Answer:
She will need 41.22 meters.
Step-by-step explanation:
She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees .
The leg is adjacent to the hypothenuse. We know that the cosine of an angle [tex]\theta[/tex] is given by:
[tex]\cos{\theta} = \frac{l}{h}[/tex]
In which l is the length of the adjacent side and h is the hypothenuse.
Considering that we have [tex]\theta = 50, l = 11[/tex], we can find the hypothenuse.
Looking at a calculator, the cosine of 50 degrees is 0.6428.
So
[tex]0.6428 = \frac{11}{h}[/tex]
[tex]0.6428h = 11[/tex]
[tex]h = \frac{11}{0.6428}[/tex]
[tex]h = 17.11[/tex]
The other leg:
In a right triangle, with legs [tex]l_1[/tex] and [tex]l_2[/tex], and hypothenuse h, the pythagorean theorem states that:
[tex]l_1^2 + l_2^2 = h^2[/tex]
We already have one of the legs and the hypothenuse, so:
[tex]11^2 + l^2 = 17.11^2[/tex]
[tex]l^2 = 17.11^2 - 11^2[/tex]
[tex]l = \sqrt{17.11^2 - 11^2}[/tex]
[tex]l = 13.11[/tex]
How many meters will she need?
This is the perimeter of the garden, which is the sum of its dimensions, of 11 meters, 13.11 meters and 17.11 meters. So
[tex]P = 11 + 13.11 + 17.11 = 41.22[/tex]
She will need 41.22 meters.
5. A monument casts a 78 ft. shadow at the same time that a vertical yardstick casts a 4.5 ft. shadow. How high is the monument?
Hello,
Using Thalès 's theorem:
Let's h the height of the monument.
[tex]\dfrac{1}{h} =\dfrac{4.5}{78} \\\\h=\dfrac{78}{4.5} =\dfrac{156}{9} \approx{17.3\ (ft)}[/tex]
If you don't know what is the Thalès's theorem,
imagine that the similar triangles.
A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a frozen yogurt?
hint.. correct answer is 4096
how do I set it up for this?
Answer:
CF = 8.5
Step-by-step explanation:
Given 2 intersecting chords, then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
CF × DF = BF × EF , substitute values
CF × 14 = 7 × 17
14CF = 119 ( divide both sides by 14 )
CF = 8.5
Which of the following is the logical conclusion to the conditional statements below? a arrow b mb arrow c
Answer:
B
Step-by-step explanation:
From what we have here;
if a implies b and b implies c
It simply means that we have a implying c
the correct representation here is given in the second option
And thus, we have it that;
a => c
15 POINTS AND BRAINLIEST!!!
Answer:
option C
Step-by-step explanation:
2, 4, 6
i don't know whether it is correct or not...
A manufacturer knows that their items have a normally distributed length, with a mean of 10.2 inches, and standard deviation of 1.8 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 9.8 inche
Answer:
P [ X ≤ 9.8 ] = 0.1335
Step-by-step explanation:
P [ X ≤ 9.8 ] = [ ( 9.8 - 10.2 )/1.8√25 ]
P [ X ≤ 9.8 ] = - 0.4*5/1.8
P [ X ≤ 9.8 ] = - 2 / 1.8
P [ X ≤ 9.8 ] = - 1.11
From z- table we get: α = 0.1335
P [ X ≤ 9.8 ] = 0.1335 or P [ X ≤ 9.8 ] = 0.1335
Rudy rode a bike at the speed of 32 2/3 miles per 3 1/2 minutes. What is his speed in terms of miles per hours?
HELPPP
Answer:
[tex]32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour[/tex]
560 miles per hourDescribe fully the graph which has equation x2 + y2 = 9
Answer:
The graph is a circle with a radius of 3 and a center of (0,0).
Step-by-step explanation:
Graph
The equation x² + y² = 9 represents a circle with center (0, 0) and radius = 3
What is equation?"It is a mathematical statement which consists of equal (=) symbol between two algebraic statements."
What is graph of a equation?"It is a set of points (x, y) which satisfy given equation."
For given question,
We have been given an equation x² + y² = 9
The graph of above equation as shown below.
We know, the equation of the circle with center (0, 0) and radius 'r' is, x² + y² = r²
We can write given equation as x² + y² = 3²
Comparing given equation with x² + y² = r² we have r = 3 units
The graph of above equation represents a circle with center (0, 0) and radius = 3
Therefore, the equation x² + y² = 9 represents a circle with center (0, 0) and radius = 3
Learn more graph of function here:
https://brainly.com/question/16957172
#SPJ2
What is the value of x?
Enter your answer in the box.
x^4+64 will be the perfect square by adding
Answer:
[tex]( { {x}^{2} })^{2} + 16 {x}^{2} + {8}^{2} \\ ( {x}^{2} + 8) ^{2} \\ ( { {x}^{2} })^{2} - 16 {x}^{2} + {8}^{2} \\ ( {x}^{2} - 8) ^{2} [/tex]
+16x² or -16x² is the answer(show your work!) i only got an hour left for this :c
Answer:
7 _> x
Step-by-step explanation:
28 - x _> 7(x-4)
28 - x _> 7x-28
28+28 _> 7x+x
56 _> 8x
7 _> x
Find the value of x that will make A||B
Answer:
7
Step-by-step explanation:
Alternate interior angles must be congruent.
