As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does, so the Claudia’s height is 132 cm.
To solve this problem, we can use the concept of similar triangles.
Let's assume Claudia's height is h cm.
Since Claudia's shadow tip moves twice as fast as she does, her shadow's length must be twice her height, or 2h cm.
According to the question, as Claudia walks away from the lamppost, her shadow moves twice as fast as she does.
This means the ratio of the length of the shadow to the distance Claudia walks is the same as the ratio of the distance the shadow moves to the distance Claudia walks.
We can set up the following proportion:
(2h) / 264 = h / x
where x is the distance Claudia walks from the lamppost.
Solve for h by cross multiplying:
2h * x = 264 * h
2hx = 264h
Divide both sides by h:
2x = 264
Divide both sides by 2:
x = 132 cm
Therefore, Claudia's height is h = 132 cm.
By using the principles of similar triangles and the given information that Claudia's shadow moves at double her pace, we establish a proportion between the heights and shadow lengths, solve the equation, and find that Claudia's height is 176 cm.
Explanation:To solve the problem of finding Claudia's height based on the information given about her shadow, we need to apply the principles of similar triangles. The situation describes a real-world application of similar triangles, where Claudia and her shadow form one triangle, and the lamppost and its shadow form another. These triangles are similar because the angles are the same: the angle of elevation to the sun is the same for both Claudia and the lamppost, and the ground provides the same angle for both bases.
Let's denote Claudia's height as h, the distance Claudia walks away from the lamppost as x, and therefore the length of her shadow will be 2x (since it moves twice as fast). The similar triangles give us the following proportion:
Height of Lamppost / Height of Claudia = Length of Lamppost's Shadow / Length of Claudia's Shadow
264 cm / h = (x + 2x) / 2x
This simplifies to:
264 / h = 3 / 2
Solving for h, we get:
2 * 264 = 3h
h = 2 * 264 / 3
h = 528 / 3
h = 176 cm
Therefore, Claudia's height is 176 cm.
What is the value of the expression when a = 5 and b = 2? a 2b−3
What is 9 x ( 3 x 5 ) = ( 9 x n ) x 5?
Answer:
n=3
Step-by-step explanation:
What is used to repair big, brass instruments
Repairing big, brass instruments requires the use of specialized tool kits made of steel alloys and brass instrument repair kits. These tools are designed to be gentle on the brass surface, ensuring the instrument's quality and longevity.
Explanation:Repairing big, brass instruments, such as trombones and trumpets, often requires the use of certain materials and techniques. Since brass is an alloy of copper and zinc, it is prone to tarnish and damage over time. Hence, it is important to use cleaning and repair tools made of similar or non-abrasive materials to avoid causing further damage to the instrument.
The most common methods of repairing dents and scratches in brass instruments involve specialist tool kits composed of various steel alloys, which are strong and durable, but also gentle on the brass surface. Additionally, using specialized brass instrument repair kits, which include various mutes, cleaning agents, and brushes, can help maintain the instrument's quality and longevity.
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The triangle PQR shown on the coordinate grid below is reflected once to map onto triangle P´Q´R´.
If vertex P’ is at (7, -6), what are the coordinates of vertex R’?
A)(5, -3)
B)(3, -5)
C) (3, -2)
D)(5, -2)
The answer is (5,-2)
To find the coordinates of vertex R' in the reflected triangle, we can use the midpoint formula. Using the given point P' at (7, -6) and the original point P at (x, y), the x-coordinate of vertex R' is 5. Similarly, using the given point P' at (7, -6) and the original point R at (x, y), the y-coordinate of vertex R' is -2.
Explanation:To find the coordinates of vertex R', we need to map the reflection of triangle PQR onto triangle P'Q'R'. Since vertex P' is at (7, -6), we can use the midpoint formula to find the coordinates of the reflected point R'.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Using the given point P' at (7, -6) and the original point P at (x, y), we can write the equation:
(x + 7) / 2 = 7
Solving for x, we get x = 5.
Similarly, using the given point P' at (7, -6) and the original point R at (x, y), we can write the equation:
(y - 6) / 2 = -2
Solving for y, we get y = -2.
Therefore, the coordinates of vertex R' are (5, -2).
The length of a rectangle is five centimeters more than its width w if the perimeter of the rectangle is 26 centimeters what is the area of the rectangle i'm square centimeters
5+3i/4-2i written as a complex number?
The expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.
How to write 5+3i/4-2i written as a complex numberTo write the expression (5 + 3i)/(4 - 2i) as a complex number, we can multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator.
The conjugate of 4 - 2i is 4 + 2i.
Multiplying both the numerator and denominator by the conjugate:
((5 + 3i) * (4 + 2i))/((4 - 2i) * (4 + 2i))
Expanding the numerator and denominator:
(20 + 10i + 12i + 6i^2) / (16 - 8i + 8i - 4i^2)
Simplifying and combining like terms:
(20 + 22i - 6) / (16 + 4)
(-14 + 22i) / 20
Now, we can simplify the expression further by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(-7 + 11i) / 10
Therefore, the expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.
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Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.
What percentage of blue pigment is in the mixture of the two inks?
45%
49%
60%
75%
Answer:
45%
Step-by-step explanation:
I took the test!
You purchase a home for $125,000. The value of the property increases by 1.9% every year. After ten years, you decide to sell the home. In the meantime, you have made renovations and improvements to the house which increase its sale value by $48,300. How much will you sell the house for, to the nearest hundred dollars?
We can use the formula:
F = P · ( 1 + i )^n
where: P = $125,000, i = 0.019 ( 1.9 %), n = 10
F = $125,000 · ( 1 + 0.019 )^10
F = $125,000 · 1.019^10
F = $125,000 · 1.207096
F = $150,887
And we have to add $48,3000 ( for renovations and improvements )
$150,887 + $48,300 = $199,187 ≈ $199,200
Answer: You will be sell the house for $199,200.
Answer:
$199,200
Step-by-step explanation:
Choose the words or phrases that best complete the sentences.
A fifth degree polynomial (could or must) have 5 linear factors. The factors (could, but do not have to be, or must) be distinct.
Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Step-by-step explanation:
The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .
For this figure, find the value of x.
x = _____?
Im not sure if i take 77 + 58 + x=180 or 77+28+x=180 or something else.
When point E (-9, 3) is rotated 180� about the origin, its coordinate becomes (3, 9).
True
False
...?
10. Mr. Falcone's pizza shop offers three sizes of pizza. The small, medium and large pizzas have diameters of 8 inches, 10 inches and 12 inches. Small Medium Large a) What is the circumference of each size of pizza? Small = _________________ Medium = ___________________ b) What is the area of each size of pizza? Small = _________________ Medium = _________________ Large = _______________ Large = _________________ c) Joey is very hungry. He says he wants to eat a 100-square-inch area of pizza. Which size(s) of pizza should he order? Why?
Answer:
Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.
The percentage decrease is 0.05%
Step-by-step explanation:
Number of pizzas sold yesterday is 65 pizzas.
The owner offers the employees a bonus if the number of pizzas sold increases by 20%
So 20% of 65 pizzas is, pizzas.
Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.
But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,
Therefore, the percentage decrease
Witch Decimal is equal to six-tenths?
0.6 0.15 0.2 0.3 0.4
Which is the most accurate name for the polygon shown?
concave pentagon
convex pentagon
concave hexagon
convex hexagon
Rock music accounted for 30.5% of the total sales of recorded music in 1999 , and 20.4% of the total sales of recorded music in 2009 . Find the average rate of change of the percentage of sales of rock music from 1999 to 2009 .
Round to the nearest hundredth of a percent. Note that the percentage sign is already given in the answer, so you do not need to enter it.
The average rate of change is
The Sky High Ski Club dues are $450 per season. This fee includes transportation to and from the slopes and lift tickets. Skis cost $159.90, boots $78.25, and poles $19. What is the total cost?
Answer:
The total cost is $707.15.
Step-by-step explanation:
The Sky High Club dues are = $450 per person
and the Skis costs = $159.90
Cost for boots = $78.25
Cost of poles = $19.00
To find the total cost we will add all the amounts.
Total cost = 450 + 159.90 + 78.25 + 19.00
= $707.15
The total cost is $707.15.
which of the following comparisons is false 4 liters< 1 gallon, 1 foot< 1 meter, 25 grams< 1 ounce, 10 kilometer< 9 miles
At a pet show, the ratio of dogs to cats is 4:3. if the number of cats is 45, find the number of dogs at the show.answer:
The number of dogs would be 60 when the ratio of dogs to cats is 4:3.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
Given that the ratio of dogs to cats is 4:3. if the number of cats is 45
We have to determine the number of dogs.
Let the number of dogs would be x
As per the given condition, we can write a proportion as
4 dogs : 3 cats = x : 45 cats
⇒ 4 / 3 = x / 45
Apply the cross-multiplication operation,
⇒ 45 × 4 = x × 3
⇒ x = (45 × 4)/3
⇒ x = 15 × 4
⇒ x = 60
Therefore, the number of dogs would be 60.
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**PLEASE HELP??? ****STUCK ON THIS!!!!
Suppose that f(w) varies inversely with w and f(w) = 0.75 when w= 8.
What is f(w) when w= 2?
A.) 12
B.) 6
C.) 3
D.) 1.5
My answer choice is C.) 3. I'm not very confident in my answer so..... :/
Answer:
C.3
Step-by-step explanation:
We are given that
f(w) varies inversely with w.
f(w)=0.75 when w=8
We have to find the value of f(w) when w=2
According to question
[tex]f(w)\propto\frac{1}{w}[/tex]
[tex]f(w)=\frac{k}{w}[/tex]
Where k=proportionality constant
Substitute the given values then, we get
[tex]0.75=\frac{k}{8}[/tex]
[tex]k=0.75\times 8[/tex]
[tex]k=6[/tex]
Substitute the value of k then, we get
[tex]f(w)=\frac{6}{w}[/tex]
Substitute the value of w=2
Then, we get
[tex]f(w)=\frac{6}{2}=3[/tex]
[tex]f(w)=3[/tex]
Hence, option C is true.
FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK
What is the equation in point slope form of the line that passes through the point (1, –2) and has a slope of 3?
y−2=3(x+1)
y+2=3(x−1)
y+1=3(x−2)
y−1=3(x+2)
1. Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.
2. A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?
a)1, –5, 25, –125, ...
b)2, 10, 50, 250, ...
c)3, –2, –7, –12, ...
d)4, 9, 14, 19, ...
becky works 16 days each month.how many days will she work in 6 months
Becky will work 96 days in 6 months.
Explanation:To find out the number of days Becky will work in 6 months, we need to multiply the number of days she works each month by the number of months. Given that Becky works 16 days each month, we can calculate the number of days she will work in 6 months as follows:
Number of days Becky works each month = 16Number of months = 6Number of days Becky will work in 6 months = 16 days/month * 6 months = 96 daysLearn more about number of days worked here:
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Create a trinomial that can be factored and write it in standard form.
To create a trinomial, use a basic factored form like (x+a)(x+b), and expand this via the distributive property. This yields as an example x²+8x+15, a trinomial in standard form.
Explanation:To create a trinomial that can be factored and to write it in standard form, we need to consider a basic factored form first. Let's use (x+a)(x+b) as our basic factored form. In this form, 'a' and 'b' are the roots of the trinomial.
To create the trinomial, we then expand this expression by using the distributive property: (x+a)(x+b) = x² + bx + ax + ab, which simplifies to x² + (a+b)x + ab. This is now our trinomial in standard form.
Let's take a concrete example. If we let 'a' be 3 and 'b' be 5, our factored form is (x+3)(x+5). Expanding this, we get x² + 5x + 3x + 15, which simplifies to x² + 8x + 15. Thus, x² + 8x + 15 is a trinomial that can be factored and is written in standard form.
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A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
If the crew members used 3 gal of paint per hour and bought 30 gal of paint for a job, then they will work 30:3=10 hours.
They start at x=0 hours with y=30 gal of paint;They end at x=10 hours with y=0 gal of paint (they worked until they used all the paint).The dependence between x and y is linear.Conclusion: the only possible sketch is A.
Answer: correct choice is A.
Integrate (2 ln x)/x ...?
The altitude dropped to the base of an isosceles triangle is a median, an angle-bisector, and a perpendicular bisector?
True
False ...?
What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3?
A.9xy2 – 6x2y + 5x3
B. 9xy2 – 6x2y – 5x3
C. 9xy2 + 6x2y + 5x3
D. 9xy2 – 6x2y + 5x3
Answer:
The answer is B.
Step-by-step explanation:
The additive inverse of the given polynomial is:
-9xy^2 - 6x^2y + 5x^3
How to find the additive inverse of a polynomial?The additive inverse of a polynomial would be another polynomial, such that when we add the two, the outcome is zero.
For a given polynomial the additive inverse is given by multiplying the given polynomial by -1.
Here we have:
p(x) = 9xy^2 + 6x^2y – 5x^3
Then the additive inverse is:
q(x) = -p(x) = -9xy^2 - 6x^2y + 5x^3
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What is 43/50 as a percent?
Which CANNOT be used in a proof?
A. Theorems
B.Postulates
C.Properties
D.Undefined Terms
The diagonals of a rhombus divide it into four triangles of equal area.
True
False
Answer:
True
Step-by-step explanation: