The distance from Mrs. Thompson's house to the library is 3/4 kilometers. Mrs. Thompson biked 1/2 kilometers. What fraction of the distance from her house to the library did Mrs. Thompson bike?

The x-intercepts [tex]$${graph}\{x \wedge 2+4 x-5[-20,20,-10,10]\}$[/tex].

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.

Given a parabola in standard form [tex]$; y=a x^2+b x+c$[/tex]

then the x coordinate of the vertex can be found using

[tex]$x_{\mathrm{vertex}}=-\frac{b}{2 a}$[/tex]

[tex]$f(x)=x^2+4 x-5$[/tex] is in standard form

with a = 1, b = 4, c = -5

[tex]$\Rightarrow x_{\text {vertex }}=-\frac{4}{2}=-2$[/tex]

substitute this value into f(x) for y coordinate

[tex]$y_{\text {vertex }}=(-2)^2+4(-2)-5=-9$[/tex]

vertex =(-2,-9) to obtain the intercepts

Let x = 0, in equation for y-intercept

let y=0, in equation for x-intercepts

[tex]$x=0 \rightarrow y=-5 \leftarrow$[/tex] y-intercept

y=0 [tex]$\rightarrow x^2+4 x-5=0$[/tex]

the factors of -5 which sum to +4 are +5 and -1

[tex]$\Rightarrow(x+5)(x-1)=0$[/tex] equate each factor to zero and solve for x [tex]$x+5=0 \Rightarrow x=-5$[/tex]

[tex]$x-1=0 \Rightarrow x=1$[/tex]

x = -1 and x = -5

x-intercepts [tex]$${graph}\{x \wedge 2+4 x-5[-20,20,-10,10]\}$[/tex].

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A function's x-intercept and y-intercept is x is 2.

With x = 0, solve for y to determine the y-intercept. It will be said that (0, y). With y = 0, solve for x to determine the x-intercept. It will be said that (x, 0).

In light of this, x=2 is our axis of symmetry.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.        

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Answer:

7.57082 or its just 7.5

Answer:

x = 7

Step-by-step explanation:

42 = 6x

x = 7

6(7) = 42

Answer:

6x = 42 ( being alternate angel)

x = 42/6

x = 7

We generally use scatter plots to observe the relationship between variables. Dots are used in a scatter plot to represent values for two different numeric variables.

Values for an individual data point are indicated by the position of each dot on the horizontal and vertical axis.  A scatter plot represents data points on a two-dimensional plane or on a Cartesian system.

On the X-axis, the independent variable is marked and the dependent variable is marked on the Y-axis. We call these plots as scatter plots or scatter diagrams. Scatter plots can be defined as one of the most useful inventions in statistical graphs. In 1833, it was presented by an English Scientist, John Frederick W. Herschel.

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Answer:

a² + 5

Step-by-step explanation:

a² = The square of a number.

Then:

Five plus the square of a number is:

a² + 5

a percent using the form % to represent the following word problem is x=12

What do u mean by percent?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage. Related Topics: mathematics percentile.

60 % of 20

60/100 = x/20

cross product

60 * 20 = 100x

divide by 100

1200/100 =x

12=x

60/100 = x/20    x= 12

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Answer: FB= .25m + .25n

Step-by-step explanation:

So I drew a diagram of what I think it looks like, and this is my best answer. Sorry if it is incorrect.

The value of x in the right angle triangle is 54 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, exterior angle theorem can be used to find the angle x.

The triangle is a right angle triangle.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the angle x using exterior angle theorem.

90 + x = 144

subtract 90 from both sides of the equation

90 + x = 144

90 - 90 + x = 144 - 90

x = 54 degrees

Therefore, the angle x is 54 degrees.

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The probability of having a total of more than 180 arrivals at the toll in the next two hours is 0.84.

The time taken to assemble follows the normal distribution.

Given mean i.e. μ = 100

Given standard deviation i.e. σ = 40

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

z=(X−μ)/σ

where X is a normal random variable, μ is the mean of X, and σ is the standard deviation of X.

For X=180

Z=(180−100)/40= 2

For X=2

Z=(2-2)/2=0

P(a<X<b)=P(X<b)–P(X<a)

P(20<X<22)=P(X<180)−P(X<2)

                   =P(Z<2)−P(Z<0)

                    =0.8413

Thus, The probability of having a total of more than 180 arrivals at the toll in the next two hours is 0.84.

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As per the given standard deviation, the probability of having a total of more than 180 arrivals at the toll in the next two hours is written as 0.84.

Here we have given that the number of arrive at a highway toll in an hour is independent of other hours and is well-estimated by a Normal distribution with an average of 100 cars per hour and standard deviation 40 cars.

Which means that

mean  = 100

And the value of standard deviation = 40

Now, we have to use the normal random variable of a standard normal distribution is called a standard score or a z-score.

Then the value of z score is calculated as

=> z=(X−μ)/σ

Apply the values on it then we get

=> z = (180−100)/40= 2

Therefore, the probability is calculated as

=> P(20 < x <22) = P(X<180)−P(X<2)

When we apply the value on it then we get,

=> P(Z<2) − P(Z<0)

=> P = 0.8413

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Swim practice will be no more than 35 laps is P≤35.

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Complete Question is: Write an inequality for each sentence.

1. Swim practice will be no more than 35 laps.

Answer:

Step-by-step explanation:

14

Answer:

14 will be your answer for that question

The sum of first square number and the first cube number would be 2.

What is the cube of a number?

A cube of a number is the number multiplied by itself three times. For example, the cube of 2 is 2 x 2 x 2 = 8. It can also be represented mathematically by raising the number to the power of 3, such as x^3 where x is the number you want to find the cube of.

The first square number is 1^2 = 1 and the first cube number is 1^3 = 1. Therefore, the sum of the first square number and the first cube number is 1 + 1 = 2.

Hence, the sum of first square number and the first cube number would be 2.

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Nasim needs  to  invest $20203.5 for the value of the account to reach $27000.

It is the interest that a person can earn from a particular amount of deposit money. And the deposit is increased gradually over the time.

given, interest rate = r = 5.8%

final amount = A = $27000

time period elapsed, t = 5 years

number of times interest applied per time period, n= 365 times

as the interest compound daily so per year interest applied = 365 days = 365 times [ as 1 year = 365 days]

we need to determine the initial invested money, P.

From the compound interest formula, A = P (1 +r/n) ∧nt

                                                  $27000 = P (1+ 0.058/365) ∧365×5

                  initial amount P = $20203.5

Nasim needs to invest $20203.5.

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Answer:

1 or 21

Step-by-step explanation:

The solution is Option B.

The transformation of the function is a reflection along the vertical y axis

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the function be represented as f ( x )

Now , the transformed function is given as g ( x )

The function g ( x ) has the x coordinates as the additive inverse

So , it must be a reflection transformation

And , the axis of transformation is y axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

Therefore , it is a vertical reflection

Hence , the transformation of the function f ( x ) is a reflection

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Using sine and cosine law, the value of x is 7.2 unit

Cosine law is a mathematical formula used to calculate the sides and angles of a triangle when the lengths of all three sides are known. It states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of their included angle.

Using cosine law, we can find the length of A which will in turn assist us in finding the value of x

a² = 12² + 10² -2(12)(10) cos80

a² = 202.32

a = √202.32

a = 14.22

Using sine law;

a / sin A = x / sin X

Substituting the values into the formula

14.22 / sin 80 = x / sin 30

x = 14.22sin30 / sin80

x = 7.2

The value of x is 7.2

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The function an = -4 + 5(n - 1) in slope intercept form is an = 5n - 9

From the question, we have the following parameters that can be used in our computation:

an = -4 + 5(n - 1)

The slope-intercept form of a linear equation is represented as

an = mn + c

Where the variable m is the slope and the variable c is the y-intercept

So, the first step in solving the question is to open the bracket in an = -4 + 5(n - 1)

This gives

an = -4 + 5n - 5

Add -5 and -9

an = 5n - 9

Hence, the representation of the equation is an = 5n - 9

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The general form of the equation of the given circle with center A is (x − h)² + (y − k)² = a².

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

Given:

The circle with center A

The general form of the equation of a circle is: x2 + y2 + 2gx + 2fy + c = 0.

The equation of the circle is given by  (x−h)² + (y−k)² = a²

Here, h and k are the x and y coordinates of the circle and a is the radius of the circle.

Thus, the standard equation of a circle is  (x−h)² + (y−k)² = a².

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Answer:

-2

Step-by-step explanation:

-2 is greater than -4 because on number line the numbers on the left of zero are negative numbers and the numbers which are very close to zero on left side are greater. So -2 is more close to zero than -4 . Hence answer will be

Implementing an expansion strategy, attracting capital, lowering tax obligations, facilitating entry into a business, and utilizing limited liability are all options are correct.

In most cases, a corporation is set up to benefit from restricted liability. This indicates that the shareholders, who are the corporation's owners, are not personally liable for the debts and liabilities of the business. The additional reasons you have provided for forming a corporation are also viable possibilities, but they are not its main objective. Establishing a corporation might be one approach to carry out an expansion strategy, which is a company's plan for growth and expansion.

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The relationship is proportional when John works for the hour allocated.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

Because the rate of change in a proportional relationship is constant (and equal to the constant of proportionality), it is a linear relationship.

In this case, when John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30.

The constant will be:

= 15 / 1 or 30/2

= $15 per hour.

Therefore, it's a proportional relationship.

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When John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30. Is the relationship proportional?

The days requried for which Jason's workout would be the same in either pool is 5 days.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Here.

Consider the number of days of Jason's workout be x, the total yard he swims be y,

We have that, he swims at the rec center pool, will complete a 200-yard warm-up, and then swim laps in a lane that is 20 yards long.

y = 200 + 20x

Jason swims at the indoor pool at his gym, he will complete a 100-yard warmup, plus the main set that consists of 40 yards per lap.

y = 100 + 40x

Equating both the equation,

200 + 20x = 100 + 40x

40x - 20x = 200 - 100

20x = 100

x = 5  days

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If a class must have a number of students ≤28 and at the same time greater than 16 then:

16≤S≤28

So the number of students may be: 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28.

Answer:

First is (14-3), but then it's addition.

Answer:

The first process in solving out such an equation is first by evaluating or removing the brackets

And then you add or subtract the equation

And I think lastly is bringing your whole answer down for analysis

192 unique keys will result from the distribution.

Distribution is the process of moving goods and services from a producer to a consumer. It involves the coordination of several activities, including transportation, storage, and delivery, in order to ensure the products reach the intended customer in a timely and cost-effective manner. Distribution also involves marketing, which helps identify customer needs and target markets. Finally, distribution requires proper management of the supply chain, so that products are delivered to the right customers when they need them.

Each of the 12 electrical locks will have a unique key, so the total number of unique keys that will result from the distribution will be 12 multiplied by the number of job site superintendents, which is 16. Therefore, the total number of unique keys will be 192.

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The expression startroot 64 r superscript 8 baseline endroot can be written as (64)1/8r8.

This expression is asking for us to take the eighth root of 64, and then multiply it by 8. To solve this we can use the formula for radicals, which states that the nth root of a number a is equal to a1/n. In this case, n is equal to 8, and a is equal to 64. Therefore, the expression can be rewritten as 641/8 x 8. This simplifies to 8r2.

To calculate this, we first need to calculate the eighth root of 64, which can be done by raising the number to the power of the reciprocal of the root. In this case, we need to calculate 64^1/8. We can use a scientific calculator to find that the eighth root of 64 is 2. To finish the calculation, we simply multiply 2 by 8, which gives us 16. We can rewrite 16 as 8r2, which is the answer to the expression.

Therefore, the simplified expression is 8r2.

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The simplified form of expression √(64r^8) is  8r^4

The correct answer is an option (b)

In this question we have been given an expression startroot 64 r superscript 8 baseline endroot.

i.e., √(64r^8)

We need to simplify this expresison.

We know that 64 is square of 8.

8^2 = 64

So, we can write given expression as,

√(64r^8)

= √(8^2r^8)

= √[8^2r^(2 * 4)]

We know that for the properties of exponents i.e., non-zero numbers a, m,n

(a^m)^n = a^(m * n)                    ............(1)

So, √[8^2r^(2 * 4)]

= √[8^2(r^4)^2]            

= √((8r^4)^2)

Square-root is nothing but the 1/2 power of number/expression.

i.e., √((8r^4)^2)

= [(8r^4)^2]^1/2

=  (8r^4)^(2 * 1/2)                  ...........(from (1))

= (8r^4)^1

= 8r^4

Therefore, √(64r^8)  =  8r^4

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The system does appear to have a solution after the changes.

The equation of the orange line after the changes is y = -x - 3. The system appears to have a solution after the changes because the equations for both lines are in the same form. The blue line has a slope of -5 and the orange line has a slope of -1. This means that the lines have the same slope and the same y-intercept. This means that the two lines are parallel and will intersect at the point (-3,3).

To calculate the point of intersection, we can plug in -3 for x in both equations and solve for y.

For the blue line: y = -(-3)^5 = 3

For the orange line: y = -(-3) - 3 = 3

This means that the point of intersection for these two lines is (-3,3). Therefore, the system does appear to have a solution after the changes.

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Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Lets solve for x.

[tex]7x-12=4(x-9)-9x[/tex]

Apply the distributive property in [tex]4(x-9)[/tex].

[tex]7x-12=4x-36-9x[/tex]

Subtract [tex]9x[/tex] from [tex]4x[/tex].

[tex]7x-12=-5x-36[/tex]

Subtract [tex]7x[/tex] from both sides of the equation.

[tex]-12=-5x-36-7x[/tex]

Subtract [tex]7x[/tex] from [tex]-5x[/tex].

[tex]-12=-12x-36[/tex]

Add 36 to both sides of the equation.

[tex]24=-12x[/tex]

[tex]-12x=24[/tex]

Divide both sides of the equation by -12.

[tex]x=-2[/tex]

Answer:

Step-by-step explanation:

Answer: Obtuse

Step-by-step explanation:

A right angle is an angle that is aqual to 90°. A 90° angle looks something like this: ∟. An obtuse angle is an angle tha mesures larger than that, like this: ⦦. An Acute angle is an angle that has a smaller angle mesaure than 90°. An acute angle looks smething like this: ⦟. Hope this helps, good luck.

On solving the provided question, we can say that - in the equation 2x + 5 the value of the equation is = 11

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here, we have

2x + 5

and given that x= 5

so answer is 11

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