How would you determine the distance between (6,8) and (2,-3)

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

lyudmila [28]

Step-by-step explanation:

$4x^3+x^2-8x-2\qquad\text{distributive}\\\\=x^2(4x+1)-2(4x+1)\\\\=(4x+1)(x^2-2)$

5 0

3 years ago

Daniel had 80 more stickers than Elle. He gave 1/4 of his stickers to Elle. She then gave 3/5 of her stickers to Daniel. In the

Pepsi [2]

Answer:

Daniel had 108 stickers at first

Step-by-step explanation:

Number of Daniel's stickers = d

Number of Elle's stickers = e

Since Daniel had 80 more stickers than Elle, d = 80 + e

e = d - 80

Daniel gave 1/4 of his stickers to Elle, Daniel is left with (d - d/4) = 3d/4

Elle now has e + d/4 = d - 80 + d/4 = (5d/4) - 80 = (5d - 320)/4

Elle now gave 3/5 of her remaining stickers to Daniel:

Elle now has:

$e_{new} = \frac{5d -320}{4} - \frac{3}{5} * \frac{5d -320}{4}\\\\e_{new} = \frac{5d -320}{4} - \frac{15d -960}{20}\\\\e_{new} = \frac{25d - 1600 - 15d + 960}{20} \\\\ e_{new} = \frac{10d-640}{20}$

Daniel now has:

$d_{new} = \frac{3d}{4} + \frac{3}{5} (\frac{5d - 320}{4} )\\d_{new} = \frac{3d}{4} + \frac{15d - 960}{20} \\d_{new} = \frac{30d - 960}{20}$

Daniel now had 92 more stickers than Elle

$d_{new} = E_{new} + 92$

$\frac{30d - 960}{20} = \frac{10d - 640}{20} + 92$

Multiply through by 20

30d - 960 = 10d - 640 + 1840

20d = -640 + 1840 + 960

20 d = 2160

d = 2160/20

d = 108

7 0

3 years ago

Whats the answer for 2x + 1 + 7x ?

lesya692 [45]

Answer:

9x+1

Step-by-step explanation:

combine 2x+7x then add the 1

6 0

3 years ago

Read 2 more answers

Which of the following is an example of parallel lines?

RSB [31]

Answer: C

Explanation: they will never touch

8 0

4 years ago

Read 2 more answers

A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is

seraphim [82]

Answer:

a) The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at 0.01% level of significance

They score is above 24 on the math portion of the exam

b)

Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

Alternative Hypothesis: H₁: μ ≠ 24

Step-by-step explanation:

Step(i):-

Given random sample 'n' = 250

Given data sample mean x⁻ = 24.5

Standard deviation = 3.3

Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school

H₀: μ = 24

Alternative Hypothesis: H₁: μ ≠ 24

test statistic

$Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{24.5 - 24}{\frac{3.3}{\sqrt{250} } } = \frac{0.5}{0.2087} = 2.397$

a) 99% or 0.01% level of significance

Level of significance ∝ = 0.01

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} =2.576$

The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance

Null hypothesis is accepted at 0.01% level of significance

They score is above 24 on the math portion of the exam

b) 95% or 0.05% level of significance

Level of significance ∝ = 0.05

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96$

The Z -value 2.397 > 1.96 at 95% or 0.05% level of significance

Null hypothesis is Rejected at 0.05% level of significance

They score is below 24 on the math portion of the exam

6 0

3 years ago