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The solution to the system of equation shown is (7, -1)

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given the equation:

4x + 8y = 20   (1)

-4x + 2y = -30  (2)

Solving by elimination method. Add equation 2 and 1:

10y = -10

y = -1

Put y = -1 in eqn 1:

4x + 8(-1) = 20

4x - 8 = 20

4x = 28

x = 7

The solution is (7, -1)

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The measure of angle a is given as 94 degrees.

In order to get the value of a, we have to use the formula for the sum of angles in a straight line.

The sum of angles that are in a straight line is given as 180

this is summed up and equated to 180

From the figure,

m∠1 = 86 degrees

m∠2 = a

we have to sum this up and equate the value to 180 degrees

86 degrees + a = 180 degrees

a = 180 - 86

a = 94 degrees

Therefore the measure of the angle a is given as 94 degrees

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Answer:

18. y = -2x + 6

19. y = -1/2x -1/2

Step-by-step explanation:

y = mx + b

18. The point (0,6) 0 is the x-intercept and 6 is the y-intercept

For now, all we care about is 6

-2 is the slope which means the line will go down 2 and right 1

m = slope

b = y-intercept

y = -2x + 6

19.

-1/2 is the slope which means the line will go down 1 and right 2

For the y-intersept, I just played with it on a graphing calculater until I got it right.

m = slope

b = y-intercept

y = -1/2x -1/2

A right angled isosceles triangle is a triangle with two sides of equal length and one right angle. To prove that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle, we can use the distance formula and the Pythagorean theorem.

The distance formula is used to calculate the distance between two points in a coordinate plane. It is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the distance formula, we can find that the distance between the points (-3, 3) and (3, -7) is:

d = √((3 - (-3))^2 + ((-7) - 3)^2) = √(6^2 + (-10)^2) = √(36 + 100) = √136

Similarly, we can find that the distance between the points (-3, 3) and (7, 9) is also √136 and the distance between the points (3, -7) and (7, 9) is √36.

Now, we can use the Pythagorean theorem, which states that in a right angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean theorem can be written as:

c^2 = a^2 + b^2

Since d1 and d2 are equal, we can say that the triangle is isosceles.

So, using the distance formula and the Pythagorean theorem, we have proven that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle.

On subtracting 3x² + 7x - 4 from 8x² - 6x + 2, the expression in standard form is obtained as 5x² - 13x + 6.

What is standard form?

To make mathematics easier for everyone to read, write, and work with, mathematicians from all around the world resolved to come to basic writing standards. The term "standard form" refers to this particular method.

The given expressions are -

a = 3x² + 7x - 4 and b = 8x² - 6x + 2.

Subtract a from b. The expression will be -

= (8x² - 6x + 2) - (3x² + 7x - 4)

= 8x² - 6x + 2 - 3x² - 7x + 4

= 5x² - 13x + 6

Therefore, the standard form is 5x² - 13x + 6.

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1 . The following formula can be used to determine the likelihood that a pupil is proficient in arithmetic but not reading:

P(math proficient and not reading proficient) = P(math proficient) - P(math and reading proficient)

We are aware that 65% of kids are fluent in both reading and mathematics, and 78% of children are proficient in arithmetic.

So, the probability that a student is proficient in mathematics but not reading is:

78% - 65% = 13%.

2 . The following formula can be used to determine the likelihood that a pupil is proficient in reading but not mathematics:

P(reading proficient and not math proficient) = P(reading proficient) - P(math and reading proficient)

We are aware that 65% of children are proficient in both reading and mathematics, and 85% of pupils are proficient readers.  So, the probability that a student is proficient in reading but not mathematics is:

85% - 65% = 20%.

3 . The formula P(math and reading proficient) = P(math proficient) + P(reading proficient) - P can be used to determine the likelihood that a student is proficient in both reading and math (math proficient or reading proficient)

We are aware that 78% of pupils demonstrate arithmetic proficiency, 85% demonstrate reading proficiency, and 65% demonstrate reading and math proficiency. Therefore, there is a 65% chance that a student will be proficient in both reading and mathematics.

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The probability that a student is proficient in mathematics but not reading is 13%. The probability that a student is proficient in reading but not mathematics is 20%.There is a 65% chance that a student will be proficient in both reading and mathematics.

1 . The following formula can be used to determine the likelihood that a pupil is proficient in arithmetic but not reading:

P(math proficient and not reading proficient) = P(math proficient) - P(math and reading proficient)

We are aware that 65% of kids are fluent in both reading and mathematics, and 78% of children are proficient in arithmetic.

So, the probability that a student is proficient in mathematics but not reading is:

78% - 65% = 13%.

2 . The following formula can be used to determine the likelihood that a pupil is proficient in reading but not mathematics:

P(reading proficient and not math proficient) = P(reading proficient) - P(math and reading proficient)

We are aware that 65% of children are proficient in both reading and mathematics, and 85% of pupils are proficient readers.  So, the probability that a student is proficient in reading but not mathematics is:

85% - 65% = 20%.

3 . The formula P(math and reading proficient) = P(math proficient) + P(reading proficient) - P can be used to determine the likelihood that a student is proficient in both reading and math (math proficient or reading proficient)

We are aware that 78% of pupils demonstrate arithmetic proficiency, 85% demonstrate reading proficiency, and 65% demonstrate reading and math proficiency. Therefore, there is a 65% chance that a student will be proficient in both reading and mathematics.

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In the scale drawing, the height of building itself is 88 .4 centimeters.

The scale drawing is a smaller edition of a large object. By using scale drawing we try to bring the large shape of image or any object within a sheet of paper or in a computer screen. The ratio of the dimension of scale drawing to the original dimension is called scale factor.

The height of observation deck of the Wills tower from ground surface = 412 meters

in the scale drawing the height of deck = 82.4 centimeters.

The actual height of Wills tower building = 442 meters

now, the height of Tower building in scale drawing = (442×82.4) / 412

  in the scale drawing the height = 88.4 centimeters

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600 mL of solution B and 3(600) = 1800 mL of solution A are used by Chau.

Let x = the amount of Solution B used

3x = the amount of Solution A used

Knowing that 13% = 0.13 and 18% = 0.18, we can create the equation shown below:

3x(0.13) + x(0.18) = 342 (Remember that the concentration of pure alcohol is 100%, or 1.00).

0.39x + 0.18x = 342

0.57x = 342

x = 600 mL

600 mL of solution B and 3(600) = 1800 mL of solution A are used by Elsa.

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Answer:

Step-by-step explanation:

9

Answer:

40

Step-by-step explanation:

This is an example of a composite function. And, in order to answer the given problem, we need to calculate first the inner function.

In this example, we have:

[tex]f(x) = x^{2} - 3x + 6\\g(x) = 5x - 10[/tex]

And, we are tasked to calculate the [tex]g(f(-4))[/tex]. Let's calculate first the [tex]f(-4)[/tex].

[tex]f(x) = x^{2} + 3x + 6\\f(-4) = (-4)^{2} + 3(-4) + 6\\f(-4) = 16 - 12 + 6\\f(-4) = 4 + 6\\f(-4) = 10[/tex]

Let's substitute this value to the function of g to get the final answer.

[tex]g(x) = 5x - 10\\g(f(-4)) = 5(10) - 10\\g(f(-4)) = 50 - 10\\g(f(-4)) = 40[/tex]

Thus, the final answer was 40.

Answer:

Step-by-step explanation:

well first you must question what 11 minus 9 is and its the x for m but do the same for o and combine the 2. i don't know if it will work i'm so past that

Answer:

25

Step-by-step explanation:

25 because i used a calculator

Answer:

------------------------------

A. rectangle

B. square

C. parallelogram

D. trapezoid

Answer:

(m,0) and (m,0),(-a,-b) and (a,b),(0,-k) and (0,k) are the required coordinates

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The value of x in the interval 0 ≤x≤ pi is 2.083 so the graph f and g have parallel tangent lines

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.  The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = tan x

and, g(x) = x²

Now, f(x) = t g(x)

and, g(x) = x²

On differentiating f(x) we get

f'(x) = t g²(x) + 1

and, g(x) = 2x

Now, the parallel tangent line

f' (x) = g'(x)

t g²(x) + 1 = 2x

since the interval for x is 0 ≤x≤ pi.

So, the value of x = 2.083

Hence, the value of x is 2.083.

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Step-by-step explanation:

[tex]7x^2-10=-17\\7x^2=-7\\x^2=-1\\x=\sqrt{-1}\\x=\sqrt{i^2}\\\boxed{x=i,-i}[/tex]

Therefore, by simply multiplying 63.8 by 4.6, we get 293.48. Once you have mastered each times table, move on to the next one.

The quantity of items in the group expands as we multiply.  Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations.  In the first and second grades, students learn how to represent, work out, and extend their counting sequences. Students start learning basic multiplication facts and times tables in the third grade.

given

Slice up the information into manageable pieces. With a straightforward picture, give the facts context. Teach your kid how to use the simpler facts as stepping stones for the more difficult ones. Once you have mastered each times table, move on to the next one.

63.8 x 4.6

by simple multiplication

= 293.48

Therefore, by simply multiplying 63.8 by 4.6, we get 293.48.

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Answer:

212 gummy bears

Step-by-step explanation:

Just add 125 and 87 together

Answer: 212

Step-by-step explanation:

Its simple addition.

