Is 24, 45, and 51 a right triangle?

Answer:

He'll earn 125 in interest after 5 years.

Step-by-step explanation:

Since it's a simple interest rate, we can use the formula to calculate the amount of interest he'll earn in those years. We have:

C = P*i*t

Where C is the amount of interest earned, P is the initial amount invested, i is the interest rate and t is the total time elapsed. For this case we have:

C = 500*0.05*5

C = 2500*0.05

C = 125

He'll earn 125 in interest after 5 years.

The solution is

The equations with one solution is

y = 0.5x - 2  ;   y = -0.5x + 4

y = 2x + 1  ;  y = 4x + 1

The equations with no solution is

y = 0.5x + 5  ;  y = 0.5x + 1

y = -x - 3  ;  y = -x + 3

The equations with infinite number of solutions is

y = 3x + 2.5  ;  y = 3x + 2.5

y = -x - 2  ;  y = -x - 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

y = 0.5x - 2   be equation (1)

y = -0.5x + 4   be equation (2)

On simplifying both the equations , we get

0.5x - 2 = -0.5x + 4

Adding 0.5x on both sides of the equation , we get

x - 2 = 4

Adding 2 on both sides of the equation , we get

x = 6

Substitute the value of x in equation (1) , we get

y = 1

The value of x is 6 and value of y is 1

b)

y = 0.5x + 5   be equation (1)

y = 0.5x + 1   be equation (2)

On simplifying both the equations , we get

0.5x + 5 = 0.5x + 1

Now , the equations are contradictory and there are no solution

c)

y = 2x + 1   be equation (1)

y = 4x + 1   be equation (2)

On simplifying both the equations , we get

2x + 1 = 4x + 1

Subtracting 2x on both sides of the equation , we get

2x + 1 = 1

Subtracting 1 on both sides of the equation , we get

2x = 0

x = 0

Substitute the value of x in equation (1) , we get

y = 1

Therefore , the value of x is 0 and value of y is 1

d)

y = 3x + 2.5   be equation (1)

y = 3x + 2.5   be equation (2)

On simplifying both the equations , we get

3x + 2.5 = 3x + 2.5

Therefore , the equations are similar and there are infinite number of solutions

e)

y = -x - 3   be equation (1)

y = -x + 3  be equation (2)

On simplifying both the equations , we get

-x - 3 = -x + 3

Now , the equations are contradictory and there are no solution

f)

y = -x - 2   be equation (1)

y = -x - 2   be equation (2)

On simplifying both the equations , we get

-x - 2 = -x - 2

Therefore , the equations are similar and there are infinite number of solutions

Hence , the system of equations are solved

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Final answer:

The solution to the system of equations is x = 1 and y = 6.

Explanation:

The given equations are:

3x + 2y = 15

y = 6x

To solve this system of equations, we can substitute the value of y from the second equation into the first equation:

3x + 2(6x) = 15

3x + 12x = 15

15x = 15

x = 1

Substituting the value of x into the second equation to find y:

y = 6(1)

y = 6

So, the solution to the system of equations is x = 1 and y = 6.

Answer:

D) the value of the exponential function will eventually exceed the value of the linear function.

Step-by-step explanation:

I ATTACHED AN IMAGE WITH THE CORRECT INFORMATION OF THE QUESTION.

To know which is the correct answer we can calculate some other values of f(x) and g(x) for higher values of x:

f(100)=210            g(100)=7.31

f(1000)=2010        g(1000)=20959.15

f(10000)=20010    g(10000)=1.63e^43

As we can observe, g(x) eventually will exceed to f(x). This is noticed when x = 1000, where g(1000)>f(1000).

Hence, the answer is:

D) the value of the exponential function will eventually exceed the value of the linear function.

Answer:

[tex]\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]

Step-by-step explanation:

The angle [tex]\theta_1[/tex] is located in Quadrant I and [tex]\cos(\theta_1)=\frac{3}{8}[/tex]

From Trigonometric ratio, In the First Quadrant

[tex]\cos \theta=\frac{Adjacent}{hypotenuse}[/tex]

Adjacent =3, Hypotenuse =8

Using Pythagoras Theorem

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\8^2=Opposite^2+3^2\\Opposite^2=64-9=55\\Opposite=\sqrt{55}[/tex]

Therefore:

[tex]\sin(\theta_1)=\frac{Opposite}{Hypotenuse}\\\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]

Answer:

No solutions

Step-by-step explanation:

The graph does not contact the x axis

There are no real answers for this reason.

Answer:

$5

Step-by-step explanation:

First you divide the 2 numbers you know.

100/20= 5

And if your not sure then you can multiply it.

5x20=100

Answer:

$35 x + $25 y ≥ $3200           x ≤ 120

Step-by-step explanation:

Because she needs to write before type the page, so that y≤x

∴ x≤120

$35 x + $25 y ≥ $3200           x ≤ 120

Final answer:

The system of inequalities for the teacher's summer work with the textbook company is 35x + 25y \\( ext{≥}) 3200, x + y \\( ext{≤}) 120, x \\( ext{≥}) 0, and y \\( ext{≥}) 0, where x is pages written and y is pages typed.

Explanation:

The system of inequalities to represent the situation where a teacher works for a textbook company during the summer, earns $35 per page for writing the material and $25 per page for typing, wants to earn at least $3200, and does not want more than 120 pages of work would be:

35x + 25y \\( ext{≥}) 3200

x + y \\( ext{≤}) 120

x \\( ext{≥}) 0

y \\( ext{≥}) 0

Here, x represents the number of pages written and y represents the number of pages typed. The first inequality ensures the teacher earns at least $3200, the second inequality ensures the total number of pages does not exceed 120, and the last two inequalities represent that the teacher cannot write or type a negative number of pages.

Answer:

64°

Step-by-step explanation:

In circle with center P, AD is diameter.

[tex] \therefore m\angle DPE + m\angle APE = 180\degree \\

\therefore (33k-9)\degree + 90\degree = 180\degree \\

\therefore (33k-9)\degree = 180\degree -90\degree \\

\therefore (33k-9)\degree = 90\degree \\

\therefore 33k-9 = 90\\

\therefore 33k= 90+9\\

\therefore 33k= 99\\

\therefore k= \frac{99}{33}\\

\therefore k=3\\

m\angle CPD = (20k +4)\degree \\

\therefore m\angle CPD = (20\times 3 +4)\degree \\

\therefore m\angle CPD =(60+4)\degree \\

\therefore m\angle CPD =64\degree \\

m\overset {\frown}{CD} = m\angle CPD\\

\therefore m\overset {\frown}{CD} = 64\degree

[/tex]

Answer:

B. 8ft

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w) where l is the length and w is the width

Substituting in the given values

48 = 2(16+w)

Divide each side by 2

48/2 = 2/2(16+w)

24 = 16+w

Subtract 16 from each side

24-16 =16+w-16

8 =w

Answer: It’s 4 they’re all wrong (pretty sure I have the same graph)

Step-by-step explanation:

A general cosine function has the form:

f(x) = A*cos(c + x)

We want to find the value of A that matches the one in the image, and we will find that A = 3

Ok, a general cosine function is:

f(x) = A*cos(c + x)

Where A is the amplitude.

To find the amplitude of a cosine function, we just need to find half of the difference between the maximum and minimum value of the function:

By looking at the given graph, we can see that the maximum is y = 3, and the minimum is y = -3

Then the amplitude is:

A = (3 - (-3))/2 = 6/2 = 3

The correct option is B.

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Answer: B) (x-1)2+(y+1)2= 25 radius = 5 miles

Step-by-step explanation:

In order to get this answer you see that you are adding a negative to x in the first part then multiplying it by 2. Second, you add y+1 then multiplying it by 2. You get the radius of 25 which equals 5 miles. Look at the graph to also check your answers to the problem.

Answer:

B) (x-1)2+(y+1)2= 25 radius = 5 miles

Step-by-step explanation:

Equation of a circle:

(x - h)² + (y - k)² = r²

(h,k) = (1, -1)

r = 5

(x - 1)² + (y - -1)² = 5²

(x - 1)² + (y + 1)² = 25

Answer:

118!

Step-by-step explanation:

On edge 2020

Answer: 8 i

Step-by-step explanation: The square root of negative 64 is 8 i. Whenever you are finding a negative square root you need to find what times what will equal that number. 8 x 8 = 64. So the square root is 8. But, since we are finding a negative square root, the answer will be 8 i. i states that 8 is the negative square root of 64.

So the answer is 8 i.

Always add i after the number when finding negative square roots.

Answer:

29 rungs

Step-by-step explanation:

In this question, we are to use the climbing statistics of a firefighter to determine the number of rungs a ladder have.

Firstly, since we do not know the number of rungs but we know we are starting from the middle rung, let the middle rung be r.

From the middle rung, he climbed 6 rungs, meaning he would be on rung x + 6 ! From here he came down ten rungs, meaning he would be on rung x + 6 - 10 = x -4

Now, he climbed 18 rungs again, making x -4+18 = x + 14

This is equal to the topmost rung i.e the topmost rung is at a position x + 14

This means that the ladder must have 14 rungs above the middle , 14 below it and the middle itself

14+ 14 + 1 = 29 rungs

The firefighter's movements on the ladder suggest that the ladder has 41 rungs, confirmed by algebraically considering the middle rung 'm' and then solving for 'm' knowing the positions relative to the top.

To solve the question, let's follow the firefighter's movement on the ladder using variables and a step-by-step approach. If we let the middlemost rung the firefighter is initially standing on be represented by 'm,' we can track the rung positions with the following moves:

The firefighter climbs up 6 rungs: new position is m + 6.

The firefighter then climbs down 10 rungs: new position is (m + 6) - 10 = m - 4.

Finally, to reach the top of the ladder, the firefighter climbs up 18 rungs: new position is (m - 4) + 18 = m + 14.

Since the final position is the top rung of the ladder, it means the middlemost rung 'm' plus 14 rungs equals the total number of rungs on the ladder. Because 'm' is the middle rung of the ladder, there must be 'm - 1' rungs below it. Therefore, the total number of rungs on the ladder is (m - 1) + m + 14. Simplifying, this becomes 2m + 13.

Now we know that 2m equals the number of rungs minus the top 14 rung positions, and since 'm' represents the middlemost rung, '2m' represents the total number of rungs on the ladder except for the top 14. Hence, the total rungs on the ladder are 2m + 14. But since 2m + 13 equals the total, the only number that satisfies this condition is when m = 14. Therefore, the ladder must have 2m + 13 = 2(14) + 13 = 41 rungs.

Answer:

The question not complete

Answer:

k = 0.5

Step-by-step explanation:

Constant of Proportionality is k = y/x

k = 0.5/1 = 0.5

The airplane is approximately 33,336.6 feet above the ground. This calculation is based on Ray's perspective from 1 mile away with an 81-degree angle of elevation to the plane. The calculated height difference between the plane and the top of the tower is approximately 1,598.5 feet.

To solve this problem, we can use trigonometry to set up a system of equations with the given angles and the known height of the tower. We'll use the following steps:

1. Use Ray's angle of elevation to the plane (81 degrees) and his distance from the tower (1 mile, which is 5280 feet) to find the height of the plane from the ground.

2. Use Ray's angle of elevation to the top of the tower (8.6 degrees) with the same distance to find the height difference between the tower and the plane.

3. Add the height of the tower to the height difference found in step 2 to get the total height of the plane from the ground.

Let's denote the height of the plane from the ground as ( h ) and the horizontal distance from Ray to the point right below the plane as ( d ). We know that [tex]\( \tan(81^\circ) = \frac{h}{5280} \)[/tex] and [tex]\( \tan(8.6^\circ) = \frac{800}{5280} \)[/tex].

Let's calculate ( h ) using these equations.

The airplane is approximately 33,336.6 feet above the ground. This calculation is based on Ray's perspective from 1 mile away with an 81-degree angle of elevation to the plane. The calculated height difference between the plane and the top of the tower is approximately 1,598.5 feet.

A 90° counterclockwise rotation is the same as a 270° clockwise rotation. A 180° rotation is the same as a reflection across both axes. A 90° clockwise rotation is the same as a 270° counter-clockwise rotation. Two separate rotations of 90° counter-clockwise and then 180° are the same as rotations of 90° clockwise and then 180°.

In mathematics, especially in geometry, transformations involve changing the position, size or shape of a figure. The question is about matching specific transformations or sequence of transformations to its equivalent transformation.

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Answer:

It's z^11

Step-by-step explanation:

To multiply exponents with the same base (z), you add the exponents so in this case you add 5 and 6 to get z^11

Answer:

[tex]z^{11}[/tex]

Step-by-step explanation:

[tex]z^{a} *z^{b}= z^{a+b} \\z^{5} *z^{6}= z^{5+6} = z^{11}[/tex]

Answer:

(x+3)^2 + (y +5)^2 = 36

Step-by-step explanation:

We can write the equation of a circle with the formula

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

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

(x+3)^2 + (y +5)^2 = 6^2

(x+3)^2 + (y +5)^2 = 36

Answer:

D; (x + 3)^2 + (y + 5)^2 = 36

Step-by-step explanation:

correct on edge

Answer:

[tex]c=-x^{2} +24x[/tex]

Step-by-step explanation:

Subtract on both sides to isolate c.

