Answer:
Step-by-step explanation:
(a - b)(a +b) = a² - b²
1 - Sin² A = Cos² A
\(LHS = \frac{1}{1- Sin A} + \frac{1}{1 + Sin A}\\\\= \frac{1*(1 + Sin A)}{(1- Sin A)(1 + Sin A)} + \frac{1*(1- Sin A)}{(1 + Sin A)(1- Sin A)}\\\\= \frac{1 + Sin A+ 1 - Sin A}{1^{2}- Sin^{2} A}\\\\= \frac{2}{1 - Sin^{2} A}\\\\= \frac{2}{Cos^{2} A}\\\\= 2 Sec^{2} A\)
2) Sec² A - Tan² A = 1
\(LHS = \frac{1}{Sec A - Tan A}\\\\=\frac{1*(Sec A + Tan A)}{(Sec A - Tan A)(Sec A + Tan A)}\\\\=\frac{Sec A + Tan A}{Sec^{2} A - Tan^{2} A}\\\\=\frac{Sec A + Tan A }{1}\\\\= Sec A + Tan A = RHS\\\\\\\)
3) LHS = Cosec² A + Cot² A
= Cosec² A + Cosec² A - 1
= 2Cosec² A - 1 = RHS
\(4) LHS = \frac{Sec A}{Cos A}- \frac{Tan A}{Cot A}\\\\ = Sec A*\frac{1}{Cos A}-Tan A*\frac{1}{Cot A}\\\\ = Sec A * Sec A - Tan A * Tan A\\\\= Sec^{2} A - Tan^{2} A \\\\= 1\)
Chose a definition for the function
Answer: D
It's D because the left piece only works when x<2 (not x≤2) and that left piece has a y-intercept of (0,2), making the left piece's equation "x+2 when x<2".
The next model of a sports car will cost 14.7% more than the current model. The current model costs $34,000. How much will the price increase in dollars?
What will be the price of the next model?
Increase in price:
Price of next model:
Answer: $4,998
Step-by-step explanation:
34000*1.147
38998-34000=4998
help asap this i cant figure out
Answer:
a = 60
2a = 120
Step-by-step explanation:
360 = 2a + 2a + a + a
360 = 6a
a = 360 / 6
a = 60
2a = 2(60)
2a = 120
Point C has a coordinate of (-4, -6) and point D has a coordinate of (1, -6), how far are they apart?
The distance between points C and D is given as follows:
5 units.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The coordinates for this problem are given as follows:
(-4, -6) and (1, -6).
Hence the distance is given as follows:
\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)
D = 5 units.
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The current in an electrical conductor varies inversely as the resistance of the conductor. If the resistance is 240 ohms when the current is 12 ampere, what is the current when the resistance is 540 ohms?
The resistance is 540 ohms, the current in the conductor is approximately 5.33 amperes.
According to the given information, the current in an electrical conductor varies inversely to the resistance of the conductor. Inverse variation can be represented mathematically as follows:
Current * Resistance = Constant
Let's denote the constant as 'k'. We can use the initial values to find the value of 'k'.
When the resistance is 240 ohms and the current is 12 amperes:
12 * 240 = k
k = 2880
Now that we have the value of 'k', we can use it to find the current when the resistance is 540 ohms:
Current * 540 = 2880
Current = 2880 / 540
Current ≈ 5.33 amperes
Therefore, when the resistance is 540 ohms, the current in the conductor is approximately 5.33 amperes.
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Despite having developed a reputation as a good cook, I'm really not one. What I am is a really good recipe follower. I put my trust in real chefs whose recipes are posted here on Recipe Masters. Turns out, though, my trust was misplaced. Sadly, my weekly supper club dinner that featured a Recipe Masters recipe for meatball sub casserole turned into a pizza delivery night. If after reading this review, any of my fellow Recipe Masters subscribers are still set on trying this casserole recipe, here is my advice: Stop after the first step, when the sauce turns into an un-stirrable glob. Don't do as I did and continue on, believing things will improve. They won't. Following this recipe is a recipe for disaster. My advice for Recipe Masters is to ensure that recipes posted here are "tried and true," as advertised. We subscribers pay a fee for access to "top-notch, no-fail recipes." If we lose faith in your recipes, we might just turn to the free recipe sites all over the internet. Which sentence best summarizes the author's point of view about the casserole recipe posted on Recipe Masters?
The author of the review is disappointed with the meatball sub casserole recipe posted on Recipe Masters, which did not turn out well despite following the recipe.
The author recommends that others should not attempt to make the recipe and believes that Recipe Masters should ensure that their posted recipes are reliable and thoroughly tested. The author also implies that the quality of the recipes on Recipe Masters is not as advertised, which could potentially lead subscribers to lose faith in the service and seek out free recipe sites instead.
Therefore, a suitable summary of the author's point of view would be: The author is dissatisfied with the meatball sub casserole recipe on Recipe Masters, which did not work out well and believes that Recipe Masters should provide reliable, thoroughly tested recipes as advertised.
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Mrs. Grubbs has the option of eating a cookie with the diameter of 14 cm or 4 smaller cookies with a diameter of 5
cm. Which option would give Mrs. Grubbs more cookie to eat?
Mrs. Grubbs would get more cookie to eat by choosing the 4 smaller cookies with diameter 5 cm each rather than the single cookie with diameter 14 cm.
To compare the amount of cookie Mrs. Grubbs would get by eating a single cookie with diameter 14 cm and 4 smaller cookies with diameter 5 cm each, we need to consider the total area of the cookies.
The area of a cookie with diameter 14 cm can be calculated as follows:
A = πr^2 = π(7 cm)^2 = 49π cm^2
where r is the radius of the cookie.
On the other hand, the area of a single small cookie can be calculated as follows:
A1 = \(πr^2\) = \(π(2.5 cm)^2\)= \(6.25π cm^2\)
where r is the radius of the small cookie.
Therefore, the total area of 4 small cookies is:
A2 = 4A1 = \(4(6.25π cm^2)\) = \(25π cm^2\)
Comparing the two options, we see that the total area of the 4 small cookies is greater than the area of the single large cookie:
A2 > A
\(25π cm^2 > 49π cm^2\)
It's worth noting that this comparison assumes that the thickness or volume of the cookies is the same for both options. If the cookies have different thicknesses, then the comparison would need to take into account the volume of the cookies instead of just the area.
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Hexagonal prism B is the image of
hexagonal prism A after dilation by a scale
factor of 2. If the surface area of hexagonal
prism B is 172 cm2, find the surface area of
hexagonal prism A, the preimage.
The surface area of hexagonal prism A is 9√3x² cm². We are given that hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2.
Therefore, all corresponding sides of prism A and prism B are in the ratio of 1:2. Let the side length of the base of hexagonal prism A be 'x'. Then, the side length of the base of hexagonal prism B is '2x'.
We know that the surface area of hexagonal prism B is 172 cm². Using the formula for the surface area of a hexagonal prism, we can write:
172 = 2(3√3)(2x)^2 + 6(2x)h
where h is the height of hexagonal prism B.
Simplifying this equation, we get:
172 = 24√3x² + 12xh
Dividing both sides by 12, we get:
14.33 = 2√3x² + h
Now, since hexagonal prism B is a dilation of hexagonal prism A by a scale factor of 2, the height of hexagonal prism A is half the height of hexagonal prism B. So, the height of hexagonal prism A is h/2.
Using the formula for the surface area of a hexagonal prism, we can write:
SA(A) = 2(3√3)x² + 6x(h/2)
Substituting h/2 for the height of hexagonal prism A, we get:
SA(A) = 2(3√3)x² + 3xh
Substituting 2√3x² + h/2 for h, we get:
SA(A) = 2(3√3)x² + 3x(2√3x² + h/2)
SA(A) = 6√3x² + 3√3x² + (3/2)xh
Substituting 2√3x² for h in the above equation, we get:
SA(A) = 6√3x² + 3√3x² + (3/2)x(2√3x²)
SA(A) = 9√3x²
Therefore, the surface area of hexagonal prism A is 9√3x² cm².
