Answer:
a < 9/20
Step-by-step explanation:
Our equation is the following: ax^2 + 3x + 5
a = unknown
b = 3
c = 5
We are concerned with the discriminant. Namely, b^2 - 4ac must be greater than 0 if we want to real roots
Lets plug in the values:
9 - 4a(5) > 0
9 - 20a > 0
9 > 20a
9/20 > a
a < 9/20
In a quadratic equation given as,
ax² + bx + c = 0
Discriminant of the equation → (b² - 4ac)
For the roots of the equation,
Roots will be real if (b² - 4ac > 0)Roots will be complex if (b² - 4ac < 0)Only one root if b² - 4ac = 0Given quadratic equation in the question is,
ax² + 3x + 5 = 0
Coefficient of x² = a
Coefficient of x = b = 3
Constant term = c = 5
If the roots of this equation are real,
b² - 4ac > 0
(3)² - 4a(5) > 0
9 - 20a > 0
20a < 9
a < [tex]\frac{9}{20}[/tex]
Therefore, for all values of 'a' less than [tex]\frac{9}{20}[/tex], equation will have two real roots.
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Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 8 feet. What is the area of the shade? The area of the shade is ft2.
Answer:
24
Step-by-step explanation:
A triangle is a three sided polygon with three edges and three vertices
There are different types of triangles. They include :
Right angled triangle - one of the angles measure 90 degreesequilateral triangle - all three sides of the triangle are equalisosceles triangle - two sides of the triangle are equalArea of a triangle = 1/2 x ( base x height)
1/2 x (6 x 8) = 24 ft²
Help me pls asp I will give 100 points
The cone and cylinder above have the same radius and height. The volume of the cylinder is 48 cm3. What is the volume of the cone?
A.
24 cm3
B.
16 cm3
C.
96 cm3
D.
144 cm3
Answer:
Option B (16 cm³)
Step-by-step explanation:
GIVEN :-
Both cone and cylinder have same radius and height.Volume of cylinder = 48 cm³TO FIND :-
Volume of coneFACTS TO KNOW BEFORE SOLVING :-
Volume of a cylinder having radius 'r' and height 'h' is [tex]\pi r^{2} h[/tex]Volume of a cone having radius 'r' and height 'h' is [tex]\frac{1}{3} \pi r^{2} h[/tex]Hence ,
Volume of cylinder = Thrice the volume of cone
[OR]
Volume of cone = One third of volume of cylinder
PROCEDURE :-
Volume of cone = [tex]\frac{1}{3} (Volume \: of \: cylinder) = \frac{48}{3} = 16cm^3[/tex]
Which set of ordered pairs demonstrates a function?
A
(-2,-4), (-1, -2), (1, 2), (2, 4)
B
(-2, 4), (1, 2), (1, -2), (2.-4)
C
(-2,4), (-1, 2). (-1, 2), (-2,-4)
D
(-2, 4). (-1, 2), (-1, -2), (-2,-4)
The set of ordered pairs from listed options demonstrating a function is given by: Option A: (-2,-4), (-1, -2), (1, 2), (2, 4)
Firstly, we need the definition a function; based on which we can distinguish the correct set of ordered pairs.
What is a function?If we have two sets A and B as:
[tex]A = \{a_1, a_2, ... \}\\B = \{b_1, b_2, ... \}[/tex]
Then, function [tex]f: A \rightarrow B[/tex] is a connection of elements of A to B such that one element of A is connected to only single element of B, and not many.
The connected pairs are then written as:
[tex]\{(a_i_1,b_j_1), (a_i_2, b_j_2), ... \}[/tex] under the function f.
Now, for the listed ordered pairs, checking if they're functions or not:
Case 1: (-2,-4), (-1, -2), (1, 2), (2, 4)Each single input is connected with single output. So it is demonstrating a function.
Case 2: (-2, 4), (1, 2), (1, -2), (2.-4)In this case, 1 is connected to 2, and -2 both. Thus, it's not representing a function.
Case 3: (-2,4), (-1, 2), (-1, 2), (-2,-4)-1 is only connected to 2, but that does't help as -2 is connected to -4 and 4 both. Thus, it doesn't represent a function.
Case 4: (-2, 4), (-1, 2), (-1, -2), (-2,-4)-2 is connected to 4 and -4, and -1 is connected to 4 and -4, so its not a function.
Thus, the set of ordered pairs from listed options demonstrating a function is given by: Option A: (-2,-4), (-1, -2), (1, 2), (2, 4)
Learn more about functions here:
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Karina ate 1/2 of the muffins. Ulysses ate 1/4 of the muffins. Zawanna ate 1/5 of the muffins. Juan ate the rest of the muffins. What fraction of the muffins did Juan eat?
Answer:
1/20
Step-by-step explanation:
Karina ate 1/2 of the muffins. Ulysses ate 1/4 of the muffins. Zawanna ate 1/5 of the muffins. Juan ate the rest of the muffins. What fraction of the muffins did Juan eat?
Let the total number of muffins = 1
Hence:
The fraction of muffins Juan ate =
1 - (1/2 + 1/4 + 1/5)
Lowest common denominator is 20
1 - ( 10 + 5 + 4/20)
1 - 19/20
= 1/20
The Fraction of muffins Juan ate is 1/20
Consider the rectangular prism.
8 cm
14 cm
6 cm
How many cubes with side lengths of a cm can fit inside the rectangular prism?
0672 cubes
1, 344 cubes
2,688 cubes
0 5,376 cubes
Answer:
672 cubes because 8×6×14 equals 672 I hope it helps
Mena is making a hamster house she cuts a hole for a window that has side length of 6 inches and 3 inches
Answer:
Perimeter: 18 Area: 18
Step-by-step explanation:
6 + 6 + 3 + 3 = 18
6 x 3 = 18
Brandon discovered that his daily routine of buying a slice of pizza and a soda at lunch was costing him more than 18,000$ per year. Choose the correct answer below. A. This statement does not make sense because this would mean that a slice of pizza and a soda costs him about 5$ a day. B. This statement makes sense because this would mean that a slice of pizza and a soda costs him about 5$ a day. C. This statement makes sense because this would mean that a slice of pizza and a soda costs him about 49$ a day. D. This statement does not make sense because this would mean that a slice of pizza and a soda costs him about 49 $ a day.
Answer:
This statement makes sense because this would mean that a slice of pizza and a soda costs him about $49 a day
Step-by-step explanation:
Given
The total spent on a slice of pizza and a soda is:
[tex]Cost > \$18000[/tex] per year
Required
Which of the options is true:
First, we calculate the daily amount spent on a slice of pizza and a soda.
Assume that the yearly cost is: $18000
The daily cost is:
[tex]Daily = \frac{\$18000}{365}[/tex]
[tex]Daily = \$49.32[/tex]
This means that he spends about $49 daily
Given f(x) = 2x ^ 2 + kx - 20 and the remainder when f(x) is divided by x - 10 is 90, then what is the value of k?
Answer:
k = -9
Step-by-step explanation:
f(x) = 2x²+kx-20
From remainder theorem,
x = 10 and f(10) = 90
f(10) = 90
Subsitute the value of x into the expression above.
f(10) = 2(10²)+10k-20 = 90
200+10k-20 = 90
Solve for k by collecting like terms
10 k = 90+20-200
10k = 110-200
10k = -90
k = -90/10
k = -9.
Hence the value of the constant is -9
Please Help me!!! The rectangle has a width of 6 in and a length of 8 in. What is the Perimeter? What is the Area? Remember: Area is length x width. P= A=
There are 8 red, 4 green and 12 yellow balls in a box. If you choose one ball from the box, what is the probability that it will be a yellow ball?
Answer:
50% percent chance the ball will be yellow
Step-by-step explanation:
Find the amount of all the balls-24 and the amount of yellow balls-12
Then divide the number of yellow balls by the number of total balls.
12÷24=0.5
0.5=50%
Gabriella bought 50 lbs of clay for her art projects. She used 18.2 lbs to make a sculpture, and 0.76 lbs for each mug. How many mugs did Gabriella make if she had 18.88 lbs of clay left over?
Answer:
24 mugs
Step-by-step explanation: 18.88/0.76 = ≈24
Answer:
24 mugs
Step-by-step explanation:
Disregard unimportant information
Set up an equation
Variable x = number of mugs
18.88 = 0.76x
Divide both sides by 0.76 to isolate variable x
24.842...
There's no such thing as a fraction or decimal of a mug so round down to the nearest whole number
24
The minute hand of a clock moves from 12:10 to 12:30 a. How many degrees does the minute hand move during this time? b.How many radians does it move during this time?
Answer:
a. 120 degrees
b. 2.0944 radians
Step-by-step explanation:
From 12:00 to 12:15 there forms a 90 degree angle. If we divide this by 3 we get that every 5 minutes the hand moves 30 degrees. Since in this scenario, the minute hand moved from 12:10 to 12:30 it, therefore, moved a total of 20 minutes so we can do the following math
20 / 5min = 4 times
4 * 30 degrees = 120 degrees
We can see that in this time it moved a total of 120 degrees. Now we can use this value to turn it into radians using the degree to radians formula
degrees * [tex]\pi /180[/tex] = radians
120 * [tex]\pi / 180[/tex] = radians
2.0944 = radians
write an expression that has 5 terms and that is equivelent to 5x+y
Answer:
5x + y - 2 + 3 - 1
Step-by-step explanation:
16. Write the equation of the line graphed below.
A. Y= 2x-2
B. Y= -1/4x+2
C. Y= 1/4x+2
D. Y= 1/4x-2
Answer:
B) y = -[tex]\frac{1}{4}[/tex]x + 2
Step-by-step explanation:
slope is -1/4
y-intercept is 2
Find the length of the third side. If necessary, write in simplest radical form. 9 6 Answer: Submit Answer
Answer:
[tex] \sqrt{81 - 36} \\ = \sqrt{45 } \\ = 3 \sqrt{5 } \\ = 6.71[/tex]
The length of the third side of the triangle will be 6.71 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The length of the third side of the triangle will be
Let x be the length of the third side of the triangle. Then we have
9² = 6² + x²
81 = 36 + x²
x² = 45
x = 6.708
x ≅ 6.71 units
More about the Pythagoras theorem link is given below.
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evaluate this expression for a=3
Can someone please help me?
9514 1404 393
Answer:
see below for a graphone possible solution: (12, 5)Step-by-step explanation:
I like a graphing calculator for creating graphs. Here, each inequality is in "slope-intercept" form, so the y-intercepts are easily located (+8 and -4).
The slope (x-coefficient) is the "rise" divided by the "run". The boundary line of the first inequality has a rise of -1 for each run of 3 to the right. The second rises 5 units for each 3 to the right. Starting from the y-intercept, additional points to plot are easily found.
Of course, the boundary line is solid for y ≥ ( ), and is dashed for y < ( ). The shading will be above the line (for higher y-values) for the first inequality, and below the line (for lower y-values) for the second inequality. That puts the double-shaded solution area in the right-side quadrant of the X where the lines cross.
There are an infinite number of solution points to choose from. One of them is (12, 5). Points with an x-value that is a multiple of 3 will be easiest to substitute into the inequalities to check.
5 ≥ (-1/3)(12) +8 ⇒ 5 ≥ 4 . . . true
5 < (5/3)(12) -4 ⇒ 5 < 16 . . . true
4(x + 8), x = 10
5(15p - 2), p = 3
(solve for both)
Answer:
1. 4(10+8) 40+32=72
2. 5(15*3-2) 5(45-2) 225-10=215
Step-by-step explanation:
What value of x makes the equation, -3 + 4x + 3(4x + 8)=4(7x + 3)-3 true?
Answer:
x = 1
Step-by-step explanation:
-3 + 4x + 3(4x + 8) = 4(7x + 3) - 3
first, solve the brackets by using the distributive property of multiplication:
3(4x + 8) = 12x + 24
4(7x + 3) = 28x + 12
rewrite equation:
-3 + 4x + 12x + 24 = 28x + 12 - 3
combine like terms:
16x + 21 = 28x + 9
subytact 21 on both sides:
16x + 21 - 21 = 28x + 9 - 21
16x = 28x - 12
subtract 28x on both sides:
16x - 28x = 28x - 28x - 12
-12x = -12
divide both sides by 12
[tex]\frac{-12x}{12} = \frac{12}{12}[/tex]
x = 1
to check, substitute 1 for x:
-3 + 4(1) + 3(4(1) + 8) = 4(7(1) + 3) - 3
-3 + 4 + 12 + 24 = 28 + 12 - 3
37 = 37
Someone find x !!!!!!
HELP ASAP DUE IN 10 MINS WILL GIVE BRAINLIEST PIC IN QUESTION
In the figure shown, l1 || l2. Which angle is congruent to ∠7? Select all that apply.
Answer:
Since congruent means that they have the same diameter , i'd say that the answer is 1
Step-by-step explanation:
I could use some help
Answer:
[tex]\boxed{50cm^2}[/tex]
Step-by-step explanation:
Hello There!
The shown figure is a trapezoid
The formula for area of a trapezoid is
[tex]A=\frac{a+b}{2} h[/tex]
where a = base 1
b = base 2
h = height
the dimensions given are
13 & 7 - bases
5 - height
so all we have to do is plug in the values into the formula
[tex]A=\frac{7+13}{2} 5\\7+13=20\\\frac{20}{2} = 10\\10*5=50\\A=50[/tex]
So we can conclude that the area of the trapezoid is 50 cm²
Which matrix represents the vertices of the rectangle after it is scaled by a factor of 3?
0 0 120
12 12 6 0
(4,4)
(0, 2)
To 12 12 67
0 12 12 6
(0,0)
(40)
To 12 12 0
0 0 12 6
DONE
the awnser is C I just got it right
Determine the slope (8grade
Answer: 1/2
Step-by-step explanation: I believe the answer is 1/2 because for (2,-6) and (4,-7) the rise over run is 1/2. I don't know though
A frying pan has a radius of 14 cm. What is the circumference of the pan?
Answer:
119.381cm
Step-by-step explanation:
C=2πr
2π * 14cm = 38πcm or 119.381cm
Please help I will mark you brainlest and give you 30 point!!
Answer:
im not sure but i think its x=6
An aquarium has 14 angel fish, 12 clownfish and
18 seahorses. What is the ratio of angelfish to
seahorses?
Answer:
Ratio= 7:9
Step-by-step explanation:
What is the ratio of angelfish to seahorses?
14 angel fish : 18 seahorses
14:18 = 7:9
If the sum of the squares of the legs of a right triangle are = to 144, the hypotenuse is...
Answer: 12
Step-by-step explanation:
H^2=144
Square root of 144
H=12
pls pls pls help with all these three asap! NO WRONG ANSWERS PLS!
Answer:
In 2014, the population is of the United States was about 318,900,000 people. Choose the best approximation of the United States Population in 2014.
people
people
Answer:
people
Step-by-step explanation:
Given
US Population in 2014: About 318,900,000
Required
Approximate
From the given options, it's seen that the population of US is to be approximated to one significant digit and the result should be presented in standard form
So, the first step is to write out the population
318,900,000
As a general rule,
Category 1: Digit 0-4 are approximated to 0
Category 2: Digit 5-9 are approximated to 1
Since, we are approximating to one significant digit, only the first digit is needed, others are to be approximated.
The first digit is 3, meaning that approximation starts from the next digit which is 1
Approximating 318,900,000 will give 300,000,000 because "1" falls in category 1 as illustrated above.
The final step is to convert 300,000,000 to standard form.
There are 8 0s after 3.
Hence,
Conclusively, the approximation of 318,900,000 is people
Step-by-step explanation:
3) The population of a type of bacteria, starts with 100, and grows at a rate of 300% every
day.
a) Write a formula that models this situation.
b) How many bacteria will there be in a week?
c) How many will there be in a month?
Pls help show work