Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].
So if the perimeter of the larger polygon is
[tex]s_1+s_2+s_3=85[/tex]
then the perimeter of the smaller polygon would be
[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]
so its perimeter would be 34 meters.
Final answer:
The perimeter of the smaller similar polygon is 34 meters, calculated by setting up and solving the proportion 2/5 = P/85.
Explanation:
When dealing with similar polygons, the ratio of their corresponding side lengths is the same as the ratio of their perimeters. Given that the ratio of the sides is 2 to 5, and the perimeter of the larger polygon is 85 meters, we can set up a proportion to find the perimeter of the smaller polygon.
Let the perimeter of the smaller polygon be P. The proportion will be 2/5 = P/85. To find P, we cross-multiply and get: 2 * 85 = 5 * P. Simplifying, we find that P equals 34 meters. Hence, the perimeter of the smaller polygon is 34 meters.
Kathy's fish tank has many different kinds of fish. In particular 1/6 of the fish are testras, and 2/5 of the fish are guppies. What fraction of kathy's fish are either testras or guppies?
Factor [tex]x^3-4x^2-3x+18=0[/tex] given that 3 is a zero.
A) [tex](x+2)(x-3)^2=0[/tex]
B) [tex](x-2)(x-3)^2=0[/tex]
C) [tex](x-2)(x-3)(x+3)=0[/tex]
D) [tex](x+2)(x-\sqrt{3})(x+\sqrt{3})=0[/tex]
Answer:
A) (x +2)(x -3)² = 0
Step-by-step explanation:
Synthetic division by (x-3) gives the quadratic x² -x -6, which has factors (x -3) and (x +2). This is confirmed by another round of synthetic division.
The resulting factorization is ...
... (x +2)(x -3)² = 0
_____
A graph confirms a double zero at x=3 and one at x=-2.
In 2000, the population of a town was 8914. The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round the answer to the nearest whole number.
Answer:
Step-by-step explanation:
Answer:
12,495 is the answer
Step-by-step explanation:
please help on this one ?
1 ║ 4 6 -1
4 10
----------------------------------------------
4 10 [tex]\boxed{9}[/tex]
⇒ The Remainder is 9
Consider that the system has infinitely many solutions. Which choice is the coefficient of y in the second equation? 5x + 10y = 15 x + __ y = 3
The pay-scale for Pedro's stores is based on the education level of his employees. The education levels are shown for the employees at his two stores.
Which matrix correctly displays the total number of employees for the two stores based on their education levels?
The total of the two matrices is found by adding corresponding elements:
[tex]\left[\begin{array}{cc}5+2&3+3\\22+17&15+27\\13+15&12+18\end{array}\right] =\left[\begin{array}{cc}7&6\\39&42\\28&30\end{array}\right][/tex]
This matches selection A.
Simplify f+g / f-g when f(x)= x-4 / x+9 and g(x)= x-9 / x+4
[tex]f(x)=\dfrac{x-4}{x+9};\ g(x)=\dfrac{x-9}{x+4}\\\\f(x)+g(x)=\dfrac{x-4}{x+9}+\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)+(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2+x^2-9^2}{(x+9)(x+4)}=\dfrac{2x^2-16-81}{(x+9)(x+4)}=\dfrac{2x^2-97}{(x+9)(x+4)}\\\\f(x)-g(x)=\dfrac{x-4}{x+9}-\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)-(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2-(x^2-9^2)}{(x+9)(x+4)}=\dfrac{x^2-16-x^2+81}{(x+9)(x+4)}=\dfrac{65}{(x+9)(x+4)}[/tex]
[tex]\dfrac{f+g}{f-g}=(f+g):(f-g)=\dfrac{2x^2-97}{(x+9)(x+4)}:\dfrac{65}{(x+9)(x+4)}\\\\=\dfrac{2x^2-97}{(x+9)(x+4)}\cdot\dfrac{(x+9)(x+4)}{65}\\\\Answer:\ \boxed{\dfrac{f+g}{f-g}=\dfrac{2x^2-97}{65}}[/tex]
The value of f+g / f-g = (2x² - 97) / 65
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)= x-4 / x+9 and g(x)= x-9 / x+4
So, f+g / f-g
f(x)+ g(x)
= x-4 / x+9 + x-9 / x+4
= (x² - 4²) + (x² - 9²) / (x+4)(x+9)
= (2x² - 97) / (x+4)(x+9)
f(x)-g(x)
= x-4 / x+9 - x-9 / x+4
= (x² - 4²) - (x² - 9²) / (x+4)(x+9)
= 65 / (x+4)(x+9)
Then, f+g / f-g
= (2x² - 97) / (x+4)(x+9) x (x+4)(x+9)/ 65
= (2x² - 97) / 65
Learn more about Function here:
https://brainly.com/question/12908735
#SPJ2
Maulik bought two horses at Rs 40,000 each. He sold one horse at 15% gain, but he to sell the second horse at a loss. If he had suffered a loss of Rs 3600 on the Whole transaction, find the selling price of the second horse.
Answer:
Answer is selling price of second horse is Rs 30400.
Step-by-step explanation:
Maulik bought one horse at Rs 40000 and sold it with a gain of 15%
So the selling price of one horse will be 40000+15% of 40000
= 40000+6000
= Rs 46000
Second horse is costing Rs 40000 and had suffered a loss of Rs 3600 on selling both so selling price of both will be = 40000×2-3600
= 80000-3600
= 76400
Now selling price of second horse will be selling price of both - selling price of first = 76400-46000 = Rs 30400
Answer:
The selling price of the second horse is Rs 30,400.
Step-by-step explanation:
Cost Price of first horse([tex]CP_{1}[/tex])= Rs. 40,000
Cost Price of second horse([tex]CP_{2}[/tex])= Rs. 40,000
Total cost price=[tex]CP_{1}+CP_{2}[/tex]=Rs (40,000+40,000)=Rs 80,000
First horse is sold at 15% gain.
This means selling price of first horse([tex]SP_{1}[/tex])= [tex]\dfrac{115}{100} \times40000[/tex]
= Rs. 46,000
also total there is a loss of Rs 3600
selling price of both the horses(SP)=80000-3600=Rs 76400
now, [tex]SP=SP_{1}+SP_{2}[/tex]
where [tex]SP_{2}[/tex] is the selling price of the second horse.
[tex]SP_{2}=SP-SP_{1}[/tex]
[tex]SP_{2}=76400-46000[/tex]
[tex]SP_{2}=30400[/tex]
Hence the selling price of the second horse is Rs 30,400.
BRAINLIEST AND 80 POINTS
A spinner is divided into 3 sections: red, blue, and green. Belinda spins the spinner 10 times. The spinner lands on red 2 times. What is the experimental probability that the spinner lands on red?
Answer:
1/5
Step-by-step explanation:
Experimental probability is the actual times it happens divided by the number of trials
Actual times red occurs:2
Trials: 10
Experimental probability: 2/10 = 1/5
Answer:1/5
Step-by-step explanation:Experimental probability is the actual times it happens divided by the number of trials
Actual times red occurs:2
Trials: 10
Experimental probability: 2/10 = 1/5
Why is the answer D? I'm having a hard time with the logic of it.
Let's assume the opposite is the case. So let's assume that a = b is true. If so, then f(a) and f(b) would be the same output. This is because we can replace 'b' with 'a', or vice versa. In other words, f(a) = f(b) would be true. But this contradicts the original inequality that f(b) < f(a)
So that is why 'a' cannot equal b. We don't know if a > b or if a < b (unless we are told if the function is strictly decreasing or increasing on the interval from x = a to x = b), so we just leave it as [tex]a \ne b[/tex]
A student raises her average grade from a 75 to a 90. What is the percent of the increase in the students average grade
Please explain as best as you can :)
Answer:
The best answer is C. y = 2/5x + 2
Step-by-step explanation:
You would start at point 2 then rise 2 units then run 5 units. (i got something else) but i went to desmos to make sure and it matched
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b).
Read two points from the graph.
y-intercept = (0, 2) → b = 2
x-intercept = (-5, 0)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{0-2}{-5-0}=\dfrac{-2}{-5}=\dfrac{2}{5}[/tex]
Therefore your answer is
[tex]\boxed{C.\ y=\dfrac{2}{5}x+2}[/tex]
Kit bought a soft drink and a sandwich for 9.00 what was the price of each ifnthe sandwich cost 3.5 times as much as the soft drink
Answer:
Sandwich = 6.75
Soft drink = 2.25
Step-by-step explanation:
9.00/4 = 2.25
2.25*3=6.75
You receive two job offers. One offers a straight commission of 6% of sales. The other offers a salary of $500 per week plus 3% of sales. How much would you have to sell per week in order for the straight commission job offer to be better? Use Gaussian elimination
Answer: $16, 666.67
Step-by-step explanation:
Job 1: 0.06x
Job 2: 0.03x + 500
0.06x > 0.03x + 500
-0.03x -0.03x
0.03x > 500
÷0.03 ÷0.03
[tex]x > \dfrac{50000}{3}[/tex]
x > 16,666.67 rounded to the nearest penny
Solve the system of linear equations by substitution.
2x=y−10
x+7=y
Answer:
-3,4
Step-by-step explanation:
The solution to the system of linear equations 2x = y - 10 and x + 7 = y by substitution is (x, y) = (-3, 4).
Explanation:To solve the system of linear equations 2x = y - 10 and x + 7 = y by substitution, follow these steps:
First, solve one of the equations for one variable. From the second equation, we get x = y - 7.Next, substitute this expression for x into the first equation: 2(y - 7) = y - 10.Simplify and solve for y: 2y - 14 = y - 10, which simplifies to y = 4.Finally, substitute y back into one of the original equations to find x: x = 4 - 7, which simplifies to x = -3.The solution to the system of equations is (x, y) = (-3, 4).
I NEED HELP ASAP LIKE NOWWW
The formula for the circumference of a circle is = 2. Use 3.14 for . Solve the formula for r. What is the radius of a circle with a circumference of 87 ? Round to the nearest tenth.
a. = 2; 13.9 cm
b. =2 π ; 27.7 cm
c. = 2 ; 546.4 cm
d. = − 2 ; 80.7 cm
The formula for the area of a triangle is = ℎ /2 Solve the formula for h. What is the height of a triangle that has an area of 25 2 and a base with a length of 10 ?
a. ℎ = 2 ; 1.25 mi
b. ℎ = 2 ; 2.5 mi
c. ℎ =2/; 0.2 mi
d. ℎ = 2/; 5 mi
Answer:
C / (2pi) = r; r= 13.9 cm
2A/b = h ; h= 5
Step-by-step explanation:
The formula for the circumference of a circle is C = 2* pi * r.
Solving for r, we need to divide by 2 * pi on each side
C/(2* pi) = 2*pi*r/ (2* pi)
C / (2pi) = r
If the circumference is 87, we can find r by substituting into the equation.
87 / (2 * 3.14) = r
87/ 6.28 = r
13.85350318=r
Rounding to the nearest tenth
r= 13.9 cm
The formula for the area of a triangle is A = bℎ /2
To solve the formula for h, we need to multiply each side by 2
2*A = bh
Then divide each side by b
2A/b = bh/b
2A/b = h
If the area of a triangle is 25 and the base of 10 , we can substitute in to find the height.
2* 25 /10 = h
50/10 = h
5 =h
Start at six create a pattern that multiplies each number by three stop when you have four numbers
Answer:
Step-by-step explanation:6*3 7*3 8*3 9*3
There are more cups in 5 gallons than in 22 quarts
Answer:
The answer is false
Step-by-step explanation:
22 quarts is 5.5 gallons
Answer: FALSE, there are 80 cups in 5 gallons and 88 cups in 22 quarts
can you please help me i really need help.
find the value of x.
a) 90
b) 158
c) 180
d) 9
Answer:
d) 9
Step-by-step explanation:
In a kite, the two shorter sides have to be equal.
Therefore
3x-5 = 22
Add 5 to each side
3x-5+5 = 22+5
3x = 27
Divide each side by 3
3x/3 = 27/3
x =9
What is the value of x in the equation 2^2x = 2^3?
A.) x = 1.5
B.) x = 3
C.) x = 64
D.) x = 0.28
Answer:
The value of x is A) 1.5
Step-by-step explanation:
In order to find this, we can first note that if the base is the same, their exponents also must be the same. Since both have a base of 2, then we can eliminate the base and simply compare their exponents.
2x = 3
Now we can solve by simply dividing both by 2.
x = 1.5
Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the ages of Harvey and Jane. Jane is a0 years old. Harvey is a1 years old.
Answer:
Jane is 12 years old and Harvey's is 36 years old .
Step-by-step explanation:
Given :
Jane is [tex]a_{0}[/tex] years old.
Harvey is [tex]a_{1}[/tex] years old.
Harvey is 3 times as old as Jane.
The sum of their ages is 48 years.
To find : The ages of Harvey and Jane.
Solution :
Jane 's age :
[tex]a_{0}[/tex]
Harvey 's age:
[tex]a_{1}[/tex]
Since we are given that sum of their ages is 48 years
⇒[tex]a_{1} + a_{0} = 48[/tex] ----(A)
We are also given that Harvey is 3 times as old as Jane.
⇒[tex]a_{1} = 3a_{0}[/tex] --- (B)
Solving (A) and (B) using substitution method
Substitute value of [tex]a_{1}[/tex] from (B) in (A) :
⇒[tex] 3a_{0}+ a_{0} = 48[/tex]
⇒[tex] 4a_{0} = 48[/tex]
⇒[tex]a_{0} = \frac{48}{4}[/tex]
⇒[tex]a_{0} = 12[/tex]
Thus , Jane 's age is 12 years .
Substitute this value in (B) to find Harvey,s age :
⇒[tex]a_{1} = 3(12)[/tex]
⇒[tex]a_{1} = 36[/tex]
Thus, Harvey,s age is 36 years .
Hence Jane is 12 years old and Harvey's is 36 years old .
Will give you brainliest!!
Answer:
Final answer is 7.
Step-by-step explanation:
Given that f(x) =7x+8.
Now we need to find the derivative of f(x) at x=5
So let's find derivative first.
[tex]f(x)=7x+8[/tex]
[tex]f'(x)=\frac{d}{dx}(7x+8)[/tex]
[tex]f'(x)=\frac{d}{dx}(7x)+\frac{d}{dx}(8)[/tex] {Using formula [f+g]'=f'+g'] }
[tex]f'(x)=7\frac{d}{dx}(x)+\frac{d}{dx}(8)[/tex] {Using formula f'(ax)=a f'(x) }
[tex]f'(x)=7(1)+0[/tex] {derivative of constant term is 0 }
[tex]f'(x)=7[/tex]
Now plug the given value of x=5
[tex]f'(5)=7[/tex]
Hence final answer is 7.
Using the information in the diagram, you can prove that segment WY ≅ segment ZX. Which reason would not appear in the proof?
AAS Congruence Theorem
Right Angles Congruence Theorem
SAS Congruence Postulate
Alternate Interior Angles Theorem
Answer: SAS congruence (choice C)
==============================================
Explanation:
Let's go through the various answer choices. I'll say whether or not they are used
A) This is used because angle WXZ = angle WYZ and angle WZX = angle ZWY are the two pairs of angles. The pair of sides are WZ = WZ which overlap (aka shared) between the two triangles. Note how the sides are not between the angled mentioned. Eg: for the triangle on the left, WZ is not between angle WXZ and angle WZX. So we can cross choice A off the list. Note: AAS is slightly different from ASA. Make sure not to confuse the two.
B) We use this to prove that the right angles (WXZ and WYZ) are congruent to each other. Both are 90 degrees. This will then feed in to choice A above, to help use AAS. We can cross choice B off the list.
C) We do not use SAS because we use AAS instead. We only have info about one pair of sides (WZ = WZ). We do not have info about another pair of sides. Therefore, this is the answer.
D) We use this fact to help set up that angle WZX = angle ZWY. The segments WY and XZ are parallel. I like to think of them as train tracks. On the inside of the train tracks are the angles WZX and ZWY, and they are on opposite sides of the transversal segment WZ, so this is why the pair of angles are alternate interior angles. They are congruent as long as WY is parallel to XZ. Like with choice B, this helps feed into choice A. We can cross choice D off the list.
Among the listed reasons, the Alternate Interior Angles Theorem would typically not appear in a proof proving that segment WY is congruent to segment ZX, unless the diagram involved parallel lines cut by a transversal. Other postulates might be used if angle and side measurements are congruent.
Explanation:In proving that segment WY ≅ segment ZX, some postulates or theorems may not appear in the proof depending on the given diagram. The Angel-Angle-Side (AAS) Congruence Theorem, the Side-Angle-Side (SAS) Congruence Postulate, and the Right Angles Congruence Theorem could all potentially appear in the proof if relevant angle and side measurements are given in the diagram.
However, the Alternate Interior Angles Theorem would typically not appear in this proof. This theorem is related to the indication that two lines are parallel when they are cut by a transversal and the alternate interior angles are congruent. This theorem does not directly involve proving the congruity of sides (or segments) as would be necessary for proving segment WY ≅ segment ZX. Unless the diagram specifically involved parallel lines cut by a transversal, this theorem would not be used.
Learn more about Congruence of Segments here:https://brainly.com/question/28636355
#SPJ2
A pizza delivery shop averages 30 minutes per delivery with a standard deviation of 4 minutes. What is the probability that a pizza takes less than 27 minutes to be delivered
Which graph type would be best for showing the height of a fifth-grade student who is taller than 25% of the other students in his class?
Answer: The bar graph could work.
Answer:
Step-by-step explanation: A box plot takes a large amount of data and clearly identifies the median, first quartile, and third quartile. The first quartile identifies the 25th percentile, and the third quartile identifies the 75th percentile.
To determine how the height of the student compares to 25% of his class, the value of the first quartile of the heights is needed.
Therefore, the best graph type to show how the student compares to 25% of his class is a box plot.
Phillip bought apples from the grocery for $2.20 per pound. If he had bought 2.5 pounds of apples on Monday and 1.2 pounds of apples on Tuesday, how much did he spend on apples in total?
Answer:
8.14$
Step-by-step explanation:
each pound is for 2.20
2.5 x 2.20 = 5.50$ on Monday
1.2 x 2.20 = 2.64$ on Tuesday
5.50 + 2.64 = 8.14$ in total
Ana age is 8 years less than 4 times her sister's age .Write an expression for Ana's age.How old is Ana if her sister is 5 years old ?
Answer: 4x - 8 ; 12 yrs old
Step-by-step explanation:
sister: x
Ana: 4x - 8
when x = 5, Ana = 4(5) - 8
= 20 - 8
= 12
Can somebody help me with this. Please see the attachment.
48
Step-by-step explanation:Let x represent the distance OC. Then CD = x+2, and DP = 16-x. The radius of circle P is ...
... CD +DP = (x+2) +(16-x) = 18
The radius of circle O is ..
... OC + CD = (x) + (x +2) = 2x+2
The length OP is ...
... OC + CP = (x) + (18) = x+18.
Now, the perimeter of ΔAOP is ...
... radius of circle O + radius of circle P + OP = 80
... = (2x+2) + 18 + (x+18) = 3x+38 = 80
Then x is ...
... x = (80 -38)/3 = 14
and the radius of circle O is
... 2x +2 = 2·14 +2 = 30
The desired sum is ...
... OB + BP = (radius of circle O) + (radius of circle P) = 30 + 18
... OB + BP = 48
Write all of the potential roots of:
p(x) = x^4 − 9x^2 − 4x + 12
So to find the potential roots, we will be using the rational root theorem. The rational root theorem is [tex]\pm \frac{p}{q}[/tex] , with p = factors of the constant and q = factors of the leading coefficient. In this case, our constant is 12 and our leading coefficient is 1:
[tex]p=1,2,3,4,6,12\\q=1\\\\\pm\frac{1,2,3,4,5,6,12}{1}\\\\\pm1,\pm\ 2,\pm\ 3,\pm\ 4,\pm\ 6,\pm\ 12[/tex]
AnswerIn short, our potential roots are: ± 1, ± 2, ± 3, ± 4, ± 6, and ± 12.
Answer:
2,4,3,6,12
Step-by-step explanation:
i just did it.