given that f(x) = 5x -2 and g(x) = x +5 find g of (-12)​

Answer:0.32$

Step-by-step explanation:2.56/8=0.32$

Answer:

10

Step-by-step explanation:

(x-3)² = 7²

so x-3 = 7

x =10

Step-by-step explanation:

the picture is so fuzzy, I can hardly read the details.

I suspect the orange line is

f(x) = 6^x

the black line is

g(x) = 6^x + k⁵

to find k we simply create

(g - f)(x) = 6^x + k⁵ - 6^x = k⁵

as we can see, the difference (up/down distance) between both functions is a constant k⁵.

the best and most reliably we can see and calculate that difference at x = 0 :

2

k⁵ = 2

[tex]k = \sqrt[5]{2} [/tex]

which is 1.148698355...

but I see, I might have misunderstood the 5 of the coordinate axis as exponent of k.

so, the function might be

g(x) = 6^x + k

and then

the difference is simply k, and

k = 2

Answer:

17/7

Step-by-step explanation:

2 3/7 = 17/7

2 times 7 = 14 + 3 = 17/7

So, the answer is 17/7

Answer:

x= -4

Step-by-step explanation:

-7(x-2)+4=46

-7x+14+4=46

-7x=46-18

-7x=28

x=28/-7

x= -4

Answer:

-4

Step-by-step explanation:

Hope it helps! =D

On solving the provided question, we can say that the linear equation formed will be y = -2x+18

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

In xx hours, Justin can iron 40x40x shirts since he can iron 40 shirts every hour. Daniel can iron 20 shirts each hour, or 20y20y shirts, in y hours. There were 360 shirts ironed in all (40x+20y):

[tex]40x+20y=360\\40x+20y=360\\x+y=14\\40x+20y= 360\\x+y=14\\40x+20y = 360 x+y = 14 20y = -40x+360 \\y = -2x+18[/tex]

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The definite integral of x * ln(x) from [tex]x = e^{1/8} \ to \ x = \frac{e^{-1/6}}{2}[/tex]

To find the definite integral of x * ln(x) from x = [tex]e^{(1/8)}[/tex] to x = [tex]e^{(1/6)[/tex] it can be evaluated using integration by substitution.

Let u = ln(x), then du/dx = 1/x and dx = [tex]e^u du[/tex]. The integral becomes:

[tex]\int e^{(1/8)} e^{(1/6) }x \ ln(x) dx = \int e^{(1/8)} e^{(1/6)} e^u u du[/tex]

= [[tex]e^{(2u)[/tex]/2] evaluated at u = ln([tex]e^{(1/6)[/tex]) and u = ln([tex]e^{(1/8)}[/tex]), which gives the final result:

[e[tex]^{(2u)[/tex]/2] evaluated at u = 1/6 - 1/8 = -1/12

[tex]= e^{(-2/12)}/2 = e^{(-1/6)}/2[/tex]

The integral is a mathematical concept that refers to the sum of the values of a function over a specific interval or region. It is a tool used to calculate the area under a curve or the total change in a quantity over a given interval.

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The test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis

A test statistic shows how closely your data’s distribution fits the distribution anticipated by the statistical test’s null hypothesis. The frequency with which each observation happens is defined by the distribution of data, which may be represented by its central tendency and variance around that central tendency.

Z= (x – y)/(x2/n1 + y2/n2) is the formula for calculating the test statistic when comparing two population means. To compute the statistic, we must first compute the sample means (x and y) and standard deviations (x and y) for each sample independently. In statistics, there are many different types of tests, such as the t-test, Z-test, chi-square test, anova test, binomial test, one sample median test, and so on. If parametric tests are applied,

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To purchase all the paint, it will cost £ 186.89.

-Following are the formulas for calculating the trapezium's area:

[tex]& A=\frac{1}{2}(a+b) h \\[/tex]

[tex]& a \| b \text { dimensions } \\[/tex]

[tex]& \therefore A=\frac{1}{2}(16+10) \times 7.6 \\[/tex]

[tex]& =98.8 \mathrm{~m}^2[/tex]

-Since 1 litre of paint covers an area of 1.9 sq m, we divide the area of the trapezium by this and multiply by the cost per litre to get the overall cost:

[tex]$& \text { Paint Used }=\frac{\text { Area }}{\text { Paint } / m^2} \\[/tex]

[tex]$& =\frac{98.8}{1.9} \\[/tex]

[tex]$& =52 \text { litres }[/tex]

-We are given that each 5 I tin of paint costs $£ 16.99$. We therefore divide the paint used by 5 and multiply by $£ 16.99$ :

[tex]$& =\frac{52}{5} \\[/tex]

[tex]$& =10.4-. > 11 \text { tins } \\[/tex]

[tex]$& \text { Cost }=11 \times 16.99 \\[/tex]

= £ 186.89

Hence, it will cost £ 186.89 to buy all the paint

Paint is only bought in 5 I tins. Hence, any fractional bit will necessitate the purchase of the whole 5 I tin

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Answer:

x = arccos(sqrt((1 + sin(x))/2)) + 2npi or x = pi - arccos(sqrt((1 + sin(x))/2)) + 2npi

Step-by-step explanation:

cos^2(x) - sin^2(x) = sin(x) can be rewritten as cos^2(x) = sin^2(x) + sin(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify the equation as

cos^2(x) = 1 - cos^2(x) + sin(x)

Solving for cos^2(x), we get

cos^2(x) = (1 + sin(x))/2

Therefore, cos(x) = sqrt((1 + sin(x))/2) or cos(x) = -sqrt((1 + sin(x))/2)

To find the possible values of x, we need to find the values of sin(x) that satisfy this equation.

For the domain [0, 2pi), the range of sin(x) is [-1, 1], so we have:

cos(x) = sqrt((1 + sin(x))/2) for -1 <= sin(x) < 1

cos(x) = -sqrt((1 + sin(x))/2) for -1 <= sin(x) < 1

So, the solution is

x = arccos(sqrt((1 + sin(x))/2)) + 2npi or x = pi - arccos(sqrt((1 + sin(x))/2)) + 2npi

where n is an integer.

Answer:

  C. 45 × 45

Step-by-step explanation:

You want to know the expanded form of 45 squared.

A square is signified by an exponent of 2:

  45 squared = 45²

The exponent tells you the number of times the base appears as a factor in the product:

  45² = 45 × 45 . . . . . . . 45 is a factor 2 times in the product

__

Additional comment

The value "45 squared" is the area of a square of side length 45.

The value "45 cubed" is the volume of a cube of side length 45.

The compound experiment is the probability of heads on a coin and 4 on a number cube which is P = ( 1/12 )

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability be represented as P

Now , the equation will be

a)

The probability of heads on a coin and 4 on a number cube

Now , the probability of tossing a heads on a coin = 1/2

The probability of rolling a 4 on number cube = 1/6

So , the compound probability P = ( 1/2 ) ( 1/6 )

On simplifying the equation , we get

P = 1/12

b)

The probability of 3 on a six spaced spinner

The value of P = 1/6

c)

The probability of rolling a 6 on a number cube

The value of P = 1/6

d)

The probability of drawing a King from a regular deck of cards

The value of P = 4/52

On simplifying the equation , we get

The value of P = 1/13

Hence , the compound probability is P = 1/12

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In a consistent system with more variables than equations, the augmented column of the reduced row echelon form (rref) contains the solution set of the system of linear equations.

The Reduced Row Echelon Form denoted as "rref"  is a matrix representation of the system in which the leading non-zero entry in each row is 1 and is called the pivot. The pivots in the rref correspond to the basic variables in the solution set, and the non-pivot variables are free variables.

In the augmented column of "rref" , the entries corresponding to the pivot columns give the values of the basic variables in the solution set, while the entries corresponding to the non-pivot columns give the coefficients of the free variables,  free variables can take any value and do not affect the solution set,

Therefore, information contained in augmented column of the rref gives the values of the basic variables and the coefficients of the free variables in the solution set of the system.

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Introduction:

Probability is a measure of the likelihood that a given event will occur. In this scenario, the event of interest is the fuel tank being empty, given the observation that the battery is flat. Evaluating the probability of this event involves finding the relationship between the fuel tank and the battery, and using this information to calculate the probability that the fuel tank is empty.

Detailed explanation:

To evaluate the probability of the fuel tank being empty given the observation that the battery is flat, we need to use Bayes' theorem. Bayes' theorem states that the probability of event A given event B can be calculated as follows:

P(A|B) = P(B|A) * P(A) / P(B)

Where P(A|B) is the probability of event A given event B, P(B|A) is the probability of event B given event A, P(A) is the probability of event A, and P(B) is the probability of event B.

In this scenario, event A is the fuel tank being empty, and event B is the battery being flat. To calculate the probability of the fuel tank being empty given the battery is flat, we need to find the values of P(B|A), P(A), and P(B).

Suppose we have the following information:

P(A) = 0.1 (the probability that the fuel tank is empty)

P(B|A) = 0.8 (the probability that the battery is flat given that the fuel tank is empty)

P(B) = 0.05 (the probability that the battery is flat)

Using these values, we can calculate P(A|B) as follows:

P(A|B) = P(B|A) * P(A) / P(B) = 0.8 * 0.1 / 0.05 = 0.16

This means that the probability that the fuel tank is empty given the battery is flat is 0.16.

In conclusion, the probability that the fuel tank is empty given that the battery is flat is lower than the probability that the fuel tank is empty, which was 0.1. This suggests that having a flat battery decreases the likelihood that the fuel tank is empty.

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On solving the provided question we can say that the sides are = 10, 9 , 8 perimeter of the triangle will be = 10 + 9 + 9/ 3 = 27 / 3 = 9 units

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

the sides are = 10, 9 , 8

perimeter of the triangle will be = 10 + 9 + 9/ 3 = 27 / 3 = 9 units

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Answer:

46

Step-by-step explanation:

18+21+12+12+23=86

22×6=132

132-86=46

46

The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable takes a value less than or equal to z.

In order to model continuous phenomena or quantities that depend on chance, such as time, length, and mass, continuous random variables are utilized.

The likelihood that the random variable takes a value inside that interval is defined as the area under the density function over an interval. Therefore, the probability that the random variable will have a value less than or equal to z is given by the area under the normal curve from negative infinity to z.

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The number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.

The number of monic polynomials of degree n in Fp[x] is pⁿ. In this case, "monic" means that the coefficient of xⁿ is 1.

In Fp[x], there are p possible values for the coefficient of each power of x, from x⁰ to xⁿ. Hence, there are pⁿ possible polynomials of degree n.

The number of polynomials that do not take on the value 0 for x ∈ Fp is pⁿ - 1 because if a polynomial is zero for all values of x in Fp, then it must be the zero polynomial. The zero polynomial is not counted because it is not monic, as it has a coefficient of 0 for the xⁿ term.

So, the number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.

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For the expressions (32 - 13) (54 -45) and (23.1 - 17)/(3.2 - 13), the inequality will be (32 - 13) (54 - 45) > (23.1 - 17)/(3.2 - 13).

For the expressions -(14/5) - 19.7 and (19.7)⁴, the inequality will be -(14/5) - 19.7 < (19.7)⁴.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The first two expressions are -

(32 - 13) (54 -45) and (23.1 - 17)/(3.2 - 13)

Solve the expression (32 - 13) (54 -45) first.

(32 - 13) (54 - 45)

Use the arithmetic operation of subtraction -

(19)(9)

Use the arithmetic operation of multiplication -

171

Now solve the expression (23.1 - 17)/(3.2 - 13).

(23.1 - 17)/(3.2 - 13)

Use the arithmetic operation of subtraction -

6.1/-9.8

Use the arithmetic operation of division -

-0.622

Now, it can be seen that -0.622 is less than 171.

Therefore, the inequality symbol > will be used.

The second two expressions are -

-(14/5) - 19.7 and (-19.7)⁴

Solve the expression -(14/5) - 19.7 first.

-(14/5) - 19.7

Use the arithmetic operation of division -

-2.8 - 19.7

- 22.5

Now solve the expression (-19.7)⁴.

(-19.7)⁴

Expand using the powers rule -

150613.848

Now, it can be seen that - 22.5 is less than 150613.848.

Therefore, the inequality symbol < will be used.

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Check the picture below.

[tex]\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{21^2+32^2-26^2}{2(21)(32)}\right)=\measuredangle J \implies \cos^{-1}\left(\cfrac{ 789 }{ 1344}\right)=\measuredangle J\implies \boxed{54.1^o\approx \measuredangle J}[/tex]

Make sure your calculator is in Degree mode.

A polynomial is even if each term is an even function. f ( x ) = 2 x 4 − 3 x 2 − 5 f(x)=2x^4-3x^2-5 f(x)=2x4−3x2−5. Odd

What is odd and even polynomial?

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Mr. Estes paid $136,000 for the SUV after the discount was applied.

Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.

We have the formula,

Selling price = (1 - markdown rate) Original price

Here,

Markdown percentage = 15%

Markdown rate = 15/100 = 0.15

Original price of the car = $160,000

Selling price = (1 - 0.15) × 160,000

                     = 0.85 × 160,000

                     = 136,000

Hence the selling price of the car is $136,000.

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given two positive numbers a and b such that b < a. it turns out that a/b is the same as the ratio (a+ b)/a=b/(a-b)

Integers are a set of counting numbers (positive and negative), along with zero, that can be written without a fractional component. As mentioned above, an integer can be either positive, negative or zero.

All natural numbers are also integers that start from 1 and end at infinity.

All whole numbers are also integers, starting from 0 and ending at infinity.

We have two positive numbers a and b and b less a . the ratio of a and b is the same of (a+b)/a .

a:b=(a+b):a

[tex]a^2=b(a+b)\\[/tex]

(a+b)(a-b)=ab

(a+b):a=b:(a-b)

The ratio of a/b = b:(a+b).

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The equation of the line is y =3x + 40

The general formula for the equation of a line is expressed s;

y = mx+ c

Given that the parameters are;

From the information given, we have that the points are;

Slope, m = 3

Intercept, c = unknown

Now, substitute the values, we get;

10 = 3(-10) + c

Now, expand the bracket

10 = -30 + c

Collect like terms

c= 40

Hence, the equation is y = 3x + 40

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The function f(x)=√x with f:R→R is injective and surjective but not bijective.

Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.

Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.

Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.

Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.

In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.

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Answer:

x = 12.5 degree

y = 220 degree

Step-by-step explanation:

The 1/2y is equal to the 110-degree angles, so to find the y, we take

110 times 2 = 220. So, the answer for y is 220.

The (4x + 20) and 1/2y must add up to 180 degrees. We know one is 110 degrees, so the (4x + 20) must be equal to 70 degrees.

4x + 20 = 70

4x = 50

x = 12.5 degree

So, x = 12.5 degrees and y = 220 degrees.

Answer:

Step-by-step explanation: