The solutions of the inequality [tex]2x^{2} + x - 6 = 0[/tex] are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form [tex]ax^{2} +bx + c = 0[/tex], the solutions are [tex]x = -b +/-\sqrt{b^{2} -4ac} /2a[/tex].
Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49
Solution 1: x = [tex]-b + \sqrt{b^{2} -4ac} /2a[/tex] = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2
Solution 2: x = [tex]-b-\sqrt{b^{2} -4ac} /2a[/tex]= (-1 - √49)/(2×2) = -8/4 = -2
So, the two solutions are 3/2 and -2.
The equation can also be written as,
[tex]2x^{2} +4x -3x-6=0[/tex]
[tex]2x(x+2) -3(x+2) = 0[/tex]
[tex](2x-3)(x+2) = 0[/tex]
x = 3/2, -2
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A cup of cereal ha 12 gram of fiber, which i 40% of the amount of fiber Jared’ doctor recommend he conume each day. How much fiber doe Jared’ doctor recommend he conume each day?
As per the given percentage, the recommended daily amount is 30 grams.
The term percentage in math is defined as a portion of a whole expressed as a number between 0 and 100 rather than as a fraction
Here we have given that a cup of cereal has 12 grams of fiber, which is 40% of the recommended daily allowance.
Then the recommended daily amount is calculated as,
Let us consider that x be the recommended daily amount.
Then it can be written as,
=> 12/x = 40/100
When we cross multiply the terms, then we get,
=> 40x = 1200
Then the value of x is calculated as,
=> x = 30
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In a company, 65% of the workers are women. If 945 people work for the company who aren't women, how many workers are there in all?
Answer:
32123456789098765443
What value of x would make Line R Q tangent to circle P at point Q?
x =
Since the value of x cannot be negative x value that makes line RQ tangent to the circle P at point Q is 6.
How to find x value?From the circle P, if Q is the tangent, It implies that at the tangent line, it is perpendicular to the radius.
Using Pythagorean theorem;
PQ² + RQ² = PR²
Where PQ = 9
RQ = 12
PR = (x + 9)
Applying (x + 9) to the formula
(9)² + (12)² = (x + 9)²
Using algebraic expression; (a + b)² = a² + 2ab + b²
x² + 18x + 81 = 36 + 144
x² + 18x + 81 = 225
x² + 18x + 81 - 225 = 0
x² + 18x - 144= 0
By employing the quadratic formula,
[tex]x =\frac{ -b+/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 1, b = 18 and c = -144
[tex]x =\frac{ -18+/-\sqrt{18^{2} - 4(1)(-144)} }{2(1)}[/tex]
[tex]x =\frac{ -18+/-\sqrt{324 + 576} }{2}[/tex]
[tex]x =\frac{ -18+/-\sqrt{900} }{2}[/tex]
[tex]x =\frac{ -18+/- 30}{2}[/tex]
[tex]x =\frac{ -18 + 30}{2}[/tex]
[tex]x =\frac{ 12}{2}[/tex]
x = 6
[tex]x =\frac{ -18 - 30}{2}[/tex]
[tex]x =\frac{-48}{2}[/tex]
x = -24
Knowing that the value of x cannot be negative then, the quadratic equation that yielded 12/2 = 6 makes the value of x = 6.
The complete question is:
What value of x would make Line R Q tangent to circle P at point Q? x =
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Answer:
x = 6
Step-by-step explanation:
edg 23
How can you isolate the term ?
3
f
3
+22=17
?
?
on both sides.
Answer: How you can isolate the term f/3 is to
subtract 22 from both sides.
Can anyone help with 1/4 of what is 1/5?
Answer: Let's set up 1/5 and 1/4 side by side so they are easier to see:
[tex]\frac{1}{5} x\frac{1}{4}[/tex]
The next step is to multiply the numerators on the top line and the denominators on the bottom line:
1 x 1
5 x 4
From there, we can perform the multiplication to get the resulting fraction:
1 x 1
5 x 4 = [tex]\frac{1}{20}[/tex]
The complete answer is below (simplified to the lowest form):
1/20
Convert 1/5 times 1/4 to Decimal
Here's a little bonus calculation for you to easily work out the decimal format of the fraction we calculated. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:
[tex]\frac{1}{20}[/tex] = 0.05
Factor the following expression
x²- 15 x 56 =
Multiply the numbers X²-15x56
x²-840
What is factor expression?A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and yWrite each term as the. prime factorization. of the coefficient or constant, listing any variables separately. For example, write. x. y. as. x. y. , and write. x. as. x. x. .Identify the factors that all of the terms have in common.Multiply those common factors.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).To learn more about factor expression refers to:
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Write to ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
Answer:
5:9
Step-by-step explanation:
just divide both sides by 5 and then you get the ratio 5:9
Answer: 5/9 g
Step-by-step explanation:
Given below are lease terms at the local dealership. What is the total cash
due at signing?
Terms:
• Length of lease: 24 months
• MSRP of the car: $27,500
• Purchase value of the car after lease: $19,500
• Down payment: $3400
Monthly payment: $425
Security deposit: $375
.
• Acquisition fee: $550
●
The total cash due at signing is $4750.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To get the cash due at signing, we just add up the following quantities:
Down payment = $3300
First Monthly payment = $475
Security deposit = $475
Acquisition fee = $500
Hence the total cash due at signing is calculated as follows:
(Total cash due at signing) = (Down payment) + (First Monthly payment) + (Security deposit) + (Acquisition fee)
= $3300 + $475 + $475 + $500
= $4750
Hence, the total cash due at signing is $4750.
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How do you change to base 5?
Change to base 5 can be done by dividing the decimal number by 5 and then taking the remainder of the division in reverse order.
The number base is the number that forms the basis for the formation of other numbers in a number system.
The number base that we use a lot every day is the decimal system, which consists of 10 numbers, from 0 to 9. This decimal system is usually called the base 10 number system. Apart from base 10, there are also other base systems, for example, base 2 (biner system), 8 (octal system), and 16 (hexadecimal system) which are usually used in computer / digital systems.
Change of base 10 numbers to other base numbers is done by:
dividing the decimal number by the intended base number, writing the remainder down, repeating the division until the remainder is zero, taking a look at the remainder in reverse order.For example, we want to change 214₁₀ to a base 5 number:
214 : 5 = 42 remainder 4
42 : 5 = 8 remainder 2
8 : 5 = 1 remainder 3
1 : 5 = 0 remainder 1
Thus 214₁₀ = 1324₅
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due tonight help please
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
An inequality is a relationship that compares two numbers or other mathematical expressions in an unfair manner. When comparing the sizes of two numbers on the number line, it is most frequently used. The graph of each equation or inequality is given the attachment.
What is graph?The graph, visual depiction of statistical information or a functional relationship between variables. Graphs serve a predictive purpose because they can highlight broad trends in the quantitative behaviour of data. However, they can be inaccurate and occasionally deceptive as mere approximations.
Most graphs have two axes: a horizontal axis for a set of independent variables and a vertical axis for a set of dependent variables. A broken-line graph is the most typical type of graph, with time usually acting as the independent variable.
16. 2y – 4x < 8
= 2y < 4x + 8
= y < 2x + 4
17. -4y > -x + 12
= y > x/4 + -3
18. | x + 3 |= y
y = | x + 3 |
19. |2x – 6| + 2 = y
y = |2x – 6| + 2
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(y+x)-:2+x; use x=1, and y=1
Value of expression (y + x) ÷ (2 + x) is 2 if x =1 and y = 1.
What is expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given
In expression
(y + x) ÷ 2 + x
x = 1
y = 1
Substituting value of x and y in the expression
(1 + 1) ÷ 2 + 1
= 2 ÷ 2 + 1
= 1 + 1
= 2
Hence, 2 is the value of expression (y + x) ÷ (2 + x) if x= 1 and y = 1.
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What strategy do you use to multiply integers?
Integer multiplication is equivalent to repetitive addition, which is adding an integer a predetermined number of times. For instance, adding 4 three times results in the number 12 (4 + 4 + 4).
What is an integer ?All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a representation of a collection of integers.
A straight line of numbers is shown visually as a number line.
This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.
The collection of integers can be shown on a number line much like other sets of numbers.
Hence, Integer multiplication is equivalent to repetitive addition, which is adding an integer a predetermined number of times. For instance, adding 4 three times results in the number 12 (4 + 4 + 4).
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An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point) Group of answer choices
7th grade
Answer:
12 × 1/3 hour
Step-by-step explanation:
1/12 tank in 1/3 hour.
1/12 is one-twelfth of the tank.
there are 12 twelfths in an unit. The tank has 12 one-twelfth parts, so you need to fill 12 times 1/12 of the tank.
Since it takes 1/3 hour to fill 1/12 of the tank, it will take 12 × 1/3 ghour tio fill the entire tank.
The expression is
12 × 1/3 hour
Is 3x 2 exponential?
No. [tex]3x^{2}[/tex] is not an exponential function. It is a quadratic function. In this, exponent is not a variable.
There is a variable in the exponential function called exponent. 3x would have been an example of an exponential function. In this function, the exponent is not variable, it is 2. Therefore this is a quadratic function, not an exponential one. The exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price that are growing or decay exponentially. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. it can be extended to the complex numbers or generalized to other mathematical objects like matrices.
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What is the inverse of y=−4x+3?
The inverse of the equation y = - 4x + 3 is y = (3 - x)/4.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, An equation y = - 4x + 3.
To find the inverse we'll first solve for 'x'.
Therefore,
y = - 4x + 3.
4x = 3 - y.
x = (3 - y)/4.
Now, we'll interchange the positions of 'x' and 'y'.
Therefore,
x = (3 - y)/4 becomes,
y = (3 - x)/4.
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Help me figure this mf out
Answer:
m∠COQ = 60°
Step-by-step explanation:
(2x)° = (3x-30)° (corr angles, l//m)
2x - 3x = -30
∴ x = 30
∴ m∠COQ = 2x°
= 60°
Is 2x3 is an exponential function?
Answer:
No it is not
Step-by-step explanation:
Hope it helps!
Isa earns a salary of $32,500 per annum. If he works an average of 34 hours a week calculate his hourly rate of pay
His hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.
What does per annum mean?Per annum denotes yearly or annually. It is a phrasing used frequently to describe interest rates. In sentences like "I have a 4% mortgage loan" or "This bond pays interest at a rate of 6%," "per annum" is frequently left out.
An illustration is when a supplier offers a credit customer a 2% early-payment discount for paying an invoice in 10 days as opposed to the full amount in 30. In this instance, the supplier forfeits 2% of the invoice amount in exchange for receiving payment 20 days early.
We recalculate the amounts and multiply both the "2%" and the "20 days" by 18 to get the rate per year. The annual rate that results is roughly 36%.
Isa works 34 hours a week
There are total 52 weeks a years
In a year the time he works is = 52 × 34 h
= 1768 hours
His annual salary is $32,500
Then his hourly rate of income = 32500/1768
= 32500/1768
= $18.38
Thus, his hourly pay rate is $18.38 if he works 34 hours a week an earns $32,500 per annum.
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A local boys club sold 136 bags of mulch and made a total of $532. It sold two types of mulch: hardwood for $4.25 a bag and pine bark for $3.75 a bag. How many bags of each kind of mulch did it sell?
The local boys club sold 91 bags of hardwood mulch at $4.25 each, and 45 bags of pine bark mulch at $3.75 each.
What is selling?Selling is the action of exchanging goods or services in exchange for money. It is the process of persuading someone to buy a product or service. Sellers use various methods to persuade potential buyers, such as advertising, discounts, and promotions. Sellers must understand the needs and wants of their customers in order to effectively sell their products or services.
This totaled $532, with 91 bags of hardwood mulch costing $385.75 and 45 bags of pine bark mulch costing $168.75.
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-4(1.75+x)=18. ;;;;;;;;;;;;;;;;
Answer:
Step-by-step explanation:
1.75+x=-9/2
7/4+x=-9/2
x=-25/4
How can we determine the end behavior of a polynomial function?
The end behavior of a polynomial function can be determined by looking at the degrees of the terms in the polynomial.
Generally, the highest degree term will indicate the end behavior of the function. For example, if the highest degree term is x^2, then the end behavior of the function will be that it will approach positive infinity as x approaches positive infinity and it will approach negative infinity as x approaches negative infinity. This can be illustrated by the following calculation:
f(x) = x^2 + 4x + 8
As x approaches positive infinity, the x^2 term will become much larger than the other terms, causing the polynomial function to approach positive infinity.
f(x) → +∞ as x → +∞
Similarly, as x approaches negative infinity, the x^2 term will again become much larger than the other terms, causing the function to approach negative infinity.
f(x) → -∞ as x → -∞
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Draw all non-isomorphic simple graphs with three vertices. Do not label the vertices of the graph. You should not include two graphs that are isomorphic. Remember that it is possible for a graph to appear to be disconnected into more than one piece or even have no edges at all.
Three non-isomorphic simple graphs with three vertices are given in the figure below.
The first is a complete graph, in which all three vertices are connected to each other. It is represented by a triangle shape.
The second graph is a graph with one vertex connected to the other two, it is represented by a line with two branches.
The third graph is a graph with no edges, it is represented by three isolated points.
Remember that two graphs are isomorphic if one can be transformed into the other by relabeling the vertices. It's important to note that these are the only three possible non-isomorphic simple graphs with three vertices.
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NEED HELP ASAP!!!!!!!!
Answer:
A = 5, B= 4, C = 2, D = 1, E= 3
Step-by-step explanation:
x^5 times x^8 = x^13 following the x^n times x^m = x^n+m [rule]
The 1 and 3 for D and E satisfy this. Each number is used only once.
Hope this helps!
what is The distance from Phoenix, Arizona, to Jacksonville, Florida, is 1 795 miles. 5.1 Use the line of best fit to predict the length, in minutes, of a direct flight from Phoenix to Jacksonville
Answer:
this is your answe
Step-by-step explanation:
The total straight line flight distance from Jacksonville, FL to Phoenix, AZ is 1,795 miles. This is equivalent to 2 888 kilometers or 1,559 nautical miles.
7 less than 2 times a number is 3. what is the number?
Evan is going to make a cake for his mother's birthday. It will take 26 minutes to make the cake batter, and the cake needs to bake in the oven for 1 hour and 13 minutes. If Evan wants the cake to be out of the oven by 12:39 P.M., what is the latest time he can start making the cake batter?
Step-by-step explanation:
calculating backwards :
12:39 pm minus 1 hour 13 minutes = 11:26 am
the cake needs to get into the oven latest at that time.
caucuses further backwards :
11:26 am minus 26 minutes = 11:00 am
Evan has to start latest at 11:00 am to have the cake ready at 12:39 pm.
Is every number a multiple of 8?
No, not every number is a multiple of 8.
Multiple:
A multiple is a number that can be produced by multiplying another number by an integer.
Integer:
An integer is a whole number with no fractional part.
For example, 1, 2, 3, 4, and 5 are integers. The number 0 is also an integer because it is not divisible by any whole number greater than 1. The largest integer that can be represented as a fractional value is called the fractional part of the value.
A multiple of 8 is a number that can be divided by 8 with no remainder.
For example, 8, 16, 24, 32, etc. are multiples of 8, but 7, 9, 15, etc. are not.
So, every number cannot be a multiple of 8.
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What does 3 2 mean in math?
Answer: In math, 3 2 would typically be written as 3^2, which means "3 raised to the power of 2" or "3 to the second power." It is the same as 3 multiplied by itself, which equals 9.
In some contexts, 3 2 could also be interpreted as "3, 2" which would be read as "3 and 2" and it can mean a collection of 3 and 2 items.
Step-by-step explanation:
What is the exponential form of 2 * 2 * 2 * 2 * 2?
How do I find the solution to a system?
If the system consists of 2 variables we can use the method of elimination or substitution to get the answer easily.
In the method of elimination from the two given sets of equations, we make one of the coefficients of a variable the same so that when in the next step when we will subtract them they will get canceled out and we will get the value of one of the variables which after substituting in one of the equation we'll get the value of another variable.
If we have more than 2 variables the method of row reduction using a matrix is the best way to solve the system. In the system we make an augmented matrix of the coefficients of the variables and row reduce them in such a way that when we multiply the matrix with the row matrix we get the values of the variables easily.
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