A wise man once said,
“400 reduced by 3 times
my age is 244." How old is
the wise man?

Answer:

y = - [tex]\frac{2}{5}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (5, 2) ← 2 points on the line

m = [tex]\frac{2-4}{5-0}[/tex] = [tex]\frac{-2}{5}[/tex] = - [tex]\frac{2}{5}[/tex]

Note the line crosses the y- axis at (0, 4) ⇒ c = 4

y = - [tex]\frac{2}{5}[/tex] x + 4 ← equation of line

Answer:

y = -2/5 +4

Step-by-step explanation:

points are :

(0 , 4 ) and ( 5,2)

midpoint = (0 + 5 )/2  and ( 4 + 2 )/2

= (2.5 , 3 )

the gradient = (2 - 4 )/ ( 5 - 0)

= -2/5

now create the equation using both gradient and midpoint

Y - y1 = m (X - x1)

y-3 = -2/5 (x - 2.5)

y = -2/5 x +1 +3

y = -2/5 +4

The measure of arc GC is 90°

Solution:

Given data:

m∠CHD = 90°

Sum of the adjacent angles in a straight line = 180°

⇒ m∠GHC + m∠CHD = 180°

⇒ m∠GHC + 90° = 180°

Subtract 90° from both sides, we get

⇒ m∠GHC = 90°

The angle measure of the central angle is equal to the measure of the intercepted arc.

[tex]m\angle GHD = m (ar \ GC)[/tex]

90° = m(ar GC)

Switch the sides.

m(ar GC) = 90°

The measure of arc GC is 90°.

Answer: D. 96

Step-by-step explanation:

1/2 (82 + 110)

1/2 (192) = 96

96°

∠X = 1/2(82 + 110)

∠X = 96°

Answer:

A. 4x^2 - 9

Step-by-step explanation:

2x * 2x = 4x^2

2x * -3 = -6x

3 * 2x = 6x

-3 * 3 = -9

-6x + 6x  = 0, so we're left with 4x^2 - 9

Answer:

B. (2x − 3)(2x + 3)(4x2 + 9)

Step-by-step explanation:

Answer:

The answer is 120

Step-by-step explanation:

length X width X height

6*4*5

120

Answer:

r=11

Step-by-step explanation:

3x11=33

so therefore r=11

Answer:

y < 1.1

Step-by-step explanation:

Step 1:  Subtract 2.1 from both sides

-4.2y + 2.1 - 2.1 > -2.52 - 2.1

-4.2y > -4.62

Step 2:  Divide both sides by -4.2

-4.2y / -4.2 > -4.62 / -4.2

Since you divided by a negative, that flips the sign.

y < 1.1

Answer:  y < 1.1

Answer: Y < 1.1

Step-by-step explanation: I took the quiz, i hope this helps! :)

m(ar ABD) = 57°

Solution:

The given question have mistake. The correct question is wiiten below.

If angle BCD = 23° and arc EF = 34°, determine arc abd using the appropriate theorems and postulates.

Given data:

m∠BCD = 23° and m(ar EF) = 34°

By central angle theorem,

The measure of a central angle is equal to the measure of the intercepted arc.

m (ar EF) = m∠ECF

m∠ECF = 34°

By vertical angle theorem,

If two lines are intersecting, then vertically opposite angles are equal.

⇒ m∠ACB = m∠ECF

⇒ m∠ACB = 34°

m∠ACD = m∠ACB + m∠BCD

              = 34° + 23°

m∠ACD = 57°

By central angle theorem,

m(ar ABD) = m∠ACD

m(ar ABD) = 57°

Answer:

$4

Step-by-step explanation:

10x = 8(x+1)

2x = 8

x = 4

Answer:

40 dollars

Step-by-step explanation:

We can say

x=amount each friend has to pay

Then, the price of the gift would be 10x because there are 10 friends and each pays x dollars. But since two friends dropped out, it will now become 8x. Also,  each of the 8 friends has to pay an extra dollar to go back to the original amount, so 8x+8 is also the price of the gift. We set these two expressions equal to each other (because they both represent the price of the gift) so

10x=8x+8. Using the subtraction property of equality (which says if a=b, then a-c=b-c) we subtract 8x from both sides to get

2x=8. Using the division property of equality (which says if a=b, then a/c=b/c) we divide by 2 on both sides to get x=4. But the question asked how much money they planned to collect, or what was the price of the gift, which is 10x, 10*4=40, 40 dollars.

Answer:

a.) equivilent to;     4 x 7x - 4 x 6         and         28x-24

b.) equivilent to;     8y + 13y          and            21y

Step-by-step explanation:

A.)

4(7x-6)     First you have to multiply everything in the parenthesis by 4 because of distribution

7x x 4 - 6 x 4                That is why it is equivilent to the  4 x 7x - 4 x 6  awnser

28x - 24                    That is the end result by simplifiying and show why it is equivient to 28x-24

B.)

8y+6y+7y                 Simplify the like terms

8y+13y                   6+7 is 13 so that is why it is eauals to 8y+13y

21y                       if you continue adding you see why it equals 21y

Answer:

yup, its positive

two times cancels out, but then the third time made it negative again

Answer:

7.5

Step-by-step explanation:

5 x 3 = 15

5.5 x 3 = 16.5

Triangle PQR has 3x the amount as ABC on each side, therefore, n = 7.5

Step-by-step explanation:

8n+4-6n/2

8n+4-3n

5n+4

Answer:

n+2

Step-by-step explanation:

to  simplify this expression 8n+4-6n/2

we have,

{8n-6n + 4}/2

{2n + 4}/2

to further simplify this expression {2n + 4}/2 , we are going to factorize 2 from the numerator ,

we have

=2(n +2)/2

the next step to simplify the 2(n +2)/2 further is to use the factorised 2 at the numerator to divide the 2 at the denominator so that we can have a simplified expression.

we have

=2(n +2)/2

=n+2

therefore  the simplified form of the expression 8n+4-6n/2 is n+2

Answer:

The decimal point should be moved Six places to the right side because there are Six zeros in 10 to the power of 6.

Step-by-step explanation:

As we have to represent the number in the form of [tex]10^{6}[/tex] we need to move the decimal Six places towards left because there are Six zeros in [tex]10^{6}[/tex] i.e. 1000000. For this purpose we will add four zeros to the left of the number.

So the number in the format mentioned in question will look like -

0.00003405 × [tex]10^{6}[/tex].

Answer:

Reflection

Step-by-step explanation:

It is reflecting across the Y axis. It is not a dialation, since it is the same shape, but not a different size. Its not rotation, because it wasnt rotated to get to the new shape. And it is not translation, because it is not exactly the same shape (the shape was mirrored)

Answer:

[tex]x=5\\\\y=2[/tex]

Step-by-step explanation:

Given Equations:

        [tex]-6y= -20 + 2x[/tex]    Equation:1

Solving Equation:1 Adding '[tex]6y[/tex]' to both the sides:

             [tex]2x+6y-20=0[/tex]  

Adding '20' both the sides:

              [tex]2x+6y=20[/tex]   Equation:2

[tex]2x - 4y=0\\[/tex]  Equation:3

Subtracting Equation:3 From Equation:2

          [tex]2x+6y-(2x-4y)=20-0\\\\2x+6y-2x+4y=20\\\\10y=20\\\\y=\frac{20}{10}\\\\ y=2[/tex]

Putting the value of 'y' in equation:3

          [tex]2x - 4y=0\\[/tex]

          [tex]2x-4(2)=0\\\\2x-8=0[/tex]

Adding '8' to both the sides

             [tex]2x=8\\\\x=8/2\\\\x=5[/tex]

SO,  

              [tex]x=5\\\\y=2[/tex]

Answer: 6 pencils

Step-by-step explanation:

You divide 6.72(amount of money he has) by 1.12(the price of each pencil). You get the answer 6 pencils.

Answer:

The answer is 22.

d=√(−9−13)2+(−17−(−17))^2

d=√(-22)^2+(0)^2

d=√484+0

d=√484

d=22

Step-by-step explanation:

Answer:If we are traveling in a car around a corner and we drive over something slippery on the road (like oil, ice, water or loose gravel) and our car starts to skid, it will continue in a direction tangent to the curve.

Step-by-step explanation:

Tangent lines are essential in real-life scenarios like physics for analyzing motion, such as object velocity and acceleration, enabling accurate predictions in various fields.

**Tangent lines** are crucial in various real-life scenarios. For instance, in **physics**, when analyzing the motion of an object along a curved path, the tangent line at a specific point helps determine the object's instantaneous velocity or acceleration. This is vital in understanding how objects move in the real world.

A practical example is when studying the trajectory of a ball thrown into the air. By using the **tangent line** at different points of its path, we can calculate the ball's velocity or acceleration at those instances, assisting in sports analytics, engineering designs, or even space exploration calculations.

Understanding **tangent lines** is essential in fields like **engineering** and **physics** as it allows for precise calculations and predictions based on the behavior of curved functions and their instantaneous rates of change.

Answer:

as long as

[tex]a^2+b^2=c^2[/tex]

then it’s valid, soo...

the first one is not valid (5,6,sqrt 223)

the second one is Not valid (7,11,sqrt 175)

the third one is correct, since [tex]6^2+15^2=261[/tex]

and [tex]\sqrt 261 = 16.1554944214[/tex] (further info)

Answer:

m = 5/2

Step-by-step explanation:

Formula for slope: [tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]

-[tex]\frac{6-(-9)}{5-(-1)}=\frac{15}{6} =\frac{5}{2}[/tex]

The height of the building is 25.38 feet

Explanation:

Let AB denotes the height of the building.

