The values of 'j' are -11,5.
What is a Quadratic Equation?
Quadratic equations are the polynomial equations of degree 2 in one variable of the type [tex]f(x) = ax^{2} + bx + c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.The standard form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex] .Here, the given equation is (2x+7)(x-5) = - 43 + jx
On simplifying the equation we get,
[tex]2x^{2} -10x+7x-35=-43+jx\\2x^{2} -3x-35+43-jx=0\\2x^{2} -3x-jx+8=0\\2x^{2} -(3+j)x+8=0.....(1)\\[/tex]
By comparing the given equation with the standard form of the quadratic equation we get,
a = 2
b = - (3 + j)
c = 8
Therefore,
[tex](-(3+j))^{2} -4\times2\times8=0\\(3+j)^{2} -64=0\\(3+j)^{2} =64\\[/tex]
Take the square root of both sides,
[tex]\sqrt{(3+j)^{2} }=\sqrt{64} \\[/tex]
3 + j = ±8
Therefore,
3 + j = 8
j = 8 - 3
j = 5
or
3 + j = -8
j = -8 - 3
j = -11
Hence, the possible values of 'j' are -11,5.
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What are exponent examples?
Answer:
An exponent refers to how many times a number is multiplied by itself.
Step-by-step explanation:
For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
Determine whether the point (1, 1) is a solution to the system of equations. Explain your reasoning in complete sentences. graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2
(1, 1) is not solution of system of equations.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
We need to check the point (1, 1) is a solution to the system of equations.
graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one.
y = 3x + 2
g = |x-1| +1
We obtain the intersection point
(0,2)
The only point of intersection of the graphs is (0, 2).
The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection
Hence, (1, 1) is not solution of system of equations.
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christine's rectangular bedroom has a perimeter of 44 feet. the llength of her bedroom is 2 more than the width. what are the dimensions of her room
Answer:
Step-by-step explanation:
44/4= 11
44-24/2=12
20/2=10
The room is 10 x 12' long
Does 5 7 11 make triangles?
It is possible to construct a triangle whose sides are 5 cm 7 cm and 11 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 5 cm 7 cm and 11 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 5 and 7
5 + 7 > 11
12 > 11
Now we add 7 and 11
7 + 11 > 5
18 > 5
Now we add 5 and 11
5 + 11 > 7
16 > 7
It is possible to construct a triangle whose sides are 5 cm 6 cm and 11cm because the sum of two sides are greater than third sides.
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30 points for this simple question
How many prime numbers are there between 1 - 2020??
Answer:
How many prime numbers are there in 2020?
There are 12 factors of 2020, of which the following are its prime factors 2, 5, and 101. The Prime Factorization of 2020 is 2^2 × 5^1 × 101^1.
...
Sum of Factors of 2020: 4284.
Step-by-step explanation:
Can you insert a formula in a table?
In a table cell, enter a formula. Choose the table cell in which you wish the result to appear.
what is sequence ?A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. A set of numbers connected by a rule is referred to as a number sequence. You can determine the following numbers in the sequence if you figure out the rule. Therefore, adding 6 each time is the rule for this sequence.
given
In a table cell, enter a formula. Choose the table cell in which you wish the result to appear.
Delete the contents of the cell if it is not empty. Click Formula under the Data group on the Layout tab of the Table Tools.
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One bag holds 11 cherries how many cherries are in 143 bags
143x11
=1573 cherries
One bag holds 11 cherries and there are 143 bags. To find out how many cherries there are, we would need to multiply the amount of cherries by the number of bags.
[tex]11\times143[/tex]
[tex]=\fbox{1573 total cherries}[/tex]
Question 6 of 10
What sentence represents the number of points in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. The number of multiple-choice question points plus the number of
short-answer question points is 80.
B. The number of multiple-choice question points plus the number of
short-answer question points is 25.
OC. The number of multiple-choice question points minus the number
of short-answer question points is 25.
D. The number of multiple-choice question points times the number
of short-answer question points is 80.
APEX
The number of multiple-choice question points plus the number of short-answer question points is 80. Therefore, the correct answer is option A.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points.
Let the number of 2 points questions be x and the number of 4 points questions be y.
A test is worth 80 points.
2x+4y=80 -------(I)
The test has 25 questions.
x+y=25 -------(II)
Therefore, option A is the correct answer.
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How do the functions from part a differ from functions you have used in algebra in the past?
The functions differ from functions that we have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
An output variable and one or more input variables are the minimum number of variables in a function.
An equation can have any number of variables and declares that two expressions are equal (none, one, or more). Although not all equations are functions, a function is frequently expressed as an equation.
It should be recalled that a function is merely an equation in which the x inserted produces precisely one from the equation.
