Answers
Answer:
[tex]-5, 18, \sqrt{13}[/tex]
Step-by-step explanation:
We can solve the first equation, f of -3. The value of the function f is [tex]\frac{1+x^2}{x+1}[/tex], and plugging in -3 gets us [tex]\frac{1+9}{1-3}[/tex], this results in 10 divided by negative 2, which is negative 5.
Now, we must solve g of negative one third. The function g is defined as [tex]|9x-15|[/tex]. Plugging in negative one third into the question gets us [tex]|9(-\frac{1}{3})-15|[/tex]
9 times negative one third is -3, and -3 minus 15 is -18. The absolute value of -18 is 18.
Now, we must solve h of negative 2, and h is defined as [tex]\sqrt{-3-8x}[/tex]. Plugging in negative 2, we have [tex]\sqrt{-3-8(-2)}[/tex]. Negative 8 times negative 2 is positive 16, and 16 minus 3 is 13. The answer is the square root of 13
Related Questions
Which of the following is a quadratic function
Answers
A quadratic a function has a form of,
[tex]f(x)=ax^2+bx+c,a\neq0[/tex]
The first function has a term [tex]x^3[/tex] which doesn't fit the profile of a quadratic function. The highest exponent on x inside a quadratic function can be 2, but here we have 3 so this is not a quadratic function, but rather a cubic function.
The second function fits the form of a quadratic function perfectly.
The third function is a bit tricky. While technically the third function could be considered quadratic if the leading term would be something like [tex]0x^2[/tex] and we did't even see it written out because multiplying with 0. But when we specified the form of a quadratic function, we strictly said that the number before [tex]x^2[/tex] aka [tex]a[/tex] cannot equal to zero. So the last function is not a quadratic function but rather a linear function.
Hope this helps :)
Step-by-step explanation:
f(x) = 4x² + x - 3
[tex]f(x) = 4x {}^{2} + 3 - 2[/tex]
r3t40 is correct
There is a pile of 55 coins consisting of nickels and dimes worth $3.90. Find the number of each if you say that the nickels are x.
Answers
Answer:
There are 32 nickels and 23 dimes.
Step-by-step explanation:
Lets say x is nickels and y is dimes
The first equation would be 55 = x + y
The second equation would be .05x + .10y = 3.90
The Solving Part:
Move y to the other side: x = 55 - y
Substitute x in the second equation: .05(55-y) + .10y = 3.90
Distribute, rearrange, and combine like terms: .05y = 1.15
Solve for y: Y = 23
Plug in 23 for y and solve: 55 - y = x ; 55 - 23 = x ; 55 - 23 = 32
x = 32
y = 23
32 nickels and 23 dimes
Answer:
There are 32 nickels and 23 dimes.
Step-by-step explanation:
Yay :) we solved the problem together :)))))
The surface areas of two similar solids are 16m2 and 100 m2. The volume of the larger one is 750m3. What is the volume of the smaller one?
Answers
Answer:
48 m^3
Step-by-step explanation:
If the scale factor of linear dimensions between two solids is k, then the scale factor for areas is k^2, and the scale factor of volumes is k^3.
Let's call the solid with 16 m^2 of area solid A, and the other one solid B.
The scale factor of areas from, A to B is (100 m^2)/(16 m^2) = 25/4
In other words, multiply the area of the solid A by 25/4 to get the area of solid B.
Let's check: 16 m^2 * 25/4 = 16 * 25/4 m^2 = 4 * 25 m^2 = 100 m^2
We do get 100 m^2 for solid B, so the area scale factor of 25/4 is correct.
The area scale factor is k^2, so we have:
k^2 = 25/4
We solve for k:
k = 5/2
Now we cube both sides to get k^3, the scale factor of volumes.
k^3 = 5^3/2^3
k^3 = 125/8
Let V = volume of smaller solid, solid A.
V * 125/8 = 750 m^3
V = 750 * 8/125 m^3
V = 48 m^3
The ratio of the volumes of two similar solid polyhedra is equal to the square root of the ratio between their edges. True or False? HELP QUICK PLSSSSS
Answers
Answer:
FALSE.The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges. This statement is false. A polyhedron is a shape that has no gaps between their edges or vertices.
Answer:
it's false
~~~~~~~~~~~
Find y' for the following.
Answers
Answer:
[tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{\sqrt{x} + 1}{\sqrt{y} + 1} = y^2[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx} \bigg[ \frac{\sqrt{x} + 1}{\sqrt{y} + 1} \bigg] = \frac{dy}{dx}[ y^2][/tex]Quotient Rule: [tex]\displaystyle \frac{(\sqrt{x} + 1)'(\sqrt{y} + 1) - (\sqrt{y} + 1)'(\sqrt{x} + 1)}{(\sqrt{y} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Rewrite: [tex]\displaystyle \frac{(x^\Big{\frac{1}{2}} + 1)'(y^\Big{\frac{1}{2}} + 1) - (y^\Big{\frac{1}{2}} + 1)'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Basic Power Rule [Addition/Subtraction, Chain Rule]: [tex]\displaystyle \frac{\frac{1}{2}x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - \frac{1}{2}y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Factor: [tex]\displaystyle \frac{\frac{1}{2} \bigg[ x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1) \bigg] }{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{2(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}= 4yy'(y^\Big{\frac{1}{2}} + 1)^2[/tex]Isolate y' terms: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = 4yy'(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}[/tex]Factor: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = y' \bigg[ 4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} \bigg][/tex]Isolate y': [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1)}{4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} = y'[/tex]Rewrite/Simplify: [tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
N
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.6 0.7257
0.7291
0.7324
0.7357
0.7389 0.7422
0.7454
0.7486
0.7517
0.7549
0.7 0.7580
0.7611
0.76420.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
Answers
I wish I could help
1 poir
Question 1. Jessica has $1,625.00 to purchase a five-year Certificate of
Deposit (CD). In the chart, there are CD rates frombankrate.com. What
would the account ending balance be at Synchrony Bank if it is
compounded quarterly? *
Use the Compound Interest Formula to calculate the ending balance. A = P(1 + 5)nt
Nationwide
Bank
Nationwide
2.01%
No
Synchrony Bank
all synchrony
1.95%
Answers
9514 1404 393
Answer:
$1790.99
Step-by-step explanation:
Given:
$1625 is invested at an annual rate of 1.95% compounded quarterly for 5 years
Find:
the ending balance
Solution:
The compound interest formula applies.
FV = P(1 +r/n)^(nt) . . . Principal P at rate r for t years, compounded n per year
FV = $1625(1 +0.0195/4)^(4·5) = $1625(1.004875^20) ≈ $1790.99
The account ending balance would be $1790.99.
If a point in quadrant IV is reflected in the y-axis, its image will lie in quadrant:
A. IV
B. II
C. I
D. III
Answers
Answer:
Option D is correct.
Step-by-step explanation:
A plane mirror shows that the image formed by it is of same size as that of object, same distance as that of object and same orientation and laterally inverted.
So, when a point is in IV quadrant and reflection is from Y axis, the image is in III quadrant.
A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation
MO-167 +800+ 224, where t represents the time in seconds that the baseball has been in the air and represents the baseball's height in feet. When factored, this
equation is -16(-7)(t+ 2).
What is a reasonable time for it to take the baseball to land on the ground?
OA 2 seconds
ОВ
7 seconds
C. 5 seconds
D.
9 seconds
Answers
9514 1404 393
Answer:
A. 7 seconds
Step-by-step explanation:
We assume your factored equation is something like ...
h(t) = -16t(t -7)(t +2)
The time it takes the ball to reach the ground is the positive value of t that makes a factor zero:
t -7 = 0 ⇒ t = 7
The ball will land on the ground in 7 seconds.
Find r given: (4,-7) and (-2, r) with a slope of 8/3
Answers
Answer:
r = -23
Step-by-step explanation:
slope = (y1-y2)/(x1-x2)
(r--7)/(-2-4) = 8/3
(r+7)/-6 = 8/3
3(r+7)=8 x -6
3r + 21 = -48
3r = -69
r = -23
Find the length of AC
Answers
Answer:
377.19 (rounded off to 2dp)
Step-by-step explanation:
since its a right angled triangle, we can use tangent
tan(x) =opp/adj
tan(5) =33/AC
AC =33/tan(5)
7. Solve for x: x/6 - y/3 = 1
Please give steps!
Answers
<=> x/6 = 1+ y/3
<=> x/6 = (3+y)/3
<=> x = (3+y)/3 x 6
<=> x = 2(3+y)
So the answer is x = 2(3+y)
Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of ±3%." The margin of error was based on a 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are ___________ confident that the ___________ of registered voters ___________ planning on voting for Robert Smith is between ___________ and ___________.
Answers
Answer:
We are 95% confident that the percentage of registered voters in the nation planning on voting for Robert Smith is between 49% and 55%.
Step-by-step explanation:
Given that :
Margin of Error = ±3%
Sample Proportion = 52%
Confidence level = 95%
The 95% confidence interval is :
Sample proportion ± margin of error
52% ± 3%
Lower boundary = 52% - 3% = 49%
Upper boundary = 52% + 3% = 55%
The interpretation is that at a given confidence level ; the popukation proportion based on the sample proportion and margin of error is in the confidence interval.
a cookie recipe calls 3 1/4 cups of flour. the recipe makes 3 dozen cookies. how much flour us needed to make 144 cookies
Answers
1 dozen = 12
144 / 12 = 12 dozen
12 dozen/ 3 = 4
They need 4 times the amount of flour:
3 1/4 x 4 = 13
They need 13 cups of flour
If there are g girls and b-boys in a room, write an expression for the total number of children in the room.
Answers
Answer:
g+b
number of girls+number of boys
if i am incorrect forgive me plz
The expression for the total number of children in a room is g+ b.
What is an expression?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
What is addition?Addition is the process of finding the total, or sum, by combining two or more numbers or variables.
According to the given question
We have
Number of girls = g
And, number of boys = b
Therefore, the expression for the total number of children in room is given by
Total number of children = g + b
Hence, the expression for the total number of children in a room is g+ b.
Learn more about expression and addition here:
https://brainly.com/question/10386370
#SPJ2
The point (3,-4) is on the terminal side of an angle 0. What is cos 0?
А. 3/4
В. -3/4
C. 3/5
D. -3/5 E. 3
Answers
9514 1404 393
Answer:
C. 3/5
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(3² +(-4)²) = √(9+16) = 5
The cosine of the angle is the ratio of the x-coordinate to this value:
cos(θ) = x/d
cos(θ) = 3/5
A truck rental is $25 plus $ 0.40/mi find out how many miles ken traveled if his bill is $59.40
Answers
Answer:
Step-by-step explanation:
C = 59.4
Fixed Cost (F) = 25
C = 25 + 0.4*x Solve for x
59.40 = 25 + 0.4x Subtract 25
34.4 = 0.4x Divide by .4
34.4/0.4 = x
x = 86 miles
SOMEONE PLS HELP ME!!!
Answers
Answer:
No
Step-by-step explanation: Bye
PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST
Answers
Answer:
32.64°
Step-by-step explanation:
From triangle Given :
The sides of the missing angle given are the Adjacent and hypotenus.
Since the triangle is right angled, we can apply trigonometry :
cosθ = adjacent / hypotenus
Cosθ = 16 / 19
θ = Cos^-1(16/19)
θ = 32.6368
θ = 32.64°
Can someone help me solve this problem ?
Answers
Answer:
B
Step-by-step explanation:
Since x= 3/4
To take the fraction on left hand side, inverse 4/3
Take π as denominator
Then cube root the entire equation on the left hand side.
Answer:
Step-by-step explanation:
Prove: Quadrilateral ABCD is a parallelogram.
m∠AEB = m∠CED
Answers
Answer:
m∠ AEB = m∠ CED ......... By Vertical Angles Theorem.
Step-by-step explanation:
Vertical Angles Theorem: Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines, are congruent. If two lines intersect each other, we have the two pair of vertical opposite angles. As shown in the figure. Here, ∠ 1 and ∠ 2 are vertical opposite angles, and also they are equal. ∠ 3 and ∠ 4 are also vertical opposite angles, and also they are equal. For, step 3. m∠ AEB = m∠ CED Therefore, the reason for this proof is Vertical Angles Theorem.
Which statement best applies to the slope of the line below?
A.
the slope is negative
B.
the slope is zero
C.
the slope is positive
D.
the line has no slope
Answers
Answer:
D
Step-by-step explanation:
fro the diagram below there line has no slope
Answer: B) The slope is zero
============================================================
Explanation:
Any horizontal line will always have a slope of 0. This is because there is no change in y (aka the rise is 0).
