=========================================================
Explanation:
We have a triangle with these side lengths
a = 31b = 72c = 78The order of 'a' and b doesn't matter, but we must have c as the largest value. Usually a,b,c are in ascending order.
Plug those values into the formula for the pythagorean theorem. If we get the same thing on both sides, then we have a right triangle.
[tex]a^2 + b^2 = c^2\\\\31^2 + 72^2 = 78^2\\\\961+5184 = 6084\\\\6145 = 6084\\\\[/tex]
We have a false statement at the end, which means the original equation is false for those a,b,c values.
Therefore, we do not have a right triangle.
Instead, this triangle is acute since the [tex]a^2+b^2[/tex] side is larger than the [tex]c^2[/tex] side
---------------
Rules to have in your notebook or on a reference sheet:
[tex]\text{If }a^2 + b^2 = c^2 \text{ then it is a right triangle}\\\\\text{If }a^2 + b^2 > c^2 \text{ then the triangle is acute}\\\\\text{If }a^2 + b^2 < c^2 \text{ then the triangle is obtuse}\\\\[/tex]
For more information, check out the converse of the pythagorean theorem.
A watering can hold 12 1/2 litres.it’s filled 11 times from a tank containing 400 litres.how much water is left in the tank
Answer:
262 1/2 liters
Step-by-step explanation:
Remaining water in tank :
Volume (tank) - 11 x Volume (watering can)400 - 11 x 12 1/2400 - 137 1/2262 1/2 litersAnswer:
262.5 litres
Step-by-step explanation:
Water taken from the tank
⇒ 11 × 12.5 litres = 137.5 litres
Water left in tank
⇒ 400 - 137.5 = 262.5 litres
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]
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
Kara wants to buy a game that is on sale. the original price of the game is p, but it is on sale for 30% off the original price. she uses the expression p(i - 0.3) to model the price. which expressions are equivalent to kara's expression? select all correct answers and the answers are
p - 0.3
1 - 0.3p
0.7p
p - 0.3p
1.3p
The expressions equivalent to kara's expression are 0.7p and p-0.3p
How to find discount of original price?Original price = pDiscount = 30%Discount price expression = p(1 - 0.3)
= p - 0.3p
= 0.7p
Check for equivalent expression
p - 0.3
Not equivalent
1 - 0.3p
Not equivalent
0.7p
Equivalent
p - 0.3p
Equivalent
1.3p
Not equivalent
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The price of a notebook is 20% less than the price of a book. By
what percent is the price of the book higher than the price of the
notebook?
HELP
Answer:
125%
Step-by-step explanation:
lets just say the book is $100. 20% less would be $80
now to go back to $100, we need to add $20 to $80
20 is 25% of 80, so add the extra 25% to 100% of 80
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.
What is the value of x?
Answer:
130° is the correct value of x.Step-by-step explanation:
In the question, there's an quadrilateral whose sum of all exterior angle is 360°.
140° + 34° + 56° + x = 360°
➝ 230° + x = 360°
➝ x = 360° - 230°
➝ x = 130°
Thus, The value of x is 130°.
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
(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]
A board 18 inches long is cut into two pieces in the ratio 1:2. Find the length of each piece.
-11+13+ 10x + 2x
I will give you brainliest
Answer:
12x + 2Step-by-step explanation:
-11 + 13 + 10x + 2x =
2 + 10x + 2x =
12x + 2
Answer:
2(6x+1)
Step-by-step explanation:
1. Add the number
-11 + 13 + 10x + 2x
2 + 10x +2x
2.Combine like terms
2 + 10x + 2x
2 + 12x
3.Arrange terms
2 + 12x
12x + 2
4.Common factor
-11 + 13 + 10x + 2x
2(6x+1)
If k (x) = x^2 and p (x) = k (x) + n, what is the value of n?
The equation k(x) = x^2 is quadratic equation, and the value of n in p (x) = k (x) + n is -6
How to determine the value of n?The equations are given as:
k(x) = x^2
p (x) = k (x) + n
From the graph, we can see that the graph of k(x) is shifted down by 6 units.
This means that the equation of p(x) is
p (x) = k (x) - 6
By comparison;
n = -6
Hence, the value of n in p (x) = k (x) + n is -6
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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=-36HELPPPPPPPPPPPPPPPPpppp
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
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]
Find two integers whose sum is 3 and product is -28 ?
Answer:
-4 and 7
Step-by-step explanation:
-4 + 7 = 3
-4•7 = -28
A Cylinder has a base diameter of 4cm and a height of 2cm. What is it’s volume in cubic cm, to the nearest tenths place
Answer: The answer is v=25.1 cm³
Step-by-step explanation:
b=4
h= 2
r= 4/2 r =2 radius is half of the diameter
V=πr²h
v= π(2)²2
v= 25.132741228718
v=25.1 cm³
Which of the following is an equation of a line perpendicular to the equation
y =3x + 1?
O A. y = 3x + 5
O B. y=x+5
X
3
O C. y = -3x+5
OD. y - 3x+5
O 5
3
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 !
(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
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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
What is 15 1/3 in radical form?
2/15
15
Answer:
∛15.
Step-by-step explanation:
15^1/3
= ∛15.
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).
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Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
1) x² + x
2) Check Below.
Explanation:
step 1 = 2 sqauresstep 2 = 6 squaresstep 3 = 12 squaresHence sequence can be created:
2, 6, 12
Find difference:
2, 6, 12
4 6
2
Find Equation:
2a = 2a = 1Then,
3a + b = 4b = 4 -3(1)b = 1Then,
a + b + c = 2c = 2 - 1 -1c = 0So Equation:
ax² + bx + c --- main formulaex² + 1x + 0 x² + x [equation]B)With Step Increasing, The step number multiplies the step number and plus the step number. That is the number of squares.
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.
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:
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
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.
Which of the following is a valid probability distribution?
Answer:
first one is the valid probability distribution