2x - 3 greater than equal to 5
PLEASE EXPLAIN IT ;)

The result of the given expression 12 5/6x - 14x + 1/6x  is -x

Given the expression

12 5/6x - 14x + 1/6x

Convert the mixed fractions into improper fractions as shown:

[tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Collect the like terms;

[tex]= \frac{77}{6} x+\frac{1}{6}x - 14x\\= \frac{77x+x}{6} - 14x\\= \frac{78x}{6} - 14x\\= 13x - 14x\\= -x[/tex]

Hence the result of the given expression is -x

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The simplified form of the expression is -x .

Given, expression [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex] .

Expression:  [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex]

Firstly solve the mixed fraction.

[tex]12\frac{5}{6} x\\= \frac{77}{6}x[/tex]

Rewriting the expression :

= [tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Solve the terms with common denominator.

= [tex]\frac{77+1}{6} x[/tex]

= [tex]13x[/tex]

Solve the like terms,

[tex]= 13x - 14x\\\\=- x[/tex]

Hence the simplified form of expression is -x .

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Yo sup??

Equation of the given line is

y=12 - 0.5x

on the y axis the x coordinate will be , therefore at x=0 we get

y=12 - 0.5*0

y=12

Therefore the coordinates of the y intercept are (0,12).

Hope this helps.

Final answer:

The y-intercept for the equation y = 12 - 0.5x is found by setting x to 0, resulting in y = 12, giving us the coordinates of the y-intercept as (0, 12).

Explanation:

The equation of a straight line is given by y = mx + b, where m represents the slope of the line, and b is the y-intercept. In your case, the equation is y = 12 - 0.5x. To find the coordinates of the intercept on the y-axis, we set x to 0 and solve for y. This gives us the y-intercept directly from the equation without needing to graph it.

For the equation y = 12 - 0.5x, when x = 0:

y = 12 - 0.5(0)

y = 12 - 0

y = 12

Therefore, the coordinates of the intercept on the y-axis are (0, 12).

The value of expression when n = 3 is 22

Solution:

Given expression is:

[tex]\frac{6(n^2 + 2)}{n}[/tex]

We have to find the value of expression when n = 3

Substitute n = 3 in given expression

[tex]\rightarrow \frac{6(3^2 + 2)}{3}\\\\Simplify\ the\ above\ expression\\\\\rightarrow \frac{6(9+2)}{3}\\\\Solve\ the\ terms\ inside\ the\ bracket\\\\\rightarrow \frac{6(11)}{3}\\\\Divide\ 6\ by\ 3 \\\\\rightarrow 2 \times 11 = 22[/tex]

Thus the value of expression when n = 3 is 22

Answer:

22

Step-by-step explanation:

area = sum of parallel sides . height/2

= (5.9 + 16.3) 4.6/2

= 22.2 . 2.3

= 51.06 m²

so the answer is A

Answer:

[tex]f(x) = (840)\times (1.05)^{x}[/tex] where f(x) is the bonus every year and x is in number of years

Step-by-step explanation:

The function that represents the situation where $840 annual bonus increases by 5% each year is given by

[tex]f(x) = (840)\times (1.05)^{x}[/tex] where f(x) is the bonus every year and x is in number of years

Final answer:

The function representing an $840 annual bonus that increases by 5% each year is f(x) = 840(1 + 0.05)ˣ

Explanation:

To write a function that represents the situation where an $840 annual bonus increases by 5% each year, we can use an exponential growth model.

The general form of an exponential growth function is f(x) = a(1 + r)ˣ, where a is the initial amount, r is the growth rate, and x is the number of time periods.

In this case, the initial bonus a is $840, the growth rate r is 5% or 0.05, and x represents the number of years. Thus, the function can be written as:

f(x) = 840(1 + 0.05)ˣ

Answer:

y = 38°

Step-by-step explanation:

If Angle x and angle y are complementary, then x + y = 90°

Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.

Solving the latter equation for x, we get x = 52°.

Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding

y = 38°

Answer:

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for the measures of angles x and y.}[/tex]

[tex]\textsf{First, x is supplementary to an angle that equals 128}^{\circ}.[/tex]

[tex]\Large\underline{\textsf{What are Supplementary Angles?}}[/tex]

[tex]\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+128^{\circ}=180^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 128 from both sides for x:}}[/tex]

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\Large\underline{\textsf{What are Complementary Angles?}}[/tex]

[tex]\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+y=90^{\circ}.}[/tex]

[tex]\textsf{Because we know x, we can solve for y.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{52^{\circ}+y=90^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 52 from both sides for y:}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\bf{What\ is\ greater: \dfrac{3}{10}, \dfrac{1}{2},\&\dfrac{2}{5}?}[/tex]

[tex]\bf{Well, let's\ turn\ our\ fractions\ into\ decimals\downarrow}[/tex]

[tex]\bullet\ \bf{\dfrac{3}{10}=0.30(also\ known\ as\ 0.3)}\\\\\bullet \ \bf{\dfrac{1}{2}=0.50(also\ known\ as\ 0.5)}\\\\\bullet \ \bf{\dfrac{2}{5}=0.40(also\ known\ as\ 0.4)}[/tex]

[tex]\bf{The\ fractions\ in\ percentages\downarrow}[/tex]

[tex]\bullet \ \mathsf{\dfrac{3}{10}=30\%}\\\\\bullet \ \mathsf{\dfrac{1}{2}=50\%}\\\\\bullet \ \mathsf{\dfrac{2}{5}=40\%}[/tex]

[tex]\text{Now that we have that out the way. Let's solve for your answer!}[/tex]

[tex]\bf{\dfrac{1}{2}}\rightarrow\dfrac{2}{5}\rightarrow\dfrac{3}{10}}}} \leftarrow( that's\ for\ GREATEST\ to\ LEAST)[/tex]

[tex]\boxed{{\bf{Answer: \dfrac{1}{2}\ would\ be\ your\ GREATEST\ or \ BIGGEST\ one}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Following the slope of the line at x= 0 the line is at y =1 , at x=, it is at Y = 1.5, so the slope is 1/2

The y intercept is where the line crosses the y a is at x =0 which is 1

The equation would be y = 1/2x+ 1

Answer:

y = 1/2x+ 1

Step-by-step explanation:

Answer:

Slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Step-by-step explanation:

The slope of the line can be determined by simplifying the given equation to its standard form.

In the standard form, y =  mx + c, m represents the slope of the line.

We are given: [tex]$ y - 2 = - \frac{2}{3}(x + 1) $[/tex]

[tex]$ \implies y = -\frac{2}{3}x - \frac{2}{3} + 2 $[/tex]

[tex]$ \implies y = - \frac{2}{3}x + \frac{(-2 + 6)}{3} $[/tex]

[tex]$ \implies y = -\frac{2}{3}x + \frac{4}{3} $[/tex]

Comparing it with the standard equation, we can see that the slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Hence, the answer.

Answer:

Step by-step explanation:

Speed v = 12km/h = 12/60km/min

Time t = 75min =

Distance d = ?

V = d/t

12/60 = d/75

Cross multiply

60d = 75 × 12

60d = 900

d = 900/60

d = 15km

Answer:

[tex]Give\ Two\ expressions\ are\ equivalent.[/tex]

Step-by-step explanation:

[tex]First\ expression=7^2+4x\\\\At\ x=2,\ value\ of\ first\ expression=7^2+4\times 2=49+8=57\\\\Second\ expression=4x+(7\times 7)\\\\Second\ expression=4x+7^2\ \ \ \ \ \ \ \ \ \ \ as\ m\times m=m^2\\\\Second\ expression=7^2+4x\ \ \ \ \ \ \ \ using\ commutative\ property\ of\ addition\\\\At\ x=2,\ value\ of\ second\ expression=7^2+4\times 2=49+8=57\\\\Hence\ these\ two\ expressions\ are\ equivalent.[/tex]

63 divided by 9 is 7, so -7+7 is 0

Hope this helped

Answer:

0

Step-by-step explanation:

using PEMDAS

63/9 = 7

-7 + 7 = 0

Answer:

This is Equivalence system of equations. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2

Answer:D

Step-by-step explanation:

Multiply the cost of the house by 0.18.

f(x) = 2([tex]2^{x}[/tex])

Step-by-step explanation:

Step 1 :

Given

When  x =0, f(x) = 2

x =1, f(x) = 4

x =2, f(x) = 8

x =3, f(x) = 16

Step 2 :

Substituting for x in the function f(x) = 2([tex]2^{x}[/tex]) we get,

When  x =0, f(x) = 2

x =1, f(x) = 4

x =2, f(x) = 8

x =3, f(x) = 16

This matches the given sequence and this shows that the function represents the given sequence .

Final answer:

The function rule for the given sequence 2, 4, 8, 16, ... is [tex]f(x) = 2^x[/tex], representing the sequence's exponential growth pattern where each term is double the previous term.

Explanation:

The given sequence is 2, 4, 8, 16, ..., which is a geometric sequence where each term is multiplied by 2 to get the next term. This pattern corresponds to an exponential function where the base is 2 and the exponent is the position of the term, which can also be thought of as the function's input, x. Therefore, the function that represents this sequence is f(x) = 2x.

The other function choices given, such as f(x) = 2x + 2 or f(x) = 2, do not correctly represent the pattern observed in the sequence. The correct function rule for the given sequence is f(x) = 2x which fits the pattern where when x is substituted for each term's position (starting from 0), the function provides the corresponding term of the sequence.

Answer:

$36.94

Step-by-step explanation:

Okay, so. This is what we do. There is two magazines and they cost 9.95 each multiply 9.95 times 2

9.95 x 2 = 19.90

Okay, then he buys a book for 14.95 we add 19.9. and 14.95

19.90 + 14.95 = 34.85

Then we have a sales tax of 6% we would multiply 34.85 time 6%

34.85 x 6% = 2.09

Then we would add. 34.85 + 2.09

34.85 + 2.09 = 36.94

Therefore your answer is $36.94

Hope this helps!!!

The answer is $36.94. You add up the total purchases, multiply them by .06, then add that number to you total purchases.

Answer:

Therefore the area of the quadrilateral =35 cm²

Step-by-step explanation:

Given, the length of one of diagonal of quadrilateral is 10 cm and perpendicular drawn from the opposite vertices to this diagonal are the length of 2.8 cm and 4.2 cm.

A diagonal divided a quadrilateral into two triangle.

Therefore the area of the quadrilateral

= sum of the area of the triangles

[tex]=(\frac{1}{2}\times 10\times 2.8+ \frac{1}{2}\times 10\times 4.2)[/tex]cm²      [ area of a triangle[tex]= \frac{1}{2}\times base\times height[/tex]]

=35 cm²

Answer:

  $2.40

Step-by-step explanation:

You have ...

  finance charge = 1.2% × unpaid balance

     = 0.012 × $200 . . . . . fill in the value of unpaid balance

  finance charge = $2.40

Answer:

A (5x + 3)(5x – 3)

B (7x + 4)(7x + 4)

E (x – 9)(x – 9)  

F (–3x – 6)(–3x + 6)

in other words, A,B,E, and F on edge-nuity. just completed with 100%

Step-by-step explanation:

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

tan(θ) (cot(θ)^2 + 1)/(tan(θ)^2 + 1) = cot(θ)

Multiply both sides by tan(θ)^2 + 1:

tan(θ) (cot(θ)^2 + 1) = ^?cot(θ) (tan(θ)^2 + 1)

(cot(θ)^2 + 1) tan(θ) = tan(θ) + cot(θ)^2 tan(θ):

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) (tan(θ)^2 + 1)

cot(θ) (tan(θ)^2 + 1) = cot(θ) + cot(θ) tan(θ)^2:

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) + cot(θ) tan(θ)^2

Write cotangent as cosine/sine and tangent as sine/cosine:

sin(θ)/cos(θ) + sin(θ)/cos(θ) (cos(θ)/sin(θ))^2 = ^?cos(θ)/sin(θ) + cos(θ)/sin(θ) (sin(θ)/cos(θ))^2

(sin(θ)/cos(θ)) + (cos(θ)/sin(θ))^2 (sin(θ)/cos(θ)) = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2

(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2 = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?cos(θ)/sin(θ) + sin(θ)/cos(θ)

The left hand side and right hand side are identical:

Answer: (identity has been verified)

By using the Pythagorean trigonometric identities and substituting the expressions of tan θ, sec θ, and csc θ, we can simplify the given expression to prove that tan θ (1 + cot2 θ) / (1 + tan2 θ) equals cot θ.

To prove that tan θ ( 1 + cot2 θ ) / ( 1 + tan2 θ ) = cot θ, we can use trigonometric identities. Recall the Pythagorean identity which states that cot2 θ + 1 = csc2 θ and tan2 θ + 1 = sec2 θ. Using these identities, we can rewrite the expression on the left side of the equation:

tan θ ( 1 + cot2 θ ) / ( 1 + tan2 θ ) = tan θ * csc2 θ / sec2 θ

Since sec θ = 1/cos θ and csc θ = 1/sin θ, and remembering that tan θ = sin θ / cos θ, we substitute these into the expression:

tan θ * csc2 θ / sec2 θ = (sin θ / cos θ) * (1/sin2 θ) / (1/cos2 θ)

With simplification, the sin2 θ in the numerator and denominator cancel out, as do the cos2 θ terms, leaving us with:

cos θ / sin θ = cot θ

Thus, the original expression simplifies to cot θ.

Answer:

The quotient is 345.5

Step-by-step explanation:

Check image

Final answer:

To find the quotient of 1,382 divided by 4, divide each place value separately. The quotient is 343 with a remainder of 2.

Explanation:

To find the quotient of 1,382 divided by 4, we divide the thousands, hundreds, tens, and ones place separately. Starting from the leftmost digit, we divide 1,382 by 4.

4 divided by 1 is 0 with a remainder of 4. Bring down the next digit 3. So, we have 43. Next, divide 43 by 4. 4 divided by 43 is 10 with a remainder of 3. Bring down the next digit 8. So, we have 38. Finally, divide 38 by 4. 4 divided by 38 is 9 with a remainder of 2.

Therefore, the quotient of 1,382 divided by 4 is 343 remainder 2.

Answer: [tex]m=-21[/tex]

Step-by-step explanation:

In order to solve the exercise, you need to remember the following properties:

1. Addition property of equality:

If [tex]a=b[/tex], then [tex]a+c=b+c[/tex]

2. Subtraction property of equality:

If [tex]a=b[/tex], then [tex]a-c=b-c[/tex]

3. Divison property of equality:

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

4. Multiplication property of equality:

If [tex]a=b[/tex], then [tex]a*c=b*c[/tex]

Then, given the following equation:

[tex]9+\frac{m}{3}=2[/tex]

You need to followw these steps in order solve for "m":

- Apply the Subtraction property of equality subtracting 9 from both sides of the equation:

[tex]9+\frac{m}{3}-9=2-9\\\\\frac{m}{3}=-7[/tex]

- Apply the Multiplication property of equality multiplying both sides of the equation by 3. Then, you get:

[tex](3)(\frac{m}{3})=(-7)(3)\\\\m=-21[/tex]

Final answer:

The volume of a pyramid with a height of 215 units and a square base of 339 units on each side is calculated using the formula V = (1/3)Bh, resulting in a volume of 1,304,688.67 cubic units.

Explanation:

To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square with each side being 339 units, then the area of the base (B) can be calculated as 339×339 square units. Given the height (h) of the pyramid is 215 units, the volume can then be calculated.

First, calculate the area of the base:
B = 339×339 = 114921 square units.

Then, use the volume formula by plugging in B and h:
V = (1/3)×114921×215 = 1,304,688.67 cubic units.

Therefore, the volume of the pyramid is 1,304,688.67 cubic units.

Answer:

  4 and 5

Step-by-step explanation:

  20 is greater than 4² = 16, and less than 5² = 25. So, the square root of 20 is between 4 and 5.

___

Your calculator will tell you that √20 ≈ 4.472, so is between 4 and 5.

Answer:

Proof in the explanation

Step-by-step explanation:

Trigonometric Equalities

Those are expressions involving trigonometric functions which must be proven, generally working on only one side of the equality

For this particular equality, we'll use the following equation

[tex]\displaystyle cos(x-y)=cos\ x\ cos\ y+sin\ x\ sin\ y[/tex]

The equality we want to prove is  

[tex]\displaystyle arccos\ \sqrt{\frac{2}{3}}-arccos\left(\frac{1+\sqrt{6}}{2\sqrt{3}}\right)=\frac{\pi}{6}[/tex]  

Let's set the following variables:

[tex]\displaystyle x=arccos\ \sqrt{\frac{2}{3}},\ y=arccos(\frac{1+\sqrt{6}}{2\sqrt{3}})[/tex]

And modify the first variable:

[tex]\displaystyle x=arccos\ \frac{\sqrt{6}}{3}}=>\ cos\ x= \frac{\sqrt{6}}{3}}[/tex]

Now with the second variable

[tex]\displaystyle y=arccos\ \frac{1+\sqrt{6}}{2\sqrt{3}}=>cos\ y=\frac{1+\sqrt{6}}{2\sqrt{3}}=\frac{\sqrt{3}+3\sqrt{2}}{6}[/tex]

Knowing that

[tex]sin^2x+cos^2x=1[/tex]

We compute the other two trigonometric functions of X and Y

[tex]\displaystyle sin \ x=\sqrt{1-cos^2\ x}=\sqrt{1-(\frac{\sqrt{6}}{3})^2}=\sqrt{1-\frac{6}{9}}=\frac{\sqrt{3}}{3}[/tex]

[tex]\displaystyle sin\ y=\sqrt{1-cos^2y}=\sqrt{1-\frac{(\sqrt{3}+3\sqrt{2})^2}{36}}}[/tex]

[tex]\displaystyle sin\ y=\sqrt{\frac{36-(3+6\sqrt{6}+18)}{36}}=\sqrt{\frac{15-6\sqrt{6}}{36}}[/tex]

Computing

[tex]15-6\sqrt{6}=(3-\sqrt{6})^2[/tex]

Then

[tex]\displaystyle sin\ y=\frac{3-\sqrt{6}}{6}[/tex]

Now we replace all in the first equality:

[tex]\displaystyle cos(x-y)=\frac{\sqrt{6}}{3}.\frac{\sqrt{3}+3\sqrt{2}}{6}+\frac{\sqrt{3}}{3}.\frac{3-\sqrt{6}}{6}[/tex]

[tex]\displaystyle cos(x-y)=\frac{3\sqrt{2}+6\sqrt{3}}{18}+\frac{3\sqrt{3}-3\sqrt{2}}{18}[/tex]

[tex]\displaystyle cos(x-y)=\frac{9\sqrt{3}}{18}=\frac{\sqrt{3}}{2}=cos\ \pi/6[/tex]

Thus, proven  

Answer:

5 + 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Multiply top and bottom by sqrt(3) + sqrt(2)

Top = (sqrt (3) + sqrt(2)) * (sqrt(3) + sqrt(2))

Top = 3 + sqrt(6) + sqrt(6) + 2

Top = 5 + 2sqrt(6)

Bottom = (sqrt (3) - sqrt(2)) * (sqrt(3) + sqrt(2))

Bottom = (3 - sqrt(6) + sqrt(6) - 2)

Bottom = 1

So, the answer is 5 + 2[tex]\sqrt{6\\}[/tex]

Answer: 5+2√6

Step-by-step explanation: attachment

Answer:

y=-3/4x+3

Step-by-step explanation:

3x+4y=12

4y=12-3x

4y=-3x+12

y=-3/4x+12/4

y=-3/4x+3

The area of flying disk is 452.16 square centimeters

Step-by-step explanation:

The disc is in circular shape so we will use the formulas for circle in this question.

Given

Circumference = C = 75.36 centimeters

We have to find the area of the disc for which we have to find the radius first.

Let r be the radius

Then

Circumference is given by:

[tex]C=2\pi r[/tex]

putting the values

[tex]75.36 = 2*3.14*r\\75.36 = 6.28r[/tex]

Dividing both sides by 6.28

[tex]\frac{6.28r}{6.28} = \frac{75.36}{6.28}\\r = 12\ cm[/tex]

The area of circle is given by:

[tex]A = \pi r^2[/tex]

Putting the values

[tex]A = 3.14 * (12)^2\\A = 3.14*144\\A =452.16\ cm^2[/tex]

Hence,

The area of flying disk is 452.16 square centimeters

Keywords: Circle, area

Learn more about circle at:

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Question:

In the right triangle shown, ∠B=60° and BC = 2√3

How long is AB?

Answer exactly, using a radical if needed.

The image of the triangle is attached below:

Answer:

The length of AB is [tex]4\sqrt{3}[/tex]

Explanation:

It is given that ∠B = 60° and BC = [tex]2\sqrt{3}[/tex]

To determine the length of AB, we shall use the cosine formula.

Because the value of the angle and its adjacent side is given and AB is the hypotenuse, we shall substitute the value of angle and adjacent side in the formula to find the value of AB.

Thus, the formula for [tex]\cos \theta[/tex] is given by

[tex]\cos \theta=\frac{a d j}{h y p}[/tex]

Where [tex]\theta=60[/tex] and [tex]adj= 2\sqrt{3}[/tex] and [tex]hyp=x[/tex]

Substituting these values in the formula, we get,

[tex]\cos 60=\frac{2 \sqrt{3}}{x}[/tex]

Interchanging, we get,

[tex]x=\frac{2 \sqrt{3}}{\cos 60}[/tex]

The value of [tex]cos 60 =\frac{1}{2}[/tex]

Substituting, we get,

[tex]x=\frac{2 \sqrt{3}}{\frac{1}{2} }[/tex]

[tex]x=4\sqrt{3}[/tex]

Thus, the value of x is [tex]4\sqrt{3}[/tex]

Hence, the length of the hypotenuse AB is [tex]4\sqrt{3}[/tex]

Answer:

  1/16

Step-by-step explanation:

Area is the product of linear dimensions.

Suppose the area of the triangle is the product of two dimensions p and q*:

  A = pq

Then the smaller triangle will have an area that is ...

  A = (1/4p)(1/4q) = (1/4)²pq = (1/16)pq . . . . . . 1/16 of the original area

__

If each of the linear dimensions of the triangle is multiplied by 1/4, the area will be multiplied by (1/4)² = 1/16.

_____

* No doubt, you have learned the area formula for a triangle is ...

  A = (1/2)bh

In the above, we might have p=1/2b and q=h. Or, there could be some other relationship between triangle dimensions and p and q.