Answer:
h(2)=-1
h(2)=-1
Step-by-step explanation:
Use the given functions to set up and simplify
h
(
2
)
Which expression is equivalent to secα(1−cos^2α) for all values of α for which secα(1−cos^2α) is defined?
sin^2a
sin atan a
tan a
csc^2a
sec^2a
By means of trigonometric functions and trigonometric formulas, the trigonometric equation sec α · (1 - cos² 2α) is equivalent to 4 · cos α - 4 · cos³ α.
How to simplify a trigonometric equation
In this problem we find the case of a trigonometric equation that must be simplified by definitions of trigonometric functions and trigonometric formulas. First, write the trigonometric equation:
sec α · (1 - cos² 2α)
Second, use the fundamental trigonometric formula:
sec α · sin² 2α
Third, use the definition of secant and the formula for the sine of the double angle:
(1 / cos α) · (2 · sin α · cos α)²
4 · sin² α · cos α
Fourth, use the fundamental trigonometric formula:
4 · (1 - cos² α) · cos α
4 · cos α - 4 · cos³ α
None of the options given are equivalent to the trigonometric equation.
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What is the solution to the system?
-4x - 2y = 8
y = x2 - 3
Will give points for answer
Answer:
Step-by-step explanation:
to find x;
-4x - 2 -1 =8
-4x + 3 = 8
+4 + 3 = +4
x + 3 = 12
-3 + -3
x = 10
to find y;
y = x2 - 3
y = (10)2 - 3
y = 20 - 3
y = 17
30 POINTS!!!!!! HELP ASAP! At cruising speed a car burns fuel at a rate of 2.5 kilograms per hour the mass of the car including the fuel when it reaches cruising speed is 1,550 kg and the mass of the car when the fuel tank is empty is 1,520 kg. the domain of the function f(t) is best described as
The domain of the function f(t) is best described as 608 ≤ t ≤ 620
How to determine the domain of the function?From the question, we have the following parameters that can be used in our computation:
Rate = 2.5 kilograms per hour
Mass of the car (including the fuel) = 1550 kg
Mass of the car (not including the fuel) = 1520 kg
Calculate the times using the rate and the masses above
So, we have the following representations
Time 1 = 1550/2.5
Time 1 = 620
Time 2 = 1520/2.5
Time 2 = 608
Express as an interval
608 ≤ t ≤ 620
Hence, the domain is 608 ≤ t ≤ 620
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Simplify 5/8x+2/3(−1/2x+24).
Answer:
[tex]\frac{7}{24}[/tex] x + 16
Step-by-step explanation:
[tex]\frac{5}{8}[/tex] x + [tex]\frac{2}{3}[/tex] ( - [tex]\frac{1}{2}[/tex] x + 24) ← distribute parenthesis
= [tex]\frac{5}{8}[/tex] x - [tex]\frac{1}{3}[/tex] x + 16 ( express fractions with common denominator 24 )
= [tex]\frac{15}{24}[/tex] x - [tex]\frac{8}{24}[/tex] x + 16
= [tex]\frac{7}{24}[/tex] x + 16
Need help asap! thanks
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of the given expression is 1479.40
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Sum of [tex]2(\frac{4}{3})^n[/tex] from n = 0 to n = 6.
This can be written as,
= [tex]2(4/3)^0 + 2(4/3)^1 + 2(4/3)^2 + 2(4/3)^3 + 2(4/3)^4 + 2(4/3)^5 + 2(4/3)^6[/tex]
= 2 x 1 + 8/3 + 2 x 16/9 + 2 x 64/27 + 2 x 256/81 + 2 x 1024/243 +
2 x 4096/729
= 2 + 2.67 + 3.56 + 4.74 + 6.32 + 8.43 + 1458
= 1479.40
Thus,
The value of the given expression is 1479.40
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NEED HELP ASAP!!!
I am 20 years older than twice my daughter's age. How old is my daughter? ( 1. 17 years ago, I was half the age I am now. How old am I? - Part of 2.)
The daughter's age is 7 years old.
What is the equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.
Let the age of the parent be x,
He/she was half of the age 17 years back, then,
x/2 = x-17
x = 34
Therefore, parent's present age is 34 years.
He is 20 years older than twice his daughter's age,
Let his daughter's age be y,
2y+20 = 34
2y = 14
y = 7
Hence, his daughter's age is 7 years old.
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7 ÷ (-9 - -8)³ how do I solve this? What’s the answer
Answer: -7
Step-by-step explanation:
7 ÷ (-9 - -8)³
(-9 - -8)³ = -1
7 ÷ -1 = -7
Answer:
-7
Step-by-step explanation:
We have to solve this according to the B O D M A S theorem.
