50 POINTS The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.

A=h(a+b)/2

Solve for b.

y + 1/4x - 9/4 is an equation of a line passing through the point (-1, 2) that is parallel to the line y = -4x + 5

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that y = -4x + 5

Here -4 is the slope and 5 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 1/4, x₁ = -1 and y₁ = 2

y - 2 = 1/4(x - (-1))

y - 2 = 1/4(x + 1)

y - 2 = 1/4x + 1/4

y + 1/4x - 9/4

You can use the point-slope form calculator to determine the equation of a line given its slope and a point on the line. You will soon understand what the point-slope form equation is and how it differs from the slope-intercept form equation.

The point-slope formula is expressed as

y - y₁ = m(x - x₁)

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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:

The first option

Step-by-step explanation:

(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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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 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:

VAT = R239.85

Step-by-step explanation:

VAT = 15%

15/100 = 0.15

R1599 × 0.15 = 239.85

VAT = R239.85

Answer:

$30.00

Step-by-step explanation:

$25.50 = y(1 - 0.15)

$25.50 = y(0.85)

($25.50) / (0.85) = y

y = $30

Answer:

$30

Step-by-step explanation:

let x = the original price

x - .15x = 25.50  

The original price - .15 of the original price is 25.25

.85x = 25.25  Divide both sides by .85

x = 30

Check:

30 - .15(30) = 25.25

30 - 4.50 = 25.25

25.25 = 25.25

Answer: [tex]3^{14}[/tex]

Step-by-step explanation:

[tex]\frac{3^{9} }{3^{-5} }[/tex]

Properties of exponents (negative exponent) says that a term can be moved from the numerator to the denominator and vice versa by flipping the sign.

So,

[tex]\frac{1}{3^{-5} } =3^{5}[/tex]

Properties of exponents (Product Rule) also say that

[tex]a^{x} *a^{y} = a^{x+y}[/tex]

So,

[tex]3^9*3^5=3^{9+5} =3^{14}[/tex]

Another way to solve this is simply using the Properties of exponents (Quotient Rule) which states

[tex]a^{x} /a^{y} =a^{x-y}[/tex]

So,

[tex]\frac{3^{9} }{3^{-5} }=3^{9-(-5)} =3^{14}[/tex]

Answer:

24

Step-by-step explanation:

to solve this you should first write it out

-8 * -3

now multiply them

the negatives cancel each other out

so

you can just do 8 * 3

and get 24

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:

[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]

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]

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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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]

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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Answer

59,000+1,700=60,000

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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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!

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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The flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.

From the information, it was stated that the recipe for cookies calls for 3 cups of flour for every 4 cups of oatmeal.

Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be:

= 3/4 × 16

= 12

Therefore, the flour that is needed for a big batch of cookies that uses 16 cups of oatmeal will be 12 cups of flour.

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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 roots of the function  x⁴+ x² = 4 x²  + 4 are ±2 or x = ±i.

A Complex number is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a function as x⁴+ x² = 4 x²  + 4

x⁴+ x² - 4 x²  - 4 = 0

x⁴+ - 3 x²  - 4 = 0

Assume u = x²

x⁴+ - 3 x²  - 4 = 0

Now using the substitution u = x² , then

u² - 3u - 4= 0 ← in standard form

(u - 4)(u + 1) = 0 ← in factored form

Then equate each factor to zero and solve for u

u - 4 = 0 ⇒ u = 4

u + 1 = 0 ⇒ u = - 1

Then convert u back into terms of x

x² = 4 ( take square root of both sides )

x = ± 2

x² = - 1 ( take square root of both sides )

⇒ x = ±i

Thus, The roots of the function  x⁴+ x² = 4 x²  + 4 are ±2 or x = ±i.

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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

Answer:

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

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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