marcela's dog gained 4.1 kilograms in two months. Two months ago, the dog's mass was 5.6 kilograms. What is the dog's current mass?

Answer:  

Part A:  The function  [tex]f(x)[/tex] has greater slope than function [tex]g(x)[/tex]

Part B:  [tex]g(x)[/tex] has a greater y-intercept than [tex]f(x)[/tex].

Step-by-step explanation:

Part A:

For finding the slope of [tex]f(x)[/tex], first we need to pick any two order pairs from the given table in form of [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] and then use the formula of slope:  [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Lets choose two points as [tex](-1, -15)[/tex] and [tex](0, -10)[/tex]

So,  [tex]m= \frac{-10-(-15)}{0-(-1)}= \frac{-10+15}{0+1}= 5[/tex]

Thus, the slope of the function [tex]f(x)[/tex] is 5.

Another function is:  [tex]g(x)=2x+8[/tex]

The function [tex]g(x)[/tex] is given in standard slope intercept form [tex]y= mx+b[/tex]. So, we will get  [tex]m=2[/tex]

Thus, the slope of the function [tex]g(x)[/tex] is 2.

So, the function  [tex]f(x)[/tex] has greater slope than function [tex]g(x)[/tex]

Part B:

For function [tex]f(x)[/tex], there is one ordered pair as [tex](0, -10)[/tex]. This point is lying on the y-axis. So, the y-intercept of [tex]f(x)[/tex] is -10.

Now, in [tex]y= mx+b[/tex] form, [tex]'b'[/tex] is represented as the y-intercept. So, for function [tex]g(x)=2x+8[/tex], the value of [tex]'b'[/tex] will be 8.

Thus, the y-intercept of [tex]g(x)[/tex] is 8.

As  [tex]8>-10[/tex],

So, [tex]g(x)[/tex] has a greater y-intercept than [tex]f(x)[/tex].

( - ∞, ∞ )

h(x) is a polynomial and is defined for all real values of x thus domain ∈ R

or ( - ∞, ∞ ) ← in interval notation

it will be 1.33= 1 1/3

-1 > -4

3 > 0

1 > -2

3 > -5

I don't understand the second one sorry.

The inequalities should be matched with the graphs that represent them as follows;

6. 4y + 3 ≤ y + 6   ↔ graph C.

7. -2y > 2   ↔ graph A.

8. y/3 < -1   ↔ graph D.

9. 3y ≤ 2y + 3   ↔ graph B.

Based on the information provided, we would determine the solution set for each of the given inequality by simplifying as follows;

4y + 3 ≤ y + 6

By rearranging and collecting like terms, we have the following;

4y - y ≤ 6 - 3

3y ≤ 3

By dividing both sides of the inequality by 3, we have;

y ≤ 1 (solid dot at point 1 and it decreases to the left).

Part 7.

-2y > 2

By dividing both sides of the inequality by -2, we would flip (reverse) the inequality symbol;

-2y/-2 > 2/-2

y < -1 (hollow dot at point -1 and it decreases to the left).

Part 8.

y/3 < -1

By cross-multiplying, we have;

y < -3 (hollow dot at point -3 and it decreases to the left).

Part 9.

3y ≤ 2y + 3

By rearranging and collecting like terms, we have the following;

3y - 2y ≤ 3

y ≤ 3 (solid dot at point 3 and it decreases to the left).

Hello!

[tex]7d + 12 -4d -3\\[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓

First this problem it should be the group like terms.

[tex]7d-4d+12-3[/tex]

Then you add similar elements.

[tex]7d-4d=3d[/tex]

[tex]3d+12-3[/tex]

You can also add or subtract by the numbers.

[tex]12-3=9[/tex]

[tex]=3d+9[/tex]

Answer⇒⇒⇒3d+9

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

we can solve this by first combining like terms: our like terms in this equation are d and plain numbers

so, this means that we can combine the d's with the d's and the plain numbers with the plain numbers

so,

7d + 12 - 4d - 3 = 0

3d+ 9 = 0

next, we have to get our plain numbers on one side of the equal sign, and our numbers with the d's on the other side of the equal sign: we do this by doing the opposite of what the number is doing on the side it is on, since the 9 is being subtracted from the left hand side, we will subtract it from both sides:

3d = -9

next, we want to get rid of the 3 next to the d

to do this, we would divide the 3 on both sides since it is being multiplied to the d on the left hand side:

d = -3

this is our final answer: d = -3

The x- intercept would be (3,0) or 3

The y-intercept would be (0,-4) or -4

In A, traveled hours will be increased if the distance traveled is increased and hence it is in direct variation.

In B, both x and y represent the length of a table and the difference is in units only. So, it is also in direct variation.

In C, more number of $1-off coupons used, more money will be saved and hence it is also in direct variation.

