What is the solution set of √
x + 7 − 1 = x?

Answer:x=23

Step-by-step explanation:

x+1+7x-5=180

8x-4=180

8x=184

x=184/8

x=23

Answer:

To show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4, we need to show that f(a x - 4) = 0 for all values of x.

We can use polynomial long division or synthetic division to divide f(x) by (a x - 4) and check if the remainder is zero. Here, we will use synthetic division:

4/a | 2   -5   -11   -4

   |     8a  12a  4a-16

   +------------------

   2   8a-5  a-11  4a-20

The last term in the bottom row of the table is the remainder, which is 4a - 20. We can see that this remainder is equal to zero if a = 5.

Therefore, if we substitute x = (5/ax - 4) into the function f(x), we get:

f(a x - 4) = 2(5/ax - 4)^3 - 5(5/ax - 4)^2 - 11(5/ax - 4) - 4

Simplifying this expression, we get:

f(a x - 4) = 0

This means that a x - 4 is indeed a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4 when a = 5.

Answer:The leading term in a polynomial is the term with the highest degree.

Step-by-step explanation:

Step-by-step explanation:

y = 3 x^2 - 4 x - 1

leading coefficient is 3  and its sign is ' + '   or positive

The blanks of the number pyramid puzzle can be filled with numbers calculated below.

A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.

Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:

m = -4 * 0.5 = -2

k = 0.5 * 1/8 = 1/16

x * (-1/8) = 8

x = 8/(-1/8)

x = -64  

y = x * 1/8

y = -64 * 1/8

y = -8

j = m * k

j =  -2 * 1/16 = -1/8

p = -48 * m

p = -48 * (-2) = 96

n = y * 8

n = -8 * 8 = -64

t = p * j

t = 96 * (-1/8) = -12

w = -1/2 * n

w = -1/2 * (-64) = 32

c = t * 1/16

c = -12 * 1/16 = -3/4

u = 1/16 * w

u = 1/16 * 32 = 2

d = c * u

d = -3/4 * 2 = -3/2

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The probability based on the information will be;

a. Likely, probability is 25%

b. Likely, probability is 25%

c. Impossible, probability is 0%

d. Unlikely, probability is 33.3%

The probability of rolling a 5 on a 6 sided die is 1/6 or approximately 16.67%.

The probability of not rolling a 5 on a 6 sided die is 5/6 or approximately 83.33%. This can also be:

= 100 - 16.67

= 83.33%

The probability of spinning an even number on a spinner with numbers 1-8 is 4/8 or 1/2 or 50%.

The probability that a white horse is George is 1/5 or 20%.

An event that has probability of 0% is something that is impossible, such as rolling a 7 on a 6-sided die. An event that has a probability of 100% is something that is certain, such as flipping a coin and getting either heads or tails.

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Answer:

Step-by-step explanation:

ex  2

        4444

2

 4444

Yes, that's correct I even tried to show you.

The 2 is the bags of candy

4 pieces of candy per bag

equals to 8 in total

b equal for the top of the bookcase to have the correct area= 5 cm2

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

L × b = 300

b = 300 / L

b = 300 / 60 = 5

Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.

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The values of x that could make the triangle into different types of triangles are:

For a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side.

Right Triangle:

A triangle is a right triangle if it satisfies the Pythagorean theorem: a² + b² = c², where c is the longest side (hypotenuse).

6² + 8² = x²

36 + 64 = x²

100 = x²

x = 10

Acute Triangle:

A triangle is acute if the sum of the squares of the two shorter sides is greater than the square of the longest side. Since we already know that the right triangle has x = 10, we can choose a value for x that is less than 10 to form an acute triangle.

Let's take x = 9:

6² + 8² > 9²

36 + 64 > 81

100 > 81

Obtuse Triangle:

A triangle is obtuse if the sum of the squares of the two shorter sides is less than the square of the longest side. We can choose a value for x that is greater than 10 to form an obtuse triangle.

Let's take x = 11:

6² + 8² < 11²

36 + 64 < 121

100 < 121

The possible values of x for each triangle type are:

Right Triangle: x = 10

Acute Triangle: x = 9

Obtuse Triangle: x = 11

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The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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Answer:

2 real zeros at x = - 2 , x = 1

Step-by-step explanation:

f(x) = x² + x - 2

to find the zeros let f(x) = 0 , that is

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 1 = 0 ⇒ x = - 1

there are 2 real zeros , x = - 2 and x = 1

Answer:

Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

The correct statement is: Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

Length, which is typically expressed in units like meters, feet, or inches, is a measurement of an object's size or the separation between two locations. It alludes to the measurement of an object's longest dimension or the separation between two ends. The term "length" can also be used to describe the extent of a line or the linear separation between two locations, such as the length of a triangle's side, a road, or a length of rope. In geometry, length is a crucial mathematical notion that is used to gauge an object's size, shape, and location.

given

The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. Here are the facts:

60° sine + (BC/AB)

Using sin 60°, whose value is 3/2, as an example:

√3/2 = (BC/AB)

Multiplying AB by both sides:

BC = AB * √3/2

The hypotenuse's length is determined by adding the squares of the lengths of the other two edges. Here are the facts:

We have the following by substituting the earlier-obtained formulas for AC and BC:

Adding 3 to both sides:

4AB2 + 9AB2 = 12AB2

AB = 3x

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

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Answer:

B.......................

Answer:

  -15

Step-by-step explanation:

You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].

The average rate of change is defined as ...

  AROC(g) = (g(b) -g(a))/(b -a)

We can evaluate this directly, or we can simplify it a bit first.

 AROC = ((3b² +3) -(3a² +3))/(b -a)

  = (3b² -3a²)/(b -a)

  = 3(b -a)(b +a)/(b -a)

  = 3(b +a)

The AROC on the interval [a, b] = [-9, 4] is then ...

  AROC = 3(4 +(-9)) = 3(-5)

  AROC = -15

__

Additional comment

In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.

The demand equation for commodity A is Xa = (4/10)Xb.

A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.

In the given question,

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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The demand equation for commodity A is Xa = (4/10)Xb.

What is demand equation?

A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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Answer:

The cone takes up one-third of the volume of the cylinder. (the cylinder is 3x bigger than the cone)

Step-by-step explanation:

Answer:

B. is right.

Step-by-step explanation:

Volume of cone = volume of cylinder/3

Therefore the volume of the cylinder is 3 x that of cone

Answer: what shape?

Step-by-step explanation:

More info please

Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

The length of the rectangle is 10.5 units.

What is perimeter?

Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.

The perimeter of a rectangle is given by the formula:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:

34 = 2l + 2(6.5)

Simplifying, we get:

34 = 2l + 13

Subtracting 13 from both sides, we get:

21 = 2l

Dividing both sides by 2, we get:

l = 10.5

So the equation to determine the length of the rectangle is:

2l + 2w = P

Substituting the known values, we get:

2l + 2(6.5) = 34

Simplifying and solving for l, we get:

2l + 13 = 34

2l = 21

l = 10.5

Therefore, the length of the rectangle is 10.5 units.

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Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.

Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.

Answer:2.04

Step-by-step explanation:

Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).