A triangle has vertices at (4.-2), (2.2), and (4.6). What are the vertices of the image of the triangle after applying the
translation (x, y)=(x - 1, y + 2)?​

Answer:

Point used by Harold was:

(7, 0)

Step-by-step explanation:

Given that

Equation of linear function used by Harold:

[tex]y = 3(x - 7)[/tex]

We know that linear equation in point slope form can be represented as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where [tex](x_1,y_1)[/tex] are the coordinates of a given point.

[tex]m[/tex] is the slope of line.

Formula for Slope, m is given as:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the two points on the line.

If slope and a point with coordinates [tex](x_1,y_1)[/tex] is know, the equation of a line can be represented in linear form as:

[tex]y - y_1 = m(x - x_1)[/tex] ....... (1)

Now, the given equation is:

[tex]y = 3(x - 7)[/tex]

Re-writing the equation with a slight modification:

[tex]y-0 = 3(x - 7)[/tex]

Now, comparing the above equation with equation (1):

We get that:

[tex]x_1=7\\y_1=0[/tex]

So, the point used by Harold is (7, 0).

Answer:

(7,0)

Step-by-step explanation:

Answer:

There are 1000 millimeters in a meter.

Step-by-step explanation:

I really hope this helps in any way.

Answer:

1,000

Step-by-step explanation:

The word millimeter has the prefix of 'milli-'.

'Milli-' means a thousand.

Applying the prefix meaning to the word, a millimeter would be a thousandth of a meter.

There are 1,000 millimeters in a meter.

Brainilest Appreciated.

Answer:

Total um of the digits of the first 25 numbers is 127

Step-by-step explanation:

Notice that:

The sum of the digits:

0+1+2+3+4+5+6+7+8+9 = 45

Also notice that the addition of:

10+11+12+13+14+15+16+17+18+19=0+1+2+3+4+5+6+7+8+9 + 10*1 = 45 + 10 = 55

And for the last 6 numbers:

20+21+22+23+24+25 = 0+1+2+3+4+5 + 2 * 6 = 15 + 12 = 27

So the total sum of all this is: 45 + 55 +27 = 127

Answer:

Step-by-step explanation:

Total marbles = 5  + 6 + 2 = 13

P( getting blue ball from first draw) = 5/13

The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4

P( getting blue ball from second draw) = 4/12 = 1/3

P(getting two blues) = [tex]\frac{5}{13}*\frac{1}{3}\\[/tex]

                                  = 5/39

Answer:

Step-by-step explanation:

surface area of cylinder=2 πr²+2πrh

=2πr(r+h)

=2π×12(12+18)

=24π×30

=720π

≈2261.9 cm²

Answer:

16 cm, 30 cm, 34 cm

Step-by-step explanation:

I got this answer simply by plugging each number into my calculator with the following equation:

[tex]\sqrt{x^{2} +y^{2} }[/tex]

When you the lower numbers into the equation, if the lengths really do give you a triangle, then you should get the largest number as your output. This can help you with any of the other questions that you may have to answer.

Only the measurements of 16 cm, 30 cm, and 34 cm could represent the side lengths of a right triangle.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,

The side lengths of a right triangle must satisfy the Pythagorean theorem, which states that the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). Therefore, we need to check which sets of measurements satisfy this condition.

Only the measurements of 16 cm, 30 cm, and 34 cm could represent the side lengths of a right triangle.

For the first set of measurements, we have:

a = 16 cm, b = 30 cm, c = 34 cm

a² + b² = 256 + 900 = 1156

c² = 1156

Since a² + b² = c², these measurements do represent the side lengths of a right triangle.

Learn more about Pythagorean triplets here:

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Answer:

x=23/3

Step-by-step explanation:

x=c+ay

7=c+3a     | *(-1)

9=c+6a

-7=-c-3a

9=c+6a

------------

9-7=c-c+6a-3a

2=3a

a=2/3

7=c+3*2/3

7=c+2

-2   -2

5=c

so   x=5+2/3*y

when y=4 then  x=5+2/3*4=5+8/3

x=15/3+8/3

x=23/3

Answer:

1080

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the intercept form of the equation of a line, then solve for y.

Intercept form

  x/(x-intercept) +y/(y-intercept) = 1

  x/-4 +y/8 = 1

__

Solving for y, we have ...

  -2x +y = 8 . . . . multiply by 8

  y = 2x +8 . . . .  add 2x

The coefficient of x is 2, so the slope is 2.

__

The graph shows you the rise is 8 for a run of 4, so ...

  slope = rise/run = 8/4

  slope = 2

Answer:

-7, -4, 3

Step-by-step explanation:

Tn = 2n² - 3n - 6

Answer:

\the zeroes are (2√3)/ 3, (√3)/4,

or -1.15, 0.43 to the nearest hundredth.

Step-by-step explanation:

I am assuming you want to find the zeroes of this function:

4√3 x^2+5x-2√3 = 0

Using the quadratic formula:

x = [ -5 +/- √((5)^2 - 4 * 4√3  * -2√3) ]  / (2 * 4√3 )

=  ( - 5 +/- √(25 - (-32*3)) / 8√3

= (-5 +/- √ 121) / 8√3

= (-5 - 11) / 8√3 or  (-5 + 11) / 8√3

=  -16/8√3 or 6/8√3

= -16√3/ 24 or  6√3 / 24

= -2√3/ 3 or √3/4.

Answer:

The information given in the question to solve it is insufficient.

The complete question related to this found at GMAT club forum is stated below:

Steve works at an apple orchard and is paid by the bushel for the apples he harvests each day. For the first 42 bushels Steve harvests each day, he is paid y dollars per bushel. For each additional bushel over 42, he is paid 1.5y. How many bushels of apples did Steve harvest yesterday?

1. Yesterday, Steve was paid $180 for the apples he harvested.

2. Today, Steve was paid $240, and he harvested 10 more bushels of apples than he harvested yesterday.

Step-by-step explanation:

1st 42 bushels Steve harvests each day:

Payment of 1 bushel = y dollar

Payment of ≤ 42 bushel = 42× y = $42y

Payment for Additional bushel after the 1st 42 bushels = 1.5y per bushel

Yesterday's Payment = $180

Today's payment = $240

Let the total number Steve harvested yesterday = p

Today he harvested 10 more bushels than he did yesterday

Total number Steve harvested today = p + 10

Now looking at the information in the question:

First statement did not tell us the amount he harvested that got him that pay, so it's insufficient. Second statement alone two is not sufficient to determine yesterdays pay.

In both statement, we were not told if he harvested more or less than 42 yesterday. Neither were we told if the additional 10 bushels was after he had harvested more than 42 bushels.

Let's assume the additional 10 bushels was after he had harvested more than 42 bushels (that is he harvested 42 yesterday) .

Difference in payment = 240-180 = 60

For the additional 10bushels, he was paid $60

10(1.5y) = 60

15y = 60

y = 60/15 = 4

If y = $4 per bushel and he was paid $180, the number he harvested will be:

4 × number of bushels = $180

4p = 180

p = 180/4 = 45 bushels

p = 45bushels isn't possible because the amount for the first bushels should either be less than or equal to 42

If we make another assumption, let's say he harvested more than 42 yesterday (42 + an additional number), we would get a different answer.

Thus the information given in the question to solve it is insufficient.

Answer:

0.

Step-by-step explanation:

Fair dice are dice that have 6 sides, and the probability of rolling a side is the same as rolling another.

Since each die has 6 sides, the most you can get from the two dice are 6 + 6 = 12. Therefore, getting a 13 is impossible. So, there is a probability of 0.

Hope this helps!

Answer:

m∠x = 98°

Step-by-step explanation:

Step 1: Find the supplementary angle in the triangle

180 - (53 + 45) = 82

Step 2: Use Supplementary Angles to solve for x

180 - 82 = 98°

Answer: 5/55

Step-by-step explanation:

1/11 x 5 = 5/55

So, the fifth equivalent fraction to 1/11 is 5/55.

The 5th equivalent fraction should be [tex]5\div 55[/tex]

Since the fraction is [tex]1\div 11[/tex]

So here the 5th equivalent should be

[tex]= 1\div 11 \times 5\div 5[/tex]

= [tex]5\div 55[/tex]

Here 5 represent the numerator and 55 represent the denominator.

Therefore, we can concluded that The 5th equivalent fraction should be [tex]5\div 55[/tex]

Learn more about fraction here: https://brainly.com/question/1786648

Answer:

Median: 15

Range: 9

25th: 14

75th: 17

IQR: 3

Answer:

1/3000

Step-by-step explanation:

3 meters to centimeters:

3 × 100 = 300

= 1/10 ÷ 300

= 1/10/300

= 1/(10×300)

= 1/3000

Answer:

C) line b and line c

Step-by-step explanation:

On edge

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The system of equations that do not have any solution is line b and line c. Hence, the correct option is C.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The equation of line a passing through (-1,0) and (1,2) are,

m = (0-2)/(-1-1) = -2/-2 = 1

y= x + c

0 = -1 + c

c = 1

Equation of line 1, y=x+1

The equation of line b passing through (-2,2) and (-1,-1) are,

m = (2+1)/(-2+1) = 3/-1 = -3

y= -3x + c

-1 = -3(-1) + c

c = -4

Equation of line 1, y=-3x-4

The equation of line c passing through (0,3) and (1,0) are,

m = (3-0)/(0-1) = 3/-1 = -3

y= -3x + c

3 = -3(0) + c

c = 3

Equation of line 1, y=-3x+3

Also, the equation of line d is y=1

The solution of two-equation is the point at which the two equations are not intersecting. Therefore, the system of equations that do not have any solution is line b and line c.

Hence, the correct option is C.

Learn more about Equation of Line:

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Answer:

1620

Step-by-step explanation:

If a number decreased by 95% is 81, then

5% is 81.

So, the number = 100/5 x 81= 20 x 81 = 1620

Hope this helps

Answer:

the answer is 1620

Step-by-step explanation:

Answer:

1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]

2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]

3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex],  the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]

4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex],  the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]

5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex],  the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]

6) For[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]

Step-by-step explanation:

This can be done using the completing the square method.

The standard equation of a circle is given by [tex](x - a)^2 + (y-b)^2 = r^2[/tex]

1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex]

[tex]x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\[/tex]

Therefore, for [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]

2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex]

[tex]x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\[/tex]

Therefore, for [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]

3)  For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex]

Divide through by 3

[tex]x^2 + y^2 + 4x + 6y = 5[/tex]

[tex]x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\[/tex]

Therefore, for [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex],  the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]

4)  For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex]

Divide through by 5

[tex]x^2 + y^2 - 2x + 4y = 6[/tex]

[tex]x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\[/tex]

Therefore, for [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex],  the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]

5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex]

Divide through by 2

[tex]x^2 + y^2 - 12x - 8y = 4[/tex]

[tex]x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\[/tex]

Therefore, for [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex],  the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]

6) For [tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex]

[tex]x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\[/tex]

Therefore, for[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]

For Plato / Edmentum

Just to the test and got it right ✅

Answer:

The correct option is;

D) x² + 72·x - 7920 = 0

Step-by-step explanation:

The time it takes the car to stop = x/24 seconds

the average speed during stopping = x/2 feet per second

Given that the car was initially travelling at x feet per second and it takes the car 165 feet to stop after the driver takes 1.5 seconds at the initial speed x before the break is applied, we have;

Total distance traveled = (x/24)×(x/2) + x×1.5 = 165

= x²/48 + 1.5·x = 165

Multiply through by 48, we have;

x² + 72·x = 7920

Which gives the equation as follows;

x² + 72·x - 7920 = 0.

Answer:

the 2nd

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

Using the rules of logarithms

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

log[tex]x^{n}[/tex] ⇔ n log x

ln e = 1

Given

4 + 5[tex]e^{x+2}[/tex] = 11 ( subtract 4 from both sides )

5[tex]e^{x+2}[/tex] = 7 ( divide both sides by 5 )

[tex]e^{x+2}[/tex] = [tex]\frac{7}{5}[/tex] ( take ln of both sides )

ln [tex]e^{x+2}[/tex] = ln ([tex]\frac{7}{5}[/tex] )

(x + 2) lne = ln ([tex]\frac{7}{5}[/tex] )

x + 2 = ln ([tex]\frac{7}{5}[/tex] ) ( subtract 2 from both sides )

x = ln([tex]\frac{7}{5}[/tex] ) - 2

Answer:

b-4/5b

Step-by-step explanation:

b is decreased by 80%

dat is 80/100×b

= b-80/100b

b-4/5b

Answer:

c)    [tex]2\frac{23}{30}[/tex]     d)[tex]1\frac{23}{24}[/tex]

7)    a.   [tex]6\frac{3}{11}[/tex]  kg                  b.   [tex]6 \frac{2}{3}[/tex]  cm               c. 20 cm

d.  [tex]9\frac{9}{10}[/tex] kg                  e. 10 g             f. [tex]23 \frac{1}{4}[/tex]  kg