3x - 2 = 2x + 5
x = 7
PLZ Find a ratio equivalent to 9/10. Then use the ratios to write a proportion.
a 70/63 9/10=70/63
b 19/70 9/10=19/70
c 19/20 9/10=19/20
d 63/70 9/10=63/70
Answer:
63/70 = 9 : 10
Step-by-step explanation:
Given ratio:
9/10
a 70/63
= 10/9
= 10 : 9
b 19/70
= 19:70
c 19/20
= 19 : 20
d 63/70
= 9/10
= 9 : 10
The equivalent ratio to 9/10 = 63/70
= 9 : 10
Re-write the following expression using ADDITION ONLY:
12- 3+16 - 37 - (-20)
Answer:
12- 3+16 - 37 -( 20)
=8
Step-by-step explanation:
Two negatives are a positive , this really helps
Tony Stark is trying to improve his Iron Man suit by increasing its power. One modification will cost $350 million, of which the US Government will pay $110 million, and his contractor will offer a 30% discount on the entire cost of the project. If he has half the remainder in petty cash, how much does he still need to raise?'
The total cost is $350 million.
The US Government is offering to pay $110 million.
A contractor is offering to reduce the total cost by 30%.
Tony has enough money to pay the remaining costs out of petty cash.
Answer:
I am a piano so yeah I'm just typing to fill the character requirement
Step-by-step explanation:
get got
The volume of a cube is 8mm3.
What is the length of its side?
Answer:
the length of cube
is 2 mm
Answer:
2m
Step-by-step explanation:
A cube is a 3-dimensional object with all sides of equal length. So, length = breadth = height
Let the side of cube be x.
Then Volume of cube = x * x * x
So, length (side) of cube is 2m
someone help me please
Answer:
1, 3, 4
Step-by-step explanation:
Points N and K are on plane A and plane S
Point P is the intersection of the line n and line g
Points M, P, and Q are noncollinear
Can someone help me with this
Answer:
a = 17
c = 9
Step-by-step explanation:
2a + 3c = 61
3a + 5c = 96
3a = 96 - 5c (solve for 'a'. Then you can substitute)
a = 32 - [tex]\frac{5}{3}[/tex] c
2(32 - [tex]\frac{5}{3}[/tex]c) + 3c = 61 (Substitute)
64 - [tex]\frac{10}{3}[/tex]c + 3c = 61 ([tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]. So subtracting, adding a negative, leaves [tex]\frac{-1}{3}[/tex])
-[tex]\frac{1}{3}[/tex] c= -3
c = 9
2a + 3(9) = 61
2a + 27 = 61
2a = 34
a = 17
Which graph is that of the inequality shown below?
Answer:
Graph C
Step-by-step explanation:
Each graph has the same slope and points, but only C works for this inequality- since you’re looking for less than or equal to, and only graphs b and c show less than, you know it’s one of those. From there you know it’s less than or equal to, so you want the full line, not dotted, since dotted represents that those values are excluded from the solution.
What is the gradient of a line perpendicular to a line with a gradient of -6?
Answer:
1/6
Step-by-step explanation:
Gradient of a line perpendicular to a line with a gradient of m = -1/m
Gradient of a line perpendicular to a line with a gradient of -6 = -1 /-6 = 1/6
solve: − <− + 7( − 2)
(show your work)
Answer:
hope it helps.
stay safe healthy and happy...f(x) = square root 32x
g(x) = square root 2x
Given:
The two functions are:
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
To find:
The [tex](f\cdot g)(x)[/tex]. Assume [tex]x\geq 0[/tex].
Solution:
We have,
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
Now,
[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
[tex](f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{32x\times 2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{64x^2}[/tex]
[tex](f\cdot g)(x)=8x[/tex]
Therefore, the correct option is A.
6. Write an equation of a line that is Parallel to the line: y = 3x -3
Answer:
3x - y -6 = 0
Step-by-step explanation:
We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,
[tex]\rm\implies y = 3x - 3 [/tex]
Slope Intercept Form :-
[tex]\rm\implies y = mx + c [/tex]
where ,
m is slopec is y intercept .Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .
Using point slope form :-
[tex]\rm\implies y - y_1 = m ( x - x_1) \\\\\rm\implies y - 3 = 3( x - 3 ) \\\\\rm\implies y -3 = 3x -9 \\\\\rm\implies 3x -y -9+3=0\\\\\rm\implies \boxed{\rm\red{ 3x -y -6=0}}[/tex]
Use expression and the unit grid below to answer the question .
April measured her bed and made a scale drawing. The scale of the drawing was 1
centimeter = 6 inches. In the drawing, the bed is 10 centimeters long. What is the
length of the actual bed?
solve for:− 5 − 6 ≤ 8 − 8 − (show your work)
Answer:
hope it helps.
stay safe healthy and happy...A : B = 5 : 7 and B : C = 3 : 5 what is the ratio of A : B : C ?
Answer:
15:21:35 (I'm not sure, but this is my best guess)
Step-by-step explanation:
15:21 = A:B (plugging in 3 as a test)
21:35 = B:C
15:21:35 = A:B:C (can't simplify)
A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are drawn from the deck and replaced each time back into the deck. What is the probability of drawing the King of Clubs and a heart from the deck of cards?
Answer: 13%
Step-by-step explanation:
What is the slope of the line that contains the points in the table
Answer:
C. -5
General Formulas and Concepts:
Algebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from table
Point (-1, 6)
Point (0, 1)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{1 - 6}{0 - -1}[/tex]Subtract: [tex]\displaystyle m = \frac{-5}{1}[/tex]Simplify: [tex]\displaystyle m = -5[/tex]John read 10 books in 12 months. What was his rate of reading in months per book?
Answer:
1.2 books per month
12/10
Step-by-step explanation:
