The sum of two numbers is 4. Three times the larger number plus two times the smaller number is 26. Find the numbers.
The larger number is and the smaller number is

Solution :-

As we know that,

Therefore ,

>> m = -2 - (-3) / -1 - (-8)

>> m = -2 + 3 / -1 + 8

>> m = 1 / 7

We have that the data are:

(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)

The slope is equal to the change in and with respect to change in X, or what rises when moving forward.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}[/tex]

The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).

Introduce the values of x and y In the equation to find the slope.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}[/tex]

Answer: 75 hours

Step-by-step explanation:

"Aisha can make 50 bars of soap in 75 hours"

The division is one of the four fundamental arithmetic operations. The time it will take to make 50 soap bars if they both work together is 25.4543 hours.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Brianna can make 50 bars of soap in 40 hours, and Aisha can make 50 bars of soap in 75 hours. Therefore, we can write,

Soaps Made Briana in an hour = 50 bars/40 hours

                                                   = 1.25 soap bars per hour

Soaps Made Aisha in an hour = 50 bars/75hours

                                                   = 0.7143 soap bars per hour

Now, together the number of soap bars they can make in an hour is,

Number of soap bars in an hour = 1.25 + 0.7143 soap bars per hour

                                                      = 1.9643 soap bars per hour

Further, the time it will take to make 50 soap bars if they both work together is,

Time is taken = Number of soaps/ Number of soaps in an hour

                       = 50 soap / 1.9643 soap bars per hour

                       = 25.4543 hours

Hence, the time it will take to make 50 soap bars if they both work together is 25.4543 hours.

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The domain of the function y = 3 ln x is (0, ∞) .

The graph of the function y = 3ln x is given below .

Then , coordinate point (1, 0)

The logarithmic function y = log x has the domain x > 0 (or) (0, ∞).

This is a logarithmic function. An important property of logarithms is that the domain cannot be denied. The same is true for x=0, since the logarithm of negative numbers is undefined.

The image attached shows the graph of this function, there you can notice its domain restriction.

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The domain of the given relation is: {x| x = –7, –6, 2, 3, 11}.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Additionally, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

In this context, we can reasonably infer and logically deduce that the domain of the given relation include the following: {x| x = –7, –6, 2, 3, 11}.

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The domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

The domain of a function is the set of inputs that are accepted by the function. The range, also known as the codomain, is the set of all the output values of the function.

Here, we are given a relation with the following set of solutions-  

{(5,-3), (2,2), (0, -3), (2,1) (5,3)}

We know that all x values will form the domain and all the y values will make up the range.

Here the x values are: 5, 2, 0, 2, 5

and the y values are: -3, 2, -3, 1, 3

Thus, the domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

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The prime factors of 6912 are 2 and 3 and the cube root of 6912 is approximately 19.05 (rounded to 2 decimal places) .

Prime numbers are numbers which do not have any factors other than 1 and itself. For example 7 is a prime number, 37 is a prime number as the factors of 7 are 1 and 7 and the factors of 37 are 1 and 37.

Prime factorization of a number is given by writing all the prime factors of as number in multiplication form.

The prime factorization of 6912 gives:

6912 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁸ × 3³

Hence the prime factors of 6912 are 2 and 3.

The cube root of 6912 = 19.0488... ≈ 19.05 (rounded to 2 decimal places)

Therefore the cube root of 6912 is approximately 19.05 .

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The value of -5*g(4)-1 is 9.

It is a question of functions.

Here, g is a function of x.

Function

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Let X and Y be any two non-empty sets; mapping from X to Y will be a function only when every element in set X has one end, only one image in set Y.

Given that:-

g(x) = 1 - (3/4)x

We have to find the value of  -5*g(4)-1

First we will find g(4),

g(4) = 1 - (3/4)*(4) = 1 - 3 = -2

-5*g(4) - 1 = -5*(-2) - 1 = 10 - 1 = 9

Hence, the value of -5*g(4) - 1  is 9.

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The interpretation of the y-intercept of the model is (d) when the attendance is 0, the number of wins is 15.2

The equation of the linear regression model is given as

y = 4.9x + 15.2

The y-intercept of the model implies that

x = 0

Substitute x = 0 in the equation of the linear regression model given as

y = 4.9x + 15.2

So, we have

y = 4.9 x 0 + 15.2

Evaluate the product

So, we have

y = 0 + 15.2

Evaluate the sum

So, we have

y = 15.2

Hence, the interpretation of the y-intercept of the model is (d) when the attendance is 0, the number of wins is 15.2

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.

and it is outdated. your teacher and the manufacturer should use joules as metric.

1 BTU ≈ 1055 joules

anyway, so, the solution has several parts.

we need to find how many pounds of water are in a gallon.

and then multiply by the amount of gallons (20 000) and the amount of degrees (2 from 70 to 72).

and after a little search on the internet we get

1 gallon of water = 8.34 pounds

so, we need to warm

20000×8.34 pounds of water by 2 degrees F.

that is

20000 × 8.34 × 2 = 333,600 BTU

if we use only the rounded value of pounds per gallons (8.3), this would be

20000 × 8.3 × 2 = 332,000 BTU

so in any case, B is the right answer (as being the closest to the real result), which is the situation with any size classification of devices : reality is somewhere close by, but never meets the exact specifications.

Answer:

1

Step-by-step explanation:

let the number be n

3n + 9 = 12

3n = 12 - 9 = 3

n= 3/3

n= 1

Answer:

no solution

Step-by-step explanation:

Multiplying the second equation by 2 gives 2x-14y=38.

Adding this to the first equation, we get 0=9, and thus there is no solution.

Answer: 12 electoral college votes

Step-by-step explanation:

4*100%=

4*100/100=

400/100=4

4*300%=

4*300/100=

1200/100=12 votes

The number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours

The given parameters can be represented using the following table of values

                              Mine 1 (x)              Mine 2 (y)   Available

Regular grade          6                            18             420

Low grade               16                             8              480

Operating cost      20500                     10200

Time                        55                              36

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 20500x + 10200y

Subject to:

6x + 18y >= 420

16x + 8y >= 540

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (26.5, 14.5)

This means that

Mine 1 hour = 26.5 hours

Mine 2 hour = 14.5 hours

Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours

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Answer:

[tex]\sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]

Step-by-step explanation:

Given equation:

[tex](x^2+2)^{\frac{5}{2}}+2x(x^2+2)^{\frac{3}{2}}+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Rewrite the exponents }\frac{5}{2} \textsf{ as } \left(\frac{1}{2} \cdot 5\right)\textsf{ and }\frac{3}{2} \textsf{ as }\left(\frac{1}{2} \cdot 3\right):[/tex]

[tex]\implies (x^2+2)^{\frac{1}{2} \cdot 5}+2x(x^2+2)^{\frac{1}{2}\cdot 3}+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left((x^2+2)^{\frac{1}{2}}\right)^5+2x\left((x^2+2)^{\frac{1}{2}}\right)^3+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies \left(\sqrt{x^2+2}\right)^5+2x\left(\sqrt{x^2+2}\right)^3+x^2\sqrt{x^2+2}[/tex]

Factor out [tex]\sqrt{x^2+2}[/tex] from each of the three terms:

[tex]\implies \sqrt{x^2+2}\left[\left(\sqrt{x^2+2}\right)^4+2x\left(\sqrt{x^2+2}\right)^2+x^2\right][/tex]

[tex]\textsf{Factor the expression in the parentheses using} \quad a^2+2ab+b^2=(a+b)^2.[/tex]

[tex]\textsf{Let }a=\left(\sqrt{x^2+2}\right)^2 \textsf {and }b=x:[/tex]

[tex]\implies \sqrt{x^2+2}\left(\left(\sqrt{x^2+2}\right)^2+x\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a^2}=a:[/tex]

[tex]\implies \sqrt{x^2+2}\left(x^2+2+x\right)^2[/tex]

[tex]\implies \sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]

The domain of the given function is; (0, 2)

The range of the given function is; (-2, 6)

We want to evaluate the function f(x) = 4x - 2 for x = 0, 1 and 2.

Step 1;

f(0) = 4(0) - 2

f(1) = 4(1) - 2

f(2) = 4(2) - 2

Step 2;

f(0) = 0 - 2 = -2

f(1) = 4 - 2 = 2

f(2) = 8 - 2 = 6

The domain is the set of all possible input values which is (0, 2)

The range is the set of all possible output values which is (-2, 6)

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Answer:

a = 2

b = 3

c= 8

Step-by-step explanation:

a) 4 = [tex]2^{2}[/tex]  We want to have all of the bases the same in the powers, so we will convert 4 to a base of 2.

b) When we divide with powers with the same baes, we subtract the exponents.  (5-2 =3)

c) [tex]2^{3}[/tex] means 2x2x2 or 8

The statement that is true is: A. segment XZ is perpendicular to segment WY.

When two lines intersect at a point to form right angles (90 degrees), both lines are said to be perpendicular to each other.

We are told that angle YXZ is equal to 90 degrees. This is the angle formed at the point where segment XZ intersects segment WY at point X.

This means that both lines are perpendicular to each other.

Therefore, the statement that is true is: A. segment XZ is perpendicular to segment WY.

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The compound inequality that represents the set of real numbers that are between -4 and 5 inclusive is the option;

D: -4 ≤ n ≤ 5

A compound inequality comprises of a sentence that makes two inequality statements that are joined by either the word 'and' or 'or'.

