If you cannot write down the first step to a problem, you should the problem to help you remember how to solve it.

Find xif f(x) = 2x + 7 and f(x) = -1.

Natali [406]

Answer: -4

Step-by-step explanation:

Solve 2x+7=-1

2x. =-8

x. =-4

8 0

3 years ago

Read 2 more answers

The sum of the first ten terms of a linear sequence is 145. the sum of the next ten term is 445. find the sum of the first four

chubhunter [2.5K]

The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

$S_n =\frac{n}{2}(2a+(n-1)d)$

The sum of the first ten terms of a linear sequence is 145

⇒ $S_{10} =\frac{10}{2}(2a+(10-1)d)$

⇒ 145 = 5 (2a+9d)

⇒ $\frac{145}{5} =2a+9d$

⇒ 29 = 2a + 9d ------- (1)

The sum of the next ten term is 445, so the sum of first twenty terms is

⇒ 145 + 445

⇒ $S_{20} =\frac{20}{2}(2a+(20-1)d)$

⇒ 590 = 10 (2a + 19d)

⇒ $\frac{590}{10}=2a+19d$

⇒ 59 = 2a + 19d -------- (2)

Now subtract (2) from (1),

⇒ 30 = 10d

⇒ d = $\frac{30}{10}$

⇒ d = 3

Substitute d in (1), we get

⇒ 29 = 2a + 9(3)

⇒ 29 = 2a + 27

⇒ 29 - 27 = 2a

⇒ 2 = 2a

⇒ a = $\frac{2}{2}$

⇒ a = 1

Thus, sum of first four terms is

⇒ $S_4 =\frac{4}{2}(2(1)+(4-1)(3))$

⇒ $S_4 =2(2+(3)(3))$

⇒ S₄ = 2(2+9)

⇒ S₄ = 2(11)

⇒ S₄ = 22.

Hence we can conclude that the sum of the first four terms of the sequence is 22.

Learn more about sum of sequence of n terms here

brainly.com/question/20385181

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6 0

1 year ago

If y is 15 times x, which equation shows the relationship between x and y?

zhannawk [14.2K]

Is= equals sign
times= multiplication

So y equals 15 times x

y= 15 * x
y= 15x

ANSWER: y= 15x (bottom choice)

Hope this helps! :)

4 0

3 years ago

The formula is: <img src="https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%7Br%7D%5E%7B3%7D%20" id="TexFor

uranmaximum [27]

Answer:

Volume of hemisphere=

$\frac{2}{3} \pi {r}^{3}$

Volume of sphere=

$\frac{4}{3} \pi {r}^{3}$

Step-by-step explanation:

$\frac{2}{3} \times \frac{22}{7} \times {8}^{3}$

Using calculator=

1072.761905

Round to the nearest tenth=

1072.8

5 0

3 years ago

the plans for your 13th birthday party are well under way. your parents agree to your guest list of 400 people. you decided it w

diamong [38]

Answer:

11 people will get both the prizes.

Step-by-step explanation:

In this question we need to find common integral multiples of 5 and 7 under 400. As you can see in the figure 35th person is the first one to get both ipod and psp. The LCM (least common multiple) of 5 and 7 which is 35 (!!! I hope you know how to LCM of two integers ).

Therefore the integral multiples of 35 will be same as the common multiples of 5 and 7. So, figuring out the number of integral multiples of 35 under 400 will give the answer.

To do that divide the number 400 with 35. On performing the division the quotient will be 11 and the remainder will be 15.

Therefore 11 persons out of 400 will get both the prizes.

Similarly if you want to find the number of person getting ipod then divide 400 with 5. The quotient will be 80. ∴ 80 people will get ipod.

And for psp, divide 400 with 7. The quotient will be 57. ∴ 57 people will get psp.

In these divisions, consider just the quotient, here remainder is of no use.

5 0

3 years ago