The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
If x represents the smallest integer, then which of the following equations could be used to solve the problem?
Ox= 2x + 6
Ox= 2x + 3
2x + 2 = x + 4

Answer:

Time = 25/9 hr

Step-by-step explanation:

Let speed of boat in still water is x km/hr

then, speed in downstream equals to "x + 3"km/hr

and speed in upstream equals to "x - 3" km/hr

We also know that time taken to travel 3km in upstream is twice as time taken to travel 4km in downstream.

so,  using time = distance/speed

              3/x- 3   = 2 × (4/x + 3)

                3x + 9 = 8x -24

                    5x = 33

                      x = 33/5 km/hr

Net speed in upstream = 33/5 - 3 = 18/5 km/hr

So, Time taken to travel 10km upstream = distance /speed

                      =  (10 × 5) / 18 = 25/9 hr

Time = 25/9 hr

The boat speed in still water is determined to be 6.6 km/hr, and it will take around 2.78 hours to travel 10 km upstream.

To determine how long it will take the man to travel 10 km upstream to his favorite fishing location, let's first define the boat speed in still water as v km/hr.

From the problem, we know:

The speed of the current is 3 km/hr.

It takes twice as long to travel 3 km upstream as it does to travel 4 km downstream.

The speed of the boat upstream relative to the shore is v - 3 km/hr, and downstream it is:

→ v + 3 km/hr.

Let t be the time it takes to travel 4 km downstream. Then time to travel 3 km upstream is 2t.

We can set up the following equations using distance = speed x time:

→ For downstream: 4 = (v + 3)t

→ For upstream: 3 = (v - 3)2t

Solve these equations:

→ From 4 = (v + 3)t, we have t = 4/(v + 3)

Substitute t in 3 = (v - 3)2t: 3 = (v - 3)2(4/(v + 3))

→ Simplify: 3(v + 3) = 8(v - 3)

→ Expand and solve for v: 3v + 9 = 8v - 24

→ 33 = 5v

→ v = 33/5

     = 6.6 km/hr

Now that we know the speed of the boat in still water is 6.6 km/hr, we can determine the time it takes to travel 10 km upstream:

→ The effective speed upstream is:

= 6.6 - 3

= 3.6 km/hr.

→ Time required to travel 10 km upstream is:

= 10 / 3.6

≈ 2.78 hours.

Answer: Dividing 185 by 4 is the first step in finding out whether the owner will be able to use a whole number of panels. Hope this helps!

Step-by-step explanation:

The owner will not be able to use a whole number of panels btw

Answer:

C = pi * d formula

C = 314 ft

Step-by-step explanation:

To find the distance around the theatre, we want to use circumference.

C= 2 * pi *r  where r is the radius

or

C = pi * d  where d is the diameter

C = pi *100

C = 100pi

Using 3.14 as an approximation for pi

C = 3.14*100

C = 314 ft

Answer:

- 406.278

Step-by-step explanation:

10 - 4(2.4 • 3.5)2 + 0.12 10 - 4(8.4)2 + 0.12 10 - 4(70.56) + 0.12

Using BODMAS rule, first operation under bracket will be done. Then after Multiplication, addition and subtraction will be solved.

= 10 - 4 (8.4) 2 + 0.1210 - 4(8.4) 2 + 0.1210 - 4 (70.56) + 0.12

= 10 - 67.2 + 0.1210 - 67.2 + 0.1210 - 282.24 + 0.12

= - 406.278

Answer:

A

Step-by-step explanation:

Since the triangles are similar then the ratio of corresponding sides = a : b

and ratio of areas = a² : b²

Here the ratio of areas = 7 : 28 = 1 : 4, hence

ratio of sides = [tex]\sqrt{1}[/tex] : [tex]\sqrt{4}[/tex] = 1 : 2

Hence

XY = 2 × DE = 2 × 4 = 8 cm

The answer is XY=2*DE=2*4=8cm, in summary, eight cenimeters.

Answer:

2x^2+4x/3x-3

Step-by-step explanation:

ape.x

The quotient of (x-2)/(x+3) divided by 2/x is (x² - 2x)/(2x + 6), which corresponds to option D. This is achieved by multiplying the first fraction by the reciprocal of the second fraction and then simplifying.

To find the quotient of (x-2)/(x+3) divided by 2/x, we'll follow these steps:

Looking at the given options, the correct answer is: (x² - 2x) / (2x + 6) (Option D)

The complete question is

which of the following is the quotient of the rational expressions shown below x-2/x+3 divided by 2/x

A. (2x - 4)/(x ^ 2 + 3x)

B. (2x - 2)/(x ^ 2 + 3x)

C. x/(2x + 3)

D. (x² - 2x)/(2x + 6)

Check the picture below, notice the angles encircled in purple.

Answer:

A

Step-by-step explanation:

∠BES = ∠GES = 40°

∠BSE = ∠GSE = 90°

ΔBES and ΔGES are similar by the AA postulate → A

The given ΔBES and ΔGES are similar triangles according to the AA similarity postulate or theorem. Option A true.

The AA similarity postulate is that " If any two triangles have a pair of angles with equal measures then they are said to be similar triangles". If two angles are equal then the third one will also be equal in both the triangles.

The given triangles are ΔBES and ΔGES

The ΔBES has dimensions as ∠BES=40° and ∠ESB=90° and the ΔGES has dimensions as ∠GES=40° and ∠ESG=90°

Thus, both the triangles have pair of angles with equal measures. I.e., ∠BES=∠GES=40° and ∠ESB=∠ESG=90°. So, they satisfy the AA similarity theorem.

Hence, the given triangles are said to be similar according to the AA similarity postulate or theorem. So, option A is true.

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6 units right is the answer, since plugging in values(since it's asking for the translation you can ignore the -3) so your answer is:

The graph is translated 6 units RIGHT

Hope this helps!

plz brainliest

Final answer:

To find a system with the same solution, multiply one of the original equations by a constant and/or add the two original equations together to derive a new equation. An example is the alternative system 6x - 8y = -36 and 9x - 2y = -24, which shares the same solution as the original.

Explanation:

To find a system of equations with the same solution as the given system:

6x + 2y = −6

3x − 4y = −18

We must ensure that the alternative system is equivalent, meaning they share the same solution. A common technique is to multiply both sides of one or both of the equations by a constant to create new equations that have the same solutions. For example, we could multiply the second equation by 2:

3x − 4y = −18 becomes 6x − 8y = −36 after multiplying by 2.

Then, to avoid having the same equation, we could add the original second equation to the first one to get a different second equation:

6x + 2y + (3x − 4y) = −6 + (−18) becomes 9x − 2y = −24.

So, the alternate system that shares the same solution as the original would be:

6x − 8y = −36

9x − 2y = −24

Answer:

1041.25 miles

Step-by-step explanation:

You just have to multiply 12.25 (which is equivalent to 12 1/4) by 85 and you'll get the answer 1041.25

Answer:

1041.248 miles

Step-by-step explanation:

Points to remember

Speed = Distance/Time

It is given that,a train traveling at an average speed of 85 miles per hour.

To find the speed of train

Speed = 85 miles/1

 = 136.794 km/1 = 136.794 km/hr

To find the distance traveled in 12 1/4 hours

Distance = Speed * time

 = 136.794 * 12 1/4

 = 136.794 * 49/4

 = 1675.7265

 = 1041.248 miles

Total area is 110 square meter

Answer:

140

Step-by-step explanation:

Answer: 56

Step-by-step explanation:

For this case we must make a conversion of centimeters to millimeters. By definition we have to:

1 cm equals 10 mm

By making a rule of three we have:

1 cm ---------> 10 mm

5.6 cm --------> x

Where "x" represents the quantity in millimeters.

[tex]x = \frac {5.6 * 10} {1} = 56[/tex]

Thus, we have that 5.6 centimeters equals 56 millimeters.

Answer:

56mm

Answer: 10 units

Step-by-step explanation:

The length of one side of the given rhombus is; C: 10 units

The half diagonals of a rhombus are the legs of a right angle triangle with the hypotenuse being the side of the rhombus.

We see that EG and FH are the diagonals of the rhombus. This means that the half-diagonals measure 8 and 6.

Using Pythagoras theorem, we can find the hypotenuse which is the length of the side of the rhombus.

Thus;

8² + 6² = c²

64 + 36 = c²

100 = c²

c² = 100

c = 10

In conclusion, the length of one side of the rhombus is 10 units

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Answer:

2

Step-by-step explanation:

According to the fundamental theorem of Algebra

A polynomial of degree 3 has 3 roots

However, complex roots occur in conjugate pairs, hence

There can only be 2 distinct complex roots.

Answer:

d. 314 in²

Step-by-step explanation:

Area of a circle=πr²where r is the radius of the circle.

A=πr²

=π×10²

=314.2 in²

Area of the circle is 314 in² to the nearest square inch.

ANSWER

d. 314

EXPLANATION

The area of a circle is calculated using the formula:

[tex]Area = \pi {r}^{2} [/tex]

It was given in the question that, the circle has radius r=10 units. We substitute this value and π=3.14 into the formula to get,

[tex]Area = 3.14 \times {10}^{2} [/tex]

[tex] \implies \: Area = 3.14 \times 100[/tex]

[tex]Area = 314 \: {in}^{2} [/tex]

The correct answer is D.

Answer:

B. [tex]f(x)=x^4-x^3+2x^2-4x-8[/tex]

Step-by-step explanation:

If [tex]2i[/tex] is a root of f(x), then the complex conjugate [tex]-2i[/tex] is also a solution. If f(x) should have exactly 2 real roots, then by the Fundamental Theorem of Algebra, the minimum degree of f(x) is 4.

Hence the first and last options are eliminated.

By the Remainder Theorem, [tex]f(2i)=0[/tex].

Let us check for options B and C.

For option B.

[tex]f(x)=x^4-x^3+2x^2-4x-8[/tex]

[tex]\implies f(2i)=(2i)^4-(2i)^3+2(2i)^2-4(2i)-8[/tex]

[tex]\implies f(2i)=16i^4-8i^3+8i^2-8i-8[/tex]

[tex]\implies f(2i)=16+8i-8-8i-8=0[/tex]

For option C

[tex]f(x)=x^4-x^3-6x^2+4x+8[/tex]

[tex]\implies f(2i)=(2i)^4-(2i)^3-6(2i)^2+4(2i)+8[/tex]

[tex]\implies f(2i)=16i^4-8i^3-24i^2+8i+8[/tex]

[tex]\implies f(2i)=-16+8i+24+8i+8\ne0[/tex]

Therefore the correct choice is B.

Answer:

5

Step-by-step explanation:

7 ducks=7/7 ducks

7/7-?=5/7

7/7-2/7=5/7

5/7=5 ducks

Answer:

C 15, 205.

Step-by-step explanation:

That would be C because 15^2 = 225. The others are all correct.

The whole number not followed by its square is (c) 15, 205

The square of a number x can be represented as:

y = x^2

Using the above equation, we have:

121  = 11^2 --- true

169  = 13^2 --- true

205  = 15^2 --- false

64  = 8^2 --- true

4  = 2^2 --- true

Hence, the whole number not followed by its square is (c) 15, 205

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Answer:

0.48

Step-by-step explanation:

convert the percent to a decimal

12%=0.12

multiply 4 by 0.12

you're left with 0.48

you can check your math by dividing .48/.12, which will give you 4

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

12 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12 as the part and 100 as the whole

We want to know what is 12% of the number 4. This means 4 is the whole and the unknown (let's make this x) is the part.

[tex]\frac{x}{4} =\frac{12}{100}[/tex]

Now you must cross multiply

x*100 = 4*12

100x = 48

Now isolate x divide 100 to both sides

100x/100 = 48/100

0.48 = x

This means that 12% of 4is 0.48

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

You can spell only one word using the letters (M,A,G,I,C) the only word able to be made would be magic.

Step-by-step explanation:

Hope this helped you! :3

Answer:Meets,Abuzz,Glows,Inner,Creepy

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Use the distributive property:

  3(x - 1)

= 3(x) + 3(-1)

= 3x  - 3

Answer

D

Step-by-step explanation:

just toke the test

That's easy.

[tex]1\cdot-\dfrac{5}{8}=-\dfrac{5}{8}[/tex]

Hope this helps.

r3t40

Answer:

A) A(p(t)) = 25πt²

B) 314 square units.

Step-by-step explanation:

Part A)

Flow of paint can be expressed by the function:

p(t) = 5t

Area of the pattern is expressed as:

A(p) = πp²

Since area is given in terms of p, we can use the expression of p to express the area of pattern in terms of time(t). Using the value, we get:

A(p(t)) = π (5t)²

A(p(t)) = 25πt²

Part B)

We have to calculate the area of the pattern after time t. Substituting the value of t in above expression, we get:

A(p(2)) = 25 x 3.14 x 4 = 314 square units.

Therefore, the area of spilled paint after 2 minutes will be 314 square units.

Answer:

A=8v

8v=A

8v/8=A/8

v=A/8 answer

Answer:

[tex]\large\boxed{-y-3(-3y+5)=8y-15}[/tex]

Step-by-step explanation:

[tex]-y-3(-3y+5)\qquad\text{use the distributive porerty}\ a(b+c)=ab+ac\\\\=-y+(-3)(-3y)+(-3)(5)\\\\=-y+9y-15\qquad\text{combine like terms}\\\\=(-y+9y)-15\\\\=8y-15[/tex]

the simplified expression is 8y−15

To simplify the expression −y−3(−3y+5), we can start by distributing the negative sign to each term inside the parentheses.

This gives us −y+9y−15. Next, we can combine like terms by adding the coefficients of the y-terms, which gives us 8y.

Finally, we combine the constant terms to get −15.

Therefore, the simplified expression is 8y−15. We simplified the original expression by distributing the negative sign and then combining like terms to obtain a more concise and equivalent expression.

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Answer: Base.

The exponent is the 2, and the 5 is the base.

Answer:

Step-by-step explanation:

The five is the base. The two tells you what to do with the base.

5^2 = 5 * 5 = 25.

Notice what you are told. The 2 tells you to use two fives. The ^ in this case means multiply.

The solutions to the inequality x^2 + 3x - 4 > 0 are all real numbers where x is less than -4 or greater than 1, represented by the intervals (x < -4) or (x > 1).

To find the values that are solutions to the inequality x2 + 3x - 4 > 0, we first need to determine the roots of the quadratic equation x2 + 3x - 4 = 0. We can do this either by factoring, completing the square, or using the quadratic formula. In this case, factoring is the simplest approach:

x2 + 4x - x - 4 = 0

(x + 4)(x - 1) = 0

Therefore, the roots are x = -4 and x = 1. Since it is a parabola opening upwards (the coefficient of x2 being positive), the inequality x2 + 3x - 4 > 0 holds true when x is either less than -4 or greater than 1.

The solution set is thus all real numbers outside the interval [-4, 1], which can be written as (x < -4) or (x > 1).

Answer:

C=1/12

1/6x=2 so 1=12x

X=1/12

Step-by-step explanation: