Solve the equation 3x - 13y = 2 for x.

Answer:

[tex]- (\frac{15 - 4\sqrt{3} }{11} )[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{3}-6}{\sqrt{3} +6} = \frac{(\sqrt{3}-6)(\sqrt{3}-6)}{(\sqrt{3} +6)(\sqrt{3} -6)}[/tex]

[tex]= \frac{(\sqrt{3})^2 - (2\times6\times\sqrt{3}) +6^{2} }{(\sqrt{3})^2 - 6^{2}} = \frac{9 - 12\sqrt{3} + 36}{3 - 36}[/tex]

[tex]\frac{45 -12\sqrt{3} }{-33} =- (\frac{15 - 4\sqrt{3} }{11} )[/tex]

Answer:

Is the equation that you need answered

y = 4x - 3 ?

That is not a real equation, therefore you can not answer that/show work

Answer:

Step-by-step explanation:

Not sure what they are looking for here.

you can plug in different x and get a y

x = 0 y = -3

x = -3 y = -15

x = 4 y = 13

Answer:

read explanation

Step-by-step explanation:

This won't give him the correct answer because if he substitutes zero into anything he will get -5.9. 0 multiplied by anything is 0 and if you put that into bot equations you get the same answer so it won't help him. he should instead try 1 or something like that.

Simple interest formula: A= P(1+Ryan)

A = 12000(1+ 0.07x4) = 15,360.00

Amount of interest = 15360-12000= 3,360.00

A= 12000(1+0.08x5) = 16,800.00

Interest = 16,800-12,000 = 4,800.00

Difference in interest = 4800 - 3360 = $1,440.00

Answer:

1440

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

16÷(100%-78%) = 16÷22% = 72.73 =70(correct to the nearest tenth)

Answer:

an individual thing or person regarded as single and complete but which can also form an individual component of a larger or more complex whole

The two numbers being asked in the question are 4 and -1.

This question can be solved using a system of linear equations. Let's call the first number x and the second number y.

From the first statement, we can create one equation: 2x + 4y = 4

From the second statement, we can create another equation: x - y = 5

To solve this system, we can use substitution or elimination method. If we multiply the second equation by 2, we get 2x - 2y = 10. Now, we can subtract the second equation from the first: (2x + 4y) - (2x - 2y) = 4 - 10, which simplifies to 6y = -6. Dividing both sides by 6, we get y = -1.

Substitute y = -1 into the equation x - y = 5, we get x - (-1) = 5. Therefore, x = 5 - 1 = 4.

So, the first number x is 4 and the second number y is -1.

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To meet or beat the sales goal, the inequality 72x + 90y ≥ 360 can be used to represent the number of games that must be sold every day. The graph of this inequality would show the region above or on the line 72x + 90y = 360.

To meet or beat the sales goal of at least $360 per day, we can set up an inequality based on the profits from selling games. Let x be the number of portable game systems sold and y be the number of standard game systems sold. The inequality representing the number of games that must be sold every day is 72x + 90y ≥ 360.

To graph this inequality, we can plot the points on a graph where each point represents a combination of x and y. Then we shade the region that satisfies the inequality, which is the region above or on the line 72x + 90y = 360.

See the graph in the attached image for visual representation.

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Final answer:

To find the percentage of weight lost, calculate the difference in weight and then divide by the original weight, multiplying by 100%. The patient has lost approximately 5.88% of their original weight.

Explanation:

To determine the percentage of weight lost by a patient who weighed 102 kg and now weighs 96 kg, we use the following steps:

So, the patient has lost approximately 5.88% of their original weight.

To factor the expression 15x - 25 using the greatest common factor (GCF), divide each term by the GCF. The factored form is 5(3x - 5).

To factor the expression 15x - 25 using the greatest common factor (GCF), we need to find the largest number that divides both terms evenly. In this case, the GCF is 5. We can then divide each term by 5 to factor out the GCF:

15x ÷ 5 = 3x

-25 ÷ 5 = -5

Therefore, the factored form of the expression 15x - 25 is 5(3x - 5).

The expression 15x - 25 is factored by finding the Greatest Common Factor, which is 5, and then dividing each term by 5 to get the factored expression 5(3x - 5).

To factor the expression using the Greatest Common Factor (GCF), we need to identify the highest number that divides both coefficients in the expression 15x - 25. In this case, both 15 and 25 are divisible by 5, so 5 is the GCF of the expression. Applying the distributive property, we factor out the GCF:

Now, the expression 15x - 25 is fully factored as 5(3x - 5).

Because the triangles are congruent we know that NM = ST = 50.

answer: 50

The length of NM line segment for the considered situation is given by: Option D: 50 mi

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\\[/tex]

(|AB| denotes length of line segment AB, and so on for others).

For these cases, the two triangles in the image are congruent.

So their corresponding sides must be of same measures.

The three sides of triangle RST are of measures 75, 67 and 50 miles

The two sides of triangle NLM are 67 miles and 75 miles. So obviously third one can be nothing except 50 miles so that the triangle NLM also have sides of same measure as of the triangle RST.

Thus, the length of NM line segment for the considered situation is given by: Option D: 50 mi

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Answer:

  see below

Step-by-step explanation:

The five linear equations produce five parallel contour lines. The value of z increases as the lines shift to the right.

Final answer:

Level curves for the function f(x, y) = 5x - y for different values of c are straight lines with a slope of 5. They can be plotted on the same coordinate axes to form a contour map, with each line corresponding to one value of c.

Explanation:

Level Curves for the Function f(x, y) = 5x - y

To find the level curves of the function f(x, y) = 5x - y for the given values of c, we set f(x, y) equal to each constant and solve for y in terms of x:

For c = -2: -2 = 5x - y → y = 5x + 2

For c = -1: -1 = 5x - y → y = 5x + 1

For c = 0: 0 = 5x - y → y = 5x

For c = 1: 1 = 5x - y → y = 5x - 1

For c = 2: 2 = 5x - y → y = 5x - 2

These equations represent lines with a slope of 5 and various y-intercepts. The level curves can be drawn on a set of coordinate axes by plotting the lines according to their y-intercepts. Each line represents a different level curve and the set of these lines can be referred to as a contour map.

Answer:

Step-by-step explanation:

3(x + 1) + 4x + 3 = 34......distribute thru the parenthesis

3x + 3 + 4x + 3 = 34....combine like terms

7x + 6 = 34....subtract 6 from both sides

7x = 34 - 6

7x = 28....divide by 7

x = 28/7

x = 4 <====

Answer:

look at the picture shown

Answer:

3/7 and 4/14

Step-by-step explanation:

a) 3/7 is not an equivalent of 6/21 because when you multiply the numerator and the denominator by 2 you get: 6/14

b) 4/14 is not an equivalent

Answer:

3/7

Step-by-step explanation:

6/21 = 6 ÷ 3 / 21 ÷ 3 = 2 / 7

6 / 21 = 4 ÷ 2 / 14 ÷ 2 = 2 / 7

6/21 = 12 ÷ 6 / 42 ÷ 6 = 2 / 7

Answer:

9

Step-by-step explanation:

The domain of a graph is the set of input values the function can take

The domain of the graphed function is (c) {x | x is a real number}

The equation of the graph is given as:

[tex]y = \sqrt[3]{x -1} + 3[/tex]

The above function is a cubic function, and a cubic function can take any real number as its input

This means that, the input values of the function [tex]y = \sqrt[3]{x -1} + 3[/tex] is the set of real numbers

Hence, the domain of the graphed function is (c) {x | x is a real number}

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The domain of the translated cube root function y = ∛(x - 1) + 3 is {x | x is a real number}, since cube root functions accept all real numbers.

The graph of the function y = ∛(x - 1) + 3, which is a cube root function, is a translated version of the parent function y = ∛x. The translation involves shifting the graph to the right by 1 unit and up by 3 units. Given that a cube root function, like y = ∛x, can accept any real number as an argument because there are real cube roots for all real numbers, the domain of the translated function would also be all real numbers. This remains true even after the function is translated. Hence, the domain of the graphed function is {x | x is a real number}.

Answer:

[tex]200.96sq.ft.[/tex]

Step-by-step explanation:

Given:

            Circumference= 50.24 ft.

We have to find the area of the circle.

Finding the radius with the help of given circumference

            Circumference of a circle= [tex]2\pi r[/tex]

                           [tex]50.24=2*\pi* r\\\\50.24=2*(3.14)*r\\\\50.24=6.28*r\\\\r=\frac{50.24}{6.28} \\\\r= 8ft.[/tex]

Area of a circle=  [tex]\pi r2[/tex]

                     [tex]=\pi *8*8\\\\=64*\pi \\\\=64*3.14\\\\=200.96sq.ft.[/tex]

Answer:  15.67

Step-by-step explanation:

Pot Santa

Answer:

15.67

Step-by-step explanation:

focus only on the underlined area

15.666666666667

round the last 6 underlined is what we are going to use to round the one before it

5 or more goes up so the six is now rounded to a seven on that part leaving you with 15.67

Answer:

D.)<-50.5, 58.1>

Step-by-step explanation:

The vector can be decomposed into its x and y components using trigonometry.

The x and y components of the vector, together with the vector length forms a right triangle, as shown in the figure attached.

The x-component of the vector is given by

[tex]sin (-41^o)=\dfrac{x}{77}[/tex]

[tex]x=77*sin (-41^o)[/tex]

[tex]x=-50.5[/tex]

And the y-component of the vector is given by

[tex]cos(-41^o)=\dfrac{y}{77}[/tex]

[tex]y=77*cos(-41^o)[/tex]

[tex]y=58.1[/tex]

Thus, the vector as an ordered pair is represent by

[tex]\boxed{ (-50.5, 58.1)}[/tex]

which is choice D.

Answer:

Triangle 1 line segment AB and triangle 2 line segment BA correspond to each other

Step-by-step explanation:

Point b and point a don't correspond to anything else

triangle 1 and 2 are congruent my answer would be a 50/50 guess between C and D If it were me id risk it and go D but it is up to you.

Answer:

-6, -7, -8, -9

Step-by-step explanation:

-2x > 10

x < -5

So x can be -6, -7, -8, -9

Any number less than -5 is a solution.

The listed ones are the solutions because they satisfy the the inequality,

-2x > 10

x = -6, -2(-6) > 10 12 > 10

x = -7, -2(-7) > 10 14 > 10

x = -8, -2(-8) > 10 16 > 10

x = -9, -2(-9) > 10 18 > 10

Final answer:

The combined probability of the coin landing tails-up and the number cube landing on a 4 is 8.33%.

Explanation:

The question involves calculating the probability of two independent events: the coin landing tails-up and the dice landing on a 4. The probability of a coin landing on tails is 0.5, and the probability of a dice landing on a particular number, say 4, is 1/6 since a dice has six faces. Since these two events are independent, their combined probability is found by multiplying the probabilities of each event.

The probability of the coin landing tails-up is 0.5, and the probability of the number cube (dice) landing on a 4 is 1/6. So, the combined probability of both events occurring is (0.5) × (1/6) = 0.0833, or 8.33% when expressed as a percentage.

The value of n from the equation 7n = 28 is n = 4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

7n = 28   be equation (1)

On simplifying the equation , we get

Divide by 7 on both sides of the equation , we get

n = 28/7

n = 4

Another equation which satisfies the relation is 4n = 16

n = 4

Therefore,  the value of n is 4

Hence , the value of the equation is 4

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Answer:

Just multiply four times twenty and youll get your answer

See picture for solution to your problem.

Answer:

700  milligrams of protein is contained in one glass.

Step-by-step explanation:

Given:

Protein present in on glass of soy milk =  7 grams

To Find:

How many milligrams of protein does one glass contain =?

Solution:

​We have to convert grams to milligrams

We know that 1 gram  =  100 milligram

then 7 grams  will be  = [tex]7 \times 100[/tex] milligrams

7 grams  =  700 milligrams

Therefore in one glass of soy milk there will be 700 milligrams of proteins

Answer:

The piecewise model of the function is

[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]

[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]

Step-by-step explanation:

we know that

The general form of absolute value equation is

[tex]f\left(x\right)=a\left|x-h\right|+k[/tex]

where

The variable a, tells us how far the graph stretches vertically, and whether the graph opens up or down

(h,k) is the vertex of the absolute value

In this problem we have

[tex]f\left(x\right)=0.7\left|x-4\right|+2[/tex]

we have

[tex]a=0.7[/tex]

The coefficient a is positive ----> the graphs open up

The vertex is the point (4,2)

Find the piecewise model

case 1) positive value

[tex]f(x)=0.7[(x-4)]+2[/tex]

[tex]f(x)=0.7x-2.8+2\\f(x)=0.7x-0.8[/tex]

Is a linear equation with positive slope

[tex](x-4)\geq 0\\x\geq 4[/tex]

The domain is the interval [4,∞)

case 2) negative value

[tex]f(x)=0.7[-(x-4)]+2[/tex]

[tex]f(x)=-0.7x+2.8+2\\f(x)=-0.7x+4.8[/tex]

Is a linear equation with negative slope

[tex](x-4)< 0\\x<4[/tex]

The domain is the interval (-∞,4)

[tex]x<4[/tex]

therefore

The piecewise model of the function is

[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]

[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]

Answer: 16x² + 8x + 1

Step-by-step explanation:

(4x + 1)(4x + 1)

This expansion can be done in two ways either by direct expansion or by indirect expansion

(1) Direct expansion

(4x + 1)(4x + 1 )

4x X 4x + 4x X 1 + 1 X 4x + 1 X 1

= 16x² + 4x + 4x + 1

= 16x² + 8x + 1

(2) Method

This can be written thus:

(4x + 1 )(4x + 1 ) = (4x + 1 )²

= (4x)² + 2( 4x X 1 ) + 1²

= 16x² + 2(4x) + 1

= 16x² + 8x + 1.

(4x + 1)(4x + 1)

4x · 4x = 16x²

4x · 1 = 4x

1 · 4x = 4x

1 · 1 = 1

16x² + 4x + 4x + 1

16x² + 8x + 1

Answer:

135m^2

Step-by-step explanation:

length = l

width = w

l + l + w + w = 48

l = w+6

w+6 + w+6 + w + w = 48

4w + 12=48

4w=36

w=9

l=15

15*9=135

Answer:

A = 135m²

Step-by-step explanation:

Write equations to represent the problem.

l = w + (6m)        The length is 6m more than the width

P = (48m)        Perimeter is 48m

***We put brackets around numbers with the "m" to avoid confusing the units with a variable.

The formula for perimeter of a rectangle is P = 2(l + w)

Substitute "l" and "P" into the perimeter formula with the equations above. Simplify, then isolate "w".

P = 2(l + w)        

(48m) = 2(w + (6m) + w)        Collect like terms (w + w = 2w)

(48m) = 2(2w + (6m))        Distribute over brackets

(48m) = 4w + (12m)        Start isolating "w"

(48m) - (12m) = 4w + (12m) - (12m)        Subtract 12m from both sides

(36m) = 4w        

4w/4 = (36m)/4        Divide both sides by 4

w = 9m        Width of rectangle

Find "l" using the formula for length. Substitute the width.

l = w + (6m)        

l = (9m) + (6m)        Add

l = 15m        Length of rectangle

Use the formula for the area of a rectangle A = lw.

Substitute the values we found for length and width.

A = lw        

A = (15m)(9m)        Multiply

A = 135m²        Area of rectangle

Therefore the area of the rectangle is 135m².

Final answer:

To create an equation yielding a solution of 8, use a variable x and the fraction 1/4. By multiplying x by 32, the equation will result in 8.

Explanation:

To write a multiplication equation with one variable and one fraction yielding a solution of 8:

Start with the fraction 1/4.

Multiply that fraction by x = 32 to get a product of 8.