Answers
Answer:
Third option is the right choice.
Step-by-step explanation:
Manipulate the right hand side.
[tex]\sec \left(x\right)\\\\=\frac{1}{\cos \left(x\right)}\\\\\mathrm{Use\:the\:following\:identity}:\quad \:1=\cos ^2\left(x\right)+\sin ^2\left(x\right)\\\\=\frac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)}\\\\\Rightarrow \mathrm{True}[/tex]
Best Regards!
Answer:
sin ^2 (x)+ cos^2(x) = 1
Step-by-step explanation:
sin ^2 (x)+ cos^2(x)
------------------------
cos (x)
We know that sin ^2 (x)+ cos^2(x) = 1
1
------------------------
cos (x)
The definition of sec is 1 /cos
= sec(x)
Related Questions
The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisions organized by age groups. If the winner is in Baseball League, find the probability that the winning team is in either the Ages 10 - 12 division or the Ages 13 - 15 division. Answer in terms of a reduced fraction. A= p(y|b)= A0 B= p(z|b)= A1 C= p(y or z |b)= A2
Answers
Answer:
0.5 or 50%
Step-by-step explanation:
Total number of championships won = 3+2+1+7+2+1=16Total Number of winners in baseball league, n(B)= 3+2+1=6Number of Wins in the Ages 10 - 12 division, n(Y) =2Number of Wins in the Ages 13-15 division, n(Z) =1The probability that the winning team is in the Ages 10 - 12 division given that it is in the baseball league:
[tex]P(Y|B)=\dfrac{P(Y \cap B)}{P(B)} \\=\dfrac{2/16}{6/16}\\=\dfrac{2}{6}[/tex]
The probability that the winning team is in the Ages 13 - 15 division given that it is in the baseball league:
[tex]P(Z|B)=\dfrac{P(Z \cap B)}{P(B)} \\=\dfrac{1/16}{6/16}\\=\dfrac{1}{6}[/tex]
Therefore:
[tex]P(Y$ or $Z|B)=\dfrac{2}{6}+\dfrac{1}{6}\\=\dfrac{3}{6}\\\\=0.5[/tex]
Jenny wants to show the gym on a scale drawing. She uses a scale of 1:75. The gym has a length of 12.3 metres. Jenny works out the length of the gym on the scale drawing is 18cm. Is she correct?
Answers
Answer:
She is wrong
Step-by-step explanation:
Let us use the scale 1 : 75 to find the length of the gym on the scale drawing.
The scale means that 1 m on the drawing represents 75 m in real life.
Therefore, if the length of the gym is 12.3 cm, then the length of the gym in the scale drawing is:
12.3 / 75 = 0.164 m
Converting to cm:
1 m = 100 cm
0.164 m = 0.164 * 100 = 16.4 cm
She is wrong.
**BRAINLIEST 20 POINTS****
Given right triangle XYZ, what is the value of sin(Y)? (Hint: Special Right)
1/2
SqRt3/3
SqRt3/2
(2SqRt3)/3
Answers
Answer:
1/2
Step-by-step explanation:
Cos 60 = [tex]\frac{adjacent}{hypotenuse}[/tex]
1/2 = [tex]\frac{XZ}{4}[/tex]
Multiplying both sides by 4
=> XZ = 2
Sin Y = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin Y = [tex]\frac{2}{4}[/tex]
Sin Y = 1/2
What is the slope of the line represented by the equation y=4/5x-3? A.-3 B.-4/5 C.4/5 D.3
Answers
Answer:
4/5
Step-by-step explanation:
y = 4/5 x -3
This is written in slope intercept form
y =mx + b where m is the slope and b is the y intercept
the slope is 4/5 and the y intercept is -3
What is the volume of this triangular prism?
Answers
195 m^3
Step-by-step explanation:
The equation for the volume of a triangular prism is...
[tex]V=\frac{1}{2}bhl[/tex]
In this equation, b is the base, h is the height, and l is the length. We simply need to plug everything in from the problem into the equation, then solve. To also make this easier, I'm going to change the 1/2 to a 0.5.
[tex]V=0.5*6*13*5[/tex]
[tex]V=[/tex]
195 m^3
TRUE OR FALSE
(b^4)^3 = b^12
Answers
Answer:
TRUE
Step-by-step explanation:
if it was b^4 x b^3 then false. but here, would would multiply b^4 by b^3 to make it 12 so true
sorry for bad explanation
Answer:
True
Step-by-step explanation:
If b=2, 2^4 is 16, and 16^3 is 4096.
Also 2^12 is 4096.
So they are equivalent.
Which function has real zeros at x = 3 and x = 7?
f(x) = x2 + 4x - 21
Cf(x) = x2 - 4x - 21
Cf(x) = x2 - 10x + 21
f(x) = x2 - 10x - 21
Answers
Answer:
f(x) = x2 – 10x + 21
Step-by-step explanation:
I got it because you substract and add the last part
Please answer for brainliest!!!Find the equation of a line that passes through the point (-2,1) and has a gradient of 3. Leave your answer in the form ax+by=c Where a, b and c are integers
Answers
Answer:
3x - y = - 7
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 3 and (a, b) = (- 2, 1) , thus
y - 1 = 3(x + 2) ← distribute
y - 1 = 3x + 6 ( subtract 6 from both sides )
y - 7 = 3x ( subtract y from both sides )
- 7 = 3x - y, that is
3x - y = - 7 ← in standard form
Does -3(x-4)= -3x=12 have one solution, many solutions, or no solutions at all?
Answers
Answer:
If the expression is:
-3x + 12 = -3x + 12, infinite solutions
If the expression is:
-3x + 12 = -3x - 12, no solutions
Step-by-step explanation:
Step 1: Distribute
-3x + 12 = 3x = 12
If both lines have the same slope and same y-int, they are the same line and therefore have infinite solutions.
If both lines have the same slope but different y-int, then they are parallel and therefore have no solutions.
Please help me with this question!!
Answers
Answer: Choice B) The conjecture is valid given the focus is on proportional equivalence of two sectors.
This is another way of saying "the two pie slices are the same percentage in area". By this, I mean the percentage of the entire cake. For instance, the shaded slice could be 20% of the entire circle area, for each circle.
It's probably easier to see this is the angle was 90 degrees (split the cake into 4 equal slices, only shade one slice). Or probably even easier if you cut the cake into two slices and only shade one slice (to form a central angle of 180 degrees). For the first example, the slice would be 25% of the whole area, while the second slice is 50%.
Choice C is close, but the two sectors are not the same area. This is because the bottom circle has a larger radius, and therefore its sector area is larger.
Identify the graph of y^2+8x=0 for theta=π/6 and write an equation of the translated or rotated graph in general form.
Answers
Answer:
parabola; (x)^2-2(square root 3) xy+3(y)^2 +16 (square root 3) x+16=0
Step-by-step explanation:
edge’s possible answer 2020
PLEASE ANSWER THIS I AM ASKING THIS QUESTION FOR SOMEONE CAUSE IM NICE AND yeah lol pls answer this question in the pic
Answers
what is the product of the polynomials below? (8x^2-4x-8) (2x^2+3x+2)
Answers
Answer:
B
Step-by-step explanation:
you can FOIL or set up a box that is 3 x 3 (which is what I recommend) to solve it.
The product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Product of polynomialsFrom the question, we are to determine the product of the given polynomials
The given polynomials are
(8x^2-4x-8) (2x^2+3x+2)
Their product can be determined as follows
[tex](8x^2-4x-8) (2x^2+3x+2)[/tex]
[tex](8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)[/tex]
Clear the brackets
[tex]16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16[/tex]
Now, collect like terms
[tex]16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16[/tex]
Simplifying
[tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Hence, the product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
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A cyclist travels at an average speed of 11mph for 3 hours. how far did she travel in miles
Answers
Answer:
She traveled 33 miles.
Step-by-step explanation:
11*3 = 33
Answer:
33
Step-by-step explanation:
11mph times 3 hours= 33 miles
Find angle x, giving your answer to 1 decimal place.
38
x
11 cm
8 cm
Answers
The value of angle x is 57.1 degrees.
Here we have given an angle is 38degee and the sides of the triangle are 11cm and 8 cm.
What is the formula for sin ratio?[tex]sin(x)=\frac{opposite side }{hypotenuse}[/tex]
Therefore by using the formula for the attached figure we have
[tex]sin(38^0)=\frac{y}{11}\\\\y=11sin(38^0)\\\\y=6.71[/tex]
Similarly, for the second triangle for the value of x
we have,
[tex]sinx=y/8=6.71/8=0.84\\\\x=sin^-1(0.84)=57.1^0[/tex]
Therefore we get the value of angle x is 57.1 degrees.
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What is the domain of the square root function graphed below?
2
6.
4
1-2
6
X
2
4
6
O x5-1
O x2-1
Oxso
x20
HELP PLS
Answers
Answer:
[tex]x \geqslant 0[/tex]
Option D is the right option.
Explanation:
Observe from the graph that the value of X starts at X=0 and the graph is going to the right infinitely.
So the domain of the function should be:
[tex]x \geqslant 0[/tex]
Hope this helps...
Good luck on your assignment..
The domain of the square root function graphed is, x ≥ 0
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The square root function are graphed below in figure.
Now, We know that;
The set of all inputs of the function is called Domain of set.
Hence, By definition of domain of function, we get;
The domain of the square root function graphed is,
x ≥ 0
Thus, The domain of the square root function graphed is, x ≥ 0
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Which statement describes the end behavior of the function f(x) = 3|x − 7| − 7? A. As x approaches negative infinity, f(x) approaches negative infinity. B. As x approaches negative infinity, f(x) approaches positive infinity. C. As x approaches positive infinity, f(x) approaches negative infinity. D. As x approaches positive infinity, f(x) is no longer continuous.
Answers
Answer:
Our expressions is f(x) = 3|x-7|-7
in positive values |x-7| is x-7 ⇒f(x) = 3x-28in negative ones |x-7| is 7-x wich is the opposite⇒f(x) = 14-3xLet's calculate the limits in +∞ and -∞
[tex]\lim_{x \to +\infty} (3x-28)=[/tex][tex]\lim_{x \to+ \infty} 3x[/tex] = +∞ [tex]\lim_{x \to- \infty} (14-3x) = \lim_{x \to- \infty} -3x[/tex] =+∞So the right staement is B
As x approaches positive infinity, f(x) approaches negative infinity.
What is a function?A relation is a function if it has only One y-value for each x-value.
The function f(x) = 3|x − 7| − 7 is a piecewise function, where the absolute value function has two cases depending on the sign of (x - 7).
When (x - 7) is positive, the function becomes 3(x - 7) - 7 = 3x - 28, and when (x - 7) is negative, the function becomes -3(x - 7) - 7 = -3x + 14.
As x approaches positive infinity, both cases approach negative infinity because the dominant term in each case is the linear term (3x or -3x) as x becomes large.
Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches negative infinity.
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Sarah pours four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then transfers half the coffee from the first cup to the second and, after stirring thoroughly, transfers half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?
Answers
Answer:
2/5
Step-by-step explanation:
4ounces of coffee in cup 1
4 ounces of cream in cup 2
In the first step pour 4/2=2 ounces of coffee from cup 1 to cup 2, getting:
2 ounces of coffee in cup 1
2 ounces of coffee and 4 ounces of cream in cup 2
In the second step we pour 2/2=1 ounce of coffee and 4/2=2 ounces of cream from cup 2 to cup 1, getting:
2+1=3 ounces of coffee and 0+2=2ounces of cream in cup 1
so the answer is 2/5
Point A is located at (0, 4) and point C is located at (-3, 5). Find the x value for point B that is located the distance from point A to point C.
Answers
Answer: If point B is on the same line and the same distance from points A and C, the location is (-1.5, 4,5)
Step-by-step explanation: For point B to be the same distance from the other two points, it must be halfway between them.
for the x-value, find the number that is halfway between 0 and -3. That is -1.5
For the y-value, find the number that is halfway between 4 and 5. That is 4.5
The coordinate for point B is (-1.5, 4.5)
cos^4a=1/8(3+4cos2a+cos4a)
Answers
Answer:
Below.
Step-by-step explanation:
cos2a = 2 cos^2 a - 1
cos^4a = 8cos^4 a - 8cos^2 a + 1
Right side of the identity =
1 /8(3 + 4cos2a + cos4a)
= 1/8( 3 + 4(2 cos^2 a - 1) + 8cos^4 a - 8cos^2 a+1)
= 1/8 (3 + 8 cos^2 a - 4 + 8 cos^4 a - 8cos^2 a + 1)
= 1/8 (8cos^4 a)
= cos^4 a = the left side.
I realised that I should have derived the identity for cos 4a as well , which i have done in the picture.
The given identity, cos⁴a = 1/8(3 + 4cos2a + cos4a) is proved.
How is proving identities done?To prove a given identity, say f(a) = f(b), we proceed to simplify any of the expressions among the L.H.S. f(a) and the R.H.S. f(b), to get the other term. If we get the simplified form as the other term, our identity holds and is proved.
How do we solve the given question?We know cos2A = 2cos²A - 1.
Going by the same formula, we derive the value of cos4A.
cos4A = 2cos²2A - 1
or, cos4A = 2(2cos²A - 1)² - 1, putting value of cos2A
or, cos4A = 2(4cos⁴A - 4cos²A + 1) - 1, (expanding (2cos²A - 1)² using the formula of (a-b)² = a² -2ab + b²)
or, cos4A = 8cos⁴A - 8cos²A + 2 - 1, (expanding)
or, cos4A = 8cos⁴A - 8cos²A + 1, (simplifying)
∴ cos4A = 8cos⁴A - 8cos²A + 1.
Given identity to us is, cos⁴a = 1/8(3 + 4cos2a + cos4a).
To prove the identity, we proceed with the R.H.S.:
= 1/8(3 + 4cos2a + cos4a)
We put values of cos2A and cos4A in this expression, to get
= 1/8(3 + 4(2cos²a - 1) + (8cos⁴a - 8cos²a + 1))
Expanding the equation, we get
= 1/8(3 + 8cos²a - 4 + 8cos⁴a - 8cos²a + 1)
Simplifying, we get
= 1/8(8cos⁴a) = cos⁴a = L.H.S.
Hence, the given identity is proved.
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If 8a^2+ 2b^2= 10 and ab = 2, then what is the value of (2a+b)^2
Answers
Answer:
13
Step-by-step explanation:
We have:
8a^2 + 2b^2 = 10
Dividing both sides by 2,
=> 4a^2 + b^2 = 5
or (2a)^2 + b^2 = 5
We also have ab = 2
=> (2a + b)^2
= (2a)^2 + 2(2a)(b) + b^2
= (2a)^2 + b^2 + 4ab
= 5 + 4(2)
= 5 + 8
= 13
PLEASE HELPPP ASAP. I WILL GIVE BRAINLIEST!!!
Answers
Answer:
Factors: 5x, 3x²y⁵ Not Factor: 10x⁴y³
Step-by-step explanation:
5x is a factor because 15x²y⁶= 5x•3xy⁶
3x²y⁵ is a factor because 15x²y⁶ = 3x²y⁵•5y
10x⁴y³ isn't a factor because 15:10=1.5 isn't integer
Which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0, -12)?
