Which statement best describes the equation (x 5)2 4(x 5) 12 = 0?.

The inequality that can be used to find m, the number of months after receiving his fish tank, when Dante will have less than 10 goldfish in his fish tank is 20 - 2m < 10

Since Dante has 20 goldfish and gives out 2 goldfish every month,

After one month, he has 20 - 2 = 20 - 1(2) gold fish left.

After 2 months, he has 20 - 2 - 2 = 20 - 4 = 20 - 2(2) goldfish left.

After 3 months, he has 20 - 2 - 2 - 2 = 20 - 6 = 20 - 3(2) goldfish left.

So, after m months, he has 20 - 2m goldfish left.

For the number of goldfish to be less than 10, we have the inequality

20 - 2m < 10

So, the inequality that can be used to find m, the number of months after receiving his fish tank, when Dante will have less than 10 goldfish in his fish tank is 20 - 2m < 10

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Answer:

The first equation must be multiplied by 18 and second equation must be multiplied by 8

Step-by-step explanation:

To eliminate x, on the addition of two equations, we multiply the first equation by -10, and the second equation by 3. Thus, option (A) –10 times the first equation and 3 times the second equation, is the right choice.

A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.

In the question, we are asked for the numbers which when multiplied by the two equations respectively, eliminate x, when the equations are added.

The two equations are:

(1/5)x + (3/4)y = 9 ... (i),

(2/3)x - (5/6)y = 8 ... (ii).

We know that to eliminate a variable from a system of equations, their coefficients need to be equal and the sign needs to be opposite.

In the question, we are asked to eliminate x.

The coefficients of x are (1/5) and (2/3).

To equalize the coefficients, we make them equal to their LCM.

LCM of (1/5) and (2/3) is 2.

To make (1/5) as 2, we need to multiply it by 10.

To make (2/3) as 2, we need to multiply it by 3.

For opposite signs, we will make of this negative.

The option with our calculations is A. –10 times the first equation and 3 times the second equation.

Thus, to eliminate x, on the addition of two equations, we multiply the first equation by -10, and the second equation by 3. Thus, option (A) –10 times the first equation and 3 times the second equation, is the right choice.

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Answer:

(c) 1.61

Step-by-step explanation:

thats what i got

Answer:

4/9

Step-by-step explanation:

See attachment for step-by-step

Answer:

3/8 = 9/24

1/3 = 8/24

3/8 > 1/3

Step-by-step explanation:

3/8 = 9/24 (multiply both numerator and denominator by 3)

1/3 = 8/24 (multiply both numerator and denominator by 8)

9/24 > 8/24

Step-by-step explanation:

[tex] \sin(22) = \frac{x}{14} \\ x = \sin(22) \times 14 = 5.2[/tex]

Answer: 30 feet is greater

Step-by-step explanation:

3 yards is 9 feet (1 yard is 3 feet). 9 < 30. 30 feet is more than 9 feet, and 9 feet is equal to 3 yards so 30 feet is greater than 3 yards

First Method:

Round [tex]\frac{3}{5}[/tex] to the closest integer, which is 1.

Round [tex]\frac{3}{4}[/tex] to the closest integer, which is also 1.

So 1 + 1 = 2.

Answer for method 1: 2

Second Method:

[tex]\frac{3}{5}[/tex] + [tex]\frac{3}{4}[/tex] = [tex]\frac{3*4}{5*4} + \frac{3*5}{4*5} = \frac{12}{20}+\frac{15}{20}=\frac{27}{20}[/tex]

[tex]\frac{27}{20}[/tex] is around 1

Answer for method 2: 1

The closest answer is 1.

Statement:

The circle has a diameter of 16 inches.

To find out:

The area of the circle.

Solution:

Answer:

C) 201 square inches

Hope you could understand.

If you have any query, feel free to ask.

Answer:

[tex]Solution,\\Here,\\Diameter(d)=16 inches\\radius(r)=16inches/2=8inches\\Now, \\ Area=\pi r^{2} \\ Area=3.14*(8inches)^{2} \\ Area=3.14*64inches^{2} \\Area=200.96inches^{2} =201inches^{2}[/tex]

Hence, Option c is correct.

Answer:

x = cd-by/ a

Step-by-step explanation:

ax + by / c = d

ax + by = cd

ax = cd-by

x = cd-by/a

Answer:

B

Step-by-step explanation:

You can multiply both sides by c to remove the fraction part.

d(c) = ax + by/c(c)

dc = ax + by

Then subtract "by" from both sides to isolate x.

dc - by = ax - by + by

dc - by = ax

Then divide both sides by a to completely isolate the variable x.

(dc - by)/a = ax/a

(dc - by)/a = x

B

Answer:

Step-by-step explanation:

1) Total = 30 students

Girls : Boys = 2 : 1

Total part = 2 + 1 = 3

Fraction of girls = 2/3

[tex]Number \ of \ girls = \dfrac{2}{3}*30 = 2*10 = 20\\\\\\Number \ of \ boys = 30 - 20 = 10[/tex]

Answer: 20 girls and 10 boys

2) Total pens = 24

Red  :Blue : Black  = 3 : 4 : 1

Total parts = 3 + 4 + 1 = 8

[tex]Number \ of \ red \ pens = \dfrac{3}{8}*24=3*3 = 9\\\\\\Number \ of \ blue \ pens = \dfrac{4}{8}*24=4*3=12\\\\\\Number \ of \ black \ pens = \dfrac{1}{8}*24=1*3=3[/tex]

Answer: 9 red pens

                12 blue pens

                 3 black pens

3) Total people = 180

Adults : boys : girls = 3 : 2 : 7

Total parts = 3 + 2 + 7 = 12

[tex]Number \ of \ adults = \dfrac{3}{12}*180=3*15=45\\\\\\Number \ of \ boys = \dfrac{2}{12}*180=2*15=30\\\\\\Number \ of \ girls = \dfrac{7}{12}*180=7*15=105\\\\[/tex]

Answer: 45 adults  ; 30 boys and 105 girls

4)Total vehicles = 12000

Cars : trucks : motorcycles = 13 : 8 : 3

[tex]Number \ of \ cars = \dfrac{13}{24}*12000=13 *500 = 6500\\[/tex]

6500 cars drove through on that day

[tex]b) Number \ of \ trucks = \dfrac{8}{24}*1200 = 8*500 = 4000[/tex]

4000 trucks

It's a

All steps are correct.

The probability that he selected the special quarter is 87.5%.

Given that Mandvil has one standard quarter and one special quarter with a Head on both sides, and he selects one of these two coins at random, and without looking at it first, he flips the coin three times, to determine, if he flips a Head three straight times, what is the probability that he selected the special quarter, the following calculation must be made:

Therefore, the probability that he selected the special quarter is 87.5%.

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Answer:  5

Step-by-step explanation:

7x^5 has the highest degree of the polynomial  

Answer:

5

Step-by-step explanation:

The highest power(Exponent) of variable x is the degree of the polynomial

Highest power = 5

Degree of the polynomial = 5

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

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

0 4x² - x

- 4x² - 4x

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

0 + 3x - 3

- 3x - 3

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

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

Answer:

[tex]the \: answer \: is \: c \: \\ {x}^{ \frac{10}{3} } = \sqrt[3]{ {x}^{10} } = {x}^{3} \sqrt[3]{x} \\ {x}^{3 } \times {x}^{ \frac{1}{3} } = {x}^{3 + \frac{1}{3} } = {x}^{ \frac{10}{3} } [/tex]

Answer: False

Step-by-step explanation: Numbers are infinite, They go on forever. 2/3 can be 20/30, 200/300, etc.

Answer

B)False

Step-by-step explanation:

Every fraction has an infinite number of equivalent fractions.

For example, the equivalent fractions for 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12, and infinite others. Hence, there are infinite equivalent fractions for a every single fraction.

Answer:

5

Step-by-step explanation:

6x^2 + 7x^3 + 8x^5 +9

Write in order from highest power to lowest power

8x^5 + 7x^3 + 6x^2  +9

The highest power ( largest exponent) is 5

The degree of the polynomial is 5

Look at the pics

Step-by-step explanation:

Answer:

4/3.28

Step-by-step explanation:

Answer:

4/3.28

Step-by-step explanation:

Answer:

We will be using the Pythagorean theorem for the first 2 and SOH CAH TOA for the other 3.

a^2 + b^2 = c^2

sin(t) = b/c;  cos(t) = a/c;  tan(t) = b/a

#4)  a^2 + 9^2 = (3sqrt(10))^2                    #5  9^2 + 27^2 = c^2

       a^2 + 81 = 90                                             81 + 729 = c^2

       a^2 = 9                                                       810 = c^2

       a = 3                                                          9sqrt(10) = c

#6    27 + 3 = 30                                        #9  cos(90) = 8/c

                                                                         8/-0.45 = c

                                                                         | 17 | = c  [not the exact value]

#7  8^2 + b^2 = 17^2                                 #8  2^2 + 15^2 = c^2

      64 + b^2 = 289                                          4 + 225 = c^2

      b^2 = 225                                                  229 = c^2

      b = 15  [not the exact value]                     15.3 = c  [not the exact value]

Sorry if something doesn't make sense and felt kind of rushed. Feel free to comment down below my answer if you have any questions and I'll try to clarify it the best I can.

Answer:

I think number one is 19

Step-by-step explanation:

The lengths of the sides and the measure of the interior angles of the

three triangles determines which of the triangles are congruent.

Correct response;

According to Side-Side-Side postulate, two triangles are congruent if

the lengths of the three sides of one triangle are equal to the lengths of

the three sides of the other triangle

The lengths of the sides of the second triangle  are;

The side length of the third triangle are;

Therefore; the second and the third triangles are congruent.

However, the side lengths of the first triangle are;

Given that the two of the sides of the first triangle are equal to 2.6

centimeters, while non of the sides of the second and third triangle are

equal, we have;

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I am sorry, I am late but for future people here is the answer. :))

Answer:

3y

Step-by-step explanation:

All three expressions have the factor 3, and all three have the factor y.  Thus, the GCF is 3y.

Check the picture below.

we can simply get the volume of the larger sphere, then the volume of the smaller sphere and subtract it from that of the larger sphere and what's leftover is the region between both.

[tex]\stackrel{\textit{\large volumes}}{\stackrel{\textit{sphere with r=6}}{\cfrac{4\pi (6)^3}{3}}~~ -~~\stackrel{\textit{sphere with r = 3}}{\cfrac{4\pi (3)^3}{3}}}\implies 288\pi -36\pi \implies 252\pi \approx \stackrel{cubic~units}{791.68}[/tex]

The region within the larger sphere and not within the smaller sphere is 789.02 cubic units.

The volume of sphere is the measure of space that can be occupied by a sphere.  If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³

Given that, there are two concentric spheres of radii 3 units and 6 units.

Now,

Volume of sphere with radius 3 units is

V₁ = 4/3×3.14×3³

= 4/3×3.14×27

= 4×3.14×9

= 113.04 cubic units

Volume of sphere with radius 6 units is

V₂ = 4/3×3.14×6³

= 4/3×3.14×216

= 902.06 cubic units

Now, difference is 902.06-113.04

= 789.02 cubic units

Therefore, the region within the larger sphere and not within the smaller sphere is 789.02 cubic units.

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Answer:

this is what to do

Step-by-step explanation:

The formula for calculating the sales tax on a good or service is selling price x sales tax rate, and when calculating the total cost of a purchase, the formula is total sale amount = selling price + sales tax.

The equation will be A(x) = 5 + 2x and the independent variable will be the number of coffee cups that are purchased.

Since the program costs $5 per month which allows her to get a discounted coffee price of $2.5 per cup.

The independent variable x, represents the number of coffee cups purchased. The dependent variable is the total monthly cost.

The function is A(x) = 5 + 2x. The cost for 10 cups will be:

= 5 + 2x

= 5 + 2(10)

= 5 + 20

= 25

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