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Describe the series of rigid motion transformations which map polygon A to Polygon A'''. Are the two polygons congruent? Explain how you know.
(someone please help me!)
The series of rigid motion transformations that map polygon A to Polygon A''' are;
A rotation of 145° about the origin to map A to A'A reflection across the x-axis to map A' to A'A translation of four units to the right and one unit downWhat is a rigid transformation?A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.
The series of rigid motion transformations that map polygon A to polygon A''' are;
Transformation from A to A'
The angle in the diagram in the question indicates the rotation of polygon A to produce polygon A' is a rotation of 145° about the origin.Transformation from A' to A''
The coordinates of the vertices of triangle, A' (0.9, 4.1), (3.1, 5.9), (5.5, (2.5) and the vertices of triangle A'' (0.9, -4.1), (3.1, -5.9), (5.5, -2.5), indicates that the transformation is a reflection about the x-axisTransformation from A'' to A'''
The arrow of the translation transformation indicates that the transformation is a translation of four units to the right and 1 unit down.Learn more about rigid transformations in geometry here:
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Mark borrowed $5,500 at 11.5 percent for five years.
How much did Mark pay in interest?
$1,150
$1,520
$1,757
$2,300
Answer:
$ 1 , 150
Step-by-step explanation:
what is the area of the shaded area. Round to the nearest whole unit.
please help!!!
Answer:
69.53 or 70(depending on rounding)
Step-by-step explanation:
The squares area is (9*2)^2 which is 324.
The circles area is 9^2 pi or 254.47 approx.
Subtract and you get 69.53 or 70
A quality control expert at a drink bottling factory took a random sample of bottles from a batch and measured
the amount of liquid in each bottle in the sample. The amounts in the sample had a mean of 503 mL and a
standard deviation of 5 mL. They want to test if this is convincing evidence that the mean amount for bottles in
this batch is different than the target value of 500 mL.
Let u be the mean amount of liquid in each bottle in the batch.
Which of the following is an appropriate set of hypotheses for their significance test?
Answer: A
Step-by-step explanation:
The correct hypothesis is Option A.
What are hypotheses in mathematics?A hypothesis is a supposition or suggested explanation for a phenomenon or issue. It is a preliminary claim that has to be examined and confirmed by logic, experimentation, or other means. A hypothesis can be used to steer the development of a theory or to make predictions about events that will happen in the future.
The appropriate set of hypotheses for this significance test is:
μ = 500 mL (null hypothesis) - The mean amount of liquid in each bottle in the batch is equal to the target value of 500 mL.
μ ≠ 500 mL (alternative hypothesis) - The mean amount of liquid in each bottle in the batch differs from the target value of 500 mL.
This is done in order to determine whether there is proof that the average volume of the bottles in this batch differs from the desired value of 500 mL.
The alternative hypothesis suggests that the mean quantity is different from the null hypothesis assumption that it is equal to 500 mL. The test will evaluate whether there is enough support for the alternative hypothesis to be accepted instead of the null hypothesis.
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Chinedu missed his school bus by 2 munutes, so he walked to school which took him 27 minutes, arriving 6 minutes late for class at 8.11am At what time should he have caught the bus?
Answer:
Step-by-step explanation:
So we know he arrived at 8:11 am. He should've arrived at 8:05 am if he rode the bus. So, we know that it took 27 minutes for him to get to school by walking. If he arrived at 8:11, then he started walking at 7:44 am. Since the school bus arrived 2 minutes before he started walking, we can say that the school bus arrived at 7:42 am.
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find the values of variables, then find the lengths of the sides of each quadrilateral
Describe a situation that matches the equation 2(-8)=16
Answer:
The little drummer boy wanted to solve a math problem for Christmas so he asked Santa and he gave him 2(-8) which the little drummer boy evaluated to equal 16.
Step-by-step explanation:
You just have to be creative.
write an equation of the line that passes through the points (0,-2),(3,13)
Answer: y = 5x-2
Step-by-step explanation:
QUICKLY HELP ME! Trigonometry
The value of tan (2∅) in the right triangle is - 960 / 644.
How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
15² + 8² = 17²
Let's find ∅ using trigonometric ratios,
tan ∅ = opposite / adjacent
tan ∅ = 15 / 8
Therefore,
tan 2∅ = 2 tan ∅ / 1 - tan² ∅
tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²
tan 2∅ = 30 / 8 ÷ 1 - 225 / 64
tan 2∅ = 15 / 4 ÷ 64 - 225/ 64
tan 2∅ = 15 / 4 ÷ -161 / 64
tan 2∅ = 15 / 4 × 64 / -161
tan 2∅ = - 960 / 644
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The value of tan (2∅) in the right triangle is - 960 / 644.
How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
15² + 8² = 17²
Let's find ∅ using trigonometric ratios,
tan ∅ = opposite / adjacent
tan ∅ = 15 / 8
Therefore,
tan 2∅ = 2 tan ∅ / 1 - tan² ∅
tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²
tan 2∅ = 30 / 8 ÷ 1 - 225 / 64
tan 2∅ = 15 / 4 ÷ 64 - 225/ 64
tan 2∅ = 15 / 4 ÷ -161 / 64
tan 2∅ = 15 / 4 × 64 / -161
tan 2∅ = - 960 / 644
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If the radius of a circle is 5 m what is the area up to the nearest tenth
Answer:79
Step-by-step explanation:
Use the formula d = ( r − c ) t to find c if d = 30 , r = 12 , and t = 5 .
C=
Given that log 2 = 0.3010 and log 7 = 0.8451, find the following (a) log 49 (b) log 560
Answer:
ok babababr
Step-by-step explanation:
skwjshehhehdhhshwhhdhwhbeujsbsgehbedheb
Answer:
Log 49= 1.6902
Log 560= 1.7481
Step-by-step explanation:
log49= log7×7
From the rules of logarithms, we have that
log a×b= log a + log b
So log49= log7×7= log7 + log7
= 0.8451 + 0.8451 = 1.6902
Log 560 = log7×8 = log7 + log8
log8= log2^3 = 3log2
log8= 3×0.3010 =0.930
log 560= 0.8451 + 0.930 = 1.7481
Please if you know the answer tell me it and the steps also thank you.
Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.
Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..
The farmers market sells bags of oranges by
the pound. What is the cost per pound for
oranges according to the following graph?
Cost in Dollars
007 (
2 4 6 8 10 12 14 16 18 x
Pounds
A. $0.04 per pound
B. $0.25 per pound
C. $0.33 per pound
D. $0.50 per pound
I
Answer:
The answer is A
Step-by-step explanation:
I just know
The correct answer is B. $0.25 per pound
How to calculate the cost per pound for oranges?In the given graph, the line coincides with the point that indicates 8 pound along x axis and $2 along y axis. This indicates that 8 pounds for oranges costs $28 pounds for oranges costs $2
∴ 1 pound for oranges will cost $ \(\frac{2}{8}\) = $ \(\frac{1}{4}\)
= $ 0.25
∴ the cost per pound for oranges is $ 0.25
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the question is . Observe and record the coordinates of the transdormation show below. How can this transformation be represented algeraically?the answer choises are A. (-x, -y)B. (-y, -x)C. (x, -y)D. (-x, y)
We need to track the movement of the coordinates.
For coodinates A and A' we have:
A(2,-6)
A'(-2,6)
we can see this indicated in the following picture:
In A, the x coordinate is equal to 2, and in A' the x coordinate has the opposite sign: .2.
The same happens with the y-coordinate. In A is -6 and in A' it has the opposite sign +6.
The same is true for points B and B':
B(7,-6)
B'(-7,6)
Fom B to B prime both the x and y coordinate change signs.
And finally, the same is true for C and C':
C(2,-2)
C'(-2,2)
From C to C' both coordinates x and y change their signs.
The expression that represent this transformation is: A. (-x, -y)
Because the number in the x and y coordinates stays the same, it just changes of sign.
A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?
Answer:
10:3
Step-by-step explanation:
Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.
For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.
So make 5/2 to a 10/4.
Take the numerator 10 & 3.
Your answer will be 10:3
No problem.
1/4r - 4 = 20
Help what does r equal
Answer:
Step-by-step explanation:
To solve for r, we need to isolate the variable r on one side of the equation.
1/4r - 4 = 20
First, we'll add 4 to both sides of the equation:
1/4r - 4 + 4 = 20 + 4
Simplifying:
1/4r = 24
Next, we'll multiply both sides of the equation by 4 to eliminate the fraction:
1/4r * 4 = 24 * 4
Simplifying:
r = 96
Therefore, the solution to the equation 1/4r - 4 = 20 is r = 96.
the mean of 5 numbers is 198. the numbers are in ratio 1:2:3:4:5 find the smallest number
Answer: 13.2
In fraction form, this is 66/5
=============================================================
Explanation:
The five values are in the ratio 1:2:3:4:5 which scales up to 1x:2x:3x:4x:5x for some positive number x.
Add up the pieces of the second ratio and set that sum equal to 198. Then solve for x.
1x+2x+3x+4x+5x = 198
15x = 198
x = 198/15
x = 66/5
x = 13.2 is the smallest number since 1x = 1*13.2 = 13.2 was the smallest value of the ratio 1x:2x:3x:4x:5x.
Hi, could someone solve this parametric system?
7х+4y – 5z = 2
3х +5y +kz = 4
X+ky +7z = k
9514 1404 393
Answer:
(x, y, z) = ((7 -2k)/(-31 +7k), (-29 +7k)/(-31 +7k), 1/(31 -7k))
Step-by-step explanation:
The system can be solved by any of your favorite methods. Treat k as you would any number.
My row reduction software says the solution is ...
(x, y, z) = ((7 -2k)/(-31 +7k), (-29 +7k)/(-31 +7k), 1/(31 -7k))
__
Clearly, k ≠ 31/7.
The augmented coefficient matrix is attached.
<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find the measure of <2
Answer:
122 Degrees
Step-by-step explanation:
Since we are given that angle 1 and 2 make a linear pair:
angle 1 + angle 2 = 180 degrees ----------------------------(1)
We have also been told that angle 2 is 6 more than twice the measure of angle 1
Which means: angle 2 = (2*angle1) + 6 -------------------(2)
From putting the value of angle 2 in (1) from (2)
angle 1 + 2*angle 1 + 6 = 180
3*angle 1 = 174
angle 1 = 58 degrees -----------------------(3)
From (1) and (3):
angle 2 + 58 = 180
angle 2 = 122 degrees
Therefore, the measure of angle 2 is 122 degrees
Please help, I am super confused
For symmetrical acceleration a is given by this formula where v is the velocity of the object and r is the object’s distance from the center of the circular path a=v to the 2nd power over r solve for r
Answer:
\(r=\frac{v^2}{a}\)
Step-by-step explanation:
\(a=\frac{v^2}{r} \\ \\ ar=v^2 \\ \\ r=\frac{v^2}{a}\)
Linear equation: Solve x1, x2, x3, in terms of y1,y2,y3
x1 + ax2 + bx3 = y1
x2 + cx3 = y2
x3 = y3
Answer:
x1 = y1 - a*y2 + (a*c - b)*y3
x2 = y2 - c*y3
x3 = y3
Step-by-step explanation:
Here we have the system:
x1 + a*x2 + b*x3 = y1
x2 + c*x3 = y2
x3 = y3
Where the variables y1, y2, and y3 are known (a, b and c are also known).
The first step is to isolate one of the variables in one of the equations, we can see that in the third equation we have x3 already isolated, so now we can just replace it on the other two equations to get:
x1 + a*x2 + b*(y3) = y1
x2 + c*(y3) = y2
Now we again want to isolate one of the variables in one of the equations, i will isolate x2 in the second equation to get:
x2 = y2 - c*y3
Now we can replace this on the other equation to get:
x1 + a*(y2 - c*y3) + b*y3 = y1
Now we canw write x1 in terms of the known variables:
x1 = y1 - a*y2 + (a*c - b)*y3
And in the process we also found that:
x3 = y3
x2 = y2 - c*y3
Then the solutions are:
x1 = y1 - a*y2 + (a*c - b)*y3
x2 = y2 - c*y3
x3 = y3