- x + y = - 3
y=x-3

Substitution method

The solutions of the given equations are:

1. x = 5, -5

2. x = -6, 4

3. x = 3, -3

4. x = 1/2, -3

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

1. x²-7= 18, by applying factorization

x² = 18 + 7

x² = 25

x = 5, -5

2. x² + 2x -24 = 0, by applying factorization

x² + 6x - 4x - 24 = 0

x(x+6)-4(x+6) = 0

(x-4)(x+6) = 0

x = 4,-6

3. 4x² + 2 = 38, by applying factorization

4x² = 36

x² = 9

x = 3, -3

4. 2x² + 5x -3 = 0, by applying factorization

2x² + 6x - x - 3 = 0

2x(x +3) -1(x+3) = 0

(2x-1)(x+3) = 0

x = 1/2, -3

Hence, The solutions of the given equations are:

1. x = 5, -5

2. x = -6, 4

3. x = 3, -3

4. x = 1/2, -3

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Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.

acc to our question-

Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.

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Answer: 9m

Step-by-step explanation:

If we draw a right triangle, we can get a triangle with an angle of 18 degrees and a base of 18.5m. To get the height, we would do TOA or tan = opp / adj:

tan18 = x / 18.5

Multiply both sides by 18.5 to isolate x:

x = 18.5 * tan18

x = 6m (approximately)

This means that the taller building is 6 meters taller, so:

15m - 6m = 9m

x = [tex]\sqrt[3]{40}[/tex]  = 3.42 ( approx.) is the value of x by given equation .

We often read numbers in words like hundred, thousand, hundred thousand, and ten million. Which number has more digits than we can read? For example, the mass of the Earth is 5972190000000000000000000 kg. This cannot be read in simple words. Therefore, exponents are used to pronounce these kinds of numbers.

Exponents can be observed in four different types: positive, negative, zero, and rational/fractional. Numerical values ​​can be interpreted  using exponents as the total number of times a base must be multiplied by the same base.

3x^3/5 = 24

3x^3 = 120

x^3 = 40

x = [tex]\sqrt[3]{40}[/tex]  = 3.42 ( approx.)

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x=-20/13 and y=77/13 are solutions of 5x+4y=-16 and y= 2x+9

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

The two equations are

5x+4y=-16 ...(1)

Five x plus 4 y equal to minus sixteen.

y= 2x+9 ...(2)

y equal to two times of x plus nine.

Substitute 2 in 1.

5x+4y=-16

5x+4(2x+9)=-16

5x+8x+36=16

13x+36-16=0

13x+20=0

13x=-20

x=-20/13=-1.53

substitute the value of x in y.

y=2(-20/13)+9

y=(-40+117)/13

y=77/13

Hence the value of x is -20/13 and y value is 77/13.

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Answer: 16,000

100,000 x 0.04 x 4

    p         x    I     x T.  

A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls, then the ratio of rolls with double prints to rolls develop would be 5:7.

What is the ratio in mathematics?

A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.

A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls.

Then the ratio of rolls with double prints to develop = 1500/2100

Simplifying the above ratio we get

                                                                       = 5/7

Hence, the ratio of rolls with double prints to rolls develop would be 5:7.

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The probability that the player will receive a blackjack from  a player is dealt 2 cards from a standard deck of 52 well-shuffled cards is 0.0483.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

Combinations of drawing 1 ace * combinations of drawing 1 face cards / all possible 2 card combinations

4C1 * 16C1 / 52C2

4 * 16 / (52 * 51/2)

=64/1326

=.0483

When a player is dealt two cards from a standard deck of 52 properly shuffled cards, the likelihood that they will get a blackjack is 0.0483.

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According to the unitary method, the cost of each postcard is $0.7.

Unitary method:

Unitary method is used to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

Given,

Claudia buys 12 postcards, 12 stamps, and 1 pen. The postcards cost twice as much as the stamps. The pen costs $14.10.

Here we need to find the cost of the postcard.

In the given question, we have two variables, the price of the postcard and the price of the stamp, since the price for the pen is known.

And we also have the total cost of the purchase that is $14.1.

Therefore, now we have to create an equation as shown:

=> (12 x postcards) + (12 x stamps) + pen = 14.1

This equation refers the total amount spent by Claudia, but here we know that each pen costs $1.5, therefore:

When we apply the value on the equation then we get,

=> (12 x postcards) + (12 x stamps) + 1.5 = 14.1

=> (12 x postcards) + (12 x stamps) = 14.1 - 1.5

Therefore, (12 x postcards) + (12 x stamps) = 12.6

Here we also know that the postcards cost twice as much as the stamps, Then it can be written as,

postcards = 2 x stamps

By apply this value on the equation then we get the value of the stamp as,

=> (12 x (2 x stamps)) + (12 x stamps) = 12.6

=> (24 x stamps) + (12 x stamps) = 12.6

=> 36 x stamps = 12.6

Then the value of on stamp is stamps = 12.6/36

Therefore, the value of the stamps is 0.35

When we apply these values, then we get,

postcards = 2 x stamps = 2 x 0.35 = 0.7

Therefore, each postcard cost $0.7.

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Answer:

Ummm I dont even kno but s1

Step-by-step explanation:

Answer:

After 12 Seconds the cable would be 42 Ft down in depth

Step-by-step explanation:

3 1/2 Ft = 1 Second

3 1/2 Ft x 12 Seconds = 42Ft in Depth

The change in the depth of the fish trap after 12 second is 30 feet.

The mathematical operation of multiplication is arithmetic. Additionally, it involves repeating the same forms of statements.

Example: 2 + 3 signifies that 2 is multiplied by 3 or that 3 is multiplied by 2 times.

Given, a cable on a fishing boat lowers a fish trap into a lake at a rate of 3 1/2 feet per second.

[tex]3\frac{1}{2}[/tex] = 5/2 feet per second.

To find the change in depth of the fish trap after 12 seconds:

Multiplied by 12 to the rate of feet per second.

5/2 x 12

= 30 feet

The change of rate is 30 feet per 12 second.

Therefore, the change in depth is 30 feet per 12 second.

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The like terms to the Linear expression: 4a-4+6a-11 is 10a - 15

A Linear equations are the equations of degree 1. It is the equation for the straight line.

Collect the like terms of the expression

4a +6a -4 -11

Add the like terms

10a -15

Therefore the like terms in the linear expression is 10a -15

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The image of the point after the rotation is:

(-6, 7)

We have the point (-7, -6) and we want to apply a rotation of 270° counterclockwise.

This is equivalent to a rotation of 90° clockwise, so we will go from the third quadrant to the second quadrant, such that:

Then the image after the rotation is:

(-6, 7)

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Answer:

4[tex]x^{4}[/tex]

6[tex]x^{5}[/tex]

Step-by-step explanation:

For the first problem.  I am not sure what is going on with the -4.  Is it being added or multiplied by 2[tex]x^{2}[/tex]?  I left it out.

[tex](2x^{2}) ^{^{2} }[/tex] means 2[tex]x^{2}[/tex] (2[tex]x^{2}[/tex]) Which is 4[tex]x^{4}[/tex]

(2[tex]x^{2})\\[/tex]([tex]3x^{3)}[/tex]  multiple the 2 and the 3 and add the exonents

6[tex]x^{5}[/tex]

The value of f(4) = 0 by the given graph.

What is graph?

Graph is  diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Given graph is straight line, and the equation of line is given as

y =mx+b

where m is the slope and as we know  y is dependent variable,

we can write it as

f(x)= mx +b

The coordinates are (4,0) and (0,2)

m = 2-0/0-4

m = -1/2

y = -1/2 x +b

we can see the line intersect the y-axis at 0,2

b =2

y = -1/2 x +2

at x =4

f(4) = -2+2=0

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Answer:

C. Both

Step-by-step explanation:

You would substitute the coordinates into the equation to find the answer.

(4,-1)

-1 + 1 = 3 (4-4)

0 = 0

(5,2)

2 + 1 = 3(5-4)

3 = 3

Answer:

no because area is multiplication, but perimeter is adding.

Answer:

  162

Step-by-step explanation:

You want the sum of the first 9 terms described by ...

  a[n] = 7n -17

There are several ways the sum can be found. Most straightforward is simply adding up the terms:

  For n=1, 7n-17 = -10

  For n=2, 7n -17 = -3

The remaining 7 terms are 4, 11, 18, 25, 32, 39, 46.

The sum is ...

  -10 -3 +4 +11 +18 +25 +32 +39 +46 = 162

The terms form an arithmetic sequence with first term -10 and last term 46. The sum will be the average term multiplied by the number of terms:

  ((-10 +46)/2)(9) = 18(9) = 162

The sum can be decomposed into the sums whose formulas we know:

  [tex]\displaystyle \sum_{n=1}^9(7n-17)=7\sum_{n=1}^9{n}-17\sum_{n=1}^9{1} =7\cdot\left.\dfrac{n(n+1)}{2}-17n\right|_{n=9}\\\\= 7\cdot\dfrac{9\cdot10}{2}-17(9)=315-153=\boxed{162}[/tex]

The linear function that represents the cost of an adult ticket in dollars for a customer who contributes x cans of pet food is of:

y = 9.5 - 0.75x.

The graph is given by the image shown at the end of the answer.

The general format of a linear function is given by the rule shown as follows:

y = mx + b.

The terms of the linear function are listed and explained as follows;

The values of these terms in this function are given as follows:

The costs for the amounts of cans are given as follows:

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A parabola has a vertex at (-3,2) and is opening left.

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

So, a parabola has a vertex at (-3,2).

Now where is the axis of symmetry?

• Parabola opens downward or upward. The concept of the axis of symmetry is that, it is a line that when you fold the graph it will be one.

• in y=a(x-h)2+k where vertex is at (h,k), the axis of symmetry is x=h

Hence the answer is X=-3

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Answer:

Step-by-step explanation:

the answer would be 73 since the angle is split in half which means that they are both equal to each other

Applying the midpoint formula, the values of a and b are:

B. a = -8, b = -12

The midpoint formula is used to find the coordinates of the midpoint of a segment, which is given as:

M(x, y) = [tex](\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].

Given the points below:

(10, a) = [tex](x_1, y_1)[/tex]

(b, 6) = [tex](x_2, y_2)[/tex]

M(-1, -1) = (x, y)

Plug in the values:

(-1, -1) = [(b + 10)/2, (6 + a)/2]

Solve the variables separately

-1 = (b + 10)/2

-2 = b + 10

-2 - 10 = b

b = -12

-1 = (6 + a)/2

-2 = 6 +a

-2 - 6 = a

a = -8

The answer is: B. a = -8, b = -12

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A manufacturing machine has a 7% defect rate. If 4 items are chosen at random,

The probability of randomly choosing atleast one defective item would be 0.3043

Given the Parameters :

   Defect rate = P(defect) = 0.07

Probability = required outcome / Total possible outcomes

   P(atleast 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.07 = 0.93

P(none is defective) = P(non defective)^4

P(none defective) = 0.93 × 0.93 × 0.93 × 0.93 = 0.7480

P(atleast one is defective) = 1 - 0.7480 = 0.252

Therefore, probability of atleast one defective item is 0.252.

Hence the answer is, the probability of randomly choosing atleast one defective item would be 0.3043

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They take out one box from the warehouse because one box is sufficient for the requirement of 36 sweaters.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

There are 7 boxes, which contain a total of 63 sweaters in a store's warehouse.

The store needs 36 sweaters.

Here one box is sufficient for the requirement of 36 sweaters because it contains 63 sweaters.

Therefore, they take out one box from the warehouse.

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Answer:

largest angle is angle L

Step-by-step explanation:

the angle across the largest side of the triangle is the largest angle

The exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]

The expression is given that

{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}

Here we have to use the trigonometric functions

Find the each values of the term

sec π/4 = 1 / cos π/4

= 1 / (1 / [tex]\sqrt{2}[/tex] )

= [tex]\sqrt{2}[/tex]

Next term is cos 2π/3

cos 2π/3 = -1 / 2

Next term is tan π/6

tan π/6 = [tex]\sqrt{3}[/tex] / 3

Next term is csc 3π/4

csc 3π/4 =  [tex]\sqrt{2}[/tex]

Substitute the values in the expression

{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}

= (    [tex]\sqrt{2}[/tex] × (-1/2) ) / ( [tex]\sqrt{3}[/tex] / 3 ×  [tex]\sqrt{2}[/tex])

= - [tex]\sqrt{3} /2[/tex]

Hence, the exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]

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Inverse    [tex]f^{-1}(x) = \frac{log(x)}{log7}[/tex]    and  [tex]f(x) = 10^{x}[/tex].

[tex]f(x) = 7^{x}[/tex]

First, replace f(x) with f(y).

Now, [tex]y = 7^{x}[/tex]  will become [tex]x = 7^{y}[/tex]

Taking log on both sides,

log(x) = y(log 7)

y = log(x)/log 7.

Similarly, [tex]f^{-1}(x) = log_{10}x[/tex]

replace f(x) with f(y).

[tex]x = f^{-1}(y) = log_{10}y[/tex]

[tex]y = 10^{x}[/tex]

Hence, [tex]f(x) = 10^{x}[/tex].

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Answer:

Since [tex]s=\frac{3}{4}ft[/tex],

27 ÷ s² = 27 ÷ [tex](\frac{3}{4})^{2}[/tex]

            = 27 ÷ [tex]\frac{9}{16}[/tex]

            = [tex]\frac{27}{1}[/tex] × [tex]\frac{16}{9}[/tex]

            = 48

∴ Mr Grant would need to buy 48 of such square tiles.

Step-by-step explanation:

what that simply means is that the area he needs the files for is 27 ft².

as the tiles are squares, each one has an individual area of s² = 3/4 × 3/4 = 9/16 ft²

how many tiles do we need ?

as b many as how often the area of one tile fits into the total area :

27 ÷ s² = 27 / 9/16 = 27/1 / 9/16 = 27/1 × 16/9 =

= 3/1 × 16/1 = 3×16 = 48

he has to buy 48 tiles.

Answer: 1. no 2. 104

Step-by-step explanation: