We can easily silve it by splitting the middle term or by using the discriminate method *
* splittingx 2 +3x -70
x2 + 10x - 7x -70
x(x + 10) -7(x +10)
(x / 7) ( x + 10)
x = 7 or -10
what is the value of the limit [tex]\lim_{x \to \5} \sqrt{x^{2}+4 }[/tex]
Answer:
Refer to the attached photo.
Step-by-step explanation:
What type of sequence is 8 16 24 and 32?
Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next item in the sequence is obtained by adding the previous term by 8.
What is meant by arithmetic sequence?The difference between consecutive terms in an arithmetic sequence, sometimes referred to as an arithmetic progression, is consistently the same.
What is the general formula to find nth term of arithmetic sequence?To find nth term we will use
[tex]a_{n}=a+(n-1)d[/tex]
where
a=first term
d=common difference
n=number of terms
In 8 16 24 and 32 since common difference d=8 between each successive term so this is a arithmetic sequence.
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What are the four 4 inequality symbols?
What is multiplicity value?
Multiplicity value is a measure of the number of times a given entity appears in a relationship.
It is expressed as either a single value (1:1, 1:N, or M:N) or as a range of values (e.g. 1..4). This value is used to define the type of relationship between two entities.Multiplicity value is a measure of the number of times a given entity appears in a relationship. It is expressed as either a single value, such as 1:1, 1:N, or M:N, or as a range of values, such as 1..4. These values are used to define the type of relationship between two entities. For example, a 1:1 relationship means that one entity is related to one other entity, such as one customer to one order. A 1:N relationship means that one entity is related to multiple other entities, such as one customer to multiple orders. An M:N relationship means that multiple entities are related to multiple other entities, such as multiple customers to multiple orders.
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given JK || MN and L is the midpoint of JM proven JKL = MNL
The triangle JKL is similar to triangle MNL by AA similarity and all three sides of the triangle are equal, so JKL = MNL.
What is the triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
JK || MN and L is the midpoint of JM,
As the line JK || MN then,
∠ MNL = ∠ JKL (The alternate angle of the parallel line are equal)
∠ LMN = ∠ LJK (The alternate angle of the parallel line are equal)
∠ JLK = ∠ NLM (The corresponding angle of the parallel line are equal)
Thus, all the sides will also be equal as the angles are equal.
Hence, the area will also be equal.
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How would you define this triangle by its angles and its sides?
Answer:
Equilateral Triangle
A triangle with all the sides equal is called an equilateral triangle.
Isosceles Triangle
A triangle with at least two sides equal is called an isosceles triangle.
Scalene Triangle
If all the sides of a triangle are unequal, i.e., if the sides are of different lengths, the triangle is called a scalene triangle.
Acute Triangle
An acute triangle is a triangle whose all the three interior angles are acute. In other words, if all interior angles are less than 90 degrees, then it is an acute-angled triangle.
Obtuse Triangle
Obtuse triangles are those in which one of the three interior angles has a measure greater than 90 degrees. In other words, if one of the angles in a triangle is an obtuse angle, then the triangle is called an obtuse-angled triangle.
Right Triangle
A right triangle is a triangle in which one of the angles is 90 degrees. In a right-angled triangle, the side opposite to the right angle (90-degree angle) will be the longest side and is called the hypotenuse. You may come across triangle types with combined names like right isosceles triangle and such, but this only implies that the triangle has two equal sides with one of the interior angles being 90 degrees.
The graph of F(x), shown below, resembles the graph of G(x) = x², but it has been changed somewhat.
Which of the following could be the equation of F(x)?
A. F(x)=2x^2+3
B. F(x)= -x^2+3
C. F(x) = 0.2x²+3
D. F(x)=x²+1
The equation of f(x) from the graph if, G(x) = x², is F(x) = 2x² + 3, so option A is correct.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given:
G(x) = x²,
As you can see from the graph, the vertex of the parabola is (0, 3),
Write the equation of a parabola as shown below,
y = a(x - 0)² + 3
y = ax² + 3
Here a is the slope of the parabola,
slope = 4 / 2 (from the graph),
slope = 2
Thus, the equation will be,
y = 2x² + 3 or F(x) = 2x² + 3
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Geometry.
