[tex]\stackrel{\textit{Pythagorean Identities}}{1+tan^2(\theta)=sec^2(\theta)}\implies tan^2(\theta ) = sec^2(\theta )-1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ csc^2(\theta )tan^2(\theta )-1~~ = ~~tan^2(\theta ) \\\\[-0.35em] ~\dotfill[/tex]
[tex]csc^2(\theta )tan^2(\theta )-1\implies \cfrac{1}{sin^2(\theta )}\cdot \cfrac{sin^2(\theta )}{cos^2(\theta )}-1\implies \cfrac{1}{cos^2(\theta )}-1 \\\\\\ \cfrac{1^2}{cos^2(\theta )}-1\implies \left[ \cfrac{1}{cos(\theta )}\right]^2-1\implies sec^2(\theta )-1\implies tan^2(\theta )[/tex]
Solve the system with elimination.
3x + y = 9
x + 2y = 3
Answer: X = 3 and Y = 0 3,0
CAN SOMEONE PLEASE ANSWER THIS QUICK I HAVE 5 MINS PLS
Answer:
$20
Step-by-step explanation:
49 is the outlier
The side of a square is 3 cm long.
What is the length of the diagonal of the square? Give a reason for your answer.
INSTRUCTION: Round your answer to two decimal places.
Answer:
approximately 4.23 cm
Simplify the expression. Write your answer as a power.
(xy)⁷
The simplified expression is
Answer:
x⁷y⁷
Step-by-step explanation:
An exponent signifies the base is a repeated factor in the product. The exponent is the number of times it is a factor.
__
The term (xy)^7 means (xy) is a factor 7 times:
= (xy)·(xy)·(xy)·(xy)·(xy)·(xy)·(xy)
The commutative and associative properties of multiplication let us rearrange this to ...
= (x·x·x·x·x·x·x)·(y·y·y·y·y·y·y)
= (x^7)(y^7)
The expression can be simplified to ...
[tex](xy)^7 =\boxed{x^7y^7}[/tex]
_____
The rule of exponents is ...
(ab)^c = (a^c)(b^c)
Find the midpoint M between V(3,7,-6) and W(-4,-8,7). Put your answer in the form (x,y,z)
Answer:
M(-1/2, -1/2, 1/2)
Step-by-step explanation:
To find the midpoint of a line segment, average the coordinates of the end points.
M = (A +B)/2
__
M = (V +W)/2
M = ((3, 7, -6) +(-4, -8, 7))/2 = (3-4, 7-8, -6+7)/2 = (-1, -1, 1)/2
M = (-1/2, -1/2, 1/2)
The midpoint between V and W is M(-1/2, -1/2, 1/2).
)The scatter plot shows the relationship between the number of hours spent practicing piano per week and the number of pieces of music the student can play:
A scatter plot is shown. The x-axis is labeled hours spent practicing and the y-axis is labeled number of pieces student can play. Data points are located at 1 and 1, 1 and 5, 2 and 10, 2 and 15, 3 and 15, 3 and 25, 4 and 40, 5 and 40, 5 and 50, 6 and 55, 6 and 70, 8 and 90, 3 and 70. A circle labeled T includes all points except for 3 and 70. Point 3 and 70 is circled and labeled as R.
Part A: What is the group of points labeled T called? What is the point labeled R called? Give a possible reason for the presence of point R. (3 points)
Part B: Describe the association between the number of hours practiced each week and the number of pieces a piano student can play. (2 points)
Part A
The group of points labeled "T" can be thought of as the main cluster of points. Your teacher might have given another name for it, but this is how I think about it. All of these points are very close to a straight line.
The point R is known as an outlier. It is fairly far from the main cluster, in that it's not near the regression line. You can think of the points in the main cluster as houses along/near a straight road. The outlier house is unfortunately far from that road.
One possible reason for point R is that the student is very talented and can pick up music really easy, thereby not needing that much practice. Another reason is that the student already had tons of prior practice and experience, so they don't need as much practice currently.
============================================================
Part B
We have a strong positive linear association with the main cluster of data points. As mentioned earlier, a straight line is very close to these points. The closer they are to the same straight line, the stronger the correlation.
We have positive correlation because as x goes up, so does y. The variables increase together. Negative correlation happens when x and y go in opposite directions (one goes up, the other goes down).
The outlier point R pulls on the regression line to make it slightly not near the main cluster. The line tries its best to be near all of the points, and that includes the outlier. In some situations, the outlier is ignored and regression is done on the other set of points.
As you can probably guess, the outlier dilutes the strength of the correlation. The further the outlier, the weaker the correlation gets.
Answer:
Here you go!
Step-by-step explanation:
A) The group of points labeled T called cluster. The point labeled R called outlier. Student because of being proficient on the piano before practice was measured.
B) A positive correlation is a relationship between two variables that tend to move in the same direction
)The number of elements in power set {1, 2, 3} is
(a) 4
(b) 6
(c) 8
(d) 9
Answer:
(c) 8Step-by-step explanation:
The number of elements in a power set = the number of subsets of a set
Formula:
Let S be a sent ,the number of elements of the power set of S =
[tex]2^{\text{card(S)} }[/tex]
Where card(S) = number of element of S itself.
=======================================
In this case :
Card(S) = 3
Then
the number of elements of the power set of S =
[tex]2^{3}=8[/tex]
Emily ran 4 1/8 miles at track practice on one day and 3 3/4 miles the next day. Her coach said she needed to run 10 miles this week. How many more miles does she need to run?
Answer
2 1/8
Step-by-step explanation 10–7 7/8=(10 – 7) + ( 0–7/8)= 3 +0 × 8 – 7/8= 3 + 08– 78= 3 + 0 – 78= 3 + -7/8 = 2 1/8
How much water is in each basket?
Answer:
E
Step-by-step explanation:
1 2/3
Divide 5/3 and you get 1 2/3
Answer:
E) 1 2/3
Step-by-step explanation:
5 divided between 3 buckets in 5/3 which in a mixed number is 1 2/3
How do I find the function rule???
x: 0, 1, 2, 3
y: 5, 4, 3, 2
Answer: y=-1x+5
Step-by-step explanation:
1. Use slope-intercept formula (y = mx + b) to find the slope which is represented by the variable 'b'.
m = ∆y / ∆x
m = -1 / 1
m = -1
y= -1x + b
2. Use any cooresponding x and y values to substitute into the formula. Ex: (x,y) → (1,4)
y = mx + b
4 = -1(1) + b
4 = -1 + b
5 = b
3. Plug in the values found into the formula.
y = -1x + 5
somebody please help me with this
Answer:
P(A) = 5/12
P(B) = 1/2
Step-by-step explanation:
A) Sum greater than 7
If the sum needs to be >7, then it can be 8, 9, 10, 11, and 12.
There are 26 out of 36 events where the sum is >7, thus P(A) = 15/36 = 5/12.
B) Sum is even
If we see in an overview of the sum distribution, there is a balanced division between odd and even numbers, thus the probability is very likely to be 1/2. Now let's make sure of it:
If the sum needs to be even, which means divisible by 2, then it can be 2, 4, 6, 8, 10, and 12.
There are 18 out of 36 events where the sum is even, thus P(B) = 18/36 = 1/2.
Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3
Determine the equation of the circle with center (-4,-2) containing the point
(4, -17).
The equation of the circle is:
[tex](x + 4)^2 + (y + 2)^2 = 17^2[/tex]
How to get the equation for the circle?The general equation for a circle of radius R and center (a, b) is:
[tex](x - a)^2 + (y - b)^2 = R^2[/tex]
Here the center is (-4, -2), and it contains the point (4, -17), so the radius is:
[tex]R = \sqrt{(4 - (-4))^2 + (-2 + 17)^2} = 17[/tex]
So the equation of the circle is:
[tex](x + 4)^2 + (y + 2)^2 = 17^2[/tex]
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The coordinates of the vertices of are E (-4, 5), F (-1, 1), and G (3, 4). Determine whether EFG is a right triangle and support your decision. Show all work.
Answer:
No, it will not be a right triangle
Step-by-step explanation:
Since E (-4, 5) and F (-1, 1) are both in-plane one and G (3, 4) in-plane two
The x's are wrong for E and F which would be a cause for not a right triangle
And the y for G is not either 5 or 1 which would help make the triangle a right triangle.
So the triangle ends up being an scalene triangle and not a right triangle
Hopes this helps :)
2x+y=26
x-y=4
Descubra o valor de x e y e explique o processo.
The correct roots of this equation is:
x = 10
y = 6
– This equation is a value substitution system. To solve it, we will: add the terms equal to x, with the sums of the equality.
2x + y = 26
x - y = 4
2x + x = 26 + 4
3x = 30
x = 30/3
x = 10
– Now, let's "take" the first equation of the system, and we'll calculate it, replacing x with its value.
2x + y = 26
2 . 10 + y = 26
20 + y = 26
y = 26 - 20
y = 6
Therefore, the roots of this equation or system is:
x = 10
y = 6
please hepl, 30 points, will give brainly
Answer:
3x(5-7)°+1(5x-7)°
3x×5-3x×7+1×5x-1×7
15x-21x+5x-7
15x+5x-21x-7
20x-14
The density of iron is 7.8 g/cm3. an iron beam has a volume of 10,504 cm³. what is the mass of the iron beam? enter your answer as a decimal in the box.
Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.
How to determine the mass of the iron beam
Let suppose that the iron beam has an uniform density, the mass of the iron beam (m), in gram, is equal to the product of its density (ρ), in grams per cubic centimeter, and its volume (V), in cubic centimeters:
m = ρ · V (1)
If we know that ρ = 10504 cm³ and V = 7.8 g/cm³, then the mass of the iron beam is:
m = (7.8 g/cm³) · (10504 cm³)
m = 81931.2 g
Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.
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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer:
X > 3
Step-by-step explanation:
When divided or multiplied by a negative number the inequality will change
What are the solutions of this quadratic equation? 6x2 6 = 12x 18 a. b. c. d.
The solution to the quadratic equation 6x² + 6 = 12x is x = 1
How to determine the solutions?The quadratic equation is given as:
6x² + 6 = 12x
Equate the equation to 0
6x² - 12x + 6 = 0
Expand the equation
6x² - 6x - 6x + 6 = 0
Factorize the expression
6x(x - 1) - 6(x - 1) = 0
Factor out x - 1
(6x - 6)(x - 1) = 0
Split
6x - 6 = 0 or x - 1 = 0
Solve for x in both instance
x = 1 or x = 1
Hence, the solution to the quadratic equation 6x² + 6 = 12x is x = 1
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quick timer
Consider the pattern below.
5+5/3+5/9+5/27+5/81
What does this pattern represent?
O an arithmetic series
O an arithmetic sequence
a geometric series
O a geometric sequence
Answer:
C
Step-by-step explanation:
g+6 ≥ 5 I need help I don't know how to do it
Answer:
you will subtract 6 from 5 then your answer will be g ≥ -1
Step-by-step explanation:
hope this helps
Find the arc length of the subtending arc for an angle of 3pi/4 radians on a circle of radius 2.5.
The arc length of the circle will be equal to 5.89 units.
What is the length of the arc?The length of the curve on the circumference of the circle making an angle with the centre is called the length of the arc of the circle.
Given that:-
Angle = 3π / 4radius = 2.5 units.The length of the arc will be calculated as:-
Arc = Angle x radius
Arc = ( 3π / 4 ) x 2.5
Arc = 5.89 units.
Therefore the arc length of the circle will be equal to 5.89 units.
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Pre-algebra Volumes. GIVING BRAINLEST! TO FIRST ANSWER. 25 POINTS!
Answer:
Choice B and Choice C
Step-by-step explanation:
Hello! This is how I solved this question:
(10 x 8 x 2) + (3 x 3 x 4) = 160 + 36 = 196ft^3
(10 x 3 x 2) + (5 x 4 x 2) = 60 + 40 = 100ft^3
(8 x 4 x 2) + (3 x 6 x 2) = 64 + 36 = 100ft^3
(8 x 10 x 3) + (4 x 5 x 2) = 240 + 40 = 280ft^3
Choice B and Choice C are the same values, and knowing that you need two of the same values for the volume of the figure must be the same. Giving you your two answers from simply multiplying and adding the answers.
Hope this helps, don't hesitate to ask if you have additional inquiries!
Find the product.
Y^5 x y^3
Please and thx
But hurry
Answer:
[tex]y^{5}\times y^{3}=y^8[/tex]
Step-by-step explanation:
exponent property :
[tex]\left( a\right)^{n} \times \left( a\right)^{m} =\left( a\right)^{n+m}[/tex]
………………………………………
[tex]\Longrightarrow y^{5}\times y^{3}=y^{5+3}=y^8[/tex]
I WILL GIVE BRAINRLY
Answer:
a
Step-by-step explanation:
f(x)-g(x)=2x square-3x+6-(3x square +4x-8)
2x square-3x+6-3x square-4x+8
-x square-7x+14
Can you please help me with these two lol. Im weak with this type of math. Brainlist to whoever helps. +40 points. lol
Answer:
See below ~
Step-by-step explanation:
Volume of prism :
Base Area x Height9 x 3 1/29 x 3.531 1/2 in³Volume of small-size box of dog treats :
3/10 x 3 1/4 x 7 1/2 x 123/10 x 13/4 x 15/2 x 123/10 x 13 x 15/2 x 31755/20351/487 3/4 in³Questions 1-4 of 4 | Page 1 of 1
Question 1 (1 point)
Of 100 boys, 34 are on the Honor Roll, 29 play sports, and 27 are on the Honor Roll and play sports.
What is the probability that a randomly selected student plays sports or is on the Honor Roll? Pick
the most simplified answer.
a
36/100
9/25
Oc 18/50
Od 3/5
Answer:
A 36/100
Step-by-step explanation:
the probability is going to be this because the rates in honor roll and sports are higher than the other 27 that do both.
Circle the correct words to complete the sentences.
1. Precipitation falls in these two forms: Solid / Liquid / Gas
2. Evaporation changes gas / liquid water to ice (solid) / water vapor (gas)
i just need to know what the answer i will give branliest
1. solid and liquid
2. Evaporation changes liquid water to water vapour.
for #1: for example, it's raining, when it rains, the rain is water (liquid).
Or it's snowing, the snow is solid.
for #2: for example, when you are making tea, you need hot water, so you add heat, then the water lessens because it's transforming to gas, and sometimes you can see it.
Answer:
1. solid and liquid
2. water vapor (gas)
Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in the table. A cylinder. Model 1 radius: 14 cm height: 48 cm diagonal: 50 cm Model 2 radius: 6 cm height: 35 cm diagonal: 37 cm Model 3 radius: 20 cm height: 40 cm diagonal: 60 cm Model 4 radius: 24 cm height: 9 cm diagonal: 30 cm In which model does the lateral surface meet the base at a right angle? Model 1 Model 2 Model 3 Model 4
The model in which the lateral surface meets the base at right angle is : Model 1.
What is a lateral surface?The lateral surface of an object is all surfaces of that object excluding its base and top.
Analysis:
To know the exact model, we check for the models in which their dimensions form a Pythagorean triplet otherwise a right-angled triangle.
For Pythagorean triplet, the square of the diagonal must be equal to the sum of squares of the other two sides.
Model 1
Diagonal = 50cm, radius = 14cm, lateral height = 48cm
[tex](50)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](48)^{2}[/tex]
2500 = 196 + 2304
2500 = 2500. Forms Pythagorean triplet
Model 2
Diagonal= 37cm, radius = 6cm lateral height = 35cm
[tex](37)^{2}[/tex] = [tex](35)^{2}[/tex]+ [tex](6)^{2}[/tex]
1369 = 1225 +36
1369 [tex]\neq[/tex] 1261
Model 3
Diagonal = 60cm, radius = 20cm lateral height = 40cm
[tex](60)^{2}[/tex] = [tex](20)^{2}[/tex] + [tex](40)^{2}[/tex]
3600 = 400 + 1600
3600 [tex]\neq[/tex] 2000
Model 4
Diagonal = 30cm, radius = 24cm, lateral height = 9cm
[tex](30)^{2}[/tex] = [tex](24)^{2}[/tex] + [tex](9)^{2}[/tex]
900 = 576 + 81
900 [tex]\neq[/tex] 657
Therefore the lateral surface model 1 meets the base at right angle
In conclusion, the lateral surface of model 1 meets the base at right angles as the dimensions form a right-angled triangle.
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Answer:
the answer is B have an amazing day
Step-by-step explanation:
One thousand unit cubes are fastened together to form a large cube with edge length 10 units; this is painted and then separated into the original cubes. The number of these unit cubes which have at least one face painted is:
Based on the number of unit cubes that are fastened together, the number of cubes which will have at least one face painted on is 488 cubes.
How many cubes will have one face painted on?The cubes formed one large cube which means that each surface is one cube deep. So two cubes will be painted.
The number of unpainted cubes per surface is therefore:
= 10 - 2
= 8 cubes
Number of unpainted cubes is:
= 8 x 8 x 8
= 512 cubes
Number of cubes with one face painted:
= Total cubes - Number of unpainted cubes
= 1,000 - 512
= 488 cubes.
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What is the simplest radical form of the expression?
(8x^7y^4)^2/3
Answer:
[tex]\large \text{$ 4 x^{\frac{14}{3}}y^{\frac{8}{3}}$}[/tex]
Step-by-step explanation:
Given expression:
[tex](8x^7y^4)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a \cdot b)^c=a^{c} \cdot b^{c}:[/tex]
[tex]\implies 8^{\frac{2}{3}} \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]
[tex]\implies 4 \cdot (x^7)^{\frac{2}{3}}\cdot(y^4)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 4 \cdot x^{\frac{14}{3}}\cdot y^{\frac{8}{3}}[/tex]
[tex]\implies 4 x^{\frac{14}{3}}y^{\frac{8}{3}}[/tex]
Expand [tex]\bf{(8x^{7}y^{4})^{\frac{2}{3} } }[/tex]
[tex]\bf{8^{\frac{2}{3} }(x^{7})^{\frac{2}{3} }(y^{4})^{\frac{2}{3} } }[/tex]
To raise a power to another power, multiply the exponents. Multiply 7 and 2/3 to get 14/3.
[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }(y^{4})^{\frac{2}{3} } }[/tex]
To raise a power to another power, multiply the exponents. Multiply 4 and 2/3 to get 8/3.
[tex]\bf{8^{\frac{2}{3}}x^{\frac{14}{3} }y^{\frac{8}{3} } }[/tex]
Calculate 8 to the power of 2/3 and you get 2/4.
[tex]\bf{4x^{\frac{13}{4} }y^{\frac{8}{3} } \ \ ==== > \ \ \ Answer }[/tex]