Given that the inequality represents the set of all real numbers that are between -4 and 5, and -4 < 5, the required set of numbers is therefore of the form;

[tex] - 4 \: \leftrightarrow \: 5[/tex]

The expression of the required set of numbers as inequalities is therefore;

The compound inequality is therefore;

D: -4 ≤ n ≤ 5

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The length of both UV and ST is [tex]3\sqrt{2}[/tex] and hence they both are congruent.

Here, we are given two lines- UV and ST.

We can find the length of the lines using distance formula. According to distance formula, distance between two points- (x1, y1) and (x2, y2) is given as-

[tex]\sqrt{(x2-x1)^{2} + (y2 - y1)^{2} }[/tex]

Here, for UV,

the two endpoints are- (1,0) and (4,3)

thus, the length of UV will be-

[tex]\sqrt{(4-1)^{2} + (3 - 0)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (3 )^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

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

Similarly, the two endpoints of ST are- (-2,-1) and (1,-4)

thus, the length of UV will be-

[tex]\sqrt{(1+2)^{2} + (-4 +1)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (-3)^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

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

So we can see that UV = ST = [tex]3\sqrt{2}[/tex], which means that both of them are congruent. Hence, option 1 is the correct answer.

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Your question was incomplete. Check for the missing figure below.

The correct option is that;

C. Leon overpaid for his purchase by $2.60 if he paid $44.64.

The vendor, who is acting as the state's agent, collects the sales tax and remits it to the state on behalf of the final customer. The use tax, on the other hand, is self-assessed and paid by the final customer.

Given that;

Purchase fuel = 12 Gallons per $2.89 per gallons (including Tax)

2 Granola Bar for $1.59 per bar

1  apple for $0.89

2 bottles of vitamin water for $1.39

The sales Tax rate is 7.5%

Required to calculate the difference amount of Actual Paid and Actual Purchase =?

Fuel = 12 x 2.89 = $34.68 (including tax)

Granola Bar = 2 x 1.59 = $3.18

Apple = 1 x 0.89 = $0.89

Vitamin Water = 2 x 1.39 = $2.78

Total Purchase excluding fuel without tax is,

= $3.18 + $0.89 + $2.78

= $6.85.

Adding sale tax on  $6.85 at the rate of 7.5% = $7.36

Hence, Total Purchase including Tax is,

$7.36 + $34.68 = $42.04

Thus, there is a clear difference that Leon paid 2.60 more than his actual purchase. He paid $ 44.64 and his actual purchase is 42.04 the difference between that is $2.60.

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The interpretation of the value of the function, [tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex], when x = 30 is that by running up 30 steps, Jayden burns [tex] 13 \frac{1}{3} [/tex] calories.

The domain of the function is the set of all real numbers

The given function is presented as follows;

[tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex]

Where;

f(x) = The number of calories burnt

x = The number of steps Jayden runs

The value of x is negative while running down the stairs

Therefore;

[tex]f(30) = \frac{1}{25} \times \left( \left |6 \times 30 \right | + 5 \times 30 \right) = 13 \frac{1}{3} [/tex]

[tex]f(30) = 13 \frac{1}{3} [/tex]

The interpretation of the above function equation is that the amount of calories Jayden burns when she runs 30 steps up the stairs is [tex] 13 \frac{1}{3} [/tex]

Given that 6•x > 5•x, the function is always positive, and has a minimum value of zero, the function can take any value for x.

The domain of the function is therefore, -∞ ≤ x ≤ ∞, which is the set of all real numbers.

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Answer:

This relation is not a function.

Step-by-step explanation:

Function

A relation is a function when each input (x-value) has a single output (y-value).

A function is one-to-one if each output (y-values) corresponds to exactly one input (x-values).

A function is many-to-one if some outputs (y-values) correspond to more than one (many) inputs (x-values).

In the given relation, one input value (x = 4) corresponds to two output values.  Therefore, this relation is not a function.

(See attached Relation Arrow Diagram).

2. The solution to the given system of equation is x = 1 and y = 6

3. The solution to the given system of equations is x = 1, y = 2

4. The simplified form of the expression is y²

5. The simplified form of the expression is 2

8. the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11

9. The multiplication yields x² - 4x - 96

10. The factored form of the expression is (x + 6)(x- 6)

11. The solutions to the given quadratic equation are x = 5 and x = -6

From the question, we are to solve the given system of equations

The given system of equation is

y = 10 - 4x      --------- (1)

2x + 3y = 20  --------- (2)

Substitute equation (1) into equation (2)

2x + 3y = 20

2x + 3(10 -4x) = 20

2x + 30 - 12x = 20

2x - 12x = 20 - 30

-10x = -10

x = -10/-10

x = 1

Substitute the value of x into equation (1)

y = 10 - 4x

y = 10 - 4(1)

y = 10 - 4

y = 6

Hence, the solution to the given system of equation is x = 1 and y = 6

3.

