Answer:
y = 48
Step-by-step explanation:
Plug in 7 for x:
y = x² - 1
y = (7)² - 1
Simplify. Remember to follow the order of operations, PEMDAS.
PEMDAS stands for:
Parenthesis
Exponents (& roots)
Multiplication
Division
Addition
Subtraction
~
First, solve the power, then subtract:
y = (7)² - 1
y = (7 * 7) - 1
y = (49) - 1
y = 48
48 is your value for y.
~
Match each of the shaded regions to one of these equalities
The inequalities that match each region are given as follows:
a) x + y ≥ 5. (Option E).
b) y ≤ x + 2. (Option A).
c) y ≥ 4. (Option D).
What are the inequalities that match each region?For item a, we have that values to the right of the line are shaded, meaning that the line is the lower bound of the interval.
The line is decreasing and has an intercept of 5, hence it is given as follows:
y = 5 - x.
As the line is the lower bound of the inequality, the inequality is defined as follows:
y ≥ 5 - x
x + y ≥ 5.
For item b, the line has an intercept of 2, hence it is given as follows:
y = x + 2.
It is an increasing line, and the values to the right of the line are shaded, meaning that the line is the upper bound and the inequality is given as follows:
y ≤ x + 2.
For item c, the lower bound is the horizontal line y = 4, hence the inequality is described as follows:
y ≥ 4.
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How do you find holes and asymptotes?
To find holes, look for places where the function is undefined. To find asymptotes, look for where the function approaches infinity or negative infinity. Additionally, look for places where the function has a vertical or horizontal line, as these are also potential asymptotes.
To find holes in a function, look for places where the function is undefined. This can occur when the denominator of a fraction is equal to zero, as the fraction becomes undefined. Additionally, look for places where the function is not continuous, as this can indicate a hole in the graph. To find asymptotes, look for places where the function approaches infinity or negative infinity. This can occur when the denominator of a fraction is equal to zero and the numerator is not. Additionally, look for places where the function has a vertical or horizontal line, as these can also indicate potential asymptotes. Asymptotes are also present when the degree of the numerator is higher than the degree of the denominator. By looking for these areas, you can identify potential holes and asymptotes in a function.
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The following histogram shows the number of items sold at a grocery store at various prices:
Histogram titled Items Sold with Price Range on the x axis and Number of Items Sold on the y axis. Bar 1 is 0 to 2 dollars and 50 cents and has a height of 2. Bar 2 is 2 dollars and 51 cents to 5 dollars and has a height of 4. Bar 3 is 5 dollars and 1 cent to 7 dollars and 50 cents and has a height of 0. Bar 4 is 7 dollars and 51 cents to 10 dollars and has a height of 1.
Which of the following data sets is represented in the histogram?
{0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}
{2, 4, 0, 1}
{2.50, 2.51, 5.00, 5.01, 7.50, 9.00, 10.00}
{0.50, 2.50, 2.50, 5.00, 5.00, 5.00, 7.51}
Answer:
i think 2.oo or 7.51 not sure
Answer:
the answer to this is a.
Step-by-step explanation:
Is negative 1 a number?
Yes, the expression represented as negative 1 is a number
How to determine the truth value of the statementFrom the question, we have the following parameters that can be used in our computation:
Is negative 1 a number?
As a general rule
Numbers are expressions, words and representations that have an arithmetic value
Using the above as a guide, we have the following:
negative 1
Mathematically, this can be represented as
-1
-1 is an integer
Hence, negative 1 is a number
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what is the slope between (-2,-19) and (-12,11)
Answer:
m = -3
Step-by-step explanation:
The slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y increase by 30 and the x decrease by 10, so the slope is
-30/10 = -3
So, m = -3
Answer:
Slope = -3
Step-by-step explanation:
Formula of slope,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Now the slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (11 -(-19))/(-12 -(-2))
→ m = (11 + 19)/(-12 + 2)
→ m = 30/-10
→ m = -(30/10)
→ [ m = -3 ]
Hence, the slope is -3.
What are examples of SAS?
The examples of SAS (Statistical Analysis System) are Mathematical Programming
Examples of mathematical programming.Mathematical Programming: Conventional Procedures.Network optimization algorithms.Project ManagementWhat is SAS ?SAS is a statistical software suite developed by the SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, criminal investigations, and predictive analytics. It is used for
Access data in almost any format, including SAS spreadsheets, Microsoft Excel spreadsheets, and database files.Manage and manipulate existing data to get the data you need. For example, data can be subdivided and combined with other data to create new columns.Present the results of your analysis in meaningful reports that you can share with others. Created reports can be saved in various formats such as HTML, PDF.Examples of SAS are :
Mathematical Programming.Examples of mathematical programming.Mathematical Programming: Conventional Procedures.Network optimization algorithms.Project Management.Local search optimization.Constraint programming..To learn more about SAS , refer:
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Mortgage Details
Principal
Loan Length
Interest Rate
Monthly Payment
A. $500.00
How much of the first
$150,000
payment for the
30 years mortgage described in
the table will go
towards principal?
4%
$716
C. $343.68
B. $372.32
D. $216.00
Answer:
Step-by-step explanation:
New houses in a neighborhood are selling for $175,000. A down payment of $18,000 is
required and a 25-year mortgage at an annual interest rate of 8% is available. Find the
monthly mortgage payment.
Selling price = 175000
down payment = 18000
interest rate = 8% = 0.08
time = 25 years = 300 months (25 * 12)
First, we will compute the total interest for the loan
I = P * R * T
I = (175000 - 18000)(0.08)(25)
I = (157000)(0.08)(25)
I = 314000
the distribution of prices for home sales in minnesota is skewed to the right with a mean of $290,000 and a standard deviation of $145,000. suppose you take a simple random sample of 100 home sales from this (very large) population. what is the probability that the mean of the sample is above $325,000?
The probability that the mean of the above sample is $325,000 is 0.0079
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Calculation:We know that, distribution of prices skewed to the right with mean $290000. Let this be x.
Random sample of 100 sales so considering 100 as y.
Standard deviation is $145000 let is be w.
SD for $145000 for 100 random sample data is
z = [tex]\frac{w}{\sqrt{y} } }[/tex] = [tex]\frac{145000}{\sqrt{100} }[/tex].
normalcdf(325000,infinity,290000,14500) = 0.0079.
The probability that the mean of the above sample is $325,000 is 0.0079.
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What is an interest group in AP Gov?
Interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.
What are interests groups?Higher Placement The College Board's Advanced Placement Program makes a college-level course and exam in United States Government and Politics available to high school students.
By organizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues, interest groups enable citizen participation in governance.
a group of individuals united by a shared interest or objective and working to sway public policy. group leaders. As adolescents gain knowledge, they frequently form their own groups. government.
Therefore, interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.
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What is inequality examples?
An example of inequality is 3 < 5.
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.
They are denoted by the symbols ≥ < > ≤. An example of inequality is 3 < 5. This simply means that 3 is less than 5.
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mark and kevin own 1/4 and 1/3 of the books on a shelf, respectively lori owns the rest of the books. if kevin owns 9 more books than mark, how many books does lori own ?
The total number of books Lori owns is 45.
To find the total number of booksLet x be the total number of books.
Mark owns 1/4 of x
Kevin own 1/3 of x
Kevin owns 9 more than Mark, so;
1/4x - 1/3x = 9
Multiplying both sides by 12
4x - 3x = 108
x = 108
The total number of books is 108
but;
Mark owns 1/4 of x = 1/4 x 108
Mark = 27
while Kevin owns 1/3 x 108
Kevin = 36
Therefore, Lori would own
108 - 36 - 27 = 45
Lori's number of books will be 45.
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Which expression is the factored form of 2x² 7x 3?
The expression 2x² + 7x + 3 can be factored as (2x + 3)(x + 1).So, the factored form of 2x² + 7x + 3 is (2x + 3)(x + 1).
To factor this expression, we can use the method of grouping. First, we rewrite the expression as:
2x² + 7x + 3
Then, we group the first and last terms and the middle term:
(2x² + 3) + (7x)
Next, we try to factor in the first group. Since 2x² + 3 can be rewritten as (2x + 1)(x + 3), we can factor the entire expression as:
(2x + 1)(x + 3) + (7x)
Finally, we can rearrange the terms to get the factored form:
(2x + 7x) + (1)(3)
This simplifies to:
(2x + 7x)(1) + (3)
Which is equal to:
(2x + 7x + 3)
And finally:
(2x + 7x + 3) = (2x + 3)(x + 1)
So, the factored form of 2x² + 7x + 3 is (2x + 3)(x + 1).
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What is the leading coefficient of the polynomial function if?
Observing the polynomial and the coefficient provided, The leading coefficient of the polynomial function is the coefficient of the highest degree term.
What do you mean by a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by leading coefficient?The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.
polynomial of the form [tex]ax^{2}+bx+c[/tex].
Since, The degree is 2 and the coefficient of [tex]x^{2}[/tex] is a.
The leading coefficient is 'a'.
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Drag and drop the correct answer choice to each answer blank.
Answer:
45n + 60 = 285
Step-by-step explanation:
n=# of weekday classes (this is an unknown value)
45n= each weekday class is 45 mins long, and when you multiply it by "n" which is the number of weekday classes, you will get a total number of minutes.
+60= we add 60 because that is how many mins it takes for the one class on the saturday. there is only one saturday class which means that you dont need a variable attached to it.
=285
this is the total number of mins from last week.
so, the total number of mins from last week has to equal the 60 min class plus however many 45 min classes there are that week.
45n+60=285
and if you really wanted to know how many weekday classes there were that week, n=5
What are the 7 types of hazards in the home?
The 7 types of hazards in the home are Psychosocial Risks,Physical
Dangers , Chemical Dangers, Biological risks, Constrained Areas,
Changing Equipment and Biohazards
Psychosocial Risks
Physical dangers include a subgroup called psychosocial hazards. For some workers, these risks might be more severe or restrictive than for others. Poor management or a lack of feedback may be the cause of these risks.
Physical Dangers
Environmental and occupational hazards are two different categories of physical risks. These include unguarded machines, heat, cold, vibration, noise, and temperature extremes. Engineering controls can lessen some physical dangers.
Chemical Dangers
Toxic, flammable, explosive, self-reactive, oxidizing, or corrosive compounds are considered chemical dangers. Chemical risks can have negative health impacts and need special handling techniques and equipment.
Biological risks
Many workplaces have biological risks, which can be harmful to people. They include waste debris, food, fungi, food, hair, skin, and saliva.
Constrained Areas
Flammable gases can accumulate in small places. These gases tend to gravitate toward lower elevations, yet they can rise to the surface if a lid is closed or if they are hanging in the air.
Changing Equipment
For workers, the moving machinery hazard provides a distinct set of mechanical risks. Injuries caused by it include crushing, shearing, tangling, air being ejected, striking, abrading, and trapping.
Biohazards
There are many danger thresholds for biohazards. Agents of biohazard level I pose little risk to people. On the other hand, biohazard class II agents may be extremely contagious and may result in serious sickness if consumed or dispersed through the air.
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Can someone please help me I’ll mark you as brainlist
A=
B=
Answer:
A = 14
B = 4
Step-by-step explanation:
You want to know the values of A and B consistent with ∆EFG being congruent to ∆HJI, given that EF=14B-15, FG=9A-28, HJ=7B+13, JI=7A.
CongruenceCorresponding sides of congruent triangles have the same measure, so we have ...
FG = JI
9A -28 = 7A
2A = 28 . . . . . . add 28-7A
A = 14 . . . . . divide by 2
and ...
FE = JH
14B -15 = 7B +13
7B = 28 . . . . . . . . add 15-7B
B = 4 . . . . . . divide by 7
The values of A and B are 14 and 4, respectively.
How do you solve a mode step by step?
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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Which of the three theorems below states that: "if two angles and non- included side of the triangle are congruent to the corresponding two angles and non- included side of another triangle,then the triangles are congruent."?
The first of the three theorems below, known as the Angle-Angle-Side Theorem or AAS Theorem, asserts that two angles and a non-included side of a triangle must be congruent with the corresponding two angles and non-included side of another triangle for the triangles to be considered congruent.
What do you mean by congruent?
Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.
Why are triangles congruent?
Two triangles are said to as congruent triangles if their dimensions and shapes match. Two congruent triangles remain congruent even if we flip, rotate, or otherwise alter one of the triangles.
Two triangles must have the same angles and, as a result, must be congruent if their sides are equal.
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Solve the quadratic equation below for the exact values of x.
Answer:
x = ± 2√5
Step-by-step explanation:
4x² - 5 = 75
4x² = 75 + 5
x² = 80 ÷ 4
x² = 20
√x² = ± √20
x = ± 2√5
help asap please!!!!!!!!!!!!!!!!!!!!!
The value of the highlighted angle using the alternate angle theorem is 130°.
What is are alternate angles?Alternate angles are angles obtained on the opposite sides of a transversal line that have the same size.
To calculate the value of the highlighted angle, we use the alternate angles theorem.
Note: Alternate angles are equal, From the diagram,the values of the two included angles are equal
Given:
Highlighted angle = 18x+4............ Equation 119x-3 = 18x+4 (Alternate angle)Solve for x
19x-18x = 4+3x = 7Substitute the value of x into equation 1
Highlighted angle = (18×7)+4Highlighted angle = 130°Hence, the value of the highlighted angle is 130°.
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What is an example of a geometric term?
An example of geometric term is ar².
When a set of numbers follow a particular order, they are said to be in sequence.
A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as
Geometric Sequence = a, ar, ar², ar³, ......, arⁿ⁻¹, arⁿ.
where,
The first term is a.
Every two consecutive terms, r is the common ratio.
The number of terms is n.
Let us take an example.
The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series and 2, 6, 18, 54 are geometric terms.
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PLEASE HELP ASAP
At a local high school, the student population is growing at 12% a year. If the original population was 242 students, how long will it take the population to reach 300 students? Round to the nearest tenth of a year.
A. 0.7 Years
B. 3.2 Years
C. 1.9 Years
Answer:
c is the closest
Step-by-step explanation:
it should take about 2 years
What does ∆ mean in math?
The symbol "≪" means "much less than," and the symbol "≫" means "much greater than."
These symbols are used to express a strong inequality between two values. For example, if you wanted to say that the value of x is much less than the value of y, you could write "x ≪ y." Similarly, if you wanted to say that the value of x is much greater than the value of y, you could write "x ≫ y."
The symbols "≪" and "≫" are used in mathematics to express a strong inequality between two values. They are similar to the familiar inequality symbols ">" (greater than) and "<" (less than), but they indicate a greater degree of inequality.
For example, if you wanted to say that the value of x is much less than the value of y, you could write "x ≪ y." This means that x is much smaller than y, and the difference between the two values is significant. Similarly, if you wanted to say that the value of x is much greater than the value of y, you could write "x ≫ y." This means that x is much larger than y, and the difference between the two values is significant.
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The question is -
What does ≪ mean in math?
What value of x would make these two solids similar? X = 27 x = 30 x = 7.75 x = 31
The value of x is 31 mm, which makes given prisms similar.
What is similarity?Similarity of a triangle is the ratio of their corresponding sides or angles which are equal.
In the given prisms,
The length of the large prism = 29 mm,
And width = x mm.
In small prism, the length = 14.5 mm,
And width = 15.5 mm.
According to given condition,
Both the prisms are similar.
By property of similarity,
The in similar figure, the ratio of corresponding sides are equal.
For the given prisms,
29 / x = 14.5 / 15.5
x = 2 × 15.5
x = 31
The required value of x is 31 mm.
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What is the translation formula?
Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.
Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.
Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.
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How do you prove two triangles are congruent with two congruent sides?
If the two triangles have the two congruent side, then the two triangles are congruent.
The term triangle refers the polygon with three side, three vertices, and three edges.
Here we have to prove that the two triangles are congruent with two congruent sides.
As we know that the term congruent refers if their sides have the same length and angles have same measure.
Based on these theory, and we have to use the another theory called SAS (Side-Angle-Side) tell that any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, if then the two triangles are said to be congruent.
According to this rule, we have clearly identifies that the given two triangles are congruent.
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A cubic polynomial P(x) has real coefficients. If 3 - 2i and are roots of P(x) = 0 , what is one additional root?
A. 3 + 2i
B. -3-2i
C. - 3 + 2i
D. -5/2
The another root for the given polynomial is 3 + 2i.
What is the conjugate of a complex number?A complex number is defined as a number containing both real and imaginary part which is written as x + iy. The conjugate of a complex number can be obtained by changing the sign of the imaginary part of the number. the product of a complex number and its conjugate is the square of its magnitude.
One of the complex roots of a polynomial is given as 3 - 2i.
Since, all the coefficients of the polynomial P(x) are real.
The another root should be the complex conjugate of the given root.
Thus, the other root is given as below,
3 + 2i
Hence, the additional root is given as 3 + 2i.
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How many term of the A. P. 16,14,12,. Are needed to give the um 60? explain why do we get two anwer
The sum of first five or twelve term in the A.P given the value 60.
The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
Here we have given that A. P. 16,14,12,.
And we need to find the number of term to get the value of 60.
While we looking into the given question we have identified that the common difference d of the A.P. is − 2
Here we also know that the terms of the A.P. are in descending order.
Now, we have to take n = 5 then then first 5 terms are 16,14,12,10,8.
Here we have identified that the sum is 60.
Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5
Here we have identified that the sum of these seven terms is 0.
Therefore, sum of first 12 terms is also 60.
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Is a triangle congruent if 1 angle of the triangle is congruent and 2 sides are congruent?
The triangles are congruent if there are two pairs of corresponding angles and one pair of corresponding sides.
What is meant by congruent ?If two shapes are congruent, we can also state that their mirror images are identical. If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence. Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. Create two circles with the same radius, cut them out, and stack them.To learn more about congruent refer to:
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What is the nature of roots of quadratic equation 2x² 4x 3 0 *?
Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary when calculated using discriminant.
Define root.In mathematics, the number that results in the original number when it is multiplied by itself is called the root.
How we can find nature of roots?We can find nature of root using discriminant.
B² - 4AC = 0 ----> Roots are equal ,real & rational
B² - 4AC > 0 , and also a perfect square --> Roots are real , distinct & rational
B² - 4AC >0 ,but not a perfect square -----> Roots are real, distinct & irrational
B² - 4AC <0 , ---> Roots are imaginary
B² - 4AC >= 0 ---> Roots are real
Given 2x² - 4x + 3 = 0
Now, Calculate Discriminant,
Here
B = -4
A = 2
C = 3
==> B² - 4AC
= (-4)² - 4 * 2 * 3
= 16 - 24
= -8 < 0
Discriminant is negative
Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary .
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