Which choices are equivalent to the quotient below check all that apply. square root of 16 over square root of 8

In decimal form this is equal to -17.22.

The most appropriate choice for arithmetic and geometric series will be given by-

P = 0, Q = 4 , R = 8, S = 16 or P = 15, Q = 9, R = 3, S = 1 are the required numbers

What is arithmetic and geometric series?

Arithmetic series are those series whose difference between two consecutive terms are same.

Geometric series are those series whose ratio between two consecutive terms are same.

Here,

P, Q and R forms an Arithmetic sequence

Let P = a - d , Q = a, R = a + d, Where a is the first term of the Arithmetic sequence and d is the common difference of the sequence.

Let S = b

Q, R and S forms a Geometric sequence

[tex]\frac{a + d}{a} = \frac{b}{a +d}[/tex]

[tex](a + d)^2 = ab\\a^2 + d^2 + 2ad = ab\\[/tex] ............... (1)

Now the sum of first and fourth number is 16

a - d + b = 16

b = 16 - a + d

Putting the value of b in (1),

[tex]a^2 + d^2 + 2ad = a(16 - a +d)\\a^2 + d^2 + 2ad = 16a -a^2+ad\\a^2+a^2 + d^2+2ad - ad - 16a = 0\\2a^2 + ad+d^2 -16a = 0[/tex]............ (2)

Sum of second and third number is 12

[tex]a + a + d = 12\\2a +d = 12\\d = 12-2a[/tex]

Putting the value of d in (2)

[tex]2a^2 + a(12 - 2a)+(12 - 2a)^2-16a = 0\\2a^2 + 12a - 2a^2+144-48a+4a^2 - 16a = 0\\4a^2-52a+144=0\\4(a^2-13a+36)=0\\a^2 -13a+36=0\\a^2-9a-4a+36=0\\a(a - 9)-4(a-9)=0\\(a-4)(a-9) = 0\\[/tex]

[tex]a - 4 = 0[/tex] or [tex]a - 9 = 0[/tex]

[tex]a = 4[/tex] or [tex]a = 9[/tex]

When a = 4,

[tex]d = 12 - 2\times 4\\d = 12 - 8\\d = 4[/tex]

[tex]b = 16 - 4+4\\b = 16[/tex]

P = 4 - 4 = 0

Q = 4

R = 4 + 4 = 8

S = 16

When a = 9,

[tex]d = 12 - 2\times 9\\d = 12 - 16\\d = -6[/tex]

[tex]b = 16 - 9-6\\b = 1[/tex]

P = 9 - (-6) = 15

Q = 9

R = 9 + (-6) = 3

S = 1

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Consider the figure,

So, we have, Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

So, here, [tex]<\text{AHB}+z=180[/tex]

Therefore, z can be calculated as,

Now, the angles DHC and

Answer:

C. Neither

Explanation:

The SSS Congruence Rule states that if the three sides of a triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SAS Congruence Rule states that if the two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles are congruent.

Notice that in the given triangles, there are two congruent sides and a non-included angle, since this does not satisfy any of the rules stated above, SSS Congruence rule or SAS Congruence rule, we'll choose "neither" as the correct answer.

a)

We need to convert 1.96 x 10^-5 meters. into standard notation.

Now, on the scientific notation, the power of ten shows how many places the decimal point has been moved.

- If the exponent is positive then the decimal point has been moved to the left.

- If the exponent is negative, then the decimal point has been moved to the right.

In this case, the power is negative 5 . So, the decimal point has been moved 5 places to the right.

Hence:

1.96 x 10^-5 = 0.0000196

b)

a. Meters

First, we need to convert kilometers into meters using the rule of three:

If 1k = 1000 meters

Then 12,100k = x

Where x = (12,100k*1000m)/ 1k

x =12000000 meters

We need to convert from standard notation to scientific notation:

12000000.0 = 1.2x10^7 meters

The decimal point has been moved 7 places to the left, so the power of then is positive 7.

b) We need to convert 12,100 kilometers into scientific notation:

12,100 = 12,100.0

Converting into scientific notation

1.21x10^4 kilometers

The decimal point has been moved 4 places to the left. Hence, the power of the is positive 4.

