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2 years ago

Find the x- and y-intercepts of the parabola y=x2+10x+4

Mathematics

1 answer:

Nuetrik [128]2 years ago

6 0

Answer:

x-intercepts: -5 +/- $\sqrt{21}$ . y-intercept: 4

Step-by-step explanation:

For x-intercepts use the quadratic equation

$x= (-b +/-\sqrt{b^2-4ac} )/2a$

Fill in your values:

$x= (-10 +/-\sqrt{100-16} )/2$

And solve

$x=-5 +/- \sqrt{21}$

For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.

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Find the equation of the tangent line to the curve 4x3+2y2−11=4xy−x at the point (−1,2).

katrin [286]

Hello : let : y = f(x) so : y' = f'(x)
calculate : f'(x) and : f'(-1) given f(-1) = 2

by derivate : <span>4x3+2y2−11=4xy−x
12x² +4yy' = 4y +4xy' - 1
4yy' - 4xy' = - 12x² +4y -1
y' ( 4y - 4x) = 4y -12x² -1 ...(*)
if x = -1 y = 2 subsct in : (*)
y' (4(2)-4(-1)) = 4(2)-12(-1)² - 1
2y' = - 9
y' = - 9/2 = f'(- 1) ( the slope of the tangent )
</span>of the tangent line to the curve <span>at the point (−1,2) is :
y - 2 = (-9/2)(x +1)</span>

5 0

3 years ago

it takes Maya 30 minutes to solve 5 logic puzzles, and it takes Amy 28 minutes to solve 4 logic puzzles. use models to show the

7nadin3 [17]

Answer:

Maya ---> $6\ minutes/puzzle$

Amy ----> $7\ minutes/puzzle$

see the procedure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

Let

m ---> the number of minutes

p ---> the number of puzzles

In this problem, the relationship between the variables m and p represent a proportional variation

$m=kp$

Maya

it takes Maya 30 minutes to solve 5 logic puzzles

we have

m=30, p=5

Determine the value of the constant of proportionality k

$k=\frac{m}{p}$

substitute the given values

$k=\frac{30}{5}=6\ minutes/puzzle$

The value of the constant k is the same that the slope or unit rate

The equation is equal to

$m=6p$

Amy

it takes Maya 28 minutes to solve 4 logic puzzles

we have

m=28, p=4

Determine the value of the constant of proportionality k

$k=\frac{m}{p}$

substitute the given values

$k=\frac{28}{4}=7\ minutes/puzzle$

The value of the constant k is the same that the slope or unit rate

The equation is equal to

$m=7p$

8 0

3 years ago

Amembership to the gym costs $ 25 per person in 1995 .the membership cost has increased by an average of $ 6 per person for each

Step2247 [10]

Answer:6x+25

109

Step-by-step explanation:

X is the amount of years since 1995

2009 is 14 years so plug in 14 for x and solve

4 0

4 years ago

A coin bank for donations for the protection of the reef contained Php 1,570. There were twice as many Php 5-coins as

kvasek [131]

Answer:

There are 144 Php 5-coins, 72 Php 10-coins and 130 Php-1 coins

Step-by-step explanation:

The amount of the coins in the coin bank = Php 1,570

The number of Php 5-coins = 2 × The number of Php 10-coins

The number of Php 5 coins = The number of Php 1-coins + 14

Let 'x' represent the number of Php-5 coins, let 'y' represent the number of Php 10-coins, and let 'z' represent the number of Php 1-coins, we get;

x = 2 × y...(1)

x = z + 14...(2)

5·x + 10·y + z = 1,570...(3)

From equation (1) equation (2), and equation three, we have;

y = x/2

z = x - 14

5·x + 10·x/2 + x - 14 = 1,570

11·x - 14 = 1,570

x = (1,570 + 14)/11 = 144

The number of Php 5-coins, x = 144

y = x/2

∴ y = 144/2 = 72

The number of Php 10-coins, y = 72

z = x - 14

∴ z = 144 - 14 = 130

The number of Php 1-coins, z = 130

6 0

3 years ago

Pls help 19 a. 100 pts

Len [333]

Answer:

dkdkkdkddkdkdkddkdkdkkkdkkkkkdkdkd

Step-by-step explanation:

3 0

3 years ago