[tex]x^{2} -24x+c\\x^{2} -24+c-c=-c\\x^{2} -24+0=-c\\x^{2} -24x=-c\\-c=x^{2} -24x[/tex]

Have c be in positive form.

[tex]-c=x^{2} -24x\\(-)(-c)=(-)(x^{2} -24x)\\c=-x^{2} +24[/tex]

if i'm not mistaken, this means that one person has to shake 38 people's hands. so, that would be 38*39, i believe.

Answer: E simple random

Step-by-step explanation:

A simple random sample in a statistics is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability

The type of sampling used in this scenario is simple random sampling(E), where each member of the population has an equal chance of being chosen.

The type of sampling used in this scenario is simple random sampling(option E).

In simple random sampling, each member of the population has an equal chance of being chosen.

In this case, since the cards are placed in a bag and three names are picked, each card has an equal probability of being selected, making it simple random sampling.

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Answer:

The area of the interior tiles must be 7 inches ² with dimensions 1.871" x 3.742".

Step-by-step explanation:

Since the interior tiles must be 3.5 larger then the border tiles to calculate the dimensions of the interior tiles we first need to find the area of the border tiles. This is shown bellow:

area border = 1*2 = 2 inches²

The area of the interior tiles is 3.5 larger than that, so we have:

area interior = 2*(area border) = 2*3.5 = 7 inches²

In order to maintain the same proportions as the border tiles we must find a width that is two times the height, so we have:

area interior = width*height = 2*height*height = 2*height²

7 = 2*height²

height² = 3.5

height = sqrt(3.5) = 1.871

width = 2*height = 2*1.871 = 3.74166

The area of the interior tiles must be 7 inches ² with dimensions 1.871" x 3.742".

The interior tiles that Ryan wants to use in his bathroom will have dimensions of 3.5 inches by 7 inches.

Ryan is using 1" x 2" tiles for the border of his bathroom and wants to use similar tiles for the interior that are larger by a scale factor of 3.5.

To calculate the dimensions of the interior tiles, you simply multiply the dimensions of the border tiles by the scale factor. Therefore, the dimensions of each interior tile will be:

2 inches (width of border tile) x 3.5 = 7 inches (width of interior tile)

c = 30 inch

Step-by-step explanation:

perpendicular (p) = 18 inch

base(b) = 24 inch

hypotenuse (h) = ?

we know by using Pythagoras theorem

h² = p² + b²

h² = 18² + 24²

h² = 324 + 576

h² = 900

h= √900

therefore h = 30 inch

Hope it will help you. :)

Answer:

(30)Pythagorean theorem a^2+b^2=c^2

Step-by-step explanation:

18^2+24^2=c^2

square root 900 and the answer is 30

sorry if wrong i tried

Answer:

$1.49 per pound of bananas at Smiths

Step-by-step explanation:

1. 10 pounds is $14.90

2. Find how much one pound costs by dividing 14.90 by 10

3. 14.90/10= 1.49

4. $1.49 per pound of bananas at Smiths

Answer:

3/5

Step-by-step explanation:

Answer:

The slope is 3/5.

Step-by-step explanation:

First remember that the formula for slope is the difference in ys / difference in xs.

m = y2 - y1 / x2 - x1

Plug in the coordinates of the two points you're given, keeping in mind that coordinates are (x,y).

m = -5 - 1 / -5 -5

m = -6 / -10

m = 6/10 = 3/5

If she goes 75 mph for 2 hours, that's 150 miles altogether. 45 mph for 1 hour is 45 miles, so 150 + 45 is 195 miles.

The total distance that Mishka covers on her road trip is 195 miles.

Two or more expressions with an Equal sign is called as Equation.

To calculate the total distance covered on the road trip

we need to add the distances traveled on the highway and side roads.

Distance on the highway = speed × time

= 75 mph × 2 hours

= 150 miles

Distance on side roads = speed × time

= 45 mph × 1 hour

= 45 miles

Total distance covered = Distance on the highway + Distance on side roads = 150 miles + 45 miles

= 195 miles

Therefore, the total distance that Mishka covers on her road trip is 195 miles.

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Answer:

C

Step-by-step explanation:

I took the test