if f(x)=x+3 g(x)=2x+6 find (f+g)(x)

Answer:

4. -2s^9

7. 8b^10

Step-by-step explanation:

First, focus on the number part of the expression. For 4), multiply -2 x -1 x -1 = -2. Then, look at the exponents. When you're multiplying exponents with the same base (in number 4, the base is s), you can add the exponents.

2+3+4 = 9; which makes it s^9. Multiply -2 x s^9, which gives you -2s^9.

Same thing for 7). Multiply all the numbers first. this gives you 8. (Remember two negatives equals a positive). Add all of the exponents of b together, which gives you 10. (when a variable has no exponent, it means that the exponent is 1.) Multiplying 8 and b^10 should give you 8b^10.

It may help to brush up on exponent rules and sign rules.

Answer:

Length of side AB = 5.6 cm

Step-by-step explanation:

From the figure attached.

In right triangle ABC,

m∠ABC = 62°

m(BC) = 12 cm

By applying Cosine rule in this triangle,

Cos62° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

Cos62°= [tex]\frac{AB}{BC}[/tex]

0.46947 = [tex]\frac{AB}{12}[/tex]

AB = 12 × 0.46947

AB = 5.63

     ≈ 5.6 cm  

Therefore, length of side AB = 5.6 cm

Length of side AB = 5.6 cm.

Since In right triangle ABC,

m∠ABC = 62°

m(BC) = 12 cm

Here we used the cosine rule

So, it is

[tex]Cos 62 = AB\div BC\\\\0.46974 = AB\div 12[/tex]

So, AB = 5.6 cm

hence, Length of side AB = 5.6 cm.

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Answer:

Complete question:

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10,000 cm^3 cubed. The base of the box is 25cm by 10cm.

How tall is the box of cereal?

Answer: 40cm

Step-by-step explanation:

Given that :

A box is normally in the shape of a cube

formula of volume of a cube;

We want to find the height(tallness)

Volume=LengthxWidthxHeight

Volume = 10,000cm^3

Base of box = 25cm by 10cm,

Base of box = Length × width

Therefore:

Length = 25cm, Width = 10cm

Volume = Lengh × Width × Height

10,000cm^3 = 25cm × 10cm × Height

10,000cm^3 = 250cm^2 × Height

Height = 10,000cm^3 ÷ 250cm^2

Height = 40cm

Answer:

384m

Step-by-step explanation:

24 x 4 = 96

96 x 4 = 384

Answer:

the real answer is 96

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

3-2x=-1.5x

3=2-1.5x

3=0.5x

X=(3÷0.5)=6

Answer:

shorter base = 6 yd

longer base = 8 yd

area of playground = 42 yd^2

Step-by-step explanation:

The question tells you that the shorter side is equal to the width, which is 6 yds. The bases of the triangles on either side are 1 yd. Since there are two, add 1 twice to 6 (6+1+1). This gives you 8 yd for the longer base. You're right about the area, just use the trapezoid area formula: 1/2h(a+b).

Answer:

74594.2 m

Step-by-step explanation:

Heron's formula

area=sqrt(p(p-a)(p-b)(p-c)) where p=(a+b+c)/2

[tex]\sqrt{641.5(641.5 - 503)(641.5 -415)(641.5 - 365)}[/tex]The total amount of area of the triangle which she has covered is 74594.17.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Area of triangle = 1/2 ×base ×height.

Given that A woman hikes 503 m, turns and jogs 415 m, turns again, and runs 365 m returning to her starting point

so the triangle which is made by the woman(no matter what kind of triangle is) has a side as

A = 503m , B = 415m , C = 365m

Now S = (A + B + C)/2

S = (503 + 415 + 365)/2

S = 641.5

Now the area of a triangle is given by

Area = [tex]\sqrt{S(S - A)(S -B)(S - C)}[/tex]

Area = [tex]\sqrt{641.5 (641.5 - 503)(641.5 -415)(641.5 - 365)}[/tex]

Area = 74594.17 hence, the area of the triangle will be this.

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Answer:

Henry=12, Bernard=18

Step-by-step explanation:

let Henry's age = x

let Bernard's age= 1.5x

according to d passage 6yrs ago x×2=1.5x

mathematically that is (x-6)2=1.5x-6

2x-12=1.5x-6

2x-1.5x=-6+12

0.5x=6

divide both sides by the co-efficient of x which is 0.5 can also be written as ½

there fore x=6÷½

x=Henry's age=12years

1.5x=Bernard's age=12×1.5=18years

Answer:

see below

Step-by-step explanation:

Because there is the right angle symbol on the chart these angles are complementary meaning thety have a sum of 90°.

Answer: 30

Step-by-step explanation:

Hi, to answer this question, first we have to multiply the number of slices of cheese (5) by the area of each slice (125.7)

125.7 (5) = 628.5 in2

Finally we have to divide that result by the area that each handful of cheese covers (21 in2)

628.5 / 21 = 29.92 = 30 handful of cheese

Feel free to ask for more if needed or if you did not understand something.  

Answer:

30

Step-by-step explanation:

Answer:

A. If none of the output values are repeated, the relation is a function

Step-by-step explanation:

The reason why A is correct stems from the concept of the vertical line test. If each x-value has their own respective output (y-value), then the relation is a function.

Choice B just states that if none of the x-values are repeated. then the relation is a function. This is not correct because it doesnt follow the vertical line test, which analyzes if any y-values are being repeated

Choice C and D doesnt have any correlation with the vertical line test because an x-value doesnt have to equal a y-value to make the relation a function. Vice versa for any y value being equal to any x-value.

Answer:

see below

Step-by-step explanation:

a. H 1, H2 ,H3  T1 ,T2, H3

b  6 possible outcomes

c 2 outcomes for the coin ( h,T) 3 outcomes for the spinner

2*3 = 6

Answer: -4

Step-by-step explanation:

Do -6 x 2 to get -12, then divide by 3 to get -4

Thats assuming this is a fraction and not an actual division sign

Considering the number of student tickets sold as x.

5x+7*120=1840

5x+840=1840

5x=1840-840

5x=1000

x=1000/5

x=200

200 student tickets were sold.

Each solution is a pair of numbers (x,y) that make the equation true. Solving a linear equation usually means finding the value of y for a given value of x. If the equation is already in the form y = mx + b, with x and y variables and m and b rational numbers, then the equation can be solved in algebraic terms.

I really hope that this helps you if u have any more questions ask. :>

Answer:

Each solution is a pair of numbers (x,y) that make the equation true. Solving a linear equation usually means finding the value of y for a given value of x. If the equation is already in the form y = mx + b, with x and y variables and m and b rational numbers, then the equation can be solved in algebraic terms.

Step-by-step explanation:

Solving an equation means finding the value or values for which the two expressions on each side of the equals sign are equal. One of the most common methods used to solve equations is the balance method.

Imagine an equation as a set of scales. The scales will stay in balance as long as the same operation (addition, subtraction, multiplication or division) is applied to both sides.

Example: y = 2x + 1 is a linear equation:

line on a graph

The graph of y = 2x+1 is a straight line

When x increases, y increases twice as fast, so we need 2x

When x is 0, y is already 1. So +1 is also needed

And so: y = 2x + 1

Here are some example values:

x y = 2x + 1

-1 y = 2 × (-1) + 1 = -1

0 y = 2 × 0 + 1 = 1

1 y = 2 × 1 + 1 = 3

2 y = 2 × 2 + 1 = 5

Well, we would find the volume of both the cylinder and the cone.

The formula to find the volume of a cylinder is V =  \pi  r^{2} h.

The formula to find the volume of a cone is V =  \frac{1}{3}  \pi  r^{2} h.

Now, when using pi (the symbol  \pi ), if the problem asks to use the approximate value of pi as 3.14, we'll use 3.14 to represent pi. If the problem asks for the exact answer, then we'll just put the pi sign next to our final answer we've gotten.

We can do both ways to solve with pi. Tho let's solve using the approximate value of pi.

One more thing. When there's an exponent in the problem, (such as  r^{2}  in the problem), that just means you would multiply the base, (which is r in  r^{2} ), by itself the number of times the exponent, (which is the number 2 in  r^{2} ), shows. For example, if it was  3^{2} , that would just mean we would multiply 3 times itself twice. So  3^{2}  would be the same as 3 times 3, which is 9. When you deal with variables in a problem, (the letters used to represent a value in the equation, such as a, b, c, d, etc.), they're solved in multiple ways. If a number is next to a variable, (for example, 3b), it would mean you are supposed to multiply the number times the variable. If a number is next to parenthesis, that would mean you would multiply the number times the answer from the parenthesis. In formulas, when all the letters and numbers are squished together in one line, that means you would multiply all of them times each other after they're individually solved. In this problem, r = radius and h = height.

So without further-a-do, let's begin! :)

So the question says that the radius of the cylinder is 10 centimeters, and the height is 20 centimeters. According to the formula given above, we would multiply the radius times itself twice, which would be 10 times 10, which equals 100, then multiply it by the height which is 20, so 100 times 20 = 2,000. If we were to find the exact volume, it would be 2,000 with the pi sign next to it, which would be 2,000 \pi . Though, let's find the volume with the approximate value of pi, 3.14. So 2,000 times 3.14 is 6280. The exact volume of the cylinder is 2,000 \pi and the approximate volume is 6280.

Now after we find the volume of the cone, we would need to find out how many times we'd need to use the cone to fill up the cylinder's volume.

To find the volume of the cone, we would do the same as last time. Since the cone's radius is 5 centimeters, and its height is 10 centimeters, we would first multiply the radius times itself twice, which would be 5 times 5, which is 25, then multiply that by the height, which would be 25 times 10, which is 250. The fraction part of the formula means this- the numerator "1" means you would multiply what you have so far times 1, and the denominator "3" means you will divide what you have so far NOW by 3. So 250 times 1 = 250, and 250 divided by 3 = 83.3333333333, though we'd say that answer up to the hundredths place, which would be 83.33. If you need the exact answer, we'd put the pi sign next to it as 83.33 \pi , and you're done.Tho we didn't find the approximate volume of the cone.So we'd trace back to what answer we had before moving on to the step with the fraction  \frac{1}{3} . Since we were on 250, we'd multiply that by 3.14, which is 785, and continue with what we did with the fraction. 785 times 1 = 785, and 785 divided by 3 = 261.666666667, and saying the answer up to the hundredths place, the approximate volume of the cone would be 261.66

Now since we know the volume of the cylinder, exact = 2,000 \pi  and approximate volume = 6280, this means this is how much of the cylinder should be filled when we use the cone to pour in the water.

We could easily determine this by division.

Finding with the exact volume, you would do 2,000 (from cylinder's volume) divided by 83.33 (from cone's volume), which is 24.0009600384, and since it's not a whole answer, you would move it up a whole number. Why you may ask? Well you can't pour 0.0009600384 of a cone's volume into the cylinder now can you? :P  So it would take 25 times of pouring the cone filled with water into the cylinder in order for the cylinder to be full using the exact volumes of both objects.

Now finding with the approximate volumes of both objects, we'd do the same we did last time. The cylinder's volume divided by the cone's volume, which is 6280 divided by 261.66, would be 24.0006114805, and saying the answer up to the hundredths place, 24.00, but for the same reason as the last one when we were using the exact volumes, we'd round 24 up a whole number, so it would approximately take 25 times to fill the cylinder with the cone.

Either way, using exact or approximate volumes, your final answer would be 25 times. =DI hope I helped! ^-^

By calculating the volume of cone and cylinder, we find that one need to 24 times use the completely filled cone to completely fill the cylinder with water.

The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.

The volume of cone will be equal to one-third of the product of the area of the base and its height.

For a cylinder, the formula is πr²h. For a cone it is 1⁄3πr²h.

Volume of cylinder = π[tex]r^{2}[/tex]h =  π * 10* 10 * 20 = 2000π

Volume of cone =  [tex]\frac{1}{3}[/tex]*π[tex]r^{2}[/tex]h = 1/3 *  π * 5 * 5 * 10 = 250 π/3

Number of times one needs to use the completely filled cone to completely fill the cylinder with water =

= Volume of cylinder/Volume of cone

= 2000π / (250π/3) = 24

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In the given diagram ∠AJF or x comes to be 76°.

Opposite Angles are angles directly opposite to each other when two lines intersect in a plane.

We know that ∠JIH+∠JID=180°

107° +∠JID=180°

∠JID=180°-107°

∠JID=73°

∠JDI=31°(given))

In triangle JDI,

∠JDI+∠JID+∠IJD=180°

31° + 73° + ∠IJD =180°

∠IJD =76°

We know that ∠IJD and angle x° are opposite angles.

So, x=76°

Therefore, In the given diagram ∠AJF or x comes to be 76°.

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Answer: Los catetos medirán 12m y 9m.

Step-by-step explanation:

Bueno, sabemos que los lados de nuestro triangulo son 6m, 8m y 10m.

Podemos usar relaciones trigonométricas para encontrar los ángulos de este triangulo.

Cos(X) = cateto adyacente/hipotenusa

Si tomamos al cateto adyacente como 8m, tenemos:

Cos(X) = 8m/10m

X = Acos(8/10)  

Esto nos dice que para que nuestro otro triangulo rectángulo sea equivalente al primero, entonces los nuevos catetos C1  y C2 tienen que ser tal que los cocientes entre los catetos y la hipotenusa se mantengan constantes:

C1/15m = 8m/10m

C1 = (8/10)*15m = 12m

C2/15m = 6m/10m  

C2 = (6/10)*15m = 9m.

Answer: [tex]726 cm^{2}[/tex]

Step-by-step explanation:

surface area(SA)= [tex]6s^{2}[/tex]

= [tex]6*(11)^{2}[/tex]

= [tex]6*121[/tex]

= [tex]726 cm^{2}[/tex]

s= the length of the side of the cube

Answer:

none of them it should be ac,cb,ab. From my point of view

Answer:

188.5 cm^2

Step-by-step explanation:

a) Your volume is correct.

b) The curved surface area of the cone is called the lateral area.

Its formula is:

LA = (pi)rs,

where pi is 3.14159...

r = radius of the base

s = slant height of the cone

Here, r = 6 cm, and s = 10 cm

LA = (3.14159)(6 cm)(10 cm)

LA = 188.5 cm^2

Answer:(x-3)(x-3)

Step-by-step explanation:

(x-3)(x-3)=x^2-6x+9

Answer:

Step-by-step explanation:

Answer:

60 degrees

Step-by-step explanation:

Since the two lines are intersecting, the angles formed by them are vertical angles. Therefore:

2x+24=144

2x=144-24=120

x=120/2=60

Hope this helps!

Step-by-step explanation:

Therefore,

2x+24= 144° [ Vertically positive angles]

Or, 2x= 144-24

Or, 2x= 120

Or, x= 120/2

Therefore, x= 60°

Answer: The actual height of the tower is 91m

[tex]\frac{14}{x}=\frac{2}{13} \\x=\frac{14\times13}{2} \\x=91 m[/tex]

The actual height of the tower is 91 m.

An indication of the relationship between the distances on a map and the corresponding actual distances.

Given that, The height of a tower on a scale is 14 centimeters. The scale is 2 cm: 13 m.

Since, 2 cm = 13 m

1 cm = 13 /2 m

Therefore, 14 cm = 14 × 13/2 = 91 m

Hence, the actual height of the tower is 91 m.

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Answer:

Arrow C.

Step-by-step explanation:

Out of three arrows, nearest arrow from the origin will be the best arrow.

Ordered pair for arrow A → (-5, 4)

Distance between A and bullseye = [tex]\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2}[/tex]

                                                    =  [tex]\sqrt{(0+5)^2+(0-4)^2}[/tex]

                                                    = [tex]\sqrt{41}[/tex]

                                                    = 6.40 units

Ordered pair for arrow B → (5, -5)

Distance between B and bullseye = [tex]\sqrt{(0-5)^2+(0+5)^2}[/tex]

                                                         = [tex]5\sqrt{2}[/tex]

                                                         = 7.1 units

Ordered pair for arrow C → (-2, -6)

Distance between C and the bullseye = [tex]\sqrt{(0+2)^2+(0+6)^2}[/tex]

                                                               = [tex]\sqrt{40}[/tex]

                                                               = 6.32 units

Distance between C and the bullseye is the shortest.

Therefore, arrow C will be the best arrow.

Answer:

6.3 cm

Step-by-step explanation:

Answer:

a) 7a/8; b) 5a/8  

Step-by-step explanation:

Given:

AP = 2PQ = 2QB

Calculations:

1. A to the midpoint of QB

        a = AP + PQ + QB

If 2PQ = 2QB.

    PQ = QB and

    AP = 2PQ

∴      a = 2PQ + 2PQ = 4PQ

    PQ = a/4

    AP = 2PQ = a/2

Let M be the midpoint of QB.

AM = AP + PQ + QM

     = a/2 + a/4 + a/8

     = 7a/8

2. Midpoints of AP and QB

Let N be the midpoint of AP

NM = NP + PQ + QM

      = a/4 +a/4 + a/8 =

      = 5a/8

Answer:

Rupees 891

Step-by-step explanation:

If you multiply 810 times 0.1 which is the decimal of 10%, you get 81 which you can add to 810 to get 891 which is the price the shopkeeper payed to buy the watch.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

  a.  16%

Step-by-step explanation:

The difference from the mean is ...

  (x - µ) = 4420 lb -3550 lb = 870 lb

Then the minimum Z-score of the traffic of interest is ...

  (x - µ)/σ = (870 lb)/(870 lb) = 1

__

The "empirical rule" tells you that 68% of a normal distribution is within 1 σ (Z = ±1) of the mean. If 68% is inside that range, then the remaining 32% is outside that range. The normal distribution is symmetrical about the mean, so half that quantity is below Z = -1, and the other half, 16%, is above Z=1.

About 16% of the cars have weights more than 4420 pounds.

Answer:

{-12,12}

Step-by-step explanation:

-|-x| = -12 multiply both sides by -1

|-x| = 12 apply rule for solving absolute value equations

-x = 12 and -x = -12 solve

x = -12 and x =12

Answer:

" Expected Payoff " ⇒ $ 0.830

Step-by-step explanation:

Consider the probability of entering 1 ticket out of the 1000 entered;

[tex]Total Tickets Entered - 1000 Tickets,\\Prize Won - 830 Dollars,\\Number of Tickets One Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 1000,\\Proportionality - 1 / 1000 = x / 830, If x = " Expected Payoff ",\\\\1 / 1000 = x / 830 - Cross Multiplication ,\\1000 * x = 830,\\x = 830 / 1000 = 0.830\\\\Conclusion ; x = 0.83[/tex]

Solution ; " Expected Payoff " ⇒ $ 0.830 ( might or might not include 0 at end )