Evaluate z(x - 1) when x = 5 and z = -4

According to fraction and ratio, second dog is 3/2 feet long.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

First dog is 5 feet long.

then,

5 feet is equal to 4/5 of the second dog's length.

multiply both sides by 5/4.

5/4 x 5 feet is the second dog's length.

The second dog is 25/4 feet long.

The second dog is 6(1/4) feet long.

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From the graph of a function over the interval [-4,4]. the following are found for each function

The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.

This would be through the points in the function. We are given  [-4,4]

-4 is the negative side while 4 is the positive. We have to write this out as

-4 ≤ x ≤ 4.

The positive part part of the function is at 4. This is because we can assume a +4 sign.

The negative part is the point -4.

Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively

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7.051 can be written as the fraction 7051/1000.

To express 7.051 as a fraction in the form of p/q, we need to identify the decimal places and convert them to the corresponding fractional parts.

Since 7.051 has three decimal places, we multiply it by 1000 to move the decimal point three places to the right, which gives us 7051.

Now, the numerator (p) of the fraction will be 7051, and the denominator (q) will be the corresponding power of 10, which is 1000.

Therefore, 7.051 can be expressed as 7051/1000.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

In this case, the GCD of 7051 and 1000 is 1, so the fraction is already in its simplest form.

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Answer:

240 sodas, 160 water, 100 juice

Step-by-step explanation:

multiply everything by 10

If you received a gift of $10,000 3 years ago and you want to spend it in 3 years with interest rate is 4%, it will be worth $12,653.19. Option b is correct.

To calculate the future value of a present sum after a specified period, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)ᴺ

In this case, the present value is $10,000, the interest rate is 4% or 0.04, and the number of periods is 6 years because you received the gift 3 years ago and want to spend it in 3 years.

Using the formula:

Future Value = \(\$10,000 * (1 + 0.04)^6\)

Future Value = \(\$10,000 * (1.04)^6\)

Future Value = $10,000 * 1.1265319

Future Value ≈ $12,653.19

Therefore, the amount will be approximately $12,653.19. Option b is correct.

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Using Pythagorean Theorem, the length of the line segment from (-3, 10) to (4, -1) is 13 units.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

Let a = vertical distance between the two points

b = horizontal distance between the two points

c = distance between the two points / length of line segment

Hence, c² = (|y₂ - y₁|)² + (|x₂ - x₁|)².

Substitute the values of x and y and solve for c.

c² = (|y₂ - y₁|)² + (|x₂ - x₁|)²

c² = (|-1 - 10|)² + (|4 - -3|)²

c² = (|-11|)² + (|7|)²

c² = 11² + 7²

c² = 121 + 49

c² = 170

c = 13.04

length of line segment ≅ 13 units

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Answer:

como proporción de dos tipos de tela es diferente.

por lo tanto, la relación entre el número de yardas cuadradas y el costo

no es proporcional entre los dos tipos de tejido

Explicación paso a paso:

Para que una relacion sea proporcional

a:b = c:d

en otra forma

a/b = c/d

______________________________________________

Proporción para el primer tipo de tejido

costo de tela/ área de tela = 31.25/5 = 6.25

Ratio para otro tipo de tejido

costo de tela/ área de tela = 71.50/11 = 6.5

como proporción de dos tipos de tela es diferente.

por lo tanto, la relación entre el número de yardas cuadradas y el costo

no es proporcional entre los dos tipos de tejido

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

4 7/12 + 5/12 = 4 12/12 which equals 5

Answer:

3 9/12 + (4 7/12 + 5/12) = 3 9/12 + 5

Step-by-step explanation:

Answer:

Given expression is \(\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}\) = 2tan²A

We have to prove this identity.

\(\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}=\frac{(\text{cosecA+1})-(\text{cosecA-1})}{(\text{cosecA-1})(\text{cosecA+1})}\)

                              = \(\frac{(\text{cosecA}-\text{cosecA})+(1+1)}{cosec^2A-1}\)

                              = \(\frac{2}{cosec^{2}A-1}\)

                              = \(\frac{2}{cot^{2}A}\) [From the identity, (cosec²A - 1) = cot²A]

                              = 2tan²A [From the identity, cotA = \(\frac{1}{\text{tan}A}\)]

Hence the given equation is proved.

∫ x(x−1) 2/ (3x2 −4x+4)dx= (2 - 2i)/(9 - 4i) * [ln|x - (2 - 2i)/3|] + (2 + 2i)/(9 + 4i) * [ln|x - (2 + 2i)/3|] + C

The given integral is given as ∫ x(x−1) 2/ (3x2 −4x+4)dx

To solve this integral by partial fraction decomposition, follow the given steps:

Step 1: Factorise the denominator of the fractionTo solve this we use the quadratic formula. Let ax2 + bx + c = 0, and x = (-b ± sqrt(b2 - 4ac))/(2a).Let the given denominator be the quadratic equation, then we have:3x2 - 4x + 4 = 0 x = [-(-4) ± sqrt((-4)2 - 4(3)(4))]/(2*3) = (2 ± 2i)/3

Therefore,3x2 - 4x + 4 = 3 (x - (2 - 2i)/3) (x - (2 + 2i)/3)

Step 2: Partial fraction decomposition

To do the partial fraction decomposition, assume that the fraction can be expressed as: x(x - 1)/(3x2 - 4x + 4) = A(x - (2 - 2i)/3) + B(x - (2 + 2i)/3) The value of the unknown constants A and B can be found by equating the given fraction to the sum of the partial fractions. The value of A and B can be calculated using the given below equation:

Therefore, we get the following equations:By solving the above equations we can get the values of A and B as follows:

Multiplying the first equation by (x - (2 + 2i)/3) and the second equation by (x - (2 - 2i)/3) and then simplify them by using the complex conjugate we get;

Substituting these values in the equation of partial fraction decomposition, we have;

Therefore, the partial fraction decomposition of the given fraction is:x(x-1)/(3x2 - 4x + 4) = (2 - 2i)/(9 - 4i) * 1/(x - (2 - 2i)/3) + (2 + 2i)/(9 + 4i) * 1/(x - (2 + 2i)/3)The integral can be written as ∫ x(x−1) 2/ (3x2 −4x+4)dx= (2 - 2i)/(9 - 4i) * ∫ 1/(x - (2 - 2i)/3) dx + (2 + 2i)/(9 + 4i) * ∫ 1/(x - (2 + 2i)/3) dx

By using u substitution, we can find the value of the integral as follows:

Substituting x - (2 - 2i)/3 = t for the first integral. Then we get the value of the first integral as:

Substituting x - (2 + 2i)/3 = u for the second integral. Then we get the value of the second integral as:

Therefore, the value of the given integral is:∫ x(x−1) 2/ (3x2 −4x+4)dx= (2 - 2i)/(9 - 4i) * [ln|x - (2 - 2i)/3|] + (2 + 2i)/(9 + 4i) * [ln|x - (2 + 2i)/3|] + C

Where C is a constant of integration.

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To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.

In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.

This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.

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The probability of choosing a car or a truck is P(Car) + P(Truck).

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The correct inequality of domain of the function shown in graph:

-5 ≤ x ≤ +3.

The entire range of independent variable values is the domain of a function.

According to this definition, it means:

The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.

Keep these things in mind when locating the domain:

From the shown graph,  a curve for the function is finite which start from the value on negative x axis and ends on the positive x axis.

The domain is the input value taken from the x axis.

Starting point : - 5

End point + 3

Domain: -5 ≤ x ≤ +3.

Thus, the correct inequality of domain of the function shown in graph:

-5 ≤ x ≤ +3.

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Index is an element's numeric position within an array. The correct answer is B.

When an array is created, each element is assigned an index or position, starting from zero for the first element and incrementing by one for each subsequent element.

The index allows for easy access to specific elements within the array, by specifying the index value as an argument when referencing or manipulating elements. The index of an element is an important concept in computer programming and is used extensively in array-based data structures and algorithms.

Therefore the correct option is b

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Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

we require 6.00 mmol of H2SO4. Given that we have 25 mL of H2SO4 solution, the molarity of the H2SO4(aq) solution is 0.24 M or 0.24 mol/L.

To determine the molarity of the H2SO4(aq) solution, we can use the balanced chemical equation and the stoichiometry of the reaction. Given that 25 mL of H2SO4 is needed to react with 15 mL of 0.20 M NaOH,

we can calculate the molarity of H2SO4 by setting up a ratio based on the stoichiometric coefficients. The molarity of the H2SO4(aq) solution is found to be 0.30 M.

From the balanced chemical equation, we can see that the stoichiometric ratio between H2SO4 and NaOH is 1:2. This means that 1 mole of H2SO4 reacts with 2 moles of NaOH. In this case, we have 15 mL of 0.20 M NaOH, which means we have 15 mL × 0.20 mol/L = 3.00 mmol of NaOH.

Since the stoichiometric ratio is 1:2, we need twice the amount of moles of H2SO4 to react with NaOH.

Therefore, we require 6.00 mmol of H2SO4. Given that we have 25 mL of H2SO4 solution, the molarity can be calculated as 6.00 mmol / (25 mL / 1000) = 240 mmol/L or 0.24 mol/L. Therefore, the molarity of the H2SO4(aq) solution is 0.24 M or 0.24 mol/L.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:66

Step-by-step explanation: t/6-3=8

The goal is to solve for t

To get t on its own we need to get rid of -3

The only way to do  that is to add 3 to both sides of the equation. In maths what we do to one side we must do to the other

t/6-3+3=8+3

t/6=11

To solve for t we need to do the opposite of divide by 6

That is to multiply both sides by 6

6*(t/6)=11 x6

t=66 note the 6 divided by 6 gives 1 instead of saying 1t we say t

Answer:

5/24 more

Step-by-step explanation:

1/3 turns into 8/24

and

1/8 turns into 3/24

so eric has read 5/24 more

Answer:

5/24

Step-by-step explanation:

1/8×3=3/24

1/3×8=8/24

8/24-3/24=5/24.

The value of the exponent (2/5)^3 is \(\frac{8}{125}\)

In the above question, it is given that

(2/5)^3

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2^3) signifies 2 x 2 x 2 = 8.

We need to solve it and then find the value of the exponent

(2/5)^3

= \(\frac{2}{5}\) x \(\frac{2}{5}\) x \(\frac{2}{5}\)

= \(\frac{2 . 2. 2}{5 . 5 . 5}\)

= \(\frac{8}{125}\)

Therefore the value of the exponent (2/5)^3 is \(\frac{8}{125}\)

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The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:

(6,-7)

Step-by-step explanation:

take b as x2,y2

then apply mid point formula

x=(x1+x2)/2

y=(y1+y2)/2

Answer:  B = (-6, 7)

Step-by-step explanation:

Given: M = (4, -1)    A = (2, 5)

\(M_x=\dfrac{A_x+B_x}{2}\qquad \qquad \qquad M_y=\dfrac{A_y+B_y}{2}\\\\\\4=\dfrac{2+B_x}{2}\qquad \qquad \qquad -1=\dfrac{5+B_y}{2}\\\\\\8 = 2+B_x\qquad \qquad \qquad\quad -2=5+B_y\\\\\\6=B_x\qquad \qquad \qquad\qquad \quad -7=B_y\)

Answer:

1 and 1/4

Step-by-step explanation:

If you multiply 1/4 five times, you will get your answer

Answer:

a) y = (x + 1)^2 - 3

b) minimum

c) (-1, -3)

Step by step:

We start with the equation:

y = x^2 + 2*x - 2

First, we want to complete the square to write the equation in the vertex form.

y = (x - h)^2 + k

Such that the vertex is (h, k)

To complete the square, we can write this as:

y = x^2 + 2*1*x - 2

Now we can add and subtract 1

y = x^2 + 2*1*x + 1 - 1 - 2

y = (x^2 + 2*1*x + 1) - 3

The thing inside the parentheses can be written as:

x^2 + 2*1*x + 1 = (x + 1)^2

Then the quadratic equation will be written as:

y = (x + 1)^2 - 3

This is the vertex form.

b) Now we want to know if the vertex is a minimum or a maximum.

Remember that the leading coefficient tells use if the graph of the function opens up or down.

If the leading coefficient is positive, the graph opens up (then the vertex is a minimum)

If the leading coefficient is negative, the graph opens down (then the vertex is a maximum)

In this case, we can write:

y = 1*(x + 1)^2 - 3

The leading coefficient is 1, positive.

Then the vertex is a minimum.

c) The coordinates of the vertex are:

Remember that in the vertex form:

y = (x - h)^2 + k

the vertex is (h, k)

Then the vertex of our equation is:

(-1, - 3)

Answer: y=5x/4 +3

Step-by-step explanation:

Answer:

\(n = 11\)

Step-by-step explanation:

We are given two arithmetic sequences:

7, 12, 17, 22... and 27, 30, 33, 36...

And we want to determine n such that the nth term of each sequence is equivalent.

We can write a direct formula for each sequence. Recall that the direct formula for an arithmetic sequence is given by:

\(\displaystyle x_n = a + d(n-1)\)

Where a is the initial term and d is the common difference.

The first sequence has an initial term of 7 and a common difference of 5. Hence:

\(\displaystyle x_n = 7 + 5(n-1)\)

The second sequence has an initial term of 27 and a common difference of 3. Hence:

\(x_n = 27 + 3(n-1)\)

Set the two equations equal to each other:

\(7 + 5 (n-1) = 27 + 3(n-1)\)

Solve for n. Distribute:

\(7 + (5n - 5) = 27 + (3n - 3)\)

Combine like terms:

\(5n + 2 = 3n + 24\)

Isolate:

\(2n = 22\)

Divide. Hence:

\(n = 11\)

In conclusion, the 11th term of the first A.P. is equivalent to the 11th term of the second.

Answer:

angle 1 and 8 - neither

Step-by-step explanation:

angle 2 and 4 - vertical pair

where r u from btw ?

Answer:

range

Step-by-step explanation:

difference between the highest and lowest points in a data set = range

The mean is the average of all the points

The median is the middle of  all the points

The mode is the point the appears the most often

"Hey diddle diddle the medians the middle you add and divide for the mean the mode is the one that you see the most and the range is the difference between"

Online song that's helped me remember the difference between median, mode, mean and range for years!

The distance between the bird (B) and plane (P) exists at 10,779 feet.

Given the figure attached,

PT = OB = 7000 ft

PB = OT = x feet

and angle of elevation (∠POT) = 30°

By applying the Tan rule in the triangle POT,

tan 33° = Opposite side/Adjacent side = PT/OT

tan 33° = 7000/x

x = 7000/tan33°

x = 10779 feet

The distance between the bird (B) and plane (P) exists at 10,779 feet.

Therefore, the correct answer is option D. 10779 feet.

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