Answer:
The 27th term is 22Step-by-step explanation:
Let the first term is a and common difference is d.
The nth term is:
aₙ = a + (n - 1)dWe have:
a₆ = 15a₉ = 16The difference of these terms is:
(a + 8d) - (a + 5d) = 16 - 153d = 1d = 1/3Then the first term is:
a + 5*1/3 = 15a = 15 - 5/3 = 13 1/3The nth term equation is:
aₙ = 13 1/3 + 1/3(n - 1) = 1/3n + 13If the nth term is 22, find n:
1/3n + 13 = 221/3n = 22 - 131/3n = 9n = 9*3n = 27A scale drawing of a rectangular park had a scale of 1 cm = 100 m. What is the actual perimeter of the park in meters?
10.1 and 8.8
Answer:
3780 m
Step-by-step explanation:
First, we find the perimeter of the scale drawing.
perimeter = 2(L + W)
perimeter = 2(10.1 cm + 8.8 cm)
perimeter = 2(18.9 cm)
perimeter = 37.8 cm
Now that we have the perimeter of the drawing, we use the scale to find the real perimeter.
1 cm (drawing) = 100 m (real)
37.8 cm × 100 m/cm = 3780 m
Answer: 3780 m
In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 23 hours. How long would it be, to
the nearest tenth of an hour, until there are 10500 bacteria present?
Answer: x = 22.7
Step-by-step explanation:Based on the given conditions, formulate: 5300x2(x divided by 23) = 10500
Divide both sides of the equation by the coefficient of variable: 2 x/23 = 10500/5300
Reduce the fraction:2 x/23 = 105/53
Convert exponential to logarithm form: x/23 = long^2 105/53
Divide both sides of the equation by the coefficient of variable:x = log^2 105/53 x 23
Rewrite the expression: x = 23 long^2 105/53
Round the number: x = 22.7
Answer: x = 22.7
A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long. At what angle is the sun above the horizon at that time?
Step-by-step explanation:
there is a right-angled triangle.
its legs (enclosing the 90° angle) are the height of the skyscraper (396 m) and the shadow (332 m).
so, we know the third side (the Hypotenuse, which is the line of sight between the end of the shadow and the top of the skyscraper) too by using Pythagoras :
c² = a² + b²
line² = 396² + 332² = 156816 + 110224 = 267040
line = sqrt(267040) = 516.7591315... m
and we know 1 angle : the 90° angle between the legs.
the other angles we can now get by using the law of the sines :
a/sin(A) = b/sin(B) = c/sin(C)
where the angles are opposite of the lines.
the line of sight is opposite of the 90° angle.
and the height of the skyscraper is opposite of the angle between the line of sight and the shadow. this angle is also the angle of the sun above the horizon, as the extended line of sight would lead directly to the sun.
so, we have
516.7591315.../sin(90) = 396/sin(angle)
as sin(90) = 1
516.7591315... = 396/sin(angle)
sin(angle) = 396 / 516.7591315... = 0.76631447...
angle = 50.02407526...°
19=5+7x i need explanation it’s two step equation btw
Answer:
x = 2
Step-by-step explanation:
subtract both sides by 5. left with 14=7x. divide both sides by 7. x=2
Answer:
[tex]\boxed{\sf x=2}[/tex]Step-by-step explanation:
[tex]\sf 19 =5+7x[/tex]
First, let's swap sides so that all variable terms are on the left hand side.
[tex]\sf 5+7x=19[/tex]
Subtract 5 from both sides:
[tex]\sf 7x=19-5[/tex]
Subtract 5 from 19:
[tex]\sf 7x=14[/tex]
Divide both sides by 7:
[tex]\sf \cfrac{7x}{7} =\cfrac{14}{7}[/tex]
[tex]\sf x=2[/tex]
_____________________________________
(Help me please!!)
Write the equation of each linear relationship in slope-intercept form. (Convert the slope to decimal form.)
X: 25, 35, 45, 55
Y: 94. 88, 82, 76
Answer:
y = -0.6x +109
Step-by-step explanation:
The slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (88 -94)/(35 -25) = -6/10 = -0.6
The y-intercept is ...
b = y -mx = 94 -(-0.6)(25) = 109
The equation of the line is ...
y = mx +b
y = -0.6x +109
State the slope and y-intercept for the graph of
- 8x + y = -12.
Answer:
y must have a numerical coefficient of 1. This equation does. If it does not, then you must divide through by whatever is in front of the y.
To read the slope, you must have x and its coefficient on opposite sides of the equal sign.
So you get
y = 8x – 12 when you add 8x to both sides
Next, the y intercept is found when x = 0
y = 8x – 12
y = 8(0) – 12
y = – 12
The y intercept is -12 or in point form (0, – 12)
Answer
slope = 8
y intercept = – 12
Step-by-step explanation:
Angelique Calculated the slope of a line that passed through points (-5,4) and (2,-3) her work is shown below. identify her error and correct her mistakes.
Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 4 ) and (x₂, y₂ ) = (2, - 3 )
m = [tex]\frac{-3-4}{2-(-5)}[/tex]
Her error was subtracting 5 from 2 instead of - 5 from 2
m = [tex]\frac{-7}{2+5}[/tex] = [tex]\frac{-7}{7}[/tex] = - 1 ← corrected solution
Please help guys this is just domain and range
Answer:
domain: x>=0
range: y>=1
Step-by-step explanation:
domain: x>=0
range: y>=1
Find the sum of all solutions to the equation $3x(x+4) = 135$.
Answer:
-4
Step-by-step explanation:
3x(x + 4) = 135
3x² + 12x = 135
3x² + 12x - 135 = 0
On dividing by 3
x² + 4x - 45 = 0
x² + (9x - 5x) - 45 = 0
x² + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x + 9)(x - 5) = 0
x = 5 & -9
Sum = -9 + 5
Sum = -4
The sum of the solutions of the given quadratic equation will be -4.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
As per the given equation,
⇒ 3x(x + 4) = 135
Multiply the 3x as,
3x² + 12x = 135
3x² + 12x - 135 = 0
Divide the above equation by 3 as
3x²/3 + 12x/3 - 135/3 = 0
x² + 4x - 45 = 0
x² + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x - 5)(x + 9) = 0
x = 5 and x = -9
Therefore the sum will be -9 + 5 = -4
Hence "The total of the quadratic equation's answers will be -4".
For more about the quadratic equation,
https://brainly.com/question/17177510
#SPJ2
Which equation shows a proportional relationship between x and y?
A. y = 3x + 1
B.y= 4x
C.y = -3x - 2
D.y=9
Answer:
A
Step-by-step explanation:
100
O () = 97 +18
or()- +2
x= +
OF (x) = 97 +2
F(x) = -27 + -
10
Answer:
9x+2
Step-by-step explanation:
the inverse of the function is the opposite. 1/9 becomes 9 and negative 2 becomes positive 2
Answer:
first option
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply through by 9 to clear the fraction )
9y + 18 = x
change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = 9x + 18
Can someone explain how to do this:
If you put 10 in to the function f(x) = 2x, what would be the output?
--
Im so lost-
Answer:
It would be 2 (10)
Step-by-step explanation:
If you replace x with 10 then you have a multiplacation problem and the output of the answer is 20
28. Which category is zero NOT a part of?
NY
A. Whole
B. Integers
C. Rational
D. Natural
Answer:
Zero is not a natural number
Step-by-step explanation:
Hope this helps!
HELP HURRY PLS
Graph y= 1/2x-3
Answer:
This is what it would look like. Hope this helps!
What is the solution to the system of equations shown below?
y = -x-2
4y + 8 = x
A. No solution
B. (2,0)
C. (0,2)
D. Infinitely many solutions
Answer:
The answer is c when u solve for x it gives 0 and for y gives 2
The quadratic function g(x)=ax^2+bx+c has the complex roots (-5+9i) and (-5-9i).
What is the value of a?
What is the value of b?
What is the value of c?
Answer:
I don't know sorry
in a sale there is a 40% discount.what is the discount on a dress that costs $150.00
Answer:
$90 or $60
Step-by-step explanation:
Brady rode his bike 70 miles in 4 hours. He rode at an average speed of 17 mph for t hours and alah
respeed of 22 mph for the rest of the time. How long did Brady
ride at the slower speed? Use the variablet to
represent the time, in hours, Brady rode at 17 mph.
Answer:66 slower speed
Step-by-step explanation:
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Answer:
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
solve this to pretty pretty pls
Answer:
3) 161
Step-by-step explanation:
Indeed this is pretty easy :D
What we need to find is the surface area of the rectangular prism excluding the area of the hole. First, let's find out the width of the box, we can do this by using the area, the length, and the height, and we can write:
[tex]V=lhw[/tex]
(Formula to find the volume of a rectangular prism)
[tex]140=(4)(7)w\\ 140=28w\\ 5=w[/tex]
Now that we have the width, can find the area of the top part of the prism:
[tex](5)(4)=20[/tex]
The area of the top part of the prism is 20, and the circle has 1/4 of the area of that:
[tex]A_{circle} = \frac{A_{top part} }{4}\\ A_{circle} = \frac{20}{4} \\ A_{circle} = 5[/tex]
So the area of the circle is 5. Now we just need to find the surface area of the rectangular prism and subtract that result with the area of the circle:
[tex]A_{circle}=5\\ SA_{rec.pri.}=2(lh+lw+wh)\\ SA_{rec.pri.}=2((4)(7)+(4)(5)+(5)(7))\\ SA_{rec.pri.}=2(28+20+35)\\ SA_{rec.pri.}=2(83)\\ SA_{rec.pri.}=166[/tex]
Subtract these two results...:
[tex]166-5=161[/tex]
And we are done!
Will someone give me explanation of this question below??
[tex]show \: that \: function \: y = ax+ {2a}^{2} \: is \: a \: solution \: of [/tex]
[tex]the \: differential \: equation[/tex]
[tex] 2( \frac{dy}{dx})^{2} + x ( \frac{dy}{dx} ) - y = 0 \\ [/tex]
Note: Don't spam and don't copy
Need answer with explanation
Don't answer if you don't know
Thank You!
If y = ax + 2a², then its derivative is dy/dx = a. Substitute y and dy/dx into the given equation and check if it results in an identity:
2 (dy/dx)² + x dy/dx - y = 0
2a² + ax - (ax + 2a²) = 0
0 = 0
This is of course true, so y = ax + 2a² is indeed a solution to the given equation.
Given the two similar triangles below, which proportion is true?
Answer:
B) 10/15 = 15/22.5
Step-by-step explanation:
For the two triangles, proportions that involve ratios of the corresponding sides are true.
Can someone please help me!!?
Answer:
Step-by-step explanation:
Domain is all the x's on the graph. The graph does go from -3 to 4 (not including the -3 but including the 4). Pay attention to the use of () as well as [] on the answers. Those answers are not weird coordinates, they are intervals where the first number is the starting place and the second number is the end. Also on the graph one end point is an open circle which means it's not included on the graph and the other endpoint is a darkened circle which means it is included. The range is all the y's. It does go from -3 to 3. Increasing means the graph is going up from left to right and decreasing means the graph is going down left to right. The graph is positive when it is above the x-axis and negative when its below the x-axis. It seems like ALL of the statements about the graph are true.
A cylinder has a height of 4 centimeters. Its volume is 12.56 cubic centimeters. What is the radius of the cylinder?
Step-by-step explanation:
hope it will help you...
Answer:
radius of cylinder = 1 cm
Step-by-step explanation:
Start with the formula for the volume of a cylinder: V = (pi)r²h, where r is the radius and h is the height. We want to solve this for the radius, r.
Dividing both sides of the Volume formula (above) by (pi)h, we get:
V
r² = -----------
(pi)h
If we now substitute 12.56 cc for V, 3.14 for pi and 4 cm for h, we get:
V 12.56 cc
r² = ---------- = ----------------- = 1 cm²
(pi)h 3.14(4 cm)
Taking the square root of both sides, we get r = 1 cm
answer in standard form PLEASE.
identify the median of 15-18
2(t+1)=10
t= ? ............................................
Answer:
4
Step-by-step explanation:
2x5=10
5-1=4
2(4+1)=10
2(x-3) < 3(2x+2)
How do I solve for x
Answer:
x < -3
Step-by-step explanation:
2(x-3) < 3(2x+2)
Use the distributive property.
(2× x)-(2×3) < (3 × 2x) + (3×2)
2x-6 < 6x+6
add 6 to both sides
2x < 6x+12
subtract 6x from both sides.
-4x < 12
divide both sides by -4
x < -3
which expression simplies to 40x10?
Answer:
i think its 4*1
Step-by-step explanation:
hope this helps
have a great day
~Zero~
Answers
Explainations
1 point
A jacket is on sale for $48 in a Texas store. The sales tax in Texas is 6,25%.
How much does the jacket cost with sales tax included? *
Answer:
$51
Step-by-step explanation:
First, we can convert the tax to a decimal by dividing by 100.
6.25% = 0.0625
Then, we can calculate the sales tax by multiplying the original amount by the tax.
48 * 0.0625 = 3
Finally, we can add the sales tax to the original amount to get our final amount of
48 + 3 = 51