Answer:
i) 2:1
ii) 1:3
iii) 5:4
Step-by-step explanation:
i) Male teachers : Female teachers
10 : 15-10
10 : 5
2 : 1
ii) Female teachers : Total teachers
5 : 15
1 : 3
iii) Do remember that two angles are called complementary if their measures add to 90 degrees.
Hence, ration of the pair of complementary angles = 50 : 90-50
= 50 : 40
= 5 : 4
Answer:
Step-by-step explanation:
Total number of teachers = 15
Given number of male teachers = 10
Therefore number of female teachers = 15 - 10 = 5
i)
Ratio of male and female teachers
[tex]\frac{male}{female} = \frac{10}{5} = \frac{2}{1}\\\\Ratio = 2 : 1[/tex]
ii)
Ratio of female teachers and total number of teachers
[tex]\frac{female}{total\ teachers} = \frac{5}{15} =\frac{1}{3} \\\\Ratio = 1 : 3[/tex]
iii)
If x and y are complementary angles, then x+ y = 90°
Given : one angle, x = 50°
Therefore, 50° + y = 90°
y = 90 - 50 = 40°
Ratio of the pair of complementary angles
[tex]\frac{x}{y} = \frac{50}{40} = \frac{5}{4} \\\\Ratio = 5 : 4[/tex]
Find the sum of the first 8 terms of the following series, to the nearest integer.
9
36,9,
4
Enter an equation in point-slope form for the line. (4, 4) and (-9, 4) is on the line..
Answer:
y=4
Step-by-step explanation:
it's a straight line on y=4
Help:
A) 3/4 + 1/7 =
B) 2/5 + 3/6 =
C) 2/5 - 1/4 =
D) -2/6 - (-1/3) =
E) 5 ½ + 6 ½ =
F) 8 ¾ + 4 ½ - 2 ¹/6=
G) 3/4 + 1/5 + 1/6 =
H) 8 ¾ + 4 ½ - 2 ¹/6 =
I) -3/12 - (-1/16) =
J) - 3/48 - (4/5) + 1/5 =
Answer:
A) 25/28
B) 9/10
C) 3/20
D) 0
E) 12
F) 11 1/12 (also as 133/12)
G) 1 7/60 ( also as 67/60)
H) 11 1/12 It's the exact same question as the other one sooo
I) -3/16
J) -53/80
Step-by-step explanation:
Just find the LCD and combine
Answer:
See below.
Step-by-step explanation:
A) 3/4 + 1/7 = 21/28 + 4/28 = 25/28
B) 2/5 + 3/6 = 12/30 + 15/30 = 27/30 = 9/10
C) 2/5 - 1/4 = 8/20 - 5/20 = 3/20
D) -2/6 - (-1/3) = -1/6 + 1/3 = 0
E) 5 ½ + 6 ½ = 5 + 6 + ½ + ½ = 12
F) 8 ¾ + 4 ½ - 2 ¹/6 = 8 + 4 - 2 + 9/12 + 6/12 - 2/12 = 10 13/12 = 11 1/12
G) 3/4 + 1/5 + 1/6 = 45/60 + 12/60 + 10/60 = 67/60 = 1 7/60
H) 8 ¾ + 4 ½ - 2 ¹/6 = 11 1/12
I) -3/12 - (-1/16) = -1/4 + 1/16 = -4/16 + 1/16 = -3/16
J) -3/48 - (4/5) + 1/5 = -15/240 - 192/240 + 48/240 = -159/240 = -53/80
An express train travel from A to B for 4 hours. A normal train travel from B to A for 10 hours. Both of them started at the same time. The average speed of the express train is greater than the average speed of the normal train 90km/h. Find the average speed of the normal train?
Answer:
The speed of the normal train is 60 kilometers per hour.
Step-by-step explanation:
Let suppose that both trains move at constant speed and cover the same distance. Then, we have the following identity:
[tex]v_{1}\cdot t_{1} = v_{2}\cdot t_{2}[/tex] (1)
Where:
[tex]v_{1}, v_{2}[/tex] - Average speeds of the express train and the normal train, in kilometers per hour.
[tex]t_{1}, t_{2}[/tex] - Travel times of the express train and the normal train, in hours.
