The expression 6x + 6 represents the amount of money Kristine earns making x custom t-shirts. The expression x − 1 represents her upfront costs. If x represents the number of t-shirts sold in both expressions, what is Kristine's profit when she sells 4 shirts?

$27
$10
$30
$33

The solution of pair of equation 2x + y = 5 and 3x - 2y = 4 is x = 2 and y = 1.

The set of equations given is linear equations that can be solved simultaneously to find the values of variables x and y.

2x + y = 5------->(1)

3x - 2y = 4------->(2)

Multiply equation (1) by 2 and then add it to equation (2)

4x + 2y = 10

3x -  2y =   4

7x + 0  = 14

7x = 14

x = 2

Putting x = 2 in (1),

2(2) + y = 5 

y = 5 - 4 = 1

Therefore, the values of x and y obtained are 2 and 1, respectively. 

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The store that offers the better value based on the unit rate is Store A.

The unit rate is the ratio of one item to the whole item.

The unit rate represents the average of a data set.

It is computed by dividing the total value by the number of units.

The cost of 5 notebooks at Store A = $6.75

The unit rate of notebooks at Store A = $1.35 ($6.75/5)

The cost of 3 notebooks at Store B = $4.50

The unit rate of notebooks at Store B = $1.50 ($4.50/3)

Thus, using the unit rate as the basis of consideration, we can conclude that Store A offers Ben a better value than Store B.

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Answer:

30 seconds.

Step-by-step explanation:

Think of it this way:

20 seconds has a two and 2/3 has a two.

1/3 must be 10 seconds.

0/3 is 0 seconds.

Which means 3/3, the full length, will take 30 seconds.

The substitution that should be used to rewrite  x⁸ + 3x⁴ + 2 = 0, as a quadratic equation is U = x⁴ .

The equation is called as quadratic if the equation has the highest degree  as 2 , it can also be called as an algebraic equation that is second degree in x .

The equation to make a quadratic is  x⁸ + 3x⁴ + 2 = 0 ;  

we have to make this given equation a quadratic equation ,

So , we substitute U = x⁴  ,  in equation ,

we get ;

⇒  (x⁴)² + 3x⁴ + 2 = 0 ;

⇒  (U)² + 3U + 2 = 0;

the equation becomes ⇒ U₂ + 3U + 2 = 0 , which is an quadratic equation,

Therefore , the substitution that should be used is U = x⁴  .

The given question is incomplete , the complete question is

What substitution should be used to rewrite  x⁸ + 3x⁴ + 2 = 0  as a quadratic equation ?

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The answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

When two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given are some questions regarding production of glucose molecules during aerobic metabolism.

1) 1 glucose molecules produces 30 ATP molecules, how many for 50 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 50 ATP molecules,

1 / 30 = x / 50

x = 5/3

x = 1.67

Therefore, there are 1.67 glucose molecules required to produce 50 ATP molecules.

2) 1 glucose molecules produces 6 ATP molecules, how many for 216 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 216 ATP molecules,

1 / 6 = x / 216

x = 36

Therefore, there are 36 glucose molecules required to produce 216 ATP molecules.

3) 1 glucose molecules produces 30 ATP molecules, how many for 450 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 450 ATP molecules,

1 / 30 = x / 450

x = 15

Therefore, there are 15 glucose molecules required to produce 450 ATP molecules.

4) Since, in one day it's 1200 times an ATP molecule is reused in a human body,

We need to find for a week, there are 7 days in a week,

Therefore, an ATP molecule is reused in a human body for a week = 1200 x 7 = 8400 times.

Hence, the answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

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No, â =1 is not equals to ¾. Since ¾ is written as 0.75 in fractional notation.

The fraction ¾, which is equivalent to 0.75, is shown by the fractional notation "â...". The bottom number, or denominator, must be multiplied by the top number in order to comprehend this fraction (top number). 4 times 3 in this instance equals 12, which is true. Find the fractional value by first dividing the numerator by the denominator. In this case, the result of 3 divided by 4 is 0.75, or 3/4.

To calculate a fractional value, use the following formula:

Fractional Value: Numerator / Denominator

The numerator is multiplied by the denominator to arrive at 12 when calculating the fractional value of 3/4. Following that, the fractional value is obtained by dividing the numerator by the denominator:

Fractional value equals 3 / 4 = 0.75

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Answer:

2.6

Step-by-step explanation:

260÷x=100

260/x=100

260=100x

x=2.6

Answer:

[tex] \sf \: 4x + 3 [/tex]

Step-by-step explanation:

Given expression,

→ (-3x + 5) - (-7x + 2)

Let's simplify the expression,

→ (-3x + 5) - (-7x + 2)

→ -3x + 5 + 7x - 2

→ (-3x + 7x) + (5 - 2)

→ (4x) + (3)

→ 4x + 3

Hence, the answer is 4x + 3.