The point-slope form of a line is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Replacing with m = 1 and the point (4, -3):

y - (-3) = 1(x - 4)

y + 3 = x - 4

Express p in terms of x : p = 5x

What is Percent?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

If 5% of an adult's daily potassium requirement is provided by each serving of Crunchy Grain cereal, then x servings will offer x times 5%.

Five times as many servings, or p, of potassium are required for an adult's daily requirement.

As a result,

p = 5x can be used to describe the proportion of potassium in an adult's daily allotment.

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The rate of yen per Indian rupee is 1.6

How do you convert currency to another currency?

Divide your current currency by the exchange rate if you are aware of it.

Assume, for instance, that you want to change 100 USD into EUR and the USD/EUR exchange rate is 0.631. Simply multiply 100 by 0.631 to do this, and the result is 63.10 EUR, which is the amount you will receive.

Given, 2000 Yen = 16 Euros

and, 40 Euros = 3,125 Indian Rupees

Find rate of yen per India rupee

1 Euro = 2000/16

1 Euro = 125 yen

And, 1 Euro = 3125/40

1 Euro =  78.125 India rupee

Now, find 1 yen = ? Indian rupee

we know,  1 Euro = 125 yen and 1 Euro =  78.125 India rupee

put the values of euro in India rupee in 1 Euro = 125 yen, we get

78.125 India rupee  = 125 yen

1 India rupee = 125 / 78.125

1 Indian rupee = 1.6 Yen

Therefore, the rate of yen per Indian rupee is 1.6

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Solution

Gievn the equation below

To find the vertex and focus of the given equation, we apply the parabola standard equation which is

Where p is the focal length and the vertex is (h,k)

Rewriting the equation in standard form gives

Relating the parabola standard equation with the given equation, the vertex of the parabola is

Hence, the vertex is (3,0)

The focus of the parabola formula is

Where

Substitute the values of h, k and p into the focus formula

Hence, the focus is (3, 1)

Collinear points are two or more points that lie on the same line.

For Example:

Point A, B and C

Given :

The cost of 3 shirts and 5 sweaters is $99 .

The cost of 6 shirts and 4 sweaters is $90.

To determine :

The sweater cost and shirt cost each.

Explanation :

Let the shirt cost be x.

Let the sweater cost be y.

Then the equation formed is

Solve the equation 1 and 2 to find x and y with the help of elimination method.

Multiply by 2 in equation 1.

Solve equation 2 and 3 by subtraction,

The value of y is 18 and now substitute the value of y in equation 2 to find x.

The value of x is 3.

Answer :

The cost of shirt is 3 dollar .

The cost of sweater is 18 dollar.

Answer:

Σmf = 23347

Σm²f = 1621631

(Σmf)² = 545082409

Explanation:

The symbol Σ means that we need to sum all the products of m and f.

So, Σmf is equal to:

Σmf =76(94) + 37(92) + 27(63) + 98(62) + 62(81)

Σmf = 7144 + 3404 + 1701 + 6076 + 5022

Σmf = 23347

Then, to find Σm²f, we need to find the square of m, so:

Σm²f = (76)²(94) + (37)²(92) + (27)²(63) + (98)²(62) + (62)²(81)

Σm²f = 5776(94) + 1360(92) + 729(63) + 9604(62) + 3844(81)

Σm²f = 542944 + 125948 + 45927 + 595448 + 311364

Σm²f = 1621631

Finally, (Σmf)² is equal to:

(Σmf)² = (23347)²

(Σmf)² = 545082409

Therefore, the answers are:

Σmf = 23347

Σm²f = 1621631

(Σmf)² = 545082409

Answer:

x = 100degrees

Explanation:

Using the theorem;

The angle at the vertex is the half of the difference of its intercepted arcs

Angle at the vertex = 15 degrees

angle at the intercepted arcs = 70degrees and x degrees

According to the theorem;

15 = 1/2(x-70)

Cross multiply

15 * 2 = x - 70

30 = x - 70

Add 70 to both sides

30 + 70 = x - 70 + 70

100 = x

Swap

x = 100degrees

Hence the value of x is 100degrees

Answer:

25 feet

Explanation:

The equation that models the pathway of the container is:

The maximum height occurs at the axis of symmetry.

First, we find the equation of symmetry:

Next, determine the value of h at t=0.

The maximum height of the container is 25 feet.

If M(h,k) is rotated 90° counterclockwise about the origin, the new position would be M'(k, -h)

M(2, 4)-> M'(4, -2)

For this problem we have the following two numbers

Let's convert the two numbers with scientific notation

Now we just need to find a number between the two given we know that:

The final answer for this case would be any number between these two numbers and it could be:

also it could be:

Or any number between the two given

Answer:

The answer is B,D, And F

Step-by-step explanation:

7.1 × 103 = 7,100

7.1 × 105 = 710,000

Because 7,100 < 710,000 < 71,000,000 then 7.1 × 105 falls between 7.1 × 103 and 71,000,000

650 --- total

650*.68=442

442 students ate green bean casserole

.68 represents the percentage

so for example, if they asked me for 50% of 1000

we need to multiply 1000*0.5

if they asked for 60% we will multiply 1000*0.6

Given:

The equaiton that model height of the driver jumps from the ledge.

Requried:

We need to find the time taken by driver to enter the water.

Explanation

You have the following equation:

5x - 3y = -45

In order to solve the previous equation for y, you proceed as follow:

5x - 3y = -45 subtract 5x both sides

- 3y = -45 - 5x multiply by -1 both sides

(-1)(-3y) = (-1)(-45 - 5x)

3y = 45 + 5x divide by 3 both sides

y = 45/3 + 5/3 x order the right side

y = 5/3 x + 15

Hence, the solution for y is y = 5/3 x + 15

The equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)

The given equation of the perpendicular line

y = (1/4)x -7

The equation is in the slope intercept form of the line

y = mx+b

Where m is the slope of the line

By comparing the given equation with the slope intercept form

The slope of  the line m = 1/4

The slope of its perpendicular line = -1/m

= -4

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

The point is given that (-2,-6)

Substitute these values in the equation

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

y+6 = -4(x+2)

Hence, the equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)

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Given the algebraic expression below

The first term of the algebraic expression is

The first term "7s" is a variable term.

The variable of the first term is "s"

The coefficient of the variable term is 7

Andrew constructed a triangle such that the measurements of angles m<1 and m<2 are congruent.

The above statement can be inferred from concept of congruency of triangles. The oppsoite sides of the two congruent angles in a traingles are also equal.

From the above statement we can deduce the type of a triangle that Andrew drew as follows:

An isoceles triangle has two equal sides and angles i.e congruent sides and interior angles. Hence,

The following information is given for the third interior angle m<3 of the isoceles triangle:

We need determine the angle measure of the angle 1. Recall that the sum of interior angles of a triangle is given as follows:

Substitute Eq1 into Eq2 as follows:

Substitute the angle measurement of angle ( 3 ) in the expression above and solve for angle ( 1 ) as follows:

Given :

The table show a proportional relationship between the number of pounds and the total cost

so,

The probability of success (a hit) is given by:

p = 0.341

The complement (a failure) of this probability is:

q = 1 - 0.341 = 0.659

Then, we can construct a probability distribution for the first hit until his nth at-bat:

For his 5th at-bat, we have n = 5, then:

Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...

Step-by-step explanation:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Draw the given graph.

STEP 2: Get the function plotted on the graph.

Number of sandwiches = 80p

Given:

Laura produces 80 sandwiches per day

To find:

The number of sandwiches that will be produced in p days

1 day = 80 sandwiches

p days = 80 × p

p days = 80p

This means that she will produce 80p number of sandwiches in p days

The slope of a line, m, comes in the equation as the coefficient of x.

In the given equation, m= -5/4. Two perpendicular lines have slopes that are the negative reciprocals of each other.

So, the slope of the perpendicular line will be +4/5.

Between the given options, letter c will be:

4x-5y=15

-5y=15-4x (divided by -5)

y=4/5x-3

Letter C

The expression is given as,

Note that the denominator of both the fractions are prime numbers. So their lowest common multiple, LCM(2,3) will be the product of the numbers,