Use substitution to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.

[tex]4x+y=14\\y=8+2x[/tex]

Answer:

45

Step-by-step explanation:

Draw an imaginary line from F to S. We then break this into 2 parts:

1. Evaluate the area of triangle SFN

The base of the triangle is FS, who has length 9. The height is the vertical line that passes through point N and FS, and that line has length 6. The area would then be 9*6/2=27.

2. Evaluate the area of rectangle SCWF

WC has length 9. FW has length 2. The area would then be 9*2=18.

The caterpillar touches 15 points with two integer coordinates, including the start point (-3, -4) and the end point (25, 38).

What is co-ordinate geometry ?

Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. In coordinate geometry, geometric figures are represented using algebraic equations and analyzed using techniques from algebra and calculus.

The caterpillar moves from (-3, -4) to (25, 38) in a straight line. We can find the equation of the line passing through these two points using the slope-intercept form of the equation of a line:

y - (-4) = (38 - (-4))/(25 - (-3)) * (x - (-3))

y + 4 = 42/28 * (x + 3)

y = 3/2 * x + 19

The caterpillar touches a point with two integer coordinates whenever x and y are both integers. To find these points, we can substitute integer values for x and solve for y. Since the slope of the line is 3/2, every time x increases by 2, y increases by 3.

Starting from x = -3, we can list the integer values of x that the caterpillar touches:

-3, -1, 1, 3, 5, ..., 25

For each value of x, we can compute the corresponding value of y using the equation of the line:

y = 3/2 * x + 1

For example, when x = -3, y = 3/2 * (-3) + 19 = 14.5, which is not an integer. When x = -1, y = 3/2 * (-1) + 19 = 17.5, which is also not an integer. However, when x = 1, y = 3/2 * 1 + 19 = 20, which is an integer. Similarly, we can find the integer values of y for all the other values of x.

Therefore, the caterpillar touches 15 points with two integer coordinates, including the start point (-3, -4) and the end point (25, 38).

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Answer: When do you need it done?

Step-by-step explanation: ?

Answer:

Step-by-step explanation:

x+y=17

x-y = 7

From equation 2, x = 7 + y

put this in equation 1.

(7+y) + y = 17

7+2y = 17

2y = 10

y = 5.

We said that x = 7+y

thus, x = 7 + 5

x = 12.

2x+2y=36

2(x+y) = 36

Thus, x + y = 18.

x+y = 18

x-y=6 using elimination (literally simplifying this)

2x = 24 (y-y=0. ELIMINATED!)

x = 12

When x = 12,

x+y=18

12+y=18

y=6.

3x = y

x + y = 20

From 1, y = 3x.

x + (3x) = 20

4x = 20

x = 5.

when x = 5,

y = 3x

y = 3(5)

y = 15.

x+y = -4

xy = -21

from 1, x = -4-y

=> y(-4-y)= -21

-y²-4y = -21

Therefore,

y² + 4y -21 = 0

y= 3 or -7.

When y = 3,

x + 3 = -4

x= -7.

When y = -7,

x + (-7) = -4

x-7=-4

x = 3.

Hope these help! :)

*fingers cracking*

The length of arc AB for the given circle is found to be 13.60 units.

Plotting two lines from the arc's ends to the circle's center, measuring the angle at the point where the two lines intersect the center, and then solving for L by cross-multiplying are useful methods for calculating an arc's length.

And use the arc length method, one may determine a circle's arc length given its radius and center angle.

So,

Radius r = 13 units

Central Angle Ф = 60 degree.

Arc length AB = 60 * 3.14 * 13 /180

Arc length AB = 13.60

Thus, the length of arc AB for the given circle is found to be 13.60 units.

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Answer:

what term?

Step-by-step explanation:

Explain the question.

By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence.

A sequence is a list of objects that is in order in mathematics. (or events). Similar to a set, it has members. (also called elements, or terms). The length of the sequence is the number of many ordered elements (potentially infinite).

Given :

The ratio between consecutive terms in the above sequence is not constant, hence it is not a geometric sequence. The series does, however, appear to rotate between positive and negative numbers.

The explicit formula for the nth term in this sequence is as follows:

a = (-1)^(n+1) * 2^(n-2) (n-2)

By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence. For instance, when n is 1, we obtain:

n = 2 results in:

so forth.

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The quantity of fuel that was utilized by the water in March is 230.4 liters.

Fuel capacity of the tanker = 460 liters

Fuel consumption rate = 5 km/ℓ

Total distance covered per full tank = fuel capacity * fuel consumption rate = 460 x 5 = 2,300 km

Number of full tanks required to make one round trip = distance per round trip / total distance covered per full tank = 18/2300

                                                                              =0.0078

Number of round trips made in March 2022 = 1/0.0078 x 2

                                                                          = 64.1

Total distance covered = number of round trips * distance per round trip                                      

                                      = 64 x 18

                                      = 1,152 km

Therefore, the total distance covered by the water tanker = 1,152 km

Quantity of fuel utilized = total distance covered / fuel consumption rate

                                       =  1152/5

                                       = 230.4 liters.

Therefore, The quantity of fuel that was utilized by the water in March is 230.4 liters.

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Your question is incomplete. The complete question is:

The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 liters. The rate of fuel consumption of the Mercedes water tanker averages 5 km/t. The prices of fuel per liter in March and June 2022 appear below:

MARCH 2022 FUEL PRICES

DIESEL

50 ppm

COST

R19,55

JUNE 2022 FUEL PRICES

DIESEL

50 ppm

Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022.

Answer:

We know that 120 can be factored as 2^3 * 3 * 5, so its totient function value can be found as follows:

φ(120) = φ(2^3) * φ(3) * φ(5)

= 2^2 * 2 * 4

= 16

Therefore, there are 16 numbers less than or equal to 120 that are relatively prime to 120

Answer: Let's use the following system of equations to represent the given information:

h + c = 131    (the total number of burgers sold is 131)

2.5h + 2.75c = 342    (the total value of the burgers sold is $342)

where h represents the number of hamburgers sold and c represents the number of cheeseburgers sold.

We can use the first equation to solve for one of the variables in terms of the other:

h + c = 131

h = 131 - c

Substituting this into the second equation, we can solve for c:

2.5h + 2.75c = 342

2.5(131-c) + 2.75c = 342

327.5 - 2.5c + 2.75c = 342

0.25c = 14.5

c = 58

So, 58 cheeseburgers were sold. We can use the first equation to find the number of hamburgers sold:

h + c = 131

h + 58 = 131

h = 73

Therefore, 73 hamburgers were sold.

Let x be the number of medium bags of chips that Bradford bought. Then, he bought 20 - x large bags of chips.

According to the problem, the total cost of the chips was $53. We can set up an equation for the total cost in terms of x:

diff

2x + 3(20-x+6) = 53

2x + 54 - 3x + 18 = 53

-x = -19

x = 19

So, Bradford bought 19 medium bags of chips and 20 - 19 = 1 large bag of chips.

Enjoy!

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] of Total battery life = [tex]\frac{1}{6} * 3600 = 600[/tex]milliamps

Assuming the battery takes 100 Milliamps per hour,

Time = Battery Capacity / Current hours

Time = 600 / 100 Mah = 6H

x is the number of HD Big View television produced daily.

y is the number of Mega Tele box television produced daily.

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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The values of ST and QR based on the information regarding the square will be 7 and 9.9

The square is a geometric figure that belongs to the parallelograms. The square has the following properties:

All four sides have the same length. The four angles measure 90. The sum of its angles is equal to 360

The diagonals are congruent. The diagonals bisect each other.

We get a PQRS square with PR=14. We are required to find ST and QR.

First, since the figure is a square, we must know that the diagonals are congruent. Therefore, we are required to find ST and QR:

PR = SQ = 14.

ST = 14/2 = 7

QR = sin 45 × 14

QR = 9.9

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After expanding the polynomial (5x² + x - 7)(x - 4) - (2x³ + 5x² - 6), b = -24

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

Since we have the polynomial (5x² + x - 7)(x - 4) - (2x³ + 5x² - 6) and we want it expressed as a polynomial in the form ax³ + bx² + cx + d, to find the value of b, we proceeda s follows.

(5x² + x - 7)(x - 4) - (2x³ + 5x² - 6)

Expanding the brackets, we have that

(5x² + x - 7)(x - 4) - (2x³ +5x² - 6) = 5x³ - 20x² + x² - 4x - 7x + 28 - (2x³ + 5x² - 6)

= 5x³ - 20x² + x² - 4x - 7x + 28 - 2x³ - 5x² + 6

Collecting like terms, we have

= 5x³ - 2x³ - 20x²- 5x² + x² - 4x - 7x + 28 + 6

= 3x³ - 24x² - 11x + 34

So, comparing 3x³ - 24x² - 11x + 34 with ax³ + bx² + cx + d, we have that

b = - 24

So, b = -24

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The upper bound of the volume of water left in the fish tank is 60 liters.

33.81 fluid ounces make up one litre (US).

One litre of water would fill about one-fourth of a gallon water bottle. Also, you should be aware that there are two different kinds of ounces used globally to measure water volume: (1 litre = 33.814 US ounces).

The maximum allowable mistake can be added to the actual value to determine the upper bound of the amount of water still in the fish tank.

The maximum error for 90 litres, rounded to one significant figure, is half of the value of the last significant figure, or 5. Hence, the actual value of 90 litres might be either 85 or 95.

The largest potential inaccuracy for 30 litres, rounded to one significant figure, is likewise 5. Hence, the actual value of 30 litres might be 25 or 35.

We subtract the lower bound of the withdrawn volume from the higher bound of the original volume to determine the upper bound of the volume of water still present in the tank.

The upper bound of the volume of water left in the fish tank can be found by adding the half of the absolute uncertainty to the measured value of 60 liters (90 - 30):

Upper bound = 60 + 0.5 x 1 = 60.5 liters (rounded to 1 significant figure)

Therefore, the upper bound of the volume of water left in the fish tank is 60 liters.

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We can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right triangle with legs of length a and b and hypotenuse of length c, we have:

a^2 + b^2 = c^2

In this case, the rectangle has dimensions of 14 centimeters by 48 centimeters, so we can let the length and width of the rectangle be the legs of a right triangle, and the diagonal be the hypotenuse. Then:

a = 14 cm b = 48 cm c = ?

We can plug these values into the Pythagorean theorem and solve for c:

14^2 + 48^2 = c^2 196 + 2304 = c^2 2500 = c^2 c = sqrt(2500) c = 50

Therefore, the length of the diagonal of the rectangle is 50 centimeters.

Answer:

50 cm

Step-by-step explanation:

the equation is d=sqrt(w^2+l^2)

so you get sqrt(14^2+48^2) which equals 50.

After answering the provided question, we can conclude that Therefore, the answer of quadratic equation is  D) [tex]$-3x^{2}+7$[/tex]

A quadratic equation is x ax² + bx + c = 0, so it's a single variable quadratic polynomial. a 0. Because this regression is of second order, the Fundamental Principle of Algebra helps to ensure that it includes at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic calculation.

This means there is at least yet another word that must be squared. The formula "ax² + bx + c = 0" is a common solution for quadratic equations. where a, b, and c are arithmetical coefficients or constants. where the parameter "X" is unidentified.

To find g(h(x))

[tex]$\begin{array}{l}{{h(x)=3x^{2}-2}}\\ {{g(h(x))=g(3x^{2}-2)}}\\ {{g(3xA^2))=-3x^2-2}+5}}\\ {{g(h(x))=-3x^{2}+7}}\end{array}$[/tex]

Therefore, the answer is D) [tex]$-3x^{2}+7$[/tex]

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The equation of the graphed function, which is composed of translations to f(x) = x³, is given as follows:

B. y = f(x + 3) - 2.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The turning point of f(x) = x³ is at the origin, while for the graphed function it is at point (-3,-2), hence the translations are given as follows:

Hence the graphed function is defined as follows:

B. y = f(x + 3) - 2.

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Answer:

1

explanation in head

Answer:

265 ft

Step-by-step explanation:

its asking what is the hypotenuse

"SOHCAHTOA"

sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent

use

soh because it has hypotenuse in it

sine equals opposite over hypotenuse

sine 49 = 200 / x

x & sine 49 can switch

x = 200/sin(49°)

x = 200/0.7547

x = 265.005962634

x = 265

using pythagorean theorem other leg is 173.85 or 174

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Therefore , the solution of the given problem of probability comes out to be there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.

The primary goal for every procedure's criteria-based methods is to ascertain the probability that a statement is true or that a specific event will occur. Chance can be represented by any number range between 0 and 1, where 0 usually represents probability and 1 usually reflects degree of certainty. A probability illustration displays the possibility that a specific event will take place.

Here,

a.

=> P(X < 90) = F(89)

We can determine: Using a computer or a spreadsheet

=> Binom.dist(89, 200, 0.48, TRUE) = 0.0016 when

=> P(X  90) = F(89) (rounded to 4 decimal places)

Therefore, there is a 0.0016 percent chance that fewer than 90 of the executives agree that workers are most effective on Tuesdays.

b.

=> P(X > 100) = 1 - P(X < 100) = 1 - F(100)

We can determine: Using a computer or a spreadsheet

=> Binom.dist(100, 200, 0.48, TRUE)

=> 0.0668 for P(X > 100) = 1 - F(100) = 1 - (rounded to 4 decimal places)

Therefore, there is a 0.0668 percent chance that more than 100 executives agree that Tuesdays are when workers are most effective.

c.

=> P(X > 82) = 1 - P(X < 82) = 1 - F(82)

We can determine: Using a computer or a spreadsheet

=> Binom.dist(82, 200, 0.48, TRUE) = 0.7569, P(X > 82) = 1 - F(82) = 1

Therefore, there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.

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`C(p,k) * C(n-p,k)`

a. Proof: We will apply the same method we used in formula (1) in our class notes on this question. For this purpose, we choose a set containing `n + 1` elements. It contains all elements of the set of `n` elements and another element `y` that has not been included in the set of `n` elements.Let the number of sets of `n` elements that contain `k` particular elements `a` be `P(n, k)`. To count the number of sets of `n + 1` elements that contain `k` elements, we use the concept of permutations with repetition, such as -{n + 1} can be placed in any of the `k` places of the k-element subsets of `{1, 2,...,n}`, or it can be one of the remaining `n-k+1` elements in each of the `P(n,k)` sets that contain `k` elements.Let us use `A` to denote the set of sets of `n` elements that do not contain the element `y` and `B` to denote the set of sets of `n` elements that contain the element `y`. Then, `P(n+1,k)=|A|+|B|=P(n,k)+(n−k+1)P(n,k−1)`.b. Proof: To count the number of `k` element subsets from a set of `n` elements, we use `C(n, k)`.Let us consider two sets, `A` and `B`, where `|A|=n-k` and `|B|=p-k`. We want to choose `k` elements from these two sets such that the number of subsets we get from `A` is `x` and the number of subsets we get from `B` is `y`. In the set `A`, we select `x` elements by choosing `k-x` elements from the remaining `n-k` elements. Similarly, in the set `B`, we select `y` elements by choosing `k-y` elements from the remaining `p-k` elements.Thus, the total number of ways of choosing `k` elements from `A` and `B` is given by `C(n-k, x) * C(p-k, y)`. The total number of ways of choosing `k` elements from `n` elements is given by `C(n, k)`. Therefore, the total number of ways of choosing `k` elements from `n` elements such that `x` elements are chosen from `A` and `y` elements are chosen from `B` is `C(n-k, x) * C(p-k, y) * C(n, k)`.To get the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B`, we must sum over all possible values of `x` and `y`. Thus, the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B` is given by: `C(p,k) * C(n-p,k)`  which is the required result.

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Answer: 130 degrees

Step-by-step explanation:

The line equals 180 degrees

50+j=180

180-50=130

Answer:

130 Degrees

Step-by-step explanation:

180-50 = 130

In the parallelogram ABCD the value of DF is 13.33 metres or DF = 40/3 metres (rounded to two decimal places).

In the parallelogram ABCD, we can draw a diagonal AC that splits the parallelogram into two congruent triangles, namely, △ABC and △ADC.

Let x be the length of DF. We can use similar triangles to find x.

Notice that △BCE and △DFE are similar triangles, since they share the same angle at E and the angles at B and D are congruent due to opposite angles in a parallelogram. Therefore, we can write the following proportion:

BC/CE = DF/FE

Substituting the given values, we have:

16/8 = x/(20-x)

Simplifying this equation, we get:

2 = x/(20-x)

2(20-x) = x

40 - 2x = x

3x = 40

x = 40/3

Therefore, DF = 40/3 meters or 13.33 meters (rounded to two decimal places).

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We can use the principle of inclusion-exclusion to find n(U), which states that for two sets A and B:

n(A union B) = n(A) + n(B) - n(A intersection B)

We can apply this to three sets r, s, and their complements r' and s':

n(U) = n(r union s)

= n(r) + n(s) - n(r intersection s)

= [n(r intersection s') + n(r intersection s)] + [n(s intersection r') + n(s intersection r)] - n(r intersection s)

= [(4 + n(r' intersection s)) + (n(r intersection s') + 7)] - 4

= n(r' intersection s) + n(r intersection s') + 3

= 7 + 3 + 3

= 13

Therefore, n(U) = 13.

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

part A)

the table shows that in 10 attempts

Blue was hit 5 times

Yellow was hit 2 times

Green was hit 2 times

Purple was hit 1 time

so the experimental probabilities are

Blue 5/10 = 1/2 = 0.5

Yellow 2/10 = 1/5 = 0.2

Green 2/10 = 1/5 = 0.2

Purple 1/10 = 0.1

part B)

the theoretical probability of Purple with an equally spaced spinner of 4 colors is 1/4 = 0.25

A proportional connection exists when two values may be expressed as y = kx, where k is a constant. To discover which ordered pairings have a proportionate connection with (0.2, 0.3).

We must find a value of k for each pair that makes this equation true. Let us begin with option A: (1.2, 2.3). If we wish to represent this combination as y = kx, we must discover the value of k that results in 2.3 = k. (1.2). When we solve for k, we get: k = 2.3 / 1.2 ≈ 1.92 As a result, (1.2, 2.3) does not have a proportionate connection with (0.2, 0.3) since the value of k is different for both couples. This procedure can be repeated for each of the others. options. Option B: (2.7, 4.3) yields: k = 4.3 / 2.7 ≈ 1.59 Option C: (3.2, 4.8) yields: k = 4.8 / 3.2 = 1.5 Option D: (3.5, 5.3) yields: k = 5.3 / 3.5 ≈ 1.51 Option E: (5.2, 7.8) yields: k = 7.8 / 5.2 = 1.5 As a result, alternatives C and E are proportional to (0.2, 0.3) since they can be represented in the form y = kx with the same k value. k = 1.5 in both situations.

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The resulting constant is 2/5 when (2-4/3) is subtracted from (-3/5 plus 5/3).

Mathematical subtraction includes calculating the difference between two numbers. It is the inverse of addition and is denoted by the symbol "-". When we subtract one number from another, we are essentially finding out how much smaller the second number is than the first number.

We can simplify the expressions inside the parentheses first:

2 - 4/3 = 6/3 - 4/3 = 2/3

-3/5 + 5/3 = -9/15 + 25/15 = 16/15

So the expression (-3/5 + 5/3) - (2 - 4/3) becomes:

(16/15) - (2/3)

To subtract these fractions, we need to find a common denominator, which is the least common multiple of 15 and 3, which is 15. Then we can rewrite both fractions with this denominator:

(16/15) - (2/3) = (16/15) - (10/15)

Now we can subtract the numerators and keep the denominator:

(16/15) - (10/15) = 6/15 = 2/5

Therefore, the resulting constant is 2/5.

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The solution of the system of equations from the graph is x = 2.

The point of intersection formula is used to determine where two lines meet, or the point at which they intersect. In Euclidean geometry, the intersection of two lines can be either an empty set, a point, or a line. Two lines must meet certain requirements in order to intersect, including being in the same plane and not being skew lines. The intersection of these lines may be determined using the intersection formula.

The solution of the system of equations can be determined from the graph by determining the point of intersection between the two lines.

From the graph we observe that the point of intersection of the two lines is at (0, 2).

Hence, the solution of the system of equations is x = 2.

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