√2x + 4 - √x = 2
please solve the solution and show how
​

Answer:

270 m^2

Step-by-step explanation:

formula for area of a triangle is base times height divided by 2

(30)x(18)÷2

30x9

270 m^2

hopes this helps

Check the picture below.

Using Pythagoras theorem to solve the right angle triangle formed between the astronaut and the earth, his distance 6412.5km

Pythagorean Theorem, states the square of the hypotenuse in a right angle triangle is equal to the sum of the squares of the other two sides. In the equation x² = y² + z², where x is the hypotenuse and y and z are the other two sides.

To find the distance of the astronaut from the space center, the height of the space center and his current location forms a right angle triangle.

We can find the distance as;

x² = y² + z²

z = radius of earth = 12800 / 2 = 6400km

x² = 6400² + 400²

x² = 41120000

x = √41120000

x = 6412.5km

The astronaut location from the earth is 6412.5km

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The value of angle m∠F is  42°.

What are the Exterior angle properties of triangle?

If in a triangle any side is extended, the outside angle or exterior angle formed results is equal to the sum of the two opposite internal angles.

Here we are given a triangle ΔGHF

m∠F = ∠HFG = 4x + 6

∠G = ∠FGH = 70°

and exterior angle ∠GHJ = -5 + 13x

Here side FH of ΔGFH is extended .

so by using exterior property of triangle i.e,

Exterior angle = sum of opposite interior angles.

∠GHJ =∠FGH + ∠GFH

-5 + 13x = 70 + (4x + 6)

13x - 4x = 70 + 6 + 5

9x = 81

x = 81/9

x = 9.

Therefore m∠F = ∠GFH = (4x+6)

m∠F = 4×9+6

m∠F = 42°

So we got the value of angle m∠F is  42°.

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There are 168 different outfits does Cai have to choose from.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Cai is trying to pick out an outfit for the first day of school.

And, He can choose from 2 pairs of pants, 3 t-shirts, 7 sweaters or hoodies, and 4 pair of shoes.

Now,

Since, He can choose from 2 pairs of pants, 3 t-shirts, 7 sweaters or hoodies, and 4 pair of shoes.

Hence, Number of possible outfits = 2 × 3 × 7 × 4

                                                      = 168

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The value of x for which JKLM is a parallelogram is 21

It is important to note that the sum of angles in a parallelogram is 360 degrees.

From the information given, we have that;

This is represented as;

JKL + KLM + LMJ + MJK = 360

substitute the values

4x + 13 + 4x - 1 + 5x - 8 + 3x + 20 = 360

collect like terms

4x + 4x + 5x + 3x = 360 - 24

Add or subtract like terms

16x = 336

Divide both sides by the coefficient of x

x = 336/16

x = 21

Hence, the value is 21

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Answer:

-8 + (-7) = -8 - 7 = -15

The sum of -8 and -7 is -15.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

The volume of the rectangular prism is 5 inches cube.

A rectangular prism is a three-dimensional shape or figure. Therefore, the volume of a rectangular prism can be represented as follows:

volume of a rectangular prism = lwh

where

Therefore,

l = 2 1 / 2 inches = 5  /2 inches

w = 1 inches

h = 2 inches

Hence,

volume of the rectangular prism = 5 / 2 × 1 × 2

volume of the rectangular prism = 10 / 2

volume of the rectangular prism = 5 inches cube

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Answer:It is 30 cubic inches.

Step-by-step explanation:

Answer:

43

133

Step-by-step explanation:

Complementary means that the two angles added together equal 90

90 - 47 = 43

Supplement means that the two angels added together equal 180

180 -47 = 133

The presented problem has a simplified value of 11/20.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Given  3/4+3/5-4/5

3/4 + 3/5 -4/5

First, solve the problem with the same denominator taking 1/5 common

3/4 +1/5(3-4)

3/4 + 1/5(-1)

3/4 - 1/5

Taking the LCM of the denominator

=> [tex]\frac{15 - 4}{20}[/tex]

=> 11/20

Therefore, the simplified value of the given problem is 11/20.

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The unitary technique yields (x, y) = (-1, 1) as the answer to the equations y = 3x + 4 and y = - 2x - 1.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. for example, 2x - 4 = 2.

by solving

y = 3x + 4

y = - 2x - 1

= 3x + 4 = -2x - 1

= 3x + 2x = -5

x= -1

putting value of x in 2nd eq.

y = 2 - 1= 1

y = 1

so The unitary technique yields (x, y) = (-1, 1) as the answer to the equations y = 3x + 4 and y = - 2x - 1.

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The simplest radical form in terms of x is √x.

The radical in the question can be represented as

∛(x∛(x∛(x√(2&x)) ) )

The formula for rational exponents is:

√(n&a*b)=√(n&a)* √(n&b)

Hence,

∛(x∛(x∛(x√(2&x)) ) )

∛x*∛(∛(x∛(x√(2&x)) ) )

∛x*√(9&x∛(x√(2&x)) )

∛x*√(9&x)*√(9&∛(x√(2&x)) )

∛x*√(9&x)*√(27&x√(2&x))

∛x*√(9&x)* √(27&x)√(27&√(2&x))

∛x*√(9&x)* √(27&x)*√(54&x)

As, √(n&x)=x^(1/n)

Hence

x^(1/3)*x^(1/9)*x^(1/27)*x^(1/54)

According to multiplying exponent rules with the same base, x^a*x^b=x^(a+b)

Hence,

x^(1/3+1/9+1/27+1/54)

x^(27/54)

x^(1/2)

√x

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The composite functions when solved accordingly gives us;

(f ° g)(x) = 75x³ + 140x²+ 87x + 18

(f ÷ g)(x) =  3x + 2

Composite functions are formed when the output of one function is used as the input of another.

Now, we are given the functions as;

f(x) = 15x² + 19x + 6

g(x) = 5x + 3

Let us factorize f(x) to get;

f(x) = 15x² + 19x + 6 = (5x + 3)(3x + 2)

(f ° g)(x) simply means; f[g(x)]

Thus, we have;

f.g(x) = (15x² + 19x + 6)(5x + 3)

f.g(x) = 75x³ + 95x² + 30x + 45x² + 57x + 18

f.g(x) = 75x³ + 95x² + 45x²+ 30x + 57x + 18

f.g(x) = 75x³ + 140x²+ 87x + 18

(f ÷ g)(x) = ((5x + 3)(3x + 2))/(5x + 3)

(f ÷ g)(x) =  3x + 2

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Answer: 36.902 Seconds

Step-by-step explanation:

(1) --> To find the time that the rocket is at a height of more than 100 feet, you need to find the time when the height of the rocket is equal to 100 feet.

(2) --> do this by setting your equation equal to 100

[tex](-\frac{1}{2} )t^2 + 15t = 100[/tex]

[tex](-\frac{1}{2}) t^2 + 15t - 100 = 0[/tex]

(3) --> From here, use the quadratic formula to solve for t

Quadratic formula:

[tex]t = - \frac{-b+-\sqrt{b^2 - 4ac} }{2a}[/tex] (solving the b+ first)

[tex]t = \frac{(-15 + \sqrt{225 - 4(-\frac{1}{2}) (-100)}}{-1}[/tex]

[tex]= \frac{(-15 + \sqrt{475})}{-1}[/tex]

[tex]= \frac{(-15 + 21.902)}{-1}[/tex]

[tex]= \frac{6.902}{-1}[/tex]

[tex]= -6.902[/tex]

(solving b-)

[tex]t = \frac{-15 - \sqrt{475}}{-1}[/tex]

[tex]= \frac{-15-21.902}{-1}[/tex]

[tex]= \frac{-36.902}{-1}[/tex]

[tex]= 36.902[/tex]

HENCE: The first solution, -6.902, is not a valid time because it is negative. The second solution, 36.902, is the time when the rocket is at a height of 100 feet. Since the rocket is at a height of more than 100 feet for the entire time after it reaches a height of 100 feet, the rocket will be at a height of more than 100 feet for 36.902 seconds.

The average score of all the students in both classes is 84.

step1

The class with 20 students had an average score of 90 on a test. The total score will be:

= 20× 90=1800

A class with 10 students had an average score of 80 on the same test. The total score will be:

=10× 80

= 800

A class with 4 students had an average score of 70 on the same test. The total score will be:

=4×70

=280

step2

Total scores = 1800 + 800+ 280=2880

Number of students = 20 + 10+4=34

The average score will be:

= Total score / Total students

= 2880/ 34=84

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The average score of all the students in both classes is 84.

step1

The class with 20 students had an average score of 90 on a b. The total score will be:

= 20× 90=1800

A class with 10 students had an average score of 80 on the same test. The total score will be:

=10× 80

= 800

A class with 4 students had an average score of 70 on the same test. The total score will be:

=4×70

=280

step2

Total scores = 1800 + 800+ 280=2880

Number of students = 20 + 10+4=34

The average score will be:

= Total score / Total students

= 2880/ 34=84

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One thing that is wrong with Sana's statement is that it is repetitive as negative three degrees Celsius is already below zero.

When temperature is measured in degrees Celsius then it means that there are temperatures above 0 degrees Celsius and those that are below it. Those temperatures above 0 degrees Celsius are positive temperatures and those below zero degrees Celsius are negative.

These negative temperatures are used for places that are very cold and the colder a place is, the lower the temperature will be below zero. This therefore means that saying a temperature is negative and saying it is below zero is the same thing.

This means that Sana was wrong to say, " temperature is negative three degrees below zero " as they could have either said that the temperature was 3 degrees below zero or negative 3 degrees Celsius.

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Answer:

To describe the shape of a cubic function, we need to consider its end behavior, any turning points it has, and any intervals over which it is increasing or decreasing.

For the cubic function 32. y = 3x³ - x - 3, the leading coefficient is 3, which means that the end behavior of the function will be determined by the sign of the term x³. Since the coefficient of x³ is positive, the function will approach positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity. This means that the graph of the function will curve upwards at both ends.

To find the turning points of the function, we can find the zeros (or roots) of the function. In this case, we can solve the equation 3x³ - x - 3 = 0 using the cubic formula or a numerical method. This will give us three real roots, which correspond to the x-values of the turning points of the function. The function will be concave upwards at the points between these roots and concave downwards at the points between the roots and the ends of the graph.

The function will be increasing on the intervals between the roots where the function is concave upwards and decreasing on the intervals between the roots where the function is concave downwards.

For the cubic function 33. y = -9x³ - 2x² + 5x + 3, the leading coefficient is -9, which means that the end behavior of the function will be determined by the sign of the term -9x³. Since the coefficient of x³ is negative, the function will approach negative infinity as x approaches positive infinity and positive infinity as x approaches negative infinity. This means that the graph of the function will curve downwards at both ends.

As with the previous function, we can find the zeros (or roots) of the function by solving the equation -9x³ - 2x² + 5x + 3 = 0 using the cubic formula or a numerical method. This will give us three real roots, which correspond to the x-values of the turning points of the function. The function will be concave upwards at the points between these roots and concave downwards at the points between the roots and the ends of the graph.

The function will be decreasing on the intervals between the roots where the function is concave upwards and increasing on the intervals between the roots where the function is concave downwards.

Step-by-step explanation:

The given trigonometrical equation is solved and proved below.

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is a trigonometrical expression as -

tan(y) + cot (y)

The given expression is -

tan (y) + cot (y)

tan (y) + cot (y) = {sin(y) / cos(y) + cos(y) / sin(y)}

tan (y) + cot (y) = {sin²(y) + cos²(y)} / {sin(y) cos(y)}

tan (y) + cot (y) = 1 / {sin(y) cos(y)}

tan (y) + cot (y) = {1/sin(y) . 1/cos(y)}

tan (y) + cot (y) = cosec(y) sec(y)

L.H.S = R.H.S

Therefore, the given trigonometrical equation is solved and proved above.

