B. Determine the principal
1. √64
2. √100
3. √169
4. √196
5. √256
how please​

Answer:

y = [tex]\sqrt{(k-a)}[/tex]

Step-by-step explanation:

k= y^2 + a

k-a= y^2

y^2 = k-a

y = (k-a)^(1/2)

y = [tex]\sqrt{(k-a)}[/tex]

Answer:

[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]

Step-by-step explanation:

To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².

[tex]\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}[/tex]

Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)

Then square root both sides to get rid of the exponents of y-term:

[tex]\displaystyle{\sqrt{k-a}=\sqrt{y^2}}[/tex]

If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:

[tex]\displaystyle{\pm \sqrt{k-a}=y}[/tex]

Therefore, the new equation written in term of y is:

[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]

number 9 is 36  12x3 is 36

The runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.

We need to select all the runners whose speeds are in a proportional relationship with each other.

We find the speed using formula, speed = distance / time

Name         Time (seconds)           Distance (miles)              Speed(mps)

Liam                   306.6                           0.5                      0.5/306.6 = 0.0016    

Taylor                756.36                          1.2                      1.2/756.36 = 0.0016

Sarah                 504.35                         0.7                     0.7/504.35 = 0.0014

Ashley               459.9                          0.75                    0.75/459.9 = 0.0016

Connor              600.5                              1                          1/600.5 = 0.0017

Nathan               942.75                         1.5                     1.5/942.75 = 0.0016

Juan                   827.82                         1.35                  1.35/827.82 = 0.0016

Katie                   429.48                          0.6                   0.6/429.48 = 0.0014

Therefore, the runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

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0.08891% percent of people have a blood pressure reading greater than 145.

acc to our question-

Hence, 0.08891% percent of people have a blood pressure reading greater than 145.

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Answer:

 3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16 

Step-by-step explanation:

Hope it helps you buddy(:

Answer: 16

You already got the answer- But whatever.

The values of [x], [y] and [z] are 2, 0 and 7.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have the following system of equation -

3x+y-4z=-22

2x+3y+4z=32

x-y+2z=16

We can write -

x - y + 2z = 16

x = 16 + y - 2z

So, we can write 3x + y - 4z = -22 as -

3(16 + y - 2z) + y - 4z = -22      ...eq[1]

and we can write 2x + 3y + 4z = 32 as -

2(16 + y - 2z) + 3y + 4z = 32      ...eq[2]

Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.

We get y = 0 and z = 7

So -

x = 16 + 0 - 14

x = 2

Therefore, the values of [x], [y] and [z] are 2, 0 and 7.

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Answer:

I think it is y = -3x + 2

Step-by-step explanation:

The percentage of variation in variable can be accounted for by the other variable is 81%.

What is variation in statistic?

The statistical distance between the values of the observations (data points) is what makes up a measure of variance. There are various ways to measure variation.

What is correlation coefficient?

A statistical indicator of the strength of a linear link between two variables is the correlation coefficient.

The formula of percentage of variation is:

(correlation coefficient × correlation coefficient × 100)%.

Given that the correlation coefficient is 0.90.

Thus the percentage of variation is (0.90 × 0.90 × 100)% = 81%

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Answer:

Step-by-step explanation:

(12-5)x4=28

Answer:

y=5x+1

Step-by-step explanation:

we already know the slope so we can put it in the slope intercept form

y=5x

And now we can put the coordinate points in there to find the y intercept

-4=5(-1)

-4=-5

We need to add 1 to make this equation true so the y intercept is 1

The equation will be

y=5x+1

Hopes this helps please mark brainliest

Answer:

y=5x+1

Steps are in the picture

Answer:

40 cm²

Step-by-step explanation:

Let,

length ( l ) = 4 cm

Height ( h ) = Width ( w ) = 2 cm

To find : Surface are of cuboid : -

Formula : -

Surface are of cuboid = 2 [ lh + hw + wl ]

Surface are of cuboid

= 2 [ ( 4 )( 2 ) + ( 2 )( 2 ) + ( ( 2 )( 4 ) ]

=  2 [ 8 + 4 + 8 ]

= 2 [ 20 ]

= 2 x 20

= 40 cm²

1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4

2. Using the function table, the test average for science class is after the second test is: 84.

3. f(4) = 79.8

4. g(4) = 80

5. Science class was higher.

The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.

The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79

Write the linear function for science class;

Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1

Slope (m) = -2

Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:

82 = -2(3) + b

82 = -6 + b

82 + 6 = b

88 = b

b = 88

Substitute m = -2 and b = 88 into g(x) = mx + b:

g(x) = -2x + 88

Part 1:

Substitute x = 2 into .f(x) = 0.2x + 79

.f(2) = 0.2(2) + 79

.f(2) = 79.4

Test average for maths class after 2 test is: 79.4

Part 2:

Using the function table, when x = 2, the test average for science class is: 84.

Part 3:

Substitute x = 4 into  .f(x) = 0.2x + 79

.f(4) = 0.2(4)+ 79

.f(4) = 79.8

Part 4:

Substitute x = 4 into g(x) = -2x + 88

g(4) = -2(4) + 88

g(x) = 80

Part 5:

Science class had a higher test 4 average of 80.

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Answer:

to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

Step-by-step explanation:

Answer:

b & d

Step-by-step explanation:

Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.

Proportion refers to the quantity of a value or variable contained in another value.

Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.

Proportions are depicted using fractions, decimals, or percentages.

The number of avocados required for 4 orders of guacamole = 6.5

The total number of orders of guacamole required = 14

The number of avocados to make 1 order = 6.5/4

The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)

Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.

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Answer:

SAS

Step-by-step explanation:

If two sides and the included and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. The included angle is the angle formed by the two sides.

EF = BC

∠ F = ∠ C

DF = AC

then the two triangles are congruent by the SAS postulate.

Answer:

SAS

Step-by-step explanation:

On triangle one and two, they both start by having a congruent side, then a congruent angle, then another congruent side, thus making these triangles congruent by Side Angle Side.

It can't be AAS because there is only one angle, we know is congruent.

It can't be SSS because there are only two sides, we know are congruent.

It can't be HL because there is no right angle, meaning these aren't right triangles.

The statement which is true about this equation is that: C. The equation has no solution.

In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.

This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.

From the information provided above, we have this equation:

3(-y + 7) = 3(y + 5) + 6

Opening the bracket, we have the following:

-3y + 21 = 3y + 15 + 6

Next, we would rearrange the equation by collecting like terms as follows:

-3y + 21 = 3y + 21 (no solution)

-3y - 3y = 21 - 21

-6y = 0

y = -0/6

y = 0

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Answer:

x = 14

Step-by-step explanation:

the inscribed angle JKL is half the measure of its intercepted arc, that is

83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction

166 = 9x + 40 ( subtract 40 from both sides )

126 = 9x ( divide both sides by 9 )

14 = x

Answer:

1) 71.83

2) 43

3) 41

4) 755.66

5) 458

6) 1757.12

7) 123 meters

Answer:

59/15

Step-by-step explanation:

8/5 + 7/3                       Multiply the numerator and denominator by the LCF of the denominator

(3/3) 8/5 + 7/3 (5/5)      Multiply

24/15 + 35/15                Add the numerators

59/15

Answer:

d+12/3

Step-by-step explanation:

*= multiply /= fraction ALL OVER= fraction over fraction

find the common denominator-

d/3+4

d/3+3*4/3

combine fractions with the common denominator

d/3+3*4/3 ALL OVER d+3*4/3

multiply

d+3*4/3 ALL OVER d+12/3

The required positive number whose product is 25 and whose sum is minimum is 5, 5

Sum of two numbers means adding two same or different number together

Let two positive numbers xy = 25

Divide both side by x

y  = [tex]\frac{25}{x}[/tex]  ----------Equation (1)

Sum of two positive numbers s = x + y  -------Equation (2)

Substitute equation (1) into equation (2)

S = x + [tex]\frac{25}{x}[/tex]

differentiate with respect to x

[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]

[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex]  ---------- Equation (3)

[tex]\frac{ds}{dx} = 0[/tex]

[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0  ⇒ [tex]x^{2}[/tex] = 25

x = 5

Differentiate equation (3) again

[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]

hence, at point x = 5,   [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex]  [tex]= \frac{50}{25} = 2[/tex]

Value of s minimum at point x = 5.

substitute the value of x into equation (1)

[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]

Therefore the required positive numbers are 5, 5.