Step-by-step explanation:

c)  [tex]8\frac{2}{3}[/tex]   -   [tex]5\frac{9}{10}[/tex]

First we will change to improper fraction and then solve

[tex]\frac{26}{3} - \frac{59}{10}[/tex]

=  [tex]\frac{260 - 177}{30}[/tex]

= [tex]\frac{83}{30}[/tex]

we will now change to mixed number

= [tex]2\frac{23}{30}[/tex]

d)  [tex]8\frac{1}{8} - 6\frac{1}{6}[/tex]

we will first change it to improper fraction and then solve

= [tex]\frac{65}{8} - \frac{37}{6}[/tex]

= [tex]\frac{390 - 296}{48}[/tex]

= [tex]\frac{94}{48}[/tex]

we can reduce the fraction

=[tex]\frac{47}{24}[/tex]

we will change it mixed number

=[tex]1\frac{23}{24}[/tex]

7)  

a.   [tex]\frac{3}{11}[/tex]   of 23

=  [tex]\frac{3}{11}[/tex]   × 23

=  [tex]\frac{69}{11}[/tex]

=[tex]6\frac{3}{11}[/tex]  kg

b. [tex]\frac{2}{3}[/tex]   of 10 cm

= [tex]\frac{2}{3}[/tex]   × 10 cm

= [tex]\frac{20}{3}[/tex]  cm

=[tex]6 \frac{2}{3}[/tex]  cm

c. [tex]\frac{5}{6}[/tex]   of 24cm

=    [tex]\frac{5}{6}[/tex]   × 24 cm

6 will divide 24

=5 × 4 cm

= 20 cm

d.  [tex]\frac{3}{10}[/tex]  of  33 kg

=  [tex]\frac{3}{10}[/tex]  ×  33 kg

=[tex]\frac{99}{10}[/tex]  kg

=[tex]9\frac{9}{10}[/tex] kg

e. [tex]\frac{2}{7}[/tex]   of  35 g

=  [tex]\frac{2}{7}[/tex]   ×  35 g

7 will go into 35

=2×5 g

=10 g

f. [tex]\frac{3}{4}[/tex]  of  31 kg

= [tex]\frac{3}{4}[/tex]  ×  31 kg

=[tex]\frac{93}{4}[/tex] kg

=[tex]23 \frac{1}{4}[/tex]  kg

Answer:

y = csc (x) + 2

Step-by-step explanation:

From the graph, we can derive the parent function y = csc(x). Notice how there are asymptotes at x = 2πk and x = π + 2πk, which is where csc(x) is undefined.

Finally, we can see a vertical shift of 2 which we can see from the mid-line of the graph which is at y = 3.

Answer:

c

Step-by-step explanation:

edg 2021

Answer:

Option C

Step-by-step explanation:

Answer:

B.

You need to subtract 1 term because you don't include the starting 5

4^10 - 1 =  4^9

You multiply 5 by 4 each time for 9 times so it is 5 x 4^9

Hope this helps

Step-by-step explanation:

Answer:

114.96 pounds at angle 81.76°

Step-by-step explanation:

Let i be the component along x-axis and j be the component along y-axis.

First force that is given is 150 acting at angle 40; [tex]F1 = 150cos170i + 150sin40j = 114.91i +96.42j[/tex]

The second force 100 is acting at angle 170;

[tex]F2 = 100cos170i + 100sin170j = -98.48i + 17.36j[/tex]

We now have the resultant force, which is: [tex]114.91i + 96.42j + (-98.48i + 17.36j) = 16.43i + 113.78j[/tex]

Magnitude of resultant:

[tex]\sqrt{16.43^{2} + 113.78^{2} }[/tex] = 114.96 pounds

Angle it makes with horizontal; inverse tangent of [tex]\frac{(113.78)}{(16.43)}[/tex] = 81.76 degrees

Hope this helps; Brainliest appreciated!

Answer:

6) g = 11p

7) This equation is an example of direct variaction because it is proportional because can make a slanted line with the equation C = 6g + 15

Step-by-step explanation:

Well to find g we seperate g and combine like terms,

[tex]81 = 6g + 15[/tex]

So we subtract 15 from both sides 66 = 6g,

66/6 = 11.

So g = 11.

Answer:

  B. 5 seconds

Step-by-step explanation:

A graphing calculator shows the answer easily.

__

h(t) = 0 = -16t^2 +400

t = √(400/16) = 5

It will take 5 seconds for the sandbag to hit the ground.