How do you graph 5x= -50

Answer:

Below

Step-by-step explanation:

Only the middle three are tri -nomials  ( three terms)

the third one reduces to  (x+ 2)^2

Answer:

3

Step-by-step explanation:

(x+2)^2

The second term of the series will be 27.

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.

Sum to infinity = a/1-r

where s = 300

r = 0.1

a = 300 (1 - 0.1)

a = 300 (0.9)

a = 270

The second term of the progression will be = ar

Second term = 270 x 0.1

Second term = 27

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The distance the ride will go for birr 1350 is 130 kilometres.

The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;

Let's use equation to represent the total amount spent on the distance covered.

Therefore,

let

Hence,

y = 50 + 10x

Therefore,

where

y = 1350

y = 50 + 10x

1350 = 50 + 10x

1350 - 50 = 10x

1300 = 10x

divide both sides by 10

x = 1300 / 10

x = 130 km

Therefore, the ride will go 130 km.

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The final function  after the transformations are applied to the graph of y =√x is y = 2√(x - 5) +1.

What is transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Rule of transformation:

g(x) = c f(x+a) + b

If c > 1, then f(x) vertically starched by c factor. If 0< c < 1, then f(x) vertically compressed by c factor.

If a>0, then f(x) is shifted horizontally a unit right side. If a<0, then f(x) is shifted horizontally a unit left side.

If b>0, then f(x) is shifted vertically b unit upward. If a<0, then f(x) is shifted vertically b unit downward.

Putting c = 2, a = -5, b = 1, and f(x) = √x

y = 2√(x - 5) +1

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The inverse of the function shown is (x + 5).

What is the inverse of the function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.

Coordinates of the given line are (8,3) and (-2,-7)

The function of the given graph for two points form is

[tex]y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )[/tex]

or, [tex]y-3 = \frac{-7-3 }{-2-8} (x-8 )[/tex]

or, y - 3 = x - 8

or, y = x -8 + 3 = x - 5

y = x - 5

To find the inverse, replace x with y and y with x then, we get

x = y - 5

y = x + 5

[tex]f^{-1}[/tex] = x + 5

Hence, the inverse of the function shown is (x + 5).

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The approximate speed-up ratio between pipelined and non-pipelined system to execute 100 instructions is 4.03

The term ratio in math defines as an ordered pair of numbers a and b, written a / b where b does not equal 0.

Here we have given that

And we need to determine the approximate speed-up ratio between pipelined and non-pipelined system to execute 100 instructions.

While we looking into the given question we have identified the following values,

=> Number of pipeline segments = stages in pipeline,

=> n = 5

Here we know that,

=> Clock cycle time per operation = clock cycle per stage = 14 ns

And the number of instructions = 100

Here the formula to calculate the startup is written as,

=> T[without pipeline] = no. of instructions × stages in pipeline × clock cycle per stage

=>  100 × 5 × 14

=> T[with pipeline] = (time for pipelined execution without stalls) + (overhead due to stalls)

=> (5 + 99) × 20 + 20 × 20 = 124 × 20

Therefore, the startup is

=> [500 x 14] / [124 x 14]

=> 4.03

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The probability that the mean height x is between 68 and 70 inches is found as 37.28%.

The z-score is written as follows:

z = (x - μ)/σ

In which,

x =  between 68 and 70 inches.

μ = mean 69 inches

σ = standard deviation 6 inches

Put the values in the formula,

Probability that the mean height x is between 68 and 70 inches

P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)

P(68 < x < 70) = (-0.16) < z < (0.16)

P(68 < x < 70) = 0.4364 - 0.0636

P(68 < x < 70) = 0.3728

P(68 < x < 70) = 37.28%

Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.

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The statement that is true about integrals is; A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

Left-Hand Sums and Right-Hand Riemann sums usually give us different approximations of the specific area under a curve.

Now, If one sum gives us an overestimated value and then the other gives us an underestimated value, then we can try to find out what exactly the actual area under the curve might possibly be. It should be noted that left-hand sum will be an under-estimate of the specific area of R. Thus, as  f is increasing, a left-hand sum will definitely use the smallest value of f on each sub-interval. This therefore tells us that any left-hand sum will not cover all of R and also any right-hand sum will be an over-estimated value of the area of R.

Thus, Since f is increasing, a right-hand sum will utilize the largest value of f on each specific sub-interval. Thus, right-hand sum will definitely cover R and others.

From the above, option A is true because if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.

Meanwhile, option B is false because if the graph is concave upwards, then the trapezoid approximation is an overestimated value, and as such the midpoint will be underestimated.

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Billy has already saved 25% of the total cost.

What is percentage?

A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.

Given that, the cost of the DVD is $64.

He saved $16 for the DVD.

The percent of saving

= Saving amount/ cost of DVD × 100%

= (16/64) × 100%

= 0.25 × 100%

= 25%.

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Answer:

one 2

one 3

two 4's

one 5

one 6

Step-by-step explanation:

We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.

[tex]_nC_r = \dfrac{n!}{r!(n-r)!}[/tex] where [tex]n[/tex] is the number of things to choose from and [tex]r[/tex] is the number of things we are choosing. Hence the equation for this problem is:

[tex]_4C_2 = \dfrac{4!}{2!(4-2)!}[/tex]

[tex]_4C_2=\dfrac{24}{2(2)}[/tex]

[tex]_4C_2 = 6[/tex]

So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:

(1, 3)     (3, 5)     (5, 7)

(1, 5)     (3, 7)

(1, 7)

Then, we can calculate the mean, or average, of each.

2           4           6

3           5

4

Finally, we can conclude that the distribution of the means for each possible set of number pairs is:

one 2

one 3

two 4's

one 5

one 6

A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is; 300a + 450b = 6000 and a + 5 = b.

