Ginger's cat gave birth to a kitten that weighed ounces when it was born. On the day Ginger sold the kitten to its new owner, it weighed ounces. How many ounces did the kitten gain before it went home with its new owner?

To divide mixed numbers like 3 1/2 and 2 1/4, first convert to improper fractions. In this case, 3 1/2 divided by 2 1/4 simplifies to 1 5/9.

To solve the problem of 3 1/2 divided by 2 1/4, you need to first convert each mixed number into an improper fraction.

3 1/2 becomes 7/2 and 2 1/4 becomes 9/4, because 3*2 + 1 = 7 (for the first number) and 2*4 + 1 = 9 (for the second number), the numerators of the fractions.

Next, in our division problem, we flip the second fraction (this is the reciprocal), and multiply it with the first. It's the same as multiplying by its inverse to divide fractions.

So, 7/2 divided by 9/4 becomes 7/2*
4/9 which equals 28/18, which can be simplified to 1 10/18 or further simplified to 1 5/9 in mixed number form.

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b + a = 14

b = 14 - a

14 - a + a = 14

14 = 14

Since we can't gain any further information after solving for b the first time, we know b = 14 - a to be the simplest form of b.

Answer: Choice A -- f(x) = (1/3)*|x|

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

The input of a function is x and the output is y = f(x)

To vertically compress a function, we will multiply the y value by some fraction smaller than 1. This is so that the y coordinates are a fraction of what they once were.

In this case, we multiply y by 1/3 so that something that has a y coordinate of y = 81 becomes y = 27 (divide by 3)

So we have y = f(x) become (1/3)*y = (1/3)*f(x) = (1/3)*|x|

Answer:

At that particular moment, the time and day could be written as: 12:34, 5/6/78.

Where as we can see numbers are in increasing order.

Answer: 5-6i

The rule is that if f(x) has real number coefficients, then a root of x = a+bi pairs up with its conjugate pair of x = a - bi. In this case, a = 5 and b = 6.

Answer:

5 -6i is also the root of  f(x).

Step-by-step explanation:

Given : If 5 + 6i is a root of the polynomial function f(x),

To find  : which of the following must also be a root of f(x).

Solution : We have given that 5+6i is the on of the root of polynomial function f(x).

It has two parts real and imaginary  part so , it is a complex number .

Real part  = 5  and 6i is imaginary part.

Complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of a + bi is a − bi.

a = 5 , b = 6.

Then by the complex conjugate defination , Another root would be 5 - 6i

Therefore, 5 -6i is also the root of  f(x).

Answer:

-1/2 or x=2

Step-by-step explanation: The first step you need to do in getting your answer is factoring ,you will factor the left side of the equation first:

(2x+1)(x-2)=0

Next, you will set the factors to equal to "0":

2x+1=0  x-2=0

Then you'll proceed to solve the problem using the basic algebraic equation problem solving steps .When you do this you'll be left with answers of x=-1/2  and x=2

Answer:

1 3/5 miles per hour

Step-by-step explanation:

Distance = rate * time

We know the distance and the time

2/5 miles = rate * 1/4 hour

Divide by 1/4

2/5   ÷ 1/4 = rate * 1/4 ÷ 1/4

Copy dot flip

2/5 * 4/1 = rate

8/5 = rate

1  3/5 miles per hour is the rate

Answer:

It is given that,  

there are 8 balls in the bag numbered 1 to 8

5 balls are  color is gray and all others are white

The gray color balls are 2,3,4,5 and 7

The white color balls are 1,6 and 8

P(X) = probability of getting white ball

P(not X) = Probability of getting gray ball

a) To find Probabilities P(X) and P(not X)

For event X, 1,,6,8 are checked and P(X) = 3/8

for event 'not X' 2,3,4,5 and 7 are checked and P(not X ) = 5/8

b) To find 1 - P(X)

1 - P(X) = 1 - 3/8 = (8 - 5)/8 = 5/8  

c)1 - P(X) is same as P(not X)

The height of the first copy is 20 cm, and the height of the second copy is 17 cm, after applying the percentages to each successive copy.

The subject of your question falls into the category of Mathematics, particularly in the domain of ratios and percentages. In order to answer your question, we must make a sequence of percentage calculations based on the original height of the photo.

Firstly, if the height of the first copy is 80% of the original photo's height, then the calculation should look like this: 0.80 * 25 cm = 20 cm. Therefore, the first copy's height is 20 cm.

