Under a dilation centered at the origin, the point (-4 , 3) has image at (8 , -6) The dilation is

24 students in arons class

Answer:

Option (C) 6.736

Step-by-step explanation:

Please look at the attached modified schematic, where I have constructed a perpendicular line to the base of the triangle.

This creates two Right triangles (i.e. one angle will always be 90°). In doing so, the 80° angle is divided into 30° and 50° angles. In doing so we also then know that on the left Right-triangle the bottom left angle will be 60° since for any Triangle all three angles must add up to 180°.

(Check your self: On the left triangle we have 90° + 30° + 60° = 180° and on the right triangle we have 90° + 50° + 40° = 180°, so we are correct).

Now let us first find the value of side named [tex]y[/tex] on the figure using Right-triangle Trigonometry. In a Right-triangle the longest side is called the hypotenuse (here denoted by the sides [tex]x[/tex] and the one valued [tex]5[/tex]).

So we have:

[tex]sin(60)=\frac{opposite side}{hypotenuse}= \frac{y}{5}\\[/tex]

so solving for [tex]y[/tex] gives:

[tex]sin(60)=\frac{y}{5}\\ y=5sin(60)\\y=\frac{5\sqrt{3} }{2}[/tex]

Similarly for the other triangle we can write:

[tex]sin(40)=\frac{y}{x}\\\\[/tex]

[tex]sin(40)=\frac{\frac{5\sqrt{3} }{2} }{x}\\[/tex]

[tex]x=\frac{\frac{5\sqrt{3} }{2} }{sin(40)}\\\\x=6.736[/tex]

So the correct option is Option (C) 6.736

Answer:

t = t₀ - 3n

Step-by-step explanation:

Let t be the temperature and t₀ be the initial temperature of the day

Let n be the number of hours after the initial temperature ( t₀) was registered

Let -3 be the constant of change of temperature ( In 4 hours it went down 12 degrees)

Now, let's write down the expression that shows the temperature change each hour, this way:

t = t₀ - 3n

After 2 hours

t = t₀ - 3 * 2 = t₀ - 6

After 5 hours

t = t₀ - 3 * 5 = t₀ - 15

After 3 hours and 30 minutes

t = t₀ - 3 * 3.5 = t₀ - 10.5

Answer:

6y+9x

Step-by-step explanation:

Combine like terms.

8y-2y=6y

4x+5x=9x

6y+9x

Answer:9x+6y

Step-by-step explanation:

8y +4y-2y+5x

=8y+4x+-2y+5x

(4x+5x)+(8y+-2y)

To convert 44.4% to a fraction, express it as 44.4/100, eliminate the decimal by multiplying by 10 to get 444/1000, and then simplify this to 111/250 by dividing both terms by their greatest common divisor.

To convert 44.4% into a fraction, start by writing the percent as a fraction with a denominator of 100, which would be 44.4/100. Since there is a decimal in the numerator, we want to eliminate it by multiplying both the numerator and the denominator by 10, transforming it into 444/1000. From here, the fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This results in the fraction 111/250, which is the simplest form of the fraction corresponding to the percent 44.4%.

Answer:

0.225 L of milk, would be required if she uses 450 m L of water.

Step-by-step explanation:

Here, to make the shake, ingredients used by Dina are:

40 m L of chocolate syrup,

200 m L of milk, and 400 m L of water.

So, here Amount of water used = 2 x ( Amount of Milk used)  .......  (1)

Now,again the amount of water used by Dona = 450 m L

Let us assume the milk used by her  = k m L

⇒ 450 m L = 2 x ( k m L)     ( from (1))

or, 450 = 2  k

⇒  k    = 450/2  = 225

⇒   k   = 225 m L

Also, 1 m L = 0.001 L

So, 225 m L = 225 x  0.001  = 0.225 L

⇒   k   = 0.225  L

Hence, 0.225 L of milk, would be required if she uses 450 m L of water.

Dona would need 0.225 liters of milk when using 450 mL of water for her chocolate shake.

