The sum of two numbers is 78. Their difference is 32. Write a system of equations that describes this situation. Solve by elimination to find the two numbers. x + y = 32 y – x = 78 50 and 24 x – y = 78 x + y = 32 54 and 24 x + y = 78 x – y = 32 55 and 23

Answer:

B

Step-by-step explanation:

Sin x°= opposite ÷ hypotenuse

Cos x°= adjacent ÷ hypotenuse

Tan x°= opposite ÷ adjacent

Ctg x°= adjacent ÷ opposite

The correct will bet cot x = adjacent ÷ opposite

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometric properties we have

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Step-by-step explanation:

The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.

Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are

±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).

Trying out a few roots until we get one that works using synthetic division, we can try

x+1 (the root is x=-1)

-1  |     1       1        -6         -14         -12

    |            -1          0          6           8

    __________________________

          1     0        -6            -8         -4

the remainder is -4, so this does not work

x+2 (the root is x=-2)

-2 |     1       1        -6         -14         -12

    |            -2          2          8          12

    __________________________

          1      -1       -4           -6         0

Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is

-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6

Using the rational roots theorem, the possible roots of x³-x²-4x-6 are

±(1,2,3,6)

Starting with

x-1 (root is x=1), we have

1 |     1       -1        -4         -6      

    |            1          0         -4        

    _____________________

          1      0       -4           -10

there is a remainder, so this is not a root

next, x-2 (root is x=2)

2 |     1       -1        -4         -6      

    |            2         2         -4        

    _____________________

          1      1       -2           -10      

there is a remainder, so this is not a root

next, x-3 (root is x=3)

3|     1       -1        -4         -6      

    |            3         6         6        

    _____________________

          1      2      2          0

x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2

Answer:

Its not nonlinear

Step-by-step explanation:

Answer:

no, it is a linear function as y has a degree of 1

Answer:

so thats 2/6 or 1/3

Step-by-step explanation:

A die has 6 sides your odds of getting 2 or lesser are 1/3 or 33%

Answer:

(6, 9) (3, 0)

Step-by-step explanation:

Solve for each option using the slope formula:

Slope formula:

m = y2 - y1 / x2 - x1

m = 4 - 5 / 1 - 4

m = -1/-3

m = 1/3

This is not 3.

m = 0 - 9 / 3 - 6

m = -9 / -3

m = 3

This has a slope of 3!

m = 0 - 0 / -6 - 3

m = 0/ -9

m = 0

This is not 3.

m = 2 - 1 / 0 - 3

m = 1/-3

m = -1/3

This is not 3.

Answer:

121

Step-by-step explanation:

Given,

a = 4

b = 5

a² + ab² + b²

= 4² + 5 x 4² + 5²

= 16 + 80 + 25

= 121

Answer:

Step-by-step explanation:

chiều dài:x,x>0

chiều   rộ:y

[tex]\left \{ {({x+y)*2=326} \atop {xy=6370}} \right.[/tex]

[tex]\left \{ {{x+y=163} \atop {xy=6370}} \right.[/tex]

[tex]\left \{ {{y=163-x} \atop {xy=6370}} \right.[/tex]

[tex]\left \{ {{y=163-x} \atop {x*(163-x)=6370}} \right.[/tex]

[tex]\left \{ {{y=163-x} \atop {163x-x^{2} =6370}} \right. \\[/tex]

[tex]\left \{ {{y=163-x} \atop {x_{1} =98; x_{2} =65}} \right.[/tex]

[tex]\left \{ {{y=65} \atop {x=98}} \right.[/tex]

Answer: [tex]V=0.0028278\ m^3[/tex]

Step-by-step explanation:

Given

Length of the pipe [tex]l=4\ m[/tex]

Inside diameter of the pipe [tex]d_i=4\ cm[/tex]

Outside diameter of the pipe [tex]d_o=5\ cm[/tex]

Volume of the pipe

[tex]\Rightarrow V=\dfrac{\pi }{4}[d_o^2-d_i^2]\\\\\text{Insert the values}\\\\\Rightarrow V=\dfrac{\pi}{4}[5^2-4^2]\times 10^{-4}\times 4\\\\\Rightarrow V=28.278\times 10^{-4}\ m^3\\\\\Rightarrow V=0.0028278\ m^3[/tex]

Answer:

-55

Step-by-step explanation:

the sqeuence seems to be subtracting by 2 everytime.

so it will be -1,-3,-5,-7,-9,-11,-13,-15,-17,-19,-21,-23,-25,-27,-29..

the answer will be 27*-2(-54) -1(because we start at -1 , not 0)

Answer:

Step-by-step explanation:

the formula for an arithmetic sequence that is explicit is

[tex]a_n=a_1+d(n-1)[/tex]  where [tex]a_1[/tex] is the first term (so -1), and d is the common difference (-2). n is the number position in the sequence. As soon as we find the formula or model for this sequence we can find any number term we want. Filling in the formula:

[tex]a_n=-1-2(n-1)[/tex] and we'll clean that up just a bit:

[tex]a_n=-1-2n+2[/tex] (I just distributed through the parenthesis) and a bit more to

[tex]a_n=-2n+1[/tex] and if we want the 21st term, fill in a 21 for n:

[tex]a_{21}=-2(21)+1[/tex] and

[tex]a_{21}=-42+1[/tex] so

[tex]a_{21}=-41[/tex]

Los tres cantos volverán a coincidir en 154 minutos.

Dado que en una granja hay un gallo, un canario y un azulejo, suponiendo que el gallo canta cada 7 minutos, que el canario lo hace cada 14 minutos y el azulejo, cada 22 minutos, si en este momento cantaran al mismo tiempo las tres aves, para determinar en cuántos minutos volverán a  coincidir los tres cantos se debe realizar el siguiente cálculo:

Debe obtenerse el múltiplo común menor entre 7, 14 y 22. Dado que todo múltiplo de 14 será también múltiplo de 7 (pues 14 no es otra cosa que dos veces 7), debe obtenerse el múltiplo común menor entre 14 y 22. Entonces, debe descomponerse ambos números en factores primos:

Posteriormente, deben multiplicarse los factores no comunes por el factor común, es decir, 7 x 11 x 2, cuyo resultado es igual a 154. Así, los tres cantos volverán a coincidir en 154 minutos.

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Answer: -2/7

|3x - 2| - 4x = 4

1) (3х - 2) - 4х = 4, if 3x - 2 >= 0

2) -(3x - 2) - 4x = 4, if 3x - 2 < 0

1)

3х - 4х = 4 + 2

-x = 6

x = -6

3х - 2 >= 0

3х >= 2

x >= 2/3 - wrong

2)

-3х + 2 - 4х = 4

-7х = 2

x = -2/7

3x-2<0

3x<2

3(-2/7)<2-right

Answer:

Step-by-step explanation:

The general form of this equation is

[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

[tex]A=45000e^{-.02t[/tex]

Answer:

3. (1-7/9)÷2 = 2/9÷2 = 1/9

reciprocal of 1/9 is 9

4. x+2/x=3

if you solve it, you get x = 1 and x = 2, so last option, 1 and 2, is the answer

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

I discounted the 2-m ramp. If we are supposed to be looking for the length of time the ride is above 38 m from the ground, that translates to 36 m from the very bottom of the circle that is the Ferris wheel (where the wheel would meet the "ground"). I first found the circumference of the circle:

C = 48(3.1415) so

C = 150.792 m

I enclosed this circle (the Ferris wheel is a circle) in a square and then split the square in 4 parts. Each square has a quarter of the circle in it. If you divide the circumference by 4, that means that the arc length of each quarter circle is a length of 37.698 m. But that doesn't put us 36 m above the ground, that only puts us 24 m above the ground (remember the diameter of the circle is 48, so half of that is 24, the side length of each of the 4 squares). What that means to us (so far, and we are not at the answer yet) is that when the height off the ground is 24 m, a car that starts at the bottom of the ride has traveled 37.698 m around the circle. Traveling in an arc around the outside of the circle is NOT the same thing as a height off the ground. Going around a circle takes longer because of the curve. In other words, if the car has traveled 37.698 m around the outside of the circle, it is NOT 37.698 m above the ground...it's only 24 m above the ground. Hence, the reason I enclosed the circle in a square so we have both the circle's curve {arc length} and height above the ground {side of the square}). As the car travels farther along the outside of the circle it gets higher off the ground. If one quarter of the circle is 24 m above the ground, we need to figure out how much farther around the circle we need to go so we are 36 m above the ground. The height difference is 36 - 24 = 12m. we need now to find how long the arc length of the circle is that translates to another 12 m (the difference between the 24 we found and the 36 total). Using right triangle trig I found that arc length to be 12.566. The total arc length on the circle that translates to 36 m above the ground is 50.26437 m.

Going back to the beginning of the problem, the circumference of the circle is 150.792, and it makes one complete revolution in 5 minutes. That means that a car will travel 30.1584 m in 1 minute. Since this is the case, we can use proportions to solve for how long it takes to get 36 m above the ground:

[tex]\frac{m}{min}:\frac{30.1584m}{1min}=\frac{50.26437m}{xmin}[/tex] and cross multiply:

30.1584x = 50.26437 so

x = 1.6667 minutes, the time it takes to reach a height of 36 m. BUT this is not what the question is asking. The question is asking how long it's HIGHER than that 36 m. Let's think.

The car starts at the bottom of the ride, gets to a height of 36 m, keeps going around the circle to its max height of 48 m, then eventually comes back down and keeps going til it's back on the ground. That means that there is a portion at the top of the wheel that is above 36 m. If it goes 50.2647 m around the circle til it's at 36 m, then when it passes the max height and drops back to 36 m, it's 50.2647 m around the other side of the circle. We just found that to travel that 50.2647 m, it took the car 1.6667 minutes. We travel this distance twice (once meeting the height going up and then again coming down) so that takes up 3.3334 minutes.

5 minutes - 3.3334 minutes leaves us off 36 m above the ground for 1.6664213 minutes.

Two options are given to Tina. We find how much she pays for each option, and the one in which she pays less offers the better value.

Tina sends 12 text messages each day in June

June has 30 days, so in June, Tina sent 12*30 = 360 text messages.

Package A:

First 100 messages cost 3p, the next 100 cost $2 and after that each costs $1.

She sends 360 messages, with:

The first 100 costing 3p.

The next 100 costing 2p.

The final 360 - 200 = 160 costing 1p.

She pays:

[tex]100*3 + 100*2 + 160*1 = 660[/tex]

Package B:

2p for each message, 360 messages, so:

360*2p = 720p.

Which package is better?

Package A costs less, thus, it offers her the better value for money in 30 days.

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Answer:

if it's area the area would be the length of the diameter of the semi circle which is the height of the triangle multiplied by the base of the triangle to find the area of the triangle then to find the area of the circle would be pie multiplied by the diameter divided by two squared

[tex]\pi \ \times 7 {}^{2} [/tex]

then the total area would be the area of the triangle plus the area of the half circle

Answer:

Step-by-step explanation:

The dimensions as a pair, appear twice for each combination.

SA = 2* 16 * 8 + 2 * 16 * 6 + 2*8* 6

That's because when you look at the figure, there are 2 places each face is positioned.

SA = 256 + 192 + 96

SA = 544

Answer:

A square shaped room contains 12m³of air.If the height of the room is 3m,what is the area of the floor. find the length too.also write the method ka answer

Step-by-step explanation:

Answer:

find the indicated functional value for the floor function: f(-3/2)

B. 0

Step-by-step explanation:

hope it helped.

° ° °

The indicated functional value for the floor function is option (C) -1 is the correct answer.

The floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted floor(x) or f(x). It gives the largest nearest integer of the specified value.

For the givens situation,

The floor function is f(-3/2).

The indicated functional value for the floor function is

⇒ [tex]f(-3/2)= f(-1.5)[/tex]

Here x = -1.5, the indicated functional value should be a greatest integer less than or equal to x.

Thus the indicated functional value of [tex]f(-1.5)[/tex] is [tex]-1[/tex].

Hence we can conclude that the indicated functional value for the floor function is option (C) -1 is the correct answer.

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Answer:

Add 1.25 litres of oil.

Step-by-step explanation:

Contents in beaker A implies;

15% of oil in 1 litre = 0.15 litres of oil

So that, there are 0.15 litres of oil and 0.85 litres of vinegar in beaker A.

Contents in beaker B implies:

55% of oil in 2 litres = 1.1 litres of oil

So that, thee are 1.1 litres of oil and 0.9 litres of vinegar in beaker B.

Half of contents of B poured into A implies that beaker A now contains:

0.15 litres + 0.55 litres = 0.7 litres of oil

0.85 litres + 0.45 litres = 1.3 litres of vinegar

The percentage of oil in A now = [tex]\frac{0.7}{2}[/tex] x 100%

                                                    = 35%

To increase the percentage of oil to 60%, then:

0.7 litres + 1.25 litres = 1.95 litres of oil

But the new total litres of the content in beaker A = 3.25 litres

So that;

[tex]\frac{1.95}{3.25}[/tex] x 100% = 60%

Therefore, to produce a mixture which is 60% oil, add 1.25 litres of oil.

Answer:

thanks for your question it is a good question but I need other part of your paper to see 3-7 questions

Step-by-step explanation:

i think there are 8 children in totally

Answer:

Step-by-step explanation:

According to the plot we have

Number of children:

Total amount of juice:

If shared equally each of the children would get:

Answer:

the answer will be 10.81

if.you round of to the nearest tenth then 10.8 feet will be the distance from slide to the monkey bar

Answer:

-14, 9 and - 54/7

Step-by-step explanation:

Answer:

(x-4)^2-9 where a=4 and b=9

Step-by-step explanation:

x^2-8x+5

x^2-8x+16-16+5

(x-4)^2-9, a=4 and b=9

Answer:

5.3 cents

Step-by-step explanation:

85/16

because all 16 ounces cost 85 cents

Answer:

5.3 cents.

Step-by-step explanation:

Answer:

11/30

Step-by-step explanation:

Answer:

One of the scenarios: