The perimeter of a rectangular concrete patio is 34 meters. the area is 70 square meters. what are the dimensions of the patio?
To find the dimensions of the rectangular patio, use the equations for perimeter and area and solve for length and width.
Explanation:To find the dimensions of the rectangular patio, we can use the given information about its perimeter and area. Let's assume the length of the patio is L and the width is W.
The perimeter is given as 34 meters, which is equal to 2L + 2W. So, we have the equation 2L + 2W = 34.
The area is given as 70 square meters, which is equal to L * W. So, we have the equation L * W = 70.
We can use these equations to solve for L and W using substitution or elimination method.
What is the value of the 7 digit in 91,764,350?
Solve for t.
q=r+rst
The equation q=r+rst can be rearranged to isolate t, with the final solution being t=(q-r)/rs.
Explanation:To solve for t in the equation q=r+rst, first, you need to isolate t on one side of the equation. You can do this by subtracting r from both sides so that you have q-r=rst. Next, divide both sides by rs, which gives you the final solution: t=(q-r)/rs.
Learn more about Algebra here:https://brainly.com/question/32436021
#SPJ3
If f(x) = 3x2 - x, find f(-2).
10
14
38
f(x) = 3x^2-x
F(-2)
replace x with -2
3(-2)^2 - -2 =
3*4 +2 = 14
Answer is 14
If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is ___.
The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2.
What is probability?Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.
As per the given,
In the first three attempts coming head in the first three times.
In the fourth attempt, the probability will be independent of the first three events.
Thus, the probability of coming ahead in the fourth time will be as,
Number of desire output/number of total output
=> 1 / 2
Hence "The coming head in the fourth time is independent of the coming head in the first three times thus the probability of coming head in the fourth time is 1/2".
For more information about the probability,
brainly.com/question/11234923
#SPJ6
Multiplying by a conjugate gives a rational number because (a + b)(a -
b.= _____.
What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD.
The value of x in the figure given is E. √70.
The answer is E. √70.
The two triangles are similar by the AAA Similarity Theorem, since they have two pairs of congruent angles, namely ∠ABD and ∠CAD, and ∠BAD and ∠CDA.
Since the triangles are similar, the ratio of corresponding sides is constant. In particular, the ratio of AD to CD is the same as the ratio of BD to AD.
We are given that AD = 14 and CD = 20, so the ratio of AD to CD is 14/20. We are also given that BD = x, so the ratio of BD to AD is x/14.
Setting these two ratios equal to each other, we get x/14 = 14/20, which simplifies to x = √70.
Here is a proof that shows why the two triangles are similar:
AAA Similarity: Triangles ABD and CAD have two pairs of congruent angles, namely <ADB> and <CAD>, because they are both right angles.
SSS Similarity: Triangles ABD and CAD have three pairs of corresponding sides that are proportional, namely AD/CD = 14/20, BD/AD = x/14, and AB/CD = √70/20. Therefore, the two triangles are similar by the SSS Similarity Theorem.
To learn more about value here:
https://brainly.com/question/28787935
#SPJ2
What did the doctor say to the guy who thought he was a wigwam one day and teepee the next? math riddle
Answer:
too tenes
This is the correct answer because it is a play on words comparing tents which describes the native american home structure of a wigwam and a teepee and tense, will which describes a physiological response to high anxiety6.
Simplify 5 - 2 · 3 + 4. 13 -5 3 21
Auto insurance options offered by AA Auto Insurance are outlined in the table below. What monthly payment would you expect for an insurance policy through AA Auto Insurance with the following options? Bodily Injury: $25/50,000 Property Damage: $25,000 Collision: $250 deductible Comprehensive: $100 deductible
a.
$43.23
b.
$46.10
c.
$54.85
d.
$64.44
In this exercise we have to use the knowledge of finance to calculate the monthly amount of insurance, so the best alternative that represents this amount is:
Option C
In this exercise we want to calculate the monthly insurance payment amount, so from the given values we find:
[tex]Payment= (Bodily Injury)+ (Property Damage)+ (Collision)+(Comprehensive)[/tex]
Substituting the values in the formula given above we find that:
[tex]Payment= 22.5 + 120.5 + 415.25 + 100 \\= 658.25\\658.25/12 = 54.854[/tex]
See more about finances at brainly.com/question/10024737
For f(x)=3x+1 and g(x)=x squared - 6 find (f- g)(x)
The expression 2/+2w is used to find the perimeter of a rectangle with length / and width w.
What is the perimeter of a rectangle with length 14cm and width 4cm?
9cm
18cm
28cm
36cm
THANKS IN ADVANCE, I MARK BRAINLIEST!!!
Answer: 36 cm
Step-by-step explanation:
Given : The expression 2l+2w is used to find the perimeter of a rectangle with length l and width w.
To find : The perimeter of a rectangle with length 14cm and width 4cm.
Substitute l=14 and w=4 in the given expression , we get
Perimeter= [tex]2(14)+2(4) =28+8=36\ cm[/tex]
Hence, the perimeter of a rectangle with length 14cm and width 4cm= 36 cm
A line goes through the points (8,9) and (2,4).
What is the slope of the line?
Write the equation of the line in point-slope form?
Write the equation of the line in slope-intercept form?
A probability experiment consists of rolling a fair 16-sided die. Find the probability of the event below of rolling a 5.
Answer:
The probability of the event below of rolling a 5 is 0.0625.
Step-by-step explanation:
Given is : A probability experiment consists of rolling a fair 16-sided die. Find the probability of the event below of rolling a 5.
Total number of faces = 16
So, there is only one way for rolling a 5 on a die
And the probability of rolling a 5 on a die = [tex]\frac{1}{16}[/tex]
= 0.0625
Solve the following equation.75 = –5(–3 – 4x)
x = 3
x = –4
x = –3
x = 5
Evaluate u + xy, for u = 20, x = 9, and y = 8.
calculate the rate of change for the quadratic function over the given interval:
f(x)=x^2 + 4x +5 ; -4 =< x =< -2
The rate of change of the quadratic function over the interval −4≤x≤−2 is 2.
To find the rate of change of the quadratic function [tex]$f(x)=x^2+4 x+5$[/tex] , over the interval −4≤x≤−2, we need to find the average rate of change over that interval.
The average rate of change of a function f(x) over an interval [a,b] is given by:
[tex]Average Rate of Change =\frac{f(b)-f(a)}{b-a}$[/tex]
So, in this case:
a=−4
b=−2
We calculate f(−4) and f(−2):
[tex]$\begin{aligned} & f(-4)=(-4)^2+4(-4)+5=16-16+5=5 \\ & f(-2)=(-2)^2+4(-2)+5=4-8+5=1\end{aligned}$[/tex]
Now we can find the rate of change:
Rate of Change = [tex]$\frac{1-5}{-2-(-4)}=\frac{-4}{-2}=2$[/tex]
The average rate of change of the function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 is -2.
The rate of change for the quadratic function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 can be calculated using the average rate of change formula. This formula is given by:
Rate of Change = [f(x2) - f(x1)] / (x2 - x1)
Where x1 = -4 and x2 = -2. We first calculate f(-4) and f(-2) by plugging these values into the function:
f(-4) = (-4)² + 4(-4) + 5 = 16 - 16 + 5 = 5
f(-2) = (-2)² + 4(-2) + 5 = 4 - 8 + 5 = 1
Now we use these results in our rate of change formula:
Rate of Change = (1 - 5) / (-2 + 4) = -4 / 2 = -2
The average rate of change of the function f(x) over the interval from x = -4 to x = -2 is -2.
Which number line represents the solutions to |x + 4| = 2?
The number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].
Further explanation:
The equation is given as follows:
[tex]|x+4|=2[/tex]
In the above equation [tex]||[/tex] represents the modulus function.
Modulus function is defined as a function which gives positive value of the function for any real value of [tex]x[/tex].
For example: The function [tex]y=|x|[/tex] is a modulus function in which [tex]y>0[/tex] and [tex]x<0[/tex] or [tex]x>0[/tex].
In the given equation [tex]|x+4|[/tex] is a modulus expression.
There are two cases formed for [tex]|x+4|[/tex].
First case: [tex]x>-4[/tex]
If [tex]x>-4[/tex] then [tex]|x+4|\rightarrow (x+4)[/tex].
Substitute [tex]|x+4|=(x+4)[/tex] in [tex]|x+4|=2[/tex].
[tex]\begin{aligned}x+4&=2\\x&=2-4\\&=-2\end{aligned}[/tex]
Therefore, for [tex]x>-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-2[/tex].
Second case: [tex]x<-4[/tex]
If [tex]x<-4[/tex] then [tex]|x+4|\rightarrow -(x+4)[/tex].
Substitute [tex]|x+4|=-(x+4)[/tex] in [tex]|x+4|=2[/tex].
[tex]\begin{aligned}-(x+4)&=2\\-x-4&=2\\-x&=2+4\\-x&=6\\x&=-6\end{aligned}[/tex]
Therefore, for [tex]x<-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-6[/tex].
This implies that the solution for the equation [tex]|x+4|=2[/tex] or the value of [tex]x[/tex] which satisfies the given equation are [tex]\fbox{\begin\\\ \math x=-2\ \text{and}\ x=-6\\\end{minispace}}[/tex].
Option 1:
The number line in option 1 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 1 is correct.
Option 2:
The number line in option 2 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=4[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 2 is incorrect.
Option 3:
The number line in option 3 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=6[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 3 is incorrect.
Option 4:
The number line in option 4 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-4[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 4 is incorrect.
Therefore, the number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].
Learn more:
1. A problem on composite function https://brainly.com/question/2723982
2. A problem to find radius and center of circle https://brainly.com/question/9510228
3. A problem to determine intercepts of a line https://brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Functions
Keywords: Functions, modulus, modulus function, number line, real line, |x+4|=2, equation, root, zeroes, solutions, absolute function, x=-6 and x=-2.
Option A is correct, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].
Modulus function always returns a positive value to the equation.
Here, [tex]|x+4|[/tex] will give positive result if [tex]x>-4[/tex] and negative value if, [tex]x<-4[/tex].
Case 1: When [tex]x>-4[/tex]
According to the given equation,
[tex]|x+4|=2\\x=2-4\\x=-2[/tex]
So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x>-4[/tex] is [tex]x=-2[/tex].
Case 2: When [tex]x<-4[/tex]
According to the given equation,
[tex]|x+4|=2\\-x-4=2\\x=-6[/tex]
So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x<-4[/tex] is [tex]x=-6[/tex].
Hence, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].
Now, according to the options, Option A is correct.
Learn more about number line here:
https://brainly.com/question/24279896?referrer=searchResults
I only need number 30 answered
Out of 100 lottery tickets, each having 50% chance of winning, 2 tickets are bought at random. what is the probability that at least one ticket will win?
Simplify using long division
The distance d in feet that dropped object falls in t seconds is givin by the equation d divided 16 = tsquared how long does it take a dropped object to fall 64 feet
Consider this equation (csc x+1)/cot x = cot x/(csc x +1) is it an identity?
(50 POINTS) Hi, I really need help on this first part of my portfolio it was due last week but I don't really get this part so if someone could explain it to me I could get the other four parts done on my own.
-------
Use the City Populations table found on the message board and select a city that is experiencing population growth. Determine the percentage growth and use that to write an exponential function to represent the city’s population, y, based on the number of years that pass, x from 2010 (i.e. 2011 means that x = 1)
City: Portland, Oregon 585,256 593,939 603,026 609,456 619,334 630621 639863
This was deleted once and idk why there is plenty of information :(
Ik this is a lot to ask of someone but I haven't had any luck with any function sites.
The formula for the area a of a triangle is a equals 1 half b where is the base and h is the height. solve the formula for h and then find the height of a triangle whose area is 1768 square inches and whose base is 52 inches. round to the nearest tenth if necessary. height = inches
Area of triangle is given as:
A = (1/2) b * h
where b is base and h is height
So given that:
A = 1768 inches^2
b = 52 inches
Rearranging the equation to find for h:
h = 2 A / b
h = 2 * 1768 inches^2 / 52 inches
h = 68 inches
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden. the dirt store sells by the cubic yards. how many cubic yards will you need to order? the store only sells in increments of 1/4 cubic yards.
Answer:
You need to buy 6.5 cubic yards.
Step-by-step explanation:
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden.
We know 1 yard = 3 feet or 1 yard = 36 inches
Then 1 inch = [tex]1/36[/tex] yard.
1 feet = 1/3 yard
The volume of the layer of the topsoil is given by:
= [tex]5(1/36)(23)(1/3)(18)(1/3)[/tex] cubic yards
[tex]2070/324=6.39[/tex] cubic yards
Now, the store only sells increments of 1/4 = 0.25 cubic yards.
So, we need to buy [tex]6.39/0.25=25.56[/tex] increments
Rounded to 26 increments.
Therefore, we need to buy 26 increments of 1/4 cubic yards.
That becomes 6.5 cubic yards.
5. The dimensions, in inches, of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x - 1. The volume is about 7.6 f3. Find the dimensions of the box in inches. Round to the nearest inch. (Hint: 1 f 1,728 in.3)
To find the dimensions of the shipping box, calculate the volume in cubic inches, then set up and solve the volume equation x(x + 5)(3x - 1), substituting the given volume after conversion from cubic feet. Solve for x, then use it to find and round the box's dimensions.
Explanation:To find the dimensions of the shipping box, we need to calculate the volume using the given dimensions in inches and compare it to the provided volume in cubic feet. Recall that the conversion factor between cubic feet and cubic inches is 1 cubic foot equals 1,728 cubic inches. Firstly, convert the volume of the box from cubic feet to cubic inches: 7.6 cubic feet are 7.6 x 1,728 cubic inches.
Next, we can set up the volume equation for the box using the given dimensional expressions: volume = width x length x height, which for this box is x x (x + 5) x (3x - 1). Now we solve the equation for x given that the volume in cubic inches is equal to 7.6 x 1,728 inches.
Once x is found, we can determine the width, length, and height by plugging x back into the expressions x, x + 5, and 3x - 1, respectively, and rounding each to the nearest inch.
If f(x)= 2x+8 and g(x) = x^4, what is (g°f)(-3)?
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x − 2, y + 8) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.
This is a number that can be divided out of each term in an expression.
Answer:
Hello!
Great question!
The correct answer would be "Common Factor."
Step-by-step explanation:
It is a common factor when it is a factor of two (or more) numbers.
The number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.
What is GCF (greatest common factor)?GCF or greatest common factor is the common number which all the term has in a group of terms. It is the number which can divide each number of the group.
For example, let a group of number as,
[tex]\{1,2,4,8,16\}[/tex]
The number which can be divided out of each term in this data is 16 which is the greater common factor of this data set.
Thus, the number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.
Learn more about the GCF here;
https://brainly.com/question/219464
#SPJ2