Solve the inequality and express your answer in interval notation. x² + 8x + 3 < 0

Bank account with an interest rate of r% per year = 2.5%

Simple Interest :

Simple interest paid or received over a certain period is a fixed percentage of the principal amount.

Simple Interest=P×[tex]\frac{r}{100} }[/tex]×T

where:

P=Principal

r= interest rate on a certain period

T= Time

Given :

Principal(P)=  £1000

Time (T)= 1 Year

Find :

the interest rate per year = r%

Now,  

Interest earned on account =  £1025 - £1000

Simple Interest= £ 25

Simple Interest=P×[tex]\frac{r}{100}[/tex]×T

25= 1000×[tex]\frac{r}{100}[/tex]×1

25×100=1000r

2500=1000r

[tex]\frac{2500}{1000} =r\\\frac{25}{10} =r\\\frac{5}{2} =r\\2.5=r[/tex]

r= 2.5%

the interest rate of r% per year. after one year the value of the account=2.5%

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The population of a city after 5 years would be 261698.

We know the the formula for the exponential growth of the population is,

P(t) = a(1+r)^t

where, a is the initial population

t is the time period

r is the rate of growth

In this question, we have a = 210000, %R = 4.5

So, r = 0.045

We need to find the population after 5 years.

t = 5

Using above formula,

P = 210000 × ( 1 + 0.045)^5

P =  210,000 × (1.045)^5

P = 210,000 × 1.25

P = 261698.2

P ≈ 261698

Therefore, the population of a city after 5 years would be 261698.

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If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.

First step is to calculate the value loss

Value loss=1/3× original  value

Value loss= 1/3× $215,613

Value loss= $71,871

Second step is to calculate the new value

New value=$215,613-$71,871

New value= $143,742

Third step is to calculate the value gained

Value gained= 1/2× new value

Valued gained=1/2× $143,742

Valued gained=$71,871

Fourth step is to calculate the current value

Current value= $143,742+$71,871

Current value=$$215,613

Therefore If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.

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The day of the month is nominal (option c).

Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable.  A nominal variable is a categorical variable that is qualitative.

A ratio scale is quantitative. A ratio scale is a variable with a true zero. An example is weight. An interval variable is a variable where each value is measured along a scale. An example of an interval variable is credit score.

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Step-by-step explanation:

3800 is the general amount, but before he can touch it, 800 and 200 are taken away from it for the described purposes.

so, what is left is

3800 - 800 - 200 = 2800

this is then the real amount he can do something with.

Answer:

easy

Step-by-step explanation:

How to solve a system of equations by elimination.

Write both equations in standard form.

Make the coefficients of one variable opposites.

Add the equations resulting from Step 2 to eliminate one variable.

Solve for the remaining variable.

Substitute the solution from Step 4 into one of the original equations.

The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value. In the graphically representation we can see the line intersect each other at point (12,6).

Given that,

The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value.

We have to create a graphic representation of this inequality system and choose a potential resolution.

x + y ≤18----->equation(1)

Amount in pennies: 5x+10y≥110------>equation(2)

solves by eq2 - 5×eq(1)

5x+10y - 5(x+y) = 120 - 5×18

5x + 10y -5x-5y  = 120 - 90

5y = 30

y=6

Then x=12

Therefore, x=12, y=6 is the point where two lines converge.

In the graphically representation we can see the equation (1) line and equation (2) line intersect each other at point (12,6).

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Answer:

$5.90

Step-by-step explanation:

(7.19)(.82)  Put these numbers in your calculator and multiply them together.

5.8958 Round to the nearest cent

$5.90

The required rate for ratio of the two different quantities i.e

Gabby worked 30/4 hours per day.

Option (c) is correct.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Gabby worked 30 hours in 4 days.

According to given question we have

The ratio of the two quantities of the different kind and in the different units is a fraction that shows how many times one quantity is of the other.

By the use of arithmetic we have,

Gabby worked 30 hours in 4 days means

4 days= 30 hours

1 days = 30/4 hours

Therefore, the required rate for ratio of the two different quantities i.e

Gabby worked 30/4 hours per day.

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Answer: 30/4 hours per day

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Let the cat have a weight of x.

Then, the dog weighs 9x.

The hamster weighs x/20.

The mouse weighs 3x/10.

So, the dog is 9/(3/10) = 30 times as heavy.

The weight of the dog is 30 times the weight of the mouse.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Let the weight of the dog be x,
A dog is 9 times as heavy as a cat,
weight of the dog = 9x - - - - -(1)

A hamster is 20 times as light as a cat
Weight of the hamster = x /20

A mouse is 6 times as heavy as a hamster.

Weight of the mouse = 6(x /20)
m(20/6) = x

Now, put x = m(20/6) in equaiton 1,
weight of the dog = 9[m(20/6)]
weight of the dog = 30m

Thus, the weight of the dog is 30 times the weight of the mouse.

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The original price is $623.51.

Let the original price be represented by x.

Since the appliance store decreases the price of a 19-In television set 29%, that means the percentage of the sales price will be:

= 100 - 29

= 71%

Therefore, the original price will be:

= 71% of x = $442.69

0.71x = $442.69

x = $442.69/0.71

x = $623.51

The price is $623.51.

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Answer:

The first option

Step-by-step explanation:

The addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.

Given 3 1/2 + 2 3/4

= 7/2 + 11/4

= (14+11) / 4

= 25/4

= 6 1/4

Given 3 1/2 - 2 3/4

= 7/2 - 11/4

Find the LCM of both denominators

= (14-11) / 4

= 3/4

Therefore, the addition and subtraction of fractions and mixed fractions can be done by finding the lowest common multiple (LCM) of the denominators before simplifying.

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The 120 feet point to point displacement and the 80° angle formed at the vertex A by the control line, AC = AB, Charlie is holding, gives the length of the control line as about 93 feet.

The given parameters are;

The distance (displacement) traveled by the plane = 120 feet (point to point)

The points on the circle, flown by the model plane = C and B

The center of the circle = A

The angle formed by AC and AB = 80°

Required;

The length of the control line.

Solution:

The control line in the description of the diagram is the line AC or AB

Therefore;

AC = AB

Taking the points C and B as the point the plane flew through, we have;

BC = 120 feet

Which gives

‹ABC = ‹ACB = (180° - 80°)/2 = 50°

From the law of sines, we have;

Which gives;

120/(sin(80°)) = AC/(sin(50°))

AC = 120×(sin(50°))/(sin(80°)) ≈ 93

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Answer:

The control line is about 86 feet long.

Hope this helps!

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

[tex]\frac{24}{96}[/tex] = [tex]\frac{6}{24}[/tex] = [tex]\frac{1}{4}[/tex]

this indicates the sequence is geometric with explicit formula

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 96 and r = [tex]\frac{1}{4}[/tex] , then explicit formula is

[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]

(a) There are 665280 ways of selection if the order of the choices matters.

(b) There are 924 ways of selection if the order of the choices does not matters.

(a)  If the order of the choices matters, then we must use the permutation formula that is

[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]

Here n is the total no. of objects and r is chosen objects

We have n = 12

               r = 6

After we substitute the value we get

[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]

[tex]^{12}P_6 = \frac{12!}{6!}[/tex]

[tex]^{12}P_6[/tex] = 665280

Thus, there are 665280 ways of selection if the order of the choices matters

(b)  If the order of the choices does not matter, then we must use the combination formula that is

[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]

After we substitute the value we get

[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]

[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!

​[tex]^{12}C_6 =[/tex] 665280/ 720

​[tex]^{12}C_6 =[/tex] 924

Thus, there are 924 ways of selection if the order of the choices does not matters.

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Answer:

VAT = R239.85

Step-by-step explanation:

VAT = 15%

15/100 = 0.15

R1599 × 0.15 = 239.85

VAT = R239.85

Answer:

It's coordinates are (1,-2)

Answer: e² - 4

Step-by-step explanation:

Differentiate of e²x - 3e-4x is e² - 4

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x} = 2e^{2x}+12e^{-4x}[/tex]

Step-by-step explanation:

Given function:

[tex]y=e^{2x}-3e^{-4x}[/tex]

[tex]\boxed{\begin{minipage}{3.7cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{\text{d}}{\text{d}x} e^{2x}-\dfrac{\text{d}}{\text{d}x}3e^{-4x}\\\\& =2 \cdot e^{2x}-(-4)\cdot 3 e^{-4x} \\\\ &= 2e^{2x}+12e^{-4x}\end{aligned}[/tex]

Answer:

[tex](x-6)^2=-1[/tex]

Step-by-step explanation:

Given equation:

[tex]-6x^2+64x-222=-8x[/tex]

When completing the square, first move the terms in x to the left and the constant to the right of the equation:

[tex]\implies -6x^2+64x-222=-8x[/tex]

[tex]\implies -6x^2+64x-222+222=-8x+222[/tex]

[tex]\implies -6x^2+64x=-8x+222[/tex]

[tex]\implies -6x^2+64x+8x=-8x+222+8x[/tex]

[tex]\implies -6x^2+72x=222[/tex]

Factor out the leading coefficient -6 from the left side, then divide both sides by -6:

[tex]\implies -6(x^2-12x)=222[/tex]

[tex]\implies \dfrac{-6(x^2-12x)}{-6}=\dfrac{222}{-6}[/tex]

[tex]\implies x^2-12x=-37[/tex]

Add the square of half the coefficient of the term in x to both sides, forming a perfect square trinomial on the left side:

[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2=-37+\left(\dfrac{-12}{2}\right)^2[/tex]

[tex]\implies x^2-12x+\left(-6\right)^2=-37+\left(-6\right)^2[/tex]

[tex]\implies x^2-12x+36=-37+36[/tex]

[tex]\implies x^2-12x+36=-1[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (x-6)^2=-1[/tex]

To solve:

[tex]\implies \sqrt{(x-6)^2}=\sqrt{-1}[/tex]

[tex]\implies x-6=\pm i[/tex]

[tex]\implies x-6+6=\pm i+6[/tex]

[tex]\implies x=6 \pm i[/tex]

Therefore, the solutions are:

[tex]x=6+i, \quad x=6-i[/tex]

valid . some trees grow flowers i belive

The measures of the triangle's unknown angles will be 50° and 100°.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

A triangle has one 30° angle, an unknown angle, and an angle with a measure that is twice the measure of the unknown angle.

Let 'a' and 'b' be the unknown angles of the triangle. Then the equation will be

∠a = 2 ∠b

We know that the angle sum of the triangle is 180°. Then the equation will be

∠a + ∠b + 30° = 180°

2∠b + ∠b = 150°

3∠b = 150°

∠b = 50°

Then the measure of the angle 'a' will be

∠a = 2 ∠b

∠a = 2 x 50°

∠a = 100°

The measures of the triangle's unknown angles will be 50° and 100°.

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Step-by-step explanation:

Parallel Lines are lines that do not intercept with eachother. They have the same slope yet have different y-intercepts.

Draw two lines not touching.

Example

[tex]y = 5x + 1[/tex]

[tex]y = 5x + 2[/tex]

No examples

[tex]y = 5x + 2[/tex]

[tex]y = - \frac{1}{5} x + 2[/tex]

Hope this helps!

Answer:

○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]

Step-by-step explanation:

We are told that:

[tex]z(x)= 15x - x^2 + 3[/tex],

and told to find an expression for [tex]z(x - 1)[/tex].

In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:

[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]

Now we can simplify:

⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex]      [Distributing 15 into the first brakets]

⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]

⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex]     [Distributing the minus sign]

⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex]          [Combining like terms]

⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]

Therefore, the first option is the correct one.

Answer:

I think it's because of the down payment and the positive slope because you are going to pay in installments by months.

Answer

59,000+1,700=60,000

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

from seeing the steps listed the answer should be b would be helpful if u posted the diagram along