The absolute value is to write the nubmer as a positive number
For example:
|-4| = 4
|-2.5| = 2.5
| 6| = 6
So, the number if was negative, we will make it positive
And the number if positive, will remain as it is
There is no need to use the number lines
So, the absolute value of 5.23 = | 5.23 | = 5.23
Is square root of 224 an irrational number ?
ANSWER
YES
EXPLANATION
We want to know if the square root of 224 is an irrational number.
An irrational number is a number that cannot be written as a fraction/ratio of two integers.
If we simplify the square root of 224:
[tex]\begin{gathered} \sqrt{224}\text{ = }\sqrt{16\cdot\text{ 28}}\text{ = 4}\sqrt{28} \\ \text{ }\Rightarrow\text{ 21.166010488}\ldots \end{gathered}[/tex]As we can see, this number cannot be written as a fraction of two numbers.
As a rule, the square root of any number that is not a perfect square is an irrational number.
So, the answer is Yes. It is an irrational number
This sequence represents the diameters of circles used to create an art project 2.5 cm, 3.1cm, 3.7cm,4.3cm let f(n) represent diameter in centimeters
The equation that represents the sequence of diameters is f(n) = 1.9+0.6n
What is arithmetic progression?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
Given the sequence that represents the diameter of a circle 2.5 cm, 3.1 cm, 3.7 cm and 4.3 cm. this sequence forms an arithmetic progression with a common difference.
nth term of an arithmetic progression is expressed as; [tex]a_{n}[/tex] = a+(n-1)*d
where, a is the first term of the sequence
n is the number of terms
d is the common difference.
Here, the first term a = 2.5 and common difference = 3.1-2.5 = 3.7-3.1 = 4.3-3.7 = 0.6
Substituting the values;
[tex]a_{n}[/tex] = 2.5 + (n-1)*0.6
= 2.5 + 0.6n - 0.6
= 1.9 + 0.6n
Hence, The equation that represents the sequence of diameters is f(n) = 1.9+0.6n
For more references on arithmetic progression, click;
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find the height of a cone with a diameter of 12m whose volume is 264m ^3 . use 3.14 for π and round your answer to the nearest meter . A. 42m B. 6m C. 7mD. 2m
find the height of a cone with a diameter of 12m whose volume is 264m ^3 . use 3.14 for π and round your answer to the nearest meter .
A. 42m
B. 6m
C. 7m
D. 2m
we have that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
V=264 m3
pi=3.14
r=12/2=6 m ------> the radius is half the diameter
substitute
[tex]264=\frac{1}{3}\cdot3.14\cdot6^2\cdot h[/tex]solve for h
[tex]\begin{gathered} h=\frac{264\cdot3}{3.14\cdot36} \\ \\ h=7\text{ m} \end{gathered}[/tex]answer is option C
If a movie is played at the rate preferred by its director, a moviegoer see 600 frames in 12.5 seconds. how many frames does a moviegoer see in 159?
A moviegoer sees 7632 frames in 159s.
An artist paints a mural on a wall at the local park The wall measures 16 1/4 meters in length. The artist paints a star every 18/20 meter. What is the total number of stars the artist paints om the mural?
The total length of the wall is
[tex]l=16\frac{1}{4}m=\frac{65}{4}m[/tex]the artist paint the star in every 18/20 meter,
so the total number of the stars are,
[tex]\frac{(\frac{64}{5})}{\frac{18}{20}}[/tex][tex]\frac{64\times20}{5\times18}=14.22[/tex]so the number of stars will be an integer. so we will round it
so the answer is 14 star.
How do I find the point slope intercept of a line
for the slope, the equation is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]in case you have two points
The equation of the line equation:
[tex]y=mx+b[/tex]If you want to find the interception in x-axis, you have to change the y for a 0, like this
[tex]0=mx+b[/tex][tex]x=-\frac{b}{m}[/tex]If you want to find the interception in y-axis, you have to change the x for a 0, like this, that is "b" in the equation
[tex]y=m(0)+b[/tex][tex]y=b[/tex]Find u · v.u = 6i − 4jv = i − j
1. m = -2; b=5
Write an equation in slope-intercept form
Answer:
y=-2x+5
Step-by-step explanation:
Slope-intercept form is y=mx+b
given the function g(x)=3x-7, determine when g(x)=-4
You have the following function:
g(x) = 3x - 7
In order to determine th value of x when g(x) = -4, you equal the previous expression to -4 and solve for x, just as follow:
g(x) = 3x - 7 replace g(x) = -4
-4 = 3x - 7 add 7 both sides
-4 + 7 = 3x simplify
3 = 3x divide by 3 both sides
3/3 = x
x = 1
Hence, the anser is x = 1
A student earned grades of C, A, B, and A in four different courses. Those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places.2.183.408.753.50
Given:
Grades the student earned = C, A, B, A
Corresponding credit hours = 4, 5, 1, 5
The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0.
Required: Grade point average (GPA)
Explanation:
Points earned = Earned grades x Corresponding credit hours
For C, points earned = 2 x 4 = 8 points
For A, points earned = 4 x 5 = 20 points
For B, points earned = 3 x 1 = 3 points
Total points earned = 8+20+3+20 = 51 points
Total credit hours = 4+5+1+5 = 15 hours
Find GPA.
[tex]\begin{gathered} \text{Grade point average\lparen GPA\rparen=}\frac{\text{ Total points of the student}}{\text{ Total credit hours}} \\ =\frac{51}{15} \\ =3.40 \end{gathered}[/tex]Final Answer: The grade point average of the student is 3.40.
find the inverse of each function. give any restrictions of the domain [tex]g(x) = - \frac{2}{\times + 2} - 3[/tex]
Answer
The inverse function is
[tex]g^{-1}(x)=\frac{5x}{4}+\frac{25}{4}[/tex]The domain of this inverse function is all real numbers.
Explanation
The question asks us to find the invers of the given function and give any restrictions of the domain if that exists.
The function is
g(x) = -5 + (4x/5)
To obtain the inverse of a function, the right approach is to write g(x) as y, then make x the subject of formula.
[tex]\begin{gathered} y=-5+\frac{4x}{5} \\ \text{Multiply through by 5} \\ 5y=-25+4x \\ \text{Rewrite the equation} \\ -25+4x=5y \\ 4x=5y+25 \\ \text{Divide through by 4} \\ \frac{4x}{4}=\frac{5y}{4}+\frac{25}{4} \\ x=\frac{5y+25}{4} \end{gathered}[/tex]We can then write this properly in terms of the inverse function
[tex]g^{-1}(x)=\frac{5x}{4}+\frac{25}{4}[/tex]The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.
The domain of this inverse function is all real numbers because there would be a real number answer for every real number value of x.
Hope this Helps!!!
Solve for x. 6 244 - 21.A. 0.53B. 0.45 C. 0.06 D. 0.24
ANSWER:
B. 0.45
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]6\cdot2^{4x}^{}=21[/tex]We solve for x:
[tex]\begin{gathered} 2^{4x}=\frac{21}{6} \\ \ln \: \mleft(2^{4x}\mright)=\ln \: \mleft(\frac{7}{2}\mright) \\ 4x\cdot\ln (2)=\ln \: \mleft(\frac{7}{2}\mright) \\ x=\frac{\ln \: \mleft(\frac{7}{2}\mright)}{4\cdot\ln (2)} \\ x=0.45 \end{gathered}[/tex]The value of x is 0.45
I need help with this
A trinomial is a polynomial that has three terms.
Let the unknown trinomial be represented by A
Thus, the difference between the two trinomials as stated in the question will be represented mathematically as;
[tex]\begin{gathered} A-(3x^2-2x+7)=5x^2+11x-16 \\ \text{Making A the subject of the formula, we have} \\ A=(5x^2+11x-16)+(3x^2-2x+7) \\ \operatorname{Re}\text{arranging and collecting the like terms, we have;} \\ A=5x^2+3x^2+11x-2x-16+7 \\ A=8x^2+9x-9 \end{gathered}[/tex]Therefore, the expression of the other trinomial is;
[tex]A=8x^2+9x-9[/tex]The correct answer is option C.
What is the estimate for each expression? Drag the number to each box.011/2Expression Estimate2+513 114 101+12 20-1009
ANSWER:
STEP-BY-STEP EXPLANATION:
We must approximate each addition or subtraction, estimating if it is close to 0, 1/2 or 1.
We operate in each case:
[tex]\begin{gathered} \frac{1}{8}+\frac{2}{5}=\frac{1\cdot5+2\cdot8}{8\cdot5}=\frac{5+16}{40}=\frac{21}{40}=0.525\approx\frac{1}{2} \\ \\ \frac{13}{14}-\frac{1}{10}=\frac{13\cdot10-1\cdot14}{14\cdot10}=\frac{130-14}{140}=\frac{116}{140}=0.82\approx1 \\ \\ \frac{1}{12}+\frac{1}{20}=\frac{20+12}{12\cdot20}=\frac{32}{240}=0.13\approx0 \end{gathered}[/tex]Find the lateral surface area of the rectangular prism. Round your answer to the tenth of necessary
48 square feet
Explanation
to find the lateral surafece, we need to add the 4 faces that make it,so
so,the total area
[tex]\begin{gathered} \text{Area}=2(\text{length}\cdot\text{width)}+2(\text{length}\cdot\text{width)} \\ \text{Area}=2(6\text{ ft}\cdot3\text{ ft)+2(3ft}\cdot\text{2 ft)} \\ \text{Area}=2(18ft^2)+2(6ft^2) \\ \text{Area}=36ft^2+12ft^2 \\ \text{Area}=48ft^2 \end{gathered}[/tex]so, the answer is 48 square feet
The weight, in pounds, of a male child can be estimated 3 using the function f(x) = 2.69x^3/4, where x represents the child's age in months. Determine the child's weight at 3 years of age, rounded to the nearest thousandth.
the modeled equation for the weight of a male child is
[tex]f(x)=2.69X^{\frac{3}{4}}[/tex]x is the age of the child in months
to calculate the child weight in 3 years
we need to convert the years to months since x is a function of months
12 months ==== 1 year
x months = 3 years
cross multiplication
12 x 3 = 1 * x
x = 36 months
Therefore, 3 years =
what does the dotted line on the geometric triangle mean?
It is line of symmetry. That is, if you draw a triangle like this,
Then you will get a trainagle similar to the first one.
A coin is flipped 3 times. What is the probability that it lands on tails exactly 3 times? Write your answer as a reduced fraction (numerator /denominator).
Note the probabilty of getting a tail when a coins is flipped 1 time is 1/2
Now for the probability when flipping a coin 3 times, the probability if the a single flipped is multiplied by itself 3 times..
Therefore, the probability of getting a tail for 3 times is :
[tex]\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}[/tex]The answer is 1/8
Another solution is to list down the possible outcomes :
HHH
THH
HTH
HHT
TTH
THT
HTT
TTT
There are a total of 8 outcomes.
and getting the probability of TTT over 8 outcomes is 1/8
List the integers from least to greatest 4, -7, 6, -2, 1
When you have negative numbers you can see that numbers in a number line to see what is the greatest and what is the least:
In a number line you put the 0 as the center and to the right you put the possitive numbers and in the left of the 0 the negative numbers, as follow:
Then you can put the numbers you have in a number line:
You get
Purle: -7
Red; -2
Blue: 1
Green: 4
Black: 6
The least number is the number that is more to the left and the greatest is the number taht is more to the right
Then so, the List the integers from least to greatest is:-7, -2, 1, 4, 6in triangle JKL j=10cm k=12cm anf l=13cm find cos K
For the given triangle, we must apply the following trigonometric relation:
[tex]\begin{gathered} k^2=j^2+l^2-2jl\cos K \\ \cos K=\frac{k^2-j^2-l^2}{-2jl} \\ \cos K=\frac{12^2-13^2-10^2}{-2\cdot13\cdot10} \\ \cos K=0.48 \end{gathered}[/tex]In the figure to the right, what value of x makes G the incenter of triangle JKL. See image below
We were given the following information:
LT = 12
GL = 13
GR = x - 3
The incenter of a triangle refers to the intersection point of all interior angle bisectors of the triangle. The incenter is equidistant to the sides, they are all the same
If triangle JKL has G as its incenter, the following will be found to be true:
[tex]|GR|\cong|GS|\cong|GT|[/tex]However, we were not given any of the above distances GR, GS & GT. We can obtain GT by using the Pythagoras Theorem on the triangle GTL as shown below:
[tex]\begin{gathered} |GT|^2=|GL|^2-|LT|^2 \\ |GT|^2=13^2-12^2 \\ |GT|^2=169-144 \\ |GT|^2=25 \\ \text{Take the square root of both sides, we have:} \\ |GT|=\sqrt[]{25} \\ |GT|=5 \\ \\ \therefore|GT|=5 \end{gathered}[/tex]Since GT equals 5, it implies that GS & GT will also equal 5
We will obtain the value of ''x'' as shown below:
[tex]undefined[/tex]A classmate claims that the function g(x)=-4ex+6 is the parent function f(x)=ex reflected across the Y axis, vertically compressed by a factor of four, translated to the left five units, and translated up six units.A) explain what the classmate described incorrectly.B) describe g(x) as a series of transformations of f(x)
Based on the function g(x), the function f(x) is multiplied by a negative number. Hence, there is a reflection across the x-axis.
If it was the "x" variable that was multiplied by a negative number for example, y = e^-x, it would have been reflection across the y-axis.
Since the number multiplied to the function f(x) is not between 0 and 1, we are stretching the function. Hence, the function is vertically stretched by a factor of 4.
Moving to the number -5 that was subtracted from the variable x, we have moved/shifted the function 5 units to the right instead of left.
Lastly, 6 was added to the entire function, therefore, we have translated the functions 6 units up.
To summarize, f(x) = e^x had undergone the following series of transformation: reflection across the x-axis, vertically stretched by a factor of 4, translated 5 units to the right, and translated 6 units up to form g(x).
Solve the inequality c+49 <-16
ANSWER
c < -65
EXPLANATION
We have the inequality:
c + 49 < -16
To solve this, we collect like terms:
c < -16 - 49
Simplify:
c < -65
That is the answer.
