Answer:
182 ft
Step-by-step explanation:
When you are not given a diagram, always draw one for yourself (see diagram).
When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:
<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse Soh
<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse Cah
<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent Toa
"θ" means the angle of reference (the angle you are talking about).
We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.
We know ∠C = 77°. This will be our angle of reference (replace θ).
The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.
Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)
cosθ = adjacent/hypotenuse
Substitute the variables specific for this problem.
cosC = b/d
Substitute the values you know.
cos77° = (41 ft) / d
Isolate "d" to the left side
dcos77° = 
Multiply both sides by "d"
dcos77° = 41 ft
dcos77° / cos77° = 41 ft / cos77° Divide both sides by cos77°
d = 41 ft / cos77° Input into calculator
d = 182.261874....... ft Unrounded answer
d ≈ 182 ft Rounded to nearest foot (whole number)
Remember d = BC. It's often easier to use one letter for calculations.
Therefore the length of BC is about 182 feet.
Answer:
is it from a textbook
Step-by-step explanation:
Answer:
Slope = 6.000/2.000 = 3.000
x-intercept = 10/3 = 3.33333
y-intercept = -10/1 = -10.00000
Step-by-step explanation:
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -10.000 and for x=2.000, the value of y is -4.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -4.000 - (-10.000) = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
The answer: 7 * 1,829 = " 12,803 " .
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<span>The following is the explanation—"in expanded form" — (as per the specfic instructions— within this very question—as to how to get the answer:
</span>____________________
Given: 7 * 1,829 = ? ; Find the solution; using "expanded form" :
____________
(7 * 9 = 63 ) ; +
(7 *20 = 140) ; +
(7 * 800 = 5,600) ; +
___________________________________________
(7 * 1,000 = 7,000) ;
___________________________________________
Now, add the the values together to solve the problem:
___________________________________________
→ 7 * 1,829 = 63 + 140 + 5,600 + 7,000 ;
{ = 203 + 5,600 + 7,000 } ;
{ = 5,803 + 7,000 } ;
= 12,803 ; which is the answer.
________________________________________________
Alternately, write out the steps as follows—using "expanded form":
________________________________________________
→ 7 * 1,829 = ?
________________________________________________
→ 7 * 1,829 = (7*9) + (7*20) + (7*800) + (1,000) ;
________________________________________________
→ 7 * 1,829 = 63 + 140 + 5,600 + 1,000 ;
{ = 203 + 5,600 + 7,000 } ;
{ = 5,803 + 7,000 } ;
= 12,803 ; which is the answer.
____
→ {Now, is our obtained answer: "12,803" ; the "correct answer"—to the problem: " 7 * 1,829 " ;} ??
→ Let us check: {Note: " 7 * 1,829 " ; is the same as: ↔ " 1,829 * 7 " .}.
→ Using a calculator, does: "7 * 1829 = ? 12,803" ?? ; Yes! ;
→ &, for that matter; does: " 1829 * 7 =? 12,803" ?? ; Yes! .
_______
Furthermore, let us check, using the "traditional format" ;
→ Does: "1,829 * 7 =? 12,803 ?? " ;
________
{NB: We are multiplying 2 (TWO) numbers together; & 1 (ONE) of these 2 [TWO] numbers is a "1-digit" ["single-digit"] number; & the "OTHER" multiplicand is a "multiple-digit" [specifically, a"4-digit"] number.}.
______
NB: Yes; using a calculator is sufficient. Below, I simply provide an alternate method to confirm whether our "obtained value" is correct.
_____
→ Does: "7 * 1,289 = ? 12,803" ?? ;
→ Using the "traditional method"; let us check; as follows:
_____
₅ ₂ ₆
→ 1, 829
<span> <u> * 7 </u> </span>
12 8 03 ;
_____
So; does: "12,803 =? 12,803" ?? ; YES!
→ This "traditional method" shows that: "7 * 1,829" ; does, in fact, equal: "12,803".
_____
{NB: Explanation of the steps used in solving the aforementioned problem using the "traditional method"—just for clarification and confirmation} :
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→Start with: "7*9= 63" ; Write down the "3" & 'carry over' the "6" ; {Note the small-sized digit, "6"; written on top of the "2"; {commonly done—to keep track);
→Then; "7*2 = 14" ; then add the "small digit 6"; to the "14" ; →"14+6 =20" ;
Write down the "0" ; & 'carry over' the "2" ; {Note the "small-sized digit, "2"; written over the "8"; (commonly done—to keep track);
→ Then; "7*8 = 56" ; then add the "small digit 2"; to the "56"; → "56+2 = 58" ; Write down the "8" ; & 'carry over' the "5" ; {Note the "small-sized digit", "5" ; written over the "1" ; (commonly done—to keep track);
→Then; "7*1 = 7" ; then add the "small digit 5"; to the "7" ; → "7+5 = 12" ; Write down the "12" ; in its entirety—since are no digits left [in the multiplicand, "1,829"] ; to "carry over".
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We get: "12,803" ; which =? "12,803" ?? ;→Yes!
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I hope my explanation of how to solve "7 * 1,829" ; using the "expanded form" is helpful. Also, i hope my explanation—albeit lengthy— of confirming that [<em>our</em>] "correctly obtained value"—which is: "12,803"— is of some help.
__
(F)=6+3F
We move all terms to the left:
(F)-(6+3F)=0
We add all the numbers together, and all the variables
F-(3F+6)=0
We get rid of parentheses
F-3F-6=0
We add all the numbers together, and all the variables
-2F-6=0
We move all terms containing F to the left, all other terms to the right
-2F=6
F=6/-2
F=-3
I don’t know if it is right but I hope this helps :)
