Answer:
x=[tex]\frac{3}{2}[/tex] and x=[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{36x^2-60x+25}=4[/tex]
=> [tex]\sqrt{36x^2-60x+25}^{2} =4^{2}[/tex]
=> [tex]{36x^2-60x+25}=16[/tex]
=> [tex]36x^2-60x+25-16=16-16[/tex]
=> [tex]36x^2-60x+9=0[/tex]
=> [tex]x_{1,\:2}=\frac{-\left(-60\right)\pm \sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}}{2\cdot \:36}\\\\\sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}=48[/tex]
=> [tex]x_{1,\:2}=\frac{-\left(-60\right)\pm \:48}{2\cdot \:36}[/tex]
=>[tex]x_{1} = \frac{-\left(-60\right)+48}{2\cdot \:36}\\\\x_{1}=\frac{60+48}{2\cdot \:36}\\\\x_{1}=\frac{108}{72} \\\\\\x_{1}=\frac{3}{2}\\[/tex]
=> [tex]x_{2}=\frac{-\left(-60\right)-48}{2\cdot \:36}\\\\x_{2} =\frac{60-48}{2\cdot \:36}\\\\x_{2}=\frac{12}{2\cdot \:36}\\\\\x_{2}=\frac{12}{72}\\\\x_{2}=\frac{1}{6}[/tex]
Two similiar rectangles have corresponding sides in the ratio 10:3. What is the ratio of their areas
Answer:
Step-by-step explanation:
The ratio of its areas is equal to
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem the scale factor is equal to the ratio 10:3
Let
z-------> the scale factor
so
z2=(10/3)2=100/9
Answer:
mee:)
Step-by-step explanation:
f;kn ef
The second hand on a clock is
8 cm long.
What is the distance the tip of the second hand travels in 10 minutes?
Answer:
8.37 cm rounded
Step-by-step explanation:
C = 2π r
C = 2π (8)
C = 16 π
C = 50.24
1/6 ( 50.24)= 8.37
Find the equation of the line through the points (-5,11) and (2,-3)
y=
Answer:
y = -2x + 1
Step-by-step explanation:
y2 - y1 / x2 - x1
-3 - 11 / 2 - (-5)
-14/ 7
= -2
y = -2x + b
-3 = -2(2) + b
-3 = -4 + b
1 = b
QUICK! WHAT IS THIS ANSWER?
Answer:
a)2x-3y
b)4(9a-4)
Step-by-step explanation:
a)we want to expand the following expression:
[tex] \displaystyle - \frac{1}{4} ( - 8x + 12y)[/tex]
well to do so we consider distributive property thus distribute:
[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y)[/tex]
reduce fraction which yields:
[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y) \\ \\ \displaystyle 2x + ( - 3y)[/tex]
simplify Parentheses:
[tex] \displaystyle \boxed{ 2x - 3y}[/tex]
b)in the expression there's a common factor of 4 therefore factor it out:
[tex] \displaystyle 9.4a - 4.4 \\ \\ \displaystyle \boxed{4(9a - 4)}[/tex]
If the two legs of a right triangle are 15 and 20, how long is the hypotenuse?
Answer:
25
Step-by-step explanation:
To solve this problem, you can use the pythagorean theorem, which is a^2 + b^2 = c^2 where a and b are legs and c is the hypotenuse. We can plug in the values of 15 and 20, and solve for c:
15^2 + 20^2 = c^2
225 + 400 = c^2
625 = c^2
c = 25
This means the hypotenuse is 25.
Question 2 of 10
What is the length of MN?
M
4x
x + 3
250"
50
N
A. 4
o
B. 1
C. 7
ОО
D. 8
Answer:
4
Step-by-step explanation:
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
The measurement of MN side is 4
What are the properties of Triangle?The properties of the triangle are:
1. The sum of all the angles of a triangle (of all types) is equal to 180°.
2. The sum of the length of the two sides of a triangle is greater than the length of the third side.
3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
Since the base angles are the same, the side have to be the same
ML = MN
4x = x+3
Subtract x from each side
4x-x = x+3-x
3x= 3
Divide by 3
3x/3 = 3/3
x = 1
We want the length of MN
MN = x+3 = 1+3 = 4
Learn more about triangles here:
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A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.
If you spin this spinner 1000 times, how many times do you expect it to land on Red?
(Hint: Find n first)
Answer:
83 times.
Step-by-step explanation:
n + 3n + 8n = 240
12n = 240
n = 20.
