Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
Answers
Answer:
* sin Ф = -15/17 * cos Ф = 8/17 * tan Ф = -15/8
* csc Ф = -17/15 * sec Ф = 17/8 * cot Ф = -8/15
Step-by-step explanation:
Lets revise the trigonometric function of angle Ф
- Angle θ is in standard position
- Point (8, -15) is on the terminal ray of angle θ
- That means the terminal is the hypotenuse of a right triangle x and y
are its legs
∵ x-coordinate is positive and y-coordinate is negative
∴ angle Ф lies in the 4th quadrant
- The opposite side of angle Ф is the y-coordinate of the point on the
terminal ray of angle Ф and the adjacent side to angle Ф is the
x-coordinate of that point
∵ The length of the hypotenuse (h) = √(x² + y²)
∴ h = √[(8)² + (-15)²] = √[64 + 225] = √[289] = 17
∴ The length of the hypotenuse is 17
- Lets find sin Ф
∵ sin Ф = opposite/hypotenuse
∵ The opposite is y = -15
∵ The hypotenuse = 17
∴ sin Ф = -15/17
- Lets find cos Ф
∵ cos Ф = adjacent/hypotenuse
∵ The adjacent is x = 8
∵ The hypotenuse = 17
∴ cos Ф = 8/17
- Lets find tan Ф
∵ tan Ф = opposite/adjacent
∵ The opposite is y = -15
∵ The adjacent = 8
∴ tan Ф = -15/8
- Remember csc Ф is the reciprocal of sin Ф
∵ csc Ф = 1/sin Ф
∵ sin Ф = -15/17
∴ csc Ф = -17/15
- Remember sec Ф is the reciprocal of cos Ф
∵ sec Ф = 1/ cos Ф
∵ cos Ф = 8/17
∴ sec Ф = 17/8
- Remember cot Ф is the reciprocal of tan Ф
∵ cot Ф = 1/tan Ф
∵ tan Ф = -15/8
∴ cot Ф = -8/15
Related Questions
Simplify 3/4(1/2×-12)+4/5
Answers
Answer: [tex]\frac{3}{8}x-\frac{41}{5}[/tex] or [tex]\frac{3}{8}x-8\ \frac{1}{5}[/tex]
Step-by-step explanation:
Given the following expression:
[tex]\frac{3}{4}(\frac{1}{2}x-12)+\frac{4}{5}[/tex]
You can follow these steps in order to simplify it:
1. You need to apply Distributive property:
[tex]=\frac{3}{8}x-9+\frac{4}{5}[/tex]
2. And now you must add the like terms. Then:
[tex]=\frac{3}{8}x-\frac{41}{5}[/tex]
Therefore you get the following answer:
[tex]\frac{3}{8}x-\frac{41}{5}[/tex] or [tex]\frac{3}{8}x-8\ \frac{1}{5}[/tex]
At the carpet store where you work, a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size. The carpet ,pad,and installation will cost $17.50 per square yard. To the nearest dollar,how much will it cost to carpet the room?
Answers
Answer: 595 Dollars
Step-by-step explanation:
16 1/2 times 18 1/2 = 305.25
one square yard = nine feet
305 devided by nine 33.9166667 (round to 34)
34 times 17.50 = 595
Answer:
$593
Step-by-step explanation:
We have been that a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size.
First of all, we will find area of carpet by multiplying both side lengths as:
[tex]\text{Area of carpet}=16\frac{1}{2}\text{ ft}\times 18\frac{1}{2}\text{ ft}[/tex]
Convert mixed fraction into improper fraction:
[tex]16\frac{1}{2}\Rightarrow \frac{16\times2+1}{2}=\frac{32+1}{2}=\frac{33}{2}[/tex]
[tex]18\frac{1}{2}\Rightarrow \frac{18\times2+1}{2}=\frac{36+1}{2}=\frac{37}{2}[/tex]
[tex]\text{Area of carpet}=\frac{33}{2}\text{ ft}\times \frac{37}{2}\text{ ft}[/tex]
[tex]\text{Area of carpet}=\frac{1221}{4}\text{ ft}^2[/tex]
[tex]\text{Area of carpet}=305.25\text{ ft}^2[/tex]
1 square feet equals 0.111 square yards.
[tex]305.25\text{ ft}^2=305.25*0.1111\text{ yards}^2[/tex]
To find the cost to carpet the room, we will multiply area of carpet by cost $17.50 per square yards.
[tex]305.25\times 0.1111\text{ yards}^2\times\frac{\$17.50}{\text{ yard}^2}[/tex]
[tex]305.25\times 0.1111\times\$17.50[/tex]
[tex]\$593.4823125\approx \$593[/tex]
Therefore, the cost to carpet the room would be $593.
What’s the value of x
Answers
Answer:
The correct answer is last option 3√2 units
Step-by-step explanation:
From the figure we can see that two small right angled triangle.
These two triangle combined to form a large right angled triangle.
To find the value of x
Consider the small triangle with hypotenuse x and one side 3 units.
The angles of this triangle be 45°, 45° and 90°, then the sides are in the ratio 1 : 1 : √2
Therefore we can write,
3 : 3 : x = 1 : 1 : √2
x = 3√2
The correct answer is last option 3√2 units
Selena is graphing the inequality x <-2
She begins by drawing a number line and placing an open circle at –2. What’s Selena’s next step?
Answers
Answer:
My man above in Correct
Step-by-step explanation:
Solve for x in the picture please
Answers
Answer: [tex]x=1[/tex]
Step-by-step explanation:
In order to find the value of "x", it is important to remember that:
[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]
We can identify in the figure that:
[tex]Tangent\ chord\ angle=(43x)\°\\\\Intercepted\ arc=AB[/tex]
Then:
[tex]43x=\frac{1}{2}AB[/tex]
Solving for AB:
[tex]2(43x)=AB\\\\AB=86x[/tex]
Now, since there are 360° in a circle, we know that:
[tex]AB+(272x+2)=360[/tex]
Then we can substitute [tex]AB=86x[/tex] into [tex]AB+(272x+2)=360\°[/tex] and solve for "x". This is:
[tex](86x)+(272x+2)=360\\\\358x=360-2\\\\x=\frac{358}{358}\\\\x=1[/tex]
Express in exponential form. log 3 a = n
Answers
Answer:
[tex]\log_3(a)=n[/tex] has exponential form [tex]3^n=a[/tex].
[tex]\log(3a)=n[/tex] has exponential form [tex]10^{n}=3a[/tex].
Please let me know if neither of my interpretations of your problem/question is correct. That is I can either assume you wrote [tex]\log_3(a)=n[/tex] or [tex]\log(3a)=n[/tex].
If something else was intended, please let me know. Thanks kindly.
Step-by-step explanation:
Let's assume: [tex]\log_3(a)=n[/tex].
The base is 3.
The exponent is n. (Just remember the logarithm is the exponent.)
So we have [tex]3^n=a[/tex]
In general these forms are equivalent:
[tex]log_b(a)=y \text{ is equivalent to } b^y=a[/tex].
[tex]\log(3a)=n[/tex] is the same as [tex]\log_{10}(3a)=n[/tex]
The base is 10 (if you don't see a base and log is written).
The exponent is n.
So we have [tex]10^n=3a[/tex].
To transform the logarithmic function log3 a = n into an exponential form, we apply the rule that if logb a = n, then b^n = a. Therefore, the exponential form is 3^n = a.
Explanation:The student's question is about transforming a logarithmic equation into an exponential form. This is a common request in mathematics, particularly in algebra and precalculus.
The given equation is log3 a = n. The exponential form of a logarithmic equation is based on this relationship: If logba = n, then the exponential form is bn = a. Applying this rule to the provided equation gives 3n = a as the exponential form.
