solution
For this case we can do the following:
[tex]\tan M=\frac{\sin M}{\cos M}=\frac{\text{opposite}}{\text{adjacent}}[/tex]For this case the opposite side is 8 and the adjacent is 6 so we got:
[tex]\tan M=\frac{8}{6}=\frac{4}{3}[/tex]The perimeters of the square and equilateral triangle shown below are equal. Which of the following is NOT a true statement about the figures. Remember: perimeter of a square = 4(one side), and perimeter of an equilateral triangle = 3(one side)
ANSWER
The incorrect option is Each side length of the square is 6 units
EXPLANATION
We are given that the perimeter of the square and the equilateral triangle are equal.
The length of the side of the square is 2x.
The perimeter of a square is given as:
P = 4 * L
=> P = 4 * 2x
P(square) = 8x
The length of side of the triangle is given as 3x - 1.5.
The perimeter of an equilateral triangle is given as:
P = 3 * L
=> P = 3 * (3x - 1.5)
P(triangle) = 9x - 4.5
Therefore, since both perimeters are equal:
8x = 9x - 4.5
Collect like terms:
9x - 8x = 4.5
x = 4.5
Now, for the options:
- The value of x is 4.5
- The perimeter of the square is 8 * 4.5 i.e. 36 units.
- Each side length of the square is 2 * 4.5 = 9 units
- Each side length of the triangle is :
3 * 4.5 - 1.5 = 13.5 - 1.5 = 12 units
So, the incorrect option is Each side length of the square is 6 units
LEVEL 1
Roses are red, violets are blue. The order of colors, is your clue.
Directions: Solve each
equation. The green
and purple equations
are fractions. Once you
have the answer, find
the number that is on
the colored line, and
put it on the matching
line next to the code.
1.8-(-3.7) =
-7.2 +4.1=-
-1.5 x (-0.2) =
-2/7 ÷ (-1/4) =___/
Code:
——-
HELP ASAP PLEASE..
Answer:
1.8-(-3.7)= 5.5
-7.2+4.1= -3.1
-1.5*(-0.2)= 0.3
-2/7÷(-1/4)= 8/7
code: 5.5,(-3.1),0.3,8/7
8 / 1/3 and 2 / 1/9 what's the generalizations can make about the equations
The generalization about the terms is that one is the cube root of the other
∛(8/9) = 2/3
What is generalizations in mathematics?Generalization can be viewed as a statement that holds true for a broad category of objects or numbers, as the method by which we arrive at a general statement, or as a means of transferring information from one context to another in the mathematics.
The equation represented as 8 / 1/3 and 2 / 1/9
is made an equated to each other and rearranged as follows
8 / 1/3 ⇔ 2 / 1/9
cross multiplying
8 * 1/9 ⇔ 2 * 1/3
8/9 ⇔ 2/3
the equation only holds true when the cube root sign is there then we have
∛(8/9) = 2/3
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6 The length of a city block running north to south in New York City is about 5 X 10-2 miles The distance from New York City to Mumbai, India, is about 7.5 X 103 miles. The distance from New York City to Mumbai is about how many times the length of a New York City north-south block? Show your work.
Just need one answer.Is it reflectional symmetry, Rotational symmetry, or is it both
This is a simple question to solve.
First, let's focus on the reflection symmetry, What is it?
Having a reflection symmetry means if we split the image in half the left side is identical to the right side. To illustrate better, we have the following picture:
As we can see above, the left side of our shape is identical to the right side, it is like a reflection, so: yes, the image has reflectional symmetry.
Now let's focus on rotational symmetry. A
Mr. Bernard paid $4,794 in social security tax on earnings of $68,000 one year. What was the social security tax rate for that year to the nearest hundredth of a percent)?6.85%7.05%7.15%7.65%None of these choices are correct.
Answer:
7.05%
Explanation:
Mr Bernard taxable income = $68,000
Amount paid as social security tax on earnings = $4,794
Let the social security tax rate = x
This gives:
[tex]\frac{x}{100}\times68,000=4,794[/tex]Next, solve for x:
[tex]\begin{gathered} 680x=4794 \\ x=\frac{4794}{680} \\ x=7.05 \end{gathered}[/tex]The social security tax rate for that year (to the nearest hundredth of a percent) is 7.05%.
Is this the correct solution for this question? I need help please
Given equation:
[tex]9x^2\text{ - 12x + 4 = 0}[/tex]Let's solve the question to identify the type of solution.
Using factorization method:
[tex]\begin{gathered} 9x^2\text{ - 12x + 4 =0} \\ 9x^2-6x\text{ -6x + 4 = 0} \\ 3x(3x-2)\text{ -2(3x-2)= 0} \\ (3x-2)(3x-2)\text{ =0} \end{gathered}[/tex]The solution is thus
[tex]\begin{gathered} 3x\text{ -2 = 0} \\ 3x\text{ = 2} \\ x\text{ = }\frac{2}{3} \end{gathered}[/tex]Hence, there is one solution and it is real.
Answer: 1 real (Option B)
Find an equation for the perpendicular bisector of the line segment whose endpointsare (-3, 2) and (7,6).
First, we need to find the midpoint. We can find it using the following equations:
[tex]\begin{gathered} Mp=(xm,ym) \\ xm=\frac{x1+x2}{2} \\ ym=\frac{y1+y2}{2} \end{gathered}[/tex]Where:
[tex]\begin{gathered} (x1,y1)=(-3,2) \\ (x2,y2)=(7,6) \end{gathered}[/tex]So:
[tex]\begin{gathered} xm=\frac{-3+7}{2}=\frac{4}{2}=2 \\ ym=\frac{6+2}{2}=\frac{8}{2}=4 \end{gathered}[/tex]Now, we need to find the slope of the line segment:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}[/tex]Since it is the line of the perpendicular bisector:
[tex]\begin{gathered} m\cdot mb=-1 \\ \frac{2}{5}mb=-1 \\ mb=-\frac{5}{2} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-ym=mb(x-xm_) \\ y-4=-\frac{5}{2}(x-2) \\ y-4=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+9 \end{gathered}[/tex]Answer:
[tex]y=-\frac{5}{2}x+9[/tex]What is 64 feet in 8 inches
Given
[tex]The\text{ actual house is 64ft long.}[/tex]To draw 64ft long house using a 8 inch scale.
Explanation:
Since the unit of inch is smaller than the unit of feet.
Then, by using the 8inches long scale.
Consider, 1 inch is equal to 8ft.
That implies,
[tex]\begin{gathered} 1inch=8ft \\ 8inch=8\times8ft \\ =64ft \end{gathered}[/tex]Hence,
8. * The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically. 9. ** f(x) = 5x – 2 and g(x) = 2x + 4. Are f(x) and g(x) parallel, perpendicular or neither parallel nor perpendicular to each other. Justify.
does the mapping diagram represent a function
It is possible to show the relationship between input and output values using a mapping diagram. If there is only one output value associated with each input value, a mapping diagram illustrates a function.
What is a mapping diagram?A mapping diagram can be used to illustrate the connection between input and output values. A mapping diagram shows a function when each input value has a single related output value.Use the following test to determine whether a relation is a function given a mapping diagram for the relation: The outputs are a function of the inputs if each input has only one line attached to it. Every element of the domain is associated with exactly one element of the range in a function, which is a unique kind of relation. A mapping demonstrates the pairings of the elements. It displays the input and output values of a function, much like a flowchart would. The two parallel columns of a mapping diagram.As it is given in the description itself, that mapping diagram shows a function when each input value has a single related output value.
Therefore, it is possible to show the relationship between input and output values using a mapping diagram. If there is only one output value associated with each input value, a mapping diagram illustrates a function.
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A function is translated from f(x)=9⋅3x−2 to g(x)=9⋅3x+4−2. What is the effect on f(x)?
Given the functions:
[tex]\begin{gathered} f(x)=9*3x-2 \\ \\ g(x)=9*3x+4-2 \end{gathered}[/tex]Let's determine the transformation that occurred from f(x) to g(x).
Apply the transformation rules for functions.
After a shift d units to theupwards, we have:
[tex]g(x)=f(x)+d[/tex]Thus, from the given translation, we can see that the function f(x) is translated 4 units to get the function g(x).
[tex][/tex]3x squared negative 4x squared plus 7x 4x squared negative 4x
ANSWER
[tex]12x^5-28x^4+44x^3-28x^2[/tex]EXPLANATION
First we have to find the partial products by multiplying each term of the first polynomial by each term of the second polynomial:
Now the second term of the second polynomial:
And now we just have to add these partial products:
The sum of 4 consecutive integers is 254. What is the value of the greatest integer?
The sum of 4 consecutive integers is 254. What is the value of the greatest integer?
Let
x -----> the first integeer
x+1 ----> second integer
x+2----> third integer
x+3 ----> fourth integer
we have that
x+(x+1)+(x+2)+(x+3)=254
solve for x
4x+6=254
4x=254-6
4x=248
x=62
therefore
the greatest integer is x+3
so
62+3=65
answer is 655. Find the perimeter for the figure. Show the set-up and allwork.
The perimeter of a polygon is given by the sum of the length of its sides. For the polygon in the picture we have the following side lengths:
[tex]7,9x,10,3x,12,4x,15,2x[/tex]Then their sum is:
[tex]7+9x+10+3x+12+4x+15+2x[/tex]We can group like terms. Like terms are terms multiplied by the same power of x. In this case we have two groups of like terms: constants and terms multiplied by x. Then we group them:
[tex](7+10+12+15)+(9x+3x+4x+2x)[/tex]We can use the distributive property in the terms with x. For example:
[tex]ax+bx+cx=(a+b+c)x[/tex]We use this and we also add the constants so we get:
[tex]\begin{gathered} (7+10+12+15)+(9x+3x+4x+2x)=44+(9+3+4+2)x \\ 44+(9+3+4+2)x=44+18x \end{gathered}[/tex]AnswerThen the answer is that the perimeter of the figure is 18x+44.
Can someone help me out with this because i looked at all the videos that my teacher gave us and none of them explained it.
The meaning of;
[tex]\frac{x}{4}[/tex]In algebra, when there is an unknown number it is generally represented by a letter (such as x,y,z etc.)
The letters x in x/4 represents an unkown number.
So, x/4 represent the unknown number x divided by 4.
For example; if x=20, then;
[tex]\frac{x}{4}=\frac{20}{4}=5[/tex]what are the solutions to this equations ? 2y = 4x + 12y = 2x - 6
Solve the following system of equations;
[tex]\begin{gathered} 2y=4x+12---(1) \\ y=2x-6---(2) \\ \text{From equation (2) substitute for y=2x-6 into equation (1) } \\ 2(2x-6)=4x+12 \\ 4x-12=4x+12 \\ \text{Collect all like terms} \\ 4x-4x=12+12 \\ 0=24 \end{gathered}[/tex]The answer is 0 = 24, which is not possible.
Hence, the system of equations has NO SOLUTION
Zoo AttendanceZoo D 234,679Zoo E 872,544Zoo F 350,952For each zoo in the table, round the attendance to the nearest hundred thousand.4 grade student
Explanation
We can round to the nearest hundreds of thousands below.
Answer:
Zoo D: 200,000
Zoo E: 900,000
Zoo F: 400,000
Hello, I am having difficulty with this problem, thanks. Find the smallest numberFind the largest rational numberFind the smallest irrational number
In order to determine which of them is the smallest number, let's convert each number into a decimal number.
[tex]\sqrt[3]{9}=2.080083823\approx2.08[/tex][tex]\sqrt{3}=1.732050808\approx1.73[/tex][tex]\sqrt{\frac{1}{4}}=\frac{1}{2}=0.5[/tex][tex](-5)^{-2}=\frac{1}{(-5)^2}=\frac{1}{25}=0.04[/tex]Upon converting, we can easily that the smallest number is the fourth number which is (-5)^-2.
On the other hand, between the 4 numbers, there are only two rational numbers and these are the 3rd and the 4th number. Between the two, the largest rational number is the 3rd number which is √(1/4) equivalent to 0.5.
Lastly, between the 4 numbers, there are only two irrational numbers and these are the first and the second number. Between the two, the smallest irrational number is √3 which is equivalent to 1.73.
What happens to the graph of y=2x^3+x^2−7x−6 as x heads toward ∞ and −∞?A. as x→∞, y→∞ as x→−∞, y→−∞B. as x→∞, y→∞ as x→−∞, y→∞C. as x→∞, y→−∞ as x→−∞, y→−∞D. as x→∞, y→−∞ as x→−∞, y→∞
Answer:
A. as x→∞, y→∞ as x→−∞, y→−∞
Explanation:
Given the function:
[tex]y=2x^3+x^2−7x−6[/tex]In order to determine the end behavior of f(x), we use the leading coefficient test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd and the leading coefficient is positive,, the graph falls to the left and rises to the right.
,• When the ,degree is odd and the leading coefficient is negative,, the graph rises to the left and falls to the right.
,• When the ,degree is even and the leading coefficient is positive,, the graph rises to the left and right.
,• When the ,degree is even and the leading coefficient is negative,, the graph falls to the left and right.
From the function, f(x):
• The degree of the polynomial = 3 (Odd)
,• The leading coefficient is 2 (Positive)
Thus, using the 1st rule of the 4 given above, we have that as x→∞, y→∞ as x→−∞, y→−∞.
The correct option is A.
Sketch the graphs for each of the following equations. 7 a. y = 5-X+7 b.y=9 c. y= 3x + 6
a)
Given:
The equation is,
[tex]y=-\frac{7}{5}x+7[/tex]The objective is to sketch the graph of the equation.
Since, the highest degree of the equation is 1, it could be a straight line. The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the equation and c represents the y intercept. Then comparing the both equations,
[tex]\begin{gathered} \text{slope, m=-}\frac{\text{7}}{5} \\ y\text{ intercept, c=7} \end{gathered}[/tex]Substitute, y = 0 in the given equation.
[tex]\begin{gathered} 0=-\frac{7}{5}x+7 \\ \frac{7}{5}x=7 \\ x=7\cdot\frac{5}{7} \\ x=5 \end{gathered}[/tex]Thus, at y = 0, the value of x = 5.
Using the coordinates (5,0) and y intercept c = 7, the graph will be,
Hence, the required graph is obtained,
6. Find all the solutions of the recurrence relation an = 2an-1 + an-2 + 2n + 1 with initial conditions a1 =7 and a2 = 19
aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
What is Recurrence relation?Recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms
aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
Homogenous case,
aₙ -2aₙ₋₁ + aₙ₋₂ with characteristic t²-2t-1=0
t=1
aₙ=C₁.(1-√2)ⁿ+C₂.(1+√2)ⁿ
Special case, Since non homogenous part is 2n+1
Let aₙ=pn+q, then
aₙ -aₙ₋₁ + aₙ₋₂=2n+1
pn+q-2(p(n-1)+q)-p(n-2)-q=2n+1
-2pn+qp-2q=2n+1
p=-1 and q=4p-1/2=-5/2
Combine both cases, aₙ = C₁(1-√2)ⁿ+C₂((1+√2)ⁿ-n-5/2
Substitute a₁=7 and a₂=19
a₁ = C₁(1-√2)+C₂((1+√2)-1-5/2
a₁ = C₁(1-√2)+C₂((1+√2)-7/2=7
(C₁+C₂)+(C₂-C₁)√2)=21/2..(1)
a₂ = C₁(1-√2)²+C₂((1+√2)²-2-5/2
= C₁(1-√2)²+C₂((1+√2)²-9/2=19
3(C₁+C₂)+2(C₂-C₁)√2)=97/2..(2)
By solving 1 and 2 we get
C₁=1/2(5/2-4√2)
C2=1/2(5/2+4√2)
aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2
Hence, aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
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It is multiple choice and you will have two boxes checked
The correct options are : x = 1.5, side length is 1.6, and side length is 3.9.
We are given a triangle. The vertices of the triangle are P, Q, and R. The lengths of the sides PQ, QR, and RP are "x + 0.1", "x + 2.4", and "3x - 0.6". The triangle is an isosceles triangle. The lengths of the sides RP and QR are equal to each other. So, we can form an equation and find the value of the variable "x".
RP = QR
3x - 0.6 = x + 2.4
2x = 3
x = 1.5
The length of the side PQ is x + 0.1 = 1.5 + 0.1 = 1.6. The length of the side QR is x + 2.4 = 1.5 + 2.4 = 3.9. The length of the side RP is 3x - 0.6 = 3(1.5) - 0.6 = 3.9.
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2 5 Evan mixed 2 pounds of nuts with 1 pounds of 3 6 7 raisins and 1 pounds of chocolate chips. How many 8 pounds did this mixture weigh? 1 3 24 B. © 6 6 3 6
Give that the nuts weigh 2 whole and a 2/3 pounds, raisins weigh 1 whole and a 5/6 ponds, and the chocolate chips weigh 1 whole 7/8 pounds.
All these ingredients are mixed to obtain the mixture.
Note that this mixture contains the above 3 things in the quantity mentioned. And there is no other stuff in the mixture.
So the weight of the individual ingredients would add up to get the weight of the mixture, therefore the weight of the mixture is calculated as,
[tex]2\frac{2}{3}+1\frac{5}{6}+1\frac{7}{8}\Rightarrow\frac{8}{3}+\frac{11}{6}+\frac{15}{8}=\frac{51}{8}=6\frac{3}{8}[/tex]Thus, the mixture weigh 6 whole and a 3/8 pounds.
Therefore, option (c) is the correct choice.
The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 202 feet, what is the area of the garden in square feet?
We have the following rectangular garden
The perimeter is 202 feet, we can do the following equality
[tex]2(x+9)+2x=202[/tex]Now we solve "x"
[tex]\begin{gathered} 2x+18+2x=202 \\ 4x=202-18 \\ x=\frac{184}{4} \\ x=46 \end{gathered}[/tex]Now, we know the longer (l = 55) and the width (w = 46)
To find the area we use the following equation
[tex]\begin{gathered} A_R=l\cdot w \\ A_R=55\cdot46 \\ A_R=2530 \end{gathered}[/tex]In conclusion, the area of the garden is 2530 square feet
Find thr value of x for which 1 II m.
The value of x is 50 for which line l is parallel to line m and the angles are equal by the properties of parallel lines that is vertically opposite angles are equal.
What is parallel lines?Two lines (in the same plane) are said to be parallel if they never collide, regardless matter how far they are extended on either side. Parallel lines travel parallel to each other, like train tracks. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.
Here,
Since l ⇵ m,
Vertically opposite angles are equal by the properties of parallel lines.
2x-5=95
2x=100
x=50
The value of x is 50, which means that line l is parallel to line m and the angles are equal according to the property of parallel lines, which states that vertically opposing angles are equal.
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Given the function k(n) = -3n + 2, and its domain is described by the set {6,-8, 4, 2}, what is therange?
The domain of a function is the set of values where the function is defined (values of x where y is defined).
The range of a function are the values of the function where is defined (values of y).
For the given function:
[tex]k(n)=-3n+2[/tex]Domain: values of n {6,-8, 4, 2}
Range: values of k(n)
n= 6
[tex]\begin{gathered} k(6)=-3(6)+2 \\ =-18+2 \\ =-16 \end{gathered}[/tex]n=-8
[tex]\begin{gathered} k(-8)=-3(-8)+2 \\ =24+2 \\ =26 \end{gathered}[/tex]n=4
[tex]\begin{gathered} k(4)=-3(4)+2 \\ =-12+2 \\ =-10 \end{gathered}[/tex]n=2
[tex]\begin{gathered} k(2)=-3(2)+2 \\ =-6+2 \\ =-4 \end{gathered}[/tex]Then, the range is: {-16, 26, -10, -4}
Simplify the expression.
(x)2(2xy3)5
2x3y15
32x7y8
32x7y15
10x3y8
Answer:
[tex]32x^7y^{15}[/tex]
Step-by-step explanation:
[tex]x^2 (2xy^3)^5 \\ \\ =x^2(2^5)(x^5)(y^{(3)(5)}) \\ \\ =x^2(32)(x^5)(y^{15}) \\ \\ =32x^7y^{15}[/tex]
1AcellusFind the area of the shaded region.Help Resources80°5 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.Enter
The formula for finding the area of the unshaded segment is given as
[tex]A=(\frac{\pi\theta}{360}-\frac{\sin \theta}{2})r^2[/tex]Given the following parameters,
π = 3.14
θ = 80°
r = 5 cm
Substituting,
[tex]\begin{gathered} A=(\frac{3.14\times80}{360}-\frac{\sin \text{ 80}}{2})\times5^2 \\ =(\frac{251.2}{360}-\frac{0.9848}{2})\times25 \\ =(0.6978-0.4924)\times25 \\ =0.2054\times25 \\ =5.135\approx5.1\operatorname{cm}^2 \end{gathered}[/tex]To find the area of the shaded portion, we would subtract the area of the unshaded segment from the area of the circle.
Area of circle = πr²
[tex]3.14\times5^2=78.5\operatorname{cm}^2[/tex]Therefore,
The area of the shaded region = 78.5 - 5.1 = 73.4 cm²
I have a question regarding a math topic on my review
The set of real numbers strictly contains the set of integers.
Every integer is a real number.
But pi is a real number and is not an integer
Hence choice A is correct