Fill in the blank to make the fractions equivalent.

8/12 = _/3

Answer:

4 copies

Step-by-step explanation:

After yesterday's sales, 1/3 of the original supply remained. After today's sales, 1/5 of that value remain. So the remaining number is ...

60·(1/3)(1/5) = 60/15 = 4

The bookstore has 4 copies of the magazine left after selling 2/3 of them on the first day and 4/5 of the remaining on the second day.

The bookstore originally has 60 copies of a magazine. On the first day, it sold 2/3 of them, which equals to 60*(2/3) = 40 copies. So, there are 60 - 40 = 20 copies left. On the second day, it sold 4/5 of what remained, that is, 20*(4/5) = 16 copies. After this, the remaining copies are 20 - 16 = 4 copies.

Learn more about Fractions here:

https://brainly.com/question/33564650

#SPJ2

She gets 10000$hope dat helped

Answer:

the answer is $841.53

explanation:

this probably won't help now but it will help others :D

Answer:

11.5 (i think)

Step-by-step explanation:

23 is the diameter and half of the diameter is the radius so 23 divided by 2 is 11.5.

Answer:

Step-by-step explanation:

In the picture you have a diameter of d = 23 cm.

The diameter is twice the radius: d = 2r.

Therefore, r = d : 2 → r = 23 cm : 2 = 11.5 cm

Answer:

option B) f(x)=x^3-6x^2+11x-6

Step-by-step explanation:

Zeros means the point at which a given function becomes zero for the value of input.

In given case, zeros of f(x) is required at points 1,2 and 3.

Graphically the point on x-axis where the function line intersects the x-axis is the zero of the function i.e. the function value is 0,

hence

f(x)=0 when x=1

x-1=0

f(x)=(x-1)

f(x)=0 when x=2

x-2=0

f(x)=(x-2)

f(x)=0 when x=3

x-3=0

f(x)=(x-3)

Thus f(x)=(x-1)(x-2)(x-3)

Writing the above polynomial in standard form:

f(x)=x^3-6x^2+11x-6 !

Answer:

a negative set of numbers? or integers

Step-by-step explanation:

integers are all the numbers in the world so that includes a negative number

Answer: 3 units

Step-by-step explanation:

the volume of a cone C = πr²h/3

C = 18π, h =2x, r = diameter/2 = 2x/2 =x

18π = π* x²* 2x/3

divide through by π

18 = x² * 2x/3

multiply through by 3

54 = 2x³

divide through by 2

27 = x³

x =∛27 = 3

x = 3 units = radius

Answer:

The Mode is 3 and Median is also 3

Step-by-step explanation:

Answer:

Mean: 2.7

Mode: 3

Median: 3

Range: 4

Step-by-step explanation:

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

Mean: 1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 5 = 30/11 = 2.7

Mode: 3

Median: 3

Range: 5 - 1 = 4

Answer:

[tex]\large\boxed{d)\ x=-5\pm\sqrt{31}}[/tex]

Step-by-step explanation:

[tex]x^2+10x=6\\\\x^2+2(x)(5)=6\qquad\text{add}\ 5^2\ \text{to both sides}\\\\x^2+2(x)(5)+5^2=6+5^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+5)^2=6+25\\\\(x+5)^2=31\iff x+5=\pm\sqrt{31}\qquad\text{subtract 5 from both sides}\\\\x=-5\pm\sqrt{31}[/tex]

Answer:

(x - 4)(x + 1)

Step-by-step explanation:

Given

x² - 3x - 4

To factor the trinomial

Consider the factors of the constant term (- 4) which sum to give the coefficient of the x- term (- 3)

The factors are - 4 and + 1, since

- 4 × 1 = - 4 and - 4 + 1 = - 3, hence

x² - 3x - 4 = (x - 4)(x + 1)

Answer:

The answer is A

Step-by-step explanation:

Answer:

A. Abrupt changes or trends in engine temperature

Step-by-step explanation:

Abrupt changes or trends in engine temperature are an indication that your vehicle may be developing a cooling system problem.

Cooling system problem occurs in engines of vehicles when the vehicle is running low on coolant. This results in an increase in temperature of the engine. If such conditions go un noticed for a long time, fatal accidents can take place.

All of the numbers in the shaded part of the line have two characteristics:

==> X >= 0

==>  X <= 20

This can be written as a single inequality with x in the middle, but when I type it, Brainly won't accept the characters, and says there's an error.

Here it is in words:

0 (less than or equal to) x (less than or equal to) 20 .

[tex]

3\sqrt{8}\cdot4\sqrt{3} \\

12\sqrt{24} \\

12\cdot2\sqrt{6} \\

\boxed{24\sqrt{6}}

[/tex]

Final answer:

The product of (3 the square root of 8)(4 the square root of 3) is simplified to 24√6, which is the final simplified form as the radical cannot be simplified further.

