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3 years ago

Solve the following system by substitution -3x+y=-5 and 3x+6y=0

Mathematics

1 answer:

Jobisdone [24]3 years ago

3 0

Answer:

$x=\frac{10}{7},\:y=-\frac{5}{7}$

Step-by-step explanation:

$\begin{bmatrix}-3x+y=-5\\ 3x+6y=0\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-3x+y=-5:\quad x=-\frac{-5-y}{3}\\\\\mathrm{Subsititute\:}x=-\frac{-5-y}{3}\\\\\begin{bmatrix}3\left(-\frac{-5-y}{3}\right)+6y=0\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}5+7y=0\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:5+7y=0:\quad y=-\frac{5}{7}\\\\\mathrm{For\:}x=-\frac{-5-y}{3}\\\\\mathrm{Subsititute\:}y=-\frac{5}{7}\\\\x=-\frac{-5-\left(-\frac{5}{7}\right)}{3}$

$-\frac{-5-\left(-\frac{5}{7}\right)}{3}=\frac{10}{7}\\\\x=\frac{10}{7},\:y=-\frac{5}{7}\\\\$

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Which inequality is represented by the graph?

bearhunter [10]

Answer:

Correct answer: y>-32x-2

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3 years ago

a disc is thrown into the air with an upward velocity of 62 ft/s.its height h in feet after t seconds is given by the function h

Korolek [52]

Given that the height of the disc is modeled by the function:
h=-16t^2+20t+6
a] The maximum height will be as follows:
At maximum height:
h'(t)=0
from h(t)
h'(t)=-32t+20=0
thus
t=20/32
t=5/8 sec
thus the maximum height will be:
h(5/8)=-16(5/8)^2+20(5/8)+6
=12.25 ft

b] How long will it take the disc to reach the maximum height?
time taken to reach maximum height will be:
from h(t)
h'(t)=-32t+20=0
thus
t=20/32
t=5/8 sec
thus time taken to reach maximum height is t=5/8 sec

c]How long does it take for the disc to be caught 3 feet off the ground?
h(t)=-16t^2+20t+6
but
h(t)=3
thus
3=-16t^2+20t+6
solving for t we get:
0=-16t^2+20t+3
factoring the above we get:
t=5/8-/+√37/8
t=-1.5256 or 2.776
since there is no negative time we pick t=2.776
Hence time taken for the disc to be caught 3 ft from the ground is 2.776 ft

3 0

3 years ago

) Una compañía invierte $15,000 al 8% y $22,000 al 9%. ¿A qué tasa debe invertir

Anna35 [415]

Usando proporciones, hay que los $12,000 restantes deben ser investidos a una tasa de 11%.

<h3>¿Qué es una proporción?</h3>

Una proporción es una fracción de la cantidad total.

De las dos primeras inversiones, el ingreso es dado por:

0.08 x 15000 = $1,200.

0.09 x 22000 = $1,980

T = 1200 + 1980 = $3,180

Por la tercera inversión, busca-se un retorno de 4500 - 3180 = $1,320.

De esa forma, la tasa x es la seguiente:

12000x = 1320

x = 1320/12000

x = 0.11.

Los $12,000 restantes deben ser investidos a una tasa de 11%.

Puede-se aprender mas a cerca de proporciones es brainly.com/question/26425852

7 0

2 years ago

X to the 2nd power =64

lawyer [7]

Answer:

Step-by-step explanation:

8 *8=64

4 0

3 years ago

Read 2 more answers

An experiment was performed to determine whether the annealing temperature of ductile iron affects its tensile strength. Five sp

Tcecarenko [31]

Answer:

There are significant differences among the mean tensile strengths for different temperatures.

Step-by-step explanation:

A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.

The hypothesis can be defined as follows:

H₀: There is no difference between the means, i.e. $\mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}$ .

Hₐ: There is a significant difference between the means, i.e.at least one of the mean is different.

Use MS-Excel to perform the analysis of variance.

Go to Data → Data Analysis → Anova: Single Factor.

A dialog box will open.

Enter the data and enter Alpha as 0.05.

Press OK.

The output is attached below.

The F-value is, 8.40458.

The p-value of the test is, 0.00139.

Decision Rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.00139 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Concluding that there are differences among the mean tensile strengths for different temperatures.

3 0

3 years ago