Unknown Numbers
Consider the following problem.
One number is 3 less than 6 times a second number.
Their sum is 46. Find the numbers
If × represents the second number, which equation is
correct for solving this problem?

Because the angles are vertical angles, the value of x is 1

The angles are given as

A = 7x + 26

B = 4x + 29

The angles are vertical angles

So, we have

A = B

This gives

7x + 26 = 4x + 29

Evaluate the like terms

3x = 3

Divide by 3

x = 1

Hence, the value of x is 1

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So the correct answer is a. f(-3)=-5.

Solution :

Cartesian coordinate system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

Cartesian Plane:

A plane consists of axes and quadrants. Thus, we call the plane the Cartesian Plane, or the Coordinate Plane, or the x-y plane. The axes are called the coordinate axes.

Abscissa and Ordinate

The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis and it is known as Abscissa.

The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis and it is known as the Ordinate.

So,

the point (-3, -5) corresponds to the graph of the function.

A point on a graph in the Cartesian coordinate system then that point consists of coordinates (x, y).

In, y=f(x) and x so (x, f(x))

x is a x-coordinate and y=f(x) is y-coordinate.

So if we have a point (-3, -5) the corresponding coordinates are x=-3 and

y=f(x)=-5. So it must be true that y=f(-3)=-5.

So the correct answer is a. f(-3)=-5.

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The wholesale price of the TV will be 0.40 x where x represents the retail price.

Percentage :

In mathematics, it is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Let the retail price of TV be x

Now, we are given that it is sold off at 60 percent discount.

Whole sale price = x - 60 % of x

Whole sale price = x - 60 / 100 x

Whole sale price = x - 0.60 x

Whole sale price = 0.40 x.

Therefore, the wholesale price of the TV will be 0.40 x where x represents the retail price of the TV.

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The value of the constant π is located between 3 and 4 on a number line

The value is given as

Value = π

As a general rule, the value of π is

π = 22/7

So, we have

Value = 22/7

Evaluate the quotient of 22/7

So, we have

Value = 3.143

The number 3.143 is greater than 3 but less than 4

This means that, 3.143 is between 3 and 4

In other words, the value of the constant π is located between 3 and 4 on a number line

Hence, the value of the constant π is located between 3 and 4 on a number line

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The number of f(x) = g(x) solutions is an option (2) The right answer is 2, thus.

A graph is a diagram or visual representation that organizes the presentation of facts or values. The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph.

For the predicament,

f(x) = In(x + 2) and g(x) = e(x - 1) throughout the range [(-2,3].

In the graph below,

plot the two functions f(x) and g(x).

These two functions cross at two locations in the range [(-2,3]).

The function's solution is revealed at the intersection point.

Consequently, we might say that the number of solutions.

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Answer:

x = 2.638

Step-by-step explanation:

Answer

Unless you need a different version of this answer?

Step-by-step explanation:

(27in(3)

x=___4_______ True

In(3)

Answer:

$5.30 for two gallons

Step-by-step explanation:

Maria need 12 fiction books.

Multiplication table: A multiplication chart is a table that shows the products of two numbers. Usually, one set of numbers is written on the left column and another set is written as the top row. The products are listed as a rectangular array of numbers.

Given that She wants to make packages that have 3 fiction books and 4 nonfiction books. She already has 9 fiction books

Step 1

Complete the rows for 3 and 4 on multiplication table

Fraction           : 3,6,9,12, 15, 18, 21, 24,27,30.

Notification     : 4,8,12,16,20,24,28,32,36,40.

Step 2

Read across the top until you reach 9. The corresponding number bottom row.

The top untill you reach 9 the corresponding number bottom row is 12

Maria need 12 fiction books.

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The bagel costs $0.89 and a muffin costs $0.75

Let B = Bagel cost

Let M = Muffin cost

Thus, from the given question parameters, the system of equations that can be used to determine the cost x is;

3B + 4M = 5.67     ------(1)

5B + 3M = 6.70    ------(2)

Multiply the 1st equation by 3 and the 2nd equation by (-4) to get;

9B +12M =  17.01     ------(3)

-20B - 12M = -26.80   ------(3)

Add equations 3 and 4 together to get;

-11B = -9.79

B = 0.89  

Plug this value for B in to the 1st equation and solve for M to get;

3(0.89) + 4M = 5.67

2.67 + 4M = 5.67

4M = 3.00

M = 0.75

Thus, a bagel costs $0.89 and a muffin costs $0.75

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The equation of the bisector of angle OAB is y=x

If E is the point of intersection of this bisector and line through A and B then the co-ordinates of E is (40/3,40/3)

Since E is the point of intersection of the bisector of angle OAB and line A and B  hence we can say OA:OB=AE:EB

Since point O is the origin hence we can say the co-ordinates of point O are (0,0) and the angle bisector of the angle OAB makes and angle of 45 degree from x axis, So by the formula of Line passing through origin (y= mx )

where ,

∅=angle made by the bisector the angle OAB to the x axis(i.e. 45 degree)

m=tan∅

now using substitution method ,

m=tan45

m=1

the equation of the bisector of angle OAB is  y=x

Now, the equation of the line passing through point A(5,0) and point B(0,8) by formula,

(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)

here , y1=0, x1=5, y2=8, x2=0

again by substitution method,

(y-0)={(8-0)/(0-5)}*(x-5)

y={8/-5}*(x-5)

8x - 5y = 40

point E is the intersection of 8x - 5y = 40 and y=x the solving these two equations by substitution method we get;

x=40/3

y=40/3

the co-ordinates of point E are  (40/3,40/3)

E is the intersection point of the bisector of the angle OAB and the line through point A and B ,

on comparing triangle OEA and triangle OEB we can say that,

OA:OB= AE:EB

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Answer:

18

Step-by-step explanation:

5*(6)-10(2)+8 = 18

Substitute k = 6 and c = 2 into the equation and solve it.

Using proportions, it is found that Jen planned to spend 19/4 hours paddleboarding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In this problem, we have that:

4 + 3/4 = 4.75 hours = 19/4.

Jen planned to spent 19/4 hours paddleboarding.

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The correct inequality will be 53.46d + 45.5 ≤ 260

What does a math inequality look like?

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Given That:

She plan to drive 350 miles and each mile cost $0.13 which is total $45.5

and she have to pay $53.46 for each day

So the correct inequality will be 53.46d + 45.5 ≤ 260

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Answer:

It's 0.4

Step-by-step explanation:

2/5 = 40/100 = 4/10 = 0.4

Hope that helps :)

Answer:

  (d)  c = ab/x

Step-by-step explanation:

You want to solve the proportion x/a = b/c for the variable c.

The usual method recommended for solving almost any kind of proportion is to first clear the fractions. You do this by multiplying both sides by the product of the denominators. This has the appearance of "cross multiplication."

  [tex]\dfrac{x}{a}=\dfrac{b}{c}\qquad\text{given}\\\\\\\dfrac{x}{a}\cdot ac=\dfrac{b}{c}\cdot ac\qquad\text{multiply by $ac$}\\\\xc=ba\qquad\text{simplify; each numerator times the opposite denominator}[/tex]

At this point, it is a "one-step" linear equation in c, so is solved by dividing by the coefficient of c, which is x.

  [tex]\dfrac{xc}{x}=\dfrac{ab}{x}\\\\\boxed{c=\dfrac{ab}{x}}[/tex]

Answer:

0.000345 in standard form would be:

3.45 times 10 to the -4 power

Step-by-step explanation:

The number tells use that we have to divide by 10 and we are working with a negativenumber equal to the power of 4.

Answer:

3.45 × 10^-4

Step-by-step explanation:

Move from the decimal point till you you get to after the first number.

Then you put the decimal point there and because it's starts with 0. i.e it is not up to one

You put minus in front of it when raising it to the power of 10

Answer:

No

Step-by-step explanation:

1/10 = 0.1

0.05 x 0.1 = 0.005

The linear functions for this problem are given as follows:

13. y = 2x/3 + 8/3.

14. y = -3x + 5.

15. y = -1/3x - 2.

16. y = 5/4x - 1/4.

17. y = 7/4x + 19/2.

A linear function is modeled by the following rule:

y = mx + b

In which:

The slope is also related with parallel and perpendicular lines, as follows:

In item 13, the line in slope-intercept form is:

y = 2x/3.

The line we want to find is parallel, hence it has the same slope, that is:

y = 2x/3 + b.

When x = -1, y = 2, hence:

2 = -2/3 + b

b = 8/3.

Hence the line is:

y = 2x/3 + 8/3.

For item 14, the line is perpendicular to:

y = 1/3x + 4.

Hence the slope is found as follows:

1/3m = -1

m = -3.

Then:

y = -3x + b.

When x = 0, y = 5, hence b = 5 and the line is:

y = -3x + 5.

For item 15, the line is perpendicular to:

y = 3x + 4.

Then the slope is found as follows:

3m = -1

m = -1/3.

