you buy 1 shirt and 3 pairs of pants for $44. your friend buys 3 shirts and 1 pair of pants for $44. what is the cost of each shirt? of each pair of pants?

[tex] \Large{\boxed{\sf 2x - y = 18}} [/tex]

[tex] \\ [/tex]

We will try to write the given linear equation in standard form.

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Standard \ Form \ of \ a \ linear \ equation \text{:}} \\ ~ \\ \tt Ax + By = C \end{array} \right] } [/tex]

Where:

[tex] \\ [/tex]

Given linear equation:

[tex] \sf y + 4 = 2(x - 7) [/tex]

[tex] \\ [/tex]

First, expand the right side of the equation:

[tex] \sf y + 4 = 2 \cdot x + 2 \cdot (-7) \\ \\ \sf y + 4 = 2x - 14 [/tex]

[tex] \\ [/tex]

Subtract 2x from both sides of the equation:

[tex] \sf y + 4 - 2x = 2x - 14 - 2x \\ \\ \sf -2x + y + 4 = -14 [/tex]

[tex] \\ [/tex]

Subtract 4 from both sides of the equation:

[tex] \sf -2x + y + 4 - 4 = -14 - 4 \\ \\ \sf -2x + y = -18 [/tex]

[tex] \\ [/tex]

Since the coefficient of x (-2) has to be positive, multiply both sides of the equation by -1:

[tex] \sf -1 \cdot (-2x + y) = -1 \cdot (-18) \\ \\ \sf -1 \cdot (-2x) + (-1) \cdot y = 18 \\ \\ \boxed{\boxed{\sf 2x - y = 18 }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Using the critical values of t=+/-2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of +/-2.093.

Critical Value Definition -

Critical value can be defined as a value that is compared to a test statistic in hypothesis testing to determine whether the null hypothesis is to be rejected or not.

If the value of the test statistic is less extreme than the critical value, then the null hypothesis cannot be rejected.

Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability \alpha if the null hypothesis is true.

Using the critical values of t=±2.201 is more "conservative" than using the critical value of ±2.093 because it is more likely to reject the null hypothesis using the greater value i-e t=±2.201.

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Answer:

Step-by-step explanation:

You want to know the measures of angles ADB and ADC given that inscribed angle BAC is 21° and exterior angle CBE is 58°.

Angle CBE is exterior to triangle CBA with remote interior angles BAC (21°) and ACB. The exterior angle is equal to the sum of the remote interior angles, so ...

  ∠CAB +∠ACB = ∠CBE

  21° +∠ACB = 58°

  ∠ACB = 37° . . . . . . . . subtract 21°

The measure of an inscribed angle is half the measure of the arc it intercepts. This means the measures of all inscribed angles that intercept the same arc are the same.

  ∠ADB = ∠ACB = 37°

  ∠BDC = ∠CAB = 21°

By the Angle Addition theorem, ...

  ∠ADC = ∠ADB +∠BDC = 37° +21°

  ∠ADC = 58°

As we just saw, ...

  ∠ADB = 37°

For angle CAD = 69°, the total of the inscribed angles with vertex A is ...

  ∠CAD +∠CAB = ∠BAD

  69° +21° = 90° = ∠BAD

This means angle BAD intercepts an arc BD of 180°, hence segment BD is a diameter.

__

The attached figure is accurately drawn.

Answer:

A , E

Step-by-step explanation:

side of the square = 10

there are 4 side in the perimeter

10 · 4 = 40

the radius of the semicircle is the value of the side of the square = 10

there are two equals semicircle, so the total perimeter of these shapes is equal to a complete circle

10 · 2 · π = 20π

total perimeter

40 + 20π

that can be expanded in

10 + 10 + 10π + 10 + 10 + 10π

Answer:330

Step-by-step explanation:

Set up cross multiplication:

33/x    10/100

Cross multiply

10*x   100*33

Divide sums

3,300/10x

Answer:

330 total cards

The roots of the quartic polynomial f(x) = x⁴ + 8x³ + 11x² - 9x + 28 are ±1, ±2, ±3, ±4, ±7, ±14, ±28

In the given problem, we have to find the roots of the fourth degree polynomial and factorize the given polynomial equation first in order to obtain three equations which are linear and quadratic equation. We can easily determine the zeros of the  fourth degree polynomial.

Generally, polynomials of fourth degrees are called quartic polynomials.

f(x) = x⁴ + 8x³ + 11x² - 9x + 28

When we factorize this, we wouldn't get a lower value because this quartic polynomial cannot be factorized.

However, we can still find the roots which are the solution to the polynomial and are

x = ±1, ±2, ±3, ±4, ±7, ±14, ±28

These values are the solution to the polynomial.

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complete question : What are the roots of f(x)=x^4+8x^3+11x^2-9x+28

3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

Given that,

The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).

We have to find how many such difference triangle are possible.

We know that,

Perimeter of the triangle is 12cm.

p=12

a+b+c=12

a+b≥c

b+c≥a

So,

a+b+c≥2c

12≥2c

c≤6

So,

a≤6,b≤6,c≤6

We get,

a=6,b=3,c=3

a=5,b=4,c=3

a=4,b=4,c=4

Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

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2. The measurement of angle 1 is 113°

3. The measure of ∠1 = 98° and ∠2 = 82°

4. The value of x is 8.

5.  The value of x is 3.

What is the supplementary angle?

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.

2.

Given that, ∠1 and ∠4 are vertical angle.

According to the vertical angle theorem, if two angles are vertical then they are congruent.

Therefore,

∠1 = ∠4

3x + 14 = 5x − 52

Subtract 5x from both sides:

3x - 5x + 14 = -52

-2x + 14 = -52

Subtract 14 from both sides:

-2x = -66

x = -33

Putting x = -33 in ∠1 = 3x + 14

∠1 = 3× 33 + 14 = 113°

3.

Given that, ∠1 = 3x + 8 and ∠2 = 2/3x + 62 are supplementary angles.

Therefore ∠1 + ∠2 = 180°

3x + 8 + 2/3x + 62 = 180°

11/3 x + 70 = 180°

Subtract 70 from both sides:

11/3 x = 110

x = 110 × (3/11)

x = 30

Putting x = 30 in ∠1 = 3x + 8 and ∠2 = 2/3x + 62

∠1 = 3x + 8 = 3×30 + 8 = 98°

∠2 = 2/3x + 62 = (2/3)×30 + 62 = 82°

4.

Given that, Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the measure of angle 3 equals 9x + 59.

Therefore,

∠2  = ∠3

13x + 27 = 9x + 59

Subtract 9x from both sides:

13x - 9x + 27 = 9x -9x +59

4x +27 = 59

Subtract 27 from both sides:

4x = 32

x = 8

5. Given that m∠ABC = 163° and ∠XYZ = 5x + 2 are supplementary angles.

m∠ABC + m∠XYZ =180°

163° + 5x + 2 =180°

165 + 5x = 180

Subtract 165 from both sides:

5x = 15

x = 3

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Answer:

2)  m∠1 = 113°

3)  98° and 82°

4)  x = 8  

    Angles = 131°

5)  x = 3

Step-by-step explanation:

If Angle 1 and Angle 4 are vertical angles, then according the Vertical Angles Theorem they are congruent.

Therefore:

⇒ m∠1 = m∠4

⇒ 3x + 14 = 5x - 52

⇒ -2x + 14 = -52

⇒ -2x = -66

⇒ x = 33

To find the measure of Angle 1, substitute the found value of x into the expression for the angle:

⇒ m∠1 = 3x + 14

⇒ m∠1 = 3(33) + 14

⇒ m∠1 = 99 + 14

⇒ m∠1 = 113°

Given:

If the angles are supplementary, they sum to 180°:

⇒ 3x + 8 + ²/₃x + 62 = 180

⇒ ¹¹/₃x + 70 = 180

⇒ ¹¹/₃x = 110

⇒ 11x = 330

⇒ x = 30

Substitute the found value of x into the expressions for the angles:

⇒ ∠ = 3x + 8

⇒ ∠ = 3(30) + 8

⇒ ∠ = 98°

⇒ ∠ = ²/₃x + 62

⇒ ∠ = ²/₃(30) + 62

⇒ ∠ = 82°

If Angle 2 and Angle 3 are vertical angles, then according the Vertical Angles Theorem they are congruent.

Therefore:

⇒ m∠2 = m∠3

⇒ 13x + 27 = 9x + 59

⇒ 4x + 27 = 59

⇒ 4x = 32

⇒ x = 8

Substitute the found value of x into the expressions for the angles:

⇒ m∠2 = 13x + 27

⇒ m∠2 = 13(8) + 27

⇒ m∠2 = 104 + 27

⇒ m∠2 = 131°

⇒ m∠3 = 9x + 59

⇒ m∠3 = 9(8) + 59

⇒ m∠3 = 72 + 59

⇒ m∠3 = 131°

Given:

If ∠ABC and ∠XYZ are supplementary, they sum to 180°:

⇒ m∠ABC + m∠XYZ = 180°

⇒ 163 + 5x + 2 = 180

⇒ 5x + 165 = 180

⇒ 5x = 15

⇒ x = 3

The side length of Figure A can be determined using the ratio of areas and the known side length of Figure B. The area of Figure A is 18 square feet and the area of Figure B is 98 square feet. The side length of Figure B is 14 feet. Using these values, the corresponding side length of Figure A can be calculated to be 7 feet.

The missing corresponding side length of Figure A can be determined using the ratio of areas and the known side length of Figure B. If two shapes are similar, then their corresponding sides are in the same ratio as their areas. Since the area of Figure A is 18 square feet and the area of Figure B is 98 square feet, the ratio of their areas is 18/98. Since the side length of Figure B is 14 feet, the corresponding side length of Figure A can be calculated by multiplying 14 feet by the ratio of 18/98, which is 0.1837. This value can be rounded to 7 feet. Therefore, the missing corresponding side length of Figure A is 7 feet. This result can be verified by calculating the area of Figure A using the known side length and the missing side length. If the two side lengths are multiplied together, the product should be equal to the area of Figure A, which is 18 square feet.

7 feet x 11 feet = 77 feet^2

77 feet^2 = 18 feet^2 (Area of Figure A)

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The tree diagram that summarizes these probabilities is Option (D).

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Here, N(S) = 10, The numbers from 0 - 9.

The probability of going to work by driving is (4/10) = 0.4.

If he drives, he has a probability of 0.1 of being late so P(NL) = 1 - 0.1 = 0.9.

The probability of going to work by walking is = 6/10 = 0.6.

if he walks, his probability of late rising to 0.25 so, P(NL) = 1 - 0.25 = 0.75.

Now we'll connect this information to the given options.

From the given options, Option (D) satisfies the given information.

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Answer:

A is the only irrational number present.

Step-by-step explanation:

The bottom two numbers can be simplified into 7 and 5. Meanwhile, B is a repeating number. A is a non-repeating and non terminating number.

Answer:

A.

Step-by-step explanation:

An irrational number is any real number that cannot be equally divided by 2 integers. (It's not a perfect square.)

No whole number multiplied by itself equals 27.

Answer:

1.5 groups.

Step-by-step explanation:

1 divided by 8/12 is 1.5

Answer:

1 1/2

Step-by-step explanation:

The figure shows a large rectangle that is divided into 12 parts of equal size.

Think of the entire rectangle as 1.

Each small rectangle is 1/12 of 1.

Now count 8 small rectangles starting at the left.

When you divide 1 by 8/12, you can fit 1 full 8/12 (8 small rectangles) and another half of 8/12 (another 4 small rectangles.

Since you can fit 1 1/2 groups of 8 small rectangles,the result is 1 1/2.

Answer: 1 ÷ 8/12 = 1 1/2

If a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.

In this question we need to prove if a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.

We know that the definition of divisibility i.e., m divides n if there exists an integer p such that n = mp

If a | c and b | d, then there exist integers x and y such that c = ax and d = by.

Consider a multiplication c * d

= (ax) * (by)

= axby

= (ab)xy

= ab(xy)

Let k be equal to the integer xy

So, cd = ab(k)

Using the definition of divisibility,  cd is divisible by ab.

Therefore, if a | c and b | d, then ab | cd.

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The total cost is $245.31.

Given,

Volume = 10[tex]m^{3}[/tex]

Width = w

Length = 2w

Base area = Length x Width = [tex]2w^{2}[/tex]

Cost of base = $15

Cost of sides = $9

Since the volume is 10[tex]m^{3}[/tex],

Volume = Base Area x Height

Height = [tex]\frac{10}{2w^{2} }[/tex] = [tex]\frac{5}{w^{2} }[/tex]

Cost of making such a container:

Cost of base =  [tex]2w^{2}[/tex] x 15 = $[tex]30w^{2}[/tex]

Cost of sides = [(2 x 2w x  [tex]\frac{5}{w^{2} }[/tex]) + (2 x w x  [tex]\frac{5}{w^{2} }[/tex])] x $9 = $[tex]\frac{270}{w}[/tex]

Overall Cost = Cost of Base + Cost of Sides

f(x) = [tex]30w^{2} + \frac{270}{w}[/tex] = [tex]30(w^{2} + \frac{9}{w})[/tex]

To get the minimum cost, we will have to find the derivative of f(x) and equate it to zero.

d(f(x))/dx = 0

[tex]2w - \frac{9}{w^{2} } = 0\\w^{3} = 4.5 \\w = 1.651m[/tex]

Putting the value of w in f(x),

f(x) = $245.31 (after calculations)

Therefore, the final answer is $245.31.

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Lauren's reasoning does not make sense because the LCM of 2 and 8 is not 16, the LCM will be equal to 8.

The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers.

It can also be computed for several different numbers.

As per the given information in the question,

Lauren says that the LCM of 2 and 8 is 16.

Now, let's check whether it is correct or not.

Let's make a factor of both numbers,

2 = 2 × 1

8 = 2 × 2 × 2

So, the LCM will be: 2 × 2 × 2 = 8

It means that the LCM of 2 and 8 is not 16, the LCM is 8.

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Answer:

third one:

x<-2 or x>2

Step-by-step explanation:

Answer:

third one

Step-by-step explanation:

]

The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.

Given that, the polygon IJKL if IJ≅KL, JK≅LI, IJ⊥JK, JK⊥KL, KL⊥LI and LI⊥IJ.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Here, the opposite sides IJ and KL are equal and the opposite sides JK and LI are equal.

Since, all the sides are perpendicular to each other makes an angle 90°

The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.

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Linear functions are those whose graph is a straight line and it has the following form. y = f(x) = a + bx.

There are several ways to represent a linear function such ad word form, function notation, tabular form, and graphical form.

The key features of a linear function identified and interpreted from a description as an increasing linear function results in a graph that slants upward from left to right and has a positive slope.

A linear function can be expressed as a point slope or a line with a slope intercept. The ordered pairs will represent points on the line where a table of values representing the function is provided. According to the values in the table, the gradient of the line is a ratio of rise to run. The gradient and initial value of the function are shown in slope intercept form.

A graph with a positive slope and a left-to-right slope is produced by an increasing linear function. A graph with a negative slope and a left-to-right slant is produced by a decreasing linear function. A graph with a constant linear function looks like a horizontal line.

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Answer: 8

Step-by-step explanation:

4+4 is the same as 4 times 2

They both equal to 8

Answer:

x = mp - np

Step-by-step explanation:

Make x the subject of m = n + x/p

m = n + x/p

subtract n from both sides:

m - n = n + x/p - n

m - n = x/p

multiply both sides by p:

p(m - n) = p(x/p)

x = p(m - n)

distribute p on right side:

x = mp - np

Answer:

3.5 cm

Step-by-step explanation:

Circumference: C = 2πr

so radius r = C/2π = 22/2π = 3.5 cm

On solving the provided question we can say that - rate is the tip of his shadow moving is [tex]d/dt ( s-x) = ds/dt - dx/dt = 25/3 - 5 = 25/3 - 15/3 = 10/3 ft/s = 10/3 ft/s[/tex]

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is what? A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

triangles and the ratios

15 ft            s

-------- = --------------

6 ft           s-x

Using cross products

[tex]15( s-x) = 6s\\15s -15x = 6s\\15s-6s = 15x\\9s = 15x\\s = 15/9 x\\s = 5/3 x[/tex]

Taking the derivative of each side with respect to time

[tex]ds/dt = 5/3 dx/dt\\We know dx/dt = 5 ft/s\\ds /dt = 5/3 * 5 = 25/3 ft/s\\a) ds/dt = 25/3 ft/s[/tex]

The length of the shadow is ( s-x)

[tex]d/dt ( s-x)\\ds/dt - dx/dt\\25/3 - 5\\25/3 - 15/3\\10/3 ft/s\\b) 10/3 ft/s[/tex]

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Answer:

b

Step-by-step explanation:

we first make

1.Subtraction/Adding

2.Mutiply/Division

Answer:

The dependent variable is the cost

Step-by-step explanation:

The dependent variable is the variable that depends on the independent variable to either increase or decrease.

In this case, the dependent variable is the cost, and the independent variable is the number of chocolate bars.

Answer:

1262(2)^x

Step-by-step explanation:

Answer:

72 = b + 24

Step-by-step explanation:

b = 48 bracelets

Answer:

Math Expert Answer

Step-by-step explanation:

So toms equation is y= 4x + 6 and addisons equation is y=10x so they will meet eachother in 1 hour. You can use a desmos calculator to input the equations for the answer

Answer:

1 hour

Step-by-step explanation:

Let's set up an equation for Tom's and Addison's distances: T(x) = 4x + 6, A(x) = 10x, where x is the amount of time since Addison started (in hours).

We solve for A(x) = T(x) and get:

10x = 4x + 6 → subtract 4x from both sides

6x = 6 → divide both sides by 6

x = 1

Therefore, it took Addison 1 hour to catch up with Tom

Explanation:

A trapezium has four sides, so it is a quadrilateral.

Any quadrilateral has all four interior angles add to 360 degrees.

K+L+M+N = 360

123+71+39+y = 360

233+y = 360

y = 360-233

y = 127

Answer:

7.5

Step-by-step explanation:
100% = 75
100% divided by 10 is 10%
75 divided by 10 is 7.5

Answer:

Law of Sines

Step-by-step explanation: