Decide whether this statement is always true, never true, or sometimes true, and explain why: In a quadratic equation of the form 0 = ax2 + bx + c, there will be two real solutions if a and c are of opposite signs

Answers

Answer 1
Answer:

Answer:

Always true

Step-by-step explanation:

Here, we want to evaluate if the given statement is true

The discriminant D can be calculated using the formula;

b^2 - 4ac

if D is greater than 0, then we will have only real roots

In a case where a and c are of opposite signs;

then -4ac will always give a positive value which can be added to b^2

This positive value will ensure that D is greater than zero and hence we can have only real roots

So this assertion is always true if a and c are of opposite signs


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The Length of a rectangle is 4 centimeters less than twice its width . The perimeter of the rectangle is 34cm. What are the dimensions of the rectangle ?

Answers

The given known values are: Length of 4 cm Width is unknown Perimeter is 34 cm Find the dimensions of the rectangle.   Since the geometric formula for perimeter is:
P= 2 (l + w)
L = 2w – 4 cm
W =?  
Derivation and solution:
34 = 2 (2w - 4) + 2w
34 =  4w – 8 + 2w

42 = 6w 42/6 = w
W = 7 cm  

34 = 2l + 2(7)
34 = 2l + 14
2l = 34 – 14
2l = 20
L = 20/2
L = 10 cm   



What is the simplest form of this expression? 2y(7y^2+1)-5y

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14y^3 -3y is the simplest form of the expression.

PLEASE HELP ME OUT IF YOU CAN

Answers

Answer:

D

Step-by-step explanation:

The following are the last 10 run scores Colin got in cricket: 5, 3, 9, 11, 4, 28, 0, 30, 0, 23 a) Work out Colin's mean score.

Answers

Answer:in  pula mea dute si invata nu mai venii aici\

Step-by-step explanation:vezii ca daca nu invetii ii zic lu mata aia creata ca folosesti brainly bai nesimtitule mars la munca nu la frecat ou bai labare.

√(x)

Consider the logarithmic equation f(x) = ln (x + 2) – 1. Round all values to the tenths place.(a) Determine any x- and y-intercepts.
(b) Determine the domain and the equation of the vertical asymptote.
(c) Make a table of values to find three other points on the graph.
(d) Graph the function. Label the three points you found in Part (c).

Answers

Hello,

A) x=0==> f(0)=ln(2)-1=-0,30685281944005469058276787854182
y=0==>ln(x+2)-1=0
==>ln(x+2)=1
==>e^ln(x+2)=e^0
==>x+2=0
==>x=-2

B)
dom f(x)={x∈IR | x>2}
x=-2 is the vertical asymptote

c)
A=(-1,-1)
B=(0,ln(2)-1=-0,30685281944005469058276787854182 )
C=(1,ln(3)-1=0,09861228866810969139524523692253)
D=(2,ln(4)-1)=0,38629436111989061883446424291635)

d) see picture



A sample of 30 11th graders were asked to select a favorite pattern out of six choices. The following display shows what their favorite color patterns were.The counts have been recorded in the accompanying table according to pattern and the number of students who selected that pattern. True or False? This frequency table can be graphically displayed as a histogram.

Answers

The counts have been recorded in the accompanying table according to pattern and the number of students who selected that pattern is True.

What is a graph?

A graph is a means to visualise a lot of data in a way that makes it simple for the user to grasp all of the information at once. The graph's line is typically a function that tracks the graph.

The name of the colour pattern will be on the x-axis of the bar graph that can best depict the circumstance, and the number of students who selected the pattern will be listed on the y-axis.

The final design must have the smallest candle and should be on the leftmost side of the equation because it is the yellow pattern. While just four students chose the first candle, it should be the second-largest candle. Given that the values of the second and third candles are 6 and 12, respectively. As a result, the third candle's length should be equal to that of the second candle.

Thus, the given statement is True.

Learn more about Graph here:

brainly.com/question/14375099

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False, the data set is not continuous. A histogram represents a continuous data set.