The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
How to determine the characteristics of the roots of a quadratic equation by discriminant
Herein we have a quadratic equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
d < 0 - conjugated complex roots.d = 0 - equal real roots (real and rational root).d > 0 - different real roots (real and irrational root).If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
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40. Se desea distribuir las bancas dentro de un salón de clases cada 1.5 m como
se muestra en la imagen, ¿de qué forma se puede saber el área requerida para
conservar la separación de las bancas?
1.5m
La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.
¿Cómo calcular el área requerida para mantener la separación?Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:
7.5 × 4.5 = 33.75Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:
1.5 × 5 = 7.5 distancia a lo largo1.5 × 3 = 4.5 distancia a lo anchoNota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:
Opciones:
A. Multiplicar (6)(4)
B. Multiplicar (7.5)(4.5)
C. Multiplicar (9)(6)
D. Multiplicar (9.5)(4.5)
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please help i just started summer school online Part F
Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.
Answer:
Step-by-step explanation:
basically all you do is
What is the area of parallelogram ABCD?
Jerry plans to keep up this saving pattern until he can no longer afford it. At that time he hopes to have enough in his account for his trip. How much will be in the account, after making the down payment, if the most he will be able to contribute in a month is $1,200?
What is the rate of change according to the table below?
x
3
4
5
6
y
21
28
35
42
Answer:
lets make this like a table
x y
3=21
4=28
5=35
so since y is bigger lets divide that by x
21/3=7
so the rate of change is 7
Hope This Helps!!!
The image of ABC is A'B'C. What transformations would result in this image?
ABC is rotated 180° around the origin, then T: ( x, y) → ( x - 1, y - 1).
ABC is reflected over the line x = 1, then is reflected over the line y = -1.
ABC is rotated -90° around the point, then T: ( x, y) → ( x + 5, y + 3).
ABC is rotated -90° around the origin, then T: ( x, y) → ( x + 5, y - 1).
(multi choice)
Triangle ABC was rotated 90° around the point, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.
Triangle ABC was rotated 90° around the point B, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.
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Which statement is true?
O When an altitude is drawn from the right angle in a right triangle it creates two similar triangles.
O When an altitude is drawn from an acute angle in a right triangle it creates three similar triangles.
O When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.
O When an altitude is drawn from an acute angle in a right triangle it creates two similar triangles.
Answer:
C) When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.
Step-by-step explanation:
The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other.
What is an equation of the line that is perpendicular to y - 4 = 2(x - 6) and
passes through the point (-3, -5)?
• A. y -5=1/2(x-4)
• B. y - 5 = -2(x- 3)
• C. y + 5 = 2(x+ 3)
O D. y +5- -1/2(x+3)
Answer:
D. y + 5 = -1/2(x + 3)Step-by-step explanation:
Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then
k ║ l ⇔ a₁ = a₂k ⊥ l ⇔ a₁ · a₂ = -1We have the euation of a line in point slope form:
(y - y₁) = m(x - x₁)Convert to the slope intercept form:
y =mx + by - 4 = 2(x - 6)
y - 4 = 2x - 12
y - 4 + 4 = 2x - 12 + 4
y = 2x - 8
The slope is m₁ = 2.
Let y = m₂x + b.
The lines is perpendicular. Therefore:
2m₂ = -1 |divide both sides by 2
m₂ = -1/2The line passes through the point (-3, -5).
Substitute to the point slope equation:
y - (-5) = -1/2(x - (-3))
y + 5 = -1/2(x + 3)
Please help with this
Answer:
(a) Horizontal line test
Step-by-step explanation:
A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.
Inverse relationThe inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.
Inverse functionIf the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.
A function will have an inverse function if it passes the Horizontal Line Test.
__
Additional comment
The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.
The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.
Which of the following angles are congruent?
Answer:
C
Step-by-step explanation:
if you rotate either of the triangles by 180 degrees, compare the angles and you will see that the answer is C
Please help, performance task: trigonometric identities
The answers are given below:
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
1. (cos x. cos y)(tan x + tan y) = sin (x+ y)
(cos x. cos y)(tan x + tan y)
= cos x. cos y (sinx/ cos x + sin y/ cos y)
= sin x cos y + sin y cos x
= sin (x+ y) [ sin ( x +y)]= sin x cos y + sin y cos x
= RHS
3. [tex]-\sin ^2\left(x\right)-\cos \left(2x\right)=0[/tex]
Using identity
[tex]-\cos ^2\left(x\right)=0[/tex]
cos ² x=0
Applying [tex]x^{n} =0[/tex] then x=0
So, cos x =0
General solution will be [tex]x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].