Secondly, the height of the next copy is said to be 85% of the FIRST copy's height. Therefore, we proceed with a similar calculation: 0.85 * 20 cm = 17 cm. This implies that the height of the second copy is 17cm.

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Answer:

We can translate Circle C (x+6, y-2) to have the same center as D. The ratio of radius to radius is 10/5=2. Scale factor 2 from C to D.

Step-by-step explanation:

Similar objects are objects which are the same shape but not the same size. This means they have the same angle measures and a scale factor between the side lengths. To show similarity, we can use transformations and proportions. We can translate to shift the object, dilation to increase or decrease size and so forth. We use proportions to find scsale factor or missing length.

We have a circle. Circles do not have a specific angles and all circles have 360 degrees. They do not have sides but do have radius. All circles are similar because all are the same shape - a fixed center with points equidistant from the center (the radius). To show similar we can translate the circle so the centers are the same and create a ratio between the radius.

We can translate Circle C (x+6, y-2) to have the same center as D. The ratio of radius to radius is 10/5=2. Scale factor 2 from C to D.

Answer:

(4,1)

Step-by-step explanation:

3x+4y=16

-4x-3y=-19

I will solve this system by elimination.  I will eliminate x

Multiply the first equation by 4 and the second equation by 3

4 (3x+4y)=4*16

12x + 16y = 64

3 (-4x-3y)=3*-19

-12x -9y = -57

Add the two modified equations together to eliminate x

12x + 16y = 64

-12x -9y = -57

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

7y = 7

y=1

We still need to find x

3x+4y = 16

Substitute y=1

3x+4(1) = 16

3x+4=16

Subtract 4 from each side

3x = 16-4

3x =12

Divide each side by 3

3x/3 = 12/3

x=4

Answer:  The required solution is (x, y) = (4, 1).

Step-by-step explanation:  We are given to solve the following system of linear equations :

[tex]3x+4y=16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4x-3y=-19~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

We will be using the method of Elimination to solve the given system as follows :

Multiplying equation (i) by 4 and equation (ii) by 3, we have

[tex]4(3x+4y)=4\times16\\\\\Rightarrow 12x+16y=64~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

and

[tex]3(-4x-3y)=-19\times3\\\\\Rightarrow -12x-9y=-57~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]

Adding equations (iii) and (iv), we get

[tex](12x+16y)+(-12x-9y)=64+(-57)\\\\\Rightarrow 7y=7\\\\\Rightarrow y=\dfrac{7}{7}\\\\\Rightarrow y=1.[/tex]

Substituting the value of y in equation (i), we get

[tex]3x+4\times1=16\\\\\Rightarrow 3x+4=16\\\\\Rightarrow 3x=16-4\\\\\Rightarrow 3x=12\\\\\Rightarrow x=\dfrac{12}{3}\\\\\Rightarrow x=4.[/tex]

Thus, the required solution is (x, y) = (4, 1).

Answer:

A. If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = - [tex]\frac{7}{2}[/tex] and c = 12

y = - [tex]\frac{7}{2}[/tex] x + 12 ← equation in slope-intercept form

given (x, 5) lies on the line, solve for x by letting y = 5

- [tex]\frac{7}{2}[/tex] x +12 = 5

multiply all terms  by 2 to eliminate the fraction

- 7x + 24 = 10 ( subtract 24 from both sides )

- 7x = - 14 ( divide both sides by - 7 )

x = 2

Answer:  9a + 6b - 21

Step-by-step explanation:

  3(3a + 2b - 7)

= 3(3a) + 3(2b) + 3(-7)

=   9a    +  6b    +   -21

Answer:

2,-3

Step-by-step explanation:

1.{(x, y): x = 2} we know x = 2

2.  {(x, y): y -3] we know y = -3

3. x,y = 2,-3

Answer:

3,4,1,2 is the order in which it goes in (go left to right)    :)

Step-by-step explanation:

Answer:

 = 420 in^2

Step-by-step explanation:

The area of a triangle is one half the base times the height

A = 1/2 bh

In this figure the base is equal to 24 inches and the height is  35 inches

Substituting what we know.

A =1/2 (24) * 35

A= 12*35

  = 420 in^2

Answer: The answer is 420

Step-by-step explanation:

24 x 35 equals 840. Then you divide by 20 and you get 420. I also took the test on iready.

