The discriminant of the quadratic equation 2x + 5x² = 1 is 24.
The discriminant of a quadratic equation is the value calculated from the coefficients of the quadratic equation and it gives information about the nature of the roots of the equation. The discriminant can be used to determine the number and type of solutions/roots of the equation.
-If the discriminant is greater than zero, the equation has two distinct, real solutions (or roots).
-If the discriminant is equal to zero, the equation has one real solution (or root).
-If the discriminant is less than zero, the equation has no real solutions (or roots), only complex solutions.
The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
Plug in the values and solve for the discriminant of the quadratic equation 2x + 5x² = 1.
b² - 4ac = (2)² - 4(5)(-1) = 24
Hence, the discriminant is 24.
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Jose has $34 to spend at the Texas State Fair. If the entrance ticket costs $12, then how much money does jose have to spend on food and games?
ONE-STEP EQUATIONS APPLICATION II 6TH MATH
WITH EQUATION!
Answer:
22
Step-by-step explanation:
34-12=22 you just basically subtract 34 and 12 and it gives you 22 but theres the equation too
What is the prouduct of 2 and 0.73
Answer:
1.46
Step-by-step explanation:
We can represent this problem as an array of dots, where each dot represents 0.73 units.
⚫️ ⚫️
We can see that the resulting product of 2 × 0.73 is just the sum of two dots. We can represent this in equation form as:
0.73 + 0.73
Finally, we can execute the addition by adding the tenths and hundredths of each number separately, then adding everything together at the end.
tenths + hundredths
(0.70 + 0.70) + (0.03 + 0.03)
1.40 + 0.06
1.46
Which of the following is a perfect square trinomial?
(A) 5x2 - 5x + 1
(B) 5x2 - 10x + 5
(C) 10x2 - 20x + 5
(D) 25x2 - 20x + 3
(E) 25x2 + 20x + 4
Answer:
B is the perfect square
Step-by-step explanation:
I need help with these questions can someone help please
Answer:you just have to find the slope
Step-by-step explanation:
so all you have to do is start by doing y=Mx+b. You start by placing down you b point on the y axis and then Do your Mx it should look something like this
How many types of angles are there in class 7?
There are basically 6 types of angles are there which are acute, obtuse, right, straight, reflex and complete angles.
If an angle is less than 90 degrees, it is known as an acute angle. If an angle is more than 90 degrees, then it is called an obtuse angle. If an angle is exactly 90 degrees, then it is called the right angle.
If an angle is precisely 180 degrees, then it is called a straight angle. If the angle is more than 180 degrees but less than 270 degrees, it is known as a reflex angle. A full 360-degree angle is called a complete angle.
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The local Dairy Queen sells four
cheeseburgers and two milkshakes for $7.90.
If two milkshakes cost $0.15 than a
cheeseburger, what is the cost of a milkshake?
While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.
what is an equation ?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. A straightforward equation shows the connection between two terms on either side of an equal sign. Additionally, simple equations incorporate one or more of the addition, subtraction, multiplication, and division arithmetic operations.
given
Let a = the cost in cents of a cheeseburger
Let b = the cost in cents of a shake
4a+2b=7 .90
2b=a+15
-a+2b=15
Subtract (2) from (1)
4a+2b=7 .90
a-2b=-15
5a=775
a=155
2b=a+15
b=170/2
b=85
While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.
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What is an equation of the line that passes through the point (-5,7) and is parallel to the line x-5y=15?
Answer: An equation of a line that is parallel to another line has the same slope as the original line. The slope of a line can be found by rearranging the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).
To find the equation of a line that is parallel to the line x - 5y = 15 and passes through the point (-5,7), we can first rearrange the equation of the original line in slope-intercept form:
x - 5y = 15
y = (1/5)x - 3
The slope of this line is (1/5). To find an equation of a line that is parallel to this line and passes through the point (-5,7), we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Substituting in the values given in the question, we get:
y - 7 = (1/5)(x - (-5))
y - 7 = (1/5)x + 1
y = (1/5)x + 1 + 7
y = (1/5)x + 8
Therefore, the equation of the line that is parallel to the line x - 5y = 15 and passes through the point (-5,7) is y = (1/5)x + 8.
Step-by-step explanation:
F(x)=5-3x find f(x+2)
Answer:
f(x + 2) = - 3x - 1
Step-by-step explanation:
substitute x = x + 2 into f(x) , that is
f(x + 2)
= 5 - 3(x + 2)
= 5 - 3x - 6
= - 3x - 1
3 times one number minus a second is 8 and the sum of the numbers is 12
Answer: 3x-y=8
Step-by-step explanation:
A water desalination plant can produce 2.8 * 10 to the power of 6 gallons of water in one day. How many gallons can it produce in 5 days?
Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.
What is the difference between factors and multiplies?A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.
Here,
So if there was 5 days, it would produce 5 times the amount above.
So 5 × (2.8 × 10⁶) = 14 × 10⁶
We must rewrite in scientific notation, so:
14 x 10⁶ = 1.4 x 10⁷
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Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.
What is the difference between factors and multiplies?A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.
Here,
So if there was 5 days, it would produce 5 times the amount above.
So 5 × (2.8 × 10⁶) = 14 × 10⁶
We must rewrite in scientific notation, so:
14 x 10⁶ = 1.4 x 10⁷
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567854+98723=?
Let's see who knows the correct answer
A coin with probability p of showing up heads is tossed n times. What is the probability that the number of heads is odd
The chance you get a odd number of heads from the first coin is 1/3,
What is the probability that the number of heads is odd? The tosses of the coin are independent (neither affects the other). Hence, the probability of a head on Flip 1 and a head on Flip 2 is the product of P(H) and P(H), which is 1/2 x 1/2 = 1/4. The same calculation applies to the probability of a head on Flip 1 and a tail on Flip 2For n≥3, if the last outcome is T, then the probability that the first (n−1)tosses do not contain two (or more consecutive heads is p n−1 and if the last outcome is H, then (n−1)th outcome must be T and the probability the first(n−2) tosses do not contain two (or more) consecutive heads is p n−2 . Hence, p n =p n−1 ×P (nth toss results in a tail)+p n−2 ×P (nth toss results in a head and (n−1)th toss results in a tail)=(1−p)p n−1+p(1−p)p n−2To learn more about probability refers to:
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An achievement exam was given to a population of 1,000 students. However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table. TEST SCORE 42 57 67 72 77 87 97 z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25 percentile rank 10 25 30 45 50 75 95 Using the table information, the test score representing the 3rd decile is: a. 67 b. 77 c. 57 d. 72 e. 97
The test score representing the 3rd decile is 67. So the option a is correct.
In the given question, an achievement exam was given to a population of 1,000 students.
However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table.
TEST SCORE 42 57 67 72 77 87 97
z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25
percentile rank 10 25 30 45 50 75 95
Using the table information, we have to find the test score representing the 3rd decile.
As we know that the 3rd decile is equal to the 30th percentile.
So that the 3rd decile have the percentile rank = 30
The test score equivalent to percentile rank 30 is 67.
So, the test score representing the 3rd decile is 67. So the option a is correct.
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(Help me please)
Lin and Noah are packing small cubes into a cube with an edge length of 1½ inches. Lin is using cubes with an edge length of ½ inch, and Noah is using cubes with an edge length of ¼ inch. Who would need more cubes to fill the 1 1/2 inch cube? Show how you know
Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.
Noah would need more cubes to fill the 1 1/2 inch cube because the cubes he is using have a smaller edge length than the cubes Lin is using. The larger the edge length of the cubes being used, the fewer number of cubes needed to fill a given space.
To see this, you can calculate the volume of the cube being filled by both Lin and Noah. The cube that Lin is filling has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Lin is using have a volume of (0.5)^3 = 0.125 cubic inches. So, Lin needs 3.375/0.125 = 27 cubes to fill the 1.5 inch cube.
The cube that Noah is filling also has a volume of (1.5)^3 = 3.375 cubic inches. The cubes Noah is using have a volume of (0.25)^3 = 0.03125 cubic inches. So, Noah needs 3.375/0.03125 = 108 cubes to fill the 1.5 inch cube.
As we can see, Noah needs 108 cubes which is 4 times more than Lin's 27 cubes.
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carmen has 92 kilograms of clay. she has 5 students in her art class. how much clay does each student get
Answer:
18.4 kg of clay
Step-by-step explanation:
92 kg for 5 students
=> 92 : 5 = 18,4 kg for 1 student
Answer: 18.4 kg
Step-by-step explanation:
DATA :
total mass of clay = 92 kg
total students = 5
how much clay does each student get?
SOLUTION:
assuming that each student got equal amount of clay, we are simply going to divide ⇒92 by 5.
⇒92 ÷ 5
⇒18.4 kg ANSWER
hope that helps...
Using the clues below, what is the value of the bigger number?
Clue 1: The sum of two numbers is ten.
Clue 2: The difference of the numbers is two.
Answer:
6
Step-by-step explanation:
Call the bigger number a, smaller b
a + b = 10
b + 2 = a
a + b + 2 = a + a = 2a = 12
a = 12 : 2
a = 6
On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).Which point is on the line that passes through (0, 6) and is parallel to the given line? (–12, 8) (–6, 6) (2, 8) (6, 0)
Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Since, We know that;
Parallel lines have same slopes and different y-intercepts
The formula of the slope of a line which passes through points (x₁ , y₁) and (x₂, y₂) is,
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Since, The given line passes through points (-12 , -2) and (0 , -4)
Hence, Use the formula of the slope above to find the slope of the given line as;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (-4 - (-2)) / (0 - (-12))
⇒ m = (-2) / 12
⇒ m = - 1/6
Since, The two lines are parallel.
Hence, Their slopes are equal
So, The slope of the parallel line = - 1/6
Here, The parallel line passes through point (0 , 6)
Since, The form of the linear equation is y = mx + b, where m is the slope and b is the y-intercept.
⇒ m = -1/6 and b = 6
Hence, The equation of the parallel line is,
⇒ y = x + 6
Now, Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line as;
Point (-12 , 8)
Substitute x = -12 and y = 8
⇒ y = (-12) + 6
⇒ y = 2 + 6 = 8
Clearly, The value of y is equal the y-coordinate of the point.
So, Point (-12 , 8) is on the line.
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Evaluate 5c+cd5c+cd5, c, plus, c, d when c=\dfrac15c=
5
1
c, equals, start fraction, 1, divided by, 5, end fraction and d=15d=15
Answer:
the value is 4
Step-by-step explanation:
2. The value of a machine depreciates by 5% every year. It is given that the initial value of the machine is RM100 000.
(a) Express its value, in RM, after n years.
(b) Hence, find its value after 10 years to the nearest ringgit.
Answer:
Step-by-step explanation:
Depreciation means wearing and tearing in the value of an asset over the years
(a) Given:
p = initial value of an asset
i% = depreciation per year
n = number of years
Depreciation after n years (d) = [tex]p(1-\frac{1}{100} )^{n}[/tex]
Value of machine after n years = p-d
(b) Given:
p = RM100000
i% = 5
n = 10
Depreciation after 10 years = [tex]100000(1-\frac{5}{100} )^{10} = 59873.69392[/tex]
Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608
Value of machine after 10 years to nearest ringgit = RM40123
I need to know the andwer to 0.03 divided by 0.81 in division of decimals
Answer: 0.0370 (Italic part repeats forever)
Step-by-step explanation:
Answer: 0.037...
Step-by-step explanation:
Find the Average Rate of Change of the table below for the interval 2 < x < 5
The AROC is 3 for the interval 2 < x < 5, which is the correct answer that would be option (A).
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The table is given in the question as follows:
x y
0 -2
1 -3
2 0
3 3
4 6
5 9
We have to determine the Average Rate of Change in the table below for the interval 2 < x < 5
As per the given table, the required AROC would be as:
⇒ (9 - 3)/(5-3)
⇒ 6/2
Apply the division operation, and we get
⇒ 3
Hence, the correct answer would be option (A).
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consider the equations t(n)=2n-5 and f(x)=2x-5
Therefore , the solution of the given problem of equation comes out to be (−∞,∞) is an interval for domain.
Analyze the equation.A mathematical equation seems to be a formula that links two statements and signifies equivalence with the equals sign (=). In algebra, a scientific claim that confirms the equality two two mathematical abstractions is referred to as an equation. For instance, the answer obd + 6 = 12 has an equal sign between the elements ptdc + 6 and 12, respectively. There is a mathematical formula that describes the connection between the two syllables on either side of a letter. Frequently, the symbol and the single variable are the same.
Here,
f(x)=2x-5 and t(n)=2n-5 are given.
A) They both depict the sequence.
B) Unless the expression is undefined, the domain of both the expression seems to be all real numbers. In this instance, the phrase is defined despite the lack of a real number.
(−∞,∞) is an interval notation.
{x|x ∈ R} is the Set-Builder Notation.
Therefore , the solution of the given problem of equation comes out to be (−∞,∞) is an interval for domain.
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find the missing part of the proof for m A. m B. m C. m D. m
Therefore, K= 66 degrees, LK length = 22 unit, and LK length = 22 unit are the answers to the specific problem of angles.
Angles are what?A geometrical angled construction is constructed from two rays that converge at the summit, or center, of both the angle and are referred to as the face and the vertex, respectively. Guess it depends on how they're situated, it is possible for two rods to create an angle together within plane. When two planes collide, an inclination is also formed. Diahedral angles are the term used to refer to them. Light beams or lines in euclidean geometry can have a wide variety of shapes or angles for the same termination. The phrase "angle" in English is based on the Latin term "angulus," which meaning "horn." the vertex.
Here,
Given: MKL M = 24 degree right triangle
K is 90 degrees, etc.
Thus,
=> ∠L + ∠M +∠K =180
=> 90 + 24 + ∠K = 180
=>∠K =180-114
K equals 66 degrees.
and
The formula for LK length is 22.
The formula for LK length is 22.
In light of this, the answer to the angle problem is
K=66 degrees, and LK length=2 units. LK length equals two units.
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Imagine you have a wood block that is 4 cm wide, 4 cm long, and 8 cm high. It
weights 200 grams.
What is the volume of the block? Be sure to include the units.
Then, imagine that you are cutting the block into 2 exactly equal halves. What is the
volume of one of the pieces (including the units)? How does its volume compare to
that of the original block?
The way that the new volume compares to the original volume of the block is that the new volume is half of the original volume.
How to find the volume of the block?The volume of a rectangular block is gotten from the formula;
Volume = length * width * height
Now, we are given;
Width = 4 cm
Length = 4 cm
Height = 8 cm
Thus;
Volume of block = 4 * 4 * 8
= 128 cm³
Now, if you are cutting the block into 2 exactly equal halves, then you can say that;
New length = 4/2 = 2cm
Thus;
Volume of cut block = 2 * 4 * 8
= 64 cm²
This is concluded to be half of the original block.
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Rewrite the expression (2t+6)+7t in the simplest form show your work.
Answer:
14t²+42t
Step-by-step explanation:
So you're basically going to use distributive property.
(2t+6)+7t is the same as, (2t)7t + 6(7t).
2t(7t)= 14t² and 6(7t)= 42t.
Combine the two answers and you get 14t²+42t.
14t²+42t is the simplest form you can get to.
Multiply = 4/7 x 5 1/4
please help me
Answer:
3
Step-by-step explanation:
[tex]\displaystyle \frac{4}{7}*5\frac{1}{4}=\frac{4}{7}*\frac{21}{4}=\frac{21}{7}=3[/tex]
Equivalent fractions for 1 3/4 and 1 4/5 using 20 as the common denominator
Answer:
35/20 and 36/20
Step-by-step explanation:
You have 50 coin that worth $8. 25. You have dime, quarter and nickel. The number of quarter i 5 more than twice the number of nickel. How many dime, quarter and nickel do you have individually
I need to know the steps to solve this.
The Constraints of the inequality are
x ≤ 2y + 500
22500 < √ 35x + 50y
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
The Company A (x) at most 500 more than twice then unit by B(y).
So, x ≤ 2y + 500
Now, the square of Company Profit will be equal to 35x + 50y
Then, the constraints will be
1. x ≤ 2y + 500
2. Company Profit² < 35x + 50y
Company Profit < √ 35x + 50y
22500 < √ 35x + 50y
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This year’s favorite to win the frog jumping event is Newton. The objective is to take the longest jumps and stop as close as possible to 120 steps. Pythagoras and Fermat are Newton’s toughest competition. ● Newton takes 4 jumps and falls short of the mark by 4 steps. ● Pythagoras takes 5 jumps and overshoots the mark by 5 steps. ● Fermat hits the mark exactly after 6 jumps. How long, in steps, is each frog’s jump?
The length of jump by Pythagoras = 25 units
The length of jump by Newton = 29 units
The length of jump by Fermat = 20 units
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the length of the jump by Pythagoras be P
Let the length of the jump by Newton be N
Let the length of the jump by Fermat be F
Now , the equation will be
The total number of steps = 120 steps
The number of jumps by Pythagoras = 5 jumps
The number of steps overshoot by Pythagoras = 5 steps
So , P ( 5 ) - 5 = 120 be equation (1)
On simplifying the equation , we get
Adding 5 on both sides of the equation , we get
5P = 125
Divide by 5 on both sides of the equation , we get
P = 25 units
The number of jumps by Newton = 4 jumps
The number of steps fell short by Newton = 4 steps
So , N ( 4 ) + 4 = 120 be equation (2)
On simplifying the equation , we get
Subtracting 4 on both sides of the equation , we get
4N = 116
Divide by 4 on both sides of the equation , we get
N = 29 units
The number of jumps by Fermat = 6 jumps
So , F ( 6 ) = 120 be equation (2)
On simplifying the equation , we get
Divide by 6 on both sides of the equation , we get
F = 20 units
Therefore , the value of P , N and F are 25 , 29 and 20 units respectively
Hence , the length of each jump is 25 , 29 and 20 units
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