What is the total population of the four cities shown in the table? Express your answer in scientific notation and in standard form.
Answers
Scientific notation is a way of writing large or small numbers that have many digits in a simplified form. The index of the base 10 exponents indicates the number of digits there are after the decimal dot.
The table shows the population of 4 cities of Texas, Houston, San Antonio, El Paso, and Corpus Christi.
To determine the total population of all cities you have to add them together, the first step is to express each given population in standard form:
Houston:
[tex]2.3\cdot10^6[/tex]This notation indicates that there are 6 digits after the decimal dot, the first one is 3 and the other five digits are zero. The positive index indicates that this number is greater than 1, so to write the number in the standard form you have to erase the decimal dot:
[tex]2.3\cdot10^6=2300000[/tex]San Antonio:
[tex]1.5\cdot10^6[/tex]The notation indicates that there are 6 digits after the decimal point, the first one is 5 and the other five digits are zero. The positive exponent indicates that this number is greater than 1, so you have to erase the decimal dot:
[tex]1.5\cdot10^6=1500000[/tex]El Paso:
This population is already given in the standard form
[tex]680000[/tex]Corpus Christi:
[tex]3.2\cdot10^5[/tex]This notation indicates that there are 5 digits after the decimal dot, the first one is 5 and the next four are zero. The exponent is positive, so as mentioned before, this number is greater than one, and to write it in the standard form you have to erase the decimal dot:
[tex]3.2\cdot10^5=320000[/tex]Now that all values are expressed in the standard form you can add them:
[tex]2300000+1500000+680000+320000=4800000[/tex]In the standard form, the total population of the four cities is 4,800,000 people
To express this value using scientific notation you have to write the decimal dot after the first digit and then count the number of digits after the decimal dot.
When you use scientific notation you have to write only the digits that are different than zero.
There are 6 digits after the decimal dot, so the exponent of the base 10 number will be 6, and the result expressed in scientific notation is:
[tex]4.8\cdot10^6\text{people}[/tex]
Related Questions
what is 9932.8 rounded to the nearest integer
Answers
ANSWER
9933
EXPLANATION
We have the number 9932.8.
We want to round it to the nearest integer.
An integer is a number that can be written without decimal or fraction.
To do that, we follow the following steps:
1. Identify the number after the decimal
2. If the number is greater than or equal to 5, round up to 1 and add to the number before the decimal.
3. If the number is less than 5, round down to 0.
Since the number after the decimal is 8, we therefore have that:
[tex]9932.8\text{ }\approx\text{ 9933}[/tex]Eduardo's school is selling tickets to a play. On the first day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108. The school took in $114 on the second day by selling 10 adult tickets and 3 child tickets. What is the price each of one adult ticket and one child ticket?
Answers
The price of one adult ticket is $9 and the price of child ticket is $8
First day of ticket sales the school sold 4 adult tickets and 9 child tickets for a total of $108
Consider the price of adult ticket as x and child ticket as y
Then the equation will be
4x+9y = 108
Similarly the school took in $114 on the second day by selling 10 adult tickets and 3 child tickets
10x+3y = 114
Here we have to use the elimination method
Multiply the first equation by 10 and second equation by 4
40x+90y = 1080
40x+12y = 456
Subtract the equation 2 from equation 1
90y-12y = 1080-456
78y = 624
y = 624/78
y = $8
Substitute the value of y in any equation
10x+3y =114
10x+3×8 =114
10x +24 =114
10x = 90
x = 90/10
x = $9
Hence, the price of one adult ticket is $9 and the price of child ticket is $8
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Consider the expression 6+(x+3)^2. Tabulate at least SIX different values of the expression.
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Considering the expression 6+(x+3)^2. the table of at least SIX different values of the expression is
x y
0 15
1 22
2 31
3 42
4 55
5 70
How to determine the he table of at least SIX different values of the expressionThe table is completed by substituting the values of x in the given expression as follows
6 + ( x + 3 )^2
for x = 0, y = 6 + ( 0 + 3) ^2 = 15
for x = 1, y = 6 + ( 1 + 3) ^2 = 22
for x = 2, y = 6 + ( 2 + 3) ^2 = 31
for x = 3, y = 6 + ( 3 + 3) ^2 = 42
for x = 4, y = 6 + ( 4 + 3) ^2 = 55
for x = 5, y = 6 + ( 5 + 3) ^2 = 70
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Solve fory.y = 6O O2y = 5y = 6.67оо3y = 94Previous
Answers
Here the chords are intersecting outside hence
[tex]\begin{gathered} 2\times(2+10)=3\times(3+y) \\ 2\times12=3(3+y) \\ 2\times4=(3+y) \\ 8=3+y \\ y=8-3 \\ y=5 \end{gathered}[/tex]Hence the answer is y=5
Shanice has 4 times as much many pairs of shoes as does her brother Ron. If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does. How many pairs of shoes will Shanice have left after she gives Ron the shoes?
Answers
Let's define:
x: pairs of shoes of Shanice
y: pairs of shoes of Ron
Shanice has 4 times as much many pairs of shoes as does her brother Ron, means:
x = 4y (eq. 1)
If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does, means:
x - 12 = 2y (eq. 2)
Replacing equation 1 into equation 2:
4y - 12 = 2y
4y - 2y = 12
2y = 12
y = 12/2
y = 6
and
x = 4*6 = 24
After she gives Ron the shoes, she will have left 24-12 = 12 pairs of shoes
evaluate B-( - 1/8) + c where b =2 and c=- 7/4
Answers
Answer: 3/8
Step-by-step explanation:
Given:
[tex]B-(-\frac{1}{8} )+c[/tex]
replace variables with their given values: b = 2 and C = 7/4
[tex]2-(-\frac{1}{8})+\frac{-7}{4}[/tex]
to make subtracting and addition easier, make each number has the same common denominator.
[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})[/tex]
Finally, solve equation.
***remember that subtracting a negative is the same as just adding and adding by a negative is the same as simply subtracting.
[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})=\frac{16}{8} +\frac{1}{8}-\frac{14}{8}[/tex]
= 3/8
Answer:
3/8
Step-by-step explanation:
2 - (-1/8) + (-7/4)
= 17/8 - 7/4
= 17/8 + -7/4
= 3/8
Michelle can wash dry and fold 5 loads of laundry in 3 1/2 hours. what is the average amount of time it takes Michelle to do one load of laundry
Answers
on a cold January day , Mavis noticed that the temperature dropped 21 degrees over the course of the day to -9C. Write and solve an equation to determine what the temperature was at the beginning of the day
Answers
Answer:
Step-by-step explanation:
At the beginning of the day, the temperature was of x.
It dropped 21 degrees to -9C. So
x - 21 = -9
x =
Find the average rate of change of the function in the graph shown below between x=−1 and x=1.
Answers
Answer:
Step-by-step explanation:
The last description actually clarifies the given equation. The equation should be written as: f(x) = 2ˣ +1. The x should be in the exponent's place.
The average rate of change, in other words, is the slope of the curve at certain points. In equation, the slope is equal to Δy/Δx. It means that the slope is the change in the y coordinates over the change in the x coordinate. So, we know the denominator to be: 2-0 = 2. To determine the numerator, we substitute x=0 and x=2 to the original equation to obtain their respective y-coordinate pairs.
f(0)= 2⁰+1 = 2
f(2) = 2² + 1 = 5
Allison earned a score of 150 on Exam A that had a mean of 100 and a standard deviation of 25. She is about to take Exam B that has a mean of 200 and a standard deviation of 40. How well must Allison score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
Answers
Allison must score 280 on Exam B to do equivalently well as she did on Exam A
Explanations:Note that:
[tex]\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \text{where }\mu\text{ represents the mean} \\ \sigma\text{ represents the standard deviation} \end{gathered}[/tex][tex]\begin{gathered} \text{For Exam A:} \\ x\text{ = 150} \\ \mu\text{ = 100} \\ \sigma\text{ = 25} \\ z-\text{score = }\frac{150-100}{25} \\ z-\text{score = 2} \end{gathered}[/tex]Since we want Allison to perform similarly in Exam A and Exam B, their z-scores will be the same
Therefore for exam B:
[tex]\begin{gathered} \mu\text{ = 200} \\ \sigma\text{ = 40} \\ z-\text{score = 2} \\ z-\text{score = }\frac{x-\mu}{\sigma} \\ 2\text{ = }\frac{x-200}{40} \\ 2(40)\text{ = x - 200} \\ 80\text{ = x - 200} \\ 80\text{ + 200 = x} \\ x\text{ = 280} \end{gathered}[/tex]Allison must score 280 on Exam B to do equivalently well as she did on Exam A
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Which of the following best represents R= A - B ?
Please help, it’s due soon!
Answers
A.
Step-by-step explanation:This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.
Hence, the answer that better represent the resulting vector is answer A.
A.
Step-by-step explanation:This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.
Hence, the answer that better represent the resulting vector is answer A.
Data Set A has a Choose... interquartile range than Data Set B. This means that the values in Data Set A tend to be Choose... the median.
Answers
The median of the given data set will be 35.
What do we mean by media?In statistics and probability theory, the median is the number that separates the upper and lower half of a population, a probability distribution, or a sample of data. For a data set, it might be referred to as "the middle" value.
So, The variability metrics for each class are listed below:
The further classifications: Class A; Class B;
Range: 30 Range: 30IQR: 12.5 IQR: 20.5MAD: 7.2 MAD: 9.2Greater variability in the data set is suggested by class B's wider interquartile range and mean absolute deviations.
Set A's median will be:
median = (20 + 32+ 36+ 37 + 50) / 5median = 175 / 5median = 35Therefore, the median of the given data set will be 35.
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Mark the drawing to show the given information and complete each congruence statement.∆acd=∆_____by______
Answers
the triangle is ACD is equal to the triangle CBE so let write all the information we have in the figure so:
And for oposit angles we know that then angle BCE = to the angle ACD, so we have two angles and ine side equal so the triangles are similar
by: ASA
Is (x + 3) a factor of 7x4 + 25x³ + 13x² - 2x - 23?
Answers
According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.
What is the remainder and factor theorem's formula?When p(x) is divided by xc, the result is p if p(x) is a polynomial of degree 1 or higher and c is a real number (c). For some polynomial q, p(x)=(xc)q(x) if xc is a factor of polynomial p. The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has a specific instance in this situation. According to the factor theorem, f(x) has a factor if and only if f=0.The remainder will be 0 if the polynomial (x h) is a factor. In contrast, (x h) is a factor if the remainder is zero.The factor theorem is mostly used to factor polynomials and determine their n roots. Factoring is helpful in real life for comparing costs, splitting any amount into equal parts, exchanging money, and comprehending time.To learn more about Factor theorem refer to:
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I really need help on this and I would really appreciate if anyone would want to help me please and thank you.
Answers
Given the equation of the parabola:
[tex]y=x^2+6x-12[/tex]To find the vertex of the parabola,
we will substitute with the value (-b/2a) into the function y
[tex]\begin{gathered} a=1 \\ b=6 \\ c=-12 \\ \\ x=-\frac{b}{2a}=-\frac{6}{2\cdot1}=-3 \\ y=(-3)^2+6\cdot-3-12=9-18-12=-21 \end{gathered}[/tex]so, the coordiantes of the vertex :
x = -3
y = -21
Joan uses the function C(x) = 0.11x + 12 to calculate her monthly cost for electricity.• C(x) is the total cost (in dollars).• x is the amount of electricity used (in kilowatt-hours).Which of these statements are true? Select the three that apply.A. Joan's fixed monthly cost for electricity use is $0.11.B. The cost of electricity use increases $0.11 each month.C. If Joan uses no electricity, her total cost for the month is $12.D. Joan pays $12 for every kilowatt-hour of electricity that she uses.E. The initial value represents the maximum cost per month for electricity.F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Answers
Answer:
The correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Step-by-step explanation:
Notice that the given function is the equation of a line in the slope-intercept form:
[tex]C(x)=0.11x+12[/tex]From this interpretation, we'll have that the correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Need help with this review question. I need to know how to find the measurements from the cyclic quadrilateral
Answers
Given a quadrilateral ABCD
A cyclic quadrilateral has all its vertices on the circumference of the circle
Also cyclic quadrilateral
has the opposites angles add up to 180°
then
[tex]\angle a+\angle c=180[/tex][tex]\angle b+\angle d=180[/tex]then
Option A
A=90
B=90
C=90
D=90
since A+C= 180
and B+D = 180
measures from Option A could come from a cyclic quadrilateral
Option B
A=80
B=80
C=100
D=100
Since A+C = 80+100 = 180
and B+D = 80 + 100 = 180
measures from Option B could come from a cyclic quadrilateral
Option C
A=70
B=110
C=70
D=110
Since A+C=70+70 = 140
And B+D =110+110=220
measures from Option C could NOT come from a cyclic quadrilateral
Option D
A=60
B=50
C=120
D=130
A+C= 60+120 = 180
B+D= 50+130 = 180
measures from Option D could come from a cyclic quadrilateral
Option E
A=50
B=40
C=120
D=150
A+C=50+120= 170
B+D=40+150 = 190
measures from Option E could NOT come from a cyclic quadrilateral
Then correct options are
Options
A,B and D
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive? 0.475 0.038 0.525 0.905
Answers
ANSWER:
0.475
STEP-BY-STEP EXPLANATION:
The probability of a person has disease given the test is positive:
P (disease) = 3.8% = 0.038
P (positive | disease) = 93.9% = 0.939
P (positive | no disease) = 4.1% = 0.041
P (no disease) = 100% - 3.8% = 96.2% = 0.962
The probability that the person has the disease given that the test result is positive is calculated as follows:
[tex]\begin{gathered} \text{ P\lparen infected \mid test positive\rparen }=\frac{\text{ P\lparen positive \mid infected\rparen }\times\text{ \rbrack P \lparen infected\rparen}}{\text{ P \lparen positive\rparen}} \\ \\ \text{ P \lparen positive \mid infected\rparen }=\text{ P \lparen positive \mid disease\rparen = 0.939} \\ \\ \text{ P \lparen infected\rparen = P \lparen disease\rparen = 0.038} \\ \\ \text{ P \lparen positive\rparen = P \lparen positive \mid infected\rparen }\times\text{ P \lparen infected\rparen }+\text{ P \lparen positive \mid no infected\rparen}\times\text{ P \lparen no infected\rparen } \\ \\ \text{ P \lparen positive \mid infected\rparen =P \lparen positive \mid no disease\rparen = 0.041} \\ \\ \text{ P \lparen no infected\rparen = P \lparen no disease\rparen = 0.962} \\ \\ \text{ We replacing:} \\ \\ \text{ P \lparen positive\rparen = }0.038\cdot0.939+0.041\cdot0.962=0.075124 \\ \\ \text{ P\lparen infected \mid test positive\rparen }=\frac{0.038\cdot0.939}{0.075124} \\ \\ \text{ P\lparen infected \mid test positive\rparen = }\:0.47497=0.475 \end{gathered}[/tex]The correct answer is the first option: 0.475
which function is best represented by this graphA) f(x) = x² - 3x + 8B) f(x) = x² - 3x - 8C) f(x) = x² + 6x + 8D) f(x) = x² + 6x - 8
Answers
Solution:
Given the graph;
The axis of symmetry and vertex of the graph are;
[tex]\begin{gathered} x=-3 \\ (-3,-1) \end{gathered}[/tex]Also, the x-intercepts are;
[tex](-4,0),(-2,0)[/tex]And the y-intercep is;
[tex](0,8)[/tex]Thus, the function that best represents the graph is;
[tex]f(x)=x^2+6x+8[/tex]CORRECT OPTION: C
The System of PolynomialsYou are aware of the different types of numbers: natural numbers, integers, rational numbers, and real numbers. Now you will work with a property of the number system called the closure property. A set of numbers is closed for a specific mathematical operation if you can perform the operation on any two elements in the set and always get a result that is an element of the set.Consider the set of natural numbers. When you add two natural numbers, you will always get a natural number. For example, 3 + 4 = 7. So, the set of natural numbers is said to be closed under the operation of addition.Similarly, adding two integers or two rational numbers or two real numbers always produces an integer, or rational number, or a real number, respectively. So, all the systems of numbers are closed under the operation of addition.Think of polynomials as a system. For each of the following operations, determine whether the system is closed under the operation. In each case, explain why it is closed or provide an example showing that it isn’t.1)AdditionType your response here:2)SubtractionType your response here:3)MultiplicationType your response here:4)DivisionType your response here:5)Determine whether the systems of natural numbers, integers, rational numbers, irrational numbers, and real numbers are closed or not closed for addition, subtraction, multiplication, and division.Type your response here: 6)Addition Subtraction Multiplication Division natural numbers integers rational numbers irrational numbers real numbers When a rational and an irrational number are added, is the sum rational or irrational? Explain.Type your response here:7)When a nonzero rational and an irrational number are multiplied, is the product rational or irrational? Explain.Type your response here:8)Which system of numbers is most similar to the system of polynomials?Type your response here:9)For each of the operations—addition, subtraction, multiplication, and division—determine whether the set of polynomials of order 0 or 1 is closed or not closed. Consider any two polynomials of degree 0 or 1.Type your response here:10)Polynomial 1 Polynomial 2 Operation Expression Result Degree of Resultant Polynomial Conclusion addition subtraction multiplication division What operations would the set of quadratics be closed under? For each operation, explain why it is closed or provide an example showing that it isn’t.Type your response here:11)Is there a set of expressions that would be closed under all four operations? Explain.Type your response here:
Answers
The Solution To Question Number 10:
The question says what operations would the set of quadratics be closed under.
Let the sets of quadratics be
[tex]\begin{gathered} p(x)=ax^2+bx+c \\ q(x)=mx^2+nx+k \end{gathered}[/tex]The set of two quadratics (polynomials) is closed under Addition.
Explanation:
[tex]\begin{gathered} P(x)+q(x)=(ax^2+bx+c)+(mx^2+nx+k) \\ =(a+m)x^2+(b+n)x+(c+k) \\ \text{which is still a quadratic.} \\ \text{Hence, the set of quadratics is closed under Addition.} \end{gathered}[/tex]The set of two quadratics is closed under Subtraction.
[tex]\begin{gathered} P(x)-q(x)=(ax^2+bx+c)-(mx^2+nx+k) \\ =(a-m)x^2+(b-n)x+(c-k) \\ \text{which is still a quadratic, provided both a}\ne m,\text{ b}\ne n\text{ } \\ \text{Hence, the set of quadratics is closed under Subtraction.} \end{gathered}[/tex]The set of quadratics is not closed under Multiplication.
[tex]\begin{gathered} P(x)\text{.q(x)}=(ax^2+bx+c)(mx^2+nx+k)=amx^4+(bn+ak)x^2+ck+\cdots \\ \text{Which is not a quadratic.} \\ \text{Hence, the set of quadratics is not closed under multiplication.} \end{gathered}[/tex]The set of quadratics is not closed under Division.
[tex]\begin{gathered} \text{Let the sets be f(x)=8x}^2\text{ and} \\ h(x)=2x^2-1 \\ \text{ So,} \\ \frac{f(x)}{h(x)}=\frac{8x^2}{2x^2_{}-1} \\ \text{Which is not a quadratic.} \\ \text{Hence, the set is not closed under Division.} \end{gathered}[/tex]
If 10 = 1+4, then 1+9= 10substitution property symmetric property transitive propertyreflexive property8*1=8Multiplicative InverseMultiplicative IdentityMultiplicative Property of ZeroAdditive Identity Property
Answers
Reflexive Property
In Math, especially in geometry, but also in other fiels.
What we have here is the Reflexive Property, that states that
If a= b+c then b+c=a
Multiplicative Identity
The multiplicative identity is the number 1, so every number times 1 is equal to itself and this property is called multiplicative identity.
In one study, it was found that the correlation between two variables is -.16 What statement is true? There is a weak positive association between the variables. There is a weak negative association between the variables. There is a strong positive association between the variables. There is a strong negative association between the variables.
Answers
The correlation could be positive, meaning both variables move in the same direction,
If it is negative, meaning that when one variable's value increases, the other variables' values decrease.
Since the correlation between the 2 variables is -16
Since -16 is a negative value
Then The answer should be
There is a weak negative association between variables
The strong negative correlation should be between 0 and -1
What is the smallest degree of rotation that will map a regular 96-gon onto itself? ___ degrees
Answers
The smallest degree of rotation is achieved through the division of the full circumference over the total number of sides
[tex]\frac{360\text{ \degree}}{96}=3.75\text{ \degree}[/tex]The answer would be 3.75°
Irene is 54 ⅚ inches tall. Theresa is 1 ⅓ inches taller than Irene and Jane is 1 ¼ inches taller than Theresa How tall is Jane
Answers
Let be "n" Irene's height (in inches), "t" Theresa's height (in inches) and "j" Jane's height (in inches).
You know Irene's height:
[tex]n=54\frac{5}{6}[/tex]You can write the Mixed number as an Improper fraction as following:
- Multiply the Whole number by the denominator.
- Add the product to the numerator.
- Use the same denominator.
Then:
[tex]\begin{gathered} n=\frac{(54)(6)+5}{6}=\frac{324+5}{6}=\frac{329}{6} \\ \end{gathered}[/tex]Now convert the other Mixed numbers to Improper fractions:
[tex]\begin{gathered} 1\frac{1}{3}=\frac{(1)(3)+1}{3}=\frac{4}{3} \\ \\ 1\frac{1}{4}=\frac{(1)(4)+1}{4}=\frac{5}{4} \end{gathered}[/tex]Based on the information given in the exercise, you can set up the following equation that represents Theresa's height:
[tex]t=\frac{329}{6}+\frac{4}{3}[/tex]Adding the fractions, you get:
[tex]t=\frac{337}{6}[/tex]Now you can set up this equation for Jane's height:
[tex]undefined[/tex]Solve the inequality 3.5 >b + 1.8. Then graph the solution.
Answers
Collect like terms
[tex]\begin{gathered} 3.5-1.8\ge b \\ 1.7\ge b \\ b\leq\text{ 1.7} \end{gathered}[/tex]An excursion boat traveled from the Ferry Dock to Shelter Cove. How many miles did ittravel?
Answers
The situation forms a right triangle:
Where x is the distance traveled.
We can apply the Pythagorean theorem:
c^2 =a^2 + b^2
Where:
c= hypotenuse = x
a & b= the other 2 sides = 5 ,12
Replacing:
x^2 = 5^2 + 12^2
x^2 = 25+144
x^2 = 169
x= √169
x= 13
Distance traveled = 13 miles
find the perimeter of the triangle whose vertices are (-10,-3), (2,-3), and (2,2). write the exact answer. do not round.
Answers
We have to calculate the perimeter of a triangle of which we know the vertices.
The perimeter is the sum of the length of the three sides, which can be calculated as the distance between the vertices.
The vertices are V1=(-10,-3), V2=(2,-3), and V3=(2,2).
We then calculate the distance between each of the vertices.
We start with V1 and V2:
[tex]\begin{gathered} d_{12}=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ d_{12}=\sqrt[]{(-3-(-3))^2+(2-(-10)^2} \\ d_{12}=\sqrt[]{(-3+3)^2+(2+10)^2} \\ d_{12}=\sqrt[]{0^2+12^2} \\ d_{12}=12 \end{gathered}[/tex]We know calculate the distance between V1 and V3:
[tex]\begin{gathered} d_{13}=\sqrt[]{(y_3-y_1)^2+(x_3-x_1)^2} \\ d_{13}=\sqrt[]{(2-(-3))^2+(2-(-10))^2} \\ d_{13}=\sqrt[]{5^2+12^2} \\ d_{13}=\sqrt[]{25+144} \\ d_{13}=\sqrt[]{169} \\ d_{13}=13 \end{gathered}[/tex]Finally, we calculate the distance between V1 and V3:
[tex]\begin{gathered} d_{23}=\sqrt[]{(y_3-y_2)^2+(x_3-x_2)^2} \\ d_{23}=\sqrt[]{(2-(-3))^2+(2-2)^2} \\ d_{23}=\sqrt[]{5^2+0^2} \\ d_{23}=5 \end{gathered}[/tex]Then, the perimeter can be calcualted as:
[tex]\begin{gathered} P=d_{12}+d_{13}+d_{23} \\ P=12+13+5 \\ P=30 \end{gathered}[/tex]Answer: the perimeter is 30 units.
Glenda borrowed $4,500 at a simple interest rate of 7% for 3 years to
buy a car. How much simple interest did Glenda pay?
Answers
Answer: I = $ 1,102.50
Step-by-step explanation: First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year,
then, solving our equation
I = 4500 × 0.07 × 3.5 = 1102.5
I = $ 1,102.50
The simple interest accumulated
on a principal of $ 4,500.00
at a rate of 7% per year
for 3.5 years is $ 1,102.50.
I need help with this practice problem solving It is trigonometry I will send another picture with the graph that is included in the problem, it asks to use the graph to solve
Answers
Given the function
[tex]f(x)=\sin (\pi x+\frac{\pi}{2})[/tex]The graph of the function is as shown below:
Given A(-9, -12), B(-2, 2), C(x, 6).and D(-5, -2), find the value ofx so that AB || CD
Answers
1) Given these line segments, let's find the slope of them. Let's begin with AB
[tex]m=\frac{2-(-12)}{-2-(-9)}=\frac{14}{-2+9}=\frac{14}{7}=2[/tex]2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:
[tex]\begin{gathered} 2=\frac{-2-6}{-5-x} \\ 2=\frac{-8}{-5-x} \\ 2(-5-x)=-8 \\ -10-2x=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-1 \end{gathered}[/tex]Thus, x=-1