Solution:
To figure out if a triangle with sides that measure 3 inches, 4 inches, and 5 inches, is a right triangle, we use the Pythagorean theorem.
According to the Pythagorean theorem, the square of the longest side of the triangle (hypotenuse) is equal to the sum of the squares of the other two sides (adjacent and opposite) of a right-triangle.
This implies that
[tex](hypotenuse)^2=(adjacent)^2+(opposite)^2[/tex]In this case, the longest side is 5 inches.
[tex]hypotenuse=5[/tex]Thus,
[tex]\begin{gathered} (hypotenuse)^2=3^2+4^2 \\ =9+16 \\ =25 \\ \end{gathered}[/tex]Since the sum of the squares of the two sides (adjacent and opposite) is exactly equal to the hypotenuse, we can conclude that the triangle is a right triangle.
Find the modulo class to which the number belongs for the indicated modulo system.14, modulo 2
Given:
Given the number 14.
Required: Modulo class where 14 belogs
Explanation:
For the case of mod 2, there are 2 modulo classes, from 0 to 1, equivalent to the remainder when a number 'n' is divided by 2.
14 is divisible by 2. So, the remainder of 14 divided by 2 gives 0. Hence 14 belongs to the modulo class [0].
Final Answer: 14 belongs to the modulo class of 0.
The following sets of data show the high temperatures in four different cities for a week in December
the data that have the greatest spread are
(3, 12, 25, 34, 51)
Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What is P(A and B)?
Given:
Events A and B are independent.
P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Required:
P(A and B).
Answer:
We have given that P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Then P(B)=
[tex]\begin{gathered} P(B)=1-P(not\text{ B}) \\ P(B)=1-\frac{2}{3}=\frac{1}{3} \end{gathered}[/tex]Hence, P(A and B)=
[tex]P(A)\cdot P(B)=\frac{3}{5}\times\frac{1}{3}=\frac{1}{5}[/tex]Final Answer:
P(A and B)=
[tex]\frac{1}{5}[/tex]You survey 100 people in your school and ask them if they feel your school has adequate parking.
Only 30% of the sample feels the school has enough parking. If you have 728 students total in your school, how many would you expect out of all the student body that felt there was enough parking?
Answer:
218 students feel there is enough parking.
Step-by-step explanation:
First, we convert 30% into a decimal by moving the decimal point over twice to get 0.30. Then, we set up this equation:
0.30 x 728 = 218.4
Now, you can't have a fraction of a person, so we round to the nearest whole number to get 218 students.
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Ab and CD are opposite sides so ab are congruent to CD 2a=34 a=17 find the value of each variable
Two segments of lines or two angles are congruent if the have the same length and the same measure, respectively. In a parallelogram, a geometric figure which opposite sides are parallel, opposite sides are congruent and opposite angles are also congruents.
In this case CD is opposite to AB, so they are congruent and have the same length. Since the segment AB measures 2a and the segment CD mesures 34, then we have the equation
[tex]\begin{gathered} 2a=34 \\ a=\frac{34}{2} \\ a=17. \end{gathered}[/tex]Similarly, the angles A and C are congruent since they are opposite, so their measurement is the same. Since the angle A measures 8b and the angle C measures 112, then we have the next equation
[tex]\begin{gathered} 8b=112 \\ b=\frac{112}{8} \\ b=14 \end{gathered}[/tex]
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is y=-0.2x + 1. Graph the equation and use it to answer questions 1 and 2. a. What is the x-intercept? What does it represent? b. What is the y-intercept? What does it represent?c. After how many hours is the battery power at 75%d. what is the percentage of battery power remaining at 3 hours?
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is given by
[tex]y=-0.2x+1[/tex]Let us graph the above equation
a. What is the x-intercept? What does it represent?
The x-intercept is the point where the line intersects the x-axis.
From the graph, we can see that the x-intercept is (5, 0)
The x-intercept represents that it takes 5 hours for the battery power to go to 0%
You can manually find out the x-intercept by substituting y = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ 0=-0.2x+1 \\ 0.2x=1 \\ x=\frac{1}{0.2} \\ x=5 \end{gathered}[/tex]Therefore, the x-intercept is (5, 0)
b. What is the y-intercept? What does it represent?
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the y-intercept is (0, 1)
The y-intercept represents that the battery power is 1 (100%) when x = 0 hours.
You can manually find out the y-intercept by substituting x = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(0)+1 \\ y=1 \end{gathered}[/tex]Therefore, the y-intercept is (0, 1)
c. After how many hours is the battery power at 75%
We need to substitute y = 0.75 (that means 75%) into the equation to find out x (number of hours)
[tex]\begin{gathered} y=-0.2x+1 \\ 0.75=-0.2x+1 \\ 0.75+0.2x=1 \\ 0.2x=1-0.75 \\ 0.2x=0.25 \\ x=\frac{0.25}{0.2} \\ x=1.25\: \text{hours} \end{gathered}[/tex]Therefore, after 1.25 hours, the battery power is at 75%
d. what is the percentage of battery power remaining at 3 hours?
We need to substitute x = 3 hours into the equation to find out y (remaining battery power)
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(3)+1 \\ y=-0.6+1 \\ y=0.4 \end{gathered}[/tex]Therefore, the remaining battery power is 40% after 3 hours.
What is the approximate area of the circle? Use 3.141 for pi and do not round your answer.
The radius of the circle is 2 units and the value of pi is 3.141.
Hence the area of the circle is given by:
[tex]\begin{gathered} A=\pi\times r^2 \\ A=3.141\times2^2 \\ A=12.564 \end{gathered}[/tex]Hence the area is 12.564 square units.
2m + 7 =9 solution please
COMPARING METHODS Consider the equation x+ 2 = 3x – 4.a. Solve the equation using algebra.
Answer: 2
We are given the equation
x + 2 = 3x - 4
To solve for x.
Firstly, we need to collect the like terms
x - 3x = -4 - 2
-2x = -6
Divide both sides by -2
-2x/-2 = -6/-2
x = -6/-2
Negative sign will cancel negative sign
x = 6/2
x = 2
The answer is 2
suppose that R(x) is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros. Answer the following.Edit: if its ok please double-check the answers.
According to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
It is given to us that -
R(x) is a polynomial of degree 12 whose coefficients are real numbers.
The zeroes of R(x) are -
-6, -2+3i, -2-3i, 5+i
We have to find out -
(a) Another zero of R(x)
(b) The maximum number of real zeroes that R(x) can have
(c) The maximum number of non-real zeroes that R(x) can have
Since R(x) is a polynomial of degree 12, there are in total 12 roots.
(a) If a non-real, complex, root 5+i exists, then so it's conjugate 5-i exists which is another zero of R(x).
(b) Now, the total number of zeroes of R(x) can be stated as -
-6, -2+3i, -2-3i, 5+i, 5-i
From the above list of zeroes, we can see that there are at least 4 non-real zeroes. So, R(x) has a total of 12 zeroes and we know that there are at least 4 non-real zeroes.
Thus, we can say that the maximum number of real zeroes that R(x) can have is 12-4 = 8 real zeroes.
(c) The non-real complex zeroes always exist in conjugate pairs. And the total number of zeroes that R(x) can have is 12. And we already have determined that R(x) can have a maximum of 8 real zeroes.
Thus, the maximum number of non-real zeroes that R(x) can have is 12-8 = 4 non-real zeroes.
Therefore, according to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
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Which expression represents the relationship between the step number n and the total number of small squares in the pattern? A Step 1 Step 2 Step 3 n²-n n2-1 n²+n n²+1
We can see in the sequence is :
[tex]0,3,8[/tex]That is a squar of side 1 minus one square so the solution will be:
[tex]n^2-1[/tex]and we can replace the first 3 steps to be sure of the answe so:
[tex]\begin{gathered} 1\to1^2-1=0 \\ 2\to2^2-1=3 \\ 3\to3^2-1=8 \end{gathered}[/tex]Solve the inequality. −2x+3>x−18 Enter the exact answer in interval notation.
Step 1
Given;
[tex]-2x+3>x-18[/tex]Required; To solve the inequality
Step 2
Bring like terms together
[tex]-2x-x>-18-3[/tex]Step 3
Simplify
[tex]-3x>-21[/tex]Step 4
Multiply both sides by -1
[tex]-3x(-1)<-21(-1)_{}[/tex]Step 5
Simplify
[tex]3x<21[/tex]Step 6
Divide by 3 and get the answer
[tex]\begin{gathered} \frac{3x}{3}<\frac{21}{3} \\ x<7 \\ In\text{ in}terval\text{ notation;} \\ (-\infty,7) \end{gathered}[/tex]Hence, the exact answer in interval notation is;
(-∞,7)
Line k has an equation of y = x + - 2/7. Line L includes the point (7,-2) and is perpendicular to
line k. What is the equation of line L? Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = -x+5
Step-by-step explanation:
y-(-2) = -1(x-7)
y+2 = -x + 7
y = -x + 7-2
y = -x + 5
calculate the female's BMI. Round your answer to one decimal place.
For the 17 year old female with:
Weight: 145 lbs
Height: 5'4''→64 inches
[tex]BMI=\frac{703w}{h^2}[/tex]w= weight (pounds)
h= height (inches)
Replace the given values in the formula to determine the girl's BMI
[tex]\text{BMI}=\frac{703\cdot145}{(64)^2}=24.89[/tex]The girl's BMI is 24.89
A helthy weight is considered to be w
If A= { 1,2,4,5,7,9} and B= {2,3,4} and U = {1,2,3,4,5,6,7,8,9} Find A’
SOLUTION
Given the sets in the question tab, the following are the solution steps to get the answer
Step 1: Write the given sets
[tex]\begin{gathered} A=\mleft\lbrace1,2,4,5,7,9\mright\rbrace \\ B=(2,3,4\} \\ U=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace \end{gathered}[/tex]Step 2: Find A'
A' denotes the complement of set A. The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. The Universal set is denoted by capital letter U.
Hence, the elements in set A' will be the elements present in the set U but not set A
[tex]A^{\prime}=\mleft\lbrace3,6,8\mright\rbrace[/tex]Evaluate the expression 25 – 14 +3.
ANSWER
14
EXPLANATION
We want to evaluate the expression given:
25 - 14 + 3
First, let us evaluate the subtraction (25 - 14). We are left with:
11 + 3
Now, evaluate:
14
That is the answer
use the function g=f+4 to find the value of g when f=1use the function u=10c to find the value of u when c=5how about this one use the function u=n-5 to find the value of u when n=7this one use the function h=g+13 to find the value of h when g =1use the function w=14f to find the value of w when f =4
Given function g=f+4
To find the value of g at f=1
substitute f=1 in the given equation
[tex]\begin{gathered} g=f+4 \\ g=1+4 \\ g=5 \end{gathered}[/tex]So, at f=1, the value of g will be 5.
(b).
At u=10c
to find the value of u at c=5
substitute the value c=5 in the given equation
[tex]\begin{gathered} u=10c \\ u=10\times5 \\ u=50 \end{gathered}[/tex]The value of u at c=5 is 50
(c).
Given function u=n-5
to find the value of u at n=7
substitute the value of n=7 in the given equation
[tex]\begin{gathered} u=n-5 \\ u=7-5 \\ u=2 \end{gathered}[/tex]So the value of u at n=7 is 2
(d).
Given function h=g+13
to find the value of h at g=1
substitute the value g=1 in the given equation
[tex]\begin{gathered} h=g+13 \\ h=1+13 \\ h=14 \end{gathered}[/tex]The value of h at g=1 is 14
(e).
Given function w=14f
to find the value of w at f=4
substitute the value f=4 in the given equation
[tex]\begin{gathered} w=14f \\ w=14\times4 \\ w=56 \end{gathered}[/tex]The value of w at f=4 is 56
the sum of z and 24 is equal to 116
Given that the sum of z and 24 equals 116, we can represent this statement as follows
We can then proceed to solve the equation by following the steps below:
[tex]z+24=116[/tex]Step 1: subtract 24 from both sides
[tex]z+24-24=116-24[/tex]Step 2: simplify the expression
[tex]z=92[/tex]Thus the value of Z = 92
Derive the following functionsa) (2x+1)⁴b) f(x) = [tex] \sqrt{6x + 3} [/tex]
Given:
18.
[tex]f(x)=\sqrt[]{6x-3}[/tex]To find the derivative of the given function, we apply chain rule first:
Therefore, the answer is :
[tex]\frac{3}{\sqrt[]{6x-3}}[/tex]Hello, I need some assistance with this homework question please for precalculusHW 23
ANSWER
slope = 1
EXPLANATION
Given:
Points (1, 2) and (8, 9).
Desired Outcome:
Slope of the line
Applying the slope formula
[tex]slope\text{ = }\frac{y_2\text{ - y}_1}{x_2\text{ - x}_1}[/tex]where:
y2 = 9,
y1 = 2
x2 = 8 and
x1 = 1
Substituting the values
[tex]\begin{gathered} slope\text{ = }\frac{9\text{ - 2}}{8\text{ - 1}} \\ slope\text{ = }\frac{7}{7} \\ slope\text{ = 1} \end{gathered}[/tex]Hence, the slope of the line containing the points (1, 2) and (8, 9) is 1.
Please ensure that you provide the important points (the x and y - intercepts, and the vertices),and please clearly label them on the Cartesian coordinate system. [15 points]
Given the piece-wise function
[tex]k(x)=\begin{cases}|x|,x\ge3 \\ \\ 2x^2-4x+3,x<3\end{cases}[/tex]The graph of
[tex]|x|\text{ for x }\ge3[/tex]Is shown below
The graph of
[tex]2x^2-4x+3\text{ for x < 3}[/tex]Is shown below
The graph of the piece-wise function is shown below
The blue curve represents the quadratic function and the red line represent the absolute function
at what price should an office equipment sales representative sell computers purchased at the cost of 19,985 and of the mark on rate is 35%?
To determine the selling price we need to add %35 to the purchased prise; that is:
[tex]19985+0.35(19985)=26979.75[/tex]Therefore the seling price should be $26,979.75
y=8x+3 ordered pairs
Answer: (1, 11) and (-1, -5), OPTION C
We are given the equation
y = 8x + 3
This implies that the value of y is a function of x
Firstly, we need to test the options
For (1, 11)
From the point given, let x = 1 and y = 11
Substitute the value of x and y in the above equation
Since, y = 8x + 3
11 = 8(1) + 3
11 = 8 + 3
11 = 11
This implies that (1, 11) satisfied the equation y = 8x + 3
For (-1, -5)
Let x = -1 and y = -5
-5 = 8(-1) + 3
-5 = -8 + 3
-5 = -5
The point (-1, -5) satisfies the equation y = 8x + 3
Hence, the answer is (1, 11) and (-1, -5)
Add (c + 3) + ( + 6) Add and Subtract polynomials
The given polynomial expression is
(c + 3) + (c + 6)
By opening the brackets, we have
c + 3 + c + 6
By collecting like terms, we have
c + c + 3 + 6
2c + 9
The final answer is 2c + 9
Some the quadratic equation by completing the square.x^2+4x-11=0First choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution separate them with commas.
By completing the square, we have:
[tex]\begin{gathered} x^2+4x=11 \\ x^2+4x+2^2=11+2^2 \\ (x+2)^2=11+4 \\ (x+2)^2=15 \end{gathered}[/tex]Take the square root of both sides
[tex]\begin{gathered} (x+2)=\pm\sqrt[]{15} \\ x=+\sqrt[]{15}-2\text{ OR x= -}\sqrt[]{15}-2 \\ x=3.8729-2\text{ OR -3.8729-2} \\ x=1.873\text{ OR -5.873} \end{gathered}[/tex]Find the equation for the line that passes through the point (-4,-3) and that is perpendicular to the line with the equation y=3/4x-1
Given,
The coordinate that lie on the line is (-4, -3).
The equation of line is y = 3/4x-1.
The standard equation of line is,
[tex]y=mx+c[/tex]Here, m is the slope of the line.
On comparing, the slope of the line y = 3/4x-1 with the standard equation of line then m = 3/4.
The relation of two perpendicular line is,
[tex]\begin{gathered} m_1\times m_2=-1_{} \\ \frac{3}{4}\times m_2=-1 \\ m_2=\frac{-4}{3} \end{gathered}[/tex]The equation of line passing through the point (-4,-3) and perpendicular to line y = 3/4x-1 is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=\frac{-4}{3}(x-(-4)) \\ y+3=\frac{-4}{3}(x+4) \\ 3y+9=-4x-16 \\ 3y=-4x-25 \\ y=\frac{-4x-25}{3} \end{gathered}[/tex]Hence, the equation of line perpendicular to y = 3/4x-1 is y = (-4x-25)/3.
Enter an equation in point-slope form for the line.Slope is -8 and (1,4) is on the line.The equation of the line in point slope form is:
y - 4 = -8 ( x - 1)
Explanations:The point slope form of the equation of a line is given as:
y - y₁ = m (x - x₁)
Where m represents the slope of the line
(x₁, y₁) are the coordinates of the point
Slope is -8 and (1,4) is on the line
m = -8
x₁ = 1
y₁ = 4
Substituting these into the equation:
y - y₁ = m (x - x₁)
y - 4 = -8 ( x - 1)
draw out the system on the bottom of the graph and chose what postulate proves the triangle is congruent hlsssaassasasa
The given postulates are:
hl: Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
sss: Two triangles have the corresponding three sides congruent (3 corresponding sides have the same measure)
aas: Two angles and a side not between those angles are congruent.
sas:Two sides and an angle between those sides are congruent.
asa: Two angles and a side between those angles are congruent.
---------------------
In the system you have two triangles that share side AC. Then one side is congrent in the triangles.
The line AC bisects angles BAD and BCD, it means taht the angle is equal up and down that line.
Then, the system has two angles and the side between those angles congruent. Triangles are congruent by asa18 in3.4.35 km5.6.15.6 amy7 mm7.8.58 yd10.2 m78-* 306.3: 243.47: 144:: 497: 8171 267*: 8417
We need to calculate the area of the circle
[tex]\begin{gathered} \text{Area of circle =}\pi r^2 \\ \text{radius of circle = 29ft,} \\ Area\text{ of circle = }\pi\text{ }\times(29ft)^2 \\ \text{Area of circle = }\pi\text{ }\times841ft^2 \\ \text{Area of circle = 84}1\pi ft^2 \end{gathered}[/tex]Therefore
The area of the circle is 841 square feet
a)Kat's equation b) Carter's equation c) After how many car washes will they both have the same amount of money? d) How much money will they each have
Answer:
a) Kat's equation is 10 + 12x = Amount
b) Carter's equation is 85 + 7x = Amount
c)
Explanation:
Kat has $10 saved up in her account and charges $12 for each car she washes, the equation representing this is:
10 + 12x
Where x is the number of cars she washes.
Carter's equation is:
85 + 7x
I