Answers
Discriminant = b² - 4ac
b = coefficient of x term = -9
a = coefficient of squared term = 4
c = constant term = 9
So, Discriminant = 81 - 4(4)(9) = -63
Since, the discriminant is negative, the equation will have complex zeros.This means its graph will not cross x-axis at any point.
So, the answer to this question is zero, option B
Related Questions
One researcher wishes to estimate the mean number of hours that high school students spend watching tv on a weekday. a margin of error of 0.23 hour is desired. past studies suggest that a population standard deviation of 1.9 hours is reasonable. estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answers
Assuming a 95% confidence interval and substituting all the values;
At 95% confidence, Z = 1.96
Therefore,
0.23 = 1.96*1.9/Sqrt (N)
Sqrt (N) = 1.96*1.9/0.23
N = (1.96*1.9/0.23)^2 = 262.16 ≈ 263
Minimum sample size required is 263 students.
Answer:the answer is 236 students
Step-by-step explanation:
) 20% of computer chips from a certain manufacturer are defective. if 100 computer chips are purchased, what is the approximate probability that at least 20 of them are defective
Answers
PLEASE HELP -Given the graph of rectangle QUAD and its reflection.
Use the coordinates of the images' vertices, Q and Q' to algebraically find the line of reflection. In your final answer, include all of your work.
Answers
Q" is located at (6,2)
they bot h have the same Y value (2) so we know it was only a reflection across the X axis
we need to find out where on the X axis it was reflected.
the distance between -5 and 6 = 11 units
11/2 = 5.5
the reflection line was 5.5 units to the right of the original Q
so the reflection line would be X = 0.5
Answer:
Q = (-5, 2)
Q' = (6, 2)
(-5 + 6/2 , 2 + 2/2) = (1/2, 2)
Vertical line through the mid point would be x = 1/2
State the domain of the relation
Answers
The domain is {-2,0,1,2,3,4}, assuming there is a point at (4,6).
the temperature at 10 am was -7°F. By noon, the temperature had dropped 12°F. By 2 pm, it had dropped another 5°F. what was the temperature at 2 pm?
Answers
Find the nth term of the sequence, then find the 20th term, 100th term and the series for each?
2/5, 1/15, -4/15,....
Answers
It's an arithmetic sequence where
[tex]a_1=\dfrac{2}{5}\ and\ d=-\dfrac{1}{3}[/tex]
nth term of the arithmetic sequence is equal:
[tex]a_n=a_1+(n-1)d[/tex]
Substitute:
[tex]a_n=\dfrac{2}{5}+(n-1)\cdot\left(-\dfrac{1}{3}\right)\\\\a_n=\dfrac{2}{5}-\dfrac{1}{3}n+\dfrac{1}{3}\\\\a_n=\dfrac{6}{15}+\dfrac{5}{15}-\dfrac{1}{3}n\\\\\boxed{a_n=\dfrac{11}{15}-\dfrac{1}{3}n}[/tex]
Other form:
[tex]a_n=\dfrac{11}{15}-\dfrac{5}{15}n\\\\\boxed{a_n=\dfrac{11-5n}{15}}[/tex]
[tex]a_{20}=\dfrac{11-5\cdot20}{15}=\dfrac{11-100}{15}=\dfrac{-89}{15}\\\\a_{100}=\dfrac{11-5\cdot100}{15}=\dfrac{11-500}{15}=\dfrac{-489}{15}=-\dfrac{163}{5}[/tex]
Leo, Kush and Mai share some money in the ratio 3:5:8
Kush receives £750 more than Leo.
Calculate total amount of money that they shared.
Answers
The ratio in which they received cash is 3:5:8
the difference in ration between Kush and Leo=£(5-3)=£2
Total ratio is: 16
thus the total amount was:
16/2×750
=£6000
99 POINTS!!!: if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then
what is the central angle,
what is the measure of the arc that 2 pieces together would intercept,
and the equation that represents
and circumference?
PLEASE HURRY!!!
Answers
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²
b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in
the measure of the arc that 2 pieces together would intercept is 9.42 in
c) The central angle of one slice is 45 degrees
Based on the family the graph below belongs to, which equation could represent the graph
Answers
Answer: Second option y=log(2x)+3
Solution:
Based on the family of graphs shown in the attached file, the equation could represent the graph is y=log(2x)+3
This graph is the graph of the funtion y=log(x) stretched horizontally by a factor of 2 and translated 3 units upward.
Michelle invests $1000 at a bank offering 3% compounded quarterly. Write an equation to model the growth of the investment.
