if f(x)=5x-2 and g(x)=2x+1, find (f+g)(x)
A.7x-3
B.3x-1
C.7x-1
D.4x-3

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.

90/18 equals 5 minutes for each window,so after 3 hours they would paint 36 windows.            180 minutes in three  hours so 180/5=36

All you have to do is add 31300000+23200000 which equals 54500000. Next subtract  54500000 from 193800000 which equals 139300000. So plant 2 is 139.3 million miles away from the sun

Let Planet 2 = X

Planet 1 = X + 31.3

Planet 3 = x +(31.3+23.2) = x + 54.5

Add the 3 distances together:

x + x +31.3 + x + 54.5 = 193.8

3x + 85.8 = 193.8

Subtract 85.8 from each side:

3x = 108

Divide both sides by 3:

x = 108 / 3

X = 36

Planet 2 = 36 million miles

Planet 1 = 36 + 31.3 = 67.3 million miles

Planet 3 = 36 + 54.5 = 90.5 million miles

36 + 67.3 + 90.5 = 193.8

( - ∞, ∞ )

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

or ( - ∞, ∞ ) ← in interval notation

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!!

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

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

Open that attachment and that should be the answer.

Answer:

1.178 x 10^35 Joule

Step-by-step explanation:

Energy produced by sun in one second = 3.8 x 10^27 J

Energy produced by sun in a year = Energy produced by sun in one second x number of seconds in one year

According to the question, the number of seconds in one year

                                                       = 31,000,000 seconds

Energy produced by the sun in one year = 3.8 x 10^27 x 31,000,000

                                                                    = 1.178 x 10^35 Joule

Thus, the energy produced by the sun in a year is 1.178 x 10^35 Joule.

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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#SPJ2

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

ANSWER

The correct answer is A

EXPLANATION

We divide the hallway into 2 rectangles as shown in the diagram attached.

The length of the longer is 25 and the with is 5 feet.

The area of this rectangle

[tex]=25\times 5[/tex]

[tex]=75[/tex] square feet

The smaller rectangle has length 6 feet and width 12 feet

The area of the smaller rectangle

[tex]=6\times 12[/tex]

[tex]=72[/tex] square feet

Adding the two areas gives the area of the hallway

[tex]=125+72=197[/tex] square feet

To convert the ratio 2.5 metres to 60 centimeters to the form 1:n we first change metres to centimeters, which gives 250 cm to 60 cm, then divide 250 by 60 to get n = 4.1667.

To find the value of n when the ratio is converted to the form 1:n, we need to express both measures in the same unit. We know that 1 metre is equivalent to 100 centimeters, so we can convert 2.5 metres to centimeters:

2.5 metres times 100 cm/metre = 250 cm

Now, we have the two measures in centimeters: 250 cm to 60 cm. Next, we divide both these numbers to find the ratio in the form 1:n.

250 cm / 60 cm = n

We simplify the ratio by dividing both numbers by 60 cm:

n = 250 cm / 60 cm = 4.1667

Therefore, the ratio of 2.5 metres to 60 centimeters expressed as 1:n is approximately 1:4.1667.

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.

If 98 - 32 = 66,

then x = 66°

0.98  0.0 = tenths 0.00 = hundredths 0.000 = thousandths

[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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(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)

-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).

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!

The given angles are known as alternate interior angles.

For line L and M to be parallel, the two given angles must be the same.

Set them to equal each other and solve for X.

7x - 7 = 4x +14

Add 7 to each side:

7x = 4x +21

Subtract 4x from each side"

3x = 21

Divide both sides by 3:

X = 21 / 3

X = 7

Answer:

7

Step-by-step explanation:

i need points

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

y + 4 = - 56(x - 8)

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 56 and (a, b) = (8, - 4)

y  + 4 = - 56( x - 8 ) ← in point-slope form

it will be 1.33= 1 1/3

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

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.

The answer is; 24/75 of the entire cake remained

If 2/5 of the initial cake was eaten, the 3/5 is what remained

MInu ate 1/3 of the 3/5 = 3/15

3/5 – 3/15 = 6/15 remained

Her brother ate; 1/5 of 6/15 = 6/75

6/15 – 6/75 = 24/75 remained

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