Scale word problem
Someone please help me!!

Correct answer: 9x -14y = -6

Linear equation: y = ax + b

Let's replace (x,y) with (1/2, 3/4) and (4,3) and have the following equations:

1/2a + b = 3/4 (1)

4a + b = 3 (2)

=> (2) b = 3 - 4a

(1) 1/2a + 3 - 4a = 3/4

=> (1) 7/2a = 9/4

(2) b = 3- 4a

=> (1) a = 9/14

(2) b = 3/7

So we have the equation: y= 9/14x + 3/7

Multiple both sides with 14

=> 14y = 9x + 6

=> 9x -14y = -6

Answer:

y = 0

x = 4

Explanation:

make x the subject,

x - 3y = 4

x = 4 + 3y __ equation 1

2x - 5y = 8

x = (8+5y)/2 __ equation 2

using substitution method:

(8+5y)/2 = 4 + 3y

8 + 5y = 8 + 6y

6y - 5y = 8 - 8

y = 0

Find x,

x = 4 + 3y

x = 4 + 3(0)

x = 4

Answer:

x = 4

y = 0

Step-by-step explanation:

x - 3y = 4      (original)

x = 4 + 3y     (rewritten)

2x -5y = 8                 (second equation)

2(4 + 3y) - 5y = 8      (substitute 4 + 3y for x)

2(4 + 3y) - 5y = 8        (distribute)

8 + 6y - 5y = 8            (combine like terms)

y = 0                           (first variable)

x - 3y = 4            (original)

x - 3(0) = 4          (substitute 0 for y)

x = 4                  (second variable)

You can double check this by plugging these numbers back into each equation; x = 4 and y = 0 is true for both.

I hope this helps!

Answer:

1. 301.6 [tex]in^{3}[/tex]

2. 576 [tex]in^{3}[/tex]

3. 274.41 [tex]in^{3}[/tex]

Step-by-step explanation:

We know that the diameter of one of the spheres must be 4 in, because the length of the box is 12 in and there are 3 spheres along each side, and [tex]\frac{12}{3} =4[/tex]. That means that the radius of a sphere is 2 in. Put 2 into the formula for the volume of a sphere, and then multiply your solution by 9, to get the total volume.

Then, you can find the volume of the box, because you know its dimentions are 12x12x4.

Subtract your answer for part 1 from your answer for part 2, and you have the solution to part 3. Hope this helps!! :-)

Answer:

r:
The function is

The remainder when f(x) is divided by x−2 is 23.

To find:The value of k.

Solution:

According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).

It is given that, the remainder when f(x) is divided by x−2 is 23. By using remainder theorem, we get

Put x=2, to find the value of f(2).Therefore, the value of k is 8.

Step-by-step explanation:

Answer:

when a fraction equals 100% it means it has the same numbers for its numerator and denominator such as 4/4 or 18/18

Step-by-step explanation:

When it has the same numbers for its numerator and denominator it will be 100%

Answer:

65 is the correct answer

With one package (less actually) she can fill the 48ft^2 of the rectangular area.

We know that Sandy needs 7.8 square feet of space per hyacinth bulb, and the hyacinth bulbs are sold in packages of 8.

The rectangular region has a surface area of:

A = 8ft*6ft = 48 ft^2

The number of hyacinth bulbs that she can put in that surface is:

N = (48 ft^2/7.8 ft^2) = 6.15

So with 6 hyacinth bulbs, she can almost complete the rectangular area, and on each package there come 8 of them, so with one package she should be fine.

If you want to learn more about areas, you can read:

https://brainly.com/question/24487155

Answer:

The answer is 7 PACKAGES

Step-by-step explanation:

I took the test!

The equation that can be used to represent Diego's and Lin's savings account is 250 = 40 + 6x and Total savings= 100 + 50x respectively.

let

Diego:

6 months ago = $40

Now = $250

250 = 40 + 6x

250 - 40 = 6x

210 = 6x

x = 210/6

x = $35

Lin:

Now = $100

Future = $50 per month

let

Total savings= 100 + 50x

Learn more about equation:

https://brainly.com/question/16863577

Answer:

Can u post a picture so I can see what your talking about!?

Answer:

-12

Step-by-step explanation:

h(x) = ½x - 14 where x = 4:

h(4) = ½(4) - 14

= 2 - 14

= -12

Answer:

1.5hours

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

-3x=-27+9

-3x=-18

x=-18/-3

x=6

Answer:

[tex]\displaystyle 6 = x[/tex]

Step-by-step explanation:

[tex]\displaystyle -3x - 9 = -27 \hookrightarrow \frac{-3x}{-3} = \frac{-18}{-3} \\ \\ x = 6[/tex]

I am joyous to assist you at any time.

Answer:

392 square inches

Step-by-step explanation:
To solve this we need to look at this quadrilateral as two shapes that share a side - a triangle and a rectangle.

You can see in the attatchment how I have drawn a dotted line indicating where they share a side.

From here we find the area of each shape seperately and add those areas together!

Rectangle:
Looking at the rectangle portion we can see that the width is 16 in and the length is 19 inches.  Don't be fooled by the long 30 inch side.  Remember, we are only looking at the portion that makes up the rectangle.

A = l*w = 16*19 = 304 inches squared

Triangle:
To find the area of the triangle, we use the formula A = (b*h)/2 where b = the length of the base and h = the height.

We can see in this attatched drawing that the height of the triangle is the same length as the width of the rectangle which is 16 inches.  

To find the base, you can do one of two things.  

1) use the pythagorian theorem (A^2 + B^2 = C^2) to solve for the missing side of the right triangle, where A is 16 inches, B is unknown and C is 19.4 inches.

2) *easier* using the information given, we can see that the longest side of this shape is 30 inches and is made up of the length of the rectangle (19 inches) and the base of the triangle (which is unkown - we can call it x)

Given that we know the total length and the length of the portion that belongs to the rectangle, we can say x = 30-19 = 11.  Therefore the base of the rectangle is 11 inches.

From here we use b*h/2
11*16/2 = 88 = area of the triangle in square inches.

Now for the easy part - add up the areas for the total!
Area (rectangle) + Area (triangle) = Area (total)
304 + 88 = 392 square inches

Answer:

c

Step-by-step explanation:

c

The vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

[tex]y=a(x-h)^2+k[/tex]

Here, (h, k) is the vertex point.

Substitute the values for h and k in the above vertex form.

[tex]f(x) = a(x -5)^2+ 3[/tex]

Use another point and substitute in values for x and f(x). Solve for a.

[tex]5 = a(6 - 5)^2 +3\\5-3=a(1)\\a=2[/tex]

Rewrite the function, using the values for h, k, and a. The function is

[tex]f(x) = 2(x -5)^2+ 3[/tex]

Hence, the vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]

Learn more about the vertex form of the parabola here;

https://brainly.com/question/17987697

Answer: 1st slot: 2 | 2nd slot: 5 | 3rd slot: 3 | correct on edge 2023!

Answer:

33.3 is your answer

Step-by-step explanation:

The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Two cones A₁ and A₂ are similar.

The radius of A₁ = 2 cm

radius of A₂ = 3 cm

The surface area of A₁ = ? cm²

surface area of A₂ = 75 cm²

Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.

Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,

(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)

We can use this relationship to solve for the surface area of A₁:

(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)

Substituting the given values, we get:

(surface area of A₁) = (2/3)² × 75

(surface area of A₁) = 4/9 × 75

(surface area of A₁) ≈ 33.3 cm²

Therefore, (surface area of A₁) ≈ 33.3 cm²

To learn more about the cone;

brainly.com/question/16394302

#SPJ7

[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]

═════════════════════

[tex]x+5[/tex]

[tex]x^{1-1} [/tex]

[tex]x^{0} [/tex]

[tex] = 1 [/tex]

─────────────────────┈

[tex](2x + 3)[/tex]

[tex]2x^{1-1} [/tex]

[tex]2x^{0} [/tex]

[tex]2\times 1 [/tex]

[tex] = 2[/tex]

══════════════════════

Step-by-step explanation:

#Carry on learning

Answer:

1/10

Step-by-step explanation:

There are ten options and Salad is one of them; therefore, the answer would be 1/10.

Answer:

6xba^2 + 6yba^7 + 48ab

Step-by-step explanation:

To do this, you have to multiply 6ab by each of the inside terms,

So you can write it out like this

6ab (xa + ya^6 + 8)

6ab(xa) + 6ab(ya^6) + 6ab(8)

Then you can simplify:

6xba^2 + 6yba^7 + 48ab

(When you multiply the same variable by itself, you turn it into an exponent)

For example x * x = x^2

Or x^4 * x^3 = x^7

Answer:

-243

Step-by-step explanation:

{3׳ykx-7 incluye

Check the picture below.

let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{42\frac{1}{2}}\implies \cfrac{42\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{85}{2}} ~\hfill \stackrel{mixed}{67\frac{3}{7}}\implies \cfrac{67\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{472}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{472}{7}~~ - ~~\cfrac{85}{2}\implies \cfrac{(2)472~~ - ~~(7)85}{\underset{\textit{using this LCD}}{14}}\implies \cfrac{944~~ - ~~595}{14}\implies \cfrac{349}{14}\implies 24\frac{13}{14}[/tex]

Answer:

105

Step-by-step explanation:

nth term=a+(n-1)d (a=first term,d=difference)

a=6,d=9-6=3

34th term=6+(34-1)3

=6+(33×3)

=6+99=105

Answer:

254.47sqft (square feet) of paint

Step-by-step explanation:

The surface area of the cylinder (282.74) minus the area of the one circle that doesn't need to be painted (28.27) is 254.47sqft which is the amount of paint he will need Mr. Jones.

Answer:

Step-by-step explanation:

Slope intercept form

y + 7 = 3(x  + 4)                 Change all the double minuses to pluses.

y + 7 =  3x + 12                  Remove the brackets.

y + 7 - 7 = 3x + 12-7           Subtract 7 from both sides

y = 3x + 5

Slope

Whatever number is in front of the x is the slope Answer: 3

y intercept

Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number.  Answer: 5

x intercept.

This occurs when y = 0

0 = 3x + 5                      Subtract 5 from both sides

-5 = 3x + 5 -5

-5 = 3x                            Divide by 3

-5/3 = 3x / 3

-5/3 = x                          

Answer: x_intercept = -5/3

Answer:

alternate angle and counter

Answer: 50 students

Step-by-step explanation:

You know that the number of students last year plus 20% of that number equals the number of students this year, which can be written as: x + 0.2x = 60 →

1.2x = 60 → x = 50 students :)

Answer: 50 students

Step-by-step explanation:

x + .2x = 60

1.2x = 60

x = 60/1.2

x = 50

Answer:

Dividing by same signs give a positive answer.

Dividing by different signs give a negative answer.

Step-by-step explanation:

Quotient is just a term for the answer given by a division problem.

positive/positive = positive

positive/negative = negative

negative/positive = negative

negative/negative = positive

Answer:

Yes, its a linear function

Step-by-step explanation:

See, all the results here are one-one which means for a distinct input there will be a distinct output.

That's why its a linear function

Answer:

Those two lines are equal