For what value of k are the roots of the quadratic equation 3x² 2kx 27/0 real and equal?
The value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation 3x²+2kx+27=0
Here, a=3,b=2k,c=27
It is given that roots are real and equal.
b²-4ac=0
(2k)²-4(3)(27)=0
4k²-324=0
4k²=324
Divide both sides by 4
k²=81
Take square root on both sides
k=±9
Hence, the value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.
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What is the slope of y =- 4 5x 3?
The slope of the given line y = -(4/5)x + 3 is -(4/5).
What is the slope of the line?The slope of a line is defined as the gradient of the line.
The slope of a line is a measure of its steepness. It is defined as the change in y (the "rise") divided by the change in x (the "run") between two points on the line.
The equation is given in the question as:
y = - (4/5)x + 3
To find the slope of a line given by the equation y = mx + b, where m is the slope and b is the y-intercept, we can just take the coefficient of x, which is m.
As per the question, the coefficient of x is -(4/5), so the slope of the line is -(4/5).
Therefore, the slope of the given line is -(4/5).
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(17, 17) (0, 13) (19, –11) (14, –17) Is this relation a function?
The relation is not a function because the element 17 is paired with two elements in the range (17 and 0). Therefore, the relation is not a function.
What is relation and function ?A relation is a set of ordered pairs that represents a relationship between two sets of objects. For example, the relation {(1, 2), (3, 4), (5, 6)} represents a relationship between the sets {1, 3, 5} and {2, 4, 6}.A function is a special type of relation in which each element in the domain is paired with exactly one element in the range. A relation is a function if each element in the domain is paired with exactly one element in the range. In this case, the relation is not a function because the element 17 is paired with two elements in the range (17 and 0). Therefore, the relation is not a function.To learn more about function refer :
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What is the relationship between the area of the base of a prism its height and its volume?
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.
What is area?The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
V=b*h
b=base area of prism
h=height of prism
The volume of a prism is calculated as V=Bh, where B is the base area and h is the height.
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A rocket-powered hockey puck moves on a horizontal frictionless table. The figure below shows the graphs of vx and vy, the x- and y-components of the puck’s velocity. The puck starts at the origin.
Part A
In which direction is the puck moving at t = 3 s ? Give your answer as an angle from the x-axis.
Express your answer using two significant figures.
On a frictionless horizontal table, the rocket-powered hockey puck moves at an angle of 61.9° above the horizontal in 3 seconds.
what are significant figures ?The significance of non-zero digits is constant. Between any two significant digits, there can be no zeros. Only the final or trailing zeros in the decimal section are important. Between any two non-zero digits, all zeros are important. Seven significant digits are seen in, for instance, 108.0097. There is never any significance for any zeros that are both to the right and left of the decimal point and a digit that is not zero.
given
Then, using the formula that relates the tangent of angle, vertical component of velocity, and horizontal component of velocity to find the direction in which the puck is moving.
Displacement is the smallest distance between the two points.
The vector representation of velocity is,
s = 1/2at2
= 1 .80 m
The puck moves at an angle 61.9° above the horizontal.
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How do you solve an inequality on a calculator?
press menu and select option,press 2 to select to a polynomial degree of 2,select the number that matches the inequality u are about to solve and lastly input the values of coefficient of x into the expression and press equal to sign on the calculator
How do we solve inequality on a calculator?A relationship between two expressions or values that are not equal to each other is called 'inequality. '
Inequality can be greater than >, less than < , great than or equal to ≥ , less than or equal to ≤.
like other equations, inequality can be solved on a calculator. This process shows how inequality can be solved on a calculator. For example if 3x²+4x+5≥0 is to be solved on a calculator, the following steps are to be taken
Step 1 : press menu and select option B( inequality option)
Step2 : press 2 to select to a polynomial degree of 2
step 3 : select the number that matches the inequality u are about to solve
step 4: input the values of coefficient of x into the expression
step 5 : press the equal to sign on the calculator.
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Geometry book page 599
Answer:
Can you make another post showing us a picture of the Geometry book page 599? I may be able to help :-)
Two balls are to be pulled from a vase that contains 7 red balls, 9 green balls, and 2 black balls. After the first ball is drawn, it is
not replaced. What is the probability that two red balls are chosen from the vase?
The probability that two red balls are chosen from the vase would be = 1/9
What is probability?Probability is defined as the concept that proves that an event may occur or not.
The number of red balls = 7
The number of black balls = 2
The number of green balls = 9
The total number of balls in the vase = 18
The probability of getting 2 red balls = 2/18 = 1/9
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Is the answer to this question A or B? I’m conflicted.
Would appreciate the reply!!
Answer: B
I have to add extra words to answer you but it’s B :))
Darcy is buying a new couch that cost $999.00. She has two payment options.
Option 1: Pay with credit card. The card charges 20.00% annual interest and Darcy expects to pay off the charge in 30 days.
Option 2: Take the store promotion of 15 monthly payments of $70 (including tax)
a) Calculate the total cost of each option
b) What is the annual interest rate being charged with Option 2?
Please show your work.
Answer:
Step-by-step explanation: a) To calculate the total cost of the couch when paid with a credit card, we need to calculate the amount of interest that will be charged. To do this, we first need to calculate the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 20/12 = 1.67%.
Next, we need to multiply the cost of the couch by the monthly interest rate to find the amount of interest that will be charged. In this case, the amount of interest is 999 * 1.67% = 16.67.
Finally, we need to add the amount of interest to the cost of the couch to find the total cost when paid with a credit card. In this case, the total cost is 999 + 16.67 = 1015.67.
To calculate the total cost of the couch when paid with the store promotion, we simply need to add up all 15 monthly payments. In this case, the total cost is 15 * 70 = 1050.00.
b) To calculate the annual interest rate being charged with Option 2, we need to divide the total cost of the couch by the number of monthly payments and then multiply by 12. In this case, the annual interest rate is (1050/15)*12 = 96%.
In the first week of July, a record 1020 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 198 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 15%.
What is the percent decrease in the number of people who went to the pool over these four weeks?The number of people in each week will be recorded below:
First week = 1020
Second week = 1020 - 100 = 920
Third week = 920 + 145 = 1065
Fourth week = 1065 - 198 = 867
The percent decrease in the number of people who went to the pool over these four weeks will be:
= (1020 - 867) / 1020 × 100
= 153 / 1020 × 100
= 15%
The percentage decrease is 15%.
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What does the notation f/x y mean?
The notation f (x) = y means that the functional value at the point x is y.
In the notation f (x) = y, we understand that the value x is to be plugged in the function given to us (which is f here) which on solving gives y as the answer or solution 'y' of that function at a point x.
For example, let us consider the function f (x) = 2x + 3 = y
Then if we find f (2), then 2 will be plugged in the function 2x +3 such that
f (2) = 2(2) + 3 = 7,
which means that 7 is the functional value, 'y' at the point 2 which is considered as x.
The question is incomplete, the complete question is f (x) = y.
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What is the vertex of the graph of f x )=[ x 5 ]- 6?
The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.
Therefore the answer is (5, -6).
The graph f(x) = |x - 5| - 6 is symmetrical about the axis x = 5.
A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is
(5, -6)
--The question is incomplete, answering to the question --
"What is the vertex of the graph of f(x) = |x - 5| - 6?"
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Use the Law of Cosines to find the values of x°and y°. Round to the nearest tenth.
The value of x° and y° are 26.8° and 86.2°.
What is rounding to tenth?
Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.
The length of sides of the triangle are 8, 6, and 5.
Assume that AB = c = 6, BC = a = 5, and AC = b = 8
m∠A = x° and m∠B = y°.
Cosine law:
c² = a² + b² - 2ab cos C ....(i)
b² = a² + c² - 2ac cos B ....(ii)
a² = b² + c² - 2bc cos A ....(iii)
Putting a = 5, b = 8, c = 6, and A = x° in law (iii)
5² = 8² + 6² - 2×8×6 cos x
25 = 64 + 36 - 84 cos x
84 cos x = 75
cos x = 75/84
x = 26.76°
x = 26.8° (nearest tenth)
Putting a = 5, b = 8, c = 6, and B = y° in law (ii)
8² = 5² + 6² - 2×5×6 cos y
64 = 25 + 36 - 60 cos y
60 cos y = 4
cos y = 4/60
y =86.177°
y =86.2°
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f(x)=x^3+8g(x)=4x^3−5x−8
find (f+g)(x)
A.
5x³-5x
B.
5x³-5x+16
C.
5x³-5x-16
The value of the sum of the functions f(x) and g(x), (f + g)(x) is 5x³ - 4x.
What is a function?The outputs for a certain set of inputs can be referred to as a function.
A function's inputs are referred to as its independent variables, while its outputs are referred to as its dependent variables.
Given, f(x) = x³ + 8 and g(x) = 4x³ - 5x - 8.
Let, f(x) = x³ + 0x + 8.
We know, (f + g)(x) = f(x) + g(x).
Therefore, (f + g)(x) = (x³ + 0x + 8) + (4x³ - 5x - 8).
(f + g)(x) = x³ + 4x³ + 0x - 4x + 8 - 8.
(f + g)(x) = 5x³ - 4x.
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HELP!!
An unsharpened pencil is in the shape of a
hexagonal prism with base area of 54 mm²
and length of 20 cm. Find the volume in
cubic millimeters. (1 cm = 10 mm)
10800 mm³ is the volume of the unsharpened pencil.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm².
The length of hexagonal prism is 20 cm.
Let us convert cm to mm
1 cm = 10 mm
20 cm =200 mm.
Volume of hexagonal prism V=Ah.
A is the base area and h is the height.
V=54×200
=10800 mm³.
Hence, volume of an unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm² and length of 20 cm is 10800 mm³.
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can anyone help me?
Answer:
a. 648
Step-by-step explanation:
Deposit= Principal= p
Interest rate = R
Time= T
Simple Interest = P x T X R X 0.01
= 5400 x 6 x 2 x 0.01
=648
How high above the water is the roadway in meters? Round to the nearest hundredth. (199 ft)
199 feet in meters
1 foot = 0.3048 meters
[tex]0.3048(meters)\times199(feet)[/tex]
[tex]=\fbox{60.66}[/tex]
2. The price of licorice is proportional to its length. It costs
$0.50 to buy 5 in. How much licorice can you get for $1.80?
The required length of licorice for $1.80 is given as 18 in.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
The price of licorice is proportional to its length. It costs $0.50 to buy 5 in; it is uncertain how much licorice you can get for $1.80.
Let the price be y and the length be x,
according to the quesiton,
y = kx,
put y = 0.50 and x = 5
0.50 = 5k
k = 0.1
Now
y = 0.1 x
for
y = 1.8
1.8 = 0.1x
x = 18
Thus, the length of licorice necessary for $1.80 is specified as 18 in.
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What is the inverse of 6?
The Multiplicative Inverse of the number 6 is "1/6" .
The Inverse (Multiplicative) of the number is the number that when multiplied by the original number gives the product as 1 .
which means the product of the number and its multiplicative inverse is 1 .
the number is given to be 6 .
So , let the multiplicative inverse of 6 be = x .
So , According to Definition of Multiplicative Inverse ,
we can write : x * 6 = 1
dividing both side by "6" .
we get ;
x = 1/6 .
Therefore , the multiplicative inverse is 6 .
The given question is incomplete , the complete question is
What is the Multiplicative Inverse of 6 ?
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What is the use of median?
Median is the only average to be used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude,
e.g., to find the average intelligence among a group of people.
It is to be used for determining the typical value in problems concerning wages, distribution of wealth, etc.
It helps us to identify if the distribution is symmetric or not.
The mean and median of a symmetric distribution are close together.
If the distribution is exactly symmetric, the mean and median are exactly the same.
In a skewed distribution, the mean is farther out in the long tail than the median.
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How can I get my SSS E1 number?
You can locate your SSS loan number scrawled on the upper right corner of your E-1 form if you applied for one in 2015 or earlier and still have a copy of it.
The personal information of an SSS member is contained on the SSS E1 form (also known as the E-1 form). Prior to receiving a social security number, a person must submit the E1 form to apply for membership in the Social Security System.
The applicant must complete the form with his personal data (such as name, date of birth, and home address), a list of dependents or beneficiaries, and, if self-employed, his profession or company.
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it took oliva 2 hour to drive 240 miles. at this rate how long does it take to drive 80 miles
Answer:
40 minutes
Step-by-step explanation:
rate = distance/time = miles/hr
rate = 240 mi/2 hr = 120 mi/hr
time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes
(0.67 hr)(60 min/hr) = 40 minutes
Which has a quotient of 1.66? Use number sense to find the answer. Select all that apply. A. 4.15÷2.5 B. 0.415÷0.25 C. 41.5÷0.25 D. 4.15÷0.25 E. 0 . 415 ÷ 2 . 5
help plssssssssssss
The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25
How to find which has a quotient?
Long division or repeated subtraction can be used to accomplish this.Finding the quotient of two integers, fractions, or algebraic words is achievable.Quotient * Dividend = Divisor
A. 4.15 ÷ 2.5
Quotient = 1.66
Divisor = Quotient * 2.5
= 1.66 * 2.5
= 4.15
So, Option A is a correct answer.
B. 0.415÷0.25
Divisor = Quotient * 0.25
= 1.66 * 0.25
= 0.415
So, Option B is a correct answer.
C. 41.5÷0.25
Divisor = Quotient * 0.25
= 1.66 * 0.25
= 0.415 ≠ 41.5
So, Option C is not a correct answer.
D. 4.15÷0.25
Divisor = Quotient * 0.25
= 1.66 * 0.25
= 0.415 ≠ 4.15
So, Option D is not a correct answer.
E. 0.415 ÷ 2
Divisor = Quotient * 0.25
= 1.66 * 2
= 3.32 ≠ 0.415
So, Option E is not a correct answer.
Hence, The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25
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How do you find the equation of a line with one point and slope of a fraction?
