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3 years ago

Use suitable identities to find the following products (x-5) (x-5)

Mathematics

1 answer:

Marrrta [24]3 years ago

7 0

Step-by-step explanation:

$(x - 5)(x - 5) \\ {x}^{2} - 5x - 5x + 25 \\ {x}^{2} - 10x + 25$

I hope it makes sense

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Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...

Mariulka [41]

Answer: $t_{n}=-15+9(n-1)$

Step-by-step explanation:

The formula for finding the nth term of an arithmetic sequence is given as:

$t_{n}=a+(n-1)d$

$a =$ first term = -15

$d =$ common difference = -6 - (-15) = 9

$n =$ number of terms

substituting into the formula , we have :

$t_{n} = -15+(n-1)9$

$t_{n}=-15+9(n-1)$

5 0

2 years ago

Please help i need to finish

elena-s [515]

Answer:

B. $\overline A \overline C \cong \overline B \overline D$

Step-by-step explanation:

The hypotenuse leg theorem (HL) requires the proof that the hypotenuse and the corresponding leg of the triangles to be equal in length. From the diagram, it can be found that $\overline D \overline C$ is a common (shared) side of both triangles, so the additional fact needed is for the hypotenuses to be the same length.

∴ $\overline A \overline C \cong \overline B \overline D$ is the additional fact needed to prove $\triangle ADC \cong \triangle BCD$

Hope this helps :)

5 0

2 years ago

Forty children from an after-school club went to the matinee.This is 25% of the children in the club.How many children are in th

Korvikt [17]

25% = 0.25

40 / 0.25 = 160

40 is 25% of 160.

There are 160 children in the club.

7 0

3 years ago

What is the length of BD?

I am Lyosha [343]

Answer:

$10\sqrt{3}$

Step-by-step explanation:

<u>Trigonometric Ratios </u>

This problem will be solved by the use of a trigonometric ratio called sine because it relates the opposite side of a given angle with the hypotenuse of the triangle.

Selecting the angle of 60° in triangle ABD:

<em>Sine Ratio </em>

$\displaystyle \sin 60^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 60^\circ=\frac{BD}{20}$

Solving for BD:

$\displaystyle BD=20\sin 60^\circ$

Since

$\sin 60^\circ=\frac{\sqrt{3}}{2}$

$\displaystyle BD=20\frac{\sqrt{3}}{2}$

Simplifying:

$\boxed{\displaystyle BD=10\sqrt{3}}$

4 0

2 years ago

A 20.3 kg person climbs up a uniform ladder with negligible mass. The upper end of the ladder rests on a frictionless wall. The

VMariaS [17]

Answer:

Q = arctan(7.1739) = 82.06

Step-by-step explanation:

Given:

- The mass of the person m = 20.3 kg

- The distance traveled up the ladder s = 1.1 m

- The gravitational constant g = 9.8 m/s^2

- The coefficient of static friction u_s = 0.23

- Total length of the ladder

Find:

The minimum angle θ, that would allow the person to climb without ladder slipping

Solution:

- Taking moments about point of ladder and wall contact A to be zero:

-F_n,b*cos(Q)*4 - F_f*sin(Q)*4+ m*g*cos(Q)*2.6 = 0

- Taking Sum of vertical forces to be zero:

F_n,b - m*g = 0

F_n,b = m*g

- The frictional force F_f is given by:

F_f = u_s*F_n,b = u_s*m*g

- Plug the values back in:

- m*g*cos(Q)*4 + u_s*m*g*sin(Q)*4 - m*g*cos(Q)*2.6 = 0

Simplify:

4*cos(Q) + 2.6*cos(Q) = u_s*4*sin(Q)

6.6*cos(Q) = 4*u_s*sin(Q)

tan(Q) = 6.6 / 4*u_s

- Plug in the values:

tan(Q) = 6.6 / 4*0.23

Q = arctan(7.1739) = 82.06

4 0

3 years ago

Use suitable identities to find the following products (x-5) (x-5)​

Use suitable identities to find the following products (x-5) (x-5)