Answer:
48.43552415324934
Step-by-step explanation:
61.73²-38.27² = 2346
[tex]\sqrt{2346}[/tex] = 48.43552415324934
a. write a sequence too described the number of blocks needed to create the figure for each step.
b. how many blocks will be needed to create the next figure?
c. describe the sequence in words
3. in a sequence, the first term is 12 and the common difference is -5. find the 4th term of sequence
Using arithmetic sequences, it is found that:
a) The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex].
b) 14 blocks will be needed to create the next figure.
c) The sequence means that the number of blocks start at 5 and increase by 3 each figure.
3) The 4th term of the sequence is of -3.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
From the figure, we have that:
The Figure 1 has 5 dots.The Figure 2 has 8 dots.The Figure 3 has 11 dots.Hence the first term and the common ratio are given as follows:
[tex]a_1 = 5, d = 3[/tex]
The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex], hence the sequence means that the number of blocks start at 5 and increase by 3 each figure.
For item b, the amount is:
[tex]a_4 = 5 + 3(4 - 1) = 14[/tex]
14 blocks will be needed to create the next figure.
For item 3, the sequence is given by:
[tex]a_n = 12 - 5(n - 1)[/tex]
Hence the 4th term is:
[tex]a_4 = 12 - 5(4 - 1) = -3[/tex]
The 4th term of the sequence is of -3.
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The answer because this question is kinda confusing
Answer: Find [tex]2^{21} = (2y)^{3}[/tex] then the solution of [tex]y^{3}[/tex] = [tex]2^{7}[/tex]
Step-by-step explanation:
Given data,
[tex]2^{21}[/tex] = [tex](2y)^{3}[/tex]
[tex](a^{m)^{n} }[/tex] = [tex]a^{m*n}[/tex] says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it's the same as multiplying the number a by itself m * n times.
we can use formula,
[tex](a^{m)^{n} }[/tex] = [tex]a^{m} a^{n}[/tex]
So,
we can write,
[tex]2^{21}[/tex] = [tex]2^{3} y^{3}[/tex]
[tex](2^{7} )^{3}[/tex] = [tex]2^{3} y^{3}[/tex]
[tex]2^{7} 2^{3}[/tex] = [tex]2^{3} y^{3}[/tex]
cancel the [tex]2^{3}[/tex] in both sides,
Then,
[tex]2^{7}[/tex] = [tex]y^{3}[/tex]
Therefore,
[tex]y^{3}[/tex] = [tex]2^{7}[/tex]
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At 7:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 28270 ft. and is descending at the rate of 550 ft/min. Airplane #2 has an elevation of 5270 ft. and is climbing at the rate of 700 ft/min.
(1) Let
t
represent the time in minutes since 7:00 am, and let
E
represent the elevation in feet. Write an equation for the elevation of each plane in terms of
t
.
plane #1:
E
(
t
)
=
plane #2:
E
(
t
)
=
(2) At what time will the two airplanes have the same elevation?
t
=
minutes after 7:00 am
(3) What is the elevation at that time?
E
=
feet
Question HelpQuestion 25: Message Message instructor
Using linear functions, it is found that:
1. The functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.2. They will have the same elevation after 18.4 minutes.
3. At that time, the elevation is of 18,150 feet.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The initial heights are the intercepts.The rates are the slopes, climbing positive and descending negative.Hence the functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.They will have the same elevation when:
E1(t) = E2(t)
28270 - 550t = 5270 + 700t
1250t = 23000
t = 23000/1250
t = 18.4.
They will have the same elevation after 18.4 minutes.
This elevation will be of:
28270 - 550(18.4) = 18150.
At that time, the elevation is of 18,150 feet.
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Use the information and diagram below to find the value of y. (Type a number answer only.)
Use the information and diagram below to find the value of x. (Type a number answer only.)
Answer:
I never took the lesson but il try!
Step-by-step explanation:
so if y is 34° and x should be 54° if I am being correct!
The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.
f(x) = 3(x2 – 8x) + 10
(StartFraction negative 8 Over 2 EndFraction) squared = 16
What is the function written in vertex form?
f(x) = 3(x + 4)2 – 6
f(x) = 3(x + 4)2 – 38
f(x) = 3(x – 4)2 – 6
f(x) = 3(x – 4)2 – 38
The function is written in vertex form the equation for is mathematically given as
f(x) = 3(x – 4)2 – 38
This is further explained below.
What is the function written in vertex form?Generally, To convert the expression "f(x) = 3x2 – 24x + 10," which is in quadratic form, into vertex form, which will look like this "y = a(x-h)2 + k," you will need to apply the technique of completing the square. This will allow you to convert the expression. In the beginning, we shall separate the x2 and x terms.
y = 3(x² - 8x) + 10
We start with a negative eight, divide that number by two to obtain a negative four, and then we square that number, which gets us sixteen. We combine these so that it forms a perfect square, and then we remove 16 so that it is not altered in any way. We will get:
y = 3(x² - 8x + 16 - 16) + 10
y = 3((x - 4)² ) - 48 + 10
y = 3(x - 4)² - 38
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Answer: option D
Step-by-step explanation:
The area of this rectangle is 54 square inches. Create an equation to find the value of n. Length is 3(n-1) and the width is n+2
Value of n is 4
The area of a rectangle is equal to the product of its length and width.
we know ,
the area of rectangle, multiply the length, , and the width, ,
and set the product equal to the area.
area of rectangle = length * width
54 = 3(n - 1) * (n + 2)
54 =( 3n - 3) * (n + 2)
multiply ( 3n - 3) with (n + 2)
we get,
54 = [tex]3n^{2} + 6n - 3n -6[/tex]
54 = [tex]3n^{2} + 3n -6[/tex]
54 = 3([tex]n^{2} + n -2[/tex])
[tex]\frac{54}{3}[/tex] = ([tex]n^{2} + n -2[/tex])
18 = ([tex]n^{2} + n - 2[/tex])
[tex]n^{2} + n - 2[/tex] - 18 = 0
[tex]n^{2} + n - 20[/tex] = 0
solve them
[tex]n^{2} + 5n + 4n -20[/tex] = 0
n (n + 5) - 4 (n + 5) = 0
(n + 5)(n -4)
then we get,
n = -5 , n = 4
value of n should not be negative . so value of n is 4
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area
Area of rectangle = Length x Breadth
A = lb
how to Factoring Quadratic Equation
Step 1: Consider the quadratic equation ax2 + b x + c = 0
Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.
(number 1)(number 2) = ac
(number 1) + (number 2) = b
Step 3: Substitute these two numbers in the formula given below:
(1/a) [a x + (number 1)] [a x + (number 2)] = 0
Step 4: Finally simplify the above equation.
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←
If a single fair die is rolled, find the probability of the following result.
An even number, given that the number rolled was 1.
Answer: so assuming this is a d6, it's 3/6
Step-by-step explanation:
on a d6, there are 6 sides (duh). three out of the six numbers are even, two four and six. so, three out of the six numbers you can roll are even.
5. The surface area of a cuboid is 518 cm².
The breadth of the cuboid is 11 cm and its
height is 9 cm. Find the length of the cuboid.
The correct answer is 8 cm.
Given the surface area = 518 cm²
breadth of the cuboid = 11 cm
height of the cuboid = 9 cm
Now let l be the length of the cuboid,
The total surface area (TSA) of a cuboid is provided by the sum of the areas of its six rectangles, where l, b, and h are the length, width, and height, respectively
Cuboid's total surface area formula,
Thus the surface area of the cuboid = 2(lb+bh+lh)
518 = 2 ( l × 11 + 11 × 9 + l × 9 )
518 = 2 (11l + 99 + 9l)
259 = 11l +99 +9l
259 - 99 = 20 l
160/20 =l
length = 8 cm
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estimate the answers to these questions by rounding the numbers the numbers
a.-28-53. b.514+-321
c. -888- - 111. d.-61.1 + -29.3
The solutions after rounding the numbers are;
a. 80
b. 190
c.780
d. 90
What is Rounding number?
Rounding means making a number simpler but keeping its value close to what it was.
The questions are given as;
a. -28 - 53
b. 514 + -321
c. -888 - - 111.
d. -61.1 + -29.3
Now, solve and rounding the numbers as;
a. -28 - 53 = 81
After rounding it we get;
81 ≈ 80
Hence, -28 - 53 = - 80
b. 514 + -321 = 514 - 321
= 193
After rounding it we get;
⇒ 193 ≈ 190
Hence, 514 + -321 ≈ 190
c. -888- - 111 = - 888 + 111
= - 777 ≈
After rounding it we get;
- 777 ≈ - 780
d. -61.1 + -29.3 = -61.1 - 29.3
= - 90.4
After rounding it we get;
- 90.4 ≈ - 90
So, The solutions are;
a. 80
b. 190
c.780
d. 90
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What is the slope of the line?
Answer: 3/-4
The slope is measured in terms of rise over run. Rise is how many units you go up or down from the point (0, 0). Run is how many units you go left to right from the point where rise left off. For this question, we go up 3 and to the left 4. SO that's a 3 on top and a -4 on the bottom.
