Find the solution for the system of linear equations by substitution: 2x - y = 3 y − x = 1

Answer: 260 m

Step-by-step explanation:

Let's say the length of NR is x m, using the similarity rule, we get the equation

175/130 = (175+175)/x

x = 260

So NR is 260 m

Answer:

Step-by-step explanation:

1/3 + 1/3 x 1/3 / 1/3 - 1/3

= 1/3 + 1/3 x 1/1 -1/3

= 1/3 + 1/3 - 1/3

= 2/3 - 1/3

= 1/3

Answer:

5/9.

Step-by-step explanation:

1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3

= 1/3 + 1/3 * 1 - 1/3 * 1/3

= 1/3 + 1/3 - 1/3 * 1/3

= 2/3 - 1/9

= 5/9.

Answer:

y=-5x-12/5

Step-by-step explanation:

First you need to find y intercept

y=mx+b

plug in the points (0,12)

12=mx+0

now plug in -5

12=-5x+0

subtract 0 from both side

12=-5x

divide -5 from both side.

x=12/-5

The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).

It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².

On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.

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Answer: its C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

20 and 35 dollars.

Step-by-step explanation:

x + x + 15 = 55

2x + 15 = 55

2x = 55 - 15

2x = 40

x = 40/2

x = 20

One of the brothers has saved 20 dollars, while the other has 35 dollars.

The surface area of the cylinder is 18.84 square feet

The given parameters are

Height, h = 2 ft

Diameter, d = 2 ft

The radius (r) is half of the diameter (d)

This is calculated as:

Radius = Diameter/2

So, we have:

r = d/2

Substitute 2 for d

r = 2/2

Evaluate the quotient i.e. divide 2 by 1

r = 1

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2

Evaluate the exponents

A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2

Evaluate the products

A = 6.28 + 12.56

Evaluate the sum

A = 18.84

Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet

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Answer:

b=67.5°

Step-by-step explanation:

hope it helps!!!

Answer:

Side AB = [tex]9\sqrt{2}[/tex]

Side AB = [tex]9\sqrt{2}[/tex]

Side CB = 36

Step-by-step explanation:

This is a special right triangle and it's also an isosceles triangle

therefore the measure of AC = AB and they are both = [tex]9\sqrt{2}[/tex]

for this special triangle the measure of hypotenuse (CB in here) is represented with [tex]x\sqrt{2}[/tex] and the legs are represented with x, each

since legs' lengths are given as = [tex]9\sqrt{2}[/tex] then x = [tex]9\sqrt{2}[/tex]

replace the x in front of [tex]x\sqrt{2}[/tex] with  [tex]9\sqrt{2}[/tex]

[tex]9\sqrt{2}[/tex] *  [tex]\sqrt{2}[/tex] = 36

If there was just one of each animal, the outcome would be that of 1 cow and 1 dog.

Option(B) is correct.

The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function.

If you own two cats worth $100 each and a cow worth $2,500. One dog, though, is worth $7000.

Cost of 1 cow = $2500

Cost of 2 cats = $100

Thus, cost of 1 cat = $100/2 = $50

Cost of 1 dog = $7000

If there was only 1 of each animal, total cost = $(2500+50+7000) = $9550.

This outcome resembles the situation of having 1 cow and 1 dog.

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2x + 2y = 42

2w + q = 35

2w + v = 29

x + q + y - v = ?

x = 7

y = 14

w = 3

q = 29

v = 23

7 + 29 + 14 - 23 =

The answer is 27

Answer: [tex]\Large\boxed{27}[/tex]

Step-by-step explanation:

Given information converted into a mathematical statement

[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]

[tex]1)~a+b+a+b=42[/tex]

[tex]2)~c+d+c=35[/tex]

[tex]3)~c+c+e=29[/tex]

[tex]4)~a+d+b-e=\mbox{?}[/tex]

Simplify each equation

[tex]1)~2a+2b=42[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Factorize 2 out of the 1) equation

[tex]2a+2b=42[/tex]

[tex]2(a+b)=42[/tex]

Divide 2 on both sides

[tex]2(a+b)\div2=42\div2[/tex]

[tex]a+b=21[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Subtract 3) equation from the 2) equation

[tex](2c +d)-(2c+e)=(35)-(29)[/tex]

Expand the parenthesis

[tex]2c+d-2c-e=35-29[/tex]

Combine like terms

[tex]2c-2c+d-e=6[/tex]

[tex]d-e=6[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~d-e=6[/tex]

[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]

Substitute values into the 3) equation to determine the final value

  [tex](a+b)+(d-e)[/tex]

[tex]=(21)+(6)[/tex]

[tex]\Large\boxed{=27}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

  j = 19.6

  k = 25.9

  J = 49°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.

The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.

  Hypotenuse = Opposite/Sin

  IJ = 17/sin(41°) ≈ 25.9

  Adjacent = Opposite/Tan

 IK = 17/tan(41°) ≈ 19.6

  Angle J = 90° -41° = 49°

In summary, ...

  j = 19.6

  k = 25.9

  J = 49°

EachEach value of time elapsed (in seconds) corresponding instantaneous velocity (in feet/second) are:2s= 96, 3s = 64, 4s= 32, 5s = 0, 6s = -32, 7s = -64. 8s= -96, 9s= -128.

Given equation:

f(t) = -16t² +160t

Velocity (v)=df(t)/dt

=-2×16t²+ 160t

=-32t+160

Hence:

-32t+160

1.     -32×(1) + 160 =    128ft/s

2.    -32×(2) + 160 =    96ft/s

3.    -32×(3) + 160 =    64ft/s

4.    -32×(4) + 160 =     32m/s

5.    -32×(5) + 160 =     0m/s

6.   -32×(6) + 160 =   -32m/s

7.    -32×(7) + 160 =    -64m/s

8.   -32×(8) + 160 =    -96m/s

9.    -32×(9) + 160 =   -128m/s

The pairs are;

2s= 96

3s = 64

4s= 32

5s = 0

6s = -32

7s = -64

8s= -96

9s= -128

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The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

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Answer: 6328723894

Step-by-step explanation:

The diagonals of the qudrilateral will not be perpendicular to each other.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.

The slope of a coordinate pair is given by the change in y divided by the change in x, that is:

For the diagonal AD the slope will be:-

Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )

For the diagonal BC, the slope will be:-

Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1

The multiplication of the two slopes will be,

M  =  ( 1 / 3 ) x -1 = ( - 1 / 3 )

Therefore,  the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.

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Answer:

The product of the slopes of the diagonals is -1.

Step-by-step explanation:

I had the question and got it right.

The minimum cost to produce the product is $7.

What are functions?

To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].

Dividing the above equation by 5, we get

[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.

Since the coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting from the above equation.

[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]

Now, we have to determine the minimum cost to produce the product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

[tex]f'(x) = 10x-70[/tex]

Now, let f'(x)=0

[tex]10x-70=0\\10x=70[/tex]

Therefore, x=7

Now, consider which is greater than 0.

Therefore, x= 7 is the minimum cost.

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Answer: The minimum cost to produce the product is $13.

I apologize for the late answer, hope this helps in the future!

Step-by-step explanation:

To complete the square, we need to rewrite the given function in the form:

f(x) = a(x - h)^2 + k

where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.

We start by factoring out the coefficient of x^2:

f(x) = 5(x^2 - 14x + 51.6)

To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:

f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)

= 5((x - 7)^2 + 13)

Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:

5(x − 7)2 + 13

The correct option is option(A) (5x-1)(x+6).

The factors of the given equation are (5x-1)(x+6).

An algebraic expression or number that divides another expression or number equally, leaving no remainder is known as factor.

The quadratic equation [tex]ax^{2} +bx+c=0[/tex]  can be expressed as the product of its linear factors as (x - k)(x - h), where h, k are the roots of the equation. This is known as factoring quadratics.

Dividing the middle term into two factors is used in quadratic factorization in this method. In splitting of the middle term, where x is the product of two factors and last term is the sum of the two factors.

Use the splitting middle term formula

[tex]5x^{2} +29x-6[/tex]

=[tex]5x^{2} +30x-x-6[/tex]

=5x(x+6)-1(x+6)

=(5x-1)(x+6)

The factors of the given equation are (5x-1)(x+6).

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Answer:

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.

The graph is in the attached image.

Answer:

12 sqrt (10)

Step-by-step explanation:

S = (12 + 11 + 7) / 2 = 15

A = sqrt (s(s-a)(s-b)(s-c))

= sqrt (15(15-12)(15-11)(15-7))

= sqrt (15*3*4*8)

= sqrt (1440)

= 12 sqrt (10)

Answer:

An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.

√64 is rational.

Hope this helps :)

❄ Hi there,

let us consider this –

Is [tex]\sqrt{64}[/tex] a rational or irrational number?

Well, to answer that we need to work out [tex]\sqrt{64}[/tex].

And we know that

[tex]\sqrt{64} =8[/tex]

and 8 is a rational number.

That's it!

❄

Answer:

m = F / a is the answer

Step-by-step explanation:

F = ma

m = F / a

Yes, the correlation coefficient is statistically significance

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.

Given,

Sample size, n = 4

Where ρ is the population correlation.

Then the number of degrees of freedom is, df = n-2 = 4-2 = 2

The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254

Here,

The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected

Suppose lr> re 0.254

Because on the sample correlation provided, we know that lrl = 0.835>=0.254.

Here, it is clear that the null hypothesis is rejected.

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The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).

Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.

Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.

According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.

64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.

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The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for.

The regression sum of squares serves as the  sum of the differences that exist between the predicted value and the mean of the variable.

The Sum of Squared Error  however states the difference between the observed  and the predictive value.

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Answer:

Option 2

Step-by-step explanation:

There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.

Using the total weight the number of red, green and yellow colour are 2, 4 and 3 respectively.

The total number of reds, yellows, and greens on a scale is 9.

The reds weighed 3 pounds each, the yellows weighed 6 pounds each, and the greens weighed 5 pounds each. The total weight is 44

pounds. There are 2 more greens than reds.

Therefore,

let

x = number of reds

number of greens = x + 2

y = number of yellow

Therefore,

x + x + 2 + y = 9

2x + y = 7

3x + 6y + 5(x + 2) = 44

3x + 6y + 5x + 10 = 44

8x + 6y = 34

Hence,

2x + y = 7

8x + 6y = 34

8x + 4y = 28

8x + 6y = 34

2y = 6

y = 6 / 2

y = 3

2x + 3 = 7

2x = 7 - 3

2x  = 4

x = 4 / 2

x = 2

Therefore,

the number red colour = 2

the number of green colour = 2 + 2 = 4

the number of yellow colour = 3

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