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The area of the  triangle to the nearest hundredth of a square meter is 0.217m²

A right triangle has a hypotenuse of 1 meter and a leg of 1/2 meter

Hypotenuse = 1

base = 0.5

We need to calculate the perpendicular

h² = b² + p²

1² = 0.5² + p²

p² = 1 - 0.25

p = √0.75

p = 0.866

area of the triangle = 1/2 base x height

area = 1/2 (0.5 x 0.866)

area = 0.2165m²

Therefore the area of the  triangle to the nearest hundredth of a square meter is 0.217m²

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The simplified for of the Algebraic expression which is the sum of two terms is 1 + 7x

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms which can either be a variable or a constant .

11 + 5(3x - 2) -8x

multiply out the bracket we have,

11 + 15x - 10 -8x

collect like terms and simplify

11 - 10 + 15x - 8x

1 + 7x

In conclusion, the expression 11 + 5(3x - 2) as a sum of two terms is 1 + 7x

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Answer:  The correct answer is x=−3 or x=5

Step-by-step explanation:

Solve for x^2−2x=15 using the quadratic equation

Step 1) Subtract 15 from both sides

x2−2x−15=15−15

x2−2x−15=0

For this equation: a=1, b=-2, c=-15

1x2+−2x+−15=0

Step 2) Use quadratic formula with a=1, b=-2, c=-15

x= (−b±√b2−4ac)/2a

x= (−(−2)±√(−2)2−4(1)(−15))/2(1)

x= (2±√64)/2

x=5 or x=−3

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The volume of solid B is 1350 [tex]cm^{3}[/tex].

What is the volume ratio?

The side length ratio raised to the third power represents the volume ratio for the two solids.

If two solids are comparable, their volumes will have a ratio that is equal to the cube of their corresponding side ratios.

Given that both solids are similar.

The volume of solid A = 400 [tex]cm^{3}[/tex]

height of solid A = 10 cm

height of solid B = 15 cm

the volume of solid B = ?

Now,

volume of solid A/ volume of solid B = (height of solid A)^3/(height of solid B)^3

or, [tex]\frac{400}{x} = \frac{10^{3} }{15^{3} }[/tex]

or, [tex]x = \frac{400*15^{3} }{10^{3}}[/tex]

or, [tex]x = \frac{400*3375 }{1000}[/tex] = 1350

Hence, the volume of solid B is 1350 [tex]cm^{3}[/tex].

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The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval  (4, −∞).

What is an increasing and decreasing functions?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We have,

[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]

[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 4, 4i, −4i, 10, 8

∴ f′(x) = 0  

   x = 4,

Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)

In interval (−∞, 4),  f′(x) < 0

Hence, the given function (f) is strictly decreasing in interval (−∞, 4)

​

In interval (4, −∞),  f′(x) > 0

Hence, the given function (f) is strictly increasing in interval  (4, −∞)

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​

Answer:

6.6

Step-by-step explanation:

you subtract 6.6 from both sides to cancel it out on one side

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By using the rule of 3 we wills ee that the percentage of students who play the trumpet is 20%

We know that there are 150 students in the marching band, that will be our 100% in this case, and we know that 30 of them play the trumpet.

These 30 students represent a percentage X that we want to find, so we can write a little system of equations and use the rule of 3.

30  = X

150 = 100%

Taking the quotient between the two equations we get:

(30/150) = X/100%

Solving for X we get:

(30/150)*100% = X = 20%

So we can say that 20% of the students play the trumpet.

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The slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a equation of a straight line as -

4x - 1 = 3y + 5

We have the equation as follows -

4x - 1 = 3y + 5

Rearranging the equation -

3y = 4x - 1 - 5

3y = 4x - 6

y = (4/3)x - 2

Refer to the graph attached.

The slope of the line is [m] = 4/3

The [y] intercept is at [c] = -2

Therefore, the slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

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