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2 years ago

7

What is the slope of a line parallel to y = 4x + 3.

2 answers:

NikAS [45]2 years ago

6 0

Answer:Using the slope-intercept form, the slope is −4 - 4 .

Step-by-step explanation:To find an equation that is parallel to y=−4x−3 y = - 4 x - 3 , the slopes must be equal.

UNO [17]2 years ago

3 0

Answer:

the slope is −4 - 4

sorry if it’s wrong

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Enter the finite geometric series from its given description, and then enter its sum.

Mama L [17]

Answer:

$a_n= 4(-5)^{(n-1)}$

-10416

Step-by-step explanation:

a = 4

r = -5

geometric series: $a_n=ar^{(n-1)} = 4(-5)^{(n-1)}$

Determine which term = -12500:

$a_n=-12500$

$4(-5)^{(n-1)}=-12500$

$(-5)^{(n-1)} = -3125$

$(5)^{(n-1)} = 3125$

$(n-1)ln(5) = ln(3125)$

$n-1 = ln(3125)/ln(5) = 5$

$n = 5 + 1 = 6$

$a_6=-12500$

Using geometric sum series formula: $S_n=\frac{a(1-r^n)}{1-r}$

Therefore, $S_6=\frac{4(1-(-5)^6)}{1-(-5)} =\frac{-62496}{6} =-10416$

4 0

2 years ago

Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x

= $64 + 192 \times x^{1} + 240 \times x^{2}$ + terms involving higher powers of x

so, the first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

Again,

$(2+x - x^{2})^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})$

Now, by inspection,

the term $x^{2}$ comes from k =5 and k = 6

for k = 5, the coefficient of $x^{2}$ is , $(-32) \times 6$ = -192

for k = 6 , the coefficient of $x^{2}$ is, $6_{C_{2}} \times 2^{4}$ = 240

so, coefficient of $x^{2}$ in the final expression = (240 - 192) = 48

3 0

3 years ago

-4x-2y=-12<br> solve the system of equations

Blababa [14]

Um there needs to be another equation

3 0

3 years ago

Dominic puts his cars in 6 rows with 5 in each row. His sister changes them into 3 rows with the same number in each row. How ma

miv72 [106K]

10 cars in each row

5 cars x 6 rows = 30

30 divided by 3 = 10 cars in each row

8 0

3 years ago

The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.35 en

trasher [3.6K]

Answer:

a) 0.3571

b) The p-value is 0.362007.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 1.35

Sample mean, $\bar{x}$ = 1.4

Sample size, n = 26

Alpha, α = 0.01

Sample standard deviation, s = 0.7

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 1.35\text{ entrees per order}\\H_A: \mu > 1.35\text{ entrees per order}$

We use One-tailed t test to perform this hypothesis.

a) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n-1}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{1.4 - 1.35}{\frac{0.7}{\sqrt{25}} } = 0.3571$

b) The p-value at t-statistic 0.3571 and degree of freedom 25 is 0.362007.

4 0

3 years ago