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Len [333]
3 years ago
8

Given right triangle ABC, what is the value of tan(A)? Five-thirteenths Twelve-thirteenths Twelve-fifths Thirteen-twelfths

Mathematics
2 answers:
WITCHER [35]3 years ago
8 0

Answer:

Twelve-fifths.

Step-by-step explanation:

The diagram is shown below

Given triangle be right angled at B,

Withe reference to \angle A,

Its opposite side is BC=12 , adjacent side is AB=5 and hypotenuse is AC=13

We are to find the value of tan(A)

We know tan=\frac{opposite}{adjacent}

Substituting the above values we get,

tan(A)= \frac{BC}{AB}=\frac{12}{5}

So the answer is Twelve-fifths.

shusha [124]3 years ago
8 0

Answer:

C. \frac{12}{13}

Step-by-step explanation:

cos(Z) = cos(C)

cos(C) = 12/13

Because adjacent side over hypotenuse side length.

Therefore, cos(Z) = 12/13.

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Need help with son's homework I will give 30 points!!! Please show work
Elis [28]

Answer:

A. ⇒ The expression is b + 3

B. ⇒ The expression is 2b - 4

C. ⇒ The Dr's office is closer by 4 miles

Step-by-step explanation:

A.

∵ The distance between Daniel's house and his school is b miles

∵ The swimming pool is 3 miles farther from his school

∴ The distance between Daniel's house and the swimming pool is b + 3

B.

∵ The distance from Daniel's house to his Dr's office is 4 less than twice the distance from home to Daniel's school

∵ The distance between Daniel's house and his school is b

∴ The expression of distance from Daniel's house to his Dr's office is

   2b - 4

C.

∵ b = 3

∴ The distance between his house and swimming pool is:

   3 + 3 = 6 miles

∴ The distance between his house and Dr's office is:

   2(3) - 4 = 2 miles

∴ The Dr's office is closer to Daniel's house than the swimming pool by:

   6 - 2 = 4 miles

6 0
3 years ago
A bakery is having a sale on cupcakes. At 11am the bakery has sold 123 cupcakes. By 2pm the bakery has sold 470 cupcakes.
Wittaler [7]

Answer:

The average rate of change is 115 cupcakes per hour approximately

Step-by-step explanation:

6 0
3 years ago
Twenty-four is 30% of what number?
IgorLugansk [536]
24 / 30 x 100 = 80

answer: <span>Twenty-four is 30% of 80</span>
7 0
3 years ago
Read 2 more answers
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
What is 3 over 4 + b = 3
FromTheMoon [43]

Answer:

2 and 1/4

Step-by-step explanation:

3/4 + b = 3

rearrange the equation

3 - 3/4 = b

3/1 - 3/4 = 14/4 - 3/4 = 11/4 = 2 and 1/4

4 0
3 years ago
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