The two triangles shown are similar. Find the value of
a
b
2.1
1.4

The y-intercept of the line y = 14 / 17 x + 14 is 14.

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Therefore, let's represent it in slope intercept form.

y = mx + b

where

Therefore, using the equation of a line in slope intercept form, the y-intercept of the equation y = 14 / 17 x + 14 is 14.

The y-intercept of a line is the value of y when x = 0.

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Answer:

  ∠A = 50°

Step-by-step explanation:

Complementary angles total 90°.

  ∠A +∠B = 90°

  (4x+6)° +(4x -4)° = 90°

  8x +2 = 90 . . . . . . . . . . divide by °, collect terms

  8x = 88 . . . . . . . . . . subtract 2

  x = 11 . . . . . . . . . divide by 8

  ∠A = (4x+6)° = (4·11+6)°

  ∠A = 50°

_____

Check

∠B = (4·11 -4) = 40°, the complement of ∠A

Answer:

4,290

Step-by-step explanation:

286.00 x 3 x 5 = 4,290

Answer:

\(92.05^{\circ}\)

Step-by-step explanation:

By the exterior angle theorem, the answer is \(m\angle Y+m\angle Z=92.05^{\circ}\).

Answer:

A

Step-by-step explanation:

exterior angle = sum of the other two angles

63.25 + 28.8

92.05°

True: Solving a system of equations using the graphing, substitution, or elimination method will find the exact same solution.

False: Elimination can never be used to solve a nonlinear system of equations (a system where one equation is not linear).

A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneously.

In Mathematics, there are three (3) main methods that are commonly used for solving a system of equations simultaneously and these include the following:

Generally speaking, the same solution would be obtained when any of the three (3) methods for solving a system of equations are used. However, it is completely false to state that the elimination method cannot be used to solve a nonlinear system of equations.

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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x^2 - 12x + 36 is a perfect square trinomial and can be written as (x-6)(x-6).

(x - 6)^2 = 44.

Take the square root of both sides to get...

x - 6 = ±√44 (Always make the square root + or - when you square root)

Add 6 to both sides...

x = √44 + 6

x = -√44 + 6

These are the 2 values of x.

You can also write it to be -0.633 and 12.633. (Once you round.)

The volume of the tank is 26635.2 ft³.

The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet.

Therefore, the volume of the tank can be calculated as follows:

volume of the tank = πr²h

where

Therefore,

volume of the tank = 3.14 × 18.8² × 24

volume of the tank = 3.14  × 353.44 × 24

volume of the tank = 26635.2384

Therefore,

volume of the tank = 26635.2 ft³

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Answer:

The journal entries are shown below:

Treasury Stock A/c Dr $5,000 (50 shares × $100)

To Cash A/c $5,000

(Being treasure stock is purchased)

Cash A/c Dr $2,600 (50 shares × $52)

(Being treasury stock is sold at higher price and the remaining amount would be credited to the paid in capital account)

Cash A/c Dr $2,300       (50 shares × $46)

Paid in capital - Treasury stock $100

Retained Earnings A/c Dr $100

(Being treasury stock is sold at lower price and the remaining amount would be debited to the retained earning account)

Answer: 110.04

Step-by-step explanation: because it is what it is

The Jenny's net pay with given bonus and over time is $675.96. Therefore, option C is the correct answer.

Given that, Jenny worked 44 hours.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

4 hours were overtime - she is paid time and a half for that.

Her regular wage is $16/hour.

Money she is getting for overtime is 16+16/2

= $24

So, total money =40×16+4×24

= 640+96

= $736

With bonus =736+50

= $786

Her tax rate is 14 percent

So, tax =14% of 786

= 0.14×786

= 110.04

Now, net pay =786-110.04 =$675.96

The Jenny's net pay with given bonus and over time is $675.96. Therefore, option C is the correct answer.

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Answer:

169

Step-by-step explanation:

13*13=169

We can split the two 13's up:

(10+3)(10+3)

Multiply 10 with 10, 10 with 3, 3 with 10, and 3 with 3.

Basically, just multiply every single term together.

100+30+30+9

100+69

169

Hope this helps!

Answer:

169

Step-by-step explanation:

Step-by-step explanation:

Recall that

\(1 + \tan^2 x = \sec^2 x\)

and

\(\dfrac{d}{dx}(\tan x) = \sec^2 x\)

so that

\(\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx\)

\(\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx\)

\(\:\:\:\:\:\:\:\:\:=\tan x - x + C\)

where C is the constant of integration.

Answer:

To find the points where the rate of change of x is half the rate of change of y, we need to solve the equations:

   dy/dx = k

   dy/dt = k

where k is a constant representing the rate of change.

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

The most appropriate choice for equation of line in slope intercept form will be given by-

2) y intercept of the line is 13 units

3) Equation of line  f(x)

x - 2y = -26

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\)  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

Here,

2) From the table, it can be seen when x = 0, y = 13

y intercept of the line is 13 units

3) The line passes through (-4, 11) and (0, 13)

Slope = \(\frac{13 - 11}{0-(-4)}\)

          = \(\frac{2}{4}\)

          = \(\frac{1}{2}\\\)

Equation of line f(x)

\(y - 11 = \frac{1}{2}(x - (-4))\)

- \(2y - 22 = x+4\\x - 2y = -22 -4\\x - 2y = -26\)

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Answer:

Step-by-step explanation:

The two purchases can be described by the equations ...

  50r +70p = 258

  90r +60p = 372

Rewriting these equations in general form facilitates the use of the cross-multiplication method of solving them.

  50r +70p -258 = 0

  90r +60p -372 = 0

According to the cross-multiplication method, we need three cross-products:

  ∆1 = (50)(60) -(90)(70) = -3300

  ∆2 = (70)(-372) -(60)(-258) = -10560

  ∆3 = (-258)(90) -(-372)(50) = -4620

The solutions are the solutions to the equations ...

  1/∆1 = t/∆2 = p/∆3

  r = ∆2/∆1 = -10560/-3300 = 3.20

  p = ∆3/∆1 = -4620/-3300 = 1.40

The cost per foot of the redwood was $3.20; of the pine, $1.40.

_____

Additional comment

Here's how this version of the "cross-multiplication" method works. For equations ...

a coefficient array can be written as ...

  \(\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right]\)

The cross-products of interest are formed from adjacent columns:

  \(\Delta1=ac-db\\\Delta2=bg-ec\\\Delta3=cd-ga\)

and the solutions are ...

  \(x=\dfrac{\Delta2}{\Delta1},\quad y=\dfrac{\Delta3}{\Delta1}\)

Using this method requires no more arithmetic operations than solving by substitution or elimination, and may require fewer: 6 products, 3 sums, and 2 quotients are needed.

To estimate the probability of hitting the bullseye at least 100 times in 2000 throws, we can use the binomial distribution formula. The probability of hitting the bullseye in a single throw can be calculated by finding the ratio of the areas of the bullseye and the entire dartboard.

The area of the bullseye (radius 1) is A_bullseye = π * 1^2 = π square units. The area of the entire dartboard (radius 5) is A_dartboard = π * 5^2 = 25π square units. Therefore, the probability of hitting the bullseye in a single throw is p = A_bullseye / A_dartboard = π / 25π = 1/25.

Now, we use the binomial distribution formula: P(X >= 100) = 1 - P(X < 100), where X is the number of bullseye hits. To calculate P(X < 100), we need to sum the probabilities from X = 0 to X = 99.

P(X < 100) = Σ [C(n, k) * p^k * (1-p)^(n-k)], for k = 0 to 99

Where n = 2000 (total throws), k = number of bullseye hits, and C(n, k) is the binomial coefficient (combinations of n elements taken k at a time).

Computing the above sum and subtracting it from 1 gives us the probability of hitting the bullseye at least 100 times. Due to the large number of calculations, using software or an online calculator can be helpful to compute this probability.

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The fractions are rewritten as so that they have a common denominator as  107/100

A fraction can be described as the part of a whole element, variable or number.

The several types of fractions are;

From the information given, we have that;

13/25 and 11/20

To rewrite the fractions, we have to determine the lowest common multiple

13/25 + 11/20

52 + 55 /100

Add the numerators , we have;

107/100

Hence, the fraction is 107/100

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Answer:

5%

Step-by-step explanation:

To find the tax, we take the price times the tax rate

2 = 40* rate

Divide each side by 40

2/40 =rate

.05 = rate

Changing to percent form

5% = rate

Answer:

tax rate = 2 / 40  = 1 /20 = 0.05 *100 = 5%

Step-by-step explanation:

Answer:

The answer to your question would be p - 0.10p

:)

Answer:

The correct answer is 0.90p.

This is  because, if  there  is a 10% price drop, the item would cost (100-10), or 90 percent of the original price.

Let me know if this helps!

[1, 3] - f is continuous on this interval.b) (1, 3) - f is continuous on this interval.c) [1, 2] - The left-hand limit of f does not exist at x = 2.d) (1, 2) - The left-hand limit of f does not exist at x = 2.e) [2, 3] - f is continuous on this interval. f ) (2, 3) - The right-hand limit of f does not exist at x = 2.

A function is a block of code that performs a specific task, and can be reused multiple times. Functions can be defined within a program, or can be imported from an external library or from another program. Functions are useful for abstracting away complex code, making it easier to read and debug. They can also help reduce code duplication and make code easier to maintain.

(a) [1, 3] – f is continuous on this interval since it is continuous at all points in the interval.

(b) (1, 3) – f is continuous on this interval since it is continuous at all points in the interval.

(c) [1, 2] – f is not continuous on this interval since it is not continuous at x = 2. The condition for continuity is not satisfied at this point.

(d) (1, 2) – f is not continuous on this interval since it is not continuous at x = 1. The condition for continuity is not satisfied at this point.

(e) [2, 3] – f is continuous on this interval since it is continuous at all points in the interval.

(f) (2, 3) – f is not continuous on this interval since it is not continuous at x = 2. The condition for continuity is not satisfied at this point.

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Complete questions as follows-

Answer:

(x-1.5)^2 -2.25

Step-by-step explanation:

divide 3 by 2 which is 1.5

(x-1.5)^2 -2.25

Answer:

parallelogram

Step-by-step explanation:

Answer:

y = -1/3x + 3

Step-by-step explanation:

Slope = -1/3

Y-intercept = (0, 3)

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

y=rx

x=17

y=r(17)

y=17r

Answer:

Step-by-step explanation:

Answer:

88.5

Step-by-step explanation:

formula = ab ×(sin∅)/2

= 18×12 × (sin 55)/2

= 88.5