Have a great day!

Question 1. 2P + 14 = 0

Step 1. You need to subtract 14 from both sides.

2p+14−14=0−14

2p=−14

Step 2. Then divide both sides by 2.

2p /2 = −14 /2

Answer:  p=−7

Question 2.  - 2/3 w + 5 = 4

Step 1. Subtract 5 from both sides.

−2 /3 w+5−5=4−5

Step 2. Then multiply both sides by 3/(-2).

( 3 /−2 )*( −2 /3 w)=( 3 /−2 )*(−1)

Answer: w=  3 /2

Question 3. 5d - 1 = - 11

Step 1. First add 1 to both sides.

5d−1+1=−11+1

5d=−10

Step 2. Divide both sides by 5.

5d /5 = −10 /5

Answer: d=−2

Hope this helps! :)

Answer:

    =sqrt(2) /3

Step-by-step explanation:

sqrt(2/9)

We can split the sqrt(a/b) = sqrt(a)/ sqrt(b)

sqrt(2/9) = sqrt(2)/sqrt(9)

We know that the sqrt(9) is 3

              =sqrt(2) /3

Answer:2/9 but not the regular one

Step-by-step explanation:

Answer:

x=34

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

Hence final answer is x=34

Step-by-step explanation:

∠ADC= ∠EDF {Vertically opposite angles are always equal}

∠ADC= 36°  {Given }

∠ADB= 36°...(i)  {Same angles}

∠ABI + ∠ABC = 180° {supplementry angles }

113° + ∠ABC = 180°  {Given }

∠ABC = 180° - 113°

∠ABC = 67°

∠ABD = 67° ...(ii)  {same angle}

We know that sum of all three angles of triangle is 180 degree so we can write:

∠ABD + ∠ADB + ∠BAD =  180°

67° + 36° + ∠BAD =  180°  {using (i) and (ii) }

67° + 36° + x°+43° =  180°  {from diagram }

146° + x° =  180°

x° =  180° - 146°

x° =  34°

Hence final answer is x=34

Answer:

A. 3 possible combinations

B. 8 4-ounce's bags and 3 3-ounce's bags

C. 2 4-ounce's bags and 11 3-ounce's bags

D. 8 4-ounce's bags and 3 3-ounce's bags

E. All solutions offer the same revenue.

Step-by-step explanation:

You have been tasked with filling 4 ounce and 3 ounce bags from a 41 ounce container of candy. Let x be the number of 4 ounce bags and y be the number of 3 ounce bags. Then

[tex]4x+3y=41.[/tex]

A. Find all integer solutions:

You get 3 possible combinations.

B. 1. 2 + 11 = 13,

2. 5 + 7 = 12,

3. 8 + 3 = 11.

The minimal number of bags is 11.

C. 1. 2·7+11·5=69 cents

2. 5·7+7·5=70 cents

3. 8·7+3·5=71 cents

The cheapest is 1st solution.

D. 1. 2·6+11·5=67 cents

2. 5·6+7·5=65 cents

3. 8·6+3·5=63 cents

The cheapest is 3rd solution.

E. 1. 2·2+11·1.50=$20.50

2. 5·2+7·1.50=$20.50

3. 8·2+3·1.50=$20.50

All solutions offer the same revenue.

Answer:

The 3rd equation on the left column  and second one on the right column.

Step-by-step explanation:

These 2 equations have same  coefficients of x and y if we divide the first one by 4 and the second by 2.

This gives the 2 equations

x^2 + y^2 - 4x + 6y - 7 = 0

x^2 + y^2 - 4x + 6y - 20 = 0

If we compete the square on these we get

(x - 2)^2 + (y + 3)^2 =  20

(x - 2(^2 + (y + 3)^2 =  33

These are in standard form . The center is the same (2, -3) but the radii are different so they are concentric.

In mathematics, concentric circles have the same center but different radii. Their general equation is (x-h)²+ (y-k)² = r², sharing the same (h, k) coordinates. Examples include equations like (x - 2)² + (y - 3)² = 4 and (x - 2)² + (y - 3)² = 9.

In mathematics, concentric circles are circles that share the same center but have different radii. The general equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. Two such equations will represent concentric circles if and only if their center coordinates (h, k) are the same.

For example, consider the equations:

(x - 2)² + (y - 3)² = 4

(x - 2)² + (y - 3)² = 9

Both these circles have the center at (2, 3) but different radii (2 and 3 respectively), making them concentric circles.

Answer: whats the question

Step-by-step explanation:

Answer:

Draw and label the points where the circles with centers A and B intersect and where the circles with centers A and C intersect.

Step-by-step explanation:

Got it right on the test

The numbers that make the statement true are:

( -14, -∞ ) or [-15, -∞).

i.e -15, -16, -17, - 18, -19, ,,,,,,,,,-∞

Given,

Nine more than twice a number is less than negative nineteen.

We need to find all numbers that make this statement true.

More than - addition.

Twice - multiplication of 2.

Less than - <

-∞.......-5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < < 3 ...........∞

Find the expression.

Let the number be M.

"Nine more than twice a number is less than negative nineteen".

We can write this statement as:

2M + 9 < -19

Find the number M.

2M + 9 < -19

2M < -19 - 9

2M < -28

M < -28/2

M < -14

Let us check the statement is true with M < -14.

2M + 9 < -19

2 x -15 + 9 = -19

-30 + 9 = -19

-21 < -19

This is true.

We see that all numbers below -14 will make the statement true.

So,

The numbers are -15, -16, -17, -18,..........-∞

Thus the numbers that make the statement true are ( -14, -∞ ) or [-15, -∞).

i.e -15, -16, -17, - 18, -19, ,,,,,,,,,-∞

Learn more about finding numbers that satisfy an inequality here:

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To solve the inequality, we need to translate the given statement into an algebraic expression and then solve for 'x' using subtraction and division.

To solve the inequality, we will translate the given statement into an algebraic expression. Let's say the number is represented by 'x'. 'Twice a number' can be written as 2x. 'Nine more than twice a number' can be written as 2x + 9.

So, the inequality becomes 2x + 9 < -19.

To solve for 'x', we subtract 9 from both sides of the inequality, giving us 2x < -28. Then, we divide both sides by 2, resulting in x < -14.

Therefore, any number less than -14 will make the statement true.

Answer:

$3.71 is your price after the tax.

Step-by-step explanation:

First, change the percentage into a decimal:

6% = 0.06

Multiply the decimal with the cost:

3.50 x 0.06 = 0.21

Add the number gotten to the original price:

3.50 + 0.21 = 3.71

$3.71 is your price after the tax.

~

Answer:

$3.71

Step-by-step explanation:

The tax = original price * tax rate

             = 3.5 * .06

             =.21

Add the tax to the original price to get the total cost

total cost = 3.5+.21

                  =3.71

The cost of the batteries is $3.71 after tax

Answer:

D. The two triangles are congruent because a translation does not change size and shape.

Step-by-step explanation:

I'm pretty sure that D is the answer. It jut basically moved , didn't change anything.

Answer:

1. The equation of line is [tex]y=-\frac{1}{2}(x)+1[/tex].

2. The correct option is D.

Step-by-step explanation:

1.

The slope intercept form of a line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

The given equation of a line is

[tex]y=2x+8[/tex]

The slope of line is 2 and y-intercept is 8.

The product of slopes of two perpendicular lines is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]2\times m_2=-1[/tex]

[tex]m_2=-\frac{1}{2}[/tex]

The slope of required line is [tex]-\frac{1}{2}[/tex] and it passes through the point (6,-2).

The equation of required line is

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

[tex]y+2=-\frac{1}{2}(x-6)[/tex]

[tex]y+2=-\frac{1}{2}(x)+3[/tex]

[tex]y=-\frac{1}{2}(x)+3-2[/tex]

[tex]y=-\frac{1}{2}(x)+1[/tex]

Therefore the equation of line is [tex]y=-\frac{1}{2}(x)+1[/tex].

2.

Translation is a rigid transformation. It means if a figure translated then the image and preimage are congruent

It the given figure two triangles are congruent because a translation does not change size and shape.

Therefore the correct option is D.

To find the percent of change from 500,000 to 10,000, subtract 10,000 from 500,000 to get 490,000, then divide that difference by the original number and multiply by 100 to get the percentage.

To find the percent of change from 500,000 to 10,000, we need to calculate the difference between the two numbers and then find the percentage of that difference relative to the original number.

Step 1: Find the difference: 500,000 - 10,000 = 490,000.

Step 2: Find the percent: (490,000/500,000) × 100 = 98%.

The percent of change from 500,000 to 10,000 is 98%.