The total Area the design is 8 square cm.
Area of rectangular design is product of length and breadth of rectangular design.
In the given question we have,
Rectangular design is made up from 6 squares .
there is 2 small squares surrounded by 4 large squares.
Area of each small square = 1 sq.cm
let the length of rectangular design be l cm
and breadth is b cm.
Area of rectangular design= l×b sq.cm
from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .
Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.
so, length of rectangular design= 4 cm
breadth of rectangular design= 2cm
Area of rectangular design= 4×2 = 8sq. cm
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What is the inverse of f(x)=(5x+2)^2 for x_> -2/5
Answer:
Step-by-step explanation:
f(x)=5x2+xf(x)=5x2+xWrite f(x)=5x2+xf(x)=5x2+x as an equation.y=5x2+xy=5x2+xInterchange the variables.x=5y2+yx=5y2+ySolve for yy.Tap for more steps...y=−1−√1+20x10y=-1-1+20x10y=−1+√20x+110y=-1+20x+110Replace yy with f−1(x)f-1(x) to show the final answer.f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110Verify if f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110 is the inverse of f(x)=5x2+xf(x)=5x2+x.Tap for more steps...f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110
Please help me with this math problem
Answer: B. ≤
Step-by-step explanation:
≤
Divide these numbers in the given ratios
36 in the ratio 4:5
the sum of three integers is 32. the sum of the first and second integers exceeds the third by 82. the third integer is 16 less than the first. find the three integers.
The values of the three integers are:
x= -9, y=66, z= -25
What is meant by an equation?In French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
In order to solve an equation with variables, you must first determine which variables' values make the equality true. Unknowns are the variables for which the equation must be solved, and equation solutions are the values of the unknowns that satisfy the equality..
Given,
Sum of three integers= 32
x+ y+ z=32 →1
And also given that,
x+ y= z+82 →2
z+16=x →3
By solving equation 1, we get
z+16+y+z=32
2z+y=16 →4
By solving equation 2, we get
z+16+y= z+82
y=82-16
y=66
By solving equation 4, we get
2z+66=16
2z=-50
z=-25
By solving equation 3, we get
x=z+16
x=-25+16
x=-9
Therefore, the three integers are x=-9, y=66, z=-25
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suppose that 47% of americans are iphone users. (a) if a random sample of 100 americans are surveyed, what is the probability that the proportion of the sample who are iphone users is between 45% and 50%? (b) if a random sample of 50 americans are surveyed, what is the probability that more than 50% of americans are iphone users?
The probability that the proportion of the sample who are iphone users is between 45% and 50% be 22.87%.
The probability that more than 50% of americans are iphone users be 11.12%.
(a)We know, p = 0.47 and n = 100. First, we should check our conditions for the sampling distribution of the sample proportion.
np = (100)(0.47) = 47 and n(1 - p) = (100)(1 - 0.47) = 53
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(0.53)/100 ≈ 0.05
P(0.45<X<0.50) = P((0.45 - 0.47)/0.05 < Z < (0.50-0.47)/0.05)
P(0.45<X<0.50) ≈ 0.2287
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 100.
(b) Now, p = 0.47 and n = 50.
np = (50)(0.47) = 23.5 and n(1 - p) = (50)(1 - 0.47) = 26.5
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(26.5)/50 ≈ 0.25
P(X>0.50) = P(Z > (0.50-0.47)/0.25)
P(X>0.50) ≈ 0.1112
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 11.12% chance that we would see a sample proportion more than 50% when the sample size is 50.
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help me please please please triangle 333333
Answer:
200 cm²
Step-by-step explanation:
Find the areas of all of the faces
17 × 2 = 34 (Top Face)
8 × 15 = 120 (Both Triangles)
15 × 3 = 30 (Bottom Face)
8 × 2 = 16 (Back Face)
Add them all together
120 + 34 + 30 + 16 = 200 cm²
Here is a set of data
2.4, 1.6, 3.2, 0.3, 1.5
Each piece of data is now doubled
Work out the new mean
Answer:
The new mean is 3.6
Step-by-step explanation:
Since each piece of data is now doubled that means the data is now
4.8, 3.2, 6.4, 0.6, 3
Add up all of the data which comes out to 18
Divide 18 by the number of numbers there are which is 5
This will get you 3.6 which is the new mean of the data
A scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x. Drag each equation to show whether it can be used to represent the ant population of Colony A, Colony B, or neither of these.
In writing the equations that describe each of the colonies A ad B we have;
y = 800e^0.25x (Colony A)y = 800e^-0.25x (colony B )What are the equations?We know that the increase or decrease of population are exponential problems. We such, we must be able to look at the problem form the exponential perspective. This is how we would be able to know how to write the appropriate equation that would be able to be used in each of the cases that have been shown in the problem.
We are told that; a scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x.
Thus;
For colony A we can write;
y = 800e^0.25x
For colony B we can write;
y = 800e^-0.25x
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mikayla lives 4 miles north and 6 miles west of the pizzeria. will the pizzeria deliver to her home?
pizzeria will not deliver to mikayla as distance is out of radius.
Coverage location of pizzeria company.According to question, as the reference with the origin of the circle, it can deliver pizzeria in the radius of 6 miles
According to given data:mikayla lives 4 miles north and 6 miles west,
So, distance of mikayla from company,
By using Pythagoras theorem
Distance = √(4)^2 + (6)^2 = √52 miles
As distance is greater than radius, pizzeria will not deliver to mikayla.
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ana and bonita are born on the same date in different years, nn years apart. last year ana was 55 times as old as bonita. this year ana's age is the square of bonita's age. what is nn?
Ana and Bonita were born nn year apart and its value of nn is 12.
Here we have to find nn which difference in the year in which Ana and Bonita were born.
Let x be the age of Ana and y be the age of Bonita.
It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:
x - 1 = 5(y -1)
x -1 = 5y - 5
5y -x = 4--------(1)
The second statement is Ana is square of Bonita's age. From this we get another equation:
x = y²-----------(2)
Putting equation 2 in equation 1 we get:
5y - y² = 4
y² - 5y +4 = 0
y² - 4y - y + 4 = 0
y(y-4) -1(y -4) = 0
(y - 4)(y -1) = 0
y = 4,1
As x = y²
x = 4² = 16 or x = 1² =1
We cannot take 1 as there is a difference in their age
So we get x = 16 and y =4
So the difference in their age = 16-4= 12
Therefore we get the value of nn as 12.
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I NEED HELP PLEASE DUE TODAY
Look at the picture for the problem
Please answer both parts
part a and b
a. The equation that represents the given data is y = 700x + 2,000.
b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.
We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.
We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.
(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)
(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)
(y - 30,000) = [(14,000)/(20)]*(x - 40)
(y - 30,000) = (700)*(x - 40)
y = 700x - 28,000 + 30,000
y = 700x + 2,000
Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.
y = 700*80 + 2,000
y = 56,000 + 2,000
y = 58,000
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graph y = 1/4 x I dont know how to do
(Excuse me if this doesn't make sense).
Your formula would be (4,1)
Your zero is (0,0)
To graph it:
If your y is 1, your x is 4
If your y is 2, your x is 8.
There's a video for this if my explanation and photo doesn't help
What is an equation of the line that passes through the points (4, -2) and (2, 3)
The slope-Intercept form of the given line is y=1.5x.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The given line passes through (4, -2) and (2, 3). Therefore, the slope of the given line can be written as,
Slope of the line, m = (-2 - 3)/(4 - 2)
= 3 / 2
= 1.5
Now, the equation of the line passing through (2, 3) can be written as,
y = mx + c
(3) = 1.5(2) + C
3 = 3 + C
3 - 3 = C
C = 0
Substitute all the value in the equation of the line,
y = m(x) + c
y = 1.5(x) + 0
y = 1.5x
Hence, the equation of the given line is y=1.5x .
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What happens if the slope is undefined? Provide an example of two points that would be on a line with an undefined slope.
What happens when the slope of a line is undefined is that, the line is a vertical line that crosses the x-axis.
The points could be (1, 5) and (1, 10)
How to explain the undefined slope?It is known that linear equations have slopes
These slopes are the average rate of change of the function
The values of these slopes can be
ZeroPositive or negativeUndefinedWhen the slope is undefined, it means that the line is a vertical line
An example of the vertices on such line is (x, y) and (x, y + n)
See that the x coordinate remains constant, while the y coordinate changed
Take for instance, a line that passes through (1, 5) and (1, 10) would have an undefined slope
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Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window.
H
HH represents the height of the tree (in centimeters),
t
tt years since Renata moved in.
H
=
210
+
33
t
H=210+33tH, equals, 210, plus, 33, t
How fast does the tree grow?
The required increasement of height of tree is 33 centimeters annually
What is function of time?Function of time is defined as the change of abject or expression of variables with time. As the time increases, there is change in shape, height, etc. is called function of time.
According to given data in the question:we have given an expression of height of tree,
H = 210 + 33t
Where t represent the time and H is height of tree.
So, Changes in the height of the tree with years,
for t = 1 year
⇒ H = 210 + 33×1 = 210 + 33 = 243 centimeters
Thus, the height of tree in increases by 33 centimeters yearly.
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I NEED HELP PLEASEEEEE ASAPPPPPPP
Answer:
7x+40=180
Step-by-step explanation:
(5x+40)+(2x)=180
7x+40=180
if you were to solve
subtract 40 from each side
7x=140
divide both sides by 7
x=20
check your answer
5(20)+40+2(20)=180
100+40+40=180
this is correct
hope this helps..and with future questions if you need to solve it
To find BCD
we know that C is 40 degrees and we know that triangle is also 180
we can also see that B is a right triangle or 90 degree
so 90+40+A=180
130+A=180
subtract 130 from 180
A=50
Explain c-a, when c = 7 and a=6
Answer:
1
Step-by-step explanation:
7-6=1
Answer:
c-a
replace x with 7 and a with 6
rewrite: 7-6
7-6 = 1
Answer: 1
Determine the total number of roots of each polynomial function. f (x) = 3x6 2x5 x4 - 2x3 6 g(x) = 5x - 12x2 3
The total number of roots for the given polynomial is for f(x)= 3x^6+2x^5+x^4-2x^3+6 is 6 and for g(x) = 5x-12x^2+3 is 2
Since for finding the number of roots, we just need to see what is the degree fro the given polynomial, where the degree of the polynomial is nothing but the highest exponent.For the function f (x) = 3x6 2x5 x4 - 2x3, here the degree is 6, and the respective function is having 6 numbers of roots, which be real roots and complex roots too.For the function g(x) = 5x-12x^2+3, here the degree is 2, so the respective function has 2 roots.
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Answer:
f (x) = 3x6 + 2x5 + x4 - 2x3 = 6 roots g(x) = 5x - 12x2 + 3 = 2 roots f (x) = (3x4 + 1)2 = 8 roots g(x) = (x - 5)2 + 2x3 = 3 roots
p(x) = (x² - 9) (x² + x - 2)
factor for zeros to plot on a graph
pls help :(
Answer:
P(x) = (x - 3)(x + 3)(x + 2)(x - 1)
Answer:
Step-by-step explanation:
Solution:To write a polynomial in standard form, simplify and then arrange the terms in descending order.Expand ( x2 − 9 )( x + 2 ) using the FOIL Method.Simplify each term.
The sum of the first three terms of a G.p is half its sum to infinity.find the positive common ratio
Bfbrbdnshdvadvsvsvsahdnagsnavs Bfbrbdnshdvadvsvsvsahdnagsnavs Bfbrbdnshdvadvsvsvsahdnagsnavs Bfbrbdnshdvadvsvsvsahdnagsnavs
Answer: What??
Step-by-step explanation:
I need help like asap !!!
only numbers and decimal points
What is the distance between (-5,-6),(-9,-4)
Answer:
The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].
Step-by-step explanation:
Distance Formula :
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Given,
The two points are
[tex](-5,-6),(-9,-4)[/tex]
To calculate the distance between two points, use the distance formula.
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Substitute the actual values of the points into the distance formula.
Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]
[tex]=\sqrt{(81-25)+(16-36)}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
help asap!!
Graph this function. f(x)=34x−2
use desmos graphing calcu
what is the slope of a line that passes through points (7,-5) and (16,7)
Doors for the small cabinets are 17.5 inches long. Doors for the large cabinets are 3.5 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 12 feet long?
Answer:
2
Step-by-step explanation:
If the doors for the small cabinets are 17.5 in long, and the doors for the large cabinets are 3.5 times longer, find the length of the large cabinet doors by multiplying the length of the small cabinet doors by 3.5:
⇒ Length of large cabinet doors = 17.5 × 3.5 = 61.25 in
1 foot = 12 inches
⇒ 12 foot = 12 × 12 = 144 inches
To find how many large doors can be cut from a board that is 12 feet long, divide 144 inches by the found length of the large door:
⇒ 144 ÷ 61.25 = 2 r 21.5
Therefore, 2 large doors can be cut from a board that is 12 feet long.
(There will be 21.5 inches of board left over).
PLEASE HELP!!
Solve x^2 – 2x = 15 by applying the quadratic formula.
Answer: The correct answer is x=−3 or x=5
Step-by-step explanation:
Solve for x^2−2x=15 using the quadratic equation
Step 1) Subtract 15 from both sides
x2−2x−15=15−15
x2−2x−15=0
For this equation: a=1, b=-2, c=-15
1x2+−2x+−15=0
Step 2) Use quadratic formula with a=1, b=-2, c=-15
x= (−b±√b2−4ac)/2a
x= (−(−2)±√(−2)2−4(1)(−15))/2(1)
x= (2±√64)/2
x=5 or x=−3
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10. Each term in a sequence is generated by
multiplying the previous term by 3 and then
adding 2. If the first term is -3, what will the 6th
term be?
a. -487
b. -165
C. -57
d. 57
e. 165
2
The 6th term is -487 i.e, option(a)
What is a Sequence ?
A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence.
There are 4 types of sequence, arithmetic sequences, geometric sequences, quadratic sequences and special sequences.
Given, the 1st term = -3
According to question, we get the term by multiplying the previous term by 3 and then adding 2.
Now, calculate the other terms.
so, the 2nd term will be
-3 * 3 + 2 = -7
3rd term
-7 * 3 + 2 = -19
4th term
-19 * 3 + 2 = - 55
5th term
-55 * 3 + 2 = -163
6th term
-163 * 3 + 2 = -487
Hence, the 6th term is -487 i.e, option(a)
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0How do we obtain the relevant equations that can be used for the problem?First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:
Area of a rectangle = Length × Width
Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:
y( y - 5) = 750
When this equation is fully expressed, we will get the following equations:
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0Therefore, options, B, C, and E are correct.
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Can somebody please answer these 3 questions please and thank you
[tex]\displaystyle \boxed{\text{First Attachment, 14}}[/tex]
Answer:
x = 30
y = 60
Step-by-step explanation:
First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.
Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.
Lastly, corresponding angles on parallel lines are congruent.
By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.
[tex]\displaystyle \boxed{\text{Second Attachment, 12}}[/tex]
Answer:
x = 65
Step-by-step explanation:
From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.
We also know there are 180 degrees in a triangle.
Lastly, we know that alternate interior angles are congruent.
Using this knowledge, we can decide that x = 65.
[tex]\displaystyle \boxed{\text{Third Attachment, 13}}[/tex]
Answer:
x = 30
Step-by-step explanation:
Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.
After placing vertical angles down from the given information, we can fill in more using corresponding angles.
Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.
Using this information, we can decide that x = 30.