Step-by-step explanation:
f(x) = x√(x+8)
When f(x) = 0,
0 = x√(x+8)
x = 0, x + 8 = 0
x = -8
f'(x) = (1)√(x+8) + x • ½(x+8)^(-½) = 0
0 = √(x+8) + 1/[2√(x+8)] (x)
-2(x+8) = x
-2x - 16 = x
x = -16/3
(-8 < -16/3 < 0)
Therefore, x-intercept of f'(x) = 0 is somewhere between the two x-intercepts, ranging from -8 to 0.
The base of a triangle exceeds the height by 7 feet. If the area is 114 square feet, find the length of the base and the height of
the triangle
Answer:
Height of the triangle = 12 feet
Base of the triangle = 19 feet
Step-by-step explanation:
Let the height of the triangle be x feet
-> Base of the triangle = (x + 7) feet
[tex]A(\triangle)= 114\: ft^2[/tex]
[tex]\because A(\triangle)=\frac{1}{2}(base)(height) [/tex]
[tex]\implies 114=\frac{1}{2}(x+7)(x) [/tex]
[tex]\implies 114\times 2= x^2+7x[/tex]
[tex]\implies 228= x^2+7x[/tex]
[tex]\implies x^2+7x-228=0[/tex]
[tex]\implies x^2+19x-12x-228=0[/tex]
[tex]\implies x(x+19)-12(x+19)=0[/tex]
[tex]\implies (x+19)(x-12)=0[/tex]
[tex]\implies (x+19)=0,\:\:(x-12)=0[/tex]
[tex]\implies x =-19,\:\:x=12[/tex]
x represents the height of the triangle.
-> x can not take negative value.
[tex]\implies x\neq -19[/tex]
[tex]\implies x = 12[/tex]
[tex]\implies x +7= 12+7=19[/tex]
Thus,
Height of the triangle = 12 feet
Base of the triangle = 19 feet
Write the first three terms of the sequence whose general term is an=(3n)!.
Answer:
3, 6, 9
Step-by-step explanation:
an=3n
a(1)=3(1)= 3
a(2)=3(2)= 6
a(3)=3(3)= 9
What is the answer for this 4² × 4²
Answer:
4squared is 16 so 16×16=256
hope it help
Answer:
4^2=16 multiplyin 16 by 16 gets you 256
Step-by-step explanation:
Find the x- and y-intercepts of the quadratic function below. Give non-integer
coordinates in fractional form.
f(x) = 2x2 - 5x + 3
-
Answer:
Step-by-step explanation:
Ryan buys some jumpers to sell on a stall.
He spends £130 buying 40 jumpers.
He sells 80% of the jumpers for £12 each.
He then puts the rest of the jumpers on a Buy one get one half price offer.
He manages to sell half the remaining jumpers using this offer.
How much profit does Ryan make?
A tree is 18 feet tall and casts a shadow
that is 22 feet long. How far is it from the
end of the shadow to the top of the tree?
Show your work.
Answer:
28.42 feet
Step-by-step explanation:
Given
Height of tree = 18 feetLength of shadow = 22 feetTo Find
Distance b/w top of tree and end of shadowSolving
This resembles a right triangle⇒ We can use Pythagorean Theorem!⇒ 18² + 22² = L²⇒ L² = 324 + 484⇒ L² = 808⇒ L = 2√202 ⇒ L = 2 x 14.21⇒ L = 28.42 feetAnswer:
28.4 feet
Step-by-step explanation:
The question can be solved by using Pythagoras Theorem.
Given:-
Height of tree :- 18 feet (Perpendicular)
length of shadow :- 22 feet (Base)
To find:-
Distance of shadow from the end to the top of the tree
Solution:-
We know the Pythagoras theorem,
Which is , H² = P² + B²
So putting the given value , we get
H² = 18²+22²
H² = 324 + 484
H = √ 808 feet
H = 28.4 feet
Julie's grades for this term test are 85' 88' and 97. In addition for the three tests that Julie already had, there will b just one more test. Julie needs to earn at least ________ point for the last test to get no less than A for the term. "A" means the average of 93 or more.
The score Julia has to have on her last test to have an A for the term is 102.
What is the least score?The first step is to determine the sum of her scores on the first three tests: 85 + 88 + 97 = 270
Now determine the score on the last test that would give an average of 93
(270 + x)/ 4 = 93
270 + x = 93 x 4
372 - 270 = x
x = 102
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I need help with this question please
[tex]v(y) = 0[/tex]
[tex] - 32t + 105 = 0[/tex]
[tex]t = \frac{ - 105}{ - 32} = 3.28[/tex]
[tex]h = - 16(3.28) {}^{2} + 105(3.28) + 17[/tex]
[tex]h = 189.26[/tex]
13, 19, 25, ...
Find the 48th term.
Answer:
so you should add 6 to 13 in case to find 19, then add 6 to 19 to get to 25.
so the first is 13 and we keep adding 6 to get to the answer. we do it 47 times. so we have 13+ (6) (47) = 295 which is the 48th term.
The 12th term of the arithmetic sequence13, 19, 25,... is 79.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, an arithmetic sequence 13, 19, 25,...
The first term a₁ = 13 and the common difference is = (25 - 19) = (19 - 13) = 6.
We know nth term of an arithmetic sequence is aₙ = a₁ + (n - 1).d.
∴ The 12th term of this arithmetic sequence is a₁₂ = a₁ + (12 - 1).d
a₁₂ = 13 + (12 - 1).6.
a₁₂ = 13 + 11.6
a₁₂ = 13 + 66.
a₁₂ = 79.
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Use the Virtual Dice Roller and roll two dice three times (or grab a pair of dice at home!).
Record the sum of the two dice for each virtual roll.
The first virtual roll is how many work shirts you have in your closet.
The second roll is how many pairs of work pants you have in your closet.
The third roll is how many pairs of work shoes you have in your closet.
Calculate and explain how many different ways can you dress every morning. Show all calculations.
The simulation of the virtual dice roller illustrates combination and sample space
There are 36 different ways you can dress every morning
How to determine the number of ways of dressing?The sample space of the two dice are:
Die 1 = {1,2,3,4,5,6}
Die 2 = {1,2,3,4,5,6}
From the above sample space, we have the sample size to be:
n(Die 1) = 6
n(Die 2) = 6
The sample size of the experiment would be:
n = n(Die 1) * n(Die 1)
Substitute known values
n = 6 * 6
Evaluate the product
n = 36
The above represents the different ways you can dress every morning.
Hence, there are 36 different ways you can dress every morning
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How do I solve it? URGANT!!!
Answer:
Step-by-step explanation:
KL = JK, so ΔJKL is an isocesles triangle, then m∠J = m∠L
KL is a tangent line, so ∠JKL = 90°,
so m∠J = 45°
Which function is shown on the graph?
U
T
30
2
2
O f(x) = sino
-14
O f(x) = jcos
OS I
2
ក
O f(x) = -cos
COS
O f(x)=- sin
Answer:
Read the explanation
Step-by-step explanation:
look at the photo
Solve the equation b(b+12) = 0. Check your solutions.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \:b(b + 12) = 0[/tex]
Here, we have two cases :
Case 1[tex]\qquad \sf \dashrightarrow \:b = 0[/tex]
Case 2[tex]\qquad \sf \dashrightarrow \:b + 12 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \:b = - 12[/tex]
Hence, 0 and -12 are the only possible solutions for given equation.
The dotted lines show how piano wire
is used to slice this cube. What will be
the shape of the cross section?
Answer:
C. rectangle (not a square)
Step-by-step explanation:
So image that the wire just sliced that piece of the cube right off:
It would give you a triangular prism,
HOWEVER, this is asking for the cross section:
The part of this triangular prism that was actually connected to the cube
and in this case, it would show that the bottom of the cut off part is rectangle.
You can also think of this as: What shape would be left over on the cube?
Cutting this piece off would give you a shape left over that is a rectangle.
Which field is required when importing vendors
Import field: Tax Identification Number, Tax Number for Customers or Vendors. Tax Identification Number (customers) or Tax ID Number (vendors).
A basket contains 4 pears, 1 pineapple, 5 bananas, 3 oranges, and 2 limes.
vin randomly selects one piece of fruit from the basket. What is the
robability that he selects an orange from the basket?
Answer:
3/15
Step-by-step explanation:
there is 15 kinds of fruit totally
4 + 1 + 5 + 3 + 2 = 5 + 5 + 3 + 2 = 10 + 3 + 2 = 13 + 2 = 15
there are 3 oranges; therefore the bility that an orange will be picked is 3 out of 15
Find the product of 4+3i and its conjugate.the answer is a +bi where
The value of a and b in the product of 4+3i and its conjugate in the format a + bi are 25 and 0.
What is conjugate?The conjugate is where we change the sign in the middle of two terms. For example:
3y + 1
conjugate of 3y + 1 is 3y - 1.
Therefore, the conjugate of 4 + 3i is 4 - 3i.
The product of 4 + 3i and its conjugate is as follows:
(4 + 3i)(4 - 3i) = 16 - 12i + 12i - 9(i)²
Therefore,
16 - 9i²
i² = -1
Hence,
16 - 9(-1) = 25
It can be written in the form a complex form → (25 + 0.i)
Therefore, a = 25 and b = 0.
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B
45°
71°
E
27°
A
D
11. What is mBAC
Answer:THE ANSWER IS B MY GUY
Step-by-step explanation:
What is the average rate of change of the function y = 3 cos x on the interval [π/2, π]?
Answer:
¹
Step-by-step explanation:
Average Rate of Change is
ts
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
Here b is pi, a is pi/2,
[tex] \cos(\pi) = - 1[/tex]
[tex] \cos( \frac{\pi}{2} ) = 0[/tex]
So we have
[tex] \frac{ - 1 - 0}{ \frac{\pi}{2} } = \frac{ - 1}{ \frac{\pi}{2} } [/tex]
Answer:
-2/pi
Step-by-step explanation:
find the rule to complete the pyramid.
Answer:
add two side by side values
Step-by-step explanation:
there are 5 values at the base of the pyramid.
4, 6, 3, 7 and 2
let's look at 6 and 3 first. when you add them together, you will get 9, which make up the upper layer of the pyramid. we can also support this statement when you add 7 with 2, which is also 9. so when you take 4 and add with 6, you will get 10, when you add 3 and 7, you will get 10.
now, let's see the second bottom layer. we get the answers as 10 in both blanks. so, add 10 with 9 and you will get 19, repeat with the other. so, the third layer will be 19, 19 and 19. to make the third layer complete, add 19 with 19, which will be 38. so, the fourth layer will be 38 and 38. add 38 with 38 and you will get 76 at the top of the pyramid.
Order the numbers from least to greatest. −34, 0.5, 23,−73, 1.2 The order of the numbers from least to greatest
Answer:
-73, -34, 0.5, 1.2, 23
Step-by-step explanation:
Hope this helps:)....if not sorry for wasting your time and may God bless you:)
how many integers from 100 to 999, inclusive, don't include the numbers 2,4,6,8? PLS HELP I WILL MARK BRAINLIEST
Answer:
243
Step-by-step explanation:
999-100= 899 integers
200s 400s 600s 800s excluded so 400 numbers excluded
899 - 400 = 499
20s 40s 60s 80s which are 40 integers x 4 = 160
499 - 160 = 339
2s 4s 6s 8s which are 4 integers x 6 x 4 ( 4 from each 100 ) = 96
339 - 96 = 243 integers
find the equation of line that is parallel to another line whose equation is 8y+5x-6=0and passes through the point (8,5)
write down the equation of line perpendicular to y=7x/4+9/4 and passes through the origin
today is the deadline please help me
1. The equation of the line that is parallel to the given line and passes through the point (8,5) is y = (-5/8)x + (65/8).
2. The equation of the line that is perpendicular to the given line and passes through the origin is y = (-4/7)x.
1. To find the equation of a line that is parallel to another line with equation 8y+5x-6=0 and passes through the point (8,5), we need to follow some steps.Steps:
First, find the slope of the given line, which can be done by rearranging the given equation into slope-intercept form (y = mx + b).8y+5x-6=0⟹ 8y = -5x + 6⟹ y = (-5/8)x + 3/4So the slope of the given line is -5/8.
Second, since we need to find a line parallel to the given line, the slope of the new line will also be -5/8.
Third, use the slope (-5/8) and the given point (8,5) to find the y-intercept (b) of the new line by using the point-slope form of the equation. y - y₁ = m(x - x₁)y - 5 = (-5/8)(x - 8)y = (-5/8)x + (65/8)
Therefore, the equation of the line that is parallel to the given line and passes through the point (8,5) is y = (-5/8)x + (65/8).
2. To write down the equation of a line perpendicular to y = 7x/4+9/4 and passes through the origin, we can follow some steps.
Steps:
First, find the slope of the given line. This can be done by rearranging the given equation into slope-intercept form (y = mx + b).y = (7/4)x + 9/4So the slope of the given line is 7/4.
Second, since we need to find a line perpendicular to the given line, the slope of the new line will be the negative reciprocal of the given line's slope.
Third, use the slope (-4/7) and the point (0,0) to find the y-intercept (b) of the new line by using the point-slope form of the equation.y - y₁ = m(x - x₁)y - 0 = (-4/7)(x - 0)y = (-4/7)x
Therefore, the equation of the line that is perpendicular to the given line and passes through the origin is y = (-4/7)x.
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Answer:
8y +5x -80 = 0y = -4/7xStep-by-step explanation:
You want the equations of lines ...
parallel to 8y +5x -6 = 0, through point (8, 5)perpendicular to y = 7/4x +9/4, through the originParallel lineThe equation of a parallel line in general form can be written using the same coefficients, and choosing a constant that makes the equation true for the given point.
8y +5x +c = 0
8(5) +5(8) +c = 0
80 +c = 0
c = -80
The equation of the desired line is 8y +5x -80 = 0.
Perpendicular lineThe given equation is in slope-intercept form, so we can identify the slope as ...
y = mx +b = 7/4x +9/4
m = 7/4
The perpendicular line will have a slope that is the opposite reciprocal of this:
m' = -1/(7/4) = -4/7 . . . . . . slope of perpendicular line
The line through the origin will have a y-intercept of 0, so the equation in slope-intercept form is ...
y = -4/7x
__
Additional comment
The attached graph shows the given lines as dashed lines, and the requested lines as solid lines in the same color. The "must pass through" points are shown.
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the elevator can accommodate at most 1500 lbs.Carl is transporting boxes that weigh 15lbs each. If carl weighs 170 lbs.Write an equation that can be used to determine the most number of boxes Carl can transport using the elevator
Answer:
15x+170≤1500
Step-by-step explanation:
it is at most 1500, so less than or equal to 1500, and the 15 lbs relies on the number of boxes so 15x and carl weighs 170 so that must be added, equaling to
15x+170≤1500
Which of the following sets of numbers is a Pythagorean triple?
42, 40, 82
42, 40, 58
41, 41, 58
40, 41, 57
HELP QUICK PLEEZ
Answer:
42,40,58
Step-by-step explanation:
I REALLY NEED HELP MY GRADES GO IN TONIGHT AND I CANT SOLVE THIS I NEED A REAL ANSWER I WILL CHECK BEFORE GIVING POINTS!!!!!!!!!!!!!!!!!
Answer:
K. 8
N. 12
A. 29
H. 5
I. -297
G. 89
T. 50
S. -7
W. 165
WHAT'S SHAKING
Answer:
K: 8
N: 12
A: 29
H: 5
I: -297
G: 89
T: 50
S: -7
W: 165
WHATS SHAKING [Answer]
Step-by-step explanation:
Please rate!!
If ((x) = x2+ 3x - 2, find f(-2).
f(x) = x² + 3x - 2
f(-2) = (-2)² + 3*(2) - 2 = 4 - 6 - 2 = - 4
Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangles, as well as the perimeter and the area in each figure.
If abc is an equilateral triangle bc must be 2cm true or false?
Answer:
I would say False
Help help math math math math math
Answer:
A
Step-by-step explanation:
You can think about it as an equation without the inequality:
y = 5 - x OR y = -x + 5
Slope = -1
Y-intercept = 5
Graph B is a horizontal line with a slope of zero and y-intercept of 2. Graph A is the only one that fits the above parameters.
Hope this helps!
Answer:
a
Step-by-step explanation: