Since consecutive terms differ by a constant k in this sequence, we have
[tex]a_8 = a_7 + k[/tex]
[tex]a_8 = (a_6+k)+k = a_6+2k[/tex]
[tex]a_8 = (a_5+k)+2k=a_5+3k[/tex]
and so on down to
[tex]a_8 = a_1 + 7k[/tex]
Solve for k :
14 = 49 + 7k ⇒ -35 = 7k ⇒ k = -5
We then do the same as above but in the reverse direction:
[tex]a_9 = a_8+k[/tex]
[tex]a_{10} = a_9+k = a_8+2k[/tex]
[tex]a_{11} = a_{10}+k = a_8+3k[/tex]
and so on, up to
[tex]a_{27} = a_8 + 19k = \boxed{-81}[/tex]
factorise fully 2ab2+ 8a2b
[tex]2 {ab}^{2} + {8a}^{2} b[/tex]
solution:[tex]2ab(b + 4a)[/tex]
to factorise first, find the highest common factor of each of the terms in the expression then, write the highest common factor (HCF) in front of any brackets atlast, fill in each term in the brackets by multiplying out.
The value of the expression after factorization will be;
⇒ 2ab (b + 4a)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2ab² + 8a²b
Now,
Factorize the expression as;
⇒ 2ab² + 8a²b
⇒ 2ab × b + 2×2×2a×a×b
⇒ 2ab (b + 4a)
Thus, The value of the expression after factorization will be;
⇒ 2ab (b + 4a)
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if a rectangle has a perimeter of 18 cm, and a height of 4 cm, what is the area?
Answer:
20 cm²
Step-by-step explanation:
Look at the diagram attached.
If the height is 4cm, we will have two sides that are 4cm for our rectangle.
We can label the other sides as x.
They are both x since opposite sides of a rectangle are equal in length.
We can make an equation with our perimeter:
[tex]2(4) + 2(x) = 18\\8 + 2x = 18\\2x = 10\\x = 5[/tex]
Now that we know the length & height, we can calculate the area:
4 × 5 = 20 cm²
Sheree purchased a digital camera for $367.99. She received a manufacturer’s $45 mail-in rebate and a $25 rebate from Jack’s Camera Store. What is the final price?
Answer:
297.99
Step-by-step explanation:
367.99-45-25=297.99
The square of a non-zero number is equal to 70% of the original number. What
is the original number?
Answer:
0.7.
Step-by-step explanation:
x^2 = 0.7x
x^2 - 0.7x = 0
x(x - 0.7) = 0
x = 0, 0.7.
After solving the quadratic equation x² = 0.7x , we get that the original number is 0.7
What is a quadratic equation?
Quadratic equation is an equation which contains one unknown variable and the highest power of this unknown variable is 2. Let x be the unknown variable then the standard quadratic equation in x is given by
ax²+bx+c =0, where a, b, c are constants and a≠0
We can solve this equation by factorizing ax²+bx+c and putting those factors equal to zero to solve for x.
Let a non zero number be x, x≠0 and given that the square of a non zero number is equal to the 70% of the original number.
As 70 % of the original number = 70/100(x) = 0.7 x
⇒ x² = 0.7 x
⇒x²-0.7 x = 0
⇒ x(x -0.7)= 0
⇒ x =0 and x - 0.7 = 0
⇒ x = 0.7, as we have given that x is a non zero number
Therefore, the original number is 0.7
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George has 4 sets of socks, and 4 sets of shoes. Each pair has a different color: White, Brown, Black, and Blue. If George selects a pair of socks (same color) and a pair of shoes (same color) at random, what is the theoretical probability that George will choose a white pair of shoes and a pair of socks that are not white
Using it's concept, it is found that there is a [tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
One out of four pairs of shoes are white.Three out of four pairs of socks are not white.Since the events are independent:
[tex]p = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]
[tex]\frac{3}{16}[/tex] probability that George will choose a white pair of shoes and a pair of socks that are not white.
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Which of the following sets of 3 side lengths could form a unique triangle?
O side lengths: 18 feet, 9 feet, 6 feet
O side lengths: 12 feet, 9 feet, 4 feet
O side lengths: 6 feet, 3 feet, 2 feet
O side lengths: 24 feet, 14 feet, 4 feet
Answer:
side lengths: 12 feet, 9 feet, 4 feet
Step-by-step explanation:
Conditions for unique triangles with 3 sides:
The sum of the two shorter sides must be greater than the third side.9 + 6 = 15
As 15 < 18 this is NOT a unique triangle
9 + 4 = 13
As 13 > 12 this IS a unique triangle
3 + 2 = 5
As 5 < 6 this is NOT a unique triangle
14 + 4 = 18
As 18 < 24 this is NOT a unique triangle
6. Which is cheaper?
A) $12 for 800ml or
B) $14 for 1 L
Answer:
A
Step-by-step explanation:
Which of the following pairs of numbers are additive inverses of each other? (A) -0.5 and -0.5 (B)-0.5 and 2 (C) 0.5 and -0.5 (D) 0.5 and 2
Answer: A) -0.5 and -0.5
Step-by-step explanation:
a packaging designer wants to find how much fabric is needed to cover the jewelry box shown the box is 12cm shown 4 cm wide and 5m high find the surface area of the box
Step-by-step explanation:
I guess you mean it is
12 cm long, 4cm wide and 5 cm high.
and the fabric goes outside on the box ? strange, but ok.
a box (like a die) has 6 sides in the form of 3 pairs of equal rectangles :
top-bottom, left-right, front-back
the surface area is the sum of all 6 rectangles.
top-bottom :
2 × 12×4 = 2 × 48 = 96 cm²
left-right :
2 × 4×5 = 2 × 20 = 40 cm²
front-back :
2 × 12×5 = 2 × 60 = 120 cm²
in total
120 + 40 + 96 = 256 cm²
NEED HELP WILL GIVE BRAINLIEST!!! PLEASE ANSWER THE TWO QUESTIONS ABOVE!
Answer:
1. 9 6/12
2. 4 3/12
Step-by-step explanation:
I did the math on it.
Answer:
3. 9 (6/12)
4. 4 (3/12)
Step-by-step explanation:
Question 3:
6 (2/6) × 1 (1/2)
multiply the whole number by the denominator
6 x 6 = 36 + 2 (numerator) = 38/6
2 x 1 = 2 + 1 = 3/2
(38/6) x (3/2)
multiply (3/2) by 3
3 x 3 = 9
2 x 3 = 6
38/6 x 9/6
38 x 9 = 342
6 x 6 = 36
19/2 = 9 (1/2) or 9 (6/12)
Question 4:
5 (2/3) × (3/4)
15 + 2 = 17
17/3 x 3/4
17 x 4 = 68
3 x 4 = 12
3 x 3 = 9
4 x 3 = 12
(68/12) x (9/12)
68 x 9 = 612
12 x 12 = 144
612/144 = 4 (1/4) or 4 (3/12)
I hope this helps! I'm sorry if this is confusing.
HELP PLEASE I WILL GIVE 10 POINTS
PLEASE HELP!! 90 POINTS!!!
Dianelys owns a small business selling ice-cream. She knows that in the last week 14 customers paid cash, 121 customers used a debit card, and 3 customers used a credit card. If next week, she is expecting 1100 customers, about how many would you expect to pay with cash? Round your answer to the nearest whole number.
Answer:
112 customers will pay cash next week
Step-by-step explanation:
1,100/138=7.97= approximately 8
Multiply the amount of customers who paid cash, 14 by 8.
pls help thanks!!!!!!
