in triangle ABC, AB = 6 cm, BC = 13cm and angle ACB = 23 degrees. Calculate angle BÁC, which is obtuse.

Answer: A

Step-by-step explanation:

Before we find the equation of the perpendicular line, we have to find the slope of the original line.

The slope-intercept form of the equation is y=mx+b, so let's change that.

[tex]-2x+3y=-6[/tex]            [add both sides by 2x]

[tex]3y=2x-6[/tex]                  [divide both sides by 3]

[tex]y=\frac{2}{3} x-2[/tex]

This gives slope as [tex]\frac{2}{3}[/tex].

There are 2 things for us to do to find the slope of a perpendicular line.

1. reciprocal

2. change sign

Let's apply those rules.

1. [tex]\frac{3}{2}[/tex]

2. [tex]-\frac{3}{2}[/tex]

Now, we can find the perpendicular lines by plugging in our new point.

[tex]y=-\frac{3}{2} x+b[/tex]          [plug in x and y]

[tex]-1=-\frac{3}{2}(6)+b[/tex]     [multiply]

[tex]-1=-9+b[/tex]          [add both sides by 9]

[tex]b=8[/tex]

Now we can plug in for our slope-intercept equation.

[tex]y=-\frac{3}{2} x+8[/tex]

Since answers are in standard form, we have to manipulate it.

[tex]y=-\frac{3}{2} x+8[/tex]        [add both sides by [tex]\frac{3}{2} x[/tex]]

[tex]\frac{3}{2}x+y=8[/tex]            [multiply both sides by 2]

[tex]3x+2y=16[/tex]

Therefore, our final answer is A.

Answer: point form: (4,3) equation form: x=4 y=3

Step-by-step explanation:

Answer:

10 years old

Step-by-step explanation:

1000b + 2500p = 60,000

1000b + 2500(10) = 60,000

1000b + 25000 = 60,000

1000b = 35,000

b = 35

they need to sell 35 basic packages to reach their goal of 60,000 dollars

The equivalent to 5a³ + 4a³ is (5+4) a³, according to the question.

What do you mean by Equivalent ?

Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.

According to the given question,

We have the given options are:

O (5+4) a³+3

O (5+4) a³

O (5.4) a³+3

O (5.4) a³

Now, we will find the equivalent,

5a³ + 4a³

Then, we will taking common factor from the given equation:

5a³ + 4a³

= a³(5+4)

So that is same as (5+4)a³.

Therefore, the equivalent to 5a³ + 4a³ is (5+4) a³.

To learn more about equivalent, visit:

https://brainly.com/question/14672772?referrer=searchResults

#SPJ1

z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

To learn more about z-score visit:

brainly.com/question/15016913

#SPJ4

Answer:At the rate of 15% the amount of interest on $2000

Step-by-step explanation:

simple amount= Principle(1+rt)

where r= rate of inetrest

t= time

principal is initial amount

therefore, amount=2000(1+15*1)

Amount = $2,300.00

Interest = Amount - Principal = $300.00

Answer:

Step-by-step explanation:

Interest = Principle * Rate * Time /100

Principle =  $2000

Rate = 15 %

Time =  1 year

I = 2000 * 15 * 1/100

I = 300

Juan has to pay $300 in a year

the inequality model will be x+2y<19

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

x + y > 11

.05x + .10y < .95

by multiplying 20 in inequality we get x+2y<19

Hence, the inequality model will be x+2y<19

Learn more about inequality here:

brainly.com/question/14098842

#SPJ1

Sam passed the marker of 483 miles, in 6 hours.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135

Simplifying the above expression gives the mile marker
M = 483 miles

Thus, the required miles are 483.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

The cost of one liter of washing up liquid would be = $1.8

Liters is a variable that is can be used to denote the measurement of a liquid.

The quantity of the washing up liquid that was given= 1.5 liters.

The cost of 1.5 liters of washing up liquid =$2.70

If 1.5 L = 2.70

1 L = X

Make X the subject of formula;

X = 1× 2.70/1.5

X = $1.8

Therefore, the cost of one liter of washing up liquid would be = $1.8

Learn more about liters here:

https://brainly.com/question/25964777

#SPJ1

Answer:

1/2

Step-by-step explanation:

Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.

Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.

Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6

3/6=1/2

The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

To know more about 30-60-90 triangle:

https://brainly.com/question/11751274

#SPJ1

Answer:

b. r = 18%

Step-by-step explanation:

0.3(0.82)^x:

0.3(0.82)^x:

The 0.82 is getting affected since it is raised to the power of x

Hence, for every iteration of x, the object is becoming 82% of itself.

100%-82%=18%

r = 18% ==> b

Option B is correct, 18% is the  rate of decay of the exponential function f(x) = 0.3(0.82)ˣ

A relation is a function if it has only One y-value for each x-value.

The exponential function f(x) = 0.3(0.82)^x can be written in the form f(x) = a(b)ˣ, where a = 0.3 and b = 0.82.

In an exponential function of the form f(x) = a(b)ˣ

the base b represents the rate of change.

If b is between 0 and 1, then the function represents exponential decay. The rate of decay r can be found using the formula:

r = (1 - b) x 100%

In this case, b = 0.82, so the rate of decay is:

r = (1 - 0.82) x 100%

= 0.18 x 100%

= 18%

Hence, option B is correct, 18% is the  rate of decay of the exponential function f(x) = 0.3(0.82)ˣ

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ2

The correct answer is C.

The equivalent ratios to tan F = EL/ EF = OS/OJ

Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.

All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.

Given that

△FEL∼△JOS

That means △FEL and △JOS are similar triangles

As we know tan θ = Opposite side / Adjacent side

From the triangle △FEL,

=> tan F = EL/EF      

By the given information,

The similar triangle's corresponding sides will have the same ratio  

=> EL/ EF = OS/OJ

Therefore

The equivalent ratios to tan F = EL/ EF = OS/OJ

Learn more about Similar triangles at

brainly.com/question/25882965

#SPJ1

Answer:

2 1/4

Step-by-step explanation:

I know bc its basic math

The x-intercept and y-intercept of the line will be at (24, 0) and (0, 6). And the line is drawn below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The linear equation is given below.

y = -(1/4)x + 6

Convert the equation into intercept form, then we have

y = -(1/4)x + 6

4y = - x + 24

x + 4y = 24

x / 24 + y / 6 = 1

The x-catch and y-capture of the line will be at (24, 0) and (0, 6) and the line is drawn underneath.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

Answer:

Step-by-step explanation:

I am not super sure about this one

Therefore , the probability that she selects none of those containing errors is 0.6798.

Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.

Here,

Number of ways of selecting 3 returns out of 59 is C(59,3).

Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).

The probability that she selects none of those containing errors is

P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798

Therefore , the probability that she selects none of those containing errors is 0.6798.

To know more about probability , visit

brainly.com/question/11234923

#SPJ4

First:

Quotient: [tex]2x^{2} -11x+58[/tex]

Remainder: [tex]-294[/tex]

Second:

Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]

Remainder: [tex]422[/tex]

Third:

Quotient: [tex]2x-3[/tex]

Remainder: [tex]12[/tex]

Answer:

x = 5

Step-by-step explanation:

Firstly, we know that corresponding angles are the same. So we can say that 25x + 5 = 26x

Let’s simplify this equation:

25x + 5 =26x

-25x -25x

5 = x

Therefore, x = 5.

Answer:

(f ○ g)(x) = 3x² + 5

Step-by-step explanation:

substitute x = g(x) into f(x) , that is

(f ○ g)(x)

= f(g(x))

= f(x² + 2)

= 3(x² + 2) - 1

= 3x² + 6 - 1

= 3x² + 5

The expression in terms of xx that represents the total amount that Hailey paid is (2912/625)xx .

What is business Mathematics?  

Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.

According to Question:

let the the subtotal on the bill was xx dollars

A tax of 8% is added on bill then Bill becomes xx + 8% of xx

The of 8% on bill = (108/100)xx

Now the Final bill = xx + (108/100)xx

                    = (208/100)xx

Hailey decides to leave a tip of 24% on the entire bill (including the tax)

So the Total Amount = (208/100)xx + 24% of Final bills

⇒

24% of (208/100)xx = (208/100)(124/100)xx

The Total amount = (208/100)xx +(208/100)(124/100)xx

Let the Amount be A

hence, expression in terms of xx that represents the total amount that Hailey paid is A = (208/100)xx +(208/100)(124/100)xx

⇒ A = (52/25)xx +(52/25)(31/25)xx

⇒ 625A = 625((52/25)xx +(52/25)(31/25)xx)

⇒ 625A = 1300xx + 1612xx

⇒ 625A = 2912xx

⇒ A = (2912/625)xx

To learn more about Business mathematics , check out

https://brainly.com/question/28960886

#SPJ1

Answer:

y=5x−2

I hope this helps!

Answer: Y=mx+b

Step-by-step explanation:

The labeled quadrants in the standard xy coordinate plane is Quadrant II

What is Quadrants?

The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.

Concept:

The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.

The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).

The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.

The labeled quadrants in the standard xy coordinate plane is Quadrant II

To learn more about Quadrant visit:

brainly.com/question/7196312

#SPJ4

The required percent decrease in the price of the skateboard is 40%.

What is the percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here, we have

Original price = $84.50

sale price = $50.70

Percent decrease = 84.50-50.70/84.50 × 100 = 40%

Hence, the required percent decrease in the price of the skateboard is 40%.

To learn more about the percentage from the given link

https://brainly.com/question/24304697

#SPJ1

Answer: Frank has to pay 56,250 dollars

Step-by-step explanation:  If Frank's repair costs 55% of the original price, that means he'll have to pay 123,750 dollars because 55% of 225,000 is 123,750. But he doesn't have to pay that amount because the car insurance is paying 30% of 225,000 which is 67,500 dollars. So the car insurance is paying 67,500 dollars out of the 123,750 dollars in damage. So you'll have the subtract 123,750 by 67,500 which is 56,250 dollars.

By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

Learn more about hypothesis test

brainly.com/question/17099835

#SPJ4