To be able to solve equations 3 and 4 by elimination, each equation needs to be multiplied by something, Drag a red number to the red box for equation 3 and a brown number to the brown box for equation 4.​

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = [tex]\pi r^{2} \frac{h}{3}[/tex]

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

[tex]r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm[/tex]

We will now find the volume of the cone.

Volume of cone  [tex]\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}[/tex]

We know the density of ice is 0.93 grams per [tex]1cm^{3}[/tex]

[tex]1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g[/tex](Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = [tex]\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}[/tex]

Volume of cone being melted = New Volume - Original volume

= [tex]\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}[/tex]

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = [tex]\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}[/tex]

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = [tex]5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}[/tex]

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= [tex]\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}[/tex]

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

Step-by-step explanation:

Answer:

The answer would be A. 3/4

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Answer:

no

Step-by-step explanation:

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The correct option is B.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The length of the sidelink b using the cosine rule can be written as,

[tex]b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}[/tex]

Hence, the correct option is B.

The complete question is:

Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?

Options are given in the image below.

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Step-by-step explanation:

Q9

a) :

First, find the common difference for the sequence. add the first term to the second term

3+3= 6

add second term to the third term

3+6=9

add third term to the fourth term

6+9=15

b) 15 +24= 39

24+39=63

39+63= 102

Q10

a) 2 , 10 , 8

b) find the common difference for the sequence. Subtract the first term from the second term.

10-2= 8

Subtract the second term from the third term

8-10= -2

c) 10

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

The first option is a worker that costs $10 per hour and produces 8lb, then this worker gives:

8lb/$10= 0.8 pounds per dollar.

The second worker costs $12 per hour, and produces 16lb per hour, so this worker gives:

16lb/$12 = 1.33 pounds per dollar.

The third option is a machine that cost $5 per hour and produces 10lb per hour, then:

10lb/$5 = 2 pound per dollar.

The last option costs $8 per hour, and produces 14 pounds per hour, then:

14lb/$8 = 1.75 pounds per dollar.

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

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Answer:

let x be thomas age

3x for huilans age since huilans age is 3 time thomas age

both of their ages add to 76

ie. x + 3x =76

solve for x

4x = 76

x = 76 ÷ 4

x = 19. thomas age

to get huilans age : take 19 × 3 = 57

Answer:

263 8/9 millilitres

Step-by-step explanation:

9.5 litres = 9500 millilitres

9500/36 = 263 8/9

Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, we have that:

Hence the number of ways by which they can go on stage is:

N = 2 x 3! = 12.

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Answer:

Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

A_n = n!A

n

=n!

In this problem, we have that:

For the first dragon, either the green or the blue dragon, hence two outcomes.

For the remaining dragons, there are 3! possible ways.

Hence the number of ways by which they can go on stage is:

N = 2 x 3! = 12.

Answer:

b = 5.3

A = 48.6

B = 41.4

Step-by-step explanation:

Attached is the Pics contain the Pythagoras Theorem and Trigonometric Identities.

So for our Right-Angled Triangle we have from Pythagoras Identity that

[tex]a^{2} +b^{2} =c^{2}[/tex]  ,, Then [tex]b^{2} =c^{2} -a^{2}[/tex]  where a=6 , c=8

by substituting,

[tex]b^2=8^2-6^2=28\\ b=\sqrt{28} =2\sqrt{7}=5.3[/tex]

Now to find A , we will use the Trigonometric Identities

Since    [tex]sin(A)=\frac{Opposite}{Hypotenuse}=\frac{a}{c} =\frac{6}{8}=\frac{3}{4} \\[/tex]

[tex]A=sin^{-1} (\frac{3}{4} )=48.6\\[/tex]

Since in any Triangle A+B+C=180

Then B=180-A-C=180-48.6-90=41.4

Answer:

First we have to find the value of x;

then we have to find the value of y;

Step-by-step explanation:

here,

2x= 12

x = 12\2

x = 6

now,

4y = 12

y = 12\4

y = 3

° the value of x is 6

° ° the value of y is 3

The required x = $2,831.49. Option B) is correct.

7-year loan of $20,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7.

When some apply there money on something so that he can get higher value in returns of his money.

for the final 4 years

20000=2500/1.08+5000/(1.08^2)+7500/(1.08^3)+x/(1.08^4)+x/(1.08^5)+x/(1.08^6)+x/(1.08^7)

x = $2,831.49

Thus the required value of x = $2,831.49.

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Answer:

There is no definitive answer to this question since different wigs are made with different kinds of synthetic fibers. Some synthetic fibers are more resistant to heat than others, so it really depends on the specific wig. In general, however, it is generally not recommended to use heat on synthetic wigs, as it can damage the fibers.

The algebraic expression that represents the reduced price is p - 125

The reduction is given as:

Reduction = $125

The original price is given as:

Original = P

The reduced price is calculated as:

Reduced price = original - reduction

This gives

Reduced price = p - 125

Hence, the algebraic expression that represents the reduced price is p - 125

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The value of  (g . f) (0) is -2 and the value of  (g . f) (1) is 1.

A function is a law that relates a dependent and an independent variable.

The value of the two functions is given

The value of  (g . f) (0)

= g(f(0))

From the table of f(x) at x = 0

= g(1)

From the table of g(x) at x =1

=-2

The value of (g . f) (1)

=  g(f(1))

From the table of f(x) at x = 1

= g(0)

From the table of g(x) at x =0

=1

Therefore, the value of  (g . f) (0) is -2 and the value of  (g . f) (1) is 1.

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same line preparations

Answer:

Parallel

Step-by-step explanation:

So the best way to compare two lines is to convert it into slope-intercept form which is given in the form of: y=mx+b where m is the slope, and b is the y-intercept, in this form it's really easy to see if they're the same line, parallel, or perpendicular.

Original Equation:

2x - y = -1

Subtract 2x from both sides

-y = -2x - 1

Divide both sides by -1

y = 2x + 1

Original Equation:

4x - 2y = 6

Subtract 4x from both sides

-2y = -4x + 6

Divide both sides by -2

y = 2x - 3

As you can see both equations have a slope of 2, but different y-intercepts, so they're not the same line, but they'll also never intersect, because they increase by the same amount, thus they are parallel

Answer:

7720 mm²

Step-by-step explanation:

area = 2 × 80 mm × 40 mm + 2 × 80 mm × 5.5 mm + 2 × 40 mm × 5.5 mm

area = 7720 mm²

Using linear function concepts, we have that from the information given:

A linear function is modeled by:

y = mx + b

In which:

From the information given, the y-intercept is of 25 and the slope is of $2.50, hence the value after t months is given by:

V(t) = 25 - 2.5t.

Thus:

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The algebraic expression for the given word problem is 12/y + 7

From the question, we are to write the algebraic expression for the given word problem

The given word problem is

"the quotient of 12 and a number y increased by 7"

First,

"the quotient of 12 and a number y" can be expressed as

12/y

Then,

"the quotient of 12 and a number y increased by 7" becomes

12/y + 7

Hence, the algebraic expression for the given word problem is 12/y + 7

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The time required to clean 200 square feet will be 80 minutes. Option B is correct.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Let x be the cleaning time for the 200 square feet area;

From the table, it is observed that for a 1 sq. foot area the time needed to clean will be 0.4 minutes.

1 square feet = 0.4 minute

200 square feet = 200 × 0.4

200 square feet  = 80 minute

The time required to clean 200 square feet will be 80 minutes.

Hence, option B is correct.

The table is attached in the attachment.

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Answer:

If this is the question about sample space, a possible answer is 24 and 64 ways in sample space.

Step-by-step explanation:

Hopefully, this is helpful :)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: 36 + 23 i[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (3 + 8i)(4 - 3i)[/tex]

[tex]\qquad \tt \rightarrow \: (3 \sdot 4)+ (3 \sdot - 3i) + (8i \sdot4) + (8i \sdot - 3i)[/tex]

[tex]\qquad \tt \rightarrow \: 12 - 9i + 32i - (24 {i}^{2} )[/tex]

[tex]\qquad \tt \rightarrow \: 12 + 23i -( 24 \sdot - 1)[/tex]

[tex]\qquad \tt \rightarrow \: 12 + 23i + 24[/tex]

[tex]\qquad \tt \rightarrow \: 36 + 23i[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex]\Large\maltese\underline{\textsf{A. What is Asked \space}}[/tex]

Perform the indicated operation and write the answer with the form a+bi.

2 numbers given, one of which is complex

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!\space\space}}[/tex]

Multiply these two numbers, just like you always multiply binomials.

[tex]\bf{(3+8i)(4-3i)}[/tex] | multiply

[tex]\bf{3\times4+3\times(-3i)+8i\times4+8i\times(-3i)}[/tex] | simplify

[tex]\bf{12-9i+32i-24i^2}[/tex] | this can be simplified A LOT

[tex]\bf{12+23i-24i^2}[/tex]  | as strange as it may seem, this can be simplified even  more, because isn't i^2 the same as -1?

[tex]\bf{12+23i-24\times(-1)}=12+23i+24}[/tex] | add 12 and 24

[tex]\bf{36+23i}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                     [tex]\bf{=36+23i}[/tex]. The answer is written in the form a+bi, as requested.

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

a gas can hold 7×10=70 litters of gas

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Let a = Adele's current age

Let t = Timothy's current age

Adele is 5 years older than Timothy:

a = t + 5       {equation 1}

In 3 years Timothy will be 2/3 of Adele's age:

(2/3)(a + 3) = t + 3     {equation 2}

Since we are looking for Adele's age, let's rearrange equation 1 to:

t = a - 5

Substitute that into equation 2 and solve for a.

(2/3)(a+3) = a - 5 + 3

(2/3)(a + 3) = a - 2

Multiply through by 3 to clear the fraction

2(a+3) = 3a - 6

2a + 6 = 3a - 6

Add 6 to both sides, subtract 2a from both sides

12 = a

Adele is 12 years old

This means Timothy is 7 years old.

Check equation 2 to verify:

(2/3)(a + 3) = t + 3

(2/3)(12+3) = 7 + 3

(2/3)(15) = 10

10 = 10

Answer is correct

Answer:

See below

Step-by-step explanation:

Isosceles because two sides are same length

                 and

Obtuse because there is an interior angle greater than 90 °

The integer that represents the horizontal translation of f(x) to g(x) is 4

The attached graph represents the missing piece in the question

From the graph, we can see that:

The function g(x) is 4 units to the left of the function f(x)

This means that:

g(x) = f(x + 4)

Hence, the integer that represents the horizontal translation of f(x) to g(x) is 4

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The velocity equation is:

[tex]v(x) = 108 - 24x[/tex]

Such that:

[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]

And the velocity is zero for x = 4.5

We know that the position equation is:

[tex]f(x) = 108*x - 12*x^2[/tex]

To get the velocity, we need to differentiate with respect to x, so we get:

[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]

Now we want to get the velocity for x = 0 and x = 2, we will get:

[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]

Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.

Finally, we need to solve:

[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]

The velocity is zero when x = 4.5

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Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

.