Answer:
n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n^2 + 2n + 4n + 8 = 143
n^2 + 6n - 135 = 0
(n + 15)(n - 9) = 0
n + 15 = 0
n = -15
n - 9 = 0
n = 9
I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.
Hope this helps!
Simplify the equation, and set it equal to zero to prepare for factoring.
Multiply the two factors in parentheses using the distributive property:
8(n2 + 2n + 4n + 8) = 1,144
Combine like terms inside the parentheses:
8(n2 + 6n + 8) = 1,144
Multiply the terms inside the parentheses by 8 using the distributive property:
8n2 + 48n + 64 = 1,144
Set the equation equal to zero by subtracting 1,144 from each side:
8n2 + 48n − 1,080 = 0
Factor out the GCF, which is 8:
8n2 + 48n − 1,080 = 0
8(n2 + 6n − 135) = 0
Divide both sides of the equation by 8:
n2 + 6n − 135 = 0
Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:
a = 1, b = 6, c = -135
The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:
6 = -9 + 15
-135 = -9 • 15
The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:
(n − 9)(n + 15) = 0
Use the zero product property, and solve for n:
n − 9 = 0 or n + 15 = 0
n = 9 or n = -15
There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9
Amanda just bought a skirt at the GAP that is usually $40 but was marked 20% off.how much did Amanda pay for the skirt?
Answer:
$32
Step-by-step explanation:
the skirt is on sale. 40 times 0.20 (because of 20 divided by 100) is 8. That means that the skirt is $32 since $40-$8=$32.
Answer:
$32
Step-by-step explanation:
discount is $8
Can someone please help me with this and show work
Answer:
29/6-16/2549/30Rationalize(1.63333333333)1*(19/30)The Hernandez family ordered one jumbo pizza with a diameter of 20 inches, cut it into 15 equal slices, and had 3 slices left over after dinner. The Mullins family ordered two medium pizzas, each with a diameter of 12 inches, cut them into 8 equal slices each, and had 6 slices left over after dinner. How much pizza did the Mullins family eat as a fraction of the pizza the Hernandez family ate?
Answer: Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex] , where r is the radius
Given, Diameter of Hernandez family's pizza = 20 inches
Radius = [tex]\dfrac{20}{2}[/tex] = 10 inches
Area of Hernandez family's pizza = [tex]\pi (10)^2=100\pi \text{ in.}^2[/tex]
Since, they divide pizza into 15 pieces , area of each slice = [tex]\dfrac{100\pi}{15}=\dfrac{20}{3}\pi\text{ in.}^2[/tex]
They left with 3 slices i.e. they ate 12 slices, area of all 12 slices = 12 x (area of each slice)
= [tex]12\times\dfrac{20}{3}\pi\text{ in.}^2= 80\pi\text{ in.}^2[/tex]
Diameter of Mullins family's pizza = 12 inches
Radius = [tex]\dfrac{12}{2}[/tex] = 6 inches
Area of Mullins family's pizza = [tex]\pi (12)^2=144\pi \text{ in.}^2[/tex]
Since, they divide pizza into 8 pieces , area of each slice = [tex]\dfrac{144\pi}{8}=18\pi\text{ in.}^2[/tex]
They left with 6 slices i.e. they ate 2 slices, area of all 2 slices = 2 x (area of each slice)
= [tex]2\times18\pi\text{ in.}^2=36\pi\text{ in.}^2[/tex]
Since, [tex]\dfrac{36\pi}{80\pi}=\dfrac{9}{20}[/tex]
Hence, Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.
Is the following relation a function?
Answer:
No, Given relation is not a function.Explanation:
We know that , if any vertical line cuts the given graph of relation at exactly one point, then the relation can be called as function.
From Given graph , we find that the vertical line through any point on x-axis greater than zero (ex : X = 5) cuts the graph at more than one point.
Hence, Given relation is not a function.
Hope this helps...
Good luck on your assignment...
What is the value of y in the solution to the system of equations? One-thirdx + One-fourthy = 1 2x – 3y = –30 –8 –3 3 8
Answer:
8 hopefully
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
What is the solution of this system of linear equations?
A. (1, 0)
B. (0,0)
C. (0, 1)
D. X=0
Graph is attached , help quick please
Answer:
The answer is C.
Step-by-step explanation:
In order to find the solution of the linear equation, you have to find the coordinates where they intersect.
So according to the graph, both lines intersect at the coordinates of ( 0 , 1 ).
(Correct me if I am wrong)
A penny is dropped from a height of 144 feet. Calculate the time between when the rock was dropped and when it landed. If we choose
"down" as positive and ignore air friction, the function is h(t) 16t2 - 144.
Answer:
3 seconds
Step-by-step explanation:
Given the function :
h(t) = 16t2 - 144.
h = height = 144 and t = time after t seconds the ball penny was dropped.
When the penny lands, h = 0
Therefore, our function becomes ;
16t2 - 144 = 0
The we can solve for t
16t^2 - 144 = 0
16t^2 = 144
Divide both sides by 16
(16t^2 / 16) = 144 / 16
t^2 = 9
Take the square root of both sides
t = 3
Therefore, the time between when the rock was dropped and when it landed is 3seconds
Answer:
t = 3 seconds
Step-by-step explanation:
A percent measures a rate
answer = no it does not measure a rate
Answer:
NO
Step-by-step explanation:
Percent is just a number out of 100
PLEASE help me with this question ASAP!!!!
Step-by-step explanation:
I believe the answer is
The fuction roughly matches the data
Answer:
The function fits very well
Step-by-step explanation:
The equation for the stats is
y=-0.039866x²+3.99375x-0.4785714
The function f(t) = -6r+ 11 has the range {- 37. - 25. - 13, -1). Select the domain values from the list
1. 2. 3. 4. 5. 6. 7. 8. Justify your choices by explaining how you determined the domain values.
answer
-6r+-11=-37
-6r=-37+11
-6r=-48
r=8
1. Arjun puts £750 into his savings account. The account earns 5% simple interest per annum. After 4 years, how much money will Arjun have in his savings account? £ 1. Connor invests £1500 of his money for 2 years at a simple interest rate of 10%. How much money will he get back in interest?
Answer:
1. 900
2. 350
Step-by-step explanation:
the formula,
A= P(1+rt)
A= final amount
P= starting amount
r= intrest rate
t= time
1. A=750(1+.05*4)
A=750(1.2)
A=900
2. A=1500(1+.1*2)
A=1500(1.1)
A=1650
But theyre
asking for how much intrest will they get back, so you subtract the new amount by the starting amount to find how much intrest was earned
1650-1500=350
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation? because both triangles appear to be equilateral because∠MNL and ∠ONP are congruent angles because one pair of congruent corresponding angles is sufficient to determine similar triangles because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
Answer:
The correct option is;
Because ∠MNL and ∠ONP are congruent angles
Step-by-step explanation:
From the diagram shown in the question, ∠MNL and ∠ONP are vertically opposite angles as they are formed by crossing of the lines LP and MO making them congruent, that is ∠MNL ≅ ∠ONP
Given that two angle of triangle LMN are congruent to two angles of triangle PON , then by the Angle Angle (AA) rule of similarity, triangle LMN and PON are similar.
The information in the diagram enough to determine that △LMN ~ △PON because∠MNL and ∠ONP are congruent angles.
What are Congruent angles?These are referred to angles which have an equal measure. From the diagram ,vertically opposite angles are formed by crossing of the lines LP and MO thus,we can deduce that ∠MNL and ∠ONP are congruent angles.
This means that there is enough information to determine that △LMN ~ △PON using a rotation about point N and a dilation.
Read more about Congruent angles here https://brainly.com/question/1563325
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Pls help me with this question
Answer:
[tex]\sqrt[5]{x^7}[/tex]
or (x ^ 1/5) ^7
or ([tex]\sqrt[5]{x}[/tex])^7
Step-by-step explanation:
x ^ 1.4
Rewriting the decimal as an improper fraction
x ^ 14/10
x ^ 7/5
The top is the power and the bottom is the root
[tex]\sqrt[5]{x^7}[/tex]
or (x ^ 1/5) ^7
or ([tex]\sqrt[5]{x}[/tex])^7
find the rules for these sequence
Answer:
start with -29, multiply each term by 4
start with 60, multiply each term by 0.1
start with 97 and multiply each term by 0.5
3.03 cells
Step-by-step explanation:
1. The first sequence begins with -29. -116 ÷ -29 = 4, -464 ÷ -116 = 4, etc. Each value is multiplied by 4 to get the next value.
2. The second sequence begins with 60. 6 ÷ 60 = 0.1, 0.6 ÷ 6 = 0.1, etc. Each value is multiplied by 0.1 to get the next value.
3. The colony starts with 97 cells. Splitting into two is the same as multiplying by 0.5.
4. Multiply 97 by 0.5, 5 times for 5 minutes.
97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03
The Goodsmell perfume producing company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to hold at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and the corresponding surface area and volume. This cylindrical perfume bottle needs to be boxed in a prism for sale on store shelves. The Goodsmell perfume producing company would like a box with the smallest possible surface area which will hold your design for the perfume bottle. Report the dimensions of the box and the corresponding area and volume. The pretty perfume company, Goodsmell’s competition, has also designed a new perfume bottle. The bottle is to be a spherical shape with a diameter of 7cm. Determine the volume and surface area of this bottle. The spherical bottle has a conical shaped lid with a diameter of 5cm and a height of 4.5cm. Given this information, calculate the volume and surface area of the lid of the spherical shaped bottle. Determine the dimensions of the smallest possible box which could be used to package Pretty Perfume’s new bottle with its spherical bottle and conical-shaped lid. However, this box is not shaped like a rectangular prism. Pretty Perfume would like to have unique packaging and have chosen to have a box shaped like a pyramid. Calculate the volume and surface area of this pyramid shaped box. The Final Product: Prepare a written report that includes: A clear and concise explanation of the process that you used to solve the problem. The calculations that you made, presented in an organized fashion. A rationale (reason) for your selection of values.
Answer:
1. r = 2.82 cm
h = 5.6 cm
The maximum volume possible to the nearest 10 mL = 140 mL
2. Size side of square base of box is 5.64 cm
Height of box = 5.6 cm
The surface area of the box is 189.96 cm²
The volume of the box is 178.13 cm³
3. The procedure for solving the problem was through noting that the shape of the cross-section of the pyramid is an isosceles triangle ans also that smallest possible box for the pretty perfume is one which fits the angle of inclination of the lid. This was found out by initially using the combined height of the perfume and the lid (placed to fit the spherical outline of the bottle) to calculate the dimensions of the pyramid, from which it was observed that the angle of inclination of the lid is larger than that of the calculated dimension, such that the lid outline would be visible and could eventually tear the perfume box
With the inclination angle, β, which is the base angle of the isosceles triangle, the angle at the top of the pyramid cross-section is calculated and the following relations are used to calculate the triangular cross-section of the pyramid
h = a·cos(α/2)
b = 2·a·cos(β)
[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]
[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]
With the calculated dimensions, a, b, and h the area, A, of the square pyramid is calculated as 2×b×a + b² and the volume, V, as 1/3×b²×h
The attached diagram shows the the cross-section of the perfume in the pyramid box.
Step-by-step explanation:
1. The surface area of the cylinder = 2πr² + 2πrh = 150 cm².........(1)
The volume of the cylinder, V = πr²h = 100 mL = 100 cm³..............(2)
From equation (2), h = 100/(π·r²)
Substituting the value if h in equation (1), we have;
2πr² + 2πr100/(π·r²) = 150
2πr² + 200/r = 150
(2πr³ + 200)/r = 150
2πr³ + 200 = 150×r
2πr³ -150·r+ 200 = 0
150 = 2πr² + 2πrh
h = (150 - 2πr²)/(2πr)
h = (75- πr²)/(πr)
Substituting the value of h in the equation for the volume, we have;
V = πr²h = πr²(75- πr²)/(πr)
V = 75·r - π·r³
At maximum volume, dV/dr = 0, we have
d(75·r - π·r³)/dr = 75 - 3·π·r²= 0
3·π·r²= 75
π·r² = 25
r = 5√π/π
h = (75- πr²)/(πr) = (75- π(5√π/π)²)/(π(5√π/π)) = (75 -25)/(5·√π)
h = 50/(5·√π)= 10·√π/π
The maximum volume = πr²h = π×25/π×10·√π/π = 250·√π/π = 141.05 cm³
The maximum volume possible = 141.05 cm³ = 141.05 mL
The maximum volume possible to the nearest 10 mL = 140 mL
The dimensions of the bottle are;
r = 2.82 cm
h = 5.6 cm
The surface area of the bottle = 2π(2.82)² + 2π×2.82 ×5.6 = 149.2 cm
2
Given that the cylindrical bottle has r = 2.82 cm and h = 5.6 cm, we have;
Size side of square base of box = 2 × 2.82 = 5.64 cm
Height of box = 5.6 cm
The surface area of the box = 2 × Area of base + 4 × Area of side
The surface area of the box = 2 *5.64^2 + 4 * 5.6 * 5.64 = 189.96 cm²
The volume of the box = Area of base × Height = 5.64^2*5.6 = 178.13 cm³
3. Diameter of spherical bottle = 7 cm = 2×r
Volume of the sphere bottle = 4/3πr³ = 4/3*3.5^3*π = 343/6·π = 179.6 cm³
The surface area of the sphere bottle = 4πr² = 4*(7/2)^2*π = 49·π = 156.94 cm²
3 i. The volume of a cone = 1/3πr²h = 1/3*(5/2)^2*4.5 = 9.385·π = 29.45 cm³
The surface area of a cone = πrS
S = √(4.5^2 + (5/2)^2) = 5.15
The surface area of a cone = π*2.5*5.15 = 40.43 cm²
3 ii. The depth of fitness of the lid on the bottle = 7/2 - √(7/2)^2 - 2.5^2) = 1.05
The total height of the spherical bottle with the conical lid = 7 + 4.5 - 1.05 = 10.45 cm
3 iii. Given that the box is shaped like a pyramid we have;
Width of the box at middle of the height of the spherical bottle = 7 cm
Height of the box = 10.45 cm
[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]
[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]
With the aid of a graphing calculator, the width of the square pyramid is found to be 12.12 cm
The volume = 1/3*12.12^2*10.45 = 511.68 cm²
The surface area = 2*12.12*√(12.12/2)^2 + 10.45^2) +12.12²= 439.7 cm²
The angle of inclination of the lid = tan⁻¹ (4.5/2.5) = 60.95°
The angle of inclination of the calculated box is tan⁻¹ (10.45/6.06) = 59.88
Since the lid is steeper, we make use of the angle of the lid
The base angles are thus = 60.95°
The angle at the top is thus 180 - 60.95*2 = 58.11°
Therefore, by the formula, we find that
a = 12.25 cm
b = 11.897 cm
h = a·cos(α/2)
h = 10.707 cm
The volume = 1/3*11.897^2*10.707 = 505.15 cm³
The surface area = 2*11.897*√(11.897/2)^2 + 10.707^2) +11.897²= 432.98 cm²
The angle at the top of the box = 2
Given that:
r = 2.82 cmh = 5.6 cmThen the maximum volume possible to the nearest 10 mL =
140 mLGiven that:
The size side of square base of box is 5.64 cmHeight of box = 5.6 cmHence, the surface area of the box is
189.96 cm²The volume of the box is :
178.13 cm³What is Surface Area?This refers to the measure of the total area of an object.
The written report:The procedural method used to solve the problem was to identify the shape of the pyramid, then finding out the smallest possible box for the pretty perfume and then using the calculated dimensions, found the answers.
Read more about surface area here:
https://brainly.com/question/76387
PLZZZ HELP WILL GIVE BRAINLIEST !!!!! NEED THIS FAST PLZZZ
Answer:
8
Step-by-step explanation:
Let's denote the number of members ordered chicken a, the number of members ordered beef b.
We have:
a + b = 12 (total number of members is 12)
10a + 14b = 136 (the chicken costs 10$, the beef costs 14$)
a + b = 12 => a = 12 - b
Substitute a into second equation, we have:
10(12 - b) + 14b = 136
=> 120 - 10b + 14b = 136
=> 4b = 16
=> b = 4
=> a = 12 - b = 12 - 4 = 8
=> Number of members ordered chicken: a = 8
What is the slope of the graph?
Answer:
-2
Step-by-step explanation:
The slope formula is
m = ( y-2-y1)/(x2-x1)
Using two points on the line (0,4) and (2,0)
m = ( 0-4)/(2-0)
= -4/2
=-2
Answer:
-2
Step-by-step explanation:
Slope is change in y over change in x
the change in y is -2 and the change in x is 1 so you do -2/1 and that as a whole number is -2.
EF is a median of trapezoid ABCD. What is the value of x?
Answer:
x = 4
Step-by-step explanation:
The midsegment ( median is equal to half the sum of the parallel bases, that is
[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values
[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2
7x - 2 = 26 ( add 2 to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
The distance from Parrot Point Airport to the Ivy Cliffs is 178 miles at and angle of 7.1 degrees northeast. There is a wind blowing southeast at 30 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly? * Round the speed to the nearest tenth of a mile per hour and angle to the nearest tenth of a degree. Where north is 0 degrees and positive is clockwise.
Answer:
The speed is 74.0 miles per hour and the angle is 65.1° north-east
Step-by-step explanation:
We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.
Since the wind is moving south east, it is at 45 south of east or a bearing of 135.
Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles
Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles
The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles
The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles
The total vertical displacement of the plane is 176.64 miles - 42.43 miles = 134.21 miles
The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles
The direction of this displacement is thus
Ф = tan⁻¹(total vertical displacement/total horizontal displacement)
= tan⁻¹(134.21/62.43)
= tan⁻¹(2.1498)
= 65.05°
= 65.1° to the nearest tenth degree.
The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.
So the speed is 74.0 miles per hour and the angle is 65.1° north-east
plz help, will give brainiest
(08.01, 08.02, 08.03 HC)
Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)
Answer:
4x^2 + 8x + 4
4(x^2 + 2x + 1) - remove GCF of 4
4(x + 1)(x + 1) - factor
4(x + 1)^2 - collect like terms
Step-by-step explanation:
Then also expand it out by distributing:
21x^3 + 35x²
Form 1:
21x^3 + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
Update:
You could also multiply two binomials and make a quadratic.
Example:
(7x + 2)(3x + 5)
7x(3x + 5) + 2(3x + 5)
= 21x² + 35x + 6x + 10
= 21x² + 41x + 10
The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The polynomial will be solved as below:-
21x³ + 35x²
Form 1:
21x³ + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
You could also multiply two binomials and make a quadratic.
E = (7x + 2)(3x + 5)
E = 7x(3x + 5) + 2(3x + 5)
E = 21x² + 35x + 6x + 10
E = 21x² + 41x + 10
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Romeo is using a common algorithm to find the product of 8,125 × 9. Drag the correct numbers to the problem to show the partial products and to complete the multiplication for Romeo.
Answer:
its harddd
Step-by-step explanation:
rightttttttt
Alguien que sepa cómo se resuelve ésto que me ayudé a solucionarlo,es urgente,doy 25 puntos
38 42 34 54
Step-by-step explanation:
7have the best mayonnaise bianco babi naive albino pig is this real or not be a posible and I am a great day for 53feet
PLEASE HELP!!!!!!!
Find the Volume of the sphere rounded to the nearest hundredth
Answer:
14130 yd^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
The diameter is 30 so the radius is d/2 = 30/2 = 15
V = 4/3 pi (15)^3
V = 4500 pi
Letting pi = 3.14
V = 14130 yd^3
Answer:
Last one
Step-by-step explanation:
The volume of the sphere is given by the relation:
V = [tex]\frac{4}{3}[/tex]*π*r³ r is the radius wich is here 30/2 = 15V= [tex]\frac{4}{3}[/tex] *π* 15³
V= 14137.166 yd³
wich is approximatively 14130yd³
The population of a city increase exponentially at a rate of x% every 5 years
In 1960 the population was 60100
In 2015 the population was 120150
Calculate the value of x
Answer:
1.1460277. Put in your decimal place given to you.
This is the percentage rate.
Step-by-step explanation:
f(x)=0=60100
55=120150
60100=a*b^0
120150/60100=60100/60100*b^5
b^5^(1/5)=5square root(120150/60100)=1.14860277
The table below shows some inputs and outputs of the invertible function f ff with domain all real numbers.
x: -14,-7,-12,9,10,-2
f(x):11,-12,5,1,-2,13
f^-1(1)+f(−14): ?
f^-1(−2): ?
PLEASE HELP!
Answer: [tex]f^{-1}(1)+f(-14)=20[/tex]
[tex]f^{-1}(-2)=10[/tex]
Step-by-step explanation:
The given table :
x: -14,-7,-12,9,10,-2
f(x):11,-12,5,1,-2,13
Since f is invertible ( given) , then [tex]f^{-1}(x)[/tex] exists.
Now , from table [tex]f^{-1}(1)=9[/tex] [ x= 9 corresponding to f(x) =1]
[tex]f(-14)=11[/tex] [ f(x) = 11 corresponding to x=-14]
then, [tex]f^{-1}(1)+f(-14)=9+11=20[/tex]
So, [tex]f^{-1}(1)+f(-14)=20[/tex]
Also, x= 10 corresponding to f(x) =-2, then
[tex]f^{-1}(-2)=10[/tex]
Show the pair of straight lines are perpendicular.
C number.
Answer:
not perpendicular
Step-by-step explanation:
perpendicular line has opposite reciprocal slope
√3x-2√3 y=13
-2√3y=13-√3x
y=-13/(2√3)+√3 x/2√3
y=1/2 x-13/2√3 ( slope is 1/2)
6x-3y+11=0
-3y=-11-6x
y=-11/-3+6x/3
y=2x+11/3 slope =2
Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12 A coordinate grid with one line labeled 8 x minus 4 y equals 12. The line passes through a point at (0, negative 3), (1, negative 1) and a point at (1.5, 0). -2 - 2
Answer:
A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2
Step-by-step explanation:
The equation of the given line is 8·x - 4·y = 12
Which gives;
8·x- 12= 4·y
y = 2·x - 3
Given that the line passes through the points (0, -3) and (1, -1), we have;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;
[tex]Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2[/tex]
y - (-3) = 2×(x - 0)
y = 2·x - 3 which is the equation of the given line
For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x - 6 to have no solution, the slope of the two lines should be equal that is m = 2
Given that the line passes through the point (1.5, 0), we have;
y - 0 = 2×(x - 1.5)
y = 2·x - 3...................(1)
For the equation, y = m·x - 6, when m = 2, we have;
y = 2·x - 6..................(2)
Solving equations (1) and (2) gives;
2·x - 3 = 2·x - 6, which gives;
2·x - 2·x= - 3 - 6
0 = 9
Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.
Answer:
short answer is 2 or d
Step-by-step explanation:
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly two of the triplets are in the starting lineup?
Answer:
990 ways to choose 6 starters out of 14 with exactly two of the three triplets.
Step-by-step explanation:
Ways to choose 2 of the triplets
= C(3,2) = 3! / (2!1!) = 3
Ways to choose the remaining 4 starters out of 11 players left
= C(11,4) = 11! / (4!7!) = 330
Total number of ways to choose 6 starters
= 3*330 = 990
In the xy-coordinate plane, a line has a slope of −5/3. If the line crosses the y-axis at (0, b), at what point does it cross the x-axis?
Answer:
([tex]\frac{3}{5}[/tex] b, 0 )
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - [tex]\frac{5}{3}[/tex] and b = b , thus
y= - [tex]\frac{5}{3}[/tex] x + b ← equation of line
The line crosses the x- axis when y = 0, substitute y = 0 into equation and solve for x, that is
- [tex]\frac{5}{3}[/tex] x + b = 0 ( multiply through by 3 to clear the fraction )
- 5x + 3b = 0 ( subtract 3b from both sides )
- 5x = - 3b ( divide both sides by - 5 )
x = [tex]\frac{3}{5}[/tex] b , thus
x- intercept = ( [tex]\frac{3}{5}[/tex] b, 0 )
Answer:
( b, 0 )
Step-by-step explanation:
Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t is the time in seconds. For which interval of time is the height of the ball less than 17 feet?
Answer:
Step-by-step explanation:
We are given the position function and need to find the value of t when h<17.
Create an inequality that represents this situation:
[tex]-16t^2+81<17[/tex] The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.
The simplest way to solve this is to subtract 81 from both sides:
[tex]-16t^2<-64[/tex] then divide both sides by -16:
[tex]t^2>4[/tex] Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is
t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.
Answer:
A on edg
Step-by-step explanation: