Answer:
15 degrees
Step-by-step explanation:
Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.
At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.
At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.
The angle of elevation you want is angle BED.
The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.
To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.
BD = 1.1 m
DE = 4.2 m
tan <BED = opp/adj
tan <BED = 1.1/4.2
m<BED = tan^-1 (1.1/4.2)
m<BED = 15
Answer: 15 degrees
Answer:
(3x - 4)(8x - 3)
Step-by-step explanation:
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 24 × 12 and sum = - 41
The required factors are - 32 and - 9
Use these factors to split the x- term
24x² - 32x - 9x + 12 ( factor the first/second and third/fourth terms )
= 8x(3x - 4) - 3(3x - 4) ← factor out (3x - 4) from each term
= (3x - 4)(8x - 3) ← in factored form
What is the value of the discriminant?
For this case, the discriminant will be given by
b ^ 2 - 4 * a * c
Where
b = 7
a = 3
c = 2
substituting
b ^ 2 - 4 * a * c = (7) ^ 2 - 4 * (3) * (2) = 25
Therefore the value of the discriminant is 25.
How many x-intercepts does this function have?
It has two intercepts with the x axis and can be found by equaling the function to zero. That is to say,
3x2 + 7x + 2 = 0
The results will be the interceptions with x.
What are the number of zeros for this function?
The number of zeros for this function is
two real number solutions
Because it is a quadratic function.
Answer: A/ alina swims about 0.7 miles per hour
Step-by-step explanation:
Answer:
2^27
Step-by-step explanation:
Given the following expression:
[(2^10)^3 x (2^-10)] ÷ 2^-7
This can be easily simplified. Let us simplify the numerator first. To do that, we have
(2^10)^3 making use of the power rule of indices that says:
(A^a)^b = A^ab where a and b are powers, we have:
2^(10x3) = 2^30
Therefore the numerator becomes:
2^30 x 2^-10. Also making use of the multiplication rule that says:
A^a x A^b = A^(a + b), we have
2^30 x 2^-10 = 2^(30 – 10) = 2^20.
Now we have:
(2^20) ÷ (2^-7)
To simplify this, we need the division rule of indices which says:
A^a ÷ A^b = A^(a – b)
Therefore we have:
(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27
