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4 years ago

The curve produced by the water coming from a hose is sketched onto a graph with zeros at 1 and 5. The point (4,

Mathematics

2 answers:

Levart [38]4 years ago

7 0

Answer

answer A and C are right

Stella [2.4K]4 years ago

6 0

Answer:

Step-by-step explanation:

From the problem, we deduct that the function has to be quadratic, because it's mention two zeros, which is proper of a polynomial expression with grade 2.

So, we can say that:

$h(x)=a(x-0)(x-5)$

Because, 5 and 0 are roots of the expression.

Also, we know that the point $(4,1)$ is on the curve, this means:

$h(4)=1$

Replacing this relation in the first expression, we have:

$1=a(4-5)$

$1=a(-1)\\a=-1$

So, the expression would be:

$h(x)=-1(x-0)(x-5)$

$h(x)=-x(x-5)$

$h(x)=-x^{2} +5x$

If we graph, we could get the vertex easier.

You can see in the image, that the vertex is at x = 2.5

Therefore, the option C is the answer.

However, the first option has this function:

h(x) = –0.25(x)(x – 5).

Which also can be solution, because, if we try x = 4:

h(4) = –0.25(4)(4 – 5)=1

Therefore, option A is also part of the answer.

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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

3 years ago

Evaluate the expression below. (8 - 7)- 4 + 3(-1) 1 -7 -1 7

Masja [62]

Answer:

answer is -1 according to calculation

4 0

3 years ago

Circle any equivalent ratios from the list below.

marysya [2.9K]

Answer:

Equivalent ratios: we can that the first ratio is equivalent to the second, then third ratio is equivalent to the forth.

Ratio: 1: 2 Value of the Ratio: 1/2

Ratio: 5: 10 Value of the Ratio: 1/2

Ratio: 6: 16 Value of the Ratio: 3/8

Ratio: 12: 32 Value of the Ratio: 3/8

We notice that if the values are equivalent the ratios are equivalent

Step-by-step explanation:

Equivalent ratios:

To get if ratios are equivalent we look for the constant between ratios

a.Ratio: 1: 2 and Ratio: 5: 10

We apply the method of comparing the first term of both ratios , and the second term of both ratios. We see the constant is 5 ( 1/5 is equal to 2/10)

We do the same with third and forth ratio

Ratio: 6: 16 compare to Ratio: 12: 32

6/12 is equal to 16/32 the constant is 2

So, we can that the first ratio is equivalent to the second, then, third ratio is equivalent to the forth.

Value of the Ratio: The value is a ratio written as a fraction.

Ratio: 1: 2 Value of the Ratio: 1/2

Ratio: 5: 10 Value of the Ratio: 5/10 if we divide both sides by 5, we can say Value of the Ratio: 1/2

Ratio: 6: 16 Value of the Ratio: 6/16 if we divide both sides by 2, we can say the value is 3/ 8

Ratio: 12: 32 Value of the Ratio: 12/32 if we divide both sides by 4, we can say the value is 3/ 8

If the values are equivalent the ratios are equivalent.

7 0

3 years ago

Read 2 more answers

work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company deci

Yuki888 [10]

Answer:

(a) S = {MR, MJ, MD, MC, RJ, RD, RC, JD, JC, DC}

(b) The probability that Roberto and John attend the conference is 0.10.

(d) The probability that John stays home is 0.60.

Step-by-step explanation:

It is provided that :

Marco (M), Roberto (R), John (J), Dominique (D) and Clarice (C) works for the company.

The company selects two employees randomly to attend a statistics conference.

(a)

There are 5 employees from which the company has to select two employees to send to the conference.

So the total number of ways to select two employees is:

${5\choose 2}=\frac{5!}{2!(5-2)!}=\frac{5\times 4\times 3!}{2\times 3!}=10$

The 10 possible samples are:

MR, MJ, MD, MC, RJ, RD, RC, JD, JC, DC

(b)

The probability of the event E is:

$P(E)=\frac{n(E)}{N}$

Here,

n (E) = favorable outcomes

N = Total number of outcomes.

The variable representing the selection of Roberto and John is, RJ.

The favorable number of outcomes to select Roberto and John is, 1.

The total number of outcomes to select 2 employees is 10.

Compute the probability that Roberto and John attend the conference as follows:

$P(RJ)=\frac{n(RJ)}{N}=\frac{1}{10}=0.10$

Thus, the probability that Roberto and John attend the conference is 0.10.

(c)

The favorable outcomes of the event where Clarice attends the conference are:

n (C) = {MC, RC, JC and DC} = 4

Compute the probability that Clarice attends the conference as follows:

$P(C)=\frac{n(C)}{N}=\frac{4}{10}=0.40$

Thus, the probability that Clarice attends the conference is 0.40.

(d)

The favorable outcomes of the event where John does not attends the conference are:

n (J') = MR, MD, MC, RD, RC, DC

Compute the probability that John stays home as follows:

$P(J')=\frac{n(J')}{N}=\frac{6}{10}=0.60$

Thus, the probability that John stays home is 0.60.

4 0

3 years ago

A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 feet longer

VladimirAG [237]

Let's say the second piece is x ft long
The first piece is 2x ft long
The third piece is x+4 ft long
All of the pieces should add up to 10ft
x+2x+x+4=10
4x= 6
x=1.5ft
The first piece is 2x ft long=3 ft long

7 0

3 years ago