From the question, we are to solve the system of equations using the elimination method

The given system of equations is

5x + 2y = 9

-5x + 4y = 3

Add the two equations

5x + 2y = 9

-5x + 4y = 3

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

0x + 6y = 12

6y = 12

y = 12/6

y = 2

Substitute the value of y into the first equation

5x + 2y = 9

5x + 2(2) = 9

5x + 4 = 9

5x = 9 - 4

5x = 5

x = 5/5

x = 1

Hence, the solution to the given system of equations is x = 1, y = 2

4. From the question, we are to simplify the expression

y⁻⁴(y³)²

First, multiply the exponents in (y³)²

(y³)² = y ³ ˣ ²

= y⁶

Thus,

The expression becomes y⁻⁴y⁶

Applying the multiplication law of indices

y⁻⁴y⁶ = y⁻⁴ ⁺ ⁶

= y²

Hence, the simplified form of the expression is y²

5.

From the question, we are to simplify

∛8

First, express 8 in exponent form

8 = 2³

Thus,

The expression becomes

∛2³

Applying one of the laws of indices,

∛2³ = (2³)¹/³

Multiplying the exponents, we get

2¹

= 2

8.

From the question, we are to subtract the polynomial

(3x² + 5x - 8) - (2x³  - 4x + 3)

Subtracting

(3x² + 5x - 8) - (2x³  - 4x + 3)

3x² + 5x - 8 -(2x³  - 4x + 3)

Open the parentheses by distributing negative

3x² + 5x - 8 -2x³  + 4x - 3

Collect like terms

-2x³ + 3x² + 5x + 4x - 8 - 3

Simplify

-2x³ + 3x² + 9x - 11

Hence, the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11

9.

From the question we are to multiply

(x + 8)(x - 12)

Applying the distributive property

x(x -12) +8(x -12)

x² - 12x + 8x - 96

Simplifying

x² - 4x - 96

10.

From the question, we are to factor

x² - 36

This can be written as

x² - 6²

From the rule of difference of two squares, we have that

a² - b² = (a + b)(a - b)

Thus,

x² - 6² = (x + 6)(x- 6)

11.

From the question, we are to find the solutions for

x² - x - 30 = 0

Solve by factoring

x² - x - 30 = 0

x² + 6x - 5x - 30 = 0

x(x + 6) -5(x + 6) = 0

(x - 5)(x + 6)  = 0

∴ x - 5 = 0 and x + 6 = 0

x = 5 and x = -6

Hence, the solutions to the given quadratic equation are x = 5 and x = -6

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Answer:

$95.88

Step-by-step explanation:

multiply 6 by 17 and get 102

multiply 102 by 0.94 and get 95.88

For the relations (tables) from left to right we have:

1) Is not a function, because the input 5 is mapped into two different values.

2) Is not a function, because the input -1 is mapped into two different values.

3) It is a function.

4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).

A relation is an operation that maps elements from one set called the domain (set of the inputs) into elements of another set, called the range (set of the outputs).

Now, a relation is a function only if each element of the domain is mapped into only one element of the range. So, if you see the same input in a table two times (related to two different outputs) then that table does not represent a function.

Then, for the tables reading from left to right, we have:

1) Is not a function, because the input 5 is mapped into two different values.

2) Is not a function, because the input -1 is mapped into two different values.

3) It is a function.

4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).

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Step-by-step explanation:

8x+20 is the answer ......

It should be noted that the wind speed is 70km per hour and the plane speed is 490km per hour.

Based on the information given, the following an be illustrated.

Let P = speed of plane

Let w = speed of wind

The appropriate equation will be:

(P + W) (3/2) = 840 ....... i

(P - W) × 2 = (840 / 2) ...... ii

P + W = 560 .....i

P - W = 420 ......ii

Subtract the equations

2P = 980

P = 980 / 2 = 490

P + W = 560

490 + W = 560

W = 560 - 490

W = 70

Therefore, the wind speed is 70km per hour and the plane speed is 490km per hour.

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The triangles ΔRST and ΔXYZ are congruent, then all the same construction make triangles congruent. All the options are correct.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If two triangles are congruent, then the ratio of the corresponding sides will be one.

The triangles ΔRST ≅ ΔXYZ. Points P and W lie on ST and YZ, respectively.

The diagram is given below.

A) If P is the midpoint of ST and W is the midpoint of YZ then ΔRSP ≅ ΔXYW is true.

B) If RP bisects ∠SRT and XW bisects ∠YXZ, then ΔRSP ≅ ΔXYW is true.

C) If RP = XW, then ΔRSP ≅ ΔXYW is true.

D) If RP ⊥ ST and XW ⊥ YZ, then ΔRSP ≅ ΔXYW is true.

All the options are correct.

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