This transformation is based on the definition of logarithms, which are the inverses of exponential functions. The logarithm of a number to a particular base is the exponent to which the base must be raised to get that number. So in this case, n is the power you need to raise 3 to in order to get a.
Learn more about Logarithms here:https://brainly.com/question/37287488
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estimate 16.667 + 7.66 by first rounding each number to the nearest tenth
Answers
Answer:
24.4
Step-by-step explanation:
16.667 + 7.66 becomes 16.7 + 7.7, which, in turn, is 24.4
Answer:
24.4
Step-by-step explanation:
The nearest tenth is the first decimal place. We look at the second decimal place. If it is 5 or above we round up
16.667 to the nearest tenth = 16.7
7.66 to the nearest tenth = 7.7
16.7 + 7.7 = 24.4
Choose the equation that represents the graph below:
Answers
Answer:
y = -2x/3 + 6
Step-by-step explanation:
y = mx+b
m = y2-y1/x2-x1
m = 2 - 6/6 - 0
m= -4/6 = -2/3
b = y-intercept = 6
Let's investigate
You have an appointment at 2 o'clock at the dentist. Then you need to catch a
train one hour after your appointment. The walk to the train station takes
20 minutes. What time will you have to leave the dentist to catch your train?
Answers
F = {(-1, 2), (3, 2), (4, 2), (0, 2)} Is F a function and why/why not?
Yes, no two ordered pairs in this list have the same first coordinate.
No, each set of ordered pairs in this list has the same second coordinate.
Yes, there is more than one ordered pair in this list.
No, there is a limited number of ordered pairs in this list.
Answers
Answer:
Yes, no two ordered pairs in this list have the same first coordinate
Step-by-step explanation:
we know that
A function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
That means that there can be only one ordered pair with the same value of x.
therefore
In this problem F is a function, because all the ordered pairs of the list don't have the same first coordinate
Consider the function represented by the equation x - y = 3. What is the equation written in function notation, with x as the
ndependent variable?
O f(x) = y + 3
Of(x) = -y-3
Of(x) = -x + 3
f(x) = X-3
Answers
Answer:
f(x)=x-3
Step-by-step explanation:
You are given x-y=3 and you want to rewrite in function notation with x being the independent. That means we need to solve for y so y can depend on x.
x-y=3
Subtract x on both sides:
-y=-x+3
Multiply both sides by -1:
y=x -3
So function notation would be f(x)=x-3
The function notation of the equation x - y = 3, with x as the independent variable, is f(x) = x - 3.
Explanation:The equation x - y = 3 is in standard form. To express this equation in function notation with x as the independent variable, we need to solve for y in terms of x. By moving y to the other side of the equation and 3 to the opposite side, we get y = x - 3. In function notation, where y is usually replaced by the function f(x), the equation becomes f(x) = x - 3.
Learn more about function notation here:https://brainly.com/question/5025688
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find the solution of x-13=25 and verify you solution using subtraction
Answers
Answer:
x = 38
Step-by-step explanation:
Add 13 to both sides, to isolate x: x = 38
We verify this solution using substitution (not subtraction):
Is 38 - 13 = 25 true? Yes, it is.
Answer:
X-13=25
get coefficient X by itself by adding 13 to both sides
X=-13+13=25+13
X=38
The volume of a cube depends on the length of its sides. This can be written
in function notation as ws). What is the best interpretation of 3) = 27?
Answers
Answer:
Step-by-step explanation:
The given question is that the volume of a cube depends on the length of its sides.This can be written in function notation as v(s). What is the best interpretation of v(3)=27.
Solution:
According to the question the volume of a cube depends on the length of its sides. According to the statement we will apply the formula of volume of a cube.
V(s)=s³
In this question we have given s=3ft.
So, we will put the value of 's' in the formula.
V(s)=s³
V(3)=3³
Multiply 3 three times to get the answer.
V(3)=3*3*3
V(3)=27 ft³
This means that the cube has a volume of 27ft³ with the length of its sides 3ft....
