Given sinθ=1/2 determine the value of sec θ. 0°<θ<90°
Given Choices
2/√3
√3/2
2
1
Answers
Answer:
[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Step-by-step explanation:
Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ. There are a few ways to go about this:
A general solution methodAll of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.
Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle). You might remember this through SohCahToa
[tex]sin(\theta)=\frac{opp}{hyp}[/tex]
In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] . While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse. So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].
While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)
This triangle represents the triangle for the unknown θ in the original sine function. We're tasked with finding the secant of that particular unknown θ.
Working toward Secant
Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].
I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex]. From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).
Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse. We already know the length of the hypotenuse, so we just need the length of the adjacent side.
Applying the Pythagorean Theorem
Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex] (where c is the length of the hypotenuse, and a & b are the lengths of the legs)
Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]
...isolating "adj" by subtraction...
[tex](adj)^2=4-1\\(adj)^2=3[/tex]
...applying the square root property...
[tex]adj=\sqrt{3}[/tex] or [tex]adj=-\sqrt{3}[/tex]
Identifying which Quadrant the triangle is in
Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.
Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].
Finding the final solution
From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Note: This method did not require knowing what the angle θ was.
Alternative method using the Unit CircleIf you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex] is associated with [tex]\theta=30^o[/tex]. If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].
This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].
Related Questions
line / is parallel to line m. the slope of line / is 4/9. what is the slope of line m?
Answers
Answer: 4/9
Step-by-step explanation:
Parallel lines have equivalent slopes.
As line 'l' and line 'm' are parallel to each other ,then the slope of line 'm' is also 4/9.
Parallel lines have the same slope. The slope of line segments is identical because they are all similarly inclined with respect to the positive x-axis. If 'l', and 'm' are the slopes of two parallel lines,
then l = m
Slope-intercept notation for lines may be expressed as y=mx+b.
In this notation, b denotes the location of the line's y-axis intercept, and slope(m) indicates the slope of the line.
The slope of 'l'=4/9
The slope of the two parallel lines is the same.
Therefore, the slope of the parallel line "m" = 4/9.
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"If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c)."
Answers
Answer:
The commutative property of addition says that changing the order of addends does not change the sum.
(a+b)+c = a+ (b+c)
( -8 + -7) + 6 = -8 + ( -7 + 6)
-15 + 6 = -8 + -1
-9 = -9
Answer:
Hence, proved (a+b) + c = a + (b+c)."
Step-by-step explanation:
first take left hand side and insert the values of a, b, and c and similarly than take right hand side.
L.H.S
(a+b)+c
(-8+(-7))+6
(-8-7)+6
-15+6
-9
R.H.S
a+(b+c)
-8+(-7+6)
-8+(-1)
-8-1
-9
hence, proved (a+b) + c = a + (b+c)."
Fireside Shop offers chimney caps for $120 less trade discounts of 25/10. The same chimney cap is being offered at Builder's Supply for $111 less trade discounts of 25/5. What is the price difference between the two companies?
Answers
The difference in price between the two companies is $81-$79.56 = $1.44
Fire side Shop
Price of Chimney cap =$120
First Discount = 25% of(120)=$30
Price after 1st Discount = $120-$30=$90
Second Discount = 10% of 90=$9
Price after 2nd Discount = $90-$9=$81
Builders' Supply
Price of Chimney Cap= $111
First Discount= 25% of 111 = $27.75
Price after 1st Discount = $111 - $27.75 = $83.75
Second Discount = 5% of $83.75 = $ 4.1875
Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56
Therefore,
a) Builders supply offers the lower price.
b) Difference in price = $81-$79.56 = $1.44
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Need help with Math (Quadratic)
Answers
Answer:
f(x) = 2(x -3)² +5 or f(x) = 2x² -12x +23
Step-by-step explanation:
The equation of a quadratic is easily written in vertex form when the coordinates of the vertex are given. Here, the point one horizontal unit from the vertex is 2 vertical units higher, indicating the vertical scale factor is +2.
__
vertex formThe vertex form equation for a parabola is ...
f(x) = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'
equationFor vertex (h, k) = (3, 5) and vertical scale factor a=2, the vertex form equation of the parabola is ...
f(x) = 2(x -3)² +5 . . . . . vertex form equation
Expanded to standard form, this is ...
f(x) = 2(x² -6x +9) +5
f(x) = 2x² -12x +23 . . . . . standard form equation
3x² - 2x + 1 = [?]
x=4
Answers
Answer:
3(4)² - 2(4) + 1 = 48 - 8 +1 = 41
x = 4
[tex] {3x}^{2} - 2x + 1 \\ \\ 3 \times {4}^{2} - 2 \times 4 + 1 \\ \\ 3 \times 16 -8 + 1 \\ \\ 48 - 8 + 1 \\ \\ 41.[/tex]
Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?
D: [–1, 5]; R: [–7, 5]
D: [–5, 7]; R: [–5, 1]
D: [–5, 1]; R: [–5, 7]
D: [–7, 5]; R: [–1, 5]
Answers
The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have an ellipse equation:
[tex]\rm x^{2}+4y^{2}-2x+16y-19=0[/tex]
We can write the above equation as:
[tex]\rm \dfrac{\left(x-1\right)^{2}}{36}+\dfrac{\left(y+2\right)^{2}}{9}=1[/tex]
The domain will be:
D: [–5, 7]
The range will be:
R: [–5, 1]
Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]
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The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.
{n | n < 3}
{n | n ≥ 3}
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
(3, ∞)
Answers
The correct representations of this solution is {n | n > 3} an open circle appears at positive 3.
Solution to inequality expressionInequalities are expressions not separated by an equal sign. Given the inequality
6 + 2n > 12
Subtract 6 from both sides
2n > 12 - 6
2n >6
Divide both sides by 2
2n/2 >6/2
n >3
Hence the correct representations of this solution is {n | n > 3} an open circle appears at positive 3.
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A rectangular aquarium is 1m 20cm long, 90cm wide and 50cm deep. How many cubic centimeters of water can it hold
Answers
Answer:
540,000 cubic centimeters
Step-by-step explanation:
1 meter and 20 centimeters is equal to 120 centimeters.
[tex]120 \times 90 \times 50 = 540000[/tex]
help Which statement describes the pattern shown?
*
1 point
Captionless Image
A. Each figure has 3 fewer squares than the one before it.
B. Each figure has 6 fewer squares than the one before it.
C. Each figure has 3 more squares than the one before it.
D. Each figure has 6 more squares than the one before it.
Answers
A pattern is a recurring arrangement of numbers, forms, colours, and so on.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
As per the pattern, Each figure has 3 more squares than the one before it.
Hence, the correct option is C.
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Helppppp meeeee pleaseeee?
Answers
Answer:
D
Step-by-step explanation:
A. The domain is not all real numbers since the domain of the inverse is the range of the square root function which is not all real numbers.
B and C. The domain is not x >= -4, that's the range since the domain and range are swapped relative to the original square root function which had a domain x >= 4 and a range x >= 0
D. This is true since the range of the square root function is x >= 0 which is now the range of the inverse.
Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to 73.7-57
0 72
0 77
17
글
Answers
Answer: [tex]\frac{1}{7^{2}}[/tex]
Step-by-step explanation:
Using the exponent rule [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex], we get that
[tex]7^{3} \cdot 7^{-5}=7^{-2}[/tex]
Then, using the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex], we get that
[tex]7^{-2}=\boxed{\frac{1}{7^{2}}}[/tex]
only 2/3 of the school districts kindergarten teachers are women. if 59 are men, how many kindergarten teachers in all are employed by the school district
Answers
Answer:
177
Step-by-step explanation:
2/3 are women.
that means the remainder, 1/3, are men.
59 = 1/3 of all kindergarten teachers (3/3 = 1 representing the "whole").
so,
59×3 = 177
is the number of all kindergarten teachers employed by the school district.
F(x)=x^2.what is g(x) ?
Answers
Answer:
Option C. [tex]g(x)=(\frac{1}{3}x)^2[/tex]
Step-by-step explanation:
Stretch transformations of functionsIn which direction is the transformation happening?Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.
Transformations on the outside
Ex. [tex]g(x)=(x^2)-3[/tex] is subtracting 3 outside, so its transformation is vertical.
Transformations on the inside
Ex. [tex]g(x)=(x-7)^2[/tex] is subtracting 7 inside, so its transformation is horizontal.
Stretch/compression transformationsFor any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.
Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.
For example, [tex]\$10*2 = \$20[/tex], but [tex]\$10*\frac{1}{2} = \$5[/tex]
For transformations, this intuition needs a small modification:
Operations outside: transformations happen "normally" as you would expect.Operations inside: transformations happen "backwards" from the natural way one might expect.Multiplying on the outside
When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.
Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).
Multiplying outside by [tex]\frac{1}{2}[/tex] , things get smaller (compress) vertically down to [tex]\frac{1}{2}[/tex] as much as (50% of) normal (toward a height of zero).
"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).
Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.
Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".
Putting 3 into the "f" function, f(3)=9. Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.
Multiplying on the inside
When multiplying inside, transformations happen horizontally, and inside things happen "backwards".
So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).
If multiplying by a number less than one (but positive), like [tex]\frac{1}{3}[/tex] , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of [tex]\frac{1}{3}[/tex]) as much as normal.
Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.
How far has the function been stretched out horizontally?Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).
Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away. Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.
Answer C multiplies inside by [tex]\frac{1}{3}[/tex], so it actually makes things 3 times bigger horizontally.
The correct answer is option C.
Verifying algebraicallyTo verify, from (3,1), put 3 into the option C g(x) -- it gives "1" as an output.
[tex]g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\[/tex]
An alternative solutionThis function could have been compressed vertically to obtain the red graph.
Note that f(3)=9.
The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function. We could compress the "f" vertically by 1/9th to transform the blue function into the red function.
Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.
Thus, an alternative answer to transform f(x) to g(x) is [tex]g(x)=\frac{1}{9}(x^2)[/tex]
Two last things:
Simplifying this function we just obtained we get [tex]g(x)=\frac{1}{9}x^2[/tex]
Returning to the function that we chose for our answer in option C, [tex]g(x)=(\frac{1}{3}x)^2[/tex]
[tex]g(x)=(\frac{1}{3}x)(\frac{1}{3}x)[/tex]
[tex]g(x)=\frac{1}{9}x^2[/tex]
Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.
What is the product? Assume x≥0.
(√3x + √5)√15x+2√30)
A. 3x√√5 +3√165x+10√√6
B. 3x√5+6√10x +5√3x +10√6
C. 3x√√5+10√6
D. 6√3x+10√6
Answers
The product of (√3x + √5)(√15x+2√30) assuming x ≥ 0 is 3√5x² + 6√10x + 5√3x + 10√6
What is the product of the expression?It follows from the task content that the expression given whose product is to be evaluated is;
(√3x + √5)(√15x+2√30)
Hence, by multiplying the terms with each other accordingly; we have;
= (√45x² + 2√90x + √75x + 2√150)
= 3√5x² + 2√90x + √75x + 2√150
= 3√5x² + 2×3√10x + √75x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 10√6
= 3√5x² + 6√10x + 5√3x + 10√6
Ultimately, the product of the expression is; 3√5x² + 6√10x + 5√3x + 10√6
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4. Three weeks later, you find a scooter on sale for $399.99, which reflects a discount rate of 30%.
What percentage of the original price is $399.99? Show the proportion to solve the equation.
What was the original price? (Hint, you will need to perform subtraction, similar to the
example).
Answers
Answer:
70%
$571.41
Step-by-step explanation:
100% means 1, or a whole thing.
Since the discount is 30% of the original price, and the original price is 100% of the original price, then
100% - 30% = 70%
With a 30% discount, you actually pay 70% of the original price.
$399.99 is 70% of the original price.
399.99 / 70% = x / 100%
70x = 100 × 399.99
x = 571.41
The original price was $571.41.
Lily pads increase by 25% every 10 days.lf a pond starts with 22 lily pads,how many will there be after 50 days?
Answers
We conclude that after 50 days, there will be 67 lily pads.
how many will there be after 50 days?
We know that the number increases by 25% every 10 days.
In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.
We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:
N = 22*(1 + 25%/100)*...*(1 + 25%/100%)
( the factor (1 + 25%/100%) appears five times)
So we can rewrite:
N = 22*(1 + 25%/100%)⁵
N = 22*(1 + 0.25)⁵ = 67.1
Which can be rounded to the nearest whole number, which is 67.
So we conclude that after 50 days, there will be 67 lily pads.
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consider the quadratic function f(x)= x^2 -8x-4 what is the value of the leading coefficient
Answers
The leading coefficient of the quadratic equation f(x)= x² – 8x – 4 will be 1.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
Then we have the quadratic equation given below.
f(x)= x² – 8x – 4
f(x)= x² – 8x + 16 – 16 – 4
f(x)= (x – 4)² – 20
Then the leading coefficient will be 1.
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find the slope of the line on the graph write your answer as a whole number or a fraction not a mixed number or decimal
Answers
Answer: 3/4
Step-by-step explanation:
Which best describes the range of the function #(x) = 2(3)x? O y>0 O y≥0 O y = 2 O y≥2
Answers
Answer:
The range of the function f(x) : is y > 0.
The correct option is (A)
Step-by-step explanation:
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
Answer: A
Step-by-step explanation:
We can rewrite [tex]8^x[/tex] as follows:
[tex]8^{x}=\left(8^{9} \right)^{x/9}=\left(\frac{1}{8^{9}} \right)^{-x/9}[/tex]
Hence, [tex]A=\frac{1}{8^{9}}=\boxed{8^{-9}}[/tex]
Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {y|–Infinity < y < Infinity}.
The function is a reflection of y = .
The function passes through the point (3, –27).
Answers
the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.Which statements are true about the function?
Here we have the function:
[tex]F(x) = -\sqrt[3]{x}[/tex]
First, this is a cubic root, so its domain is the set of all real numbers (same for the range). And we know that the cubic root is an increasing function, so if we put a negative sign before it, we will have a decreasing function.
Then the correct options are:
The function has a domain of all real numbers.The function has a range of {y|–Infinity < y < Infinity} (this is the same as saying that the range is the set of all real numbers.The fourth option is incomplete, so we can't conclude if it is true or not, it would be true if it said:
"The function is a reflection over the x-axis of y = ∛x"
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Answer:
b, c, d
Step-by-step explanation:
Rob bought a pair of jeans at 30% off the original price. If the original price was $55, how much did he pay for the jeans?
Answers
Answer:
$38.50
Step-by-step explanation:
(100-30)% of $55
= 70% of $55
= $38.50
Hope this helps :)
Two fire trucks on the ground on either side of a burning building or 1.3 miles apart. they each measure the angle of elevation to the fire which are 58° and 52°. How far is each truck from the fire? Please help ASAP thank you so much!
Answers
The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.
Distance of each truck from the fireUsing sine rule, we find the length of AB and BC as shown in the image.
a/sin A = b/sin B = c/sin C
Angle C = 180 - (58 + 52) = 70⁰
1.3/(sin 70) = b/(sin 52)
b = (1.3sin 52) / (sin 70)
b = 1.09 mile
c = (1.3sin 58) / (sin 70)
c = 1.1732 miles
Bisect angle C, and use sine rule again to find the lengths of bisected line AB.
1.09/(sin 90) = x/[sin (90 - 58)]
1.09/(sin 90) = x/(sin 32)
x = (1.09 sin 32)/(sin 90)
x = 0.578 mile
Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile
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Write the mathematical expression for cost of each item if y items cost a
total of $25.00.
Answers
Simplify this expression:
12a−8−5a+12
Answers
12a - 8 -5a + 12
arranging like terms
12a - 5a - 8 + 12
a ( 12-5) - 8 - 12
a(7) - 4(2 - 3)
a(7) -4(-1)
a(7) + 4
7a + 4
simplifing the expressions
Answer:
12a-5a-8+12
=(12-5)a+4
=7a+4
What is the value of x?
Answers
The value of x in the segment is 3
How to determine the value of x?Using the secant and segment theorem, we have:
x * (x + 21) = (x + 1) * (x + 1 + 14)
Evaluate the sum
x * (x + 21) = (x + 1) * (x + 15)
Expand
x^2 + 21x = x^2 + 15x + x + 15
Subtract x^2 from both sides
21x = 15x + x + 15
Evaluate the like terms
5x = 15
Divide both sides by 5
x = 3
Hence, the value of x is 3
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Which of the following is the graph of y = log3 x - 1
Answers
The options are not mentioned , but the correct graph is plotted and attached with the answer.
What is a function ?A function is a mathematical statement that relates a dependent variable with an independent variable .
It is given to find among the options which is the correct graph for
y = log₃ (x-1)
The options are not mentioned , but the correct graph is plotted and attached with the answer.
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juan tiene 400 y rosa 350. ambos se compran
Answers
What is the value of log5^125?
Answers
Step-by-step explanation:
I'm going to assume you mean
[tex]log(5^{125})[/tex] which can be rewritten as [tex]125 log(5)[/tex] since if you start with [tex]log(a) = x = > 10^x=a\\(10^x)^c=a^c\\c *log(a^c)[/tex]since when you do (10^x)^c you're just multiplying the exponent which is represented by the x but is equal to the log you just multiply the log which is why you can bring it in front.
You can then approximate the value of log(5) using a calculator and multiply by 125 to get around 87.371
A linear function on a coordinate plane passes through (minus 2, 3), (minus 1, 0), (0, minus 3), and (1, minus 6)
Which equation describes the line graphed above?
A.
B.
C.
D.
Answers
The equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The options are missing.
The options are:
A) y = 3x - 3
B) y = -3x + 3
C) y = 3x + 3
D) y = -3x - 3
From the points [tex]\left(-2,3\right)[/tex] and [tex]\left(-1,0\right)[/tex]:
[tex]\rm y\ =\ \dfrac{3}{-1+2}\left(x+1\right)[/tex]
y = 3(x + 1)
y = 3x + 3
Thus, the equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
Learn more about the straight line here:
brainly.com/question/3493733
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