Given f(x) = -2x^2 + 4, determine the slope of the secant line over the interval [-1, 2].
Answer: -2
Step-by-step explanation:
We know that the slope of a secant line over a interval [a,b] is given by :-
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Given f(x) =[tex]-2x^2 + 4[/tex]
Then, the slope of the secant line over the interval [-1, 2] is given by :-
[tex]m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1[/tex]
Hence, the slope of the secant line over the interval [-1, 2] is -2.
Write this in a Algebraic expression. (Use x as your variable) The sum of x squared and y
Answer:
x^2+y
Step-by-step explanation:
simply because you have x squared and a variable y that needs to be added.
using addition formula solve tan 15
Answer:
2 - [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) = [tex]\frac{tanA-tanB}{1+tanAtanB}[/tex] and the exact values
tan45° = 1 , tan60° = [tex]\sqrt{3}[/tex] , then
tan15° = tan(60 - 45)°
tan(60 - 45)°
= [tex]\frac{tan60-tan45}{1+tan60tan45}[/tex]
= [tex]\frac{\sqrt{3}-1 }{1+\sqrt{3} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 + [tex]\sqrt{3}[/tex] is 1 - [tex]\sqrt{3}[/tex]
= [tex]\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL
= [tex]\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}[/tex]
= [tex]\frac{-4+2\sqrt{3} }{-2}[/tex]
= [tex]\frac{-4}{-2}[/tex] + [tex]\frac{2\sqrt{3} }{-2}[/tex]
= 2 - [tex]\sqrt{3}[/tex]
Round 9.62 to the nearest whole number
Answer:
10
Step-by-step explanation:
Anything greater than 9.49 would be rounded to 10, if it were 9.49, it would be rounded to 9. But only look at the numbers after the decimal.
i.e. ;
7.23 = 7
3.33 = 3
8.89 = 9
14.56 = 15
26.91 = 27
The length of a rectangle is 5 mm less than 4 times the width. If the perimeter is 75 mm, what is the length of the rectangle?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}[/tex]
Step-by-step explanation:
Let the width of a rectangle be 'w'
Length of a rectangle be 4w - 5
Perimeter of a rectangle = 75 mm
First, finding the width of the rectangle ( w )
[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 2(5w - 5)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 10w - 10}}[/tex]
[tex] \dashrightarrow{ \sf{10w - 10 = 75}}[/tex]
[tex] \dashrightarrow{ \sf{10w = 75 + 10}}[/tex]
[tex] \dashrightarrow{ \sf{10w = 85}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}[/tex]
[tex] \dashrightarrow{ \sf{w = 8 .5 \: mm}}[/tex]
Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle
[tex] \sf{length \: of \: a \: rectangle = 4w - 5}[/tex]
[tex] \dashrightarrow{ \sf{4 \times 8.5 - 5}}[/tex]
[tex] \dashrightarrow{ \sf{34 - 5}}[/tex]
[tex] \dashrightarrow{ \sf{29 \: mm}}[/tex]
Length of a rectangle = 29 mm
Hope I helped!
Best regards! :D
9x + 8y when x = 4 and and y = -5
━━━━━━━☆☆━━━━━━━
▹ Answer
-4
▹ Step-by-Step Explanation
9x + 8y = ?
Substitute the value for x in:
9(4) + 8y
Substitute the value for y in:
9(4) + 8(-5)
Multiply:
9 * 4 = 36
8 * -5 = -40
9x + 8y = 36 - 40 = -4
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Solve for x x - 8.9 = 7.18 x =
Answer:
x = 16.08
Step-by-step explanation:
x - 8.9 = 7.18
Add 8.9 to each side
x - 8.9+8.9 = 7.18+8.9
x = 16.08
write -0.1... as a fraction
Answer:
THE ANSWER IS :
-(1/10)
List the next three numbers for the sequence: 7, 7 /2 , 7 /4 , 7/ 8
Answer:
7/16, 7/32, 7/64
Step-by-step explanation:
PLEASE GIVE BRAINLIEST OR AT LEAST A THANKS!
Answer:
7/16, 7/32, 7/64
Step-by-step explanation:
7, 7 /2 , 7/ 4 , 7/ 8
We multiply by 1/2 each time
7/8 *1/2 = 7/16
7/16*1/2 = 7/32
7/32 *1/2 = 7/64
Use the stem and leaf plot above to answer the following question.
Lower quartile :
Medial:
Upper quartile:
Answer:
Lower quartile - (20+32) divided by 2 = 26
Median - (43+46) divided by 2 = 44.5
Upper quartile - 51
Step-by-step explanation:
64
-2/3(6/5x-7/10)17/20
What is an example of polynomials that are in standard form?
Answer:
standard form means that the terms are ordered from biggest exponent to
lowest exponent. The leading coefficient is the coefficient of the first term in a
polynomial in standard form . For example, 3x^4 + x^3 - 2x^2 + 7x.
The growth of a city is described by the population functionwhereis the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at
Complete question:
The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at
Answer:
27,800
Step-by-step explanation:
We need to obtain the initial population(P0) and constant value (k)
Population function : p(t) = P0e^kt
At t = 0, population = 19,000
19,000 = P0e^(k*0)
19,000 = P0 * e^0
19000 = P0 * 1
19000 = P0
Hence, initial population = 19,000
At t = 3; population = 23,000
23,000 = 19000e^(k*3)
23000 = 19000 * e^3k
e^3k = 23000/ 19000
e^3k = 1.2105263
Take the ln
3k = ln(1.2105263)
k = 0.1910552 / 3
k = 0.0636850
At t = 6
p(t) = P0e^kt
p(6) = 19000 * e^(0.0636850 * 6)
P(6) = 19000 * e^0.3821104
P(6) = 19000 * 1.4653739
P(6) = 27842.104
27,800 ( nearest whole number)
In the given diagram if AB || CD, ∠ABO = 118° , ∠BOD = 152° , then find the value of ∠ODC.
please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
90°
Step-by-step explanation:
Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.
Therefore,
∠ABO + ∠BOP = 180° (by interior angle Postulate)
118° + ∠BOP = 180°
∠BOP = 180° - 118°
∠BOP = 62°.... (1)
Since, ∠BOP + ∠POD = ∠BOD
Therefore, 62° + ∠POD = 152°
∠POD = 152° - 62°
∠POD = 90°.....(2)
∠POD + ∠ODC = 180° (by interior angle Postulate)
90° + ∠ODC = 180°
∠ODC = 180° - 90°
[tex] \huge\red {\boxed {m\angle ODC = 90°}} [/tex]
Can the sine rule relationship in trigonometry be used with non right angled triangle?
Answer:
Yes
Step-by-step explanation:
The sine rule works on all triangles (not just right-angled triangles) where a side and it's opposit angles are known.
Suppose a bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles. What is the probability of picking a green marble, replacing it, and then picking a brown marble? The probability of a student having a skateboard is 0.49 and the probability of having rollerblades is .57. What is the probability that a student has both a skateboard and roller blades? If 50% of your friends like coffee and 70% like hot cocoa, what is the probability that one of your friends likes both coffee and hot cocoa?
Answer:
1. There are a total of 19 marbles in the bag. The probability of picking a green marble out of them is 4/19 since there are only 4 green ones. The probability of picking a brown marble after replacing what has been initially picked is 1/19. The final probability is the product of the two probabilities and that is 4/361.
2. ?
3. 60%
Step-by-step explanation:
solve for q
-9 = q - 4.8
q = ?
(Thank you :3)
Answer:
[tex]-4.2=q[/tex]
Step-by-step explanation:
To do this you would just add 4.8 to both sides to get rid of the -4.8 so then the equation would look like [tex]-4.2=q[/tex] and that would be our answer.
Answer:
q=-4.2
Step-by-step explanation:
-9 = q - 4.8
Add 4.8 to each side
-9+4.8 = q - 4.8+4.8
-4.2 = q
q=-4.2
If y = x + 5 and x = 3 then y =
Answer:
y=8
Step-by-step explanation:
if you subsitute 3 into x then it will be y=3+5 which equals 8, so y= 8
please help me with this question.
Answer:
[tex] \purple{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{ {x}^{11} } \\ y = {x}^{ - 11} \\ \frac{dy}{dx} = \frac{d}{dx} {x}^{ - 11} \\ \frac{dy}{dx} = - 11{x}^{ - 11 - 1} \\ \frac{dy}{dx} = - 11{x}^{ - 12} \\ \\ \frac{d}{dx} \bigg(\frac{dy}{dx} \bigg) = \frac{d}{dx} ( - 11 {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11\frac{d}{dx} ( {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11( - 12{x}^{ - 13} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = 132{x}^{ - 13} \\ \\ \huge \red{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
what value should go in the red box
Answer: y = 4
Step-by-step explanation: If y = x + 2, then the value of y will correspond
to the values that are located in the x-column.
