If m<1 = (7x-19), and m<2 = (x + 5)°, find m2

The value of x for the equation is 8 to roundoff the nearest ten-thousand  = 8.0000.

A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). For instance, the base ten logarithms of 100 equals 2, because ten raised towards the power of two equals 100: log 100 = 2.

Solving for x  the equation  log₂4 x=5.

log₂4 x=5

witting this as :

4x = 2⁵

4x  = 32

x = 32/4

x = 8

The value of x for the equation is 8 to roundoff the nearest ten-thousand  = 8.0000

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Answer:

1. -8/11

2. -1 3/7

Step-by-step explanation(Q1):

Using order of operations, start with parentheses and work with exponents second. Then, M/D/A/S.

[tex]5-3\\=2\\=2^{3}\\=\boxed{8}\\3^2\\=9\\=1+9-21\\1+9\\=10\\=10-21\\=\boxed{-11}\\=\frac{8}{-11}[/tex]

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Step-by-step explanation(Q2):

Given x = 3, y = -2

[tex]4\left(3\right)\\=12\\=12+\left(-2\right)\\12+\left(-2\right)\\=12-2\\=10\\\downarrow\\2\left(-2\right)\\=-4\\=-4-3\\=\left(-4\right)-3\\=-7\\=\frac{10}{-7}\\=-\frac{10}{7}\\\\\bold{Long~Division}\\7 \div 10 = 1\\1 \times 7 = 7\\7 - 10 = 3\\= 1,R3\\\\\frac{10}{7}\\=1\frac{3}{7}\\=-1\frac{3}{7}[/tex]

The numeric values of the function are given as follows:

The function is missing, and is given as follows:

It asks for the following numeric values:

f(-3), f(2), f(5).

To find the numeric value of a function, we replace each instance of the variable by the desired value.

Hence, for this function, the numeric values are:

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The amount of the shed that Jack would have built when Kyle finishes the shed is 8/25.

A fraction is a non- whole number that consists of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.

When Kyle finishes building the shed, he would have finished building 1 of the shed. In order to determine the amount of shed Kyle needs to build in order to build one shed, divide 1 by 5/8.

1 ÷ 5/8

= 1 x 8/5 = 8/5

The amount of shed that Jack will have built when Kyle finishes the shed is:

8/5 x 1/5 = 8/25

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The perimeter of triangle 8 is 41 feet and 3 inches while the area is around 81.42 feet².

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

The given object is a triangle with sides of 13 ft 4 in,13 ft 4 in, and 14 ft 7 in.

A perimeter is the sum of all sides of the triangle.

There fore,

Perimeter = 13 ft 4 in + 13 ft 4 in + 4 ft 7 in

⇒ 41 feet 3 inches.

Now the area is given as 1/2 × base × height.

Here base = 14 ft 7 in and height = 11 ft 2 inch

Now,

1 inch = 1/12 ft so 7 inch = 7/12 feet and 2 inches = 2/12 feet.

So,

Area = 1/2 × (14 + 7/12) × (11 + 2/12)

Area = 81.42 feet²

Hence "The perimeter of triangle 8 is 41 feet and 3 inches while the area is around 81.42 feet²".

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Answer:

[tex]f(x)=-x^2 + 11x - 24[/tex]

Step-by-step explanation:

Well for this problem, you want to start off by writing it in factored form.

In factored form, you can represent a quadratic as: [tex]f(x)=a(x-b)(x-c)[/tex], where x=b, and x=c are zeroes of the function, since plugging them into the function makes one of the factors zero, and multiplying zero by the other factors will just give you zero.

The "a" in front of the two factors generally defines the stretch/compression of the function.

So let's start by plugging in the zeroes into the function, and then we can solve for "a" later: [tex]f(x) = a(x-3)(x-8)[/tex]

Now let's use one point on the graph, which is not a root/zero to solve for "a". It's important to not use a zero/root since if we use that point the entire thing will be zero regardless of the value of "a"

Luckily we have one point provided that is not a zero and is: (4, 4)

So let's plug it in: [tex]4=a(4-3)(4-8)\\4=a(1)(-4)\\4=-4a\\a=-1[/tex]

So now let's plug this into the factored form to get: [tex]f(x)=-(x-3)(x-8)[/tex]

using foil to multiply these two factors you get: -[x^2 -8x - 3x + 24]

Now combine like terms

-[x^2 - 11x + 24]

distribute the negative sign

-x^2 + 11x - 24

[tex] \large \bf \implies{y = { - x}^{2} + 11x - 24}[/tex]

Let standard form of quadratic equation be

If passes through (3,0) , (8,0) and (4,4)

The measure of ∠B round to the nearest whole number is 76°.

Cosine is the trigonometric function that is equal to the ratio of the side adjacent to the acute angle in a right angled triangle.

Mathematically,

           Cos = Base/Hypotenuse

Now given that, a triangle ABC,

AB = 21

BC = 7

∠C = 90°

Thus, we have

hypotenuse = AB

Base = BC

Perpendicular = AC

So, for angle B

CosB = Base/Hypotenuse

⇒ CosB = BC/AB

Put the values we get,

⇒ CosB = 7/21

or,

CosB = Cos(75.53°)

⇒ B = 75.53°

Now the nearest whole number to 75.53° is 76°

Thus, we get

B = 76°

Thus, the measure of ∠B round to the nearest whole number is 76°.

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The value of the fraction expression 4 x 37/10 is 14 8/10 not 12 7/10

The equation is given as:

4 x 3 7/10 = 12 7/10

Remove the result

So, we have

4 x 3 7/10

Express 3 7/10 as an improper fraction

So, we have

4 x 37/10 = 4 x 37/10

Evaluate the product of 4 and 37

So, we have

4 x 37/10 = 148/10

Evaluate the quotient of 148 and 10

So, we have

4 x 37/10 = 14 8/10

Hence, the value of the fraction expression 4 x 37/10 is 14 8/10 not 12 7/10

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The values of the missing sides of the similar shapes are:

x = 7

y = 10

z = 20

Similar shapes have side lengths whose ratios are the same, or have proportional side lengths.

Use the following ratios to find the missing lengths of the two similar shapes in the given diagram:

35/14 = 17.5/x

Cross multiply

(35)(x) = (17.5)(14)

35x = 245

Divide both sides by 35

35x/35 = 245/35

x = 7

35/14 = 25/y

Cross multiply

(35)(y) = (25)(14)

35y = 350

35y/35 = 350/35

y = 10

35/14 = z/8

(35)(8) = 14z

280 = 14z

z = 280/14

z = 20

Therefore, the values of the missing sides of the similar shapes are:

x = 7

y = 10

z = 20

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Answer:

45 feet

Step-by-step explanation:

Set up Ratios

1/2 in/5 ft = 4 1/2 in/x

Solve for x by cross-multiplying:

[tex]\frac{1/2}{5}[/tex] times [tex]\frac{4 1/2}{x}[/tex]

4 1/2 times 5 = 22 1/2

1/2 times x = 1/2x

22 1/2 = 1/2x

45 = X

Therefore the actual length of the bus is 45 feet.

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Answer:

x=42

y=12

Step-by-step explanation:

The real root of the number √0.49 is given by 0.7.

We are given the expression:

√0.49

We need to find the root of the number.
For this, we will make the factors of the number and then solve the expression accordingly.

First, we know that 0.49 can also be written as 49 / 100

Now, we also know that:

49 = 7 × 7 and 100 = 10 × 10

So, the square root of 49 will be 7 and 100 will be 10.

So, we get the root of the number as:

√0.49 = 7 / 10

√0.49 = 0.7

Therefore, the real root of the number √0.49 is given by 0.7.

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The coordinates of the images of the points are B'(x, y) = (0, 2), C'(x, y) = (3, 4), Z'(x, y) = (4, 3) and X'(x, y) = (4, 1), respectively.

In this problem we find four points set on Cartesian plane, each of which has to be transformed by using the following transformation rule about the origin:

(x', y') = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

(x, y) - Coordinates of the original point.

θ - Angle of rotation, in degrees.

If we know that B(x, y) = (- 2, 0), C(x, y) = (- 4, 3), Z(x, y) = (- 3, 4), X(x, y) = (- 1, 4) and θ = 90°, then the coordinates of the resulting point:

B'(x, y) = (- 2 · cos (- 90)° - 0 · sin (- 90°), - 2 · sin (- 90°) + 0 · cos (- 90°))

B'(x, y) = (0, 2)

C'(x, y) = (- 4 · cos (- 90°) - 3 · sin (- 90°), - 4 · sin (- 90°) + 3 · cos (- 90°))

C'(x, y) = (3, 4)

Z'(x, y) = (- 3 · cos (- 90°) - 4 · sin (- 90°), - 3 · sin (- 90°) + 4 · cos (- 90°))

Z'(x, y) = (4, 3)

X'(x, y) = (- 1 · cos (- 90°) - 4 · sin (- 90°), - 1 · sin (- 90°) + 4 · cos (- 90°))

X'(x, y) = (4, 1)

Finally, we proceed to graph the locations of the points, both original and resulting, by means of a graphing tool.

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Answer:

-24

Step-by-step explanation:

-7 - 17 = -24.

Answer:

-24

Step-by-step explanation:

[tex]for~q - 7, q = -17\\-17-7\\=-24[/tex]

The numbers are 88, 90 and 92. So the first number in this sequence is 88.

Given that

The sum of 3 consecutive even numbers is 270 .

What is consecutive numbers?

      Let the numbers be n, n+2, and n+4.

      n+(n+2)+(n+4) = 270

      3n+6 = 270

      3n = 264

      n = 264/3

      n=88

First number = x = 88

Second number = x + 2 = 88 + 2 = 90

Third number = x + 4 = 88 + 4 = 92

Therefore, the first number is 88.

Hence, the numbers are 88, 90 and 92.

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[tex]\sqrt{x}[/tex] = [tex]\sqrt{x+1}[/tex] has no real roots.

[tex]\sqrt{x}[/tex] = [tex]\sqrt{x+1}[/tex]

squaring both the sides

x = x+1

0 = 1

which is not true

hence false.

Therefore, no real roots.

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Answer: 21

Step-by-step explanation:

The given expression can be written in its simplest form by using the rule of negative exponent.

As the negative exponent is applied to the second term, which also has a power, we will first multiply the powers. As we know that (x^n)^m=x^nm, hence,

(x^2/3)^-1=x^2/3*-1=x^-2/3

Now the expression will become 5x^-2/3

Now solving the second term for the negative exponent, the rule of negative exponent states that when a base term has a negative exponent, the negative sign can be solved by inversing the base term. We know that x^-a=1/x^a, therefore

5x^-2/3=5/x^2/3

The simplest form of the expression is 5(x²/₃)⁻¹=5/x^2/3

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Taking into account definition of perimeter and system of equations,  the length and width of the frame is 32 inches and 21 inches respectively.

The perimeter of a two-dimensional figure is the distance around the figure. That is, the perimeter of a flat geometric figure is called the length of its contour.

So, the perimeter is the measurement obtained as a result of the sum of the sides of a flat geometric figure. So to calculate the perimeter of a figure it is necessary to know two basic variables:

A rectangle is a flat geometric figure with four sides, of which two sides that are opposite parallel to each other have the same length and the remaining two have another length. The expression to calculate the perimeter of a rectangle is:

Perimeter= 2×(length + width)

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know that:

So, the system of equations to be solved is

[tex]\left \{ {{2x(L+W)=106} \atop {L=2xW-10}} \right.[/tex]

From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

2×(2×W - 10 + W)=106

Solving:

2×(3×W - 10)=106

2×3×W - 2×10=106

6×W - 20=106

6×W=106 + 20

6×W=126

W=126 ÷6

W= 21

Remembering that L= 2×W - 10, you get:

L= 2×21 - 10

Solving:

L= 32

Finally, the length and width of the frame is 32 inches and 21 inches respectively.

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Just by adding the second row to the first one in the matrix, we can see that the solution of the system of equations is x = 0.5 and y = 20.

Here we have the system of equations:

300x - y = 130

200x + y = 120

And we want to solve it using a matrix equation. Remember that we could add the two rows, subtract them, etc to remove one of the variables.

Here is really simple to see that if we add the two rows (or the two equations, depending on how you see the system) the variable y will be removed.

Then we can add the second row to the first one to get.

(300x + 200x) + (-y + y) = (130 + 120)

Now our matrix will look like:

500x + 0y = 250

200x + y = 120

With the first row we can find the value of x, it just is:

x = 250/500 = 0.5

And with taht we can find the value of y:

200*0.5 + y = 120

100 + y = 120

y = 120 - 100 = 20

Just by adding two rows, we can see that the solution of the system of equations is x = 0.5 and y = 20.

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Answer:

7 = b.

8 = a.

Answer:

8x+8

Step-by-step explanation:

perimeter = lengths of all sides added up

we want all sides to add up to 6x + 4

so far, we have 2x-7 and -4x + 3

side 1 + side 2 + side 3 = perimeter = 6x + 4

2x - 7 + (-4x + 3) + side 3 = 6x + 4

-2x -4 + side 3 = 6x + 4

add (2x+4) to both sides to isolate side 3

side 3 = 8x + 8

Answer:

hope u will be clear from the given definition

value of x =  25

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is the expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log 4x =2

now convert this equation to exponential form

=> 4x = 10²

=> 4x = 100

=> x = 100 / 4

=> x = 25

Thus solution for this equation is x =25.

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Answer:

-429

Step-by-step explanation:

Answer:

2751

Step-by-step explanation:

2+5 times 12 times 54 minus 10 minus 475 minus 6

2+3240-10-475-6=2751

Answer:

option a 0.06 bared

Let the number be x

x=18

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Answer:    X=18

Step-by-step explanation:

The factoring of the expression 3 x²-2=5 x is (x - 2) (3x +1)

By ordering the values, we get:

3x² - 5x - 2 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Factor 5 from 5x:

3x² - 5x - 2 = 0

3x² + (- 6 + 1) x - 2 = 0

2. Apply the distributive b:

3x² - 6x + 1x - 2 = 0

3. Groups the first two terms and the last two terms:

(3x² - 6x) + 1x - 2 = 0

4. Factorize the greatest common denominator (GCM) of each group:

3x(x - 2) + x - 2 = 0

5. Simplify the common term (x - 2) with the distributive property:

(x - 2) (3x +1)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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The two numbers are 12 and 20

Let the small number be x

Let the large number be y

We have that;

y = 8 + x      (1)

But;

x + y = 32    (2)

Now, substitute the value of y as 8 + x in equation (2)

x + 8 + x = 32

collect like terms

2x + 8 = 32

2x = 32 - 8

2x = 24

Make 'x' the subject

x = 24/ 2

x = 12

But;

y = 8 + x

y = 8 + 12

y = 20

Thus, the two numbers are 12 and 20

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