A line passes through the origin and has a slope of 4. What is the equation of the line that is parallel to the first line and passes through the point (1, –2)? A. y = 4x + 9 B. y = –4x + 2 C. y = 4x – 6 D. 2003-10-03-00-00_files/i0160000.jpg

The equation of line which is perpendicular to the given line and has a given point is required.

The equation of the line is [tex]y=\dfrac{1}{2}x+2[/tex].

The given line is

[tex]y-4=-2(x+3)\\\Rightarrow y-4=-2x-6\\\Rightarrow y=-2x-2[/tex]

The slope of the given line is [tex]m_1=-2[/tex]

For a line to be perpendicular we have the condition

[tex]m_1m_2=-1\\\Rightarrow m_2=\dfrac{-1}{-2}\\\Rightarrow m_2=\dfrac{1}{2}[/tex]

The point is [tex]P(2,3)[/tex]

The equation will be

[tex]y=m_2x+c\\\Rightarrow 3=\dfrac{1}{2}\times 2+c\\\Rightarrow c=3-1=2[/tex]

[tex]y=\dfrac{1}{2}x+2[/tex]

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The equation of the line passing through point P(2,3) that is perpendicular to the line y-4=-2(x+3) is y = (1/2)x + 2.

To find the equation of the line passing through point P(2,3) that is perpendicular to the line y-4=-2(x+3), we need to find the slope of the perpendicular line first. The given line has a slope of -2. The slope of the perpendicular line will be the negative reciprocal of -2, which is 1/2.

Now that we have the slope, we can use the point-slope form of the equation of a line. The equation is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we have y - 3 = (1/2)(x - 2).

This simplifies to y - 3 = (1/2)x - 1, and further simplifies to y = (1/2)x + 2.

Answer:

[tex]1\frac{4}{5}[/tex]

Step-by-step explanation:

3 times 3/5

[tex]3 \cdot \frac{3}{5}[/tex]

To multiply whole number by fraction , then we multiply 3 with the numerator

[tex]\frac{3 \cdot 3}{5}[/tex]

[tex]\frac{9}{5}[/tex]

Now write the fraction in mixed form

when we divide 9 by 5, the quotient is 1 and 4 is the remainder

[tex]\frac{9}{5}[/tex]

[tex]1\frac{4}{5}[/tex]

The college will receive an amount of $5436.56.

Compound interest is different from simple interest. In compound Interest, interest amount will vary each year. Interest is calculated first on the principal amount and then interest is the accumulated interest on the previous year.

Compound interest compounded continuously means interest is accumulating not within a month or year, but continuously.

If compound interest is compounded continuously, then the formula for calculating the final amount is,

A = P e^rt

where A is the final amount, P is the principal amount, r is the rate of interest and t is the time period.

Here, P = $2,000

r = 5% = 5/100 = 0.05

t = 20 years

A = 2000 × e^(0.05 × 20)

   = 2000 × e^1

   = 2000e

The value of e = 2.7182818..

A = 2000 × 2.7182818

   = 5436.5636 ≈ 5436.56

Hence by the amount deposited by philanthropist, if the interest is compounded continuously, the college will receive $5436.56.

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Answer:

[tex]m<R=87\°[/tex]

[tex]m<Q=93\°[/tex]

Step-by-step explanation:

we have that

[tex]m<R=(8x-1)\°[/tex]

[tex]m<Q=(9x-6)\°[/tex]

[tex]m<R+m<Q=180\°[/tex] ------> by supplementary angles

Substitute the values and solve for x

[tex]8x-1+9x-6=180\°[/tex]

[tex]17x-7=180\°[/tex]

[tex]17x=187\°[/tex]

[tex]x=11\°[/tex]

Find the value of angle R

[tex]m<R=(8*11-1)\°=87\°[/tex]

Find the value of angle Q

[tex]m<Q=(9*11-6)\°=93\°[/tex]

The measure of angle Q and R can be obtained by supplementary angle. The supplementary angle is defined as the addition of two angle is [tex]180^{\circ}[/tex].

The angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].

Given:

The equation for unknown angle is,

[tex]8x -1 + 9x - 6 = 180[/tex]

The supplementary angle is,

[tex]\angle R+\angle Q=180^{\circ}[/tex]

Compare the above equation.

[tex]\angle R=(8x-1)^{\circ}\\\angle Q=(9x-6)^{\circ}[/tex]

Solve the given expression.

[tex]\begin{aligned}8x -1 + 9x -6 &= 180\\ 17x - 7 &= 180 \\17x &= 187 \\x&=11\\\end[/tex]

Calculate the Angle R.

[tex]\angle R=(8\times 11-1)\\\angle R=87^{\circ}[/tex]

Calculate the Angle Q.

[tex]\angle Q=(9\times 11-6)\\\angle Q=93^{\circ}[/tex]

Thus, the angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].

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Final answer:

The exact value of tan(30°) is found using the sine and cosine values of 30°, resulting in tan(30°) being approximately 0.577.

Explanation:

To find the exact value of tan(30°), we look at the relationship between the sides of a 30-60-90 triangle or use the definitions of sine and cosine. The sine of 30° (sin(30°)) is 0.500, and the cosine of 30° (cos(30°)) is 0.866. The tangent is the ratio of sine to cosine, so:

tan(30°) = sin(30°) / cos(30°) = 0.500 / 0.866

When you calculate that ratio, you get tan(30°) = approximately 0.577, which is the exact value for tangent of 30 degrees.

Answer:

C) A line perpendicular to a given line through a point not on a line.

Step-by-step explanation:

In the given construction we draw a perpendicular line from a point which is not on line.

Please see the attachment for construction and naming of point.

Thus, C is correct option. " a line perpendicular to a given line through a point not on a line".

The next thing that Carlotta should do for the next step is A. Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc

An equilateral triangle simply refers to the triangle that has all its sides to be equal. An equilateral triangle also means a triangle where all the angles are 60°.

Since she has already constructed the line segment and arc that's shown in the diagram, then the next thing to do is to place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.

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Answer:

The estimated area of figure is 30 square units.

Step-by-step explanation:

We need to find the area of the irregular shape.

Draw a quadrilateral as shown below.

It is a trapezium with bases 5 units and 7 units, and height 5 units.

Area of a trapezoid is

[tex]Area=\frac{a+b}{2}\times h[/tex]

where, a, b are bases and h is height.

Substitute a=5,b=7 and h=5 in the above formula.

[tex]Area=\frac{5+7}{2}\times 5[/tex]

[tex]Area=6\times 5[/tex]

[tex]Area=30[/tex]

Therefore, the estimated area of figure is 30 square units.

Final answer:

To find the total number of games in a 64-team knockout soccer tournament, we observe that the number of games played in each round is half of the previous round, starting from 32 games in round one. By summing the games from all rounds, we determine that a total of 63 games are played in the tournament.

Explanation:

To calculate the total number of games played in a knockout soccer tournament with 64 teams, we can notice that in each round, half of the teams get eliminated and thus the number of games played is halved. Starting with the first round where 32 games are played, we can sum the total number of games for each subsequent round until we reach the final game.

Here's the pattern of games played per round until the final:

The total number of games played in the tournament is the sum of the games played in each round:

32 + 16 + 8 + 4 + 2 + 1 = 63 games

Therefore, the total number of games played in the regional soccer tournament is 63 games.

Answer: y = -(1/2)x

Step-by-step explanation: Direct variation of y with x means that:

y = k*x

where k is a real constant.

We know that when y = -4, the value of x is 8. So we can replace these values in the equation and find the value of k.

-4 = k*8

now we divide by 8 into both sides:

-4/8 = k*8/8 = k

-1/2 = k

So the equation is:

y = -(1/2)x

The equation is k = y/x and the value of k is  -1/2

The equation that can be used to represent direct proportion is y = kx

Where:

When k is made the subject of the formula, the equation becomes:

k = y/x

k = -4/8 = -1/2

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To find g'(a), take the derivative of G(x) with respect to x. Substitute x-values into g'(a) to find slope of tangent line. Use slope and point to write equation of tangent line.

To find g'(a), we need to take the derivative of G(x) with respect to x. The derivative of G(x) is the slope of the tangent line to the curve at any given point. In this case, G(x) = x^2 - 7x + 7, so g'(a) = 2a - 7.

For the point (0, 7), we substitute x = 0 into g'(a) to find the slope of the tangent line at that point:

Therefore, the equation of the tangent line at (0, 7) is y = -7x + 7.

Similarly, for the point (6, 1), we substitute x = 6 into g'(a) to find the slope of the tangent line at that point:

Therefore, the equation of the tangent line at (6, 1) is y = 5x - 29.

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The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.

Given :

To solve this kind of problems first let x be in degree. So, angle A, angle B and angle C beecomes:

[tex]\rm \angle A = 7x[/tex]    -----  (1)

[tex]\rm \angle B = 18x[/tex]  ----- (2)

[tex]\rm \angle C = 11x[/tex]   ----- (3)

From the properties of triangle, the sum of interior angles of a triangle is [tex]180^\circ[/tex].

[tex]\rm \angle A +\angle B+\angle C = 180^\circ[/tex]  --- (4)

Now, put the values of [tex]\rm \angle A,\;\angle B,\;and \; \angle C[/tex] in equation (4).

[tex]7x+18x+11x=180^\circ[/tex]

[tex]36x = 180^\circ[/tex]

[tex]x = 5[/tex]

Now, put the value of x in equation (1), (2) and (3).

[tex]\rm \angle A = 7\times 5 = 35^\circ[/tex]

[tex]\rm \angle B = 18\times5 = 90^\circ[/tex]

[tex]\rm \angle C = 11\times5=55^\circ[/tex]

The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.

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Final answer:

To make $2.50 using one dollar bills, quarters, and dimes, there are 7 different combinations.

Explanation:

To make $2.50 using one dollar bills, quarters, and dimes, we can use the concept of combinations. Let's break it down:

So, there are 7 different combinations to make $2.50 using one dollar bills, quarters, and dimes.

"The correct answer is ""Glanced.""

To determine which of the given words is a verb, we need to understand the function of each word in a sentence. A verb is a word used to describe an action, state, or occurrence, and it can change form to match the tense, mood, voice, aspect, person, and number of the subject.

 Let's analyze each word:

 - Europe: This is a proper noun, as it refers to a specific geographical location, the continent of Europe.

- Pretty: This is an adjective, as it describes a noun, modifying it to indicate that something has a pleasing appearance.

- Cup: This is a noun, as it names a thing, which in this case is a container used to hold liquids for drinking.

- Glanced: This is a verb, as it describes an action. ""Glanced"" means to look quickly or briefly at something. It is the past tense of the verb ""glance.""

 Therefore, ""Glanced"" is the verb among the options provided."