Find the values of x and y
(5x+4) (3x-24) (2y) 114

Answer:

6

Step-by-step explanation:

The union is defined as the set of all elements in at least one of the sets.

[tex]A \cup B=\{1,2,3,4,5,7\}[/tex]

So, there are 6 elements.

The height of the pole is 7.1 feet.

Given that a light display for a wedding with two 10-foot strands of lights and top of a pole and to two stakes on the ground forming two right triangles.

The Pythagorean theorem, also known as the Pythagoras theorem, explains the relationship between the three sides of a right triangle.

The two sides of triangle are equal that is x and and the third side is 10.

Now, we will apply the pythagoras theorem, we get

B²+P²=H²

Here B=P+x and H=10

x²+x²=(10)²

2x²=100

Now, we will divide both sides with 2, we get

2x²/2=100/2

x²=50

Now, we will take square root on both sides, we get

√x²=√50

x=√50

x=7.07106781

The Round to the nearest tenth is x=7.1 feet.

Hence, the height of the pole when wedding with two 10-foot strands of lights and the lights will be attached to the top of a pole and to two stakes on the ground forming two right triangles is 7.1 feet.

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The equation of teh second line is y = -1/3x + 5/3

The first equation is given as

y = -1/3x + 14

The slope of the above equation is

m = -1/3

Parallel lines have equal slope

So, the slope of the other line is

m = -1/3

The equation is then calculated as

y = m(x - x1) + y1

So, we have

y = -1/3(x + 7) + 4

Expand

y = -1/3x - 7/3 + 4

Evaluate

y = -1/3x + 5/3

Hence, the equation of teh second line is y = -1/3x + 5/3

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The student's GPA is of 2.33.

Grade Point Average (GPA) is the measure used to summaries your academic achievement at Griffith.

Given:

A worth 4​ points,

B worth 3​ points,

C worth 2​ points,

D worth 1 point

The GPA is

= 3(3) + 1(3) + 2(4) + 2(2)/9+3+4+2

=9+3+8+4/18

=2.33

Hence, The student's GPA is of 2.33.

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Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is [tex]\frac{2}{x}[/tex].

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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Answer:

        92.5 and 94.5

___________________

         [tex]187 \div 2 = 93.5\\\mathrm{Split\:93.5\:into\:two\:integers\:by\pm1}\\93.5 - 1 = 92.5\\93.5 + 1 = 94.5[/tex]

→ Thus, we have our two integers.

_________________________

Answer:

[tex]\frac{350}{11} weeks[/tex]

Step-by-step explanation:

Let V be the volume of water in the lake and w be the number of weeks to empty the lake

Since it takes 14 weeks to empty the lake by water release, the empty rate = V/14

But at the same time the river is replenishing the lake at a rate of V/25 since it will take 25 weeks to fill the empty lake

               [tex]\frac{1}{14} - \frac{1}{25} = \frac{1}{w}[/tex]

              [tex]25 - 14 = \frac{350}{w}[/tex]  ==> [tex]11 = \frac{350}{w}[/tex]

                  11w = 350

                    w = [tex]\frac{350}{11 }[/tex] weeks

Answer:

see explanation

Step-by-step explanation:

using the rules of exponents

[tex]\frac{1}{a^{m} }[/tex] = [tex]a^{-m}[/tex]

then

[tex]\frac{1}{32}[/tex] = [tex]\frac{1}{2^5}[/tex] = [tex]2^{-5}[/tex]

and

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , so

[tex](2^{-5}) ^{-3x}[/tex]

Answer:

x=6

Step-by-step explanation:

2(x+3)-8=10

use 2 to multiply the one in the bracket

(2x+6)-8=10

group like terms

2x-2=10

send all constant terms to one side of the equation

2x=10+2

2x=12

divide both side by the coefficient of x

2x/2=12/2

x=6

Answer on Question #54875

–

Math

–

Statistics

and Probability

A normal population has a mean of 0.1 and standard deviation 2.1. Find the probability that the

mean of a sample of size 900 will be negative.

Solution

In accordance with the given problem, we have the following data:

μ

=

0

.

1

,

σ

=

2

.

1

and

n

=

900

. It is known that

푥

~

M

(

μ

,

σ

2

)

and

z

~

N

(

0

,

1

)

Answer:

The room should be 460.65 [tex]m^{2}[/tex].

Step-by-step explanation:

First, you have to convert the percentage to a fraction.

11% = 0.11

Then add one to that number.

0.11 + 1 = 1.11

Multiply the number with the original room size.

415 * 1.11 = 460.65 ([tex]m^{2}[/tex])

Answer:

w≈8.33

Step-by-step explanation:

Greetings !

Firstly recall rectangle area formula

Thus,

[tex]area \: of \: rectangle \: = length \: \times \: width[/tex]

Given values:-

require value:-

solution/ work-out:-

[tex]width = \: \frac{area \: of \: rectangle}{length} [/tex]

[tex]w = \frac{125}{15} [/tex]

[tex]w = 8.333...[/tex]

Hope it helps !!!

Answer:  380.5

Step-by-step explanation: you can type it into desmos graphing calculator

Step-by-step explanation:

remember, a parallelogram is a quadrilateral with 2 pairs of parallel and equal sides, and 2 pairs of correspondingly equal angles. and its diagonals are intersecting each other in their midpoint.

with that in mind

(i)

because ABCD is a parallelogram, AD = BC, and AB = CD.

and angle A = angle C (and angle B = angle D).

therefore, as AE = FC, this also means that ED = BF.

via SAS (side angle side) it is clear that the triangles ABE and CDF are congruent.

therefore, EB = DF.

as ED is part of AD, and BF is part of BC, it is also clear that ED || BF.

together with ED = BF this means that EB || DF.

so, we have with BEDF 2 pairs of parallel and equal sides. and that is a parallelogram.

(j)

BCDE and ABCG are parallelograms.

so, BC = DE = AG, CD = BE, AB = CG.

due to the midpoint intersection rule of the diagonals of parallelograms, we also know

GE = CG = AB, DG = BG.

and as CG || AB, then also GE || AB.

together with AB = GE that means that AE = BG and AE || BG.

so, we have with ABGE again 2 pairs of parallel and equal sides. and that is a parallelogram.

The solution for the given system of equations is (3,5) and (-4,12).

Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.

⇒x+y=8; let's assume this equation as A

⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B

From equation A

⇒y=8-x

From equation B

⇒y=[tex]x^{2}[/tex]-4

Equating both the values of y

⇒8-x=[tex]x^{2}[/tex]-4

⇒[tex]x^{2}[/tex]-8-4+x=0

⇒[tex]x^{2}[/tex]-12+x=0

{solving quadratic equation}

⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}

⇒[tex]x^{2}[/tex]+4x-3x-12=0

⇒x(x+4)-3(x+4)=0

⇒(x-3)(x+4)=0

Therefore, the value's of x=3,-4

⇒if x=3

From  equation A

⇒y=8-3=5

For x=3 ; y=5

⇒if x=-4

From  equation A

⇒y=8-(-4)=12

For x=-4 ; y=12

Therefore,The solution for the given system of equations is (3,5) and (-4,12).

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The number of different digits that appear when [tex]\frac{1}{110}[/tex] is written as a recurring decimal is two digits i.e 9,0.

Given the fraction [tex]\frac{1}{110}[/tex]

Recurring decimal:  

A repeating decimal, also known as a recurring decimal, is a decimal representation of a number whose digits are periodic (repeating at regular intervals) and whose infinitely repeated portion is not zero. It is possible to demonstrate that a number is rational if and only if its decimal representation repeats or terminates.

⇒[tex]\frac{1}{110}[/tex]=0.0090909090.....

Therefore,The number of different digits that appear when [tex]\frac{1}{110}[/tex] is written as a recurring decimal is two digits i.e 9,0.

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Answer:

a. $2850

b. $6720

Step-by-step explanation:

a.

3000(1-0.05) = $2850

b.

7000(1-0.04) = $6720

We get that value of AC after adding AB and BC as 12 x + 20.

We are given that:

AB = 8 x + 2 and BC = 4 x + 18

We need to find AC.

For this, we will add AB and BC.

Adding AB and BC, we get that:

AB + BC = AC

Substituting the values of AB and BC in the equation which are given to us:

AC = 8 x + 2 + 4 x + 18

Combining the like terms, we get that:

AC = 12 x + 20.

Therefore, we get that value of AC after adding AB and BC as 12 x + 20.

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The correct answer is option A that is 74.

First, we need to put the expression in the form of mathematical equation. A mathematical equation may be defined as the combination of numbers and arithmetic symbols which are related to each other according to the expression given. The expression in the form of mathematical expression can be written as:

(9 - 2/3×√9)² + (1-6)²

Solving the brackets separately.

(9 - 2/3×3)² + (-5)²

Now in the next step, simplify the equation.

=>(9 - 2)² + 25

=>(7)² + 25

=>49 + 25

=>74.

Therefore, the required answer is 74.

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the first derivative of the given function is:

f'(x) = (2x²- 12x - 2)/( 2x² - 2)²

The quotient rule says that, if f(x) = g(x)/h(x), then:

f'(x) = ( g'(x)*h(x) - g(x)*h'(x) )/h(x)²

In this case we know that:

g(x) = x² + x - 2

h(x) = 2x² - 2

The derivatives are:

g'(x) = 2x + 1

h'(x) = 4x

Replacing that we get:

f'(x) = ( g'(x)*h(x) - g(x)*h'(x) )/h(x)²

      = ( (2x + 1)*(2x² - 2) - ( x² + x - 2)*(4x) )/( 2x² - 2)²

Expanding the denominator we get:

f'(x) = ( 4x³ - 4x + 2x² - 2 - 4x³ + 4x² - 8x)/( 2x² - 2)²

f'(x) = (2x²- 12x - 2)/( 2x² - 2)²

That is the first derivative of the given function.

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Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.

Here, we are given that Tanisha mowed 5 lawns last week in 7/ 12 hours each.

Thus, the total time taken by her to mow 5 lawns = 5(7/12)

= 35/ 12 hours

Now, this week she mows the five lawns in 5/12 hours each

Thus, the total time taken by her = 5(5/12)

= 25/12 hours

Therefore, the difference between the time taken by her last week and this week will be-

35/ 12 - 25/ 12

= (35 - 25)/ 12

= 10/ 12

= 5/6

Thus, Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.

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Answer: 30

Step-by-step explanation: just do 6*5, 6 faces for five die is thirty faces

There are 30 faces on 5 dice in total.

Given that a standard die has 6 faces on it, we need to determine the number of the faces on 5 dice.

A standard die has 6 faces. If you have 5 dice, each with 6 faces, you can calculate the total number of faces by multiplying the number of dice by the number of faces on each die:

Total number of faces = Number of dice × Number of faces on each die

Total number of faces = 5 dice × 6 faces/die

Total number of faces = 30 faces

So, there are 30 faces on 5 dice.

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Answer:

225 students

Step-by-step explanation:

600 students, and [tex]\frac{3}{8}[/tex] of students walk to school

[tex]600 * \frac{3}{8} = 225[/tex]

225 students can be expected to walk to school

Answer:

[tex]\dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{4+\sqrt{3}}{3+\sqrt{-3}}[/tex]

[tex]\textsf{Apply radical rule}:\quad \sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}\sqrt{-1}}[/tex]

[tex]\textsf{Apply imaginary number rule}:\quad \sqrt{-1}=i[/tex]

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i}[/tex]

Multiply by the conjugate of the denominator:

[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i} \cdot \dfrac{3-\sqrt{3}i}{3-\sqrt{3}i}[/tex]

[tex]\implies \dfrac{(4+\sqrt{3})(3-\sqrt{3}i)}{(3+\sqrt{3}i)(3-\sqrt{3}i)}[/tex]

[tex]\implies \dfrac{12-4\sqrt{3}i+3\sqrt{3}-\sqrt{3}i\sqrt{3}}{9-3\sqrt{3}i+3\sqrt{3}i-\sqrt{3}i\sqrt{3}i}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-4\sqrt{3}i-3i}{9-3i^2}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3i^2}[/tex]

[tex]\textsf{Apply imaginary number rule}:\quad i^2=-1[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3(-1)}[/tex]

[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{12}[/tex]

Separate the fractions:

[tex]\implies \dfrac{12+3\sqrt{3}}{12}-\dfrac{(3+4\sqrt{3})i}{12}[/tex]

Simplify:

[tex]\implies \dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]

The cost of the dryer will be $450

In the given sum the combined cost of the washer and dryer is $813

let the cost of the dyer be x

the cost of the washer will be (87 - x) as it is mentioned in the question washer costs $87 less than the dryer

According to the problem :

∴  x + (x-87) = 813

=> x+x-87 = 813

=> 2x - 87 = 813

=> 2x = 813 +87

=> 2x = 900

=> x = 900/2

=> x = 450

So the cost of the dryer is $450

The cost of the washer is = x - 87 = 450 - 87 = $363

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The number 67 and 113 are not the multiples of 3,6 and 7.

Multiples are the results of multiplying one whole number from another whole number.

Now, for the given question;

As, 67 and 113 are not completely divisible by 3. They are not multiple of 3.

67 and 113 are not entirely divisible by 6. So, they are also not the multiple of 6.

Now, 67 and 113 are also not entirely divisible by 7. Thus, they are also not the multiple of 7.

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Answer:

2.4 hours or 2 hours and 24 minutes

Step-by-step explanation:

Distance = rate times time

d = rt

1200 = 500t  Divide both sides by 500

2.4 = t

It will take 2.4 hours.  We can convert the .4 into minutes by using a unit multiplier 60 minutes = 1 hour.

[tex]\frac{.4hours}{1}[/tex] x [tex]\frac{60minutes}{1hour}[/tex]  The words hours cancel out and we are left with

.4 x 60 = 24 minutes.

You didn't provide a lot of info regarding the given question, however if you are looking to solve for t:

_______________________________________________

Isolate the variable by dividing each side by factors that do not contain the variable.

Solution's Exact Form:

[tex]t=-\frac{1}{243},-\frac{243}{32}[/tex]

_______________________________________________

Hope this helps! If not, please provide further info if you can regarding this question and I'll see what else I can do to help. If this did help however, lmk! Thanks and good luck!

Answer:

The sides are 62, 69, and 49

Step-by-step explanation:

x + (x + 7) + (x - 13) = 180

3x - 6 = 180

3x = 186

x = 62