A) A = 1000(1.03)4t
B) A = 1000(1+.03
4
)t
C) A = 1000(1+.03
4
)4t
D) A = 1000((1.03)
4
)4t
Answers
is what I got
Answer:
C. [tex]1000( \frac{1+.03}{4})^{4t}[/tex]
Step-by-step explanation:
Simplify radical expression. Leave in radical form. the squarefoot of 7(the squarefoot of 14+the squarefoot 3)
Answers
1- You have the following radical expression given in the problem above:
(√7)(√(14)+√(3))
2- When you apply the distributive property, you obtain:
(√7)(√(14))+ (√7)(√(3))
3-Simpliying, you have:
(7√2)+(√21)
4- Therefore the answer is: (7√2)+(√21)
A store manager set up a cardboard display to advertise a new brand of perfume. The display is a square pyramid whose base is 18 inches on each side.The height of each triangular face of the pyramid is 12 inches. How much card word was used to make the display?
A. 516 B.756
C.612 D.1080
D is not the answer I tried the teacher marked it wrong
Answers
please award brainly
The surface area of the cardboard display is the sum of the area of the square base and the four triangular faces, totaling 756 square inches. This corresponds to answer B.
The student wishes to calculate he amount of cardboard used to create a square pyramid display. To find this, we need to determine the surface area of the pyramid, which includes the base and the four triangular faces.
Firstly, we calculate the area of the square base. The base length is given as 18 inches. The formula for the area of a square is side length squared:
Base area = 18 inches × 18 inches = 324 square inches.Next, we find the area of one triangular face using the formula for the area of a triangle (base × height / 2). The base of each triangle is the same as the side of the square base, and the height is given as 12 inches:
Triangular face area = (18 inches × 12 inches) / 2 = 108 square inches.Since there are four identical triangular faces, we multiply the area of one triangle by four:
Total area of triangular faces = 4 × 108 square inches = 432 square inches.Finally, we add the area of the base to the total area of the triangular faces:
Total surface area = 324 square inches (base area) + 432 square inches (triangular faces area) = 756 square inches.Therefore, the amount of cardboard used for the pyramid display is 756 square inches, which corresponds to answer B.
what happens when you add 1 to a number
Answers
Which expression represents the volume of the box? use the formula v=lwh 3x+1, 2x-1 ×+2
Answers
(3x+1) by (2x-1) by (x+2) will be:
volume, V=lwh
plugging the values we get:
V=(3x+1)(2x-1)(x+2)
Expanding the above we get:
V=(3x+1)(2x^2+3x-2)
V=3x(2x^2+3x-2)+1(2x^2+3x-2)
V=6x^3+9x^2-6x+2x^2+3x-2
V=6x^3+11x^2-3x-2
Hence the expression for the volume will be:
V=6x^3+11x^2-3x-2
Linda bought circular table clothe that was a radius of 3 feet. What is the circmference to the nearest foot of linda's table cloth? (using Pie 3.14
Answers
[circumference]=2*pi*r
for r=3 ft
[circumference]=2*pi*3-----> 18.84 ft-------> nearest foot-----> 19 ft
the answer is
19 ft
The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?
Answers
If we look at y = mx + b and y = 8x -b we can see the similarities
y = mx + b
y = 8x - 1
m = slope = 8
b = y-intercept = -1
Slope = 8
Answer:
8
Step-by-step explanation:
I just took the test.
The penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20 meters. One penguin swims half way around the island before hopping out.
How far did the penguin swim?
Answers
Answer:
10pi
Step-by-step explanation:
The answer is 10pi
What do you notice about the median and mean?
Answers
Which is the equation of an ellipse centered at the origin with foci on x-axis, x-intercepts +7, -7 and y-intercepts +2,
-2?
Answers
foci on x-axis-------> is a ellipse with horizontal major axis
the equation is
(x²/a²)+(y²/b²)=1
major axis is the x-axis with length 2a
2a=14--------> a=7
minor axis is the y-axis with length 2b
2b=4-----> b=2
the equation is
(x²/a²)+(y²/b²)=1------> (x²/7²)+(y²/2²)=1-----> (x²/49)+(y²/4)=1
the answer is
(x²/49)+(y²/4)=1
see the attached figure
Answer:
It's B on edge.
Step-by-step explanation:
Question 21 [t-interval] a random sample of size 18 is drawn from a population that is normally distributed. the sample mean is 58.5, and the sample standard deviation is found to be 11.5. determine a 95% confidence interval about population mean.
a. [52.78,64.22]
b. [53.78,63.22]
c. [53.18,63.81]
d. [54.04,62.96]
Answers
Answer:
Option a. [52.78,64.22]
Step-by-step explanation:
We are given that a random sample of size 18 is drawn from a population that is normally distributed.
Sample mean is 58.5, and the sample standard deviation is found to be 11.5 i.e., X bar = 58.5 and s = 11.5
The pivotal quantity for calculating 95% confidence interval is;
[tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
So, 95% confidence interval about population mean is given by;
P(-2.110 < [tex]t_1_7[/tex] < 2.110) = 0.95
P(-2.110 < [tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.110) = 0.95
P(-2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]{Xbar - \mu}[/tex] < 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
P(X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]\mu[/tex] < X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
95% confidence interval about [tex]\mu[/tex] = [ X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] , X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ]
= [ 58.5 - 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] , 58.5 + 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] ]
= [ 52.78 , 64.22 ]
Therefore, 95% confidence interval about population mean is [52.78 , 64.22].
PLZ HELP ASAP CIRCLES
Answers
[tex] x^{2} -16x+ y^{2} -36=0 \\ \\ x^{2} -2(x)(8)+ y^{2} = 36 \\ \\ x^{2} -2(x)(8)+ 8^{2}+ y^{2} =36 +8^{2} \\ \\ (x-8)^{2}+y^{2}=100 [/tex]
Thus, we can say now:
Center of the circle is (8,0) and its radius is 10.
6(z+2)-2(2z+5)=18 show step by step
Answers
Note:
Parenthesis, Exponents (and roots), Multiplication, Division, Addition, Subtraction)
Because you are trying to isolate the z (variable), you cannot do parenthesis. Instead, distribute 6 to z and 2, and -2 to 2z and 5
6(z + 2) = 6z + 12
-2(2z + 5) = -4z - 10
6z + 12 - 4z - 10 = 18
Next, combine like terms. Combine terms with common variables together, as well as constants.
6z - 4z = 2z
12 - 10 = 2
2z + 2 = 18
Next, isolate the z, do the opposite of PEMDAS. Note that there is an equal sign. What you do to one side, you have to do to the other.
2z + 2 = 18
subtract 2 from both sdies
2z + 2 (-2) = 18 (-2)
2z = 18 - 2
2z = 16
isolate the z, divide 2 from both sides
2z = 16
2z/2 = 16/2
z = 16/2
z = 8
8 is your answer for z
hope this helps
A taco stand sells tacos for $3.25 each. The stands expenses for the day are $210. Define your variables and write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then slice the inequality. Provide your conclusion as a complete sentence.
Answers
Let P= profit
let n= no. of tacos sold per day
Sol'n:
P= 3.25n-210
the profit needs to be positive, thus
3.25n>210
n>210/3.25
n> 64.615
they can only sell whole tacos, therefore they must sell at least 65 tacos to make a profit and that profit is:
P=3.25n-210
P=3.25*65 - 210
P= 211.25 -210
P= 1.25
$1.25 profit
Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk 2 quarts of orange juice 16 cups of milk 32 oz of lemonade . how many gallons of beverages did he buy
Answers
1 pint=0.125 gallons
1 quart=0.25 gallons
1 cup = 0.0625 gallons
1 oz = 0.0078125 gallons
thus amount of :
milk bought
0.125*2=0.25 gallons
orange juice bought:
0.25*2=0.5 gallons
milk bought:
16*0.0625=1 gallon
lemonade bought:
32*0.0078125=0.25 gallons
Thus total gallons made was:
0.25+1+0.5+0.25
=2 gallons
The amount of beverages did he buy will be 2 gallons.
What is conversion?Conversion means to convert the same thing into different units.
Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk, 2 quarts of orange juice, 16 cups of milk, and 32 oz of lemonade.
We know the conversion
1 pint = 0.125 gallons
1 quart = 0.25 gallons
1 cup = 0.0625 gallons
1 oz = 0.0078125 gallons
Then the amount of beverages did he buy will be
Milk bought
0.125 x 2 = 0.25 gallons
Orange juice bought:
0.25 x 2 = 0.5 gallons
Milk bought:
16 x 0.0625 = 1 gallon
Lemonade bought:
32 x 0.0078125 = 0.25 gallons
Thus total gallons made will be
→ 0.25 + 1 + 0.5 + 0.25
→ 2 gallons
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Identify the coefficient of each term of the polynomial.
-2x+9
what is The coefficient of the first term is ....
what isThe coefficient of the second term is
Answers
The coefficient is a known number, written as a digit, whereas the variable is an unknown number, written as a letter to signify an unknown number.
So, the coefficient in the first term (or part of the equation) is -2. The coefficient in the second term is 9, and the variable in this equation is x.
Final answer:
The coefficient of the first term '-2x' in the polynomial is -2, and the coefficient of the second term '9' is 9.
Explanation:
In the polynomial -2x+9, each term has a coefficient. A coefficient is a number that multiplies the variable. The variable in the first term is x, and it is being multiplied by -2. Therefore, the coefficient of the first term is -2. The second term is a constant and does not have a variable associated with it. However, by convention, we can think of this term as 9 times x0, since any number raised to the zero power is 1. The coefficient of this constant term is 9.
A surveyor wants to measure the distance from the north end (point b ) to the south end (point c) of a body of water. He creates a right triangle by using point A which is 17.5 m due west of point c and at a 30 degree angle with point b. Find the distance across the lake
Answers
The distance across the body of water from point b (north end) to point c (south end) can be found using trigonometry and the sine ratio. Given that the angle is 30° and the distance from point A to point b is 17.5 m, the distance across the water (from point b to point c) is 8.75m.
Explanation:The problem at hand is a trigonometry problem which can be solved by using the sine ratio. In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle is given as 30°, and we are asked to find the distance from point b (north end) to point c (south end), which is the side opposite to the 30° angle. Therefore, we can set up the following equation using the sine ratio: sin(30°) = opposite/hypotenuse.
In this instance, the hypotenuse is the distance from point A to point b, which is given as 17.5 m. Thus, the equation becomes sin(30°) = distance from point b to point c / 17.5 m. Solving this for the distance from point b to point c would mean multiplying both sides by 17.5 m, giving us: distance from point b to point c = sin(30°) * 17.5 m.
Upon calculation, we find that sin(30°) equals 0.5, so therefore the distance from point b to point c, which is the distance across the body of water is 0.5 * 17.5m = 8.75 m.
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A rectangle floor is 24 feet long and 9 feet wide. what is it’s area of the floor in square yards?
Answers
The rectangle is 24 ft (length) by 9 ft (width):
Area = 24 * 9 => Area = 216 sq. yds.
Final answer:
The area of a rectangle floor that is 24 feet long and 9 feet wide is 216 square feet, which is equivalent to 24 square yards when converted using the fact that there are 9 square feet in a square yard.
Explanation:
The student is asking about the area of a rectangle when the dimensions are given in feet and the answer is required in square yards. To convert the area from square feet to square yards, we need to know the conversion factor between these two units of measurement.
It's established that 1 square yard is equal to 9 square feet. Thus, the area of the floor in square feet is calculated by multiplying the length by the width:
Area in square feet = Length in feet × Width in feet
= 24 ft × 9 ft
= 216 square feet
Next, we convert the area into square yards by dividing by 9:
Area in square yards = Area in square feet ÷ Conversion factor
= 216 sq ft ÷ 9 (sq ft/sq yd)
= 24 square yards
Therefore, the area of the floor in square yards is 24 square yards.
Find f. f ''(x) = −2 + 24x − 12x2, f(0) = 4, f '(0) = 18
Answers
Answer:
f(x) = -x⁴ + 4x³ - x² + 18x + 4
Step-by-step explanation:
If we take the integral of f''(x) with respect to x, we get that f'(x)= -2x + 12x² - 4x³ + C.
Substituting in f'(0)=18, we get C=18.So, f'(x) = -2x + 12x² - 4x³ + 18.If we take the integral of f'(x) with respect to x, we get that f(x) = -x² + 4x³ - x⁴ + 18x + C.
Substituting in f(0) = 4, we get C=4.So, f(x) = -x⁴ + 4x³ - x² + 18x + 4To find the function f, we need to integrate its second derivative, then use the given initial conditions to solve for the constant of integration and find the exact function f(x).
Explanation:To find the function f, we need to integrate its second derivative. We integrate each term of the second derivative separately, using the power rule for integration. So, f''(x) = -2 + 24x - 12[tex]x^2[/tex] becomes f'(x) = -2x + 12[tex]x^2[/tex] - 4[tex]x^3[/tex] + C, where C is the constant of integration. Then, we integrate f'(x) to find f(x), again using the power rule for integration. Finally, we use the given initial conditions, f(0) = 4 and f'(0) = 18, to solve for the constant of integration and find the exact function f(x).
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what is the volume of the cube shown below? 2 1/4
Answers
The volume of the given cube is 11.4 cubic units.
What is volume of cube?The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object.
The edge of the given cube is [tex]2\frac{1}{4}[/tex] =2.25 units.
We know that, the volume of a cube is a³, where a is an edge.
Here, volume = (2.25)³
= 11.390625
≈ 11.4 cubic units
Therefore, the volume of the given cube is 11.4 cubic units.
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the function f(x)=2^x. the function f(x)= 2^x+k and K < 0. which of the following statements is true