Use Heron's formula to find the area of the triangle. Round to the nearest square foot.Side a=7 feetSide b=7 feetSide c=5 feet
Answers
The area is approximately 16 square feet.
Step - by -Step Explanation
What to find? Area of the triangle using Heron's formula.
Given:
• Side a=7 feet
,• Side b=7 feet
,• Side c=5 feet
The Heron's formula is given below:
[tex]\text{Area}=\sqrt[]{p(p-a)(p-b)(p-c)}[/tex]Where P is the perimeter of the triangle.
a, b and c are the sides of the triangle.
We need to first find the half perimeter of the triangle.
P = a+b+c /2
= 7+7+5 /2=19/2 = 9.5
Substitute the value of p, a, b and c into the formula and simplify.
[tex]\text{Area}=\sqrt[]{9.5(9.5-7)(9.5-7)(9.5-5)}[/tex][tex]=\sqrt[]{9.5\times2.5\times2.5\times4.5}[/tex][tex]=\sqrt[]{267.1875}[/tex][tex]\approx16\text{ square f}eet[/tex]Hence, the area of the triangle is approximately 16 square feet.
Related Questions
question will be in picture
Answers
ANSWER:
C. 50 fewer people will attend for every dollar the admission price increases.
STEP-BY-STEP EXPLANATION:
The equation in its slope and y-intercept form is as follows
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]We have the following equation
[tex]n=800-50p[/tex]We can see that in this case the slope is - 50, therefore the answer would be 50 fewer people will attend for every dollar the admission price increases.
discriminant of the equation x squared minus 5x equals -2 is
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Recall that the "discriminat" of a quadratic equation of the form:
a x^2 + b x + c = 0
is given by the formula: b^2 - 4 a c
So for our equation:
x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:
x^2 - 5 x + 2 = 0
Now we recognize:
a = 1
b = - 5
c = 2
and write the discriminant
b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17
Then, the discriminat of the equation is: 17.
5LATR이S20What is the value of sinEnter an exact value or round to the nearest hundredth.(5)
Answers
Sine:
[tex]\sin (x)=\frac{opposite}{hypotenus}[/tex]Using the calculator (in radians), we can get the value:
[tex]\sin (\frac{\pi}{3})\approx0.87[/tex]solve the system of equations using elimination (1/2)x+(1/3)y=4(1/3)x+y=-2
Answers
EXPLANATION
Let's consider the system of equations:
(1) (1/2)x + (1/3)y = 4
(2) (1/3)x +
my questions is about. latitude and longitude
Answers
Answer
Option B is correct.
The latitude and longitude of the point X is 42.5°N, 77.5°W
Hope this Helps!!!
PLS HELP ME WITH THIS
Answers
Equation of the line in slope-intercept form = y = 8x − 1
How to calculate the equation of the line?
Given:
Co-ordinates of the first line (x, y)=(0,-1), (1,7), (2,15), (3,23),(4,31)
We know that,
[tex]\text{slope }=m=\frac{y_2-y_1}{x_2-x_1}\\\\= > \frac{7+1}{1-0}\\\\=8[/tex]
The slope - intercept form of a line is given by,
y = mx + b ---(1)
Let us substitute ( x, y )= (0, -1) in (1)
-1 =(8)*0+b
-1= b
b = - 1 ----(2)
Let us substitute m and b in the slope-intercept equation (1)
y = 8x − 1
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The system of equations y = -2 + 5 and y = x - 1 is graphed. What is the solution to
the system of equations?
(3,2)
(0,5)
3
2
4-5-3
234
(2, 3)
(1,0)
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Given
We have the system of equations:
[tex]\begin{gathered} y\text{ = -x + 5} \\ y\text{ = x - 1} \end{gathered}[/tex]The solution to the system of equation as determined from the graph is the point where the two lines intersect
From the graph, we can determine the point of intersection to be (3, 2)
Answer: (3, 2) Option A
I need to write to objective function and the constraints
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Let's define:
x: number of Traveler bicycles made
y: number of Tourister bicycles made
The objective function is:
Maximize 300x + 600y
Subject to the following restrictions:
x + y ≤ 300
x + 3y ≤ 360
Equation fraction X over 9 equals 7
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Answer:
x/9= 7
×ing by 9 on both sides
x=9×7
x=63
Step-by-step explanation:
If ∆ABC is congruent to ∆PQR, find the length of QR.
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If ∆ABC is congruent to ∆PQR, find the length of QR.
Given that If ∆ABC is congruent to ∆PQR:
The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.
When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.
From the triangle ABC, the side BC = 4,
Hence the PQR, the side QR = 4 since they are congruent
Find the linear equation of the plane through the point (1, 3, 10) and parallel to the plane x+6y+2z+4=0
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The most appropriate choice for equation of plane will be given by-
Required equation of plane is [tex]x + 6y +2z=39[/tex]
What is a plane?
A surface which is spanned by two linearly independent vectors is called a plane.
The general equation of plane is [tex]ax + by + c =d[/tex] where
[tex](a,b,c)[/tex] are the components of normal vectors.
Equation of the plane parallel to [tex]x + 6y +2z=-4[/tex] is
[tex]x +6y+2z=c[/tex] [As the perpendicular vector of two parallel planes are same]
The required plane passes through (1, 3, 10)
Putting [tex]x=1, y=3,z=10[/tex] in [tex]x + 6y+2z=c[/tex]
[tex]1 + 6 \times 3 + 2\times 10 = c\\1 + 18+20=c\\c=39[/tex]
So, Required equation of plane is [tex]x + 6y +2z=39[/tex]
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The functions rands are defined as follows.r(x)=32-4s(x) = -2x+4Find the value of s(r(-5)).s(r(-5)) = 00/0
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With the use of factorization, we can state that s and r have values of -2 and 3, respectively.
What is factorisation?The process of breaking or decomposing an entity (such as a number, a matrix, or a POLYNOMIAL) into a product of another entity, Or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring.The given values are
r(x)= 3x-4 s(x)= -2x+4Solving with the help of factotisation.
s(r(-5))(2x-4)(3x-4-5)2x+4(3x-9)6x² - 6x - 36Dividing the eqn by 6
x²-x-6taking common factors= x(x-3) + 2(x-3)(x+2)(x-3)x= -2,3hence,from above solving we can say that values of s and r are: 2,3
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Use the graph of the function below to answer the questions.i just need help with b and c
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Answer:
a) Yes
b) -3, 0, 2
c) [-1, -3], [3, -4], [5, -1]
Explanation:
a) From the graph, we can see that f(3) = -4.
Therefore, f(3) is negative
b) From the graph, we can see that the values of x for which f(x) = 0 are -3, 0, and 2.
c) From the graph, we can see that the values of x for which f(x) < 0 are -1, 3, and 5.
Using the interval notation, we'll have [-1, -3], [3, -4], [5, -1]
Ben has a 6 3/5 pound bag of granola. He wants to give his friends 3/4 pound of granola each. To how many friends can Ben
give granola?
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Answer:21 to each of his 3 friends
Step-by-step explanation:
I need a run down on how to do multi step equations.Number 3 only
Answers
Answer:
x=-7
Explanation:
Given the equation:
[tex]8x-2=-9+7x[/tex]To solve equations of this form, the goal is to try to bring all the terms containing the variable (letter x or any letter) to one side of the equation and the constants to the other side.
First, subtract 7x from both sides.
[tex]\begin{gathered} 8x\textcolor{red}{-7x}-2=-9+7x\textcolor{red}{-7x} \\ x-2=-9 \end{gathered}[/tex]Next, add 2 to both sides.
[tex]\begin{gathered} x-2+2=-9+2 \\ x+0=-7 \\ \implies x=-7 \end{gathered}[/tex]The value of x is -7.
Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30N, and the other east and at an angle of 30 degrees northward and a tension force of 40 N. Find the components of the net force on the cart. Show all work.
Answers
The net force on the cart is 62N
and the vertical component =36.64 N
the horizontal component= 50N
What is revolution of vector?
The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component
30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.
40N tension isN 30° E which means
the vertical component= 40 sin60=36.64N
Horizontal component= 40 cos 60= 20N
sum of vertical = 36.64N +0= 36.64N
sum of horizontal= 30N+20N= 50N
60° was used for tension 40N because the angle of vector must always lie on the horizontal axis
therefore the net force F is obtained by using Pythagoras theorem
F= √(50^2+36.64^2)
= 62N to the nearest whole number.
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What is g(f(x)) if f(x) = 3x + 2 and g(x) = -2x + 4?
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⇒g(f(x)) means that in the function g(x) insert/plug in what f(x) is equal to in the place of x. f(x)= 3x+2 meaning in the place of x in g(x) insert 3x+2 and simplify.
[tex]g(f(x))=-2(3x+2)+4\\g(f(x))=-6x-4+4\\g(f(x))=-6x[/tex]
Attached is the solution of what g(f(x)) is equal to.
PLEASE HELP URGENT:
Graph the following function:
y=3sin(2x−π/2)−2
Drag the black dot to shift your graph in the desired direction. Use the blue draggable dot to change the period. Drag the orange dot to change the amplitude and/or reflect with respect to the x-axis. The horizontal distance between the vertical dotted green lines corresponds to one period.
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A graph of this sine wave function y = 3sin( 2x + π/2) - 2.
A sine wave, also known as a sinusoidal wave or simply a sinusoid in mathematics, is a basic waveform that is frequently employed to describe periodic oscillations, with each interval's displacement amplitude being directly proportional to the sine of the displacement's phase angle.
This mathematical expression can be used to model or depict a sine wave mathematically:
y = asinbx
Where a represents the amplitude of a sine wave, b represents the periodicity.
After that, we would use the lowest common denominator (LCM) to solve the sine wave function given:
y = 3sin( 2x - π/2 ) - 2
y = 3sin( ( 2(2x) - π)/2) - 2
y = 3sin( ( 4x - π)/2 ) - 2
In conclusion, this sine wave function has an amplitude of 3 and a periodicity is 2.
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which coordinate is a solution to the system of inequalities
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I need to know the answer for this question?
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The probability of the first sock being blue is 1/3 and the second sock being white is 1/4.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So,
Red socks: 10White socks: 6Blue socks: 8Total number of socks: 10 + 8 + 6 = 24
Formula: P = favourable events/Total number of events
Probability of picking a blue sock first:
P = 8/24P = 1/3Probability of picking a white sock at second:
P = 6/24P = 1/4Therefore, the probability of the first sock being blue is 1/3 and the second sock being white is 1/4.
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Determine the distance between M(4, 0) and N(-2, -3).
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Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Step 2
let
P1=M(4,0)
P2=N(-2,-3)
replace
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(-2-4)^2+(-3-0)^2} \\ \text{distance}=\sqrt[]{(-6)^2+(-3)^2} \\ \text{distance}=\sqrt[]{36+9} \\ \text{distance}=\sqrt[]{45} \\ \end{gathered}[/tex]I hope this helps you
If there is more then one element in the set, separate them with commas
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Answer:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
Explanation:
The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Then, the outcome for the event that the select number is 2 is
Event that the number chosen is 2 = {2A, 2B, 2C}
Therefore, the answers are:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
evaluate(if possible) the sine,cosine, and the tangent of the real number
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Find the cos equation given amplitude: 6, period: 2π, vertical shift: 0, and horizontal shift:OA. y = 6 cos 0 + 2OB. y = 6 cos 0 - 2OC. y = 6 cos (0+²)OD. y = 6 cos (0-3)Reset Selection2T3
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Given: A cosine function with amplitude: 6, period: 2 pie, vertical shift: 0, and horizontal shift-
[tex]\frac{2\pi}{3}[/tex]Required: To determine the function.
Explanation: The cosine function is defined as-
[tex]y=Acos(Bx-C)+D[/tex]where
[tex]\begin{gathered} A=Amplitude \\ \frac{2\pi}{B}=Period \\ \frac{C}{B}=Phase\text{ shift} \\ D=Verical\text{ shift} \end{gathered}[/tex]Hence, the required function is-
[tex]y=6cos(x-\frac{2\pi}{3})+0[/tex]Final Answer: The function is-
[tex]y=6cos(x-\frac{2\pi}{3})[/tex]Hence, Option D is correct.
Sammy is 5 years younger than twice Lizzy's age. Sammy os 15 years old. How old is Lizzy?
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Answer:
Lizzy is 40
Step-by-step explanation:
15 + 5 + 20
20 x 2 = 40
Answer:
35
Step-by-step explanation:
15 x 2= 30 + 5=35
the five is because he is 5 years younger than lizzy
adding to her age
5
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2
If log₁/2x = -1, then the value of x is
a) 2
b) 1/2
c)-1
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The value of the variable 'x' in logarithmic expression is: 2
What is logarithm?
In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.
According to the question, the given logarithmic expression are as follows:
[tex]log_{1/2}x = -1[/tex]
Using standard logarithmic property, we get
x = (1/2)^-1
⇒x = 2
Hence, the logarithmic value of the variable 'x' is: 2
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solve for B 25+ 7/9=74
Answers
To solve this equation, we need to follow the next steps:
1. Subtract 25 to both sides of the equation:
[tex]25-25+\frac{7}{9}b=74-25[/tex][tex]\frac{7}{9}b=49[/tex]We obtained this result doing the corresponding operations (25 - 25 = 0), and (74 - 25 = 49).
2. Multiply by 9/7 to both sides of the equation:
[tex]\frac{9}{7}\cdot\frac{7}{9}b=\frac{9}{7}\cdot49\Rightarrow\frac{9}{9}\cdot\frac{7}{7}b=9\cdot\frac{49}{7}\Rightarrow b=9\cdot7\Rightarrow b=63[/tex]To check if the solution for this equation is b = 63, we can substitute this val
find the radius of the circle given the central angle and the area of the Shaded sector
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we have the following formula for the area of a sector of a circle:
[tex]A_s=\frac{\theta\cdot\pi}{360}\cdot r^2_{}[/tex]In this case, we have the following information:
[tex]\begin{gathered} A_s=60\pi \\ \theta=24\degree \end{gathered}[/tex]then, using the formula and solving for r, we get the following:
[tex]\begin{gathered} 60\pi=\frac{24\cdot\pi}{360}\cdot r^2 \\ \Rightarrow360\cdot60\pi=24\pi\cdot r^2 \\ \Rightarrow21600\pi=24\pi\cdot r^2 \\ \Rightarrow r^2=\frac{21600\pi}{24\pi}=900 \\ \Rightarrow r=\sqrt[]{900}=30 \\ r=30 \end{gathered}[/tex]therefore, the measure of the radius is r = 30
Find the domain and range of the following graph in interval notation. 5+ 4 3 2 1 -5 4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5+ a Domain: Range: NOTE: If you do not see an endpoint, assume that the graph continues forever in the same direction. Entry example: [2,3) or (-00,5). Enter -oo for negative infinity and oo for infinity.
Answers
The domain of the function of the graph is the set of all x values of the graph for which the function is defined.
The range of the function is the set of all y values shown in the graph.
Hence, the domain is (-∞, ∞)
The range is (-∞, 0].
A total of $7000 is invested: part at 7 % and the remainder at 15 %. How much is invested at each rate if the annual interest is $510?
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The total invested = $7000
Part of the money at 7% and the reminder at 15%
Let the part at 7% = x
So, the part at 15% = 7000 - x
Given the annual interest = $510
so,
7% of x + 15% of ( 7000 - x ) = 510
0.07 * x + 0.15 * ( 7000 - x ) = 510
0.07 x + 0.15 * 7000 - 0.15 x = 510
0.07 x + 1050 - 0.15x = 510
0.07 x - 0.15 x = 510 - 1050
-0.08 x = - 540
divide both sides by -0.08
x = -540/-0.08 = 6,750
7000 - x = 7000 - 6750 = 250
So, the part that is invested at a rate of 7% = $6,750
And the part that invested at a rate of 15% = $250