To find out how much milk would be required if 450 mL of water is used, we should first look at the ratio of water to milk in the original recipe. Dona used 400 mL of water for 200 mL of milk, which is a 2:1 ratio of water to milk. If she uses 450 mL of water, maintaining the same ratio, we would calculate the amount of milk required as follows:

Determine the proportion of milk to water used originally: 200 mL milk / 400 mL water = 1/2.

Using the proportion, calculate the new amount of milk for 450 mL water: (1/2) * 450 mL = 225 mL.

Convert the milk from milliliters to liters: To do this, we know that 1 liter is equivalent to 1,000 milliliters. Therefore, we divide 225 mL by 1,000 to convert to liters.

225 mL / 1,000 = 0.225 liters of milk is needed.

There are different ways through which you can earn money through a share, either from Exxon or from any other company. These are:

-Through obtaining profits by collecting dividends, which are sums of money that each company pays to shareholders as a way to distribute profits.

-Through the maintenance of the share in the investment portfolio, when it rises in value, it will also cause the shareholder's wealth to rise.

-Through the short investment, seeking to earn money through the "bet" for the fall in the value of the share.

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Daniel bought 2 spoons and 5 forks.

Step-by-step explanation:

Given,

Amount spent on utensils = $40

Cost of each spoon = $5

Cost of each fork = $6

Total items bought = 7

Let,

x be the number of spoons bought

y be the number of forks bought

x+y=7           Eqn 1

5x+6y=40    Eqn 2

Multiplying Eqn 1 by 5

[tex]5(x+y=7)\\5x+5y=35\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](5x+6y)-(5x+5y)=40-35\\5x+6y-5x-5y=5\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=7\\x=7-5\\x=2[/tex]

Daniel bought 2 spoons and 5 forks.

Keywords: linear equation, elimination method

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Daniel bought 2 spoons and 5 forks by using a system of equations and solving for the number of each utensil.

The question involves determining how many spoons and forks Daniel bought given that spoons cost $5, forks cost $6, he bought a total of 7 utensils, and spent $40. To solve this, we can use a system of equations where s represents the number of spoons and f represents the number of forks.

The first equation represents the total number of utensils bought:

s + f = 7

The second equation represents the total amount spent:

5s + 6f = 40

To find the values of s and f, we can solve the system of equations. Subtracting the first equation from the second equation (multiplied by 5) gives:

5s + 6f = 40
-(5s + 5f = 35)
------------------
f = 5

Substituting f = 5 into s + f = 7, we get s = 2. Hence, Daniel bought 2 spoons and 5 forks.

Answer: f(x)= -2x - 3

Step-by-step explanation

Good morning,

Answer:

4.5/25 = 0.18

Step-by-step explanation:

4.5/25 = (4.5×4)/(25×4) = 18/100 = 0.18.

:)

The answer to the division question 'What is 4.5 divided by 0.25' is 18, because a whole (1) can be expressed as 4 parts in 0.25 decimal representation, and when multiplied by 4.5 it gives 18 parts.

The student has asked: 'What is 4.5 divided by .25'. This is a division question within the subject of Mathematics.

To solve this, you will need to divide 4.5 by 0.25. If we perform this division, we get 18. Therefore, 4.5 divided by 0.25 equals 18.

This is because if take a whole (which is 1 in decimal and represents 4 parts in 0.25 decimal representation), and we multiply it by 4.5, we get 18 parts of 0.25.

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The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed

Step-by-step explanation:

Given

Distance = d = 45 miles

Time = t = 3/4 hour

The unit rate is defined as the distance per unit time. In this case, the unit rate can also be called speed.

So,

[tex]s = \frac{d}{t}\\s = \frac{45}{\frac{3}{4}}\\s = 45 * \frac{4}{3}\\s = 60\ miles\ per\ hour[/tex]

Using this unit rate we can see if the car can travel 65 miles in 1.25 hours or not

Given

Distance = d1 = 65 miles

Speed = s = 60 miles per hour

Putting the values in the formula for speed

[tex]s = \frac{d_1}{t_1}\\60 = \frac{65}{t_1}\\t_1 = \frac{65}{60}\\t_1 = 1.08\ hours[/tex]

As we can see that 1.08 is less than 1.25 so the driver will reach the meeting before time if he drives on a constant speed of 60 miles per hour

Hence,

The unit rate is 60 miles per hour and the driver will reach before time with the calculated constant speed

Keywords: Speed, unit rate

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Answer:

  10. Statement: Point P lies on line C'D'. Reason: The coordinates of P satisfy the equation of line C'D'.

Step-by-step explanation:

The equation for line C'D' in statement 8 appears to be in error. It should be ...

  [tex]y=\dfrac{-s}{2t-r}x+\dfrac{2st}{2t-r}[/tex]

The coordinates of point P given in statement 9 are in error (they cannot be negative). They should be ...

  P = (2/3(r+t), 2/3s) . . . . . without the minus signs

This point will satisfy the equation of line C'D'. Here is the algebra. (Notice we have multiplied each term on the right of the above equation by (-1/-1).

  [tex]y=\dfrac{s}{r-2t}x-\dfrac{2st}{r-2t}\\\\\dfrac{2}{3}s=\dfrac{s}{r-2t}\cdot\dfrac{2}{3}(r+t)-\dfrac{2st}{r-2t}\qquad\text{substitute P for (x, y)}\\\\s(r-2t)=s(r+t)-3st\qquad\text{multiply by $\frac{3}{2}$(r-2t)}\\\\sr-2st=sr-2st\qquad\text{P satisfies the equation for line C'D'}[/tex]

So, step 10 should say, in effect, P lies on C'D'.

_____

Comment on the proof

IMO it is unfortunate that this proof has so many mistakes. Properly done, it is a nice demonstration that the medians are concurrent. It also demonstrates that the location of the centroid is 1/3 of the distance along the median toward the vertex.

Answer:

answer is E      

    Statement: Point P lies on line C'D'. Reason: The coordinates of P satisfy the equation of line C'D'.

Step-by-step explanation:

Answer:

0.01707779886

Step-by-step explanation:

Just do 27/1581

Answer:

$2.046

Step-by-step explanation: I think..don't take my word.

Answer:

2

Step-by-step explanation:

plug it in

(4*3-4)+(-10+4)

8+(-6) = 2

Answer: (4x-y) + (-10 + y) = 2 , if x=3 and y=4

Step-by-step explanation:

We can substitute the known values for x and y

(4(3) - 4) + (-10 + 4) = 12 - 4 -10 +4 = 2

The solution to the inequality is:

[tex]x>\frac{-1}{2}[/tex]

Solution:

Given inequality is:

[tex]16x-33x<37x+27[/tex]

We have to find the solution to given inequality

[tex]\mathrm{Add\:similar\:elements:}\:16x-33x=-17x[/tex]

[tex]-17x<37x+27[/tex]

[tex]\mathrm{Subtract\:}37x\mathrm{\:from\:both\:sides}[/tex]

[tex]-17x-37x<37x+27-37x[/tex]

Simplify the above inequality

[tex]-54x<27[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

Remember that, change the inequality sign if you divide or multiply both sides by a negative number

If you divide or multiply both sides by a positive number,the inequality sign will not change

[tex]\left(-54x\right)\left(-1\right)>27\left(-1\right)\\\\54x>-27[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}54[/tex]

[tex]\frac{54x}{54}>\frac{-27}{54}\\\\x>-\frac{1}{2}[/tex]

Thus the solution to inequality is found

Answer:

p - 3000 = 16000

Step-by-step explanation:

none of the options given are correct

The correct equation representing the situation is p - 3000 = 16000, where p is the original price of the car.The correct answer is option D

To determine the correct equation that describes the given situation, we need to understand the relationship between the original price of the car and its discounted price.

Let p represent the original price of the car.

The problem states that the original price was reduced by $3,000, resulting in a discounted price of $16,000.

This relationship can be represented by the equation:

p - 3000 = 16000

Rearranging this equation, we find:

p = 16000 + 3000

Therefore, the best equation that represents the situation is:

p - 3000 = 16000

The correct answer is option D

Answer:

If you're trying to solve for r. r=35

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

r+2r=105

(r+2r)=105(Combine Like Terms)

3r=105

3r=105

Step 2: Divide both sides by 3.

3r/3 = 105/3

r=35

The measure of the angle x is 70 degrees because the sum of the two interior angles is equal to the exterior angle.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

As we know,

The sum of the two interior angles is equal to the exterior angle.

15 + 35 = x

x = 70 degrees

Thus, the measure of the angle x is 70 degrees because the sum of the two interior angles is equal to the exterior angle.

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Answer:

The amount of change in the balance of the account is an increase of $3160.57.

Step-by-step explanation:

i) first deposit is given as $1250

ii) second deposit is given as $3040.57

iii) first withdrawal is given as $400

iv) second withdrawal is given as $400

v) third withdrawal is given as $400

vi) first penalty removed is $35

vii) second penalty removed is $35

viii) therefore the change to the balance is given by

$1250 + $3040.57 - $400 - $400 - $400 + $35 + $35 = $3160.57

viii) Therefore the amount of change in the balance of the account is an increase of $3160.57.

Answer:

Step-by-step explanation:

B) 33

Answer:

B) 33

Step-by-step explanation:

This is a dilation.

Good morning ☕️

Answer:

Step-by-step explanation:

9f²-12f+4 = (3f)²-2×(3f)×(2)+2² = (3f-2)²

:)

Answer:

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

Step-by-step explanation:

Looking at the graph

For x=-2 ---> f(x)=3

For x=2 ---> f(x)=1  

so

we have the points

(-2,3) and (2,1)

Find the slope

[tex]m=(1-3)/(2+2)=-\frac{1}{2}[/tex]

The equation of the line in slope-intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=-\frac{1}{2}[/tex]

[tex]b=2[/tex] ---> see the graph

substitute

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

Answer: +-6.32

Step-by-step explanation:

x = +- √40

x = +-6.324

Note that +- means plus or minus.

Answer:

$546

Step-by-step explanation:

50 + 28 = 78 x 7 = 546

Answer:

600

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = 8x + 8

f(x+1) = 8(x+1) + 8

= 8x + 8 + 8

= 8x + 16

Answer:

f(x+1) = 8x + 16

Step-by-step explanation:

f(x+1) = 8(x + 1) + 8 = 8x + 8 + 8 = 8x + 16

Based on the calculations below, the slope of this graph is equal to 2/3.

In Mathematics and Euclidean Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

By substituting the given data points (0, -2), and (3, 0) into the formula for the slope of a line, we have the following;

Slope of graph = (0 - (-2))/(3 - 0)

Slope of graph = (0 + 2)/(3 - 0)

Slope of graph = 2/3

Based on the graph, the slope is the change in y-axis with respect to the x-axis, and it is equal to 2/3.

Complete Question;

Using the graph, determine the value of the slope.

What is the slope?

The line passing through the point (4, -6) and perpendicular to the line y=1/4x+4 has an equation in point-slope form of y + 6 = -4(x - 4) and in slope-intercept form, it is y = -4x + 10.

In Mathematics, lines that are perpendicular have slopes that are negative reciprocals of each other. This means if one line has a slope of m, the line perpendicular to it will have a slope of -1/m. The given line has a slope of 1/4, so the line perpendicular to it will have a slope of -4 (negative reciprocal of 1/4).

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Thus, the equation of a line passing through the point (4, -6) with a slope of -4 can be expressed as y - (-6) = -4(x - 4), which simplifies to y + 6 = -4x + 16 or y = -4x + 10.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Therefore, based on our previous findings, the equation of the line in slope-intercept form is y = -4x + 10.

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