The solution of the quadratic equation using quadratic formula are x = (√181 - 19)/2 or x = (-√181 - 19)/2.
What are Quadratic Equations?Quadratic equations are defined as the polynomial equations with the highest degree of the variable being 2.
The standard form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is,
-x² - 19 = 45
Subtracting both sides by 45,
-x² - 19 - 45 = 0
Multiplying throughout by -1,
x² + 19 + 45 = 0
Quadratic formula for the general quadratic equation is,
x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] / 2a
Here, [tex]\sqrt{b^2-4ac}[/tex] is called discriminant.
Discriminant of given equation = [tex]\sqrt{19^2-(4*1*45)}[/tex] = √181
x = (-19 ± √181) / 2
x = (√181 - 19)/2 or x = (-√181 - 19)/2
Hence the solutions are x = (√181 - 19)/2 or x = (-√181 - 19)/2.
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Which theorem or postulate proves that △ABC and △DEF are similar? The two triangles are similar by the ________
The two triangles are similar by the Angle- Angle and also SIde -Side postulates.
A postulate is defined as a statement that is assumed to be true without any proof.
A theorem is defined as a true statement and is supported by a proof (or can be proven).
Here, two triangles can be said to be similar through many postulates :
1. △ABC and △DEF are similar if
angle ABC is equal to angle DEF; and
angle BCA is equal to angle EFD
(or any other two corresponding angles are same)
This can be said that △ABC and △DEF are similar with Angle- Angle (AA) postulate.
2. △ABC and △DEF are similar if
side AB/ BC is proportional to side DE/ EF;
(or ratio of two corresponding sides are similar)
This can be said that △ABC and △DEF are similar with Side Side (SS) postulate.
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In the library at Lenape Elementary School, there are
3
8
as many fiction books as there are nonfiction books. There are 44 books in the school library. How many books are fiction books?
With given expression, Fiction books will be calculated as 12.
What are expressions exactly?
In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.
Now,
According to given conditions
Let non-fiction books=n
then fiction books are=3/8n
given that n+3/8n=44
11n/8=44
n=32
then 3/8n=12
hence,
Fiction books will be 12.
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Right Question:-
In the library at Lenape Elementary School, there are 3/8 as many fiction books as there are nonfiction books. There are 44 books in the school library. How many books are fiction books?
What is the net of the triangular prism?
The net of the triangular prism is a combination of the two triangles and three rectangles.
A prism is a solid figure having two bases that are the same in size and shape, flat faces, and a continuous cross-section. The two bases of a prism, which can be triangles, rectangles, or any other polygon, determine the name of the prism in question.
Prisms having triangle bases, for instance, are referred to as triangular prisms, whereas those with square bases are referred to as square prisms, and so on. Three rectangle lateral sides and two triangular bases make up a triangular prism.
A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
ELECTRIC CAR For every hour x that Eva’s electric car charges, she can drive the car 7.5 miles. Eva needs to drive at least 60 miles tomorrow.
Part A
What inequality represents the situation in terms of x hours?
Multiple choice question.
A)
60x≥7.5
B)
7.5x≤60
C)
7.5x≥60
D)
60x≤7.5
Part B
Select the correct choices to complete the sentence.
Part B
What is the least amount of time that Eva will need to charge her car?
, 1 of 1.
Select Choice
0
1
2
3
4
5
6
7
8
9
hours
Answer: Part A: Option C) 7.5x≥60
Part B: 8 hours
Step-by-step explanation:
Part A: To represent the situation in terms of x hours, we can use the formula:
Distance driven ≤ distance the car can travel per hour × hours the car is charged
Since Eva needs to drive at least 60 miles and the car can travel 7.5 miles per hour of charging, we can write the inequality as:
60 ≤ 7.5x
The correct answer is (C) 7.5x ≥ 60.
Part B: To find the least amount of time that Eva will need to charge her car, we can solve the inequality from Part A as follows:
7.5x ≥ 60
x ≥ 8
This means that Eva will need to charge her car for at least 8 hours to be able to drive at least 60 miles.
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the sum of two numbers is 40.The smaller number is 8 less than the larger number.what are the numbers
Answer:
x = 24
y - 16
Step-by-step explanation:
Answer:
[tex]\huge\boxed{\sf x = 16, \ y = 24}[/tex]
Step-by-step explanation:
Let the smaller number be x and larger number be y.
