A rectangular city is 6 miles long and 11 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles. How far is it to the closest tenth of a mile? Answer: The distance is approximately ________ miles.

The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

Answer: F.) 7 triangles

Step-by-step explanation:

Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath

Of those 4 "see through triangles", there are 3 equal to ΔABC

Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.

That's 4 + 3 = 7 total triangles

Answer:

≈5089.3801 (5089.4)

Step-by-step explanation:

the formula is πr^2 x h

so, V=πr2h=π·92·20≈5089.3801

Answer:

Step-by-step explanation:

6089.9

Answer:

A

Step-by-step explanation:

f(-2)=3(4)+1

      =13

Answer: A

Step-by-step explanation:

Do it step by step : f(-2)= 13, f(1)= 4

Answer:

Let's call the growth rate of the tomato plant "g". We know that the height difference between the tomato plant and the bean plant decreases by 0.1 cm per day, so we can write the following equation:

1.5 - 0.85 - (10 * g) = 0

Solving for g:

g = (1.5 - 0.85) / 10 = 0.065 cm/day

So the tomato plant grows at a rate of 0.065 cm per day, and will reach the height of the bean plant in no more than 10 days.

The tomato plant will grow 0.165 cm per day.

Solution:

Given,

Height of bean plant = 1.5 cm

Height of tomato plant = 0.85 cm

The growth rate of bean plant = 0.1 cm/ day

The bean plant will grow 1.5 + (0.1* 10) in 10 days = 2.5 cm

So, the tomato plant will have to grow (2.5 - 0.85) cm in 10 days = 1.65 cm

Since, the tomato plant will grow steadily,

Hence, 1.65/ 10 = 0.165

Therefore, the tomato plant will grow at a rate of 0.165 cm per day

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Answer:

\(2) \: \: \frac{11}{2} \)

Step-by-step explanation:

\( \frac{4}{5} + \frac{18}{20} \\ \\ \frac{4}{5 \times 4} + \frac{18}{20} \\ \\ \frac{4}{20} + \frac{18}{20} \\ \\ \frac{4 + 18}{20} \\ \\ \frac{22}{20} \\ \\ \frac{11}{2} \)

Answer:

\(y = \frac{x}2 + 2.5\)

Step-by-step explanation:

Step 1) Finding the slope
The line is perpendicular to \(y = 1 - 2x\), therefore, its slope is equal to the negative invert of \(y\)'s slope.

\(y\)'s slope is -2 (the coefficient to \(x\)), and, therefore, the line's slope is \(m = [-(-2)]^{-1} = 2^{-1} = \frac12\)

Step 2) Building the Equation

We can now substitute the slope, along with the given point's coordinates, into the formula \(y - y_1 = m(x - x_1)\) :

\(y - 3 = \frac12(x - 1)\\\to y - 3 = \frac{x}2 - \frac12\\\to y = \frac{x}2 + 2.5\)

Answer:

which graph best represents y = -x2 + 6x - 1?

Step-by-step explanation:

hich is the graph of the linear function that is represented by the equation y= 1/2x-2 ?

Answer:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  ( 3 , 8 )

Focus:  ( 3 , 31 /4 )

Axis of Symmetry:  x = 3

Directrix:  y = 33/4

x                      y

1                      4

2                     7

3                     8

4                     7

5                     4

Step-by-step explanation:

Below is a picture of the graph

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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The transformation h(x)=3x^2-7 will cause the graph of f(x)=x^2 to stretch vertically by a factor of 3 and shift 7 units downward.

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

f(x) = x^2

h(x) = 3x^2 - 7

This means that

h(x) = 3f(x) - 7

This in other words, the transformation "stretches" the graph of f(x) = x^2 vertically by a factor of 3 and "translates" it vertically by shifting it downward by 7 units.

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The rational numbers are given as follows:

To order the rational numbers, we must convert the fractions to decimal, dividing the numerator of the fraction by the denominator.

The conversion of each number is given as follows:

Hence they are ordered as follows:

7/15, 6/10, 5/3, 25/5.

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Answer:

0.07142857142 ≈ 7.14

Answer: 20 hrs

Step-by-step explanation:

Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

The value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

The value of angle x and angle y is calculated by applying principle of angles formed by parallel lines as follows;

The value of angle adjacent x = 102⁰

The value of angle x   is calculated as;

x = 180 - 102 ( sum of angles on a straight line)

x = 78⁰

The value of angle y is calculated as follows;

y = 115⁰ (corresponding angles are equal)

Thus, the value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

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The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

The spring will stretch 4.1 inches

Step-by-step explanation:

Direct Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y = kx

Where k is the constant of proportionality.

Let's call:

y = distance a spring stretches

x = weight attached to the spring

We know when x=80 pounds, y=6 inches, thus:

6 = 80k

Solve for k:

\(k=\frac{6}{80}=\frac{3}{40}\)

The equation is now:

\(\displaystyle y = \frac{3}{40}x\)

When x=55 pounds are attached:

\(\displaystyle y = \frac{3}{40}\cdot 55\)

Calculating:

y = 4.1 inches

The spring will stretch 4.1 inches

Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Answer:

a = b = 3√2

Step-by-step explanation:

Use trigonometry:

\( \sin(45°) = \frac{a}{6} \)

Cross-multiply to find a:

\(a = 6 \times \sin(45°) = 6 \times \frac{ \sqrt{2} }{2} = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} \)

Use the Pythagorean theorem to find b:

\( {b}^{2} = {6}^{2} - {a}^{2} \)

\( {b}^{2} = {6}^{2} - ( {3 \sqrt{2}) }^{2} = 36 - 9 \times 2 = 36 - 18 = 18\)

\(b > 0\)

\(b = \sqrt{18} = 3 \sqrt{2} \)

After answering the given query, we can state that The expression for the difference between a number s and -6 is: s - (-6) or s + 6

In numbers, you can multiply, split, add, or take away. The following is how a phrase is made together: Numeric number, expression, and arithmetic operator The elements of a mathematical expression are integers, factors, and functions.   It is feasible to use contrasting words and terms. Any mathematical declaration containing variables, integers, and a mathematical action between them is known as an expression, also known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.

The expression for the difference between a number s and -6 is:

s - (-6)

or

s + 6

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Answer:45%

Step-by-step explanation:

Answer:

z(195) = (195-200)/50 = -0.1

z(205) = (205-200)/50 = +0.1

P(195 < x < 205) = p(-0.1 < z < 0.1) = 0.0797

Step-by-step explanation:

step by step is in they're

Using the normal distribution and the central limit theorem, it is found that there is a 1 = 100% probability that the sample mean will be within 65 of the population mean.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

We want the probability that the sample mean will be within 65 of the population mean, hence:

\(Z = \frac{65}{s}\)

\(Z = \frac{65}{5}\)

\(Z = 13\)

The probability is P(|Z| < 13), which is the p-value of Z = 13 subtracted by the p-value of Z = -13.

Looking at the z-table:

1 - 0 = 1

1 = 100% probability that the sample mean will be within 65 of the population mean.

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The appropriate hypothesis test is a two-sample t-test for independent samples.

The appropriate hypothesis test in this scenario is a two-sample t-test for independent samples. Since the population standard deviations are known, we can use the Z-test instead.

The test statistic can be calculated using the formula:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

x1 and x2 are the sample means for Manufacturer A and Manufacturer B, respectively.

s1 and s2 are the population standard deviations for Manufacturer A and Manufacturer B, respectively.

n1 and n2 are the sample sizes for Manufacturer A and Manufacturer B, respectively.

Plugging in the given values:

x1 = 179, x2 = 178, s1 = 1, s2 = 5, n1 = n2 = 108

t = (179 - 178) / sqrt((1^2 / 108) + (5^2 / 108))

t = 1 / sqrt(0.00926 + 0.0463)

t ≈ 1 / sqrt(0.05556)

t ≈ 1 / 0.2357

t ≈ 4.241

To determine whether there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different, we compare the calculated t-value to the critical value from the t-distribution at the desired significance level (0.05).

The decision depends on the degrees of freedom for the test, which is calculated as (n1 + n2 - 2) = (108 + 108 - 2) = 214.

Using a t-table or statistical software, we find that the critical value for a two-tailed test with a significance level of 0.05 and 214 degrees of freedom is approximately ±1.972.

Since the calculated t-value of 4.241 exceeds the critical value of 1.972, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the voltage of the batteries made by the two manufacturers is different at the 0.05 significance level.

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Answer:

346.93

Step-by-step explanation:

The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.

Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

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When solving a linear system of equations, you are looking for the points of intersection between the equations

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

Solving a system of linear equations

Also, we have the following from the options

The general rile is that

Slope = rate of change

x and y intercepts = when y and x equals 0

points of intersection = solution to the system

Hence, you are looking for the points of intersection between the equations

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Question

When solving a linear system of equations, you are looking for which of the following?

Slope

y-intercept

x-intercept

Points of intersection