The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?

3x – 4 and 2x + 15
3x + 4 and 2x – 15
2(x – 2) and 3(x + 5)
2(x + 2) and 3(x – 5)

Final answer:

To find the area between two curves, calculate the definite integral of the difference between the two functions over the interval of interest.

Explanation:

To find the area between two curves, you need to calculate the definite integral of the difference between the two functions over the interval of interest. Let's say the two curves are f(x) and g(x), and you want to find the area between them from x = a to x = b. You can write the integral as follows:

Area = ∫(f(x) - g(x)) dx from a to b

Then you can evaluate this integral using integration techniques, such as u-substitution or integration by parts, to find the area between the two curves.

The solution of the equation [tex]13+\frac{w}{7}=-18[/tex] is [tex]\boxed{w=-217}[/tex].

Further explanation:

Given:

The equation is [tex]13+\frac{w}{7}=-18[/tex].

Calculation:

Method (1)

The given equation is as follows:

[tex]\boxed{13+\dfrac{w}{7}=-18}[/tex]  

The above equation is a linear equation that has one degree.

The equation with one variable can be solved by moving all terms in to the one side and simplify the equation for the value of variable.

Subtract [tex]13[/tex] on both sides in the equation (1) to obtain the value of [tex]w[/tex] as follows,

[tex]\begin{aligned}13+\dfrac{w}{7}-13&=-18-13\\13-13+\dfrac{w}{7}&=-31\\ \dfrac{w}{7}&=-31\end{aligned}[/tex]  

Now, multiply [tex]7[/tex] on both sides of the above equation as,

[tex]\begin{aligned}7\times \dfrac{w}{7}&=-31\times7\\w&=-217\end{aligned}[/tex]

Therefore, the value of [tex]w[/tex] is [tex]-217[/tex].

Method (2)

To obtain the solution of the equation (1), take least common multiple of the denominator of the left hand side of the equation as,

[tex]\begin{aligned}13+\dfrac{w}{7}&=-18\\ \dfrac{(13\times7)+w}{7}&=-18\\ \dfrac{91+w}{7}&=-18\end{aligned}[/tex]  

Now, multiply by [tex]7[/tex] on both sides of the above equation to obtain the value of [tex]w[/tex] as follows,

[tex]\begin{aligned}7\times\left(\dfrac{91+w}{7}\right)&=7\times(-18)\\91+w&=-126\end{aligned}[/tex]

Subtract [tex]91[/tex] on both sides of the above equation as follows,

[tex]\begin{aligned}91+w-91&=-126-91\\w&=-217\end{aligned}[/tex]

Therefore, the value of [tex]w[/tex] is [tex]-217[/tex].

Thus,  the solution of the equation [tex]13+\dfrac{w}{7}=-18[/tex] is [tex]\boxed{w=-217}[/tex].

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations

Keywords: Equation, 13+(w/7)=-18, variables, subtract, linear equations, one degree, multiply least common multiple, linear equation, mathematics.

To compare the selling prices in store A and store B for the tool described:

Let's denote the list price of the tool as x dollars.

In Store A:

- Original selling price = List price - $50

- Current selling price = 90% of the original selling price

In Store B:

- Original selling price = 90% of the list price

- Current selling price = Original selling price - $50

Now, we can calculate the selling prices for both stores and compare:

For Store A:

Original selling price in Store A = x - 50

Current selling price in Store A = 0.9(x - 50)

For Store B:

Original selling price in Store B = 0.9x

Current selling price in Store B = 0.9x - 50

To determine which quantity is greater, we need to compare the expressions for the current selling prices in both stores. We will simplify the expressions to make the comparison easier.

Store A:

0.9(x - 50) = 0.9x - 45

Store B:

0.9x - 50

Comparing the simplified expressions, we see that:

0.9x - 45 is greater than 0.9x - 50

Therefore, Store A has a greater current selling price for the tool compared to Store B.

So, the correct answer is:

A) Quality A is greater.

Answer:

[tex]2 \frac{2}{5}[/tex]

Step-by-step explanation:

Try dividing 12 and 5. What a surprise it doesn't work. 5×2=10. 12÷5=10 r2. r2=[tex]\frac{2}{5}[/tex]. 2+[tex]\frac{2}{5}[/tex]=[tex]2 \frac{2}{5}[/tex].

Without additional details about the kite CDFG, such as angle measures or side lengths, it is impossible to provide an exact measure for Angle D.

The question asks to find the measure of angle D in a kite named CDFG. Without additional information such as angle measures or side lengths, it is impossible to determine the exact measure of Angle D. However, we know in a kite, there are two pairs of adjacent sides that are equal, and one pair of opposite angles (the angles between the unequal sides) are equal. Typically, the diagonals of a kite are perpendicular, and one of the diagonals bisects the other. This information still does not provide enough context to solve for the measure of angle D without more specific details about the lengths of the sides or measures of other angles.

Answer:

Option (a) is correct.

a(x)b(x) = (ab)(x)

To produce a quadratic equation the two linear equation must be multiply.

Step-by-step explanation:

Given :  a(x) and b(x) are linear functions with one variable.

We have to choose from the given option the correct expression that will produce a quadratic equation.

Quadratic equation is an equation which is in the form of [tex]ax^2+bx+c[/tex] where [tex]a\neq0[/tex]

Since given a(x) and b(x)  are linear equation in one variables so to get square term we must multiply the two linear equations.

Let a(x)=3x+1

and b(x)= 8x+1

then when we multiply we get,

[tex]a(x)\times b(x)=(3x+1)\times (8x+1)=24x^2+11x+1[/tex]

Thus, To produce a quadratic equation the two linear equation must be multiply.

Thus, a(x)b(x) = (ab)(x) is correct.

Option (a) is correct.

Answer:

315 cm<2 399.9 cm<2

Step-by-step explanation:

Answer:

L = 315 cm2 ; S = 399.9 cm2

Step-by-step explanation:

Lucky guess on my quiz!

Answer: B. intersecting chords

Step-by-step explanation:

When two chords intersect then inscribed angles are formed.

We know that the inscribed angle theorem tells that the measure of an inscribed angle is half the measure of its intercepted arc.

The measure of an angle formed by intersecting chords is half the sum of the measures of the intercepted arcs.

Answer:

[tex]13/28[/tex]

Step-by-step explanation:

Let

x-----> the shaded area

we know that

[tex]x+\frac{1}{4}+\frac{2}{7}=1[/tex]

Because the complete circle represent the [tex]100\%[/tex]

and

[tex]100\%=100/100=1[/tex]

solve for x

Multiply by [tex]28[/tex] both sides

[tex]28x+7+8=28[/tex]

[tex]28x=28-15[/tex]

[tex]28x=13[/tex]

Divide by [tex]28[/tex] both sides

[tex]x=13/28[/tex] ----> fraction irreducible

Answer:

C

Step-by-step explanation:

The selling price for 10 hats, calculated by applying the cost function f(x) to find the cost and then the selling price function g(x), is $8.

The selling price of 10 hats can be found by first calculating the cost of materials to make those hats using the function f(x) = 0.5x + 1, and then applying the g(f(x)) function to find the selling price, where g(x) = x + 2.

First, we calculate the cost for making 10 hats:
f(10) = 0.5  imes 10 + 1 = 5 + 1 = 6.

Now, we use the selling price function g to calculate the selling price for 10 hats:
g(f(10)) = g(6) = 6 + 2 = 8.

Therefore, the selling price for 10 hats is $8.

Final answer:

The cosine, cosecant, secant, and cotangent functions are all trigonometric functions. They are continuous everywhere except where the denominator is zero.

Explanation:

The cosine, cosecant, secant, and cotangent functions are all trigonometric functions. These functions are defined for all real numbers except when the denominator becomes zero. Therefore, they are continuous everywhere except where the denominator is zero.

For example, the cosine function, denoted as cos(x), is continuous for all real numbers. It has a periodic nature and oscillates between -1 and 1.

Similarly, the cosecant function, denoted as csc(x), is continuous everywhere except at the points where sin(x) is equal to zero. The secant function, denoted as sec(x), is continuous everywhere except at the points where cos(x) is equal to zero. The cotangent function, denoted as cot(x), is continuous everywhere except at the points where tan(x) is equal to zero.

1/30 in decimal form can be rounded to 0.033.

To convert the fraction 1/30 into decimal form, you simply divide the numerator (1) by the denominator (30). This can be done using a calculator or by manual division.

1 ÷ 30 = 0.03333... (repeating)

So, 1/30 as a decimal is approximately 0.033 when rounded to three decimal places.

Here are the steps to understand it better: