Answer:
m<x = 48
m<y = 132
Step-by-step explanation:
Since x and y are supplementary angles, that means their sum is 180 degrees.
And we are given that y is 12 less than 3 times the measure of x. With this information we can make a system of linear equations.
x + y = 180
y = 3x - 12
So now plug in the value of y into the first equation.
x + y = 180
x + (3x - 12) = 180
x + 3x = 192
4x = 192
x = 48
And then plug this computed value of x back into the first equation to find the measure of y.
x + y = 180
48 + y = 180
y = 180 - 48
y = 132
So the measures of the angles are as follows:
m<x = 48
m<y = 132
Cheers.
Find the sum of 1st 50 odd natural numbers
[tex] \Large{ \boxed{ \mathbb{ \pink{SOLUTION:}}}}[/tex]
The AP would be like:
1, 3, 5, 7........[50 terms]Now,
➝ First term = 1
➝ Common difference = 2
➝ No. of terms = 50
By using formula,
[tex] \large{ \boxed{ \rm{S_n = \frac{n}{2} \bigg(2a + (n - 1)d \bigg)}}} [/tex]
Here,
a = First termn = number of termsd = common difference Sn = sum of n termsProceeding further,
➝ S50 = 50/2{ 2 × 1 + (50 - 1)2 }
➝ S50 = 25{ 2 + 49 × 2 }
➝ S50 = 25{ 100 }
➝ S50 = 2500
⛈️ Sum of 50 terms of AP = 2500
Shortcut trick:- n^2
Then, Sum of 50(n) terms = 50^2 = 2500
☘️ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
Answer:
2500
Step-by-step explanation:
The Sum of First 50 Odd Natural Numbers:
1+3+5+7+9+11+13+15+17+19+21+23+25+27+29+31+33+35+37+39+41+43+45+47+49+51+53+55+57+59+61+63+65+67+69+71+73+75+77+79+81+83+85+87+89+91+93+95+97+99
= 2500
The perimeter of a rectangle can be found using the equation P=2L + 2W , where P is the perimeter, L is the length, and W is the width of the rectangle. Can the perimeter of the rectangle be 60 units when its 11 units and its length is 24 units?
Step-by-step explanation:
From the question
Perimeter = 2L + 2W
L = 24 units
W = 11 units
Substitute the values into the above formula
That's
P = 2(24) + 2(11)
P = 48 + 22
P = 70 units
Therefore the perimeter of the rectangle cannot be 60 units since the values when substituted into the above formula will give us 70 units
Hope this helps you
Can someone help me on Domain and Range
Answer:
Its the second option.
Step-by-step explanation:
The domain and range are just the x (domain) and y (range) values
A rectangular prism is 12 cm long, 6 cm wide, and 5 cm high.
What is the volume of the rectangular prism?
O A. 23 cubic cm
B. 72 cubic cm
C. 162 cubic cm
D. 360 cubic cm
Answer:
D. 360 cubic cm.
Step-by-step explanation:
The volume = l * w * h
= 12 * 6 * 5
360 cu cm.
The volume of the rectangular prism is 360 cubic cm
A rectangular prism is a three-dimensional shape. It also known as a cuboid.
Characteristics of a rectangular prism
It has six faces. Opposite sides are identical It has 12 sides It has 6 verticesVolume = length x width x height
12 x 6 x 5 = 360 cubic cm
A similar question was solved here: https://brainly.com/question/12449923?referrer=searchResults
The area of a rectangle is 180 square centimeters. If the length of the rectangle is 15 cm, what is its width?
Answer:
[tex]width=12[/tex]
Step-by-step explanation:
The formula for the area of a rectangle:
[tex]Area=length*width[/tex]
Insert the known values:
[tex]180=15w[/tex]
Solve for w. Isolate the variable by dividing both sides by 15:
[tex]\frac{180}{15}=\frac{15w}{15} \\\\12=w[/tex]
w is equal to 12, so the width of the rectangle is 12 cm.
:Done
please answer will mark brainliest need to find the slope!
Answer:
0.3
Step-by-step explanation:
please give an answer Rationalise the denominator and find the values of a and b. 7−4√3/7+4√3 = a + b √3
Answer:
a = 97, b = - 56
Step-by-step explanation:
Given
[tex]\frac{7-4\sqrt{3} }{7+4\sqrt{3} }[/tex]
To rationalise multiply numerator/ denominator by the conjugate of the denominator.
The conjugate of 7 + 4[tex]\sqrt{3}[/tex] is 7 - 4[tex]\sqrt{3}[/tex]
= [tex]\frac{(7-4\sqrt{3})(7-4\sqrt{3}) }{(7+4\sqrt{3})(7-4\sqrt{3}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{49-28\sqrt{3}-28\sqrt{3}-48 }{49-48}[/tex]
= [tex]\frac{97-56\sqrt{3} }{1}[/tex]
= 97 - 56[tex]\sqrt{3}[/tex]
with a = 97 and b = - 56
Answer:
a = 97, b = - 56
Step-by-step explanation:
Simplify the following expression. (3m/4-2)+8
A. 8m/4
B. 9m/4
C. 3m+24/4
D. 3m+28/4
Answer:
C. 3m+24/4
Step-by-step explanation:
Given that (3m/4 - 2) + 8
Then we solve
= (3m/4 - 8/4) + 8
= (3m - 8)/4 + 32/4
= (3m - 8 + 32)/4
= 3m + 24 /4
Therefore the answer is C
Alternatively, we can simplify the equation by
Given that, the equation is ( 3m/4 - 2 ) + 8
We then remove parenthesis
= 3m/4 - 2 + 8
= 3m/4 + 6
= 3m/4 + 24/4
Then add the numerators and leave the denominator
= 3m + 24 /4
This also equals option C.
Hence, it can be concluded that, the correct answer is Option C: (3m + 24)/4
Square root of 4489 by division method
Consider first two digits and then the next two digits.If there are three digits in the given number then first consider the first digit and then the take two digits together
6 | 4489 | 6x
36
12x | 889 |
Now the number 889 has 9 in units place so take a share number which has 9 at the end (ex.3*3=9 and 7*7=49)
So put 7 in the place of x and multiply the x value with 12x(that is 127) u will get the remainder as 0
Therefore the square root of 4489 is 6x*6x i.e. 67*67=4489
A shopkeeper gained Rs 8 by selling a pen by allowing 10% discount. Hw would have gained Rs 20, if he had not allowed discount. What was the cost price of the pen?
Answer:
Cost of the pen = Rs.100
Step-by-step explanation:
Let the marked price = x
When the shopkeeper is selling for x, his gain = Rs. 20
Cost price = Marked price - Gain = x - 20 --------(I)
After discount:
Discount = 10%
Marked price after discount = (100 - 10)% of x = 90% of x
= 0.9 * x = 0.9x
When the shopkeeper is selling for 0.9x, his gain = Rs.8
Cost price = Marked price - gain = 0.9x - 8 -------(II)
From (I) and (II)
x - 20 = 0.9x - 8
x = 0.9x - 8 + 20
x = 0.9x + 12
x - 0.9x = 12
0.1x = 12
x = 12/0.1
x = 120
Marked price of pen = Rs.120
Cost price = 120 - 20
Cost price = Rs. 100
Simplify the expression.
-50 + 3r + 50 - 3r
Answer:
0
Step-by-step explanation:
Group like terms= 3r-3r-50+50
Add similar elements= -50+50
Answer=0
I hope this helps!
The inverse of f(x) is a function A.true B.false
Answer:
True
Step-by-step explanation:
Answer:
A. True
Step-by-step explanation:
The graph passes the horizontal line test, so the inverse relation is a function.
__
The horizontal line test requires any horizontal line intersect the graph in at most one place.
find the equation of the line perpendicular to the line x=9 that passes through the point (9,-1)
Answer:
y = -1
Step-by-step explanation:
Notice that the line x = 9 is a vertical line, therefore a line perpendicular to it will be a horizontal line of the form y = constant number.
Since we want it to go through the point (9, -1), then we know that that y value needs to be "-1", and the equation of the line will be given by the expression:
y = -1
Answer:
y =1
Step-by-step explanation:
[tex](9,-1)=(x ,y)\\\\x =m_1 =9\\m_2 = \frac{-1}{m_1} = \frac{-1}{9} = -\frac{1}{9} \\\\Substitute \:the \:values\:into ;\\y =mx+b\\\\-1 =-\frac{1}{9} (9) +b\\-1 = -1+b\\-1+1 = b\\0 =b\\m= 1 \\Substitute\:the\:new\:values\:into ;\\y = mx+b\\y = 1 x +0\\ y= 1[/tex]
A fashion designer created a sketch of a square scarf. The design has one large triangle and two congruent smaller triangles. The shaded portion shows the part made from red silk. The sketch of the scarf has a scale of 5 inches = 3 feet. How much red silk does the fashion designer need to make the scarf? which i the answer : 2.25 ft2 4.5 ft2 6.25 ft2 12.5 ft2
Answer:4.5 ft squared
Step-by-step explanation:
3*1.5/2=4.5
explanation:
Answer:
my name is yeff
Step-by-step explanation:
What is the solution to this equation?
X/5 = 15
A. x = 10
B. x = 75
C. X = 3
D. x = 20
Answer:
B. x=75
Step-by-step explanation:
First, write out the equation as you have it:
x/5=15
Then, multiply both sides of the equation by 5/1:
5/1(x/5)=15(5/1)
Your result is:
x=75
Answer:-75 on a pex quiz 1.4.3
Step-by-step explanat
The engineers who designed an arch used the function h(x) = -0.005061x^2 + 0.499015x to describe the height of the arch (h) a distance of x from each end. Determine the distance between the ends of the arch, and the height of the arch.
Answer:
1) The distance between the ends of the arch is approximately 98.6
2) The eight of the arc is approximately 12.3
Step-by-step explanation:
1) The function for the height of the arch, h(x) = -0.005061·x² + 0.499015·x
Where;
x = The distance from the ends of the arch = 0, which gives;
0 = -0.005061·x² + 0.499015·x
Factorizing the above equation, we get;
0 = x·(-0.005061·x + 0.499015)
Which gives;
x = 0 or (-0.005061·x + 0.499015) = 0
-0.005061·x + 0.499015 = 0 gives;
-0.005061·x = -0.499015
x = -0.499015/(-0.005061) ≈ 98.6
Therefore, the height of the arch is zero at distance x = 0 and x = 98.6
Which gives the distance between the ends of the arch = 98.6
2) The height of the arc function h(x) = -0.005061·x² + 0.499015·x, whereby the coefficient of x² is negative, shows that it is ∩-shaped, the coordinates height and therefore, the height, is given by equating the derivative of the function to zero as follows;
d(h(x))/dt = d(-0.005061·x² + 0.499015·x)/dt = 2×(-0.005061)×x + 0.499015
d(h(x))/dt = 0 gives;
2×(-0.005061)×x + 0.499015 = 0
x = -0.499015/(2×(-0.005061)) ≈ 49.3
Therefore, the height of the arc, is the height at the point where x = 49.3
Therefore, we find the height of the arc from the height equation as follows;
h(x) = -0.005061×(49.3)² + 0.499015×49.3 ≈ 12.3
The eight of the arc is approximately 12.3.
Two points in a rectangular coordinate system have the coordinates (5.5, 2.9) and (−3.5, 4.8), where the units are centimeters. Determine the distance between these points.
Answer:
The distance between these points is approximately is 9.198 units.
Step-by-step explanation:
Let be (5.5, 2.9) and (-3.5, 4.8) the location of the points in Cartesian plane. The straight line distance between both points ([tex]d[/tex]) is determined by the Pythagorean Theorem, which is described below:
[tex]d = \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex]
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Horizontal components of each point, dimensionless.
[tex]y_{A}[/tex], [tex]y_{B}[/tex] - Vertical components of each point, dimensionless.
If [tex]A = (5.5, 2.9)[/tex] and [tex]B = (-3.5,4.8)[/tex], the distance between these points is:
[tex]d = \sqrt{(-3.5-5.5)^{2}+(4.8-2.9)^{2}}[/tex]
[tex]d\approx 9.198[/tex]
The distance between these points is approximately is 9.198 units.
not so good with mathematics
Answer:
2n-7
Step-by-step explanation:
the product of 2 and a number is 2 times a number, so number is n. (this is multiplicaiton) it then becomes 2n. 7 less than that is 2n-7. (If it's less than, it goes after the variables 2n)
Explanation:
7 less --> -7
product of 2 and a number --> 2x
Answer:
2x-7
I hope this Helps!!
Solve for b
4b+8=3b
B=?
Answer:
[tex]\huge\boxed{b=-8}[/tex]
Step-by-step explanation:
[tex]4b+8=3b\\\\4b+8-8=3b-8\\\\4b=3b-8\\\\4b-3b=3b-3b-8\\\\\boxed{b=-8}[/tex]
Answer:
b = -8
Step-by-step explanation:
4b+8=3b
Subtract 4b from each side
4b-4b+8=3b-4b
8 = -b
Multiply each side by -1
-8 = b
Please answer this question I will mark you the brainlest
please ............☺️☺️
Answer:
Hope it helps u .
mark as brainlist
An opera house has a seating capacity of 872 people with each ticket costing 50 Rupees .If the opera house is running for 15 days ,how much money will it make?
Answer:
654000 Rupees
Step-by-step explanation:
If we assume that the opera house was full every day then it would be 872 x 50 for the price of 1 day
872 x 50 = 43600
We multiple that number by the amount of days open so is would be 43600 x 15
43600 x 15 = 654000
Therefore it will make 654000 Rupees
1. Five times a whole number x is subtracted from 62 The result is less than 40
Find the three lowest values
2. if 7.3 is subtracted from Y the results is less than 3,4 find the range of value of Y
3. solve the following equation
a.4b= 3 (3b+15)
b. 5( a+2)=4(a - 1)
Answer:
Step-by-step explanation:
1. Symbolically, we get: 62 - 5x < 40
2. y - 7.3 < 3.4. Solve for y by adding 7.3 to both sides, obtaining:
y < 10.7 This is both the 'range' and the 'solution'
3a) 4b = 9b + 45, or -5b = 45, or b = -9
3b) 5a + 10 = 4a - 4
Combining like terms results in a = -14
The thickness of one sheet of paper is 〖8 × 10〗^(-3)
Work out the thickness of 250 sheets of paper.
Answer:
1/2048 or 4.8828125*10^(-4)
Step-by-step explanation:
First, figure out the thickness of 1 sheet of paper in number format:
[(8*10)]^(-3)=(80)^(-3) or (1/(80)^(3))=1/512000
Now, multiply 1/512000 by 250 to find the thickness of 250 sheets of paper:
250(1/512000)=1/2048
In scientific notation, this is written as 4.8828125*10^(-4).
Find the distance between the points (0, 2) and (-9, -10).
Answer:
15
Step-by-step explanation:
OPTION 1:
We can use the distance formula to find the distance between these two points.
[tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
X2 is -9, X1 is 0, Y2 is -10, and Y1 is 2, so we can substitute inside the equation.
[tex]\sqrt{(-9-0)^2 + (-10-2)^2}\\\\\sqrt{9^2 + -12^2}\\\\\sqrt{81 + 144}\\\\\sqrt{225}\\\\15[/tex]
OPTION 2:
We can look at the change in x and the change in y and use the Pythagorean Theorem to find the missing length of the hypotenuse.
The x changes by 9, and the Y changes by 12.
[tex]a^2+b^2=c^2[/tex] is the Pythagorean Theorem. We know a and b, so we can substitute inside the equation.
[tex]9^2 + 12^2 = c^2\\\\81+144=c^2\\\\225=c^2\\\\c=15[/tex]
Hope this helped!
Answer: The distance is 15 units.
Step-by-step explanation:
Find the difference in the x and y coordinates and square them and add them together.
(0,2) and (-9,-10) The x coordinates are 0 and -9 and the y coordinates are 2 and -10.
0-(-9) = 9
2-(-10) = 12
9^2 + 12^2 = d^2
81 + 144 = d^2
225 = d^2
d = [tex]\sqrt{225}[/tex]
d= 15
Solve for "X"
16 = 9 + x - 3
Answer:
x = 10
Step-by-step explanation:
Step 1: Write out equation
16 = 9 + x - 3
Step 2: Combine like terms
16 = x + 6
Step 3: Subtract 6 on both sides
10 = x
Step 4: Rewrite
x = 10
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 10}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{16 = 9 + x - 3}[/tex]
Subtract 3 from
⇒[tex] \sf{16 = 6 + x}[/tex]
Swap the sides of the equation
⇒[tex] \sf{6 + x = 16}[/tex]
Move 6 to right hand side and change it's sign
⇒[tex] \sf{x = 16 - 6}[/tex]
Subtract 6 from 16
⇒[tex] \sf{x = 10}[/tex]
Hope I helped!
Best regards!!
f(x) = 17 - 2x
Find f(a + 7)
Answer:
-2a + 3
Step-by-step explanation:
We can substitute a + 7 for x:
f(a + 7) = 17 - 2(a+7) = 17 - 2a - 14 = -2a + 3
PLEASE HELP!! Which equation can be used to solve 2 6 0 1 * x1 x2 = 2 -3
Answer:
Equation :
[tex]\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}\0.5}&-3\\ 0&1\end{bmatrix}}\begin{bmatrix}2\\ -3\end{bmatrix}[/tex]
Step-by-step explanation:
To isolate the following matrix, we will have to divide either by matrix 1, or the co - efficient of the matrix shown below. By doing so we will have to take the inverse of the co - efficient of that same matrix on the other side. In other words,
[tex]\begin{bmatrix}x_1\\ x_2\end{bmatrix}[/tex] - Matrix which we have to isolate,
[tex]\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}2&6\\ \:0&1\end{bmatrix}^{-1}\begin{bmatrix}2\\ -3\end{bmatrix}[/tex] - Equation used to solve the matrix
Now as you can see this equation is not any of the given options. That is as we have to simplify it a bit further,
[tex]\begin{bmatrix}2&6\\ 0&1\end{bmatrix}^{-1} = \frac{1}{\det \begin{bmatrix}2&6\\ 0&1\end{bmatrix}}\begin{bmatrix}1&-6\\ -0&2\end{bmatrix} = \frac{1}{2}\begin{bmatrix}1&-6\\ -0&2\end{bmatrix} = \begin{bmatrix}\frac{1}{2}&-3\\ 0&1\end{bmatrix}[/tex]
We know that 1 / 2 can be replaced with 0.5, giving us the following equation to solve for x1 and x2,
[tex]\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}\0.5}&-3\\ 0&1\end{bmatrix}}\begin{bmatrix}2\\ -3\end{bmatrix}[/tex]
As you can see our solution is option d.
Answer: d
Step-by-step explanation: on edge
Mattie bought a piece of rope that was 10.8 yards long. She needs to cut 8 equal pieces. How long will each pie be?
Answer:
Your answer will be 1.35
5x-4=-3-x so ya can yall help
Step-by-step explanation:
5x-4=-3-x
5x+x=4+(-3)
6x=1
x=1/6
Answer:
[tex] \boxed{ \huge{ \bold{ \sf{x = 0.16}}}}[/tex]Step-by-step explanation:
[tex] \sf{5x - 4 = - 3 - x}[/tex]
Move constant to R.H.S and change it's sign
Similarly, Move variable to L.H.S and change it's sign
⇒[tex] \sf{5x + x = - 3 + 4}[/tex]
Collect like terms
⇒[tex] \sf{6x = - 3 + 4}[/tex]
Calculate
⇒[tex] \sf{6x = 1}[/tex]
Divide both sides of the equation by 6
⇒[tex] \sf{ \frac{6x}{6} = \frac{1}{6} }[/tex]
Calculate
⇒[tex] \sf{x = 0.16}[/tex]
Hope I helped!
Best regards!!
please help and leave answers
Answer:
The other guy got it
Step-by-step explanation
Answer:
[tex]\huge \boxed{\mathrm{36\sqrt{3} +72 \ mm^2}}[/tex]
Step-by-step explanation:
The height of the triangle is important to find the area of the rectangle.
We can split the triangle in half, we get a right triangle.
Apply Pythagorean theorem to solve for the height.
3² + b² = 6²
b² = 6² - 3²
b² = 36 - 9
b² = 27
[tex]b= 3\sqrt{3}[/tex]
The length of the rectangle is 3 + 3 + 3 + 3 = 12 mm
The width is 3 + [tex]3\sqrt{3}[/tex] + 3 = [tex]3\sqrt{3}+6[/tex] mm
The area of a rectangle is length × width.
[tex]12(3\sqrt{3}+6)[/tex]
Distribute.
[tex]36\sqrt{3} +72[/tex]
The area of the rectangle is [tex]36\sqrt{3} +72[/tex] mm².