Can you guys please help me with this two questions
Answers
Answer:
1. C) 5.50x + 10
2. 54
Step-by-step explanation:
1. C) 5.50x + 10
You have a static fee of $10 which does not need to be attached to a variable as it will not change. You also have a fee of $5.50, which may be charged depending on the amount of classes. Since this is dependent on something, it includes a variable.
Therefore, your terms are:
5.5x
10
Simply add them together for your equation.
[tex]5.5x+10[/tex]
2. 54
To solve, simply plug in 8 to your equation which you created in part 1. This is possible because x stands for the amount of classes and, as the question tells us, 8 is the amount of classes.
[tex]5.5(8)+10\\44+10\\54[/tex]
Tom just received a new job offer. He is told that his starting salary will be $75,000 per year. He is told his salary will probably be $81,000 in four years. We'll use this information to try to anticipate his future earnings in any given year.Assume that Y= Tom's salary amount in dollars and x= the number of years worked. Step 1.Use the data given to find the rate of change, or the salary increase per year.( hint: compute the slope.) We are now going to use a line to model Tom's salsry growth. Step 2. Use the data given and the slope value from Step 1 to write the slope-intercept form of the line. Step 3. Based on your equation from Step 2, What will Tom's salary be in ten years?
Answers
Answer:
Part 1) The rate of change is [tex]2,000\ \$/year[/tex]
Part 2) The equation of the line into slope intercept form is [tex]y=2,000x+73,000[/tex]
Part 3) Tom's salary would be [tex]\$93,000[/tex] in ten years
Step-by-step explanation:
Let
x ------> the number of years worked
y -----> Tom's salary amount in dollars
we have the points
A(1, 75,000) and B(4,81,000)
step 1
Find the rate of change (slope)
The slope is equal to
[tex]m=(81,000-75,000)/(4-1)=2,000\ \$/year[/tex]
step 2
Find the equation of the line into slope-intercept form
we know that
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have that
[tex]m=2,000\ \$/year[/tex]
point A(1, 75,000)
substitute
[tex]75,000=(2,000)(1)+b[/tex]
[tex]b=75,000-2,000=73,000[/tex]
The equation of the line is
[tex]y=2,000x+73,000[/tex]
step 3
What will Tom's salary be in ten years?
For x=10 years
Substitute in the linear equation
[tex]y=2,000(10)+73,000=\$93,000[/tex]
Answer:
The increment in salary is $1500 each year. The slope intercept form is [tex]y=1500x+75000[/tex] and the salary in 10 years will be $90000.
Step-by-step explanation:
Consider the provided information.
The starting is $75,000 per year.
Let x is the number of years worked and y is Tom's salary amount in dollars.
When he has 0 yr of experience, his salary is $75000 per year.
it can be written as (0,75000).
His salary will probably be $81,000 in four years.
It can be written as (4,81000).
STEP 1:
Find the rate of change by using the formula slope=[tex]m=\frac{rise}{run}[/tex].
Determine the rise by subtracting 75000 from 81000.
Rise = 81000 - 75000 = 6000
Now determine the run by subtracting 0 from 4.
Run = 4 - 0 = 4
Substitute the respective values in the above formula.
[tex]slope=m=\frac{6000}{4}\\slope=m=1500[/tex]
Therefore, the rate of change, or the salary increase per year is $1500.
STEP 2:
Write the slope intercept form by using the formula:
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute m = 1500 and [tex](x_1,y_1)=(0,75000)[/tex] on the above formula.
[tex](y-75000)=1500(x-0)\\y-75000=1500x\\y=1500x+75000[/tex]
Thus, the slope intercept form is [tex]y=1500x+75000[/tex].
STEP 3:
The salary in 10 years. can be calculated as:
Substitute the value of x = 10 in [tex]y=1500x+75000[/tex].
[tex]y=1500(10)+75000\\y=15000+75000\\y=90000[/tex]
Hence, the salary in 10 years will be $90000.
Find the arc length of the given circle.
Answers
Answer:
Arc length = (30/360)(2π)(14)
= (7/3)π cm = about 7.33 cm
Please help ASAP
this table shows how many students from high schools attended a foot ball game.
A student is randomly selected.
what is the probability that a student attended the game, given that the student is from North Beach? Round your answer to two decimal places.
Answers
In total, there are 200 students from North Beach.
Of those 200 students, 110 attended the game.
Because it is only asking for the probability that a student from North Beach attended, the answer would be 110 / 200, or 0.55.
Therefore, the answer would be C.
Hope this helps! :)
Answer:
0.314
Step-by-step explanation:
Given:
total number of students=350
total number of students that attented= 170
students that attended from North beach =110
probability that a student attended the game, given that the student is from North Beach= 110/350
=0.314 !
Triangle ABC has coordinates A(2, 4), B(5, 6), and C(1, 4). If the triangle is rotated 180° clockwise about the origin, what are the coordinates of B'?
Answers
Answer:
B'(-5,-6)
Step-by-step explanation:
The mapping for 180° clockwise rotation about the origin is:
[tex](x,y)\to (-x,-y)[/tex]
The find the image of B(5,6), we plug in x=5 and y=6 into the rule.
[tex](5,6)\to (-5,-6)[/tex]
Therefore the coordinates of B' are (-5,-6).
Point B with coordinates (5, 6) will have coordinates (-5, -6) after a 180° clockwise rotation about the origin.
Triangle ABC has coordinates A(2, 4), B(5, 6), and C(1, 4). If the triangle is rotated 180° clockwise about the origin, we need to find the coordinates of B'.
To rotate a point (x, y) 180° about the origin, we can multiply the coordinates by -1. So, the coordinates of B' after rotation will be (-5, -6).
Select the correct answer.
If a line crosses the y-axis at (0, 1) and has a slope of 4/5, what is the equation of the line?
Answers
Answer:
5y - 4x = 5. This gives you your points with a slope of 4/5
Answer:
[tex]y=\frac{4}{5}x+1[/tex]
Step-by-step explanation:
We are given the slope, and the y-intercept. So we can use the slope-intercept equation. Which is as follows:
[tex]y=mx+b[/tex]
where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of [tex]y[/tex] when [tex]x=0[/tex]).
The information that we have is that the slope of the line is:
[tex]m=\frac{4}{5}[/tex]
and that the line crosses the y-axis at (0, 1).
From this point we can find the y-intercept [tex]b[/tex], because b is the value of [tex]y[/tex] when [tex]x=0[/tex].
And since the line passes through (0, 1) when [tex]x = 0[/tex], [tex]y =1[/tex]. Thus, the y-intercept is:
[tex]b=1[/tex]
substituting the values of the slope and the y-intercept into the equation:
[tex]y=mx+b\\y=\frac{4}{5}x+1[/tex]
the answer is: [tex]y=\frac{4}{5}x+1[/tex]
Given a triangle with a = 12, A = 13°, and B = 12°, what is the length of c? Round to the nearest tenth.
Answers
Answer:
=5.1 units
Step-by-step explanation:
To use the sine rule to find the length of c we first need to find the angle at C.
C=180-(13+12)
C=180-25
C=155°
a/Sin A=c/Sin C
Calculating for the value of c using the sine rule:
12/Sin 13=c/Sin 155
c=12 sin 155
=5.07 units
Thus to 1 decimal places, the value of c is 5.1 units.
Betsy can clean a/b of the house in an hour. How long will it take her to clean the whole house?
Answers
Answer:
[tex]b/a\ hours[/tex]
Step-by-step explanation:
we know that
Betsy can clean a/b of the house in an hour
The whole house (100%) correspond to the number 1
so
using proportion
Find out how long will it take her to clean the whole house
[tex]\frac{(a/b)}{1}=\frac{1}{x} \\ \\x=1/(a/b)\\ \\x=b/a\ hours[/tex]
Use the zero product property to find the solutions to the equation 6x^2- 5x = 56.
Answers
Answer:
[tex]\large\boxed{x=-\dfrac{8}{3}\ or\ x=\dfrac{7}{2}}[/tex]
Step-by-step explanation:
[tex]6x^2-5x=56\qquad\text{subtract 56 from both sides}\\\\6x^2-5x-56=0\\\\6x^2+16x-21x-56=0\\\\2x(3x+8)-7(3x+8)=0\\\\(3x+8)(2x-7)=0\iff 3x+8=0\ \vee\ 2x-7=0\\\\3x+8=0\qquad\text{subtract 8 from both sides}\\3x=-8\qquad\text{divide both sides by 3}\\\boxed{x=-\dfrac{8}{3}}\\\\2x-7=0\qquad\text{add 7 to both sides}\\2x=7\qquad\text{divide both sides by 2}\\\boxed{x=\dfrac{7}{2}}[/tex]
p(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply. (MORE THAN ONE ANSWER)
x + 3 is a factor of the polynomial.
x - 3 is a factor of the polynomial.
-3 is the constant term of the polynomial.
p(x) can have at most 3 linear factors.
Answers
Answer:
x+3 is a factor of P
Step-by-step explanation:
By the factor theorem:
P(a)=0 <-> x-a is a factor of P.
You have P(-3)=0.
This implies x-(-3) is a factor of P.
Note: x-(-3)=x+3.
We know this from the factor theorem, which states that if f(a) = 0, then (x - a) is a factor.
Thus we know that (x - -3) is a factor, which simplifies to (x + 3).
All the other answer options do not have to be true, because (x - 3) doesn’t have to be factor, -3 doesn’t have to be the constant of the polynomial, and p(x) can have any number of linear factors, which means the only answer you should select as definitely true is the first option.
I hope this helps! Let me know if you have any questions :)
Which of the given expressions results in 0 when evaluated at x = 5?
OA. 5x(x – 7)
OB. (x - 3)(x - 5)
Oc. (x + 7)(x - 2)
OD. (x + 5)(x - 8)
Answers
Answer:
B
Step-by-step explanation:
Look for an expression with (x - 5 ) as this will give zero when x = 5, that is
x - 5 = 5 - 5 = 0
The only expression with a factor of (x - 5 ) is B
Clyde simplified ( j^-8)^-2
Answers
ANSWER
[tex]{j}^{16} [/tex]
EXPLANATION
The given expression is
[tex]( {j}^{ - 8} )^{ - 2} [/tex]
To simplify this expression, we use the law of exponents.
Recall that:
[tex] {(a}^{m} )^{n} = {a}^{mn} [/tex]
We need to multiply the exponents to get:
[tex]( {j}^{ - 8} )^{ - 2} = {j}^{ - 8 \times - 2} [/tex]
[tex]( {j}^{ - 8} )^{ - 2} = {j}^{16} [/tex]
Therefore after simplification, Clyde got:
[tex]{j}^{16} [/tex]
Answer:
Clyde should have applied the power of a power rule and multiplied the exponents instead of adding them. The simplified form should be j to the 16th power.
Step-by-step explanation:
The exponents should be multiplied.
The simplified form should be j^16
In each of the following pairs, determine the temperature change, and whether the temperature increased or decreased. a. 45° F to –10° F b. 35° C to 80° F c. –19° C to 49° C d. 137° C to 0° C e. 5° C to 19° F f. 68° F to 29° C
Answers
A: decreased
B: increased
C: increased
D: decreased
E: decreased
F: increased
Answer:
∵ Change = final value - initial value,
If change > 0, then the value is increased,
if change < 0, then the value is decreased,
a. 45° F to -10° F,
Change = -10° F - 45° F = -55° F < 0° F,
Thus, temperature is decreased,
b. 35° C to 80° F
∵ 35° C = 95° F ( by the formula (°C × 9/5) + 32 = °F )
Change = 80° F - 95° F = -5° F < 0° F,
Thus, temperature is decreased,
c. -19° C to 49° C,
Change = 49° C - (-19)° C = 68° C > 0° C,
Thus, temperature is increased,
d. 137° C to 0° C,
Change = 0° C - 137° C = -137° C < 0° C,
Thus, temperature is decreased,
e. 5° C to 19° F,
∵ 5°C = 41°F
Change = 19° F - 41° F = -22° F < 0° F,
Thus, temperature is decreased,
f. 68° F to 29° C,
∵ 29°C = 84.2°F
Change = 84.2°F - 68° F = 16.2° F > 0° F,
Thus, temperature is increased.
If R(x) = 2x - 5 and g(x) = x2 - 4x - 8, find (f + g(%).
O A (f+9)(x) = x2 - 2x-3
O B. (f+g)(x) = x2 - 2x-13
O C. (*+ g)(x) = 3x2 - 4x- 13
O D. (f+ g)(x) = x2 + 2x-3
C
PREVIOUS
Answers
Answer:
OB. (f+g)(x) = x^2-2x-13
Step-by-step explanation:
Given
f(x) = 2x-5
and
g(x) = x^2-4x-8
We have to find (f+g)(x)
So,
(f+g)(x) = f(x) + g(x)
= 2x-5 + (x^2-4x-8)
= 2x-5+x^2-4x-8
= x^2+2x-4x-5-8
=x^2-2x-13
Therefore, Option B is correct ..
What is the first term in this expansion?
1.) 2x^15
2.) 2^15x^15
3.) 10y^15
4.) 10^15y^15
Answers
Answer:
2¹⁵x¹⁵ (2nd option)
Step-by-step explanation:
When you expand (2x+10y)¹⁵ you would get:
32,768x¹⁵ + 2,457,600x¹⁴y + 86,016,000x¹³y² + 1,863,680,000x¹²y³+
27,955,200,000x¹¹y⁴+307,507,200,000x¹⁰y⁵ + 307,507,200,000x¹⁰y⁵ + ... so on and so forth.
Since you are not interested in anything else but the first term, observe that the first term is:
32,768x¹⁵
That is equal to: 2¹⁵x¹⁵
What happened there is you need to distribute the exponent to the coefficient of the term as well, so you need to distribute it to 2 as well.
Which of the following is a function?
A. {(1,1), (2,5), (-2,5), (1,-1)}
B. {(-1,1), (-2,1), (-1,3), (-4,1)}
C. {(-1,1), (-1,2), (-1,3), (-1,4)}
D. {(-1,1), (-2,2), (-3,3), (-4,4)}
Answers
Answer:
D
Step-by-step explanation:
Reminder: A function returns ONLY ONE y value for each input value.
We immediately discard possible answer A, since 2 points have input 1 with different outputs.
Same for B: discard this.
Same for C: discard this.
D is a function. All of the inputs are unique (no duplication).
6. The sum of 3 consecutive odd integers is 87. Find the equation used to solve this
problem. Find the three integers.
An +n + 2 +n +4-87:
n-27, n + 2 - 29, n + 4- 31
B
n
+n +1 +n + 2 - 87:
n=28, n + 1 = 29, n + 2 = 30
Cn +n +1+n + 2 = 87;
n = 29, n + 1 = 30. n + 2 = 31
Dn+n + 2 +n + 4-87;
n = 29,0 + 2 = 31, n + 4 = 33
Answers
Answer:
A
n=27, n+2=29, n+4=31
The correct option is A: n + n + 2 + n + 4 = 87; n -27, n + 2 - 29, n + 4 - 31.
Let's denote the three consecutive odd integers as n, n + 2, and n + 4. The sum of these integers is given as 87.
The correct equation to represent this situation is:
n + (n + 2) + (n + 4) = 87
Now let's solve for n:
3n + 6 = 87
Subtract 6 from both sides:
3n = 81
Divide both sides by 3:
n = 27
n + (n + 2) + (n + 4) = 87
27 + 29 + 31 = 87
The three consecutive odd integers are 27, 29, and 31.