Three times a number is less than 96.

The first step would be to multiply the bottom equation by -1 to eliminate x, then you would combine like terms, like 5y + 2y, and 16 + 10.

Answer:

Subtracting the 2 equations

Step-by-step explanation:

3x + 5y = 16

3x + 2y = 10

Subtract it;

3y = 6

Divide both sides b 3;

y = 2

Substitute y;

3x + 5y = 16

3x + 5(2) = 16

3x + 10 = 16

Subtract 10 from both sides;

3x = 6

Divide both sides by 3;

x = 2

(x, y) = (2, 2)

A polar graph that is a limacon has a formula similar to [tex]r=a+bcos\theta[/tex]

Option B is correct.

A  limacon has a formula similar to [tex]r=a+bcos\theta[/tex]

Case 1 .  If  a < b  or  [tex]\frac{b}{a}>1[/tex]

Then the curve is limacon with an inner loop.

Case 2.  If  a>b   or   [tex]\frac{b}{a}<1[/tex]

Then the limacon does not have an inner loop.

Here, given that,  [tex]r=3+4cos\theta[/tex]

It is observed that,  a < b  or [tex]\frac{b}{a}>1[/tex]

Therefore, the curve is limacon with an inner loop.

Hence, option B is correct.

Learn more:

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Answer:

60 liters of 20% solution & 20 liters of 60% solution

Step-by-step explanation:

80*0.3=.2x+0.6(80-x)

24=0.2x+48-0.6x

-24=0.2x-0.6x

-24=0.4x

24=0.4x

60=x

Hope this helps!! This is step by step btw!

Answer:

∑ₙ₌₀°° (-3x)ⁿ / n!

R = ∞

Step-by-step explanation:

Maclaurin series is:

∑ₙ₌₀°° f⁽ⁿ⁾(0) xⁿ / n!

Find the nth derivative and evaluate at x=0:

f(x) = e⁻³ˣ

f⁽ⁿ⁾(x) = (-3)ⁿ e⁻³ˣ

f⁽ⁿ⁾(0) = (-3)ⁿ

The Maclaurin series is therefore:

∑ₙ₌₀°° (-3)ⁿ xⁿ / n!

∑ₙ₌₀°° (-3x)ⁿ / n!

Use ratio test to find the radius of convergence.

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│[(-3x)ⁿ⁺¹ / (n+1)!] / [(-3x)ⁿ / n!]│< 1

lim(n→∞)│(-3x) n! / (n+1)!│< 1

lim(n→∞)│3x / (n+1)│< 1

0 < 1

The radius of convergence is infinite.

Answer:

1. (0,5), (0,9), (10,4), (10,0), (5,0)

2. [tex]Q_{max}=912[/tex]

[tex]Q_{min}=300[/tex]

Step-by-step explanation:

1.

In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.

The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.

0+y=5

y=5

(0,5)

The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:

0+2y=18

[tex]y=\frac{18}{2}[/tex]

y=9

(0,9)

The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:

10+2y=18

2y=18-10

2y=8

[tex]y=\frac{8}{2}[/tex]

y=4, so the oint is

(10,4)

The next point is the intercept between the lines x=10 and y=0, so the point is:

(10,0)

The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:

x+0=5

x=5

so the point is:

(5,0).

2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.

(0,5)

Q=60(0)+78(5)

Q=390

(0,9)

Q=60(0)+78(9)

Q=702

(10,4)

Q=60(10)+78(4)

Q=912

(10,0)

Q=60(10)+78(0)

Q=600

(5,0)

Q=60(5)+78(0)

Q=300

So now we compare the answers and pick the minimum and maximum results.

We get that:

[tex]Q_{max}=912[/tex]

when x=10 and y=4

and

[tex]Q_{min}=300[/tex]

When x=5 and y=0

The feasible region is the possible set of a constraint

(a) The coordinates of the vertices at the feasible region

The constraints are given as:

[tex]\mathbf{x \ge 0}[/tex]

[tex]\mathbf{y \ge 0}[/tex]

[tex]\mathbf{x \le 0}[/tex]

[tex]\mathbf{x + y\ge 5}[/tex]

[tex]\mathbf{x + 2y\ge 18}[/tex]

See attachment for the graph of the constraints

From the graph, the vertices are:

[tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]

(b) The minimum and the maximum values of objective function Q

The objective function is:

[tex]\mathbf{Q=60x +78y}[/tex]

Substitute [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex] in Q

[tex]\mathbf{Q=60(0) +78(5) = 390}[/tex]

[tex]\mathbf{Q=60(0) +78(9) = 702}[/tex]

[tex]\mathbf{Q=60(5) +78(0) = 300}[/tex]

Hence, the maximum and the minimum values are 702 and 300, respectively.

Read more about feasible regions at:

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Answer: the function is a liner

Step-by-step explanation: trust

Answer:

The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800

Step-by-step explanation:

We are given:

Principal Amount (P) = $5000

Years (t) = 5

Rate (r) = 3% or 0.03

We need to find New Amount (A)

The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Since amount is compounded continuously so n=1

Putting values and finding A

[tex]A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.03}{1})^{1*5}\\A=5000(1+0.03)^5\\A=5000(1.03)^5\\A=5000(1.16)\\A=5800[/tex]

So, New Amount (A) = $5800

The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800

Answer:

80$

Step-by-step explanation:

Answer:

3 x y − 7 y 2 − 6 x + 20 y + 5

Step-by-step explanation:

Answer:

substitution

Step-by-step explanation:

Answer: y>-2

Step-by-step explanation:

8y-3(y-2) < 2y+4(2y+4)

8y-3y+6 < 2y+8y+16

6-16<2y+8y-8y+3y

-10<5y

y>-2

Answer:

(−∞,−2)

Step-by-step explanation:

Start by simplifying each side as much as possible by distributing and combining like terms to get

8y−3(y−2)8y−3y+65y+6>2y+4(2y+4)>2y+8y+16>10y+16

Subtract 10y from both sides to collect the variables on the left, then subtract 6 from both sides to collect all the constants on the right.

5y+65y+6−10y−5y+6−5y+6−6−5y>10y+16>10y+16−10y>16>16−6>10

Divide each side by −5 to solve for y. Since −5<0, the inequality changes direction.

−5y−5y−5y>10<10−5<−2

In interval notation, we write this as (−∞,−2).

Answer:

1.1

Step-by-step explanation:

6-4.9=1.1

Hope I helped!

Please mark Brainliest!!!

Answer:

1.1

Step-by-step explanation:

it's easy you just subtract.

Answer:

Its A

Step-by-step explanation:

Answer:

It will take 35.46 quarters for the account to grow to $3000.

Step-by-step explanation:

Since the annual rate is compounded quarterly, this can be calculated using the formula for calculating the future value as follows:

FV = PV * (1 + r)^n ............................ (1)

Where;

FV = future value or the amount the deposit expected to grow to = $3,000

PV = Present value or the amount place in the savings = $2,000

r = Quarterly rate = Annual rate / 4 = 4.6% / 4 = 0.046 / 4 = 0.0115

n = number of quarters it will take for the loan to grow to $3000 = ?

Substituting the values into equation (1) and solve for n, we have:

$3,000 = $2,000 * (1 + 0.0115)^n

$3,000 / $2,000 = (1.0115)^n

1.50 = (1.0115)^n

Loglinearise both sides, we have:

log(1.50) = n log(1.0115)

0.176091259055681 = n * 0.00496588710682352

n = 0.176091259055681 / 0.00496588710682352

n = 35.4601816891322

Rounding to the nearest hundredth, which also implies to rounding to 2 decimal places, we have:

n = 35.46

Since the the annual rate is compounded quarterly, it will therefore take 35.46 quarters for the account to grow to $3000.

Suppose that $2000 is placed in a savings account at an annual rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, it will take him 8.86 years for the account to grow to $3000

From the information given:

By using the compound interest formula:

[tex]\mathbf{A = P( 1+\dfrac{r}{n})^{nt}}[/tex]

replacing the values from above, we have:

[tex]\mathbf{3000= 2000( 1+\dfrac{0.046}{4})^{4t}}[/tex]

[tex]\mathbf{\dfrac{3000}{2000}= ( 1+\dfrac{0.046}{4})^{4t}}[/tex]

[tex]\mathbf{\dfrac{3000}{2000}= ( 1+0.0115)^{4t}}[/tex]

[tex]\mathbf{\dfrac{3000}{2000}= ( 1.0115)^{4t}}[/tex]

[tex]\mathbf{log(\dfrac{3000}{2000})= 4t \times log ( 1.0115)}[/tex]

[tex]\mathbf{0.17609= 4t \times0.004966}[/tex]

[tex]\mathbf{t = \dfrac{0.17609}{4 \times 0.004966 }}[/tex]

t = 8.86 years to the nearest hundredth.

Learn more about compound interest here:

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Answer: 84

Step-by-step explanation: Multiply 75 by 3. That is 225, and is the value the three numbers must add up to. 73+68=141. 225-141 is 84.

Answer:

Step-by-step explanation:

Step one:

given that the first 3 hours the train travels at a speed of 45 mph.

i.e Time = 3 hours

    speed =45 mph

    distance=?

we know that speed = distance/time

distance= speed*time

distance= 45*3

distance=135miles

Step two:

For the nex two hours it travels at 55 mph

i.e time= 2hours

   speed= 55mph

  distance=?

distance= speed*time

distance= 2*55

 distance= 110mile

Step three:

Hence for a total of 5 hours drive, the total distance covered is

135+110= 245miles

Answer:

2/3

Step-by-step explanation:

1/2 dresses = 36x1/2 = 18

18 dresses in 3/4 hr. ==> 1/4hr ==> 18/3 = 6

1hr ==> 6x4 = 24

fraction = 24/36 = 2/3

Answer:

I am not really good at this but...if I had to choose the ones that make sense

A and B

Step-by-step explanation:

Your are incresing the amount is going up, so if you go backwards you woild have to the negatuves.

Then again I woild not trust my math for the second answer cause I am no good at math.

Answer:

Graph A

Step-by-step explanation:

3x+y=5

y=-3x+5

4x-y=2

-y=-4x+2

4=2x-2

Answer:

7 trophies for $49.00

5 trophies for $30.00

-----------------------------------

Explination:

It says that she wants to pay no more than 7 dollars for each trophy she buys, which means 7 and less. So we have to multiply 7 x the number of trophies, And if it gives you the excact number or less its correct.

So we multiply

7 x 7 = 49 (The excact number, correct)

9 x 7 = 63 (The price they are selling it at is higher, incorrect)

12 x 7 = 84 (The price they are selling it at is higher, incorrect)

5 x 7 = 35 (Paying less, Correct)

3 x 7 (The price they are selling it at is higher, incorrect)

---------------------------------------------------------------------------------------

Its really easy if you put your mind into it! Goodluck <3

Hi! I believe your answer is 0.42, (simplified form of 0.42424242424) which is 14/33 (or [tex]\frac{14}{33}[/tex] ) as a decimal. I hope this helps you! Good luck and have a great day. ❤️✨

Answer:

15 hours

Step-by-step explanation:

Kelsey + 4 sisters = 5 girls

Each of the 5 girls spent three hours cleaning

Usually, I would do 5 x 3 = c, but since we need to use a division equation, we should use c / 5 = 3 OR c / 3 = 5.

c/5 = 3

3 x 5 = 15

Check:     15/ 5 = 3

Answer:

Determination of the Finance Charge, Carry-over balance, Minimum Payment for each of the next two months:

Finance Charge:

First month = $7.91

Second month = $7.72

Carry-over balance:

First month = $487.59

Second month = $475.50

Minimum Payment:

First month = $20.32

Second month = $19.81

Starting balance (Carry-over balance + Finance charge):

First month = $507.91

Second month = $495.31

Step-by-step explanation:

a) Data and Calculations:

Credit Finance = $500

APR = 18.99%

Minimum monthly payment = 4% of the balance

Monthly rate of interest = 0.1899/12 = 0.015825

Finance Charge:

First month = $7.91 ($500 * 0.015825)

Second month = $7.72 ($487.59 * 0.015825)

Carry-over balance:

First month = $487.59($507.91 - $20.32)

Second month = $475.50 ($495.31 - $19.81)

Minimum Payment:

First month = $20.32 ($507.91 * 4%)

Second month = $19.81 ($495.31 * 4%)

Starting balance (Carry-over balance + Finance charge):

First month = $507.91 ($500 + $7.91)

Second month = $495.31 ($487.59 + $7.72)

9514 1404 393

Answer:

  $7,358

Step-by-step explanation:

Assuming the interest is compounded annually, the amortization formula is useful here.

  A = Pr/(1 -(1+r)^-t)

A is the annual scholarship, P is the principal invested at rate r for t years.

  A = $100,000(0.04)/(1 -1.04^-20) = $7,358.18

The university could give $7,358 in scholarships each year.

Answer:

y(1,6) x(-4,6) z(1,1)

Step-by-step explanation:

Answer:

X(-8,6)Y(-3,6)Z(-3,1)

Step-by-step explanation:

just moving the coordinate over to the left 4 times

Answer:

Step-by-step explanation:

S=

S = 55√3

Answer:

s=✓3(1+2+3+...10)

s=✓3[10/2×(10+1)]

here, applying sum of 1st n natural number is n/2×(n+1)

so, s=✓3×5×11

hence, s=55✓3.

Answer:

Andre says: "I think the number of paper clips in the box is less than 1000.

The equality that shows Andre's statement, or information:

p p p (for the number of clips)

So,

p>1000

1000>p

Hope that helps...