[tex]6x^2-x=2\implies 6x^2-1x-2=0 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{-1}x\stackrel{\stackrel{c}{\downarrow }}{-2}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]x = \cfrac{ -(-1) \pm \sqrt { (-1)^2 -4(6)(-2)}}{2(6)}\implies x = \cfrac{1\pm\sqrt{1+48}}{12} \\\\\\ x = \cfrac{1\pm\sqrt{49}}{12}\implies x = \cfrac{1\pm 7}{12}\implies x = \begin{cases} \frac{8}{12}\to &\frac{2}{3}\\[1em] -\frac{6}{12}\to &-\frac{1}{2} \end{cases}[/tex]
A man flies a kite 354 feet in the air when he runs out of string, what is the angle of elevation if he had 200 yards of string to begin with
Answer:
Step-by-step explanation:
Assuming the string is straight (it will not be so due to gravity and wind load)
θ arcsin(354 / (200(3)) = 36°
Plot the point (6, 0) on the coordinate plane.
Answer:
Just go to the 6 on the bottom line, and add a point
Answer:
see below
Step-by-step explanation:
(6,0)
The first coordinate is the x coordinate. Since it is positive we go to the right 6 units. The second coordinate is the y coordinate. We go up zero units
Charlie and Daniella each began a fitness programme. On day one, they both ran 500m. On each subsequent day, Charlie ran 100m more than the previous day whereas Daniella increased her distance by 2% of the distance run on the previous day.
(a) Calculate how far Charlie ran on day 20 of his fitness programme. (1) Daniella ran on day 20 of her fitness programme. On day n of the fitness programmes, Daniella runs more than Charlie for the first time.
b) Find the value of n
Answer:
a) 2400m on the 20th day for Charlie.
1) 728.41m of 20th day for Daniella.
Didn't find n, sorry.
Charlie ran 2400m on day 20 of his fitness program and Daniella ran 728m on day 20 of her fitness program.
It is given that Charlie and Daniella on day one both ran 500m on each subsequent day.
Charlie ran 100m more than the previous day.
Daniella increased her distance by 2% of the distance run on the previous day.
It is required to calculate how far Charlie and Daniella ran on day 20 and the value of n.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Charlie ran 500m on the first day:
[tex]\rm a_1 = 500[/tex]
[tex]\rm a_2 =600[/tex] ( because charlie ran 100m more than the previous day)
It is an arithmetic progression in which the difference between two consecutive terms:
d = 600 - 500 ⇒ 100
and [tex]\rm a_n = a+d(n-1)[/tex]
[tex]\rm a_2_0 = 500+100(20-1)\\\\\rm a_2_0 = 2400m[/tex]( ∵ n = 20 )
Daniella ran 500m on the first day:
[tex]\rm b_1 = 500[/tex]
[tex]\rm b_2 = 500+ 500\times2 \%[/tex] (because Daniella increased her distance by 2% of the distance run on the previous day)
We can write [tex]\rm n^t^h[/tex] terms:
[tex]\rm b_n= 500(1+2\%)^n^-^1[/tex]
[tex]\rm b_2_0= 500(1+2\%)^2^0^-^1[/tex]
[tex]\rm b_2_0= 500(1+0.02)^1^9\\\\\rm b_2_0 = 500\times 1.02^1^9\\\\\rm b_2_0 = 500\times1.456 \Rightarrow 728.40 \approx 728 m[/tex]
[tex]\rm b_n > a_n[/tex] (given in the question)
[tex]\rm500(1+2\%)^n^-^1 > 500+100(n-1) \ \ or \\\\\rm500(1+2\%)^n^-^1 > 100n+400[/tex]
The above expression is not true for all the values of 'n' ie. 'n' can not be determined.
Thus, Charlie ran 2400m on day 20 of his fitness program and Daniella ran 728m on day 20 of her fitness programme.
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math models help PLEASE!
(20x5+10)-(8x8-4)
a . 58
b. 50
c. 40
Answer:
Answer is C, 40
Step-by-step explanation:
(100)-(60)
Solve for x: -2x - 4> 8
X<-6
X> -6
0x<-2
X>-2
Answer:
x < -6
Step-by-step explanation:
-2x - 4 > 8
the first step is to add 4 to both sides since we need to get x alone on one side
-2x - 4 > 8
+4 +4
so we are left with -2x > 12
we still need to get x alone so we have to divide -2 from both sides
always remember that if you divide by a negative number the inequality flips!! so instead of > it will be <.
-2x/-2 = x
12/-2 = -6
so the answer is x < -6
If 882 grams of FeS2 is allowed to react with 528 grams of O2 according to the following equation, how many grams of Fe2O3 are produced?
FeS2 + O2 → Fe2O3 + SO2
Balance the reaction:
a FeS₂ + b O₂ => c Fe₂O₃ + d SO₂
Matching up the atoms on either side gives the system of equations
• Fe: a = 2c
• S: 2a = d
• O: 2b = 3c + 2d
We have 3 equations with 4 unknowns. Suppose we fix one of the variables, say a = 2. Then
2 = 2c ===> c = 1
2•2 = d ===> d = 4
2b = 3•1 + 2•4 ===> b = 11/2
and so the balanced reaction is
2 FeS₂ + 11/2 O₂ => Fe₂O₃ + 4 SO₂
or
4 FeS₂ + 11 O₂ => 2 Fe₂O₃ + 8 SO₂
Look up the molar masses of each component element:
• Fe: 55.845 g/mol
• S: 32.06 g/mol
• O: 15.999 g/mol
Then the molar masses of the reactants are
• FeS₂: 119.965 g/mol
• O₂: 31.998 g/mol
Convert the given masses to moles:
• (882 g FeS₂) (1/119.965 mol/g) ≈ 7.35 mol FeS₂
• (528 g O₂) (1/31.998 mol/g) ≈ 16.5 mol O₂
In the balanced reaction, 4 moles of FeS₂ combine with 11 moles of O₂, or equivalently 1 mol FeS₂ is needed for every 11/4 = 2.75 mol O₂. Now,
(16.5 mol O₂) / (2.75 mol O₂) = 6
while
(7.35 mol FeS₂) / (1 mol FeS₂) = 7.35
which means the reaction consumes all of the available O₂ and we're left with 7.35 - 6 = 1.35 mol FeS₂.
For every 11 mol O₂ among the reactants, 2 mol Fe₂O₃ are produced. Then 16.5 mol O₂ makes for
(11 mol O₂) / (2 mol Fe₂O₃) = (16.5 mol O₂) / x
===> x = 3.00 mol Fe₂O₃
which has a mass of
(3.00 mol Fe₂O₃) (160. g/mol) ≈ 479 g Fe₂O₃
To find the mass of Fe2O3 produced, we convert the given masses of FeS2 and O2 into moles and use the molar ratio in the balanced chemical equation. The mass of Fe2O3 produced is 1170.68 grams.
To solve this problem, we need to convert the given masses of FeS2 and O2 into moles. From the balanced chemical equation, we can see that the molar ratio between FeS2 and Fe2O3 is 1:1.
This means that the number of moles of Fe2O3 produced will be equal to the number of moles of FeS2. We can use the molar mass of Fe2O3 to convert moles to grams.
First, we calculate the number of moles of FeS2 and O2:
Moles of FeS2 = 882 g / 120.17 g/mol = 7.34 mol
Moles of O2 = 528 g / 32 g/mol = 16.5 mol
Since the molar ratio between FeS2 and Fe2O3 is 1:1, we know that 7.34 moles of FeS2 will produce 7.34 moles of Fe2O3.
Now, we can calculate the mass of Fe2O3:
Mass of Fe2O3 = Moles of Fe2O3 x Molar mass of Fe2O3
Mass of Fe2O3 = 7.34 mol x 159.69 g/mol = 1170.68 g
Therefore, 1170.68 grams of Fe2O3 are produced.
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If you deposit $400 into an account that offers a 5% interest rate. How much interest will you earn after 1 year?
Answer:
Answer: The answer is $20
Multiply 400 by .05 or 5%.
If you wanna know 6 years it would be 536 usd
Explanation:
This would be an compound interest. Meaning that your gain every year would increase exponentially.
The equation to calculate this would be: Kn = K0⋅
(1+p100)n Kn is your savings after the period nK0 is your starting deposit p is the percentage n is the period of interest for your example we would have.
Kn=400⋅
(1+5100)6
Step-by-step explanation:
CREDIT FOR ANSWER GOES TO
calderonj4588
1
21314 JEG B 10
3
Which is the best estimate of -14
of-14; (-20)
ם
10
-42
-28
OOOO
28
42
Step-by-step explanation:
OOOO
BYE
Carly spent $150 on supplies and $125 on labor for her home. She could not spend more than $500 total. Which of these is a valid statement?
Answer:
she could spend up to $225 on more supplies
Step-by-step explanation:
the total amount of supplies and labor has to be less than or equal to $500. If she spent $150 and $125=$275 on supplies and labor, the equation would be 150+125+x≤ 500. Isolate x, to get x≤ $225. The value of x has to be less than or equal to $225.
Select the best appropriate choice below.
Decide whether you have enough information to determine that the triangles are congruent.
If they are congruent, explain why by selecting the appropriate reason.
. .
•ASA Triangle Congruence Theorem
•SAS Triangle Congruence Theorem
•SSS Triangle Congruence Theorem
•AAS Triangle Congruence Theorem
•HL Triangle Congruence Theorem
•Not Enough Information To Determine Triangles Congruent
PLEASE HELP ;-;
Numeros comprendidos entre 20
One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, and nineteen/Uno, dos, tres, cuatro, cinco, seis, siete, ocho, nueve, diez, once, doce, trece, catorce, quince, dieciséis, diecisiete, dieciocho y diecinueve
You need spoons, cones, and bowls for your store. The spoons come in packs of 100, cones come in packs of 60, and cups come
in packs of 80.
1. How many spoons, cones, and cups will you have if you order 8 packs of each?
2. How many customers will you be able to serve? Will every person need a cup, spoon, and a cone?
3. If you estimate that you will have 1500 customers next week, how would you change your order to make sure everyone can be served?
Step-by-step explanation:
Number 1
Number of spoons= no of boxes × individual no of spoons
= 100 × 8 = 800 spoons.
Number of cones = no of cones in a box × no of boxes
= 60 × 8 = 480
Number of cup = no of cups in a box × no of boxes
= 80 × 8 = 640.
Total = 800 + 480 + 640 = 1920
Number 2
If everyone needs a cup, spoon and cones, it means they all need 3 items.
no of people you can serve = 1920 ÷ 3
= 640 people.
How much did i paint if i painted 3/4 of 3/4 of a wall
Answer:
(4) 1/4x = 3/4 (4)
1x=3
Step-by-step explanation:
3/4 x
÷ = ÷
1/4 1
(4) 1/4x = 3/4 (4)
1x=3
Find the equation of this line.
y=3/4x+1/4
I hope this helped :)
Answer:
Step-by-step explanation:
two points on the line are (-3,-2) and (5,4)
slope=(4-(-2))/(5-(-3)=(4+2)/(5+3)=6/8=3/4
eq. of line is
y+2=3/4(x+3)
4y+8=3x+9
4y=3x+9-8
4y=3x+1
y=3/4 x+1/4
Determine whether the graph represents a proportional relationship. A graph is shown. The x-axis is labeled from 0 to 16. The y-axis is labeled from 0 to 16. Four points are shown on the graph on ordered pairs 0, 2 and 1, 6 and 2, 10 and 3, 12. These points are joined by a line. The label on the x-axis is Number of Cars. The title on the y-axis is Number of Wheels. Yes, it is a proportional relationship because the graph goes through the origin Yes, it is a proportional relationship because the graph is a straight line No, it is not a proportional relationship because the graph is not a straight line No, it is not a proportional relationship because the graph does not go through the origin
Answer:
no its not a proportion
Step-by-step explanation:
because the line has to be straight unless the graph is scrap
Answer:
"Yes, it is a proportional relationship because the graph is a straight line"
Step-by-step explanation:
Your welcome ^^
I'll mark brainiest.. no links
Answer:
20.5
Step-by-step explanation:
Use Pythagorean theorem,
[tex]x^2 = 14^2 +15^2 \\\\\implies x^2 =421\\\\\implies x =\sqrt{421}\\\\\implies x =20.5[/tex]
Find the area of the figure. (Sides meet at right angles.)
4 m
Бm
4 m
10 m
8 m
Please verify how [tex]\frac{1-cos(x)}{sin(x)} =\frac{sin(x)}{1+cos(x)}[/tex]
Answer/Step-by-step explanation:
[tex]\frac{1-\cos \left(x\right)}{\sin \left(x\right)}=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}[/tex]
When you have an equation like this, you can start from either side. So, let us start from the left side.
[tex]\underline{\mathrm{Left\:side:}} \quad\frac{1-\cos \left(x\right)}{\sin \left(x\right)}[/tex]
[tex]\sf{Rewrite\: using \:Trig \:identities=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}}\\\\\mathrm{Therefore,\: it \:is \:true}[/tex]
Answer of what is QS
Check the picture below.
and let's not forget that the midsegment of a triangle is always half its parallel base.
[tex]\stackrel{midsegment}{AB}=\cfrac{\stackrel{base}{QS}}{2}\implies 16=\cfrac{QS}{2}\implies 32=QS[/tex]
solve pls brainliest
Answer:
-3
Step-by-step explanation:
using pemdas, we first divide -18 by 6 to get -3. next, we subtract -3 from -6: -6-(-3)=-6+3=-3
Answer: -3
Step-by-step explanation:
For this, you want to use PEDMAS
This is Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction. The first step would be to divide -18/6. This will come out to -3
1) Company A charges $55 per hour and a service charge of $250 and Company B charges $60
per hour and a service charge of $225. At what time are they equal?
Answer:
5 hours
Step-by-step explanation:
54,392 rounded to the hundreds place
Answer:
54,400
Step-by-step explanation:
The diameter of Pilar's bike wheel is 24 inches.
How far does Pilar's bike travel when the wheel makes
10 complete rotations?
The distance Pilar's bike travel when the wheel makes 10 complete rotations is 753.6 inches
Since the wheel is circular in nature, we will take the circumference to determine the distance travelled for 1 revolution
Circumference of a circle = πr²
r is the radius of the wheel.
Given that d = 24 in, r = 24/2 = 12in
C = 2(3.14)(12)
C = 75.36 in
Hence the distance completed by 1 revolution is 75.36. If Pilar's bike makes 10 revolutions, hence the required distance will be:
D = 10 * 75.36
D = 753.6in
Hence the distance Pilar's bike travel when the wheel makes 10 complete rotations is 753.6 inches
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What is the value of m
35.6 355⅝5555555555555555555545455555555
12(6x + 10) + x = 9x + 5(1 – x) can u solve this?
Answer:
-115/69
Step-by-step explanation:
12(6x + 10) + x = 9x + 5(1 - x)
72x + 120 + x = 9x + 5 - 5x
73x + 120 = 4x + 5
69x = 5 - 120
69x = -115
x = -115/69
Question
Find the area of the parallelogram.
Area =
units²
Answer:
9 units²
Step-by-step explanation:
Parallelogram area = base × height
Base = 3 units
Height = 3 units
Area = 3 × 3
Area = 9
The area of the parallelogram is 9 units².
Here, we have,
We know that,
Parallelogram area = base × height
here, from the given figure we get,
Base = 3 units
Height = 3 units
so, we get,
Parallelogram area = base × height
Area = 3 × 3
Area = 9
Hence, The area of the parallelogram is 9 units².
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Find the factorization of the polynomial below.
81x2 + 72x + 16
Answer:
9 x + 42.
Step-by-step explanation:
Answer:
72x+178" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.017px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">72x+17872x+178
At a candy factory, a machine is putting candy into a container. the graph shows the amount of candy (in pounds) in the container vs time (in minutes). SEE GRAPH BELOW AND ANSWER THE FOLLOWING QUESTIONS PLEASE.
A.) What is the amount of candy in the container at 0 minutes?
B.)Choose the stament that best describes how the time and candy are related then fill in the blank.
B 1.) As time increases the amount of candy in the container decreases. At what rate is the amount of candy decreasing?
_____ pounds per minute?
B 2.) As time increases the amount of candy in the container increases. At what rate is the amount of candy increasing?
____pounds per minute?
Answer:
A) 20 pounds
B.2) (increasing) 60 pounds per minute
Step-by-step explanation:
A) The graph shows the container has 20 pounds in it at x=0 minutes.
__
B) The graph goes up to the right (is increasing).
At minute 0, the container has 20 pounds.
At minute 1, the container has 80 pounds.
The increase in one minute is 80-20 = 60 pounds per minute.
The initial amount of candy in the container is 2 pounds. As time increases, the amount of candy in the container decreases at a rate of 1 pound per minute.
A.) The amount of candy in the container at 0 minutes is 2 pounds.
B1.) As time increases, the amount of candy in the container decreases. The rate at which the amount of candy is decreasing is 1 pound per minute.
B2.) As time increases, the amount of candy in the container increases. However, this option is not applicable in this case as the graph shows a decreasing trend.
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1. Un restaurant ofrece 14 entradas, 8 platos principales y 7 postres. ¿De cuántas formas un cliente puede ordenar una comida?
2. ¿Cuántos grupos de 4 letras se pueden formar con las letras de la palabra TECNICA?
3. ¿Cuántos números de 4 dígitos se pueden formar con los primeros 7 números naturales?
4. ¿Cuántos partidos distintos se pueden realizar dados 5 equipos de futbol?
5. ¿De cuántas formas pueden colocarse los 11 jugadores de un equipo de fútbol teniendo en cuenta que el portero no puede ocupar otra posición distinta de la portería mientras que los otros 10 pueden jugar en cualquier otra posición que no sea portero?
6. En el palo de señales de un barco se puede izar tres banderas rojas, dos azules y cuatro verdes. ¿Cuántas señales distintas pueden indicarse con la colocación de las nueve banderas?
Usando técnicas de conteo, se encuentra que
1. Un cliente puede ordenar una comida de 784 formas.
2. 420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.
3. 840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.
4. 10 partidos distintos se pueden realizar.
5. Pueden colocarse de 3,628,800 formas.
6. 1260 señales distintas pueden indicarse.
Item 1:
La técnica usada es el principio fundamental de conteo, que afirma que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] maneras de seren realizadas, el número total de maneras de ser realizadas es:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
En este problema, [tex]n_1 = 14, n_2 = 8, n_3 = 7[/tex], por eso:
[tex]T = 14 \times 8 \times 7 = 784[/tex]
Un cliente puede ordenar una comida de 784 formas.
Item 2:
El orden es importante, ya que TECN es una palabra diferente de NCET, por lo tanto, la fórmula de permutaciones se usa para resolver este problema.
Fórmula de permutaciociones:
El número de permutaciones de x elementos en un conjunto de n elementos es dada por:
[tex]P_{n,x} = \frac{n!}{(n - x)!}[/tex]
En este problema, 4 letras de 7, enconteces:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
La letra C se repite dos veces, o sea:
[tex]T = \frac{P_{7,4}}{2} = \frac{840}{2} = 420[/tex]
420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.
Item 3:
Permutaciones de 4 dígitos de 7, sin repeticiones, o sea:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.
Item 4:
El orden no es importante, ya que Time 1 x Time 2 es la misma partida de Time 2 x Time 1, por lo tanto, la fórmula de combinaciones se usa para resolver este problema.
Fórmula de combinaciones:
El número de combinaciones de x elementos en un conjunto de n elementos es dada por:
[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]
En este problema, combinaciones de 2 elementos de un conjunto de 5, entonces:
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
10 partidos distintos se pueden realizar.
Item 5:
El número de arreglos de n elementos viene dado por
[tex]A_n = n![/tex]
En este problema, arreglo de 10 elementos, o sea:
[tex]A_{10} = 10! = 3628800[/tex]
Pueden colocarse de 3,628,800 formas.
Item 6:
El número de arreglos de n elementos, con repeticiones de [tex]n_1, n_2, \cdots n_n[/tex] elementos viene dado por
[tex]A_n^{n_1,n_2,\cdots,n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
En este problema, [tex]n = 9, n_1 = 3, n_2 = 2, n_3 = 4[/tex], por eso:
[tex]A_9^{3,2,4} = \frac{9!}{3!2!4!} = 1260[/tex]
1260 señales distintas pueden indicarse.
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Determine f(4)+2×g (2)
Answer:
4f+4g
Step-by-step explanation: