solve for x please help ! (show work)

Answer:

(14,2) and (-6/5,-28/5)

Step-by-step explanation:

The distance, d, from two points (x,y) and another point (a,b) can be calculated using

d=sqrt((x-a)^2+(y-b)^2).

Our point (a,b) is (2,7) and d=13.

Making substitutions:

13=sqrt((x-2)^2+(y-7)^2)

We are also given the relation between x and y is given as x-2y=10.

Adding 2y to both sides gives: x=10+2y

Make this insertion into our equation:

13=sqrt((10+2y-2)^2+(y-7)^2)

Simplify inside:

13=sqrt((8+2y)^2+(y-7)^2)

Square both sides:

169=(8+2y)^2+(y-7)^2

Expand binomial squares:

169=64+32y+4y^2+y^2-14y+49

Combine like terms:

169=5y^2+18y+113

Subtract 169 on both sides:

0=5y^2+18y-56

We could try to factor

0=(5y+28)(y-2)

So y=2 or y=-28/5

Recall x=10+2y

So if y=2, then x=10+2(2)=10+4=14.

So if y=-28/5, then x=10+2(-28/5)=10+(-56/5)

=50/5 +-56/5

=-6/5.

So two points satisfying given criteria is

(14,2) and (-6/5,-28/5).

Answer:

The bus will take 81 minutes to complete the trip.

Step-by-step explanation:

To determine how many minutes will the bus take to complete the trip if a bus completes half a trip at 40 km per hour and the other half at 50 km per hour, and the whole trip was 60 km, the following calculation must be performed:

60/2 = 30

30/40 = 3/4 of an hour = 45 minutes

30/50 = 3/5 of an hour = 36 minutes

45 + 36 = 81

Therefore, the bus will take 81 minutes to complete the trip.

Answer:

297 square feet

Step-by-step explanation:

Let w represent the width of the garden.

Since the length is 24 ft longer than the width, it can be represented by w + 24.

Use the perimeter formula, p = 2l + 2w. Plug in the perimeter and w + 24 as l, then solve for w:

p = 2l + 2w

84 = 2(w + 24) + 2w

84 = 2w + 48 + 2w

84 = 4w + 48

36 = 4w

9 = w

So, the width is 9 ft. Add 24 to this to find the length:

24 + 9 = 33

So, the length is 33 ft.

Find the area of the garden with the formula A = lw:

A = lw

A = (33)(9)

A = 297

The area of the garden is 297 square feet.

It will take Fred 42 minutes to type and spell check 60 pages.

Given the following data;

To find how long it takes him to type and spell check 60 pages;

We would use direct proportion to express the work described and solve for the unknown variable (time).

[tex]9 \;minutes : 13 \;pages\\\\X \;minutes : 60 \;pages[/tex]

Cross-multiplying, we have;

[tex]9[/tex] × [tex]60[/tex] [tex]= 13[/tex] × [tex]X[/tex]

[tex]540 = 13X\\\\X = \frac{540}{13}[/tex]

X = 41.54 ≈ 42 minutes

Therefore, it will take Fred 42 minutes to type and spell check 60 pages.

Find more information: https://brainly.com/question/89674

Step-by-step explanation:

ae=ec

ec=1+2=3

then ae=3

Answer:

6-most likely (AC=6)

Step-by-step explanation:

Because the 2 sides, AE and EC *look the same. Also you can look at the opposite sides.

*This is what I think

Answer:

35 lbs is the final weight

Step-by-step explanation:

20 +23 = 43 lbs

Then they had to remove 8 lbs

43 - 8 =35

35 lbs is the final weight

9514 1404 393

Answer:

Step-by-step explanation:

The reduced side ratios, shortest to longest are ...

  AC : AT : CT = 8 : 9 : 15

  OD : OG : DG = 5 : 6 : 10

These are different ratios, so the triangles are not similar.

Answer:

2.67

Step-by-step explanation:

To solve this problem do 16.02 / 6.

Answer:

Step-by-step explanation:

[tex]4 + \frac{4}{4} [/tex]

= 4 + 1

= 5 (Ans)

Answer:

This depends whether you want to make the fraction bigger or smaller.

Step-by-step explanation:

If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.

However, if you want to make the fraction bigger, then you would multiply.

Hope this helps! :)

Answer:

Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.

Step-by-step explanation:

We have,

[tex]a:b=3:6,a+b=96[/tex]

Introduce variable [tex]x[/tex] such that [tex]a=3x,b=6x[/tex]

The sum [tex]a+b=96[/tex] is therefore [tex]9x=96\implies x=10.\overline{6}[/tex]

So,

[tex]a=3\cdot10.\overline{6}=\boxed{32}[/tex] (sadia's age)

[tex]b=6\cdot10.\overline{6}=\boxed{64}[/tex] (father's age)

Hope this helps :)

Answer:

7/12

Step-by-step explanation:

There are 12 roses - 5 white = 7 pink

7 pink / 12 total

Answer:

it is

[(2+3+4+6)-2*4]:4=1.75

I THINK

Step-by-step explanation:

Answer:

There isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average .

Step-by-step explanation:

This is a one sample mean test ;

H0 : μ = 2.7

H1 : μ > 2.7

Given the data :

2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3

Sample size, n = 12

The sample mean, xbar = ΣX / n = 33/12 = 2.75

The sample standard deviation, s = 1.215 ( from calculator)

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (2.75 - 2.7) ÷ (1.215/√(12))

T = 0.05 / 0.3507402

T = 0.1426

The critical value from Tscore ;

df = 12 - 1 = 11

Critical value = 1.796

Since ; Test statistic < Critical value ;WE fail to reject the Null and conclude that there isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average

9514 1404 393

Answer:

  $7641.24

Step-by-step explanation:

The amortization formula tells the payment amount.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where principal P is paid off in t years with n payments per year at interest rat r.

Using the given values, we find ...

  A = $7000(0.165/12)/(1 -(1 +0.165/12)^-12) = $7000×0.01375/(1 -1.01375^-12)

  A = $636.77

The total of 12 such payments is ...

  $636.77 × 12 = $7641.24

You will pay a total of about $7641.24.

_____

Additional comment

Since the payment amount is rounded down, the actual payoff will be slightly more. Usually, the lender will round interest and principal to the nearest cent on each monthly statement. The final payment will likely be a few cents more than the monthly payment shown here.

Step-by-step explanation:

After putting the values:-

answer:

another number is -47/22

explanation:

let one number be x and the other be y

-11/21 × y = 47/42

y = -47/22

Answer:

- [tex]\frac{47}{22}[/tex]

Step-by-step explanation:

let n be the other number , then

- [tex]\frac{11}{21}[/tex] × n = [tex]\frac{47}{42}[/tex] ( divide both sides by - [tex]\frac{11}{21}[/tex] )

n = [tex]\frac{\frac{47}{42} }{-\frac{11}{21} }[/tex]

   = [tex]\frac{47}{42}[/tex] × - [tex]\frac{21}{11}[/tex] ( cancel 21 and 42 )

   = [tex]\frac{47}{2}[/tex] × - [tex]\frac{1}{11}[/tex]

   = - [tex]\frac{47}{22}[/tex]

Answer:

2 times as large

Step-by-step explanation:

For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that  V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128

For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus

V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256

To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in

π * 256 / (π *128) = 2

Answer:

B. 550

Step-by-step explanation:

550 is the smallest number that becomes 600 when rounded to the nearest hundred

Answer:

F F → F

Step-by-step explanation:

The statement is given as:

A triangle has four sides, and a rectangle has three sides.

It is again a false statement since a triangle is a polygon with three sides and a rectangle is a polygon with four sides.

Hence, the answer is:

                F  F → F

Answer:

90m^2

Step-by-step explanation:

image shows a trapezium,

area of trapezium = h(a+b)/2 = 9(8+12)/2 = 90

Answer:

29

12+8+9 =29

Step-by-step explanation:

additional question

add tose measure

Answer:

Hello,

60L

Step-by-step explanation:

Quantity of water /Quantity of milk =2/1

Quantity of mixture= Quantity of water +Quantity of milk =60L

Quantity of milk =40 L

Quantity of water =20 L

Let say x the quantity of water to be added

New ratio =1/2=40/(20+x)

20+x=80 (cross products)

x=60 (L)

Answer:

x1 = 3

Step-by-step explanation:

first set up the proportion (write as fractions):

(y1/x1) = (y2/x2)

then fill in the variables:

4/x1 = 8/6

now cross multiply:

8 • x1 = 6 • 4

simple algebra:

8 • x1 = 24

x1 = 24/8

x1 = 3

If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.

In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."

In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:

x1 / y1 = x2 / y2

Plugging in the given values:

x1 / 4 = 6 / 8

Now, cross-multiply to solve for x1:

x1 * 8 = 4 * 6

x1 = 24 / 8

x1 = 3

Therefore, the value of x1 is 3.

Learn more about ratios here:

https://brainly.com/question/32531170?

#SPJ3

Answer: 1,526.04 yd³ (this is what i got on my calculator others may vary use any rounding you need)

VOLUME of CONE is: V= Pir² h / 3

Pi= 3.14

r= 9

h= 18

V= (3.14) x (9)² x (18)

9²= 81

3.14 x 81= 254.34 x 18= 4,578.12

4,578.12 / 3= 1,526.04 <-- answer

Step-by-step explanation:

2., 3., 4., 5.

yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.

you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).

2.

(-4, 6) to (10, -10)

in x the distance is 10 - -4 = 14. half is 7.

in y the distance is |-10 - 6| = |-16| = 16. half is 8.

so the midpoint is

(-4 + 7, 6 - 8) = (3, -2)

remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).

3.

(-3, -8) to (-6.5, -4.5)

in x distance : -3 - -6.5 = 3.5. half is 1.75

in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75

midpoint is

(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)

4.

(3, 7) to (-8, -10)

x : 3 - -8 = 11. half is 5.5

y : 7 - -10 = 17. half is 8.5

midpoint is

(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)

5.

(-6, -13) to (-6.4, -3.8)

x : -6 - -6.4 = 0.4. half is 0.2

y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6

midpoint is

(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)

6.

(-1, 7) to (5, 1)

x : -1 - 5 = |-6| = 6. 1/3 is 2.

y : 7 - 1 = 6. 1/3 is 2.

1/3 from C to D

(-1 + 2, 7 - 2) = (1, 5)

7.

2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).

again

(1, 5)

8.

2/3 of the way from C to D.

so, we need to double what we added in 6.

(-1 + 4, 7 - 4) = (3, 3)

9.

1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).

again

(3, 3)

10.

exactly. Pythagoras.

the square root of the sum of the squares of the coordinate differences.

distance = sqrt((x1 - x2)² + (y1 - y2)²)

11.

(6, 8) to (-1, 8)

distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7

12.

(5, -6) to (5, 6)

sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12

13.

(-2, 0) to (11, 0)

sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13

14.

(1, -5) to (9, 1)

sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10

15.

ST and MT are basically the same equation.

MT is half of ST.

ST equation based on 2 points :

y – yS={(yT – yS)/(xT – xS)}(x – xS)

M = (xS + (xT - xS)/2, yS +(yT - yS)/2)

so, let's put that into the general equation :

y - yM={(yT - yM)/(xT - xM)}(x - xM)

y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))

16.

the two corners farthest away are (5, 10) and (9, 6).

what distance from (0, 0) is now bigger ?

since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.

5² + 10² = 125

9² + 6² = 117

so, the corner (5, 10) is the farthest away.

Answer:

Hi,

If you don't know how to derivate, i can show you using

lim (f(x+h)-f(x))/h if h ->0

Step-by-step explanation:

[tex]f(x)=2x^2+3x-2\\\\f'(x)=4x+3\\\\f'(1)=4*1+3=7\\\\f'(3)=4*3+3=15\\\\f'(5)=4*5+3=23\\[/tex]

Step-by-step explanation:

18

there are 7 vertices in this shape

Answer:

7.

Step-by-step explanation:

The vertices are the points where the lines meet.

According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:

[tex]C = 0.99 + xy + 0.2z[/tex]

Cost:

0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.

Thus, the cost starts at:

[tex]C = 0.3*3.3 = 0.99[/tex]

y kilograms of cucumbers, at x dollars per kilogram.

Considering this, the cost will now be of:

[tex]C = 0.99 + xy[/tex]

0.2 kilograms of carrots, at z dollars per kilogram:

Now, we have to consider this for the cost, so:

[tex]C = 0.99 + xy + 0.2z[/tex]

A similar example is given at https://brainly.com/question/14544759

Answer:

A≈795.77ft²

Step-by-step explanation:

C=100ft

Area of circle=C^2/4pie

100/4×22/7≈795.77472ft²