Consider the function graphed to the right.

The solution of system of equations x is 1 and value of y is 6.

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

The  system of equations are y = 2x² - 5x+9 and y = 2x² + 5x - 1

Subtract both the equations

y-y=2x² - 5x+9 -2x² - 5x +1

0=-10x+10

10x=10

Divide both sides by 10

x=1

Now plug in x value in any of the equation.

y=2(1)² - 5(1)+9

y=2-5+9=6

Hence, the solution of system of equations x is 1 and value of y is 6.

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Due to length restrictions, we kindly invite to read the explanation for further details on how to go across the maze with linear functions.

In this problem we find a maze formed by representations of linear functions on Cartesian plane, of which we must determine the slope of each line until finish is reached. This can be done by understanding the following instructions based on results from secant line formula:

The procedure to go across the maze is shown below:

FAIL

SUCCESS

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20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A

It is necessary to multiply, distribute, add, or take in mathematics. The following is the way an expression is put next to each other: Number, expression, and logical operator The ingredients of a mathematical expression include numerals, variables, and equations (such as addition, subtraction, multiplication or division etc.) It is conceivable to contrast statements with phrases. An phrase, often known as an arithmetic operation, is any logical statement that abstract, numbers, and a mathematical operation between those. For instance, the word m in the formula given is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

3x-2x+0.5x  =  1/2 (16x+30y-20)

6(x+4)-2(x+5)  =  1.5%

3(x+4)-2(x+4) +0.5(x+4) =  1.5

20(2/5x+3/4y-1/2) = 2(2x+7)

20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A .

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The value of n(B) in the set is 23

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

n(A) = 108, n(A ∪ B) = 160, and n(A ∩ B) = 43,

The value of n(B) is calculated as

n(A u B) = n(A) + n(B) - n(A n B)

Substitute the known values in the above equation, so, we have the following representation

160 = 108 + n(B) - 43

This gives

n(B) = 160 + 43 - 180

Evaluate

n(B) = 23

Hence, the solution is 23

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Answer:

The range is -11,-4,3,10

Step-by-step explanation:

The set of pairs for which x and y vary inversely is given as follows:

{(-1, -2/7), (4, 1/14), (6, 1/21)}

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse relation, the relation is modeled as follows:

y = k/x.

Meaning that when x increases, y decreases at a constant rate.

The constant is then given as follows:

k = yx.

Hence the third relation is then the relation for which x and y vary inversely, as:

k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.

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Answer:

5

Step-by-step explanation:

The parrot was 12.5 miles from its nest 30 minutes ago.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Average speed = distance/ time

Since the parrot can fly 5 miles in one hour,

So it can fly 5/2 = 2.5 miles in 30 minutes. (apply the division operation)

So 30 minutes ago, the parrot was 15 - 2.5 = 12.5 (apply the subtraction operation)miles from its nest.

Thus, the parrot was 12.5 miles from its nest.

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In Venn diagram All three papers 39,exactly two of the papers 189, exactly one of the papers 251 and  The Guardian alone 142.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.

They frequently serve to visually group objects while highlighting how they differ and how they are similar.

(I) All three papers

(G∪P∪T) = G + P+T+G∩P+G∩T+P∩T-(G∩P∩T)

290=142+181+117+75+60+54-(G∩P∩T)

(G∩P∩T)=39

(ii) exactly two of the papers = 60+75+54=189

(iii) exactly one of the papers =251

(iv) The Guardian alone =142.

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Answer:

YOUR ANDWER MIGHT BE D

Step-by-step explanation:

Therefore , the solution of the given problem of probability comes out to be likelihood that the full batch will be approved is therefore 0.832.

Probability theory is an area of mathematics that focuses on calculating the probability that a claim is accurate or that a particular occurrence will occur. Chance can be represented by any number range between 0 and 1, where 1 often denotes certainty and 0 typically denotes possibility. A probability diagram shows the possibility that a specific event will occur. The numerals 0 and 1, fractions with a ranging of 0% to 100%, or a few more characters can all be used to indicate probabilities.

Here,

Given that we've done it

Amount of CDs: 2100

50 faulty CDs total.

If every component of the sample is acceptable, the complete batch is accepted.

Therefore, we shall apply the "Binomial Theorem"

If there is no flaw, let p be the likelihood of success.

So, => p = 2100 - 50 / 2100

=> p = 2050/2100

=> p =0.97

q is the likelihood of a failure, or defect.

So,

=> q = 50/2100

=> q = 0.02

hence, the number of CDs chosen is 6.

Consequently, it is => P(X=6) = (0.97)6 = 0.832.

The likelihood that the full batch will be approved is therefore 0.832.

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The arena should be financed by selling $  320   million in bonds and borrowing $  480   million.

==========================================================

Work Shown:

Something like x = 27 means "27 million dollars of bonds were sold".

