a pair of integers whose sum is -12​

Answer:

Step-by-step explanation:

Add 0.32 and 0.18 to get 0.5.

0.5=0.25 - 1.95

subtract 1.95 from 0.25 to get —1.7.

0.5=—1.7

compare 0.5 and —1.7.

flase

Answer:

y = (1/4)x² - (5/4)x + 1

Step-by-step explanation:

The x-intercepts of the quadratic equation are simply it's roots.

Thus, we have;

(x + 1) = 0 and (x - 4) = 0

Now, formula for quadratic equation is;

y = ax² + bx + c

Where c is the y intercept.

At y-intercept: (0,1), we have;

At (-1,0), thus;

0 = a(1²) + b(1) + 1

a + b = -1 - - - (1)

At (4,0), thus;

0 = a(4²) + b(4) + 1

16a + 4b = -1

Divide both sides by 4 to get;

4a + b = -1/4 - - - (2)

From eq 1, b = -1 - a

Thus;

4a + (-1 - a) = -1/4

4a - 1 - a = -1/4

3a - 1 = -1/4

3a = 1 - 1/4

3a = 3/4

a = 1/4

b = -1 - 1/4

b = -5/4

Thus;

y = (1/4)x² - (5/4)x + 1

Answer:

4

Step-by-step explanation: This one is easy if you have 6 groups of ones then times it by 4 and you will get 24.

Answer:

N= 4

C=5

T=22

K=1

Step-by-step explanation:

Edge 2021

Answer:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Step-by-step explanation:

Given

[tex]$$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,[/tex] for some integer k[tex]\}[/tex]

[tex]$$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,[/tex] for some integer k},

[tex]$$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,[/tex] for some integer k},

and

[tex]$$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,[/tex]for some integer k}.

Required

Is [tex]\{0, 1, 2, 3\}[/tex] a partition of Z

Let

[tex]k = 0[/tex]

So:

[tex]$$A _ { 0 } = 4 k[/tex]

[tex]$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0[/tex]

[tex]$$A _ { 1 } = 4 k + 1$$,[/tex]

[tex]A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1[/tex]

[tex]A _ { 2 } = 4 k + 2[/tex]

[tex]A _ { 2} = 4 *0 + 2$$ \to A_2 = 2[/tex]

[tex]A _ { 3 } = 4 k + 3[/tex]

[tex]A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3[/tex]

So, we have:

[tex]\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}[/tex]

Hence:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Answer:

Can u explain more pls?

Step-by-step explanation:

Answer:

Square

Step-by-step explanation:

Answer:

x × 3 + 5[tex]x^{2}[/tex] - x- 5

reorder the terms

3x + 5[tex]x^{2}[/tex] - x - 5

collect like terms

2x + 5[tex]x^{2}[/tex] - 5

reorder the terms

Solution

5[tex]x^{2}[/tex] + 2x -5

Answer:

[tex] {x}^{3} + 5 {x}^{2} - x - 5 \\ {x}^{2} (x + 5) - 1(x + 5) \\ (x + 5)(x - 1) \\ \\ (x + 5)( {x}^{2} - {1}^{2} ) \\ (x + 5)(x - 1)(x + 1) \\ [/tex]

Answer:

D

Step-by-step explanation:

Answer:

g(x)=f(x+3)+5

Step-by-step explanation:

12 1/2 years

Step-by-step explanation:

Let the unknown be n. Then 40+n = 3(5+n).

Performing the multiplication:

40+n = 15+3n

Isolate n and combine the constant terms:

25=2n, so n= 25/2 years

Answer:

It might be $17 for how much he has left.

Step-by-step explanation:

$20+$5-$10+5-$3=$17

Answer:

[tex]2^{3}[/tex]×5×3×[tex]x^{2}[/tex]×[tex]y^{4}[/tex]

Step-by-step explanation:

[tex]8xy^{4}[/tex]= [tex]2^{3}[/tex]×[tex]x[/tex]×[tex]y^{4}[/tex]

6[tex]x^{2} y[/tex]= 2×3×[tex]x^{2}[/tex]×[tex]y^{}[/tex]

10[tex]x^{2} y^{2}[/tex] = 2×5×[tex]x^{2}[/tex]×[tex]y^{2}[/tex]

[tex]2^{3}[/tex]×5×3×[tex]x^{2}[/tex]×[tex]y^{4}[/tex]

Answer:

57.3 minutes

Step-by-step explanation:

We know that the temperature as a function of time of an object is described by the equation:

[tex]T(t) = T_a + (T_0 - Ta)*e^{-k*t}[/tex]

Where:

k is a constant

Tₐ =  room temperature = 68°F

T₀ =  initial temperature of the object = 375°F

Replacing these in our equation we will get

T(t) = 68°F + (375°F - 68°F)*e^{-k*t} = 68°F + (307°F)*e^{-k*t}

And we know that after 25 minutes, at t = 25min, the temperature of the casserole is 190°F

then:

T(25min) = 190°F = 68°F + (307°F)*e^{-k*25 min}

Now we can solve this for k:

190°F = 68°F + (307°F)*e^{-k*25 min}

190°F - 68°F = (307°F)*e^{-k*25 min}

(122°F)/(307°F) = e^{-k*25 min}

Now we can apply the natural logarithm in both sides:

Ln( 122/307) = Ln(e^{-k*25 min}) = -k*25min

Ln( 122/307)/(-25 min) = k = 0.0369 min^-1

Then the temperature equation is:

T(t) = 68°F + (307°F)*e^{-0.0369 min^-1*t}

Now we want to find the value of t such that:

T(t) = 105°F = 68°F + (307°F)*e^{-0.0369 min^-1*t}

We can solve this in the same way:

105°F - 68°F =  (307°F)*e^{-0.0369 min^-1*t}

37°F =  (307°F)*e^{-0.0369 min^-1*t}

(37°F)/(307°F) = e^{-0.0369 min^-1*t}

Ln( 37/307) = -0.0369 min^-1*t

Ln( 37/307)/( -0.0369 min^-1 ) = 57.3 min

So after 57.3 minutes, the temperature of the casserrole will be 105°F

The length of JD is 19

The distance between two ends of a line segment can be used to calculate its length. It is the path that connects the two points and has a known length.

Given

JD = JP-DP = 57-38 =19

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Answer:

X= 115 is the answer

because it is corresponding angel they are equal

Answer:

X = 115 since the x and the other angle looks like they correspond to each other

Step-by-step explanation:

Answer:

D. 160

Step-by-step explanation:

9514 1404 393

Answer:

  a) 230

  b) 300

  c) 2×10^-2

  d) 1.1×10^-6

Step-by-step explanation:

a) 0.26 × 890 ≈ 1/4 × 900 ≈ 225 ≈ 230

b) 1.95/(.67×10^-2) ≈ 2/(2/3)×10^2 ≈ 300

c) 2010×10^-5 ≈ 2×10^3×10^-5 = 2×10^-2

d) 9.98×10^-4/(9×10^2) = 9.98/9×10^(-4-2) ≈ 1.1×10^-6

__

YMMV depending on how you do the rounding and approximate multiplication and division.

The first one can be done multiple ways. For most accurate results, increasing one number while decreasing the other is recommended. (You don't want to compute 0.3×900, for example.)

Answer:

The height of the tank in the picture is:

Step-by-step explanation:

First, to know the height of the tank, we're gonna change the unit of the volume given in liters to cm^3:

So:

Now, we must calculate the height of the tank that we don't know (the other part that isn't with water), to this, we can use the volume formula clearing the height:

Now, we must clear the height because we know the volume (1200 cm^3):

Height = volume of a cube / (long * wide)

And we replace:

Remember this is the height of the empty zone, by this reason, to obtain the height of the whole tank, we must add the height of the zone with water (7 cm) that the exercise give us:

In this form, we calculate the height of the tank in 19.5 cm.

[tex]\displaystyle\ y^4 +5y^2+9=(y^2+3)^2-y^2=(y^2-y+3)(y^2+y+3)[/tex]

Answer:

Solution given;

[tex] y^{4}+5y²+9[/tex]

keeping [tex]y^{4} and 9 together [/tex]

[tex]y^{4}+9+5y²[/tex]

[tex](y²)²+3²+5y²[/tex].....[I]

we have

a²+b²=(a+b)²-2ab

or

a²+b²=(a-b)²+2ab

same like that

[tex](y²)²+3²=(y²+3)²-6y² or (y²-3)²+6y²[/tex]

remember that while adding or subtracting the left term 5y² either adding 6y²or subtracting 6y²

should make the term perfect square

while subtracting it makes perfect square

so

we take

(y²)²+3²=(y²+3)²-6y²

again

substituting value of

(y²)²+3² in equation 1 and it becomes

(y²+3)²-6y²+5y²

solve like terms

(y²+3)²-y²

again

we have

a²-b²=(a+b)(a-b)

by using this.

(y²+3+y)(y²+3-y)

rearrange it

(y²+y+3)(y²-y+3) is a required factorisation form.

Answer:

36 spuare units

Step-by-step explanation:

A= 1/2 b*h

b=8

h=9

A=1/2(8*9)

A=1/2(72)

A=36

Answer:

Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°

Step-by-step explanation:

To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.

180 - 100 = 80

Angle a is 80°.

Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.

After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.

Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.

So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.

Answer:

Slope of AB = 2

Slope of CD = 2

equal slopes means the lines are parallel

Step-by-step explanation:

Use slope formula

m = [tex]\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )}[/tex]

line AB = [tex]\frac{(5-1)}{(2-0)}[/tex] = [tex]\frac{4}{2}[/tex] = 2

line CD - [tex]\frac{(15-7)}{(4-0)}[/tex] = [tex]\frac{8}{4}[/tex] = 2

Answer:

a) The greatest number that divides 36, 45, and 63 without leaving a remainder is 9

b) The greatest number which exactly divides 90, 120, and 150 is 30

c) The greatest capacity of the bucket is 10 liters

d) The greatest number of people to whom the items can be distributed equally is 40 people

ii) 2 kg of wheat flour, 3 kg of corn and 4 kg of rice

e) The greatest number of children to whom the 48 orange, 80 bananas, and 144 apples can be distributed equally is 16

ii) 3 oranges, 5 bananas and 9 apples each

f) 5 mangoes at a time from the basket containing 120 mangoes

7 mangoes at a time from the basket containing 168 mangoes

g) The greatest length of each squared marble is 2 m

Step-by-step explanation:

a) The greatest number that divides 36, 45, and 63 without leaving a remainder = The highest common factor of 36, 45, and 63, which is given as follows;

36 = 9 × 4

45 = 9 × 5

63 = 9 × 7

Therefore, The greatest number that divides 36, 45, and 63 without leaving a remainder  = The highest common factor of 36, 45, and 63 = 9

b) 90 = 30 × 3

120 = 30 × 4

150 = 30 × 5

The greatest number which exactly divides 90, 120, and 150 is 30

c) The factors of the volumes are;

50 l = 10 × 5 l

60 l = 10 × 6 l

70 l = 10 × 7 l

Therefore, the greatest capacity of the bucket = 10 liters

d) The masses of the items are

The factors of 80 = 40 × 2

120 = 40 × 3

160 = 40 × 4

Therefore the items can be distributed equally to 40 people

ii) Each person gets 2 kg of wheat flour, 3 kg of corn and 4 kg of rice

e) 48 = 16 × 3

80 = 16 × 5

144 = 16 × 9

Therefore, the greatest number of children = 16

ii) Each child gets 3 oranges, 5 bananas and 9 apples

f) The factors of 120 = 24 × 5

168 = 24 × 7

Therefore;

The greatest number of mangoes which is to be taken out of the basket with 120 mangoes = 5 mangoes each (24 times)

The greatest number of mangoes which is to be taken out of the basket with 168 mangoes = 7 mangoes each (24 times)

g) The area of the floor = 12 m × 10 m = 120 m²

The factor of 120 m² which is a perfect square is 4 therefore, we have;

The side length of each squared marble, s = √4 = 2

The side length of each squared marble, s = 2 m

Answer:

La probabilidad es P = 0.4

Step-by-step explanation:

Sabemos que la caja tiene:

3 bolas de color primario (1 roja, 1 amarilla, 1 azul)

2 de color secundario (1 verde, 1 naranja)

Como la bola la sacaremos al azar, todas las bolas tienen exactamente la misma probabilidad de salir.

Queremos obtener la probabilidad de sacar una bolita de color secundario.

Esta probabilidad se calculará como el cociente entre el número de bolitas que cumplen este requisito (es decir, ser de color secundario, sabemos que hay dos de esas) y el número total de bolitas en la caja ( son 5)

La probabilidad es:

P = 2/5 = 0.4

Escribiendo esto en porcentaje (solo se lo multiplica por 100%) tenemos:

40%

Es decir, hay un 40% de posibilidades de sacar una bolita de un color secundario.

Answer:

90

Step-by-step explanation:

You are looking for the highest common factor for 270 and 360.  

Factor the 2 numbers

270 = 2 * 5 * 3  * 3 * 3

360 = 2 * 2 * 2 * 3 * 3 * 5

Each of the numbers has a 5

Each of the numbers has two threes

Each of the numbers has one 2

So the answer is 2 * 3*3 * 5

Answer:

(2x - 3) ^2 - 11x - 6

Step-by-step explanation:

Answer:

A. All men

Explanation

The probability of all men = 0.4219 while the probability of 2 women and 1 man = 0.14

The question says we have three times as much men as women

The probability it is a man that was chosen = 3/4

The probability of choosing a woman = 1/4

a. The probability that the chosen persons are all men = (3/4)³

= 0.4219

b. The probability of 2 women and 1 man

3 * 0.75 *0.25²

= 0.14

Hence the probabilities are  a. 0.4219 and b.  0.14

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Answer:

[tex]{ \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^{3} - {3x}^{2} + kx - 1}} \\ { \tt{f(1) : {(1)}^{3} - 3 {(1)}^{2} + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}[/tex]

Answer:

k = 3

Step-by-step explanation:

If x-1 is a factor of x³ - 3x² + kx - 1 then value of x is 1.

f (x ) = x³ - 3x² + Kx - 1 , then

plug 1 as x in the expression.

expand exponents

combine like terms

Add 3 to both side