Show how the model in problem 7 would change if
pl>lql. Draw the model, labeling p, q, and p + q.
Then write an addition equation using integers that
could represent p, q, and p + q.

Answer:37

Step-by-step explanation:

<UYW=<UYV+<VYW=36+2x=110

2x=110-36=74

x=74/2=37

The foci of the hyperbola is  (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].

The two fixed points that are located inside each curve of a hyperbola are known as its foci, and they are important for the formal description of the curve.

Here the given equation of the hyperbola is [tex]4y^2-x^2=16[/tex] .

Now writing the given equation into standard form then,

=> [tex]4y^2-x^2=16[/tex]

=> [tex]-x^2+4y^2=16\\[/tex]

=> [tex]\frac{-x^2}{4}+\frac{4y^2}{4}=\frac{16}{4}[/tex]

=> [tex]\frac{-x^2}{4}+y^2=4[/tex]

=> [tex]\frac{-x^2}{4\times4}+\frac{y^2}{4}=1[/tex]

=> [tex]\frac{-x^2}{16}+\frac{y^2}{4}=1[/tex]

Here we know that [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex] then a=2 and b=4 , (h , k)=(0,0)

Then c=[tex]\sqrt{a^2+b^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}[/tex].

Then foci is (0,0+c) and (0,0-c) then,

=> (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex]

Hence the foci of the hyperbola is  (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].

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Hence, the simplified expression for the area of a rectangle in standard form is 8x³ + 2x² - 12x - 3.

Having four sides, four corners, & four right angles (90°), a rectangle is an enclosed 2-D shape. A rectangle has four equal and parallel opposite sides. Having length and width as its two dimensions, a rectangle is a two-dimensional form. The length and breadth of a rectangle are determined by its longer and shorter sides, respectively.

The equation A = length x width determines the area of a rectangle. When we replace the provided length and width expressions, we obtain:

A = (4x + 1) (2x² - 3)

By combining like terms and the distribution property of multiplication, we may make this expression simpler:

A = 8x³ - 12x + 2x² - 3

A = 8x³ + 2x² - 12x - 3

So, the area of the rectangle as a simplified expression in standard form is 8x³ + 2x² - 12x - 3.

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Answer: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that is only divisible by 1 and itself.

Step-by-step explanation:

For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on, are prime numbers because they can only be divided by 1 and themselves without any remainder.

However, 4 is not a prime number because it can be divided by 1, 2, and 4, and 6 is not a prime number because it can be divided by 1, 2, 3, and 6.

Answer:

A prime number is a number that can be multiplied by one and itself~
eg- 2,3,5,7,11
Let me know if this helps

, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Interval  [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval  [tex](-4, -3).[/tex]

Interval  [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval  [tex](-3, -2).[/tex]

Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval  [tex](-€2, -1).[/tex]

Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]

Interval  [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Therefore, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

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Answer:  d.  25 square inches

Step-by-step explanation:

The singer sold 512 music downloads.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

Let's use the following variables:

CD = the number of CD singles sold

DL = the number of music downloads sold

From the problem, we know the following:

CD + DL = total number of singles sold

CD = 456

The profit from selling CD singles is 35p = £0.35 per CD single

The profit from selling music downloads is 17p = £0.17 per music download

The total profit is £246.64

Using the information above, we can set up two equations based on the profits earned from selling CD singles and music downloads:

0.35 * CD = profit from CD sales

0.17 * DL = profit from download sales

And we know that the sum of these two profits equals the total profit:

0.35 * CD + 0.17 * DL = 246.64

Substituting CD = 456, we get:

0.35 * 456 + 0.17 * DL = 246.64

Simplifying this equation, we get:

159.6 + 0.17 * DL = 246.64

0.17 * DL = 87.04

DL = 512

Therefore, the singer sold 512 music downloads.

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The opposite of the oppsite of 28,or (-28), is equivalent to the option (c) 28

The opposite of a number is the number with the opposite sign.

For example, the opposite of 28 is -28, and the opposite of -28 is 28.

So, the opposite of the opposite of 28, or (-28), is the opposite of -28, which is 28.

This means that the answer is (c) 28.

To explain it further, think of the number line. 28 is a positive number, so its opposite is a negative number, which is -28.

Now, the opposite of -28 is a positive number, which is 28. So, the opposite of the opposite of 28 is 28.

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Answer:

asdfasdfasdf

Step-by-step explanation:

asdf

According to the solving this algebra approximately 1.43 quarts of pure antifreeze to the initial 5 quarts of 10% antifreeze solution to obtain a 30% antifreeze solution.

what is algebra?

Mathematical operations are applied to abstract symbols rather than concrete numbers in the field of algebra, which also includes other formal manipulations. The area of mathematics known as geometry is concerned with the qualities of the space that objects are in as well as the shape of the objects themselves.

According to the given information:

Let Q be the number of quarts of pure antifreeze to be added.

Let 0.10(5) be the amount of antifreeze in the initial 5 quarts of the 10% antifreeze solution, which is 0.5 quarts.

To obtain a 30% antifreeze solution, the amount of antifreeze in the final solution should be 0.3(5+Q) quarts.

Since we are only adding pure antifreeze, the amount of antifreeze in the final solution will be the sum of the antifreeze in the initial solution and the antifreeze we add:

0.5 + Q = 0.3(5+Q)

Now we can solve for Q:

0.5 + Q = 1.5 + 0.3Q

0.7Q = 1

Q = 1/0.7

Q ≈ 1.43

Therefore, we need to add approximately 1.43 quarts of pure antifreeze to the initial 5 quarts of 10% antifreeze solution to obtain a 30% antifreeze solution.

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Answer:(-3, -7)

Step-by-step explanation: (7-3,-) look the middle is (3,-6)        and instead on   7 is 6 bec in 7-

Answer:

To find the number of bracelets Alia can make, we need to divide the total length of the silver chain she has by the length of each bracelet.

Total length of silver chain = 36 1/4 inches

Length of each bracelet = 7 1/4 inches

To divide fractions, we need to invert the second fraction and multiply:

(36 1/4) ÷ (7 1/4) = (145/4) ÷ (29/4) = (145/4) x (4/29) = 5

Therefore, Alia can make 5 bracelets with the given amount of silver chain.

Answer:

5 bracelets

Step-by-step explanation:

Given Information:

Clearly, the number of bracelets possible (say x) multiplied by the amount of chain required for 1 bracelet will result in the total chain length (36 1/4).

Now, we can divide 7 1/4 on both sides to find value of x (total bracelets).

Therefore, Alia can make 5 bracelets.

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Answer:32+ 1.21

Step-by-step explanation:

if you really want an awser you would take all the nubers and sfhgkjfqipjghwpkrejvhbwptijgbqkejnvwpigtnjuvrepiufgnjwrekjbhartio

Yes, it is true that Triangle FGH is a right triangle.

We check whether the Pythagorean theorem holds true for these sides to determine if this triangle is a right triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the right triangle's legs.

a² + b² = c²

If this is a right triangle, the hypotenuse will be the longest side, and the other two sides will be the legs. We have these when we incorporate the Pythagorean theorem.

6²+(√45)² = 9²

36+45 = 81

which implies that  right triangle because the assertion is true.

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Answer:The expression −4x−2y−3 can be written as −4/x^2y^3.

Multiplying both numerator and denominator by -1, we get 4/x^2y^3.

Hence, option A, −4x^2y^3, is equivalent to −4x−2y−3.

Step-by-step explanation:

Answer:  y = -2 - 2 * (x - 1).

Step-by-step explanation: The pattern is a linear function with a slope of -2 and an intercept of -2. The slope of a line is the change in y over the change in x. In this case, the change in y is -2 and the change in x is 1. Therefore, the slope is -2/1 = -2. The intercept is where the line crosses the y-axis, which is at y = -2 when x = 1. Therefore, the equation of the line is y = mx + b where m is the slope and b is the intercept. Substituting m = -2 and b = -2 gives us y = -2 - 2 * (x - 1).

Hope this helps, and have a great day!

The solution set of the equation x^2+3x-4=6 is {-5, 2}.

The answer of the given question are as follows :-

Para encontrar el conjunto de soluciones de la ecuación x^2+3x-4=6, debemos primero llevarla a su forma canónica. Restando 6 de ambos lados, obtenemos:

x^2+3x-10=0

Luego, podemos resolver esta ecuación utilizando la fórmula cuadrática:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

donde a = 1, b = 3, y c = -10.

Reemplazando estos valores, obtenemos:

x = (-3 ± sqrt(3^2 - 4(1)(-10))) / 2(1)

x = (-3 ± sqrt(49)) / 2

x = (-3 ± 7) / 2

x1 = 2

x2 = -5

Por lo tanto, el conjunto de soluciones de la ecuación x^2+3x-4=6 es {-5, 2}.

Translation in english :-

To find the solution set of the equation x^2+3x-4=6, we must first bring it to its standard form. Subtracting 6 from both sides, we get:

x^2+3x-10=0

Then, we can solve this equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 3, and c = -10.

Substituting these values, we get:

x = (-3 ± sqrt(3^2 - 4(1)(-10))) / 2(1)

x = (-3 ± sqrt(49)) / 2

x = (-3 ± 7) / 2

x1 = 2

x2 = -5

Therefore, the solution set of the equation x^2+3x-4=6 is {-5, 2}.

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Answer:

the possible answers are 80 and 140

Step-by-step explanation:

since one angle has a measure of 20 in isosceles triangle let this be vertex angle and other two as base angles then

in isosceles triangle base angles must be equal to each other so

x+x+20 = 180

2x+20 = 180

2x = 160

x=80

so the base angles are equal to 80

now if you suppose 20 as base angle then other base angle should also be 20 since it is an isosceles triangle and the vertex angle can be calculated as

20+20 + x = 180

x = 140

Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.

Here we have a linear equation that relates the wind temperature with the wind's velocity.

The linear equation is:

y = -0.36*x + 12.6

Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:

y = -0.36*19 + 12.6

y = -6.84 + 12.6

y = 5.76

So your answer is correct.

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The statement that is true, given that ΔCBX ≅ ΔSML, would be G. XC ≅ ML.

Given that ΔCBX ≅ ΔSML, we can use the properties of congruent triangles to determine which statement is true. The correspondence between the vertices of the two triangles is as follows:

C ↔ S

B ↔ M

X ↔ L

XC ≅ ML is true because XC corresponds to the side connecting vertices X and C in ΔCBX, and ML corresponds to the side connecting vertices M and L in ΔSML. Since the triangles are congruent, their corresponding sides are congruent.

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Answer:

396 in²

Step-by-step explanation:

To answer this question we need to use pythagorean theorem (a² + b² = c²)

In our case, a would be 14 and b would be 17

Now we have to multiply this by 18

Which rounded would be 396

Hope this helps, have a lovely day! :)

Para preparar un pastel, Anita tenía un paquete de harina de 1 1/3 kg:  0.83 kg

Primero, debemos convertir 1 1/3 kg a una fracción común. 1 1/3 kg es igual a 4/3 kg o 1.33 kg. Luego, podemos simplificar 3/6 a 1/2.
Ahora podemos restar 1/2 de 1.33 kg para encontrar la cantidad de harina que sobró.
1.33 kg - 1/2 kg = 1.33 kg - 0.5 kg = 0.83 kg
Entonces, Anita le sobró aproximadamente 0.83 kg de harina después de preparar su pastel.
Es importante recordar que la medición y las cantidades de los ingredientes son cruciales al preparar cualquier receta de cocina. Es importante seguir las instrucciones cuidadosamente para obtener resultados exitosos en la cocina.

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Answer: To solve this problem, we can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal, r is the interest rate as a decimal, and t is the time in years.

We are given that the interest rate is 1.95% = 0.0195, the time is 30 years, and the final amount in the account is $800. Let P be the principal we are trying to find.

First, we can use the formula to find the total interest earned over the 30-year period:

I = P * r * t

I = P * 0.0195 * 30

I = 0.585P

Next, we can use the fact that the final amount in the account is the sum of the principal and the interest:

800 = P + 0.585P

800 = 1.585P

P = 504.71

Therefore, the principal was $504.71 and the interest earned over the 30-year period was:

I = 0.585P

I = 0.585 * 504.71

I = 294.29

So the interest earned was $294.29.

Step-by-step explanation:

Answer:

the total mass of the 250 objects is 1.3 kilograms.

Step-by-step explanation:

To find the total mass of the 250 objects, we need to multiply the mass of each object by the number of objects:

Total mass = mass per object x number of objects

The mass per object is given as 5.2x10^-3 kg, and the number of objects is 250. So, we can calculate the total mass as follows:

Total mass = 5.2x10^-3 kg x 250

Total mass = 1.3 kg

The volume of the cone is  2119. 5 cubic centimeters

The formula used for calculating the volume of a cone is expressed as;

V = πr² h/3

Given that the parameters are namely;

Now, substitute the values, we have;

Volume , V = 3.14 × 15² × 9/3

Divide the values, we have;

Volume = 3.14 × 225 × 3

Multiply the values, we get;

Volume, V = 2119. 5 cubic centimeters

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