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2 years ago

Solve fro the Equation below: 7+2(x-3)=-3(x+1)-4

1 answer:

4 0

7 + 2x - 6 = -3x - 3 - 4
2x + 1 = -3x - 3 - 4
2x + 1 = -3x - 7
2x + 1 + 3x = -7
5x + 1 = -7
5x = -7 - 1
5x = -8
x = -8/5.

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Let f(x)=4x+9. Write a function g whose graph is a reflection in the y-axis of the graph of f. g(x)= ?

frez [133]

Answer:

$g(x)=-4x+9$

Step-by-step explanation:

So we know that:

$f(x)=4x+9$

To reflect across the <em>y-axis</em>, instead of x, use -x. Therefore:

$g(x)=f(-x)=4(-x)+9$

Simplify:

$g(x)=-4x+9$

And that's our answer :)

3 0

3 years ago

Solve the inequality.

mr Goodwill [35]

Answer:

the first one, v < 1 23/25

Step-by-step explanation:

multiply both sides by 6 and divide by 5

v < 48/25, or v < 1 23/25

5 0

2 years ago

Read 2 more answers

If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta

Ivahew [28]

Step-by-step explanation:

We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.

$\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}$

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

PQ = Opposite side
QR = Adjacent side
RP = Hypotenuse
∠Q = 90°
∠C = θ

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

$\rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}}$

Since, we know that,

cosθ = 5/13
QR (Adjacent side) = 5
RP (Hypotenuse) = 13

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

$\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}$

$\rule{200}{3}$

$\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}$

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

$\rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}}$

Where,

Opposite side = 12
Hypotenuse = 13

Therefore,

$\sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}}$

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

$\rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}}$

By substituting the values, we get,

$\rule{200}{3}$

$\sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}}$

∴ Hence, the required answer is 17/7.

6 0

2 years ago

Please help me on these questions and explain it thanks

Korolek [52]

ABC = 180-120=60
ACB = 180-(40+60)=80
Therefore ECD= 80 as ACB and ECD are vertically opposite angles

the solution is A as that is where the graphs intersect each other

6 0

3 years ago

Un depósito se llena de agua a diario para dar de beber a los animales de una granja. Según requerimiento se sacaron 3/8 del agu

Nostrana [21]

Answer:

5/24

Step-by-step explanation:

The question in English is

A tank is filled with water daily to give water to the animals on a farm. As required, 3/8 of the water was taken from the tank to give to the horses and 1/3 of what was left in the tank was given to the pigs. The remainder of the tank was distributed in two equal amounts to give water to the birds and pets. What is the fraction of the water that pets receive to drink?

1) 3/8 of the water was taken from the tank to give to the horses

At this point in the tank there are 1-3/8=5/8 of the water of the tank

2) 1/3 of what was left in the tank was given to the pigs

At this point in the tank there are

(1-1/3)*5/8

(2/3)(5/8)=10/24 of the water of the tank

3) The remainder of the tank was distributed in two equal amounts to give water to the birds and pets

The remainder is equal to 10/24

divided by 2

(10/24)/2=10/48

4) The fraction of the water that pets receive to drink is 10/48

simplify

10/48=5/24

8 0

2 years ago