Step-by-step explanation:
here we have to know that, if A/B=A'/B' is equal to 1 it means it doesn't cut. if it isn't equal to 1, it does.
A=3 B=4
A'=4 B'=3
3/4=4/3 it cuts. Now, they are straight lines because we don't have x² or anything, so they can just intersect once between them.
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ? The population of Town C in 2000 was of the population in 2005. The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005
This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.
Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient
Statement 1 and Statement 2 combined:
Let X= the population in 2000
Let Y= the population in 2005
Let Z= the population in 2010
From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y
Multiply both sides by 3 to get [tex]3X=2Y[/tex]
Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]
=>[tex]Y=1.5X[/tex]
As per statement 2, let's first determine the increase in the number of people from 2000 to 2005
If [tex]Y=1.5X[/tex], we know
X= the population in 2000
1.5X= the population in 2005
[tex]1.5X-X=0.5X[/tex]
So, the population increased [tex]0.5X[/tex] from 2000 to 2005
So, from 2005 to 2010, the population increased at least 0.5X
1.5X= the population in 2005
[tex]1.5X+0.5X=2.0X[/tex]
So, the population in 2010 was at least 2.0X
In other words, the population at least doubled from 2000 to 2010
So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?
(1) The population of Town C in 2000 was 2/3 of the population in 2005.
(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
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What is the nth term rule of the quadratic sequence below?
6
,
20
,
40
,
66
,
98
,
136
,
.
.
.
Answer:
3n² + 5n - 2
Step-by-step explanation:
Given sequence:
6, 20, 40, 66, 98, 136, ...
Calculate the first differences between the terms:
[tex]6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136[/tex]
As the first differences are not the same, calculate the second differences:
[tex]14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
Therefore, the n² term is: 3n²
Compare 3n² with the given sequence:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]
The second operations are different, therefore calculate the differences between the second operations:
[tex]3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18[/tex]
As the differences are the same, we need to add 5n as the second operation:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]
Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.
Therefore, the nth term of the quadratic sequence is:
3n² + 5n - 2
A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers use coupons. 36 times out of 40 these results were considered accurate to within 2.5%. what is the confidence interval?
The confidence interval comes out to be (0.685,0.735).
Calculating the Confidence Level and Other Terms
The confidence level can be calculated as follows,
z = [tex]\frac{36}{40} * 100%[/tex]%
z = 90 %
The margin error is given as, E= 0.025
The p value in this case is 0.71
Calculating the Confidence Interval
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
Confidence interval can be obtained by using the following formula,
(p-E, p+E) = (0.71-0.025, 0.71+0.025).
Therefore, the confidence interval is (0.685, 0.735).
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In a class test containing 20 questions, 5 marks are given for every correct answers, ( -2 ) marks given for every incorrect answers and zero mark for question not attempted. Anju gets 9 correct answer and 11 incorrect answers. What is her total score?
Answer:
she has 23 points
Step-by-step explanation:
hope this helps and mark brainliest please
A local business has an area reserved behind the store for a parking lot that is 78 meters long by 19 meters wide. The stalls of the lot are at 90° angles to a required aisle that bisects the lot. The aisle is 8 meters by 78 meters.
An area reserved for a parking lot is 78 meters long by 19 meters wide. 2 stalls and an aisle are in the reserved area. The aisle is 78 meters long and 8 meters wide.
Use the layout of the parking lot to answer the questions.
What is the total area available for cars to park?
m2.
If the parking spaces are compact, they have an area of 12.5 m2. How many compact parking spaces will fit in the lot?
.
If the parking spaces are not compact, they will be 3 meters by 5.5 meters. How many noncompact parking spaces will fit in the lot?
.
The total area available for cars to park will be 858m².
How to calculate the area?The area of the parking lot will be:
= 78 × 19
= 1482m²
The area of aisle will be:
= 8 × 78
= 624m²
The available area will be:
= 1482m² - 624m²
= 858m².
The compact parking spaces that will fit in the lot will be:
N × 12.5 = 858
N = 858/12.5
N = 68
The non compact parking spaces that will fit in the lot will be:
N × 16.5 = 858
N = 858/16.5
N = 52
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4. In the triangle ABC, angle A = 90° and
sec B = 2
a.Work out the size of angles B and C.
b.Find tan B.
c. Show that 1 + tan² B = sec² B.
Step-by-step explanation:
here the answers is it helpful
help me please!!!! 15 points
Answer:
17 sq. cm
Step-by-step explanation:
1st you split into 2 smaller shapes
Smaller shape:
A = lw
= 1(2)
= 2
Bigger Shape:
A = lw
= 3(5)
= 15
Add them together
15 + 2 = 17
−5(−5x+3)−5x+5= -50
Solve for X
Answer:
x = -2
Step-by-step explanation:
you can fist distribute -5 into the parenthesis
25x - 15 - 5x + 5 = -50
then combine like terms
20x - 10 = -50
add 10 to both sides
20x = -40
lastly divide both sides by 20
x = -2
that is your answer
1/8 of passengers of a train were children. if there were 40 children travelling in the train on a certain day, how many adults were there in the train?
280 adults were there in the train.
What is linear equation definition and example?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of linear equation is y=mx + b. noun. 20. A polynomial equation of the first degree (such as x = 2y - 7)Given,
Total children are in the train = 40
1/8 are children in train and no of children in train ,
∴ 1/8 × x = 40
x = 40 × 8 ⇒ 320
The no of passenger in train = 320
in total passenger, 40 are children .
So, rest adults passengers are = 320 - 40 ⇒ 280
There fore, 280 adults were there in the train.
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In the figures below show a similar shape, how long is the side 7x - 5 ?
Answer:30
Step-by-step explanation:
To solve the problem, I will have to solve the equation for the first shape.
5^2 + 4^2 = 25 + 16 = 41
The second shape seems to be 2.5 times bigger than the first shape.
7x - 5 + 24 = 102.5
+5 +5
7x + 24 = 107.5
-24 -24
7x = 83.5
7 7
x = 11.9285714286
x = 11.9^2
11.9^2 = 141.61
Looking at the angles we know, there's a 4 and a 24 so the second shape is 6 times larger than the first shape. There's also a 5 which means the solution to the problem, 7x - 5, should be 30.
7x - 5 = 30
+5 +5
7x = 35
7 7
x = 5
linear slope help pls
A slope is also known as the gradient of a line. The slope of the given linear table is $250 per car.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the linear table is,
m = ($4,000 - $2,500)/(12-6) = $250 per cars
Hence, the slope of the given linear table is $250 per car.
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Suppose that the relation H is defined as follows.
H= = {(2, 7), (2, -1), (-8, -2)}
Give the domain and range of H.
Write your answers using set notation.
domain = = 0
range = 0
X
Answer:
Domain = {-8, 2}Range = {-2, -1, 7}Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
Simplify [4 -⅓ ( 64 ⅓ - 64 ⅔) ]
Answer:
-3*4^2/3.
Step-by-step explanation:
[4 -⅓ ( 64 ⅓ - 64 ⅔) ]
= 1/4^1/3 ( 4 - 4^2)
= 1 / 4^1/3 * -12
= -12/ 4^1/3
= -12 * 4^2/3 / 4
= -3*4^2/3
Given that AABC~ ADEF, solve for x.
Answer:
GIVEN THAT THE TRIANGLES ARE SIMILAR THEREFORE we can use similarity theorem.
Step-by-step explanation:
[tex] \frac{30}{5} = \frac{24}{x} \\ 30x = 120 \\ \frac{30x}{30} = \frac{120}{30} \\ x = 4[/tex]Hope this helps!
If h(x)=-3x - 10, find h(-3)?
Answer:
h(-3)=-1
Step-by-step explanation:
h(x)=-3x - 10
Let x = -3
h(-3)=-3(-3) - 10
= 9-10
=-1
The price of a car is £2750.
In a sale, the price is reduced by 20%
Work out the price of the car in the sale
Answer: $2200
Step-by-step explanation:
20% = 0.2
2750 x 0.2 = 550
2750 - 550 = 2200
OR
2750 x (1-0.2) =
2750 x (0.8) = 2200
Answer:
£2200
Step-by-step explanation:
Formula:
20% off
so:
2750x0.20= x Price of car with 80% off
2750-x= Price of car with 20% off
Find answer:
(look in image to see my work on 2750x0.20, I used Microsoft Whiteboard)
2750x0.20=550.00
2750-550=2200
The price of the car 20% off is £2200
Cindy works at Jurassic Park and has been tasked to design a container in the shape of a rectangular prism for the incoming baby dinosaurs. The scaled model of the container has dimensions 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model. By what amount should Cindy increase each dimension of the scaled model?
The amount Cindy should increase for each dimension of the scaled model will be 12 meters.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
Given that:-
The scaled model of the container has dimensions of 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model.The scale model will be solved as follows:-
Present volume = 2 x 4 x 6 = 48 cubic meters
Let the lengths be increased by x meters now the new volume will be:-
( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84
( x² + 6x + 8 ) ( 6 + x ) = 48 x 84
( x³ + 44x + 12x² - 3984 ) = 0
By solving the cubic equation we will get the value of x = 12 meters.
Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.
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expand -2/20 (1 - 2x + 2)
The expansion of the expression is [tex]\frac{4x - 6}{20}[/tex]
How to expand the expressionGiven the expression;
-2/20 (1 - 2x + 2)
= [tex]\frac{-2}{20}[/tex] × (1 -2x +2 )
Open up the bracket by multiply with -2, we have
= [tex]\frac{-2 + 4x -4}{20}[/tex]
Collect like terms in the numerator
= [tex]\frac{4x - 6}{20}[/tex]
Thus, the expression of the expression is [tex]\frac{4x - 6}{20}[/tex]
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lol please help me goodness gracious
To find x = [tex]\frac{1}{2} (AB+CD)[/tex]
[tex]x=\frac{1}{2} (46+25)\\\ x=\frac{1}{2} (71)\\ x =35.5[/tex]
Hope it helps!
ΔXYZ was reflected to form ΔLMN.
Triangle X Y Z is reflected to from triangle L M N. Angle Z Y X is 86 degrees and angle Y X Z is 38 degrees. Angle L N M is 56 degrees and angle N M L is 86 degrees.
Which statements are true regarding the diagram? Check all that apply.
ΔXYZ ≅ ΔLMN
∠Y ≅ ∠M
∠X ≅ ∠L
∠Z ≅ ∠L
YZ ≅ ML
XZ ≅ LN
ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Reflection is a rigid transformation, hence it produces congruent figures with congruent angles.
∠Y + ∠X + ∠Z = 180 (angle in a triangle)
86 + 38 + ∠Z = 180
∠Z = 56°
Also:
∠N + ∠M + ∠L = 180 (angle in a triangle)
86 + 56 + ∠L = 180
∠L = 38°
ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN
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Bill's Roast Beef sells 8 times as many sandwiches as Pete's Deli. The difference between their sales is 434 sandwiches. How many sandwiches did each sell?
Okay, so let's call B = the number of sandwiches Bill sells
and P = the number of sandwiches Pete sells
Since Bill sells 7 times as many sandwiches as Pete, then
B = 7P
And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then
B - P = 434
So, now we can substitute for B from the equation above B = 7P
x = bill's
y = pete's
x = 8y
B - P = 434
7P - P = 434
6P = 434
P = 72.33
Therefore, Pete sells 72.33 sandwiches
Bill sells 7 x 72.33 = 506 sandwiches.
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2,307,419 = two million, three hundred seven thousand, four hundred nineteen
Write each number below in word form.
Ex: 1, 750, 064
218,502
384,057
TOUR
4,012,923
one million, seven hundred fifty thousand, sixty-four
two hundred eighteen thousand, five hundred two
Hello!
The numbers should be written as :
1,750,064
one million, seven hundred fifty thousand, sixty-four
218,502
two hundred eighteen thousand, five hundred two
384,057
three hundred eighty-four thousand, fifty-seven
4,012,923
four million, twelve thousand, nine hundred twenty-three
AB ≅ BC and AD ≅ CD
Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
The additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
How to illustrate the information?From the information, Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
In this case, the additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
Also, the additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem is that AX and CX are congruent.
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Answer:
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
✔ AC and BD are perpendicular.
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
✔ AX and CX are congruent.
Step-by-step explanation:
right on edge
Gianna is substituting t = 2 and t = 7 to determine if the two expressions are equivalent.
5 (2 t + 3) 5 t + 25
Which statement is true?
Answer:
LHS5(2t+3)
=5×(2×2+3)
=5×7
=35
RHS5t+25
=5×7+25
=35+32
=67
Therefore,LHS≠RHS
SO,the statement is false
15. Find the coordinates of the circumcenter of triangle ABC With the vertices A(3,-1) B(-3,-11) C(3,-8)
The coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).
How to determine the coordinates?In order to determine the coordinates of the circumcenter of triangle ABC with the given vertices, let its circumcenter be P(x, y). Thus, PA = PB = PC.
By squaring all sides of triangle ABC, we have:
PA² = PB² = PC²
From PA² = PB², we have:
(x - 3)² + (y - (-1))² = (x - (-3))² + (y - (-11))²
(x - 3)² + (y + 1)² = (x + 3)² + (y + 11)²
x² - 6x + 9 + y² + 2y + 1 = x² + 6x + 9 + y² + 22y + 121
-12x - 20y = 120
-3x - 5y = 30 ..........equation 1.
From PB² = PC², we have:
(x - (-3))² + (y - (-11))² = (x - 3)² + (y - (-8))²
(x + 3)² + (y + 11)² = (x - 3)² + (y + 8)²
x² + 6x + 9 + y² + 22y + 121 = x² - 6x + 9 + y² + 16y + 64
12x + 6y = -57 ..........equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
x = -2.5 and y = -4.5.
Therefore, the coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).
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Grayson buys milk and oranges at the store.
• He pays a total of $40.68.
.
• He pays a total of $2.52 for the milk.
• He buys 8 bags of oranges that each cost the same amount.
How much does each bag of oranges cost?
Answer: 4.77
Step-by-step explanation:
40.68-2.52=38.16/8=4.77
This is what I do :
40.68 - 2.52 = 38.16
38.16 ÷ 8 = 4.77
Each bag of oranges costs $4.77
help me please im in a rush i need help
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Area of shaded region = 34 cm²
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Area of shaded region = Area of bigger rectangle - Area of smaller rectangle.
Area (big) :
[tex] \qquad❖ \: \sf \:13 \times 6[/tex]
[tex] \qquad❖ \: \sf \:78 \: \:c m {}^{2} [/tex]
Area (small) :
[tex] \qquad❖ \: \sf \:11 \times 4[/tex]
[tex] \qquad❖ \: \sf \:44 \: \: cm {}^{2} [/tex]
Area of shaded region :
[tex] \qquad❖ \: \sf \:78 - 44[/tex]
[tex] \qquad❖ \: \sf \:34 \: \: cm {}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Area of shaded region = 34 cm²
6. It takes a delivery truck 2 hours to travel 70 km to deliver a new fridge. The truck drives part of
the way on the highway at 80 km/h and the rest on city roads in traffic at only 20 km/h. (6 marksT)
a) How far did the truck travel on each road?
4
Answer:
40 km on the highway
30 km on the city roads
Step-by-step explanation:
Let x = highway
Let y = city road
The time formula: time = distance / speed.
1) Since we do not know the distance travelled on the highway and city roads but we do know the total time taken, we can say x + y = 70. Set the distances x and y and all equated to 2 hours, since we do not know them, nor do we know the time. This is called a system of equations.
x + y = 70
x/80 + y/20 = 2
2) Solve the system of equations using substitution.
x = 70 - y
---------------
70 - y/80 + y/20 = 2
70 + 3y/80 = 2
y = 30
---------------------------------
x + 30 = 70
x = 70 - 30
x = 40
Therefore, the delivery truck travelled 40 km on the highway and 30 km on the city roads.
Using a stopwatch, Tyrone determines it takes him 58.2 minutes to travel 30 miles to work. The stopwatch measures to hundredths of a minute. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of feet per second Tyrone traveled on his way to work?
The number of feet per second Tyrone traveled on his way to work is 45.36 ft/s
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
1 mile = 5280 ft, 1 min = 60 sec
30 mile = 30 mile * 5280 ft per mile = 158400 ft
58.2 min = 58.2 min * 60 sec per min = 3492 sec
Speed = distance / time = 158400 ft / 3492 sec = 45.36 ft/s
The number of feet per second Tyrone traveled on his way to work is 45.36 ft/s
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The marks price of an article is 4500.after allowing some percent of and levying 10% VAT it is sold at 4400, find the discount percent
The discount percent for the given transaction is calculated as; 6.11%
What is the percentage Discount?We are given;
Mark Price; M.P = 4500
Now, formula for discount amount is;
Discount amount = %Discount * M.P
Discount amount = x% * 4500 = 45x
Also;
Selling price is;
S.P = M.P - Discount Amount
S.P = 4500 - 45x
VAT = Vat% * S.P
VAT = (10%*4500) - 45x
VAT = 450 - 45x
S.P with VAT = S.P + VAT Amount = 4500 - 45x + 450 - 45x = 4950 - 90x
Thus;
4950 - 90x = 4400
Solving for x gives;
x = 6.11%
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