In D, if the speed is increased, then the time to travel 60 miles will be decreased. Hence it is not in direct variation.

Answer:

x = time it takes to travel 60 miles, and y = speed traveled

Step-by-step explanation:

2 and 5 8th   Convert  to improper fraction.

so, after you convert it. It should be like this

11/12 divided by 21/8

then use reciprocal so it will be

11/12 multiply by 8/21

then you got 88/252

then simplify it, 88 divided 4, and 252 divided 4

so the answer is 22/63.

The division of 11/12 by 2 and 5/8 (or 21/8) results in the fraction 22/63 after simplification.

To solve this problem, we first need to express everything as a fraction. So, '2 and 5/8' can be written as 21/8 (that is 2 whole and 5/8).

The question is asking us to divide 11/12 by 21/8. To perform division with fractions, we multiply by the reciprocal of the divisor. So, we rewrite this as 11/12 multiplied by 8/21.

Performing this multiplication gives us 88/252. This can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4, to get 22/63.

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Hey there!!

Given equation :

... ( x - 3 ) ( 3x - 4 )

... ( x ) ( 3x ) + ( x ) ( -4 ) + ( -3 ) ( 3x ) + ( -3 ) ( -4 )

... 3x² - 4x - 9x + 12

... 3x² - 13x + 12

Hope my answer helps!!

We are given the results of an election:

Candidate Fraction of votes

Johnson = [tex]\frac{1}{9}[/tex]

Smith  = [tex]\frac{7}{18}[/tex]

Dragovic = [tex]\frac{1}{2}[/tex]

Now, we need to find the difference between the fractions of votes received by Dragovic and Johnson.

Therefore, difference is :

[tex]\frac{1}{2} - \frac{1}{9}[/tex]

Taking common denominator of 2 and 9 is 18.

[tex]=\frac{1\times9}{2\times 9} - \frac{1\times 2}{9\times 2}[/tex]

[tex]=\frac{9}{18} - \frac{2}{18}[/tex]

[tex]=\frac{9-2}{18}[/tex]

[tex]=\frac{7}{18}[/tex]

Therefore, the difference between the fractions of votes received by Dragovic and Johnson is [tex]\frac{7}{18}[/tex].

Answer:

Step-by-step explanation:

7/18

Answer:

p^2 + 3p - 10

Step-by-step explanation:

Use the so-called "foil" method of multiplication of binomials:

p^2 -2p + 5p - 10, or p^2 + 3p - 10

Given:-

... ( p+5 )( p-2 )

When we have an equation like,

( a + b ) ( a - c )

... a² + ba - bc - ac

We have,

( p+5 )( p-2 )

... p² - 2p + 5p - 10

... p² + 3p - 10 Is the answer.

Hope it helps!

can be simplified as 5-9+7=-4+7=3

Q: evaluate (+5)-(+9)-(-7

A: if you remember how to add integers correctly, your answer would have been 3

(i added a picture to help you a little bit more)

hope this helps! ❤ from peachimin

(6, 2 )

substitute x = 5 into the equation and solve for y

6y + 8 = 20 ( subtract 8 from both sides )

6y = 12 ( divide both sides by 6 )

y = [tex]\frac{12}{6}[/tex] = 2

the ordered pair is (5, 2 )

plug in 5

4(5)=6y+8

20=6y+8

12=6y

2=y

(5,2)

Answer:

A. 4.26 in^2

Step-by-step explanation:

Step 1: Find the area of the sector DBC. Here we have to use the formula.

Area of a sector = Central Angle/360 *π[tex]r^{2}[/tex]

The area of the sector DBC = (54/360)*3.14*[tex]8^{2}[/tex]

= 30.16

Step 2: Area of segment CFD = Area of the sector DBC - Area of the ΔCBD

= 30.17 - 25.9

Area of segment CFD = 4.27in^2

Answer:

4.24 in ^2

Step-by-step explanation:

extra added: Use 3.14 for the value of π. Round your answer to the nearest hundredths if necessary.

I say when she starting to put weight on the trampoline for the first part she making energy you see. Same thing with the second picture she charging up the energy more and more  then when she jumps all that energy is being released making her jump up in the air higher so i say the  3rd picture first then 2nd then first because she preparing the energy to jump then she is adding more energy after that she releases it and jumps high

yes it is, -4x+9=13, subtract 9 from both sides, -4x=4, divide by negative 4 from both sides, x= -1. Hope I helped!

-4x + 9 =  13

-4x =  4

 x = -1

Answer is Yes

x = - 1 is  a solution

Final answer:

Alice hit 10 home runs and Peter hit 8 home runs that season. The width of the parallelogram is 16 meters and the length is 20 meters.