Answer:
he will have 29 nickles
Step-by-step explanation:
I just solved it on paper, hope it helps and if it's right
the following are ages in years of members in a group: 8,11,8,19,6,7,3x,11,11. If the mean age is 9, find x
I WILL GIVE YOU 5 STARS ON YOUR PROFILE COMMNET I WILL ALSO GIVE A THANK YOU ON YOUR ACC AND COMMENT!!!!
Answer:
The answer is C. 2.94
Step-by-step explanation:
All you have to do is take 588 and divide it by 200 which gives you the answer of 2.94.
Using factoring, what is the solution to the equation 2x2 + 3x – 5 = 0
RSM find all 2-digit natural numbers that have exactly 3 factors
Answer:
25 and 49
Step-by-step explanation:
25 = 1, 5, 25
49 = 1, 7, 49
Hope this helps!
The table shows some ordered pairs that belong to quadratic function h.
What is the range of h?
Question 10 options:
All real numbers greater than or equal to -5
All real numbers greater than or equal to 0
All real numbers
All real numbers greater than or equal to -2
Answer: All real numbers greater than or equal to -5
Step-by-step explanation:
The vertex has a y coordinate of -5, and all the other outputs are more than -5.
A large food distributor claims that 45% of all individuals who purchase eggs from its grocery stores choose standard white eggs, 25% choose standard brown eggs, 20% choose organic eggs, and 10% choose free-range eggs. To investigate this claim, researchers collected data from a random sample of the distributor's customers in a large city. The results were 274 white, 159 brown, 126 organic, and 41 free-range egg purchases. Are the data from the sample consistent with the distributor's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion.
The statistical test at the 5% significance level shows that we fail to reject the null hypothesis.
How to compute the statistical test?From the information given, the level of significance is 0.05 and n is 600. The degree of freedom will be:
= 4 - 1 = 3
The test statistic will be:
= ∑(O - E)²/E
= 6.92
The critical value is also given as 7.815 from the table. Since the test statistic is lesser than the critical value, we fail to reject the null hypothesis.
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Find the area of the shaded sector. round to the nearest tenth. Please help!!
Answer:
Step-by-step explanation:
Remark
If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.
So the way to solve this problem is to multiply the entire area of the circle by (81/360)
Area of the sector = (81/360) * pi * r^2
pi = 3.14
r =8.91 cm
Area of the sector = (81/360) * 3.14 * 8.91^2
Area of the sector = 56.09
Rounded to the nearest tenth, the answer is 56.1
Answer: 56.1 cm^2
The figures are similar. Find x.
Pls help meee
A Premier League footballer is value £30 million and after a bad season his transfer value depreciates by 20%. His next season is a good one and his transfer value appreciates by 20%. how Find the value of the footballer after his good season.
How to work out Sir
Answer:
£28.8 Milllion
Step-by-step explanation:
£30,000,000 × 0.8 = £24,000,000 (Depreciates by 20%)
£24,000,000 × 1.2 = £28,800,000 (Appreciates by 20%)
Is it possible for a sixth degree polynomial function with integer coefficients to have no real zeroes? Choose all that apply: Yes No
Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, [tex]\pm i, \pm 2i, \pm 3i[/tex], a sixth degree function with no real zeros is formed, so the answer is Yes.
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please help me!!!!!!!
The distance between you and train 1 at time t is
20.6 km + (0.2 km/h) t
and the distance between you and train 2 at time t is
59.7 km - (2.1 km/h) t
The trains are an equal distance away from you when
20.6 km + (0.2 km/h) t = 59.7 km - (2.1 km/h) t
Solve for t :
(2.3 km/h) t = 39.1 km
t = 17 h
at which point they are
20.6 km + (0.2 km/h) (17 h) = 24 km
away from you.
Which expression is equivalent to startfraction (3 m superscript negative 2 baseline n) superscript negative 3 baseline over 6 m n superscript negative 2 baseline endfraction? assume m not-equals 0, n not-equals 0.
The expression that is equivalent to the given statement was reduced.
The given expression is:
[tex]\frac{(3m^{-2}n)^{-3} }{6mn^{-2} }[/tex]
What are some important power rules?Some important power rules are:
[tex](ab)^n=a^nb^n[/tex]
[tex](a^{m} )^n=a^{mn}[/tex]
[tex]a^m.a^n=a^{m+n}[/tex]
[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]a^{-m} =\frac{1}{a^m}[/tex]
So, the given expression can be written as:
[tex]\frac{3^{-3} m^{6} n^{-3} }{6mn^{-2} }[/tex]
=[tex](\frac{3^{-3} }{6} )*(\frac{m^{6} }{m} )*(\frac{n^{-3} }{n^{-2} } )[/tex]
=[tex](\frac{1}{3^{3} *6} )*m^{5} *(\frac{1}{n^{3} *n^{-2} } )[/tex]
=[tex]\frac{m^5}{162n}[/tex]
Hence, the expression that is equivalent to the given statement was reduced.
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Help!
Square pyramids A and B are similar. In pyramid A, each base edge is 20 cm. In pyramid B, each base edge is 5 cm and the volume is 25 cm.
a. Find the volume of pyramid A.
b. Find the ratio of the surface area of A to the surface area of B.
c. Find the surface area of each pyramid.
Answer:
Below in bold.
Step-by-step explanation:
a) The volumes will be in the ratio of the cubes of the edges.
So volume of A / volume B = 20^3 / 5^3
Volume A / 25 = 8000/125
Volume a = (25* 8000) / 125
= 8000/ 5
= 1600 cm^3.
b) ratio of the surface area of A to surface area of B
= 20^2 : 5^2
= 400:25
= 16:1.
c. The volume of pyramid B is 25 cm*3 so it' height is 25 / area of its base = 25/5^2
= 1 cm.
Now its slant height = √(1^2 + (2.5)^2)
= √7.25
= 2.6926 cm
So surface area = 25 + 4 * 1/2 * 5 * 2.6926
= 51.926
= 51.93 cm^2 to nearest hundredth.
and the surface area of pyramid B = 51.926 * 16
= 830.82 cm^2 to nearest hundredth.
Calvin has a gift card which he is using to buy candy (x), and he has been tracking how much money (y) he spends. He noted that after buying 4 pieces of candy (in all) he has $28.00 left on his card and then after buying 10 pieces of candy (in all) he has $25.00 left on his card. Write the equation of the line that represents his spending on candy.
Answer:
Negative Correlation
Step-by-step explanation:
The plot looks like it's going downwards. If it was an equation, it'd be something with y = -x +b.
how to I write a one solution function??
Answer this for 20 points and brainliest
Answer:
D
Step-by-step explanation:
If you are solving for something like this, set the given full integer equal to x times the percent given
In 1983, a winter hat cost $12.95. today, a winter hat costs $24.50. if the cpi is 219, what is the percent relation of the actual price of a winter hat to the expected price? a. the actual price is 39.3% higher than the expected price. b. the actual price is 15.8% higher than the expected price. c. the actual price is 13.6% lower than the expected price. d. the actual price is 29.8% lower than the expected price.
The actual price is 13.6% lower than the expected price.
What is cpi?CPI or Consumer Price Index is a measure of determining retail inflation in an economy, based on price variations in a fixed basket of goods and services, over overtime periods.
Let's suppose the expected price is x.
The percent relation of the actual price of a winter hat to the expected price is given by;
CPI = ( expected price ) : ( price in 1983 ) × 100
219 = ( x : 12.95 ) × 100
Divide both sides by 100.
x : 12.95 = 2.19
x =2.19 × 12.95
x = $28.36 ( expected price )
p = ( 24.50 × 100 ) / 28.36
p= 2450/28.36
p = 86.4 %
100 % - 86.4 % = 13.6 %
Hence, the actual price is 13.6% lower than the expected price.
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