All categories

2 years ago

Multiply and simplify: (1 - 5i)(1 -2i)

Mathematics

1 answer:

balu736 [363]2 years ago

7 0

Answer:

-9-7i

Step-by-step explanation:

1) Use the FOIL Method : (a+b)(c+d)=ac+ad+bc+bd

1-2i-5i-10

2) Collect Like Terms

(1-10)+(-2i-5i)

3) Simplify

-9-7i

You might be interested in

Which expression is equivalent to

maksim [4K]

The answer is C . -7r^2 + 12r -8

5 0

2 years ago

ΔEFG is located at E (0, 0), F (−7, 4), and G (0, 8). Which statement correctly classifies ΔEFG?

MariettaO [177]

Answer:

ΔEFG is an isosceles triangle.

Step-by-step explanation:

Given:

E (0, 0),

F (−7, 4),

G (0, 8)

ΔEFG

Solution:

Distance formula

Distance d = $\sqrt{(x_2-x_1)^2 +( y_2-y_1)^2$

Step 1: Finding the length of EF

By using distance formula,

$EF = \sqrt{(-7 - 0)^2 + (4-0)^2}$

$EF = \sqrt{(49) + (16)}$

$EF = \sqrt{(49) + (16)}\\EF = \sqrt{65}\\$

Step 2: Finding the length of FG

By using distance formula,

$FG = \sqrt{(0-(-7))^2+(8-4)^2}\\FG = \sqrt{(7)^2 +(4)^2}\\FG = \sqrt{49 +16}\\FG = \sqrt{65}$

Step 2: Finding the length of GE

$GE= \sqrt{(0-0)^2 + (0-8)^2}\\\\GE =\sqrt{(-8)^2}\\GE = \sqrt{64}\\GE = 8$

Thus we could see that the sides EF = FG

So it is a isosceles triangle.

6 0

2 years ago

A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average len

Gnom [1K]

Answer:

$t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723$

E. -0.723

$df=n-1=93-1=92$

$p_v =2*P(t_{(92)}$

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

Step-by-step explanation:

Information provided

$\bar X=5.97$ represent the sample mean for the length

$s=0.4$ represent the sample standard deviation

$n=93$ sample size

$\mu_o =6$ represent the value that we want to test

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the lathe is in perfect adjustment (6cm), then the system of hypothesis would be:

Null hypothesis: $\mu = 6$

Alternative hypothesis: $\mu \neq 6$

since we don't know the population deviation the statistic is:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing in formula (1) we got:

$t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723$

E. -0.723

P value

The degrees of freedom are given by:

$df=n-1=93-1=92$

Since is a two tailed test the p value would be:

$p_v =2*P(t_{(92)}$

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

5 0

2 years ago

Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq

Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

$\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9$

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

$125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9$

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0

3 years ago

Those who have taken the Algebra EOC please answer.

Dennis_Churaev [7]

Step-by-step explanation:

To me yes.

Algebra is mostly memorization. If you know the formulas and know how to apply it, you should do good.

I say use this. Algebra topics are like building on top each other.

Heart of Algebra:

Review what the purpose of x in algebra.
Then learn things like combining like terms, and solving for x.
Since you know the basics of x, you can then review linear equations( imo, a big content of algebra). Stuff like slope, different linear forms, graphs of linear equations, and mostly linear equation word problems
Then you can review system of equations. since you know how to manipulate linear equations, etc.

Then move on to other algebra topics dealing with algebra like

functions, and different types of them
exponents, and radicals rules
inequalities.
sequences.
These aren't the heart of algebra but study them they are useful and it important to know them.

Since you learned different function rules, we can move on to learning exponetial functions, graphs, and word problems.

Then finally, learn most hard thing in Algebra: Quadratics.

Pratice,practice, and practice and you will pass.

Try to memorize the formulas and know when to apply it.

Good Luck

7 0

2 years ago