Explanation:

The product of (3 the square root of 8) and (4 the square root of 3) involves using properties of radicals and multiplication. First, simplify the square root of 8 to 2√2 because 8 is 4 times 2, and 4 is a perfect square whose square root is 2. Now the expression becomes (3∙2√2)∙(4√3). We then multiply the coefficients (3∙2) and (4), which is 24, and the radicals √2 and √3 which is √6. The final product is 24√6, which cannot be simplified further as 6 is not a perfect square.

Answer:

C. 12.5,114,125

Step-by-step explanation:

:3:3:3:3::33

Answer:

D

Step-by-step explanation:

We have to find the list of equivalent numbers

A.1.25,[tex]1\frac{1}{4}[/tex],12.5%

[tex]1\frac{1}{4}=\frac{5}{4}=1.25[/tex]

12.5%=[tex]\frac{125}{1000}=0.125[/tex]

Given numbers are not equivalent

Hence, option A is false.

B.0.125,[tex]\frac{1}{4}[/tex],12.5%

[tex]\frac{1}{4}=0.25[/tex]

12.5%=[tex]\frac{125}{1000}=0.125[/tex]

Given numbers are not equivalent.

Hence, option B is false.

C.12.5,[tex]1\frac{2}{12}[/tex],125%

[tex]1\frac{2}{12}=\frac{14}{12}=1.167[/tex]

125%=[tex]\frac{125}{100}=1.25[/tex]

Given numbers are not equivalent.

Hence, option C is false.

D.1.25,[tex]1\frac{1}{4}[/tex],125%

[tex]1\frac{1}{4}=\frac{5}{4}=1.25[/tex]

125%=[tex]\frac{125}{100}=1.25[/tex]

Given numbers are equal.

Hence, option D is true.

Answer:

Option A. 30 days

Step-by-step explanation:

Find the area of the brownie pan

The area of the trapezoid is equal to

step 2

To calculate the number of days, divide the total area of the brownie pan by 30 square centimeters of brownie

so

Answer:

x ≈ 4.1 cm

Step-by-step explanation:

The segment from the centre to the chord is a perpendicular bisector

The third side of the triangle = 14.6 ÷ 2 = 7.8

We now have a right triangle with legs x and 7.8 with hypotenuse 8.8

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 7.8² = 8.8²

x² + 60.84 = 77.44 ( subtract 60.84 from both sides )

x² = 16.6 ( take the square root of both sides )

x = [tex]\sqrt{16.6}[/tex] ≈ 4.1 ( nearest tenth )

Answer:

4.1

Step-by-step explanation:

⇒The missing side of the triangle is 7.8 cm

We use Pythagoras theorem to solve x

a² = b² + c²

In this case, a = 7.8 cm and c = 8.8 cm

→ 7.8² = x² + 8.8²

( Rearrange )

→ x² = 8.8² - 7.8²

( Simplify )

→ x² = 77.44 - 60.84

( Simplify )

→ x² = 16.6

( Square root )

→ x = 4.074309757

For this case we have to subtract the two distances (subtract the polynomials) and the difference will be given by the shorter miles of the second route.

[tex]6x ^ 2 + 2x-2- (5x ^ 2-8x-6) =[/tex]

Taking into account that:

[tex]- * + = -\\- * - = +\\6x ^ 2 + 2x-2-5x ^ 2 + 8x + 6 =[/tex]

Adding similar terms:[tex]6x ^ 2-5x ^ 2 + 2x + 8x-2 + 6 =\\x ^ 2 + 10x + 4[/tex]

So, the correct option is C

ANswer:

Option C

For this case we have that by definition, the area of a triangle is given by:

[tex]A = \frac {1} {2} b * h[/tex]

Where:

b: It's the base

h: It's the height

Substituting the values, according to the given data:

[tex]225 = \frac {1} {2} (15) * h\\225 = 7.5h[/tex]

Dividing between 7.5 on both sides of the equation:

[tex]h = \frac {225} {7.5}\\h = 30[/tex]

Thus, the height of the triangle is 30ft

Answer:

30ft

Answer: 30 feet.

Step-by-step explanation:

The formula used to calculate the area of a triangle is:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

In this case you know that the area of this triangle is 225 ft² and its base is 15 ft. Then, you can substitute these values into the formula [tex]A=\frac{bh}{2}[/tex] and solve for the height "h":

[tex]225ft^2=\frac{(15ft)h}{2}[/tex]

[tex](2)(225ft^2)=(15ft)h[/tex]

[tex]h=\frac{(2)(225ft^2)}{15ft}[/tex]

[tex]h=30ft[/tex]

Answer:

a. x² + x - 30 = (x + 6)(x - 5)

b. -3x² + 23x - 14 = -[(3x - 2)(x - 7)]

c. 2x² - 5x + 4 can not factorize by this way

d. 6x² + 10x - 24 = 2[(3x - 4)(x + 3)]

Step-by-step explanation:

* To factor a trinomial in the form ax² ± bx ± c:

- Look at the c term

# If the c term is positive

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will have the same sign (sign of b)

∵ a = h × k ⇒ h , k are the factors of a

∴ rk + hs = b

∴ (hx + r)(kx + s) ⇒ if b +ve  OR  (hx - r)(kx - s) ⇒ if b -ve

# If the c term is negative

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will not have the same sign

∵ a = h × k ⇒ h and k are the factors of a

∴ rk - hs = b OR hs - rk = b

(hx + r)(kx - s) OR (hx - r)(kx + s)

* Now lets solve the problem

a. x² + x - 30

∵ ax² + bx + c

∴ a = 1 , b = 1 , c = -30

∵ c is negative

∴ r and s have different signs

∵ a = h × k

∵ 1 = 1 × 1

∴ h = 1 , k = 1

∵ c = r × s

∵ c = -30

∴ r × s = -30

∵ 6 × -5 = -30

∴ r = 6 , s = -5

∴ hs = 6

∴ rk = -5

∵ hs - rk = 6 - 5 = 1 ⇒ same value of b

∴ (x + 6)(x - 5)

* x² + x - 30 = (x + 6)(x - 5)

b. -3x² + 23x - 14 ⇒ take -1 as a common factor

∴ -(3x² - 23x + 14)

∵ ax² + bx + c

∴ a = 3 , b = -23 , c = 14

∵ c is positive

∴ r and s have same sign (-ve) because b is negative

∵ a = h × k

∵ 3 = 3 × 1

∴ h = 3 , k = 1

∵ c = r × s

∵ 14 = 2 × 7

∴ r = 2 , s = 7

∴ hs = 3 × 7 = 21

∴ rk = 2 × 1 = 2

∵ hs + rk = 21 + 2 = 23 ⇒ same value of b

∴ (3x - 2)(x - 7)

* -3x² + 23x - 14 = -[(3x - 2)(x - 7)]

c. 2x² - 5x + 4

∵ ax² + bx + c

∴ a = 2 , b = -5 , c = 4

∵ c is positive

∴ r and s have same sign (-ve) because b is negative

∵ a = h × k

∵ 2 = 2 × 1

∴ h = 2 , k = 1

∵ c = r × s

∵ 4 = 2 × 2

∴ r = 2 , s = 2

∴ hs = 2 × 2 = 4

∴ rk = 2 × 1 = 2

∵ hs + rk = 4 + 2 = 6 ⇒ not same value of b

∴ We can not factorize it

* 2x² - 5x + 4 can not factorize by this way

d. 6x² + 10x - 24 ⇒ take 2 as a common factor

∴ 2(3x² + 5x - 12)

∵ ax² + bx + c

∴ a = 3 , b = 5 , c = -12

∵ c is negative

∴ r and s have different signs

∵ a = h × k

∵ 3 = 3 × 1

∴ h = 3 , k = 1

∵ c = r × s

∵ -12 = -4 × 3

∴ r = -4 , s = 3

∴ hs = 3 × 3 = 9

∴ rk = -4 × 1 = -4

∵ hs - rk = 9 - 4 = 5 ⇒ same value of b

∴ (3x - 4)(x + 3)

* 6x² + 10x - 24 = 2[(3x - 4)(x + 3)]

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

[tex]4<c<20[/tex]

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

[tex]a+b>c\\ \\a+c>b\\ \\b+c>a[/tex]

Use this rule in your case. So, if a=12 and b=8, then

[tex]12+8>c\\ \\12+c>8\\ \\8+c>12[/tex]

Hence, you get

[tex]c<20\\ \\c>-4\\ \\c>4[/tex]

From these inequalities, you can state that

[tex]4<c<20[/tex]

So, c must be smaller than 20 inches and greater than 4 inches.

Answer:

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c----> the length of the third side of triangle

Applying the triangle inequality theorem

1) 12+8 > c

20 > c

Rewrite

c < 20 in

2) 8+c > 12

c > 12-8

c < 4 in

therefore

4 in < c < 20 in

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

T= O/A

Tan(46)= x/35

Tan(46)×35= x= 36.2435... ft

the answer is A i believe

the like terms are 9x and 7x, if you are told to simplify, you write, "12y+16x"

12y + 9x + 7x

The like terms are 9x and 7x. This is because they both have the x variables attached to the number. This means that you can add only 9x and 7x (not 12y because it isn't a like term) together like normal numbers (except with an x at the end so you would get: 12y + 16x

Hope this helped!