Then:

y = -1/3x + b.

When x = 0, y = -2, hence b = -2 and the line is:

y = -1/3x - 2.

For item 16, the line is perpendicular to:

y = 4 - 4/5x.

Then the slope is found as follows:

-4m/5 = -1

m = 5/4.

Hence:

y = 5/4x + b.

When x = 1, y = 1, hence:

1 = 5/4 + b

b = -1/4.

Then the line is:

y = 5/4x - 1/4.

For item 17, the line is perpendicular to:

y = 13/7 - 4/7x

Then the slope is found as follows:

-4m/7 = -1

m = 7/4.

Hence:

y = 7/4x + b.

When x = -2, y = 6, hence:

6 = -14/4 + b

b = 19/2.

Hence the line is given by:

y = 7/4x + 19/2.

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Answer:58.73

Step-by-step explanation:

28.37+30.36=58.73

The number of children wearing both black and orange costumes is 7.

Let P denote the universal set, the number of children going to a party.

Then n(P) = 46

Let B denote the number of children wearing black costumes to the party.

Then n(B) = 18

Let O denote the number of children wearing orange costumes to the party.

Then n(O) = 12

We are asked to find how many children will wear both orange and black. That is to find n(B ∩ O).

We are also given that half of the guests are wearing costumes that are neither black nor orange.

Then n(B ∪ O)' = n(P)/2 = 46/2 = 23, where n(B U O)' denotes the complement of n(B U O).

We also know that n(B ∪ O) = n(P) - n(B U O)' = 46 - 23 = 23

⇒ n(B U O) = n(B) + n(O) - n(B ∩ O)

⇒ 23 = 18 + 12 - n(B ∩ O)

⇒ 23 = 30 - n(B ∩ O)

⇒ n(B ∩ O) = 30 - 23 = 7

⇒ n(B ∩ O) = 7.

Therefore, the number of children wearing both black and orange costumes is 7.

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According to the solving the non of the quadratic equations equivalent.

4X² + 5x - 3.

A quadratic equation seems to be a second-order polynomial equation in a variable, x ax2+bx+c=0, with a 0 as the coefficient. The fundamental theorem of algebra ensures that it has at least one solution as it is a second-order polynomial problem. The solution could be straightforward or difficult.

Equivalent equations are those that have the same solutions or roots. An equivalent equation is produced by adding or subtracting the identical number or expression from both sides of an equation. Equivalent equations are produced by multiplying and dividing both sides of such an equation by the same non-zero value.

3 ⁢X² + 5 x − 7 ⁢+ ( X² + 4 ).

Simplifying this equation:

3 ⁢X² + 5 x − 7 +  X² + 4

= 4X² + 5x - 3

According to the solving the non of the quadratic equations equivalent.

4X² + 5x - 3.

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I understand that the question you are looking for is:

Which expression is equivalent to the given expression?

3 ⁢X² + 5 x − 7 ⁢+ ( X² + 4 ).

A. - 4X² + 5X − 4

B. X² + 4

C. X² + 28

D. - 4 ⁢X² + 5x − 28

Answer:

The answer to the inequality is

x < -5

x > 15

The height of the building is 23.09m.

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Answer: -1.4,1 1/25,1.25

Step-by-step explanation:

-1.4,1 1/25,1.25

1 1/25=

1+0.04=1.04

Order: -1.4, 1.04, 1.25 ==> -1.4,1 1/25,1.25

Answer:

[tex]3.4196 \times 10^{7}[/tex]

Step-by-step explanation:

Given expression:

[tex](4.12 \times 10^{-9})(8.3 \times 10^{15})[/tex]

Remove the parentheses:

[tex]\implies 4.12\times 10^{-9} \times 8.3 \times 10^{15}[/tex]

Collect like terms:

[tex]\implies 4.12 \times 8.3 \times 10^{-9} \times 10^{15}[/tex]

Multiply the numbers 4.12 and 8.3:

[tex]\implies 34.196 \times 10^{-9} \times 10^{15}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 34.196 \times 10^{(-9+15)}[/tex]

[tex]\implies 34.196 \times 10^{6}[/tex]

Scientific notation is written in the form  [tex]\boxed{a \times 10^n}[/tex]

where [tex]1\leq a < 10[/tex]  and [tex]n[/tex] is any positive or negative whole number.

To convert 34.196 × 10⁶ into scientific notation, move the decimal point to the left by one place and increase the power of 10 by 1:

[tex]\implies 34.196 \times 10^{6}=3.4196 \times 10^{7}[/tex]