Is the product of 2/5 and 5 greater or less than 2/5? Is it greater or less than 5? explain your reasoning.

Answer:

 Option (b) is correct.

[tex](f-g)(x)=-x^2+3x+7[/tex]

Step-by-step explanation:

Given : Functions [tex]f(x) = 3x +1[/tex] and[tex]g(x) = x^2-6[/tex]

We have to choose the correct option from the given options that represents (f-g)(x)

Consider the given functions

[tex]f(x) = 3x +1[/tex] and[tex]g(x) = x^2-6[/tex]

then , (f - g)(x) = f(x) - g(x)

Substitute, we have,

[tex]f(x) - g(x)=3x+1-(x^2-6)[/tex]

Applying plus - minus rule[tex]-(-a)=a[/tex], we have,

[tex]f(x)-g(x)=3x+1-x^2+6[/tex]

Simplify and write in standard form, we have,

[tex]f(x)-g(x)=-x^2+3x+7[/tex]

Thus, The[tex](f-g)(x)=-x^2+3x+7[/tex]

Ms. Franco hourly wage is approximately $33.42

Data

To solve this problem, we have to trace back to know her gross pay and then divide it by the total number of hours worked.

Sum of all her net pay and all taxes.

[tex]709.54+87.45+38.45=835.44[/tex]

Her total gross pay is $835.44

This is the amount she earned working for each hour.

Since she worked for a total of 25 hours, let's divide her gross pay by 25

[tex]\frac{835.44}{25}=33.4176[/tex]

Ms. Franco hourly wage is approximately $33.42

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Matias and Hannah can make 8 identical centerpieces using all the flowers, with each centerpiece composed of 9 carnations, 10 lilies, and 8 rosebuds, arranged harmoniously.

Matias and Hannah can make the greatest number of identical centerpieces by finding the largest number that can divide into the quantities of all three types of flowers without remainder. They have 6 dozen carnations (72 carnations), 80 lilies, and 64 rosebuds. The highest common factor that divides into 72, 80, and 64 is 8. This means they can make 8 centerpieces, with each centerpiece containing 9 carnations, 10 lilies, and 8 rosebuds.

Describing the centerpiece based on the description in the hypothetical art reference: The centerpiece would feature a balanced and harmonious arrangement of flowers with the carnations drawing the viewer's attention at the center. Similar to the composition in Chittenden's paintings, the various flower types, such as lilies and the delicate rosebuds, would be distributed to complement each other in the arrangement, creating an aesthetically pleasing and symmetrical display for the school dance buffet tables.

Line segment AB is longer than segment CD.

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

Two line segments AB and CD have endpoints at A (-5, 11), B(3, 5), C (9, 3) and D (2, 10).

To find the distance:

The distance of two points

= √ {(x₂-x₁)² + (y₂-y₁)²}

The distance of segment AB

= √ {(3+5)² + (5-11)²}

=  √ {(8)² + (-7)²}

=  √(64 + 49)

= √(64 + 49)

= √113

= 10.63 unit.

The distance of segment CD

= √ {(2-9)² + (10-3)²}

=  √ {(-7)² + (7)²}

=  √(49 + 49)

= √98

= 9.9 unit.

Clearly, distance of AB > distance of CD

Therefore, distance of AB > distance of CD.

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The variable 'm' represent the slope.

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Given:

y= mx + b

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

So the change in y coordinate with respect to the change in x coordinate can be written as,

m = Δy/Δx

where, m is the slope

The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,

y = mx + b

where,

m is the slope, such that m = tan θ = Δy/Δx

θ is the angle made by the line with the positive x-axis

Δy is the net change in y-axis

Δx is the net change in x-axis

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Answer:

OPTION B

Step-by-step explanation:

Answer:

The correct option is A. 2 seconds

Step-by-step explanation:

The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32·t – 16·t²

Now, we need too find the time after which the fired projectile touches the ground.

So, The fired projectile when touches the ground, The height of the projectile will become 0

⇒ Find the required time t when h = 0

⇒ 0 = 32·t - 16·t²

⇒ 0 = t × (32 - 16·t)

⇒ t = 0 or 32 - 16t = 0

⇒ 16t = 32

⇒ t = 2

So, t = 0 or t = 2

t cannot be 0 because initially the projectile is in the air as it has been already fired

⇒ t = 2 seconds

Therefore, The correct option is A. 2 seconds

Answer:

[tex]m\angle D=29.05[/tex]

Step-by-step explanation:

We have been given an image of a right triangle and we are asked to find the measure of angle D.

We can see from our given triangle that the opposite side of angle D measures 25 ft and adjacent side of angle D is 45 ft.

Since we know that tangent represents the relation between the opposite and adjacent sides of a right triangle.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

Upon substituting our given values in above formula we will get,

[tex]\text{tan}\angle D=\frac{25}{45}[/tex]

[tex]\angle D=\text{tan}^{-1}(\frac{25}{45})[/tex]

[tex]\angle D=29.054604099077[/tex]

Upon rounding our answer to nearest hundredth we will get,

[tex]\angle D\approx 29.05[/tex]  

Therefore,the measure of angle D is 29.05 degrees.

Given is square root of a negative real number, i.e. [tex] \sqrt{-0.25} [/tex]

When we find square root of positive real numbers, we get Real answers.

But when we find square root of negative real numbers, we get Imaginary answers. To solve them, we can split the given negative number into product of -1 and the number itself but with positive sign. e.g. -4 = -1 x 4.

For square root of -1, we use english letter 'i' called Imaginary unit i.e. [tex] \sqrt{-1} = i [/tex]

Now we can use -0.25 = -1 x 0.25

[tex] \sqrt{-0.25} =\sqrt{-1*0.25} \\\\
\sqrt{-0.25} =\sqrt{-1}*\sqrt{0.25} \\\\
\sqrt{-0.25} =i*0.5 \\\\
\sqrt{-0.25} =0.5i [/tex]

Hence, "0.5i" is the final answer.

The square root of -0.25 is not a real number because the square root of a negative number is not defined within the set of real numbers.

The square root of a negative number is not a real number. In the case of √(-0.25), the expression is undefined within the set of real numbers because taking the square root of a negative number results in a complex number. The square root of a negative number is typically represented using the imaginary unit "i" in the complex number system. Therefore, √(-0.25) is not a real number.

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The given expression is 3y (-5y³-11y²+y-8)

We use distributive rule to distribute 3y to the terms -5y³-11y²+y-8.

The distributive rule states :To multiply a sum by a number, multiply each term of the sum.

This can be applied to multiply a monomial and polynomial.

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms.In multiplication exponents are added.

3y (-5y³-11y²+y-8) =[tex] -15y^{4} -33y^{3} +3y^{2} -24y [/tex]

Answer:

The answer was actually s = 8p! Just tried it out on the ttm website. Hope that this helps!

Portion = 8 grams of sugar

The amount of sugar you have is dependent on how many portions of cereal you have (each one is 8), so this would be Sugar = 8 grams multiplied by how many portions you have. :)

The larger is 14 the smaller is 8

Let the larger number be L and the smaller be S
So we know that

1) L+S=22
And
2)4L=7S
From equation 1) we get L=22-S

Substitute this into equation 2) to get 4(22-S)=7S
88-4S=7S
88=11S
S=8. The smaller number is 8

As they total 22 the larger number is 14.
Check: 4x14=7x8. Yes

Solution 2:

Let x= larger number
And let y= smaller. umber

Now we are told that:
4x=7y--------eq1
We are also told that:
x + y=22-----eq2

Substitution method looks easier.

From eq1 x=(7/4)y. Substitute this into eq2
(7 /4)y +y=22
(7/4)y+(4/4)y=22
(11/4)y=22 multiply each side by 4
11y=88
y=8

From eq2, x+8=22
x=14

Hope this helps

Final answer:

To find the two numbers where four times the larger is equal to seven times the smaller, and the sum is 22, we set up a system of equations and solve them. We find that the larger number is 14 and the smaller number is 8.

Explanation:

To solve the question "Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. What are the numbers?", we use a system of equations. First, we assign variables to the unknowns: let x be the larger number and y be the smaller number. According to the problem, we have two equations:

4x = 7y (because four times the larger number is equal to seven times the smaller)

x + y = 22 (because the sum of the numbers is 22)

Now, we can solve for one of the variables. Let's isolate y in the second equation:

y = 22 - x

Substitute this expression for y into the first equation:

4x = 7(22 - x)

Expand and solve for x:

4x = 154 - 7x

11x = 154

x = 14

Then we find y by substituting x back into the equation y = 22 - x:

y = 22 - 14

y = 8

Therefore, the larger number is 14 and the smaller number is 8.