Let BC denotes the distance between the fire truck and the building.

Let AC denotes the length of the ladder.

Using the Pythagorean theorem, we have,

[tex]AC^2=AB^2+BC^2[/tex]

where AC = 30, BC = 16

Substituting the values, we have,

[tex]30^2=AB^2+16^2[/tex]

Simplifying the terms, we get,

[tex]900=AB^2+256[/tex]

Subtracting both sides by 256, we get,

[tex]644=AB^2[/tex]

Taking square root on both sides of the equation, we get,

[tex]\sqrt{644}=AB[/tex]

[tex]25.38=AB[/tex]

Thus, the height of the building is 25.38 feet

Answer:

Step-by-step explanation:

a fire truck parks 16ft away fromm a building. the truck extends its ladder 30 feet. how far up the building from the trucks roof does the ladder reach

Answer:

  (g◦f)(x) = 2x +1

Step-by-step explanation:

(g◦f)(x) = g(f(x)) = g(2x -1) = (2x -1) +2

(g◦f)(x) = 2x +1

__

Substitute f(x) for the argument in the function g(x) and simplify.

Bob has 49 quarters and 11 dimes.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Let there be x quarters.

Then there are 60 - x dimes so using cents as the unit, we get

25x + 10(60 - x) = 1335

25x + 600 - 10x = 1335

15x = 735

x= 49

and 60 - x = 60 - 49 = 11

Hence, Bob has 49 quarters and 11 dimes.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ5

Final answer:

By setting up a system of two equations, where q stands for the number of quarters and d for the number of dimes, and solving this linear system, we find that Bob has 49 quarters and 11 dimes.

Explanation:

To solve this problem, we can set it up as a system of equations. Let's call the number of quarters q and the number of dimes d. We have two pieces of information:

Now, we can multiply the second equation by 10 to eliminate decimals:

2.5q + d = 133.5

Using the first equation (q + d = 60), we can express d as d = 60 - q. Substituting this into the second equation:

2.5q + (60 - q) = 133.5

Simplifying, we get:

1.5q = 73.5

Divide both sides by 1.5 to find q:

q = 49

Now, plug q back into the first equation to find d:

d = 60 - 49 = 11

So, Bob has 49 quarters and 11 dimes.

Answer:

24x^4+18x^3-15x^2 -42x-24

Step-by-step explanation:

(6x^2-3x-6)(4x^2 +5x+4)=

6x^2*4x^2 +6x^2*5x+6x^2*4

-3x*4x^2 - 3x*5x-3x*4

- 6*4x^2 -6*5x-6*4=

24x^4+30x^3+24x^2-12x^3-15x^2 -12x

-24x^2-30x-24=

24x^4+18x^3-15x^2 -42x-24

Answer:

About 95% of data lies between 15.6 and 32.4

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 2.4

Standard Deviation, σ = 4.2

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Empirical Formula:

We have to find the percentage of data lying between 15.6 and 32.4

[tex]15.6 = 24 - 2(4.2) = \mu - 2\sigma\\32.4 = 24 + 2(4.2) = \mu + 2\sigma[/tex]

Thus, we have to find the percentage of data lying within two standard deviations of the mean. By Empirical formula about 95% of data lies between 15.6 and 32.4

Answer

[tex]\angle \ LMN=49\textdegree[/tex]

Step-by-step explanation:

The diagonals of kite KLMN meet at 90°

Since, LK and KN are congruent,[tex]\angle KLM[/tex] and[tex]\angle KNM[/tex] form a set of opposite congruent angles. Congruent angles are equal.

All interior angles of a kite add up to 180°, therefore:-

[tex]\angle LMN=360\textdegree - 2\times106\textdegree-99\textdegree\\=49\textdegree[/tex]

Answer:

∠LMN = 49°

Step-by-step explanation:

Given that

∠LKN = 99°

∠MNK = 106°.

Because, the lengths of LK and KN are congruent.

LK=KN because congruent lines are equal

Hence, ∠MNK=∠MLK = 106°

Adding all angles together, we have

∠MNK + ∠MLK + ∠LKN + ∠LMN = 360°

By substituton;

We have

106° + 106° + 99° + ∠LMN = 360°

311° + ∠LMN = 360°

Collect like terms

∠LMN = 360° - 311°

∠LMN = 49°

Answer:

1(18 + 6)/4

Step-by-step explanation:

1(18 + 6)/4

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Final answer:

The numerical expression for 1/4 of the sum of 18 and 6 is calculated by adding 18 and 6 to get 24, then multiplying by 1/4 to get 6.

Explanation:

The numerical expression for 1/4 of the sum of 18 and 6 is found by first adding 18 and 6 to get their sum, which is 24. Then, to find 1/4 of this sum, you multiply 24 by 1/4. The calculation step-by-step is as follows:

Therefore, the numerical expression for 1/4 of the sum of 18 and 6 is 6.