Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.

A system of equations. x plus 5 y equals 21. x plus y equals 9.

The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.

The quadratic equation is  3x² - 27.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Given:

The roots are 3 and -3

We have

α= 3   and β=-3

So,

α+β = -b/a  and αβ = c/a

α+β = 0 =-b/a and  αβ= -9 = c/a

Comparing from above

a=1, b= 0 and c=-9

Also, the leading coefficient is 3.

Then the quadratic equation is,

= 3(ax² + bx + c)

= 3( x² +0x- 9)

Hence, the quadratic equation is 3x² - 27.

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Angle DAB will be equal to angle CAB

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

AC is a straight line and forms one of the sides of the triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

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Answer:

D. [tex](x + 1)(x^2 + 3)[/tex]

Step-by-step explanation:

Hello!

We can group the first two terms and the last two terms.

Factoring by grouping is the process of breaking down larger polynomials to smaller ones to factor. We can then combine like factors.

In the second step, we can see that we can rewrite [tex]x^3 + x^2[/tex] as [tex]x^2(x + 1)[/tex], as both the two terms share a common factor of [tex]x^2[/tex]. We can pull out [tex]x^2[/tex] from that expression. Similarly, [tex]3x[/tex] and [tex]3[/tex] share a common factor of [tex]3[/tex], so we can pull that out.

In quadrilateral PQRS, ∠P and ∠S are opposite angles.

Answer:

C

Step-by-step explanation:

cos 30=12/x

[tex]x = 8 \sqrt{3} [/tex]

cos60=y/x

[tex]y =4 \sqrt{3} [/tex]

Answer:

x = [tex]8\sqrt{3}[/tex]

y = [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

• tan 60° = 12/ y         [tan θ = opposite/ adjacent]

y = 12/ tan 60°  

y = [tex]4\sqrt{3}[/tex]

• x² = y² + 12²             [Pythagoras's theorem]

x² = ( [tex]4\sqrt{3}[/tex] )² + 144

x = [tex]\sqrt{(4\sqrt{3})^{2} \space\ + \space\ 144}[/tex]

x = [tex]8\sqrt{3}[/tex]

Answer:

A

Step-by-step explanation:

Use the Pythagorean Theorem: a^2 + b^2 = c^2

The cable will be the hypotenuse, so c = 11.3 m

One leg is the distance of the anchor, so a = 4.2 m

(4.2)^2 + b^2 = (11.3)^2

17.64 + b^2 = 127.69

Subtract 17.64 from both sides

b^2 = 110.05

Square root both sides

b = ~10.5 m

Answer:

x = -15

Step-by-step explanation:

Answer:

If the denominators are equal for all of the fractions, you can simply look at the numerator and order them. If the denominators aren't equal, you'll have to find the lcm (lowest common multiple), for example, if we have the fractions 3/6 and 1/4, we would find the lcm of 6 and 4, which is 12 and multiply the numerators accordingly. So the fractions would then become 6/12 and 3/12, this makes it easier for you to figure out their order from least to greatest.

Goodluck for your finals :)

Answer:

the answer are A and Y , B and X.

 A and X are two independent events  , Option A is the correct answer.

Probability is the likelihood of an event to happen

A two way table is given

The two events will be independent when

If A is the first event and B is the second event , then

P(A) = P(A|B)

Here the P(A) = 30/100 = 0.3

P(B) = 20/100 = 0.2

P(A|X) = 15/50 = 0.3

P(A) = P(A|X)

Therefore A and X are two independent events , Option A is the correct answer.

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Answer:

See below

Step-by-step explanation:

4(x + 5) = 9x + 4x − 34

4x + 20 = 9x + 4x − 34   [Distributive]

4x + 20 =  13x − 34         {Combine Like Terms]

4x - 13x + 20 = 13x - 13x − 34  [Subtractive:  -13x both sides]

-5x + 20 = - 34            [Combine Like Terms]

-5x + 20 - 20 = -34 - 20     [Subtractive:  - 20 both sides]

-5x  = -54               [Combine Like Terms]

x = -54/-5             [Division Property:  divide both sides by -5]

x =  - 10 4/5            

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given information:

We can assume that 3 pupils play the flute only as we have also been told that 6 pupils play both instruments.

To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:

⇒ total number of pupils - pupils who play instruments

⇒ 20 - (3 + 6 + 6)

⇒ 20 - 15

⇒ 5

Therefore, 5 pupils do not play the piano and/or flute.

To calculate probability:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore:

[tex]\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}[/tex]

The substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an exponential function:

[tex]\rm N = N_oe^{-kt}[/tex]

Plug N = N⁰/2

[tex]\rm N_o/2 = N_oe^{-kt}[/tex]

[tex]\rm \dfrac{1}{2} = e^{-0.15t}[/tex]

Solving for t:

t = 4.62≈ 4.7 days

Thus, the substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15

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Answer:

  6/x²

Step-by-step explanation:

Rational expressions are added the same way numerical fractions are added. Their sum is the quotient of the sum of numerators, and the common denominator.

__

The given fractions already have the same denominator, so we simply add their numerators.

  [tex]\dfrac{2}{x^2}+\dfrac{4}{x^2}=\dfrac{2+4}{x^2}=\boxed{\dfrac{6}{x^2}}[/tex]

The true statements about ∠MJK and ∠MJL are

The statement is given as:

∠MJK and ∠MJL are a linear pair of angles and the angles are also supplementary

As a general rule, linear pair angles are adjacent angles that add up to 180 degrees. This means that:

The above means that, the following options are true:

(e), (f) and (h)

Also, the converse of the statement is:

∠MJK and ∠MJL are supplementary angles and the angles are also  linear pair of angles

This is false because not all supplementary angles are  linear pair angles

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Answer: A stretch by a factor of 2 for the exponential growth function f(x)= a(9/4)^x occurs when a =✔ 2

A stretch by a factor of 11/3  for the exponential decay function f(x)= a(3/5)^x occurs when a =✔ 11/3

A shrink by a factor of 1/3 for the exponential growth function f(x)= a(7)^x occurs when a =✔ 1/3

A shrink by a factor of 2/5  for the exponential decay function f(x)= a(2/9)^x occurs when a =✔ 2/5

Step-by-step explanation:

The exponential growth equation is stretched and compressed by a scale factor k = 2 , 11/3 , 1/3 and 2/5

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential growth equation be represented as A

Now , the value of A is

For the exponential growth function f(x)= a(9/4)ˣ, a stretch by a factor of 2 occurs when a = 2

For the exponential decay function f(x)= a(3/5)ˣ, a stretch by a factor of 11/3 occurs when a = 11/3

For the exponential growth function f(x)= a(7)ˣ, a shrink by a factor of 1/3 occurs when a = 1/3

For the exponential decay function f(x)= a(2/9)ˣ, a shrink by a factor of 2/5 occurs when a = 2/5

Hence , the exponential equation is solved

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Answer:

the answer is C, 5a^6b

Step-by-step explanation:

The length of lake is 4500 feet.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.

Here, In ΔABE and ΔDCE

          ∠ABE = ∠DCE         { each 90⁰ }

          ∠AEB = ∠CED         { vertically opposite angle}

By AA similarity, we get

          ΔABE ≈ ΔDCE

Now, AB/CD = BE/CE

       AB/500 = 1800/200

       AB/500 = 9

        AB = 9 X 500

       AB = 4500 feet.

Thus, the length of lake is 4500 feet.

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Answer:

x^4 - 3x^2 - 4.

Step-by-step explanation:

Imaginary roots  occur as conjugate pairs  so a 4th roots is -i.

So in factor form we have:

f(x) = (x - 2)(x + 2)(x - i)x + i)

     = (x^2 + 1)(x - 2)(x + 2)

     = (x^2 + 1)(x^2 - 4)

      = x^4 - 3x^2 - 4.

Answer:b.f(x) = x^4 – 3x^2 – 4

Step-by-step explanation:

Answer:

pm = 4

M is the mid point of PQ which means that pm = mq

so MQ = 4

PQ = PM + MQ

= 4 + 4

= 8

the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

To do this, we can think on the situation as a right triangle, where the hypotenuse is 4 miles, the angle that we look at measures 10.5°, and the change in elevation (let's call it x) will be the opposite cathetus to that angle.

Then we can use the relation:

Sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know, we get:

sin(10.5°) = x/4mi

x = sin(10.5°)*4mi = 0.73mi

So the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

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Answer:

50

Step-by-step explanation:

So you can think of this by grouping it like this:

(1-2) + (3-4) + (5-6) + ... + (97-98) + 99

which is equal to: (-1) + (-1) + (-1)... + (-1) + 99

(each group is equal to -1, and 99 won't have a pair since it's the last one)

then, find how many groups of -1 there are:

the groups start at 1 and end at 98, but there are two in each group, so 98/2 = 49. this means there are 49 groups.

so now, you know that there are 49 -1s, so 49 * (-1) = -49.

finally, you can't forget the extra 99 that didn't have a pair, so -49 + 99 = 50.

The answer is pretty simple but I put it in a picture below

Answer:

[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].

Step-by-step explanation:

Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.

Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:

[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].

Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:

[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].

Answer:

D

Hope this helps!

We can see that the area of the triangle is: 5.65in².

A triangle is actually known to be a shape that has three sides, three angles and three vertices. It's also known as a plane shape.

In order to find the area of the triangle, we will use Pythagorean Theorem: c² = a² + b².

Where c = hypotenuse = 6in.

b = 2in.

6² = a² + 2²

36 = a² + 4

a² = 36 - 4 = 32

a = √32

Area of the triangle = ½ × base × height.

Where base = √32

height = 2

Thus: A = ½ × √32 × 2

A = √32 = 5.65in².

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Answer:

6 + (7 + 8) = 21

Step-by-step explanation:

the associative property of addition is: (a + b) + c = a + (b + c)

So the equivalent addition sentence would be:

(6 + 7) + 8 = 6 + (7 + 8) as they both equal 21

Based on the calculations, the equation for the curve of best fit is equal to y = -30.17x + 14.49.

From the table of data points, we have the following:

Mathematically, the standard equation of a straight line is given by:

y = ax + b       ....equation 1.

Thus, the equations that can be used to model the given data points are:

∑y = na + b∑x             ....equation 2.

∑xy = a∑x + b∑x²       ....equation 3.

Substituting the parameters into the equations, we have;

50.9 = 6a + 16b             ....equation 4.

24.6 = 16a + 35b       ....equation 5.

Solving eqn. 5 and 6 simultaneously, we have:

Substituting the value of a and b into eqn. 1, we have;

y = ax + b

y = -30.17x + 14.49.

Therefore, the equation for the curve of best fit is equal to y = -30.17x + 14.49.

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