The two equations that can be used to find the height are as follows
12 / 4 = h /5
5 / 4 = h / 12
We have given that,
Amelia is 5 feet tall and casts a 4-foot shadow. A tree next to her casts a 12-foot shadow.
What is the similar triangles?Similar triangles are not necessarily the same in size. Corresponding angles of similar triangles are congruent. The sides of a similar triangle are a ratio to each other.
The tree casts a shadow of 12 ft. Let's establish the proportion base on similar triangles. The height of the tree is h. Therefore,
h / 12 = 5 / 4
Therefore, h / 12 = 5 / 4
cross multiply
4h = 60
divide both sides by 4
h = 60 / 4
h = 15 ft
Therefore, the two equations that can be used to find the height are as follows
12 / 4 = h /5
5 / 4 = h / 12
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Answer:
i am on ttm
Step-by-step explanation:
12/4=h/5
5/4=h/12
1. Calculate the equation of the line through the points (1, 1), (4, 3), (10, 7) and (40, 27).
Answer:
y = (2/3)x + 1/3
Step-by-step explanation:
Check that a single straight line will actually go through all four of these points. Going from (1, 1) to (4, 3), the 'rise' is 2 and the 'run' is 3, which would make the slope, m, equal rise/run = 2/3. Going from (4,3) to (10, 7), m = rise/run = 4/6 = 2/3 (again).
Let's find the slope-intercept form of the equation of this line: y = mx + b
Arbitrarily choose the point (1, 1). Here x = 1, y = 1 and m = 2/3. Then
we have
1 = (2/3)(1) + b, or 1 = 2/3 + b, so that b must be 1/3.
The equation in question is y = (2/3)x + 1/3
Line a goes through the points (- 3, 4) and (1, 2) . Line b goes through the point (6, 2) and (8, 1) . Are lines a and b parallel, perpendicular, or neither?
Answer:
They are parallel
Step-by-step explanation:
Find slope of point A
(-3,4), (1,2)
2-4=-2 1-(-3)=4
slope of a= -2/4 or -1/2
Find slope of point B
(6,2), (8,1)
1-2=-1, 8-6=2
slope of b= -1/2
Both have different slopes, and it can't be perpendicular because they have different denominator values.
Answer:
Step-by-step explanation:
(-3,4) (1,2)
difference is (y2 - y1) /( x2 - x1)
-2 / -4
-1/2 is the slope
(6,2) (8,1)
same as the last
-1 / 2
these lines have the same slope so they are parallel, if their slopes were reciprocals (-1/2 and 2) they would be perpendicular.
NEED HELP ASAP 40 POINTS GEOMETRY QUESTION PLEASE GIVE FULL ANSWER!!!Which of the lines listed below is perpendicular to the line with the equation
Answer:
Step-by-step explanation
Tyra, Elle, Tran, and Ann share equally in the rental of a car. If the total cost of the rental is C dollars, which expression represents Tyra's share of the cost?
Answer:
c/4
Step-by-step explanation:
Since it's equally shared, and the total cost is C, then the answer is c/4
At what point(s) does the parabola,
y
=
x
2
−
2
, intersect the line,
y
=
−
x
Answer:
Please check the formatting when posting. I'm assuming these are the equations:
y=x^2 - 2
y=−x
Step-by-step explanation:
We can either graph the equations or solve them. I use graphing - see the attachment. The lines intersect at (-2, 2) and (1,-1)
1. Graphing
See attached graph
(-2, 2) and (1,-1) are the intersection points
2. Solving
y=x^2 - 2 Use y=−x in this equation:
-x = x^2 - 2
0 = x^2 + x - 2
0 = (x+2)(x-1)
x = -2 and +1
(-2, 2) and (1,-1) are the intersection points
Jared and Casey splurged on a special dinner for their anniversary. Their dinner cost $262.57,
and the local sales tax is 4%. If they left a 20% tip on the $262.57, how much in total did
they pay?
They paid a total of $325.5868
what is the range of a parabola that opens down with a vertex at (1,-3)
Answer:
-3 to -infinity
Step-by-step explanation:
Drag each tle to the correct box
Arrange the solutions of the mathematical expressions from least to greatest according to their values in scientific notation
MAGAKAKASUNOD NA PO YAN
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A square with an area of 144cm is reduced by a factor of 1/3. How long are the new sides of the square?
Answer:
9.797. . .
Step-by-step explanation:
2/3 of 144 is 96
[tex]\sqrt{96} = 9.797...[/tex]
Julie is a cashier. She can ring up 12 customers in 9 mintesutes. At the rate, how many minutes does it take for her to ring up 4 customers?
Answer:
5.2
Step-by-step explanation:
ok so we need to find the unit rate( how many customers per minute) and thats 12 divided by 9 which is 1.3 minutes per customer so now we need to find what 1.3 minutes is x4 customers. This brings us to 5.2.
Problem Solving
4. A school club sells 43 raffle tickets on Monday and
39 raffle tickets on Tuesday. How many more raffle
tickets did it sell on Monday than on Tuesday?
Answer:
They sold 4 more raffle tickets on monday than they did on tuesday.
Step-by-step explanation:
Answer: they sold 4 more raffle tickets on monday than tuesday.-
Step-by-step explanation:
Which point would be a solution to the system of linear inequalities shown below?
Y>2/3x-4
Y<−4x−6
the state of California keeps track of how many millions of students are learning English as a second language each year: English Learners are shown in millions in the table.
find an equation for the median fit line
√x - 5+ x = 7
please help me out :)
on a map of the northwest territories,4.0cm represents 920km. how far is it from tuktoyaktuk to fort smith is the distance on the map js 6.0cm
Answer:
1380 km
Step-by-step explanation:
Each 4 cm = 920 km
6 cm is 1.5 x 4, so multiply 920 x 1.5
Complete the sentence below.
If 8^x= 8^3, then x =
[tex]8^x = 8^3\\\\\implies \ln(8^x) = \ln(8^3)\\\\\implies x \ln(8) = 3 \ln (8)\\\\\implies x = 3\\\\[/tex]
5/12 of the pupils in yr9 say their favourite colour is red. There are 180 pupils in yr9. How many students said red is their favourite colour?
Answer:
75 students
Step-by-step explanation:
180*5/12=75
What is -2 1/2 times 3 3/4?
Answer:
-6 3/8
Step-by-step explanation:
Step-by-step explanation:
-2 1/2 mixed number change fraction= -3/-4 = 3/4.
3 3/4 = 15/12 = 5/4.
3/4 x 5/4= 15/16.
Given that AABCDEF, solve for X.
B
A. 10
o
B. 6
C. 17
0 0
Answer:
D
Step-by-step explanation:
Given Δ ABC is similar to Δ DEF then the ratios of corresponding sides are in proportion, that is
[tex]\frac{EF}{BC}[/tex] = [tex]\frac{DE}{AB}[/tex] , substitute values
[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{30}[/tex] ( cross- multiply )
30x = 5 × 42 = 210 ( divide both sides by 30 )
x = 7
The ratio remains same
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{30}{42}[/tex]
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{15}{21}[/tex]
[tex]\\ \sf\dashrightarrow 15x=105[/tex]
[tex]\\ \sf\dashrightarrow x=7[/tex]
how many 7 digit numbers are there where all the digits are different and are in increasing order
Answer:
36
Step-by-step explanation:
Usually, when we talk about an n-digit number, we mean one that has no leading zeros. If we use all 9 non-zero digits, the single number having increasing digits is ...
123456789
We cannot swap any digits and have the digits remain in increasing order. The only thing we can do to create different numbers is remove different pairs of digits.
There are 9C2 = 9·8/(2·1) = 36 different ways to choose 2 digits from 9. Thus, there are 36 possible 7-digit numbers with the digits in increasing order.
__
Additional comment
The first few are 1234567, 1234568, 1234569, 1234578, 1234579, 1234589, ...
The point F( – 4,6) is translated 6 units right. What are the coordinates of the resulting point, F'?
i.e
[tex]\\ \sf{:}\Rrightarrow -4+6=2[/tex]
New co-ordinates:-
[tex]\\ \sf{:}\Rrightarrow F(2,6)[/tex]
What is the quotient of 8.44 and 0.04?
10 pts
8.44/0.04=211
hope this helps!
Answer:
211
Step-by-step explanation:
8.44 divided by 0.04 = 211
Find the equation of the line that goes through ( 2, 4 ) and ( 4, 6 ).
Answer:
y=x+2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-4)/(4-2)
m=2/2
m=1
y-y1=m(x-x1)
y-4=1(x-2)
y=x-2+4
y=x+2
What is the slope-intercept equation for the line below?
5
(5.4)
(0, 2)
y
O A. - - x + 2
B. yo * +2
C. v - -** +2
D. v=x+2
HELP?!!!!
Answer:
[tex]y=\frac{2}{5}x+2[/tex]
Step-by-step explanation:
(x1, y1) = (5, 4)
(x2, y2) = (0, 2)
First, find the slope. The slope formula is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
I marked the 2 points above in that form, so you can plug those in here:
[tex]m=\frac{2-4}{0-5}\\\\m=\frac{-2}{-5}\\\\m=\frac{2}{5}[/tex]
The slope of this line is 2/5. Next, you can use that slope and whichever known point you want to find the y-intercept. Slope-intercept form is:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Plug in the slope we found for m and whichever point you want for (x, y):
[tex]2=\frac{2}{5}0+b[/tex]
Now, solve for b:
[tex]2=0+b\\b=2[/tex]
In this particular case, there wasn't much to be done. We already had a point at x = 0, and that is already our y-intercept. For similar problems though, that's how you would do it.
Finally, with both the slope and the y-intercept, you can write the equation:
[tex]y=\frac{2}{5}x+2[/tex]
Answer 75-82 pls it would be amazing!!!!!
Answer:
75-82=-7
Step-by-step explanation:
e
© There is a bag with only milk and dark chocolates.
5
The probability of randomly choosing a dark chocolate is
5/12
There are 25 dark chocolates in the bag and each is equally likely to be chosen.
Work out how many milk chocolates there must be.
Answer:
I think it's 35, because if there's 25 dark and you divide 25 by 5 you get 5, so 1/12 is equal to 5
I want a picture of magnitic force and electric force
Answer:
Step-by-step explanation:
123
Samir bought 6 equally priced pencils for $2.10.
How much will 10 of these pencils cost?
$1.26
$2.63
$2.86
$3.50
Price of 6pencils=2.10
Price of one pencil
[tex]\\ \sf\longmapsto 2.10/6=0.35[/tex]
Price of 10pencils
[tex]\\ \sf\longmapsto 0.35(10)=\$3.5[/tex]
The cost of ten pencils is $3.50.
Given
Samir bought 6 equally priced pencils for $2.10.
Unit rate;A rate is a ratio that is used for comparing two different kinds of quantities which have different units.
The cost of 1 pencil is;
[tex]\rm =\dfrac{2.10}{6}\\\\=0.35[/tex]
Therefore,
The cost of 10 pencils is;
[tex]= 10 \times 0.35\\\\=3.50[/tex]
Hence, the cost of ten pencils is $3.50.
To know more about unit rate click the link given below.
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I NEED HELP PLEASE! Thank you
Answer:
A
Step-by-step explanation:
21 -6×3
-6×3=-18
21-18
=3
Can you please factorise 7-x²
Answer:
Can't factorize with rational numbers
Step-by-step explanation:
The best you could do is [tex](\sqrt{7}+x)(\sqrt{7}-x)[/tex] but [tex]\sqrt{7}[/tex] is irrational.
Answer:
Step-by-step explanation:
7-x²
If we treat this as the difference of 2 squares we get
(√7 - x)(√7 + x)