solve this simultaneous equation m+2n=10 and 2n+3m=18​

Answer:

-65

-61

20ab - 3bc - 3ac

Step-by-step explanation:

1.) Find the sum of 72−104+5and -32+ 4-10.

72 - 104 + 5 = - 27

- 32 + 4 - 10 = - 38

Sum of (-27 and - 38) = - 27 + (-38) = - 65

2.) What should be added to 32+32+3 to get 3+3

32 + 32 + 3 = 67

3 + 3 = 6

67 + x = 6

x = 6 - 67

x = - 61

3.) Subtract the sum of 12ab –10bc –18ac and 9ab +12bc + 14ac from the sum of ab + 2bc and 3bc –ac

(12ab –10bc –18ac) + (9ab +12bc + 14ac)

12ab + 9ab - 10bc + 12bc - 18ac + 14ac

= 21ab + 2bc - 4ac

(ab + 2bc) + (3bc - ac)

ab + 2bc + 3bc - ac

ab + 5bc - ac

(21ab + 2bc - 4ac) - (ab + 5bc - ac)

21ab + 2bc - 4ac - ab - 5bc + ac

21ab - ab + 2bc - 5bc - 4ac + ac

20ab - 3bc - 3ac

Answer:

Yes!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for this is:

6(6 + x) = 3(3 + 25) and

6(6 + x) = 3(28) and

36 + 6x = 84 and

6x = 48 so

x = 8

Answer:

The flag pole is 38.96 feet tall.

Step-by-step explanation:

The angle of depression from the top of the flagpole to an object on the ground is 33°.

The object is 60 feet from the base of the cliff.

We need to find the height of the flag pole.

Here, base, B = 60 feet

We know that,

[tex]\tan\theta=\dfrac{P}{B}[/tex]

Put all the values to find P.

[tex]P=B\times \tan\theta\\\\P=60\times \tan(33)\\\\P=38.96\ ft[/tex]

So, the flag pole is 38.96 feet tall.

Answer:

See below

Step-by-step explanation:

[tex]x+7\leq2[/tex] or [tex]\frac{x+14}{4}\geq3[/tex]

[tex]x\leq -5[/tex] or [tex]x\geq-2[/tex]

Therefore, on the number line, you would have a closed dot at x=-5 with an arrow going to the left, and then you would have a closed dot at x=-2 with another arrow going to the right.

Answer:

A

Step-by-step explanation:

Answer: x=6

Step-by-step explanation:

Let's solve your equation step-by-step.

4+3(2x−4)=28

Step 1: Simplify both sides of the equation.

4+3(2x−4)=28

4+(3)(2x)+(3)(−4)=28(Distribute)

4+6x+−12=28

(6x)+(4+−12)=28(Combine Like Terms)

6x+−8=28

6x−8=28

Step 2: Add 8 to both sides.

6x−8+8=28+8

6x=36

Step 3: Divide both sides by 6.

6x

6

=

36

6

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]4+3 (2x-4)=28[/tex]

Distribute 3 to the parenthesis:

[tex]4+6x-12=28[/tex]

Add 12 to both sides:

[tex]4+6x-12=28[/tex]

          +12      +12

[tex]4+6x=40[/tex]

Subtract 4 from both sides:

[tex]4+6x=40[/tex]

-4            -4

[tex]6x=36[/tex]

Divide both sides by 6

[tex]6x=36[/tex]

/6      /6

[tex]x=6[/tex]

Hope this helps!

(a) 8:30 am

(b) 17 minutes

(c) 10:15

Answer:

a

Step-by-step explanation:

because

Answer:The equation that is given, h = –16t 2 + 64t + 8, represents the general formula of the motion which is h(t) = h0 + v0t - 16t² where h0 is the initial height (8 feet), v0 is the initial velocity  (+64 ft/s) and t is time in seconds. To determine the time when the ball is at the maximum height, we need to determine the vertex of the parabola which is done as follows:

vertex = time at maximum height = -b/2a = -64 / 2(-16) = 2 seconds

The maximum height can be calculated by substituting the time we obtained to the function.

h = –16t 2 + 64t + 8

h = –16(2)^2 + 64(2) + 8 = 72 feet

Step-by-step explanation:

Answer:

[tex]S' = (-5,-5)[/tex]

[tex]Q"=(-5,-5)[/tex]

Step-by-step explanation:

Given

[tex]S = (5,-5)[/tex]

[tex]Q= (5,5)[/tex]

Solving (a): Reflect S across y-axis

The rule to reflect across y-axis is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]S(5,-5) \to S'(-5,-5)[/tex]

Hence:

[tex]S' = (-5,-5)[/tex]

Solving (b): Reflect Q across x and y-axis

The rule to reflect across x-axis is:

[tex](x,y) \to (x,-y)[/tex]

So:

[tex]Q(5,5) \to Q'(5,-5)[/tex]

The rule to reflect across y-axis is:

[tex](x,y) \to (-x,y)[/tex]

So:

[tex]Q'(5,-5) \to Q"(-5,-5)[/tex]

Hence:

[tex]Q"=(-5,-5)[/tex]

i dont get it either

Step-by-step explanation:

Complete the square:

x ^2 - 2x + y ^2 + 4y + 1 = 0

(x - 1)^2 + (y + 2)^2 + 1 = 1 + 4

(x - 1)^2 + (y + 2)^2 = 4 = 2^2

Hence the center is (1, -2) and the radius is 2. (D)

Answer:

[tex] \frac{15 \sqrt{209} }{209} [/tex]

Step-by-step explanation:

Objective: Understand and work with trig identies.

Recall multiple trig identies and manipulate them to get from cosecant to secant.

Given

[tex] \csc(a) = \frac{60}{16} [/tex]

Apply reciprocal identity csc a = 1/sin a.

[tex] \sin(a) = \frac{16}{60} [/tex]

Apply pythagorean identity to find cos a.

[tex]( \frac{16}{60}) {}^{2} + \cos(x) {}^{2} = 1[/tex]

[tex] \frac{256}{3600} + \cos(x) {}^{2} = 1[/tex]

[tex] \cos(x) {}^{2} = \frac{3600}{3600} - \frac{256}{3600} [/tex]

We can simplify both expression

[tex] \cos(x) {}^{2} = \frac{225}{225} - \frac{16}{225} [/tex]

[tex] \cos(x) = \frac{ \sqrt{209} }{15} [/tex]

Cosine is positve on quadrant 1 so that cos(a)

Apply reciprocal identity sec a= 1/ cos a.

The answer is

[tex] \sec(a) = \frac{15}{ \sqrt{209} } [/tex]

Rationalize the denominator.

[tex] \frac{15}{ \sqrt{209} } \times \frac{ \sqrt{209} }{ \sqrt{209} } = \frac{15 \sqrt{209} }{209} [/tex]

Answer:

b=36 and c=144

Step-by-step explanation:

b+144=180, b=36

b+c=180, c=180-36=144

Answer:

Let the first integer be 'n.' Then n(n+2)+38=(n+2)^2. Solve using the quadratic equation: n=17. The two odd integers are 17 and 19.

Step-by-step explanation:

The integers are -39 and -38.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex] where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

Given;

The product of two consecutive positive odd integers is 38 less than the square of the greater integer

Now, let the numbers be x and x+

So, the equations will be

x(x+1)-38=(x+1)^2

x^2+x-38=x^2+1+2x

x=-39

x+1=-38

Therefore, the integer numbers will be -39 and -38.

Learn more about numbers here;

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Answer:

6n-1

Step-by-step explanation:

The Equivalent polynomial is 6n-1.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

We have,

To divide (18n² - 9n+ 1) by (3n-1).

Now, performing the division we get

                   3n-1   |  18n² - 9n+ 1  | 6n -1

                                18n² - 6n

                              _________

                                         -3n + 1

                                          -3n +1

                                          _______

                                                  0

Thus, the quotient is 6n -1.

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Answer:

c = 60°

Step-by-step explanation:

Since the measures are among a 90° angle, we need to subtract 30° from 90° which equals 60°

c = 60°

Answer:

49

Step-by-step explanation:

(3m + 58) + (8m + 155) = 180

11m + 213 =180

11m = -33

m = -3

PCM = 3m + 58 = -9 + 58 = 49

Answer:

Step-by-step explanation:

Let's FOIL this out and get it into standard quadratic format:

[tex]h(t)=-4.9t^2+490[/tex]. The lack of a linear term in the middle means therewas no upwards velocity, consistent with the object being dropped straight down as opposed to thrown up in the air tand then falling in a parabolic path. The -4.9t² represents the acceleration due to gravity, and the 490 represents the height from which the object was dropped. The constant in a quadratic that is modeling parabolic motion always represents the height from which the object was dropped (or launched). That's how you know.

The requried initial height of the object is 490 meters.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The object is dropped from a height of 49 meters.

We know this because the initial height is given by the first term of the expression in the parentheses, which is 49. When the object is dropped from the helicopter, t is equal to zero. Substituting t=0 into the equation for h gives:

h(0) = (49 + 4.9(0))(10 - 0) = 49(10) = 490

Therefore, the initial height of the object is 490 meters.

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Answer:

should be 3/7 I think that's right

Answer:

factorise form of

x²+2x = x(x+2)

Answer:

(y+8)(y+2)

Step-by-step explanation:

y^2 + 10y + 16

What two numbers multiply to 16 and add to 10

8*2 = 16

8+2 =10

(y+8)(y+2)

Answer:

x = 5

Step-by-step explanation:

9 - 2x = - 1

9 + 1 = 2x

10 = 2x

x = 5

Answer:

hope it helps

have a good day

Step-by-step explanation:

q

Answer:

if the solutsion are r1,r2 then the factored form is

y=a(x-r1)(x-r2) where a is a constant

so

r1=-1/3

r2=4

y=a(x-(-1/3))(x-4)

y=a(x+1/3)(x-4)

so it will be

y=a(x+1/3)(x-4)

a is a constant

Step-by-step explanation:

Answer:

Your welcome! :)

Step-by-step explanation:

17: 35000

18: 0.0029

19: 0.000003

20: 1.5

Answer:

the answer is plane try I'm pretty sure it's that.

Answer:

2x+y=4

2times-1 is -2

2x+-2=4

2x=4

x=2

Answer:

-74 10/5

Step-by-step explanation:

first you will write the decimal number in fraction form which will be,

-74.5 = -745/10

now, on diving we will get,

74 as quotient and 5 as remainder, 10 as divisor.

now mixed fraction is, quotient divisor/remainder

the answer will be -74 10/5

•you can solve it to get the fraction you got previously as, =(-74 X10 + 5)/5 you will get the fraction in question.

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Hope my answer helps.