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2 years ago

Question 5 (1 point)

Mathematics

2 answers:

Ivanshal [37]2 years ago

6 0

$\huge{{x}^{2} + 6x + 9}$

Step-by-step explanation:

Using Binomial Theorem:

$\boxed{{(a+b)} ^n= \sum_{k=0}^{n}\binom{n}{k} a^{n-k}b^{k}}$

$(a+b) ^2 =a^{2} + 2ab +b^{2}$

The answer seems to be $x^{2} + 6x + 9$ ...

fredd [130]2 years ago

4 0

Answer:

a) x² + 6x + 9

Step-by-step explanation:

When we square something, we multiply it by itself:

⇒ (x + 3)² = (x + 3)(x + 3)

Using the FOIL method: (a + b)(c + d) = ac + ad + bc + bd

⇒ (x + 3)(x + 3) = x² + 3x + 3x + 9

= x² + 6x + 9

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A is true but f(x) is wrong need help

MrRissso [65]

Answer:

f(x)=-18x^2

Step-by-step explanation:

Given:

1+Integral(f(t)/t^6, t=a..x)=6x^-3

Let's get rid of integral by differentiating both sides.

Using fundamental of calculus and power rule(integration):

0+f(x)/x^6=-18x^-4

Additive Identity property applied:

f(x)/x^6=-18x^-4

Multiply both sides by x^6:

f(x)=-18x^-4×x^6

Power rule (exponents) applied"

f(x)=-18x^2

Check:

1+Integral(-18t^2/t^6, t=a..x)=6x^-3

1+Integral(-18t^-4, t=a..x)=6x^-3

1+(-18t^-3/-3, t=a..x)=6x^-3

1+(6t^-3, t=a..x)=6x^-3

That looks great since those powers are the same on both side after integration.

Plug in limits:

1+(6x^-3-6a^-3)=6x^-3

We need 1-6a^-3=0 so that the equation holds true for all x.

Subtract 1 on both sides:

-6a^-3=-1

Divide both sides by-6:

a^-3=1/6

Raise both sides to -1/3 power:

a=(1/6)^(-1/3)

Negative exponent just refers to reciprocal of our base:

a=6^(1/3)

3 0

2 years ago

The function A(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its othe

Brut [27]

Answer:

$b(a) =\frac{a}{7} -5$

Step-by-step explanation:

Given

$A(b) = 14 * \frac{b + 5}{2}$

Required

Determine the inverse function b(a)

Write A(b) as a

$a = 14 * \frac{b + 5}{2}$

Swap a and b

$b = 14 * \frac{a + 5}{2}$

$b = 7(a + 5)$

Divide both sides by 7

$a + 5 = \frac{b}{7}$

Maka a the subject

$a =\frac{b}{7} -5$

Swap a and b again

$b =\frac{a}{7} -5$

Hence:

$b(a) =\frac{a}{7} -5$

4 0

3 years ago

Use the circle to answer the questions

insens350 [35]

Answer:

Diameter: 10.8 cm

Circumference (in terms of π): 10.8π cm

Circumference (approximate): 33.91 cm

Step-by-step explanation:

Hi there!

We're given:

The radius (5.4 cm)

1) Determine the diameter

$d=2r$

Multiply the radius 5.4 cm by 2

5.4 × 2 = 10.8

Therefore, the diameter of the circle is 10.8 cm.

2) Determine the circumference of the circle

$C=\pi d$

Plug in the diameter 10.8

$C=10.8\pi$

Therefore, the circumference of the circle in terms of π is 10.8π cm.

3) Determine the approximate circumference of the circle

$C=10.8\pi\\C=10.8(3.14)\\C=33.91$

Therefore, the approximate circumference of the circle is 33.91 cm.

I hope this helps!

5 0

3 years ago

Triangles L M N and L K N are connected at side L N. A line is drawn from point M to point K and intersects side L N at point P.

lesya692 [45]

The true statement is Line MK is the perpendicular bisector of LN and ML is ≅ MN.

<h3>What is perpendicular?</h3>

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

Δ LMN and Δ LKN are connected at side LN.

As per the information,

Line MK is the perpendicular bisector of LN. and ML ≅ MN.

Learn ore about this concept here:

brainly.com/question/25397944

#SPJ1

8 0

1 year ago

An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty y

Kay [80]

Answer:

$t=\frac{(14-20)-0}{\sqrt{\frac{5^2}{31}+\frac{6^2}{31}}}}=-4.28$

Now we can calculate the p value with the following probability:

$p_v =2*P(t_{60}$

The p value is a very low value so then we have enough evidence to reject the null hypothesis and we can conclude that people under the age of forty have vocabularies that are different than those of people over sixty years of age.

Step-by-step explanation:

Information given

$\bar X_{1}=14$ represent the mean for sample 1 (younger)

$\bar X_{2}=20$ represent the mean for sample 2 (older)

$s_{1}=5$ represent the sample standard deviation for 1

$s_{f}=6$ represent the sample standard deviation for 2

$n_{1}=31$ sample size for the group 2

$n_{2}=31$ sample size for the group 2

t would represent the statistic

System of hypothesis

We want to test if that people under the age of forty have vocabularies that are different than those of people over sixty years of age, the system of hypothesis are:

Null hypothesis: $\mu_{1}-\mu_{2}=0$