Apply the distributive property to create an equivalent expression.
4\left(3 + \dfrac14c - \dfrac12d\right) =4(3+
4
1
​
c−
2
1
​
d)=

Answer:

-12

Step-by-step explanation:

f(-3)= -(-3)2 + 6(-3)

= -(-6) -18

= 6 - 18

= - 12

The value of the quadratic function f(x) = -x² + 6x at x = -3 will be negative 27.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = -x² + 6x

The degree of the function is 2. So, the function is a quadratic function.

The value of the function at x = -3 will be calculated as,

f(-3) = -(-3)² + 6(-3)

Simplify the equation, then we have

f(-3) = -(-3)² + 6(-3)

f(-3) = - 9 - 18

f(-3) = - 27

The worth of the quadratic capability f(x) = - x² + 6x at x = - 3 will be negative 27.

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120 says is 1/3 of a year.

Interest = 1500 x 0.15 x 1/3 = $75

Proceeds = 1500 - 75 = $1425

Answer: Interest = 1500 x 0.15 x 1/3 = $75

Proceeds = 1500 - 75 = $1425

Step-by-step explanation:

Hope this helps:)

Answer:

I am pretty sure its 60 i am sorry if its wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.24

Answer:

2/4 .   4/6 .   2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/4=1/4

4/6=2/3

5/8

3/6

6/9=3/6

Answer:

Each person will be getting [tex]2\frac{2}{5}[/tex] pieces  of licorice

Step-by-step explanation:

If we have 12 pieces of licorice

To divide it equally among 5 people following formula will be used

Pieces to be given to each person = [tex]\frac{total\, pieces}{total\,people}[/tex]

                                                           = [tex]=\frac{12}{5} \\2.4\\[/tex]

So

Each person will be getting [tex]2\frac{2}{5}[/tex] pieces  of licorice

Keywords: Algebra

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Answer:

Perpendicular

Step-by-step explanation:

Put all the points on a graph.

Parallel means that the lines that have the same slope and different y-intercepts. Lines that are parallel to each other will never intersect.

On the graph we made we can see that the lines will have to intersect because the points are in positions that no matter which points we chose to connect together, they would intersect with the other line.

Answer:

Step-by-step explanation:

3(x - 4)(x + 5) = 0

Dividing through by 3

(x - 4)(x + 5) = 0

(x - 4) = 0 or x + 5 = 0

x - 4 = 0 or x + 5 = 0

x = 4 or x = - 5

Answer:

Part 1) [tex]a=-\frac{1}{4c^6}[/tex]

Part 2) [tex]a=-\frac{1}{4c^{-6}}[/tex]

Step-by-step explanation:

Part 1) we have

[tex]a=2b^{3}[/tex] ----> equation A

[tex]b=-\frac{1}{2}c^{-2}[/tex] ----> equation B

substitute equation B in equation A

[tex]a=2(-\frac{1}{2}c^{-2})^{3}[/tex]

Applying property of exponents

[tex](x^{m})^{n}=x^{m*n}[/tex]

[tex]x^{-m} =\frac{1}{x^{m}}[/tex]

[tex]a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}[/tex]

therefore

[tex]a=-\frac{1}{4c^6}[/tex]

Part 2) we have

[tex]a=2b^{3}[/tex] ----> equation A

[tex]b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}[/tex] ----> equation B

substitute equation B in equation A

[tex]a=2(-\frac{c^{2}}{2})^{3}[/tex]

Applying property of exponents

[tex](x^{m})^{n}=x^{m*n}[/tex]

[tex]x^{-m} =\frac{1}{x^{m}}[/tex]

[tex]a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})[/tex]

simplify

[tex]a=-\frac{c^{6}}{4}[/tex]

therefore

[tex]a=-\frac{1}{4c^{-6}}[/tex]

Based on the cost of the car and the interest rate as well as the period, Jaclyn's monthly payment would be A. $298.81.

First find the amount she financed:

= Cost of car - down payment

= 11,000 - 1,000

= $10,000

Then find the monthly interest and number of periods:

= 4.8%/12                                                          = 3 years x 12

= 0.4%                                                               = 36 months

Monthly payment would be:

Amount financed = Amount x ( 1 - (1 + rate)^-number of periods) / rate

10,000 = A x ( 1 - (1 + 0.4%)⁻³⁶) / 0.4%

10,000 = A x 33.4658758899

Amount = 10,000 / 33.4658758899

= $298.81

In conclusion, option A is correct.

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Answer:

22.95

Step-by-step explanation:

91.80÷4=22.95

Therefore, 99.80÷4 is 22.95

Answer: 38

Step-by-step explanation:

Divide 38000/1000

Answer:

Step-by-step explanation: How many 10,000 are in 200,000

Answer:

43.5 ft

Step-by-step explanation:

Given: Julie is 6 feet tall

           She stands 15 feet from the flagpole.

