Is the answer true or false?

Answer:

The greatest four-digit number that is divisible by 6 is 9996

Step-by-step explanation:

9,996 / 6 = 1,666

Answer:

a = -6

b = -8

c = 12

Step-by-step explanation:

Quadratic equations follow the general structure:

ax² + bx + c = 0

In this equation, "a" and "b" serve as coefficients which modify the variables and "c" represents the y-intercept. Since the given equation is in the quadratic form, you can easily identify which values match the variables.

-6x² - 8x + 12 = 0

a = -6

b = -8

c = 12

Answer: If they worked together, it would take 31.5 minutes

Step-by-step explanation:

There's a certain formula for equations like this:

[tex]\frac{1}{t1} +\frac{1}{t2}=\frac{1}{tb}[/tex]

t1= the time it took for the first person to complete the task.

t2= the time it took for the second person to complete the task.

tb= the time it took for both of them to complete the task.

We have the values for both t1 and t2, but not for tb.

t1= 45

t2= 105

tb= x

[tex]\frac{1}{45} +\frac{1}{105} = \frac{1}{x}[/tex]

Now it's simple algebra, and all we need to do is solve for x

The LCM for both fractions is 315, so now we multiply BOTH sides of the equation by 315.

[tex]\frac{315}{45} + \frac{315}{105} = \frac{315}{x}[/tex]

This will simplify nicely, so now we just need to get x on the other side.[tex]7 + 3 = \frac{315}{x} \\\\\ 10*x = \frac{315}{x} * x[/tex]

[tex]10x = 315 \\\\x = 31.5[/tex]

Answer:

Q1: Third Choice. 15√3

Q2: Fourth Choice. 15√3

Q3: First Choice. 12√10

Step-by-step explanation:

Given expression

8√3 + 7√3

Simplify by addition

Remember that terms with the same radical part can add together directly

= (8 + 7) √3

[tex]\Large\boxed{=15\sqrt{3} }[/tex]

Given expression

√15 × √45

Factorize each radical

= √(3 × 5) × √(9 × 5)

= √3 × √5 × √9 × √5

Simplify necessary radicals

= √3 × √5 × 3 × √5

= 3 × √3 × √5 × √5

Simplify by multiplication

When radicals multiply, combine them under one radical sign

= 3√3 × √(5 × 5)

= 3√3 × 5

[tex]\Large\boxed{=15\sqrt{3} }[/tex]

Given expression

15√10 - 3√10

Simplify by subtraction

Remember that terms with the same radical part can subtract each other directly

= (15 - 3) √10

[tex]\Large\boxed{=12\sqrt{10} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: 3/8

Step-by-step explanation:

1/2 is also 4/8 so you subtract 4/8 from 7/8 to get 3/8

The pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5

The complete question is added as an attachment

Function 1

f(x) = 5x - 11 and g(x) = (x + 11)/5

Represent 5x - 11 with y in f(x) = 5x - 11

y = 5x - 11

Swap x and y

x = 5y - 11

Add 11 to both sides

x + 11 = 5y

Divide by 5

y = (x + 11)/5

Express as a function

g(x) = (x + 11)/5

From the question, we have:

f(x) = 5x - 11 and g(x) = (x + 11)/5

This means that the function g(x) is an inverse of the function f(x)

Hence, the pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5

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The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.

In this problem we have the shape of an ellipse centered at origin, whose vertex form is shown below:

x² / a² + y² / b² = 1        (1)

Where a, b are the lengths of the semiaxes, in feet.

An oblate spheroid is generated by revolving half of the ellipse about the y-axis. Oblate spheroids are a kind of ellipse:

x² / a² + y² / b² + z² / a² = 1       (2)

Where a, b, c are the lengths of the semiaxes, in feet.

And the volume of the oblate spheroid is:

V = (4 / 3) · π · a² · b      (3)

If we know that a = 3 ft, b = 2 ft, then the volume of the oblate spheroid is:

V = (4 / 3) · π · (3 ft)² · (2 ft)

V ≈ 75.398 ft³

The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.

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Answer:

28/57

Step-by-step explanation:

odds in favor of event occurring = (probability event occurs)/(probability event does not occur)

Let p = probability event occurs.

Then the probability the event does not occur is 1 - p.

Let the odds = a/b.

a/b = p/(1 - p)

a(1 - p) = bp

a - ap = bp

bp + ap = a

p(a + b) = a

p = a/(a + b)

p = 28/(28 + 29)

p = 28/57

As per the given scenario, the probability of event E is 28/57 or approximately 0.4912.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

If the odds in favor of an event E are "a to b," then the probability of E is given by:

P(E) = a / (a + b)

In this case, the odds in favor of E are 28 to 29, which means that there are 28 favorable outcomes for E and 29 unfavorable outcomes against E.

So, using the formula above, we can compute the probability of E as:

P(E) = 28 / (28 + 29)

P(E) = 28 / 57

Therefore, the probability of event E is 28/57 or approximately 0.4912.

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Answer:

Step-by-step explanation:

(-8 - 0)/(-4 - 8)= -8/-12 = 2/3

The slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.

The slope or gradient between two points in the Cartesian coordinate system. The slope exists the amount of slant a line retains and can maintain a positive, negative, zero, or undefined value.

Using the slope formula [tex](y_2 - y_1)/(x_2 - x_1)[/tex]

[tex]x_1 = 8, y_1 = 0[/tex] and [tex]x_2 = -4 , y_2= -8[/tex]

slope [tex]= (y_2 - y_1)/(x_2 - x_1)[/tex]

= ((-8) - 0) / ((-4) - (8))

= (-8) / (-12) = (-2) / (-3)

= 0.66667

Therefore, the slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.

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Answer:

no mode

Step-by-step explanation:

no number appears more than once

therefore there is no mode

Answer:

50°

Step-by-step explanation:

Note EFGH is an isosceles trapezoid.

∠HGF=77° (base angles of an isosceles trapezoid are congruent)

∠EGH=27° (angles in a triangle add to 180°)

∠FGE=50° (angle subtraction postulate)

If the price of 1 cubic foot of hay is $10 then the money needed is $15.

Given the price of 1 cubic foot of hay be $10 and the amount of hay be $1.50.

We are required to find the amount of money needed to buy the hay.

We know that the amount of money that can be spend on something is the product of price of one unit and number of units.

Product is the result when two numbers are multiplied with each other.

Total money =Price of 1 cubic foot*$1.50

=10*1.50

=$15

Hence if the price of 1 cubic foot of hay is $10 then the money needed is $15.

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Question is incomplete, the right question is as under:

1.5 cubic foot hay is required to fill a room completely. Calculate the amount we have to pay to fill the room completely if the price of 1 cubic foot is $10?

Answer: 480

Step-by-step explanation:

72/3 is 5% of the number we are looking for.
72/3=24
24*20 will be 100%
480 is 100%

72 is 15% of what number?

Quantity          %

  72---------------15

   x---------------100

We solve

[tex]\boldsymbol{\sf{x=\dfrac{72\times100 }{15}=\dfrac{7200}{15}=480 }}[/tex]

Answer: 72 is 15% of 480.

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Answer:

  A.  (-1, -4)

Step-by-step explanation:

The vertex can be found by converting the equation from standard form to vertex form.

Considering the x-terms, we have ...

  y = (x^2 +2x) -3

where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...

  y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2

  y = (x +1)^2 -4

Compare this to the vertex form equation ...

  y = a(x -h)^2 +k

which has vertex (h, k).

We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).

On the attached graph, the vertex is the turning point, the minimum.

Answer:

Step-by-step explanation:

6x-6>y

put y=6

6x-6>6

6x>12

x>12/6

x>2

(3,6) is one solution.

Using the binomial distribution, there is a 0.0874 = 8.74% probability that not enough seats will be available.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

n = 15, p = 0.85.

The probability that not enough seats will be available is P(X = 15), as the only outcome in which not enough seats will be available is when all 15 people who bought the ticket show up, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 15) = C_{15,15}.(0.85)^{15}.(0.15)^{0} = 0.0874[/tex]

0.0874 = 8.74% probability that not enough seats will be available.

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The zeros which are the roots of the polynomial expressions are:

x = -4; x = - 2;  x = 4 - 2√5;  x = 2(2 + √5)

The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.

For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.

From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:

Using the rational root theorem:

[tex]\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }[/tex]

[tex]\mathbf{=(x+2) (x^3-4x^2-36x-32) }[/tex]

By factorization, we have:

= (x + 2) (x + 4) (x² - 8x - 4)

The zeros which are the roots of the polynomial expressions are:

x = -4; x = - 2;  x = 4 - 2√5;  x = 2(2 + √5)

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Answer:

32: X=54

31: Xx54+74

The time at Sydney when Dan rings his friend is 1 : 30 am (option B).

The first step is determine the time difference between London and Sydney.

Time difference = time at Sydney - time at London

( 12 + 10pm) - 12pm

22pm - 12pm = 10 hours

The second step is to add the time difference to the time it was when Dan rang.

15 : 30 pm + 10pm = 25 : 30

We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30

25 : 30 - 24 = 1 : 30 am

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Answer:

True

Step-by-step explanation:

This is true in an equilateral triangle.

The amount received net of expenses is $397865 and the percentage of the sale price was 10%.

Given that Bourassas decides to sell a house for $ 440,000. You will be charged a real estate fee of 8% of the sale price, property insurance of 1.4% of the sale price, and an escrow fee of $ 775.

The declared retail price is $ 440,000.

Real estate commission = 8% of the sale price

Real Estate Fee = (8/100) × 440000

Real Estate Fee = 8 × 4400

Real Estate Fee = $ 35,200

Security insurance costs of the title = 1.4% of the sale price

Cost of title insurance = (1.4 / 100) × 440 000

Cost of title insurance = 1.4 × 4400

Title Insurance Cost = $ 6160

The escrow fee assigned is $ 775.

(a) In determining the amount received after deducting the sale price of the property commission, title insurance and escrow fees, we receive

Amount received after fees = sale price - real estate commission - title insurance - escrow fees

Amount received after fees = 440000-35200-6160-775

The amount received after fees = $397865

(b) To find the percentage of sale price, add together all the terms real estate commission, title insurance and escrow fees and divide by the sale price we get

Percentage of selling price=((35200+6160+775)/440000)×100

Percentage of sale price = (42135/440000) × 100

Percentage of sale price = 9.57

Percentage of sale price = 10% (rounded down)

Hence Bourassas decides to sell a house for $440,000, then the amount Bourassas will receive after expenses is $397,865 and the percentage of the sale price of expenses is 10%.

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So, making x subject of the formula, x = [m - 2pt³ ±√(m²  - 4pt²m)]/{2t⁵}

Since p = √(mx/t) - t²x

So, p + t²x = √(mx/t)

Squaring both sides, we have

(p + t²x)² = [√(mx/t)]²

p² + 2pt²x + t⁴x² = mx/t

Multiplying through by t,we have

(p² + 2pt²x + t⁴x²)t = mx/t × t

p²t + 2pt³x + t⁵x² = mx

p²t + 2pt³x + t⁵x² - mx = 0

t⁵x² + 2pt³x - mx + p²t = 0

t⁵x² + (2pt³ - m)x + p²t = 0

Using the quadratic formula, we find x.

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]

where

Substituting the values of the variables into the equation, we have

[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

So, making x subject of the formula,  [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

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Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.

The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.

Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:

Side CD equals side DB.

Side CD = 5x - 17

Side DB = 3x + 1

Make both segments equal to each other. Therefore, we would have the equation:

5x - 17 = 3x + 1

Solve for x

Add both sides by 17

5x - 17 + 17 = 3x + 1 + 17

5x = 3x + 18

Subtract 3x from both sides

5x - 3x = 3x + 18 - 3x

2x = 18

Divide both sides by 2

2x/2 = 18/2

x = 9

CD = 5x - 17

Plug in the value of x

CD = 5(9) - 17

CD = 45 - 17

CD = 28 units.

DB = 3x + 1

Plug in the value of x

DB = 3(9) + 1

DB = 27 + 1

DB = 28 units.

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Answer:

53 mph   and  71 mph

Step-by-step explanation:

bus 1 rate = x

bus 2 rate = x + 18

rate times time = distance

( x    +    x+18) * 6 = 744

(2x+18) * 6 = 744

2x + 18 = 124

2x = 106

x = 53       the other bus is  53 + 18 =  71  mph

Answer:

84,08964 [gr.].

Step-by-step explanation:

for more details see in the attachment.

Answer:

(3+3) x (3+1)

Step-by-step explanation:

free

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

[tex] \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } [/tex]

[tex]f(4) = 2(3) {}^{4} = 2 \times 81 = 162[/tex]

[tex]f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6[/tex]

[tex]f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} [/tex]

[tex]f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96[/tex]

[tex]y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} [/tex]

[tex]y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5[/tex]

[tex]s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38[/tex]

[tex]s = 2500.e {}^{0.07 \times 20} = 10138[/tex]

Answer:

SAS and SSA

Kindly award branliest

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.

The criterias that guarantee congruence are :

[tex] \qquad \large \sf {Conclusion} : [/tex]