Which Expression is Equivalent to (f+g)(4)?

A) F(4) + G(4)
B) F(X) + G(4)
C) F(4 + G(4))
D) 4(F(X) + G(X))

Answer:

transitive property

Step-by-step explanation:

Generally proofs flow naturally from one step to the next.  Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.

From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]

For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]

What changed between line 8 and 9?  The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.

So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?

Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].

The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).

Recall that the transitive property states:

[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

There are three parts,

1. the first part needs a=b

2. the second part needs b=c

3. the third part produces a=c

Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.

Statement 8 is like the second part, and statement 9 is like the third part.

Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:

Original transitive property:  [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

Updated transitive property:  [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]

In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true.  The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.

From calculations, we can say that the given tiles will not fit together perfectly.

If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.

Expression for the measure of the interior angle of a polygon,

Interior angle of a polygon = [(n - 2) * 180]/n

Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°

Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°

Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°

To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°

Sum of all interior angles = 108° + 120° + 135° = 363°

Therefore, given tiles will not fit together perfectly.

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Answer:

298.97 minutes

Step-by-step explanation:

2^x = 1 000 000      where 'x' is the number of 15 minute periods

x = 19.931      15 minute periods = 298.97 minutes

The equation will be a linear equation from (2, 5) to (4, 10) will be y = 2.5x.

Mathematics is replete with functions, which are necessary for the construction of intricate connections.

A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.

Use the information in the table to find the constant of proportionality and write the equation.

The equation will be a linear equation from (2, 5) to (4, 10) will be

(y – 5) = [(10 – 5) / (4 – 2)] (x – 2)

 y – 5 = 2.5x – 5

       y = 2.5x

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Answer:

2.5 and y=2.5x

Step-by-step explanation: i got that question on an edguenity assignment

The inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies

Let's suppose b is the price of each box of supplies.

Total cost for a 25 number of boxes = $25b

25b ≤ 375

Thus, the inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

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The measure of x will be 18.81 units.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

The given information are;

Perpendicular = 4

Base = x

Then, Tan ∅ = Perpendicular /Base

Tan 12 = 4/x

x = 4 /0.212

x = 18.818

Hence, the measure of x will be 18.81 units.

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Answer:

Point Form:

(9,12)

Equation Form:

x = 9

y = 12

Step-by-step explanation:

Answer:

[tex]\fbox{x = 9, y = 12}[/tex]

Step-by-step explanation:

[tex]\textsf {Let's solve by substitution.}[/tex]

[tex]\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}[/tex]

[tex]\textsf {Substitute for x in the first equation of the system.}[/tex]

[tex]\implies \mathsf {-5(2y-15)+4y=3}[/tex]

[tex]\implies \mathsf {-10y+75+4y=3}[/tex]

[tex]\implies \mathsf {-6y=-72}[/tex]

[tex]\implies \textbf {y = 12}[/tex]

[tex]\implies \mathsf {x = 2(12) - 15}[/tex]

[tex]\implies \mathbf {x = 9}[/tex]

[tex]\textsf {The solution is : x = 9, y = 12}[/tex]

Its the first one

--------------------

Answer:

  $24 = $0.40(60)

Step-by-step explanation:

Match the input value and its location in the equation.

__

  $24 = $0.40(60)

_____

Additional comment

When input is liters and output is dollars, the constant of proportionality must have units of "dollars per liter." The dollar sign of these units is not shown in the left panel, but is shown on the answer choices. If you understand units conversion, this should not be a mystery. (The mystery is why the curriculum materials are inconsistent.)

Answer:

DF

Step-by-step explanation:

Paint a picture in your head reflecting the triangle. Just hold A and flip it so A = E , D = B

Answer:

The exponent is 2, so the degree is 2

The scale factor for triangle ABC to A'B'C' is 2

The complete question is in the attached image

From the attached image, we have the following corresponding sides

AC = 4 cm

A'C' = 8 cm

The scale factor is then calculated as:

Scale factor = A'C'/AC

This gives

Scale factor = 8cm/4cm

Evaluate the quotient

Scale factor = 2

Hence, the scale factor for triangle ABC to A'B'C' is 2

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The nature of a graph, which has an even degree and a positive leading coefficient will be up left, up right position

The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.

Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.

The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.

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Answer:

508.02

HOPE THIS HELPS

Todo <3

Step-by-step explanation:

Construct OD and BD. Then, in quadrilateral ABOD, angles ODA and OBA are right angles and thus angle DOB is 130 degrees (since angles in a quadrilateral add to 360 degrees).

So, this means arc DB also measures 130 degrees. Hence, by the inscribed angle theorem, angle BCD is 65 degrees.

Answer:

(2,3) ; (-2.11)

Step-by-step explanation:

Answer:

(2, 3); (-2, 11)

Step-by-step explanation:

f(x) = x² - 2x + 3

f(x) = -2x + 7

f(x) = f(x)

x² - 2x + 3 = -2x + 7

x² = 4

x = ±2

x = 2

f(2) = -2(2) + 7 = -4 + 7 = 3

x = -2

f(-2) = -2(-2) + 7 = 4 + 7 = 11

Answer: (2, 3); (-2, 11)

Answer:

-21

Step-by-step explanation:

The solution to the given quadratic expression is x = -1 and x = 5

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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Answer:

Step-by-step explanation:

Exponent law:

    [tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]

    [tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]

       First convert radical form to exponent form and then apply exponent law.

 [tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]

[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]

                      [tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]

Answer:

b

Step-by-step explanation:

when u plug in -6 u get the equation equal to 0 which means x+6 is a factor of that function.

Answer:

option B, -(4x - 3)(x - 2)

Step-by-step explanation:

-4x^2 + 11x - 6

4x * x = 4x^2

x * -3x = -3x

-4x * -2 = -8x

-3 * -2 = -6

Answer:

B

Step-by-step explanation:

Used elimination method.

first plugged in (0,0)which remove A,D

than saw the line is not solid so chose B

Answer:

In the circle, the measure of the arc AC is 21°.

Step-by-step explanation:

Concept: We can use the Inscribed Angle theorem to get the measure of AC.

Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.

Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

3x - 1.5 = 0.5(3x + 9)

6x - 3 = 3x + 9

3x = 12

x = 4

Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,

intercepted arc AC is 21°.

Hence the intercepted arc AC is 21°.

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Answer:

[tex]y=[1]cos([\frac{2\pi }{3}]x)[/tex]

Step-by-step explanation:

Looking at the graph, we can see the domain to be from (0 , 2π).

Now we have to find one period that corresponds to cos(x).

The half-period of cos(x) for this graph appears to be pi/3 and adding another pi/3 gets us 2pi/3 to be our cosine period.

b = 2pi/3

a is the same range as cos(x). Range: (0,0)

y = [a] * cos ([b]*x)

y = [1] * cos([2pi/3]x)

Using proportions, it is found that:

a) 5 people are needed.

b) Yes.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Item a:

Each person works for 32 hours, and 150 hours are needed, hence the number of people needed is given by:

150/32 = 4.6875.

However, an integer number is needed, hence 5 people are needed.

Item b:

With 30 hours, the number of people needed is given by:

150/30 = 5.

Which remains the same.

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Answer:

-282

Step-by-step explanation:

Any altitude below sea level would have a negative sign in front of it.

Answer:

Please see attachment.

The first one is a quadrilateral that is not a parallelogram.

The second one is a triangle with a right angle.

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

300-6x

Step-by-step explanation:

Trust me

Answer:

6x^2 + 17x + 5

Step-by-step explanation:

(2x + 5)(3x + 1)

= 6x^2 + 2x + 15x + 5

= 6x^2 + 17x + 5

The expression (2x+5)(3x+1) is a product of two binomials. To expand this product, we multiply each term in the first binomial by each term in the second binomial, using the distributive property of multiplication.

When we multiply 2x by 3x, we get 6x^2.

Then we multiply 2x by 1, which gives us 2x.

Next, we multiply 5 by 3x, which gives us 15x.

Finally, we multiply 5 by 1, which gives us 5.

Putting these terms together gives us the expanded form of the expression:

(2x+5)(3x+1) = 6x^2 + 2x + 15x + 5

Simplifying, we can add the 2x and 15x terms to get 17x, giving us the final simplified expression:

(2x+5)(3x+1) = 6x^2 + 17x + 5.

Less workers = more hours

OR the answer might be worded as

More workers = less hours