So we could say something like
slope = rise/run = 0/1 = 0
The run can be anything we want, and we'd still get 0 every time.
------------
Another way to see this is to pick two points from this line. Whichever points are selected, they are plugged into the slope formula
m = (y2-y1)/(x2-x1)
You'll find that the y2-y1 expression turns into 0. Why? Because y1 and y2 are the same, so they subtract to 0. It doesn't matter what x2-x1 turns into.
write your answer in simplest radical form
Answers
Answer:
a = 3√6 in
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Adjacent = 3√2 in
Opposite = a =?
The value of 'a' can be obtained by using the tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 60 = a / 3√2
√3 = a / 3√2
Cross multiply
a = √3 × 3√2
Recall:
c√d × n√m = (c×n) √(d×m)
Thus,
√3 × 3√2 = (1×3)√(3×2)
√3 × 3√2 = 3√6
a = 3√6 in
Evaluate the functions
Answers
Answer:
Step-by-step explanation:
Which equation is correct?
1
A. cos x =
sin a
1
B. tan x=
CSC 2
C. sec =
COS
1
D. cot 2 =
sec
SUBMIT
Answers
It’s a reciprocal identity
The requried secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x. Option C is correct.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The correct equation is option C: sec x = 1/cos x.
This is because the secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x.
Learn more about trig ratios here:
https://brainly.com/question/14977354
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Please help explanation if possible
Answers
Answer:
Step-by-step explanation:
so d = 2r which means r = 5cm.
A = πr^2 = π(5)^2 = 25π = (25)(3.14) = 78.5 cm^2.
So input 78.5
Answer:
see below
Step-by-step explanation:
so d = 2r which means r = 5cm.
A = πr^2 = π(5)^2 = 25π = (25)(3.14) = 78.5 cm^2.
So input 78.5
HOPE IT HELPS YOU
Use the given information to determine which of the following relationships
can be proved and why.
L= 20
ME ZP
ML = PO
A. ALMN - A OPQ, because of AAS.
B. ALMNE A OPQ, because of ASA.
C. We cannot prove any relationship based on these data.
D. ALMN=A OPQ, because of SAS,
Answers
Answer:
B. ∆LMN ≅ ∆OPQ because of ASA
Step-by-step explanation:
Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.
From the information given, we have:
Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.
Also, included side in both triangles are congruent (ML ≅ PO).
Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.
which of the following is the formula in solving for the area of a circle?
A.A=2πr
B.A=πr²
C.A=πd
D.A=2πr²
Answers
The area of circle is πr²
Answer:
πr²
Step-by-step explanation:
The answer is πr² where,
π = pi, 3.14...
r = radius
This is the most common way of solving for the area of the circle.
A local church holds an annual raffle to raise money for a new roof. They sell only 500 tickets at $50 each. This year's prizes include: $3,000 in cash, four $100 Amazon gift cards, and two $75 Visa gift cards. You buy one ticket. What is your mathematical expectation for this game
Answers
Answer:
The expectation for an event with outcomes:
{x₁, x₂, ..., xₙ}
Each one with probability:
{p₁, p₂, ..., pₙ}
Is:
Ev = x₁*p₁ + ... + xₙ*pₙ
There are 500 tickets sold.
1 of these, wins $3,000 (this is the event x₁)
4 of these, wins $100 (this is the event x₂)
2 of these, wins $75 (this is the event x₃)
The others do not have a prize.
So the probability of winning the $3000 is equal to the quotient between the number of tickets with that prize (1) and the total number of tickets (500)
p₁ = 1/500
Similarly, the probability of winning $100 will be:
p₂ = 4/500
And for the $75 prize:
p₃ = 2/500
Then the probability of not winning is:
p₄ = 493/500
Then the expected value for a single ticket is:
Ev = $0*493/500 + $75*2/500 + $100*4/500 + $3000*1/500
Ev = $7.1
If you take in account that you pay $50 for the ticket, the actual expectation should be:
E = $7.10 - $50 = -$42.90
by selling a purse for rupees 250 Rajan loses one sixth of what cost should find the cost price of the first her loss percentage
Answers
Answer:
300, 16.67%
Step-by-step explanation:
Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%