           The edges of the square line up with the top and bottom of the flagpole.

Picture drawn to show side and angle formed by Julie and flagpole.

Lets assume the height of flagpole be "h".

As given, the edges of the square line up with the top and bottom of the flagpole.

∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.

Now, finding the height of flagpole by using tangent rule.

we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]

Remember, both the angle are equal.

∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]

We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]

Solving the equation now

⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]

Multiplying both side by 15

⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]

Multiplying both side by (h-6)

⇒ [tex]6\times (h-6) = 15\times 15[/tex]

Distributive property of multiplication

⇒ [tex]6h-36= 225[/tex]

Adding both side by 36

⇒[tex]6h= 225+36[/tex]

Dividing both side by 6

⇒[tex]h= \frac{261}{6}[/tex]

∴ [tex]h= 43.5\ feet[/tex]

Hence, the height of flagpole is 43.5 feet.

The height of the flagpole is given by the length of the hypotenuse side

formed by the right triangle Julie forms with the cardboard.

Response:

The triangle formed by the edges of square lined up with the top and

bottom of the flagpole is a right triangle.

The altitude of the right triangle formed with the height of the flagpole as the base = 15 feet

Length of a leg of the right triangle = √(15² + 6²) = 3·√(29)

The other angle formed by the right triangle = (90° - arctan(15/6))

h × sin(arctan(15/6)) = 3·√29

[tex]h = \mathbf{\dfrac{3 \cdot \sqrt{29} }{sin(arctan(15/6))} } = 17.4[/tex]

Height of the flagpole, h = 17.4 feet

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The speed of a boat in still water (b) is 50km/h. It takes the same time (t) for the boat to travel 10km (x) upstream as it does to travel 20km (y) downstream. Find the speed of the current.​

upstream speed (u) = speed in still water (b) - stream speed (s) = b-s = 50-s

downstream speed (d) = speed in still water (b) + stream speed (s) = 50+s

time (t) = x/u = y/d

10/(50-s) = 20/(50+s)

10(50+s) = 20(50-s)

500 + 10s = 1000 - 20s

30s = 500

stream speed (s) = 500/30 = 16.6 km/h

Answer:

25*3 or 25(3)

Step-by-step explanation:

Understanding arithmetic operations, like multiplication, and the order of operations, is essential in algebra. Parentheses dictate the order, as seen in '2 + (3 x 5)', resulting in 17. For algebraic manipulation, this understanding helps when working with variables and complex expressions like cubing exponentials or solving simultaneous equations.

When faced with the phrase '25 multiplied by 3 algebraic expression', we might interpret this as the task of multiplying an algebraic expression by 25. Considering the examples provided, the manipulation of parentheses greatly influences the outcome of mathematical expressions.

The expression 2 + (3 x 5) includes parentheses, which indicate that multiplication should occur before addition, following the order of operations (PEMDAS/BODMAS). Here, the product of 3 and 5 is 15, and adding 2 results in 17.

However, if we were to apply the principle of algebraic multiplication to an unknown variable, say 'x', the expression would be 25x. If 'x' was the expression (2 + (3 x 5)), then 25x would be 25 times 17, or 425, after applying the order of operations within the parentheses.

Applying this method to simultaneous equations or Cubing of Exponentials, we can see the importance of understanding the principles of algebra and arithmetic operations.

When cubing exponentials, for example, you multiply the exponent by 3. This concept is crucial for solving more complex algebraic problems like those involving unknowns and linear equations.

Common difference = [tex]\frac{1}{5}[/tex]

Solution:

Given arithmetic sequence:

[tex]$-2,-1\frac{4}{5} ,-1\frac{3}{5} , -1\frac{2}{5} , ....[/tex]

Let us first convert the improper fraction into mixed fraction.

[tex]$-2,-\frac{9}{5} ,-\frac{8}{5} , -\frac{7}{5} , ....[/tex]

Difference between two numbers in an arithmetic sequence is the common difference.

[tex]$a_2-a_1=-\frac{9}{5}-(-2)=-\frac{9}{5}+2=\frac{1}{5}[/tex]

[tex]$a_3-a_2=-\frac{8}{5}-\left(-\frac{9}{5}\right)=-\frac{8}{5}+\frac{9}{5}=\frac{1}{5}[/tex]

[tex]$a_4-a_3=-\frac{7}{5}-\left(-\frac{8}{5}\right)=-\frac{7}{5}+\frac{8}{5}=\frac{1}{5}[/tex]

Common difference = [tex]\frac{1}{5}[/tex].

Hence the common difference of the arithmetic sequence is [tex]\frac{1}{5}[/tex].

Common difference of the given arithmetic sequence is equal to [tex]\frac{1}{5}[/tex]

The given arithmetic sequence is in mixed numbers. Converting them into proper fractions, we get:

[tex]First\ term = t_1 = -2\\\\Second\ term = t_2 = -1\frac{4}{5} = -\frac{(5\times1)+4}{5} = -\frac{9}{5}\\\\Third\ term = t_3 = -1\frac{3}{5} = -\frac{(5\times1)+3}{5} = -\frac{8}{5}\\\\Fourth\ term=t_4 = -1\frac{2}{5} = -\frac{(5\times1)+2}{5} = -\frac{7}{5}[/tex]

The sequence can thus be rewritten as [tex]-2, -\frac{9}{5}, -\frac{8}{5}, -\frac{7}{5}[/tex]

To find the common difference of the given arithmetic sequence, subtract any two consecutive numbers of the sequence. The difference between two consecutive numbers is always a constant and is termed as the common difference.

Hence,

[tex]d_1= t_2-t_1=(-\frac{9}{5} -(-2)= \frac{-9+10}{5}= \frac{1}{5} \\\\d_2=t_3-t_2= (-\frac{8}{5} -(-\frac{9}{5} )= \frac{-8+9}{5} = \frac{1}{5}\\\\d_3=t_4-t_3= (-\frac{7}{5} -(-\frac{8}{5} )= \frac{-7+8}{5} = \frac{1}{5}[/tex]

[tex]d_1=d_2=d_3 = d[/tex]

Common difference [tex]d=\frac{1}{5}[/tex]

a. The perimeter of the figure is 4x+34.

b. The total area of figure is 24x+40.

Step-by-step explanation:

Given,

Length of figure = 12

Width of figure = x+5+x = 2x+5

a. Perimeter = Length + Length + Width + Width

Perimeter = [tex](12)+(12)+(2x+5)+(2x+5)[/tex]

Perimeter = [tex]12+12+2x+5+2x+5 = 4x+34[/tex]

The perimeter of the figure is 4x+34.

b. Total area = Length * Width

Total area = [tex]12(2x+5) = 24x+60[/tex]

The total area of figure is 24x+40.

Keywords: area, perimeter

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The division of 5/5/8 by 1/2/9 in simplest form is 405/88 after converting the mixed numbers to improper fractions, then multiplying by the reciprocal, and simplifying.

To find the simplest form of the division of two mixed numbers, first, both mixed numbers must be converted to improper fractions. Dividing by a fraction is the same as multiplying by its reciprocal. So, when dividing 5/5/8 by 1/2/9, we first turn these into improper fractions.

5/5/8 becomes 45/8 (since 5*8+5=45) and 1/2/9 becomes 11/9 (since 1*9+2=11). Now the problem is 45/8 divided by 11/9. To divide these fractions, we multiply by the reciprocal: 45/8 * 9/11 = (45*9)/(8*11) = 405/88.

To simplify 405/88, we find the Greatest Common Divisor (GCD) of the numerator and the denominator, which is 1 in this case, so the fraction is already in its simplest form, which is 405/88.

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 1/2/9 is 9/2/1. So, the expression becomes 5/5/8 multiplied by 9/2/1. To multiply fractions, we multiply the numerators together and the denominators together. So, (5 x 9) / (5 x 2) x 8 / 1 = 45/10 x 8/1 = 360/10 = 36.

The equation with no fractions is:

30x + 80 = 36

Solution:

Given that the equation is:

[tex]\frac{3}{4}x+2=\frac{9}{10}[/tex]

We have to rewrite the equation such that there is no fraction

From given expression,

[tex]\frac{3}{4}x+2=\frac{9}{10}[/tex]

Simplify the left hand side of equation

[tex]\frac{3x+8}{4} = \frac{9}{10}[/tex]

Cross multiply to get a simpler equation

[tex]10(3x+8) = 9 \times 4\\\\Simplify\ the\ above\ expression\\\\30x + 80 = 36[/tex]

Thus the equation is rewritten with no fractions

To rewrite the equation 3/4x + 2 = 9/10 without fractions, we multiply every term by the lowest common denominator (20) to get 15x + 40 = 18. Then, we isolate x by subtracting 40 from both sides to get 15x = -22. We solve for x by dividing both sides by 15, resulting in x = -22/15.

The aim is to rewrite the equation 3/4x + 2 = 9/10 without fractions. To get rid of the fractions, we'll multiply each term by the lowest common denominator (LCD). In this case, the LCD is 20 because it's the smallest number both 4 and 10 can both go into. The equation thus becomes: 20*(3/4x) + 20*2 = 20*(9/10)

This simplifies to: 15x + 40 = 18

Now, to isolate x, we start by subtracting 40 from both sides:

15x + 40 - 40 = 18 - 40

So, 15x = -22. Finally, to solve for x, we divide by 15:

x = -22/15

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Answer:

The total cost is calculated to be $105,000.

Step-by-step explanation:

Here,

The cost of per acre land= $60,000

Jack is willing to purchase= 1 ¾acres = [tex]\frac{4*1+3}{4} =\frac{7}{4}=1.75[/tex] acres

Then,

By unitary method,

The cost of one acre land is $60,000 .

The cost of 1.75 acres is    = $[tex]1.75*60,000[/tex]

The total cost of land is =$105,000.

So, Jack has to pay $105,000 to purchase 1.75 acres of land.

To find the total cost of 1 ¾ acres of land purchased at $60,000 per acre, multiply the price by the number of acres. Jack will pay $105,000 for the land.

Jack purchased 1 ¾ acres of land at $60,000 per acre. To calculate the total cost, multiply the price per acre by the total number of acres:

Total Cost = Price per acre x Number of acres

Total Cost = $60,000 x 1.75 = $105,000

Answer: 3 1/2

Step-by-step explanation:

Yo sup??

y=3x+12

y-12=3x

x=y/3 - 4

f(y)=y/3 - 4

or

f(x)=x/3 - 4

where f(x) is the inverse of y.

Hope this helps

The inverse relation of [tex]\( y = 3x + 12 \)[/tex] is [tex]\( x = \frac{y - 12}{3} \)[/tex].

To find the inverse of the relation [tex]\( y = 3x + 12 \)[/tex], we start by expressing it in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:

[tex]\[ y = 3x + 12 \][/tex]

Next, solve for [tex]\( x \)[/tex]:

[tex]\[ y - 12 = 3x \][/tex]

[tex]\[ x = \frac{y - 12}{3} \][/tex]

Thus, the inverse relation is:

[tex]\[ x = \frac{y - 12}{3} \][/tex]

To verify, substitute [tex]\( x \)[/tex] with [tex]\( \frac{y - 12}{3} \)[/tex] back into the original equation:

[tex]\[ y = 3 \left( \frac{y - 12}{3} \right) + 12 \][/tex]

[tex]\[ y = y - 12 + 12 \][/tex]

[tex]\[ y = y \][/tex]

Therefore, the answer is [tex]\( x = \frac{y - 12}{3} \)[/tex].

Answer:

B

Step-by-step explanation:

[tex]22.8 \times 9.8 = 216.58 \\[/tex]

Answer:

4x^4

Step-by-step explanation:

Cubed and squared are the same thing

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The polygon is rhombus

In geometry, the definition of a polygon is given as a closed two-dimensional figure with three or more straight lines. The Greek word "Polygon" consists of Poly meaning "many" and gon meaning "angle". We see many different polygons around us. For example, the shape of a honeycomb is a hexagon. Each polygon is different in structure, they are categorized based on the number of sides and their properties. Thus, all polygons are closed plane shapes.

Given:

angle measures: 80°, 100°, 80°, 100°

As, the sum of angles is 360

= 80+ 80 +100 +100

= 160 +200= 360

Also, pair opposite angles are equal.

Hence, the given polygon is rhombus.

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To find the cost of gas for Sally's commute, you would multiply the number of gallons she uses daily by the cost per gallon. Assuming a daily use of one gallon at $4 per gallon, Sally would spend $4 per day, $20 per week (5-day workweek), and $1,040 per year (52 workweeks). This does not account for variable factors such as days off or gas price changes.

The student is asking about the cost of gasoline for commuting to and from a job. Since we do not have the exact distance Sally travels or the efficiency of her vehicle, we cannot compute the exact cost per day, week, or year. However, if we assume Sally uses one gallon of gas per day at a cost of $4 per gallon, here's how you calculate the costs:

These calculations are based on the premise of daily one-gallon gas usage and do not take into account vacations, days off, or possible fluctuations in gas prices.

Answer:

x=4.5 inches

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The perimeter of a hexagon is the sum of its six length sides

Let

x ----> the length of a shorter side

y ---> the length of a longer side

The perimeter of the hexagon is equal to

[tex]P=4x+2y[/tex]

[tex]P=52\ in[/tex]

so

[tex]52=4x+2y[/tex] ---->equation A

Each longer side measure 1 in. less than 4 times the length of a shorter side

so

[tex]y=4x-1[/tex] ----> equation B

substitute equation B in equation A

[tex]52=4x+2(4x-1)[/tex]

Solve for x

[tex]4x+8x=52+2\\12x=54\\x=4.5\ in[/tex]