That is:
B ⇒ Brackets
O ⇒ Of
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Also, we know that,
( + ) × ( + ) = ( + )
( - ) × ( - ) = ( + )
( + ) × ( - ) = ( - )
Let us solve it now.
7 ÷ ( - 9 - ( - 8 ) )³
7 ÷ ( - 9 + 8 )³
7 ÷ ( - 1 )³
7 ÷ ( - 1 )
- 7
What is 375 grams of a 12% solution?
The value of 375 grams of a 12% solution is 45 grams.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Based on the information given, it should be noted that in order to calculate the value of the grams, we simply need to multiply the value of the percentage that's is given by the number of grams that's given.
In this case, the value of the gram will be:
= Percentage given × Total grams
= 12% × 375 grams
= 0.12 × 375 grams
= 45 grams.
Therefore, the value will simply be 45 grams.
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Answer:
45
Step-by-step explanation:
375*0.12=45
What is W= x/y-z for x?
Answer:
[tex]x = wy - wz[/tex]
Step-by-step explanation:
this equation looks like this
[tex]w = \frac{x}{y - z}[/tex]
to solve for x you can multiply both sides by y - z
this would cancel out the y - z on the bottom
this would make it
[tex]w(y - z) = x[/tex]
now you must distribute and switch the x to the other side
[tex]wy - wz = x[/tex]
[tex]x = wy - wz[/tex]
Write the expression as a single logarithm.
7log6z - 1/2log6x +3log6y
The value of the logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
As per the given logarithm,
7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex]
Since,[tex]alog_{b}c = log_{b}c^\frac{1}{a}[/tex]
Thus,
7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex] =d [tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]dddd
Since,[tex]log_{a}b+log_{a}c=log_{a}bc[/tex]
Therefore,
[tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]= [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].
Hence "The value of the given logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex]".
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Sam runs at a velocity of 18m/s due east. A strong wind traveling at 8m/s blows on bearing 230° calculate the resultant velocity using Cosine law
Answer is he run with 11m/s.
Multiply. 2u*3u^2 please help me
Answer: 6u^3
Step-by-step explanation:
You have to add the exponents when you multiply them.
But before that, you can multiply the coefficients of 2 and 3 so you get 6.
Now you have u and u^2 left.
u = u^1
u^2 = u^2
1+2 =3
Kinda urgent
Will mark brainliest
:)
The function rule for the transformation of the graph f(x) = 2x
reflection over the x - axis (x, y) → (x, -y)
f(x) = -2xvertical compression of a factor of 1/4
g(x) = -x/2How to find the required transformationConsidering the given function f(x) = 2x that requires reflection and vertical compression
The transformation rule for reflection over the x - axis
(x, y) → (x, -y)
comparing to the equation y = f(x) = 2x
-y = -2x
hence f(x) = -2x
vertical compression involves multiplying by 1/4
= 1/4 * f(x)
= 1/4 - 2x
= -x/2
Hence g(x) = -x/2
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please find the gradient
Answer:
-2
Step-by-step explanation:
use the formula
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Reagan is running toward school twice as fast as her brother. If her brother is running at 2meterspersecond, how much time will it take Reagan to run 28meters?
Write your answer as a whole number.
The time taken by the Reagan to cover the distance of 28 meters will be 7 seconds.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that Reagan is running toward school twice as fast as her brother. If her brother is running at 2 meters per second.
The time taken to cover the distance of 28 meters will be calculated as,
R = 2B
Brother's speed = 2 m / s
Reagan's speed = 2 x 2 = 4 m/s
The time will be,
T = Distance / Speed
T = 28 / 4
T = 7 seconds
Therefore, the time taken by Reagan to cover the distance of 28 meters will be 7 seconds.
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Pythagoras theorem
How do i find the n
Answer:
n = 44
Step-by-step explanation:
the 'dashes ' through the 2 legs of the triangle indicate they are congruent.
then n = 44 mm
A company has 11 male and 8 female employees, and needs to nominate 2 men and 2 women for
the company bowling team. How many different teams can be formed?
There 1540 teams can be formed.
What is combination?A combination is a combination of n things taken k at a time without repetition.
Given that, A company has 11 male and 8 female employees, and needs to nominate 2 men and 2 women for the company bowling team.
The formula for a combination of choosing r unique ways from n possibilities is:
nCr = n!/r!(n - r)!
