Given the function ƒ(x) = 3x + 5, find ƒ(4) and x such that ƒ(x) = 38.

Select one:
A. 17; 11
B. 20; 13
C. 12; 15
D. 24; 9

Answer:

Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.

Step-by-step explanation:

Let us consider the system of equation below.

[tex]4x-5y=3[/tex]

[tex]3x+5y=13[/tex]

Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.

Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.

As the given system of equation

[tex]4x-5y=3[/tex][tex]......[1][/tex]

[tex]3x+5y=13[/tex][tex]......[2][/tex]

Adding Equation 1 and Equation 2

[tex]4x-5y+3x+5y=3+13[/tex]

[tex]7x=16[/tex]

[tex]x=[/tex][tex]\frac{16}{7}[/tex]

Putting [tex]x=[/tex][tex]\frac{16}{7}[/tex] in Equation [1]

[tex]4x-5y=3[/tex][tex]......[1][/tex]

[tex]y=[/tex][tex]\frac{43}{35}[/tex]

Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.

For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.

As the given system of equation

[tex]4x-5y=3[/tex][tex]......[1][/tex]

[tex]3x+5y=13[/tex][tex]......[2][/tex]

Solving the equation 2 for x variable

[tex]3x=13-5y[/tex]

[tex]x=\frac{13-5y}{3}[/tex]

Plugging [tex]x=\frac{13-5y}{3}[/tex] in equation [1]

[tex]4(\frac{13-5y}{3}) -5y=3[/tex]

[tex]y = \frac{43}{35}[/tex]

Putting [tex]y = \frac{43}{35}[/tex] in Equation 2

[tex]3x+5y=13[/tex][tex]......[2][/tex]

[tex]x = \frac{16}{7}[/tex]

So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.

Similarly, using graphing method, it would take a certain time before we identify the solution of the system.

Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.

Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

Keywords: substitution method, system of equations, elimination method

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The substitution and graphing methods are less efficient methods than elimination method for this system as there is extra amount of steps we have to take to solve the same system of equations 4x-5y=3  , 3x+5y=13

We have equations

4x-5y=3  ... (1)

3x+5y=13 ...(2)

Substituting the value of 5y = 13-3x from equation (2) into equation(1)

4x-(13-3x)=3

4x-13+3x=3

7x= 3+13

7x= 16

x = [tex]\frac{16}{7}[/tex]

Substitute the value of x = [tex]\frac{16}{7}[/tex] in y value, we get

[tex]5y=13-3(\frac{16}{7} )\\y=\frac{43}{35}[/tex]

4x-5y=3

3x+5y=13

Adding both the equations, we get

[tex]7x=16\\x=\frac{16}{7}[/tex]

Put the value of x in any one of the above equation, we get

[tex]3\frac{16}{7} +5y=13\\y=\frac{43}{35}[/tex]

So, the Elimination method is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation and it is less time consuming.

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Answer:

x=(3+sqrt(7)*i)/4, (3-sqrt(7)*i)/4.

Step-by-step explanation:

Apply the quadratic formula.

Answer:

[tex]x = \frac{3 +/- i \sqrt{7} }{4}[/tex]

Step-by-step explanation:

[tex]2x^{2} -3x + 2 = 0[/tex]

a =2 b = -3 c = 2. Substitute these into the quadratic formula [tex]x = \frac{-b +/- \sqrt{b^{2}- 4ac} }{2a}[/tex].

[tex]x = \frac{-(-3)+/- \sqrt{(-3)^{2} - 4(2*2)} }{2(2)}[/tex] Simplify.

[tex]x = \frac{3+/-\sqrt{(9)^{2} - 4(4) } }{4}[/tex] Keep simplifying...

[tex]x = \frac{3+/-\sqrt{9-16} }{4}[/tex] Simplify again...

[tex]x = \frac{3 +/-\sqrt{-7} }{4}[/tex] There will be an imaginary number because the number under the [tex]\sqrt{}[/tex] is negative, so

[tex]x = \frac{3+/-i\sqrt{7} }{4}[/tex]

Answer:

5x^2-6x-10

Step-by-step explanation:

(2x^2-2x)-(-3x^2+4x+10)

2x^2-2x+3x^2-4x-10

5x^2-2x-4x-10

5x^2-6x-10

Solving for x...

3/4x+2=5/4x-6

8=2/4x

8=1/2x

x=16

To find the value of x in the given equation, we can eliminate the fractions, combine like terms, and solve for x. The value of x is 16.

To find the value of x in the equation 3/4x+2=5/4x-6, we need to isolate x on one side of the equation. We can do this by first getting rid of the fractions. Multiplying each term in the equation by the LCD (Least Common Denominator) of 4 will help us eliminate the fractions. Then, we can combine like terms and solve for x.

Finally, we can divide both sides by 2 to solve for x: (32/2) = 2x/2, resulting in x = 16.

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Answer:

Step-by-step explanation:

The school store sells packs of 12 pens for $2.40.  

Select the three unit rates that describe this sale.

There is more than one correct answer

$0.20 per pen

$2.40 per pack of pens

5 pens per dollar

120 pens per $24

HOPE THIS HELPED ;3

Answer:

50.3% of profit.

Step-by-step explanation:

English muffins are on sale for $1.99 per package, but only if you buy five packages.

Therefore, the price of five packages of muffins on sale is $(1.99 × 5) = $9.95.

There is a $1.00 discount per package on sale.

So, the ordinary price per package of muffins is $(1.99 + 1) = $2.99.

Therefore, the ordinary price of five packages of muffins is $(2.99 × 5) = $14.95.

Hence, the percentage of profit that I will make when I purchase the package of muffins in the sale is [tex]\frac{14.95 - 9.95}{9.95} \times 100\% = 50.25\%[/tex] ≈ 50.3 % (Answer)

Answer:

[tex]15x\geq 105[/tex]

Step-by-step explanation:

Hence, the inequality represents how long Johnny needs to work to afford his new bike is

[tex]15x\geq 105[/tex]

What is the inequality?

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

Here given that,

Johny earns $[tex]15[/tex] per hour dog walking. So, he wants to earn at least $[tex]105[/tex] to buy a new bike.

So, the inequality is

[tex]15x\geq 105[/tex]

Hence, the inequality represents how long Johnny needs to work to afford his new bike is

[tex]15x\geq 105[/tex]

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Answer: The answer is 0.2

Step-by-step explanation:

1 divided by 5 is 0.2 because 1 goes into 5 0.2 times.

Hope this helps!

Answer:

4.9%

Step-by-step explanation:

To find the percentage you first find the decrease in price, divide it by the original price then multiply it by 100.

(14. 44-13. 72)

= -------------------- ×100

14. 44

0. 72

= -------- × 100

14. 44

= 0. 72× 6. 925207759

= 4. 986149584

~ 4. 9

Answer: $63.90

Step by Step explanation:

$1,278 + 5% = 63.90

Answer: 14 cakes

Step-by-step explanation:

We have the following data:

Number of gallons the baker has: [tex]4 gallons \frac{16 cups}{1 gallon}=64 cups[/tex]

Number of cups the baker used for one cake: [tex]4,5 cups[/tex]

Now, we can use the Rule of three  to find the maximum number of cakes the baker can completely decorate:

[tex]4.5 cups[/tex]-----​[tex]1 cake[/tex]

[tex]64 cups[/tex]-----​[tex]?[/tex]

Then:

​[tex]?=\frac{(64 cups)(1 cake)}{4.5 cups}[/tex]

​[tex]?=14,2 cakes \approx 14 cakes[/tex]

Answer:

Step-by-step explanation:

9,899,399+2082

=9901481

Final answer:

To find out what 9,899,399 increased by 2,082 is, add the two numbers together, resulting in 9,901,481.

Explanation:

The question asks what the result will be if the number 9,899,399 is increased by 2,082. To find the result, we simply need to add the two numbers together. This type of problem involves basic arithmetic operations and is fundamental in understanding how to manipulate and work with numbers.

To calculate the result:

Start with the original number: 9,899,399.

Add the increase: 2,082.

Perform the addition: 9,899,399 + 2,082 = 9,901,481.

Therefore, when the number 9,899,399 is increased by 2,082, the result is 9,901,481.

Answer:

Step-by-step explanation:

This kinda looks like the limiting definition of a derivative.  

Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x.  That looks like this:

f(2 + h) = 2(2 + h) - 3 which simplifies to

f(2 + h) = 4 + 2h - 3 which simplifies to

2h + 1

From that we are subtracting f(2).  What we are doing with that is evaluating f(x) with 2 in place for x.  That looks like this:

f(2) = 2(2) - 3 which simplifies to

f(2) = 4 - 3 which simplifies to

f(2) = 1.  Now put those together over h to get:

[tex]\frac{f(2+h)-f(2)}{h}=\frac{2h+1-1}{h}=\frac{2h}{h}=2[/tex]

-x + 2y = -4

-x = -2y - 4

x = 2y + 4

5(2y + 4) - 4y = 8

10y + 20 - 4y = 8

6y + 20 = 8

6y = -18

y = -3

-x + 2y = -4

-x + 2(-3) = -4

-x - 6 = -4

-x = 2

x = -2

The coordinate pair is (-2, -3) (x = -2, y = -3.)

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Answer:

81/16

Step-by-step explanation:

Answer:

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-4)/(-2-10)

m=-9/-12

m=9/12

m=3/4

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

m=(y2-y1)/(x2-x1)

m=(8-1)/(7-(-7))

m=7/(7+7)

m=7/14

m=1/2

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

m=(y2-y1)/(x2-x1)

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

m=2/1

m=2

Final answer:

The slope of a line between two points is found using the formula slope (m) = (y2 - y1) / (x2 - x1), with an example given for points A (10,4) and B (-2,-5), resulting in a slope of 3/4.

Explanation:

The slope of a line passing through two points (A and B) can be determined using the formula slope

(m) = (y2 - y1) / (x2 - x1).

This formula calculates the rate of change in the y-values with respect to the x-values, resulting in a description of the steepness of the line.

For example, let's find the slope for points A (10,4) and B (-2,-5). Applying the formula, we have:

m = (y2 - y1) / (x2 - x1) = (-5 - 4) / (-2 - 10) = (-9) / (-12) = 3/4

The slope between points A and B is 3/4. This process can be repeated for other pairs of points to find the respective slopes.

Answer:

Charnessa has 4 times as many apples as Luke. Luke has -8 apples.

Hope this is what you were looking for :)

Option B

12 over quantity x minus 7, x ≠ 7, x ≠ −3

Solution:

Given that we have to simplify quantity 12 x plus 36 over quantity x squared minus 4 x minus 21

So we have to simplify,

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 }[/tex]

We have to find the restrictions on the variable

The above given Rational function is defined, for

[tex]{x}^{2} - 4x - 21\ne0\\\\(x+3)(x-7)\ne0\\\\x\ne -3,x\ne7[/tex]

In order to simplify the above expression, we need to factor both the numerator and the denominator

[tex]\rightarrow \frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ {x}^{2} - 4x - 21}[/tex]

For the denominator, we need to split the middle term of the quadratic to get factored form,

[tex]\rightarrow \frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ {x}^{2} - 7x + 3x- 21}[/tex]

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ x(x - 7) + 3(x- 7)}[/tex]

Fcatoring the denominator part,

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ (x + 3)(x - 7)}[/tex]

Cancel out common factors to get,

[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12}{x - 7} \\\\where\\\\x\ne -3,x\ne7[/tex]

Thus option B is correct. 12 over quantity x minus 7, x ≠ 7, x ≠ −3

The simplified expression is 12 / (x - 7) with restrictions x ≠ 7, x ≠ -3. The correct answer is option b.) 12 over quantity x minus 7, x ≠ 7, x ≠ −3.

The expression((12x + 36) / (x² - 4x - 21)) and finding the restrictions on the variable.

First, we factor both the numerator and the denominator.

The numerator can be factored as 12(x + 3).

The denominator can be factored by finding two numbers that multiply to -21 and add to -4, which are -7 and 3.

Thus, the denominator factors to (x - 7)(x + 3). Our expression then simplifies to (12 / (x - 7)), after cancelling out the (x + 3) terms.

To find the restrictions on the variable, we note that the original denominator, (x² - 4x - 21), cannot be zero, as division by zero is undefined.

Setting (x - 7)(x + 3) to zero gives us the restrictions x ≠ 7 and x ≠ -3, to ensure the denominator is not zero.

Therefore, the simplified expression is 12 / (x - 7), with the restrictions x ≠ 7, x ≠ -3.

Hey, I'd like to give you a professional response.

First we need to re-group terms.

1. 2(3+g)−g=−4(g+1)

Let's also expand the terms.

6+2g−g=−4g−4

Simplify 6+2g-g to 6 + g.

6+g=-4g-4

Add 4g to BOTH sides.

6+2g−g=−4g−4

Simplify 6+g+4g to 6+5g.

6+5g=-4

Now subtract 6 from both sides.

5g = -4-6

Simplify -4 - 6 to -10.

Now you have 5g = -10.

g = -10/5 (Divide both sides by 5)

Simplify -10/5 to 2.

G = 2

Let's check our answer.

First let g = 2.

2+2 X (3-2) = -4 X (-2 + 1)

2 + 2 X 1 = -4 X (-2 +1)

2 + 2 X 1 = -4 x -1

2+2 = -(-4)

Remove the parentheses,

4 = 4 This problem has been checked.

Area of the rectangle: 14.5 x 22 = 319 square meters.

Area the goat can reach ( area of a circle): 3.14 x 2.5^2 = 19.625 square meters.

Now subtract the area of the circle from the area of the rectangle:

319 - 19.625 = 299.375 square meters.  (Round the answer as needed.)

Answer:

OPTION D: NEITHER

Step-by-step explanation:

The given equation is: 7x - 2y = - 5

To find a solution to this, we substitute the options and compare LHS and RHS.

OPTION A: (1, 5)

LHS = 7(1) - 2(5) = 7 - 10 = -3

RHS = - 5

LHS [tex]$ \ne $[/tex] RHS.

So, this option is eliminated.

OPTION B: (-1, 1)

LHS = 7(-1) - 2(1) = -7 - 2 = - 9

RHS = - 5

Again, LHS [tex]$ \ne $[/tex] RHS.

So, this Option is eliminated as well.

OPTION C: It says both A and B. Clearly, this is eliminated as well.

Therefore, the answer is: OPTION D: NEITHER.

NOTE: This is a two variable equation. So, we need a minimum of two equations to determine the solution. Since, only one equation is given here, we use the help of options.

                               Question # 1 Solution:

As the expression [tex]13v + 8f +6b+3m[/tex] represents her cost, in dollars for the arrangements when she buys

Which statement is true?

A.The term 13v represents the cost of 13 vases.

B.The coefficient 6 represents the cost of b stems of wood bark.

C.The term 8f represents the cost of f stems of flowers at $8 per stem.

D.The coefficient 3 represents the number of packages of marbles she buys.

Choosing the correct statement:

As the formula for cost of any item can be calculated by multiplying the cost of one item with the total number of items.

So, if f represents the stems of flowers, and the cost of f stems of flowers at $8 per stem. Then according to the formula for cost of any item, the statement C is true i.e. "The term 8f represents the cost of f stems of flowers at $8 per stem" is the correct statement.

                           Question # 2 Solution

As the inequality is given as:

                                12x + 9x - 3 ≤ 3(2x + 14)

and we have to find the value of x.

So,

12x + 9x - 3 ≤ 3(2x + 14)

Step 1: Simplify both sides of the inequality

21x - 3 ≤ 6x + 42

Step 2: Subtract 6x from both sides.

21x - 3 - 6x ≤ 6x + 42 - 6x

15x - 3 ≤ 42

Step 3: Add 3 to both sides.

15x - 3 + 3 ≤ 42 + 3

15x  ≤ 45

Step 4: Divide both sides by 5

15x/5 ≤ 45/5

3x  ≤ 9

x ≤ 9/3

So, x ≤ 9/3 is the right answer. Please note that x ≤ 9/3 can also be written as x ≤ 3.

Hence, option A i.e. x ≤ 9/3 is correct. The solution graph is also attached in figure a.

                               Question # 3 Solution

As we have to find the correct statements from the given graph that represents John's weight (in pounds) as a function of time t, measured in days since January 1, 2017.

So, here are the correct statements that validate the graph:

Keywords: inequality, equation, graph, rate of change, function

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Answer:

Jamie has 11/15 yards of Green Felt more than Blue Felt

Step-by-step explanation:

Green felt- Blue felt

= 5/6- 1/10

= 25/30- 3/30  ( taking LCM)

= 25 - 3/30

=22/30

=11/15 yards

LCM= 2*3*5= 30

Factors of 6= 2*3

Factors of 10= 2*5

Answer:

In order to determine the density of a solid , it is necessary to determine the mass and the volume

Step-by-step explanation:

Answer:

density of a solid?

Answer

Density of a solid

Mass/Volume

So (i) measure the mass, and (ii) measure the volume, and then take the quotient.

Of course, the mass is easy to measure. The volume is a little harder to assess, especially if it is an irregularly shaped solid, however, volume displacement of a liquid would be a quite feasible means.

Step-by-step explanation:

Density of salt is in the picture above please mark me brainliest

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Answer:

The answer is 10/27

Step-by-step explanation:

5/6 times 4/9 is equal to 10/27

Answer:

The solution is the point (-5,-3)

Step-by-step explanation:

The complete question is

Consider the linear system of equations y = 2/5x - 1 and 2x -3y + 1 = 0

The solution of the system of equations is?

we have

[tex]y=\frac{2}{5}x-1[/tex] ----> equation A

[tex]2x-3y+1=0[/tex] ----> equation B

Solve by substitution

substitute the equation A in equation B

[tex]2x-3(\frac{2}{5}x-1)+1=0[/tex]

solve for x

[tex]2x-\frac{6}{5}x+3+1=0[/tex]

[tex]2x-\frac{6}{5}x+4=0[/tex]

Multiply by 5 both sides to remove the fraction

[tex]10x-6x+20=0[/tex]

[tex]4x+20=0[/tex]

subtract 20 both sides

[tex]4x=-20[/tex]

divide by 4 both sides

[tex]x=-5[/tex]

Find the value of y

[tex]y=\frac{2}{5}(-5)-1[/tex]

[tex]y=-3[/tex]

The solution is the point (-5,-3)

The question involves solving a system of linear equations from high school algebra. Substituting Y from the first equation into the second and solving for x, we find that x = -5 and Y = -3.

The student is asking about solving a system of linear equations, which is a concept in algebra that falls under high school mathematics. To find the solution to the given linear system, we can use either substitution or elimination methods. Let's use substitution since the first equation has Y isolated.

From the first equation Y = 2/5x - 1, we substitute for Y in the second equation, which gives us 2x - 3(2/5x - 1) + 1 = 0. Simplifying, we get 2x - 6/5x + 3 + 1 = 0, which further simplifies to 4/5x + 4 = 0. Solving for x gives x = -5. Substituting x back into the first equation to find Y yields Y = 2/5(-5) - 1, so Y = -3. Therefore, the solution to the system of equations is x = -5 and Y = -3, which is the point where the two lines intersect.

Option A and Option B

The equivalent expressions for 24k + 36q - 12 are 12(2k + 3q - 1) and 3(8k + 12q - 4)

Solution:

Given that we have to factor 24k + 36q - 12

To factor a number or expression containing variables means to break it up into smaller numbers or expressions that can be multiplied together to get the original number or expression

Given expression is:

24k + 36q - 12

So for numbers 24 , 36 and 12: the factors that divides all these numbers 24, 36 and 12 completely are 12 and 3 and also 2

In the above expression we take 12 common term

12(2k + 3q - 1)

So option A is correct

We can also take out 3 as common term

3(8k + 12q - 4)

So option B is also correct

Thus the equivalent expressions are: 12(2k + 3q - 1) and 3(8k + 12q - 4)

Answer:

y-3=14/17(x-2)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(17-3)/(19-2)

m=14/17

y-y1=m(x-x1)

y-3=14/17(x-2)

Answer:

Step-by-step explanation:

line l