Answer:
Any value of kStep-by-step explanation:
The quadratic expression can be factored into two binomials if it has two real roots.
Two real roots possible with non-negative discriminant:
D ≥ 0As D = b² - 4ac, we get the following inequality
k² - 4(3)(-8) ≥ 0k² + 96 ≥ 0k² ≥ - 96This is true for any value of k
k ∈ (- ∞, + ∞)Answer:
(-∞, ∞) or [tex]k \in \mathbb{R}[/tex]
Step-by-step explanation:
Binomial: two terms connected by a plus or minus sign.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
If a quadratic expression factors into two binomials, it will have two real roots. Therefore, the discriminant will be greater than zero.
Given quadratic expression:
[tex]3x^2+kx-8[/tex]
[tex]\implies a=3, \quad b=k, \quad c=-8[/tex]
Substitute the values of a, b and c into the discriminant, set it to > 0:
[tex]\implies k^2-4(3)(-8) > 0[/tex]
[tex]\implies k^2+96 > 0[/tex]
As k² ≥ 0 for all real numbers,
[tex]\implies k^2+96 \geq 96[/tex]
Therefore, the values of k are (-∞, ∞) or [tex]k \in \mathbb{R}[/tex]
if a-1/a=5 then find the value of a square +1/asquare
Answer:
3
Step-by-step explanation:
Calculating a
a - 1 / a = 5a - 1 = 5a4a = -1a = -1/4Substitute in the 2nd equation
a² + 1 / a²(-1/4)² + 1 / (-1/4)²1/2 + 1 / 1/23/2 / 1/23A caterer charges a setup fee of $40, plus $15 per
person. How much will the caterer charge if 22
people attend the party, and the customer has a
coupon for $100 off the total?
What is the area of triangle PQR rounded to the nearest tenth of a square meter? Drawing is not to scale.
Answer:
A 31.3
Step-by-step explanation:
just took the test
Answer:
27.0m^2
Step-by-step explanation:
Use the formula A = 0.5 * a * b * sin (x)
this formula is used for obtuse angles where a & b are the sides (12,7) and x is the angle between them.
Fill in the blanks:
A = 0.5 * 12 * 7 * sin (40)
use demos scientific calculator
A= 26.99
round up
27.0 m^2
what is the mean of the data set 17,9,11,7
Answer:
11
Step-by-step explanation:
Mean - add all the numbers up and divide by the amount of numbers you have.
Add all the numbers up-
17 + 9 + 11 + 7 = 44
Divide by the amount of numbers you have, since you have 4, divide by 4
44/4 = 11
11 would be your answer!
I hope it helps! Have a great day!
Muffin ^^
can someone please help me with this question
Answer:
88 [tex]in^2[/tex]
Step-by-step explanation:
2(2 x 6 + 4 x 6 + 4 x 2)
[tex]2[/tex][tex](wl+hl+hw)[/tex]
In 1932, the average house in the united states cost $3,900. today, the average cost of a house is $350,000. what is the percent of change in the average price of a house in the united states (round to the nearest whole percentage)?
Answer:
8,874%
Step-by-step explanation:
Find percent of change by finding the differnce between the original price and new price. You can then use a proportion "change/original = percent/100"
i need help it is overdue ):
Answer:
x = 4[tex]\sqrt{3}[/tex] , y = 4
Step-by-step explanation:
using the cosine and sine ratios in the right triangle and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 4[tex]\sqrt{3}[/tex]
and
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 8 ( divide both sides by 2 )
y = 4
There are 25 white tiles in a box. what percent of tiles what percent of tiles will ally use to tile her laundry room floor (6ft by 6ft)
Answer: 100%
Step-by-step explanation:
Jill went shopping from 3:45 pm to 5:00 om for how long did she shop
kyle has x -3ounce blue marbles and 5 ounce green marbles. lara has 5-ounce green marbles and 3-ounces of blue marbles. is it possible for kyle and lara to have the same number of green marbles and the same total bag weight ,y? explain
Answer:
yes
Step-by-step explanation:
if x=6, 6-3=3 , so it is possible if x is 6
Which of the following lines has a negative slope?
Answer:
The second option, or the one attached.
Step-by-step explanation:
This line has a negative slope because the line is going "down the stairs" from the top-left to the bottom-right.
Answer:
negative, the arrows pointing directly to it,
Review the graph of function f(x). On a coordinate plane, a graph has maximum point at open circle (0, 4), and curves down and then repeats with smaller curves at intervals of 2 pi in both the positive and negative x -axis. A point is at (0, negative 2). Which statement identifies and explains Limit of f (x) as x approaches 0? The limit Limit of f (x) as x approaches 0 = –2 because the value of the function at x = 0 is –2. The limit Limit of f (x) as x approaches 0 does not exist because there is an open circle at (0, 4). The limit Limit of f (x) as x approaches 0 = 4 because both the left-hand and right-hand limits equal 4. The limit Limit of f (x) as x approaches 0 does not exist because there is oscillating behavior around x = 0.
The true statement is that (b) The limit [tex]\lim_{x \to 0} f(x)[/tex] does not exist because there is an open circle at (0, 4).
How to interpret the limit of f(x)?From the graph of the function (see attachment), we have the following highlight:
There is an open circle at point (0,4), the maximum point of the function f(x) and when x = 0
When there is an open circle in the graph at x = 0, then the function has no limit at this point
This is so because the value is exclusive of the function values
Hence, the limit [tex]\lim_{x \to 0} f(x)[/tex] does not exist because there is an open circle at (0, 4).
Read more about limits and continuity at:
https://brainly.com/question/12212916
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Answer:
C - The limit Limit of f (x) as x approaches 0 = 4 because both the left-hand and right-hand limits equal 4.
Step-by-step explanation:
Precalc Edge 2023
your class wants to sell school spirit cups with the school logo on them .you teacher asks you to design this new cup such that a stack of 10cups will be 125 cm tall. describe key measurements of the school spirit cups and explain how they will meet the reqiured specifications
The class can make the school cup of 120.5 cm tall.
What is Equation?Equations include two sides on the left and right connected with equal to sign.
We can find the key measurements of the cups using the formula,
x + 10y = 125
where x is the height of one cup without including the lip length and y is the lip length.
x + y is the height of one cup.
There are various ways to form the measurement of x and y here.
Let y, the lip length of the cup be 1 cm tall. Then,
x + 10 = 125
⇒ x = 115
Length of 1 cup will be 115 + 1 = 116 cm.
Suppose length of lip, y be 0.5 cm. Then,
x + (10 × 0.5) = 125
x + 5 = 125
x = 125 - 5
x = 120 cm
Length of 1 cup will be 120 + 0.5 = 120.5 cm.
Similarly, we can have many measurements for the height of one cup.
Their logo can be placed in the middle of the cup taking the height of 80 cm leaving 20 cm on the top and bottom.
Hence the class can make the school cup of 120.5 cm tall.
To learn more about Equations, click :
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You supply a good at a price of $5. You also earn a profit at this price. This means that your marginal cost could be _____. $2.00 $5.00 $10.00
[tex]$5.00[/tex][tex]Hello[/tex] [tex]There![/tex]
Your answer is..:$[tex]5.00[/tex]
Hopefully, that helps you!!
[tex]OwoSokka[/tex]
again another Pythagorean Theorem i need help on, please and thank you
You commented that part of the instruction included "If the theorem cannot be applied, explain the reason."
The theorem cannot be applied. Since this is not a right triangle, we cannot solve using the Pythagorean Theorem unless we are given a height. If we have the height of this triangle, then we can break it into two different right triangles and solve.
What is a right triangle? A right triangle is a triangle that has an angle measurement of 90 degrees.
In summary, this is an isosceles triangle and the Pythagorean Theorem only applies to right triangles.
Please help In triangle ABC, m∠A=47∘ and m∠B=70∘. What is the measure of angle C?
Answer: <C = 63°
Step-by-step explanation:
The interior angles in all triangles always equal 180°
47 + 70= 117
180 - 117 = 63°
<C = 63°
hope this helps :)
According to the line plot, how many tadpoles were measured?
10 tadpoles
3 tadpoles
4 tadpoles
9 tadpoles
Answer:
10 Tadpoles were mesured in the line plot
Answer:
10 tadpoles
Step-by-step explanation:
look at the diagram
count the x's
you get your answer
pls answer (10 points given)
Answer:
C
Step-by-step explanation:
Its not greater than or equal to and its less than 6.
Answer:
A. x < 3
Step-by-step explanation:
2x < 6
Simplify:
2x < 6 <== divide both sides by 2
/2 /2
x < 3
Rules:
Open circle: < (going left) or > (going right)
Closed circle: ≤ (going left) or ≥ (going right)
For our answer: x < 3
It would be an open circle going left. The only number line that illustrates this is line A.
Hope this helps!
a cylindrical tank has a diameter of 24 dm And a height of 30, dm.how many litters of a water can it hold when full (1 dm³ = 1 L)
heath records the number of winners of three ring toss games. According to heaths experiments, what is the probability a player will win the game
How much closer is it to travel from Aurora to Clifton directly than from Aurora to Clifton through Burlington?
Answer:
40m
Step-by-step explanation:
The total distance from Aurora to Clifton through Burlington is: 65 + 72 = 137
137 - 97 = 40
So it is 40 m closer to travel from Aurora to Clifton directly than from Aurora to Clifton through Burlington.
what is 7/5 as a simple thing?
please b quick
The display on a calculator reads 9.378 E - 5. Which value does this represent?
a. 937,800,000
b. 937,800
c. 0.00009378
d. 0.000009378
Answer: C.0.0009378
Step-by-step explanation:
9.378E-5 is basically 9.378 x 10∧-5. Move the decimal to right 5 times.
no links please help!!!
Answer:
5. During the day, the temperature on the surface of Mars rises at a rate of 9 degrees C every hour
a. In 2 hours: 18 a. in 3 hours: 27 in n hours: 9n
b. y=9n
c. 108
d. -540
6. Kaite saves 5 dollars every week, so far she has saved a total of $63
a. y=5x+63
b. 25
hope it helps
What is the measure of the radius, c, rounded to the nearest hundredth? use an appropriate trigonometric ratio to solve. 5.88 cm 8.09 cm 12.36 cm 17.01 cm
The measure of the radius, c, rounded to the nearest hundredthis 12.36cm
Trigonometry identityThe given figure is a pentagon. The measure of one of the interior angle is 108 degrees.
The triangle in the pentagon is right angle.
Measured acute ange = 108/2 = 54 degrees
Using the trig identity
sin 54 = 10/c
c =10/sin54
c = 10/0.8090
c = 12.36 cm
Hence the measure of the radius, c, rounded to the nearest hundredthis 12.36cm
Learn more on trigonometry identity here; https://brainly.com/question/7331447
Answer:
12.36
Step-by-step explanation:
If P = (4,7), Find:
r 180° (P)
([?], [])
Answer: (-4,-7)
Step-by-step explanation:
For what values of a is the expression true? |a+5|=a+5
Answer:
a>=-5
Step-by-step explanation:
when a+5>/=0
a>/=-5 because the if the contents of the absolute value are equal to the same expression in the absolute value if the expression is non negative. So we find the values of a when the expression is nonnegative.
Every second, an elevator either has a 50% chance of going up and a 50% chance of going down. If the elevator starts at floor 15, what is the probability that, after 5 seconds, the elevator is at floor 18?
Using it's concept, it is found that there is a 0.1563 = 15.63% probability that, after 5 seconds, the elevator is at floor 18.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Starting at floor 15, these are the following outcomes that result in the elevator being at floor 18 in 5 seconds, each with [tex]0.5^5[/tex] probability:
4 up, 1 down.3 up, 1 down, 1 up.1 down, 4 up.1 up, 1 down, 3 up.2 up, 1 down, 2 up.5 outcomes, hence the probability is:
[tex]p = 5 \times (0.5)^5 = 0.1563[/tex]
0.1563 = 15.63% probability that, after 5 seconds, the elevator is at floor 18.
More can be learned about probabilities at https://brainly.com/question/14398287
What type of triangle is defined by the following set of side lengths
11, 9 , 7
Question 4 options:
Acute
Obtuse
Right
Not a triangle
Answer:
it looks like a triangle but it is not it is called a Nonigon
IMAGE IS DOWN BELOW
SOMEONE PLEASE HELP ME WITH THIS
ILL GIVE YOU BRAINLIST ANSWER
Answer:
13.0 cm
Step-by-step explanation:
We proceed by Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
We are given a = 1 and b = 13
[tex]1^2 +13^2 =c^2\\c=\sqrt{170}\\[/tex]
c ≈ 13.0
This is the answer rounded to the nearest tenth.
