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natima [27]
2 years ago
12

Each dot on the dot plot shows the number of people in a 12-person random sample who are shorter than 5 feet tall.

Mathematics
1 answer:
qwelly [4]2 years ago
5 0

Answer:

15

Step-by-step explanation:

sucks to suck

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Simply the following expression by combining like terms 5w + 7v - 8w + v - w + 2y
Dafna11 [192]
-4w + 8v + 2y = -4w + 8v + 2y
7 0
2 years ago
How do you illustrate<br>quadratic equation<br>in one variable?​
soldi70 [24.7K]

Step-by-step explanation:

Quadratic Equation

Quadratic equation is in the form

ax2+bx+c=0

Where

a, b, & c = real-number constants

a & b = numerical coefficient or simply coefficients

a = coefficient of x2

b = coefficient of x

c = constant term or simply constant

a cannot be equal to zero while either b or c can be zero

Examples of Quadratic Equation

Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.

1. 3x2+2x−8=0

2. x2−9=0

3. 2x2+5x=0

4. sin2θ−2sinθ−1=0

5. x−5x−−√+6=0

6. 10x1/3+x1/6−2=0

7. 2lnx−−−√−5lnx−−−√4−7=0

For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.

Roots of a Quadratic Equation

The equation ax2 + bx + c = 0 can be factored into the form

(x−x1)(x−x2)=0

Where x1 and x2 are the roots of ax2 + bx + c = 0.

Quadratic Formula

For the quadratic equation ax2 + bx + c = 0,

x=−b±b2−4ac−−−−−−−√2a

See the derivation of quadratic formula here.

The quantity b2 - 4ac inside the radical is called discriminat.

• If b2 - 4ac = 0, the roots are real and equal.

• If b2 - 4ac > 0, the roots are real and unequal.

• If b2 - 4ac < 0, the roots are imaginary.

Sum and Product of Roots

If the roots of the quadratic equation ax2 + bx + c

= 0 are x1 and x2, then

Sum of roots

x1+x2=−ba

Product of roots

x1x2=ca

You may see the derivation of formulas for sum and product of roots here.

4 0
3 years ago
I need help finding the are of this
Allisa [31]

Answer:

78.5

Step-by-step explanation:

3.14*5*5=78.5

3 0
3 years ago
1. Emma used elimination to solve this system of linear equations. 3x + 5y = -17 2x + 4y = 6 Which equation did Emma have after
Gwar [14]

Answer:

2y=52

Step-by-step explanation:

1st equation *(-3) and 2nd *(2)

-6x-10y=34

6x+12y=18

eliminate -6x and 6x

add both equations

2y=52

6 0
3 years ago
Read 2 more answers
What is the area of an acute angle​
snow_lady [41]
The acute angle inside the triangle is 57 degrees. The one labeled “1” is 123 degrees.
7 0
3 years ago
Read 2 more answers
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