Find two positive integers whose sum is 16 and the sum of squares is minimum.

Step-by-step explanation:

let's use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

so,

5.4/sin(K/2) = 12.3/sin(M1)

8.2/sin(K/2) = x/sin(M2)

M1 + M2 = 180 (as complementary angles or linear pair)

M2 = 180 - M1

sin(K/2) = 5.4×sin(M1)/12.3

sin(K/2) = 8.2×sin(M2)/x

therefore

5.4×sin(M1)/12.3 = 8.2×sin(180 - M1)/x

since sin(a) = sin(180 - a)

5.4×sin(M1)/12.3 = 8.2×sin(M1)/x

and then

5.4/12.3 = 8.2/x

x×5.4 = 8.2×12.3

x = 8.2×12.3/5.4 = 18.67777777... ≈ 18.7

Step-by-step explanation:Step-by-step explanation:

let's use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

so,

5.4/sin(K/2) = 12.3/sin(M1)

8.2/sin(K/2) = x/sin(M2)

M1 + M2 = 180 (as complementary angles or linear pair)

M2 = 180 - M1

Answer:

x=9

y=-5

Or

(9,-5)

Step-by-step explanation:

-x+y=-14

+x.    +x

y=x-14

2x-3(x-14)=33

2x-3x+42=33

-x+42=33

   -42. -42

-x=-9

/-1. /-1

x=9

-(9)+y=-14

+9.      +9

y=-5

Hopes this helps please mark brainliest

Answer: 150 square inches

Step-by-step explanation:

Set up the proportional ratios (convert feet to inches first):

30 ft = 360 inches (there are 12 inches in 1 foot)

20 ft = 240 inches (I'm assuming there is an error in the question and the width is 20 ft, NOT 20 inches!)

360/15 = 240/x

x is the width of the scaled down rectangle

solve for x:

360x = 3600

x = 10 in

Now calculate Area = length x width

A = 15 x 10 = 150 square inches

The train will catch up with the dog in 1.996 seconds

The problem is solved using the formula for speed which is

distance / time

speed of the train = length of track / time

= 1900 / 40

= 475 m/s

speed of the dog is given to be 6 m/s

The relative velocity = 475 - 6 = 469 m/s

The time to catch up is calculated using relative velocity

469 * time = 936 meters

time = 936 / 469

= 1.996 seconds

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The boys in the class that wear glae are 6 people.

The boys in the class that wear glae can be calculated as follows:

First we should calculate how many boys there are in the class. We can calculate it by multiplying the percent of the boys to the total students.

Boys in the class = [tex]\frac{20}{100} X 50[/tex] = 10 people.

Thus, we can calculate the boys who wear the glae by multiplying the percent of the boys wearing glae of the boys in the class.

Boys wear glae = [tex]\frac{60}{100} X 10[/tex] = 6 people.

Hence, The boys in the class that wear glae are 6 people.

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The equation of the line into slope-intercept form is y = x/3 - 6

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have the following equation that can be used in our computation:

9y−3x= −54

Rewrite properly

This gives

9y - 3x = -54

Divide through the equation by 3

So, we have the following representation

9y/3 - 3x/3 = -54/3

Evaluate

3y - x = -18

To rewrite as slope-intercept form is to make y the subject

So, we have

3y = x - 18

Divide through the equation by 3

So, we have the following representation

y = x/3 - 6

Hence, the equation is y = x/3 - 6

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For minima,

C'(x) = 0

6x-30 = 0

x = 5

If C"(x) >0, then minima

So, C"(x) = 6 > 0

So, for x = 5 , thr value of C(x) will be minimum.

Option C is correct

Answer:

B

Step-by-step explanation:

product means multiplication and quotient is division , then

product of 8 and the quotient of 6 and w is

8 ([tex]\frac{6}{w}[/tex] )

Answer:

Graph

Step-by-step explanation:

graph the line x=1 (vertical line passing through point (1,0))with a dotted line and shade everything to the right of the line. Then graph the line y=x (line with slope 1 passing through origin) with a dotted line, shading everything above the line.

Answer:

8 hours

Step-by-step explanation:

We can use an algebraic equation to solve this problem.

7.5x + 10 = 70

7.5x + 10 (-10) = 70 (-10)

7.5x (/7.5)= 60 (/7.5)

x = 8

Answer: 41.7 feet from pitcher to 1st

13.2 feet from pitcher to 2nd

58 degrees to turn from home to 1st

distance from pitcher to the line from home to 1st is 57.5(sin45) = 57.5(.707) = 40.66

construct a right triangle with legs 40.66 and 50-40.66 = 9.34.  then sum the legs' squares, and take the square root to get 41.72 feet

distance from home to 2nd = hypotenuse of a right triangle with sides 50 and 50, and angle of 45 degrees

50^2 + 50^2 = 2(2500) = 5000.  sqr5000= 70.71,  subtract 57.5.    70.71-57.5= 13.21 feet from pitcher to 2nd

Step-by-step explanation:

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]y=-\cfrac{2}{3}x-1\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( -\cfrac{2}{3}x-1 \right)} \\\\\\ 3y=-2x-3\implies {\Large \begin{array}{llll} 2x+3y=-3 \end{array}}[/tex]

The mean is 76 and the standard deviation is 7.

What is mean and standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

In mathematics, particularly in statistics, there are various types of means. Each mean summarizes a particular set of data, frequently to help determine the overall significance of a particular data set.

Let, 95% of students in statistics scored between 62 and 90 points.

Here,

Mean = [tex]\frac{62+90}{2} = \frac{152}{2} = 76[/tex]

And the standard deviation is,

SD = [tex]\frac{90-76}{2}= \frac{14}{2} = 7[/tex]

Hence, the mean is 76 and the standard deviation is 7.

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Answer: 144 dresses in 1440 minutes.

Step-by-step explanation:

Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.

The rate is 120min/12dresses. Let's simplify it.

12/120 = 10min/1dress (or just 10)

Lets use this rate for 144 dresses

10 x 144 = 1140

It will take 1440 minutes to sell 144 dresses.

Answer:

The conclusion is false.

Step-by-step explanation:

If the conclusion is false, then the whole conditional is false even if the hypothesis is true.

Total earning = Salary + 10% of sales

According to question, we have

14000 = 9500 + 10% of sales

4500 = 0.1 sales

sales = 4500*10 = 45000

So, her total sales was Rs 45000

Answer:

739

Step-by-step explanation:

2217 (weight) / 3 ( # of blocks)

Answer:

20 dollar tip (rounded) assuming the bill is 68.37

Step-by-step explanation:

just multiply 68.37 by 0.25, and you get 17.09 or 20 dollars rounded to TENS place.

The depth of snowdrift changed from Thursdays to Friday by -4 inches

The change of depth of snowdrift from Monday to Thursday = -8  inches

From Thursday to Friday, the depth changed by half as much

The equation is the mathematical statement that shows the relationship between two expression with and equal sign. The equation may consist of variables, numbers and arithmetic operators

Then the equation will be

The change of depth of snowdrift from Thursday to Friday = -8 /2

Here we have to use the division

Divide the terms

The change of depth of snowdrift from Thursday to Friday = -4 inches

Hence, depth of snowdrift changed from Thursdays to Friday by -4 inches

The complete question is :

From Monday to Thursday, the depth of a snowdrift changed by -8 inches. From Thursday to Friday, the depth changed by half as much. What is the change in the depth of the snowdrift from Thursday to Friday?

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Answer:

y = 4x - 6

Step-by-step explanation:

linear equation:

y = mx + b

1. find the slope m

first select two point

im gonna take point 1 (-1,-7) and point 2 (3,9)

m = (y2-y1)/(x2-x1)

m = (9-(-7))/(3-(-1)) = 16/4 = 4

2. find b

first select a point

im gonna reuse point 2 (3,9)

y = mx + b

9 = 5(3) + b

9 = 15 + b

b = 9 - 15 = -6

3. keep x y, substitute m,b to linear equation

y = 4x - 6

The price per cup for a 2-pint bucket of paint costs $11.08 is $2.77.

It should be noted that 1 pint = 2 cup

In this case, 2-pint bucket will be:

= (2 × 2)

= 4 cups.

Therefore, 4 cups cost $11.08.

The price per cup will be:

= Total cost / Number of cups

= $11.08 / 4

= $2.77

The price is $2.77.

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4.21 x 10-9) (7.8 x 1015) = 32.838 * 10^6" ; the correct option is second.

4.21 * 10 ^ -9 * 7.8 * 10 ^ 15 = 32.838 * 10^6

so the correct option is second

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Answer:

4

Step-by-step explanation:

Let x be the unknown number.

[tex]\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}[/tex]

Solve the found equation for x:

[tex]\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}[/tex]

Therefore, the number squared is:

[tex]\implies x^2=2^2=4[/tex]

Answer:

Step-by-step explanation:

Let the number of 2 liter cans be x and 5 liter cans be y.

Number of cans:

Amount of paint:

Solve the system by elimination, double the first equation and subtract from the second one:

Find x:

Using the theories of Application of derivative,we got that  59.11221inches³/sec  is rate of volume changing when the radius is 2.3 inches.

We are given rate of change of radius (dr/dt)=0.6inches

We know very well that volume of sphere is given by (4/3)πr³

where r is the radius of the sphere.

Now, differentiating the volume with respect to radius, we get

=>dV/dr=4πr²

=>dV/dt=(dv/dr)·(dr/dt)

=>dV/dt=4πr².(dr/dt)

We are given that dr/dt=0.6inches/sec

So, dV/dt=4πr²·(0.6)

Now, putting values of r=2.3

 dV/dt=4π(2.3)²×(0.6)

=>dV/dt=4×3.14×2.3×2.3×0.6

=>dV/dt=59.11221inches³/sec

Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.

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The required value of the expression (2x − 12) + (1/2 xy - 10) for x = 8 and y = 2 is 2. Option D is correct.

First, let us understand the algebraic expression and how is it formed:

A multitude of strategies is used to build algebraic expressions utilizing variables and constants. It is a term-based mathematical expression that comprises variables, constants, and algebraic operations such as addition, subtraction, and so on.

We are given:

(2x − 12) + (1/2 xy - 10)

We need to find the value of the given expression for x = 8 and y = 2.

Substitute the values of x and y in the given expression, we will get;

(2 * 8 − 12) + (1/2 * 8 * 2 - 10)

= (16 − 12) + (8 - 10)

= 4 + (-2)

= 4 - 2

= 2

So, the obtained value is 2.

Thus, the required value of the expression (2x − 12) + (1/2 xy - 10) for x = 8 and y = 2 is 2. Option D is correct.

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The solution of this Algebraic Equation is -1.0

What is an Algebraic Equation?

An algebraic equation is a mathematical statement which establishes two expressions equal to each other. An algebraic equation is generally composed of a variable, coefficients, and constants.

Solution:

According to the question,

the algebraic equation given is,

(8.7 + x)/1.1 = 7

By cross multiplying

8.7 + x = 7.7

x = -1.0

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The probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.

What is probability?

Probability shows the likelihood of an event happening.  It can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No. of total no of cards =5

The probability the card drawn is a 3  =1/5

                                                             =0.2000

Therefore the probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.                      

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