The longer leg of the right triangle is 8 more than the shorter leg. The hypotonuse is 8 more than the longer leg. FInd all 3 sides
Answer:
4[tex]\sqrt{13}[/tex]
4[tex]\sqrt{13}[/tex] + 8
4[tex]\sqrt{13}[/tex] + 16
Step-by-step explanation:
as per the given information:
shorter leg = x
longer leg = x + 8
hypotonuse = x + 8 + 8
remember the Pythagorean theorem, which states
x^2 + y^2 = n^2
where x and y are the legs and n is the hypotenuse
so now one can set up an equation:
x^2 + ( x + 8 )^2 = ( x + 16 ) ^2
simplify and solve using inverse operations:
first preform the square
x^2 + x^2 + 16x + 64 = x^2 + 32x + 256
then preform inverse opertations and simplify
2x^2 + 16x + 64 = x^2 + 32x + 256
-x^2 -x^2
x^2 + 16x + 64 = 32x + 256
-16x -16x
x^2 + 64 = 16x + 256
- 64 -64
x^2 = 16x + 192
-16x -16x
x^2 - 16 = 192
x^2 -4^2 = 192
remember the differnt ways of writing a special square
(x - 4) (x + 4) = 192
x = 4[tex]\sqrt{13}[/tex]
now add 8 to find the longer leg
4[tex]\sqrt{13}[/tex] + 8
an add another 8 to find the hypotenuse
4[tex]\sqrt{13}[/tex] + 8 + 8
4[tex]\sqrt{13}[/tex] + 16
Communities A,B and C are faced with acute water problem. The distance between communities A and B is 5km and that of A and C 7km. The angle between path AB and AC is 45degrees. If a well is dug for the three communities such that it would have equal distance to the path linking each communities. (a) Indicate by a way of sketching the exact place to dig the well? (b) Measure the distance between communities B and C?
Answer:
a) by finding the incentre
b) 5 km
Step-by-step explanation:
Let the communities A, B and C be shown by the three points of the triangle as shown in the figure below. As the angle between the path Ab and Ac is 45 degrees this is an isosceles triangle having two angles equal. As this is an isosceles triangle it must also have two sides equal .
a) the in center point can be used to have equal distance to the path linking each communities.
We take a compass and draw arcs on the two sides of the vertex and placing the compass on the arcs bisect each angle made by the triangles arms.
Joining the bisectors the lines meet at a point which is highlighted by a circle in the diagram.
This is the incentre which is equidistant from each vertex.
b) Using Pythagorus theorem
c² = a² + b²
7²= 5² + b²
b²= 24
b= 4.89= 5 km
The path between B and C is also 5 km.
−5(3p+3)+9(−7+p) please solve this help.
iinstall microsoft math and do you task
Donner un encadrement d’amplitude 10^-p des réels donner, l’entier p étant précisée pour chaque cas
Solve the equation, justify
each step with an algebraic
property.
10 + 8x = -78
Answer:
x=-11
Step-by-step explanation:
10+8x=-78
minus 10 from both sides
8x= -88
-88/8 = -11
x= -11
Answer:
Your answer is: x = -11
Step-by-step explanation:
Hope this helped : )
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!!!!!!
Answer:
$1.30
Step-by-step explanation
yup its 100% sure
can u brainliest i really need it
:) <3
Solve for q.
HEELLPP
When do you use a Vertex Form y=a(x – h)2 + k ? What information do you get from a Vertex Form?
Answer:
The vertex
Step-by-step explanation:
Vertex form shows you the vertex of a quadratic equation.
the y coordinate of the point is determined by k.
the x coordinate is determined by:
(x-h)=0
x-h=0
+h +h
x=h
Sum of twice a number and 15 is greater than 3
The number with the algebraic sum of its double and 15 is greater than 3 is described by; x > -6
From the question given;
The Sum of twice a number and 15 is greater than 3.In essence;
Let the number in discuss be; x so the we have;2x + 15 > 3By solving;
2x > 3 -152x > -12x > -6.Read more on inequalities;
https://brainly.com/question/14361489
Which of the following is arranged in the correct order?
A. |31| > |-41| > |-3| > |5|
B. |-41| > |31| > |5| > |-3|
C. |-41| > |31| > |-3| > |5|
D. |31| > |5| > |-3| > |-41|
Answer:
it's B.
Step-by-step explanation:
41>31>5>3
LOTS OF POINTS!!! HELP WITH 7 ANd EXPLAIN!!
Answer:
w=4
Step-by-step explanation:
The surface area of a prism is SA= 2lw+2lh+2hw
We are trying to find out the width if the SA is 240 square inches, length is 12 inches, and the height is 5 inches. Let's plug these numbers into the equation.
240=(2*12*w)+(2*12*5)+(2*5*w)
24w+120+10w
240= 34w+120
-120 -120
120= 34w
120/34 = 34w/34
w is approximately equal to 3.5 which can be rounded to 4
w=4
Hope this is right! It was confusing at first but I understood it!
Please help I don’t understand
Answer:
y = -2x+4
Exp:
Slope (m) =
ΔY
ΔX
=
-2
1
= -2
θ =
arctan( ΔY ) + 360°
ΔX
= 296.56505117708°
ΔX = 2 – 1 = 1
ΔY = 0 – 2 = -2
Distance (d) = √ΔX2 + ΔY2 = √5 = 2.2360679774998
Equation of the line:
y = -2x + 4
When x=0, y = 4
When y=0, x = 2
solve the equation. x^2+49=0
a.) no real solution.
b.) x= 7
c.) x= -7
d.) x= -7 and x= 7
Answer:
C
Step-by-step explanation:
-7 squared is -49, -49 plus 49 is 0.
sometime outiers can have a significant effect on statistics and sometime they don't . Use the following distribution to determine which statistics are affected by outliers. Round to the nearest hundredth.
Can someone double check this?
Answer:
you good my guy
Step-by-step explanation:
Triangle ABC is graphed in the xy-coordinate plane, as shown.
You may interact with the applet to help answer the questions,
Triangle ABC is reflected across the y-axis to form
AA'B'C'. What are the coordinates of B' after the
reflection?
А
B' (2, - 1)
A 6
5
B
B' (2, 1)
4.
С
B'(-2, 1)
3
С
2
D
B' (1, 2)
1
-8-7 -6 -5 -4 -:B
-1.
1
1 2 3 4
5 6 7
-2
-3
-4
-5
-6
-7
to
Answer:
that will be A
Step-by-step explanation:
Kenny had a total of 140 minutes to read, do homework, and play video games. he spent x minutes reading. he spent 2(x + 5) minutes doing homework and he spent 25 minutes playing video games. How many minutes did Kenny spent reading?
Answer:
35 min
Step-by-step explanation:
given that the total time spent is 140min
and that the time spent reading is x minutes
and also that the time spent doing home work is 2(x+5)
the time spent playing video game is 25
the expression for the total time is given as
total = reading +homework +video game
140=x+2(x+5)+25
solving for x we have
140=x+2x+10+25
140=3x+35
140-35=3x
105=3x
x=105/3
x=35
kenny spent 35 min reading
Time spend for reading is 35 minutes
Given that;
Total number of minutes Kenny have = 140 minutes
Time spend for reading = x
Time spend for homework = 2(x + 5) = 2x + 10
Time spend for games = 25 minutes
Find:
Time spend for reading
Computation:
Total number of minutes Kenny have = Time spend for reading + Time spend for homework + Time spend for games
140 = x + 2x + 10 + 25
3x + 35 = 140
3x = 105
x = 105 / 3
x = 35
So,
Time spend for reading = 35 minutes
Learn more:
https://brainly.com/question/23129403?referrer=searchResults
Which statement about the ordered pairs (3, -8) and (4, 4) is true for the equation 3x - y/4 = 11?
A. Neither ordered pair is a solution.
B. Both ordered pairs are solutions.
C. (4, 4) is a solution to the equation but not (3, -8).
D. (3, -8) is a solution to the equation but not (4, 4).
Answer:
Neither ordered pair is a solution.
Step-by-step explanation:
If we substitute an ordered pair which is the correct solution, we will obtain the value at the right hand side of the equation.
Now let us try it;
Substitute (3,-8)
3(3)-(-8)/4 = 9 +8/4 =17/4
Again;
3(4) - 4/4 = 8/4 =2
Hence, none of the ordered pairs is a solution.
Could someone help me out pls? I’m taking a test and I’d love help on this thanks <3
Answer:
AC = DE
Step-by-step explanation:
Which situation requires the use of the cube root?
A. Determine the surface area of a cube given the side
B. Determine the volume of a cube given the side
C. Determine the side of the cube given the volume
D. Determine the volume of a sphere given the radius
Answer:
C
Step-by-step explanation:
Mathematically, the volume of a cube of side L is given as;
V = L^3
Now, given V and we want to find L, what we shall simply do is to find the cube root of both sides
By finding the cube roots of both sides, we can easily get the value of the side of the cube in question
Anyone want to help me with math
Solve 1−2/5 < 5x+2/5−4x
Answer:x > 1/5
Step-by-step explanation:
Which value of x satisfies the equation |-2x|=10
Answer:
Step-by-step explanation:
First you will divide I-2xI on both sides that should look like this:
-2x/-2 = 10/-2
when you divide it your -2‘s should cancel out and you should be left with
-x=10/-2
when You divide 10/-2 you should get -5
10/-2= -5
your answer should look like this then
-x=-5
-5 is just one of your answers the other is 5
To get rid of the negative on the -X you have to didvide it by both sides
-x/-x=-5/-x
your answer should be
X= 5
your final answers are
-5 or 5
The value of x is "5".
Equation:[tex]|-2x|=10[/tex]
x=?
[tex]\to |-2x|=10\\\\\to 2x=10\\\\\to x=\frac{10}{2}\\\\\to x= 5[/tex]
Therefore, the final answer is "5".
Learn more about the equation here:
brainly.com/question/18681264
Which linear function has the same slope as the one that is represented by the table? x y Negative one-half One-fifth Negative one-fifth StartFraction 7 Over 50 EndFraction One-fifth StartFraction 3 Over 50 EndFraction One-half 0 y = negative one-half x + StartFraction 1 Over 10 EndFraction y = negative one-fifth x + one-half y = one-fifth x minus one-half y = one-half x minus StartFraction 1 Over 10 EndFraction
Answer:
B
Step-by-step explanation:
hope this helps
Answer:
B.
Step-by-step explanation:
Solve each system by using substitution
X= Y - 2 4X + Y = 2
Answer:
10
Step-by-step explanation:
Answer:
(0, 2 )
Step-by-step explanation:
Given the 2 equations
x = y - 2 → (1)
4x + y = 2 → (2)
Substitute x = y - 2 into (2)
4(y - 2) + y = 2
4y - 8 + y = 2
5y - 8 = 2 ( add 8 to both sides )
5y = 10 ( divide both sides by 5 )
y = 2
Substitute y = 2 into (1) for corresponding value of x
x = 2 - 2 = 0
Solution is (0, 2 )
Minute Math 10
Please help me.
Answer:
Step-by-step explanation:
1. False
2. True
3. False
4. 12/2, 8/8, 2^2
5. 0.375
6. Through the middle vertically
7. a
Which transformation can be used to accomplish this?
A. Dilation
B. Rotation
C. Reflection
D. Translation
Solve for f.
8 = 2f + 2
Answer:
f = 3
Step-by-step explanation:
8 = 2f + 2
-2 -2
6 = 2f
/2 /2
3 = f
What is the product of (-6)(-7)(-1)?
042
O-14
O 14
O 42
Answer:
-42
Step-by-step explanation:
(-6)(-7)(-1)
42(-1)
-42
(3x – 70)
(3y + 40)°
120°
X
Answer:
x=250
Step-by-step explanation:
Find the area of the isosceles triangle
Slope: 13cm
Base: 10cm
Answer:
65
Step-by-step explanation:
A=hbb
2=13·10
2=65