Determine the measure of

Step-by-step explanation:

we use the point-slope approach :

y - y1 = m(x - x1)

m is the slope, and (x1, y1) is a point on the line.

so,

1.

y - 2 = 7(x - 1) = 7x - 7

y = 7x - 5

2.

y - -1 = -1×(x - 3) = -x + 3

y + 1 = -x + 3

y = -x + 2

3.

y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)

y = -4x - 3

4.

y - 5 = 5/3 × (x - 3) = 5x/3 - 5

y = 5x/3 or 5/3 × x

Answer:

1. [tex]7x-y=5[/tex]

2. [tex]x+y=2[/tex]

3. [tex]4x+y=-3[/tex]

4. [tex]5x-3y=0[/tex]

Step-by-step explanation:

Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.

[tex]y-k=m(x-h)[/tex]

[tex]y-2=7(x-1)[/tex]

[tex]y-2=7x-7[/tex]

[tex]7x-y=5[/tex]

[tex]y+1=-1(x-3)[/tex]

[tex]y+1=-x+3[/tex]

[tex]x+y=2[/tex]

[tex]y-5=-4(x+2)[/tex]

[tex]y-5=-4x-8[/tex]

[tex]4x+y=-3[/tex]

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

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

[tex]3y-15=5x-15[/tex]

[tex]5x-3y=0[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf 6x+-2y^{2}+4xy^{2}+3x^{2} +5xy^{2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Group\:like\:terms \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =3x^2+6x-2y^2+4xy^2+5xy^2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Sum\:similar\:elements:\:4xy^2+5xy^2=9xy^2 \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf 3x^2+6x-2y^2+9xy^2 \end{gathered}$} }[/tex]

The lengths of the other two sides of the right triangle are 12 and 13

From the question, we are to determine the lengths of the other sides of the triangle

From the given information,

The other sides have lengths that are consecutive integers

Thus,

If the length of the other side is x

Then,

The hypotenuse will be x + 1

By the Pythagorean theorem, we can write that

(x+1)² = x² + 5²

(x+1)(x+1) = x² + 25

x² + x + x + 1 = x² + 25

x² - x² + x + x = 25 - 1

2x = 24

x = 24/2

x = 12

∴ The other leg of the right triangle is 12

Hypotenuse = x + 1 = 12 + 1 = 13

Hence, the lengths of the other two sides are 12 and 13

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Answer:

r=8.74038744 m
and surface area=1303.76211 m2

Step-by-step explanation:

Answer: Option (4)

Step-by-step explanation:

From the diagram, we know that

[tex]\sin 60^{\circ}=\frac{BC}{15}\\\\\cos 60^{\circ}=\frac{AB}{15}[/tex]

This means we can eliminate options 1 and 2.

Now, if we multiply both sides by 15, we get

[tex]15\cos 60^{\circ}=7.5[/tex].

This gives us Option (4).

Answer:

Step-by-step explanation:

already

Answer:

To solve this problem we first subtract 3 from both sides, giving the inequality -cw+3-3<= 15-3. We then simplify the equation to -cw<= 12. Next, we divide both sides by -c and flip the inequality. We flip the inequality because we are dividing by a negative. Now we have the inequality -cw/-c >= 12/-c. Lastly, we simplify to w >= -12/c.

Answer: B

The main word that gives the answer away is product, which means to multiply.

Answer:

11.4 feet

Step-by-step explanation:

1/1.9 = h/w  (h= height, w=width)

Solving for w, gives you the formula

w = (1.9)h

This means the width is 1.9 times the height.

Use the formula to find the width where the height is 6 feet.

h = 6

w = (1.9)(6) = 11.4

The width is 11.4 feet.

Answer:

18

Step-by-step explanation:

3*3*3 = 27, assuming all 3 digits can occupy each space

However, 0 cannot start a number, so it becomes:

3*3*2, which is 18.

a. Sean drank at a rate of 5 milliliters per second.

b. It took Sean 55 s to drink all the slushy.

Since Sean darnak at a constant rate and originally there were 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters of slushy remained.

The rate at which Sean drank, r = Change in volume of slushy/time for change

= (275 mL - 210 mL)/13 s

= 65 mL/13 s

= 5 mL/s

So, Sean drank at a rate of 5 milliliters per second.

The time it takes Sean to drink all the slushy is given by

T = V/r where

So, T = V/r

= 275 mL/5 mL/s

= 55 s

So, it took Sean 55 s to drink all the slushy.

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The solution will illustrate that the equation has one solution at x=0.

Given that  adds 2 to both sides, the equation 4x = 3x results.

An algebraic equation may be described as a mathematical declaration wherein expressions are set the same as every other.

The equation is 4x=3x.

As given that add 2 on both sides, we get

4x+2=3x+2

Now, we will subtract 3x from both sides, we get

4x+2-3x=3x+2-3x

x+2=2

Further, we will subtract 2 from both sides, we get

x+2-2=2-2

x=0

Hence, When adds 2 to both sides, the equation 4x = 3x results that the equation has one solution x=0.

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Answer:

B, C, A

Step-by-step explanation:

Don't really know how to explain this.

Answer:

The length and the width of the rectangle are 10 inches and 6 inches respectively.

In the question, we are given that the length of a rectangle exceeds its width by 4 inches, and the area is 60 square inches.

We are asked for the length and the width of the rectangle.

We assume the width (w) of the rectangle to be x inches.

Its length (l), exceeds its width (w) by 4 inches.

Thus, its length (l) = x + 4 inches.

Now, the area can be calculated using the formula, A = l*w, where A is its area, l is its length, and w is its width.

Thus, the area = (x + 4)x = x² + 4x.

But, we are given that the area is 60 square inches.

Putting the value, we get a quadratic equation:

x² + 4x = 60.

or, x² + 4x - 60 = 0,

or, x² + 10x - 6x - 60 = 0,

or, x(x + 10) - 6(x + 10) = 0,

or, (x - 6)(x + 10) = 0.

By the zero-product rule, we get:

Either, x - 6 = 0, or, x = 6,

or, x + 10 = 0, or, x = -10, but this is not possible as the width of a rectangle cannot be negative.

Thus, the width = x = 6 inches.

The length = x + 4 = 10 inches.

Thus, the length and the width of the rectangle are 10 inches and 6 inches respectively.

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[tex]\frac{7}{30}[/tex] units of time is left.

To find how much time is left:

Given - Tony is given [tex]\frac{9}{10}[/tex] hour to mow a lawn. he only uses [tex]\frac{2}{3}[/tex]  the given time to mow the lawn.

Simplify subtract   [tex]\frac{9}{10}[/tex]  by  [tex]\frac{2}{3}[/tex]  as follows:

[tex]\frac{9}{10}-\frac{2}{3} =\frac{27-20}{30} =\frac{7}{30}[/tex]

Therefore, [tex]\frac{7}{30}[/tex] units of time is left.

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2000 feet can be represented as 20 blue whales in a row of each 100 feet.

What is a blue whale?

I feet = 30.48 centimeters

To explain what the length of 2000 feet looks like:

Take the example of a blue whale of 100 feet.

Now, imagine placing up 20 blue whales one behind the other.

20 × 100 feet = 2000 feet

Therefore, 2000 feet can be represented as 20 blue whales in a row of each 100 feet.

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Based on definition of unit circle and angle properties on Cartesian plane, we find the following results: A: π/5, B: 3π/7, C: 4π/3.

Units circles are commonly used to understand angles and trigonometric functions in a simple way. Vectors in a unit circle are ordered pairs of polar form: (x, y) = (cos θ, sin θ).

To solve this problem, we must take these tips into account:

Then, we have the following results: A: π/5, B: 3π/7, C: 4π/3.

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Answer:

20 units

Step-by-step explanation:

The stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.

According  to the question,

Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. She sets aside $1000 to refurnish her apartment, and decides to invest the other $2000.

If the stock decreases at a rate of 15% per year for eight years. In order to find the stock worth when she sells it eight years later we have the formula

Value of stock after 'n' years = Principal[1-Rate/100]ⁿ

Value of stock after '8' years = 2000[1-15/100]⁸

= 2000[1-0.15]⁸

=2000[0.85]⁸

=2000[0.2725]

=545$

Hence, the stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.

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The double number line that shows the other values of packages and pencils is A. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48.

It should be noted that a number line simply means a line which numbers are marked a intervals to illustrated numerical operations.

In this case, the double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48 illustrate this information

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Considering the given proportions, the correct statements are:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The table gives these following proportions:

Hence the correct statements are:

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The perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2) is 4.828

We can determine the perimeter of a triangle with vertices by utilizing the distance formula.

Given that, we have the vertices (x₁,y₁), (x₂, y₂), (x₃, y₃). Then the length of each sides can be expressed as follows:

SIde AB = [tex]\mathbf{\sqrt{(x_1 -x_2)^2 +(y_1 -y_2)^2}}[/tex]

Side AC = [tex]\mathbf{\sqrt{(x_1 -x_3)^2 +(y_1 -y_3)^2}}[/tex]

Side BC = [tex]\mathbf{\sqrt{(x_2 -x_3)^2 +(y_2 -y_3)^2}}[/tex]

Replacing the values of the coordinates into the given formula above the perimeter of the triangle is 4.828

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Las cuentas de Dmitri de menor a mayor se ordenan: retiro, cheques y ahorros.

Para organizar las cuentas bancarias de Dmitri de menor a mayor debemos observar cuidadosamente los valores de cada una. Adicionalmente para organizarlas por valor absoluto nos fijamos únicamente en el número sin tener en cuenta el símbolo, en ese caso el valor de cheques pierde su símbolo negativo.

Entonces las cuentas quedarían organizadas así:

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Answer:

a₈ = - 10935

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-15}{5}[/tex] = - 3 , then

a₈ = 5 × [tex](-3)^{7}[/tex] = 5 × - 2187 = - 10935

The amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.

A fractional betting or game allows the gambler to calculate the winning from their betting when it is compared with their stake.

The number on the left-side represents the winning, while the number on the right side of the fractional odds represents the stake (investment).

When the gambler wins, they receive 10x their stake.  The expected amount to be won is computed as the total stakes, multiplied by the winning probability and the fractional odds.

Fractional odds of winning = 10/1

Chance of winning = 1/12

Number of independent games played = 150 times

Bet each time = $20

Total bets = $3,000 ($20 x 150)

Amount won = $2,500 ($3,000 x 1/12 x 10/1)

Thus, the amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.

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How much do you expect to win?

Answer: C: [tex]D\cap F = \{2, 4, 6, 8\}[/tex]

Step-by-step explanation:

Let's first find the specific numbers that are in sets D and F.

[tex]D=\{0,1,2,\ldots\}[/tex], as D has all whole numbers.

[tex]F=\{2,4,6,8\}[/tex], as all of these numbers are even, greater than or equal to two, and less than nine.

Since all the numbers in F are whole numbers, all of them would be in D. Hence, the intersection of both would just be {2, 4, 6, 8}.

[tex]D\cap F = \{2, 4, 6, 8\}[/tex]

There will be total 14 hard centred and 14 soft centred choclates in the box.

The ratio is the division of the two numbers.

For example, a/b where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2

Hard centred/ Soft centred = 5/2

And total

Hard centred + Soft centred = 49

Now let say hard centred is H and soft centred S

H/S = 5/2 and H + S = 49

Now H = (5/2)S put into second equation

(5/2)S + S = 49

S(7/2) = 49

S = 14 now put into second equation

H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.

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