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Answer:

The answer is a)2  and b)93

Step-by-step explanation:

we know that, x=3 and y=5

now, as per the question,

a) 4x-2y

=4(3)-2(5)

=12-10

=2

b) 2x^+3y^

=2(3)^+3(5)^

=2*9+3*25

=18+75

=93

therefore, a)2 and b)93

Answer:

663

Step-by-step explanation:

5967/9=663

Answer:

663

Step-by-step explanation:

        663

9 l 5967

    -54

        56

        -54

           27

          -27

           0

hopes this helps

Answer: C

Step-by-step explanation:

The value of x is 16

A modulus function gives the magnitude of a number irrespective of its sign. It is also called the absolute value function. In mathematics, the modulus of a real number x is given by the modulus function, denoted by |x|. It gives the non-negative value of x. The modulus or absolute value of a number is also considered as the distance of the number from the origin or zero.

Given here, the equation x=|-16| but we know that modulus function only measures the magnitude therefore x cannot be negative thus x=16

Hence, The value of x is 16

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The length of 'Added metal bar' will be;

⇒ Approximately 5.4 m

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

The sides of box are;

⇒ a = 4 meters

⇒ b = 2 meters

⇒ c = 3 meters

Now,

Let the length of Added metal bar = d

By the formula of 3D Pythagoras theorem, we get;

⇒ d² = a² + b² + c²

⇒ d² = 4² + 2² + 3²

⇒ d² = 16 + 4 + 9

⇒ d² = 29

⇒ d = √29

⇒ d = 5.38

⇒ d = 5.4 meters

Thus, The length of ''Added metal bar'' is ''Approximately 5.4 m''.

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2r+r+s+2s =2×r + r×1 + s×1 + 2×s

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

2r+r+s+2s

=2×r + r×1 + s×1 + 2×s

Hence,

each sum as the product of two factors 2r+r+s+2s =2×r + r×1 + s×1 + 2×s

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Answer: B. 80%

Step-by-step explanation:

P(not green) means that Joseph will pick a marble that is either red, yellow, or purple.

First, we must find the total number of marbles by adding every marble of every color: 2 + 6 + 15 +7 = 30

Now, we need to find the total of marbles that are not green: 2 + 15 + 7 = 24

Now, to solve, we set up this fraction: not green/total marbles = 24/30 = 0.8

0.8 is equivalent to 80% when in percent form. Hope this helps!

Answer: B. 80%  

hope this helped :)

Answer:

Below

Step-by-step explanation:

The bottom will be   5 cubes (= 1 2/3  in)   X  6 cubes ( =2inches )

     = 5 x 6 = 30 cube layer

there will be  9 layers high ( 1/3 inch x 9  = 3 inches)

30 cubes/layer * 9 layers = 270 cubes

The cost of 2 orders of fries and 4 drinks is $5.68 and the cost to get f orders of fries and d drinks is $0.92f+0.96d

When something is calculated on its one unit, then it is called its unit rate. for example: If 5 mangoes is of $50 then cost of 1 mango is 50/5 = 10 here $10 is unit rate for mangoes.

Given that, At the fast food restaurant, an order of fries costs $0.92 and a drink costs $0.96.

We have here unit rates of fries and drinks,

So, when 1 pack of fries costs $0.92, then cost of 2 pack of fries = 2×0.92 = $1.84

Similarly, when 1 drink costs $0.96, then the cost of 4 drinks = 4×0.96 = $3.84

Total cost = $5.68

Similarly, the cost to get f orders of fries = $0.92f

And, the cost of d drinks = $0.96d

Total cost =  $0.92f+0.96d

Hence, we get the answer as = a) $5.68 and b) $0.92f+0.96d

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Answer:

Cynthia is the faster runner.

Bianca is 3.4 miles behind when Cynthia crosses the finish line.

Step-by-step explanation:

slope = Δy/Δx = miles/min = speed of the runner

C's speed = 1/7 = .14 mi/min   (slope of the line shown in the graph)

B's speed = (7-5)/(57.4-41) = 0.122 mi/min   (from the data in the table)

C runs faster.  (she has the greater slope)

Find how much time it takes C to finish the race:

t = distance/speed = (26.2 mi) / (0.14 mi/min) = 187.14 min

Find how far B has gone in 187.14 min:

d = speed x time = (0.122 mi/min)(187.14 min) = 22.8 mi

How far behind is B:

26.2 mi - 22.8 mi = 3.4 miles (B is 3.4 miles behind when C finishes the race)