What numbers are divided by -10 that equal 5?

Answer:

[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]

Step-by-step explanation:

we would like to solve the following trigonometric equation:

[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]

the left hand side can be rewritten using angle sum indentity of sin which is given by:

[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]

therefore Let

Thus substitute:

[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]

simplify addition:

[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]

keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:

[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]

take inverse trig and that yields:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]

add π to both sides of the second equation and that yields:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]

sin function has a period of 2nπ thus add the period:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]

divide I equation by 4 and II by -4 which yields:

[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]

recall that,-½(nπ)=½(nπ) therefore,

[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]

by using a calculator we acquire:

[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]

hence,

the general solution for: for the trig equation are

[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]

Answer: a = -8

Step-by-step explanation:

Given

-8a - 5 = -7a + 3

Subtract 3 on both sides

-8a - 5 - 3 = -7a + 3 - 3

-8a - 8 = -7a

Add 8a on both sides

-8a - 8 + 8a = -7a + 8a

a = -8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a = -8

Step-by-step explanation:

-8a-5=-7a+3                    Add 5 to both sides.

- 8a = - 7a + 3 + 5           Combine

-8a = - 7a + 8                  Add 7a to both sides

-8a + 7a = 8                    Combine

-a = 8                              Multiply by - 1

a = - 8                          

When you get a weird number like this, you should check it.

LHS = -8(-8) - 5

LHS = 64 - 5

LHS = 59

RHS = -(7*-8) + 3

RHS = -(-56) + 3

RHS = 56 + 3

RHS = 59

So a = - 8 must be right.

Answer:

x=10, y=24

[tex]\left(34-y\right)^2+y^2=676[/tex]

Step-by-step explanation:

Answer:

x = 10 and y = 24

Step-by-step explanation:

Perimeter of triangle = sum of the 3 sides of the triangle

:. x + y + 26 = 60

x + y = 60 - 26

x + y = 34 ---- (1)

From Pythagoras theorem,

x² + y² = 26²

x² + y² = 676 ---- (2)

From equation (1): y = 34 - x

:. x² + (34 - x)² = 676

x² + 1,156 - 68x + x² = 676

x² + x² - 68x + 1,156 - 676 = 0

2x² - 68x + 480 = 0

x² - 34x + 240 = 0

(x² - 24x) - (10x + 240) = 0

x(x - 24) -10(x - 24) = 0

(x - 24)(x - 10) = 0

x = 24 or 10

y = 34 - x

y = 34 - 10 = 24

:. x = 10 and y = 24

Answer:

11

Step-by-step explanation:

Let the number be x

2x + 14 = 4x - 8                  Add 8 to both sides

2x + 14 + 8 = 4x                 Combine

2x + 22  = 4x                     Subtract 2x

22 = 2x                              Divide by 2

11 = x

===========================================================

Explanation:

Refer to the diagram below.

There's a lot of info given to us that we don't need (and won't use).

The only key piece of info we'll really use is the fact that angle XZY is 27 degrees.

Draw in segments RU and RT to form quadrilateral TRUZ

Focusing solely on this quadrilateral, we see that the angles T and U are 90 degrees each (since the tangents are perpendicular to the radii at the point of tangency). Furthermore, we see that angle Z is 27 while angle R is x

For any quadrilateral, the four angles always add to 360 degrees

T+R+U+Z = 360

90+x+90+27 = 360

x+207 = 360

x = 360-207

x = 153

That means angle R of quadrilateral TRUZ is 153 degrees.

Furthermore, it means angle TRU is 153 degrees.

By extension, it indicates that minor arc TU is 153 degrees.

That makes arc TSU = 360 - (minor arc TU) = 360 - 153 = 207 degrees

By Joining TR and UR we got 2 right angles and a Quadrilateral

now

In a Quadrilateral sum of angles=360°

[tex]\\ \large\sf\longmapsto x+90+90+27=360[/tex]

[tex]\\ \large\sf\longmapsto x+180+27=360[/tex]

[tex]\\ \large\sf\longmapsto x+207=360[/tex]

[tex]\\ \large\sf\longmapsto x=360-207[/tex]

[tex]\\ \large\sf\longmapsto x=153°[/tex]

Answer:

The age of E is 40

Step-by-step explanation:

When E didn't join them, the average age was 30,that is six years ago. But present making 36.

But when E joined, the average age is now 40.

Answer:

E is 56 years old

Step-by-step explanation:

I assume E joined them now.

(A - 6 + B - 6 + C - 6 + D - 6)/4 = 30

(A + B + C + D + E)/5 = 40

(A + B + C + D - 24)/4 = 30

A + B + C + D - 24 = 120

A + B + C + D = 144

(A + B + C + D + E)/5 = 40

A + B + C + D + E = 200

144 + E = 200

E = 56

Answer:

Option B, $2020.00

Step-by-step explanation:

Volume of the pool,

12×5×14.5+4×5×7

= 1010 ft³

each cubit foot costs $2, so 1010 ft³ will cost,

1010×$2

= $2020

Answer:

f(5) = -2

Step-by-step explanation:

f (x) = -x + 3

Let x = 5

f(5) = -5+3

f(5) = -2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{f(x) = -x + 3}\\\huge\boxed{\rightarrow}\huge\text{ f(x) = -5 + 3}\\\huge\boxed{\rightarrow}\huge\text{ y = -5 + 3}\\\huge\boxed{\rightarrow}\text{ y = -2}\\\\\\\boxed{\boxed{\huge\text{Answer: \bf f(x) = -2}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

Less than 360 degree

Step-by-step explanation:

I think so

From my knowledge:

²−2−15=0

x=5

x=-3

Answer:

Not a function fails the vertical line test

Step-by-step explanation:

This is not a function.  The value of x = -1  goes to two different values of y

This would fail the vertical line test

Answer:

the first one

Step-by-step explanation:

use the vertical line test. the horizontal line would intersect at two points.

Answer:

x=19.86

Step-by-step explanation:

use cosine,

cos 19°=x/21

x=cos 19° * 21

x=19.86

Answer:

0.028x-6-0.48x-2+0.552x

(0.028-0.48+0.552)x-6-2

0.1x-8

The simplified expression, when evaluated for x=36, is -4.4, when following expression and evaluate for x=36 b= 0.02(1.4x - 300)-0.2(2.4x+10)+0.552x

To simplify the expression and evaluate it for x=36, let's break it down step by step:

0.02(1.4x - 300) - 0.2(2.4x + 10) + 0.552x

First, let's simplify the terms within each set of parentheses:

0.02 * (1.4 * 36 - 300) - 0.2 * (2.4 * 36 + 10) + 0.552 * 36

Next, perform the multiplications and additions/subtractions within each set of parentheses:

0.02 * (50.4 - 300) - 0.2 * (86.4 + 10) + 0.552 * 36

0.02 * (-249.6) - 0.2 * (96.4) + 19.872

Now, evaluate the remaining multiplications:

-4.992 - 19.28 + 19.872

Finally, perform the additions and subtractions:

-4.992 - 19.28 + 19.872 = -4.4

Therefore, the simplified expression, when evaluated for x=36, is -4.4.

To know more about  simplified , here

https://brainly.com/question/28595186

#SPJ2

Answer:

27

Step-by-step explanation:

Triangle proportionality theorem: when you draw a line parallel to one side of a triangle, it'll intersect the other two sides of the triangle and divide them proportionally

[tex]\frac{26}{39}=\frac{18}{x}[/tex]

Cross multiply and you get 702=26x

x=27

Answer:

x=27

Step-by-step explanation:

-We can use the triangle proportionality theorem: if line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

-we write the proportion and solve for x

[tex]\frac{39}{26} =\frac{x}{18}[/tex]

[tex]x= \frac{39*18}{26}[/tex]

x= 27

Answer:

1.

= Here,

Narasimha invest = 120,000

Madhu 135,000

pavan =

Answer:

X= –3, y=26

Step-by-step explanation:

3X+Y=17====> –2(3X+Y)=–34===> –6X–2Y=–34

X+2Y=49

Aight so let's head to the sum

–5X=15===> X=–3

–3+2Y=49===> 2Y=52===> Y=26

Answer:

here's the answer to your question

Answer:

B

Step-by-step explanation:

Area of shaded region + Area of unshaded region = Area of circle

Area of the unshaded sector=256*pi-32*pi=224*pi

Answer:

radius Is 16

total area becomes pi r ^ 2 = 16^2 pi = 256pi

remaining area becomes

256 pi - 32 pi = 224 pi option b

brainliest pls

Answer:

Step-by-step explanation:

16x^2 = (4x)^2

49 = 7^2

16x^2 - 49 = (4x)^2 - (7)^2

0.7% percent is the answer

[tex]\\ \sf \longmapsto 39+4+q=-14[/tex]

[tex]\\ \sf \longmapsto q+43=-14[/tex]

[tex]\\ \sf \longmapsto q=-14-43[/tex]

[tex]\\ \sf \longmapsto q=-57[/tex]

the value of 4 tenths x hundreds.

4000

Answer:

40

Step-by-step explanation:

4/10 x 100 = 40

Answer:

[tex]y=4x-2[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

We're given that the slope is 4. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=4x+b[/tex]

Now, to determine the y-intercept, plug in the given point (1,2) and solve for b:

[tex]2=4(1)+b\\2=4+b\\b=-2[/tex]

Therefore, the y-intercept is -2. Plug this back into [tex]y=4x+b[/tex] as b:

[tex]y=4x+(-2)\\y=4x-2[/tex]

I hope this helps!

Answer:

The curved surface area of the cone is approximately 329.9 cm²

Step-by-step explanation:

The parameters of the right circular cone are;

The radius of the cone, r = 7 cm

The slant height of the one, l = 15 cm

The curved surface area of a cone, CSA = π·r·l

Therefore;

CSA = π × 7 cm × 15 cm = 105·π cm² ≈ 329.9 cm².

Answer:  43,2

Step-by-step explanation:

[tex]\bf 3\sqrt{216 }=3\cdot 6\sqrt{6}=18\sqrt{6} \approx43.2 \\\\ \sqrt{216} =\sqrt{ 2^{3}\cdot 3^3}=\sqrt{2^2\cdot 3^2\cdot 3\cdot 2}=3\cdot 2\sqrt{3\cdot 2} =6\sqrt{6}[/tex]

Answer:

Rate of change, is also another word for slope.

Slope --> y2 - y1 / (x2-x1)

Assuming the table is already in xy, the cords are in xy form too.

1) (8,8)

2) (11,10)

Plug points into slope eq

--> 10 - 8 = 2

----> 11 - 8 = 3

2/3 Is the slope/rate of change.

Answer:

The answer is the last one, (X^2-2)/3!

Step-by-step explanation:

To get the inverse of a function, you switch the variables and solve for y. Doing this produces the last choice.

Area = Side^2

Area =( 4x + 2 )^2

Area = (4x)^2 + 2(4x)(2) + (2)^2

Area = 16x^2 + 16x + 4

Thus the correct answer is option B .

Answer:

u can solve ur self but let me help you

Step-by-step explanation:

simply:subtract 525ml from 512.6 liters