Answer with Step-by -step explanation:
Sequence A;4,7,10,13,16
[tex]a_2-a_1=7-4=3[/tex]
[tex]a_3-a_2=10-7=3[/tex]
The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.
Common difference, d=3
a=4
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=a+5d=4+5\times 3=19[/tex]
[tex]a_7=a+6d=4+6(3)=22[/tex]
[tex]a_8=a+7d=4+7(3)=25[/tex]
Sequence B: 5,10,20,40,80,...
[tex]a_1=5,a_2=10,a_3=20[/tex]
[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]
[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]
The ratio of two consecutive terms is equal. Therefore, it forms geometric sequence.
Common ratio, r=2
a=5
[tex]a_n=a r^{n-1}[/tex]
[tex]a_6=ar^5=5(2)^5=160[/tex]
[tex]a_7=ar^6=5(2^6)=320[/tex]
[tex]a_8=ar^7=5(2^7)=640[/tex]
Sequence C:2,5,10,17,26,..
a1=2
[tex]a_2=5=2+3=a_1+3[/tex]
[tex]a_3=10=5+5=a_2+5[/tex]
[tex]a_4=17=10+7=a_3+7[/tex]
[tex]a_5=26=17+9=a_4+9[/tex]
From the following pattern
We can get
[tex]a_6=a_5+11=26+11=37[/tex]
[tex]a_7=a_6+13=37+13=50[/tex]
[tex]a_8=a_7+15=50+15=65[/tex]
graph:y-10=-2(x-10)grgrgrgrggrgrgrgrgrgrrgrrggr
Answer: 14
Step-by-step explanation:
y -1 0 = -6
Ans -2 (x-10) = 14
Hope I could help :)
Please help ASAP!!!
A rectangle is formed by placing two identical squares side by side. the area of the rectangle is 892 cm2. What is the perimeter of the square?
Answer:
288 cm^2
Step-by-step explanation:
If you have 2 congruent squares, side by side, the perimeter is 6*sidelength.
We divide 72 by 6 to find sidelength, and get 12.
We square 12 to find the area of a square, and get 144.
Multiply by 2 to find the area of the rectangle, and get 288 cm^2
What are reciprocals?
Answer:
In mathematics,reciprocal is an expression or function so related to another that their product is unity; the quantity obtained by dividing the number one by a given quantity.
Answer:Rh
Step-by-step explanation:mama
can someone help me in this problem
Answer:
8a³b
Step-by-step explanation:
Graph the image of AUVW after a translation 11 units left and 3 units down.
A wooden frame is to be constructed in the form of an isosceles trapezoid, with diagonals acting as braces to strengthen the frame. The sides of the frame each measure 5.3 feet, and the longer base measure 12.7 feet. If the angles between the sides and the longer base each measure 68.4 degrees, find the length of one brace to the nearest tenth of a foot.
Answer:
11.8 ft
Step-by-step explanation:
Since the length of one side, l = 5.3 ft, the longer base b = 12.7 ft and the one brace, d form a triangle with angle between the longer base and side being the angle facing the brace is θ = 68.4°, we use the cosine rule to find the length of thee brace.
So d² = l² + b² -2lbcosθ
So, substituting the values of the variables into the equation, we have
d² = (5.3 ft)² + (12.7 ft)² -2(5.3)(12.7)cos68.4°
d² = 28.09 ft² + 161.29 ft² - 134.62(0.3681)
d² = 189.38 ft² - 49.56 ft²
d² = 139.82 ft²
taking square-root of both sides, we have
d = √139.82 ft²
d = 11.82 ft
d ≅ 11.8 ft to the nearest tenth of a foot.
-3x+20+7x=80 what is x? and how do I get it?
Answer:
x = 15
Step-by-step explanation:
-3x+20+7x=80
Combine like terms
4x+20 = 80
Subtract 20 from each side
4x+20 -20 = 80-20
4x = 60
Divide by 4
4x/4 = 60/4
x = 15
help pls i need this asap
Answer:
I got 45 degrees
Step-by-step explanation:
knowing that where T is is 90 degrees and a triangle always= 180 degrees I just split 90 in half and got 45. I could be wrong but I hope this helps :)
3
JK, KL, and IJ are all tangent to o (not drawn to scale). JA = 8, AL = 11, and
CK = 10. Find the perimeter of AJKL.
Answer:
[tex]P = 58[/tex]
Step-by-step explanation:
The image if the circle and triangle can be found online
Given
[tex]JA = 8[/tex]
[tex]AL = 8[/tex]
[tex]CK = 10[/tex]
Required
The perimeter of JKL
Since the mid-points of the tangents are A, B and C respectively.
[tex]JK = JB + BK[/tex]
Where
[tex]JB = JA = 8[/tex]
[tex]BK = CK = 10[/tex]
So:
[tex]JK =8+10 =18[/tex]
[tex]JL = JA + AL[/tex]
[tex]JL = 8+11 = 19[/tex]
[tex]KL = CL + CK[/tex]
Where
[tex]CL =AL = 11[/tex]
So:
[tex]KL = 11+10 = 21[/tex]
So, the perimeter (P) is:
[tex]P = JK+ KL +JL[/tex]
[tex]P = 18 + 19 + 21[/tex]
[tex]P = 58[/tex]
Last question, so please help me out ASAP!
Answer:
5/18
Step-by-step explanation:
conditional probability formula:
A|B (a given b) = (A∩B)/(B)
so
Moderate|college (moderate given college)= (moderate∩college)/college
moderate∩college= 15
college= 11+15+28= 54
15/54= 5/18
What the hcf of 24 and 180
Answer:
12
Step-by-step explanation:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
If a line has a slope of 3, what is the slope of a line perpendicular to it?
Answer:
- [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]
Here m = 3 , then
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{3}[/tex]
What is the measure of _X in degrees?
O A. Cannot be determined
O B. 20°
O C. 40°
O D. 70°
What is the length of Line segment B C?
Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses?
Answer:
134inches
Step-by-step explanation:
Convert 2feet to inches
1foot= 12 inches
2feet= 12x2inches
=24inches
24inches is to 1 birdhouse
24inches x 6 equals six birdhouses
134inches
Answer:
He will need 162 inches
Step-by-step explanation:
6×2ft is 12 feet. Convert ft into inches for every 1 foot you have 12 inches. A total of 144in. Now multiply 6×3in which equals 18in. Add 144+18=162
Which equation shows the distributive property? (a) 6 x 3 + 6 x 8 = 6 x (3 + 8) (b) 5 + (22 + 19) = (5 + 22) + 19 (c) 20 x 10 = 10 x 20 (d) 45 + 7 = 7 + 45
help me please
If you input 3 into the equation below, what is the resulting y-value?
y=9
Answer:
It will still be 9. y=9 is a horizontal line. No matter the x value, the answer will be the same.
Step-by-step explanation:
Which of the following is true about similar right triangles ?
A. Corresponding angles are not equal.
B. Corresponding trigger number trigonometric ratios are in proportion
C.Corresponding trigonometric ratios are equal
D.Corresponding sides are equal
Answer:
b
Step-by-step explanation:
because its alternation
The option (C) Corresponding trigonometric ratios are equal is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
We have a statement:
Which of the following is true about similar right triangles?
As we know from the definition the two triangles have the same shape, but it is not compulsory to have the same size.
The ratio of the corresponding sides is in the same proportions
The corresponding trigonometric ratios are equal.
Thus, the option (C) Corresponding trigonometric ratios are equal is correct.
Learn more about the similarity of triangles here:
brainly.com/question/8045819
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A credit card has a nominal annual interest rate of 18%, and interest is compounded monthly. The cardholder uses the card to make a $30 purchase.
Which expression represents the balance on the card after 5 years, in dollars, assuming no further charges or payments are made?
Answer:
30 [tex](1 + \frac{.18}{12})^{5*12}[/tex]
Step-by-step explanation:
The inequality – x2 - 6 <0 has
Answer:
X es igual a 3
Step-by-step explanation:
x2 - 6 = 0
(3)2 - 6 = 0
the pythagorean theorem equation
Answer:
(Altitude)^2+(Base)^2=(Hypotenuse)^2
help plzzzzzzzzzzzzzzzzzzzzz
What percent of all students are middle schools
1 Select the correct answer. Kalid simplified a polynomial expression as shown. (6x3 + 8x2 − 7x) − (2x2 + 3)(x − 8) step 1 (6x3 + 8x2 − 7x) − (2x3 − 16x2 + 3x − 24) step 2 6x3 + 8x2 − 7x − 2x3 − 16x2 + 3x − 24 step 3
Answer:
So, the step1 is correct.
Step-by-step explanation:
The expression is
[tex](6 x^3 + 8 x^2 - 7 x)-(2x^2 + 3)(x- 8)\\\\(6 x^3 + 8 x^2 - 7 x) - (2x^3 - 16 x^2 + 3 x - 24)\\\\6 x^3 + 8 x^2 - 7 x - 2 x^3 - 16 x^2 + 3 x - 24\\\\4 x^3 - 8 x^2 - 4 x - 24[/tex]
So, the step 1 is correct.
change from improper fraction to mix number 51/7
Answer:
7 3/7
Step-by-step explanation:
what is the perimeter of semicircle with radius of 3cm
Answer:
198/7
Step-by-step explanation:
perimeter of semi circle= (pi) x r + d
= 22/7 x 3 + 6
= 198 cm
Answer:
15.42 cm
Step-by-step explanation:
perimeter of semicircle = πr + 2r
=3.14*3 + 2*3
=9.42 + 6
=15.42
Solve 3x + 8 = 2x + 21
what is the scale factor from figure a to figure b
Scale factor from figure a to figure b = DIVIDE BY 3
{Check:- 33/3 = 11 & 15/3 = 5}
hope this helps :)
Answer:
1/3
Step-by-step explanation:
These two quadrilaterals are similar because figure A's sides are 3 times figure B's sides. Figure A's bottom is 15, while figure B's bottom is 5. To get from 15 to 5, we multiply by 1/3. This is the scale factor. All the other sides of figure A are also 3 times bigger than figure B's.
randy is a car salesman who earns a base pay of $39,800 and is a paid commission of 18% for each car he sells. if x represents total sales in dollars, which equation best represents randys total pay in dollars
Answer:
39,800+x0.18= his total pay
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Biffy Out!!!
A light bulb consumes 3600 watt-hours per day. How many watt-hours does it consume in 4 days and 18 hours?
Answer:
17,100
Step-by-step explanation:
A light bulb consumes 3600 watts per day
Therefore the number of watts consumed in 4 days 18 hours can be calculated as follows
3600= 24 hours
x= 1 hour
= 3600/24
= 150 watts in an hour
3600×4
= 14,400
150×18
= 2,700
Total watts
= 14,400+2700
= 17,100
Hence the number if watss produced in 4 days 18 hours is 17,100 watts