Lisa’s pet shop has 2 fish tanks. Tank A contains smaller fish who are fed 1 gram of food each per day. Tank B contains larger fish who are fed 2 grams of food each per day. If tank B contains 2/3 (fraction) the number fo fish thank Tank A contains, will Lisa ever feed both tanks the same amount of food?

Answer:

[tex]4(x+3.5)^{2}=0[/tex]

Step-by-step explanation:

we have

[tex]4x^{2}+28x+49=0[/tex]

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](4x^{2}+28x)=-49[/tex]

step 2

Factor the leading coefficient

[tex]4(x^{2}+7x)=-49[/tex]

step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]4(x^{2}+7x+3.5^2)=-49+(3.5^2)(4)[/tex]

[tex]4(x^{2}+7x+12.25)=0[/tex]

step 4

Rewrite as perfect squares

[tex]4(x+3.5)^{2}=0[/tex]

The equation by completing the square is [tex]\[ (x + \frac{7}{2})^2 = 0 \].[/tex]

To complete the square for the quadratic equation [tex]\(4x^2 + 28x + 49 = 0\)[/tex], we need to follow these steps:

Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. This gives us:

[tex]\[ x^2 + 7x + \frac{49}{4} = 0 \][/tex]

Next, we need to find the value to complete the square. This is done by taking half of the coefficient of [tex]\(x\)[/tex], which is [tex]\(\frac{7}{2}\)[/tex], and squaring it:

[tex]\[ \left(\frac{7}{2}\right)^2 = \frac{49}{4} \][/tex]

We add and subtract this value to the equation to complete the square:

[tex]\[ x^2 + 7x + \frac{49}{4} - \frac{49}{4} + \frac{49}{4} = 0 \][/tex]

Now, we can rewrite the equation as a perfect square trinomial and a constant:

[tex]\[ (x + \frac{7}{2})^2 - \frac{49}{4} + \frac{49}{4} = 0 \][/tex]

Simplify the equation by combining the constants:

[tex]\[ (x + \frac{7}{2})^2 = 0 \][/tex]

Answer:

[tex](x,y) -----> (x+9,y-12)[/tex]

Step-by-step explanation:

we know that

[tex]A(7, 3) ----> A'(16,-9)[/tex]

The rule of the translation is equal to

[tex](x,y) -----> (x+a,y+b)[/tex]

Find the values of a and b

[tex](7,3) -----> (7+a,3+b)[/tex]

we have that

[tex]7+a=16[/tex] ----> [tex]a=16-7=9[/tex]

[tex]3+b=-9[/tex] ---->[tex]b=-9-3=-12[/tex]

substitute the values of a and b

[tex](x,y) -----> (x+9,y-12)[/tex]

That means----> The translation is 9 units right and 12 units down

Answer:

Option D:

(x, y) -> (x + 9, y minus 12)

Step-by-step explanation: Honestly all people want are the answers so I don't really care to write an explanation.

Answer:

87067=90000

Step-by-step explanation:

because 7 is bigger than 8 so its90000

Answer:

90,000

Step-by-step explanation:

Answer:

c. -51 i know bc i used a math app and it is always right

Step-by-step explanation:

welcome

Answer:

21g

Step-by-step explanation:

you multiply the 7 and the 3 together and get 21

Answer:

D.BC and Pn are corgruent.

Step-by-step explanation:

Pair of segments in the figures that are congruent : BC and PN.

In geometry, congruent means identical in shape and size. Congruence can be applied to line segments, angles, and figures. Any two line segments are said to be congruent if they are equal in length.

Given in the figure,

Two polygons ABCDEF and JKLMNP

where

AB≅MN

BC≅PN

CD≅PJ

DE≅JK

EF≅KL

FA≅LM

Hence, BC and PN is the pair of segments in the figures that are congruent.

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Answer:

54

Step-by-step explanation:

34 + 4 ⋅ 5  (by PEDMAS, do multiply first)

=  34 + 20

= 54

Answer:

54 :)

Step-by-step explanation:

Answer:

x = 127

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6, thus

sum = 180° × 4 = 720°

Sum the interior angles and equate to 720 for x

120 + 100 + 128 + 133 + 112 + x = 720, that is

593 + x = 720 ( subtract 593 from both sides )

x = 127

Answer:

C

Step-by-step explanation:

The function is formed of 2 straight lines

The equation of a straight line in slope- intercept form is

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

Calculate the slope using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (2, - 2) ← endpoints of left line

m = [tex]\frac{-2+5}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = [tex]\frac{1}{2}[/tex] x - 3 for x <  2 ( arrow on line points left )

Repeat

with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (3, 1) ← 2 points on right line

m = [tex]\frac{1+2}{3-2}[/tex] = [tex]\frac{3}{1}[/tex] = 3, thus

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 1), then

1 = 9 + c ⇒ c = 1 - 9 = - 8

y = 3x - 8 for x ≥ 2 ( arrow on line points right )

The weakest correlation is indicated by a correlation coefficient that is close to 0. This shows that there is little to no predictable relationship between the two variables.

The data set with the weakest correlation will have a correlation coefficient value closest to zero. The correlation coefficient is a measure of the relationship between two variables. Its value ranges from -1 to 1. A value of -1 indicates a perfect negative correlation, a value of 1 indicates a perfect positive correlation, and a value of 0 indicates no correlation. The direction of the correlation is indicated by whether the value is positive or negative, whereas the strength of the correlation is indicated by how close the value is to -1 or 1.

For example, consider two variables, hours of sleep and performance on a test. If the correlation coefficient is close to 1, this suggests that as one variable increases (hours of sleep), the other variable (test performance) also increases. This would be a strong positive correlation. But if the correlation coefficient is close to 0, there is a weak or no correlation, meaning the variables (for example, shoe size and hours of sleep) do not move together in a predictable way.

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Answer:

59

Step-by-step explanation:

The three interior angles in a triangle will always add up to 180°, so:

180-93-28=59

The measure of the third angle is 59 degrees.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given are two angles of a triangle.

First angle = 28 degrees

Second angle = 93 degrees

We know that, the sum of the all the three interior angles of a triangle is 180 degrees.

Let x be the measure of third angle.

x + 28 + 93 = 180

x + 121 = 180

Subtracting 121 from both sides,

x = 180 - 121 = 59 degrees

Hence the third angle is 59 degrees.

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Answer:

I think is B .3 < x

hope it helps!

Answer:

-3< X is the correct answer. sorry if i'm to late:(

Step-by-step explanation:

Answer:

1 unit

Step-by-step explanation:

If point J is the midpoint of segment FG with endpoints F(1,4) and G(5,12), then its coordinates are

[tex]x_J=\dfrac{x_F+x_G}{2}=\dfrac{1+5}{2}=3\\ \\y_J=\dfrac{y_F+y_G}{2}=\dfrac{4+12}{2}=8[/tex]

If point K is the midpoint of segment GH with endpoints G(5,12) and H(-1,4), then its coordinates are

[tex]x_K=\dfrac{x_G+x_H}{2}=\dfrac{5+(-1)}{2}=2\\ \\y_K=\dfrac{y_G+y_H}{2}=\dfrac{12+4}{2}=8[/tex]

The measure of JK is

[tex]JK=\sqrt{(3-2)^2+(8-8)^2}=\sqrt{1^2+0^2}=1\ unit[/tex]

Given the coordinates of their endpoints, you find that the points of interest, J and K, have coordinates J(3,8) and K(2,8), respectively. You can then apply the distance formula to find the distance between these two points, resulting in 1.

To find the distance between two points, we can apply the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Given that J is the midpoint of FG, the coordinates of J can be found using the midpoint formula ((x1 + x2) / 2, (y1 + y2) / 2). By applying this formula, we find that J = ((1 + 5) / 2, (4 + 12) / 2) = (3,8).

Similarly, the coordinates of K, as the midpoint of GH, are K = ((5 + (-1)) / 2, (12 + 4) / 2) = (2,8).

Now we can plug the coordinates of J and K into the distance formula to find JK: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((2 - 3)^2 + (8 - 8)^2) = sqrt((1)^2 + 0) = sqrt(1) = 1.

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The greatest whole possible whole number length of the unknown side is 9 inches

Solution:

Two sides of an acute triangle measure 5 inches and 8 inches

The length of the longest side is unknown

We have to find the length of unknown side

The longest side of any triangle is a hypotenuse

For a acute triangle we know:

If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition that relates these three sides are given as:

[tex]c^2<a^2+b^2[/tex]

Here in this sum,

a = 5 inches

b = 8 inches

c = ?

Substituting we get,

[tex]c^2< 5^2+8^2\\\\c^2 < 25 + 64\\\\c^2 < 89\\\\c < 9.4[/tex]

On rounding to nearest whole number,

c < 9

Hence, to the greatest whole possible whole number length of the unknown side is 9 inches

Answer:

The greatest whole possible whole number length of the unknown side is 9 inches

Step-by-step explanation:

Answer:

100,000,000

Step-by-step explanation:

did some research to solve this one, i recommend looking more into to it to ensure that this is the correct answer ;)

The sum of the first 1000 consecutive odd counting numbers is 1,000,000.

To find the sum of the first 1000 consecutive odd counting numbers, we need to recognize a pattern and utilize a simple formula.

Step 1: Identify the Sequence of Odd Numbers

The first few odd counting numbers are:

1, 3, 5, 7, 9, 11, 13, ...

Step 2: Determine the Formula for the Sum

The sum of the first n odd counting numbers can be calculated using the formula:

Sum = n²

This means that the sum of the first n consecutive odd numbers is equal to the square of n.

Step 3: Apply the Formula to Our Problem

In this case, we want to find the sum of the first 1000 odd numbers. Therefore, we set n to 1000:

Sum = 1000²

Step 4: Calculate the Value

Now, we perform the calculation:

Sum = 1000 * 1000 = 1,000,000

Answer:

E

Step-by-step explanation:

Question:

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to  [tex]\frac{1}{2}[/tex].

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4

5n = 3d and 2n - 4 = d - 2

3n = 5d and 2n - 4 = d - 2

Answer:

5n = 3d and 2n – 4 = d – 2

Solution:

Let n be the numerator of the fraction and d be the denominator of the fraction.

Given the numerator and denominator of a fraction are in the ratio of 3 to 5.

This can be written as n : d = 3 : 5.

⇒ [tex]\frac{n}{d}= \frac{3}{5}[/tex] – – – – (1)

Do cross multiplication, we get

⇒ 5n = 3d

When the numerator and denominator are decreased by 2, the fraction is equal to [tex]\frac{1}{2}[/tex].

⇒ [tex]\frac{n-2}{d-2}= \frac{1}{2}[/tex]

Do cross multiplication, we get

⇒ 2(n –2)=1(d – 2)

⇒ 2n – 4 = d – 2

Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.

Answer:

5n = 3d and 2n – 4 = d – 2 is the answer

Step-by-step explanation:

Answer:

Dividing 4 × 1  by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100

Step-by-step explanation:

i) the value of 4 in 64.723 is given by 4 × 1 = 4, because 4 is the one's place

ii) the value of 4 in 9.048 is is given by 4 × 0.01 = [tex]\dfrac{4}{100}[/tex] = 0.04, because 4 is in the hundredth's place

iii) the value of 4 in 64.723 is 100 times the value of 4 in 9.048 which we get by dividing 4 × 1  by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100

Answer:

100

Step-by-step explanation:

Final answer:

The fraction for 45 divided by 20 is written as 45/20, which can be simplified by dividing both the numerator and the denominator by their greatest common divisor, 5. This results in a simplified fraction of 9/4.

Explanation:

To find the fraction for 45 divided by 20, you can write it directly as a fraction, which is 45/20. This fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 45 and 20 is 5. To simplify the fraction, we divide both the numerator and denominator by 5.

Simplified fraction:
45 ÷ 5 = 9
20 ÷ 5 = 4
So, the simplified fraction for 45 divided by 20 is 9/4.

Answer:

Ali would run 2.8 miles in 24 minutes.

Answer:

A is 198

B is 22

Step-by-step explanation:

22 × 9 = 198

22 + 198 = 220

Answer:

The volume of required foam is 0.1 cm³  

Step-by-step explanation:

Given as :

The volume of box = v = 113.14 cm³

The radius of the crystal ball = r = 3 cm

Let The volume of required foam = V cm³

According to question

Volume of  crystal ball = [tex]\dfrac{4}{3}[/tex] × π × radius³                        where π = 3.14

i.e Volume of ball = [tex]\dfrac{4}{3}[/tex] × π × 3³

Or, Volume of ball = [tex]\dfrac{4}{3}[/tex] × π × 27

Or, Volume of ball = [tex]\dfrac{4}{3}[/tex] × 3.14 × 27

Or, Volume of ball = 4 × 3.14 × 9

Or, Volume of ball = 113.04 cm³

Again

∵ volume of crystal ball = v' = 113.04 cm³

So ,  The volume of required foam = volume of box - volume of crystal ball

Or, V =  v - v'

Or, V = 113.14 cm³ -  113.04 cm³

∴   V = 0.1 cm³

So, The volume of required foam = V = 0.1 cm³

Hence, The volume of required foam is 0.1 cm³  . Answer

Answer:

B and B for plato

Step-by-step explanation:

Final answer:

The probability of picking a 1 and then a 12 from a deck of cards numbered 1-12 with replacement is 1/144, since each event is independent and each card has an equal chance of being selected.

Explanation:

The student asked about the probability of selecting a 1 and then a 12 from a deck of cards numbered 1-12, with replacement in between the picks. To find this, we need to consider the events independently, since the card is replaced after the first draw, meaning the probability of the second draw is unaffected by the first.

The formula to calculate the probability of independent events is P(A and B) = P(A) × P(B), where P(A) is the probability of the first event and P(B) is the probability of the second event occurring. Since each card has an equal chance of being picked from the deck, and there are 12 cards in total, the probability of picking any specific card, like a 1 or a 12, is 1/12.

Therefore, the probability of picking a 1 first and then a 12 is P(1 and then 12) = P(1) × P(12), which is equal to (1/12) × (1/12) = 1/144. So, the final probability is 1/144, or about 0.00694.

Answer:

Step-by-step explanation:

No. Of quarters n(Q)= 3

No. Of dimes n(D) = 5

No. Of nickels n(N) = 2

Total T = 3+5+2 = 10

Prob(D) = n(D)/T = 5/10 = 1/2

Now there are 9 left since it is not replaced back

Prob(Q) = 3/9 = 1/3

Prob(D and Q) = 1/2 × 1/3 = 1/6

The probability you will pick a dime and then a quarter without putting the dime back in your pocket is 1/6

Probability is the likelihood or chance that an event will occur

If you have 3 quarters, 5 dimes, and 2 nickels in your pocket, the total coins you have will be:

Total outcome = 3 + 5 + 2

Total outcome = 10

Probability of picking a dime = 5/10 = 1/2
Probability of picking a quarter = 3/9 = 1/3

Pr( a dime and then a quarter without putting the dime back in your pocket) = 1/2 * 1/3 = 1/6

Hence the probability you will pick a dime and then a quarter without putting the dime back in your pocket is 1/6

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To find the scale factor, compare the corresponding dimensions of the two shapes. Divide the dimension of shape A by the corresponding dimension of shape B to calculate the scale factor.

In order to find the scale factor applied to shape B to make shape A, we need to compare the corresponding dimensions of the two shapes. The scale factor is determined by dividing the dimension of shape A by the corresponding dimension of shape B. In this case, we compare the lengths of the shapes, so the scale factor is determined by dividing the length of shape A by the length of shape B.

Let's calculate the scale factor:

Therefore, the scale factor is 2/3 for all dimensions of shape B to make shape A.

Answer:

y=4x-4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-8)/(1-3)

m=-8/-2

m=4

y-y1=m(x-x1)

y-8=4(x-3)

y=4x-12+8

y=4x-4

Answer:y - 4x + 4 = 0

Step-by-step explanation: Formula for equation of a line passing through two coordinates is

y - y₁                 y₂ - y₁

______  =       ______

x - x₁                  x₂ - x₁

Therefore,            y₂ -y₁                                                                                                  

        y - y₁      =      ____      ×    ( x - x₁ )

                             x₂ - x₁

where x₁ =3, y₁ =8, x₂ = 1 and y₂ 0

Now substitute for the value

y - 8 = 0 - 8

         ______    x     ( x - 3 )

           1 - 3

Therefore y - 8 = -8/-2 × (x - 3 )

y - 8 = -8/-2 × (x - 3)

y -8 = 4 × (x - 3 )

y - 8 = 4( x - 3 )

y - 8 = 4x - 12, when the brackets are open,

So y = 4x - 12 + 8

    y = 4x - 4

Therefore the equation of the line is

y - 4x + 4 = 0

Answer

It would be 2 liters

Answer:

1.99 liters is the correct answer

Step-by-step explanation:

Answer:

$ 150

Step-by-step explanation:

Given:

Cost price of a microwave = $105

Discount % = 30

Question asked:

what was the price of the microwave before sale = ?

Solution:

Let the price of the microwave before sale = [tex]x[/tex]

Price before sale - 30 % discount = cost price of  microwave (by Javier)

[tex]x - 30\% of x = 105[/tex]

[tex]x - \frac{30x}{100} = 105[/tex]

[tex]\frac{70x}{100} = 105\\[/tex]

Multiplying both side by 100

[tex]70x = 105 \times 100[/tex]

[tex]70x = 10500[/tex]

Dividing both side by 70

[tex]x = \frac{10500}{70} \\x = 150[/tex]

x = price of the microwave before sale = $ 150

Thus, price of the microwave before the sale = $150