Answer: To find the values of k for which the line y = x + k is tangent to the circle x^2 + y^2 = 25, we need to substitute y = x + k into the equation of the circle and solve for x.

x^2 + (x + k)^2 = 25

Expanding the square, we get:

x^2 + x^2 + 2xk + k^2 = 25

2x^2 + 2xk + k^2 = 0

Now we can solve for x by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 2, b = 2k and c = k^2

x = (-2k ± √(4k^2 - 42k^2)) / 2*2

x = (-k ± √(-3k^2)) / 4

Since the square root of a negative number is not a real number, we can see that there is no real value of x that will make the equation true. Therefore, the line y = x + k is never tangent to the circle x^2 + y^2 = 25

Answer:

Step-by-step explanation:

To find the values of k that will make the line y = x + k tangent to the circle x^2 + y^2 = 25, we need to set the equation of the line equal to the equation of the circle and solve for k.

First, we'll substitute y = x + k into the equation of the circle:

x^2 + (x + k)^2 = 25

Next, we'll expand the square on x + k:

x^2 + x^2 + 2xk + k^2 = 25

Now we'll combine like terms:

2x^2 + 2xk + k^2 = 25

We'll rearrange the equation so that x^2 is on one side

2x^2 + 2xk + k^2 - 25 = 0

Now we'll divide by 2

x^2 + xk + k^2/2 - 25/2 = 0

Now we'll complete the square

x^2 + xk + (k^2/2 - 25/2) = 0

x^2 + xk + (k^2/2 - 25/2) + (25/2) = (25/2)

(x + k/2)^2 = 25/2

Now we'll take the square root of both sides

x + k/2 = +-sqrt(25/2)

Now we'll solve for x

x = sqrt(25/2) - k/2 or x = -sqrt(25/2) - k/2

Now we'll substitute these values of x into the equation y = x + k and find the value of k.

x = sqrt(25/2) - k/2

y = x + k

y = sqrt(25/2) - k/2 + k

y = sqrt(25/2)

x = -sqrt(25/2) - k/2

y = x + k

y = -sqrt(25/2) - k/2 + k

y = -sqrt(25/2)

So the line y = x + k is tangent to the circle x^2 + y^2 = 25 when k = sqrt(25/2) or k = -sqrt(25/2)

Answer:

-------------------------------

See the correct solution below:

According to the information, it can be inferred that the city of Montgomery collected 320 tons of plastic in the month of June.

To calculate how many tons of plastic the city collected in June we must take into account the following information.

Taking this information as a reference, we must perform the following operation to find the amount of plastic that Montgomery collected in June:

So, the city of Montgomery collected 320 tons of trash in the month of June.

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Answer:

Greatest Common Factor

Step-by-step explanation:

Answer:

greatest common factor

Step-by-step explanation:

The ultimate grade for the course is determined by the average of all completed assignments. Answer is 92.

You must first add up all of your grades if your instructor or professor employs a total points system.Afterward, tally the number of points available for each of those grades.

Your class grade can be calculated by dividing your earned points by the total points available.Follow these steps if you want to accomplish it by hand:The letter grade's value is calculated by dividing it by the course's total number of credits.Do this for each class, then add them all up.

Subtract the total by the number of credits.

75% of the test score would be 76 x 0.75 = 57

80-57 = 23

They need 23 more points to get an 80

The 23 is 25% of the final exam grade so they would need to score a 23 x 4 = 92 on the final exam

answer: 92

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Answer:

angle SRQ or angle QRS

Step-by-step explanation:

R is the middle angle, so it will always be in between the other two variables :)

Answer:

AB ≈ 13 cm

Step-by-step explanation:

∠ CAB = 90° - ∠ CAD = 90° - 45° = 45°

using the cosine ration in right triangle ABC

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{9}{AB}[/tex] ( multiply both sides by AB )

AB × cos45° = 9 ( divide both sides by cos 45° )

AB = [tex]\frac{9}{cos45}[/tex] ≈ 13 cm ( to the nearest whole number )

The weight of the rice bags should be less than the weight of 48.35 ounces. Inequality can be written as x < 48.35 ounces.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

That One machine fills each bag with approximately 48 ounces of rice. After the bags are filled; another machine weighs each bag. A bag is discarded if the weight differs by more than 0.35.

The inequality for the bags can be written as

x < 48.35 Ounces

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Answer:

the two hundred degrees angle is the reflex angle.

Step-by-step explanation:

reflex angle is and angle that is more than 180 degrees and less than 360 degrees.

the 200 degree angle is above 180 and lower than 360 degrees. The 100 is lower than 180 so I can't be it

Answer:

Step-by-step explanation:

45 peaches + 55 peaches + 60 peaches = 160 peaches total

17 pounds + 21 pounds + 25 pounds = 63 pounds total

63 pounds / 160 peaches = about 0.39 pounds per peach

Both the car and the train are traveling at the same speed because they both cover the same distance in different amounts of time.

In this scenario,

the car is traveling at a speed of 0.6 miles per minute

and the train is traveling at a speed of 0.75 miles per minute.

Therefore, both are traveling at the same speed of 6 miles in 10 minutes or 6 miles in 8 minutes.

With this in mind, it can be seen that they both travel at the same speed and none is faster.

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