The variables x and y respectively represents  cans of soup and frozen dinners and a and b represents number of cans of soup and frozen dinners.

Let cans of soup be denoted by x

Let each frozen dinner be denoted by y

Now, we are told that each can of soup has 300 mg of sodium and each frozen dinner has 450 mg. Thus;

x = 300

y = 450

It is said that Samuel purchased 5 more frozen dinners than cans of soup  and they all collectively contain 6000 mg of sodium.

Let the no. of cans of soup be 'a' and no. of frozen dinner be 'b'. Thus, we will have the equation as;

ax + by = 6000

a(300) + b(450) = 6000  

300a + 450b = 6000      ------(1)

We are told that Samuel purchased 5 more frozen dinners than cans of soup. This can be represented by the equation;

a + 5 = b    ------(2)

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Answer:

idrk i would at least need how many hours he gardens and how many hours he mows the lawn, for just mowing the lawn he would need to do that for 20 hours completely, for gardening he would need to work 15 hours.

Step-by-step explanation: yaaa

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.

1. First, we need to find the vector-valued function r(t) using the given parameter.

2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:

y = √(4 − (1+sin t)2 − (1 − sin t)2).

3. We can now substitute this expression into the vector-valued function to obtain:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k

4. The space curve represented by the intersection of the surfaces is a helix in a graph.

The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.

The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.

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Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by

f(x) = Σ[∞], n=1 cnyn(x)

To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).

cn = (f,yn) = ∫[0,4]f(x)yn(x)dx

Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by

cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx

Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.

cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx

= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx

= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx

= 1/2 ∫[0,2] (x+2)yn(x) dx

Therefore, the coefficient Cn is given by

Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

1 dozen of Rose costs = $30.96

1 dozen of chrysanthemums costs = $17.80

1 dozen of of tulips costs = $ 21.10

Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips

                         = 16 * 30.96 + 40 * 17.80 + 20 *21.10

                         = $1629.36

There is a 6% sales tax on all order = 6% of 1629.36 =  $ 97.76

Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.

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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.

What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
                        = 16 * 30.96 + 40 * 17.80 + 20 *21.10
                        = $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 =  $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.

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From the given Isosceles trapezoid ABCD, the three correct statements are:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.

Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.

Thus, three correct statements are -

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Answer:

Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)

Good luck;)

Step-by-step explanation:

Answer: t is the dependent variable  and x the independent variable

Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.

x is the independent variable as we can use whatever values we want for x it is not affected by t

Answer:

Read explanation :)

Step-by-step explanation:

Activity 1: When it says direction it refers to the tiles going horizontal and vertical for example the 4 and 9 going vetical to make vertical you must first add 4 + 9 which equals 13 then add a 2 under the 9 so it equals 15. And for 8 and 4 horizontal you must add 8 + 4 which equals 12 so add a three in between the 8 and 4 and for the 7 there is a two on the right of it so add 7 + 2 to equal 9 then add 6 to equal 15 then add a 1 in between the 8 and the 6 to equal 15 and add the 5 in the middle.

Activity 2: On the addition table on the left side of the table the number is the number you add to the number on top for example: the 2 at the top of the table plus the 6 on the same vertical line going down so it would be 2 + 6 which equals 8 as it tells you the answer and for 7 on the left side of the table and 3 at the top of the table with the vertical line would be 7 + 3 which equals 10.

Your Welcome Hope This Helps You.

The statement that is the best interpretation of the mean is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

The data of the number of days members visited a certain fitness center varied from 0 to 7.

The mean of the random variable x = 3.12

The mean of the random variable is also known as the long-run average value of a random variable.  

Hence, we conclude that the best interpretation of the mean in the given question is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

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4% is  the percentage rate of increase or decrease in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                    The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 420( 1.04)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

    1 + r = 1.04

      r = 0.04 ⇒  4%

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The n expressed in terms of r and p is n=r/p.

How to solve the word problems?

Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:

You must frequently create two distinct linear equations in two variables in order to solve these issues.

So, it is expressed as:

r=pn

n=r/p

Hence, The n expressed in terms of r and p is n=r/p.

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An expression that shows number of cookies each friend got is c/5.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, Cole has c oatmeal cookies. He lets 5 of his friends share them fairly.

Total number of cookies =c

Sharing among 5 friends

Number of cookies each friend got =Total number of cookies/5

= c/5

Therefore, an expression that shows number of cookies each friend got is c/5.

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In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.

What is an Agreement?

This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.

Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.

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The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.

It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.

On this note, since the given expression is;

2log2 + 2log4

It follows from factorisation that we have;

2 ( log 2 + log 4 )

Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;

= 2 ( log ( 2 × 4 ) )

= 2 log 8.

Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.

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The general anti derivative or indefinite integral of the function

cos2x - sec²x is 1/2 sin2x + tan x + C .

The given function is of the form : cos2x - sec²x

Now we will use the indefinite integral on the above expression:

∫cos2x - sec²x

This can be broken into :

∫cos2x -  ∫sec²x

Now we will integrate them separately:

∫cos2x, we will use u-substitution.

Let 2x = u

Differentiation both sides we get:

2 dx = du

or, dx = 1/2 du

Hence we will use this value:

∫cos2x

= ∫cos u · 1/2du

= 1/2 ∫ cos u du

=1/2 sin u + C , where C is a constant.

Again we will do the second part of the integral:

∫sec²x

= tan x + C

Hence the required integral will be:

1/2 sin2x + tan x + C .

Now we will use differentiation to check the integral

d/dx (1/2 sin2x + tan x + C )

= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)

= cos 2x + sec² x

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