In other words, for the first column, we know that 2 = x.
So if y = x + 2, then y = 2 + 2 or y = 4.
Kim is watching a satellite launch from an observation spot 6 miles away. Find the angle of elevation from Kim to the satellite, which is at a height of 0.7 miles.
Answer:
Angle of elevation from Kim to the satellite launch = 6.654°
Step-by-step explanation:
The distance from Kim to the satellite launch
= 6 miles
Height of the satellite launch
= 0.7 miles
Angle of elevation from Kim to the satellite launch = b
Tan b = height of satellite/distance from Kim
Tan b= 0.7/6
Tan b= 0.1166667
b = tan^-1 (0.1166667)
b= 6.654°
Angle of elevation from Kim to the satellite launch = 6.654°
What is 0=3x^2-16x +15 solved for x? there should be two numbers
Answer: x = ⅓ or 5
Step-by-step explanation:
From the quadratic equation, we are asked to find the root of the equation. Therefore, we may use any of the methods.
Here I am using grouping method.
3x² - 16x + 15 = 0
3x² - 15x -x + 15 = 0, we now factorize
3x( x - 5 ) - ( x - 5 ) = 0, we now collect like terms.
( 3x - 1 )( x - 5 ) = 0
Now to find x, we equate each in brackets to zero and then solve.
3x - 1 = 0
x = ⅓ , and if
x - 5 = 0
x = 5, .
Now , the solution of the equation will be
x = ⅓ or 5
Solve this equation: Y/9 + 5 = 0.
Answer:
y = -45
Step-by-step explanation:
Y/9 + 5 = 0
y/9 = -5
y = -45
To the nearest meter, how many meters are in 160 inches?
Answer:
4
Step-by-step explanation:
When you convert 160 inches to meters you get 4 meters
Answer:
4.064 Meters
Step-by-step explanation:
PLEASE HELP! A) 9 B) 8.6 C) 26.3 D) 5.7
Answer:
x = 9.0
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 39 = 7/x
x cos 39 = 7
x = 7/cos 39
x =9.007316961
x = 9.0
Suppose x and y are related by the given equation and use implicit differentiation to determine dydx.x7y+y7x=7.
Looks like the equation is
[tex]x^7y+y^7x=7[/tex]
Differentiate both sides with respect to [tex]x[/tex], taking [tex]y[/tex] to be a function of [tex]x[/tex].
[tex]\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0[/tex]
[tex]7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0[/tex]
Solve for [tex]\frac{\mathrm dy}{\mathrm dx}[/tex]:
[tex](x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}[/tex]
Jackie ordered a set of wood and metal clothes pins. Of the 276 pins, 172 were wood. What percentage of the clothes pins were wood? Round to the nearest hundredth.
Answer:
62.32%
Step-by-step explanation:
172/276 * 100%
= 62.32%
If the sin 30° is 1 over 2, then the cos ____° = _____.
Answer:
Below.
Step-by-step explanation:
(sine) [tex]sin=30=1/2[/tex]
[tex]=cos [90-30][/tex]
Which means cos=60
Same as:
(cosine) [tex]cos=60=1/2[/tex] or [tex]Sin30=Cos 60=1/2[/tex]
Hence, the answer is...
cos 60° = ½....
By:✨ RobloxYt ✨
The value of the trigonometric ratio cos60 is 1 / 2.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the value of sin 30° is 1 over 2. The value of cos(90-30) will be calculated as:-
sin(30) = cos(90-30) = cos60
sin(30) = cos(90-30) = 1 / 2
Hence, the value of the cos60 is 1 / 2.
To know more about Trigonometry follow
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simplify 2⁰+5¹+4³/7
Answer:
10
Step-by-step explanation:
2^0 = 1
5^1 = 5
4^3 = 4 x 4 x 4
=> 16 x 4
=> 64
=> 1 + 5 + 64 / 7
=> 6 + 64 / 7
=> 70 / 7
=> 10
So, the answer is 10
The number to which a base is raised to is called the ___. This tells you how many times to multiply the base together
Answer:
Exponent
Step-by-step explanation:
The base tells what number is being repeatedly multiplied, and the exponent tells how many times the base is used in the multiplication. Exponents and have special names. Raising a base to a power of is called “squaring” a number. Raising a base to a power of is called “cubing” a number.