Calculate the ratios in the table using the side lengths that you recorded in Part C.
Answers
Step-by-step explanation:
The ratios are;
\dfrac{BC}{AB} = \dfrac{3}{5}
AB
BC
=
5
3
\dfrac{AC}{AB} = \dfrac{4}{5}
AB
AC
=
5
4
\dfrac{BC}{AC} = \dfrac{3}{4}
AC
BC
=
4
3
\dfrac{DE}{AD} = \dfrac{3}{5}
AD
DE
=
5
3
\dfrac{AE}{AD} = \dfrac{4}{5}
AD
AE
=
5
4
\dfrac{DE}{AE} =\dfrac{3}{4}
AE
DE
=
4
3
koGiven that the lengths of the sides are;
\overline {AB}
AB
= 20
\overline {BC}
BC
= 12
\overline {AC}
AC
= 16
\overline {AD}
AD
= 10
\overline {DE}
DE
= 6
\overline {AE}
AE
= 8
The ratios are;
\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{BC}{AB} = \dfrac{12}{20} = \dfrac{3}{5}
Hypothenus
Length opposite ∠A
=
AB
BC
=
20
12
=
5
3
\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AC}{AB} = \dfrac{16}{20} = \dfrac{4}{5}
Hypothenus
Length adjacent ∠A
=
AB
AC
=
20
16
=
5
4
\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{BC}{AC} = \dfrac{12}{16} = \dfrac{3}{4}
Length adjacent ∠A
Length opposite ∠A
=
AC
BC
=
16
12
=
4
3
\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{DE}{AD} = \dfrac{6}{10} = \dfrac{3}{5}
Hypothenus
Length opposite ∠A
=
AD
DE
=
10
6
=
5
3
\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AE}{AD} = \dfrac{8}{10} = \dfrac{4}{5}
Hypothenus
Length adjacent ∠A
=
AD
AE
=
10
8
=
5
4
\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{DE}{AE} = \dfrac{6}{8} = \dfrac{3}{4}
Length adjacent ∠A
Length opposite ∠A
=
AE
DE
=
8
6
=
4
3
Related Questions
What is an equation of the line that passes through the points (8,-5) and (8, –2)?
Answers
Slope Formula (Between 2 points)
[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
Let these be the following:
[tex] \displaystyle \large{(x_1,y_1 )= (8, - 5)} \\ \displaystyle \large{(x_2,y_2 )= (8 ,- 2)} [/tex]
Substitute these points in.
[tex] \displaystyle \large{m = \frac{ - 2 - ( - 5)}{8 - 8} } \\ \displaystyle \large{m = \frac{ - 2 + 5}{0} }[/tex]
Since the denominator is 0. The slope is undefined. However, we can still find the equation of a line but not in y-isolated form.
Since for all y-values give same x-values. This means that the line will always pass at (8,y) where y is set of real numbers.
The line has to be vertical since a x-value can export many y-values.
Hence, the equation of a line would be x = 8
Solve the simultaneous
equation log(x+2) +log2=2log y and log(x-3y+3)=0
Answers
Answer:
that's is my answer for the question
Simplify the complex fraction: -1 5/6 / -1/12
Answers
Answer:
[tex] = \frac{11}{3} = 3 \frac{2}{3} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1\frac{5}{6} }{ - \frac{1}{12} } = \frac{ - \frac{11}{6} }{ - \frac{1}{2} } [/tex]
[tex] \frac{ - \frac{11}{6} }{ - \frac{1}{2} } = \frac{ \frac{11}{6} }{ \frac{1}{2} } [/tex]
[tex] = \frac{11}{3} = 3 \frac{2}{3}[/tex] ✅
3. Consider the multiplication operations below and choose whether the fosuit com
be rational, Inational, or both.
Irrational
Expressions
Rational
8. VE
О
tvo. V
V3.12
о
Answers
Answer:
1st expression= rational 2nd expression= rational 3rd expression = irrational
Step-by-step explanation:
The first and second expressions are rational because they both equal whole numbers (4 and 3) while the last expression equals a decimal that goes on forever with no end, thus making it irrational.
HURRY WILL GIVE BRANLIEST!!!!!!!
Answers
Answer:
√17
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a ratio of two integers. Or in other words, an irrational number can't be expressed as a fraction. You really cant divide one integer by another integer to get √17, so that makes it an irrational number.
Laura borrowed a total of $21,000 from two different banks to start a business. One bank charged the equivalent of 5% simple interest, and the other charged
6.5% interest. If the total interest after 3 years was $3240, determine the amount borrowed from each bank.
Let x represent the principal on the business loan at 5%.
Then, (ID is
he
remaining amount borrowed at 6.5%
X
Answers
The amount borrowed from the first and second bank is 19000 and 2000 respectively.
Recall :
Simple interest = P×R×T
Total principal, P = 21000
Bank 1 :
Let, Principal, P = x
Rate, R = 5%
Time, T = 3
Bank 2 :
Principal, P = (21000 - x)
Rate, R = 6.5%
Time, T = 3
Total interest paid = 3240
Bank A interest + Bank B interest = total interest paid
[x × 5% × 3] + [(21000-x) × 6.5% × 3)] = 3240
0.15x + 4095 - 0.195x = 3240
-0.045x = 3240 - 4095
-0.045x = - 855
x = 19000
Hence,
19000 was borrowed from Bank 1
(21000 - 19000) = 2000 was borrowed from bank 2
Learn more : https://brainly.com/question/20831630
3n-(2+n) what’s the value of n to make the expression equal to 6
Answers
Answer:
4
Step-by-step explanation:
3n-(2+n) = 6
3n-2-n = 6
2n-2 = 6
2n = 8
n = 4
Answer:
n=4
Step-by-step explanation:
Start by writing the equation without parenthesis. Since there is a negative sign, everything in the parenthesis changes sign: 3n-2-n=6
Combine like terms: 2n-2=6
move -2 to the other side: 2n=8
divide both sides by 2: n=4
Question 9 What is the predecessor of - 5?
Question 11. Write the following integers in their increasing order. - 3,0,- 6,5, – 4, 6, 3, -8
Question 15. Find the sum of the following integers: (a) (-8) + (+ 5) + (-3) + (-2) (B) (- 7) + (- 9) + (+4) + (+3)
Answers
Step-by-step explanation:
1) -4
2) -8, -6, -4, -3, 0, 3, 5
3) (a) -8 + 5 - 3 - 2
-13 + 5
-8
(b) -7 - 9 + 4 + 3
-7 - 9 + 7
-9
Graph the line with slope 2 passing through the point (-5, 2)
Answers
Answer:
Equation is y=2x+12
The image is a picture of the graph(it's not the best but it's something.
an advertising company charges $40 per half page advertisement and $75 per full page advertisement, Michaeld has a budge of $800 to purchase 13 advertisements.
a) Define a variable for each unknown. write a system of equations to represent the situation.
b) How many half -page advertisements does Michael purchase? show your work.
c) How many full-page advertisement does Michael purchase? show your work.
Answers
40h + 75f = 800
h+f=13
B) multiply the second equation by -75, so -75h = -975
Then solve 40h = 800
-75h = -975
You get -35h = -175. Divide both sides by -35 and you get 5. So 5 half page ads
C) Substitute 5 for h in the first equation
40(5) + 75f = 800
200 + 75f = 800
Subtract 200 from both sides
75f = 600
Divide both sides by 75
f = 8
So 8 full page ads
Check: 8+5=13
40(5) + 75(8) = 800
Hope this helped!!
what is the range of this function ??? please explain
Answers
Answer:
B. (2, 3, 4)
Step-by-step explanation:
The range of a function is the list of y values. In this instance, the y values present in this function are 2, 3, and 4. Therefore, the answer is B. (2, 3, 4).
Can I have some help, please?
Answers
Answer:
[tex]-3(t+1)(8t-3)[/tex]
Step-by-step explanation:
First, factor both the denominators completely:
[tex]9-24t\\= 3(3-8t)\\= 3(-8t+3)\\= -3(8t-3)[/tex]
[tex]8t^2+5t-3\\= 8t^2+8t-3t-3\\= 8t(t+1)-3(t+1)\\= (8t-3)(t+1)[/tex]
Now, we can see that the factors of the first denominator are -3 and 8t-3.
The factors of the second denominator are t+1 and 8t-3.
To find the LCD, multiply all of these factors together:
[tex]-3(t+1)(8t-3)[/tex]
Notice how we only multiply 8t-3 in the equation once. This is because it was present in both denominators, unlike the other factors.
I hope this helps!
corey paid for a dinner and left a 15% or $3.45 in tips. How much was the original bill without counting the tip?
Answers
Answer:
19.55 $
Step-by-step explanation:
3.45$×10=34.5=150% of his money overall
34.5÷3=11.5
11.5×2=23= 100% of his money
23-15%=19.55$
$23
Step-by-step explanation:
15% of x = 3.45
= 15/100 = 3.45/x
x= 23
in a class of 7 students there are 4 that play soccer.
if the teacher picks 3 students what is the probability that none of them play soccer
Answers
Answer:
Step-by-step explanation:
The total number of ways to draw 3 students is 7*6*5 = 210
Order does not matter. There are 3 students that don't play soccer.
P(3 don't play soccer) = 3*2 * 1 / 210 = 1/35 = 0.02857
The second term of arithematic proggresions 7. and the sum of the first four termd is 12 find
a) first term
b)common difference
Answers
Answer:
a) a1=15 first term
b) d=-8 common difference
Step-by-step explanation:
1)a1+d=7
2)a1+a2+a3+a4=12
a1+a1+d+a1+2d+a1+3d=12
4a1+6d=12
2a1+3d=6
We have the system of equations where a1+d=7 and 2a1+3d=6
3a1+3d=21
2a1+3d=6
Subtract the second equation from the first one
a1=15
d=-8
First term = 15
Common difference = -8
Let the first term be a and common difference be d.
Therefore,
a+d = 7 - eq. 1
a+(a+d)+(a+2d)+(a+3d) = 12 - eq. 2
4a + 6d = 12
4a + 4d + 2d = 12
Dividing both sides by 2,
2a + 2d + d = 6
2 (a+d) + d = 6
Substituting value of (a+d) in the above equation,
2*7 + d = 6
d = 6 - 14
d = -8
Substuting value of d in eq. 1
a+d = 7
a + (-8) = 7
a = 7 + 8
a = 15
To learn more about arithematic proggresions:
https://brainly.com/question/24016699?referrer=searchResults
which is not a whole number “8, -10, 0, 18/3”?
Answers
Answer:
-10 I guess its this maybe
Which function below has the following domain and range?
Answers
Answer:
The first choice.
Step-by-step explanation:
Domain = x value (first value in a coordinate pair: (x,y))
Range = y value
A function cannot have a repeating Domain value.
This eliminates the last option since -4 is used twice.
The second option has 11 as a y value but it is not in the range.
The third option has 10 as an x value but it is not in the domain.
!Can some1 help! !Help FAST!
What is the algebraic expression for the word phrase "4 times a number minus 9"?
A. 4(y-9)
B. 4y-9
C. 4(9-y)
D. 9-4y
Answers
Answer:
4y-9
Step-by-step explanation:
y is the number, 4 times the number = 4y
so 4y-9
Write 96% as a fraction.
Answers
Answer:
Directly, it would be 96/100. However, we can reduce it to become 48/50 = 24/25.
(underlined is simplest answer)
24/25
Step-by-step explanation:
96%
=96/100
=24/25
answer
In a survey of small business owners, a response to which of the following questions would be qualitative?
a. How much did your business have in profits last year?
b. How long have you owned a business?
c. What type of business do you own?
d. How many businesses do you own?
Answers
For the considered survey, the questions whose response is going to be qualitative is given by: Option C: "What type of business do you own?"
What is qualitative data?
Qualitative data tells about the quality or characteristic. It is tough to express it numerically or not at all expressible numerically. They are usually catagorical.
In contrast, there is quantitative data which can be expressed numerically.
Option A, Option B and Option D will get answers which would be in numbers. Thus, their responses would be quantitative.
Option C's question will get response as type of business that the business owners own. So its not in numbers and tells about the characteristic of businesses.
Thus, for the considered survey, the questions whose response is going to be qualitative is given by: Option C: "What type of business do you own?"
Learn more about qualitative and quantitative data here:
https://brainly.com/question/12929865
| در
please help if you can :)
Answers
Answer:
v=-14.4
Step-by-step explanation:
Isolate v.
add - 3.1 to the other side
-7.9+3.1=-4.8
Now the problem is: -4.8 = v/3
Next, multiply both sides by 3
-4.8 times 3 = -14.4
v = -14.4
Answer:
-14.4
Step-by-step explanation:
-7.9 = -3.1 + (v/3)
- 4.8 = v/3
v = -14.4
caterpillar crawls 25 inches in one minute. How many inches does it crawl in 5 minutes?
Answers
Answer:
125 inches
Step-by-step explanation:
In one minute caterpillar crawls 25 inches. So in 5 minutes we have 5 times 25 inches is 125 inches.
By equation
Additional: 25 + 25 + 25 + 25 + 25 = 125 (inches)
Mutiplication: 25 * 5 = 125 (inches)
The caterpillar crawls 125 inches in 5 minutes
because it is said that the caterpillar crawls 25 inches in one minute so we can use multiplication 25 x 5 = 125
There are □ terms in the sequence 1000,2000, 3000, 4000, ...., 500000
Answers
Answer:
500
Brainliest, please!
Step-by-step explanation:
We are adding 1000 each time.
500000/1000 = 500
Answer:
Step-by-step explanation:
[tex]Number\ of\ terms\ =\dfrac{500000-1000}{2000-1000} +1\\\\=\dfrac{499000}{1000} +1\\\\=499+1\\\\=500\\[/tex]
What exactly is Maths? And why do we die from maths? Please answer... This is a serious question though.
Answers
Answer:
it's because if you know maths you can go very far like being successful and have a chance for ur career or dreamMath is the the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering. You can D1E from math if its just too hard...
(1.) Find the equation of the line passing through the points (-4,-6 ) and (-5,5).
(2.) Find the equation of the line with slope -8 that passes through the point (3, -8).
Answers
Answer:
1) y=-11x-50 2)y=-8x+16
Step-by-step explanation:
1. y=mx+b- it is the main equation for a line'
If we take the first point and use its coordinates we have -6=-4m+b
If we take the second point and use its coordinates we have 5=5m+b
These equations are simultaneous for our line because the line passes through both points
-6=-4m+b
5=-5m+b
If subtract the second one from the first equation
-6-5= -4m+b- (-5m+b)
-11= m
b= -6-44=-50
y=-11x-50
2) y=mx+b
-8=-8*3+b
b=16
y=-8x+16
true or false |-7|>-|-7| HELPP I BEGG YOU
Answers
Answer:
False
Step-by-step explanation:
Those straight lines that look like this -> |
Represent absolute value.
All absolute value means is the distance a number is from zero.
For example: -2 is 2 numbers away from zero.
5 is 5 numbers away from zero.
-7 is 7 numbers away from zero.
So when something says |-7| that is the same value as 7
So 7 = 7
NOT 7>7 (that doesn't make sense)
Rational or Irrational: -4 √81
Answers
Answer:
it is rational
Step-by-step explanation:
Answer:
it's rational number
I hope it's helps you
What is the area of BCD?
A. 36 square units
B. 32 square units
C. 16 square units
D. 72 square units
Answers
Answer:
36
Step-by-step explanation:
The length is 12, and the height is 6
A = 1/2 * b*h
So area = 1/2 * 72 = 36
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
(8)/(r+2)+(8)/(r-2)=3
Answers
Answer:
- 2/3, 6
Step-by-step explanation:
√5 • -4√20
PLEASE SHOW STEP BY STEP ON HOW YOU SOLVED THE EQUATION
Answers
Answer:
-40
Step-by-step explanation:
[tex] \sqrt{5} \times - 4 \sqrt{20} [/tex]
Multiplication is commutative.
[tex] - 4 \sqrt{20} \times \sqrt{5} [/tex]
Apply Profuct Rule
[tex] - 4 \sqrt{100} [/tex]
Simplify sqr root of 100
[tex] - 4 \times 10 = - 40[/tex]
Hi ;-)
√5 · (-4√20) = -4√(5 · 20) =
= -4√100 = -4 · 10 = -40