So we have 20 reds in 240 spins
So by proportion the number expected in 1000 spins
= 20 * 1000/240
= 1000/12
= 83 1/3
So its 83 reds.
ahmed is sitting on a dock watching a float plane in a harbour. At a certain time, the plane is 350 m above the water and 470 m from Ahmed. Determine the angle of elevation of the plane measured from Ahmed, to the nearest degree
Answer:
The angle of elevation of the plane measured from Ahmed is approximately 36.67°
Step-by-step explanation:
The given parameters of the float plane are;
The height of the float plane above the water, y = 350 m
The horizontal distance of the float plane from Ahmed, x = 470 m
Given that Ahmed is sitting on the dock, by the water, by trigonometric ratios, we have;
The height of the float plane, the distance of the plane from Ahmed and the line of sight forming the angle of elevation of the plane measured from Ahmed, form a right triangle
[tex]tan\angle X = \dfrac{Opposite \ leg \ length}{Adjacent \ Leg\ length}[/tex]
Therefore
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
Where;
θ = The angle of elevation of the plane measured from Ahmed
y = The leg of the right triangle opposite the reference angle
x = The leg of the right adjacent to reference angle
Therefore;
θ = arctan(y/x) which gives;
θ = arctan(350/470) ≈ 36.67°
The angle of elevation of the plane measured from Ahmed, θ ≈ 36.67°.
What is the area of trapezoid DEFG with coordinates D (4, 3), E (4, 0), F (2, 1), and G (2, 3)?
10 square units
5 square units
3 square units
2 square units
The area of the trapezoid is 10 square units
How to find the area of a trapezoid?The formula for finding the area of the trapezoid is expressed as:
A = 0.5(a+b)h
where:
a and b are the sides
h is the height
Given the following
a = 3
b = 2
h = 4
Determine the requried volume of the trapezoidSubstitute
A = 0.5(3 + 2)*4
A = 0.5(20)
A = 10 square units
Hence the area of the trapezoid is 10 square units
Learn more on area of trapezoid here: https://brainly.com/question/1463152
Answer:
B) 5 Square Units
Step-by-step explanation:
Answered from another colleague :)
B1 = 2
B2 = 3
H = 2
A = 1/2 (B1 + B2) H
1/2 (2+3) 2
1/2 (5) 2
(2.5)2
5
see screenshot below
Answer:
[tex] \displaystyle B) {x} = \log_{6} 118[/tex]
Step-by-step explanation:
we would like to solve the following exponential equation:
[tex] \displaystyle 2 \cdot {6}^{x} = 236[/tex]
to do so divide both sides by 2 which yields:
[tex] \displaystyle {6}^{x} = 118[/tex]
take log of base 6 in both sides so that we can solve the equation for x by using [tex]\log_ab^c=c\log_ab[/tex] and that yields:
[tex] \displaystyle \log_{6} {6}^{x} = \log_{6} 118[/tex]
use the formula:
[tex] \displaystyle {x} = \log_{6} 118[/tex]
hence,
our answer is B)
Answer:
[tex]\boxed{\sf Option \ B }[/tex]
Step-by-step explanation:
A equation is given to us and we need to find out the value of x . The given equation is ,
[tex]\sf\dashrightarrow 2 \times 6^x = 236 [/tex]
Transpose 2 to RHS , we have ,
[tex]\sf\dashrightarrow 6^x = \dfrac{236}{2} [/tex]
Simplify ,
[tex]\sf\dashrightarrow 6^x =118 [/tex]
Use log both sides with base "6"
[tex]\sf\dashrightarrow log_6 ( 6^x) = log_6 118 [/tex]
Using the property of log ,
[tex]\sf\longmapsto \bigg\lgroup \red{\bf log_p q^r = r log_p q}\bigg\rgroup[/tex]
[tex]\sf\dashrightarrow x \ log_6 6 = log_6 118 [/tex]
Again we know that ,
[tex]\sf\longmapsto \bigg\lgroup \red{\bf log_p p= 1}\bigg\rgroup[/tex]
We have ,
[tex]\sf\dashrightarrow x \times 1 = log_6 118 [/tex]
Therefore ,
[tex]\sf\dashrightarrow\boxed{\blue{\sf x = log_6 118 }} [/tex]
Hence option B is correct .
Brian can type 50 words per minute. He needs to finish typing his 700-word essay and already has 375 words typed. Write and solve an equation to determine the number of minutes (m) that it will take Brian to finish writing his essay. (Round your answer to the nearest tenth)
What is the midpoint of AB?
A
F GHI
B
+
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
3 4 5 6 7
5 6 7 8 9
+
+
point F
point G
point H
O point
Answer:
the answer is point G
It is found that Point G is the midpoint of AB.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
We are Given two points A and B which are located at -6 and 8 on the number line. We need to find the midpoint of AB.
First we have to calculate the distance between AB which can be calculated as;
8-(-6)=14 units
Now, to find the midpoint we have to divide the total distance by 2.
Hence, the mid point of AB is 7 units apart from both points A and B then G.
Learn more about midpoint here;
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ANSWER ASAP ILL MARK BRAINLIEST!!! if the vertex of a parabola is (-1,-9) what is the equation of the axis of symmetry?
Answer:
x = -1
Step-by-step explanation:
the equation of the axis of symetry =>
x = -1
We have to find,
The equation of the axis of symmetry.
The answer will be,
→ x = -1
Therefore, this is the equation.
Can someone help me with this math homework please!
9514 1404 393
Answer:
(-1, 1)
Step-by-step explanation:
Find the differences between an f(x) value and the previous one
3 -18 = -15
0 -3 = -3
3 -0 = 3
6 -3 = 3
3 -6 = -3
Where the differences are positive, the function is increasing on the interval. Here, it is increasing on the intervals (-1, 0) and (0, 1). Then the longest increasing x-interval is (-1, 1).
Y=1/3mx^3 – (m–1)x^2 + 3(m–2)x +1/3
Answer:
not true
Step-by-step explanation:
i just wants points mate
please help!! i have no idea!
Answer:
θ = 60.34
Step-by-step explanation:
[tex]\frac{\left(12.8\cdot \:sin\left(90\right)\right)}{sin\left(52.3\right)}[/tex] = 16.177
[tex]\frac{\left(16.177\cdot \:sin\left(90\right)\right)}{18.6}[/tex] = θ = .869
[tex]arcsin\left(.869\right)[/tex] = 60.34
Answer:
60.4°
Step-by-step explanation:
There are two right triangles.
One right triangle (on the left side) has an acute angle measuring 52.3°.
Its opposite leg measures 12.8 cm.
We can find the length of its hypotenuse, x.
sin 52.3° = opp/hyp
sin 52.3° = 12.8 cm/x
x * sin 52.3° = 12.8 cm
x = 12.8 cm/sin 52.3°
x = 16.2 cm
Now we use the hypotenuse of the left side triangle which is a leg of the right side triangle.
For the right side triangle, we are looking for angle Θ. We know the opposite leg, 16.2 cm and the hypotenuse, 18.6 cm.
sin Θ = opp/hyp
sin Θ = 16.2/18.6
sin Θ = 0.8698
Θ = sin^-1 0.8698
Θ = 60.4°
(4 x 10 ^ 7) ÷ (8 x 10 ^ 4) in standard form PLZ ANSWER QUICK
Answer:
4.67×10
4
=4.67×10000=46700
[tex]4.67 \times {10}^{4} [/tex]
[tex] = \: 4.67 \times 1000[/tex]
[tex] = \: 46700[/tex]
Which expression is equivalent to
8x^7y^8? Assume x>0.
Answer:
2x^3y^3Sqrt2 is the expression
Quanto falta para a fração 8/6 chegar a 2 inteiros? respondem rapido pfv
Answer:
4/6
Step-by-step explanation:
8/6 + 4/6 = 12/6
12/6 = 2.
Which of the following is a statement? (a) The fishes are beautiful (b) Study mathematics. (c) x is a capital of country y. (d) Water is essential for health.
Answer:
its letter a
Step-by-step explanation:
I hope you help
Two-Fifths of a number is 48. What is 3/4 of the SAME number?
Need help urgently
Answer:
[see below]
Step-by-step explanation:
"Two-Fifths of a number is 48."
(2/5)n = 48
((2/5n)(5/2) = 48 *(5/2)
n = 120
------------------------------------
120 * (3/4) = 90
Hope this helps you.
Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
]
Answer:
im not completely sure if the question is just asking how many gallons of gas berto is able to buy but if it is than he is able to buy 3.2 gallons of gas
Step-by-step explanation:
just do how much money he has divided by how much gas costs to see how much gas he will be able to buy
Answer: (3.2, 12)
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Quadrilateral LMNO is a rectangle. Find MN.
A.
7
B.
10
C.
18
D.
27
Answer:
there is no diagram ......
Plz help : ) I don't understand
Write the ratio:
0.15
to
0.6
as a fraction in lowest terms.
Answer:
The ratio 15 : 60 can be reduced to lowest terms by dividing both terms by the GCF = 15 :
15 : 60 = 1 : 4
basically 1/4
Step-by-step explanation:
Make x the subject of the formula
mx=y
(-6)+(-1)+4+9+...+64 sequence
Answer:
n
Step-by-step explanation:
hb
What is the minimum perimeter of a rectangle with an area of 625 mm^2
Question 2 options:
100 mm
125 mm
156.25 mm
312.5 mm
Show your work:
Answer:
100 mm
Step-by-step explanation:
Square root the area to find the length of each side
[tex]\sqrt[]{625} =25[/tex]
Multiply 25 by 4 to get the sum of all four sides for the perimeter
25 x 4 = 100
How many solutions does-3x = -x – 2x have?
Answer:
infinite solutions
Step-by-step explanation:
-3x = -x – 2x
Combine like terms
-3x = -3x
Add 3x to each side
-3x+3x = -3x+3x
0 =0
This is always true so there are infinite solutions
using trig solve for the missing angle
Answer:
The answer is 26.4