1. Reasoning What is the advantage of using coordinates O(0,0),
E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0)?
Using coordinates O(0,0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0) has the advantage of allowing the graph to be stretched or shrunk uniformly in both the x- and y-directions by a factor of 2. This can be useful if the scale of the graph needs to be adjusted, or if the graph needs to be compared to another graph with a different scale. It can also make the graph easier to read if the values of the variables being plotted are very large or very small.
By using coordinates that are multiples of the original coordinates, the shape of the graph is preserved, but the scale is changed. This can be useful if the purpose of the graph is to compare the relationships between different variables, rather than to provide an accurate representation of the actual values of the variables.
530$ sales 9% commission rate what’s the commission?
Answer:
$47.70
Step-by-step explanation:
To find what a number is in percent form, divide it by 100
9% ÷ 100 = 0.09
Multiply this by $530 to find the commission
530 × .09 = 47.7
$47.70
a ball of radius 17 has a round hole of radius 3 drilled through its center. find the volume of the resulting solid.
Refer to the photo taken.
Convert 190 centimeters into yards.
Round your answer to the nearest
hundredth.
Answer: 190 cm = 2.07787 yards, rounded to the nearest hundredth, 2.08 yards.
Step-by-step explanation:
divide 190 cm by 91.44 to get your answer.
if 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor
Probability that at least one of them is a universal donar is 0.5263.
What is probability ?
What is probability explain?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given,
Probability of getting a universal donor is 0.072.
X be the “random variable” which “describes the number of universal donors” in the “sample of 10 people”.
X follows a “binomial distribution” with n=10 and p=0.072
P(X=x) = ([tex]{n}C^{x}[/tex])*([tex]p^{x}[/tex])*([tex]q^{n-x}[/tex]) ; x=1(1)10 ; q=1-p
Required probability,
P(X≥1)= 1 - P(X=0)
= 1 - (10C0)*([tex]0.072^{0}[/tex])*([tex]0.928^{10}[/tex])
= 1 - 0.4737 = 0.5263
Probability that at least one of them is a universal donar is 0.5263.
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the question is in the picture
Answer:
Sienna
Step-by-step explanation:
Sienna achieved higher scores of 15-17 much more consistently than Willem, who often scored just 12 or 13.
Find dy/dx for the function y=3x^0
Answer:0
Step-by-step explanation:
So this is an exponential equation. And the dy/dx is impossible because anything time 0 is 0. So there is no Rise over run, most commonly known as your slope.
Option. A ) 0 is correct
It is given that,y = 3x⁰ = 3
we have asked to differentiate the function y with respect to x.
for constants, the slope is always zero and the graph looks like a line parallel to the x-axis
[tex]dy/dx[/tex] = 0
therefore, the differentiation of y=3 is 0.
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help me out on this
The standard form of the complex number is respectively 2√3 i - 15 + √300 i,4 - 7 i, and -14 + 9 i.
What is a complex number?Complex numbers are helpful in finding the square root of negative numbers.
A complex number is the sum of a real number and an imaginary number.
(a)
As per the given, 2√-3 - 15 + √-300
Since, √-1 = i thus,
2√3 i - 15 + √300 i
(b)
As per the given, (15 - 10i)/(2 + i)
By rationalization,
(15 - 10i)/(2 + i) x (2 - i)/(2 - i)
⇒ (30 - 15 i - 20 i + 10 i²)/(2² - i²)
⇒ (30 - 10 - 35 i)/(4 + 1)
⇒ 4 - 7 i
(c)
As per the given, 3(2 + i) - 4(5 - 2i)
⇒ 6 + 3i - 20 + 8i
⇒ -14 + 9 i
Hence "The complex number has the following conventional forms: 2√3 i - 15 + √300 i,4 - 7 i, and -14 + 9 i".
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Question Says Graph f(x)-0.5x-3
Picture below please help!
Answer:
Step 1: f(0) = -2
I also attached the graph in the explanation!
Step-by-step explanation:
f(x) = 0.5^x -3
f(0) = 0.5^0 - 3
f(0) = 1 - 3
f(0) = -2
I attached the graph below.
Consider the functions f(x) = 23x + 5 and g(x) = 32x + 7. what do the slopes indicate about the lines?
As per the given function, the line of the functions has the same intersecting point (-0.2, 0).
The term function in math refers a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we have the consider the functions f(x) = 23x + 5 and g(x) = 32x + 7.
And we need to find the slopes indicate about the lines.
While we looking into the given functions,
f(x) = 23x + 5
g(x) = 32x + 7
Now, we have to identified that the slope of the function f(x) is 23 and the slope of the function g(x) is 32.
And now we have to apply some sample values on the function, then we get the following table of values.
And by using the table we have to plot the graph then we get the graph like the following.
Through graph we have identified that both functions has the same intersecting point (-0.2, 0).
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4 sin[ (π/6)x ] + 1 how do you put that as a graph
Answer:
Step-by-step explanation:
Kim purchased a new phone for $410, she put down $50 when she purchased it. If she pays a monthly bill of $35, which equation can used to determine how many months, m, it will take her to pay it off?
A 50m + 35 = 410
B 360 = 35 + m
C 35m + 50 = 419
D 50m - 35 = 410
Answer:
C
Step-by-step explanation:
I'm guessing you misspelled 410 as 419, but the equation is y=mx+b
Kim wants the money amount she puts in to pay off her $410 phone, or in other words, add up to $410.
The constant, or b, is 50. The m is 35, and the x is the months.
35m + 50 = 410
Answer: C. 35m + 50 = 410
Step-by-step explanation:
We know the cost is 410, so it will be = 410
We know that she pays 35 each month, which mean it is 35m
She put down 50 at the beginning, so it is + 50
So our equation is
35m + 50 = 410
How many real roots does the quadratic equation x2 5x 7 0 have?
The equation x^2 - 5x + 7 = 0 has no real roots.
We know that the general form of a quadratic equation is:
ax^2 + bx + c =0
The equation we have is:
x^2 - 5x + 7 = 0
On comparing the given equation with the general form of a quadratic equation, we get that:
a = 1, b= -5, and c = 7
If D = b^2 - 4ac < 0, then the roots of the quadratic equation are imaginary or there are no real roots.
Therefore, b^2 - 4ac = (-5)^2 - 4x1x7 = -3<0.
Hence, we conclude that the nature of the roots of the give equationis imaginary, thus it has no real roots.
The question is incomplete, the complete question is x^2 - 5x + 7 = 0
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Can 3 year olds spell?
Simple 3-letter words or alphabets may be spelled verbally by kids as young as 3 years old
What is alphabets?An alphabet is a standardized system of fundamental written graphemes that correspond to the phonemes of certain spoken languages. a group of letters or other symbols used to write one or more languages, especially if they are organized in a regular sequence. a set of symbols or signals used to represent letters.
Simple 3-letter words or alphabets may be spelled verbally by kids as young as 3 years old. Early exposure to the alphabet and the spelling tools it contains, like as songs and reading aloud to them, provides the foundation for their comprehension of how letters combine to form words.
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The tree diagram represents an
experiment consisting of two trials.
P(A and C) = [ ? ]
Answer:
0.2
Step-by-step explanation:
[tex]P(A \cap C)=P(A)P(C)=(0.5)(0.4)=0.2[/tex]
Daniel has a yearly income of $41,300 and claims 4 exemptions. The amount allowed for each exemption is $900. His local tax is4 3/4%. How much local income tax should be withheld from his weekly earnings? (Round your answer to the nearest cent.)
Answer:
$34.37.
Step-by-step explanation:
To calculate Daniel's local income tax withholding, we first need to determine his taxable income. To do this, we subtract the value of his exemptions from his yearly income: $41,300 - (4 x $900) = $37,500.
Next, we need to convert the local tax rate of 4 3/4% to a decimal by dividing it by 100: 4 3/4% = 0.0475.
Finally, we can calculate Daniel's local income tax withholding by multiplying his taxable income by the local tax rate: $37,500 x 0.0475 = $1,793.75.
To find the amount of local income tax that should be withheld from Daniel's weekly earnings, we simply divide his total local income tax by the number of weeks in a year: $1,793.75 / 52 = $34.37. Therefore, Daniel's local income tax withholding from his weekly earnings should be $34.37.
Points a, b, and c are collinear. If bc = 8. 5 and ac = 13. 2, select all possible values of ab.
What is the formula to find asymptotes?
Answer:
Step-by-step explanation:
ormula for finding the asymptote of hyperbola is
y-k =+/- b/a( x-h).
Find the area in quare centimeter of a rectangular orchard 3. 28m long and 75mm wide
Answer:
24.6 cm^2
Step-by-step explanation:
3.28m = 328 cm
75mm = 0.075 cm
Area of rectangle: L x W
328 times 0.075 = 24.6 cm^2
CAN ANYONE PLS HELP ME WITG THIS MATHEMATICS????
Answer:
- 3 19/30----------------------
Simplify the given expression:
1/5 - 3/4 (2 5/9) ÷ 1/2 = Convert mixed number into fraction1/5 - 3/4 × 23/9 × 2 = Cancel 2's and 3's and simplify1/5 - 23/6 = Common denominator is 5*6 = 301/5(6/6) - 23/6(5/5) = 6/30 - 115/30 = Bring to common denominator(6 - 115)/30 = Simplify- 109/30 = Convert fraction into mixed number- 3 19/30 AnswerRidgid motions to prove
Answer:
5. ∠HTS
6. DI
7. UF
8. ∠E
Step-by-step explanation:
5. We are given that ΔTSR ≅ ΔTSH, and according to CPCTC (corresponding parts of congruent triangles are congruent), ∠RTS corresponds with ∠HTS. Therefore, ∠RTS ≅ ∠HTS.
6. We are given that ΔECD ≅ ΔDJI, and according to CPCTC (corresponding parts of congruent triangles are congruent), segment DE corresponds with segment DI. Therefore, DE ≅ DI.
7. We are given that ΔVUT ≅ ΔVUF, and according to CPCTC (corresponding parts of congruent triangles are congruent), segment UT corresponds with UF. Therefore, UT ≅ UF.
8. We are given that ΔPQR ≅ ΔEFG, and according to CPCTC (corresponding parts of congruent triangles are congruent), ∠P corresponds with ∠E. Therefore, ∠P ≅ ∠E.
How do we integrate the information?
Integration services are precise design and implementation tasks that connect the functionality and/or data of two or more applications with existing or future Information systems architecture.
Integrate to combine, mould, or mix into a working or cohesive whole.
information is a stimulus that, to its recipient, has significance in a particular setting. Info that is entered into and stored in a computer is referred to as data in a wide sense. It is possible to read data that has undergone processing, such as formatting and printing, once again as info.
You may include sources into your writing in three different ways:
Quoting: This refers to using another author's identical words in your writing without modifying them.
Giving a summary entails outlining the main ideas of a source.
Putting another author's thoughts into your own words is known as paraphrasing.
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What is mode maths example?
The mode for a particular set of observations is 5 since it occurs the majority of the time.
What is mode?The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.
Here,
given set of observation:
5, 7, 8, 5, 7, 6, 9, 5, 10, 6
Mode is the number which occurs the highest time.
So here 5 occurs the highest times(3 times).
So,5 is the mode.
The mode for given set of observation is 5 as it occurs most time.
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