight)
O 125 (base eight)
Answer:
divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125
Carlos has 275% as much money as Mariame. Together they have $90. How much money does Mariame have?
Answer:
$24.
Step-by-step explanation:
Let's say Carlos has $c of money, and Mariame has $m of money.
c = 2.75m
c + m = 90
2.75m + m = 90
3.75m = 90
m = 24
c + 24 = 90
c = 66
So, Mariame has $24 and Carlos has $66.
Hope this helps!
Please help with 4.)
WILL MARK BRAINLIEST X
Answer:
a) More.
b) Less.
c) More.
Step-by-step explanation:
a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.
b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.
c) The same exact thing as part a.
Hope this helps!
What is the circumference of a circle with a diameter of 100m. A 100m B 157m C 300 m D 314m
Answer:
C = 314 m
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
Using 3.14 for pi
C = 3.14 * 100
C = 314 m
Answer:
The answer is option D.
314mStep-by-step explanation:
Circumference of a circle = πd
Where d is the diameter
From the question
d = 100m
Circumference of the circle is
100π
= 314.2
Which is 314m to the nearest whole number
Hope this helps you
in a quiz bhaskar scored -60,20and0and tamanna scored 20,0and60 in three successive rounds.who socred more
Answer:
Tamanna scored more.
Step-by-step explanation:
Bhaskar scored -60, 20 and 0. His total score is therefore:
-60 + 20 + 0 = -40
Tamanna scored 20, 0, 60. His total score is therefore:
20 + 0 + 60 = 80
Therefore, Tamanna scored more.
a system of linear equations is given by the tables. One of the tables is represented by the equation y= -1/3x + 7
the equation that represents the other equation y= x +
the solution of the system is ( , )
Answer:
Other equation: y = 1/3x + 5
Solution: (3, 6)
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Identify tables
1st table is the unknown equation
2nd table is the known equation (found using y-intercept 7)
Step 2: Find missing equation
m = (6 - 5)/(3 - 0)
m = 1/3
y = 1/3x + b
5 = 1/3(0) + b
5 = b
y = 1/3x + 5
Step 3: Find solution set using substitution
1/3x + 5 = -1/3x + 7
2/3x + 5 = 7
2/3x = 2
x = 3
y = 1/3(3) + 5
y = 1 + 5
y = 6