In addition, there is the following relationship between average speeds:
[tex]v_{1} = v_{2} + 90[/tex] (2)
By (2) in (1), we have the following expression for the average speed of the normal train:
[tex](v_{2} + 90) \cdot t_{1} = v_{2}\cdot t_{2}[/tex]
[tex]90\cdot t_{1} = v_{2} \cdot (t_{2} - t_{1})[/tex]
[tex]v_{2} = \frac{90\cdot t_{1}}{t_{2}-t_{1}}[/tex]
If we know that [tex]t_{1} = 4\,h[/tex] and [tex]t_{2} = 10\,h[/tex], then the average speed of the normal train is:
[tex]v_{2} = 90\cdot \left(\frac{4\,h}{10\,h - 4\,h} \right)[/tex]
[tex]v_{2} = 60\,\frac{km}{h}[/tex]
The speed of the normal train is 60 kilometers per hour.
Which of the following statements describes the process for solving 4x ≥ -24?
A. Divide both sides of the inequality by 4 and flip the symbol.
B. Divide both sides of the inequality by -24 but don't flip the symbol.
C. Divide both sides of the inequality by 4 but don't flip the symbol.
D. Divide both sides of the inequality by -24 and flip the symbol.
Answer:
C. Divide both sides of the inequality by 4 but don't flip the symbol.
Step-by-step explanation:
When you solve an inequality, you have to get the x by itself. So, in this inequality, the first thing you would do is divide both sides of the inequality by 4. The new and solved equation would look like this:
x ≥ -6
Because multiplying by a negative, dividing by a negative, or having negatives on both sides of the inequality was not involved in solving for x, flipping the symbol is not needed.
I really hope this helps! Have an amazing day :3
PR and SU are parallel lines.
Which angles are alternate interior angles?
Answer:
Alternate interior angles are on opposite sides of the transversal, and between the parallel lines
Step-by-step explanation:
Which 3 expressions are equivalent to the
expression : 3x-12-2(x+12)
Answer:
second option , third option and last option
Step-by-step explanation:
3x - 12 - 2(x + 12)
=3x - 12 -2x - 24
=x - 36
Can I get some help please
Answer:
domain { -8,-5}
Range { -7,-1,1}
Step-by-step explanation:
The domain is the input values
{ -8,-5}
We do not list repeated values
The range is the output values
{ -7,-1,1}
Answer: domain { -8,-5}
Range { -7,-1,1}
Step-by-step explanation:
Which formula will correctly calculate the length of side, t, in the triangle?
Answer:
t = [tex]\sqrt{r^2 + s^2}[/tex]
Step-by-step explanation:
Below is the following calculation:
It is given that the one side of the triangle is t. Thus, let the other sides are "r" and "s". Thus, the best way to find the side of a triangle is to use the Pythagorean theorem. Here, let t is the hypotenuse.
Below is the formula:
t = [tex]\sqrt{r^2 + s^2}[/tex]
Mohamed and Miguel go to the movie theater and purchase refreshments for their friends. Mohamed spends a total of $18.25 on two bags of popcorn and three
drinks. Miguel spends a total of $27.50 for four bags of popcorn and two drinks.
a) Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
b) Using your system from part a), determine and state the price of one bag of popcorn and the price of one drink.
If pi is rounded to a whole number, what is a reasonable estimate for the circumference of a circle with a diameter of 18 cm?
57 cm
50 cm
54 cm
56 cm
Answer:
54 cm
Step-by-step explanation:
Hi there!
1) Round pi
π = 3.14159265...
Rounded to a whole number ⇒ 3
2) Determine the circumference
C = πd where d is the diameter
Plug in the diameter
C = 18π
Plug in π
C = 18(3)
C = 54
Therefore, a reasonable estimate for the circumference of this circle would be 54 cm.
I hope this helps!
What type of function is represented by the table of values below?
х
1
2
3
4
5
у
2
4
8
16
32
A. exponential
B. quadratic
C. cubic
D. linear
Answer:
Step-by-step explanation:
This is exponential. I'll show you how I found it. After many attempts at other types of functions, I realized the points were either forming a quadratic or an exponential. Definitely not a line.
the standard form of an exponential function is
[tex]y=a(b)^x[/tex] so we sub in coordinates from the table to determine what the equation is and then test it on another set of points to see if it works. Using the first coordinate of (1, 2):
[tex]2=a(b)^1[/tex] so
[tex]a=\frac{2}{b}[/tex] . The next coordinate is (2, 4), so:
[tex]4=\frac{2}{b}(b)^2[/tex] which simplifies down to
4 = 2b so
b = 2. Now we plug in 2 for b and solve for a:
a = 2/2 which is 1. So the equation, if this is exponential, is
[tex]y=1(2)^x[/tex] Let's test the next point in line and see if it works, (3, 8):
[tex]8?=?1(2)^3[/tex] and yes, 8 is equal to 2 cubed. And the next point says that 16 should equal 2 to the 4th, and it does, as well. So this is exponential...growth to be specific.
Find the volume of the composite solid below.
4 ft
3 ft
-
4 ft
10 ft
Answer:
173.3ft
Step-by-step explanation:
We'll start by the rectangle below
so remember the formula: l · w · h
10 · 4 · 3 = volume
volume = 120 ft
Rectangular pyramid
Volume = [tex]\frac{1}{3}[/tex] b · h
Volume = 1/3 40 · 4
Volume = 1/3 160
Volume = 53.3 ft
120 + 53.3 = 173.3 ft
A model with 1 shaded part and 3 unshaded parts. Write the unit fraction depicted in the model as a percent.
Answer:
shaded =25 %
un shaded = 75 %
Step-by-step explanation:
Total parts = 4
shaded part = 1
un shaded parts = 3
percentage of shaded part
[tex]=\frac{1}{4}\times 100 % = 25 %[/tex]
= 25 %
Percentage of un shaded parts
[tex]= \frac {3}{4}\times 100 = 75 %[/tex]
= 75 %
Find the surface area of
the prism.
12 in.
6 in.
5 in.
The surface area is in.2.
Answer:
324
Step-by-step explanation:
SA = 2 ( lw + hl + hw )
l = length
w = width
h = height
Given Dimensions
l = 6
w = 5
h = 12
* plug in to SA formula *
SA = 2 ( (6)(5) + (12)(6) + (12)(5) )
(6)(5) = 30
(12)(6) = 72
(12)(5) = 60
SA = 2 ( 30 + 72 + 60 )
30 + 72 + 60 = 162
SA = 2(162) = 324
If f(x)=2(x)2 +5w/(x+2)
(2) =
F(2)=
Answer:
16+5w/4
Step-by-step explanation:
There are five peanut brittle to every two chocolate if there is a box of 28 sweets how many cholocate are there
Answer:
8 chocolates
Step-by-step explanation:
im not really good at math and didnt use an equation but if you add 5 and 2 together until 28 and then count up how many 2's you added, you should get the answer! sorry if this isnt helpful <3
Use the Law of Sines. Find m2c to the nearest tenth.
с
35
30°
B
58
A
a. 124.0°
b. 162.4°
C.
56.0°
d. 17.6°
Answer:
Step-by-step explanation:
Set up the Law of Sines as follows:
[tex]\frac{sinC}{58}=\frac{sin30}{35}[/tex] and
[tex]sinC=\frac{58sin30}{35}[/tex] and
sinC = .8285714286 so
C = 56.0°
In the diagram below. De and Ef are tangent to 0. Which equation could be solved to find y, the measure of DGF? O A. ;(-127) = 53 OB. }(v + 127) = 53 O c. }(y-53) = 127 OD. } (x + 53) = 127
Answer:
A
Step-by-step explanation:
The tangent- tangent angle DEF is half the difference of the measure of the intercepted arcs , that is
[tex]\frac{1}{2}[/tex] (y - 127) = 53 → A
The intercepted arcs of y is 1/2(y -127) = 53.
What is intercepted arc?
The intercepted arc exists the arc that exists inside the inscribed angle and whose endpoints exist on the angle. The vertex of an inscribed angle can be anywhere on the circle as stretched as its sides intersect the circle to construct an intercepted arc.
Let, DE and EF exist as tangents to O.
The value of y will be evaluated as follows:
For angle created outside of circle by intersection:
Two tangents or two secants or a tangent and a secant, the formula for angle created outside will be:
An angle formed outside = 1/2(Difference of Intercepted Arcs)
An angle formed outside exists ∠DEF = 53°
Intercepted arcs exist y and 127°
Hence, 53 = 1/2(y -127)
Therefore, the correct answer is option C). 1/2(y -127) = 53.
To learn more about intercepted arcs refer to:
https://brainly.com/question/1626547
#SPJ2
PLEASE HELPP HELP I WOULD REALLY APPRECIATE IT THANK U
Answer:
33
Step-by-step explanation:
180 minus 114 minus 33
soln,
x°+114°+33°=180° ( because sum of all angles of triangles is equal to 180°)
or, x°+147=180°
or, x°=180°-147°
hence, x°= 33°
What is the surface area of the right cone below?
12&3 A P E X
Answer:
A
Step-by-step explanation:
A=πr(r+h2+r2)=π·3·(3+11.622+32)≈141.38125
What is the slope of the line whose equation is y-4=5/2(x-2)?
Answer:
5/2
Step-by-step explanation:
We know,
Equation of the slope is, y = mx + c. Where m is the slope.
y - 4 = 5/2*(x-2)
y = 5/2*(x-2) + 4
y = (5/2)x - 5 + 4
y = (5/2)x - 1
y = (5/2)x + (-1) [y = mx + c form]
Slope, m = 5/2
Hope this will help. Please mark me brainliest.
Simplify 52⋅(x−2)52⋅(x-2). Apply the distributive property. y−4=5/2x+5/2⋅−2 Combine 5252 and x
y−4=5x2+5/2⋅−2 Cancel the common factor of 2.Factor 2 out of −2
y−4=5x2+52⋅(2(−1))y-4=5x2+52⋅(2(-1))
Cancel the common factor.
y−4=5x2+52⋅(2⋅−1)y-4=5x2+52⋅(2⋅-1)
Rewrite the expression.
y−4=5x2+5⋅−1y-4=5x2+5⋅-1
Multiply 55 by −1-1.
y−4=5x2−5
Add 44 to both sides of the equation.
y=5x2−5+4y=5x2-5+4
Add −5-5 and 44.
y=5x2−1
Reorder terms.
y=52x−1
THE ANSWER IS M = 5/2
does anyone know how to do this
9514 1404 393
Answer:
y = -1/2x +4
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis, at y=4.
The slope is found by following the line to the right until it meets another grid line crossing point. That is 2 units to the right and down 1 unit.
The slope is ...
m = "rise"/"run" = -1/2
Then the slope-intercept equation is ...
y = mx + b . . . . . slope m, y-intercept b
y = -1/2x +4
b to the power of -3
write that as a positive exponent
explain
Answer:
1/b^3
Step-by-step explanation:
b^-3 is like writing:
1
---
b^3 since negative exponents are made into fractions
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Solve each equation. Leave the answer as an improper fraction.
16x2 = 49
NEXT QUESTION ASK FOR HELPTURN IT IN
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Answer:
Given : isosceles right triangle hypotenuse = 8 cm
To find : leg of isosceles right triangle
Solution
isosceles right triangle
Hence Perpendicular = base
Both legs are of Equal length
Applying Pythagoras theorem
Perpendicular² + base² = Hypotenuse²
Hypotenuse = 8 cm given
=> Perpendicular² + base² = 8²
Perpendicular = base = x
=> x² + x² = 64
=> 2x² = 64
=> x² = 32
=> x = 4√2
legs of isosceles right triangle whose hypotenuse is 8 cm
are 4√2 cm
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
If you know two corresponding sides of two triangles and you know that the corresponding angles are equal, how can you find out if they are similar triangles?
a.
the other angles are proportional
c.
ratios of the sides will be equal
b.
the vertical angles will be congruent
d.
ratio of the sides will not be equal
Please select the best answer from the choices provided
A
B
C
D
Answer:
The answer is A) the other angles are proportional.
Explanation:
If you already know what 2 of the 3 sides are of each triangle, it only makes sense that the 3rd side would be proportional to those of the 1st triangle.
For which segment is B a midpoint?
Answer:
AC with endpoints at A(1; -1) and C(5; 3)
Which is a solution to the equation |10-5y|=20
How do you find the equation of a line of a triangle when given the area and one set of coordinates?
What is 2x/3 - 4 =x ?
Step-by-step explanation:
2x/3 -4 = x
multiply both side by 3
2x - 12 = 3x
-x = 12
x = -12