The area of a rectangular painting is 1/6 square yard. The width is 2/3 yard. What is the length of the painting use the formula A=e x w

By using the equation of the line and properties of perpendicular lines, we find that the equation of the line is equal to y = - 2 · x - 6.

Herein we need to find a line that passes through point (- 5, 4) and is perpendicular to a given line in implicit form: x - 2 · y = - 4. The complete procedure is shown below. First, rewrite the equation of the perpendicular line into explicit form:

x - 2 · y = - 4

2 · y = x + 4

y = (1 / 2) · x + 2

Second, determine the slope of the new line:

m · m' = - 1

(1 / 2) · m' = - 1

m' = - 2

Third, calculate the intercept of the new line:

b = y - m · x

b = 4 - (- 2) · (- 5)

b = 4 - 10

b = - 6

Fourth, complete the new equation of the line:

y = - 2 · x - 6

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we have that

the distance city B to city C is equal to

405+401=806 miles4

therefore

the answer is

The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.

For the given question;

The inequality of the function is given as;

= x² - 4x + 3

Find the factors;

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

x = 1 and x = 3 are the zeros of the equation.

Now, to graph the equation find the point;

Put x = 0; y = 3

Put x = 1; y = 0

Put x = 2, y = -1

Plot the points on the graph and join the points with solid line.

The vertex of the parabola is found at (2, -1).

Thus, the graph of the parabola is plotted.

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i think 16? 1/2+1/2=1 so 8*2=16

64 ^ (-2/3)

Rewrite 64 as 4^3

(4^3) ^ (-2/3)

Using the power rule a^b^c = a^(b*c)

4 ^(3*-2/3)

4^ -2

We know that a^ -b = 1/ a^b

1 / 4^2

1/16

Answer:

168.28

Step-by-step explanation:

Answer:

Answer is - 4  1/15

Step-by-step explanation:

-6 2/5 = -32/5

-32/5   + 7/3       to add fractions they must have the same denominator

- 96/15   + 35/15   =  ( -96 + 35) / 15 = - 61/15  = - 4  1/15

The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46

Compound interest:

A = P(1 + r/n)^nt

= 2,000(1 + 0.04/365)^(365×6)

= 2,000.00(1 + 0.000109589041095)^(2190)

= 2000(1.0.000109589041095)^2190

= 2000 (0.00010958904109589)

= $2,542.46 to the nearest cent

Simple interest:

S.I = principal × rate × time

= 2,000 × 0.04 × 6

= $480

Total = Principal + simple interest

= $2,000 + $480

= $2,480

To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest

= Compound interest - Simple interest

= $2,542.46 - $2,480

= $62.46

In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.

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1) To find the scale factor for these triangles, we need to write a pair of ratios and then solve for x:

Now, we can plug x=8 into those:

Answer:

n=2.4

Step-by-step explanation:

The value of n is ∛14.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).

To solve the equation −8 + n³= 6

Add 8 to both sides of the equation to isolate the term with n:

−8 + n³ + 8 = 6 + 8.

Simplifying the equation gives: n³ = 14.

Take the cube root of both sides to solve for n.

Taking the cube root of n³ = 14

∛(n^3) = ∛14.

Therefore, n = ∛14.

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Answer: 6 blue, 6 yellow, 6 red

Step-by-step explanation:

A fair stack of cards is an equal amount of cards.

3 colors, 18 total

18 / 3 = 6

Therefore 6 of each

Value of x =5 and value of y =2

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself. For instance, it is much simpler to write 5^7 than it is to write 5 5 5 5 5 5.

[tex]3^{x}-3^{y}=234\\ 3^{x-y}.3^{y}-3^{y}=234\\ 3^{y}(3^{x-y}-1)=234\\ 3^{y}(3^{x-y}-1)=3^{2}.26\\[/tex]

Now, by comparison, we get:

[tex]3^{y}=3^{2}\\ y=2\\ Also, \\3^{x-y} -1=26\\ 3^{x-y}=27\\ 3^{x-y}=3^{3}\\ x-y=3\\ x-2=3\\x=5[/tex]

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For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.

As given in the question,

Revenue for selling x units of a product is R = 113.95 x

Cost of producing x units is C = 93 x + 750

For profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x >93x-93x +750

⇒20.95x > 750

Divide by 20.95

⇒x > 750/20.95

⇒x>35.7995

Nearest whole number is 36.

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of

C =93x + 750 the value of x is 36units.

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The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.

The fraction of counters Adam have now is 4/9.

This is an expression which consists of a numerator and a denominator

A numerator is the upper of top value of a fraction

A denominator is the lower or bottom value of a fraction

Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley

= 18 - 10

= 8

Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has

= 10/18

= 5/9

Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has

= 8 / 18

= 4/9

In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9

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Answer:

y = -3/2x +11

Step-by-step explanation:

First you have to change the equation from standard form to slope form.

y = mx + b

2x-3y=7 --> subtract 2x from both sides

-3y = -2x + 7 --> now divide both sides by -3 to get y by itself

y = 2/3x - 7/3  --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.

now you have to use point slope form y - y1 = m (x - x1)

x1 and y1 would be your point. 2 is x1 and 8 is y1

y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope

next distribute the -3/2

y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self

now you have y = -3/2x + 11

9.16

1) Considering 14, and 6 the data. Let's calculate the Geometric Mean of it

2) To do that we just need to multiply those numbers, and since there are two of them take the square root of that product, between those 2 numbers

3) So the Geometric mean is 9.16 (approximately).

The powers can be used in the following manner using multiplicative identity.

Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.

The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.

When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.

Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.

Thus, we came to the logical conclusions.

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Answer:

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

Step-by-step explanation:

The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.

Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.

5x +3y= 15

3y= -5x +15

Divide both sides by 3:

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

Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]

The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.

Slope of perpendicular line= [tex] \frac{3}{5} [/tex]

Substitute the value of the slope into the equation:

[tex]y = \frac{3}{5} x + c[/tex]

To find the value of c, substitute a pair of coordinates the line passes through.

When x= -1, y= 2,

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

Solve for c:

[tex]c = 2 + \frac{3}{5} [/tex]

[tex]c = \frac{13}{5} [/tex]

Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].

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Answer:

1 hour, 28 minutes, 15 seconds

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

divide the after tax price by the before tax price

15.93/14.75=1.08

then subtract 1 from 1.08 (the 1 is the base price of the pizza) and convert the difference to percent to get the answer of 8% tax rate

It should be noted that the z-score for the sample mean that's given is 0.5.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

The following can be seen from the information illustrated:

Mean ( u ) =55

Standard Deviation ( sd )=12

Number ( n ) = 4

Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)

Z = (58-55)/12/ Sqrt ( 4 )

Z = 3/6= 0.5

Therefore, the z score is 0.5.

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Answer: f(-7)=-9

Step-by-step explanation:

The logarithms in terms of a and b are:

a) log 72 = 3a + 2b

b) log √27 =  [tex]\frac{3}{2} b[/tex]

c) log 360 = 3a + 2b + log 5

         nˣ = a ⇔ logₙ a = x , log stands for logarithm here.

       Where,

         Two positive real numbers are a and n. x is a real number.

Given:

log 2 = a

log 3 = b

a) log 72

= log (2³ × 3²)

= log 2³ + log 3²   [ By product rule of logarithms, log mn = log m + log n]

= 3log 2 + 2log 3   [By power rule of logarithms, log mⁿ = nlog m]

Replacing with the values of log 2 and log 3.

= 3a + 2b

b) log √27

= [tex]\frac{1}{2}[/tex] log 27    [By power rule of logarithms, log mⁿ = nlog m]

=  [tex]\frac{1}{2}[/tex] log 3³

= [tex]\frac{1}{2} *3 log3[/tex]

= [tex]\frac{3}{2} log 3[/tex]

= [tex]\frac{3}{2} b[/tex]

c) log 360

= log (2³ × 3² × 5)  

= log 2³ + log 3² + log 5 [By product rule of logarithms,log mn = log m +  log n]

= 3log 2 + 2log 3 + log 5  [By power rule of logarithms, log mⁿ = nlog m]

= 3a + 2b + log 5

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Answer:

A

Step-by-step explanation:

The centroid cuts the median in a 2:1 ratio from vertex to side.

Answer:

See below

Step-by-step explanation:

40 ÷ 50 =   40/50 = 4/5 = .8  

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

Numerous different coordinate systems can be used to describe geometrical figures.

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Explanation:

x = width

2x = length, since it is twice as long as it is wide

area = length*width = 2x*x = 2x^2

Set this equal to the area of 450 sq ft and solve for x

2x^2 = 450

x^2 = 450/2

x^2 = 225

x = sqrt(225)

x = 15 feet is the width

2x = 2*15 = 30 feet is the length

Check:

area = length*width = 30*15 = 450

The answers are confirmed.

Answer:

1 : Grouping Symbol

2 : Operator

3 : Order of Operations

4 : Exponent

5 : Variable

6 : Term

7 : Coefficient

8 : Constant

9 : Numerical Expression

10 : Variable Expression

11 : Equation

12 : Inequality

13 : Evaluate

14 : Open Sentence