9,12,18 is a right triangle and so is 30,72,90

Answer:

No congruency statement can be made because the side lengths are unknown.

Step-by-step explanation:

For two triangles to be considered congruents they have to similar and of the same size.

In this case, we can say both triangles are similar (same shape) since their internal angles are the same (90°, 30° and 60°), but we cannot say if they are congruent (same size in addition to being similar) because we don't know anything about the length of their sides, they could be the same, or not.

Answer:

a. [tex]d=2.0t[/tex]

b. 26 meters

c. picture attached

Step-by-step explanation:

- Since the turtle travels 2.0 meters per minute, it will travel a total distance of [tex]2.0t[/tex] in [tex]t[/tex] minutes. We know that the total distance is [tex]d[/tex], so we can equate both total distances to create our rule:

[tex]d=2.0t[/tex]

- To find the distance of the turtle after 13 minutes we just need to replace [tex]t[/tex] with 13 in our rule:

[tex]d=2.0t[/tex]

[tex]d=2.0(13)[/tex]

[tex]d=26[/tex]

The turtle cover a distance of 26 meters after 13 minutes.

- To graph the function we are going to evaluate our function at two points, and then we are joining those two points with a line (check the attached picture)

We already know that the turtle cover a distance of 26 meters after 13 minutes, since the distance depends on the time our point will have coordinates (time, distance) (13 minutes, 26 meters) (13, 26)

Notice that when time is zero, distance is zero as well, so our second point is (0, 0)

Now we can join the points using a line:

Answer:

Any number times zero is zero.

Step-by-step explanation:

Simplify the following:

0 g f

Hint: | Any number times zero is zero.

0 g f = 0:

Answer:  0

#3 When you set the proportion make sure you pick sides that oppose same angle and take them in same order (for example big triangle first and small second)

( 2x+2)/10= (x-2+3)/(x-2);

(2x+2)(x-2)=10(x+1);

2x^2 -4x+2x-4=10x+10;

2x^2 -2x-4-10x-10=0;

2x^2 -12x-14=0; divide by 2

X^2 -6x-7=0; factor

(X-7)(x+1)=0 so x=7 and x=-1

Reject x=-1 because we can’t have negative dimensions so x=7 is the solution

Answer: $8

Step-by-step explanation:

If 2.00 was 25%, then 25% * 4 = 100

2 * 4 = 8

Answer:

y=1/2(x-6)^2+3/2

Step-by-step explanation:

General equation of parabola centered at (h,k) and axis of symmetry is parallel to y-axis is given as

(x-h)^2=4p(y-k)^2

where

vertex is at (h,k)

p shows the distance of focus from vertex, f = (h, k + p)

and directrix is given at y = k - p

if value of p is >0 then the focus is above vertex

if value of p<0 then focus is below vertex

Given:

focus= (6,2)

directrix y=1

Comparing above with standard formula of parabola, we get

Also distance p is half the distance from the (6,2) to the directix y=1 which is  

1/2=p

As p>0, that means given parabola focus lies above vertex

hence parabola opens upwards

Finding vertex of parabola:

As focus is is at (6,2) and also 1/2 above the vertex so we get vertex at

V=(6,2-1/2)

V=(6,1.5)

Now by comparing above with the standard formula of parabola we have

h=6, k=1.5

Putting values in the formula we get

(x-6)^2=4(1/2)(y-1.5)

(x-6)^2=2(y-1.5)

(x-6)^2=2y-3

Or by re-arranging the terms equation can also be written as

f(x)=1/2(x-6)^2+3/2 !

The equation for a parabola with a focus at (6,2) and a directrix at y=1 is y = (x²-12x+37)/2. It is derived using the definition of a parabola.

The equation of a parabola can be derived using the definition of a parabola: the set of all points that are equidistant from a given point (the focus) and a given line (the directrix). The distance between a point (x,y) on the parabola and the focus (6,2) is equal to the absolute value of the difference between y-coordinate of the point and y-coordinate of the directrix line.

Mathematically, the distance to the focus is (x-6)² + (y-2)² and the distance to the directrix is |y-1|. For any point on the parabola, these distances are equal, so we have (x-6)² + (y-2)² = (y-1)². Solving for y, we obtain the quadratic equation y = (x²-12x+37)/2, which represents the equation of a parabola with a focus at (6,2) and a directrix at y=1.

https://brainly.com/question/29045743

#SPJ3

Answer:

Step-by-step explanation:

x+2y=-2

2y = - x -2

y = -1/2 x -1 ... (The first line)   red

y=1/2x-5 ( the second line ) bleus

the solution to the system of equations is (4 ; -3) intersection of two line