(90 POINTS) How can you find the length of RT using similarity? Explain your reasoning.
Answer:
RT = 26
Step-by-step explanation:
Based on the figure we can say :
ΔABC ~ ΔTSR (by SAS similarity)Scale factor :
AB/SR = 12/24 = 1/2Hence, as the proportions are the same :
CA/RT = 1/213/RT = 1/2RT = 13 x 2RT = 26The triangle ABC and RST will be similar triangles. Then the length of RT will be 26 units.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If the two triangles are similar, the ratio of the corresponding sides will be constant.
The triangle ABC and RST will be similar triangles.
RT / 13 = 24 / 12
RT = 26
More about the triangle link is given below.
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Let's find 1/4+1/12
First, write the addition so the fractions have denominator 12.
Then add.1/4+1/12=?/12+1/12=?\?
Answer:
[tex]\frac{4}{12}[/tex] or [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12}[/tex]
After sitting out of a refrigerator for a
while, a turkey at room temperature (
68°F) is placed into an oven. The oven
temperature is 305°F. Newton's Law of
Heating explains that the temperature of
the turkey will increase proportionally to
the difference between the temperature of
the turkey and the temperature of the
oven, as given by the formula below:
T = Ta + (To − Ta)e-kt
Ta
=
the temperature surrounding
the object
To
=
the initial temperature of the
object
t
=
the time in hours
T
=
the temperature of the object
after t hours
k = decay constant
The turkey reaches the temperature of
108°F after 3 hours. Using this
information, find the value of k, to the
nearest thousandth. Use the resulting
equation to determine the Fahrenheit
temperature of the turkey, to the nearest
degree, after 4.5 hours.
Answer:
The value of k to the nearest thousandth is -0.133
The of the turkey to the nearest degree after 4.5 hours is 186F
Step-by-step explanation:
If f(x) = 5x, what is ƒ¹ (x)?
Answer:
15,625
Step-by-step explanation:
If f(x) = 5x then f ¹ you must label all numbers in the equation to make it easier, once done you will have 25(5¹)=125¹
125x125=15,625
The inverse function of the given function is x/5.
What is inverse function?Inverse function is represented by f⁻¹ with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
Given that, f(x)=5x
Now, y=5x
Replace x by y and y by x, we get
x=5y
y=x/5
and f⁻¹(x)=x/5
Therefore, the inverse function of the given function is x/5.
Learn more about the inverse function here:
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find the remainder when x³-2x²+4x-2 is divided by (x-1/2)
Answer:
[tex]\sf \bf {remainder}: -\dfrac{3}{8}[/tex]
In order to find remainder:
Follow this short technique:
Set the divisor which is x-½ to zero.
x - 1/2 = 0
x = 1/2
Then insert this following into dividend.
x³ -2x² + 4x - 2insert x = ½
(½)³ - 2(½)² + 4(½) -2simplify
-3/8Answer:
-3/8
Step-by-step explanation:
Let's assume x - 1/2 is a zero of the polynomial :
Substitute x = 1/2 (the zero) in the equationx³ - 2x² + 4x - 2(1/2)³ - 2(1/2)² + 4(1/2) - 21/8 - 2(1/4) + 2 - 21/8 - 1/2-3/8-3/8 is the remainder.
Mrs Tilley Keeps a variety of poultry. This pie chart shows the numbers of What each kind:
27 Geese, 72 Hens, 45 Turkeys and 36 Ducks.
32. What percentage of the poultry are hens?
33. What percentage of the poultry are geese?
34. What fraction of the poultry are ducks?
35. What fraction of the poultry are turkeys?
Answer:
32. 40%
33. 15%
34. 1/5
35. 1/4
Step-by-step explanation:
Question 32
% Hens = No. of hens / Total poultry% Hens = 72 / 27 + 72 + 45 + 36% Hens = 72 / 180 = 2/5% Hens = 40%Question 33
% Geese = No. of geese / Total% Geese = 27/180 % Geese = 3/20% Geese = 15%Question 34
% Ducks = No. of ducks / Total% Ducks = 36/180% Ducks = 1/5Question 35
% Turkeys = No. of turkeys / Total% Turkeys = 45/180% Turkeys = 1/4Answer:
32. 40%
33. 15%
34. 1/5
35. 1/4
Step-by-step explanation:
Given:
27 Geese72 Hens45 Turkeys36 Ducks⇒ Total poultry = 27 + 72 + 45 + 36 = 180
[tex]\sf Percentage = \dfrac{Part}{Whole}\times 100[/tex]
[tex]\implies \sf Hens = \dfrac{72}{180}\times 100=40 \%[/tex]
[tex]\implies \sf Geese= \dfrac{27}{180}\times 100=15 \%[/tex]
[tex]\sf Fraction= \dfrac{Part}{Whole}[/tex]
[tex]\implies \sf Ducks=\dfrac{36}{180}=\dfrac{36 \div 36}{180 \div 36}=\dfrac{1}{5}[/tex]
[tex]\implies \sf Turkeys=\dfrac{45}{180}=\dfrac{45 \div 45}{180 \div 45}=\dfrac{1}{4}[/tex]
Which equation shows the area, in square centimeters, of the shaded figure?
Answer:
[tex]3\times8=24[/tex]
Step-by-step explanation:
Notice that the shaded figure has a width of 3 cm and a length of 8 cm. The area of the rectangle is equal to the product of the width and length, so [tex]8\:\text{cm}\times3\:\text{cm}=24\:\text{cm}^2[/tex] would be the area of the shaded figure.
(U^3 v^4)^4 * (2u^4 v^2)^2
Simplify
Show all work
I give brainliest ,.
1) apply exponent to the terms inside the bracket - multiply exponents
[tex](u^3v^4)^4\\\\(u^1^2v^1^6)[/tex]
[tex](2u^4v^2)^2\\\\(4u^8v^4)[/tex]
2) multiply the two terms together - add exponents
[tex](u^1^2v^1^6)(4u^8v^4)\\\\4(u^1^2^+^8)(v^1^6^+^4)\\\\4u^2^0v^2^0[/tex]
ТУ
Which quadratic function is represented by the graph?
6
5
4
O FUX) = - (x + 1)(x – 5)
O f(x) = - (x – 11x + 5)
3
2-
14
O f(x) = -5(x + 1)(x - 5)
2 3 4 5 x
3 -5 -5 -4 -3 -2 -21
-2
O f(x) = -5(x - 1)(x + 5)
+
-3
4
6
Answer:
the first one
Step-by-step explanation:
because I know the answer
The quadratic function represented in the graph is f(x) = -5 (x - 1) (x + 5).
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given a graph of a quadratic function.
The graph is directed downwards. So the leading coefficient is negative.
The function touches the X axis at two points, x = -5 and x = 1.
So -5 and 1 are the zeroes of the function.
So the function can be factored as,
f(x) = (x + 5)(x - 1)
So the quadratic equation is,
f(x) = -5 (x - 1) (x + 5)
Hence the equation of the given quadratic equation is f(x) = -5 (x - 1) (x + 5).
Learn more about Quadratic Equations here :
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HELPPPPPPPPPPPPPPPPpppp
What is the value of y in the solution to this system of equations?
3x + 2y = -12
2x + y = 4
A.
B.
C.
D.
-36
-12
4
20
Answer:
x= 20,y= −36
Step-by-step explanation:
3x+2y=−12
2x+y=4
Subtract 2x
from both sides of the equation.
y=4−2x
3x+2y=−12
Replace all occurrences of y
with 4−2x
in each equation.
Tap for more steps...
−x+8=−12
y=4−2x
Solve for x
in −x+8=−12
.
Tap for more steps...
x=20
y=4−2x
Replace all occurrences of x
with 20
in each equation.
Tap for more steps...
y=−36
x=20
The solution to the system is the complete set of ordered pairs that are valid solutions.
(20,−36)
The result can be shown in multiple forms.
Point Form:
(20,−36)
Equation Form:
x=20,y=−36
Multiply 2 with (1) and 3 with (2)
6x+4y=-24--(1)6x+3y=12--(4)Subtract
y=-24-12y=-36Which graph shows a negative slope and a positive y-intercept?
Answer:
The last one ( bottom left)
Step-by-step explanation:
negative slope means the line is going downwards
positive y intercept means the line hits the y axis on a positive number
I need help with this math problem brainliest for the best answer
Answer:
It is the first one
Hope this helps!
Answer:
I believe it is 4x+10y=200, x+y=38
Explanation:
PLEASE ANSWER NUMBER 30 PLEASE!!
Answer:
d) x ≤ 3
Step-by-step explanation:
8 is the GCF of what two numbers?
Answer:
16 and 24
Step-by-step explanation:
The largest factor for both numbers have in common is 8, so GCF(16,24) = 8
The circle below is centred at O.
AB is a tangent to this circle.
Work out the size of angle y.
Justify your answer.
O
42°
y
A
B
Not drawn accurately
Answer:
y = 48°
Step-by-step explanation:
angle A = 90°
interior angles of a triangle = 180°
therefore
y = 180 - 42 - 90
y = 48°
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Given ❒➣ Mid point of a circle➣ Tangent AB➣ Angle "o" of 42⁰➣ Angle "A" of 90⁰ (cuz it is the perpendicular of traingle given in circle)﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Note ❒➣here tangent AB with point O (mid point of circle) forming a traingle➣we have to find "y" in the given figure (angle B)﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Concept used ❒➣The sum of interior angles of traingle is of 180⁰➣to find the missing angle ( y ) we will use this theorem➣this Concept is also know as Sum theorem﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Assumption ❒➣angle B = y﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Let's solve ❒[tex] \large \pmb{➪ \: } \rm \pink{ \angle \: OAB+\angle \:ABO+\angle \:BOA = 180 \degree}[/tex]
➣let's substitute value now .....[tex] \pmb{➪ \: 90 + y +42 = 180 } \\ \pmb{➪ \:132 + y = 180 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 180 - 132 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 48 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Hence the size of angle is
[tex] \large \boxed{✥\underline{ \boxed{ \sf{y = 48 \degree \: \pmb{\green{✓}} }}}✥}[/tex]
▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
Hope it helps !
.......................................................
Answer:
What are we suppose to answer...
write the equation of the line passing through the point (2,- 1) with a slope of 3
Answer:
Y= 3X-7
Step-by-step explanation:
the equation of the line has the formular
Y-Y1= M (X-X1)
here, M= slope= 3
X1=2 Y1= -1
Y--1= 3(X-2)
Y+1= 3X-6
Y= 3X-6-1
Y= 3X-7
Answer:
y=3x-7
Step-by-step explanation:
1. Use The Slope Formula
y=mx+b
m=slope
b=y-intercept
2. Fill in the given values
y=3x+b
3. Use the given points to solve for b
-1=3*2+b
-1=6+b
-7=b
4. Final equation
y=3x-7
A gym charges membership dues of $25 per month. Part A
Complete the table to show how the total cost in dollars, C, and the
number of months, m, of gym membership are related. What is the cost of the blue section
you can turn this into an equation: [tex]c=25m[/tex], where c is the cost and m is number of months.
solve for blue.
[tex]c=25m\\\\c=25(14)\\\\c=350[/tex]
The blue section costs $350.
Paul drove for one and a half hours at 65 mph before he realized he had forgotten his wallet. After Paul drove home and grabbed the wallet, he realized that he had only three hours to go one hundred eighty miles. At what speed should he drive to cover the distance in time?
Radius & Diameter
Easy: 51
A. Choose the correct choice.
1) A circle has a circumference of 1211 yd. What is the diameter of the circle?
a) 12 yd
b) 6 yd
c) 18 yd
2) A wire of length 281 in is bent to form a circle. What is the radius of the circle?
a) 28 in
b) 19 in
C) 14 in
3) A circular park has a circumference of 361 yd. Find its diameter.
a) 18 ya
b) 36 yd
c) 12 ya
4) The tip of the minute-hand travels 2211 in in one hour. Find the length of the minute-hand.
a) 11 in
b) 10 in
c) 22 in
5) The circumference of a bicycle wheel is 6n in. Find the diameter of the wheel.
a) 12 in
b) 6 in
c) 3 in
B. Find the radius and diameter in each question.
S.No
Circumference
Radius
Diameter
6.
10л ft
7.
24n in
8.
341 ya
9.
407 in
10.
167 ft
Answer:
a,c,b,a,b
Step-by-step explanation:
6.
7.
8.
9.
10.
Circumference
10π ft
24π in
34π yd
40π in
16π ft
Radius
5 ft
12 in
17 yd
20 in
8 ft
Diameter
10 ft
24 in
34 yd
40 in
16 ft
A board 18 inches long is cut into two pieces in the ratio 1:2. Find the length of each piece.
Which one of these numbers is a composite number a.17 b.51 c.97 d.89
Step-by-step explanation:
The correct answer here is 51
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Which one of these numbers is a composite number: 17, 51, 97, or 89?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Composite numbers are divisible by 3 or more numbers.
17 is divisible by 1 and 17 only, so it's not composite.
51 is divisible by 1, 51, 3, and 17, so it's composite.
97 and 89 are divisible by two numbers only, so they are not composite.
So we conclude that the answer is
51
Good luck with your studies.[tex]\rule{300}{1}[/tex]
What is the radius of a hemisphere with a volume of 281,250 2.14 cm^3
Answer:
:
Answer:the radius would be 88cm
Step-by-step explanation:
radius. r = base circumference. C = volume. V = curved surface area.
giving the following sequence: 21, 24.5, 28 write an equation for the nth term
Answer:
tₙ = (3.5x + 17.5)
Does anyone knows this? I need help. Please explain
Answer:
you can put a point on (0,1) and (-1,0) and put a line through the two points
Step-by-step explanation:
PLEASE HELP FAST I'LL MARK YOU AS BRAINLIST
The volume of a cube-shaped container is 8000cm³. What is the AREA of the base?
Answer: 400
Step-by-step explanation: cube root 8000 then that times itself
Given g(x) =(x² +5)/3x find g(p + 4) Please answer with work
Answer:
g(p + 4) = [p² + 8p + 21 / 3p + 12]
Step-by-step explanation:
Function :
g(x) = (x² + 5) / 3x
Substitute x = p + 4 :
⇒ g(p + 4) = [(p + 4)² + 5] / 3(p + 4)
⇒ g(p + 4) = [p² + 8p + 16 + 5 / 3p + 12]
⇒ g(p + 4) = [p² + 8p + 21 / 3p + 12]
Find the area of the figure. Round to the nearest TENTH.
Answer:
Step-by-step explanation:
12 multiplied by 9 is 108. That gives us the square. The triangle base is 9. The height is 7. 7 multiplied by 9 is 63. 63 divided by 2 is 31.5. 108 add 31.5 is 139.5 cm squared.
Answer:
A=L*B
=12*9
=108
A=0.5base *H
=0.5(9)*7
=31.5
A=108+31.5
A=139.5
If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why.
Answer:
This is less chocolate ice cream per cup of milk than in the first mixture (2 scoops of chocolate ice cream per cup of milk), so the first mixture has stronger chocolate flavor. 2 scoops of chocolate ice cream with 1 cup of milk will taste the same as 4 scoops of chocolate ice cream with 2 cups of milk.
Step-by-step explanation:
Answer:
If you did 3 scoops of ice-cream and 2 cups of milk you would have 2times the amount of milk and only 1 1/2 times the amount of ice-cream then if you did 1 cup of milk and 2 scoops of ice-cream.
Step-by-step explanation:
To solve this question, we will have to use the aspect of mathematics that is referred to as rates or proportions.
In the first mix, what we have is that we are going to mix 2 scoops of chocolate ice cream with 1 cup of milk. What is noticeable here is that we have 2 scoops of chocolate per 1 cup of milk or there is a 2 to 1 ratio of chocolate ice cream to cup of milk.
Now in the second mix, we are mixing 3 scoops of chocolate with 2 scoops of milk. What we have here is a ratio of 3 to 2. This means that we are having a ratio of 1.5 to 1 of the number of scoops of chocolate ice cream to number of cups of milk.
Looking at this, we can deduce that a 2 to 1 ratio is a greater value compared to a 1.5 to 1 ratio. This is the reason why we are having a stronger chocolate flavor in the first mix than the chocolate flavor in the second mix