Write what the expressions below best represent within the context of the word problem How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?

Answer:  The correct option is (A) A dilation factor of 2.

Step-by-step explanation:  We are shown two similar polygons in the figure.

We are to select the transformation that was performed on PQRS to form P'Q'R'S'.

We can see clearly from the figure that two polygons have same shape but different sizes.

So, the only transformation possible from PQRS to P'Q'R'S' is dilation.

To find the dilation factor, we need the lengths of any two corresponding sides of PQRS and P'Q'R'S'.

From the graph, we note that

PQ = 2 units  and P'Q' = 4 units.

Therefore, the dilation factor is given by

[tex]D_f\\\\\\=\dfrac{\textup{length of a side of the dilated figure P'Q'R'S'}}{\textup{length of the corresponding side of the original figure PQRS}}\\\\\\=\dfrac{P'Q'}{PQ}\\\\\\=\dfrac{4}{2}\\\\=2.[/tex]

Thus, the required transformation is a dilation with dilation factor of 2.

Option (A) is CORRECT.

Answer:

[tex]-9\sqrt{11}[/tex]; None of the above; [tex]3\sqrt{7}[/tex]

Step-by-step explanation:

For the first question:

[tex]5\sqrt{11}-12\sqrt{11}-2\sqrt{11}[/tex]

Treating the radicals as a variable, we combine like terms:

[tex]5\sqrt{11}-12\sqrt{11}-2\sqrt{11}\\\\=-7\sqrt{11}-2\sqrt{11}\\\\-9\sqrt{11}[/tex]

For the second question:

[tex]5(10-4\sqrt{2})[/tex]

We use the distributive property:

[tex]5(10-4\sqrt{2})\\\\5\times 10-5\times4\sqrt{2}\\\\50-20\sqrt{2}[/tex]

This is not one of the choices available.

For the third question:

[tex]\sqrt{3}\times \sqrt{21}[/tex]

We will first find the prime factorization of 21.  21 = 3*7:

[tex]\sqrt{3}\times \sqrt{3\times7}[/tex]

These can all be written under one radical:

[tex]\sqrt{3\times 3\times 7}[/tex]

For square roots, we want pairs of factors.  We have a pair of 3s, so this comes out, giving us

[tex]3\sqrt{7}[/tex]

Answer: Answer of First Question is -9√11, answer of second Question is 'None of the above' and answer of third question is 3√7

Step-by-step explanation:

since, in first question, given expression is,

5√11-12√11-2√11

And, we can write, 5√11-12√11-2√11=-9√11

In other words, negative 9 square root of 11

Thus, option third is correct.

In second question, given expression is,

5(10-4√2),

And we can write, 5(10-4√2)=50-20√2

In other words, 50 minus 20 square root of 2.

Thus, Option fourth is correct.

In third question, given expression,

√3×√21,

And we can write, √3×√21=√3×√3×√7=3√7

Thus, third option is correct.

Answe

-5x³ + 4x² - 5x

Step-by-step explanation:

got it right on the quiz

Final answer:

The number of ways 12 cheerleaders can line up is calculated using permutations, specifically 12!, which is the product of all positive integers from 1 to 12.

Explanation:

The number of ways the 12 cheerleaders can line up down the football field can be calculated using the concept of permutations. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. For 12 cheerleaders, each of whom is distinct, the number of different ways they can line up is the same as the number of permutations of 12 objects, which is given by the factorial of the number of objects.

The formula for permutations of n objects is n! (n factorial), where n represents the total number of objects. Therefore, for 12 cheerleaders, the expression for the number of ways they can line up is:

12!

This is calculated as 12 × 11 × 10 × 9 × ... × 3 × 2 × 1. The value of 12! (12 factorial) gives us the total number of possible arrangements for the 12 cheerleaders.

Answer:-7, 7.

Step-by-step explanation:

-7+7= 0

Simple as that :) Plz mark brainliest

[tex] nPk=\dfrac{n!}{(n-k)!}\\\\
\dfrac{ 10P6}{10P4}=\dfrac{\dfrac{10!}{4!}}{\dfrac{10!}{6!}}=\dfrac{10!}{4!}\cdot\dfrac{6!}{10!}=5\cdot6=30 [/tex]

there are 6 sections and the sections are 4 x 4

 so the correct expression can be 6x4x4

Answer:

6 x 4 x 4

Step-by-step explanation:

IN order to calculate the total area or the cardboard you just have to make a simple multiplication, the carboard is divided in equal sized squares, 6 equal sizd squares, and each one of them has a 4 inches side, so to calculate the area of the cardboard you just calculate the area of one square and then multiply it by the number of squares.

Area of one square= 4x4

Number of squares=6

Total area of the carboard= 6x4x4

A rectangle is a parallelogram because each pair of sides is parallel and the same length as each other

For a parallelogram, the following are true

Two of the interior angles are equal

Only two o fits sides are parallel

A parallelogram is a quadrilateral figure with opposite parallel sides.

For a rectangle, all the interior angles are 90 degrees, a

Hence we can conclude that a rectangle is a parallelogram because each pair of sides is parallel and the same length as each other

Learn more on properties of rectangle here: https://brainly.com/question/1214882

Answer:

398 ( did it on college bridge)

Step-by-step explanation:

The required value of the expression is 412 which is determined by substituting for x = 4 and y = 6.

Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.

The expression is given in the question as:

(4x−12)+(12xy−10)(4x-12)+(12xy-10)

To find the value of the expression for a given value of x and y, we can substitute the values of x and y into the expression and evaluate it.

(4x−12)+(12xy−10)(4x-12)+(12xy-10)

Substituting x=4 and y=6 into the expression, we get:

(4(4)−12)+(12(4)(6)−10)(4(4)−12)+(12(4)(6)−10)

This simplifies to:

(16−12)+(12(24)−10)(16−12)+(12(24)−10)

This further simplifies to:

4+(12(24)−10)(4)+(12(24)−10)

4+(12(24)−10)(4)+(12(24)−10)

4+288+120 = 412

Therefore, the value of the expression for x = 4 and y = 6 is 412.

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ2

To estimate the number of units in the entire apartment complex that have 3 rats, we can use the proportion of units in the sample that have 3 rats and apply it to the total number of units in the complex.

To determine how many units in the entire apartment complex have 3 rats, we can use the concept of sampling. Since the apartment caretaker checked 9 units and recorded the number of rats in each, we can calculate the proportion of units with 3 rats in these 9 units. We can then apply this proportion to the entire apartment complex to estimate the number of units with 3 rats.

Out of the 9 units checked, there were 3 units with 3 rats. So the proportion of units with 3 rats in the sample is 3/9 = 1/3.

To estimate the number of units with 3 rats in the entire apartment complex, we can multiply the proportion of units with 3 rats in the sample (1/3) by the total number of units in the complex: 1/3 * 150 = 50. So, approximately 50 units in the entire apartment complex have 3 rats.

Answer:

D) EAC is equilateral triangle

Step-by-step explanation:

Given :

AEC is a triangle in which B∈ AC and D∈EC

Such that,

∠ABE = 90°,

∠ADE = 90°,

Also, BC = CD

We have to prove that :

Δ ABE is congruent to Δ EDA

Proof :

If EAC is an equilateral triangle,

By the property of equilateral triangle,

EA = AC = EC

If AC = EC

⇒ AB + BC = ED + CD

⇒ AB + CD = ED + CD

⇒ AB = ED

Also, AE = AE ( common segment )

Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,

Then, the other legs must be equal,

That is, BE = DA,

Hence, by SSS postulate of congruence,

Δ ABE ≅ Δ EDA

Therefore, option D is correct.

Answer:

The answer is 10 ft.  

Step-by-step explanation:

make a triangle 6ft tall, 8ft long (90 degrees to the other line) and draw a line to complete the triangle.  This is a type of 3,4,5 triangle, a 6,8,10.  The other way to do it is sqrt(6^2+8^2) = sqrt(36+64) = sqrt (100) = 10.

When x=7 , the first equation y = 200 + 350x has the greater value.

To determine which equation has the greater value when x=7, we need to evaluate both equations at x=7 and compare the resulting y values.

For the first equation [tex]\( y = 200 + 350x \):[/tex]

[tex]\[ y = 200 + 350 \times 7 \]\[ y = 200 + 2450 \]\[ y = 2650 \][/tex]

For the second equation y=3x

[tex]\[ y = 3 \times 7 \]\[ y = 21 \][/tex]

Comparing the values, we see that y=2650 for the first equation and y=21 for the second equation.

Answer:

(C)

Step-by-step explanation:

It is given that The steepest side of the model, AB, measures 4 inches, thus

From ΔABC, using the trigonometry, we have

[tex]\frac{AC}{AB}=sin45^{\circ}[/tex]

Substituting the given value, we have

⇒[tex]\frac{AC}{4}=sin45^{\circ}[/tex]

⇒[tex]AC=4{\times}\frac{1}{\sqrt{2}}[/tex]

⇒[tex]AC=2\sqrt{2}[/tex]

Now, from ΔACD, we have

[tex]\frac{AC}{AD}=sin30^{\circ}[/tex]

⇒[tex]\frac{2\sqrt{2}}{AD}=\frac{1}{2}[/tex]

⇒[tex]AD=4\sqrt{2}[/tex]

Therefore, the length of AD will be [tex]4\sqrt{2}[/tex]

thus, option C is correct.

Mitch's salary increases by $10,000 but he has to repay $2,000 for his loan. Therefore, he ends up with an extra $8,000 per year.

Mitch receives a 25% increase on his previous pay of $40,000 which equates to an additional $10,000 for the year (25% of $40,000 is $10,000), giving him a new salary of $50,000.

However, Mitch must pay 4% of his new salary towards his Study Assist loan. 4% of $50,000 equals $2,000. So he must repay $2,000 for his loan.

Therefore, the extra pay that Mitch actually keeps after paying his loan is $10,000 (rise in salary) minus $2,000 (loan repayment) which is $8,000 for the year. He ends up with $8,000 extra compared to his initial salary.

https://brainly.com/question/32197511

#SPJ12