A quadratic equation, y = ax^2 - 6x + 10, has exactly one real root. Calculate the value of a.
Answer:
a = 0.9
Step-by-step explanation:
For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.
For the given equation:
\(y = ax^2 - 6x + 10\),
• a = a
• b = -6
• c = 10.
Substituting these values into the formula for discriminant, we get:
\((-6)^2 - 4(a)(10) = 0\)
⇒ \(36 - 40a = 0\)
⇒ \(36 = 40a\)
⇒ \(a = \frac{36}{40}\)
⇒ \(a = \bf 0.9\)
Therefore the value of a is 0.9 when the given quadratic has exactly one root.
3. Write the inequality that best represents the relationship shown on this number line:
girl name are April, may, June, what is the name the mother?
mary is the 4th childs nam,e
Solve.
3x+2y−z=8
2x+2z=−4
x+3y=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
How to resolve a system of linear equations
In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:
x = 4 - 3 · y
Second, substitute x in the first two equations:
3 · (4 - 3 · y) + 2 · y - z = 8
12 - 9 · y + 2 · y - z = 8
- 7 · y - z = - 4
2 · (4 - 3 · y) + 2 · z = - 4
8 - 6 · y + 2 · z = - 4
- 6 · y + 2 · z = - 12
Third, clear z in the first equation derived in the previous step:
z = 4 - 7 · y
Fourth, substitute z in the second equation derived in the second step:
- 6 · y + 2 · (4 - 7 · y) = - 12
- 6 · y + 8 - 14 · y = - 12
- 20 · y = - 20
y = 1
Fifth, calculate y and x:
z = 4 - 7 · 1
z = - 3
x = 4 - 3 · 1
x = 1
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
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there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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Logan wants to save 35% of his weekly paycheck he earns $125 a week how much does he plan to save each week enter the correct answer in the box
Answer:
35%
Step-by-step explanation:
Logan wants to save 35% of his weekly paycheck he earns $125 a week how much does he plan to save each week enter the correct answer in the box, he wants to save 35%, how much does he plan to save, 35% easy. JK its 125 - 81.25 which is $43.75.
Find the domain of the rational expression: 6-x/4x+20
The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.
To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.
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The dimensions of a cylinder are shown in the diagram
Round to the nearest whole number , what is the total surface area of the cylinder in cubic centimeters
Answer:
S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3
If a storage tank is holding 450 litres when it is three quarters full, how much will it contain when it is two thirds?
Answer:
400 litres
Step-by-step explanation:
help a girl out :)
could you find the 2 endpoints of the minor axis and show work of how you got it? thank you :)
Answer:
If a>b then the major axis of the ellipse is parallel to the x -axis (and, the minor axis is parallel to the y -axis)
if a<b then the major and minor axes of the ellipse with respect to the x and y -axes are reversed
Step-by-step explanation:
ABC DEF. Find the length of median FQ.
Soln,
we Know that,
FQ/CP = QE/PA
or,FQ/27= 24/18
or,18FQ=648
or,FQ= 648/18
or,FQ=36
PLEASE HELP pleaseeeee
Answer:
C
Step-by-step explanation:
On a number cube from 1 to 6, there are only two numbers available that are equal to or greater than 5: 5 and 6. Out of the six possible options, only two options could meet these conditions. Therefore, the probability is 2/6. However, this can be further simplified as both 2 and 6 can be divided by two, which would equal 1/3.
At the Old Fort Boise Days Car Show there were 15 Pontiacs, 18 Chevrolets, 12 Fords ,and 5 Ramblers. What was the ratio of the Chevrolets to the Pontiacs?
a.
15:18
c.
6:5
b.
5:6
d.
18:50
Answer:
6:5
Step-by-step explanation:
Think of a two-digit number. What is the probability that it has different digits?
Answer:
9/10
Step-by-step explanation:
The first two digit number is 10 and the last is 99. That's a total of 99-10+1 numbers in all. That simplifies to 90. (Just like if we wanted to see how many numbers was 3,4,5, we would do 5-3+1=3 to get the total number.
Anyways, let's consider first how many 2 digjt numbers whose digits are equal. You have 11 22,33,44 55,66,77,88,99 which is 9 numbers total.
So the amount of 2 digits number whose digits differ is 90-9=81.
The probability that a 2 digit number have different digits is 81/90.
This can reduce. Divide top and bottom by 9 giving 9/10.
What is the breakdown of this equation 2(4+6)+13=
Answer: 6+4 =10 and 2 +10 =12 so the breakdown is 12+13
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
use pemdas
parenthesis
exponets
multiply
divide
add
first add what's in the parenthesis then multiply your answer times 2 then add 13 and you'll get 33.
hope this helps mark brainliest plz
porfavor me ayudarian es urgente
Answer: no exact answer
Step-by-step explanation:
The result of fraction multiplication are:
2/3 x 2/5 = 4/15
4/2 x 6/3 = 4
2/4 x 3/6 = 1/4
2/3 x 6/3 = 4/3
Given that, simplify the following:
2/3 x 2/5
4/2 x 6/3
2/4 x 3/6
2/3 x 6/3
For the expression 2/3 x 2/5:
To multiply fractions, we multiply the numerators together and the denominators together.
So, (2 x 2)/(3 x 5) = 4/15.
For the expression 4/2 x 6/3:
Again, we multiply the numerators together and the denominators together.
Thus, (4 x 6)/(2 x 3) = 24/6 = 4.
For the expression 2/4 x 3/6:
Following the same process, we multiply the numerators and denominators.
Therefore, (2 x 3)/(4 x 6) = 6/24 = 1/4.
Lastly, for the expression 2/3 x 6/3:
Similarly, we multiply the numerators and denominators together.
Hence, (2 x 6)/(3 x 3) = 12/9 = 4/3.
Therefore, the result of fraction multiplication are:
2/3 x 2/5 = 4/15
4/2 x 6/3 = 4
2/4 x 3/6 = 1/4
2/3 x 6/3 = 4/3
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What is the deposit of $40
The integer form is + 40.
The integer form is - 25
What is an integer?An integer is a whole number from the set of negative, non-negative, and positive numbers.
Therefore, integers can be written without fractional components.
Hence, integers may include negative or positive numbers . Examples are -1, 2, 5, -8, 9 and many more.
A deposit of 40 dollars means gain. Therefore, the integer form is + 40.
A loss of 25 pounds mean loss. Therefore, the integer form is - 25
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Select all the correct answers.
Which expressions are equivalent to the given expression.
y^-8y^3x^0x^-2
Answer:
\(x^{-2}y^{-5}\)
Step-by-step explanation:
The options are not given; however, the question can still be solved
Given
\(y^{-8}y^3x^0x^-2\)
Required
Simplify
Start by rewriting the expression
\(y^{-8} * y^3 * x^0 * x^{-2}\)
Apply the following laws of indices: \(a^x * a^y = a^{x+y}\)
This gives:
\(y^{-8+3} * x^{0-2}\)
Evaluate the exponents
\(y^{-5} * x^{-2}\)
\(x^{-2}y^{-5}\)
Hence, \(x^{-2}y^{-5}\) is equivalent to \(y^{-8}y^3x^0x^-2\)
Answer:
The answer is- (Drumroll)
Step-by-step explanation:
The answers are \(x^-2y^-5\), and \(1/x^2y^5\)
I need help please!:D
Answer:
1 & 2
Step-by-step explanation:
Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ:(a + b)^2,(a – b)^2,(a - b)(a + b)
Answer:
because you have to distrubute the 2 to the letters inside the () or else youll get a diff answer thats wrong
Step-by-step explanation:
Jim paints the surface of a shelf. the surface has an area of 90 square inches. the width of the shelf is 6inches. what is the length of the shelf. please show me how to work
I WILL GIVE BRAINLIEST IF YOU ARE CORRECT!!!
The matrix below shows the cost of four different baseballs, including tax, at two different stores. COST OF A BASEBALL Store A Store B Little League $4.23 $3.71 High School $7.41 $6.35 College $10.59 $8.45 Major League $13.77 $15.89 What is the difference in cost between 10 high school baseballs from Store A and 10 high school baseballs from Store B?
$1.06
$5.20
$10.60
$13.76
Answer:
$10.60
Step-by-step explanation:
Cost:
| Store A | Store B |
| --------------------- | ----------- | ----------- |
| Little League | $4.23 | $3.71 |
| High School | $7.41 | $6.35 |
| College | $10.59 | $8.45 |
| Major League | $13.77 | $15.89 |
| --------------------- | ----------- | ----------- |
Hopefully this table is correct. I'll edit my answer if anything is wrong there.
If the cost of the cost of 1 high school baseball from Store A is x, then the cost of 10 is 10x:
\(x=7.41\\10x=10(7.41)=74.10\)
$74.10
Same for the other store:
\(y=6.35\\10y=10(6.35)=63.50\)
$63.50
Finally, find the difference:
\(74.10-63.50=10.60\)
The difference in cost is $10.60.
How would 5,000,000,000 + 70,000,000 + 70,000 + 700 + 8 be written in standard form? OA) 57,778 OB) 570,078 OC) 577,000,078 OD) 5,070,070,708. please help this is due today
Answer:
D) 5,070,070,708
Step-by-step explanation:
5,000,000,000
70,000,000
70,000
700
8
5,070,070,708
Salve this proportion 15/35=g/7
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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if the system of linear equations above has no solutions and a is constant then what is the value of a
The value of x is 6.
What is system of linear equations?
A collection of one or more linear equations involving the same variables is known as a system of linear equations in mathematics. For instance, the system of three equations 3x + 2y - z = 1, 2x - 2y + 4z = -2, -x + y - z = 0 has the three variables x, y, and z.
A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.
Graphically, a system of linear equations that has no solution indicates two parallel lines-that is, two lines that have the same slope but different y-intercepts.
To have the same slope, the x-and y-coefficient must be the same.
To get from -2/3 to -8 you multiply by 12, so multiply -1/2x by 12 as well to yield 6x.
Because the other x-coefficient is a, it must be that a = 6 and (D) is correct.
Note that, even though it is more work, you could also write each equation in slope-intercept form and set the slopes equal to each other to solve for a.
Hence, the value of x is 6.
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SOMEONE HELP ME PLS!
Answer:
are u sure this is the question ⁉️
Answer:
x=10 or 4
Step-by-step explanation:
square root of x-7²=x-7
x=3+7 or -3+7=10 or4
Batman uses 5 gallons of gas to drive his Batmobile 140
miles. If he travels at the sanie rate, how many miles can he
drive on 7 gallons of gas?
Write answer as a number only
Answer:
196 miles
Step-by-step explanation:
if he goes 140 miles with 5 gallons, each gallon lets him go 28 miles.
140miles/5gallons=28miles/1gallon
then 7 gallons lets you go 196 miles
brainliest please :)
-3a-3=-2n+3p solve for a
Answer:
a=−2n3−p−1a=-2n3-p-1
Answer:
a=−2n3−p−1a=-2n3-p-1
Step-by-step explanation:
Order the set of numbers from least to greatest. {63, -34, 36, -27, -13, and 12}
Answer:
-34, -27, -13, 12, 36, 64.
Step-by-step explanation:
The further left you go on a number line the less the number is the further right you go the greater the number is. Hope this helped!! Give brainliest.