Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees
Direction of a vectorThe direction of a vector is the degree at which the vector is moving with respect to the horizontal.
Given the coordinate point (-3, 21), the direction is expressed as:
theta = arctan(y/x)
Substitute
theta = arctan(21/-3)
theta =arctan(-7)
theta = -81.7 degrees
Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees
Learn more on direction of vector here: https://brainly.com/question/3184914
#SPJ2
Verify each identity.
I need help with the Precalculus.
1)
[tex]\bf \cfrac{cot(x)}{sin^2(x)}=\cfrac{csc^2(x)}{tan(x)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{cos(x)}{sin(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{cos(x)}{sin(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the left-hand-side} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{1}{sin^2(x)}~~}{\frac{sin(x)}{cos(x)}}\implies \cfrac{1}{sin^2(x)}\cdot \cfrac{cos(x)}{sin(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the right-hand-side}[/tex]
2)
[tex]\bf \cfrac{cos^2(x)+tan(x)}{sec(x)}=cos^3(x)+sin(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~cos^2(x)+\frac{sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}\implies \cfrac{~~\frac{cos^3(x)+sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}~\hfill \textit{doing the left-hand side} \\\\\\ \cfrac{cos^3(x)+sin(x)}{\underline{cos(x)}}\cdot \cfrac{\underline{cos(x)}}{1}\implies cos^3(x)+sin(x)[/tex]
(Economics) Real Gross Domestic Product is adjusted for _____ changes.
a. price
b. time
c. government
(will mark brainliest)
C.Government is the answer
Answer:A-Price
Step-by-step explanation:
Real Gross Domestic Product is adjusted for Price changes.
Unlike Nominal GDP Real GDP accounts for the change in prices and provides a better figure than nominal GDP. Real GDP differentiate GDP in different years more significant because it permits comparisons of the real volume of services and goods without taking inflation.
In 1990 the enrollment at Trenton East High School was 840. From 1990 through 1996 the enrollment increased at an average rate of 24 students per year. Write a linear model for the enrollment at Trenton East High School. Let x represent the number of years since 1990. Trenton East was built to hold 900 students. Write a linear inequality that represents the possible number of years since 1990 when the school's enrollment was less than the maximum capacity for which the school was built. Solve the inequality.
Answer:
X x 26= 26x +840
Step-by-step explanation:
Answer:
See below in bold.
Step-by-step explanation:
Linear model:
E = 24x + 840 where E is the enrolment .
If there are 900 students then
900 = 24x + 840
24x = 900-840 = 60
For E < 900 we have the inequality
24x < 60
x < 2.5
As we are dealing in years our answer is
x < 3 years .
find any points of discontinuity for y=x^2/x^2+1
Answer:
The function is continuous for all real numbers
Step-by-step explanation:
We have the following function
[tex]y=\frac{x^2}{x^2+1}[/tex]
Note that the denominator of the function is:
[tex]x^2 +1[/tex]
This expression is different from zero for all real numbers, since for [tex]x^2 +1[/tex] then [tex]x^2 =-1[/tex], there is no number in the real numbers whose square root is equal to -1.
For this reason the function is defined for all real numbers and has no discontinuity.
This function is always positive, continuous and has horizontal asymptote
[tex]y = 1[/tex]
Observe the attached image
You invest $2000 in an account that is compounded annually at an interest rate of 5% . You never withdraw money from the account. How much money will be in the account after 4 years?
$2,431 is the answer to this problem I think
In Triangle JKL the measure of angle J = 40 and the measure of angle L is 3 times the measure of angle K. Find the measure of angle K and angle L.
The measure of angle K and angle L is 35 degrees and 105 degrees
Given information:In Triangle JKL the measure of angle J = 40 and the measure of angle L is 3 times the measure of angle K.
Calculation of measure of angle K and angle L:here we assume the angle K be x
So Angle L be 3x
Now
J + K + L = 180
40 + x + 3x = 180
40 + 4x = 180
4x = 180 - 40
4x = 140
x = 35 degrees
So, the angle K be 35 degrees
And, angle L should be 3(35) 105 degrees
learn more about the triangle here: https://brainly.com/question/11067716
which of the following describes the graph of
y = -x^2 + 3x + 10
A| The graph has zeroed at x = -2 and x= 5 and it opens downward.
B| The graph has zeros at x = 2 and x = -5 and it opens upward
C| The graph has zeroed at x = 2 and x = -5 and it opens downward
D| the graph has zeroed at x = -2 and x = 5 and it opens upward
The answer is D because that’s the answer lol
Jacob has 24 pieces of gum. He gives 3/4 of them away. How many pieces of gum does he have remaining?
Answer:
Step-by-step explanation: 6?
A company mixes pecans, cashews, peanuts, and walnuts to make a batch of mixed nuts. About 15.4% of the mixed nuts in a batch are pecans. If a batch contains 77 pounds of pecans, how many pounds of mixed nuts are in a batch altogether? Enter your answer in the box.
Answer:
500 lb
Step-by-step explanation:
You have to make a proportion:
[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]
77 lb is part of the whole weight ( which we don't know) so 77 will go on top
The problem tells us that 15.4% of the total weight is pecans so 15.4 will go over 100 (since % are out of 100)
[tex]\frac{77}{x} = \frac{15.4}{100}[/tex]
Then you cross multiply giving you: 7700 = 15.4x
then you divide 15.4 to both sides to isolate x which will give you 500
Final answer:
To find the total weight of a batch of mixed nuts where pecans make up 15.4% and weigh 77 pounds, we set up a proportion and solve for the total weight, resulting in 500 pounds for the whole batch.
Explanation:
The question asks how many pounds of mixed nuts are in a batch altogether if 77 pounds are pecans, which represent 15.4% of the mix. To find the total weight, we need to set up a proportion where 15.4% corresponds to 77 pounds, and we want to find 100% (the whole mix).
We can set up the equation like so: 15.4 / 100 = 77 / x, where x stands for the total weight of the mixed nuts. To find x, we solve for x using algebra: x = 77 / (15.4 / 100). When you perform the calculation, the result is x = 500 pounds. So, the batch of mixed nuts weighs 500 pounds in total.
128 + 0 = ?
128 - 0 = ?
128 x 0 = ?
128 / 0 = ?
Answer:
1.=128 2.= 128 3.= 0 4.= 0
Step-by-step explanation:
Answer:
128 + 0 = 128
128 - 0 = 128
128 x 0 = 0
128 / 0 = 0
The area of the shaded triangles in the fractal shown form a geometric sequence. The area of the largest triangle (not shaded) is 1 square unit. Find the areas of these shaded triangles. Orange: 1/4 square units Blue: _____ square units Green: _____ square units
Answer:
Blue: 1/16 square units
Green: 1/64
yes
1/3
Step-by-step explanation:
The areas of these shaded triangles. Orange: 1/4 square units, Blue: 1/16 square units, Green: 1/64 square units
What is a fraction?A fraction represents a part of a whole number of equal parts.
The area of the largest triangle is given as 1 square unit.
The area of the triangle is colored and follows a geometric sequence with the common ratio of 1/4.
The area of the non-shaded triangle is given by 1 square unit.
The area of the orange triangle
1 × 1/4 = 1/4 square units.
The area of the blue triangle
1/4 × 1/4 = 1/16 square units.
The area of the green triangle
1/16 × 1/4 = 1/64 square units.
Learn more about fractions:
https://brainly.com/question/10354322
A bicycle manufacturer uses the given expression to model the monthly profit from sales of a new model of bicycle, where x is the selling price of one bicycle, in dollars. At what selling prices for the bicycle will the manufacturer make neither a profit nor a loss?
Answer:
The manufacturer will have no profit or loss when the selling price equals $200 or $100.
Step-by-step explanation:
The expression to model the monthly profit from sales of a new model of bicycle is
-x^2 + 300x -20,000
Let
f(x) -----> the monthly profit in dollars
x -----> s the selling price of one bicycle in dollars
[tex]f(x)= -x^{2}+300x-20,000[/tex]
we know that
The manufacturer will make no profit nor a loss when the profit is equal to zero
so
f(x)=0
[tex]-x^{2}+300x-20,000=0[/tex]
Multiply by -1 both sides
[tex]x^{2}-300x+20,000=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]a=1\\b=-300\\c=20,000[/tex]
substitute in the formula
[tex]x=\frac{300(+/-)\sqrt{-300^{2}-4(1)(20,000)}}{2(1)}[/tex]
[tex]x=\frac{300(+/-)\sqrt{10,000}}{2}[/tex]
[tex]x=\frac{300(+/-)100}{2}[/tex]
[tex]x=\frac{300(+)100}{2}=200[/tex]
[tex]x=\frac{300(-)100}{2}=100[/tex]
therefore
The manufacturer will have no profit or loss when the selling price equals $200 or $100.
To find the selling prices at which the manufacturer will make neither a profit nor a loss, set the profit expression equal to zero and solve for x, giving a selling price of $5.
To determine the selling prices at which the manufacturer will make neither a profit nor a loss, we set the profit expression equal to zero:
0 = 100x - (500 + 20x)
Solving for x, we get x = 5. This means the selling price for the bicycle to break even is $5.
Please help me fill in the blank with the correct word from each statements' parentheses:
1. In an observational study, randomization of subjects _____ (occurs, does not occur).
2. A survey makes inferences about a population from_____ (a sample, a study, an experiment) of the population.
3. In an experiment, a treatment is imposed on those being studied to discern any differences in____ (a control, a response, an independent) variable.
Answer:
1. does not occur
2. a sample
3. an independent
Step-by-step explanation:
The correct answer for this question would be Occurs, Sample and an independent variable.
What is meant by survey?A survey is a type of research that involves gathering data from a predetermined group of people in order to get knowledge and insights about a variety of issues.
1) In an observational study, randomization of subjects has to occur to get a lot of diverse information from all the participants.
2) In a survey, randomly a sample is chosen from the population and all the inferences about the population are made from studying this sample only.
3) In a survey a treatment is imposed on all the participants so as to neutralize all the qualities they have which are quite different from the others.
Learn more about survey on:
https://brainly.com/question/25257437
#SPJ2
What is the solution of the inequality x^2-9x+18 less then or equal to zero? Graph solution.
ANSWER
[tex]3\le x\le6[/tex]
EXPLANATION
The given inequality is
[tex] {x}^{2} - 9x + 18 \leqslant 0[/tex]
This is the same as
[tex](x - 3)(x - 6) \leqslant 0[/tex]
The corresponding equation is
[tex](x - 3)(x - 6)= 0[/tex]
By the zero product principle,
[tex]x = 3 \: or \: x = 6[/tex]
We now plot the boundaries and test for the region that satisfies the inequality.
See attachment.
From the graph the solution is
[tex]3\le x\le6[/tex]
Kevin sold a house for $57,000 his fee or sales commission for selling the house was $2,679. What percent of the price of the price of the house was Kevin's commission
Answer:
4.7%
Step-by-step explanation:
Kevin's commission was 4.7% of the price of the house.
Calculate the percentage by dividing Kevin's commission by the selling price: $2,679 / $57,000 = 0.047.Multiply the result by 100 to get the percentage: 0.047 * 100 = 4.7%.The quotient of a numder and -5 is 6. what is the number?
Answer:
B
Step-by-step explanation:
Make an equation.
[tex]\frac{x}{-5}=6[/tex]
[tex]x=-30[/tex]
Answer:
B, -30
Step-by-step explanation:
Timothy built a base for a circular tabletop. The base can support a tabletop with a radius of at least 6 inches, but not more than 23 inches. What is the smallest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. square inches What is the largest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. square inches
Answer: The smallest possible area of the tabletop=[tex]113\text{ square inches}[/tex]
The largest possible area of the tabletop =[tex]1662\text{ square inches}[/tex]
Step-by-step explanation:
Given: The minimum radius of the tabletop = 6 inches
The maximum radius of the tabletop = 23 inches
We know that the area of circle is given by :-
[tex]A=\pi r^2[/tex], where r is the radius of the circle.
Now, the smallest possible area of the tabletop that will fit on Timothy’s table is given by :-
[tex]A_s=(3.14159265359) (6)^2=113.097335529\approx113\text{ square inches}[/tex]
The largest possible area of the tabletop that will fit on Timothy’s table is given by :-
[tex]A_s=(3.14159265359) (23)^2=1661.90251375\approx1662\text{ square inches}[/tex]
Answer:
113 square inches
1,662 square inches
Step-by-step explanation: Have a good day :)
When Mario has to leave the house for a while, he tethers his mischievous puppy to the corner of a 12 ft-by-8 ft shed in the middle of his large backyard. The tether is 18 feet long. Which description fits the boundary of the locus of points in the yard that the puppy can reach?
A a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
B a three-quarter circle of radius 18 ft, quarter circles of radii 12 ft and 8 ft
C semicircles of radii 18 ft, 10 ft, and 6 ft
D semicircles of radii 18 ft, 12 ft, and 8 ft
Answer:
a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
i took the test and i got this as the right answer
Answer:
A a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
In order to calculate this, you have to remember that you have a tether that is 18 ft long, thetered to a point, this would make a circle with a radius of 18 ft, but as the center of the circle would be where the theter is knotted, the shed forbids to make a full circle, it rather creates a 3/4 circle, and the dog can acces the other points of the shed, with le length of the theter, that is 8 ft after the long side, and 12 feet after the short side, creating another quarter circle with a radius of 8 and 12 ft.
Identify the measure of arc BG◠. HELP ASAP!! I'm so confused!
Answer:
arc BG = 14°
Step-by-step explanation:
∠BMG = [tex]\frac{1}{2}[/tex] ( arc BG + arc JS) = 30
Multiply both sides by 2
arc BG + arc JS = 60, that is
arc BG + 46° = 60° ( subtract 46° from both sides )
arc BG = 14°
Answer:
arc BG= 14°
Step-by-step explanation:
It is given in the figure that mJS = 46∘ and m∠BMG = 30∘.
If two chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. So,
m∠BMG = 12 (mJS +mBG)
Substitute the given values and solve for mBG.
30∘ = 12 (46∘ + mBG)
Multiply by 2.
60∘ = (46∘ + mBG)
Subtract 46∘.
14∘ = mBG
Therefore, mBG = 14∘.
Which of the following functions is quadratic?
Answer:sd
D. [tex]f\left(x\right)=2x^2+3x-5[/tex]
Step-by-step explanation:
Given choices are:
[tex]f\left(x\right)=\frac{2}{x^2}[/tex]
[tex]f\left(x\right)=3\left(3-x\right)[/tex]
[tex]f\left(x\right)=7^2[/tex]
[tex]f\left(x\right)=2x^2+3x-5[/tex]
Now we need to find about which of them is the quadratic function.
We know that quadratic function is written in form of [tex]f\left(x\right)=ax^2+bx+c[/tex]
Last choice looks similar to that form.
Hence coorect choice is D. [tex]f\left(x\right)=2x^2+3x-5[/tex]
Answer:
D. f(x) = 2x^2 + 3x - 5
Step-by-step explanation:
A company makes concrete bricks shaped like rectangular prisms. Each brick is 15 inches long, 10 inches wide, and 5 inches tall. If they used 15000 in cubed of concrete, how many bricks did they make?
Answer:
20 bricks
Step-by-step explanation:
So if you multipy the dimentions given, you get 750 inches squred. You now take 15,000 and divide it by 750 to get 20. This is your answer.
A company makes 20 concrete bricks.
How many bricks did the company make?Given:
A company makes concrete bricks shaped like rectangular prisms.Each brick is 15 inches long, 10 inches wide, and5 inches tall.They used 15000 in cubed concrete.Find:
How many bricks did they make?Solution:
A company makes concrete bricks shaped like rectangular prisms.
So, the volume of the brick = 15*10*5 = 750[tex]inches^{3}[/tex]
Now, to find how many bricks they make we have to divide 750[tex]inches^{3}[/tex] from 15000.
Number of brick = 15000/750 = 20
Hence, the number of bricks that the company makes is 20.
To learn more about rectangular shape, refer to:
https://brainly.com/question/27922897
#SPJ2
If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ? negative square root of 10 negative 2 square root of 10 2 square root of 10 over 7 negative 2 square root of 10 over 7
Answer:
negative 2 square root of 10 over 7
Step-by-step explanation:
Describe the error(s) that occurred and show the correct solution.
Answer:
[tex]-x^{2}+4x[/tex]
Step-by-step explanation:
we have
[tex](x^{2}+x)-(2x^{2} -3x)[/tex]
step 1
Eliminate the parenthesis
[tex]x^{2}+x-2x^{2} +3x[/tex]
The symbol of the term 3x is incorrect, must be positive instead of negative
so
[tex]-(-3x)=+3x[/tex]
Group terms that contain the same variable
[tex](x^{2}-2x^{2})+(x+3x)[/tex]
Combine like terms
[tex]-x^{2}+4x[/tex]
Which expression is equivalent to root 2/cubed root 2
Answer:
It's the second choice ⁶√2.
Step-by-step explanation:
Convert to fractional exponents:
√2 = 2^1/2
∛2 = 2^1/3
√2 / ∛2
= 2^1/2 / 2^1/3 = 2^(1/2-1/3)
= 2^(1/6)
Now change back to radicals:
= ⁶√2.
Solve each exponential equation by using properties of common logarithms. When necessary, round answers to the nearest hundredth. 7 ^3x-1 = 5 ^x-1
x ≈ 12.33
x ≈ -3.09
x ≈ 0.08
plss help mee
Final answer:
To solve the exponential equation 7^(3x-1) = 5^(x-1) using properties of common logarithms, we can take the natural logarithm (ln) of both sides. By expanding and isolating x, we can solve for x approximately as x ≈ 0.08.
Explanation:
To solve this exponential equation, you can take the natural logarithm of both sides. The natural logarithm (ln) cancels out the exponential function. So, taking the ln of both sides, we have:
ln(7^(3x-1)) = ln(5^(x-1))
Using the property of logarithms, we can bring down the exponents:
(3x-1)ln(7) = (x-1)ln(5)
Now, we can solve for x by isolating it. Let's expand the equation:
3xln(7) - ln(7) = xln(5) - ln(5)
Combining like terms:
3xln(7) - xln(5) = ln(7) - ln(5)
Factoring out x:
x(3ln(7) - ln(5)) = ln(7) - ln(5)
And finally, dividing:
x = (ln(7) - ln(5))/(3ln(7) - ln(5))
Using a calculator or a math software, we can approximate the value of x to the nearest hundredth to find:
x ≈ 0.08
Please help!!!!!!!!!!!!!!!
86 which equals 90 and then you divide by two
Answer:
x = 53.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8}{10}[/tex]
x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{10}[/tex] ) ≈ 53.1°
Amelia ran a total of 60 miles in the first 3 months of her new running program. She ran equal distances in the first and second months, but ran twice that distance in the third month. How far did she run in the third month?
15 miles
20 miles
40 miles
30 miles
she ran 15 miles in the first month and 15 in the second but because it doubled in the third month she ran 30 miles. 15+15+30=60 miles total
At the foootball game 8 1/5 of the fans wore team T-shirts.Of those wearing team T-shirts,1/4 also wore team hats.Wgat fraction of the fans at the football game wore both a team T-shirts and team hat?
Answer:
The fraction of the fans at the football game that wore both a team T-shirts and team hat is [tex]2\frac{1}{20}[/tex]
Step-by-step explanation:
Let
x----> total fans
we know that
[tex]8\frac{1}{5}x[/tex] ----> wore team T-shirts
Convert to an improper fraction
[tex]8\frac{1}{5}x=8\frac{8*5+1}{5}=\frac{41}{5}x[/tex]
Multiply by 1/4
[tex]\frac{41}{5}x*\frac{1}{4}=\frac{41}{20}x[/tex]
convert to mixed number
[tex]\frac{41}{20}x=\frac{40}{20}+\frac{1}{20}=2\frac{1}{20}x[/tex]
therefore
The fraction of the fans at the football game that wore both a team T-shirts and team hat is [tex]2\frac{1}{20}[/tex]
Find the solution set of this system:
y=−3x
x2−4=y
(4,12), (−1,3)
(−1,−3) only
(4,12) only
(−4,12), (1,−3)
Answer:
(−4, 12), (1, −3)
Step-by-step explanation:
y = −3x
x^2 −4 = y
so
x^2 −4 = −3x
x^2 + 3x - 4 = 0
(x + 4)(x - 1) = 0
x + 4 = 0; x = -4
x - 1 = 0; x = 1
when x = 1, y = -3(1) = -3
when x = -4, y = -3(-4) = 12
Answer
(-4 , 12), (1 , -3)
ANSWER
(−4,12), (1,−3)
EXPLANATION
The system has equations:
y=−3x
[tex] {x}^{2} - 4 = y[/tex]
We equate the two equations to get:
[tex] {x}^{2} - 4 = - 3x[/tex]
[tex]{x}^{2} + 3x - 4 = 0[/tex]
[tex]{x}^{2} + 4x - x - 4 = 0[/tex]
[tex]x(x + 4) - 1(x + 4) = 0[/tex]
[tex](x + 4)(x - 1) = 0[/tex]
[tex]x = - 4 \: or \: x = 1[/tex]
When x=1,
y=-3(1)=-3
when x=-4, y=-3(-4)=12
The solution is (1,-3) and (-4,12)
please solve!!!!!!!!! Thanks!
Answer:
a) 60°b) 80°c) 100°d) 50°e) 30°Step-by-step explanation:
The key here is that AB ║ EC. This makes arc AE have the same measure as arc BC. Since those have the same measure as AB and the three arcs together make a semicircle, each has measure 180°/3 = 60°.
Then the various arc measures are:
AB = 60°BC = 60°CD = 80° (given)DE = 100° . . . . . since CDE is 180°EA = 60°Then your answers are ...
a) AE = 60°
b) ∠ABD = (1/2)(DE +EA) = (1/2)(100° +60°) = 80°
c) ∠DFC = (1/2)(CD +EB) = (1/2)(80° + (60° +60°)) = 100°
d) ∠P = (1/2)(DA -AB) = (1/2)(100° +60° -60°) = 50°
e) ∠PAB = (1/2)(AB) = (1/2)(60°) = 30°