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garik1379 [7]
2 years ago
14

Chelsea is graphing the function f(x) = 20(One-fourth)x. She begins by plotting the initial value. Which graph represents her fi

rst step?
Mathematics
2 answers:
natta225 [31]2 years ago
8 0

Answer:

C

Step-by-step explanation:

Alenkinab [10]2 years ago
4 0

Answer:

c

Step-by-step explanation:

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Which of the following is the expansion of (3c + d2)6?
vovangra [49]

Answer: Option A) 729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12} is the correct expansion.

Explanation:

on applying binomial theorem,  (a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r

Here a=3c, b=d^2 and n=6,

Thus, (3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r

⇒ (3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6

⇒(3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}

⇒(3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}

⇒(3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}

3 0
2 years ago
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Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain.
Vlad [161]
Elsa's answer is incorrect since there is a solution of the given equation. In the given logarithmic problem, we need to simplify the problem by transposing log2(3x+5) in the opposite side. The equation will now be log2x-log2(3x+5)=4. Using properties of logarithm, we further simplify the problem into a new form log (2x/6x+10)=4.  Then transform the equation into base form 10^4=(2x/6x+10) and proceed in solving for x value which is equal to 1.667. 
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2 years ago
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Beth wants to make exactly 60 blueberry muffins. Each batch makes 6 muffins, She has already made 2.5 batches. How many more bat
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Answer: 4.5

You need that many more batches

8 0
2 years ago
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Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10
charle [14.2K]

Answer:

Maximum number of long sleeved shirt that can be purchase is, 8

and

Minimum number of long sleeved shirt that can be purchased is, 0

Step-by-step explanation:

let y represents the number of short sleeves  and x represents the number of long sleeves.

As per the given condition:

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt.

we have;

x+y\geq 25              or

y\geq 25 -x    ....[1]

Since, long sleeves shirt are $ 10 each and short sleeves shirt are $ 5 each.

then;

Total cost of long sleeves is 10x and

the total cost of short sleeves is 5y

Also; the club can spend no more than $ 165

then;

10x+5y\leq 165                  

 5y\leq 165 -10x or

y\leq 33-2x ......[2]

Solving the inequality equation with the graph :

Plot equation [1] and [2]; we get the maximum at point (8 , 17)

so, x= 8.

If we take minimum value of x =0 then y is between 25 and 33.

so, the solution area is between the lines to the left of where the lines intersect.

Therefore, the maximum number of long sleeved shirts can be purchased is 8 and the minimum number of long sleeved shirt can be purchased is 0






6 0
2 years ago
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Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?
quester [9]
X^3-7x^2-5x+35

= x^2(x-7) - 5 (x-7)   now by definition 

=(x^2-5)(x-7)

hope this helps
8 0
1 year ago
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