Condition # 1:x + y = 40 ----------------(1)
Condition # 2:x = y - 8 ------------------(2)
Put Eq. (2) in (1)
y - 8 + y = 40
2y - 8 = 40
Add 8 to both sides2y = 40 + 8
2y = 48
Divide both sides by 2y = 48/2
y = 24Put y = 24 in Eq. (2)
x = 24 - 8
x = 16[tex]\rule[225]{225}{2}[/tex]
How to convert Nm to ft-lbs
We can convert the unit Nm to ft-lbs by using the formula 1Nm = 0.71 Lbs-ft.
We are provided with the unit Nm that means Newton meter.
we have to covert it into Lbs - ft.
Now, we know, from the standard conversion rates that one newton is equal to 0.2 lbs and one meter is roughly equal to 3.2 feet.
So, if we want to do the unit conversion, we should write,
= Lbs-ft
= 0.2 Lbs(3.2)ft
1Nm = 0.71 Lbs-ft.
Now, the above mentioned relation is our formula for the conversion of the two unit.
So, now we can write that, 1 Nm(Newton - meter) is equal to 0.71 Lbs-ft.
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Graph the lines : y = -3x + 2 and y = 2x - 3
At what ordered pair do the lines cross?( , )
(1, -1) is the required point of intersection of the lines
Equation and graph of a straight lineThe equation of a line in slope intercept form is expressed as y = mx + b
where
m is the slope of the line
b is the y-intercept of the line
Given the following equations of the line y = -3x + 2 and y = 2x - 3, the point where the line intersects will be the solution to the given equations as shown in the graph attached.
Hence the solution to the given equation by graphical method is (1, -1)
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Which is the solution set for –7 ≤ 4x + 1 ≤ 5?
Responses
x ≥ –2 and x ≤ 1
x ≥ –2 and x ≤ 1
x≥−3/2
and x≤3/2
, x ≥ − 3 2 , and , x ≤ 3 2
x ≤ –2 or x ≥ 1
x ≤ –2 or x ≥ 1
x≥−3/2
or x≤3/2
Answer:
Inequality form: -2 ≤ x ≤ 1
Interval Notation: [-2, 1]
Step-by-step explanation:
Move all terms not containing x from the center section of the inequality.
Answer:
yes
Step-by-step explanation:
yes
write a rule for a translation 3 units right and 5 units down followed by a reflection of y=x
We swap the x- and y-coordinates of the translated point, and then shift the x-coordinate 3 units to the right and the y-coordinate 5 units down.
The formula for translating 3 units right and 5 units down if we start at a position (x, y) is:
(x, y) → (x + 3, y - 5)
In other words, we multiply the x-coordinate by 3 and the y-coordinate by 5.
We switch the point's x- and y-coordinates in order to reflect the generated image across the line y = x. Finally, the rule is:
(x, y) → (y - 5, x + 3)
This entails switching the x- and y-coordinates of the translated point, followed by a 3 unit rightward and a 5 unit downward translation.
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PLEASE ANSWER SOON!!!! SP is a radius of the circle. What is the length of BR?
Using the given radius we know that the length of the line BR is 6.5 units.
What is the radius?A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments.
The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."
The radius of a circle is the separation between its center and circumference.
Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.
So, according to the given image:
SP is the perpendicular bisector of line BA.
And line BA is 13 units.
SP intersects BA st R.
Then, the length of BR will be:
= 13/2
= 6.5
Therefore, using the given radius we know that the length of the line BR is 6.5 units.
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The graphs of function f ang g represent the height of an object being launched into the air as a function of time. Which object was in the air longer?
Function g lingered for a while.
What does the physics projectile equation mean?h = v 0 y 2 2 g . This equation, which only depends on the vertical component of the initial velocity, specifies the maximum height of a projectile above its launch site.
What is the projectile's maximum height formula?The projectile formula's maximum height from the graph is H = u 2 sin 2 2 g.
An item named g was launched from a higher location when x=0... g(0)> f(0).
A higher point was reached by the object of g.
When the object was launched, f's slope was greater than g's slope.
The launch velocity of object f was greater.
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couple more and im done guys
Sorry I don't know good luck
9. 12 in. 24 in. 8 in. 20 in.
The two dimensions that should follow the sequence, 12 in. 24 in. 8 in. 20 in., are 4 in. and 16 in.
What is a sequence?A sequence is an ordered list of numbers that follow a specific pattern.
Related events or things that follow each other in an orderly form are described as sequences.
24 inches are 12 inches more than 12 inches (24 -12).
20 inches are 12 inches more than 8 inches (20 - 8).
16 inches are 12 inches more than 4 inches (16 - 4).
The common difference between the dimensions is 12 inches and the sequence reduces in value by 4 inches from the previous length and width to the next.
Thus, we can identify some patterns in any sequence, whether they are arithmetic, geometric, quadratic, or special sequences.
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Question Completion:Which two dimensions should follow this sequence?
you can compare two marginal distributions to see if the corresponding two variables are related. true/false
Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two variables.
Comparing two marginal distributions can help you identify if there is a relationship between two variables. You can plot the distributions and look for evidence of a relationship such as a linear trend or a pattern of higher or lower values compared to one another. Additionally, you can use statistical tests such as the Pearson correlation coefficient or Spearman's rank correlation coefficient to measure the strength of the relationship between the two variables.
Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two .
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what is the rank of a 4 x 5 matrix whose null space is three-dimensional?
The rank of the 4 x 5 matrix is 2 whose null space is three-dimensional
Matrix is defined as a rectangular array of rows and columns.
Rank of a matrix is defined as the maximum number of linearly independent columns (or rows ) that the matrix has.
Rank–nullity theorem is defined as a theorem described in linear algebra, which says that the dimension of the domain of a map is the sum of its rank and its nullity.
The rank-nullity theorem states that for a matrix A,
rank(A)+nullity(A)= number of pivot columns of A
That implies (the number of pivot columns) - (the null space dimension) = rank
The rank-nullity theorem states that for any matrix A, the rank of A plus the dimension of the null space of A equals the number of columns of A. In other words:
rank(A) + dim(null(A)) = number of columns of A
In this case, we have a 4 x 5 matrix A with null space of dimension 3. Therefore, we can solve for the rank of A as follows:
rank(A) + dim(null(A)) = number of columns of A
rank(A) + 3 = 5
rank(A) = 2
So the rank of the 4 x 5 matrix is 2.
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If CE=8 and ED=4, what are the possible lengths for AE and EB in the figure below?
2 and 16
6 and 2
4 and 4
2 and 30
Answer:
Step-by-step explanation:
eay ma boi
what is ml to quarts?
One millimeter is equal to 0.00106 of U.S. liquid quarts. Simply multiply any number of ml with the given value of liquid quarts to convert and find volume.
An object's or space's three-dimensional extent can be measured using a volumetric unit of measurement. Capacity is measured by volume. Consequently, the volumetric unit is essentially a unit for gauging the size or extent of an object or space.
Typically, the unit is used to describe the volume of products or liquids. To measure a quantity of something, use the International System of Units. Despite the fact that people speak different languages, the SI Units are used globally to communicate the measurements used in research settings.
Cubic meters, liters, and milliliters are the three most popular SI units for measuring volume. Specifically, the cubic meter as the unit of volume in the SI system.
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the probability of at least one head in two flips of a coin is
Answer:
[tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
When each time a coin is flipped, there are two possible outcomes.
The chance for either heads or tails being chosen is one half.
Thus, the number of times the coin can be flipped and land on heads or tails is [tex]\frac{1}{2}[/tex].
Hope it helped!
Un determinado día, Ana ha pagado 3,6 € por 3 dólares, y Alvaro ha pagado 8,4 € por 7
dólares. A Halla la ecuación de la recta que nos da el precio en euros, y, de x dólares
La ecuación de la recta es y = 1.2x + 0, o simplemente y = 1.2x. Y el precio en euros de 10 dólares es de 12 €.
La ecuación de la recta que nos da el precio en euros, y, de x dólares se puede hallar utilizando la fórmula de la pendiente de una recta, que es m = (y2 - y1) / (x2 - x1). En este caso, los puntos dados son (3, 3.6) y (7, 8.4).
Primero, calculamos la pendiente de la recta:
m = (8.4 - 3.6) / (7 - 3)
m = 4.8 / 4
m = 1.2
Luego, utilizamos la fórmula de la ecuación de la recta, y = mx + b, para encontrar el valor de b. Podemos utilizar cualquiera de los puntos dados para esto. Usaremos el punto (3, 3.6).
3.6 = 1.2(3) + b
3.6 = 3.6 + b
b = 0
Por lo tanto, la ecuación de la recta es y = 1.2x + 0, o simplemente y = 1.2x.
Esta ecuación nos da el precio en euros, y, de x dólares. Si queremos encontrar el precio en euros de una cierta cantidad de dólares, simplemente sustituimos el valor de x en la ecuación y resolvemos para y. Por ejemplo, si queremos encontrar el precio en euros de 10 dólares, sustituimos x = 10 en la ecuación:
y = 1.2(10) = 12
Por lo tanto, el precio en euros de 10 dólares es de 12 €.
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What does it mean if a function is continuous?
The absence of unexpected values or discontinuities is referred to as a function's continuous nature.
A continuous function is one in which a shift in the argument causes a continuous change in the value of the function, which is a change without a noticeable jump. This shows that there are no abrupt changes in value or discontinuities. More exactly, a function is continuous if it is possible to guarantee that, even with arbitrarily small changes to its parameter, its value won't change dramatically. Any function that is discontinuous is referred to as such.
A function is referred to as continuous if it is constant for all values of x inside its domain. The ability to simulate and evaluate physical occurrences and mathematical relationships involving smoothly varying numbers makes continuous functions crucial in many branches of mathematics and science.
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what is summation notation calculator online
The summation notation calculator is a instrument is frequently referred to as a sigma notation calculator since it makes it simple to calculate the sum of a set of integers, also known as Sigma.
The consecutive addition of a group of numbers is known as a summation. One of the four fundamental arithmetic operations, along with subtraction, multiplication, and division, is addition. For a few numbers, particularly integers, it is easy to do, but with fractions and real numbers, it can be more difficult. This is where our summation calculator might be useful. The numbers can be manually entered or copied and pasted, separated by any non-numerical sign, with the exception of the minus and dot. There are shortcuts for computing the sums of particular sequences.
The lower and upper bounds, a mathematical formula to be used to compute each member of the sum series, and lastly the name of the variable to be used in the sigma expression must all be entered in the "Sigma notation" mode.
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The sum of two numbers is 49. The smaller number is 21 less than the larger number. What are the numbers?
Answer:
35,14
Step-by-step explanation:
I am so sorry if this is wrong
Answer: I would have to guess 35, 14
Step-by-step explanation:
6(5 + 9r) - 4h use r = 8 and h = 4
SAVINGS If $10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years? Round to the nearest dollar.
The extra income earned in monthly compounding is $142.04.
What is compound effect?Compounding is defined as calculating interest on both the amount borrowed plus previous interest.
Given is that $10,000 is deposited into a savings account which is compounded monthly followed by compounded annually.
Annual compounding for 30 years -
Total money after annual compounding for 30 years -
T{A} = 10000 + (10000 x 0.023/1)^(30 x 1)
T{A} = $19,781.95
Monthly compounding for 30 years -
Total money after annual compounding for 30 years -
T{A} = 10000 + (10000 x 0.023/1)^(30 x 1)
T{A} = $19,923.99
Extra interest earned -
E = 19,923.99 - 19,781.95 = $142.04
Therefore, the extra income earned in monthly compounding is $142.04.
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(worth 25 points and will give brainlist if you're right.) Question 1 options: Factor xy-y+3x-3. Fill in the blanks using the correct sign: (y+ ) (x+ )
(Please help as soon as you can, closing today.)
So, the signs we need to fill in are: (y + 3)(x - 1)
How do you teach a young kid about factors?Factors are sets of digits that when added together, yield another integer. For instance: Since 2 + 3 Equals 6, the digits 2 and 3 seem to be factors of 6. Many things can affect a number!
To factor xy - y + 3x - 3, we can group the first two terms and the last two terms:
(xy - y) + (3x - 3) = y(x - 1) + 3(x - 1)
Notice that (x - 1) is a common factor of both terms, so we can factor it out:
y(x - 1) + 3(x - 1) = (x - 1)(y + 3)
So, we have:
xy - y + 3x - 3 = (x - 1)(y + 3)
To fill in the blanks, we use the factors we found:
(x - 1)(y + 3) = y(x - 1) + 3(x - 1) = xy - y + 3x - 3
So, the signs we need to fill in are:
(y + 3)(x - 1) = xy - y + 3x - 3
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Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. a) Ages of people at a Little League game. b) Number of siblings of people in your class. c) Pulse rates of college-age males. d) Number of times each face of a die shows in 100 tosses.
Expect distributions of these variables are:
a) Ages of people at a Little League game are unimodal and skewed.
b) Number of siblings of people in your class is unimodal and skewed.
c) Pulse rates of college-age males unimodal and roughly symmetric.
d) Number of times each face of a die shows in 100 tosses is approximately uniform.
a) Age distribution during a Little League game is likely to be unimodal and skewed. The age range of attendees. This is because Little League has an upper age restriction and the majority of players will fall inside that range, with just a small number being outliers. As a result, the distribution is likely to be unimodal, with the majority of participants falling within a relatively small age range, and being skewed toward older ages.
b) How many siblings are in your class? The distribution of siblings in a class is probably unimodal and skewed. This is because the majority of people either have no siblings or have one or two siblings, with just a small minority having three or more. As a result, the distribution will be unimodal, with the majority of individuals falling within a very small range, and tilted in the direction of the lower numbers.
c) Males in college-age pulse rates: These men's pulse rate distributions are probably unimodal and roughly symmetric. It is doubtful that there would be different groups or outliers that would result in a bimodal distribution, even though there may be some natural variation in pulse rates. There is also no reason to assume that one tail of the distribution will be longer or more dispersed than the other, hence the distribution is probably symmetric.
d) Number of times each die face is revealed in 100 throws: The distribution of the number of times each die face is revealed in 100 throws is probably quite uniform. Each face has an equal chance of appearing on each toss, and throughout 100 tosses, each face is expected to do so roughly the same amount of times, assuming a fair die. As each face should appear nearly equally often, the distribution should be quite consistent.
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A cell phone carrier charges a monthly fee of $20 and also charges customers $0.05 per text message. The function C(t)=0.05t+20 represents the cost, C, per month based on t text messages in a month.
Which best describes the domain of the function?
A. all real numbers
B. all real numbers that are multiples of 0.05
C. all whole numbers
D. all whole numbers from 0 to 20
The domain that describes the function is,
All whole number
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
C(t) = 0.05t + 20
C(t) represents the total cost per month and t is the number of text.
Now,
t is the domain of the function C(t).
C(t) can not be in negative value so, t has to be a positive number.
And,
t can be any positive real number.
Now,
All real numbers included negative numbers.
All real numbers that are multiples of 0.05 included negative numbers.
Thus,
All whole number describes the domain of C(t).
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The equation of Pilar's line of fit is `c=-1t+120`
How many more cups of hot chocolate would Pilar expect to sell if the temperature decreased by `15°`F?
If the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.
What is an equation?
An equation is a statement that shows the equality of two expressions by using an equal sign (=). It expresses a mathematical relationship between two or more variables or quantities.
Regarding the second question, to find out how many more cups of hot chocolate Pilar would expect to sell if the temperature decreased by 15°F, we can plug in t = 15 into the equation c = -t + 120 and calculate the difference between the original value of c and the new value.
c(Original) = -15 + 120 = 105
c(New) = -(15+15) + 120 = 90
The difference is:
c(New) - c(Original) = 90 - 105 = -15
Therefore, if the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.
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can the tangent constraint be applied between a line and an arc?
Answer:
yes
Step-by-step explanation:
You can compare two marginal distributions to see if the corresponding two variables are related.a. Trueb. False
The given statement is false.
You can compare two marginal distributions to see if the corresponding two variables are related - False.
Comparing marginal distributions can only disclose information about the distribution of each variable individually, not whether the variables are connected or not.
To see if two variables are connected, we must look at their joint distribution or conditional distribution. To examine the degree and direction of a link between two variables, statistical approaches such as correlation analysis or regression analysis can be utilised.
As a result, comparing marginal distributions is insufficient to tell whether two variables are connected or not.
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