The variable x has the restriction of [tex]0 \le x \le 480[/tex] since $480 million is the ceiling for the bonds.

The variable y has the restriction of [tex]0 \le y \le 640[/tex] since $640 million is the ceiling for the money borrowed from the insurance company.

The two amounts, x and y, must add to 800 to represent the $800 million total that needs to be raised.

x+y = 800

y = 800-x

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

Let's calculate the interest for each item. Use the simple interest formula.

Bonds at 7% interest rate:

i = P*r*t

i = x*0.07*1

i = 0.07x

Borrowed money at 2% interest rate:

i = P*r*t

i = y*0.02*1

i = 0.02y

Total annual interest = 0.07x+0.02y = 32

The 32 at the end represents the $32 million of interest payout. This amount of money is paid to the bondholders and to the insurance company, and is done so yearly.

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

Apply substitution to solve for x.

0.07x+0.02y = 32

0.07x+0.02(800-x) = 32 ...... plug in y = 800-x

0.07x+16-0.02x = 32

0.05x+16 = 32

0.05x = 32-16

0.05x = 16

x = 16/(0.05)

x = 320

They should sell $320 million in bonds.

320 million = 320,000,000

Note how x = 320 is in the interval [tex]0 \le x \le 480[/tex]

y = 800-x

y = 800-320

y = 480

They should borrow $480 million at an interest rate of 2%

480 million = 480,000,000

Note how y = 480 is in the interval [tex]0 \le y \le 640[/tex]

Answer:

The arena should be financed by selling $320 million in bonds and borrowing $480 million.

Step-by-step explanation:

Simple interest is calculated by multiplying the principal by the interest rate (in decimal form) and the time (in years).

Let x be the amount raised by selling bonds that pay an annual simple interest rate of 7%.

Therefore:

As the total cost of the sports arena is $800 million, the amount raised from borrowing money from the insurance company at an annual simple interest rate of 2% is (800 - x).  Therefore:

To determine whether the arena can be financed so that the annual interest is $32 million, equate the sum of the two expressions for interest to 32 and solve for x:

[tex]\implies 0.07x+0.02(800-x)=32[/tex]

[tex]\implies 0.07x+16-0.02x=32[/tex]

[tex]\implies 0.05x+16=32[/tex]

[tex]\implies 0.05x=16[/tex]

[tex]\implies x=320[/tex]

As x is the amount raised by selling bonds, then the amount in bonds that should be sold is $320 million.

To calculate the amount to borrow, subtract the amount in bonds sold from $800 million:

[tex]\implies 800-320=480[/tex]

Therefore, the amount to be borrowed from an insurance company is $480 million.

As both these amounts are less than the maximum limits set, they are both valid.

The measure of the angle K is equal to 12.2° approximately to the nearest tenth, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle KLM, by sine rule;

k/sinK = m/sinM = l/sinL

We first derive the angle K as follows:

5.8/sin28° = 2.6/sinK

sinK = (2.6 × sin28°)/5.8

sin K = 0.2105

K = sin⁻¹(0.2105)

K = 12.1517

Therefore, the measure of the angle K is equal to 12.2° approximately to the nearest tenth, using the sine rule.

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The servings that can be made from two quarts is 24

To convert the recipe's milk measurement from cups to quarts,

We first need to determine how many cups are in a quart.

There are 4 cups in a quart.

So, 3 cups of milk is equivalent to

3 / 4 = 0.75 quarts of milk.

Since the recipe uses 0.75 quarts of milk to make 9 servings,

Then each serving uses 0.75 / 9 = 0.083 quarts of milk.

Now, 2 quarts of milk is equivalent to 2 / 0.083 = 24 servings.

Therefore, from two quarts of milk, 24 servings can be made using this recipe.

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The total amount spent on tickets by Edgar is $15.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the cost of one game ticket and y be the cost of one ride ticket.

From the table, we can form two linear equations regarding the total amount spent by Erica and Penny.

10x + 5y = 10

15x + 10y = 16.25

Multiplying the first equation throughout with 2,

20x + 10y = 20

Subtracting 15x + 10y = 16.25 from the above equation,

(20x + 10y) - (15x + 10y) = 20 - 16.25

5x = 3.75

x = 0.75

Substituting x = 0.75 in 10x + 5y = 10,

7.5 + 5y = 10

5y = 2.5

y = 0.5

Cost of a game ticket is $0.75 and cost of a ride ticket is $0.50.

Total cost by Edgar = (12 × 0.75) + (12 × 0.5) = $15

Hence the total money spent by Edgar for both game and ride tickets is $15.

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The equation the line is, y = 3/8 *x - 23/8, equation of the line in POINT-SLOPE form that passes through the given points (5,-1) and (-3,-4).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (5,-1) and (-3,-4)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

now, solving we get,

3x-8y = 23

equation of the line in POINT-SLOPE form is,

y = 3/8 *x - 23/8

Hence, the required equation is, y = 3/8 *x - 23/8

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The value of x is approximately 3.875.

Given that angle JKL is inscribed in a circle and the measure of angle JKL is (16x-2)°, we can use the property of inscribed angles to find x. Inscribed angles that subtend the same arc have equal measure.

Let's call the measure of angle JKL "m". Then, the measure of angle JKL = m, the measure of angle KJL = m, and the measure of angle JLK = m.

The sum of the angles in a triangle is 180°, so we have:

m + m + m = 180°

3m = 180°

m = 60°

Substituting the value of m into the equation for the measure of angle JKL:

60° = (16x - 2)°

60 = 16x - 2

62 = 16x

x = 3.875

So, the value of x is approximately 3.875.

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Answer: False.

Step-by-step explanation:

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. This means that the polygon has a "cave" or indentation on its interior. However, the fact that a polygon is concave does not automatically mean that one of its diagonals will be drawn outside the polygon. Whether a diagonal is drawn inside or outside the polygon depends on the specific arrangement of the vertices, and cannot be determined solely based on the fact that the polygon is concave.

The surface area of the pyramid is 300 square inches.

The surface area of a square pyramid can be calculated by:

The area of the square base is

10 inches * 10 inches = 100 square inches.

Based on the given parameters:

The area of each triangular face is:

(10 inches * 10 inches) / 2 = 50 square inches.

So, the total surface area of the pyramid is:

100 square inches + 4 * 50 square inches = 300 square inches.

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The cost of the cloth to cover the top surface of the box is 1,750.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Given the rectangular wooden box,

length = 7 m

breadth = 5 m

the top surface of the box is in the shape of a rectangle, to cover the surface with cloth we need to calculate the area of the surface to find the total cloth needed to cover,

area of rectangle = l*b

l = length, b = breadth

A = 7*5

A  = 35 m²

area of the cloth needed  is 35 m²

cost of 1 square meter = 50

cost for 35 m² cloth = 50*35

cost for 35 m² cloth =  1,750

Hence the required cost is 1,750.

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The proportional relationship modeling the number of eggs needed to make x pies is given as follows:

y = 3x.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

3 large eggs, hence the constant of the proportional relationship is given as follows:

k = 3.

Then the equation of the proportional relationship is given as follows:

y = 3x.

Which is a linear function with a slope of 3 and an intercept of zero.

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Answer:

Answer: 0, 1, 1, 2, 2, 4, 5, 6, 7, 0, 8, 9

Step-by-step explanation:

1. Start by writing five digits less than 3: 0, 1, 1, 2, 2

2. Then write four digits greater than 3: 4, 5, 6, 7

3. Finally, add three more digits of any value: 0, 8, 9

Answer:

see below

Step-by-step explanation:

a=50 because it's cut out of a full circle = 360, and it tells you what's left = 310

so 360-310=50

Answer:

b, education

Sana makatulong

The surface area of the square pyramid is given by S = 323.6 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the square pyramid be S

Now , the equation will be

The base of the square pyramid a = 10 inches

The height of the lateral face h = 10 inches

The base area of the pyramid = a²

The lateral surface area of the pyramid = 2a √ ( ( a²/4 ) + h² )

So , the total surface area of square pyramid S = a² + 2a √ ( ( a²/4 ) + h² )

Substituting the values in the equation , we get

The base area of the pyramid = 100 inches²

The lateral surface area of the pyramid = 2 ( 10 ) √ ( ( 100/4 ) + 100 )

On simplifying the equation , we get

The lateral surface area of the pyramid = 223.6 inches²

The total surface area of square pyramid S = 100 inches² + 223.6 inches²

The total surface area of square pyramid S = 323.6 inches²

Hence , the surface area of the pyramid is 323.6 inches²

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Lilianna spend d= 7 minutes total to the park. Therefore, option C is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is d(3/4+1)=12 1/4.

Now, d(3/4+1)= 49/4

d(7/4)=49/4

d=49/4 ×4/7

d= 7

Thus, she spent d= 7 minutes total in the park.

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?

The graph will be piecewise. Then the graph of the function is given below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

S(n) = 0.50n + 3.5, if 1 ≤ n ≤ 14

S(n) = 0                 , if n ≥ 15  

The graph will be piecewise. Then the graph of the function is given below.

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Answer:

Step-by-step explanation:

W(40)x25  

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\angle B=180^{\circ}-115.5^{\circ}-27.2^{\circ} \longrightarrow \boxed{\angle B=37.3^{\circ}}[/tex]

Using the Law of Sines:

[tex]\frac{AC}{\sin 37.3^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{AC=\frac{76\sin 37.3^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

[tex]\frac{BC}{\sin 27.2^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{BC=\frac{76\sin 27.2^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

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

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.