The simplified sum of the second and forth integers are

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 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 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 statements a, c and d are true.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

From the figure we understood that h is the height and r is the radius.

The volume of the cone is 1/3πr²h

V= 1/3πr²h

When volume is 47 then we need to find the height

47= 1/3π(3)²h

47=3×3.14h

47=9.42h

h=4.92=5

So if the volume is 47cm³ then the height of the cone is 5cm approximately is true

Now let us find the statement 2 is true or not

V= 1/3π(3)²(10)

V=3×3.14×10

V=94.2 cm³

So the second statement is not true

The equation V= 1/3π(3)²h is the volume of the cone and h=3V/π(3)² an be used to find the height of the cone is true.

Hence, the statements a, c and d are true.

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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:

$390

Step-by-step explanation:

780/2 = 390

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)

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

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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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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Using the given function in variable 'x', substitute x=y and y =x to find the inverse, The answer is y=-3x/4 +1/2.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. The most common symbol for a function is an arrow with the letter "f" written above it (f: X → Y), where "X" is the set of inputs and "Y" is the set of outputs. A function assigns a unique output to each input, and the inputs and outputs can be any mathematical objects, such as numbers, vectors, or polynomials.

To find the inverse of a function, you first need to make sure that the function is invertible, which means that it has a unique inverse. A function is invertible if and only if it is a bijection, that is, it is both a function (meaning that it assigns a unique output to each input) and a surjection (meaning that every element of the output set is the image of at least one element of the input set) and an injection (meaning that no two different inputs have the same output). Once you have verified that the function is invertible, you can find its inverse by "reversing" the input and output.

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

replacing input and output,

x = -4/3y + 2/3

3x-2 = -4y

y = -3x/4 + 1/2

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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: C

Step-by-step explanation:

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:

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

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 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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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

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 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:

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 simplified inequality for this problem is given as follows:

0.65x - 0.35y + 0.65z ≥ 0.

Hence the value of A is of:

0.65.

The inequality for this problem is defined as follows:

(x + z)/(x + y + z) ≥ 0.35.

Cross multiplication would work in this case, as the right term is a constant, however if it was a rational expression it would not work.

Thus the first step is leaving the right side as 0, as follows:

(x + z)/(x + y + z) - 0.35 ≥ 0.

Then the least common factor is applied to the left side, as follows:

[x + z - 0.35(x + y + z)]/(x + y + z) ≥ 0.

Applying the distributive property and combining the like terms, we have that:

(0.65x - 0.35y + 0.65z)/(x + y + z) ≥ 0.

Now cross multiplication can be applied, hence the simplified inequality is:

0.65x - 0.35y + 0.65z ≥ 0.

The coefficient A has a value of 0.65, which is the term that multiplies x.

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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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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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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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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.

Answer: 11,295,063

Step-by-step explanation:

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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