Evaluate the first operation 6^2?options: 12, 36, 6-1, 62
The operation
[tex]6^2[/tex]means that
[tex]6^2=6\times6[/tex]since 6 times 6 is equal to 36, the answer is option 2.
Can you help me find the answer to my homework questions thankyouuuu
In this problem, we have an exponential decay function of the form
[tex]y=a(1-r)^x[/tex]where
y is the area in km2
x is the number of years
a=3,800 km2 (initial value)
r=6.25%=6.25/100=0.0625
substitute given values
[tex]\begin{gathered} y=3,800(1-0.0625)^x \\ y=3,800(0.9375)^x \end{gathered}[/tex]For x=12 years
substitute
[tex]\begin{gathered} y=3,800(0.9375)^{12} \\ y=1,752\text{ km}^2 \end{gathered}[/tex]therefore
The answer is 1,752 square kilometersSI imi triangles. 16. JK 17 ST J X K 4 6 L R Р 12 M P TTTT 20. DB
16.
In the given triangles,
[tex]\begin{gathered} \angle JLK=\angle PLM\text{ (Vertically Opposite Angle)} \\ \angle LJK=\angle LPM\text{ (Given)} \end{gathered}[/tex]Hence form AA critesion,
[tex]\Delta JLK\approx\Delta PLM[/tex]From the property of similar triangles,
[tex]\begin{gathered} \frac{JK}{PM}=\frac{JL}{PL} \\ \Rightarrow\frac{x}{12}=\frac{4}{6} \\ \Rightarrow x=8 \end{gathered}[/tex]Thus, the requried value of JK is 8.
Solve the compound inequality.2u+6<18
Given:
An inequality 2u+6<18
To find:
We have to solve the given inequality.
Solution:
Subtract 6 from both sides to get:
[tex]\begin{gathered} 2u+6-6<18-6 \\ 2u<12 \end{gathered}[/tex]Divide by 2 both sides:
[tex]\begin{gathered} \frac{2u}{2}<\frac{12}{2} \\ u<6 \end{gathered}[/tex]Thus, the solution to the inequality is u < 6.
6 cm 4 cm 10 cm What is the area of the figure in square centimeters? TOTAL AREA= find the area of all the shapes and ADD together. To find the area 1/2 of a circle , you need the area of a circle and divide by 2. USE YOUR FORMULA CHART.
Notice that since the bottom side of the figure has a length of 10cm while the part that corresponds to the rectangle is only 6cm long, then the base of the triangle is 4cm long. The height of the triangle is 4cm long, since it is the same as the height of the rectangle. Additionally, the diameter of the semicircle turns out to be equal to 4cm, then its radius (which is half the diameter) must be 2cm long.
Use these data to find the area of each figure:
Semicircle
The area of a semicircle is half the area of a circle:
[tex]\begin{gathered} A=\frac{1}{2}\pi r^2 \\ =\frac{1}{2}\pi(2cm)^2 \\ =2\pi cm^2 \\ \approx6.28cm^2 \end{gathered}[/tex]Rectangle
[tex]\begin{gathered} A=w\times l \\ =6\operatorname{cm}\times4\operatorname{cm} \\ =24cm^2 \end{gathered}[/tex]Triangle
[tex]\begin{gathered} A=\frac{1}{2}b\times h \\ =\frac{1}{2}4\operatorname{cm}\times4\operatorname{cm} \\ =8cm^2 \end{gathered}[/tex]Total area:
[tex]\begin{gathered} A=6.28cm^2+24cm^2+8cm^2 \\ \Rightarrow A=38.28cm^2 \end{gathered}[/tex]Therefore, the total area of the figure is:
[tex]38.28cm^2[/tex]Don't understand how to find this answer. Can't find my notes for it.
Given that
The two sides of the triangle are 6x and 3x+9 and the two angles are 65 degrees each.
Explanation -
According to the property of the triangle " If the two angles of the triangle are equal then the sides opposite to them will be equal."
Then, we have
AB = BC -------------because angle A = angle B = 65
Substituting their values
6x = 3x + 9
6x - 3x = 9
3x = 9
x = 9/3 = 3
x = 3
So side AB will be,
AB = 6(3) = 18 units.
So opption D is correct.
Hence the final answer is 18.disjointed and overlapping events
Answer:
1. P = 0.269 or 26.9%
2. P = 0.372 or 37.2%
Step-by-step explanation:
First, let's calculate the total number of students:
So, we know that the number of students is 662.
Now, let's evaluate the probabilities:
1. Student will begin college during summer AND attend an in-state college.
P = 178/662
P = 0.269 or 26.9%
2. Student will begin college in summer GIVEN THAT he is attending an in-state college.
In this case, the total number of students will be the number of students who will attend an in-state college.
P = 178/479
P = 0.372 or 37.2%