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3 years ago

6

AC is a straight segment as shown in the diagram below. If the distance between points A and C is 67 miles, determine the distan

ce between points A and B.

1 answer:

GuDViN [60]3 years ago

7 0

Answer:

43

Step-by-step explanation:

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Complete The Square:<br> (Z^2)-19z=66

Musya8 [376]

To solve the equation using complete square method we proceed:
z^2-19z=66
but
c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4

(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3

8 0

3 years ago

A half-acre building lot is five times as long as it is wide. What are its dimensions?

Gnoma [55]

we know that

A half-acre is equal to----------> $2,023.43\ m^{2}$

Let

x---------> the length side of the building lot

y--------> the width side of the building lot

A------> Area of the building lot

x=5y-------> equation 1

$A=2,023.43\ m^{2}$

$A=x*y$

$2,023.43=x*y$ --------> equation 2

substitute equation 1 in equation 2

$2,023.43=[5y]*y$

$5y^{2}= 2,023.43\\y^{2}= 404.686\\y= 20.11\ m$

<u>Find the value of x</u>

$x=5y---> x=5*20.11--> x=100.55 m$

therefore

<u>the answer is</u>

the dimensions of the building lot are 100.55 m* 20.11 m

6 0

3 years ago

Mario is paid a salary of $500 plus 8% of sales. Calculate his total income if his sales total $10,890 in the

Gre4nikov [31]

Answer:

His total income is of $1,371.2.

Step-by-step explanation:

His salary is of $500, plus 8% of his sales.

In this question:

Sales of $10,890. So his salary is given by:

$S = 500 + 0.08*10890 = 500 + 871.2 = 1371.2$

His total income is of $1,371.2.

7 0

3 years ago

I need help with those two problems. Thanks for helping!

natima [27]

Answer:
1. To solve for “b,” you must isolate the variable. The result is 2A/h=b
2. In this question, we must solve for “F.” 9/5(C)+32=F

4 0

3 years ago

What is this equal<br> how can I solve similar trigonometric integrals like this one

Angelina_Jolie [31]

Answer:

ln|sec θ + tan θ| + C

Step-by-step explanation:

The integrals of basic trig functions are:

∫ sin θ dθ = -cos θ + C

∫ cos θ dθ = sin θ + C

∫ csc θ dθ = -ln|csc θ + cot θ| + C

∫ sec θ dθ = ln|sec θ + tan θ| + C

∫ tan θ dθ = -ln|cos θ| + C

∫ cot θ dθ = ln|sin θ| + C

The integral of sec θ can be proven by multiplying and dividing by sec θ + tan θ, then using ∫ du/u = ln|u| + C.

∫ sec θ dθ

∫ sec θ (sec θ + tan θ) / (sec θ + tan θ) dθ

∫ (sec² θ + sec θ tan θ) / (sec θ + tan θ) dθ

ln|sec θ + tan θ| + C

3 0

3 years ago