Given f(x)=x-7 and g(x)=x² <br>find g(f(4))

Triangle DEF has vertices D(0,0), E(7,0), and F(3,7).

Leni [432]

Answer:

(3, 1.7)

Step-by-step explanation:

The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.

Two lines are perpendicular if the product of their slopes is -1.

The slope of the line joining D(0,0), F(3,7) is:

$m_1=\frac{7-0}{3-0}=\frac{7}{3}$

The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)$

The slope of the line joining E(7,0), and F(3,7). is:

$m_1=\frac{7-0}{3-7}=-\frac{7}{4}$

The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)$

The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:

x = 3, y = 1.7

4 0

3 years ago

Write 425% as a fraction or mixed number in simplest form.

Temka [501]

Answer:

17/40

here! hope this helps!

8 0

2 years ago

Find the measure of unknown angle

Lemur [1.5K]

Answer:

Step-by-step explanation:

z = 102 degree (opposite angles of a parallelogram are equal)

z + x + 34 = 180 degree 9sum of adjacent angles of a parallelogram is 180 degree)

102 + x + 34 = 180

x = 180 - 136

x = 44 degree

y + 102 + x = 180 degree (sum of interior angles of a triangle is 180 degree)

y + 102 + 44 = 180

y = 180 - 146

y = 34 degree

3 0

2 years ago

Read 2 more answers

All the fourth-graders in a certain elementary school took a standardized test. A total of 85% of the students were found to be

Aneli [31]

Answer:

There is a 2% probability that the student is proficient in neither reading nor mathematics.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a student is proficient in reading

B is the probability that a student is proficient in mathematics.

C is the probability that a student is proficient in neither reading nor mathematics.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a student is proficient in reading but not mathematics and $A \cap B$ is the probability that a student is proficient in both reading and mathematics.

By the same logic, we have that:

$B = b + (A \cap B)$

Either a student in proficient in at least one of reading or mathematics, or a student is proficient in neither of those. The sum of the probabilities of these events is decimal 1. So

$(A \cup B) + C = 1$