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HELP!!!!!
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
g(x) = 3x-6
g(x) = 3x+6
g(x)=3*-6
g(x)=3*+6
The answer is g(x) = 3x - 6
The height of a tank is 3 meter and volume is 12 million centimeters. find the area of the square base of the tank in square meters
Answer:
75
Step-by-step explanation:
answer?.......................
When we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.
The given function is [tex]y=2-\sqrt{x}[/tex].
We need to find which is the graph of the given function from the options.
What are coordinates?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Take, x=0, 1, 4, 9, 16, 25, 36,....
Now, when x=0, y=2.
When x=1, y=1.
When x=4, y=0.
When x=9, y=-1
So, when we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.
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which system of equations is represented by the graph?
A. y=x² + 3x
y = -x² + x + 18
B. y=x²
y = -x² +18
C. y=x²
y = x² + 18
D. y=x²
y=-x²-x-18
Answer:
B
Step-by-step explanation:
We see the graph of y=x², so eliminate A.
Since the second graph opens downwards, the coefficient of x² must be negative, so eliminate C.
Also, the axis of symmetry is x = 0, so eliminate D.
This leaves us with B
Solve using a proportion.
A carpet store charges $150 to install 12 square yards of carpet. How much should it cost to
install 24 square yards?
A. $250
B. $300
C. $3,600
D. $192
Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.
Answer:
if the ratio allowance/chores is constant, it is proportional
Step-by-step explanation:
The values x and y are directly proportional if they satisfy the equation ...
y = kx
for some constant k, the constant of proportionality.
__
If the relation that produces ordered pairs (chores, allowance) is directly proportional, all of the ratios (allowance)/(chores) will have the same value: the constant of proportionality (k).
If the ratios are not constant, Carlos's allowance is not directly proportional to the number of chores he completes.
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
From unit conversion, it is found the following results:
6km ≈ 3.73 mi
2.5 L≈ 0.66 gal
90 lb ≈ 40.82 kg
Unit Conversion
Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others. Because of this, it is important to know converting them.
For solving this question you need some information as:
1 km = 0.621371 mi ( unit for length and distance)
1 L = 0.2641722 gallons (unit for volume)
1 lb = 0.453592 kg (unit for mass)
Therefore,
If 1 km = 0.621371 mi, you will have:1 km -------- 0.621371 mi
6 km -------- x mi
x= 6* 0.621371
x=3.73 mi
Thus, 6km ≈ 3.73 mi.
If 1 L = 0.2641722 gallons, you will have: 1 L-------- 0.2647122 gal 2.5L -------- x gal x= 2.5* 0.2647122 x=0.66 galThus, 2.5 L≈ 0.66 gal.If 1 lb = 0.453592 kg, you will have: 1 lb-------- 0.453592 kg 90 lb -------- x kg x= 90* 0.453592 x=40.82 kgThus, 90 lb≈ 40.82 kg.Read more about unit conversion here:
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Easy Question For Ya'll
The statements and reasons that complete the proof are:
4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]
5. ΔPQS ≅ ΔQRT [ASA congruence theorem]
What is the ASA Congruence Theorem?When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.
We are given the following:
QT ≅ PS [a pair of congruent sides]
∠T ≅ ∠S [a pair of congruent angles]
Thus, since QT is parallel to PS, therefore:
∠SPQ ≅ ∠TQR [alternate interior angles theorem]
Therefore, we can now state that ΔPQS ≅ ΔQRT based on the ASA congruence theorem.
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Answer:
HOW IS THAT EASY??!?!?!?!?!?
Step-by-step explanation:
The statements and reasons that complete the proof are:
4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]
5. ΔPQS ≅ ΔQRT [ASA congruence theorem]
What is the ASA Congruence Theorem?
When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.
We are given the following:
QT ≅ PS [a pair of congruent sides]
∠T ≅ ∠S [a pair of congruent angles]
Thus, since QT is parallel to PS, therefore:
∠SPQ ≅ ∠TQR [alternate interior angles theorem]
Therefore, we can now state that ΔPQS ≅ ΔQRT based on the ASA congruence theorem.
Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of
The possible values of x are 5 and -1/12
Complete questionGiven that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
How to determine the possible values of x?The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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if sin theta=-3/5 in quadrant III what is cos theta
Answer:
Just simply input in your calculator arcsin of -5/6. Arcsin is the sign that looks like sin to the power of -1, even though it doesn't mean sin to the power of -1. This comes out to 303.6 degrees. So, it actually isn't in quadrant 3, it's in quadrant 4.
Step-by-step explanation:
9
If g = 8, what is the value of the expression 2+3?
OA.
B.
815
(11)
OC. 7
OD. 19
The value of the expression, g/2 + 3 when x = 8 is: 7.
How to Evaluate an Expression?Given the expression, g/2+3, to find it's value when g = 8, plug in the value of g into the expression and solve.
g/2 + 3
8/2 + 3
Divide
4 + 3
= 7
The value of the expression is: 7.
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What's an algorithm ?
Answer:An algorithm is a set of instructions for solving a problem or accomplishing a task.
Step-by-step explanation:
Any series of well defined steps that shows a procedure for solving a given type of problem is called an algorithm.
Step-by-step explanation:
Hope it helps you !!URGENT, please help I am so lost
Answer:
Using the concept of linear equations, we find that we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze.
Step-by-step explanation:
Let x = amount of 20% antifreeze
Let y = amount of 70% antifreeze
Given that the total amount of antifreeze is 80 gallons
So, x + y = 80
Also given that the purity of the total antifreeze is 60%.
0.65x + 0.90y = 0.70(x + y)
65x + 90y = 70(x + y)
Simplify and solve the system of equations
65x + 90y = 70x + 70y
65x -70x+ 90y-70y = 0
-5x + 20y = 0
Now we have the following system of equations:
x + y = 50
-5x + 20y = 0
Multiply the first equation by 5 to get opposite coefficients for x;
add the equations to eliminate x
5x + 5y - 5x + 20y = 250
25y = 250
y = 10
Since the total mixed gallons is 50,
x = 50 - 10 = 40
So we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze
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1. Select all the true statements.
A. √-I is an imaginary number.
-1
B. There are no real numbers that satisfy the equation x = √√-1.
C. Because √-I is imaginary, no one does math with it.
D. The equation x² = -1 has real solutions.
E. √-T = -1 because -1 -1 = -1.
Answer:
A , B , D
Step-by-step explanation:
the nth term of the sequence is 3n + 2. Find the first three terms of the sequence
Answer:
5, 8, 11, ...
Step-by-step explanation:
f(n)=3n+2
the first three terms will be f(1), f(2), and f(3).
f(1)=3(1)+2=5
f(2)=3(2)+2=8
f(3)=3(3)+2=11
Hope this helps!
If not, I am sorry.
If b = 7, then the value of c is...
7[tex]\sqrt{2}[/tex]
Step-by-step explanation:The triangle shown is a 45-45-90 triangle. This name comes from the fact the 3 angle measurements are 45, 45, and 90 degrees.
If needed, you could find the missing angle using the equation: 180 - (45 + 90) = x.
Special Right Triangles
Special right triangles allow us to use formulas and shortcuts to find missing sides easily. Another type of special right triangle is the 30-60-90 triangle. While both of these are special right triangles, they have different formulas.
Formulas
All 45-45-90 triangles have 2 types of sides: the legs (a and b) and the hypotenuse (c).
c = b[tex]\sqrt{2}[/tex]b = a a = bIn these triangles, both of the legs are congruent.
Solving for c
Since we are given b, we can just plug the b-value into the formula that solves for c.
c = 7[tex]\sqrt{2}[/tex]The answer cannot be simplified further, so this is the final answer.
Answer:
Second option
Step-by-step explanation:
It is a right triangle isosceles
a = b = 7
c = hypotenuse
[tex]c =\sqrt{7^{2}+7^{2} } =\sqrt{49+49} =\sqrt{2(49)}=7\sqrt{2}[/tex]
Hope this helps
please help me solve this LCM
Note that
[tex]x^2 - y^2 = (x - y) (x + y)[/tex]
and
[tex]x^2 + 2xy + y^2 = (x + y)^2[/tex]
Then their LCM is [tex]\boxed{x + y}[/tex].
On tax-free weekend, Ben buys school supplies totaling $47.50. He has a sale coupon for 15% off his entire purchase. What will Ben final cost be after the 15% discount?
HELP, FAST!!!
choose an equation for the graph
Answer:
The equation of the graph is y = -lx - 4l - 1.
Step-by-step explanation:
As the values of y are same before and after (4, -1)
the slope of the graph is change on point (4, -1)
the equation of first line is
y - (-1) = 1 (x -4)
the equation of the second line is:
y - (-1) = -1 (x - 4)
As value of y should remain same in both equations
therefore: y - (-1) = - lx - 4l
y = - lx - 4l -1
The equation of the graph is y = -lx - 4l - 1.
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