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irina [24]
2 years ago
6

Write a cubic function whose graph goes through the points: (-5, 0) (1, 0) (2, -2) (4, 0)​

Mathematics
1 answer:
never [62]2 years ago
4 0

Answer:

Step-by-step explanation:

From points (-5,0),(1,0),(4,0) we know it has the form

y=(x+5)(x-1)(x-4)

y=(x^2+4x-5)(x-4)

y=x^3-4x^2+4x^2-16x-5x+20

y=x^3-21x+20

Then it must pass through the point (2,-2) so

-2=[2^3-21(2)+20]b

-2=[8-42+20]b

-2=[-14]b

b=1/7 so the equation is

y=(x^3-21x+20)/7

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What is the value of E?
kozerog [31]
Hello!

∠E and the angle measuring 119 degrees (we'll refer to this as ∠A) can be classified as supplementary angles. Supplementary angles are two angles whose measures add to a sum of 180 degrees (a straight line). Therefore, we can conclude that sum of ∠E and ∠A is 180 degrees. We can use this information to create the following equation:

∠E + 119 = 180

Now subtract 119 from both sides of the equation:

∠E = 61

We have now proven that ∠E is equal to 61 degrees.

I hope this helps!
8 0
3 years ago
Read 2 more answers
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
2 years ago
Based on Pythagorean identities, which equation is true? A. Sin^2 theta -1= cos^2 theta B. Sec^2 theta-tan^2 theta= -1 C. -cos^2
Arturiano [62]

Answer:

D

Step-by-step explanation:

our basic Pythagorean identity is cos²(x) + sin²(x) = 1

we can derive the 2 other using the listed above.

1. (cos²(x) + sin²(x))/cos²(x) = 1/cos²(x)

1 + tan²(x) = sec²(x)

2.(cos²(x) + sin²(x))/sin²(x) = 1/sin²(x)

cot²(x) + 1 = csc²(x)

A. sin^2 theta -1= cos^2 theta

this is false

cos²(x) + sin²(x) = 1

isolating cos²(x)

cos²(x) = 1-sin²(x), not equal to sin²(x)-1

B. Sec^2 theta-tan^2 theta= -1

1 + tan²(x) = sec²(x)

sec²(x)-tan(x) = 1, not -1

false

C. -cos^2 theta-1= sin^2

cos²(x) + sin²(x) = 1

sin²(x) = 1-cos²(x), our 1 is positive not negative, so false

D. Cot^2 theta - csc^2 theta=-1

cot²(x) + 1 = csc²(x)

isolating 1

1 = csc²(x) - cot²(x)

multiplying both sides by -1

-1 = cot²(x) - csc²(x)

TRUE

3 0
3 years ago
Bart makes $1,000 per month plus his commission on sales. He gets 6 percent of everything he sells. If he sells an $850 mattress
mamaluj [8]
$1,051. You first multiply 850 by 0.06, or 6 percent, to get $51. then add to his monthly salary. Hope this helps
8 0
3 years ago
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A parallelogram with the sides of 6 and 10 has a area of 30 square root of 2. Find the measure of each angle of the parallelogra
Vinvika [58]
a=10,b=6,A=30 \sqrt{2} 
\\
\\A=ah_a=ab\sin\theta
\\30 \sqrt{2} =10\times6\times\sin\theta
\\
\\ \sin\theta= \frac{ \sqrt{2} }{2} 
\\
\\ \theta=45^o
\\ \theta_1=180^o -\theta=180^o-45^o=135^o

7 0
2 years ago
Read 2 more answers
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