Answers
Answer:
add the y coordinates of the two lines and divide by 2
Step-by-step explanation:
½[0+(-12)]
½[0-12]
½[-12)
y co-ordinate of the midpoint is -6
Choose the best estimate for the division problem below.
8.3 /0.7
A. 12
B. 10
c. 9
Answers
Answer:
12
Step-by-step explanation:
8.3 / .7
Multiply each by 10 to get rid of the decimal
83/7
We know that 84/7 =12 so this is close to 12
Please help 6TH GRADE MATH HELP ME OUT PLEASE
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
d. 7/20
▹ Step-by-Step Explanation
[tex]\frac{1}{4} + \frac{1}{10} \\= Common denominator is 20\\\\\frac{1}{4} = \frac{5}{20} \\\\\frac{1}{10} = \frac{2}{20} \\\\\frac{5}{20} + \frac{2}{20} \\\\= \frac{7}{20}[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Please help me with this. When dividing fractions, the ________ term becomes the reciprocal. A. Second B. First C. Neither D. Both
Answers
Answer:
The second term becomes the reciprocal and then you multiply the first term by the second term
Answer:
A. second
Step-by-step explanation:
When dividing fractions, we always take the second term and flip that. In other words, we convert the second term into its reciprocal. Remember the phrase "flip the guy, and multiply!" Essentially, the "guy" just refers to the second term.
For example, if we have 1/3 ÷ 2/5, in order to solve this, we flip the second term, which is 2/5 so that it becomes 5/2 and then multiply:
1/3 ÷ 2/5 = 1/3 × 5/2 = 5/6
The answer is thus A.
~ an aesthetics lover
Write the equation of the line that passes through (2, 3) and is parallel to the line 12x – 5y = 2.
Answers
Answer:
The answer is
5y - 12x = - 9Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
12x - 5y = 2
5y = 12x - 2
Divide both sides by 5
y = 12/5x - 1/5
Comparing with the above formula
Slope / m = 12/5
Since the lines are parallel their slope are also the same.
Slope the parallel line = 12/5
Equation of the line using point (2,3) is
[tex]y - 3 = \frac{12}{5} (x - 2) [/tex]
Multiply through by 5
That's
5y - 15 = 12(x - 2)
5y - 15 = 12x - 24
We have the final answer as
5y - 12x = - 9Hope this helps you
WILL GIVE BRAINLIEST!!!!! PLEASE ANSWER FAST
Answers
Plz Help!!! I really do not get this lesson and I really need to pass it to move onto the next I am kind of getting it, I want to make sure my answer is correct. IS it sas?
Answers
Answer:
SSS
Step-by-step explanation:
I think it would be SSS (side, side, side)... let me know if I'm wrong and I'll try again:)
Check out the diagram below. I've marked the angles and sides that are congruent. Notice how the marked sides are not between the marked angles for either triangle. So we're dealing with AAS instead of ASA. The order is important. If we wanted to use ASA, then we would have to know DE = TU, both of those sides are between the marked angles.
The tax rate as a percent, r, charge on an item can be determined using the formula c/p - 1 = r, where c is the disk cost of the time and p is the price of the item before tax. Louise rewrites the equation to solve for the final cost of the final item C = p(1+r). What is the final cost of a $40 item after an 8% tax is applied?
Answers
Answer:
The final cost is $43.2
Step-by-step explanation:
We have the following equation:
[tex]C=p(1+r)[/tex]
Where C is the final cost, p is the price before tax and r is the tax rate.
So, to calculated the final cost for a $40 item after 8% tax, we need to replace p by 40 and r by 0.08 and calculate the value of C as:
[tex]C=40*(1+0.08)=43.2[/tex]
Therefore, the final cost is $43.2
Answer: $43.20
Step-by-step explanation: The simplest way to do it (my way) is i first used (1 + r), which is (1 + 8%), that gave me 1.08, then I did the total amount, $40x1.08, which equals $43.20. This may not be the right way to do it, but it is the simplest.
Hope this helped :)