A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 7 cm more than the shorter leg and the hypotenuse 14 cm more than the shorter leg. How long should the sides of the triangle be?
Answers
Given the information about the right triangle we have the following:
since we have that the longer leg is 7cm more than the shorter leg, then:
\(b=a+7\)and also the hypotenuse is 14 cm more than the shorter leg, therefore:
\(c=a+14\)with these two expressions, we can find the value of the shorter leg:
\(\begin{gathered} b=a+7 \\ c=a+14 \\ c^2=a^2+b^2 \\ \Rightarrow(a+14)^2=a^2+(a+7)^2 \\ \Rightarrow a^2+28a+196=a^2+a^2+14a+49 \\ \Rightarrow a^2+a^2+14a+49-a^2-28a-196=0 \\ \Rightarrow a^2-14a-147=0 \\ \Rightarrow(a-21)\cdot(a+7)=0 \end{gathered}\)we have then that a=21 or a=-7. We choose a=21 since distances cannot be negative. Now we can find the value of b and c and check if they match using the pythagorean theorem again:
\(\begin{gathered} a=21 \\ b=a+7=21+7=28 \\ c=a+14=21+14=32 \\ c^2=a^2+b^2 \\ \Rightarrow c^2=21^2+28^2=1225 \\ \Rightarrow c=\sqrt[]{1225}=35 \\ c=35 \end{gathered}\)therefore, the sides of the triangle should be 21 cm, 28 cm and 35 cm long
Related Questions
What is the slope of the following line: y=3x−7
Answers
Answer:
The slope is 3
Step-by-step explanation:
If sin 0 = 0.7342, the value of 0, correct to 2 decimal places, is:
Answers
The sine function is one of the trigonometric functions used to solve problems involving angles. The value of angle 0 is \(47.24^{o}\).
Trigonometric functions deals with the determination of the value of an unknown angle by the application of some functions, which are either sine, cosine or tangent of the angle.
The value of the sine of a given angle can be determined by the use of a calculator or figures table.
Given that an angle 0, then;
Sin 0 = 0.7342
divide both sides by sin to have;
0 = \(Sin^{-1}\) 0.7342
= 47.2397
0 = \(47.24^{o}\)
Therefore, the value of angle 0 is \(47.24^{o}\).
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Need help with question #7
Answers
The coordinates of A with respect to the base s are (1, -1, 2, 3).
To find the coordinates of A = (5 3 3 1) with respect to the base s, we need to express A as a linear combination of the vectors in s.
That is, we need to find real numbers a, b, c, and d such that:
(5 3 3 1) = a(1 1 1 1) + b(1 -1 1 0) + c(1 -1 0 0) + d(1 0 0 0)
Expanding the right-hand side and collecting like terms, we get:
(5 3 3 1) = (a + b + c + d)(1 1 1 1) + (-b - c)(1 -1 1 0) + (-c)(1 -1 0 0) + (-d)(1 0 0 0)
Equating corresponding entries, we get the following system of equations:
a + b + c + d = 5
a - b - c = 3
a - b = 3
a = 1
Solving this system of equations, we get:
a = 1
b = -1
c = 2
d = 3
In order to understand this problem, we need to know what a basis is in linear algebra.
A basis is a set of vectors that are linearly independent and span a vector space.
In other words, any vector in the space can be expressed as a linear combination of the basis vectors.
In this problem,
We are given a basis for the vector space M2(R), which is the space of all 2x2 matrices with real entries.
The basis is given as s = {(1,1,1,1), (1,-1,1,0), (1,-1,0,0), (1,0,0,0)}.
We are asked to find the coordinates of a given vector A = (5,3,3,1) with respect to the basis s.
To do this, we need to express A as a linear combination of the basis vectors, where the coefficients of the linear combination are the coordinates of A with respect to the basis s.
We start by writing out the general form of the linear combination:
A = a(1,1,1,1) + b(1,-1,1,0) + c(1,-1,0,0) + d(1,0,0,0)
where a, b, c, and d are the coefficients we need to find.
We then equate the corresponding entries of A and the linear combination:
5 = a + b + c + d
3 = a - b - c
3 = a - b
1 = a
Therefore, the coordinates of A with respect to the base s are (1, -1, 2, 3).
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Which of the points (s, t) is not one of the vertices of the shaded region of the
set of inequalities shown below?
ss 20 -0.5t
s 12-t
ss 24-t
S>O
t>0
Answers
Answer:
24,0
Step-by-step explanation:
Please I really need help
Answers
Answer:
85°
Step-by-step explanation:
The two angles are known as vertical angles, which are always congruent
Answer:
∠DEB = 85°
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
Angles AEC and DEB are vertically opposite angles, therefore:
∠AEC = ∠DEB
As ∠AEC = 85° then ∠DEB = 85° also.
Which of the following terms describes the 3 in the expression 3x+7?
Answers
It's Coeficent
,.,.,..,.,
Good afternoon guys and god bless!! does anyone know the answer to this?
Answers
Answer:
The answer to the question provided is horizontal or 0.
Step-by-step explanation:
Good afternoon and God bless you too <3
Which expression is NOT equivalent to -20?
O
A
(-80)
4
80
В
— (0)
ОО
с
(30)
80
ор
80
(-4)
Answers
Answer:
Which expression is NOT equivalent to -20? O A (-80) 4 80 В — (0) ОО с (30) 80 ор 80 (-4 -
Step-by-step explanation:
7(4p+2q+3r) apply the distributive property to create an equivalent expression
Answers
Answer:
28p + 14q + 21r
Step-by-step explanation:
7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside
= 28p + 14q + 21r
For what values of x and y must ABCD be a parallelogram?
Answers
Because the parallel sides have to be equal and these inputs make the side equal.
Question:
Given the demand equation p=190/q+10 where 10<0<85, for what value of q is | n | a maximum? For what value is it minimum?
Answers
The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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When rounded to the nearest tenth, which number has the greatest value?
Group of answer choices
6,543.677
6,543.847
6,543.876
6, 543.725
Answers
Answer:
C
Step-by-step explanation:
6,543.900 would be the number with the greatest value when rounded
Rewrite as an exponential equation.
Log3 1/81 = -4
Answers
Answer:
3`⁴ = 1/81
Step-by-step explanation:
________________
Reduce the fraction below to their lowest term 70/3 =
Answers
Step-by-step explanation:
70 ÷ 3 = 23 1/3
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answers
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
graph the line with slope -3/4 passing through the point (2,-1)
Answers
Answer:
Step-by-step explanation:
Slope of the line:
\(m = \frac{y-y1}{x-x1} \\\)
Given:
slope = -3/4
point (x1,y1) = (2, -1)
Substitute and solve
\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)
1/2 is the y-intercept
(0,1/2)
Since we have 2 points already, we can then graph the line.
(2, -1) and (0, 1/2)
Please help me with this proof.
Answers
Answer:
See below
Step-by-step explanation:
For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.
\((x - 2) { }^{2} = 0\)
How many solutions does this equation have?
Answers
Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft3/s. Initially, the balloon has 2 ft3 of hydrogen.
Answers
(a) The linear function that models the volume of hydrogen in the balloon at any time t is V(t) = 2 + 0.5t.
(b) It will take 26 seconds to completely fill the balloon.
What is the Linear function?A linear function is defined as an equation in which the highest exponent of the variable is always one.
(a) To find the linear function V that models the volume of hydrogen in the balloon at any time t, we can use the following formula:
V(t) = V₀ + rt
where V₀ is the initial volume of hydrogen in the balloon, r is the filling rate (in this case, 0.5 ft³/s), and t is the time (in seconds).
Substituting the given values, we have:
V(t) = 2 + 0.5t
Therefore, the linear function that models the volume of hydrogen in the balloon at any time t is V(t) = 2 + 0.5t.
(b) If the balloon has a capacity of 15 ft³, it will take some time t to completely fill the balloon. At this point, the volume of hydrogen in the balloon will be equal to the capacity of the balloon, which gives us the equation:
V(t) = 15
Substituting the linear function we found in part (a), we have:
2 + 0.5t = 15
Solving for t, we get:
0.5t = 13
t = 26 seconds
Therefore, it will take 26 seconds to completely fill the balloon.
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The question seems incomplete, the complete question would be as:
Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 ft³/s. Initially, the balloon has 2 ft³ of hydrogen.(a) Find a linear function V that models the volume of hydrogen in the balloon at any time t.V(t) = (b) If the balloon has a capacity of 15 ft³, how long does it take to completely fill the balloon?
Lieutenant James made an average of 3 arrests per week for 4 weeks. How many arrests does she need to make in the fifth week to raise her average to 4 arrests per week?
Answers
Answer:
5
Step-by-step explanation:
We want the average arrests to be 4. It can be done by calculating the average between the average arrests and arrests during the 5th week, so we get:
Avg(1,2,3,4,5) = (Avg(1,2,3,4) + A(5)) / 2
Where Avg(x) is the average of arrests in given weeks, and A(x) is the number of arrests in a given week.
Solving for A(5) => A(5) = 2*Avg(1,2,3,4,5) - Avg(1,2,3,4) = 2 * 4 - 3 = 8-3 = 5
Given the following angles, what ray is the common side of ZCFD and ZDFE?ERay FDRay FERay FC
Answers
We will consider two angles as follows:
\(<\text{ CFD > \& < DFE >}\)We are to determine the rays that have a common side to both < CFD > and < DFE >.
We will go ahead and make combination of pairs for each angle < F > common to both.
\(CF\text{ , FD }\)\(&\)\(DF,\text{ FE}\)The common sides of the angle rays would contain similar letters! From the two combinations for each ray-angles we can see that the side:
\(FD\text{ = DF}\)Hence, the ray common to both < CFD > and < DFE > is :
\(\textcolor{#FF7968}{FD}\)
a triangle is shown drag graphs to the table to ahow the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y = x.
Answers
The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.
How to reflect the triangle based on the transformation rule?By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (x, -y)
(1, -3) → (1, -(-3)) = (1, 3)
(3, -2) → (3, -(-2)) = (3, 2)
(4, -5) → (4, -(-5)) = (4, 5)
By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (-x, y)
(1, -3) → (-1, -3)
(3, -2) → (-3, -2)
(4, -5) → (-4, -5)
By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;
(x, y) → (y, x)
(1, -3) → (-3, 1)
(3, -2) → (-2, 3)
(4, -5) → (-5, 4)
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What is the probability of getting a vowel if you randomly pick a letter from the English alphabet?
Answers
Find the area of the shaded region. Round results to the nearest unit.
Answers
Answer: 211 in²
Step-by-step explanation:
To find the area of the shaded region, you want to find the area of the rectangle, then subtract the area of the circle and the triangle. First, we need to find the area of the triangle. We know that there is a circle because 2 halves make a full circle.
Area of Circle
A=πr²
A=π(6)² [exponent]
A=36π [multiply]
A=113
-------------------------------------------------------------------------------------------------------
Area of Triangle
A=bh/2
A=(18)(12)/2 [multiply]
A=216/2 [divide]
A=108
Now that we have the area of the shapes, let's find the area of the entire rectangle.
A=lw
A=(36)(12) [multiply]
A=432
With the area of the rectangle, we can subtract the areas.
432-108-113=211
The area of the shaded region is 211 in².
sorry if i got it wrong
Help pls pls help pls
Answers
Answer:
D. 118°
Step-by-step explanation:
90 + 28 = 118
good luck, i hope this helps :)
Answer:
D
Step-by-step explanation:
give them brain, they're correct.
find the angle vector of 7j +10 k,i +6j+6k,-4i+9j+6k
Answers
Answer:
Right angled and isosceles
y = -4x - 3
y = -2x + 1
Answers
I hope this helps you :)
For each of the shapes below, state whether it is a regular polygon, an
irregular polygon or neither.
ASAAP NEED HELLPPP
Answers
Answer:
regular: Eirregular: A, B, Dneither: CStep-by-step explanation:
You want to identify the given shapes as a regular or irregular polygon, or neither.
Regular polygonA regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.
Polygon E is a regular polygon.
PolygonA polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.
Any simple polygon that is not a regular polygon is an irregular polygon.
Polygons A, B, D are irregular polygons.
CircleA circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.
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Hamburger costs $1.49 for 1/2 pound. How much would the hamburger cost for a whole pound?
Answers
Answer:$2.98
Step-by-step explanation:
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30