Explanation:

To solve this problem, we need to set up an equation. Let's say that Alice hit x home runs. Then, Peter hit twice the difference of home runs Alice hit and 6, or 2(x - 6). Together, they hit 18 home runs. Setting up the equation, we have x + 2(x - 6) = 18. Solving for x, we get 3x - 12 = 18, 3x = 30, and x = 10. So, Alice hit 10 home runs and Peter hit 2(10 - 6) = 8 home runs that season.

To find the length and width of a parallelogram, we need to use the information given in the problem. Let's say the width of the parallelogram is W. The length of the parallelogram is then 4 meters more than the width, or W + 4. The perimeter of a parallelogram is given by the formula 2(length + width), so we have 2(W + W + 4) = 72. Simplifying the equation, we get 4W + 8 = 72. Subtracting 8 from both sides, we get 4W = 64. Finally, dividing both sides by 4, we find that the width of the parallelogram is 16 meters and the length is 16 + 4 = 20 meters.

Solution-

A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row.

As all the lights start out off, in the first pass all bulbs will be turned on.

In the second pass all the multiples of 2 will be off and rest will be turned on.

In the third pass all the multiples of 3 will be off, but the common multiple of 2 and 3 will be on along with the rest. i.e all the multiples of 6 will be turned on along with the rest.

In the fourth pass 4th light bulb will be turned on and so does all the multiples of 4.

But, in the sixth pass the 6th light bulb will be turned off as it was on after the third pass.

This pattern can observed that when a number has odd number of factors then only it can stay on till the last pass.

1 = 1

2 = 1, 2

3 = 1, 3

4 = 1, 2, 4

5 = 1, 5

6 = 1, 2, 3, 6

7 = 1, 7

8 = 1, 2, 4, 8

9 = 1, 3, 9

10 = 1, 2, 5, 10

11 = 1, 11

12 = 1, 2, 3, 4, 6, 12

13 = 1, 13

14 = 1, 2, 7, 14

15 = 1, 3, 5, 15

16 = 1, 2, 4, 8, 16

so on.....

The numbers who have odd number of factors are the perfect squares.

So calculating the number of perfect squares upto 1800 will give the number of light bulbs that will stay on.

As,  [tex]\sqrt{1800} =42.42[/tex]  , so 42 perfect squared numbers are there which are less than 1800.

∴ 42 light bulbs will end up in the on position. And there position is given in the attached table.

Old holiday light strings with bulbs that act as open switches will go out entirely if one bulb fails, while new versions with bulbs that short circuit will keep the remaining bulbs lit. Each bulb in an old 40-bulb series string on 120 V would be 3 V, while in a new 39-bulb series string it would be approximately 3.08 V per bulb. In a series circuit, a 60 W bulb would be brighter than a 100 W bulb.

When holiday lights wired in series have a bulb that burns out, in the old versions with bulbs that act like an open switch, the entire string of lights will go out. This is because the electrical circuit is broken, and current cannot flow through the circuit anymore. If the string operates on 120 V with 40 identical bulbs, the normal operating voltage of each bulb when all are functioning is 120 V / 40 bulbs = 3 V per bulb.

In contrast, newer versions are designed so that when a bulb burns out, it acts like a closed switch. This means the rest of the bulbs will stay lit because the circuit remains closed, allowing current to continue flowing. If one bulb short circuits and there are 39 remaining bulbs, each bulb will have an operating voltage of 120 V / 39 bulbs ≈ 3.08 V per bulb.

Regarding two household lightbulbs rated 60 W and 100 W connected in series, the one with the higher resistance (which is typically the lower-wattage bulb) will be brighter because it drops more voltage across it compared to the higher-wattage bulb with lower resistance.

I think it is 1.6m but I'm not sure

[tex]\bf 2\sqrt{54}+5\sqrt{24}\qquad \begin{cases} 54=2\cdot 3\cdot 3\cdot 3\\ \qquad 2\cdot 3\cdot 3^2\\ \qquad 6\cdot 3^2\\ 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 6 \end{cases}\implies 2\sqrt{6\cdot 3^2}+5\sqrt{2^2\cdot 6} \\\\\\ 6\sqrt{6}+10\sqrt{6}\implies \stackrel{\textit{adding like-terms}}{16\sqrt{6}}[/tex]

The simplest radical form of the equation [tex]2\sqrt{54} + 5\sqrt{24}[/tex] is [tex]16 \sqrt{6}[/tex].

We have to determine, the simplest radical form [tex]2\sqrt{54} + 5\sqrt{24}[/tex].

To convert the given equation into radical form following all the steps given below.

Equation; [tex]2\sqrt{54} + 5\sqrt{24}[/tex].

                   [tex]= 2\sqrt{54} + 5\sqrt{24}\\\\=2 \sqrt{2 \times 3 \times 3 \times 3} + 5\sqrt{2 \times 2 \times 2\times 3}[/tex]

        [tex]=2 \sqrt{2 \times 3 \times 3 \times 3} + 5\sqrt{2 \times 2 \times 2\times 3}\\\\= 2 \sqrt{2 \times 3 \times 3^2} + \sqrt{2^2\times 2 \times 3} \\\\[/tex]

                   [tex]= 2\times 3\ \sqrt{2 \times 3 } + 5 \times 2 \sqrt{2 \times 3}\\\\= 6 \sqrt{6} \ + 10 \ \sqrt{6}\\\\= 16\sqrt{6}[/tex]

Hence, The required simplest radical form of the equation [tex]2\sqrt{54} + 5\sqrt{24}[/tex] is [tex]16 \sqrt{6}[/tex]

To know more about the Radical form click the link given below.

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IQ scores and GPAs are positively correlated with a strong relationship. Similarly, IQ and SAT scores are positively correlated with a strong relationship. Because the variable IQ is in both sets, there is likely to be a relationship between the other two variables, GPAs and SAT scores.

Correlation is a measure which describes if an association or relationship exists between two variables. Since there is a positive relationship between IQ and both GPA and SAT score, then GPA and SAT should correlate.

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The equation of the line that passes through the points (6,0) and (2,-7) is '7x - 4y = 42' when transformed into the standard form.

In mathematics, especially in linear algebra, the standard form of the line is a way of describing a specific line on the plane. We can get this by using two points through which the line passes. In this case, we have the points (6,0) and (2,-7).

First, we calculate the slope using the formula (y2 - y1) / (x2 - x1). Substituting our values, we have (-7 - 0) / (2 - 6) = -7 / -4 = 7/4. So, the slope is 7/4.

Next, we find the y-intercept (b) by substituting one of the points into the equation y = mx + b. Using the point (6,0), we get 0 = 7/4 * 6 + b. Solving for b, we find that b = -21/2.

The equation is then y = 7/4x - 21/2. To convert this to the standard form, we multiply all parts by 4 to remove the fraction. The equation then becomes 4y = 7x - 42. After arranging, we obtain our final equation: 7x - 4y = 42.

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0.98  0.0 = tenths 0.00 = hundredths 0.000 = thousandths

5w + 9z = 2z + 3w

Subtract 2Z from each side:

5w + 7z = 3w

Subtract 5w from each side:

7z = -2w

Divide both sides by -2:

w = 7z / -2

We have been given an equation  and we are asked to find value of w from our given equation.

[tex]5w+9z=2z+3w[/tex]

First of all we will subtract 3w from both sides of our equation.

[tex]5w-3w+9z=2z+3w-3w[/tex]

[tex]5w-3w+9z=2z[/tex]

Now let us subtract 9z from both sides of our equation.

[tex]5w-3w+9z-9z=2z-9z[/tex]  

[tex]5w-3w=2z-9z[/tex]

[tex](5-3)w=(2-9)z[/tex]

[tex]2w=-7z[/tex]

Now let us divide both sides of our equation by 2.

[tex]\frac{2w}{2}= \frac{-7z}{2}[/tex]

Upon cancelling 2 from left side of our equation we will get,

[tex]w=\frac{-7}{2} z[/tex]

Therefore, we can see that [tex]w=\frac{-7z}{2} [/tex].

First, you need to add 367 and 863. That should equal 1230. Then, subtract 8631 from 1230. That should get you -7401. So, there’s you’re answer. To check it, add them together. Hope this helps :)

Answer: The another number should be -7401.

Step-by-step explanation:

Since we have given that

sum of 367 and 863 is equal to sum of 8631 and another number.

Let the another number be 'x'.

According to question, it becomes,

[tex]367+863=8631+x\\\\230=8631+x\\\\1230-8631=x\\\\-7401=x[/tex]

Hence, the another number should be -7401.

Trey is given expression: [tex]\frac{12}{15} +\frac{1}{10}.[/tex].

He got the answer [tex]\frac{13}{25}[/tex].

Solution: The denominators of the given expression are 15 and 10.

Therefore, in order to add the fractions, we need to find common denominator of 15 and 10.

Common denominator is the least common denominator.

Least common denominator of 15 and 10 is 30.

Therefore, Trey need to make both denominator as 30.

12/15 would become 12×2/15×2 = 24/30.

1/10 would become 1 × 3/ 10 × 3 = 3/30.

On adding 24+3, we get 27.

So, 24/30 + 3/30 = 27/30.

And 27/30 could be written in simplest fractions as 9/10.

But Trey got answer 13/25.

Therefore, Trey answer incorrect.

He must find common denominator (LCD) first and then add the fractions.

If 98 - 32 = 66,

then x = 66°