The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Answers
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
Related Questions
Use the graph below to write the formula (in factored form) for a polynomial of least degree.negative even degree function. Y intercept at -3. x intercepts at -3,-2,3 and 4If you have a non-integer coefficient then write it as a fraction. Organize factors (left to right) from smallest zero to largest. Answer:
Answers
A polynomial function is in standard form when the terms in its formula are ordered from highest to lowest degree.
The factored form of a polynomial function as a function of "x" is expressed as:
[tex]f(x)=(x-a)(x-b)(x-c)(x-d)[/tex]where a, b, c, and d are the x-intercepts or zeros of the polynomial function.
From the given graph, the zeros of the polynomial graph are the point where the curve cuts the x-axis. The zeros of the polynomial are at x = -3, -2, 3 and 4
The factors of the polynomial function will be (x+3)(x+2)(x-3)(x-4)
The formula (in factored form) for a polynomial of least degree will be:
[tex]\begin{gathered} f(x)=(x-(-3))(x-(-2))(x-3)(x-4) \\ f(x)=(x+3)(x+2)(x-3)(x-4) \end{gathered}[/tex]Express 80 as the product of its prime factors Write the prime factors in ascending order.
Answers
Answer:
2×2×2×2×5
Step-by-step explanation:
Express 80 as the product of its prime factors Write the prime factors in ascending order.
2 × 2 × 2 × 2 × 5
2×2×2×2×5 = 80
Suppose that $250 is deposited into an account that pays 4.5% interest compoundedquarterly. Using A = P(1 +r/n)nt where t is the number of years, r the interestrate as a decimal, and n the number of times interest is compounded per year, find outhow many years it takes (to the nearest whole year) to reach $1000, and type youranswer into the box.
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31 years
Explanation:We would apply the compound interest forula:
[tex]A=P\mleft(1+\frac{r}{n}\mright)^{nt}[/tex]A = future amount = $1000
P = principal = $250
r = rate = 4.5% = 0.045
n = compounded quarterly = 4 times
n = 4
t = time = ?
Inserting the values into the formula:
[tex]\begin{gathered} 1000\text{ = 250(1 + }\frac{0.045}{4})^{4\times t} \\ 1000=250(1+0.01125)^{4t} \\ \text{divide through by 250} \\ \frac{1000}{250}=\text{ }(1+0.01125)^{4t} \\ 4\text{ = (1}.01125)^{4t} \end{gathered}[/tex][tex]\begin{gathered} \text{Taking log of both sides:} \\ \log 4=log(1.01125)^{4t} \\ \log 4=4t\lbrack log(1.01125)\rbrack \\ 0.6021\text{ = 4t(}0.0049) \end{gathered}[/tex][tex]\begin{gathered} 0.6021\text{ = }0.0196t \\ \text{divide both sides by 0.0196} \\ \frac{0.6021}{0.0196}=\frac{0.0196t}{0.0196} \\ 30.72\text{ = t} \\ To\text{ the nearest whole number, t = 31 years} \end{gathered}[/tex]It takes 31 years to reach $1000.
Find the missing side of the right triangle. Leave your answer in simplest radical form. show work
Answers
Applying the Pithagorean Theorem
we have
[tex]12^2=x^2+(8\sqrt[]{2})^2[/tex]solve for x
[tex]\begin{gathered} 144=x^2+128 \\ x^2=144-128 \\ x^2=16 \\ x=\sqrt[]{16} \end{gathered}[/tex]x=4 miWriting an Equation Assume that the ball rebounds the same percentage on each bounce. Using the initial drop height and the height after the first bounce, find the common ratio,r.Note: Round r to three decimal places. Use this formula:common ratio = height on first bounce/initial heightheight on first bounce = 54 in Dropped from 72in (6 feet)
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The common ratio = 0.750 (3 decimal places)
Explanation:
Initial drop height = 72 inches
Height after the first bounce = 54 inches
common ratio = r = height on first bounce/initial height
r = 54/72
r = 0.75
The common ratio = 0.750 (3 decimal places)
Find the area when length = 5.2
(Equilateral Triangle)
Answers
Answer: 3√3 / 4
Step-by-step explanation:
A = 8^2√3 where s √3
A = ( √3)^2 * √3 / 4
A = 3√3/4
Evaluate the expression when x= -1/4 and y= 31. 2xyI don't understand his question.
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The expression is 2xy
we will substitute x and y by the given values
x = -1/4 and y = 3
[tex]2xy=2\times(\frac{-1}{4})\times(3)[/tex]We put the values of y in the expression
Now we will calculate the value
[tex]2xy=\frac{2\times-1\times3}{4}[/tex]We will multiply the numbers in the numerator
[tex]2xy=\frac{-6}{4}[/tex]We will simplify the fraction by divide up and down by 2
[tex]\begin{gathered} 2xy=\frac{-\frac{6}{2}}{\frac{4}{2}}=\frac{-3}{2} \\ 2xy=-\frac{3}{2} \end{gathered}[/tex]can you help me with key attributes of quadratic function
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The shape of a quadratic function is a parabola.
The domain of a quadratic function is the set of all real numbers.
The range of the quadratic function is the set of all y values at or above the vertex for a parabola open upwards.
In the given parabola, y=0 is the y coordinate of the vertex of the parabola.
Therefore, the range is R=[0, ∞).
The domain is (-∞, ∞).
Find 164.4% of 289 round to the nearest tenths
Answers
Answer:
475.1
Step-by-step explanation:
Percent means per hundred so 164.4 % means [tex]\frac{164.4}{100}[/tex] When you divide by 100 you move the decimal 2 places to the left
1.644 x 289 = 475.116 This rounded to the nearest tenths is
475.1
Which function is the result of vertically stretching ƒ(x) = x2 by a factor of 2 and translating it 4 units upward?Question 8 options:A) y = –4x2 + 2B) y = 2x2 + 4C) y = 2x2 – 4D) y = 4x2 + 2
Answers
To find the result function,
First stretch it, multiplying it by the factor we want to stretch.
So f(x) = x²
Stretching the function by a factor of 2:
g(x) = 2* f(x)
g(x) = 2* x²
On the other hand, to translate a function 4 units upward, we need to sum it to the function, so the result function is:
g(x) = 2x² + 4
The answer is option B.
Nancy is the proud owner of a new car. She paid $1,500 upfront and took out a loan for the rest of the amount. The interest rate on the loan is 5%. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, how much money did Nancy borrow?.1st Question: Assume that x represents the amount of money Nancy borrowed. Write an expression that represents the amount borrowed (the principal) plus the interest owed on that amount.
Answers
1st Question:
Assume that x represents the amount of money Nancy borrowed. The interest rate on the loan is 5%. This means that the amount of interest that on the loan would be
5/100 * x = 0.05x
An expression that represents the amount borrowed (the principal) plus the interest owed on that amount is
x + 0.05x
= 1.05x
Secondly
She paid $1,500 upfront and took out a loan of $x for the rest of the amount. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, it means that
1500 + 1.05x > 16,213.02
Subtracting 1500 from both sides of the equation, we have
1500 - 1500 + 1.05x > 16213.02 - 1500
1.05x > 14713.02
Dividing both sides of the inequality by 1.05, we have
1.05x/1.05 = 14713.02/1.05
x > 14012.4
The amount borrowed is greater than $14012.4
Find the slope of line segment AB where the coordinates of A are
(3,-3) and B are (1,2).
A: -2/5
B: -5/2
C: 2/5
D: 5/2
Answers
The slope formula is y2-y1 over x2-x1 from there you should get your answer. Hope this helps.
A hot air balloon was descending at a rate of 25 feet per minute and was known to be at an altitude of 425 feet above the ground 21 minutes after it began its descenta) determine the slope-intercept form of the equationb) How high was the balloon when it began its descent (0 minutes)c) How many minutes did it take to land?
Answers
We can model the problem as a linear equation of the form:
[tex]y=mx+b[/tex]Where:
m = Slope (Rate of change)
b = y-intercept (Initial value)
a)
Since it is descending at a rate of 25ft per minute, the slope is:
[tex]m=-25[/tex]So, the equation is:
[tex]y=-25x+b[/tex]b) We know that the ballon was 425ft above the ground 21 minutes after it began its descent, so:
[tex]\begin{gathered} y=425,x=21 \\ so\colon \\ 425=-25(21)+b \\ 425=-525+b \\ b=950 \end{gathered}[/tex]Therefore, the balloon was 950ft when it began its descent, so, we can conclude that the y-intercept is 950, now the equation is complete
[tex]y=-25x+950[/tex]c) We need to know for which value of x, y is equal to 0, so:
[tex]\begin{gathered} y=0 \\ 0=-25x+950 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 25x=950 \\ x=\frac{950}{25} \\ x=38 \end{gathered}[/tex]The balloon will land after 38 minutes
A person buys a 900-milliliter bottle of soda from a vending machine. How many liters of soda did the person buy?
Answers
Answer: 0.9 Liters.
Step-by-step explanation:
Divide the volume value by 1000.
900 ÷ 1000
Because 1000 mililiters are the same that one liter.
Given ABC below, with m B=25°, a = 9, and c = 16, find the area of the triangle.
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It is given that the sides of the triangle are a =9 and c=16 . The angle is given mB=25 degree.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times9\times16\times\sin 25=72\sin 25^{\circ}[/tex][tex]A=30.428sq\mathrm{}\text{unit}[/tex]Thus the area of triangle is 30.428 sq.unit.
Solve the quadratic equation by completing the square.x^2+18x+75=0First choose the appropriate form and fill in the blanks with the with the correct numbers. Then solve the equation. If there is more than one solution, separate them with commas.
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we have the quadratic equation
x^2+18x+75=0
complete the square
x^2+18x=-75
x^2+18x+81=-75+81
x^2+18x+81=6
rewrite as perfect squares
(x+9)^2=6
Find out the solutions
square root both sides
[tex]x+9=\pm\sqrt[\square]{6}[/tex][tex]x=-9\pm\sqrt[\square]{6}[/tex]The first solution is
[tex]x=-9+\sqrt[\square]{6}[/tex]The second solution is
[tex]x=-9-\sqrt[\square]{6}[/tex]URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Jimmy ran 20 meters west
from home and then turned
north to jog 25 meters. Jimmy
ran 45 meters, but could have
arrived at the same point by in
a straight line. How many
meters could he have using a
line distance?
A. 3.5 meters
B7 meters
C. 32 meters
D. 45 meters
Answers
Answer:
32m
Step-by-step explanation:
The distance he would've covered is 32m if he ran through a straight line.
What is Pythagoras's Theorem?
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
Let's substitute the values into the equation and solve.
Jimmy would've jogged 32m if he ran through a straight line.
Learn more on Pythagoras theorem here;
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AlgebraGraphing Linear EquationsHow Did The Poet Write To His Love?Graph each set of equations on its given coordinate plane:Graph: x-3y-mx+BGraph: x = -2X-2y=-2xGraph: y=-3x - 4Graph: x=-4Graph: y =Graph: x=-5Graph: x = -5y=x-sy = 3x - 4y = 4y1yosy-X + 3--
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This lines are 2 lines that cross over the same intercept in the y-axis.
they both have the y-intercept: -4
they also have the same slope but one on them is negative which makes the line cross each other at the y-intercept.
The graph should be:
Could you explain to me on what to do for this question
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1. First you need to know the value of the three internal angles in the triangle:
The mising thriangle cam be find as follow:
The angle in green is 180º
You have the value of a part of that angle (6+25x) then the other part of the angle is:
[tex]180º-(6+25x)=180º-6-25x=174º-25x[/tex]Then you have the three internan angles:
44
18x-3
174-25x
You must know that the internal angles of a triangle always gonna sum 180º, then:
[tex]180=44+(18x-3)+(174-25x)[/tex]You can clear the x, as follow:
[tex]180=44+18x-3+174-25x[/tex][tex]180=215-7x[/tex]Then so, x=5Eighth grade 0.12 Exterior Angle Theorem FMP What is m_1? 1 470 670 Q m21 =
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we know that
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
so
Applying the Exterior Angle Theorem
m<1=67+47
m<1=114 degreesIs my answer correct help me please
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3(-2) + 4
-6 + 4
whichever number has the greater value, that’s the sign you use. In this case it’s 6
6-4=2
Keep the negative
-2 is the answer
Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
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Home Liquidators marks up its merchandise 35% on cost, the company's equivalent markup on the selling price is 25.9%.
What is an equivalent value?An equivalent value represents equality.
Equivalent values show that two paired mathematical expressions are equal.
How is the markup on the selling price determined?The markup on the selling price can be derived by equating the markup on cost with the markup on the selling price as follows:
Markup on cost = 35%
Cost = 100%
Selling price = 135%
Markup on selling price = 25.9% (0.35/1.35 x 100)
Thus, we can describe Home Liquidators' markup on the selling price as equivalent to 25.9% or simply 26%.
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Ronald purchased a brand new phone for $450.00. Since phones are taxablehe had to pay a sales tax of 45%. much sales tax did Ronald pay for the phone ?
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please let me know of question 4 is correct which is not true30 > 1030 < 1010 > 3010 < 30
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Number 4
The meaning of the symbols are
> means greater than
< means less than
For the first statement, 30 is greater than 10. It is true
For the second statement, 30 is less than 10. It is not true
For the third statement, 10 is greater than 30. It is not true
For the fourth statement, 10 is less than 30. It is true
Find the length of the given side for the congruent triangles ABC and A'B'C'.
The length of side AC
The length of side AC is ____.
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ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
congruent triangle - Congruent triangles are those whose two sides and included angle match those of another triangle's matching sides and angle.
rules -
Each of the three sides is equal.A comparable side and two angles share the same properties.The angle between the two sides is also equal, and there are two equal sides.(given)
AB = 17 cm
BC = 34 cm
Using the trigonometric functions
cos x = B/H
cos(81°) = B/34
B = Cos(81°) x 34
B = 5.31.
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
To know more about triangle
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you have a table that shows a linear relationship, when can you read the value for b,in y = mx + rectly from the table without drawing a graph or doing any calculations? Complete the explanati there is a point ( (select) vy) in the table, then y = b because at the y-Intercept the value of x select) (select) 0 y
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y=mx+b
Where:
m= slope
b= y-intercept
b= has coordinate points (0,y) where the line crosses the y-axis.
So:
If there is a point (0,y) in the table y=b because at the y-intercept the value of x is 0.
Isaiah is a plumber. One day he receives a house call from a potential customer in a differentcity. The distance on a map between his home and the customer's home is 8 inches. What isthe actual distance between Isaiah's home and the customer's home if the scale of the map is1 inch = 1 mile?
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Given:
The distance on a map between his home and the customer's home, D=8 inches.
In the map, 1 inch=1 mile.
The actual distance between Isaiah's home and the customer's home is,
[tex]\begin{gathered} \text{Actual distance=8 inches}\times\frac{1\text{ mile}}{1\text{ inch}} \\ =8\text{ miles} \end{gathered}[/tex]Therefore, the actual distance between Isaiah's home and the customer's home is 8 miles.
Eddie has already written 23 pages, and he expects to write 1 page for every additional hour spent writing. After spending 21 hours writing this week, how many pages will Eddit have written in Total?
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EXPLANATION
Eddie has written ----->23 pages
He expects to write---> 1 page/additional hour
After spending 21 hours writing this week:
Eddy will have written:
Total pages are written =
Pages already written + Total additional hours*Pages/hours
Total pages written = 23 + 21 hours * 1 page/hour
Total pages written = 23 + 21
Total pages written = 44 pages
Answer: Eddie will have written 44 pages this week.
1 Select the correct answer from each drop-down menu. 500 N 520 and = < In the figures
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x = (internal angle)
y,z = (externals)
Then
Angle x= < x= 180° - 50° -45° = 85°
Angle y= 180° - (180° - Angle z =
Then answers are
Angle x= 85°
Angle y= 137°
Angle z= 128°
Translate to an algebraic expression.10 more than dThe translation is
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10 more than d is the same as d plus 10, so the algebraic expression is:
d + 10
Answer: d + 10