The recursive formula for the sequence 13, 3, -7, -17 is 3 + 10n.
How to illustrate the information?It should be noted that the nth term for an arithmetic sequence is illustrated by the formula:
= a + (n - 1)d.
where a = first term = 13
d = common difference = 3 - 13 = 10
n = number of terms
Therefore, the recursive formula will be:
a + (n - 1)d.
= 13 + (n - 1)10
= 13 + 10n - 10
= 3 + 10n
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Using Pythagoras' Theorem please solve it.
[tex] \huge\underline\mathcal{Answer \: - }[/tex]
Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.
therefore ,
[tex](25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0[/tex]
now using quadratic formula ,
[tex]x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]
here , a = 17 , b = 70 , c = -552
substituting the values in the equation above ,
[tex]x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ [/tex]
after simplifying we get ,
[tex]\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ [/tex]
since length can't be negative , therefore the other value will be neglected and hence ,
[tex]\boxed{value \: of \: x \: = \: 4 \: cm}[/tex]
hope helpful ;-;
======================================================
Work Shown:
As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.
[tex]a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\[/tex]
Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\[/tex]
Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.
This makes x = 4 the only possible solution.
----------------
If x = 4, then,
vertical leg = x+3 = 4+3 = 7horizontal leg = 4(x+2) = 4*(4+2) = 4*6 = 24This is a 7-24-25 right triangle.
We can confirm this using the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark[/tex]
"-2+8" > "-2" heeeeelpp
Answer: Yes this equation means 6 is greater than -2, making this a true statement if that was what you're asking for.
A 100ml tub of ice cream costs £1.50. Work out how much 500ml tub of ice cream would cost.
Answer:
Answer: 7.5 or 7 1/2.
What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
a. Ø
b. {all reals}
c. {1/7}
Answer:
A
Step-by-step explanation:
(-8x + x) + 15 = -7x +12
-7x +15 = -7x + 12
15 = 12 There are no solutions
What is the equation of the line that passes through the point (−3,1) and has a slope of −3?
For the data in the table, write an equation for the direct variation.
The equation of direct variation is,
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}[/tex]Substitute the values of y and x.
[tex]\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}[/tex]So, the obtained equation will be y=1.35(x).
Let's check with the values of x.
1) If x=4
[tex]\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}[/tex]2) If x=2
[tex]\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}[/tex]3) If x=-2
please show work out
find the dimension of A34×b41 matrix]
A34 should represent either a square matrix with number of columns=number of rows =34 or the 4th element in the 3rd row in the matrix A [which is not possible in the given matrix since each row has only 3 elements]
The dimension of a matrix is given as (the number of rows it has, say a) x (the number of columns it has, say b) [read as a by b].. The given matrix has 4 rows and 3 columns, so its dimension is 4x3.
For a matrix A of dimension axb to be multiplied with a matrix B of dimension cxd, the number of columns of matrix A should be equal to the number of rows of matrix B, that is b = c should be satisfied. In this case both matrices are of the same dimension 2x3 but 3 (number of columns in first matrix) is not equal to 2 (number of rows in second matirx). So these matrices cannot be multiplied as their dimensions do not match.
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3 movie tickets cost $36. At this rate, what is the cost per ticket?
Answer:
12
Step-by-step explanation:
36 divided by 3 is 12
(5y-23) (2x+13) 47 (3x) find the values of c and y
The value of variable x and y are 24 and 19 respectively.
How to find angles?We have to find the variables x and y of the angles.
Therefore,
using angles in a triangle,
2x + 13 + 47 + 5y - 23 = 180
2x + 5y = 180 - 13 - 47 + 23
2x + 5y = 143
Using corresponding angles,
180 - (2x + 13) = 47 + 3x
180 - 2x - 13 = 47 + 3x
180 - 47 - 13 = 3x + 2x
120 = 5x
x = 120 / 5
x = 24
Hence,
2(24) + 5y = 143
5y = 143 - 48
5y = 95
y = 95 / 5
y = 19
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please help need this asap!!!!! PLEASE SOMEONE ANSWER I WILL GIVE EXTRA POINTS!!!
The area of the circles are as follows:
254.34 km²1962.5 mm²379.94 m² 907.46 cm²How to find area of a circle?The area of a circle can be found as follows;
area of a circle = πr²
where
r = radiusTherefore,
a.
area of the circle = πr²
diameter = 18km
r = 18 / 2
r = 9 km
Hence,
area of the circle = πr²
area of the circle = 3.14 × 9²
area of the circle = 254.34 km²
b.
area of the circle = 3.14 × 25²
area of the circle = 3.14 × 625
area of the circle = 1962.5 mm²
c.
area of the circle = 3.14 × 11²
area of the circle = 3.14 × 121
area of the circle = 379.94 m²
d.
area of the circle = 3.14 × 17²
area of the circle = 3.14 × 289
area of the circle = 907.46 cm²
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Express each phrase as a rate and unit rate.
(Round your answer to the nearest hundredth.)
1) 7 calculators cost $120.00
Answer:
$100.00
Step-by-step explanation:
5 and above ex: 150 =200 140=100 under 5 keep the first letter then turn the other numbers into 0's 5 and above make the first number go up one then turn the rest of the numbers in to 0's
what is an example of data organization and analysis
The answer choices which represents an example of data organisation and analysis are;
Choice A; Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation.
Choice C. Running a weather station.
Choice E; Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.
Data organisation and Analysis.The concept above as the name implies involves the process of gathering data in a bid to further carry out analysis and consequently, draw inferences from such analysis.
Therefore, the answer choices A, C and E represent such activities which involve data organisation and analysis.
Complete question:
What is an example of data organisation and analysis?
Check all that apply.
A. Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation
B. Rejecting extreme data
C. Running a weather station
D. Transferring the weather data to a computer application
E. Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.
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An example of data organization and analysis include:
A. drawing a pie chart to show the percentage of sunny days rainy days and cloudy days without precipitation.
E. summing the number of days with precipitation summing the number of sunny days and summing the number of cloudy days without precipitation
What is data organization?Data organization and analysis are accomplished by a process of categorizing and organizing data based on its category and how it is studied. A is an example of data organizing and analysis.
Drawing a pie chart to display the percentage of sunny days, rainy days, and cloudy days without precipitation - in this example, data organization is done through charts and graphs, with data classification visible. e is another example.
Summing the number of days with precipitation, sunny days, and cloudy days without precipitation - in this example, data organizing is done solely through summation of numbers, with no graphs or charts to graphically portray the data.
In conclusion, the correct options are A and E.
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Which of the following activities are examples of data organization and analysis?
Check all the apply.
A. Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation
B. Rejecting extreme data
C. Running a weather station
D. Transferring the weather data to a computer application
E. Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.
A =
h(a + b)/2 solve for b
Answer: b = (−ah+2a)/h
Step-by-step explanation:
Step 1: Flip the equation.
Step 2: Add (-1)/2ah to both sides.
Step 3: Divide both sides by h/2.
NAME
DATE
PERIC
Lesson 3: More about Constant of Proportionality
Cool Down: Fish Tank
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table
as you answer the questions.
1.
How many gallons of water will be in the fish tank after 3 minutes? Explain your
reasoning.
2.
How long will it take to fill the tank with 40 gallons of water? Explain your reasoning
3. What is the constant of proportionality?
The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality then the constant of proportionality exists r = 1.6.
What is meant by constant of proportionality?The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality.
Given
x y
0.5. 0.8
1. 1.6
3. 4.8
25. 40
To estimate the constant of proportionality uses the following formula:
y = r x
Where r is the constant of proportionality;
Simplify the value of r, we get
r = y/x
Substitute the values of x = 0.5 and y = 0.8, in the above equation then
r = 0.8/0.5
r = 1.6
When x = 1 ; y = 1.6
r = 1.6/1
r = 1.6
When x = 3; y = 4.8
r = 4.8/3
r = 1.6
When x = 25 ; y = 40
r = 40/25
r = 1.6
The value of r exists constant.
Therefore, the constant of proportionality exists r = 1.6.
The complete question is:
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table and answer the question below.
time (minutes) water (gallons)
0.5 0.8
1
3
40
What is the constant of proportionality?
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what is 0.4111111… as a fraction
Which numbers I have to put in the boxes
Question
Solve 2y−18x=−26 for y.
Answer:
-26
Step-by-step explanation:
If x is a positive integer, this expression is equivalent to what?
Given:
[tex]\text{ Th expression is }4x^{\frac{1}{2}},\text{ x is a positive integer.}[/tex]Required:
Which option is equivalent?
Explanation:
The equivalent for is
[tex]\begin{gathered} =4x^{\frac{1}{2}} \\ =4\sqrt{x} \end{gathered}[/tex]Answer:
Option B is correct answer.
Which is larger, 52 or 33?
Answer:
52
Step-by-step explanation:
52 is a bigger number than 33?
Of 85 entries in the parade, 19 were
marching bands. How many entries were
not marching bands?
Question 5Which of the following is equivalent to (2 – 2) (x - 1)
May I please get help with this. I have tried multiple times but still could not get the correct answers for them
ANSWER
[tex]\frac{2}{5}[/tex]EXPLANATION
To find the scale factor of the model to the sculpture, we have to divide one set of measurements of the model and sculpture.
Let us divide the length of the model by that of the sculpture:
[tex]\begin{gathered} \frac{10}{25} \\ \Rightarrow\frac{2}{5} \end{gathered}[/tex]That is the scale factor of the model to the real sculpture.
please help me solve this
It is to be noted that:
The current total bid for Empire design is $3,060,000The current total bid for Build-EM-UP-CO is $ 3,120,000.What is a bid?Bidding is an individual or business's offer to establish a price for a product or service or a demand that something be done. Bidding is a method of determining the price or worth of something. Bidding may be done by a person who is influenced by a product or service in a given setting.
The calculations are given as follows:
Given:
Proposal of Empire design:
$30000 x b
$ 60000/ I beam
Proposal of Build-EM-UP-CO.
$32000 x b
$ 40000/ I beam
Empire Design
Since b = 9ft; and number of I beams = 6, Hence
Total bid = (300,000 * 9) + (60,000 * 6)
= $3,060,000
Build-EM-UP-CO.
Recall that b = 9ft; and number of I beams = 6, Hence
Total Bid = (320,000 * 9) + (40,000 * 6)
Therefore,
Total bid = $3,120,000.
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Full Question:
For full details of the question, see the attached image
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $456. What was the simple interest rate of the bonds?
5.7%
Explanaton:let amount invested = Principal = $8000
time = 1 year
rate = ?
Interest = $456
To get the rate, we'll apply simple interest formula:
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \end{gathered}[/tex][tex]\begin{gathered} 456\text{ = 8000}\times R\times1 \\ 456\text{ = 8000R} \\ \text{divide both sides by 8000:} \\ \frac{456}{8000}\text{ =}\frac{8000R}{8000} \\ \\ R\text{ = 0.057} \\ In\text{ percent, rate = 0.057}\times100 \\ \text{Rate = 5.7\%} \end{gathered}[/tex]Hence, the simple rate of the bonds is 5.7%
Please help me find out what 758x92 is
Answer:69736
Step-by-step explanation:
In the figure ZX = 2x + 1 YW = 3x - 1 and YX = 1, find perimeter of VYZ
The perimeter of triangle VYZ is 12 units.
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the whole sides of the triangle.
In other words, the perimeter of a triangle is the total distance covered by its boundaries or the sides.
Therefore,
perimeter of ΔVYZ = VY + ZY + ZV
Therefore,
VY = ZY = ZV = XW
Hence,
YW = YX + XW
Therefore,
XW = YW - YX
YW = 3x - 1
YX = 1
Hence,
XW = 3x - 1 - 1
XW = 3x - 2
Therefore,
perimeter of ΔVYZ = 3x - 2 + 3x - 2 + 3x - 2
perimeter of ΔVYZ = 9x - 6
ZX = YW
2x + 1 = 3x - 1
2x - 3x = - 1 - 1
-x = -2
x = 2
Therefore,
perimeter of ΔVYZ = 9(2) - 6
perimeter of ΔVYZ = 18 - 6
perimeter of ΔVYZ = 12 units
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0.8-2x=-1.4
Solve for x
Answer:
x= -0.3
Step-by-step explanation:
0.8-2x=1.4 Set up equation
-2x=1.4-0.8 Put Like terms together
-2x=0.6 Subtract like terms
x=0.6/-2 Divide
x=-0.3 Answer
Find the equation of the line that contains the point (-1,-6) and is parallel to the line 4x + 7y=11. Write the equation in slope-intercept form, if possible.
answer box to complete your choice.
Answer:
y = -4/7x - 46/7
Step-by-step explanation:
4x+7y=11
7y=11-4x
y=-4/7x + 11/7
Slope or parallel line: -4/7
Point=(-1,-6)
y+6 = -4/7(x+1)
y = -4/7x - 46/7
:]
Which system is responsible for carrying this oxygen to the muscles?
Answer:
The circulatory system
Step-by-step explanation:
Is this math? lol
:]
Choose the statements that are true about a cube with side length 1 unit.
It has a volume of 6 cubic units.
It has a volume of 1 cubic unit.
It has a volume of 3 cubic units.
It is called a "one block."
It can be used to measure volume.
It is called a "unit cube."
The answer to the mentioned statement are :
first statement is WRONG
the second statement is RIGHT
The third statement is also WRONG
the fourth statement is RIGHT
fifth statement is RIGHT
sixth statement is WRONG
The side of the given cube is 1 unit.
This means that the Length= Breadth = Height = 1 unit because it is cube
This means that the volume can be described as
( side ) ³
that is 1 × 1 × 1 = 1 cubic unit
thus the first statement is WRONG
However the second statement is RIGHT
The third statement is also WRONG
since it is a cube whose volume is 1 cubic unit
thus we can say that it is one block
Thus the fourth statement is RIGHT
fifth statement is RIGHT
sixth statement is WRONG
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