In this instance, the functions are different from the ones we have used in algebra in the past since they may be coupled and focus more on rotation than on where they travel.
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A map has a scale of 1 cm to 10 km. What would the distance be in kilometres if the distance displayed on the map is 7.211102550928 cm?
The real distance by means of scales used in the map that is described in the statement is approximately equal to 72.11102550928 kilometers.
How to predict the real distance from a map by using scales
Scales are a useful resource to represent any system in a size different than real. Maps are usually created from application of scales. Mathematically speaking, scales are described by following mathematical ratio:
r = s / R
Where:
r - Map scale, in centimeters per kilometer.s - Scale distance, in centimeters.R - Real distance, in kilometers.If we know that r = 0.1 centimeters per kilometers and s = 7.211102550928 centimeters, then the real distance derived from the distance shown in the map that is described in the statement is:
R = s / r
R = (7.211102550928 cm) / (0.1 cm / km)
R = 72.11102550928 km
By using scales on the map, the real distance is approximately equal to 72.11102550928 kilometers.
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use the distributive property to simplify the expression
1/2( 2n +4+6m)
Answer:
n + 2 + 3m
Step-by-step explanation:
[tex]\frac{1}{2} (2n+4+6m) = (\frac{1}{2}*2n)+(\frac{1}{2}*4)+(\frac{1}{2}*6m)\\ =n+2+3m[/tex]
Start at 10. Create a pattern that multiplie each number by 10 top when you have 5 number
So, the sequence is 10, 100, 1000, 10000, 100000
A pattern that multiplies each number by 10 to get the next number in the sequence would be as follows:
Start with 10.
Multiply 10 by 10 to get 100.
Multiply 100 by 10 to get 1000.
Multiply 1000 by 10 to get 10000.
Multiply 10000 by 10 to get 100000.
This pattern creates a sequence of numbers that increases exponentially, with each number being 10 times larger than the previous one. The pattern can be represented by the following rule: "Each number in the sequence is the previous number multiplied by 10."
So, the sequence is:
10, 1010 = 100, 10010 = 1000, 100010 = 10000, 1000010 = 100000
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physical activity is important for good health and can reduce the risk of many diseases. During 31 days last summer a cyclist rode the same number of miles every day for a total of 1,085 miles how many miles did she ride each day
Answer:
Below
Step-by-step explanation:
1085 miles / 31 days = 35 miles/day
Scalar multiplication quiz
the Matrix multiplication of the given question is [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]
What is matrix?
The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.
A =-1/3 [tex]\left[\begin{array}{cc}27&-9\\-15&24\\\end{array}\right][/tex]
A = [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]
Hence the Matrix multiplication of the given question is [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]
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One morning, jasmine biked to her grandmother's house in 45 minutes. It was foggy when jasmine biked back home that evening, so she biked 4 mph slower. The trip home took jasmine 1 hour and 10 minutes. How far apart are jasmine's house and her grandmother's house?.
The distance between Jasmine’s house and her grandmother’s house is 504 miles.
To find the distance, we can use this following formula:
X = V x T
Where: X = distance, V = Velocity, and T = Time
Since we know that Jasmine rode her bike to see her grandma in the morning and the trip took her 45 minutes, the first equation would be X = V x 45.On her trip back home, it was foggy, which caused her cycling speed to decrease by 4 mph that took her 1 hour and 10 minutes or 70 minutes. Therefore, the second equation would be X = (V-4) x 70.By using the following equations above, we can assume that
V x 45 = (V-4) x 70
45 V = 70 V – 280
25 V = 280
V = 11.2 mph
Now that we have the velocity, we can find the distance =
X = V x T
X = 11.2 mph x 45 minutes
X = 504 miles
Thus, the distance between Jasmine’s house and her grandmother’s house would be 504 miles
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Answer:
Step-by-Step answer:
8 2/5 miles
Find the area of the irregular figure to the nearest tenth of a unit
The area of the irregular figure is equal to 27.5 square units.
How to determine the area of an irregular figure
Irregular figures are the result of combining of two or more geometric figures. The irregular figure shown in the image is the result of seven figures, triangles and rectangles, whose area formulas are:
Triangle
A = 0.5 · w · l
Rectangle
A = w · l
Now we proceed to calculate the area of the irregular figure:
A = 0.5 · 1 · 5 + 2 · 5 + 0.5 · 2² + 2 · 3 + 0.5 · 1 · 2 + 3 · 1 + 0.5 · 3 · 2
A = 2.5 + 10 + 2 + 6 + 1 + 3 + 3
A = 27.5
The irregular figure has an area of 27.5 square units.
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Please help with this
Consequently, x = 1, 2, 3, 4, 5, 6,..., and no matter what x number we enter, 7 + x is always more than 2x.
what is expressions ?A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.
given
substituting the value of x
7+x > 2x
so x = 1
x = 2
x = 3
x= 4
x= 5
Consequently, x = 1, 2, 3, 4, 5, 6,..., and no matter what x number we enter, 7 + x is always more than 2x.
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if In = 5 x" (1+x)0.5 dx ,n= 0,1,2....
where the integral is for x e [0,1].
By first finding a bound on the integrand, which of these is an upper bound on In?
Pick ONE option
O 1/(n+1)
O 1/2(n+1)
O 1/(n+1) + 1/(n+2)
O N^N
The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).
To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
0
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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Kenny is using division to write a fraction equivalent to 30/100 she tried to divide the numerator and denominator by three she got stuck what advice would you give her
The advice I will give Kenny that was using division to write a fraction equivalent to 30/100 after she tried to divide the numerator and denominator by three, is to also divide them by factor of 10.
How can fraction equivalent be obtained?The concept that will be used is division,
The given values is 30/100, if we divide the numerator and denominator by three, we have 10/100.
Then we can also divide the numerator and denominator of 10/100 by factor of 10, then we will have 1/10.
It should be noted that Division in mathematics is the process of dividing an amount into equal parts.
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can you please help me i really need it
Maximum number of bracelets Tara can make is 6.
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
Tara has a plastic string that is 3 3/4 feet.
And, She will cut the string to make bracelets that are each 5/8 feet long.
Now,
To find maximum number of bracelets Tara can make, we can draw the point at equal distance 5/8 feet to reach 15/4 feet.
Then, Calculate the number of points to draw which is equal to the maximum number of bracelets Tara can make.
That is,
Maximum number of bracelets Tara can make = 15/4 ÷ 5/8
= 15/4 × 8/5
= 6
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d/4-9=-3
show work
show check
Answer:
d = 24
Step-by-step explanation:
d/4 - 9 = -3
d/4 - 9 + 9 = -3 + 9
d/4 = 6
d/4 * 4 = 6*4
d = 24
Check:
(24)/4 - 9 = -3
6 - 9 = -3
-3 = -3 (Correct)
Hope this helps!
What is mirror image class 9 maths?
An object that appears to be identical but is really turned the opposite way in the plane perpendicular to the mirror surface is called a mirror image.
It appears as an optical phenomenon as a result of reflection from surfaces like water or mirrors. People might be able to see a reflection of themselves in the mirror behind the glass. The "mirror image" is produced when light rays strike the mirror-like surface and reflect back. One that is commonly misinterpreted is the notion that the reflection is reflected from left to right. Mirrors are turned from left to right rather than from front to back.
When looking at printed surfaces from the inside out, as well as in the reflections of mirrors and other reflecting surfaces, one may notice two-dimensional mirror images. After gazing at what is effectively a two-dimensional object when we first glance at a card, we notice a left-right reversal in the mirror when we turn the card such that the lettering is facing a mirror (like the text on a card).
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what is the value of this equation
[tex](15 ^{ \frac{1}{5} } ) {}^{5} [/tex]
The value of the given equation with a fractional index is 15.
What are fractional indices?
We can determine how many times a term has been multiplied by itself using an index, which is a small number. Powers of a term that are fractions are known as fractional indices.
The fractional power's two components both have significance. The number's or letter's root serves as the fraction's denominator. The power to raise the answer is contained in the fraction's numerator.
For example,
A value raised to the power of ½ means we have to find the square root.
A value raised to the power of ⅓ means we have to find the cube root
Some of the rules of fractional indices are
[tex]a^{1/m} * a^{1/n} = a^{1/m + 1/n} \\\a^{1/m} / a^{1/n} = a^{1/m - 1/n} \\\a^{1/m} * b^{1/m} =( ab)^{1/m}\\\a^{1/m} / b^{1/m} =( a/b)^{1/m}[/tex]
[tex](a^\frac{1}{m}) ^\frac{1}{n} = a^\frac{1}{mn}[/tex]
For the given question,
[tex](15^\frac{1}{5} )^5[/tex] = [tex]15^\frac{5}{5} =15^1 =15[/tex]
Therefore the value of the given equation with a fractional index is 15.
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compare the end behavior of the functions g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20 and h(x) = "-3x^4" - 16x - 1. Explain your reasoning.
The end behavior of the functions g(x) and h(x) are the same and both functions approach negative infinity as x becomes large in either direction.
What is end behavior?Generally, The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity. To compare the end behavior of g(x) and h(x), we can look at the leading term of each function, which is the term with the highest degree.
In the function g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20, the leading term is -3x^4, so as x approaches positive or negative infinity, the function will approach negative infinity.
In the function h(x) = -3x^4 - 16x - 1, the leading term is also -3x^4, so as x approaches positive or negative infinity, the function will also approach negative infinity.
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Given: ∠MPN is a right angle, NP is a perpendicular bisector to MO
Prove: △MNP ≅ △ONP
Given that ∠MPN is a right angle, we know that MP and NP are perpendicular to each other. Since NP is also a perpendicular bisector of MO, it bisects MO at a 90-degree angle.
Also given that NP is a perpendicular bisector of MO, we know that NP is equidistant from M and O. Therefore, NP is the midpoint of MO and so MN = NO.
Since MP and NP are perpendicular and MN = NO, it follows that △MNP is similar to △ONP.
Therefore, we can conclude that △MNP ≅ △ONP
tara has 3 boxes of books each box has 48 books tara divides the books amongst 3 friends how many books will each friend get
Each friend will get 48 books. The solution is obtained using arithmetic operations.
What are arithmetic operations?
There are four basic operations which are listed as follows:
Addition(‘+’): This operation deals with finding the sum.Subtraction(‘-’): This operation deals with finding the difference. Multiplication(‘×’): This operation deals with finding the product.Division(‘÷’): This operation deals with finding the quotient.Now, Tara has 3 boxes of books and each box contains 48 books.
So, the total books that Tara has is equal to 3×48= 144.
Thus, Tara has total 144 books.
Tara divides the books among 3 friends.
So, the number of books that each friend will get is equal to 144÷3= 48
Hence, each friend of Tara will get 48 books.
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Which trig ratio is 5/11?
Answer:
cos(T) = 5/11
Step-by-step explanation:
cos = adjacent(5)/hypotenuse(11)
So whatever "cosine" of something to choose, the adjacent side to the angle needs to be five. It cannot be the right angle, therefore only the option "T" remains, as eleven would always be the hypotenuse for any angle.
can someone post the back of the paper on Quiz 3-1 Parallel Lines, Transversals, and Special Angle Pairs
The following statements are true:
Segment DEF is parallel to ABC
The line segment AB is parallel to DE
Line FC is parallel to AD
the line that is skewed to DE is BC
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)
Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;
DEF is parallel to ABC
CADF is parallel to CBEF
For the lines, the lines that are parallel to each other are:
AD is parallel to BE
AB is parallel to DE
FC is parallel to AD
Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC
The missing image is attached with the answer below.
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Find the range for the measure of the third side of a triangle when the measures of the other two sides are 18 ft and 23 ft.
Answer:
The measure of the third side of a triangle, when the measures of the other two sides are 18 ft and 23 ft, must be greater than the difference between the measures of the other two sides (which is 18 ft - 23 ft = -5 ft) and less than the sum of the measures of the other two sides (which is 18 ft + 23 ft = 41 ft).
This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.
Therefore the range of the measure of the third side of a triangle with side lengths 18 ft and 23 ft is:
(-5 ft < x < 41 ft)
or
[x > -5 ft and x < 41 ft].
It is also important to note that any value of x within this range will produce a valid triangle, however, any value less than -5 or greater than 41 will not.
Step-by-step explanation:
What are the mathematical concepts used to calculate insurance premiums?
The mathematical concepts used to calculate insurance premiums include probability, actuarial science, risk assessment, pricing models, financial models, and statistical analysis.
Probability:
To calculate premiums, insurance companies use statistical data to determine the likelihood of a claim occurring. Probability is used to estimate the likelihood of certain events happening, such as accidents, illnesses, or natural disasters, and to determine the likelihood of a claim being made.
Actuarial Science:
Actuarial science is the application of mathematical and statistical methods to assess risk and uncertainty in insurance, finance, and other industries. Actuaries use mathematical models to analyze data and make predictions about future events, which is crucial in determining insurance premiums.
Risk Assessment:
Insurance companies use risk assessment to determine the level of risk associated with insuring a particular individual or group. Factors such as age, health, occupation, and location are considered when assessing risk, and premiums are adjusted accordingly.
Pricing models:
Pricing models are used to determine the cost of insurance based on the perceived level of risk. Pricing models like Loss Ratio, Pure Premium, and Captive pricing are used to arrive at the insurance premium.
Financial Models:
Financial models are used to determine the long-term financial stability of an insurance company and to ensure that the company has enough funds to pay out claims. Actuaries use financial models to calculate the amount of money an insurance company needs to set aside in order to pay claims and to determine the long-term financial health of the company.
Statistical Analysis:
Insurance companies use statistical analysis to evaluate data on claims and losses, and to identify patterns that can be used to predict future claims and losses. This analysis is used to identify trends in claims, to identify high-risk groups, and to set premiums.
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