The hypotenuse of a right triangle is 5 feet. One leg of the triangle is 3 feet. What is the length of the other leg (rounded to the nearest hundredth)?

Answer:

Step-by-step explanation:

Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...

  f + t = 60

  f - t = 10

Adding these two equations, we get ...

  (f +t) +(f -t) = (60) +(10)

  2f = 70 . . . . . eliminate parentheses

  f = 35 . . . . . . divide by 2

She has 35 5-lb weights, and 25 3-lb weights.

Answer: 10 Acme and 15 Zenith.

She can buy 10 Acme and 15 Zenith calculators.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A math teacher wants to buy 25 new scientific calculators for the classroom.

Acme and Zenith makes two different type of calculators.

Acme calculators cost $15 each.

Zenith calculators cost $12 each.

The math teacher has $330 to spend.

Let x represents the number Acme calculators and y represents Zenith.

Now, we have the system of equations,

x + y = 25

So, y = 25 - x

And 15x + 12y = 330

Substituting the value of y,

15x + 300 - 12x = 330

3x = 330 - 300

3x = 30

x = 10

So, y = 15

Therefore, 10 Acme and 15 Zenith calculators.

To learn more about the system of equation;

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Answer:

7x + 14y

Step-by-step explanation:

7(x + 2y)

Multiply 7 by the values inside the parenthesis (x + 2y)

7x + 14y

Hope this helps :)

Answer:

Center (h, k) = (0, 6)

Radius, r = 3 units

Step-by-step explanation:

The given equation of the circle is: [tex]$ x^2 + y^2 + 12y + 27 = 0 $[/tex]

STEP I: Move the constant term to the right hand side.

To do that we subtract 27 on both the sides, we get:

[tex]$ x^2 + y^2 + 12y = -27 $[/tex]

STEP II: Divide the co - effecient of 'x' by 2 and square it.

Here there is no 'x' term. Its co-effecient is 0.

STEP III: Add the result on both sides.

Since, we got 0 in the previous step, there would no change in the equation

STEP IV: We repeat the process for 'y'.

Here, the co-effecient of 'y' is: 12.

Dividing by 2 and squaring it will yield:

[tex]$ \frac{12}{2} = 6; \hspace{5mm} 6^2 = 36 $[/tex]

STEP V: Adding 36 to both the sides of the equation, it becomes:

[tex]$ x^2 + y^2 + 12y + 36 = -27 + 36 $[/tex]

[tex]$ \implies x^2 + y^2 + 12y + 36 = 9 $[/tex]

We have arrived at perfect squares.

STEP VI: Write in the form of perfect squares.

[tex]$ (x - 0)^2 + (y - 6)^2 = 3^2 $[/tex]

STEP VII: Compare it with the standard form.

[tex]$ (x - h)^2 + (y - k)^2 = r^2 $[/tex]

We get: The centre of the circle: (h, k) = (0, 6) and

the radius of the circle, r = 3 units.

For this case we have that by definition, a linear equation is of the form:

[tex]ax + b = 0[/tex]

The variable (s) involved in the equation always have exponent 1.

Some examples of linear equations are:

[tex]x + 5 = 3y\\y + 6 = 3x\\y = 2x + 2[/tex]

Answer:

In a linear equation the variables have exponent 1.

[tex]y = 2x + 2[/tex]

Answer:

The third dot

Step-by-step explanation:

I did this question before :)

Answer:

-6/5

Step-by-step explanation:

-2 2/5=-12/5

1/2*-12/5=-12/10=-6/5

Option "D. y=x−12" and "E. y=1/4x" are the functions whose graphs include the point (16,4)

Step-by-step explanation:

In order to find the functions whose graph includes the point we will put the point in the functions one by one

So,

A. y=2x

Putting x = 16 and y = 4

[tex]4 = 2(16)\\4\neq 32[/tex]

B. y=x^2

Putting x= 16 and y=4

[tex]4 = (16)^2\\4 \neq 256[/tex]

C. y=x+12

Putting x= 16 and y=4

[tex]4 = 16+12\\4 \neq 28[/tex]

D. y=x−12

Putting x= 16 and y=4

[tex]4 = 16-12\\4 = 4[/tex]

E. y=1/4x

Putting x= 16 and y=4

[tex]4 = \frac{1}{4} * 16\\4 = 4[/tex]

Hence,

Option "D. y=x−12" and "E. y=1/4x" are the functions whose graphs include the point (16,4)

Keywords: Functions, graphing

Learn more about functions at:

#learnewithBrainly

Answer:

Step-by-step explanation:

The answers are D and E

Answer:

The answer is given in the graph attached.

Step-by-step explanation:

i) The answer is given in the graph attached.

Answer:

1. X= 25.9 meters

2.X= 21.3 meters

Step-by-step explanation:

1. Tan 50°= X/21

2. Tan 12°= X/100

Answer:

[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]

Step-by-step explanation:

The general form of the quadratic equation is

[tex]ax^2+bx+c=0[/tex]

You are given the quadratic equation

[tex]0=\dfrac{1}{2}x^2-3x[/tex]

It can be rewritten in standard form as

[tex]\dfrac{1}{2}x^2-3x=0[/tex]

Hence,

[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]

Answer:

y=1/2x -2. Hope this helps!

Answer:

Answer: The perimeter of the red polygon is 26 cm.

Step-by-step explanation:

Answer:

Tangents from an external point are equal. This can be used to find the perimeter

Perimeter = 22+22+22+22+27+27+98+98

= 338 in.

Hope this helps!

Step-by-step explanation:

We are asked to draw a triangle.

The information we are given with is AB is a line segment with length 3.9 cm.

∠CAB = 50°.

∠ABC = 63°.

With the given details we need to draw triangle using given angles. We need protractor and ruler to draw the triangle.

Step 1: Draw the line segment of length 3.9 cm using ruler and mark as AB.

Step 2: Using protractor, we need to mark the angle. Keep the center of the protractor at the A and mark with a point at 50°.

Step 3: Draw a line from a passing through the marked point.

Step 4: Repeat step 2 with marking at 63° and step 3 on the other side.

Step 5: Mark the intersection point as C.

Answer:

x = 3

Step-by-step explanation:

Given

3x = x + 6 ( subtract x from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

Step-by-step explanation:

3x = x + 6.....subtract x from both sides

3x - x = x - x + 6

2x = 6 ...divide both sides by 2

(2/2)x = 6/2

1x = 6/2

x = 3 <=====

Answer: the formula is

(-4) + (-5) = -9

(-9) + (-5) = -14

Step-by-step explanation:

Answer:

an  = 1 − 5n

Explanation:

a1  = 1 − 5 (1) = −4

a2  = 1 − 5 (2) = −9  

a3  = 1 − 5 (3) = −14

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

(-3,4) it shows that -3 =x and 4 =y

2x + y ≥ -2

Inserting both values into the equation

2(-3) + 4

-6 +4

-2

Answer confirms equation

Answer:

1.75, 0.4375

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

r = 28 ÷ 112 = 7 ÷ 28 = 0.25

Thus the sequence is geometric.

To obtain a term in the sequence multiply the previous term by 0.25

7 × 0.25 = 1.75

1.75 × 0.25 = 0.4375

The next 2 terms in the sequence are 1.75, 0.4375

Answer:

The  length of the rectangle is[tex](4+7y^3)[/tex] and its  width is[tex]3y^2[/tex]

Step-by-step explanation:

Given:

The Area of the rectangle =[tex]12y^2+21y^5[/tex].

Width is the greatest common factor of  [tex]12y^2[/tex] and[tex]21y^5[/tex]

To Find:

The length and width of the rectangle = ?

Solution:

Step 1: Finding the greatest common factor of [tex]12y^2[/tex]and[tex]21y^5[/tex]

[tex]12 y^2[/tex]= 2 x 3 x 3 x y x y

[tex]21y^5[/tex] = 3 x 7 x y x y x y x y x y

Thus the greatest common factor is [tex]3y^2[/tex] which is the width

Step 2: Finding the length and width

The area of the rectangle  = length x breath

width x length=  [tex]12y^2+21y^5.[/tex]

Taking[tex]3y^2[/tex] commonly from each term, we get

width x length= [tex](3y^2)(4 + 7y^3)[/tex]

Answer:

i would say wait abought 50 mins

Step-by-step explanation:

i dont know whow to explain i might be wrong but its some whaere around 50 mins irl

Using Newton's Law of Cooling with a cooling constant of 0.035, it will take approximately 42.53 minutes for the brownies to cool from 400 degrees F to 160 degrees F.

To estimate the time it would take for brownies to cool from 400 degrees F to 160 degrees F using Newton's Law of Cooling, we can use the equation [tex]T(t) = T_s + (T_0 - T_s)e^{(-kt)[/tex], where T(t) is the temperature of the object at time t, T_s is the surrounding temperature, T_0 is the initial temperature of the object, and k is the cooling constant (0.035 in this case).

First, set T(t) = 160 degrees F (the desired temperature), T_s = 70 degrees F (room temperature), and T_0 = 400 degrees F (initial temperature of brownies). Plug in the values into the equation: 160 = 70 + (400 - 70)e^(-0.035t).

Simplify and solve for t. Subtract 70 from both sides: 90 = 330e^(-0.035t). Divide both sides by 330: 90/330 = e^(-0.035t), which simplifies to 0.2727 ≈ e^(-0.035t).

Take the natural logarithm of both sides to solve for t: ln(0.2727) = -0.035t. Solving for t gives t ≈ -ln(0.2727)/0.035, which calculates to approximately t ≈ 42.53 minutes.

Hence, the brownies should cool to 160 degrees F in about 42.53 minutes.

Answer:

x=8

Step-by-step explanation:

First you want to distribute -6 to (2x+6) which you will then get -12x-36=-132. Now you want to get x by itself by getting rid of -36, so add 36 on both sides of the equation to get -12x=-96. Isolate x by dividing by -12 on both sides of the equation which will leave you with the equation x=8

Dot bikes 7m+10 miles this week.

Step-by-step explanation:

Distance of one loop = m miles

Distance of 2 loops = 2m

Distance of 3 loops = 3m

Distance covered on Sunday = 10 miles

Total distance = Monday + Wednesday + Friday + Sunday

Total distance = 2 loops + 2 loops + 3 loops + 10 miles

Total distance = 2m + 2m + 3m + 10

Total distance = (7m+10) miles

Dot bikes 7m+10 miles this week.

Keywords: addition, distance

Learn more about distance at:

#LearnwithBrainly

Good evening ,

Answer:

Step-by-step explanation:

From the table :

f(x) = g(x) only when x = -1 then -1 is the only solution

f(-1) = 9 = g(-1)

note : the equation could have some other solutions not shown in the table

:)

Answer:

Step-by-step explanation:

a - 7 = 3(b + 2)

a - 7 = 3b + 6

a - 7 - 6 = 3b

a - 13 = 3b

(a - 13) / 3 = b <====

Answer:

-13-1/4 b

Step-by-step explanation:

b is on the outside of the fraction not with the four.

-13-\frac{1}{4b}

Answer:

5z+1

Step-by-step explanation:

(3z-4)+(2z+5)

3z-4+2z+5

3z+2z-4+5

5z-4+5

5z+1

Answer:

5z+1

Step-by-step explanation:

3z-4+2z+5

Group like terms

3z+2z+5-4

Simplify

5z+1

Answer:

Step-by-step explanation:

it seems to me that if he wants the same rate of acceleration as the first trip, then he would need the same amount of soil as the first trip.

Therefore, he should reduce the amount of soil by one half and apply the same force. <====

Because the first time it was half full.....and since the second trip was all the way full, if he reduced it by one half, it would contain the same amount as the first trip....so he can then get the same rate of acceleration.

Answer:

A.

Step-by-step explanation:

According to Newton's second law of motion, an object with a larger mass requires more force to accelerate it at a certain rate than an object with less mass. This means that an object with a larger mass requires more force to accelerate.

To move the wheelbarrow at the same rate of acceleration for the second trip, the amount of soil must be the same as in the first trip. Since the gardener first filled only one-half of the wheelbarrow with soil, the gardener must reduce the amount of soil by one-half and apply the same amount of force.

Amount spent by the wife is $70

Step-by-step explanation:

Given:

the total amount  = $200

Amount spent on Lunch = $15.00

They buy three items at $20.00 each

The wife spends twice what her husband spends

They return home with $20.00 cash.

To Find:

Amount spent by the wife  = ?

Solution:

Initially after spending $15.00 on lunch they balance cash with them will be

200 - 15.00 = $185

Then they are buy 3 items each of which costs $20.00

So the balance after buying the 3 items will be

= 200 - 3(20)

= 185- 60.00

= $125

Now the wife is spending twice what her husband spends

so let the amount spent be the husband be x then the amount spent by the wife will be 2x.

Now  after spending 2x+x amount they are  left with $20.00

that is

125 -2x+x  = 20

125 -3x = 20

125 -20 = 3x

105 = 3x

[tex]x = \frac{105}{3}[/tex]

x = 35

So the wife will be spending 2(35) = $70

Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders

Solution:

Let "a" be the orders served by Teresa

Let "b" be the orders served by Charlie

Let "c" be the orders served by Justin

Teresa, Charlie, and Justin served a total of 153 orders

Therefore,

a + b + c = 153 -------- eqn 1

Justin served 4 times as many orders as Charlie

Orders served by Justin = 4( orders served by Charlie )

c = 4b ---------- eqn 2

Teresa served 9 more orders than Charlie

orders served by Teresa = 9 + orders served by Charlie

a = 9 + b ----------- eqn 3

Let us solve eqn 1 and eqn 2 and eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

9 + b + b + 4b = 153

9 + 6b = 153

6b = 153 - 9

6b = 144

b = 24

Substitute b = 24 in eqn 3

a = 9 + 24

a = 33

Substitute b = 24 in eqn 2

c = 4(24)

c = 96

Thus Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders

Answer:

Nonrigid

Segment lents are not

Step-by-step explanation:

Answer:

answer in picture

Step-by-step explanation: