We can conclude that cosθ = sin(90° - θ) for any right triangle with angle θ and its complementary angle (90° - θ).
To prove that cosθ = sin(90° - θ), we can use the properties of right triangles and their angles.
Consider a right triangle ABC, where angle A is θ, angle B is (90° - θ), and angle C is 90°.
According to the definition of trigonometric functions in a right triangle:
- cosθ = adjacent side (AB) / hypotenuse (AC)
- sin(90° - θ) = opposite side (AB) / hypotenuse (AC)
From the given definitions, we can see that both cosθ and sin(90° - θ) have the same ratio of side lengths, which is AB/AC.
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3 pitchers of berry were made and 1/5 serving size how many were made
The total number of berry pitchers made is 15/5 or 3.
If the serving size of berry pitchers is 1/5, it means that each pitcher represents 1/5 of a full serving. To determine the total number of pitchers made, we need to calculate how many times 1/5 fits into the whole serving.
Let's assume that the total number of pitchers made is represented by "x". We can set up the following equation:
x * 1/5 = 3
To solve for "x," we multiply both sides of the equation by 5:
5 * (x * 1/5) = 5 * 3
This simplifies to:
x = 15/5
Thus, the total number of berry pitchers made is 15/5 or 3.
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Use the Distributive Property to find (g−7)(g−2) all i need is the answer
Answer: [tex]g^2-9g+14[/tex]
Step-by-step explanation:
(g-7)(g-2)
[tex]g^2 - 2g-7g+14[/tex]
[tex]g^2-9g+14[/tex]
Use FOIL method.
26. Find the circumference and area. Give exact answers.
The area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.
From the given figure, legs of triangle measure the same, that is 10 units.
Let the diameter of the circle be x.
By using Pythagoras theorem,
x²=10²+10²
x²=100+100
x²=200
x=10√2 units
Radius = 5√2 units
We know that, area of a circle = πr²
= 3.14×(5√2)²
= 3.14×50
= 157 square units
We know that, circumference of a circle = 2πr
= 2×3.14×5√2
= 31.4√2 units
Therefore, the area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.
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solve 6x²-42=0 with the exact values of x
Answer:
X=-√7 and √7
Step-by-step explanation:
To solve the equation 6x² - 42 = 0, we can begin by rearranging it to isolate the variable term:
6x² = 42
Then, we can divide both sides by 6:
x² = 7
To get the exact values of x, we need to take the square root of both sides:
x = ±√7
Therefore, the exact values of x are √7 and -√7.
Jane is converting the given equation in Standard Form to the General Form. At which step did she make her first mistake?
Answer:
Step 4
Step-by-step explanation:
In step 3, 16 + 9 = 25, so step 4 should subtract 25 from both sides. Also, y² became -y² in step 4 which is incorrect.
Answer: Step 4
The table describes the quadratic function h(x).
x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
What is the equation of h(x) in vertex form?
h(x) = (x + 2)2 − 3
h(x) = (x + 1)2 − 2
h(x) = (x − 1)2 + 2
h(x) = (x − 2)2 + 3
The equation of h(x) in vertex form is given as follows:
h(x) = (x + 2)² - 3.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence it's coordinates are given as follows:
(-2,-3).
Then the equation is:
h(x) = a(x + 2)² - 3.
When x = 0, h(x) = 1, hence the leading coefficient a is obtained as follows:
1 = a(2)² - 3
4a = 4
a = 1.
Hence the equation is:
h(x) = (x + 2)² - 3.
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tamikas math teachers plots student grades on their weekly quizzes against the number of hours yhe say they study on the pair of coordinate axes and then draws the lines of best fits. what is the meaning of the x-value on the line when y = 100
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
We have,
Assuming that the line of best fit represents the trend between the number of hours students study and their quiz grades,
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
In other words,
If a student studies for this amount of time, they are predicted to achieve a quiz score of 100 based on the trend shown by the line of best fit.
Thus,
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
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In Austin TX the cost of housing for a family of four is $1600 per month. How much more would the family need to bring home annually in order to cover the cost of increased housing
The family would need to bring home an additional $2400 annually to cover the increased cost of housing.
The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.
The current monthly cost of housing is $1600 so the annual cost is:
$1600/month x 12 months = $19,200/year
Let's assume the family needs to cover an increased housing cost of $200 per month.
The new monthly cost of housing would be:
$1600/month + $200/month = $1800/month
The new annual cost of housing would be:
$1800/month x 12 months = $21,600/year
The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:
$21,600/year - $19,200/year = $2400/year
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Show that the union of a nonempty directed family of subgroups of a group G is a subgroup of G?
H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.
Let [tex]\mathcal{H}[/tex] be a non-empty directed family of subgroups of a group G. We need to show that the union [tex]H=\bigcup_{H_i\in\mathcal{H}}H_i[/tex] is a subgroup of G.
First, note that H is non-empty since[tex]\mathcal{H}[/tex] is non-empty. We also have [tex]1_G \in H_i[/tex] for all [tex]H_i\in\mathcal{H}[/tex], so [tex]1_G \in H.[/tex]
To show that H is closed under multiplication, let [tex]h_1,h_2\in H[/tex]. Then there exist [tex]H_{i_1},H_{i_2}\in\mathcal{H}[/tex] such that [tex]h_1\in H_{i_1}[/tex] and [tex]h_2\in H_{i_2}.[/tex] Since [tex]\mathcal{H}[/tex] is directed, there exists[tex]H_{i_3}\in\mathcal{H}[/tex] such that [tex]H_{i_1}\cup H_{i_2} \subseteq H_{i_3}[/tex]. Thus, [tex]h_1,h_2\in H_{i_3},[/tex]and since [tex]H_{i_3}[/tex] is a subgroup, we have [tex]h_1h_2\in H_{i_3} \subseteq H[/tex]. Therefore, H is closed under multiplication.
Finally, to show that H is closed under taking inverses, let h\in H. Then there exists [tex]H_i\in\mathcal{H}[/tex] such that [tex]h\in H_i[/tex]. Since [tex]H_i[/tex]is a subgroup, we have [tex]h^{-1}\in H_i \subseteq H[/tex]. Therefore, H is closed under taking inverses.
Since H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.
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Actually answer and don't ask for brainliest
A hotel survey showed that nearly 30% of the guests staying at the hotel were there for personal reasons. The remainder of the guests were at the hotel on business.
Use the table of randomly generated letters to answer the questions about this scenario. The letter P represents personal reasons, and B represents business reasons.
BBB PBB BPB PPB BBP
BBP PBB PPB PBB BBP
BBP BPB BBB BBB BBB
PPB BPB PBP BPB BBP
BPB PBP PPB PBB BBB
Based on this data, the estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is .
The estimated probability that it takes at least four guests to find one who is staying for personal reasons is .
Answer:
The estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is 0.25.
The estimated probability that it takes at least four guests to find one who is staying for personal reasons is 0.125.
Please help!! I don’t understand trigonometric functions
The horizontal transformations are defined as follows:
cos(ax).
They are classified as follows:
Stretch if |a| < 1.Compression if |a| > 1.The vertical transformations are defined as follows:
acos(x).
They are classified as follows:
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Prove: If A and B are m × n matrices such that Ax = Bx for all x ∈ R
n, then A = B.
From matrix property it can be showed that A=B.
Given,
If A,B and x are matrices with x≠0 and AX=BX
Now,
X must be non-singular matrix because
A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]
AI = BI
= I( identity matrix )
⇒A = B
Hence Proved, A = B .
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The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answe B 6-10 5 5-5-5 25 + 25 + 25 + 25 + 25 + 25 5+5+5+5+5+5
The expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
Calculating the expression that represents the surface area of the cube?From the question, we have the following parameters that can be used in our computation:
The cube
The side length of the cube is
Side length = 5
The surface area of the cube is calculated as
SA = 6 * Side length²
So, we have
SA = 6 * 5²
Expand
SA = 6 * 25
Further expand
SA = 25 + 25 + 25 + 25 + 25 + 25
Hence, the expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
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Complete question
The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answer
(a) 5 5 - 5 - 5
(b) 25 + 25 + 25 + 25 + 25 + 25
(c) 5 + 5 + 5 + 5 + 5 + 5
The figure is attached
Find the area of the regular polygon below and round your answer to the nearest tenth.
Explain your reasoning. Show all your work.
1) What is the perimeter of the regular polygon?
2) What is the apothem length? Show all your work and explain how you found the apothem.
3) What is the area of the regular polygon? Show your work.
7 sides each side is 10 in long
The area of the regular polygon is 311.5 in2.
We are given that;
A polygon
Now,
To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.
To find the apothem length, we need to use some trigonometry.
The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.
To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.
A = (1/2)708.9 ≈ 311.5 in2.
Therefore, by the area the answer will be 311.5 in2.
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Books in the clearance section at Reading Central Bookmart cost $6.00 for paperbacks and $12.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $53.00 or less?
A.
12p + 6h > 53
B.
6p + 12h < 53
C.
12p + 6h < 53
D.
6p + 12h < 53
Can someone help me with this pls its due td pls
The measures are given as follows:
x = 2.m < A = 110º.m < ABD = 34º.How to obtain the measures?On a parallelogram, the opposite sides are congruent, hence the value of x is obtained as follows:
2x = 4
x = 2.
Opposite angles are congruent, meaning that they have the same measure, hence the measure of angle A is given as follows:
m < A = m < C = 110º.
Consecutive angles are supplementary, meaning that the sum of their measures is of 180º, hence the measure of angle B is given as follows:
m<B = 180º - 110º = 70º.
Considering the angle addition postulate, the measure of angle ABD is given as follows:
m < ABD = 70 - 36
m < ABD = 34º.
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l want the steps.
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The first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
How to solve1. To find the first derivative of the parametric curve x = 1/(t-1) and [tex]y = t^2/(t-1)[/tex], we can use the chain rule.
2. Let's differentiate each component separately.
3. Differentiating x with respect to t, we have:
dx/dt = [tex]-1/(t-1)^2[/tex]
4. Differentiating y with respect to t, we have:
dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2[/tex]
5. Therefore, the first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
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Points z1 and z2 are shown on the graph. (10 points)
complex plane, point z sub 1 at 4 to the right of the origin and 6 units up, point z sub 2 at 5 units to the left of the origin and 2 units up
Part A: Identify the points in standard form and find the distance between them.
Part B: Give the complex conjugate of z2 and explain how to find it geometrically.
Part C: Find z2 − z1 geometrically and explain your steps.
Answer:
Part A: The point z1 is at (4, 6) and the point z2 is at (-5, 2). The distance between them is √((4-(-5))^2 + (6-2)^2) = √(9^2 + 4^2) = √(81 + 16) = √97.
Part B: The complex conjugate of z2 is (-5, -2). Geometrically, it can be found by reflecting the point z2 across the x-axis.
Part C: To find z2 − z1 geometrically, you can draw a vector from z1 to z2. The coordinates of this vector are (-5-4, 2-6) = (-9, -4). So z2 − z1 = -9 - 4i.
You purchased a home this year for $315,000. You applied for homestead exemption
and were able to take off $50,000 of the appraised value for taxes. The taxes in your
county are 1.22%. What is the monthly payment added to your mortgage for
property taxes? Please round to the nearest cent and do not put a dollar sign or
spaces in your answer.
The monthly payment added to your mortgage for property taxes is $270.25, rounded to the nearest cent. It is a good idea to budget for property taxes when purchasing a home, as they can be a significant expense that should not be overlooked.
To calculate the monthly payment added to your mortgage for property taxes, we can use the following steps:
1) Find the taxable value of the home by subtracting the exemption from the appraised value:
Taxable value = $315,000 - $50,000 = $265,000
2) Calculate the annual property tax by multiplying the taxable value by the tax rate:
Annual property tax = $265,000 x 0.0122 = $3,243
3) Divide the annual property tax by 12 to get the monthly payment:
Monthly property tax payment = $3,243 / 12 = $270.25
It's important to note that property tax rates can vary depending on where you live, so it's a good idea to check with your local tax authority to get an accurate estimate of your property tax bill.
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Helppppp pleaseeeeeeee
To achieve a 1 in row 1, column 1, divide row 1 by 4 in the given matrix, resulting in the updated matrix. This row operation preserves the system of linear equations represented by the matrix.
To get a 1 in row 1, column 1 of the given matrix, you can perform the following valid row operation:
R1 = (1/4) * R1
This operation scales row 1 by a factor of 1/4, resulting in the new matrix:
1 , -3/4 , -43/4
3 , -2 , -30
By dividing each element in row 1 by 4, the value in row 1, column 1 becomes 1. This row operation maintains the equivalence of the system of linear equations represented by the matrix.
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Nicole correctly calculates that the Coach will spend $14,800 after 12 months if he chooses the Five-Year Plan. She then claims the total cost of the Five-Year Plan will be $74,000, because 5x $14,800 $74,000. The Coach says that Nicole made a mistake. Do you agree that Nicole made a mistake? Explain your reasoning. ANSWER FAST WHOEVER GIVES CORRECT ANSWER I WILL GIVE BRAINLIST!
I agree that Nicole made a mistake because the total cost of the Five year plan is $ 34, 000 and not $ 74, 000.
How was the mistake made ?The total cost of the Five year plan would be:
= Payment per month for the five year plan x Number of months in year x number of years + Down payment
= 400 x 12 x 5 + 10, 000
= 4, 800 x 5 + 10, 000
= $ 34, 000
The mistake that Nicole made was to multiply the $ 14, 800 that was the cost of the five year plan in one year, by five years. This was wrong because it meant including a new down payment in every one of the five years instead of just once.
She should have multiplied $4, 800 by 5 years and then added the down payment which is paid just once.
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Please someone help me 28th this, eleven people are entered in a race if there are no ties in how many ways can first and second place come?
solve by using elimination. 12x + 36y = −3
−12x − 36y = 0
The given system of equations has no solution.
Given that a system of equations, 12x + 36y = −3 and −12x − 36y = 0, we need to solve it,
We know for a system of equations =
a₁x + b₁y = c₁ and a₂x + b₂y = c₂
If a₁ / a₂ = b₁ / b₂ = c₁ / c₂ then the system has infinite solutions.
If a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂ then the system has no solutions.
If a₁ / a₂ ≠ b₁ / b₂ then the system has a unique solution.
comparing the coefficients given,
-12/12 = -1
-36/36 = -1
-3/0 = -3
We get here the condition of a₁ / a₂ ≠ b₁ / b₂, which means that the system has no solution.
Hence the given system of equations has no solution.
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please show work I don't understand how to do this
so first I would move -6x to the other side and -2 at the same time it would look like this
24+2=6x+7x
and simplify
26= 13x
divide both sides by 13 to find x
2= x
What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.
Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.
Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
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Silverton County is home to a declining population of sage grouse, an endangered species of land bird similar to turkeys. Every decade, the Silverton Wildlife Center publishes its estimate of the county's sage grouse population. The most recent estimate, published this year, concluded that there are about 115,000 sage grouse in the county, and the population is expected to decrease by a factor of 1/4 each decade.
Write an exponential equation in the form y=a(b)x that can model the estimated population of sage grouse in Silverton County, y, in x decades.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]
How to write an exponential equation in the form y=a(b)x that can model the estimated population of sage grouse in Silverton CountyGiven that the population is expected to decrease by a factor of 1/4 each decade, we know that the common ratio, b, is 1/4.
Since the most recent estimate is about 115,000 sage grouse, we can assign this value to the initial population, a.
Therefore, the exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]
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Please help quickly! (Will mark Brainliest)
Hello!
area
= (b x h)/2
= (18in x 7in)/2
= 126in²/2
= 63in²
Answer:
63 in²
Step-by-step explanation:
1/2 bh=area of the triangle
Can someone please answer and provide an explanation for these problems?
Step-by-step explanation:
The way you can think about volume is that we have some cross sectional area times the height of the solid.
27.
The volume of a square based pyramid is
[tex]v = {s}^{2} ( \frac{h}{3} )[/tex]
where h is the height of the pyramid
s is the side length of the square base.
S=7
h=12
[tex]v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196[/tex]
28. The volume of a rectangular prism
[tex]v = l \times w \times h[/tex]
where l is length
w is width
h is height
[tex]v = 11 \times 11 \times 8 = 968[/tex]
29.
Use the same formula in 27
[tex]v = 100(3) = 300[/tex]
30.
Volume of a Cylinder is
[tex]v = \pi {r}^{2} h[/tex]
where r is the radius of the circle
where h is the height
r is half of the diameter
The diameter is 22, thus the radius is 11.
[tex]v = {11}^{2} (8)(\pi)[/tex]
[tex]v = 968\pi[/tex]
pi is approximately 3.14
[tex]v = 3041.06[/tex]
31. Volume of A Sphere
[tex] \frac{4}{3} \pi {r}^{3} = v[/tex]
The radius is half of diamter, thus r=7
[tex] \frac{4}{3} \pi( {7}^{3} ) = 1436.76[/tex]
I need to know how to solve number 4 in order to get a solution
Answer: 11x16x5=880
This means the answer is C
Solve:{2x-y=5
{4x+2y=-2