Answers
Answer:
X=7
Step-by-step explanation:
108=10x+2+4x+8
108=14x+10
108-10=14x
98=14x
Divide by 14
X=7
Related Questions
Stealth Bank has deposits of $700 million. It holds reserves of $70 million and has purchased government bonds worth $215 million. The bank's loans have a market value of $490 million. What does Stealth Bank's net worth, or equity capital, equal?
Answers
Answer:
$75 million
Step-by-step explanation:
Given that:
Reserve value = $70 million
Purchased government bond = 215 million
Market value of loan = $490 million
Net worth :
Assets - liability
Assets = (Market value of loan + purchased government bond + reserve value)
(490 million + 215 million + 70 million)
275 million + 70 million
= $775 million
Liability = Deposits = $700 million
Net worth = ($775 - $700) million
Net worth = $75 million
there are 3 arms for every 2 eyes. If there are 6 eyes, how many arms are there?
Answers
Answer:
There are 9 arms.
Step-by-step explanation:
A pair of eyeglasses cost $347.89. The frames of the glasses are $97.86. How much do the lenses of the eyeglasses cost.
Answers
Answer:
$250.03
Step-by-step explanation:
cost of lenses = total cost - cost of frames
cost of lenses = $347.89 - $97.86
cost of lenses = $250.03
The graph of f(x)= 3/1+x^2 is shown in the figure to the right. Use the second derivative of f to find the intervals on which f is concave upward or concave downward and to find the inflection points of f.
Answers
Answer:
Concave Up Interval: [tex](- \infty,\frac{-\sqrt{3} }{3} )U(\frac{\sqrt{3} }{3} , \infty)[/tex]
Concave Down Interval: [tex](\frac{-\sqrt{3} }{3}, \frac{\sqrt{3} }{3} )[/tex]
General Formulas and Concepts:
Calculus
Derivative of a Constant is 0.
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Second Derivative Test:
Possible Points of Inflection (P.P.I) - Tells us the possible x-values where the graph f(x) may change concavity. Occurs when f"(x) = 0 or undefinedPoints of Inflection (P.I) - Actual x-values when the graph f(x) changes concavityNumber Line Test - Helps us determine whether a P.P.I is a P.IStep-by-step explanation:
Step 1: Define
[tex]f(x)=\frac{3}{1+x^2}[/tex]
Step 2: Find 2nd Derivative
1st Derivative [Quotient/Chain/Basic]: [tex]f'(x)=\frac{0(1+x^2)-2x \cdot 3}{(1+x^2)^2}[/tex]Simplify 1st Derivative: [tex]f'(x)=\frac{-6x}{(1+x^2)^2}[/tex]2nd Derivative [Quotient/Chain/Basic]: [tex]f"(x)=\frac{-6(1+x^2)^2-2(1+x^2) \cdot 2x \cdot -6x}{((1+x^2)^2)^2}[/tex]Simplify 2nd Derivative: [tex]f"(x)=\frac{6(3x^2-1)}{(1+x^2)^3}[/tex]Step 3: Find P.P.I
Set f"(x) equal to zero: [tex]0=\frac{6(3x^2-1)}{(1+x^2)^3}[/tex]Case 1: f" is 0
Solve Numerator: [tex]0=6(3x^2-1)[/tex]Divide 6: [tex]0=3x^2-1[/tex]Add 1: [tex]1=3x^2[/tex]Divide 3: [tex]\frac{1}{3} =x^2[/tex]Square root: [tex]\pm \sqrt{\frac{1}{3}} =x[/tex]Simplify: [tex]\pm \frac{\sqrt{3}}{3} =x[/tex]Rewrite: [tex]x= \pm \frac{\sqrt{3}}{3}[/tex]Case 2: f" is undefined
Solve Denominator: [tex]0=(1+x^2)^3[/tex]Cube root: [tex]0=1+x^2[/tex]Subtract 1: [tex]-1=x^2[/tex]We don't go into imaginary numbers when dealing with the 2nd Derivative Test, so our P.P.I is [tex]x= \pm \frac{\sqrt{3}}{3}[/tex] (x ≈ ±0.57735).
Step 4: Number Line Test
See Attachment.
We plug in the test points into the 2nd Derivative and see if the P.P.I is a P.I.
x = -1
Substitute: [tex]f"(x)=\frac{6(3(-1)^2-1)}{(1+(-1)^2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(3(1)-1)}{(1+1)^3}[/tex]Multiply: [tex]f"(x)=\frac{6(3-1)}{(1+1)^3}[/tex]Subtract/Add: [tex]f"(x)=\frac{6(2)}{(2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(2)}{8}[/tex]Multiply: [tex]f"(x)=\frac{12}{8}[/tex]Simplify: [tex]f"(x)=\frac{3}{2}[/tex]This means that the graph f(x) is concave up before [tex]x=\frac{-\sqrt{3}}{3}[/tex].
x = 0
Substitute: [tex]f"(x)=\frac{6(3(0)^2-1)}{(1+(0)^2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(3(0)-1)}{(1+0)^3}[/tex]Multiply: [tex]f"(x)=\frac{6(0-1)}{(1+0)^3}[/tex]Subtract/Add: [tex]f"(x)=\frac{6(-1)}{(1)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(-1)}{1}[/tex]Multiply: [tex]f"(x)=\frac{-6}{1}[/tex]Divide: [tex]f"(x)=-6[/tex]This means that the graph f(x) is concave down between and .
x = 1
Substitute: [tex]f"(x)=\frac{6(3(1)^2-1)}{(1+(1)^2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(3(1)-1)}{(1+1)^3}[/tex]Multiply: [tex]f"(x)=\frac{6(3-1)}{(1+1)^3}[/tex]Subtract/Add: [tex]f"(x)=\frac{6(2)}{(2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(2)}{8}[/tex]Multiply: [tex]f"(x)=\frac{12}{8}[/tex]Simplify: [tex]f"(x)=\frac{3}{2}[/tex]This means that the graph f(x) is concave up after [tex]x=\frac{\sqrt{3}}{3}[/tex].
Step 5: Identify
Since f"(x) changes concavity from positive to negative at [tex]x=\frac{-\sqrt{3}}{3}[/tex] and changes from negative to positive at [tex]x=\frac{\sqrt{3}}{3}[/tex], then we know that the P.P.I's [tex]x= \pm \frac{\sqrt{3}}{3}[/tex] are actually P.I's.
Let's find what actual point on f(x) when the concavity changes.
[tex]x=\frac{-\sqrt{3}}{3}[/tex]
Substitute in P.I into f(x): [tex]f(\frac{-\sqrt{3}}{3} )=\frac{3}{1+(\frac{-\sqrt{3} }{3} )^2}[/tex]Evaluate Exponents: [tex]f(\frac{-\sqrt{3}}{3} )=\frac{3}{1+\frac{1}{3} }[/tex]Add: [tex]f(\frac{-\sqrt{3}}{3} )=\frac{3}{\frac{4}{3} }[/tex]Divide: [tex]f(\frac{-\sqrt{3}}{3} )=\frac{9}{4}[/tex][tex]x=\frac{\sqrt{3}}{3}[/tex]
Substitute in P.I into f(x): [tex]f(\frac{\sqrt{3}}{3} )=\frac{3}{1+(\frac{\sqrt{3} }{3} )^2}[/tex]Evaluate Exponents: [tex]f(\frac{\sqrt{3}}{3} )=\frac{3}{1+\frac{1}{3} }[/tex]Add: [tex]f(\frac{\sqrt{3}}{3} )=\frac{3}{\frac{4}{3} }[/tex]Divide: [tex]f(\frac{\sqrt{3}}{3} )=\frac{9}{4}[/tex]Step 6: Define Intervals
We know that before f(x) reaches [tex]x=\frac{-\sqrt{3}}{3}[/tex], the graph is concave up. We used the 2nd Derivative Test to confirm this.
We know that after f(x) passes [tex]x=\frac{\sqrt{3}}{3}[/tex], the graph is concave up. We used the 2nd Derivative Test to confirm this.
Concave Up Interval: [tex](- \infty,\frac{-\sqrt{3} }{3} )U(\frac{\sqrt{3} }{3} , \infty)[/tex]
We know that after f(x) passes [tex]x=\frac{-\sqrt{3}}{3}[/tex] , the graph is concave up until [tex]x=\frac{\sqrt{3}}{3}[/tex]. We used the 2nd Derivative Test to confirm this.
Concave Down Interval: [tex](\frac{-\sqrt{3} }{3}, \frac{\sqrt{3} }{3} )[/tex]
the number of employees for a certain company has been decreasing each year by 5%. if the company has 540 employees and this rate continues, find the number of employees in 13 years.
Answers
Answer:
Step-by-step explanation:
540
1=513
2=487.35
3=462.9825
4=
5=
6=
7=
8=
9=
10=
11=
12=
13=
Suppose a,b,c represent three positive whole numbers. if a+b=13 and b+c=22 and a+c=19 what is the value of c
Answers
Answer: C = 14
Step-by-step explanation: You can assume the A is less than B, and if you just go down in numbers such as A=6 and B=7 (To solve A + B = 13), you will eventually get to A=5 and B=8. If you do B = 8 + C = 14 ( That you get after subtracting 8 by 22 ) You should get 22, and to proof check it, you do A + C which is going to be 5 + 14 and you get 19 thus proving that C = 14.
The tree in Lisa’s backyard is 7.4 m high. How high is it in centimeters?
Answers
Answer:
740 cm
Step-by-step explanation:
Answer: 740 centimeters
Step-by-step explanation:
All you have to do is multiply the length value by 100 giving you 740.
On a number line, between which two consecutive whole numbers would the square root of 277 be located
Answers
9514 1404 393
Answer:
16 and 17
Step-by-step explanation:
16² = 256
(√277)² = 277
17² = 289
The root of 277 is between 16 and 17.
Juan is 1 1/4 feet shorter than maria.maria is 1/3 foot taller than Luis. if Luis is 62 inches tall, how tall are maria and Juan.
Answers
Answer:
Maria is 58 inches tall and Juan is 42 inches
Step-by-step explanation:
A certain fraction has the value 3/4. If its numerator is decreased by 7 and its denominator is increase by 4, the resulting fraction has the value 1/2. Find the original fraction
Answers
Answer:
n = 16 - 7
n = 9
Step-by-step explanation:
If the numerator of a fraction is increased by 3, the fraction becomes 3/4."
Cross multiply
4(n+3) = 3d
4n + 12 = 3d
"If the denominator is decreased by 7, the fraction becomes 1."
Cross multiply
1n = d - 7
n = (d-7)
In the 1st equation replace n with d-7
4(d-7) + 12 = 3d
4d - 28 + 12 = 3d
4d - 3d - 16 = 0
d = 16 is the denominator
then n = 16 - 7
n = 9
9/16 = the original equation
The process for rationalizing a denominator in a variable expression is the same as in a numeric expression. Here’s a real-world example. The kinetic energy of the car of a rollercoaster is given by the formula k = one-half m v squared where k is kinetic energy, m is the mass of the car, and v is the velocity of the car. Solving this formula for v, we get v = StartRoot StartFraction 2 k Over m EndFraction EndRoot Which formula gives the velocity of the car in simplest form?
Answers
Answer:
It's B
Step-by-step explanation:
Got it right on EDGE2020
The value of velocity of the car will be v = √(2km) / m. Then the correct option is B.
What is kinetic energy?If the object of mass m is moving with speed v. Then the kinetic energy of the object will be
KE = (1/2) mv²
The process for rationalizing a denominator in a variable expression is the same as in a numeric expression.
Here’s a real-world example.
The kinetic energy of the car of a rollercoaster is given by the formula
k = 1/2 m v²
Where k is kinetic energy, m is the mass of the car, and v is the velocity of the car.
Solving this formula for v, we get
[tex]\rm v = \sqrt{\dfrac{2k}{m}}[/tex]
Simplify the equation, we have
[tex]\rm v = \sqrt{\dfrac{2km}{m^2}}\\\rm v = \dfrac{\sqrt{2km}}{m}[/tex]
Then the correct option is B.
The complete question is attached below.
More about the kinetic energy link is given below.
https://brainly.com/question/12669551
#SPJ2
Write the following in Scientific Notation. -18,500,000,000,000
Answers
Answer:
Its 1.85 x 10 to the 13th power
Step-by-step explanation:
help pls :)))))))))))))))))
Answers
Which set if degrees = 180
Would be C. Because 30 + 60 + 90 would equal 180
Answer:
I think all measure can be used.
10 1/8 - 3 5/6=.......?
Answers
Answer:
6 7/24
Step-by-step explanation:
Nicole is making a cake that uses 3/4 cup of flour and 1 and 1/8 teaspoons if nicole uses 1 cup of flour how much salt would she need
Answers
Answer:
1.5 teaspoons
Step-by-step explanation:
1/(3/4)
=4/3
9/8*4/3
=1.5 teaspoons
PLS GIVE BRAINLIEST
Select the choice that translates the following verbal phrase correctly to algebra: (2 points)
the difference of m and 7 increased by 15
a.) m − (7 + 15)
b.) 7m + 15
c.) (m − 7) + 15
d.) m − 7 ÷ 15
Answers
what is one thousandth less than 0.061
Answers
Answer:
0.06
Step-by-step explanation:
0.061 - 0.001 = 0.060 = 0.06
What fraction is equivalent to .9?
Answers
Answer:
9/100
Step-by-step explanation:
00.9=9/100
9%
000000
000000
000
1. Matthew decided that he would like to spend his summer working and saving his money. He begins the summer with no money in his account, but he is getting paid $160.00 per week to mow lawns. His brother Dillon began the summer with $345.00 and has decided that he will referee soccer games. He will make $45.00 per week. After how many weeks will Matthew and Dillon have the same amount of money?
Answers
the anwer is no matthew will not have the same amount of money
Answer: 3 weeks.
Step-by-step explanation: Matthew's pay goes up by $160 a week, so that's y=160x.
Dillon's pay is $45 a week, but started out with $345. So, that's y=45x+345.
So, they will have the same amount of money after 3 weeks.
I need help on this...
Answers
Answer:
The answer would be C.
Step-by-step explanation:
X is greater than and equal to -2. So it would be a closed circle and it would be going to the right.
Answer:
C
Step-by-step explanation:
when x is greater than AND equal to -2
the numberline will show a closed circle on -2 and a line to the right (because greater than means positive and all numbers to the right increase)
Pls help me in these questions i will mark u brainliest.
Answers
Answer:
each angle is 83
Step-by-step explanation:
166÷ 2 = 83
check
83+83=166
hope it helps!!
Answer:
sum of two vertically angle =166°
X=166°/2 = 83°.
hence, each angle is equal to 83°.
X=
Turn these numbers into decimals
1. 4/12 2. 89/100 3.7/9 pls i need help
Answers
Answer:
.333 .89 .778
Step-by-step explanation:
1. 4 divided by 12 = .333
2. 89/100= .89
3. 7/9 = .778
Answer:
1. 0.333 repeated
2. 0.89
3. 0.777 repeated
Step-by-step explanation:
You just divide 4 by 12 or 7 by 9
Also, just a tip, if you have a number over 100 like 89/100 0.89 would be the decimal, for example 26/100 would be 0.26
Bryce had a $25 gift card to use on songs and games at an online media store. Songs cost $2 each and games cost $5 each. Bryce spent all the money on the gift card to download 8 items. Solve the system to determine how many games he purchased. Let s represent the number of songs and g represent the number of games. s + g = 8 2s + 5g = 25 Bryce purchased games.
Answers
Answer:
Bryce purchased 3 games.
Step-by-step explanation:
To find the number of songs and games that Bryce downloaded, we need to solve the following system of equations:
s + g = 8
2s + 5g = 25
We know that:
s + g = 8 → 2s + 2g = 16 → 2s = 16 -2g
2s + 5g = 25 → 16 - 2g + 5g = 25
→3g = 25 - 16
→3g = 9
→ g = 3
Therefore, bryce downloaded 3 games and 5 songs!
Answer:
.
3x + 2y = 16,
Step-by-step explanation:
What is 19,998 divided by 1,000,000,000,000,000,000,000,000,000,000,000
Answers
Answer:
1.9998e-29
Step-by-step explanation:
Can someone help me simplify this!!!
Answers
Answer:
The answer is in the picture i put, its an equation so 8 can't write it
Write an ordered pair that is a solution to the equation of the line y=x+5
Answers
Answer:
(1,6)
(2,7)
(4,9)
(8,13)
Step-by-step explanation:
What role do animals have in the carbon cycle?
Group of answer choices
use water and release oxygen
use sugar and release carbon
use carbon and release oxygen
use carbon and release nitrogen
Answers
Answer:
use sugar and release carbon
Step-by-step explanation:
Animals they eat and then release carbon through respiration. Nitrogen is only in the nitrogen cycle, and the only living organisms that can release oxygen are plants because humans and animals cannot photosynthesize. LOL!
a small airplane flies 1 015miles with an average speed of 290 mph. 1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of Boeing 747?
Answers
Answer:
The Boeing 747 had an average speed of 580 mph.
Step-by-step explanation:
Constant speed motion
An object is said to travel at constant speed if the ratio of the distance traveled by the time taken is constant.
Expressed in a simple equation, we have:
[tex]\displaystyle v=\frac{d}{t}[/tex]
Where
v = Speed of the object
d = Distance traveled
t = Time taken to travel d.
From the equation above, we can solve for d:
d = v . t
And we can also solve it for t:
[tex]\displaystyle t=\frac{d}{v}[/tex]
The small airplane travels 1015 miles at a constant speed of v=290 miles/hour. The time it took to arrive its destiny was:
[tex]\displaystyle t=\frac{1015}{290}[/tex]
t = 3.5 hours
The Boeing 747 left from the same point 1.75 hours after the small plane and traveled the same distance. It needed a time t' = 3.5 - 1.75 = 1.75 hours, thus its speed must have been:
[tex]\displaystyle v=\frac{1015}{1.75}=580[/tex]
The Boeing 747 had an average speed of 580 mph.
8) Eugene borrows $250 at a 4% annual interest rate. If he does not
make any payments, how much simple interest will he owe in 18 months?
A) $10
B) $15
C) $18
D) $20
Answers
Answer:
The simplest interest will be $15 ⇒ B
Step-by-step explanation:
The rule of the simple interest is I = Prt, where
P is the initial amountr is the rate in decimalt is the time∵ Eugene borrows $250 at a 4% annual interest rate
∴ P = 250
∴ r = 4% = 4 ÷ 100 = 0.04
∵ The time is 18 months
→ Change the time to year because the rate is annual
∵ 1 year = 12 months
∴ t = 18 ÷ 12 = 1.5 years
→ Substitute the values of P, r, and t in the rule above to find the interest
∵ I = 250 × 0.04 × 1.5
∴ I = 15
∴ The simplest interest will be $15
Find the value of the variable, x
Group of answer choices
6
3
15
5
Answers
Answer:
I think you might have a mistake for the numbers you put there.
But the answer is about 15
Step-by-step explanation:
I did the calculation and got 14, but 15 is the closeest answer