A factory used 99.19 kilograms of tomatoes to make 7 batches of pasta sauce. What quantity of tomatoes did the factory put in each batch?

Answer:

Ans:

i) y-int (0 , 2) and x-int (-2/3 , 0)

ii) y = 3x + 2

Step-by-step explanation:

we know:

m = 3 & point (0,2)

i

y-int is (0,2) because where x is 0 it intersects the y-axis

ii

from this we can sub it into the point slope formula which is:

y - y1 = m (x - x1)          (y1 and x1 being the values from a point lying on the line)

y - 2 = 3 (x - 0)

y - 2 = 3x

y = 3x + 2     < this is the equation

if you also need to find the x-int then:

to find x-int make y = 0 and solve for x

y = 3x + 2                     3x = - 2

0 = 3x + 2                       x = -2/3

therefore x-int is (-2/3,0)

Answer:

x = -1.4 and x=2

Step-by-step explanation:

The solutions are where the graphs intersect

The graphs appear to intersect at x = -1.4 and x=2

For the first equation, recall that sin²(θ) = (1 - cos(2θ))/2. Then

2 sin²(θ) = 2 + cos(2θ)

1 - cos(2θ) = 2 + cos(2θ)

2 cos(2θ) = -1

cos(2θ) = -1/2

2θ = arccos(-1/2) + 2nπ   or   2θ = 2π - arccos(-1/2) + 2nπ

(where n is any integer)

2θ = 2π/3 + 2nπ   or   2θ = 4π/3 + 2nπ

θ = π/3 + nπ   or   θ = 2π/3 + nπ

In the interval [0, 2π), the solutions are θ = π/3, 2π/3, 4π/3, 5π/3.

For the second equation, rearrange the previous identity to arrive at

cos(2θ) = 1 - 2 sin²(θ) = 2 cos²(θ) - 1

Then

cos(2θ) + 7 cos(θ) = 8

2 cos²(θ) - 1 + 7 cos(θ) = 8

2 cos²(θ) + 7 cos(θ) - 9 = 0

(2 cos(θ) + 9) (cos(θ) - 1) = 0

2 cos(θ) + 9 = 0   or   cos(θ) - 1 = 0

cos(θ) = -9/2   or   cos(θ) = 1

Since |-9/2| > 1, and cos(θ) is bounded between -1 and 1, the first case offers no solutions. This leaves us with

cos(θ) = 1

θ = arccos(1) + 2nπ

θ = 2nπ

so that there is only one solution in [0, 2π), θ = 0.

Answer:

sum of two numbers is 30

Step-by-step explanation:

let three numbers are x,y,z

average =x+y+z/3

x+y+z/3=16

x+y+z=48......(1)

The sum of two numbers is 18.

according to condition:

let x=18

subtitute x=18 in (1)

18+y+z=48

y+z=48-18

y+z=30

Answer:

If we put x=17/4

f(4×17/4-15)=8×17/4-27

f(2x=34-27

f(x)=7.

Hope i helped you.

Answer:

(x-7) and (x+12) are the factors and the rest are non factors...

Answer:

√x-x-2x³+√x+x

= 2√x-2x³

= -2x³+2√x

which is option A

Answer: D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Answer:

The choose C. 2

[tex]( \frac{4 ^{ \frac{5}{4} } \times 4^{ \frac{1}{4} } }{4 ^{ \frac{1}{2} } } )^{ \frac{1}{2} } = 2[/tex]

Answer:

2

Step-by-step explanation:

inside the parenthesis is equivalent to 4^(5/4 + 1/4 - 1/2) = 4¹ = 4

√4 = 2

The system of inequalities that is graphed is:

y ≤ - (2/3)*x

y < x - 3

So the correct option is B.

First, we can see that for both of the inequalities the shaded part is below the lines.

You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.

Only with that, we conclude that the correct option is B.

y ≤ - (2/3)*x

y < x - 3

If you want to learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1

Answer:

it's answer is

[tex] \frac{25}{18} [/tex]

Answer:

[tex]f=-\frac{15}{4}[/tex]

Step-by-step explanation:

The first thing to do when solving any equation is to isolate the unknown variable. In this case we should start by trying to isolate f on the left side. We can do this by subtracting 1/4 from both sides, as this will move it to the other side while keeping the equation equal:

[tex]f+\frac{1}{4} =-\frac{7}{2} \\\\f+\frac{1}{4} -\frac{1}{4} =-\frac{7}{2} -\frac{1}{4} \\\\f=-\frac{7}{2} -\frac{1}{4}[/tex]

Now that we have isolated the f, we can simplify the other side. We can't subtract them right away as they have different denominators, but we can solve this by multiplying the 7/2 by 2 so that its denominator is 4, allowing us to subtract the numerators:

[tex]f=-\frac{7}{2} -\frac{1}{4} \\\\f=-\frac{7*2}{2*2} -\frac{1}{4} \\\\f=-\frac{14}{4}-\frac{1}{4} \\\\f=\frac{-14-1}{4} \\\\f=-\frac{15}{4}[/tex]

Hope this helped!

Answer:

25 workers

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

,

Answer:

13⁰

Step-by-step explanation:

to draw it on a number line, write the number -12⁰, then jump forward 25 times which will end you up at 13⁰ since

-12 + 25 = 13⁰

Answer:

[tex]i)36\\ii)7[/tex]

Step-by-step explanation:

[tex]i) As\ our\ first\ expression,\ we\ have:\\ab^2\\Substituting\ a=4, b=-3:\\ab^2=4*(-3)^2=4*-3*-3=4*9=36\\ii)Next,\ we\ have:\\(a-b)(a+b)\\Hence,\\Substituting\ a=4,\ b=-3:\\(a-b)(a+b)=(4-3)(4+3)=1*7=7\\Note:\\You\ can\ also\ use\ the\ algebraic\ identity: (a+b)(a-b)=a^2-b^2[/tex]

Answer:

Given that, a = 4 and b = -3

Now,

Answer:

x=12

Step-by-step explanation:

3x/6 + 2 = 8

Subtract 2 from each side

3x/6 + 2-2 = 8-2

3x/6 =6

Multiply each side by 6/3

6/3 * 3/6 x = 6 *6/3

x = 36/3

x = 12

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \frac{3x}{6} \: + \: 2 \: = \: 8 }}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \frac{3x}{6} \: = \: 8 \: - \: 2 }}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \frac{3x}{6} \: = \: 6 }}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \frac{3x}{6} \: + \: 6}}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \frac{3x \: + \: 36}{6} \:}}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \frac{3x \: + \: \cancel{36} \: \: ^{6} }{ \cancel6} \:}}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \: x \: = \: \frac{36}{6} }}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \: x \: = \: \cancel\frac{{36}{ \: ^{6} }} {6} }}} }}} \\ [/tex]

[tex]\large\bf{{\red{ \longrightarrow \:\large\rm{{\blue{ \: x \: = \: 6 }}} }}} \\ [/tex]

Answer:

4

Step-by-step explanation:

if x+2 is a factor of the above expression then,

x=-2

so putting the value of x in above expression we get,

(-2)^3+2×(-2)^2+2×(-2)+k=0

or,-8+8-4+k=0

k=4

Answer:

Step-by-step explanation:

If (x + 2) is a factor of a polynomial then ( - 2 ) is the zero of that polynomial ⇒ ( - 2 )³ + 2( - 2 )² + 2( - 2 ) + k = 0 ⇒ k = - 4

Answer:

39/250

Step-by-step explanation:

15 3/5 = 78/5 and percent means per 100, so

(78/5)/100 = (78/5)(1/100)

=78/500 = 39/250

Answer:

The shopping time (in minutes) of the nine shoppers are:

15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged  everything from least to greatest.)

We can see, that 3 shoppers shopped for 15-20 minutes.

And, 3 shoppers shopped for 21-26 minutes.

And finally, 3 shoppers shopped for 27-32 minutes.

So the answer for all 3 of the boxes is 3.

Let me know if this helps.

Answer:

-

Step-by-step explanation:

Forget using calculators.

Test each point by plugging its coordinates into the equation, and checking if the equation holds true.

Don't bother testing (-3,0), because you can't take the square root of -3.

Answer:

(4−3i)x^2

=4x^2 - 3ix^2

Answer:

h(x) = 2x^2 +14x -60

Step-by-step explanation:

A quadratic is of the form

h(x) = ax^2 + bx +c

h(3) = h(-10) = 0

This tells us that the zeros are at x=3 and x = -10

We can write the equation in the form

h(x) = a( x-z1)(x-z2) where z1 and z2 are the zeros

h(x) = a(x-3) (x- -10)

h(x) = a(x-3) (x+10)

FOIL

h(x) = a( x^2 -3x+10x-30)

h(x) = a(x^2 +7x -30)

Let a = 2

h(x) = 2x^2 +14x -60

It means

zeros are 3 and -10

Form equation

Multi ply by 2

Option D

Answer:

b

Step-by-step explanation:

2x4=8 3x2=6 2x2=4

there all diviseble by 2

therfore ur answer is b

Answer:

the answer is 4

Step-by-step explanation:

9514 1404 393

Answer:

  (a) 5.82 cm (correctly shown)

  (b) 10.53 cm

Step-by-step explanation:

a) The length BC can be found from the law of sines:

  BD/sin(C) = BC/sin(D)

  BC = BC·sin(C)/sin(D) = (6 cm)sin(48°)/sin(50°) ≈ 5.82 cm

__

b) The angle ABD is the sum of the angles shown:

  angle ABD = 50° +48° = 98°

We know the lengths BA and BD and the included angle ABD, so we can use the law of cosines to find AD.

  AD² = BA² +BD² -2·BA·BD·cos(98°)

  AD² ≈ 8² +5.82² -2(8)(5.82)(-0.139173) ≈ 110.8411

  AD ≈ √110.8411 ≈ 10.53 . . . . cm

Answer:

z=-(51p+84)/(d+p)

Step-by-step explanation:

-p*(51+z)=dz+84

-51p-pz=dz+84

-51p-84=dz+pz

z=-(51p+84)/(d+p)

Answer:

1)17

2)33

3)9

4)27

5)1252

6)50

Step-by-step explanation:

Answer:

Swimming pool

Step-by-step explanation:

Let's say that we invite x people. The cost of the bowling alley will be $15 for the room, and we add $5 dollars for each person. Therefore, we can represent the cost of the bowling alley as

5 * x + 15

Similarly, the cost of the swimming pool is

4 * x + 12

To find the maximum of the function, one thing we can do is set the expressions of the cost equal to 40. This will give us the amount of people we can invite for exactly 40 dollars. Because cost increases with amount of people, this will give us the maximum number of people we can invite with $40.

We thus have

5 * x+ 15  = 40

subtract 15 from both sides to isolate the x and its coefficient

25 = 5 * x

divide both sides by 5 to isolate x

25/5 = x = 5

We can therefore invite 5 people to the bowling alley

4 * x+ 12  = 40

subtract both sides by 12 to isolate the x and its coefficient

28 = 4 * x

divide both sides by 4 to isolate x

x = 7

Therefore, we can invite 7 people to the swimming pool. As 7 > 5, we can invite more people to the swimming pool.

A quicker way to solve this could be by looking at the cost of each location. Because the bowling alley costs more both per person and for the room, and there is no way to decrease the cost except by decreasing the amount of people, there is no way that the bowling alley could get as many people as the swimming pool with the same amount of money

Answer:

angleABC=isosceles triangle

angleB=(180-50)÷2=65

angle B=angleX(alternative angle)

angleB=65degree

Step-by-step explanation:

sec⁴B - sec²B = sec²B(sec²B - 1)

= (1 + tan²B)(tan²B)

= tan⁴B + tan²B

= Right-hand side (Proven)

Answer:

321

Step-by-step explanation: