Factor 9y 2 - 12y + 4.

Answer:

20

Step-by-step explanation:

:D

The value of the x is 20.

We have given that,

[tex]81^5 = 3^x[/tex]

We have to determine the value of x.

3^4 = 81

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b, and the exponent or power n, and pronounced as b raised to the power of n.

exponent 4 x 5 = 20

so, 3^20 = 81^5

Therefore the value of the x is 20.

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You would need  1/12 cups of water in order to make only 1/6 of the recipe

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by addition, subtraction, dividing, and multiplying built-in functions.

When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe,

If a recipe requires 2/4 cup of water, then a fraction of the recipe requires 1/6 cup of water.

So the fraction of the recipe requires 1/6 cup of water as

⇒ 1/6×2/4

⇒  2/24

⇒  1/12

Hence, you would need  1/12 cups of water in order to make only 1/6 of the recipe.

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The scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm

To find the scale factor between two similar rectangular prisms, we can compare their volumes. The scale factor is the ratio of the cube root of the volumes.

Let's denote the volume of the first rectangular prism as V1 and the volume of the second rectangular prism as V2.

[tex]V1 = 40 mm^3\\V2 = 135 mm^3[/tex]

The scale factor (SF) can be calculated as follows:

[tex]SF = (V2)^{(1/3)} / (V1)^{(1/3)[/tex]

Plugging in the given values:

[tex]SF = (135)^{(1/3)} / (40)^{(1/3)[/tex]

To simplify the calculation, we can rewrite the values as prime factorization:

[tex]135 = 3^3 * 5\\40 = 2^3 * 5[/tex]

Now, let's calculate the cube roots:

[tex]SF = (3^3 * 5)^{(1/3) }/ (2^3 * 5)^{(1/3)}[/tex]

Using the property of exponents [tex](a^{(m/n) }= (a^m}^{(1/n)})[/tex]:

[tex]SF = (3^{(3/3)} * 5^{(1/3)}) / (2^{(3/3)} * 5^{(1/3)})[/tex]

Simplifying the fractions:

[tex]SF = 3 * 5^{(1/3)} / 2 * 5^{(1/3)[/tex]

The [tex]5^{(1/3)}[/tex] terms cancel out:

SF = 3/2

Therefore, the scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm.

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Answer:  The correct option is (B) 3.

Step-by-step explanation:  We are given to find the length of the leg s in the triangle shown in the figure.

From the figure, we note that

the given triangle is a right-angled one, where

length of the hypotenuse, h = √18 units,

length of one leg, p = 3 units

and

length of the other leg, s = ?.

From Pythagoras theorem, we have

[tex]h^2=p^2+s^2\\\\\Rightarrow (\sqrt{18})^2=3^2+s^2\\\\\Rightarrow 18=9+s^2\\\\\Rightarrow s^2=18-9\\\\\Rightarrow s^2=9\\\\\Rightarrow s=3.[/tex]

Thus, the length of the leg s is 3 units.

Option (B) is CORRECT.

Answer:

Option A) EF = 15 units.  

Step-by-step explanation:

We are given the following information in the question:

ΔABC ≅ ΔDEF

AB = 12, BC = 15, and AC = 17

If two triangles are congruent then they have the following properties:

AB = DE

BC = EF

AC = DF

[tex]\angle A = \angle D \\\angle B = \angle E \\\angle C = \angle F[/tex]

Hence, by congruency:

BC = EF

EF = 15 units.

Thus, option A is the correct answer.

Answer: 5/9 will be the fraction of the space will be for storage and baking.

Step-by-step explanation:

Since area of bakery will be used as our storefront, where customers come to visit= 100/225

Thus, the total area of bakery = 225  

And, the area will be used our storefront, where customers come to visit= 100

So, the remaining area which is used for storage and baking = 225 - 100 =125

So the part of area which is used for storage and baking= the remaining area which is used for storage and baking/ total area

=125/225= 5/9

which is the simplest form.

Answer:

3*4*7

Step-by-step explanation:

There is total of 84 combinations

In modified boxplots, a data value is a potential outlier if it is outside the range of Q3 + (1.5)(IQR) or Q1 - (1.5)(IQR). The IQR is the spread of the middle 50% of the data, calculated as Q3 - Q1.

In modified​ boxplots, a data value is​ a potential outlier if it is above Q3 + (1.5)(IQR) or below Q1 - (1.5)(IQR). The interquartile range (IQR) is crucial in this determination, representing the spread of the middle 50 percent of the data. It is found by subtracting the first quartile (Q1) from the third quartile (Q3). For example, if Q1 is 2 and Q3 is 9, the IQR is 7. Any data value greater than 9 + (1.5)(7) or less than 2 - (1.5)(7) would be considered a potential outlier.

Constructing a box plot involves identifying these five key values: minimum value, first quartile, median, third quartile, and maximum value. The box plot visually represents the data's spread, with whiskers extending to the most extreme values within the acceptable range, and separate marks for potential outliers.

To find the value of 'x' that makes the function r(x) = 19, we need to solve the equation -5x - 1 = 19 for 'x'. After doing so, we obtain x = -4.

This question involves finding the value of 'x' in a mathematical function provided, in order to get a specific output. The function provided is r(x) = -5x - 1 and the question states that the output r(x) should be 19. We can setup the equation -5x - 1 = 19 and solve for 'x'.

Adding 1 to both sides of the equation, we obtain -5x = 20. Dividing both sides by -5 gives x = -4. So, the value of 'x' that makes the function r(x) = 19 is x = -4.

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Final answer:

The second and third terms of the arithmetic sequence are -12 and -17, found by adding the common difference of 5 to each succeeding term in the sequence.

Explanation:

The question is asking to find the second and third terms of an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between the consecutive terms is constant. This constant difference is known as the common difference. In the given arithmetic sequence (-7, _, _, -22, -27), we can find the common difference by subtracting two successive terms. For this sequence, the difference between -27 and -22 is -27 - (-22) = -27 + 22 = -5. This implies that to find the previous terms, we should add 5 to each term going backwards.

Starting with -22 and adding 5, we get -17 for the third term. Similarly, adding 5 again for the second term, we get -12. Therefore, the second and third terms of the arithmetic sequence are -12 and -17, respectively.

To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, use the perimeter and area formulas for a rectangle.

To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, we can use the perimeter formula for a rectangle. Let L and W represent the length and width of each pen. The total fencing length will be 2L + 3W, and since it is given as 630 feet, we have 2L + 3W = 630. We can rearrange this equation to solve for one variable in terms of the other, substitute it into the area formula for a rectangle, and then find the maximum value using the first derivative test.

Using the equation 2L + 3W = 630, we can solve for L in terms of W: L = (630 - 3W) / 2. Substituting this into the area formula A = LW, we get A = (630 - 3W)W / 2. Taking the first derivative of A with respect to W, we have dA/dW = 630/2 - 3W/2. Setting this equal to zero, we find W = 105. Substituting this back into the equation 2L + 3W = 630, we can solve for L: 2L + 3(105) = 630, and simplifying gives L = 210/2 = 105.

Therefore, the dimensions of each pen that produce the greatest enclosed area are 105 feet by 105 feet.

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Answer:

The statement is false.

Step-by-step explanation:

To begin an indirect proof, you assume the converse of what you intend to prove is true. This is false.

Rather the correct answer is that to begin an indirect proof, you assume the inverse of what you intend to prove is true.

The converse can be either true or false, depending on what the original statement is, so assuming the converse is pointless.

The distance covered by the vehicle in 6 hours will be 600 km.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

If you drive at 100km/hr for 6 hours.

Then the distance covered by the vehicle in 6 hours will be given as,

100 = Distance / 6

Distance = 100 x 6

Distance = 600 km

The distance covered by the vehicle in 6 hours will be 600 km.

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The correct answer is 24.

[tex]\large\text{Hey there!}[/tex]

[tex]\large\text{Step 1: You have to \underline{\bf{CROSS MULTIPLY}}}[/tex]

[tex]\mathsf{\dfrac{14}{x}=\dfrac{56}{16}}\\\\\mathsf{14\times16=56\times x}\\\\\mathsf{14(16)= \ \bf{\underline{224}}}\\\\\mathsf{56(x)=\underline{\bf{56x}}}[/tex]

[tex]\huge\text{We get: \bf{\underline{224 = 56x}}}[/tex]

[tex]\large\text{Step 2: }\large\text{\bf{\underline{FLIP}}}\large\text{ the new equation around}[/tex]

[tex]\huge\text{\bf{\underline{56x = 224}}}[/tex]

[tex]\large\text{Step 3: \bf{\underline{DIVIDE}}}\large\text{ both of your sides by 56}[/tex]

[tex]\mathsf{\dfrac{56x}{56}=\dfrac{224}{56}}\\\\\mathsf{Cancel\ out: \dfrac{56x}{56}\ because\ that\ gives\ us\ 1}\\\\\mathsf{Keep: \dfrac{224}{56}\ because\ it\ gives you\ the\ value\ of\ x }\\\\\mathsf{\dfrac{224}{56}=4}\\\\\mathsf{x=4}[/tex]

[tex]\boxed{\large\text{So, the reason why x = 4 for this equation is because } \mathsf{\dfrac{14}{4}}\ \& \ \dfrac{56}{16}\ \large\text{ are equal to each}}\\\boxed{\large\text{other. }}[/tex]

[tex]\mathsf{\dfrac{14}{4} = 3.5}[/tex]

[tex]\mathsf{\dfrac{56}{16} = 3.5}[/tex]

[tex]\huge\text{\bf{3.5 = 3.5}} \ \checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dag\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Final answer:

The question involves using the Pythagorean theorem to find the missing side 'X' in a right triangle with sides 'X', 4, and 7. 'X' is calculated by rearranging the theorem to X² = c² - b² and plugging in the known values. The equation simplifies to X = √33.

Explanation:

The student is asking for an equation to solve for the missing side of a right triangle, where the sides are given as 'X', 4, and 7. The Pythagorean theorem, which states that a² + b² = c², is the appropriate tool for solving this problem. Since the triangle is right-angled, we assume 'X' is one leg, 4 is the other leg, and 7 is the hypotenuse as it is the longest side.

To find 'X', we rearrange the theorem to solve for the unknown leg (X) as follows: X² = c² - b². Plugging the values into the equation gives us X² = 7² - 4² which simplifies to X² = 49 - 16, hence X² = 33. Consequently, X can be found by taking the square root of 33, which we rewrite as X = √33.

Answer: [tex]3x+4y=16[/tex]

Step-by-step explanation:

Given equation of a line = [tex]3x + 4y = 15[/tex]

i.e. [tex]4y = 15-3x[/tex]

i.e. [tex]y=\dfrac{15}{4}-\dfrac{3}{4}x[/tex]

i.e. [tex]y=-\dfrac{3}{4}x+\dfrac{15}{4}[/tex]  (1)

It is in intercept form [tex]y=mx+c[/tex]   (2) , where m is slope.

By comparing (1) and (2) the slope of line : [tex]m=-\dfrac{3}{4}[/tex]

Also the parallel lines have same slope .

The equation of a line passing through a point (a,b) and having a slope of 'm' is given by :-

[tex](y-b)= m(x-a)[/tex]

Then the equation of the line that passes through (8,-2) and having slope of [tex]m=-\dfrac{3}{4}[/tex] is given by :-

[tex](y-(-2))=- \dfrac{3}{4}(x-8)[/tex]

[tex]4(y+2)=-3(x-8)[/tex]

[tex]4y+8=-3x+24[/tex]

[tex]3x+4y=24-8[/tex]

[tex]3x+4y=16[/tex]

Hence , the  equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is [tex]3x + 4y = 15[/tex] is [tex]3x+4y=16[/tex]

.