Solve the following system of equations.
(15 Points)
x + 3y = -5 & 5y - 10 = -20x

[tex] \sf \: 3x + x \sqrt{3} - 2 = 0 \\ \\ \sf \longrightarrow 3x + \sqrt{3} x = 2 \\ \\ \sf \longrightarrow \sqrt{3}x ( \sqrt{3} +1 ) = 2 \\ \\ \sf \longrightarrow \sqrt{3} x = \frac{2}{ \sqrt{3} + 1 } \\ \\ \sf \longrightarrow x = \frac{2}{ \sqrt{3}( \sqrt{3} + 1) } \\ \\ \sf \longrightarrow x = \frac{2}{3 + \sqrt{3} } \\ \\ \tt{You\:can\:stop\:here\:if\:you\:\bold{don't}\:want\:to }\\ \tt{ \:simplify\:in\:decimal\:form.}\\ \\ \sf \longrightarrow x = \frac{2(3 - \sqrt{3} )}{(3 + \sqrt{3})(3 - \sqrt{3} )} \\ \\ \sf \longrightarrow x = \frac{6 - 2 \sqrt{3} }{ {3}^{2} - {( \sqrt{3}) }^{2} } \\ \\ \sf \longrightarrow x = \frac{6 - 2(1.732)}{9 - 3} \\ \\ \sf \longrightarrow x = \frac{2.536}{6} \\ \\ \leadsto \underline{\boxed{\sf{\pink{x \approx 0.4226}}}}[/tex]

Answer:

No

The sides of the triangle do not satisfy the Pythagorean Theorem.

Step-by-step explanation:

If we are given the three sides to a triangle, and we are asked to find out if it is a right triangle, we will have to see if the sides of the triangle satisfies the Pythagorean Theorem. The Pythagorean Theorem is:

a² + b² = c²

where c is the hypotenuse and a and b are the other two sides.

So we can see from the image that 28 would be the length of the "hypotenuse" and 19 and 20 would be the lengths of the other two sides. Lets see if these values satisfy the Pythagorean Theorem:

19² + 20² = 28²

361 + 400 = 784

761 ≠ 784

So no, the triangle is not a right triangle because the sides does not satisfy the Pythagorean Theorem.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

a and e

Step-by-step explanation:

Answer:

A, D, and E

Step-by-step explanation:

Step-by-step explanation:

You can write an equation of a line conveniently by point-slope form. It's in the form of [tex]y -a = m(x -b)[/tex] where [tex](b,a)[/tex] is the coordinates of a point that's on the line and [tex]m[/tex] is the slope of the line.

Now choose a point (It doesn't really matter which one) and plug that in the equation. I'll choose [tex](-3,7)[/tex] where [tex]a = 7[/tex] and [tex]b = -3[/tex]

[tex]y -a = m(x -b) \\ y -7 = m(x -(-3)) \\ y -7 = m(x +3)[/tex]

The next thing we have to do now is finding the slope, [tex]m[/tex], where it's equal to [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}\\[/tex]. I'll make [tex](-3,7)[/tex] point 1 and [tex](3,3)[/tex] point 2.

[tex]m = \frac{3 - 7}{3 -(-3)} \\ m = \frac{3 - 7}{3 +3} \\ m = \frac{-4}{6} \\ m = -\frac{2}{3}[/tex]

Now let's plug that to our equation.

[tex]y -7 = m(x +3) \\ y -7 = -\frac{2}{3}(x +3)[/tex]

Now we have the equation but out of all the choices it seemed that all of them are in slope-intercept form all you have to do now is make our equation rewrite it in slope-intercept form.

[tex]y -7 = -\frac{2}{3}(x +3)\\ y -7 = -\frac{2}{3}x -\frac{2}{3}(3) \\ y - 7 = -\frac{2}{3}x -2\\ y = -\frac{2}{3}x +5[/tex]

[tex]y = -\frac{2}{3}x +5\\[/tex] is your equation.

It is easiest to solve this system by elimination.

4x-8y=44

(2x+4y=-6) -2    ----> multiply the second equation by -2 to create equations where the x coefficients are opposites

     4x-8y=44

(+) -4x-8y=12

-16y=56

y = -7/2

now substitute the value of y into one of the above equations and solve for x

4x – 8(-7/2) = 44

4x + 28 = 44

4x = 16

X = 4

So, the solution is (4, -7/2)

The solution of the  system of equations 4x-8y=44 and 2x+4y=-6is (4, -3.5).

Two or more expressions with an Equal sign is called as Equation.

The given system of equation is 4x-8y=44 ...(1)

and 2x+4y=-6...(2)

To eliminate y term we have to multiply equation 2 with 2.

4x+8y=-12..(3)

Now add equation 1 and 3.

4x-8y+4x+8y=44-12

8x=32

Divide both sides by 8

x=4

Now plug in x value in equation 1

4(4)-8y=44

16-8y=44

Subtract 16 from both sides

-8y=44-16

-8y=28

Divide both sides by 8

y=-28/8

y=-7/2

=-3.5

Hence, the solution of the  system of equations is (4, -3.5).

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Answer:

6/5

Step-by-step explanation:

hi! when dividing fractions, we use the KCF rule, which stands for keep,change,flip. we keep the first fraction the same, change the division symbol to multiplication, and flip the second fraction to its reciprocal. therefore, we now have:

9/10 * 4/3

now, we can multiply the numerators and denominators.

36/30

we can simplify this.

6/5

Answer:

She buys 20 Stamps of $0.15 and 40 Stamps of $0.35.

Step-by-step explanation:

40 x 0.35 = 14

20 x 0.15 = 3

$14 + $3 = $17

40 ($0.35) + 20 (0.15) = 60 stamps

Answer:  x = 9/5 or  [tex]1\frac{4}{5}[/tex]

35 1/5 is the perimeter of the square and the triangle.

Step-by-step explanation:

The square has 4 sides, so the perimeter of the square is 4(x+3)

The triangle has 3 sides so the perimeter is 3(3x-1)

The perimeters are equal, so 4(x+3) = 3(3x-1)

Solve by distributing and then

4x +12 = 9x - 3  subtract 4x from both sides and add 3 to both sides

4x-4x +12 -3 = 9x-4x -3 +3  cancel the zero sums and combine similar terms.

9 = 5x  divide both sides by 5

x =  9/5

Check:  4(9/5 +3) = 3[3(9/5) -1]

36/5 + 3   = [3( 27/5  -1 ]   27/5 -3  -3 equivalent -15/5  27/5 -15/5 = 12/5

36/5 = 3(12/5)  = 36/5   TRUE!  simplify to mixed numbers

35 1/5 is the perimeter of the square and the triangle.

Answer:

u,

Step-by-step explanation:

Answer:

m=slope  y = intercept

m= y2-y1 / x2-x1

       2-1   /   2-0  =  1 /2

now pick one of the points and put in for y and x

use (2,2)    2= 1/2(2) +b

                  2=1 + b

              2-1 =1-1 +b   subtract 1 from each side

                  1 = b   This is your y intercept

Step-by-step explanation:

The equation of the line passing through points  (0,1) and (2,2) will be y = ( 1 / 2) x + 1

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope= 2-1   /   2-0  =  1 /2

Now pick one of the points and put in for y and x use (2,2).

2= 1/2(2) +b

2=1 + b

2-1 =1-1 +b   subtract 1 from each side

1 = b   This is your y-intercept

The equation will be written as:-

y = ( 1 / 2) x + 1

Therefore, the equation of the line passing through points  (0,1) and (2,2) will be y = ( 1 / 2) x + 1.

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Given:

Length of taller tree = 50 feet

Length of shorter tree = 20 feet

Length of shadow of taller tree = 18 feet

To find:

The length of shadow of shorter tree.

Solution:

Since, two trees standing side by side in the sunlight, therefore the length of trees are proportional to their shadows.

Let the length of shadow of shorter tree be x feet.

Using the given information, we get

[tex]\dfrac{50}{18}=\dfrac{20}{x}[/tex]

By cross multiplication, we get

[tex]50\times x=20\times 18[/tex]

[tex]50x=360[/tex]

[tex]x=\dfrac{360}{50}[/tex]

[tex]x=7.2[/tex]

Therefore, the length of shadow of shorter tree is 7.2 feet.

Answer:

46;&74)474:&48&4:&48&

Step-by-step explanation:

For example if you have a function f(x) = x - 1, then x = 1 is a zero of this function because using it as x gives 1 - 1 = 0. The Riemann Zeta function has some zeros that are easy to find which are of little interest but there are some other ones that are harder to find which is why the are called non-trivial.

Answer:

D

Step-by-step explanation:

Slope

All answers agree that the slope = - 3

y intercept

So far what you know is that the line is

y = -3x + b

The point shows that

5 = -3*2 + b                    Combine right

5 = -6 + b                        Add 6 to both sides

5 + 6 = -6+6 + b             Combine

11 = b

So the y intercept = 11

Answer: y = -3x + 11              D

Answer:

49

Step-by-step explanation:

98-x2=0

-98    -98

[tex]\frac{x2}{2}[/tex]     [tex]\frac{98}{2}[/tex]

    49

Answer:

24% finished, 76% did not

Step-by-step explanation:

12cars/50 total +24%, and then just subtract 100% by the 24 to get 76% for the remaining percent

Answer:

24% finished and 76% did not

Step-by-step explanation:

you have the ratios:

12/50 and 38/50

These have to be turned into percentages so they need to have a denominator of 100

to do this, figure out what you have to multiply the denominator by to get 100

In this case, 50 times 2 is equivalent to 100.

Then, whatever you multiplied the denominator by, you multiply the numerator by

In this case, 12 times 2 is 24 and 38 times 2 is 76

Once you have the end products, take the numerator and add a percentage sign to it

Chat me if you have anymore questions

Given parameters:

  Equation:

          (x-4)²=9

Problem, solve the equation by factoring and extracting the root

Solution:

    Given equation:

                  (x-4)²=9

         subtract 9 from both sides to equate to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  Now, this is similar to the concept of difference of two squares;

          x² - y² = (x + y)(x-y)

Here x  = x-4 and y = -3

  So input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 4+3) = 0

              (x -7)(x -1) = 0

S0,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

If we extract the square roots;

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; this is not the only solution to the problem

So we cannot solve it by extracting the square root.

The solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root. The equation can only be solved by factoring

Given the expression;

(x-4)²=9

This expression can be solved by factoring

Factoring the expression on the left hand side

(x-4)(x-4)=9

x²-4x-4x+16 = 9

x² - 8x + 16 - 9 = 0

x² - 8x + 7 = 0

x² -x - 7x + 7 = 0

x(x-1) -7(x-1) = 0

x-7 = 0 and x - 1 = 0

x = 7 and 1

This shows that the expression can be solved by factoring

The other way is by squaring both sides

(√x-4)² = ±√9

x - 4 =±√9

x = -9+4 and x = 9 + 4

x = -5 and 13

Since the solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root

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Answer:

Since we are given that angle Y = angle Z

The magnitude of the angles will also be equal

∠Y = ∠Z

(x + 10) = (2x - 90)

90 + 10 = 2x - x

100 = x

Answer:

i am pretty sure it's -14.92

Step-by-step explanation:

Answer:

B!!!

Step-by-step explanation:

Answer:

625

Step-by-step explanation:

625

Answer:

[tex]g(n-7)=\frac{n^{2}-14n+43}{7n-49}[/tex]  → (a)

Step-by-step explanation:

We need to evaluate g(n - 7), where

Replace x by (n - 7) to evaluate it

∵ x = (n - 7)

∴ [tex]g(n-7)=\frac{(n-7)^{2}-6}{7(n-7)}[/tex]

→ Let us find (n - 7)²

∵ (n - 7)² = (n - 7)(n - 7) = (n)(n) + (n)(-7) + (-7)(n) + (-7)(-7)

∴ (n - 7)² = n² + (-7n) + (-7n) + 49 = n² + -14n + 49

∴ (n - 7)² = n² - 14n + 49

→ Find 7(n - 7)

∵ 7(n - 7) = 7(n) - 7(7)

∴ 7(n - 7) = 7n - 49

→ Now let us write then in the form above

∵ [tex]g(n-7)=\frac{n^{2}-14n+49-6}{7n-49}[/tex]

→ Add the like terms in the numerator

∴  [tex]g(n-7)=\frac{n^{2}-14n+43}{7n-49}[/tex]

The correct answer is (a)

Using the sum of the internal angles of a triangle and supplementary angles, it is found that the measure of angle 1 is of 121º.

The sum of the three internal angles of a triangle is of 180º.

Hence, the measure of the remaining interior angle is given by:

60º + 61º + x = 180º

x = 59º.

Two angles are supplementary if the sum of their measures is of 180º.

An interior angle is supplementary with it's respective exterior angle, hence:

m<1 + 59º = 180º

m<1 = 121º.

The measure of angle 1 is of 121º.

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Answer:

D is correct

Step-by-step explanation:

p=q  then q is the same as p and if r=p that is true

Answer:

A function with a graph that is symmetric about the origin is called an odd function. Note: A function can be neither even nor odd if it does not exhibit either symmetry. For example, f(x)=2x f ( x ) = 2 x is neither even nor odd

Step-by-step explanation:

The difference between the longest and shortest light bulb lifetime was five years is correct interpretation so option (B) will be correct.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

In other meaning, standard deviation shows the deviation of the value of data from the mean.

Standard deviation is how much-given data is deviate from the mean of it.

So the difference between the longest to shortest gives an idea about this deviation.

Hence "The difference between the longest and shortest light bulb lifetime was five years is a correct interpretation".

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Answer:

9x + 4

Step-by-step explanation:

Step 1: Write expression

4x - 2 + 5x + 6

Step 2: Combine like terms (x)

9x - 2 + 6

Step 3: Combine like terms (constants)

9x + 4

Answer:

9x + 4

Step-by-step explanation: