Answer:
1.16 m (approximately)
Step-by-step explanation:
Let x be the width of the path.
Total area = (5+2x)(3+2x) = 39
Expand and simplify
4x²+ 16x+15-39 = 0
4x² + 16x - 24 = 0
Simplify
x² + 4x -6 = 0
Rational factoring does not work, so use quadratic formula
x = +/- sqrt(10) -2
= 1.16 or -5.16 (reject)
= 1.16 m (approximately)
What is the equation of the line that passes through the point (-7, -4) and has a
slope of 1?
Answer:
Y=x+3
Step-by-step explanation:
we have :
x1= -7
y1= -4
m=1
as we know Y-y1=m(X-x1)
Y+4=(X+7)
Y+4=X+7
Y=X+7-4
Y=X+3
Find the y-coordinates of the points that are 10 units away from the point (-1,6) that have an x-coordinate of 7
Answer:
y = 0 or 12
Step-by-step explanation:
[tex]Let \ (x _ 1 , y _ 1) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ coordinates \ \\\\Distance \ between \ the \ points = \sqrt{(x_2 - x_1)^2 + (y_ 2 -y_1)^2}\\\\[/tex]
[tex]Given : distance = 10 \ units , (x_1 , y _ 1 ) = ( - 1 , 6 ) \ and \ (x_2 , y _ 2 ) = (7 , y )\\\\[/tex]
[tex]Substituting \ the \ values \ \\\\10 = \sqrt{(7 -(-1))^2 + (y - 6)^2}\\\\10 = \sqrt{(7 + 1)^2 + ( y - 6 )^2}\\\\10 = \sqrt{8^2 + ( y - 6)^2 }\\\\10 = \sqrt{64 + (y -6)^2 } \\\\Squaring \ both \ sides \\\\10^2 = (\sqrt{64 + (y -6)^2 })^2\\\\100 = 64 + ( y -6)^2\\\\100 - 6 4 = ( y -6)^2 \\\\36 = ( y - 6 )^2\\\\\sqrt{36} = y - 6\\\\\pm 6 = y - 6 \\\\So, \\\\\ y - 6 = 6 => y = 12\\\\\ \ \ \ y - 6 = - 6 => y = 0[/tex]
The y coordinate of the point is P ( 7 , 12 ) or P ( 7 , 0 ) where the distance of the point is 10 units from Q ( -1 , 6 )
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P ( 7 , y )
Let the second point be Q ( -1 , 6 )
Now , the distance between P and Q is D = 10 units
So , on simplifying the equation , we get
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
10 = √ [ ( 7 - ( - 1 ) )² + ( y - 6 )² ]
Squaring both sides of the equation , we get
100 = ( 8 )² + ( y - 6 )²
Subtracting 64 on both sides of the equation , we get
( y - 6 )² = 36
Taking square roots on both sides , we get
y - 6 = ±6
Adding 6 on both sides , we get
y = +6 + 6 = 12
or y = -6 + 6 = 0
So , the coordinates of the point P is P ( 7 , 12 ) or P ( 7 , 0 )
Hence , the distance formula is solved and coordinates of the point P is P ( 7 , 12 ) or P ( 7 , 0 )
To learn more about distance between 2 points click :
https://brainly.com/question/18234495
#SPJ2
Type the correct answer in the box. Use numerals instead of words. Tony bought a new car at a cost of $20,000. The value of the car decreases by approximately 12% each year. Formulate the equation that gives the value, A(+), of the car xyears since Tony bought the car. A(t)-
9514 1404 393
Answer:
A(x) = 20000(0.88)^x
Step-by-step explanation:
The general form of these exponential equations is ...
A(x) = a·b^x
where 'a' is the initial value, and b is the annual growth factor. x is the elapsed time in years.
The growth factor is ...
growth factor = 1 + growth rate
Here, the growth rate per year is -12%, so the growth factor is ...
b = 1 -12% = 88% = 0.88
Of course, the initial value is a=20,000, so the equation is ...
A(x) = 20000(0.88)^x
PLSSS HURRY AND NO LINKS!!
The strongest winds of Hurricane Isabel extended 50 miles in all directions from the center.
What is the area of the hurricane in square miles? Leave your answer in terms of pi.
Answer:
Area of the hurricane = 7853 or 3.14 x 50 squared
PLEASE help! I really appreciate it thanks!
Answer:
h=A-πr²÷2πr
Step-by-step explanation:
Making h subject
A=2πrh+πr²
A-πr²=2πrh
A-πr²÷2πr=h
h=A-πr²÷2πr
Answer:
The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
Step-by-step explanation:
To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].
Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].
Given tan(A)=5 and tan(B)=9, find the value of tan(A−B).
Answer:
tan= 4
Step-by-step explanation:
This is actually very easy, basically u have 5 - 9.
So you have positive nine and a negative sign, which is used for subtraction, so in the integers rule, positive- negative= negative
so its 4.
I HOPE ITS RIGHT, IM 11
If tan(A)=5 and tan(B)=9 the value of tan(A−B) will be -0.086.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle. The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
It discusses how triangle side lengths and angles relate to one another. Using trigonometric formulas and functions, it is mostly used to determine the unknown side lengths and angles of a right-angled triangle. Six different functions are frequently employed in trigonometry.
It is given that tan(A)=5 and tan(B)=9
As we know,
[tex]\rm tan(A -B) = \frac{tan A - tan B}{1- tan A tan B}[/tex]
Substitute the given values we get,
tan(A -B) = (tan A - tan B)/(1 + tan A tan B)
tan(A -B) = (5-9) / (1 + 5 × 9)
tan(A -B) = (-4) / (1 + 45)
tan(A -B) = -4 / 46
tan(A -B) = -2/23
tan(A -B) = - 0.086
Thus ,if tan(A)=5 and tan(B)=9 the value of tan(A−B) will be -0.086.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ2
The times of first sprinkler activation for a series of tests with fire prevention sprinkler systems using an aqueous film-forming foam were (in sec)
27 41 22 27 23 35 30 33 24 27 28 22 24
(see "Use of AFFF in Sprinkler Systems," Fire Technology, 1976: 5). The system has been designed so that true average activation time is at most 25 sec under such conditions. Does the data strongly contradict the validity of this design specification? Test the relevant hypotheses at significance level .05 using the P-value approach.
Answer:
We reject H₀, we have enough argument to explain that the production line is out of control. Is producing sprinkler out of specification
Step-by-step explanation:
Data information:
27 41 22 27 23 35 30 33 24 27 28 22 24
sample size n = 13
sample mean x = 27.92
sample standard deviation s = 5.39
The manufacturing process under control will always produce an output with normal distribution, in this case as n < 30 we will use t-student distribution in our test.
Hypothesis Test:
Null Hypothesis H₀ x = 25
Alternative Hypothesis Hₐ x > 25
The Alternative hypothesis indicates that the test is a one-tail test.
Significance level is α = 0.05
From z-table and for α = 0.05 and df = n - 1 df = 13 - 1 df = 12
p-value = 1.782
t(s) = ( x - 25 ) / s/√n
t(s) = ( 27.92 - 25 )/ 5.39/√13
t(s) = 2.92*3.605/ 5.39
t(s) = 1.95
From t-table df = 12 we find that 1.95 corresponds to a p-value < 0.05
then as p-value < 0.05 we are in the rejection region for H₀ then we reject H₀. We can deduce that the production line for sprinkler is given products out of specification
Classify the questions as statistical or not statistical.
How many houseplants
does each house on my
block have?
How many hours did Ryan
study last Saturday?
How many hours do students
in my class study every day?
How many cars does each
person in my neighborhood
own?
How many bags do I own?
How many students in my
class own 2 bags?
Answer:
1- statistical
2- statistical
4 - statistical
remaining others are non statistical in my opinion
Solve for X in the triangle. Round answer to the nearest TENTH (GIVING BRAINLEST TO BEST ANSWER :D )
Answer:
What ever.....
tan46 = x/8
x = 8×tan46
x = 8,28424251
Complete equation describing how X and Y are related.
Answer:
[tex]2[/tex]
Step-by-step explanation:
Every time the x-value increases by 1, the y-value increases by 2. Therefore, the slope of the line must be equal to [tex]2/1=\boxed{2}[/tex] (rise/y-values over run/x-values). In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents the slope of the line, [tex]b[/tex] represents the y-intercept, and [tex](x,y)[/tex] represents any point the line passes through.
Since [tex]m[/tex] represents the slope of the line, the value of
While the question only asks for this value, it's good to note that the equation of the function is [tex]y=2x+7[/tex] (find 7 by substituting any ordered pair in the table with [tex]m=2[/tex]).
Answer:
y = 2x + 7
Step-by-step explanation:
y = mx + b
For every increase of 1 in x,
there is an increase of 2 in y
m = 2
When x is 0,
y is 7
b = 7
y = 2x + 7
GIVING OUT BRAINLIEST HELP MEE PLEASE!! 10 PNTS ASWELL!!
Answer:
option 2
Step-by-step explanation:
4)
Equation of a Circle with centre ( a , b) and radius r
[tex](x - a)^2 + (y-b)^2 = r^2\\[/tex]
Given centre = ( -3 , 4), r = 5
Therefore Equation
[tex](x - ( - 3))^2 + (y-4)^2 = 5^2\\\\(x + 3)^2 + (y-4)^2 = 25[/tex]
5)
Centre = ( 2 , 0) , radius, r = 3
[tex](x - 2)^2 + (y-0)^2 = 3^2\\\\(x -2)^2 + y^2 = 9[/tex]
Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 red & 6 black balls
respectively. 1 of the bags is selected at random and a ball is drawn from it. If the ball
drawn is red, find the probability that it is drawn from the third bag.
Answer:
[tex]Probability = \frac{4}{15}[/tex]
Step-by-step explanation:
B1 = first bag
B2= second bag
B3 = third bag
Let A = ball drawn is red
Since, there are three bags.
Probability of choosing one bag= P(B1) = P(B2) = P(B3) = 1/3.
From B1: Total balls = 10
3 red + 7 black balls.
Probability of drawing 1 red ball from it , P(A) = 3/10.
From B2: Total balls = 10
8 red + 2 black
Probability of drawing 1 red ball is, P(A) = 8/10
From B3 : Total Balls = 10
4 red + 6 black
Probability of drawing 1 red ball, P(A) = 4/10 .
To find Probability given that the ball drawn is red, that the ball is drawn from the third bag by Bayes' rule.
That is , P(B3|A)
[tex]=\frac{\frac{1}{3} \times \frac{4}{10}} { \frac{1}{3} \times \frac{3}{10} + \frac{1}{3} \times\frac{8}{10} + \frac{1}{3} \times \frac{4}{10}}[/tex]
[tex]=\frac{4}{30} \times \frac{30}{15}\\\\=\frac{4}{15}[/tex]
Therefore, the probability that it is drawn from the third bag is 4/15.
Answer:
4/15
Step-by-step explanation:
Solution of conditional probability problem:
Given:
Bags (3R,7B), (8R,2B), (4R,6B)
Let
P(R,i) = probability of drawing a red AND from bag i
P(R, 1) = 3/10 * (1/3) = 3/30
P(R, 2) = 8/10 * (1/3) = 8/30
P(R, 3) = 4/10 * (1/3) = 4/30
Let
Let P(R) = probability of drawing a red from any bag
P(R) = sum P(R,i) for i = 1 to 3 using the addition rule
= 3/30 + 8/30 + 4/30
= 15/30
= 1 / 2
Conditional Probability of drawing from the third bag GIVEN that it is a red
= P(3 | R)
= P(R, 3) / P(R)
= 4/30 / (1/2)
= 8/30
= 4 / 15
(Since all bags contain 10 balls, by intuition, 4 red from third / 15 total red = 4/15)
HELP THIS IS DUE SOON MATH
Answer: the answer is x= -11.
what are two solutions of x^2-2x-4=-3+9
Answer:
x^2-2x=10
a few more steps...
the answer is 1+the square root of 11
All of the following statements have the same value except..?
1. six below zero
2. the opposite of six
3. negative six
4. the absolute value of six
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
Let's consider each of the statements.
1. Six below zero.
⟹ Any number below zero will be negative. So, the value will be [tex]\boxed{-6}[/tex]
____________________
2. The opposite of six.
⟹ The opposite of 6 wil be negative 6. The value again will be [tex]\boxed{-6}[/tex]
____________________
3. Negative six.
⟹ Negative six in numerical form is [tex]\boxed{-6}[/tex]
____________________
4. The absolute value of six.
⟹ Here they've asked the absolute value of 6 which will be [tex]\boxed{6}[/tex]
____________________
⏩ So, the statement which doesn't have the same value will be ⇻ [tex]\boxed{statement \ 4}[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex]RainbowSalt2^{2}2^{2}[/tex]
What is 2+2-35x62+88-1x675
[tex]\longrightarrow{\blue{ -2753}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]2 + 2 - 35 \times 62 + 88 - 1 \times 675[/tex]
[tex] = 2 + 2 - 2170 + 88 - 675[/tex]
[tex] = 92 - 2170 - 675[/tex]
[tex] = 92 - 2845[/tex]
[tex] = - 2753[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Miranda's financial aid stipulates that her tuition not exceed $1500. If her college charges a $55 registration fee for the term plus $275 per course, what is the greatest number of courses for which Miranda can register? Miranda can register for at most how many courses?
Answer:
5
Step-by-step explanation:
275x5= 1375
1375+55=1430
Making of a muffin requires 32 ounces of sugar. Convert ounces to pounds?
Answer:
2 pounds
Step-by-step explanation:
1 pound = 16 ounces
x pound = 32 ounces
[tex]x = \frac{32}{16} = 2 \ pounds[/tex]
Answer:
the answer to 32ounces is 2 pounds
pleaseeeee helpppppppppppp
9514 1404 393
Answer:
maximum height: 26.5 ftair time: 2.5 secondsStep-by-step explanation:
I find the easiest way to answer these questions is to use a graphing calculator. It can show you the extreme values and the intercepts. The graph below shows the maximum height is 26.5 ft. The time in air is about 2.5 seconds.
__
If you prefer to solve this algebraically, you can use the equation of the axis of symmetry to find the time of the maximum height:
t = -b/(2a) = -(40)/(2×-16) = 5/4
Then the maximum height is ...
h(5/4) = -16(5/4)² +40(5/4) +1.5 = -25 +50 +1.5 = 26.5 . . . feet
__
Now that we know the vertex of the function, we can write it in vertex form:
h(t) = -16(t -5/4)² +26.5
Solving for the value of t that makes this zero, we get ...
0 = -16(t -5/4)² +26.5
16(t -5/4)² = 26.5
(t -5/4)² = 26.5/16 = 1.65625
Then ...
t = 1.25 +√1.65625 ≈ 2.536954
The cannon ball is in the air about 2.5 seconds.
if 1 foot= 0.37 metres and 1 miles = 5180 feet, find the number of kilometres in 15 miles
Help is very much needed!!
Answer:
DE = 24
Step-by-step explanation:
The midsegment DE is half the length of the third side AC , that is
DE = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 48 = 24
An umbrella sprinkler is positioned on a ceiling at a point whose x- coordinate is 0. Negative values of a indicate distances, in meters, to the left of the position of the sprinkler, and positive values indicate distances to the right. The path of water from the sprinkler can be modeled by the quadratic function
w(x) = -1/4(x^2 -12 ) where w(x) is the height of the water, in meters, at position x.
Required:
Which equivalent expressions displays the height of the ceiling as a constant or coefficient?
Answer:
-1/4x² + 3
Step-by-step explanation:
Given that:
Path of sprinkler is modeled by the quadratic function :
w(x) = -1/4(x^2 -12 )
w(x) = height of the water, in meters, at position x
The height of ceiling as a constant or Coefficient = w(x)
Expanding w(x)
-1/4(x^2 -12 )
-1/4 * x² + 1/4 * 12
-1/4x² + 3
The height of ceiling is -1/4x² + 3
What Are the values of x and y?
Answer:
y = 72.5
x = 35.
Step-by-step explanation:
First Off, Let's Divide the question.
Let's Find the variable y :
there are 2 y(s), so it is 2y.
equation: 2y +35 =180.
I put 180 because A straight Line is always 180.
2y+35=180
1. Subtract both sides.
2y = 145
y = 72.5
Next,Find x
So y + y + x = 180.
We already know y, which is 72.5
72.5 +72.5 + x = 180
72.5 +72.5
x + 145 = 180
x = 35.
Hope This Helps!
Tập nghiệm của phương trình 2^x=-1 là
Step-by-step explanation:
Tập nghiệm của [tex]2^x=-1[/tex] là tập rỗng nha bạn. Vì 2 là số dương nên mũ mấy cũng dương hết.
Which graph represents the function f(x) = 2^x+ 3?
Answer:
Where's the graph?
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Some of the images in the diagram are images of polygon 1 from similarity transformations ?
Polygon and polygon are similar to polygon 1.
Answer: 3 and 4
Step-by-step explanation:
- 10 + x < - 2 what is the solution of the inequality shown below
Answer:
x<8
Step-by-step explanation:
Fourth-grade classrooms in several elementary schools are randomly assigned to different antibullying training programs at the beginning of the school year. The school district keeps track of the number of incidents of bullying in each classroom.
This study is an example of __________ study.
Answer:
experimental study.
Step-by-step explanation:
This study is an example of an experimental study.
The type of training program is the independent variable. The number of incidents of bullying is the dependent variable.
Since the participants of our study are affected directly in the research (the fourth-grade children) by not training against anti-bullying, the study is experimental research.
An independent variable is one that is somehow controlled or adjusted to evaluate the effects of a different variable, the dependent. Since we control whether we do bullying training here or not, our kind of training program is our independent variable, which is our dependent variable since we measure its impact on instances of bullying no.
Find the value of x and the value of y.
Please help :(
Answer:
Step-by-step explanation:
chia hình tứ giác thành 1 hình chữ nhật và một tam giác vuông từ đó y=4/sin(45)= 4,7 ; x=3+4/tan(45)=5,469
Anyone please help, how to do it
Answer:
Step-by-step explanation: