The height of the flagpole, found using the ratio of the sides of similar triangles is 12.975 meters
What are similar triangles?Similar triangles are triangles in which two angles of one triangle are congruent to two angles in the other triangle, such that they have the same shape.
The parameters that can be used to find the height of the flagpole are;
Distance of the mirror from the flagpole = 8.65 meters
Distance of Feng on the other side of the flagpole = 1.1 meters
The height from Feng's eyes to the ground = 1.65 meters
According to the law of reflection, the angle of incident and the angle of reflection are the same
The angle made by Feng and the ground = Angle made by the flagpole and the ground = 90°
The triangle formed by the Feng and the flagpole are therefore similar by AA similarity postulate
The ratio of corresponding sides of similar triangles are the same, therefore;
[tex]\dfrac{1.65}{Height\, of \, the \, flagpole} = \dfrac{1.1}{8.65}[/tex]
[tex]Height\, of \, the \, flagpole = \dfrac{1.65}{1.1} \times 8.65 = 12.975[/tex]
Height of the flagpole = 12.975 meters
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The charge in dollars for cab rides in one city is modeled by f(c) = 4 + 2.5m, when m is the number of miles traveled. What is the charge for a 4-mile ride?
16 miles out of 40 miles
The 16 miles out of 40 miles. Then the percentage will be 40%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The 16 miles out of 40 miles. Then the percentage is calculated as,
P = (16 / 40) x 100
P = 0.40 x 100
P = 40%
The 16 miles out of 40 miles. Then the percentage will be 40%.
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The missing part of the question is given below.
Determine the percentage.
write an equation of the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9
An equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
Given that, the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Here, slope of a line y=-1/5x-9 is m=-1/5.
The slope of a line perpendicular to given line is m1=-1/m2
So, slope =5
Substitute m=5 and (x, y)=(7, 10) in y=mx+c, we get
10=5(7)+c
⇒c=-25
Substitute m=5 and c=-25 in y=mx+c, we get
y=5x-25
Hence, an equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
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If x=6 what is 4x
??????????????
Answer:
24
Step-by-step explanation:
6*4=24
Find the equation of the line, in lope-intercept form, containing the point ( 5,2. 2) and (9,2. 6)
The equation of the line, in slope-intercept form, containing the point ( 5,2. 2) and (9,2. 6) is y=0.025x+2.375 where 0.025 is the value of slope and 2.375 is the y-intercept.
What is an example of a slope intercept form?Take into account the slope-intercept form of the equation y = 6 x + 9 y=6x+9. The x and y intercepts are known. When x = 0, the y-intercept also happens, and when y equals 0, the x-intercept also happens. By setting the value of y to 0, we may find the x-intercept.
What is the slope and y-intercept?The values of the slope and y-intercept reveal details of the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
To calculate the equation of line containing points (5,2.5) and (9,2.6) we will use the formula y=mx+b
Here, m = (y2-y1)/(x2-x1)
So, m = (2.6-2.5)/(9-5)
m= 1/40
m=0.025
Now finding b by using formula y=mx+b using x= 5 and y= 2.5
2.5=(0.025)(5)+b
2.5=(0.125)+b
b=2.375
so equation of line is y=0.025x+2.375 in slope-intercept form.
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42 out of the 84 teachers in a school staff meeting were first-year teachers. What percentage of the teachers in the meeting were first-year teachers? Write your answer using a percent sign (%).
when finding 6.1 divided by 0.1 how is the decimal point moved?
well, let's just divide them anyway and check it out.
hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets one "0".
That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61. We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.
if the equation x^2 + 16x + c = 0 has only one real solution, the value of c must equal
If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.
Discriminant:The quadratic formula includes the discriminant, which comes after the square root. The discriminant of a quadratic equation is important because it indicates the quantity and kind of solutions.
The formula for the Discriminant of a Quadratic Equation ax²+bx +c = 0 is given by
Discriminant Δ = b² - 4acHere we have
x² + 16x + c = 0 equation has only one real solution
Compare given equation with ax²+ bx + c = 0
=> a = 1, and b = 16
As we know when an equation has only one real solution
then its Discriminant will be equal to zero
=> b² - 4ac = 0
By the above values,
=> 16² - 4(1)c = 0
=> 256 - 4c = 0
=> 4c = 256
=> c = 256/4
=> c = 64
Therefore,
If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.
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if 14 meter of ribbion cost 19$ how much will 21 meters cost
Answer: 21 meters cost $28.5
Step-by-step explanation:
divide 19 by 14 and multiply by 21
21 meters cost $28.5
for the trapezoid below,solve for x. X= blank
Answer:
180-125 = x
x= 55 ( allied angle)
What is the solution of the equation?:
-2(3x+1)-2x=-4(2x)-4
it doesn't have solution
Jermaine plays classical guitar at a local restaurant in the evenings. If jermaine plays 23 songs per evening, how many songs does he play in 73 evenings?.
Answer:
1679 songs
Step-by-step explanation:
23
x73
----------------------------
69
+ 1610
-------------------------------
1679
what is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)?
The surface area, A, is changing at a rate of 288 km/min decreasing.
Given,
Base length, l = 6 km
Height, h = 10 km
dl/dt = -9 km/min
dh/dt = 12 km/min
Surface area of a prism, A = 2 × (lw + lh + wh)
For a square prism,
Length, l = width, w = 6km
A = 2 × (l² + lh + lh)
= 2(l²) + 4lh
A = 2(l²) + 4 lh
= 2 × (l² + 2lh)
dA/dt = 2 × (2I × dI/dt + 0 × dh/dt + 2 × 2h × dl/dt + 2l × dh/dt)
dA/dt = 2 × (2l × dl/dt + 0 + 2 × 2h × dl/dt + 2l × dh/dt)
= 2 × (2(6) × (-9) + 2(10) × (-9) + 2(6) × (12))
= 2 × (- 108 + -180 + 144)
= 2 × -144
= -288 km/min
The rate of change of the surface area, A is decreasing by 288 km/min.
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Question is incomplete. Completed question is given below;
The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 9 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 12 kilometers per minute. At a certain instant t_0t 0 t, start subscript, 0, end subscript, the base's side is 6 kilometers and the height is 10 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?
One angle measures 27°, and another angle measures (8d − 9)°. If the angles are complementary, what is the value of d?
d = 72
d = 21
d = 3
d = 9
Answer:
d = 9°
Step-by-step explanation:
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
soln
27° + (8d – 9)° = 90°
27° + 8d – 9° = 90°
27°–9° + 8d = 90°
18° + 8d = 90°
8d = 90° – 18°
8d = 72°
divide both sides by (8)
d = 9°
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amelia paid a weekly salary of $500 to sell jewelry at international Diamond Center in addition,she makes a total of 12% of commission off all of her sales. How much does Amelia make this week if she sells $22,540 worth of jewerly this week?
Answer:
Step-by-step explanation:
Pls answer it quickly
The two-column method can be used to prove that the triangles ΔACD and ΔBCD are congruent is presented as follows;
Statements [tex]{}[/tex] Reasons
1. AC ≅ BC [tex]{}[/tex] 1 Given
2 D is the midpoint of AB [tex]{}[/tex] 2 Given
3. CD ≅ CD [tex]{}[/tex] 3 Reflexive property → CD = CD
4 ∠ACD ≅ ∠BCD [tex]{}[/tex] 4 Median line of an isosceles triangle bisects the vertex angle
5 ΔACD ≅ ΔBCD [tex]{}[/tex] 5. SAS congruency postulate
What is the two-column method used to prove statements in geometry?The two-column method consists of two columns, including a statement column and a reasons column, in which each statement made is provided with an accompanying reason.
The reasons in the prove for the congruency of the triangles, ΔACD and ΔBCD are as follows;
Reflexive property
The reflexive property of equality indicates that the value of a number or measure is equal to itself, therefore, the length of the segment CD is the same as the length of the segment CD.
Median of an isosceles triangle
In an isosceles triangle, two sides are congruent. The median segment drawn from the altitude of an isosceles triangle forms two congruent segment at the base, such that the two triangles formed by the median line are congruent, by Side-Side-Side, SSS congruency postulate, therefore, the angles formed at the vertex of the triangle by the median segment are also congruent
SAS congruency postulate
The Side-Angle-Side congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.
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If [tex]$4^x = 3$[/tex], what is [tex]$4^{2x-2}?$[/tex]
[tex]4^x=3 \\\\[-0.35em] ~\dotfill\\\\ 4^{2x-2}\implies 4^{2x}\cdot 4^{-2}\implies (4^x)^2\cdot \cfrac{1}{4^2}\implies \cfrac{(4^x)^2}{16}\implies \cfrac{(3)^2}{16}\implies \cfrac{9}{16}[/tex]
Adelyn is planning to sell popcorn to raise money for a fundraiser.
She will need to rent a popcorn popper and will also need to purchase popcorn kernels, oil, salt, and bags.
She has at most $90 to spend on the fundraiser.
The rental of the popcorn popper costs $50.
The cost of popcorn kernels, oil, salt, and bags is $0.25 per serving.
Which inequality could be used to find out how many servings of popcorn that Adelyn will be able to make?
Answer: 50 + 0.25 is less than 90
Step-by-step explanation:
What is the equation in STANDARD FORM of the line that passes through the points (-4, 47) and (2, -16)?
A) y = -10.5x + 5
B) 2x + 21y = 105
C) 2x -21y = 979
D) 21x + 2y = 10
:)
The equation of the straight line is 2y + 21x = 10. The correct option is (D).
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given points are (-4, 47) and (2, -16) respectively.
The equation of the straight line passing through them can be written as,
(y - 47)/(x - (-4)) = (-16 - 47)/(2 - (-4))
=> (y - 47)/(x + 4) = -63/6
=> (y - 47)/(x + 4) = -21/2
=> 2(y - 47) = -21(x + 4)
=> 2y - 94 = -21x - 84
=> 2y + 21x = -84 + 94
=> 2y + 21x = 10
Hence, the standard form of the straight line passing through given points is 2y + 21x = 10.
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what goes in the missing box
Answer:
10
Step-by-step explanation:
in the first one, 6 16 8, (6×8)/3=16
in the third one, 9 21 7, (9×7)/3=21
using the same comcept, 5 ? 6, (5×6)/3=10
so, ?=10
Find the equation of the line that passes through (4,4) and is parallel to y = 3 x + 4.
The line's equation that is parallel to the given line is= 3x - 8
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
The line's equation in the form of the slope intercept is,
y = mx + c
m is the line's slope, and c is its y-intercept.
line equation provided that,
Therefore, the line's slope is
Finding the equation of the line that crosses (4,4) and runs parallel to the provided lines is necessary.
Because all parallel lines have the same slope.
Equation for the necessary line is,
Replace point (4,4) in the line above.
In order for the line equation to become,
3x - 8
Hence, The line's equation that is parallel to the given line is= 3x - 8
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Caroline is planting flowers in her garden. She plants her first 7 flowers in 4 minutes. After 12 minutes, she has planted 21 different flowers. If caroline keeps planting flowers at this rate, how long will it take her to plant all 70 flowers that she has?.
It will take 40 minutes for her to plant all 70 flowers that she has. By using proportions, we can find this value.
How to calculate a word problem using proportions?To calculate a word problem using proportions is as follows:
Consider the details of the word problem in proportions as
a : b = c : d
Here, a: b is the ratio of an event, and c : d is the ratio of another event.
Then, to find the value of c we need to reframe the above proportion into
c = ad/b
This is also said to be a cross formula in terms of word problems.
Calculation:It is given that, Caroline is planting flowers in her garden.
She plants her first 7 flowers in 4 minutes.
After 12 minutes, she planted 21 different flowers.
Then, she takes x minutes for planting 70 flowers.
(Since the rate of planting is the same)
So, we can write
70 : 21 = x : 12
⇒ x = (70× 12)/21 = 40 minutes
Therefore, Caroline takes 40 minutes for planting all 70 flowers.
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Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.
Help please
The given statements are:
angle A = angle O (note the single tickmarks)side AC = side OM (these sides share a similar tickmark)angle C = angle M (note the double tickmarks)We can then use the ASA congruence theorem to prove the triangles are congruent, aka they are mirror copies of one another.
Each "A" refers to facts (1) and (3) shown above. Fact (2) is the "S" of ASA.
ASA = angle side angle
2/3x- 12 for x=18
show work
At the beginning of an experiment, a scientist has 176 grams of radioactive goo. After 135 minutes, her sample has decayed to 11 grams. What is the half-life of the goo in minutes? Find a formula for G ( t ) , the amount of goo remaining at time t . G ( t ) = How many grams of goo will remain after 32 minutes?
Answer:
The amount of goo remaining after 32 minutes is approximately 54.7 grams.
Step-by-step explanation:
The half-life of a substance is the amount of time it takes for half of the substance to decay. To find the half-life of the goo in the experiment, we need to solve the equation G ( t ) = G ( 0 ) / 2 for t , where G ( 0 ) is the initial amount of goo and G ( t ) is the amount of goo remaining after time t .In this case, G ( 0 ) = 176 grams and G ( 135 minutes ) = 11 grams, so we can write the equation as follows:11 grams = 176 grams / 2Solving for t , we get:t = 135 minutes * ( 1 / 2 ) = 67.5 minutesThis is the half-life of the goo in the experiment.To find the amount of goo remaining after time t , we can use the equation G ( t ) = G ( 0 ) * ( 1 / 2 ) ^ ( t / t1/2 ) , where G ( 0 ) is the initial amount of goo, t is the time at which we want to find the amount of goo remaining, and t1/2 is the half-life of the goo.In this case, G ( 0 ) = 176 grams, t = 32 minutes, and t1/2 = 67.5 minutes, so we can plug these values into the equation to find the amount of goo remaining after 32 minutes:G ( 32 minutes ) = 176 grams * ( 1 / 2 ) ^ ( 32 minutes / 67.5 minutes )This equation tells us that the amount of goo remaining after 32 minutes is approximately 54.7 grams.
help pls
Write the equation of the line in slope-intercept form that is perpendicular to
y = -x – 18 and passes through (-6, 11).
Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
The line in slope-intercept form that is perpendicular to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex].
As we know the slope of line is
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y intercept.
Given points are [tex](-6,11)[/tex].
If we want to describe the perpendicular line to the original line then the slope of line is
[tex]m_2=-\frac{1}{m_1}[/tex]
In our given slope of line
[tex]y = -x -18[/tex]
where [tex]m_1=-1[/tex]
So,
[tex]m_2=-\frac{1}{m_1}\\\\m_2=-\frac{1}{-1}\\\\m_2=1[/tex]
Now for the slope of second line we use the point slope from the construct equation then,
[tex]y-y_1=m_2(x-x_1)\\\\y-11=1(x-(-6))\\\\y-11=x+6\\\\y=x+6+11\\\\y=x+17[/tex]
Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].
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please help meeeee!!
Answer:
f(2) = 9
Step-by-step explanation:
to evaluate f(2) substitute x = 2 into f(x) , that is
f(2) = 4(2) + 1 = 8 + 1 = 9
How do you solve this
Answer:
(f+g), (f-g), (f·g), domain is [-3, 3]f/g, domain is [-3, 3)Step-by-step explanation:
Given f(x) = √(3+x) and g(x) = √(3-x), you want the domains of various combinations of f and g.
DomainsThe domain of each of these functions is the interval on which it is defined. The domain of the square root function is all argument values greater than or equal to zero.
Domain of fThe argument of the square root will be non-negative when ...
3 +x ≥ 0
x ≥ -3 . . . . . . subtract 3
-3 ≤ x . . . . . . written using left-pointing arrow
Domain of gThe argument of the square root will be non-negative when ...
3 -x ≥ 0
3 ≥ x . . . . . add x
x ≤ 3 . . . . . written using left-pointing arrow
Intersection of domainsAny combination of functions f and g will only be defined on the domain where both f and g are defined. That is, the domain will be the intersection of the domains of f and g:
(-3 ≤ x) ∩ (x ≤ 3) = -3 ≤ x ≤ 3
Domain of f+gThe domain of f+g is the intersection of the domains of f and g.
[-3, 3]
Domain of f-gThe domain of f-g is the intersection of the domains of f and g.
[-3, 3]
Domain of f·gThe domain of f ·g is the intersection of the domains of f and g.
[-3, 3]
Domain of f/gThe domain of f/g is the intersection of the domains of f and g, excluding the value of x that makes g(x) = 0. That value is x=3.
[-3, 3)
__
Additional comment
The graphs of the combinations of functions are attached. You notice the graph of f/g tends to infinity as x → 3. It is undefined at x=3.
Neha drives a car that gets 25 miles per gallon when she is driving in the city and 40 miles per
gallon when she is driving on the highway. Her car's fuel tank will hold 15 gallons of gas. What
equation can we write to represent all the combinations of city miles and highway miles she can
drive on one tank of gas?
1. Record an equation that is a prediction.
Answer:
C/25 + H/40 = 15
Step-by-step explanation:
Let's call C the number of city miles, and H the number of highway miles.
The total gas used is therefore:
C/25 + H/40
The fuel tank holds 15 gallons, so:
C/25 + H/40 = 15
how many ways are there to list the letters of the word mathematics so that no two consecutive letters are the same?
There are 22 different ways to organize the word mathematics because no two consecutive letters are the same.
Explain the term combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the ordering of the selection is irrelevant. You can choose the components of combos in any order.Total number of ways to organize the word "mathematics".
The same letter does not appear twice.
The following word has the letters 2M, 2A, 2T, H, E, I, C, and S.
We will first organize H,E,I,C,S in five different ways;
−H−E−I−C−S−
No, we could arrange 2M, 2T, and 2A as we have 6 gaps;
= 6!/(2!.2!.2!)
So there are a total of;
= 5 x 6!/(2!.2!.2!)
= 22.5
= 22 ways
Thus, there are 22 different ways to organize the word mathematics because no two consecutive letters are the same.
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