An 18-foot flagpole casts a shadow 12 feet long forming a triangle as shown in the diagram. You are 5.75 feet tall and cast a shadow as shown. How long is the shadow you cast given the triangles shown are similar?
A. 3.83
B. 8.63
C. 11
Answers
Answer:
Option (A)
Step-by-step explanation:
From the picture attached,
ΔABC and ΔDEF are the similar triangles.
Therefore, by the property of similar triangles, their corresponding sides will be proportional.
[tex]\frac{AB}{DE}= \frac{BC}{EF}= \frac{AC}{DF}[/tex]
[tex]\frac{5.75}{18}=\frac{BC}{12}[/tex]
BC = [tex]\frac{12\times 5.75}{18}[/tex]
BC = 3.83 ft
Option (A) will be the correct option.
Related Questions
Mr. James asked his students that which of the following equations can be formed using the expression x = 5:
a)2 x + 3 = 13
b)3x + 2 = 13
c)x –5 =
1d)4x –9 = 21
Answers
Answer:
[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]
help me with finding distance pls
Answers
Answer:
5.7
Step-by-step explanation:
First find the coordinates of the points
A ( 2,2)
B ( -2,-2)
The distance is
d = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( (-2-2)^2 + (-2-2)^2 )
= sqrt( (-4)^2 + (-4) ^2)
= sqrt( 16+16)
= sqrt( 32)
=5.656854249
To the nearest tenth
5.7
Answer:
5.65
Step-by-step explanation:
(2,2) (-2,-2)
√(x2 - x1)² + (y2 - y1)²
√(-2 - 2)² + (-2 - 2)²
√(-4)² + (-4)²
√(16) + (16)
√32
= 5.65
The length of xy (the minor arc) is 15 cm. What is the circumference of OZ?
O A. 94.2 cm
O B. 426 cm
O C. 180 cm
O D. 540 cm
O E. 360 cm
O F. 450 cm
Answers
Answer:450
Step-by-step explanation:
The correct answer is option (F) 450 cm
The formula to find the arc length of the circle:
For a circle with radius 'r' and the central angle 'θ' (in radians), an arc length 's' is,
s = r × θ
The formula of the circumference of the circle:C = 2 × π × r
We have been given that the length of xy (the minor arc) is 15 cm and angle = 12°.
⇒ θ = 0.209 radians
Let r be the radius of the circle.
xy = 15
⇒ r × θ = 15
⇒ r × 0.209 = 15
⇒ r = 71.77 cm
The circumference of the circle is,
C = 2 × π × r
⇒ C = 2 × π × 71.77
⇒ C = 450.95
⇒ C ≈ 450 cm
Therefore, the circumference of the circle is option (F) 450 cm
Learn more about circle here:
https://brainly.com/question/12832946
#SPJ2
If ABCD is dilated by a factor of 2, the
coordinate of A' would be:
Answers
Answer: -5, -1
Step-by-step explanation:
→WILL GIVE BRAINLIEST←
In a survey of adults aged 57 through 85 years, it was found that 86.6% of them used at least one prescription medication. Complete parts (a) through (c) below.
a. How many of the 3149 subjects used at least one prescription medication?
(Round to the nearest integer as needed.)
b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.
(Round to one decimal place as needed.)
Answers
Answer:
a. 2,727
b. (85.6%, 87.6%)
Step-by-step explanation:
The percentage of the adults aged 57 through 85 that used at least one prescription medication = 86.6%
a. The expected number of the 3,149 subjects aged 57 through 85 that used at least one prescription medication = 3,149 × 86.6/100 = 2,727.034 ≈ 2,727 (subjects)
b. The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is given as follows;
[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p} \cdot (1-\hat{p})}{n}}[/tex]
Where;
[tex]\hat p[/tex] = 86.6/100= 0.866
n = 3,149
z = The z-value at 90% confidence level = 1.645
Therefore, we get the following confidence interval of the percentage of adults (rounded to one decimal place as required);
[tex]\left (0.866 - 1.645\times \sqrt{\dfrac{0.866 \times (1-0.866)}{3,149}}\right) \times 100 \% \approx 85.6 \%[/tex]
[tex]\left( 0.866 + 1.645\times \sqrt{\dfrac{0.866 \times (1-0.866)}{3,149}} \right) \times 100 \% \approx 87.6 \%[/tex]
The 90% confidence interval, of the percentage C.I. ≈ (85.6%, 87.6%).
HELP ME ASAP PLEASEEEEEEEE
Answers
Answer:
5 : -1.5
10: -4
y = 1 -.5x
noticed the pattern of subtracting .5 .... then plugged in x = 4
and saw that -2 had to be combined with "1" to end up with a "-1"
Step-by-step explanation:
PERE
Given: ZABC is a right angle and ZDEF is a right angle.
Prove: All right angles are congruent by showing that ZABC = ZDEF.
What are the missing reasons in the steps of the proof?
ZABC, ZDEF are
right angles
M2ABC = 90°
m2DEF = 90°
m2ABC = m_DEF
ZABC = ZDEF
Given
A
B
A:
B:
C:
Intro
Answers
Answers:
A) Definition of right anglesB) SubstitutionC) Definition of congruence=========================================
Explanation:
A) The term "right angle" is another way of saying "90 degree angle". This is a definition. Think of a definition in a dictionary. B) The substitution property allows us to replace one thing for another, as long as the two things are equal. The transitive property works as a similar idea.C) If two angles have the same measure, then they are congruent. This is the definition of congruence (or one form of it).In this exercise we have to use the knowledge of angles, in this way we can say that:
A) Right angles
B) Substitution
C) Congruence
So punctuating some necessary definitions we have that:
A) This alternative is a right angle, that is, an angle that has 90 degrees.
B) The substitution property allows us to replace one thing for another, as long as the two things are equal.
C) IIn this alternative, we are dealing with congruent angles, that is, angles that have the same measure, normally less than 90 degrees.
See more about angles at brainly.com/question/15767203
Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17
Answers
Given:
The table of values is:
x : -7 -5 -3 -1
y : 5 9 13 17
To find:
Whether the given data is linear and then find the equation.
Solution:
The given data is linear if the slope and rate of change is constant.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the slope formula. we get
[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]
[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]
[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]
Since the rate of change is constant, i.e., 2, therefore the given data is linear.
The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-5=2(x-(-7))[/tex]
[tex]y-5=2(x+7)[/tex]
[tex]y-5=2x+14[/tex]
Adding 5 on both sides, we get
[tex]y-5+5=2x+14+5[/tex]
[tex]y=2x+19[/tex]
Therefore, the equation for the given data is [tex]y=2x+19[/tex].
In a restaurant you are making a mix for a large batch of marinade that will go on some beef. The recipe calls for 12 gallons of water but you lost the gallon container and all you have left to measure is a bottle that is a quart. How many quarts would it take to make 12 gallons?
Answers
an object in geometry with no width, lengh or height is a(n):
Answers
Answer:
A point.
Step-by-step explanation:
An object in geometry that has width, length or height is simply a point. A point is yet just a dot.
help me pleaseeeeeeeeeee
Answers
Answer:
top left questions answer is B
the area of the triangle is A
Volume of the cylinder is B
The area of the triangle for q 17 is A
Answer:
1. b
2.a
17.c
Step-by-step explanation:
Given: `bar(DE)` and `bar(DF)` are midsegments of `Delta` ABC as shown. Prove: A midsegment of `Delta`ABC is half the length of the side of `Delta`ABC to which it is parallel. Match each statement to its corresponding reason. Scroll down to see all the choices. Drag the items on the left to the correct location on the right.
Answers
Answer:
here
Step-by-step explanation:
Someone, PLEASE HELP! ):
Answers
Answer:
i dont see anything
Step-by-step explanation:
CANNNN SOMEONEEEEE HELPPPP MEEE OUTTTTT !!!!!
Answers
Answer:
sin X = 21/ 29
Step-by-step explanation:
Since this is a right triangle
sin X = opp side/ hypotenuse
sin X = 21/ 29
Answer:
[tex]\boxed{\sf sinX =\frac{21}{29}}[/tex]
Step-by-step explanation:
We need to find out the value of sinX using the given triangle . Here we can see that the sides of the triangle are 21 , 29 and 20.
We know that the ratio of sine is perpendicular to hypontenuse .
[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]
Here we can see that the side opposite to angle X is 21 , therefore the perpendicular of the triangle is 21. And the side opposite to 90° angle is 29 . So it's the hypontenuse . On using the ratio of sine ,
[tex]\sf\longrightarrow sinX =\dfrac{ p}{h}=\dfrac{ZY}{ZX}[/tex]
Substitute the respective values ,
[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ X =\dfrac{21}{29}}}[/tex]
Hence the required answer is 21/29 .
Which is the graph of f(x) = -(x + 3)(x + 1)?
Ту
6
4
4
2
2
21
WB
2
4
B
X
6
WA
UB
-6
2
B
X
2.
-2
2
6+
2
4 6
Answers
Answer:
See attachment
Step-by-step explanation:
A function is given to us and we need to tell which graph represents the given function. The function given to us is,
[tex]\tt: \implies f(x) = -( x + 3 )( x + 1 ) [/tex]
Let's find out at which points do the graph Intersects x axis / finding the roots. For that substitute f(x) = 0 , we have ,
[tex]\tt: \implies -(x +3)( x + 1 ) = 0 [/tex]
Equate each factor by 0 ,
[tex]\tt: \implies \boxed{\blue{ \tt x = -1,-3 }} [/tex]
Therefore the graph will intersect x axis at x is equal to -1 and x is equal to -3 .
On looking at the given graphs in the options the second graph intersects x axis at -1 and -3 .
Hence the second option is correct .
{ See attachment }
The graph of the function is graph (b)
The function is given as:
f(x) = -(x + 3)(x + 1)
The above equation means that:
The function is a quadratic functionThe function is reflected across the x-axisThe function has its zeros at x = -3 and x = 1Hence, the graph of the function is graph (b)
Read more about quadratic functions at:
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Question 1 of 10
Classify the following triangle. Check all that apply.
121
11
599
70
10
A. Equilateral
B. Obtuse
C. Isosceles
D. Scalene
E. Acute
OF Right
PREVIOUS
Answers
Answer:
Acute and scalene
Step-by-step explanation:
All the three interior angles of triangle are less than 90 then it is an acute triangle.
All the sides have different length then it is Scalene triangle. In Scalene triangle, all the sides have different length and so all the angles are of different
Explanation:
You have the right idea. The triangle is acute since all three angles are less than 90 degrees. The triangle is also scalene because all three sides are different lengths.
For a triangle to be equilateral, the three sides must be the same length. So we can rule out choice A.
We can rule out choice B since none of the angles are larger than 90 degrees. This contradicts choice E.
We can rule out choice C because we don't have exactly two sides the same length. This contradicts choice D.
We can rule out choice F because we don't have a 90 degree angle. This contradicts choice E.
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answers
Answer:
Step-by-step explanation:
I answered this in your question from yesterday. See #24317186
Which shows one way
to determine the factors of x3 - 12x2 - 2x + 24 by grouping?
Answers
Answer:
[tex]x^3 - 12x^2 - 2x + 24[/tex]
[tex]x^2(x - 12) - 2(x -12)[/tex]
[tex](x - 12)(x^2 -2)[/tex]
Step-by-step explanation:
Answer:
[tex](x^2-2)(x-12)=0[/tex]
Step-by-step explanation:
Factoring by grouping is a way of determining the factors of a polynomial equation. One firsts groups terms by putting them in parenthesis. Then one will take a common factor out of the parenthesis. Finally, one will group the coefficients and the grouped terms respectively, thus rewriting the polynomial equation as the product of its factors.
One is given the following equation:
[tex]x^3-12x^2-2x+24=0[/tex]
Group the different terms in the equation:
[tex](x^3-12x^2)+(-2x+24)=0[/tex]
Factor, write a common factor that both terms in the parenthesis share, outside of the parenthesis.
[tex]x^2(x-12)-2(x-12)=0[/tex]
Factor the equation again. Group the like terms together, and the coefficients together.
[tex](x^2-2)(x-12)=0[/tex]
plzzz helppp i need to pass this classs
Answers
D. X=130 but im not sure if this is correct
Answer:
C
Step-by-step explanation:
x + 40 + 100 + x=360. (sum of angles at a point)
2x+140=360
2x=360-140
2x=220
x=220/2
x=110⁰
The cars of a circular Ferris wheel at an amusement park are equally spaced about the wheel's circumference. They are numbered consecutively beginning with 1. The cars numbered 14 and 30 lie on opposite ends of a diameter. How many cars are on the Ferris wheel?
Answers
Answer:
32 cars
Step-by-step explanation:
we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32
Math step-by-step:
30-14=16
16×2=32
You have 80$ panted cost 29$ And shirts cost 12$. Mom told you to buy one pair of pants and use the rest of the money to buy shirts. Use this information to write and solve and inequality how many shirts can you buy
Answers
Answer: 4 Shirts
Step-by-step explanation:
Given
Person has [tex]\$80[/tex]
Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]
Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts
Spent money must be equal or less than the total money. The inequality becomes
[tex]\Rightarrow 80\geq29x+12y[/tex]
For 1 pair of pants that is, 1 pants
[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]
That is maximum number of shirts that can be bought are 4.
Match each cone's measures to its corresponding volume.
Answers
Answer:
base area=16π in² height=6 in ⇒ base area= πr²
16π²=π(r)²
r=4 in
v=1/3 ×π (4)²×(6)
v=32π in²
-------------
v=1/3 π(12/2)²×5
v=1/3π(31)×5=
v=60π in³
-------------
v=1/3 π×(25×4)=
v=100π/3 in³
OAmalOHopeO
In Owen's class, there are 15 girls and 12 boys. Write the ratio of boys to girls.
Answers
Answer:
4 : 5
Step-by-step explanation:
boys : girls
12 15
Divide each by 3
12/3 : 15/3
4 : 5
Answer: 4:5
Step-by-step explanation:
To simplify the ratio 12:15, divide both numbers by the GCF of the 2 numbers (3). This gives you the simplified ratio, 4:5.
Enter the equation of the line in slope-intercept form.
Slope is 4, and (5,2) is on the line.
The equation of the line is y =
Answers
Answer:
y = 4x -18
Step-by-step explanation:
y-2 = 4(x-5)
y = 4x -20+2
y = 4x -18
Answer:
y = 4x-18
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 4x+b
Substitute the point in the equation and solve for b
2 = 4(5)+b
2 = 20+b
2-20 = b
-18 =b
y = 4x-18
Which of the following steps is involved in solving 3 x plus 8 equals 14 ?
A. 3 x plus 8 minus 8 equals 14
B. 3 x plus 8 equals 14 minus 8
C. 3 x plus 8 plus 8 equals 14 plus 8
D. 3 x plus 8 minus 8 equals 14 minus 8
Answers
Answer:
3 x plus 8 minus 8 equals 14 minus 8
Step-by-step explanation:
3x+8 = 14
Step 1 subtract 8 from each side
3x+8-8 = 14-8
The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the cheetah ran in hours. Solve f divided by g of 3, and interpret the answer.
Answers
Correct question is;
The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the cheetah ran in hours. Solve (f/g)(3), and interpret the answer.
Answer:
26 is the cheetahs rate in miles per hour.
Step-by-step explanation:
We are given;
f(x) = 6x + 8
g(x) = x − 2
Thus;
f/g = f(x)/g(x)
> (6x + 8)/(x − 2)
Since we are looking for (f/g)(3), then we have;
> (6(3) + 8)/((3) − 2) = 26
Since f(x) is distance and g(x) is time, then, we know that distance/time = speed. Thus, the interpretation is 26 mph which is the speed of the cheetah.
Answer:
26; the cheetah's rate in miles per hour
Step-by-step explanation:
I just took the test
Find the value of x given in the right triangle
Answers
Answer:
44.4
Step-by-step explanation:
Using SOH
sin(x)=7/10
x= 44.427
Answer:
x ≈ 44.4°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{10}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{7}{10}[/tex] ) ≈ 44.4° ( to the nearest tenth )
Need help with adding these!! *prob easy I’m just not good* see photo!
Answers
Answer:
2x+8w
I hope this will help you
If f(x) = 2x + 3 and g(x) = 3x - 9, find (f + g)(x).
Answers
Answer:
5x-6
Step-by-step explanation:
f(x) = 2x + 3
g(x) = 3x - 9
f(x) + g(x) = 2x + 3 + 3x-9
= 5x-6
Ryan rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 74 cents for each mile driven. Ryan had to pay $133.17 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
157 miles
Step-by-step explanation:
total cost = flat fee + cost per mile * miles
133.17 = 16.99 + .74 * m
Subtract 16.99 from each side
116.18 = .74m
Divide each side by .74
116.18 / .74 = .74m/.74
157 = m
