Answer:
Step-by-step explanation:
Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as
Hypotenuse² = one leg² + other leg²
Therefore,
h² = (3a)³ + (4a)³
h² = 27a³ + 64a³
h² = 91a³
Taking square root of both sides,
h = √91a³
The formula for determining the perimeter of a triangle is expressed as
Perimeter = a + b + c
a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is
√91a³ + (3a)³ + (4a)³
= √91a³ + 91a³
Aiden buys six packs of baseball cards. Each pack contains nine baseball cards. He already has 242 baseball cards at home. Is it reasonable (does it make sense) to say that Aiden has around 300 baseball cards now? Why or why not?
Step-by-step explanation:
No of packs = 6
Cards in a pack = 9
Total cards = 9 x 6 = 54
1) Use the factor theorem to determine if 3x-4 is a factor of f(x)=3x^2+2x-8
2) Find the value of K so that x+6 is a factor of 6x^3+kx^2-7x-6
Step-by-step explanation:
put f(4/3)= 3(4/3)^(2) +2(4/3)-8 =0
so 3x-4 is a factor
similarly, k=35
To make sandwiches for a picnic, Amy buys 1 loaf of bread for $4.19 and 4 pounds of turkey at $6.95 per pound. Amy calculates the total cost as $31.99.
Which equation best shows whether or not Amy’s estimate is reasonable?
It is reasonable because 4 + 1 + 4 × 6 = 29.
It is reasonable because 4 + 4 × 7 = 32.
It is not reasonable because 4 + 1 + 4 + 6 = 15.
It is not reasonable because 4 + 4 × 7 = 56.
PLEASE AWNSER ASAP I WILL GIVE BRAINLIEST
Answer:
I am sure it is because 1×$4.19+4×$6.95=$31.99. do it yourself. you will see.
What is the domain of the function y = log(x +
3)?
(-0,00) (-0,00)
(-00,-3)
(0,00)
(-3,00)
DONE
Answer:Find the domain of y = log(x + 3)
Logarithms can only be taken for positive numbers. So you must have
x + 3 > 0
x > – 3 ✔
So the domain of the function is
D = {x ∈ R: x > – 3}
or using the interval notation
D = (– 3, +∞)
I hope this helps :).
SOLVE USING ELIMINATION *20 POINTS*
1. 3x - y = 28
3x - y = 14
a. (8,-4)
b. (-7,7)
c. (7,-7)
d. (-4,8)
2. x+ 4y 13
2x + 3y 6
a. (3,5)
b. (-3,4)
C. (4,5)
d. (4,4)
3. 12r-9y 30
6x + 15y = 54
A. x = 4 and y 2
B. x = 2 and y = 4
C. x = 14 and y 2
D. x = 37/7 and y =26/7
4. x + 3/2 y = -3
6/7x + 7y = -8
A. (27/8, -1/4)
B. (9/2, -5)
C. (-3/11, -10/11)
D. (-63 / 40, -19/20)
1. No answer ( may be due to incorrect question)
2. x = -3
y = 4
3. x= 4
y = 2
4.x = -63/40
y= -19/20
Step 1
Multiply equation 1 by the coefficient of x in equation 2
Multiply equation 2 by the coefficient of x I'm equation 1
(after completing this step you will derive equation 3 and 4 )
Step 2
Subtract equation 4 from equation 3
Step 3
Divide both sides of the equation by the coefficient of y
Step 4
substitute your value for y in equation 1 or 2
(after this you will derive the values of x)
Note : This method is for the Elimination of x
I hope it helps
Answer: A. X = 11
Step-by-step explanation:
x - 7 = 4
11 - 7 = 4
A salsa recipe uses green pepper, onion, and tomato in the extended ratio 2 : 5: 9. How many cups of onion are needed to make 160 cups of salsa?
Answer:
50 cups
Step-by-step explanation:
So rewrite the ratio to be 2x : 5x : 9x
16x = 160
x = 10
5 * 10 = 50
This is only right if the 5 in the ratio is for onions.
The equation of the circle with center (3, -2) and radius 7 is
(X blank) + (y blank)
Answer:
Step-by-step explanation:
(x-3)^2 + (y+2)^2 = 7^2
Answer:
[tex] (x - 3)^{2} + { (y + 2)^{2} = 49[/tex]
Step-by-step explanation:
Center of the circle = (3, - 2) = (h, k)
Therefore, h = 3, k = - 2
Radius r = 7
Equation of circle in centre radius form is given as:
[tex](x - h)^{2} + {(y - k)}^{2} = {r}^{2} \\ \therefore \: (x - 3)^{2} + { \{y - ( - 2) \}}^{2} = {7}^{2} \\ \red{ \boxed{ \bold{\therefore \: (x - 3)^{2} + (y + 2)^{2} = 49}}}[/tex]
can somebody help with number 4 asap please
Answer:
x ≈ 41
Step-by-step explanation:
All the angles in a quadrilateral add together to equal 360°
So set up the equation:
a + b + c + d = 360°
Now fill in the values we know:
x + _ + 4x + 2x - 10 + 85 = 360
7x + 75 = 360
Now subtract both sides by 75:
7x + 75 - 75 = 360 - 75
7x = 285
Divide both sides by 7:
7x / 7 = 285 / 7
x = 40.714
Round:
x = 41
Now to check our answer, substitute 41 for x in the equation:
(41) + _ + 4(41) + 2(41) - 10 + 85
(41) + 164 + 82 - 10 + 85 = 362
The answer is close to 360, so we know it is correct
Answer:
x=40 and
+_ is 5
Step-by-step explanation:
Sum of the angles of any quadrilateral is 360.
4x +2x-10 +85 +x+_ = 360 combine like terms
7x + 75 = 360 subtract 75 on each side
7x = 360-75
7x = 285 divide by 7
x = 40.71
Now plug in back into equation x = 40:
4*40+ 2*40 -10 + 85 +40 + _ = 360
missing number is +5
If r = 10 and s = 31, find R. Round to the nearest tenth
Answer: c 17.9°
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
I took the test
How do you answer the picture below?
Answer:
42cm²
Step-by-step explanation:
because if the perimeter of the rectangle is 28 then the length is 5, 5 - 11 = 6, the formula for finding the trapezium is to add the 2 parallel sides, half them, then times them with the length so your sum will look like this, 5+9=14, (i knew the other side was 9 as the length of AB is the same as the length of FC, which is the one of the parallel sides of the trapezium) then we do 14÷2=7, finally we times 7 by 6 which is 42cm²
helpp plzzz pt.3 yeahh
AB = 4.5
Step-by-step explanation:
We can cross multiply the sides in order to find the length of AB. Make sure you don't go diagonal, so you can't do 3/6. You can do 3/4 and 3/x, then match it to the same pattern.
This is the one I chose...
[tex]\frac{4}{3} =\frac{6}{x}[/tex]
Notice how I put them in the same order.
Now we can cross multiply...
[tex]4*x[/tex]
= 4x
[tex]6*3[/tex]
= 18
[tex]4x=18[/tex]
Divide by 4.
x = 4.5
The length of AB is 4.5.
Factorise fully
x^3-x
Answer:
x(x + 1)(x - 1)
Step-by-step explanation:
[tex] {x}^{3} - x \\ = x( {x}^{2} - 1) \\ x(x + 1)(x - 1) \\ [/tex]
Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice cream.
What will Ari think about Freeze Zone's milkshakes?
Choose 1 answer:
A
They have too much caramel.
B
They have too little caramel.
C
They are just right.
HELP ME ASAP I AM GIVING BRAINETEST
Answer:
1 and 1/6
Step-by-step explanation:
7 / 6 has a greater numerator so simplify to 1 whole and one sixth
find the smallest 4 digit number that is a perfect square and perfect cube
Answer:
1024 is the smallest four digit number which is a perfect square.
Step-by-step explanation:
So the least number to be added to 1000 is 24. Therefore, 1000+24 = 1024 is the smallest four digit number which is a perfect square.
Answer:
1024
Step-by-step explanation:
So the least number to be added to 1000 is 24. Therefore, 1000+24 = 1024 is the smallest four digit number which is a perfect square.
PLZ MARK ME BRAINLIEST
In the diagram, which pair of angles are alternate interior angles?
5/6
1 2
43
8/ 7
22 and 25
21 and 27
25 and 23
27 and 24
I needs halp
What is the square root of 25
Answer:
the square root of the number 25 is 5
Step-by-step explanation:
A cylindrical container has a radius of 3 centimeters and a height of 12 centimeters. The container is filled with water up to the height of 7 centimeters. Find the volume of empty space in the cylinder.
Answer:
volume of empty space = 141.3 cm³
Step-by-step explanation:
volume of empty space = volume of the cylinder - volume of water
First, we need to calculate the volume of the container
volume of a cylinder = πr²h
where r = radius of the container and h is the height of the container
r = 3cm and h = 12 cm π is a constant which is ≈ 3.14
volume of a cylinder = πr²h
=3.14 × 3²×12
=3.14×9×12
=339.12 cm³
We will proceed to find the volume of water
since liquid will take the shape of its container,
then volume of water = πr²h
r is the radius of the container and h is the height of the water
r = 3cm and h = 7cm
volume of water = πr²h
= 3.14 ×3²×7
=3.14×9×7
=197.82 cm³
volume of empty space = volume of the cylinder - volume of water
=339.12 cm³ - 197.82 cm³
= 141.3 cm³
OR
WE CAN SOLVE DIRECTLY
height of empty space = height of container - height of water
= 12 - 7
=5 cm
volume of empty space = πr²h
=3.14×3²×5
=3.14×9×5
=141.3 cm³
volume of empty space = 141.3 cm³
The volume of the empty space in the cylinder is equal to the difference between the volume of the cylinder and the volume of water in the cylinder.
The volume of the cylinder can be calculated using the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get:
V = π(3 cm)^2(12 cm)
V ≈ 339.3 cubic centimeters
The volume of water in the cylinder can be calculated by multiplying the cross-sectional area of the cylinder by the height of the water:
V_water = πr^2h_water
where V_water is the volume of water and h_water is the height of the water.
Substituting the given values, we get:
V_water = π(3 cm)^2(7 cm)
V_water ≈ 197.9 cubic centimeters
Therefore, the volume of empty space in the cylinder is:
V_empty = V - V_water
V_empty ≈ 339.3 - 197.9
V_empty ≈ 141.4 cubic centimeters
So, the volume of empty space in the cylinder is approximately 141.4 cubic centimeters.
How long is the wire that supports the tree?
Answer:
¿Qué alternativas habrías planteado para evitar la expansión de las guerrillas en todo el territorio colombiano?
Answer:
2.3 ft
Step-by-step explanation:
i looked it up on boogle.
Plsss help (Cuz i'm dumb:D) Calculate the surface area of the prism below, shape below
the measure angles of a hexagon are 4x,5x,6x,7x,8x,and9x calculate the size of the smallest angle
Answer:
Step-by-step explanation:
Sum of interior angles of polygon = (n -2) * 180
Sum of interior angles of hexagon = (6-2)*180 = 4* 180 = 720
4x + 5x +6x +7x + 8x +9x = 180
39x = 180
x = 180/39
x=4.61
Smallest angle = 4x = 4*4.61 = 18.44
What are the solutions to the quadratic equation x? - 16 = 0?
N
OX= 2 and x = -2
O X= 4 and x = -4
O x = 8 and x = 8
OX= 16 and x = -16
Answer:
[tex]x^2 = 16[/tex]
[tex]x = \pm 4[/tex]
Thus the answer is (b)
The solutions to the given quadratic equation are +4 and -4. Therefore, the option B is the correct answer.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given quadratic equation is x²-16=0.
Now, x²=16
x=±√16
x=±4
x=+4 or x=-4
Therefore, the option B is the correct answer.
To learn more about the solution of quadratic equation visit:
https://brainly.com/question/18305483.
#SPJ7
Sample space of S{A, B, C, F, G, M, T, Z}, subset A{A, G, M}, subset B{A, B, F, G, T, Z). Determine AUB.
AUB means combination of elements in A and B without writing one element twice
AUB={A,B,F,G,M,T,Z}
Which rules could describe the rotation? Select two options
Parallel lines t and u are cut by two transversals, r and s, which intersect line u at the same point.
What is the measure of angle 2?
25°
42°
46°
88°
Answer:
42
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
hope this helps!
A yearbook staff has 30 members. In how many different ways can an editor, photographer, designer, and advisor be selected?
Answer:
the answer is 30 different ways
Step-by-step explanation:
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.5-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.9% or largest 1.9%. a) What is the minimum head breadth that will fit the clientele? b) What is the maximum head breadth that will fit the clientele?
Answer:
a) min = 4.4251
b) max = 8.5743
Step-by-step explanation:
Given:
Mean, u = 6.5
Standard deviation = 1
To get our values, we are to use the inverse of the standard normal table.
a) The minimum head breadth that will fit.
P(Z < z) = 1.9%
P(Z < z) = 0.019
P(Z < -2.0749) = 0.019
z = -2.0749
From the z-score formula, we have:
[tex] \frac{x - \mu}{\sigma} = Z_0_._0_1_9 [/tex]
Let x be the breath of heads.
Making x the subject of the formula, we have:
[tex] x = z * \sigma + \mu [/tex]
We already have:
z = -2.0749
u = 6.5
s.d = 1
Substituting figures, we have:
x = (-2.0749 * 1) + 6.5
x = 4.4251
The minimum head breadth that will fit the clientele is 4.4251
b) The maximum head breadth that will fit.
P(Z > z) = 1.9%
1 - P(Z < z) = 0.019
P(Z < z) = 1 - 0.019 = 0.981
P(Z < 2.0749) = 0.981
From the z-score formula, we have:
[tex] \frac{x - \mu}{\sigma} = Z_0_._0_1_9 [/tex]
Let x be the breath of heads.
Making x the subject of the formula, we have:
[tex] x = z * \sigma + \mu [/tex]
We already have:
z = 2.0749
u = 6.5
s.d = 1
Substituting figures, we have:
x = (2.0749 * 1) + 6.5
x = 4.4251
x = 8.5743
The maximum head breadth that will fit the clientele is 8.5743
| 2p -1 | =45, what are the values of p?
Answer:
p = 23 and p = -22
Step-by-step explanation:
| 2p -1 | =45
Absolute value equations have 2 solutions, one positive value and one negative
2p-1 = 45 and 2p-1 = -45
Add 1 to all sides
2p-1+1 = 45+1 and 2p-1+1 = -45+1
2p = 46 2p = -44
Divide by 2
2p/2 = 46/2 and 2p/2 = -44/2
p = 23 and p = -22
Jake made a wooden cone with a diameter of 6 inches and a height of 4.5 inches. What is the volume of this cone?
Answer:
42.42in³
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cone
Step one
We know that the volume of a cone is
V= 1/3πr²h
Given data
Diameter d= 6 inches
Radius r= diameter/2= 6/2= 3 inches
Height h = 4.5 inches
Step two
Substituting our given data we have
Volume = 1/3*3.142*3²*4.5
V= 1/3*3.142*9*4.5
V= 127.251/3
V= 42.42in³
NEED HELP ASAP 20 MINUTES LEFT ON TIMER
Simplify:
28x^4 over 27 divided by 20 over 24x^3
Answer:
(56/45)x^7
Step-by-step explanation:
28x^4 20
---------- ÷ ----------- becomes
27 24x^3
28x^4 24x^3
---------- * ----------- if we invert the divisor fraction and then multiply.
27 20
We get: (28)(24)
-------------- x^7
(27)(20)
which reduces to (7)(24) x^7 (7)(8)x^7
--------------- = ------------- = (56/45)x^7
27(5) 9(5)
Answer:
(56/45)x^7
Step-by-step explanation:
28x^4 20
---------- ÷ ----------- becomes
27 24x^3
28x^4 24x^3
---------- * ----------- if we invert the divisor fraction and then multiply.
27 20
We get: (28)(24)
-------------- x^7
(27)(20)
which reduces to (7)(24) x^7 (7)(8)x^7
--------------- = ------------- = (56/45)x^7
27(5) 9(5)