A characteristic of parallel lines is that they have the same slope.
So for the line
[tex]y=\frac{5}{4}x-7[/tex]The slope is
[tex]m=\frac{5}{4}[/tex]Any line parallel to this one will have the same slope:
[tex]y=\frac{5}{4}x+b[/tex]Foe example, let's say that the parallel line has to pass through the point (2,3)
Using the point slope form you can determine the equation as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{5}{4}(x-2) \\ y-3=\frac{5}{4}x-\frac{5}{2} \\ y=\frac{5}{4}x-\frac{5}{2}+3 \\ y=\frac{5}{4}x+\frac{1}{2} \end{gathered}[/tex]The line
[tex]y=\frac{5}{4}x+\frac{1}{2}[/tex]is parallel to
[tex]y=\frac{5}{4}x-7[/tex]26. Find the perimeter of the polygon.3 ina. 15 inb. 21 inc. 9 in
To find the perimeter of the regular polygon, that in this case is a pentagon, multiply 5 by the sidelength of the pentagon, it means 5 times 3.
[tex]\begin{gathered} P=5\cdot3 \\ P=15 \end{gathered}[/tex]The perimeter of the polygon is 15in
I need to know the system of equation in the photo
Solution:
The graph has a solution (4,-1);
That is, the system of equation must satisfy x=4 as y=-1.
LINE 1 has its y-intercept;
[tex]\begin{gathered} (0,1) \\ \end{gathered}[/tex]LINE 2 has its y-intercept as;
[tex](0,-5)[/tex][tex]\begin{gathered} x+2y=2 \\ 2y=-x+2 \\ y=-\frac{1}{2}x+\frac{2}{2} \\ y=-\frac{1}{2}x+1 \\ \\ x-y=5 \\ y=x-5 \end{gathered}[/tex]Thus, the system of equation that satisfy the graph is;
[tex]\begin{gathered} x-y=5 \\ x+2y=2 \end{gathered}[/tex]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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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
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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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
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
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
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:
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
Find the quotient. 1 5 – 2. + 3 1 55+3= 2 (Type a whole number, fraction, or mixed number.)
we have
[tex]5\frac{1}{2}\colon3[/tex]Convert mixed number to an improper fraction
5 1/2=5+1/2=11/2
substitute
(11/2):3=11/(3*2)=11/6
convert to mixed number
11/6=6/6+5/6=1+5/6=1 5/6
answer is
11/6 or 1 5/6
5. 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.
Question 4 (5 points)
In Brock's class of 24 students, 10 students report that math is their favorite class, 25% of the students report that science is
their favorite, and 1/3 prefer reading.. Show your work and/or explain your answer: Which subject is favored by the greatest
number of students? (5 points)
Mathi is favored by the greatest i.e 10 students, using percentage
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The % sign is used to denote it.
There are 24 students in Brock's class
10 students say math is their favorite class , 25% say that science is their favorite class and 1/3 prefer reading.
Now you have to find out if more students prefer math or science. Well since the information tells you that 10 students prefer math, you need to find out that 25% of students prefer science and 1/3 prefer reading.
For 1st case, math favorite have 10 students,
For 2nd case, 25% of 24 is 24*25/100
=24*1/4
=6
And for 3rd case, who prefer reading is 1/3rd of students which is 24*1/3
=8
So Most students like math.
Hence, Mathi is favored by the greatest i.e 10 students.
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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]Suppose that f is a one-to-one function, and f^-1 is its inverse. Suppose also that h(x) = 4 and g(x) = x^2 +xsecx. Then which of the following do we NOT know to be true?
Given:
The functions are,
h(x) = 4,
g(x) = x²+xsecx
The objective is to find which of the following is not known to be true.
Let's consider option (A).
[tex]\begin{gathered} (f\circ f^{-1}\circ h)(x)=(f(f^{-1})\circ h)(x) \\ =h(x) \\ =4 \end{gathered}[/tex]Thus, option (A) is true.
Let's consider option (B).
[tex]\begin{gathered} (g\circ h\circ f^{-1})(x)=(g(h(x))f^{-1})(x) \\ =(g(4))f^{-1})(x) \\ =((4^2+4\sec 4)f^{-1})(x) \\ =((16+4\sec 4)f^{-1}(x)) \end{gathered}[/tex]Since, the obtiaed answe doesn't matches with the given options.
Hence, option (B) is not true.
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%.
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]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. * 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.
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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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
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 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,
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 65Find the volume for the solid picture. ROUND TO THE NEAREST HUNDREDTH
The given picture is in the shape of the cuboid
The general expression for the voulme of cuboid is : Length x Breadth x Height
In the given picture of cuboid we have :
Length = 9.6 in
Breadth = 6.75 in
Height = 2 in
So, the volume of given picture is :
[tex]\begin{gathered} \text{ Volume of Cuboid = Length}\times Breadth\times Height \\ \text{ Volume of Cuboid = 9.6}\times6.75\times2 \\ \text{Volume of Cuboid = }129.6in^3 \end{gathered}[/tex]To round off to the nearest hunredth : 129.6 will become 129.60
So, the volume of given solid picture is 129.60 in³
Answer : The volume of given solid picture is 129.60 in³
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.
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
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]
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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What is the first step to solving the following equation?5x – 11 = 42
Answer:
add 11 on both sides
Step-by-step explanation:
to solve this, you want x alone on one side. To achieve this, you first add 11 on both sides, so you only have the 5x alone.
Second step then is something to get only one x on the left side ;-)
(divide both sides by 5)
Answer:
the first step is to get the x term by itself on one side