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3 years ago

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Solve the equation. \dfrac32 + b = \dfrac74 2 3 +b= 4 7 start fraction, 3, divided by, 2, end fraction, plus, b, equals, sta

rt fraction, 7, divided by, 4, end fraction b=b=b, equals

2 answers:

sveticcg [70]3 years ago

4 0

Answer:

1/4

Step-by-step explanation:

Xelga [282]3 years ago

3 0

Given:

The equation is

$\dfrac{3}{2}+b=\dfrac{7}{4}$

To find:

The value of b.

Solution:

We have,

$\dfrac{3}{2}+b=\dfrac{7}{4}$

Subtracting both sides by $\dfrac{3}{2}$ , we get

$b=\dfrac{7}{4}-\dfrac{3}{2}$

$b=\dfrac{7-2(3)}{4}$

$b=\dfrac{7-6}{4}$

$b=\dfrac{1}{4}$

Therefore, the value of b is $\dfrac{1}{4}$ .

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A helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. Angle ABC

In-s [12.5K]

Please consider the attached graph.

We have been given that a helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. The measure of angle ABC is 150°. We are asked to find the area of triangle ABC.

We will use trigonometric area formula to solve our given problem.

$A=\frac{1}{2}a\cdot c\cdot\text{sin}(b)$ , where angle b is angle between sides a and c.

For our given triangle $a=5,c=8$ and measure of angle b is 150 degrees.

$A=\frac{1}{2}(5)\cdot (8)\cdot\text{sin}(150^{\circ})$

$A=5\cdot 4\cdot(0.5)$

$A=10$

Therefore, the area of the triangle ABC is 10 square kilo-meters and option 'c' is the correct choice.

6 0

3 years ago

(sqrt3-sqrt3i)^4

Ludmilka [50]

The increasing order of the complex numbers is (√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ = (-1 + √3i)¹² < (√3 - √3i)⁴.

<h3>Absolute values of the complex numbers</h3>

The absolute values of the complex numbers are determined as follows;

(sqrt3-sqrt3i)^4 = (√3 - √3i)⁴

$|z| = \sqrt{(\sqrt{3} )^2 + (\sqrt{3 }\times1 )^2} } \\\\|z| = \sqrt{6}$

(-1+sqrt3i)^12 = (-1 + √3i)¹²

$|z| = \sqrt{(-1)^2 + (\sqrt{3)^2} } \\\\|z| = \sqrt{4} \\\\|z| = 2$

(sqrt 3-i)^6 = (√3 - i)⁶

$|z| = \sqrt{(\sqrt{3})^2 + (-1)^2 } \\\\|z| = \sqrt{4} \\\\|z| = 2$

(sqrt2-sqrt2i)^8 = (√2 - √2i)⁸

$|z| = \sqrt{(\sqrt{2} )^2 + (\sqrt{2})^2 } \\\\|z| = 2$

(sqrt2-i)^6 = (√2 - i)⁶

$|z| = \sqrt{(\sqrt{2})^2 + (-1)^2} } \\\\|z| = \sqrt{3}$

Increasing order of the complex numbers;

(√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ = (-1 + √3i)¹² < (√3 - √3i)⁴.

Learn more about complex numbers here: brainly.com/question/10662770

#SPJ1

3 0

2 years ago

Evaluate <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%5E%7B-2%7Dx%5E%7B-3%7Dy%5E%7B5%7D%20%7D" id="TexFormula1" title="\

Irina18 [472]

Answer:

$\bf C)\: -\cfrac{1}{32}$

Step-by-step explanation:

$\tt \cfrac{1}{2^{-2}x^{-3}y^5}$

$\tt x=2\\y=-4$

~

Substitute ''x'' with '2' & 'y' with "-4":-

$\tt \cfrac{1}{2^{-2}\times \:2^{-3}\left(-4\right)^5}$

First let's solve $\tt 2^{-2}\times \:\:2^{-3}\left(-4\right)^5$

$\tt 2^{-2}\times \:2^{-3}=\boxed{\cfrac{1}{32} }$

$\tt \cfrac{1}{32}\left(-4\right)^5$

Calculate exponents:- -4^5= -1024

$\tt \cfrac{1}{32}\left(-1024\right)$

Remove parentheses, apply rule:- $\tt a\left(-b\right)=-ab$

$\tt-\frac{1}{32}\times \:1024$

$\tt \cfrac{1}{32}\times \cfrac{1024}{1}$

Apply fraction rule:-

$\tt -\cfrac{1\times \:1024}{32\times \:1}$

$\tt \cfrac{1024}{32}$

Divide numbers:-

$\tt -32$

Now that we're done factoring the denominator let's bring down the numerator which is ' 1 ':-

$\tt -\cfrac{1}{32}\;\; \bf Answer$

<u>☆-------☆-------☆-------☆</u>

3 0

2 years ago

Read 2 more answers

(2x+5y-z)+(-6x-4y+7z)

11111nata11111 [884]

Answer:

-4x + y + 6z

Step-by-step explanation:

2x + 5y - z + (-6x - 4y + 7z) < distribute positive 1 to (-6x - 4y + 7z)

2x + 5y - z - 6x - 4y + 7z < combine like terms to get the answer

2x - 6x = -4x

5y - 4y = y

-z + 7z = 6z

our new expression is:

-4x + y + 6z we cannot simplify this any further, so this is our answer

8 0

3 years ago

Melissa earns a 2% commission on the first $750 of sales she makes each week. She earns a 3% commission on the amount of her sal

gizmo_the_mogwai [7]

Answer:

0.02(750)+0.03(x−750)=37.5

Step-by-step explanation:

Given data

Melissa earns a 2% commission on the first $750 of sales

= 0.02(750)

She earns a 3% commission on the amount of her sales that are greater than $750 each week

let the amount of her sales be x

= 0.03(750-x)

Melissa earned $37.50 in commissions last week.

= $37.5

Her total earnings is $37.5

37.5= 0.02(750)+ 0.03(x-750)

37.5= 15+0.03x- 22.5

37.5-15+22.5= 0.03x

45= 0.03x

x= 45/0.03

x= 1500

8 0

3 years ago