find the quotients in the exponential forms by using laws of indices.
8^{2} ÷2^{10}=?

The system of equation have one solution.

x² + y² = 25

x² - 6 = 0

x² = 6

x = √6

Therefore, let's substitute the value of x in equation (i)

x² + y² = 25

(√6)² + y² = 25

y² = 25 - 6

y² = 19

hence,

y = √19

Therefore, the system of equation have one solution.

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Answer:

7x - 9x = 26

Step-by-step explanation:

9 times a number = 9x

7 times the number = 7x

=26 because it says so

and 9x subtracted from 7x is 7x - 9x

The computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.

It should be noted that the subtraction line is simply used to subtract numbers.

In this case, the computation of the subtraction implies that 99.09 minus 98.29 will be 0.80.

When subtracting the numbers on the number line, we will move towards the left hand side of the number line.

An illustration of the number line is given.

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The value of a is (c) 86

The given parameter is:

Angle C = 86

By vertical angle theorem, we have:

Angle A = Angle C = 86

This implies that:

Angle A = 86

The arc A subtends angle A

This means that:

Arc A = 86

Hence, the value of a is (c) 86

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Answer:

(C) 496

Step-by-step explanation:

area = 100 yd × 372 yd = 37,200 yd²

37,200 yd² / 75 yd² = 496

Answer: (C) 496

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Random note:}[/tex]

[tex]\large\textsf{(We will solve for your given question as well because it}\\\large\textsf{pops up in solving for your question.)}[/tex]

[tex]\huge\textbf{Solving for your original answer:}[/tex]

[tex]\mathbf{5 + 10x = 20}[/tex]

[tex]\mathbf{10x + 5 = 20}[/tex]

[tex]\huge\textbf{SUBTRACT 5 to BOTH SIDES:}[/tex]

[tex]\mathbf{10x + 5 - 5 = 20 - 5}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{10x = 20 - 5}[/tex]

[tex]\mathbf{10x = 15}[/tex]

[tex]\huge\textbf{DIVIDE 10 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{10x}{10}=\dfrac{15}{10}}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{x = \dfrac{15}{10}}[/tex]

[tex]\mathbf{x = \dfrac{15\div5}{10\div5}}[/tex]

[tex]\mathbf{x = \dfrac{3}{2}}[/tex]

[tex]\mathbf{x = 1 \dfrac{1}{2}}[/tex]

[tex]\mathbf{x = 1.5}[/tex]

[tex]\huge\textbf{Therefore, the overall answer should be:}[/tex]

[tex]\huge\boxed{\star\boxed{\mathsf{\ x= \dfrac{3}{2} \ }}\star}[/tex]

[tex]\huge\textbf{And to answer your question, the very}\\\\\huge\textbf{first step in solving for this equation}\\\\\huge\textbf{[5 + 10x = 20] is:}[/tex]

[tex]\huge\boxed{\textsf{Option D. Subtract 5 to both sides}}\huge\checkmark\\\\\\\\\\\large\text{Look at the explanation above to see how we chose that.}\\\\\large\text{Remember: addition opposite is subtration \& subtraction opposite}\\\large\text{is addition, whereas multiplication is division \& divsion is}\\\large\text{is multiplication.}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

30+20+50 = 100 ml total. 20 ml is orange juice.

So, 30/100 reduce by dividing top and bottom by 30 gives

3/10 is the proportion of orange juice in the fruit cocktail.

Hope this helps! :)

Answer:

3/10

Step-by-step explanation:

First, find the total amount of liquid for a drink with 30 mls of orange juice
Assume volumes can be added
30+20+50 = 100 ml
the percentage/proportion of orange juice in the drink is the number of mls of orange juice divided by the total volume
so
30/100
which can be reduced to 3/10

Answer: 6

Step-by-step explanation:

    We will set up a proportion to solve. Let x be equal to ?.

[tex]\displaystyle \frac{3}{5} =\frac{x}{x+4}[/tex]

    Now, we will cross-multiply.

3 * (x + 4) = 5 * x

3x + 12 = 5x

12 = 2x

6 = x

The  size of the sample should be obtained at 2401 in order to be 95% confident

Given that:

Margi of error, [tex]ME=0.02[/tex]

Population proportion, [tex]p=0.50[/tex]

To Find: The size of the sample that should be obtained in order to be 95% confident

Let the size of the sample be n

Using formula,

[tex]n=(p*(1-p))*(z(0.05/2)/ME)^{2} \\n=(0.5*(1-0.5))*(1.96/0.02)^{2} \\n=0.25*9604\\n=2401[/tex]

Therefore, the size of the sample should be obtained at 2401 in order to be 95% confident

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The angle through which ΔABC is rotated is; Option A: 48°

Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but preserves its length and shape. Thus, a rotational transformation is formed by two reflections.

In the given question, image ABCD is reflected over lines I, then m at an angle of 24° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 24 * 2 = 48°

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Answer:

Step-by-step explanation:

Since the new line is parallel to the one that has a slope of 1, we can write:

y = 1x + b for the new line

Remember that y=mx+b, where m is the slope and b the y-intercept, the value of y when x=0.

We need to find a value of b that forces the line through point (1,-1).  Use (1,-1) in the equation and solve for b:

y = 1x + b

-1 = 1*(1)+b

b = -2

The equation of the line parallel to one with slope of 1 and going through point (1,-1) is:

y = 1x - 2

The only option that represents the correct repeating decimal is; Option C; 0.35 + 0.0035 + 0.000035

We want to find the option that is equal to the repeating decimal 0.353535.

Option A; 35 + 0.35 + 0.0035

When we add the above, we arrive at 35.3535 which is not equal to 0.353535. Thus, option A is incorrect.

Option B; 0.0035+ 0.000035 + 0.00000035

When we add the above, we arrive at 0.00353535 which is not equal to 0.353535. Thus, option B is incorrect.

Option C; 0.35 + 0.0035 + 0.000035

When we add the above, we arrive at 0.353535 which is not equal to 0.353535. Thus, option C is correct.

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Answer:

1.) C - 0.35+0.0035+0.000035+...

2.) The first term of the geometric series is 0.35.

3.) The common ratio of the geometric series is 0.01

4.) The simplified fractional representation of 0.353535... is 35 / 99

Step-by-step explanation:

Edge

Answer:

y = 3x - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-(-6)}{2-0}[/tex] = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6

y = 3x - 6 ← equation of line L

Answer:

Hence the expression [tex]$$(m+11)(m-4)=m^2+7m-44$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}[/tex]

_____________

[tex]{\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$[/tex]

The equation of the trend line is y = 3x + 15

Start by entering the table of values in a graphing calculator.

From the graphing calculator, we have the following summary:

The equation of the trend line is represented as:

y = bx + a

Where

b = SP/SSX = 52.5/17.5 = 3

a = MY - bMX = 25.5 - (3*3.5) = 15

This gives

y = 3x + 15

Hence, the equation of the trend line is y = 3x + 15

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The time taken to burn off the entire pizza by walking is 568.32 minutes.

2,368 = 125 × w

2,368 = 125w

w = 2,368 / 125

w = 18.944

Total time needed to burn all calories = 30 minutes × 18.944

= 568.32 minutes

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Option 3 and 4. The two options that shows the correct representation of the inequality are:

–3(2x – 5) < 5(2 – x)

We have to open up the brackets by multiplying the sides

= -6x + 15 < 10 - 5x

Hence the  third option is certified to be correct.

Next this inequality has to be shown on a number line.

To do this we have to solve the inequality completely

From -6x + 15 < 10 - 5x

we have to take like terms

-6x+5x < 10 - 15

-x < -5

x<5

The sign of inequality has to be reversed given that the coefficient of x was negative.

Hence x>5. The number line would start from the right and it would move towards the right

From the solution here, we can see that the two correct options are

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The least distance from point P to line l is approximately equal to 3.536 units.

There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:

Vector parallel to the line l

[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]

[tex]\overrightarrow{AB} = (3, - 3)[/tex]

A vector from one point on the line l to the point P

[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]

[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]

Now we proceed to find the vector distance by using the following vectorial formula:

[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]

[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]

[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]

[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]

[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]

The magnitude of the vector distance is determined by Pythagorean theorem:

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]

d ≈ 3.536

The least distance from point P to line l is approximately equal to 3.536 units.

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The measure of angle QS based on the information given when Point R is between points Q and S is 11x + 35.

From the information given,

PR = 3x + 7

QR = 8x + 28

The value of QS will be:

PR + QR

= (3x + 7) + (8x + 28)

= 11x + 35

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Answer:

b = 24 meter

Step-by-step explanation:

Using Pythagoras theorem:

a² + b² = c²

Here given: a = 10 m, b = ?, c = 26 m

Insert values

10² + b² = 26²

b² = 26² - 10²

b² = 676 - 100

b² = 576

b = √576

b = 24

Answer:24

Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.

so according to formula,h squared=b squared+p squared

so,26 squared=10 squared+p squared.

in order to find p

p squared=26 squared -10 squared

which gives us 576

and p squared =576

the square on the p will go on the other side and become an underroot.

take the underoot of 576

which gives us p=24.

so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula

1 gallon (gal) = 128 fluid ounce (fl oz)

1 hour (hr) = 60 minutes (min)

Convert 1 fl oz/min to gal/hr.

[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]

Answer: 2.96% rounded

Step-by-step explanation: 10/30) x (9/29) x (8/28)  =  720 / 24,360 = 6/203 = 2.96%

Answer:

56.8 m²

Step-by-step explanation:

This shape is clearly a trapezium / trapezoid. So :  

Area of a trapezium is given by the formula :

[tex]\frac{a+b}{2} h[/tex]

Substitute values given in diagram :

a = 4.2

b = 10

h = 8

[tex](\frac{4.2+10}{2} )8[/tex]

7.1 × 8 = 56.8

Units will be m² as this is area

Giving us our final answer of 56.8 m²

There are 84 possible student body governments

The given parameters are:

Senior = 7

Junior = 3

Sophomore = 4

The number of student body governments is calculated as:

n = Senior * Junior * Sophomore

This gives

n = 7 * 3 * 4

Evaluate

n = 84

Hence, there are 84 possible student body governments

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The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

Lets simplify the problem,

Let assume  the "tens" digit be x

Then the "units" difference =  (x-1), according to the condition.

Hence, the number itself is N = 10x + (x-1).

Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.

From the last statement of the problem, we have this equation

[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]

Simplify and find "x"

[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].

Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

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The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

The lines are given as:

y = -14x + 3 and y = -32x+3

Substitute y = -32x+3 in

-32x+3 = -14x + 3

Evaluate the like terms

-18x = 0

Divide by -18

x = 0

Substitute x = 0 in y = -14x + 3

y = -14(0) + 3

Evaluate

y = 3

Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)

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Answer:

Here you go with your correct answer

Answer:

Slope=14.000/2.000=7.000

x-intercept = 300/-7 = -42.85714

 y-intercept = 300/1 = 300.00000

Step-by-step explanation:

Answer: [tex]6.2 *10^9[/tex]

Step-by-step explanation:

Scientific notation is large numbers expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10

So the first number cannot be 6200 or 62 or 0.6, it has to be 6.2 because 6.2 > 1 and 6.2 < 10

count your numbers right of the decimal and you should get:

[tex]6.2 *10^9[/tex]

Answer:

l = (S/pi)-r^2

Step-by-step explanation:

Just rearrange the equation.

S = pi*l + pi * r^2

S-pi*r^2 = pi*l

l = (S-pi*r^2)/pi

l = (S/pi)-r^2