The most appropriate choice for distance formula will be given by Area of rectangle is 40 sq units
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Here,
Let A = (-1 , -4), B = (-1, 6), C = (3, 6) and D = (3, -4)
Length of AB =
[tex]\sqrt{((-1)-(-1))^2 + (-4-6)^2}\\\sqrt{100}\\10 units[/tex]
Length of BC =
[tex]\sqrt{((-1)-3)^2 + (6-6)^2}\\\sqrt{16}\\4 units[/tex]
Length of rectangle = 10 units
Breadth of rectangle = 4 units
Area of rectangle = [tex]10 \times 4[/tex] = 40 sq units
Fourth option is correct
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Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
A.
Overall it has a relation that there are more sold cups when the temperature is lower. On the other hand, based on the 40 degrees part, that have to different values of two different days, we can say is not the only factor.
B.
The best lineal approach is the line created with the points at 20 and 80 degrees. First the slope:
[tex]m=\frac{y1-y2}{x1-x2}=\frac{20-10}{20-80}=\frac{10}{-60}=-\frac{1}{6}[/tex]Now the intercept with y axis, b:
[tex]\begin{gathered} y=mx+b \\ 20=20(-\frac{1}{6})+b \\ 20+\frac{20}{6}=b=23.33=\frac{70}{3} \end{gathered}[/tex]The final line formula is:
[tex]y=-\frac{x}{6}+\frac{70}{3}[/tex]find the other binomial p squared -13 p +36 =(p-9)
To find the other factor of the polynomial
[tex]p^2-13p+36[/tex]We need to find two integers which multiplication gives 36 and addition is -13.
This integers would be -9 and -4, then we have
[tex]p^2-13p+36=p^2-9p-4p+36[/tex]now we factor the right term using common factors:
[tex]\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}[/tex]Hence:
[tex]p^2-9p-4p=(p-9)(p-4)[/tex]Therefore, the other binomial we are looking for is (p-4).
74. Noam wants to put a fence around his rectangular garden. His garden measures 35 feet by 50 feet. Thegarden has a path around it that is 3 feet wide. How much fencing material does Noam need to enclose thegarden and path?A. 97 ftB. 194 ftC. 182 ftD. 146 ft
Given:
The length of the rectangular garden, l=50 feet.
The breadth of the rectangular garden, b=35 feet.
The width of the path around the garden, w=3 feet.
The figure can be drawn as,
So, the length of the fence, L=l+2w.
The breadth of the fence, B=b+2w
The perimeter of the fence can be calculated as,
[tex]\begin{gathered} P=2(L+B) \\ =2(l+2w+b+2w) \\ =2(l+b+4w) \\ =2(50+35+4\times3) \\ =2(50+35+12) \\ =2\times97 \\ =194\text{ ft} \end{gathered}[/tex]Therefore, the perimeter of the fence is 194 ft.
Option B is correct.
Which expressions simplify to a rational answer.
Question is attached below
The expression that simplify to rational number are as follows:
1 / 4 + 1 / 2 2.√9 3.7.(1 / 3) 7. √81 How to find rational numbers?A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0.
In a simpler terms, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.
Rational numbers can also be expressed in decimal form.
Rational numbers have terminating decimals.
Therefore, let's find the rational simplification in the options.
1 / 4 + 1 / 2 = 3 / 4 2.√9 = 2 × 3 = 93.7.(1 / 3) = 21 × 1 / 3 = 77. √81 = 7 × 9 = 72learn more on rational numbers here:https://brainly.com/question/7129080
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The answer for the bottom question need a fast quick answer
Area of a circle is
[tex]A=\pi\cdot r^2[/tex][tex]\begin{gathered} d=2r \\ d=22 \\ r=\frac{22}{2} \\ r=11 \end{gathered}[/tex][tex]\begin{gathered} A=\pi(11)^2 \\ A=380.133ft^2 \end{gathered}[/tex]The area of the garder is 380.13 square footsIf a square foot cost $ 1.25
[tex]\begin{gathered} 1ft^2\to1.25\text{dollars} \\ 380.13ft^2\to x \\ x=\frac{380.13ft^2\cdot(1.25dollar)}{1ft^2} \\ x=475.16\text{dollar} \end{gathered}[/tex]To cover the garden they need to buy $475 in mulchHow many tiles of 8 cm² is needed to cover a floor of dimension 6 cm by 24 cm? A. 6 B. 12 C. 18 D. 24
Answer:
18 tiles.
Step-by-step explanation:
24x6= 144
144/8= 18
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1. A coat at the Utopian Coat factory cost $99.99. The sales tax is 7%. Find the sales tax and the total cost of the jacket. (Round to the nearest cent).
The Solution:
Given that a coat costs $99.99 and the sales tax is $75.
We are required to find the actual sales tax and the total cost of the coat.
Step 1:
We shall find the sales tax.
[tex]\begin{gathered} \text{ Cost of the coat=\$99.99} \\ \\ \text{Sales tax of 7\% }=\frac{7}{100}\times99.99=0.07\times99.99 \\ \\ =6.999\approx\text{ \$7.00 (or 700 cent)} \end{gathered}[/tex]Thus, the sales tax is $7.00 or 700 cents.
Step 2:
We shall find the total cost of the coat.
The total cost of the coat is the sum of the coat's cost and the sales tax.
[tex]\text{ The total cost=99.99+6.999=106.989}\approx\text{ \$106.99}[/tex]Therefore, the correct answers are:
Sales tax =$7.00 or 700 cents.
Total cost = $106.99 or 10699 cents..99 or 10699 cents.
4. Ifline m has the equation y = 3x - 1, and line k is perpendicular to m and goes through the point (-4,3), find the equation of line k.
Answer:
The equation of the line k is
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Explanation:
Given that k is perpendicular to line m, defined as:
y = 3x - 1
the slope of k is the negative reciprocal of the slope of line m.
The slope of m is 3
The negative reciprocal of m is -1/3 (this is the slope of k)
Therefore, k is in the form
[tex]y=-\frac{1}{3}x+b[/tex]Since this line passes through the point (x, y) = (-4, 3), we can use this to obtain the value for the y-intercept, b
[tex]\begin{gathered} 3=-\frac{1}{3}(-4)+b \\ \\ 3=\frac{4}{3}+b \end{gathered}[/tex]Solving for b by subtracting 4/3 from both sides
[tex]\begin{gathered} b=3-\frac{4}{3} \\ \\ =\frac{5}{3} \end{gathered}[/tex]The equation is therefore,
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Which of the following are equal to sec x? Choose all that apply. 3 answers
Verify each option
A ---> 1/sinx=cscx -----> is not the answer
B ---> 1/cosx=secx ----> is the answerC ---> cosx/tanx=cosx/(sinx/cosx)=cos^2x/sinx -----> is not the answer
D ---> tanx/sinx=(sinx/cosx)/sinx=1/cosx=secx -----> is the answerE ---> cotxsinx=(cos/sinx)sinx=cosx ----> is not the answer
F ----> tanxcscx=(sinx/cosx)(1/sinx)=1/cosx=secx ----> is the answertherefore
The answer is
options B, D and FAnswer:
B, D, E.
Step-by-step explanation:
B: [tex]\frac{1}{cos(x)}[/tex]
D: [tex]\frac{tan(x)}{sin(x)}[/tex]
E: [tex]tan(x) csc (x)[/tex]
Price of PensWhat is the slope ofthe line?Price ($)0-NW A o ovo2Give your answer asa fraction in simplestform.11 2 3 4 5 6 7 8 9Number of Pens
Solution
For this case we can select the following two points:
(0,0) and (4,6)
We can find the slope using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-0}{4-0}=\frac{3}{2}[/tex]then the answer after simplify would be:
3/2
The figure shows the measures of various angles of a roof and it supports. Find the measure of angle 1, the angle between an eave and a horizontal support beam.
Answer:
35 degrees.
Explanation:
The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.
Since the sum of the angles in a triangle is 180 degrees, hence:
110 + (base angles) = 180
110 + (<1 + <1) = 180 (since base angles are the same)
110 + 2<1 = 180
2<1 = 180-110
2<1 = 70
Divide both sides by 2
2<1/2 = 70/2
<1 = 35 degrees
Hence the angle between an eave and the horizontal support beam is 35 degrees.
-Given that f(x) = 6(x - 1). Choose the correct statement. A. f-1(12) = 3.5 B. f-1(3) = 1 c. f-16) = 3 D. f-1(9) = 2.5
Given that function is f(x) = 6(x - 1).
Let y = 6(x - 1). Replace x with y and then solve for y.
[tex]\begin{gathered} x=6(y-1) \\ \Rightarrow x=6y-6 \\ \Rightarrow6y=x+6 \\ \Rightarrow y=\frac{x+6}{6} \end{gathered}[/tex]Thus, f^-1(x) = (x + 6)/6.
[tex]f^{-1}(12)=\frac{12+6}{6}=3[/tex][tex]f^{-1}(3)=\frac{3+6}{6}=1.5[/tex][tex]f^{-1}(6)=\frac{6+6}{6}=2[/tex][tex]f^{-1}(9)=\frac{9+6}{6}=2.5[/tex]Thus, option D is correct.
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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i need help solving this with the statements and reasons
Given that:
[tex]\bar{AB}\mleft\Vert \mright?\bar{DC}[/tex]To prove that:
[tex]\Delta ABE\cong\Delta\text{CDE}[/tex]We know that congruent parts of congruent triangles are congruent
[tex]\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}[/tex]Given that E is the midpoint of AC, therefore,
[tex]\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}[/tex]By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent
5(3a-1) - 2(3a+2)=3(a+2) + vselect two expressions that are equivalent to v.
Let's solve the equation for v to identify the expressions:
[tex]\begin{gathered} 5(3a-1)-2(3a+2)=3(a+2)+v \\ 15a-5-6a-4=3a+6+v \\ 9a-9=3a+6+v \\ v=9a-3a-9-6 \\ v=6a-15 \\ v=3(2a-5) \end{gathered}[/tex]Therefore the equivalent expressions are D and E
How many solutions will each equation have?x^2+6x+5
To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.
[tex]\begin{gathered} x^2+6x+5=0 \\ (x+5)(x+1)=0 \\ x+5=0 \\ x=-5 \\ x+1=0 \\ x=-1 \end{gathered}[/tex]This equation has 2 solutions which are -5 and -1.
STATEMENTREASON1. DBC - RST1. Given2. ZABC - ZDBC+ ABD2. Angle addition therom3.3. Ifa=b+cand c>0,thena > b4. ABC > RST4. SubstitutionWhich of the following statements would complete the proof in line 3?O ZABC> ZABDO LABC> DBCO ZDBC> ZABD
Answer
Option B is correct.
Angle ABC > Angle DBC
Explanation
Since it's been proven that
Angle ABC = Angle ABD + Angle DBC
Since Angle ABD > 0,
Angle ABC > Angle DBC is the part that completes the proof that
Angle ABC > Angle RST
Hope this Helps!!!
The wholesale price for a pair of shoes is $3.50. A certain department store marks up the wholesale price by 60%. Find the price of the pair of shoes in the department store
Given
Wholesale price for a pair of shoes = $3.50.
Wholesale price by 60%.
Find
price of the pair of shoes in the department store
Explanation
Price in deparrtmental store is 60% more than wholesale
[tex](1+60\%\text{ \rparen of wholesale }[/tex]so ,
[tex]\begin{gathered} 1.6\times3.50 \\ 5.60 \end{gathered}[/tex]Final Answer
Therefore , the price of the pair of shoes in the department store is $5.60.
estimate 794 divided by 18=?
Answer:
C 40
Step-by-step explanation:
794 is about 800
18 is about 20
800/20=40
Given a regular octagon and a regular nonagon, which one has the greater interior angle?(Type your answer as the name of the polygon)
Answer:
Nonagon
Explanation:
Each of the interior angles of a polygon is calculated using the formula:
[tex]\frac{180^0\mleft(n-2\mright)}{n}[/tex]An Octagon has 8 sides, therefore:
[tex]\begin{gathered} Each\; \text{Interior Angle=}\frac{180^0(8-2)}{\square} \\ =\frac{180\times6}{8} \\ =\frac{1080^0}{8} \\ =135^0 \end{gathered}[/tex]A Nonagon has 9 sides, therefore:
[tex]\begin{gathered} Each\; I\text{nterior Angle=}\frac{180^0(9-2)}{9} \\ =\frac{180\times7}{9} \\ =\frac{1260^0}{9} \\ =140^0 \end{gathered}[/tex]Therefore, the nonagon has a greater interior angle.
Consider the following relation. y= 2x-4
Find four points contained in the inverse. Express your values as an integer or simplified fraction.
ASAP PLEASE¡
Four points that are contained in the inverse function include the following:
Point = (0, 4).Point = (1, 4.5).Point = (2, 5).Point = (4, 6).What is an inverse function?An inverse function refers to a type of function that is obtained by reversing a mathematical operation in a given function (f(x)).
In order to determine the inverse of the given function, we would interchange both the input value (x) and output value (y) as follows:
y = 2x - 4
x = 2y - 4
Subtracting 4 from both sides, we have:
x + 4 = 2y - 4 + 4
2y = x + 4
Dividing both sides by 2, we have:
y = (x + 4)/2
y = x/2 + 4
When x = 0, we have:
y = x/2 + 4
y = 0/2 + 4
y = 4
Point = (0, 4).
When x = 1, we have:
y = x/2 + 4
y = 1/2 + 4
y = 4.5
Point = (1, 4.5).
When x = 2, we have:
y = x/2 + 4
y = 2/2 + 4
y = 5
Point = (2, 5).
When x = 4, we have:
y = 4/2 + 4
y = 0/2 + 4
y = 6
Point = (4, 6).
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72bz +96b2h + 90xbz + 120xbh +
Factoring
Factor the expression:
[tex]72b^2z+96b^2h+90xbz+120xbh[/tex]Divide the expression into two halves:
[tex](72b^2z+96b^2h)+(90xbz+120xbh)[/tex]Factor b^2 from the first group and xb from the second group:
[tex]b^2(72z+96h)+xb(90z+120h)[/tex]Now find the greatest common multiple of 72 and 96:
72= 2*2*2*3*3
96=2*2*2*2*2*2*3
Now we take the common factors with their least number of repetitions:
GCF=2*2*2*3=24
Now we find the GCF of 90 and 120:
90=2*3*3*5
120=2*2*2*3*5
GCF=2*3*5=30
Taking the GCF of each group:
[tex]\begin{gathered} b^224(3z+4h)+xb30(3z+4h) \\ =24b^2(3z+4h)+30xb(3z+4h) \end{gathered}[/tex]Now we finally take out 3z+4h from both groups:
[tex]\mleft(3z+4h\mright)(24b^2+30xb)[/tex]This last expression can be further factored by taking out 6b from both terms:
[tex]6b(3z+4h)(4b+5x)[/tex]This is the final expression factored as much as possible
can you help me figure out the equation in the drop down menus
To find:
The piecewise function for the graph.
Solution:
From the graph, it is clear that when x is less than -1, the graph passes through (-1, -3) and (-2, -5).
It is known that the equation of a line passes through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]So, the equation of line passing through (-1, -3) and (-2, -5) is:
[tex]\begin{gathered} y-(-3)=\frac{-5-(-3)}{-2-(-1)}(x-(-1)) \\ y+3=\frac{-2}{-1}(x+1) \\ y+3=2x+2 \\ y=2x-1 \end{gathered}[/tex]So, the first drop down is "2x - 1", and second drop down is "x is less than or equal to -1".
Now, the graph passes through (1, 5) and (2, 6). So, the equation of the line is:
[tex]\begin{gathered} y-5=\frac{6-5}{2-1}(x-1) \\ y-5=x-1 \\ y=x+4 \end{gathered}[/tex]So, the third drop down menu is "x + 4" and the fourth drop down menu is "x is greater than or equal to 1".
Brenda is preparing food for a picnic. She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich
For 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is Brenda who must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, and 45 minutes to make a dozen cookies.
If she makes [x] sandwiches and [y] dozen cookies, then the total time she would take to make them can be written as -
t = 4x + 3y
For 6 sandwiches and 3 dozen cookies, we can write -
t(6, 3) = 4 x 6 + 3 x 3 = 24 + 9 = 33 minutes
t(6, 3) = 33 minutes
Therefore, for 6 sandwiches and 3 dozen cookies, the total time taken by Brenda would be 33 minutes.
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{Complete question is given below -
She must make at least 6 sandwiches and at least 3 dozen cookies. It takes her 4 minutes to make a sandwich, x, and 45 minutes to make a dozen cookies, y.}
Solve graphically by the intersection method. Give the solution in interval notation.5x+2<2x−4
The green line represents 5x + 2
The purple line represents 2x - 4
The orange-colour line represents the intersection of the lines above, which is the solution to the inequality:
5x + 2 < 2x - 4
The intersection is represented by a broken line, to signify the strict < in the equation
Ms. Mistovich and Ms. Nelson are having a competition to see who can get morestudents to bring in extra tissues for their classroom. Ms. Mistovich starts with 4 boxesand each week she gets two more boxes from her students. Ms. Nelson starts with 1box and each week she gets 3 more boxes from her students. Write a system ofequations to represent the situation. (1 pt)y=2x+4y=3x+1Ooy=2x+4y=2x+3y=4x+2y=3x+1y=2x+3y=4x+1o
To write an equation, it is enough to know the rate of change (slope) and the initial value (y-intercept).
The equation of a line of slope m and y-intercept b is:
[tex]y=mx+b[/tex]For Ms. Mistovich, the initial value is 4 and the rate of change is 2.
For Ms. Nelson, the initial value is 1 and the rate of change is 3.
Therefore, the equations that model this situation, are:
[tex]\begin{gathered} y=2x+4 \\ y=3x+1 \end{gathered}[/tex]Expand the polynomial. 1. (m^2-n)(m^2+2n^2)2. (a-2)(4a^3-3a^2)
1)
The given polynomial is
[tex](m^2-n)(m^2+2n^2)[/tex]Multiply as follows:
[tex](m^2-n)(m^2+2n^2)=m^2(m^2+2n^2)-n(m^2+2n^2)[/tex][tex]=m^2\times m^2+m^2\times2n^2-n\times m^2-n\times2n^2[/tex][tex]=m^4+2m^2n^2-m^2n-2n^3[/tex]Hence the required expansion is
[tex](m^2-n)(m^2+2n^2)=m^4+2m^2n^2-m^2n-2n^3[/tex]2)
The given polynomial is
[tex](a-2)(4a^3-3a^2)[/tex]Multiply as follows:
[tex](a-2)(4a^3-3a^2)=a(4a^3-3a^2)-2(4a^3-3a^2)[/tex][tex]=a\times4a^3-a\times3a^2-2\times4a^3-(-2)\times3a^2[/tex][tex]=4a^4-3a^3-8a^3+6a^2[/tex][tex]=4a^4-11a^3+6a^2[/tex]Hence the required expansion is
[tex](a-2)(4a^3-3a^2)=4a^4-11a^3+6a^2[/tex]select all of the following equations which represent a function?
To verify that something is a function, we use the horizontal line rule. That is, if the horizontal line passes through two points, then the graph is not a function, like this:
Then the circles and the ellipses are not functions. Then the functions in the problem would be:
1, 3 and 6.
Find the x-intercepts and y-intercept of the following
function.
f(x) = (x+7) (x + 1)(x − 2)
Write your answer in coordinate pairs of the form (x, y).
Provide your answer below:
x-intercept: ().(
]).() and
y-intercept:
Step-by-step explanation:
there are 3 x-intercepts (the x- values when y = 0). because y is only 0, when one of the 3 factors is 0.
and that is the case for
x = -7
x = -1
x = 2
so, formally, the x- intercepts are
(-7, 0), (-1, 0), (2, 0)
the y intercept is the y- value when x = 0.
(0 + 7)(0 + 1)(0 - 2) = 7×1×-2 = -14
the y-intercept is formally
(0, -14)
Find the 100-th term of the following sequence
3, 10, 17, 24, …
Also find the sum of the first 100 terms.
Answer:
696
Step-by-step explanation:
*nth term = 7n - 4
n = 100
7 × 100 - 4 = 696
So the 100th term of the following sequence is: 696
*To find the nth term:
They all increase by 7 so it is 7n3 - 7 = -4 so then it is 7n - 4Answer:
Below in bold.
Step-by-step explanation:
This is an arithmetic sequence with a1 = 3 and d = 7.
So, 100th term
= a1 + d(n - 1)
= 3 + 7(100-1)
= 696.
Sum (100) =
(n/2)[2a1 + d(n - 1)]
= 50(6 + 99*7)
= 50 * 699
= 34950.