10x +7

because minus and minus equals plus 7x + 3x equals 10x and 2 plus 5 is 7

Answer:

a = 97° , b = 19°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(a)

a is an exterior angle of the triangle , then

a = 40° + 57° = 97°

(b)

57° is an exterior angle of the triangle , then

b + 38° = 57° ( subtract 38° from both sides )

b = 19°

Sara have 5 cents and jon have 0.05 cents with him.

A fraction is a number that represents a part of a whole or a ratio of two numbers. It is written in the form of "a/b" where a is the numerator and b is the denominator. The numerator represents the number of parts that are being considered and the denominator represents the total number of parts in the whole. The fraction can be simplified by dividing both numerator and denominator by their greatest common factor.

Given Martin have 0.5 cents and it is mentioned that Sara have 10 times as much money as marting

so Sara have 10*0.5 cents

=> 5 cents

so sara have 5 cents

Given that jon have 1/10 fraction as much money as Martin have

so jon have 1/10 *0.5

=> 0.1*0.5

=> 0.05 cents

so Jon have 0.05 cents.

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Complete question:

Martin ha 0. 50 cent Sara ha 10 times as much as Martin and Jon has one tenth as much money as Martin . How many cents Sara and jon have

The magnitude and direction of vector <4, 2> are 2√5 and 26.6°, respectively.

In this problem we find the representation of a two-dimension vector, that is, a vector of the form <x, y>. Vectors are described both by magnitude and direction:

Magnitude - This can be found by Pythagorean theorem:

r = √(x² + y²)

Direction - This can be determined by following inverse trigonometric function:

θ = tan⁻¹ (y / x)

Where θ is expressed in degrees.

If we know that x = 4 and y = 2, then the magnitude and direction of the vector <4, 2> are, respectively:

r = √(4² + 2²)

r = √20

r = 2√5

θ = tan⁻¹ (2 / 4)

θ = tan⁻¹ (1 / 2)

θ ≈ 26.565°

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If two polynomials have different degrees, the degree of the sum is the maximum of the degrees of each polynomial.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Thus, position 26 would have 1378 tiles.

Pattern rule equation:

A pattern rule equation is a mathematical formula that describes how a pattern is created. It defines the relationship between the position number (p) and the number of tiles (n) in the pattern.

The pattern rule equation is a useful tool to predict the number of tiles in a certain position, for example, position 26 as I mentioned in my previous answer.

It's also useful to predict the total number of tiles in a pattern or to identify the position number of a specific number of tiles.

In the pattern rule equation n = 53p, n is the number of tiles and p is the position number. To find the number of tiles in position 26, we can substitute 26 for p in the equation:

n = 53p

n = 53(26)

n = 1378

So there would be 1378 tiles in position 26.

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Check the picture below.

[tex]tan(\theta )=\cfrac{\stackrel{opposite}{282}}{\underset{adjacent}{137}}\implies \theta =tan^{-1}\left( \cfrac{282}{137} \right)\implies \theta \approx 64^o[/tex]

Make sure your calculator is in Degree mode.

The figures P', P", and P"" have been drawn below in the coordinate plane. The solution has been obtained using transformation.

What is transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation.

The shape in two dimensions before any alteration is known as a pre-image or inverse image. The shape after transformation is the image.

Cyrus is planning a design to paint on his bass drum.

He starts with figure P and translates it 3 units to the right to form figure P'. This means he moves 3 units closer to the y-axis.

Then he reflects figure P' across the y-axis to form figure P".

Then he dilates figure P" using a scale factor of 2 to form figure P"". This means that the figure is twice of P".

The center of dilation is at the origin.

From this, the below figure has been obtained.

Hence, the figures of P', P", and P"" in the coordinate plane have been constructed.

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Using subtraction, weight put on by kitten is 1,298.43.

When we subtract from the group, the total number of items falls or gets less. The minuend, subtrahend, and difference are the elements of a subtraction problem.

It involves calculating the difference between two numbers. The icon looks like this: (minus). In this operation, we take a number and divide it by a smaller number. In other words, we divide one integer by another.

Weight of kitten when Madison brought her = 787.37 grams

Current weight of Madison = 2085.8 grams

Using subtraction,

Total weight Kitten put on = (2085.8 - 787.37)grams

= 1,298.43

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To decorate her house, Jessica buys this plant which is Boston Fern.

Sure! A plant with green leaves that Jessica can consider buying is a Boston Fern. Boston Ferns are known for their lush, bright green fronds that provide a beautiful, natural touch to any indoor space. They are popular houseplants because they are relatively easy to care for and can purify the air.

To care for a Boston Fern, place it in a location with indirect light and maintain a consistent level of moisture in the soil, avoiding letting the soil dry out completely or become waterlogged. They also benefit from regular misting to increase humidity levels.

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All the required values are given below.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

To find the percentages:

12 is 150% of,

= 12 x 100/ 150

= 8.

5 is 50% of,

= 5 x 100/50

= 10

10% of m number is 300,

m = 300 x 100/ 10

m = 3000

5% of k number is 72,

k = 72 x 100/5

k = 1440

20 is 80% of,

= 20 x 100/80

= 25

Therefore, all the required values are given above.

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The complete table is answered along with solutions is given above.

Given is the table as shown in the image.

{ 1 } -

D = 4

R = D/2 = 2

H = 10

Area = πR² = 4π

Volume = πR²h = 40π

D = 6

R = D/2 = 3

H = 10

Volume = πR²h = 63π

Area = πR² = 9π

Therefore, the complete table is answered along with solutions is given above.

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The simplified expression of 2(5+3x)+(x+10) is 7x + 20

From the question, we have the following parameters that can be used in our computation:

2(5+3x)+(x+10)

Open the brackets

so, we have

10 + 6x + x + 10

Evaluate the like terms

7x + 20

Hence, the expression is 7x + 20

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congrats man!!

good job!! you did great on it

Value of log 1 is 0 for base 10.

In mathematics, logarithmic functions, also referred to as log functions, are the inverse function of exponentiation. A logarithm, by definition, is a measurement that shows how much a base (fixed number) is raised to get a given number.

The two different kinds of logarithmic functions, in general. The base of the logarithmic function in common logarithmic functions is 10. The base of the logarithmic function in a natural logarithmic function is e.

Hence, the value of log 1 is 0 for base 10.

Correct question :

What is the value of log 1 for base 10?

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A triangle is a 3 sided Polygon whose internal angle sum up to 180 degrees. It can be constructed by knowing those angles.

To construct a perfect triangle you can follow the following procedure have a brief idea on the angles of the triangle and if the angles are not available get to know about the length of each side of the triangle. If you know the each and every angle of the triangle you can proceed to the construction of triangle. Initially draw a baseline with the given dimension let us say this line is XY. Now from either left or right side of xy with the given angle draw a slanting line even if the length of the line is not known. From this from the other side draw another slanting line from the given angle and extend it up to the point where it touches the previous line. Now you have the triangle created for you. You can name the new point with the letter Z.

Now you have the triangle XYZ constructed.

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On a graph, indicate the coordinate plane point (3,4). It's  contains of two coordinate are x , y coordinate

Identify the first four positive units and draw the y-axis.

The x-axis is then drawn, and the first four positive units are labeled.

The x-coordinate is 3, thus.

The y-coordinate is 4, thus.

Plotting (3,4) requires us to start at the beginning.

The x-coordinate being positive 3, we shift 3 units to the right.

The y-coordinate being positive 4, we shift 4 units to the right .

The point's x-value indicates how it travels to the right or left along the x-axis. The rectangular axis, often known as the Cartesian plane, has this axis as its major horizontal line.

The point's y-value indicates how it goes up or down along the y-axis. The rectangular axis, often known as the Cartesian plane, is centered on this axis.

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Answer:  y = 5x + 3 in standard form

Step-by-step explanation:

The required values of a and b are approximately 15.4 and 14.6, respectively, and Michael's speed is approximately 14.6 meters per second.

Following the given condition
Race 1: Michael wins by 1 second, so time is given as:
[tex](50/b)=(50/a)+1[/tex]

Race 2: Michael wins by 0.1 seconds over 47 meters, so time is given as:
[tex]47/a+0.1=50/b[/tex]

From Race 1, we get [tex]a=b+50/b-50.[/tex]

Substitute the value of a in terms of b into the Race 2 equation:
[tex]\dfrac{47}{b+50/b-50}+0.1-\dfrac{50}{b}[/tex]

Now, solve for b:

[tex]b\approx14.6\\[/tex]   (discard the negative solution as speed cannot be negative)

Now, calculate the value of a using the equation from Race 1:
[tex]a=b+50/b-50 \approx15.4[/tex]

Therefore, the values of a and b are approximately 15.4 and 14.6, respectively, and Michael's speed is approximately 14.6 meters per second.

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Each ticket cost 54$.

$332 (the total cost of the tickets) less $5 (the service charge) equals the cost of 9 tickets.

Round your estimate to the nearest even number: If you want it to be an even $100, deduct $4 rather than $5. Then multiply by a whole number to get 9 + 2 = 10. You now have simple numbers. $10 is equivalent to $100 divided by 10 tickets.

3. $104 (the total cost of the tickets) less $5 (the service charge) equals the cost of 8 tickets.

STEP 1: $5 off of $104 equals $99

$99.00 is equal to the cost of 9 tickets.

Step 2: Divide $99 by 9 to get $11.

Consequently: The Price/Ticket is $54.

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Answer:

700 meters.

Step-by-step explanation:

The actual distance between the two points can be determined by using the scale of the map. If the scale of the map is 1:10,000, it means that one unit of measurement on the map represents 10,000 units of the same measurement in reality.

Therefore, if the distance between the two points on the map is 7cm, the actual distance is 7cm * 10,000 = 70,000cm or 700 meters.

So, the actual distance between the two points is 700 meters.