Rational numbers, Real numbers, Natural numbers, whole number
Explanation:[tex]49\text{ can also be written as }\frac{49}{1}[/tex]Rational numbers can be written as a fraction. 49 can be written as a fraction
Real numbers consists of natural numbers, whole umbers, integers and rational numbers.
Since it is already a rational number, then it is also a real number
Natural numbers are counting numbers from 1 to positive infinity. 49 is between 1 to positive infinity.
Hence, it is a natural number
whole numbers start from 0 to positive infinity. 49 is between 0 to positive infinity.
Hence, it is a whole number
Irrational numbers cannot be written in the form of fraction. SInce 49 can be written as fraction, it is not an irrational number
Hence, the set(s) of numbers would you find the number 49 are Rational numbers, Real numbers, Natural numbers, whole number
The table shows the cost of shampoo at a discount store Cost $ 2.95 $4.50 $6.05 Number of bottles 1 2 3is the cost of the shampoo bottles proportional to the amount of bottles ?
Answer:
Not proportional
Explanation:
First, we determine the unit rate for each of the pairs of points.
[tex]\begin{gathered} UnitRate=\frac{\text{Cost}}{\text{Number of bottles}} \\ \frac{2.95}{1}=\$2.95\text{ per bottle} \\ \frac{4.50}{2}=\$2.25\text{ per bottle} \\ \frac{6.05}{3}=\$2.02\text{ per bottle} \end{gathered}[/tex]We see that the unit rates are not the same.
Therefore, the cost of the shampoo bottles IS NOT proportional to the number of bottles
Pls help fast !!!!!!!
The required solution of the function f(x) = -3x + 5 at x = -2 is 11.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given function,
f(x) = -3x + 5
Substitute x with -2 to find f(-2).
f(-2) = -3(-2) + 5
f(-2) = +6 + 5
f(-2) = 11
Thus, the required solution of the function at x = -2 is 11.
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Определите количество сторон правильного многоуголь
ника, если угол, смежный с углом многоугольника, составляет 2/3 угла многоугольника
Answer:
n=6
Step-by-step explanation:
Угол многоугольника 2х, смежного угла х.
2х+х=180.
3х=180.
х=60° .
Углы многоугольника 120°.
Формула углов правильного многоугольника.
аₙ=(n-2)/n * 180.
120=(n-2)/n *180. после преобразования
3(n-2)=2n.
n=6.
Answer: n=6.
Step-by-step explanation:
Point O is the midpoint of DG. The coordinates of points D and O are (-4, 0) and (-1,-5) respectively
What are the coordinates of point G
Coordinates of Point G is (1,-10)
To find Coordinates :
O is midpoint of DGCoordinates of O (-1,-5)Coordinates of D (-4,0)Let the coordinates of G are (x,y)
To find coordinates of G
[tex]\frac{x + (-4)}{2} = -1[/tex] [tex]\frac{y + 0}2} = -5[/tex]
= x + (-2) = -1 y+0 = -5 * 2
x = -1 + 2 y = -5 * 2
x = 1 y = -10
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Write an equation (-5,-2) and (-4,-3)
The equation from (-5, -2) and (-4, -3) is y = -1x - 7
What is Equation of line?
A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It can be expressed in a variety of ways and provides the line's slope, x-intercept, and y-intercept.
Given:
P1: (-5, -2)
P2: (-4, -3)
Find:
The equation for the line that passes thru P1 & P2
Solution:
y = mx + b
Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept
m = ( y2 - y1 ) / ( x2 - x1 )
= ( -3 + 2 ) / ( -4 + 5 ) )
= -1 / 1
∴ m = -1
Using either P1 or P2, plug in one of their respective x- and y-values into:
y = -1 x + b
For (-5, -2)
-2 = -1 ( -5 ) + b
-2 = 5 + b
-7 = b
∴ b = -7
∴ y = -1x - 7 is the equation of the line that passes thru both points (-5, -2) and (-4, -3)
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The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 5 to 3. If there were 4440 total votes, how many yes votes were there?
Total votes of the residents of the city = 4,440
Ratio of yes to no = 5:3
Yes votes = 4,440 * 3/5 = 2,664
No votes = 4,440 - 2,664 = 1,776
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he needs to walk the dog 6 times more}
Shen runs each lap in 4 minutes. He will run at least 48 minutes today. What are the possible numbers of laps he will run today?Use n for the number of laps he will run today.Write your answer as an inequality solved for n.
From the statement, we know that:
0. Shen runs each lap in 4 minutes,
,1. he will run ,at least, 48 minutes today ⇒ t ≥ 48 min.
(1) From point 1, we know that Shen's speed is:
[tex]s=\frac{1\text{ lap}}{4\text{ min}}=\frac{1}{4}\cdot\frac{\text{lap}}{\text{min}}.[/tex](2) The speed (s) times the time (t), we get the # of laps (n):
[tex]n=s\cdot t\ge\frac{1}{4}\cdot\frac{\text{laps}}{\text{min}}\cdot48\text{ min}=\frac{48}{4}\text{ laps}=12\text{ laps}\Rightarrow n\ge12\text{ laps.}[/tex]Answern ≥ 12
Determine which integer will make the inequality 20 > 4x + 16 true.
Answer:
-1
Step-by-step explanation:
That's my best shot.
There are 12 girls and 24 boys in a class. What is the ratio of boys to total number of students in the class?
Answer: 1:2
24 is half of 48
what is the absolute value of 1 -32 1?what is the opposite of 6 on the number line?
Given data:
The given number is | -32| .
The value of given modulus function is,
[tex]|-32|=32[/tex]The opposite of 6 on number line is -6.
Thus, the value of first number is 32, and second is -6.
N N Which of the following is an equation of line k in the xy-plane above? (A) y=-x-4 (B) y = x+2 (C) 2y - 3x = -8 (D) 2y - 3x = -4
Answer:
[tex]2y-3x=-8[/tex]Explanation:
Given the graph in the attached image;
The intercept of the line on the y-axis is at;
[tex]\begin{gathered} y=-4 \\ At\text{ point;} \\ (0,-4) \\ \text{ intercept b is;} \\ b=-4 \end{gathered}[/tex]At the x=2, the value of y is;
[tex]\begin{gathered} y=-1 \\ at\text{ point;} \\ (2,-1) \\ \end{gathered}[/tex]The slope of the line can be calculated using the two points on the graph;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-4)}{2-0}=\frac{-1+4}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]The slope intercept equation of a straight line is of the form;
[tex]y=mx+b[/tex]substituting the slope m and intercept b we have;
[tex]y=\frac{3}{2}x-4[/tex]As this is not among the given options, let us solve further;
multiply through by 2 and move the x term to the left side;
[tex]\begin{gathered} y(2)=\frac{3}{2}x(2)-4(2) \\ 2y=3x-8 \\ 2y-3x=-8 \end{gathered}[/tex]Therefore, from the given options the correct equation for the line is C;
[tex]2y-3x=-8[/tex]pleaseeee help!! !!!!!
Answer: it’s c
Step-by-step explanation: dude that’s ez
find the area of the shaded region. Note that the total radius from the center out to the edge of the shaded region is 8+3 = 11.
Given
The figure.
To find the area of the shaded region.
Explanation:
It is given that,
The radius of the whole circle is 11cm.
And, the radius of the small circle is 3cm.
Then,
The area of the shaded region is,
[tex]\begin{gathered} Area\text{ of the shaded region}=Area\text{ of the whole circle-area of smaller circle} \\ =\pi(11^2)-\pi(3^2) \\ =121\pi-9\pi \\ =112\pi \\ =112\times\frac{22}{7} \\ =351.85cm^2 \end{gathered}[/tex]Hence, the area of the shaded region is 351.85cm^2.
Mona borrowed $6,000 for college expenses. After 2 1/2 years she will have paid $750 in interest. What is the interest rate?
Simple interest is represented by the expression:
[tex]\begin{gathered} I=p\cdot r\cdot t \\ I=\text{interest earned after t years} \\ p=\text{ money borrowed} \\ r=\text{annual rate of interest} \\ t=\text{ the length of time you borrow} \end{gathered}[/tex]Understanding this expression, we can substitute our values:
[tex]750=6,000\cdot r\cdot2.5[/tex]Isolating our variable of interest (r):
[tex]\begin{gathered} r=\frac{750}{6,000\cdot2.5} \\ r=0.05 \end{gathered}[/tex]The interest rate is 0.05 or 5%
Instructions: Identify the type of sequence and write the explicit rule.
SOLUTION:
Case: Sequences
Method:
3, 12, 48, 192,...
Step1:
The sequence is increasing exponentially
Type: Geometric/Exponential Sequence
Step 2:
The Explicit rule is gotten from the formula:
[tex]a_n=ar^{n-1}[/tex]a= 3,
r= (12/3)
r= 4.
The rule, therefore:
[tex]a_n=3(4)^{n-1}[/tex]Final answer:
Type: Geometric sequence
Explicit rule
[tex]a_n=3(4)^{n-1}[/tex]How much money should you invest at 5.3% annual simple interest rate to have $7200 in 9 months?
Answer:
181 132$
Step-by-step explanation:
Co - initial capital
I - interest
r - 5.3% annual simple interest
t - time
I = Co * r * t
7200 = Co * 0.053 * 9/12
Co = 181 132$
'g & & eggs 1 10 15 2015-2016 time {uash. bpeed (m/sec) The graph represents the elapsed time for running with connected speed schedules for two different racers. As the speed increases what happens to the elapsed time for racer B? * 6 Points) Enter your answer
The relationship between the speed and the elapsed time is a negative relationship. That means as the speed increases, the time elapsed decreases. Thats why the line goes downward from left to right.
For racer B, as the speed increases, the time elapsed decreases at a rate lesser than that of racer A.
The distance from Earth to the sun is about 9.3 × 107 miles. The distance from Jupiter to the sun is about 4.84 × 108 miles. How much closer is the Earth to the sun than Jupiter to the sun?
The earth is 3.91×10^8 miles closer to the sun than jupiter
What is distance?Distance is the space or gap between two points or bodies. It is a scalar quantity and measured in cm, m, km, miles e.t.c
The distance between the earth and the is 9.3×10^7 miles and the distance of Jupiter from the sun is 4.84×10^8 . This shows that the earth is closer to sun than Jupiter.
The dimension of how closer the earth is to the sun than Jupiter is therefore
( 4.84×10^8)-(9.3×10^7)= 3.91×10^8 miles
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18) Find the greatest common factor (GCF) for list of terms: 10x3y5, -15x4y8, 20x5y6
10x3y5,
-15x4y8,
20x5y6
[tex]undefined[/tex]greatest common factor of 10, 15, and 20 is 5
greatest common factor of x^3, x^4 and x^5 is x^3
greatest common factor of y^5, y^8 and y^6 is y^5
Therefore the greatest common factor of all is:
5x^3y^5
[tex]5x^3y^5^{}[/tex]Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive integer value. x^2=4(x-9)
Given the following equation:
[tex]x^2=4(x-9)[/tex]First of all, we note that the quadratic equation is written in the general form shown below;
[tex]ax^2+bx+c=0[/tex]We shall now attempt to re-write the equation given in the form shown above. This is shown as follows;
[tex]\begin{gathered} x^2=4(x-9)_{} \\ We\text{ shall now expand the parenthesis;} \\ x^2=4x-36 \\ We\text{ shall now collect all like terms;} \\ \text{Subtract 4x and add 36 to both sides to both sides} \end{gathered}[/tex][tex]\begin{gathered} x^2-4x+36=4x-4x-36+36 \\ x^2-4x+36=0 \end{gathered}[/tex]We now have our quadratic equation as shown above.
Comparing this with the general form of a quadratic equation, we can now identify a, b and c as follows;
[tex]\begin{gathered} a=1 \\ b=-4 \\ c=36 \end{gathered}[/tex]ANSWER:
a = 1
b = -4 and
c = 36
Factor f(x) = 4x² - 576 = 0
4x^2 - 576 = (2x - 24)(2x + 24)
Because of conjugated binomials
(a + b)(a - b) = a^2 - b^2
2x is the square root of 4x^2
24 is the square root of 576
answer:
(2x - 24)(2x + 24)
Find the value of x. Round lengths of segments to the nearest tenth andangle measures to the nearest degree.
Answer:
7.8
Explanation:
The length x, the side with length 6, and the angle of 40 degrees are related by the trigonometric function cosine, so
[tex]\cos 40=\frac{6}{x}[/tex]Because x is the hypotenuse and 6 is the adjacent side.
Solving for x, we get
[tex]\begin{gathered} x\cos 40=x\cdot\frac{6}{x} \\ x\cos 40=6 \\ \frac{xcos40}{\cos40}=\frac{6}{\cos 40} \\ x=\frac{6}{\cos 40}=\frac{6}{0.766}=7.8 \end{gathered}[/tex]Therefore, the value of x is 7.8
The temperature of a mixture changes by -5.2 Fahrenheit between 8am and 11am. At 6pm the temperature is 14.5 Fahrenheit, which is half of what it was at 11am. What was the temperature at 8am of the mixture. I have this equation , but not sure is correct. 1/2(x-6.8)= -3.1
Explanation
Let us have a sketch of the question
If the temperature at 6 pm is 14.5 F
And the temperature at 11am is twice that of 6pm
Then the temperature at 11am will be
[tex]2\times14.5F=29F[/tex]Since the temperature of a mixture changes by -5.2 Fahrenheit between 8 am and 11 am.
Then the temperature at 8 am will be
[tex]\begin{gathered} \theta_{11am}-\theta_{8am}=-5.2 \\ 29F-\theta_{8am}=-5.2F \\ \theta_{8am}=29F+5.2F \\ \theta_{8am}=34.2F \end{gathered}[/tex]Therefore, the temperature at 8 am will be 34.2 F
(2x^3+13x^2+16x+5)÷(x^2+9x+5)
The answer will be (x-1). (2x-1). The polynomial equation P(x) = 0 has roots, or solutions, that may be found by setting each factor to 0 and figuring out what x is. Factor the polynomial equation to find the solution. Set each variable to 0. x - 6 = 0 or x + 1 = 0 or 2x4 = 0
Finding polynomial roots (zeroes) is the focus of this solution.
What is quadratic equations?Due to the fact that the variable is squared, the word "quadratic," which means "square," was coined (like x2).
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a). See examples of how to solve different equations using the formula.
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
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Use synthetic division to find the function value. Then, check your work using a graphing calculator.
we have the function
f(x)=x^4-x^3-7x^2+45x-39
Find out f(-5)
so
Use synthetic division
x^4-x^3-7x^2+45x-39 : (x+5)
x^3-6x^2+23x-70
-x^4-5x^3
-------------------------------
-6x^3-7x^2+45x-39
6x^3+30x^2
----------------------------
23x^2+45x-39
-23x^2-115x
------------------------
-70x-39
70x+350
------------------
311 ----------------> remainder
therefore
f(-5)=311
Verify
using a graphing tool
For x=-5 ------------> f(x)=311 is ok
Find the value of x in the triangle shown below.227ASCAssChoose 1 answer:MY= 45Col= 9MY= 5ProProD2 = 53Tea
The given triangle is a right triangle as shown by the square symbol inside. With this, we can solve the length "x" of this triangle using the Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]where c = length of the hypotenuse and "a" and "b" are any of the remaining sides.
In our triangle, we have 7 as our hypotenuse and 2 as the length of the one side. Let's apply these values in the formula above.
[tex]\begin{gathered} 7^2=2^2+b^2 \\ 49=4+b^2 \\ 49-4=4+b^2-4 \\ 45=b^2 \\ \sqrt[]{45}=\sqrt[]{b^2} \\ \sqrt[]{45}=b \\ 3\sqrt[]{5}=b \end{gathered}[/tex]Therefore, the value of x is √45.
I need help on this one! Please and thank you!
Given:
[tex]\cos \theta\text{ =- }\frac{1}{8}[/tex]Solving for the angle measure:
[tex]\begin{gathered} \theta\text{ = }\cos ^{-1}(-\frac{1}{8}) \\ =\text{ }97.181 \end{gathered}[/tex]Hence, we can find the exact value of sin theta:
[tex]\begin{gathered} But\text{ }\theta\text{ is in the third quadrant.} \\ \sin (97.181\text{ -180) = sin(-82.8190}) \\ =\text{ -0.992} \end{gathered}[/tex]Hence, the exact value of sin theta is -0.992
Simplify the absolute value 8|cos | if = sin−1 8/x for some real number x. (Give your answer in terms of .)
The absolute value of 8|Cosθ| is 8√(x² - 8²)/|x|.
The value of the angle θ is Sin−1 (8/x). We need to find the absolute value of 8|Cosθ|.
θ = Sin−1 (8/x)
Sinθ = 8/x
We know the trigonometric identity that Sin²θ + Cos²θ = 1.
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
(8/x)² + Cos²θ = 1.
Cos²θ = 1 - (8/x)²
Cos²θ = (x² - 8²)/x²
Cosθ = √[(x² - 8²)/x²]
Cosθ = √(x² - 8²)/x
Multiply both the sides with 8.
8Cosθ = 8√(x² - 8²)/x
Apply modulus on both the sides.
A modulus function is one that returns the absolute value of a number or variable.
8|Cosθ| = 8√(x² - 8²)/|x|
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Sort the sequences into categories. Determine which sequences are arithmetic and which are geometric. Drag each label to the correct location on the table. Each label can be used more than once. Arithmetic Sequence Geometric Sequence (90, 87, 84, 81, 78, ...) (4, 12, 36, 108, 324, ...) (8,1,1/8,1/64,1/512,...) (3, 10, 17, 24, 31,...) (1,1.4,1.8, 2.2, 2.6, ...) (3,1.5, 0.75, 0.375,...)
Given the sequences we are asked to identify whether they are geometric or arithmeti. This can be seen below.
Explanation
For an arithmetic sequence
[tex]T_2-T_1=T_3-T_2^[/tex]For a geometric sequence
[tex]\frac{T_2}{T_1}=\frac{T_3}{T_2}[/tex]Therefore;
Answer:
[tex]\begin{gathered} Arithmetic\text{ sequence}\Rightarrow90,87,84,81,78,.. \\ Geometric\text{ sequence}\Rightarrow4,12,36,108,324,... \\ Geometric\text{ sequence}\Rightarrow8,1,1/8,1/64,1/512,... \\ Arithmetic\text{ sequence}\Rightarrow3,10,17,24,31..... \\ Arithmetic\text{ sequence}\Rightarrow1,1.4,1.8,2.2,2.6.... \\ Geometric\text{ sequence}\Rightarrow3,1.5,0.75,0.375,... \end{gathered}[/tex]