I hope this helps! :) I'm a huge Algebra nerd!!! I love Algebra. :)
Functions of a polynomial. graph f(x)=(x+5)^2
Using a transformation of the parent function y = x², the graph of f(x) = (x + 5)² is given at the end of the answer.
What are transformations on the graph of a function?Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.
Examples of transformations are as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.For this problem, the parent function is given by:
f(x) = x².
Which has a parabolic graph with vertex at (0,0).
For f(x) = (x + 5)², we have that x -> x + 5, meaning that the function is shifted 5 units left, meaning that the parabola has a vertex at (0,-5), and the graph is given at the end of the answer.
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from the graph of each parabola, determine whether the parabola opens upward or downward, and find the vertex, axis of symmetry, and range of the function. find the maximum and minimum value of the function and the intervals on which the function is increasing and decreasing. URGENT 20 POINTS!
A quadratic function is one that has the formula f(x)=ax2+bx+c, where a, b, c, and an are all real values and a 0 a 0. The conventional form of a quadratic function is this form.
The quadratic function's graph is a U-shaped curve known as a parabola.
Below is a graph of the equation y=x2y=x2; it is a parabola.
The parabola rises if a>0a>0 in f(x)=ax2+bx+cf(x)=ax2+bx+c. In this case, the vertex is the smallest or lowest point of the parabola.
The vertex of the y=x2y=x2 graph is (0, 0). (0,0).
The parabola opens downhill if a0a0 in f(x)=ax2+bx+cf(x)=ax2+bx+c is true. The maximal or highest point of the parabola in this instance is called the vertex.
The value of cc for an equation in standard form yields the graph's yy-intercept.
The axis of symmetry is the line that divides the parabola into two symmetric sections and runs through the vertex.
In the case of the graph y=ax2+bx+cy=ax2+bx+c, where a=0a=0, the equation for the axis of symmetry is x=b2ax=b2a.
The yy-axis, with x=0x=0, is the axis of symmetry in all of the graphs above. The axis of symmetry in the graphs below is different (marked in red.) As you can see, cc still provides the yy-intercept.
If you write a quadratic function like x=f(y)=ay2+by+cx=f(y)=ay2+by+c, instead of writing yy as a function of xx, you obtain a parabola with a horizontal axis of symmetry.
Hence, that the xx-intercept in this situation is cc. When aa is positive, the graph opens to the right; when aa is negative, it opens to the left.
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x shares pay 8% dividend and y shares pay 9%. Reiko has invested 200000 more on x shares than she has on y shares. Her total earnings for the year for the two investments is 271000. How much did she invest in x shares
The amount Reiko invested in x shares is 1,700,000 based on 8% annual dividend
How do represent the amounts invested in each share?
The fact that Reiko invested 200,000 more on x shares means that if we assume that he invested Z on y shares then the amount invested in x shares is Z+200000
return on x shares=(Z+200,000)*8%
return on x shares=0.08Z+16000
return on y shares=Z*9%=0.09Z
total return=0.08Z+16000+0.09Z
total return=0.17Z+16000
total earnings=271000
271000=0.17Z+16000
271000-16000=0.17Z
255000=0.17Z
Z=255000/0.17
Z=1,500,000
Z+200,000=1,500,000+200,000=1,700,000
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work this out please
Answer:
1/16
Step-by-step explanation:
32= 2^5
Thus:
(2^5) ^-4/5
= (2)^ - 4
= (16) ^ - 1
= 1/16
John's test grade is 5 points less than twice Ariana's test grade. If x represents Ariana's test grade, write an expression for John's test grade.
In linear equation, 2x - 5 is an expression for John's test grade.
What is linear equation in one variable?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let Ariana's test grade = x
twice Ariana's test grade = 2x
then, John's test grade = 2x - 5
an expression for John's test grade = 2x - 5
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what is the simplifed form of the following expression? (3/5)^3
Answer:
Step-by-step explanation:
The simplified form of the expression (3/5)³ = 27/125
Step-by-step explanation:
The given expression is (3/5)³
3/5 is a proper fraction.
(3/5)³ can be written as,
(3/5)³ = 3³/5³
To find 3³ and 5³
3³ = 3*3*3 = 27
5³ =5*5*5 =125
esse rode his bike for 2 hours at a constant rate. During the first 1.5 hours, he rode 12 miles. How many miles did Jesse ride his bike during the last half hour? (Enter an exact number.)
mi
In the last half hour 4 miles did Jesse ride his bike.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Jesse rode his bike for 2 hours at a constant rate.
First 1.5 hours, he rode 12 miles.
According to given question we have
1.5 hours=12 miles
1 hours=12/1.5
0.5 hours=12*0.5/1.5
0.5 hours=4 miles
Therefore, in the last half hour 4 miles did Jesse ride his bike.
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Christa and Megan have sales jobs at different companies. Christa earns $18 for each successful sales call she
makes plus 3% commission on her sales. Megan earns $21 for each successful sales call she makes plus 3.5%
commission on her sales. In July, Christa made 35 successful sales calls and Megan made 29 successful sales calls.
They each had the same sales, in dollars, for July, and they made the same total salary that month. Which equation
can be used to find x, the amount Christa and Megan each had in sales in July?
The equation that shows the amount Christa and Megan each had in sales in July is 630 + 0.03x = 609 + 0.035x
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let x represent the amount Christa and Megan each had in sales in July. Hence:
For Christa = 18(35) + 0.03x
For Megan = 21(29) + 0.035x
630 + 0.03x = 609 + 0.035x
The equation that shows the amount Christa and Megan each had in sales in July is 630 + 0.03x = 609 + 0.035x
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As the x-value increases
by 2, the y-values increases
by 60.
Answer: 30
Step-by-step explanation:
Slope: y/x
y/x =
+60/+2=
60/2=30
chapter 7 /pt3
10.Find the value of each trigonometric ratio.
Solve the equation.
Question 1, 9.3.1
-6y+6= -2(4y + 4)
Solve
Solution : y = -7
One Variable in the linear equation :
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equations in two variables, it has two solutions.
-6y+6= -2(4y + 4)
-6y = -8y -8 -6
-6y +8y = -14
2y = -14
y = -14/2
y = -7
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If A={2,3,4}and B {1,3,5,7} what will be AnB
Answer:
A∩B = { 3 }
Step-by-step explanation:
A∩B means "the intersection of A and B" as in "all elements that appear in BOTH sets".
Only 3 appears in both sets.
Brainly User
11/01/2016
Mathematics
Middle School
answered
By recycling 1 ton of paper,6,953 gallons of water are saved. How many gallons of water are saved by recycling 4 tons of paper?
The number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812
What is proportion?Proportion can be defined as the mathematical comparison of two numbers.
It is also said to be an equation defining two given ratios as equivalent to each other.
From the information, we have that;
By recycling 1 ton of paper, 6, 953 gallons of water was saved
To determine the gallons of water that would be saved after recycling 4 tons of paper, we have to;
If 1 ton of paper = 6, 953 gallons of water
Then 4 tons of paper = x
cross multiply
x × 1 = 6953 × 4
multiply through
x = 27, 812 gallons
The number of gallons that would be saved after the recycling would be
27, 812 gallons
Thus, the number of gallons that would be saved after the recycling 4 tons of paper would be 27, 812
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An engineering school reports that 53% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 31% are both male and between the ages of 18 and 20.
What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?
Your answer should be to two decimal places.
The probability of a random probability of a random student being chosen who is a female and is not between the ages of 18 and 20 will be 0.06.
How to calculate the probability?From the information, 53% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 31% are both male and between the ages of 18 and 20.
Probability to females = 100% - 53% = 47%
Therefore, the probability of a random student being male or between the ages of 18 and 20 will be:
= 37% - 31%
= 6%
Therefore, the probability of a random student being female or between the ages of 18 and 20 will be 6%.
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Find the length of the segment AB with the endpoints as A(-3,7) and B(6,14).
Round to 1 decimal.
AB=
The length of AB is 11.40 units.
The length of two points can be calculated using the distance formulae.
The distance formulae comes under the Co-ordinate geometry section.
The distance between two points is measured by squaring the sum of the difference between the x and y co-ordinates and then applying the square root to the result.
Here the two points given are A(-3,7) and B(6,14).
The length of the line segment AB is = √(-3-6)²+(7-14)²
= √(-9)²+(-7)²
= √81+49
= √130
= 11.40 units
So, the length of line segment AB is 11.40 units.
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about how many pizzas does mr. t's pizzeria sell each week ? remember , there are 7 days in a week
Answer:
Is there any more information than that? if there Is I might be able to help
Joyce saved $150 on an item that was 35
%
off. What was the original price?
Write answer to the nearest cent.
$202.50 is your answer
help meeeeeeeeeeeeeeee please !!
Answer: 59
Step-by-step explanation:
How to do domain and range
Answer:
bjuk
Step-by-step explanation:
ftftrtt987652123456789
Please please please please please help me