With the slope and one point of the line, Using the formula of equation of line with slope and a point, The answer is [tex](y-y_1)= m (x-x_1)[/tex] .
What do you mean by equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.
What do you mean by slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
points= ([tex]x_1 , y_ 1[/tex])
slope = m
Required equation,
[tex](y-y_1)= m (x-x_1)[/tex]
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The average test score of RSM students in September increased by 10%. In October it increased by another 15%. By what percent did the average score on the test increase during the two months? PLS PROVIDE SHOW OF STEPS!
The percent that the average score on the test increased during the two months is 12.5%.
By what percent did the average score on the test increase during the two months?It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..
The average of the increase will be:
= (10% + 15%) / 2
= 25% / 2
= 12.5%
The average is 12.5%.
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Your mom wants to buy you a box of Squishmallows for $54.99. She has a 25% coupon.
a) What is the amount of discount? Make sure you round to the nearest cent.
b) What is the sale price?
Answer:
a) $13.75
b) $41.24
Step-by-step explanation:
Original price: $54.99
Discount: 25%
Amount of discount: 25% of $54.99 = 25/100 × $54.99 = 0.25 × $54.99 = $13.75
Sale price: $54.99 - $13.75 = $41.24
32^1/25 x 2^x = 8^1/4. work out the exact value of x.
Answer:
The exact value of x is 2.Step-by-step explanation:
To find the exact value of x, we need to solve the given equation for x. The equation is:
32^1/25 x 2^x = 8^1/4
To solve this equation, we need to rewrite it in a form that allows us to isolate the variable x. We can start by using the properties of exponents to simplify the left-hand side of the equation. We can use the property that says that raising a number to a fractional power is the same as taking the square root of that number, raised to the power of the denominator of the fraction. So, we can write:
(32^1/25)^2 = (32^1/25)^25/25 = 32^1/25
This simplification allows us to rewrite the left-hand side of the equation as follows:
32^1/25 * 2^x = (32^1/25)^2 * 2^x
Next, we can use the property of exponents that says that the product of two numbers raised to the same power is equal to the product of the numbers, raised to that power. So, we can rewrite the left-hand side of the equation as follows:
(32 * 2)^1/25 * 2^x = (32^1/25)^2 * 2^x
Then, we can use the property of exponents that says that raising a product to a power is the same as raising each factor to that power. So, we can rewrite the left-hand side of the equation as follows:
(32^1/25) * 2^(1/25 + x) = (32^1/25)^2 * 2^x
Finally, we can use the property of exponents that says that the exponent of a power is equal to the product of the exponents of the base and the power. So, we can rewrite the left-hand side of the equation as follows:
(32^1/25) * 2^(1/25 * 25 + 1 * x) = (32^1/25)^2 * 2^x
Since the right-hand side of the equation is already in a form that allows us to isolate the variable x, we can now use the property of exponents that says that raising a number to a power and then taking the square root of that number is the same as
What are the steps of copying?
The steps of copying involve selecting the text you want to copy, copying the text using the option from the right click menu or alternatively using the keyboard shortcut ctrl + c.
What is a clipboard?The clipboard is a section of memory that the computer temporarily saves data when you copy or cut it from its original location. When you paste something, the previously copied or cut data is retrieved from the clipboard and added to the new location.
What is the difference between copying and cutting the text?Text that is copied remains in its original location; a copy of the original text is created and kept in the clipboard. When you cut text, the original text is removed from its original location and put in the clipboard. When you copy or trim text, the original text is kept, but the original location is lost. In all cases, the copied or chopped text can be put into another location.
These steps can be used to copy text or other objects in a computer program:
By highlighting it with your pointer, you may choose the text or object that you wish to copy.
Use the keyboard shortcut "Ctrl+C" or the context menu when you right-click the highlighted text or object to choose "Copy" from the context menu.
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jackson wants to test an assumption on the number of red candies in a bag of fruity tooty's candy. the company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims. what should jackson state for the null hypothesis and alternative hypothesis?
Jackson should correctly phrase both the alternative hypothesis and the null hypothesis as follows:
b. )
p = 0.20 indicates a null result.
A different result: p ≠ 0.20
What exactly is null hypothesis?
A specific type of statistical hypothesis known as a null hypothesis claims that no statistical significance can be established in a given set of facts. One can assess the truthfulness of a hypothesis through the use of sample data in hypothesis testing. It is represented by the letter H0 and is also sometimes referred to as the "null."
The conjecture, also known as the null hypothesis, is a tool used in quantitative analysis to examine the validity of beliefs about markets, economies, and investment strategies.
A null hypothesis is a form of speculation that asserts that specific characteristics of a population or data collection method are not distinct from one another in statistics.
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