Hillsboro Street and Manchester Avenue intersect. If the diagonal distance across the
intersection is 73 feet and Hillsboro Street is 55 feet wide, how wide is Manchester Avenue?

Equation of a line in the standard form that passes through the points (3, 0) and (0, -2) will be [y = (2/3)x - 2].

As per the question statement, a straight line passes through the points (3, 0) and (0, -2).

We are required to determine the equation of the above mentioned line in it's standard form.

To solve this question, we need to know the formula to write the standard equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as [tex][(y-y_{1})=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}(x-x_{1})][/tex].

Here, let (x₁, y₁) be (3, 0) and (x₂, y₂) be (0, -2).

Therefore, equation of our concerned line passing through the two points (3, 0) and (0, -2), by substituting [(x₁, y₁) = (3, 0)] and [(x₂, y₂) = (0, -2)] in the above mentioned formula, will be [(y - 0) = {(-2 - 0)/0₂ - 3)}(x - 3)]

Or, [y = {(-2)/(-3)}(x -3)]

Or, [y = (2/3)(x - 3)]

Or, [y = (2/3)x - 2]

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Step-by-step explanation:

the area of a triangle is

length × width

in our case

(x + 10) × x = 50

x² + 10x = 50

x² + 10x - 50 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case that is

x = (-10 ± sqrt(10² - 4×1×-50))/(2×1) =

= (-10 ± sqrt(100 + 200))/2 =

= (-10 ± sqrt(300))/2 = (-10 ± sqrt(100×3))/2 =

= -5 ± sqrt(100×3/4) = -5 ± sqrt(25×3) =

= -5 ± 5×sqrt(3)

x1 = -5 + 5×sqrt(3) = 3.660254038...

x2 = -5 - 5×sqrt(3) = -13.66025404...

x2 gives us negative values for length and width. that does not make any sense for actual lengths of objects.

so,

x = 3.660254038...

1. 8/3
2. 16/3
3. 123

*some words for 20 symbols*

The number of days Henry can go on vacation is 7 days.

Given that, Henry knows it will cost $300 per day that he's on vacation plus $650 for miscellaneous activities.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of days be x.

Henry has $2750 dollars in his savings account.

So equation is 300x+650=2750

The obtained equation can be solved as follow

300x=2750-650

⇒ 300x = 2100

⇒ x = 2100/300

⇒ x = 7

Therefore, the number of days Henry can go on vacation is 7 days.

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Answer:

8x−3y=−24

Step-by-step explanation:

Based on the given figures, the line of reflection will be c. Reflection across x-axis.

If it looks like the line of reflection is a horizontal line as is the case here, the way to find the line of reflection is by finding the midway point between corresponding points on the graph.

For instance, use the coordinates of D and D' and C and C'.

The coordinates of D and D' are:

D = (-1, 1)

D' = (- 1, -1)

The Midpoint can be found to be:

= ( (x₁ + x₂) / 2, (y₁ + y₂) / 2)

= ( (-1 + (-1)) / 2), ( (1 + (-1)) / 2

= (-1, 0)

The coordinates of C and C' are:

C = (4, 1)

C' = (4, -1)

The Midpoint can be found to be:

= ( (x₁ + x₂) / 2, (y₁ + y₂) / 2)

= ( (4 + 4) / 2), ( (1 - (-1)) / 2

= (4, 0)

The line of reflection is therefore the x-axis because the value of y is 0 and the x = axis is the line that crosses y at 0.

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The number of tacos sold in August, September and October is 103, 206, 618 respectively.

Let the number of veggie tacos sold by Tina in October be x

Then, number of veggie tacos sold in September is twice that of veggie tacos sold in october = 2x

Number of veggie tacos sold in August is thrice that of veggie tacos sold in September = 3 x 2x = 6x

Total veggie taco during the three months by Tina = 927

6x + 2x + x = 927

9x = 927

x = 927/9

x = 103

Tacos sold in August = 6x =  618

Tacos sold in September = 2x = 206

Tacos sold in October = x =103

Therefore, the number of tacos sold in August, September and October is 103, 206, 618 respectively.

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A) g(6)

g(6) = 8 -2.5*6

g(6) = 8 - 15

g(6) = -7

B) g(0)

g(0) = 8 -2.5*0

g(0) = 8 - 0

g(0) = 8

C) g(-6)

g(-6) = 8 -2.5*-6

g(-6) = 8 + 15

g(-6) = 23

Answer:

2y + 1 maybe??????

Step-by-step explanation:

hope its correct if not please tell me

Answer: p= -5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

carry the one over to the right side and subtract it to get an amount of -10.

then carry the -4p to the left and add it with -2p. which comes out to be 2p

now the equation reads as 2p=-10

continue to divide 2 to get p alone and divide -10 by 2 as well.

now p=-5 because a negative divided by a postive is a negative.

Answer:

=============================

We can observe that:

1. AB and CD are horizontal segments, since both endpoints have same y-coordinates:

2. AB and CD are of same length:

It means the ABCD is a parallelogram, since two opposite sides are parallel and of same length.

The area of parallelogram is:

We know the length of the base, it is found above, 2 units.

The height is the difference of y- coordinates:

The area is:

In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes. Then There are 29 nickels and 12 dimes in the piggy bank.

We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.

Let x be the number of nickels and y be the number of dimes.

We know that, 1 dollar = 20 nickels

and 1 dollar = 10 dimes

So, we get an equation

0.05x + 0.1y = 2.65                   ...........(1)

Also the number of nickels is 7 less than three times the number of dimes.

x = 3y - 7                      .................(2)

Substitute above value of x in equation (1)

0.05(3y - 7) + (0.1)y = 2.65

0.15y - 0.35 + 0.1y = 2.65

0.25y = 2.65 + 0.35

0.25 y = 3

y = 12

Substitute above value of y in equation  (2)

x = 3(12) - 7

x = 29

Therefore, there are 29 nickels and 12 dimes in the piggy bank.

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The time period in years T = 4 years

The simple interest amount = $252

The rate of interest per year as percentage  = 7%

The principal amount = $900

The simple interest I = PTR

Where I is the interest amount

P is the principal Amount

T is the time period involved in years

R is the rate of interest per year as a percent

Substitute the values in the equation

252 = 900 × T × (7 / 100)

252 = 900 × T × 0.07

252 = 63 × T

Move the 63 to other side

T = 252 / 63

T = 4 years

Hence, the time period in years T = 4 years

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Using combinations,  there are a total of 20 distinct voting combinations.

We now have five bands. We'll refer to them as A, B, C, D, and E.

John will choose two bands from the available five if he is required to vote for his favorite and second-favorite.

We must pair bands and discover every possible combination in order to determine the TOTAL number of different possibilities.

The results/totals are as follows:

AB, AC, AD, AE

BA, BC, BD, BE

CA, CB, CD, CE

DA, DB, DC, DE

EA, EB, EC, ED

Thus, there are a total of 20 distinct voting combinations.

Since you already know that each of the five initial bands (A, B, C, D, and E) will result in a multiple of four, you may accomplish it more simply without listing by taking the five bands.

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Answer: y = 1/9

Step-by-step explanation:

7/3y=21

7= 21 x 3y

7/21 = 3y

1/3 = 3y

1/9 = y

Answer:

you can use the angle addition postulate I think that's what it's called

Answer:

1. x = 0 , x = 3

2. x = -2 , x = 2

3. (x - 1)²

The Yes or No to for digit in the hundreds place is to the value of the digit in the thousands place are-

3a. 8,556 ; No ,    3b. 6,855 ; No ,  3c. 5,568 ; Yes     , 3d. 5,656 ; No

As per the place value system,

Thousand    Hundred    Tens    Ones

3a. 8,556

Thousand value of number = 8000

Hundred value of number = 500

1/10 × 8000

800 ≠ 500

No, the digit at hundreds place is not 1/10 of the digit at thousand place.

3b. 6,855

Thousand value of number = 6000

Hundred value of number = 800

1/10 × 6000

600 ≠ 800

No, the digit at hundreds place is not 1/10 of the digit at thousand place.

3c. 5,568

Thousand value of number = 5000

Hundred value of number = 500

1/10 × 5000

500 = 500

Yes, the digit at hundreds place is 1/10 of the digit at thousand place.

3d. 5,656

Thousand value of number = 5000

Hundred value of number = 600

1/10 × 5000

500 ≠ 600

No, the digit at hundreds place is not 1/10 of the digit at thousand place.

Thus, the condition of yes and no for the given number are obtained.

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The complete question is-

3. For items 3a-3d,

Choose yes or no to tell if the digit in the hundreds place is 1/10 the value of the digit in the thousand place.

thousands place.

3a. 8,556

3b. 6,855

3c. 5,568

3d. 5,656

Answer: 9 units to the right and 5 units down

Step-by-step explanation:

1) Measure the length.

You can find that you can match point C with point W. Next find how much it goes to the right and left.

Right from (C->W): 9 squares

Down from (C->W): 5

2) Fill in the blank

9 units to the right and 5 units down

Answer:

ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.

Step-by-step explanation:

The triangles are congruent as the measures of their corresponding sides and angles are the same.

To determine the translation of ΔABC to ΔNKW, find the change in the x and y values from one of the points of ΔABC to its corresponding point of ΔNKW.

Therefore:

ΔABC ≅ ΔNKW because when ΔABC is translated 9 units right and 5 units down, it results in the other triangle.

Answer:

See explanation

Step-by-step explanation:

First add all the weights, 21+10.2+14.3=45.5oz

Then you divide 45.5 by 25 which equals 1.82oz

Answer:

140 degrees

Step-by-step explanation:

isosceles triangle   so two angles are equal    20 and 20

ALL of the angles sum to 180 degrees

20+ 20 + vertex = 180

vertex = 140°

The four consecutive integers in the question are; 51, 52, 53, 54

Let the four consecutive integers in the question be;

x, x + 1, x + 2 and 2(x + 4)

Now, we are told that the sum of these four consecutive integers is 264. Thus;

x + x + 1 + x + 2 + 2(x + 3) = 264

Expanding the bracket gives;

3x + 3 + 2x + 6 = 264

5x + 9 = 264

5x = 264 - 9

5x = 255

x = 255/5

x = 51

Thus;

Second integer = 51 + 1 = 52

Third integer = 51 + 2 = 53

Fourth Integer = 51 + 3 = 54

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Answer:

5/15 of 1/3

Step-by-step explanation:

15/15-10/15=5/15

The probability for at least one white gumball is 0.196

Consider the following:

First jar:100 whites, 25 green

Total=100+25

       =125 gumball

P(White)=100/125=0.8

Second jar:50 whites, 150 blue

Total=50+150

       =200 gumballs

P(White)=50/200=0.25

Third jar:500 whites, 10 red

Total=500+10

         =510

P(White)=500/500=0.98

Now, probability for at least one white is

              =P(white in jar 1)*P(white in jar 2)*P(white in jar 3)

              =0.8*0.25*0.98

              =0.196

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Answer:

x = 7

Step-by-step explanation:

3x + 9x = 6x +42

12x = 6x +42

12x - 6x = 6x -6x +42

6x = 42

[tex]\frac{6x}{6} = \frac{42}{6}[/tex]

x = 7

Answer: because it is out of 12

Step-by-step explanation:

Answer:

B. )r ≤ −24. 32

Step-by-step explanation:

Width of the rectangle is 2.5, Length is 10 and perimeter is 25

Given

Length of rectangle is 5 greater than double of width

let us say width = w

According to the question length L = 5 + 2w

Perimeter is 10 times the width

P= 10w

we know that perimeter of a rectangle is 2(L+W)

Substituting the values in the formula we get

10w = 2(5+2w + w)

10w = 10 + 6w

w= 2.5

From this length L = 5+2(2.5)

                            L = 10

Perimeter P = 10W

P= 10(2.5)

P= 25

Hence the length is 10, width is 2.5 and perimeter is 25

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