Without using a calculator evaluate:
- 81 + 203²

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

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.

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:

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

Answer:

$.08 per pound

Step-by-step explanation:

Take the total cost and divide by the number of pounds

6.80 / 88 lbs

$.077272727 per pound

Rounding to the nearest cent

$.08 per pound

Look at the pics

Step-by-step explanation:

360÷9=40°

2x+40=180

2x=180-40

2x=140

x=140÷2

x=70

angle is

2×70=140°

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

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:

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:

It's good

Step-by-step explanation:

7 x 60 = 420.

So, she will get the complete money

2(x - 6) + 6 = 4x - 4

Multiply 2 with x - 6

2x - 12 + 6 = 4x - 4

2x - 6 = 4x - 4

Change the position of them

2x - 4x = -4 + 6

- 2x = 2

Take -2 to other side and divide

[tex]x \: \: = \frac{2}{ - 2} [/tex]

x = -1 answer

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:12+h

Step-by-step explanation:

Explanation:

We assume the problem statement is telling us that the order of points on segment QR is Q, A, B, R, and that QA = AB = BR. This means that

  QB = QA +AB = 2BR

  BR = 1/2(QB)

The area of the triangles will be ...

  A = 1/2bh

For triangle PQB, the area is ...

  ar(PQB) = 1/2(QB)h . . . . . h is the perpendicular distance from QR to P

For triangle PBR, the area is ...

  ar(PBR) = 1/2(BR)h = 1/2(1/2QB)h . . . . h is the same as above

  ar(PBR) = 1/2ar(PQB)

__

Essentially, you're showing the base of the smaller triangle is 1/2 the base of the larger one and using that to show the area of the smaller triangle is 1/2 the area of the larger one. (Both have the same height.)

Answer:

5 weeks

Step-by-step explanation:

x(number of weeks)

5+2x=15

2x=10

x=5

(verification)

5+2*5=15

15=15

Answer:

BD = 4.99 units

Step-by-step explanation:

Consider the triangle ABD only. The angle formed is 31 degrees which occurs between two sides that are AD and BC. We know that for a right angled triangle, the angle can always be taken as an angle between hypotenuse and base. Thus, The perpendicular sides is then 3 units, where base is BD and Hypotenuse is AD Using formula for tanθ tanθ = Perpendicular/Base tan31 = 3/BD 0.601 = 3/BD BD = 3/0.601 BD = 4.99 units

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:

4/3.28

Step-by-step explanation:

Answer:

4/3.28

Step-by-step explanation:

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:  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:

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.

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

Answer:

51.428

Step-by-step explanation:

hope it helps alot

Answer:

62.83m

Step-by-step explanation:

The formula for circle circumference is

[tex]2 \times \pi \:\times r[/tex]

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

Learn more about equations on:

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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.