It took six people four days to build a wall.
a) Working at the same rate, how long would it have taken eight people to build the wall?
b) Working at the same rate, how many people would have been needed if the wall had
to be completed in two days?
Answer:
a=5 days, 3 hours
b= 3 people
Divide and simplify
x^2−9/x^2−16/x^2+5x+6/x-4
step by step pls
thanks
Answer:
Step-by-step explanation:
Answer:
[tex]\frac{(x+2)(x+3)^2(x-3)}{(x-4)^2(x+4)}[/tex]
Step-by-step explanation:
i'm going to assume what you have looks like
[tex]\frac{x^2-9}{\frac{x^2-16}{\frac{x^2+5x+6}{x-4}}}[/tex]
Let's start by factoring everything
x²-9= (x+3)(x-3)
x²-16= (x+4)(x-4)
x²+5x+6=(x+3)(x+2)
x-4= x-4
which means what we have looks like
[tex]\frac{(x+3)(x-3)}{\frac{(x+4)(x-4)}{\frac{(x+3)(x+2)}{x-4}}}=\frac{(x+3)(x-3)}{(x+4)(x-4)}\div\frac{x-4}{(x+3)(x+2)}=\frac{(x+3)(x-3)}{(x+4)(x-4)}*\frac{(x+3)(x+2)}{x-4}=\frac{(x+3)^2(x-3)(x+2)}{(x+4)(x-4)^2}[/tex]
And I think that's as simplified as it can get
if sec theta = 5/3 and the terminal point determined by theta is in quadrant 4, then:
Answer:
A. csc 0 = -5/4 or B. cos 0 = 3/5
Answer:
B or A
Step-by-step explanation:
sec(theta) = 1/cos(theta)
cos(theta) = adjacent side / hypotenuse.
The csc(theta), the sin(theta) and the tan(theta) in quad 4 are all minus
Since the cos(theta) is positive in quad 4, B is going to be the answer.
The value for sin(theta) should be sin(theta) = - 4/5 not 2/5
Tan(theta) = - 4/3
Note: 4 is found by using the Pythagorean Theorem because the trigonometric functions are all defined by the sides of a right triangle.
a^2 + b^2 = c^2
a = the adjacent side = 3
b = the opposite side = b
c = the hypotenuse = 5
3^2 + b^2 = 5^2
9 + b^2 = 25
b^2 = 16
b = 4
A triangle and a rectangle are shown below.
The area of the rectangle is 5 times the area of the triangle.
Work out the width(w) of the rectangle
Answer:
10 cm
Step-by-step explanation:
From the diagram,
Applying,
lw = 5/2(bh)..................... Equation 1
Where l = length of the rectangle, w = width of the rectangle, b = base of the triangle, h = height of the triangle.
make w the subject of the equation
w = 5(bh)/2l............... Equation 2
From the diagram,
Given: l = 12 cm, b = 6 cm, h = 8 cm
Substitute into equation 2
w = 5(6×8)/(2×12)
w = 10 cm
Hence the width of the rectangle is 10 cm
hey there, please help me. thank you
Answer:
S.S.S
Step-by-step explanation:
When three sides of a triangle are respectively equal to three corresponding sides of another triangle, they are said to be congruent .
hope it is helpful to you
Please answer its fill in the blanks
the words are at the bottom
Answer:
1. Grassland
2. grass
3. Temperate grassland
4. prairies
5. steppe
6. tropical grassland
7. savanna
8. intermountain grassland
9. mixed prairie
10. tallgrass prairie
Step-by-step explanation:
someone help please, giving brainlist to anyone who answers <3
Answer:
65 seats
Step-by-step explanation:
1. Approach
To answer this question, one has to find the rate at which seats are added to each row. Then one must find the number of seats in the first row. Using this information, one can form an equation to find out how many seats are in any given row when given the row number. Finally, one can substitute (20) into the equation to find out how many seats are in the row (20).
2.Find the rate at which seats are added
One is given the row number and the corresponding number of seats in the row. This information is presented in the formate ([tex]x,y[/tex]), as the following is,
(3, 31), (6, 37)
Where (x) is the row number and (y) is the number of seats.
To find the rate at which seats are added, one must solve for the rate of change. This can be done using the following formula,
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute in the given information and solve for the rate of change,
[tex]\frac{37-31}{6-3}[/tex]
Simplify,
[tex]\frac{37-31}{6-3}\\=\frac{6}{3}\\=2[/tex]
Seats are added at a rate of (2) seats per row.
3. Find the equation
The easiest way to write the equation of this situation is to use the equation of a line is in the slope-intercept form. This form is as follows,
[tex]y=mx+b[/tex]
Where (m) is the slope of the line and (b) is the (y-intercept). As one found in (step (2)) the slope of the line is (2). Substitute this into the equation,
[tex]y=2x+b[/tex]
One is given that (3, 31) is a part of this scenario, substitute this point into the equation and solve for the unknown,
[tex](31)=2(3)+b[/tex]
Simplify,
[tex]31 = 6+b[/tex]
Inverse operations,
[tex]31=6+b\\25=b[/tex]
Substitute this into the equation to complete the equation,
[tex]y=2x+25[/tex]
4.Find how many seats are in the row (20)
Now that one has the equation to find the number of seats where (x) represents the row number and (y) represents the number of seats. Substitute in the row number (20) to solve to find the number of seats in the row.
[tex]y=2x+25[/tex]
[tex]y=2(20)+25[/tex]
Simplify,
[tex]y=2(20)+25\\y=40+25\\y=65[/tex]
ANSWER PLEASE!!!!!!!!!!!!!
Answer:
It would be a negative linear association if not then nonlinear association.
Step-by-step explanation:
Find the 7th term in the
sequence
,
32
1, 3, 9,...
Hint: Write a formula to help you.
1st term • Common Ratio desired term – 1)
Enter
Answer:
243
Step-by-step explanation:
formula is
Un = ar^n-1
U7 = ar^7-1
U7 =ar^6
U7 =1/3 ×3^6
where a=1/3 and r= 3
U=243
sin theta =12/13 then find tan theta.
I hope this is help full to you
Answer:
tan(θ) = 12/5
Step-by-step explanation:
According to Pythagoras,
sin(θ) = Opposite / Hypotenuse
tan(θ) = Opposite / Adjacent
(Hypotenuse)^2 = (Opposite)^2 + (Adjacent)^2
or, (Adjacent)^2 = (Hypotenuse)^2 - (Opposite)^2
or, (Adjacent)^2 = 13^2 - 12^2
or, (Adjacent)^2 = 169 - 144
or, (Adjacent)^2 = 25
or, Adjacent = 5
So, tan(θ) = 12/5
Hope this will help. Please mark me brainliest.
The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism.
Answer:
I don't see the triangular prism.
Step-by-step explanation:
here is the problem if you want to help them
If θ is an angle in standard position and its terminal side passes through the point (6,1), find the exact value of
sec
θ
secθ in simplest radical form.
Given:
θ is an angle in standard position.
Its terminal side passes through the point (6,1).
To find:
The exact value of secθ in simplest radical form.
Solution:
If θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:
[tex]\sec\theta =\dfrac{Hypotenuse}{Base}[/tex]
[tex]\sec\theta =\dfrac{\sqrt{x^2+y^2}}{x}[/tex]
It is given that θ is an angle in standard position and its terminal side passes through the point (6,1), then the exact value of secθ is:
[tex]\sec\theta =\dfrac{\sqrt{6^2+1^2}}{6}[/tex]
[tex]\sec\theta =\dfrac{\sqrt{36+1}}{6}[/tex]
[tex]\sec\theta =\dfrac{\sqrt{37}}{6}[/tex]
Therefore, the exact value of secθ is [tex]\dfrac{\sqrt{37}}{6}[/tex].
A bag contains 60 marbles of different colours. The probability of randomly selecting a red marble is 5/12. How many red marbles does the bag contain?
Answer:
25 red marbles
help ...........................................
thanks,,,,
Answer:
(1,0) (0,-3)
Step-by-step explanation:
x then y a baby crawls before it walks.
A school painted 1/2 of a wall with 3 colors.Each color takes up the same amunt of space on the wall.What fraction of the wall does each color occupy?
Answer:
1/6
Explanation:
This is because if you were to take up the entire wall with these same proportions, you would need six colors.
Complete the equation of the line through (-8,-2)(-4,6)
use exact numbers
Answer:
y = 2x + 14
Step-by-step explanation:
Hope this helps!!!
First, you have to find the slope by using
In other words,
The slope is 2.
Then you plug the rest into point-slope form (you can use either of the points, I used the first one)
Remember that m is the slope.
Distribute the slope to the parenthesis
Isolate the y variable
Answer:
2x+14
Step-by-step explanation:
The ratio of men to women working for a company is 4 to 7. If there are 165 employees total, how many women work for the company?
Answer: 105
Step-by-step explanation:
Given
The ratio of men to women working for a company is 4:7
There are total of 165 employees
Suppose, there is 4x men and 7x women such that the ratio remains constant
[tex]\therefore 4x+7x=165\\\Rightarrow 11x=165\\\Rightarrow x=15[/tex]
[tex]\text{Men= }4\times 15=60\\\text{Women= }7\times 15=105[/tex]
The value of a car is deprecting at the rate of 12% Find the correct value of car when cost of car was rs 350000
please i need help
Answer:
The cost of the car is $ RS 308,000.
Step-by-step explanation:
Given that the value of a car is deprecting at the rate of 12%, to find the correct value of car when cost of car was $ RS350,000 last year, the following mathematical calculation must be performed:
100 - 12 = 88
88/100 = 0.88
350,000 x 0.88 = X
308,000 = X
Therefore, the cost of the car is $ RS 308,000.
What is the value of the expression. -(2 1/2 - 7) - 6 1/2?
Answer:-2
Step-by-step explanation:
State the mathematical properties of all the steps in the equation below.
(2x + 3) − 7 = 8 + x Problem Statement.
(2x + 3) + (−7) = 8 + x _____________
((2x + 3) + (−7)) + 7 = (8 + x) + 7_____________
(2x + 3) + (−7 + 7) = (8 + x) +7 _____________
(2x + 3) + 0 = (8 + x) + 7 _____________
2x + 3 = (8 + x) + 7 _____________
2x + 3 = 7 + (8 + x) _____________
2x + 3 = (7 + 8) + x _____________
2x + 3 = 15 + x _____________
(2x + 3) + (−3) = (15 + x) + (−3) _____________
2x + (3 + (−3)) = (15 + x) + (−3) _____________
2x + 0 = (15 + x) + (−3) _____________
2x = (15 + x) + (−3) _____________
2x = (−3) + (15 + x) _____________
2x = (−3 + 15) + x _____________
2x = 12 + x _____________
2x + (−x) = 12 + x + (−x) _____________
2x + (−x) = 12 + 1 · x + (−x) _____________
2x + (−x) = 12 + 1 · x + (−1) · x _____________
2x + (−x) = 12 + (1 + (−1))x _____________
2x + (−x) = 12 + 0 · x _____________
2x + (−x) = 12 + 0 _____________
2x + (−x) = 12 _____________
2x + (−1) · x = 12 _____________
(2 + (−1)) · x = 12 _____________
1 · x = 12 _____________
x = 12 Solution
Answer:
173*3*j3
Step-by-step explanation:
naksbvajahagcgaja
Answer:
HIHHIHIHIHIHIHIHIH
Step-by-step explanation:
IHIHIHIHIHIHIHIHIH
Find the mean of the data.
The number of trophies won by
each team in the district.
1, 3, 1, 5, 7, 8, 10
Mean: [? ] trophies
Answer:
5
Step-by-step explanation:
Una máquina de bolas de chicle tiene 23 chicles verdes, 52 chicles rojos, 34 chicles azules, 61 chicles amarillos y 30 chicles rosas. ¿Qué porcentaje de los chicles son rojos?
Answer:
creo que es 96%
Step-by-step explanation: sume todo los chiles excepto los chiles rojos y luego con la suma de todos los chiles los reste con los chiles rojos.
What is the area of the triangle shown below?
Answer:
12
Step-by-step explanation:
Each half of the isosceles triangle is a right triangle with side lengths 3, 4, 5.
A = bh/2
A = 8 * 3/2
A = 12
PLEASE HELP FINDING TRIANGLE ANGLE
Answer:
x = 146
Step-by-step explanation:
The exterior angle of the triangle is equal to the sum of the opposite interior angles
x = 48+98
x = 146
Answer:
The sum of all the angles in a triangle is 180 degrees,
We know the measures of two angles, 48 and 98
if we add those and then subtract their sum from 180, we can find the third angle which will help us find the exterior angle x
48+98=146
180-146 = 34
now, we have to do 180-34 to find the measure of x.
why? any straight line is 180 degrees.
180-34 = 146
x = 146
hope this is correct and it helps you.
round to the nearest whole number than add 4.208 + 2.482
4.208 + 2.482= 6.69 so rounding that would be 7
4.208 + 2.482 = 6.69
When we round it to the nearest, it becomes 7.
Hope it helps you..
If using the method of completing the square to solve the quadratic equation
x^2– 10x + 21 = 0, which number would have to be added to "complete the
square"?
Answer: 25
Step-by-step explanation: The number that is added to both sides is the number that is needed to create a perfect square trinomial.
The question is, what is that number?
Well, it comes from a formula. The number that is added to both sides always comes from half the coefficient of the middle term squared.
So half of -10 squared or -5 squared which is 25.
So 25 is added to both sides.
Help me please thank u
Answer:
your answer to this question is C.
the price of a ring was increased by 30% to £325 what was the price before the increase
Please answer these tree questions in detail...
Will give Brainliest for the best...
Want answer in detail ASAP
Answer:
Step-by-step explanation:
14.
A.
x = 5.0081818181..
10x = 50.08181818181....
100x = 500.81818181818...
100x - x = 500.8181818... - 5. 008181818....
99x = 495.81
[tex]x = \frac{495.81}{99} = \frac{495.81 \times 100}{99 \times 100} \\\\\\x= \frac{49581}{9900}[/tex]
[tex]x = \frac{5509}{1100}[/tex]
14.
B.
[tex]\sqrt{50} - \sqrt{98} + \sqrt{162} \\\\\sqrt{ 2 \times 25} - \sqrt{ 2 \times 49} + \sqrt{2 \times 81}\\\\\sqrt{ 2 \times 5^2} - \sqrt{ 2 \times 7^2} + \sqrt{2 \times 9^2}\\\\5\sqrt2 - 7 \sqrt 2 - 9 \sqrt 2\\\\\sqrt{2} ( 5 - 7 + 9 ) \\\\7\sqrt2[/tex]
15.
[tex]\frac{3 + \sqrt5}{4 - 2\sqrt 5} \\\\= \frac{3 + \sqrt5}{4 - 2\sqrt 5} \times \frac{4 + 2\sqrt5}{4 + 2\sqrt5}\\\\[/tex] [tex][ \ rationalizing \ the \ denominator \ ][/tex]
[tex]=\frac{(3 + \sqrt5)(4 + 2\sqrt5)}{(4 -2 \sqrt5)(4 + 2\sqrt5)}\\\\=\frac{12 + 6 \sqrt5 + 4\sqrt5 + 2(\sqrt5)^2}{(4)^2 - (2\sqrt5)^2}[/tex] [tex][ \ (a - b)(a +b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{12 + 10 + 10\sqrt5}{16 - (4 \times 5)}\\\\=\frac{22 + 10\sqrt5}{16 - 20 }\\\\=\frac{22+ 10 \sqrt5 }{-4}[/tex]
[tex]= \frac{11}{-2} + \frac{5 \sqrt5}{-2}\\\\= -\frac{11}{2} + \frac{-5 }{2} \sqrt5\\\\[/tex]
[tex]a = - \frac{11}{2} , \ b = -\frac{5}{2}[/tex]
16
[tex]\frac{\sqrt7 + 1 }{\sqrt7 - 1} - \frac{\sqrt7 - 1}{\sqrt7 + 1}\\\\[/tex]
[tex]\frac{(\sqrt 7 + 1 )( \sqrt7 + 1)}{(\sqrt7 - 1 )(\sqrt7 + 1)} - \frac{(\sqrt7 - 1)(\sqrt 7 - 1)}{(\sqrt7 + 1)(\sqrt7 - 1)}[/tex] [tex][ \ LCM \ of \ denominators : (\sqrt7 -1)(\sqrt7 + 1) \ ][/tex]
[tex]\frac{(\sqrt 7 + 1 )^2 -( \sqrt7 - 1)^2}{(\sqrt7)^2 - 1^2}[/tex] [tex][ \ (a \pm b)(a \pm b) = (a \pm b)^2 \ (a-b)(a+b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{(7 + 1 + 2\sqrt7) - ( 7 + 1 - 2\sqrt7)}{7 - 1}\\\\=\frac{8 + 2\sqrt7 - 8 + 2\sqrt7}{6}\\\\= \frac{4 \sqrt7}{6}\\\\= \frac{2 \sqrt 7}{3}[/tex]
Write an equation of the line and interpret the slope:
Answer:
Equation = y=3x+12
Slope is 3
Step-by-step explanation: