Answers
Given:
The quadratic equation is:
[tex]-5x^2-3x-2=0[/tex]
To find:
The discriminant of the given equation and the number of real solutions.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the value of discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then the quadratic equation has no real roots or two imaginary roots.
If D=0, then the quadratic equation has two equal real roots.
If D>0, then the quadratic equation has two distinct real roots.
We have,
[tex]-5x^2-3x-2=0[/tex]
Here, [tex]a=-5,b=-3,c=-2[/tex]. So, the discriminant of the given equation is:
[tex]D=(-3)^2-4(-5)(-2)[/tex]
[tex]D=9-40[/tex]
[tex]D=-31[/tex]
Since D<0, therefore the number of real solutions is 0.
Hence, the value of the discriminant is -31 and the number of real solutions is 0.
Related Questions
The area for the circle below is
cm2.
Use 3.14 for π and type your answer to the nearest tenth.
r = 5cm
PLEASE HELP
Answers
Answer:
a = 78.5 cm²
Step-by-step explanation:
a = πr²
a = 3.14 * 5²
a = 3.14 * 25
a = 78.5 cm²
The roots of 7x^2 + x - 5 = 0 are a and b. Compute (a - 4)(b - 4). Thank you!
Answers
Answer:
Step-by-step explanation:
a = 7 ; b = 1 ; c = -5
D = b² - 4ac
= 1 - 4*7*(-5)
= 1 + 140
= 141
x =( - b ± √D ) / 2a
= (-1 ± √141)/2*7
= (-1±√141) / 14
[tex]a = \frac{-1+\sqrt{141} }{14}= \frac{-1+11.87}{14}= \frac{10.87}{14}=0.78\\\\b = \frac{-1-\sqrt{141}}{14}= \frac{-1-11.87}{14}= \frac{-12.87}{14}=3.59\\\\\\[/tex]
(a -4 )(b -4) = (0.78 - 4)(-3.59-4) = (-3.22)(-7.59)
= 24.4398
7/9 × 27/5 whats the answer?
Answers
Answer:
21/5 when simplified
Answer:
4 1/5
Step-by-step explanation: 6 20 5 58
7/9 × 27/5 = (7×27) / (9 × 5)
= 189 / 45 divide numerator and denominator by 3
= 63 / 15 simplify
= 4 3/15
= 4 1/5
Answer the question in the picture
Answers
Answer:
10 ^3 * 10 ^2
1/ 10 ^5
10*10*10*10*10
Step-by-step explanation:
10 ^4^1 = 10 ^(4*1) = 10 ^4
10 ^3 * 10 ^2 = 10 ^(3+2) = 10 ^5
1/ 10 ^5 = 10 ^5
10 ^3^2 = 10 ^(3*2) = 10 ^6
10*10*10*10*10 =10 ^5
Which best describes the strength of the model?
O a weak positive correlation
O a strong positive correlation
O a weak negative correlation
O a strong negative correlation
Answers
Answer:
A weak positive correlation
Step-by-step explanation:
The table of values of the women's age to shoe size is presented as follows;
Women's Age and Shoe Size
[tex]\begin{array}{ccc} Age&&Shoe \, size\\18&&7\\30&&10\\52&&6\\64&&9\end{array}[/tex]
We get;
The correlation coefficient, r, is given as follows;
[tex]r = \dfrac{\sum \left(x_i - \overline x \right ) \cdot \left(y_i - \overline y \right )}{\sqrt{ \sum \left(x_i - \overline x \right )^2 \cdot \sum \left(y_i - \overline y \right )^2}}[/tex]
From MS Excel, we have;
[tex]\sum \left(x_i - \overline x \right ) \cdot \left(y_i - \overline y \right )[/tex] = 2
[tex]\sqrt{ \sum \left(x_i - \overline x \right )^2 \cdot \sum \left(y_i - \overline y \right )^2}[/tex] = √13,000 = 10·√130
∴ r = 2/(10·√130) ≈ 0.01754
Therefore, given that the calculated correlation coefficient, r is positive and less than 0.2 (weak), we have
The correlation is a weak and positive.
Which of the following equations represents the graph of a line that is perpendicular to the graph of y = kx + b (where k and b are constants) and goes through the point (3, -4)?
Answers
Answer:
Step-by-step explanation:
When you ask "which of the following"
you must include the choices
PLEASEEE I nEEED THE ANSWER TnT
NOTE: pls ignore another language just read the english one... ASAP
Answers
Answer:
x -1 1 3
y -2 -4 2
Step-by-step explanation:
y=x^2-x-4
when x=-1
y=(-1)^2-(-1)-4
y=1+1-4
y=-2
when x=1
y=(1)^2-(1)-4
y=1-1-4
y=-4
when x=3
y=(3)2-(3)-4
y=9-3-4
y=9-7
y=2
Where are the asymptotes of f(x) = tan (4x-pi) from x=0 to x= pi/2
A. X= pi/4, x=3pi/4
B. 0, x=pi/4
C. X=pi/2, x=3pi/2
D. X= 3pi/8, x=5pi/8
Answers
Step-by-step explanation:
the asymptotes of f(x) :
(4x-π) = π/2
4x = 3π/2 => x = 3π/8
(4x-π) = 3π/2
4x=5π/2 => x = 5π/8
the answer is
D. X= 3pi/8, x=5pi/8
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1,
,
1,
3
O-3
mp
Answers
Answer:
1/3
Step-by-step explanation:
If it was supposed to be a negative answer, there would be negative numbers in the sequence. So that narrows it do to 3 and 1/3. And now we know that 27*3 isn't 9 but 27*1/3=9 and so on.
Answer:
your answer will have to be 3
Step-by-step explanation:
from 27 to 9, we divided by 3
from 9 to 3, we divided by 3
from 1 to 1/3, we divided by 3
from 1/3 to 1/9, we divided by 3
from 1/9 to 1/27, we divided by 3
so basically the common ratio will have to be 3
what is the answer to 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Answers
Answer:
m=-2
Step-by-step explanation:
A plane and a line not in that plane which are parallel to the same line, are parallel to each other. Always, sometimes, or never
Answers
Answer:
a line and a plan are considered parallel if they have no points in common if two parallel planes are cut by a third plane then the lines of intersection are parallel
Given f(x) = x − 7 and g(x) = x2 . What does f(g(4)) =
Answers
Answer:
9
Step-by-step explanation:
f(x) = x − 7
g(x) = x^2
Find g(4) = 4^2 = 16
Then find f(g(4)) = f(16) = 16 -7 = 9
Answer:
f(g(4)) = 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationComposite FunctionsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x - 7
g(x) = x²
Step 2: Find f(g(4))
Substitute in x [Function g(x)]: g(4) = 4²Evaluate exponents: g(4) = 16Substitute in x [Function f(x)]: f(g(4)) = 16 - 7Subtract: f(g(4)) = 94.5c=9
C=
Pls help me
Answers
Answer:
c =2
Step-by-step explanation:
4.5c/4.5=9/4.5
c =2
Dndnfncjfnffnvn n nfjfjcn n nffjcn ndndjcn ncdncn nun n job chfj
The ratio of the populations of town A and B is 6:5, while the ratio of the populations of town B and C is 3:4. If the total population of the three towns is 53000, find the population of each town.
Answers
Answer:
The population of town A = 18,000
The population of town B = 15,000
The population of town C = 20,000
Step-by-step explanation:
Given;
A:B = 6:5
B:C = 3:4
total population = 53,000
A + B + C = 53,000
[tex]\frac{A}{B} = \frac{6}{5} \\\\A = \frac{6B}{5} \\\\\Also;\\\\\frac{B}{C} = \frac{3}{4} \\\\C = \frac{4B}{3} \\\\then;\\\\\frac{6B}{5} +B+ \frac{4B}{3} = 53,000\\\\multiply \ through \ by \ "15"\\\\18B + 15B + 20B = 795,000\\\\53B = 795,000\\\\B = \frac{795,000}{53} \\\\B = 15,000[/tex]
Now solve for A and C;
[tex]A = \frac{6 \times 15,000}{5} = 18,000\\\\C = \frac{4 \times 15,000}{3} = 20,000[/tex]
Hello help me with these ones pls
Answers
Answer:
(-1,3)
Step-by-step explanation:
Solve for x in the first equation
3x = 6 - 3y
9x - 5y= -24
Replace all occurrences of x with 2 - y in each equation
9(2 - y) - 5y = -24
x = 2 - y
Simplify the left side
18 - 4y = -24
x = 2 - y
Solve for y in the first equation
-14y = -42
x = 2 - y
y=3
x = 2- y
Replace all occurrences of y with 3 in each equation
x=-1
y=3
(-1,3)
Hope this helps!
Please give brainliest :)
If you need more help with these types of equations reach out to me!
Simplifying
3x + 6 = 9x + -24
Reorder the terms:
6 + 3x = 9x + -24
Reorder the terms:
6 + 3x = -24 + 9x
Solving
6 + 3x = -24 + 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
6 + 3x + -9x = -24 + 9x + -9x
Combine like terms: 3x + -9x = -6x
6 + -6x = -24 + 9x + -9x
Combine like terms: 9x + -9x = 0
6 + -6x = -24 + 0
6 + -6x = -24
Add '-6' to each side of the equation.
6 + -6 + -6x = -24 + -6
Combine like terms: 6 + -6 = 0
0 + -6x = -24 + -6
-6x = -24 + -6
Combine like terms: -24 + -6 = -30
-6x = -30
Divide each side by '-6'.
x = 5
Simplifying
x = 5
Find the Area of the shaded region of the circle. Leave answers in terms of Pi. (Image attached). Thank you!!!
Answers
Answer:
I've attached the Answer
Answer:
56Pi
Step-by-step explanation:
Area of small circle:
Pi*r^2
25Pi
Area of large circle:
Pi*r^2
81Pi
Area of the 2D doughnut :
Large -small circle = 81Pi-25Pi
12) A family stayed at a hotel for n nights. The cost was $80 per night plus a one-time fee of $20. Write an expression that represents the total cost of their hotel stay? PLEASE HELP
Answers
Answer:
80n+20=total cost
Step-by-step explanation:
We don't know the value of n, but we don't need it for an expression. We know that the family has to pay $80 per night that they stay at the hotel. Modeling this would look like: 80n (80*n for nights). Also, we know that the family MUST pay a $20 fee. So, we can add that on to the expression to look like this, 80n+20=total cost.
Hope this helps!
Have a nice evening.
x
+
5
y
=
20
x
+
3
y
=
14
Answers
Answer:
A) x + 5y = 20
B) x + 3y = 14
Multiplying A) by -1
A) -x -5y = -20 then adding B)
B) x + 3y = 14
-2y = -6
y = 3
x = 5
Step-by-step explanation:
Two jackets have a combined cost of $98. Jacket a costs $12 less than jacket b. How much does each jacket cost?
Answers
Answer:
Jacket A costs 43$
Jacket B costs 55$
Step-by-step explanation:
According to the Question,
Given, Two jackets have a combined cost of $98. Jacket 'A' costs $12 less than jacket 'B'. Thus, if the jacket B Cost 'X' So, Jacket A costs 'X-12'.Therefore, Jacket A + Jacket B = 98
X-12+X = 98
2X = 110
X = $55 ( Cost of jacket B) & Cost of Jacket A is 55-12 = 43$ .
graph: y=-4sin(2x)+1 where the x axis starts at 30
Answers
Answer:
We want to graph:
y = -4*sin(2*x) + 1
Such that the x-axis starts at x = 30
This is trivial to do if we use a program to graph or if we graph by hand, here we just need to draw the x-axis such that it crosses the y-axis at the point (30, 0)
Then let's graph the equation in that axis, we will get an image like the one you can see below.
The Gala Restaurant uses the equation 30n - C + 200 = 0 to determine the cost for a room rental, where a represents the cost. in dollars, which depends on n. the number of people attending. Express the equation in slope y-intercept form: C = mn + b
Answers
Given:
The equation is:
[tex]30n-C+200=0[/tex]
To find:
The slope intercept form of the given equation.
Solution:
We have,
[tex]30n-C+200=0[/tex]
We need to write the given equation in the form of [tex]C=mn+b[/tex].
Adding C on both sides, we get
[tex]30n-C+200+C=0+C[/tex]
[tex]30n+200=C[/tex]
Interchanging the sides, we get
[tex]C=30n+200[/tex]
This equation is in the form of [tex]C=mn+b[/tex], where m is 30 and b is 200.
Therefore, the slope intercept form of the given equation is [tex]30n-C+200=0[/tex].
10 points!!!!! Do 14 and 15 only hurry please.
Answers
Answer:
8. x = 16
9. x = 10
14.
m ∠RSU = 130°
m ∠UST = 50°
15.
m ∠RSU = 124°
m ∠UST = 56°
Step-by-step explanation:
8.
Given ∠DEF is bisected by EG. That is , ∠DEG = ∠GEF
That is , (x + 15)° = 31°
x = 31 - 15 = 16
9.
Given ∠DEF is bisected by EG. That is , ∠DEG = ∠GEF
That is ,
(6x - 4)° = 56°
6x = 56 + 4
6x = 60
x = 10
14.
13x + 5x = 180° [straight line angles ]
18x = 180
x = 10
m ∠RSU = 130°
m ∠UST = 50°
15.
4x + 12 + 2x = 180° [ straight line angles]
6x = 180 - 12
6x = 168
x = 28
m ∠RSU = 4(28) + 12 = 112 + 12 = 124°
m ∠UST = 2(28) = 56°
Answer:
14. 13x+5x
=18x
180(angles on a st. line)= 18x
180/18
=10
RSU=13*10=130
UST=5*10=50
Why does the congruency of all angles not prove the congruency of two triangles?
Answers
Draw an equilateral triangle with side lengths 5 inches each. Each interior angle is 60 degrees (this is true of any equilateral triangle).
Now draw an equilateral triangle of 10 inches each. The angles will be the same as before. We can see that the triangles are not congruent. Congruent triangles must have the same side lengths, but clearly the second one is larger than the first.
This is an example of why knowing solely the congruency of the angles is not enough to prove the triangles congruent or not. We would need to know something about the sides (whether they are congruent or not) to be able to determine overall triangle congruency.
Answer:
Because even though the angles may be the same, the lengths can be different. In an isosceles triangles, this may be the case.
Step-by-step explanation:
which graph shows the solution to this system of linear inequalities?
Answers
Answer:
c or b
tep-by-step explanation:
PLZ HELP ILL GIVE BRAINLIEST IF RIGHT!!!
Rosa has already written 11 pages ,and she expects to write 3 pages for every additional hour spent writing. How many hours will Rosa have to spend writing this week in order to have written a total of 47 pages?
Answers
Answer:
12 hours
Step-by-step explanation:
pages total = pages written + pages per hour * number of hour
47 = 11 + 3*h
Subtract 11 from each side
47 -11 = 11 +3h -11
36 = 3h
Divide by 3
36/3 = 3h/3
12 = h
A countertop for a kitchen is modeled with the dimensions shown below. An 18-inch by 21 inch rectangle will be removed for the sink. What is the area of the top of the installed countertop to the nearest square foot.
Answers
Complete Question
A countertop for a kitchen is modeled with the dimensions shown below. An
18-inch by 21-inch rectangle will be removed for the installation of the sink.
8 ft
2 ft
Sink
18 in
21 in
5 ft
2 ft
What is the area of the top of the installed countertop, to the nearest square foot?
Answer:
19 square foot
Step-by-step explanation:
A countertop for a kitchen is modeled with the dimensions shown below. An 18-inch by 21 inch rectangle will be removed for the sink. What is the area of the top of the installed countertop to the nearest square foot.
Convert from inches to feet
18 inches
1 inch = 0.0833 feet
18 inch = x
Cross Mulitiply
x = 18 × 0.0833 feet
x = 1.5 feet
21 inches
1 inch = 0.0833 feet
21 inch = x
Cross Mulitiply
x = 21 × 0.0833 feet
x = 1.75 feet
Area 1 = 2 ft × 8 ft = 16 ft²
Area 2 = 2 ft × 3 ft = 6 ft²
Area of a sink = Length × Width
= 1.5 ft × 1.75 ft
= 2.625 square feet
Area 1 - Area of sink
= 16 ft² - 2.625 ft²
= 13.375 ft²
Area of the top installed part =
Area 2 + 13.375 ft²
= 6 ft² + 13.375 ft²
= 19.375 ft²
Approximately ≈ 19 ft²
Help please guys thank you so much
Answers
Answer:
Step-by-step explanation:
Clara gave (1/2) of formal dresses to her sister. After giving, she has 1/2
of formal dresses (1- 1/2 = 1/2).
Number of formal dresses that Clara has = [tex]\frac{1}{2}*d=\frac{1}{2}d[/tex]
Clara bought 4 more dresses
[tex]\frac{1}{2}d + 4 = 12[/tex]
Solve the following quadratic equation. *
x^2+12x-45=0
Answers
Answer:
9 over 5
Step-by-step explanation:
Answer:
Step-by-step explanation:
x^2 + 12 - 45 = 0
solving by middle term break method
x^2 + (15 - 3) - 45 = 0
x^2 + 15x - 3x - 45 = 0
x(x + 15) - 3(x + 15) = 0
(x + 15)(x - 3) = 0
either x + 15 = 0 OR, x - 3 = 0
x + 15 = 0
x = 0 -15
x = -12
x - 3 = 0
x = 0 + 3
x = 3
therefore x = -12,3
i have done solution for the given question in two different methods.
the solution done in note copy is by using quadratic formula.
Solve the equation below for x. cx - 4 = 7
Answers
Answer:
x = [tex]\frac{11}{c}[/tex]
Step-by-step explanation:
Given
cx - 4 = 7 ( add 4 to both sides )
cx = 11 ( isolate x by dividing both sides by c )
x = [tex]\frac{11}{c}[/tex]
What is the area of the figure shown below, in terms of π ?
(?+?π)square units