2 men out of 11 men = 11C2 = 11!/2!(11-2)! = 55
2 women out of 8 men = 8C2 = 8!/2!(8-2)! = 28
Number of teams = 55*28 = 1540
Hence, There 1540 teams can be formed.
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75 − 3.5y − 4y = 4y + 6 for y. please show how you got
Answer:
y=6
Step-by-step explanation:
75-3.5y-4y=4y+6
Combine like terms on each side
75-7.5y=4y+6
Add 7.5y to both sides since it is the inverse of subtraction
75-7.5y=4y+6
+7.5y. +7.5y
75=11.5y+6
Isolate y on one side by subtracting 6 from both sides
75=11.5y+6
-6. -6
69=11.5y
Divide both sides by 11.5
69=11.5y
/11.5. /11.5
6=y
hopes this helps please mark brainliest
in the figure pictured below DF=3 BF =14 GF =8 find the lengths of:
A. cf
B. ef
C. ag
The lengths of CF, EF and A.F are 6 units, 28 units and 16 units, respectively
How to determine the lengths of these sides?From the question, the given parameters to solve the question are represented as
DF = 3
BF = 14
GF = 8
The point F in the triangle is the centroid of the triangle
This means that the point F divides the lines that passes through it in the ratio 1 : 2 or 2 : 1 (as the case may be)
The claim above also means that
CF = 2 * DF
EF = 2 * BF
A.F = 2 * GF
Substitute the known values in the above equation, so, we have the following representation
CF = 2 * 3 = 6
EF = 2 * 14 = 28
A.F = 2 * 8 = 16
Hence, the lengths are 6 units, 28 units and 16 units
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How do I write a two-column proof for this problem?
Given: Isosceles △ABC with legs AB and AC, BD ⊥DC and CE⊥BE
Prove: BD ≅ CE
BD ≅ CE is proved and is shown below.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are two triangles as shown in the figure.
Triangles ΔMPN and ΔSTU are congruent. We can write -
2x - y = 13
2x - 50 = 24
Now -
2x - 50 = 24
2x = 74
x = 3The measurements of [x] and [y] are 37 and 61 respectively.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is isosceles △ABC with legs AB and AC, BD ⊥DC and CE ⊥ BE.
In △BDC and △CEB, we can write -
∠D = ∠E = 90°
BC = BC {Common}
∠B = ∠C {Angles opposite to equal sides are equal}
By SAS criteria △BDC ≅ △CEB.
So, we can write -
BD ≅ CE
Therefore, BD ≅ CE is proved and is shown above.
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Find the y-intercept of the line x+y=7.
Answer:
(0,7)
Step-by-step explanation:
Simplify quantity x squared plus 5 x plus 4 end quantity over quantity x plus 4 (5 points) x − 1 x + 1 x2 + 1 x2 − 1
Answer:
Step-by-step explanation:
there is no oblique asymptote
A jar holds 20 cookies, 13 are chocolate-chip cookies, and 7 are brussel-spout-with-turnip-chips cookies. You pick 4 cookies at random. What is the probability that you get exactly 2 of the brussel-spout-with-turnip-chips cookies?
The probability that exactly 2 of the brussel-spout-with-turnip-chips cookies is picked at random is 0.05 approximately to two decimal place.
Probability of an eventTo calculate the probability of an event, we identify an event of the required outcome result and the total number of results or possible outcomes that can occur, and thus divide the number of required outcomes by the total number of possible outcomes.
The total possible outcomes = 20
probability of picking a chocolate-chip cookies = 13/20
probability of picking brussel-spout-with-turnip-chips cookies = 7/20
probability of getting exactly 2 brussel-spout-with-turnip-chips cookies when 4 cookies are picked at random considering the they are not replaced after each pick is calculated as follows;
(13/20) × (13/20) × (7/20) × (7/20)
8281/160000
0.0518.
Hence, from our calculations by simplification the probability of getting exactly 2 brussel-spout-with-turnip-chips cookies when 4 cookies are picked at random is 0.05 approximately to two decimal place.
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100 POINTS AND BRAINLIEST
For what values of c does the quadratic equation -x^2+4x+c=0
1. Have no real roots?
2. Have two roots with the same sign?
3. Have one negative root and one root equal to 0?
4. Have two roots with opposite sides?
Answer:its c
Step-by-step explanation:
Answer:
1. c < -4
2. -4 < c < 0
3. c = 0
4. c > 0
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}[/tex]
Given quadratic equation:
[tex]-x^2+4x+c=0[/tex]
Question 1If the quadratic equation has no real roots, then the discriminant is less than zero:
[tex]\implies b^2-4ac < 0[/tex]
[tex]\implies (4)^2-4(-1)(c) < 0[/tex]
[tex]\implies 16+4c < 0[/tex]
[tex]\implies 4c < -16[/tex]
[tex]\implies c < -4[/tex]
Question 2If the quadratic equation has two real roots, then the discriminant is greater than zero:
[tex]\implies b^2-4ac > 0[/tex]
[tex]\implies (4)^2-4(-1)(c) > 0[/tex]
[tex]\implies 16+4c > 0[/tex]
[tex]\implies 4c > -16[/tex]
[tex]\implies c > -4[/tex]
Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root. If c < 0 there would be 2 sign changes and therefore a maximum of 2 negative roots.
Therefore, for the two roots to have the same sign, -4 < c < 0.
Question 3If c = 0 then:
[tex]\implies -x^2+4x=0[/tex]
[tex]\implies -x(x+4)=0[/tex]
[tex]\implies x(x+4)=0[/tex]
Therefore, the roots would be 0 and -4 so there would be one negative root and one root equal to zero.
Question 4Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.
Therefore, for the equation to have two roots with opposite signs, c > 0.
Does anyone know how to do this pls
Haha ITS MATHXL
Anyways, constant rate of +90 and currently has 1560.
Say y will be the amount of students, and x is how many years later.
y=90x+1560
So for a), the answer is y=90x+1560
For b), plug in 3 for x, since 2017 is 3 years after 2014.
y=90(3)+1560
y=270+1560
y=1830
Amount of students in 2017: 1830
For c), plug in 2010 for y.
2010=90x+1560
Subtract 1560 both sides
450=90x
Divide both sides by 90
x=5
Answers
a) y=90x+1560
b) 1830
c) 5 Years Later, or 2019
Hope this helps!
larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920. What is the discount rate? Round to the nearest tenth of a percent if needed.
If larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920. Then the discount rate is 30%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
larry and Donna bought a sofa at the sale price of $1,344.
original price of the sofa was $1,920
We need to find the original rate
1920-1344/1920
576/1920
0.3
Now we have to multiply with 100 as it it hundredth part
0.3×100
30
Hence, the discount rate of sofa is 30%.
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Write an equation of the line that passes through the pair of points. (5/12, −1), (−3/4, 1/6)
Answer:
[tex]y=-x-\frac{7}{12}[/tex]
Hope this helps!
(9√-81)(-10√64) is the answer -6480i? im confused
[tex]i=\sqrt{-1}[/tex]
Solving the Question[tex](9\sqrt{-81})(-10\sqrt{64})[/tex]
⇒ Take out i from the first square root:
[tex]= (9i\sqrt{81})(-10\sqrt{64})[/tex]
⇒ Evaluate the square roots:
[tex]= (9i\times9)(-10\sqrt{64})\\= (9i\times9)(-10\times 8)[/tex]
⇒ Multiply:
[tex]= (81i)(-10\times 8)\\= (81i)(-80)\\= -6480i[/tex]
Answer-6480i
due to road works and a diversion on the m1, Anjam's drive from Sheffield to Watford took a lot longer than planned. He left Sheffield at 10.15am and arrived in Watford 3.55pm in minutes how long did it take anjam?
The minutes when Anjam travel from Sheffield at 10.15am and arrived in Watford 3.55pm in minutes is 320 minutes.
How to calculate the time?It is important to note that the question is simply about the calculation of the time involved. Based on this situation, it should be noted that:
60 minutes = 1 hour.
Given that due to road works and a diversion, Anjam's drive from Sheffield to Watford took a lot longer than planned. He left Sheffield at 10.15am and arrived in Watford 3.55pm in minutes.
The time for the journey will be:
= 3.35pm - 10.15am
= 5.20 hours.
We will change this to minutes:
= (5 × 60) + 20
= 320 minutes
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what is the 5/6 of 24?
Answer: 20
Step-by-step explanation:
Use 1 as the denominator to convert any number to a fraction:
24/1
The fraction 5/6 and our new fraction, 24/1, are now side by side, and we can multiply those two fractions to find the answer now that we have converted 24 into a fraction.
Multiply the numerators and denominators after converting the entire number to a fraction.
5*24/6*1 = 120/6
In this instance, it is possible to further simplify our new fraction. To do that, we must determine the two numbers' highest common factor.
So. GCF is 6.
We can now divide both the new numerator and the denominator by 6 to simplify this fraction down to its lowest terms.
120/6 = 20.
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Answer:
20
Step-by-step explanation:
what is the 5/6 of 24?
we can solve by multiplying 5/6 by 24
5/6 × 24 =
20