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Natali5045456 [20]
3 years ago
8

The difference of two numbers if four and their product is 60

Mathematics
1 answer:
cricket20 [7]3 years ago
4 0

Answer:

The two numbers are 10 and 6.

Step-by-step explanation:

Let's begin by calling these two numbers x and y, and setting up a system of equations.

x-y=4

x*y=60

Now, you can rearrange the first equation to find the value of x expressed through y.

x=y+4

Now, you can substitute this into the second equation.

(y+4)*y=60

y^2+4y=60

y^2+4y-60=0

(y-6)(y+10)=0

y=6

x=6+4=10

Hope this helps!

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Write and solve your own word problem for 1.3 x 2.79? solve without using a calculator
vaieri [72.5K]

Answer:

The answer is 3.62

Step-by-step explanation:

Here is a word problem that you can use.

Jimmy has exactly 2.79 points. His other friend Robert has 1.3 times his points.  How many points does Robert have?

(And yes, I wrote this problem myself and I do not mind you using it! )

Hopefully this helped!

5 0
2 years ago
Read 2 more answers
Describe the steps to dividing imaginary numbers and complex numbers with two terms in the denominator?
zlopas [31]

Answer:

Let be a rational complex number of the form z = \frac{a + i\,b}{c + i\,d}, we proceed to show the procedure of resolution by algebraic means:

1) \frac{a + i\,b}{c + i\,d}   Given.

2) \frac{a + i\,b}{c + i\,d} \cdot 1 Modulative property.

3) \left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)   Existence of additive inverse/Definition of division.

4) \frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}   \frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}  

5) \frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}  Distributive and commutative properties.

6) \frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)} Distributive property.

7) \frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}} Definition of power/Associative and commutative properties/x\cdot (-y) = -x\cdot y/Definition of subtraction.

8) \frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}} Definition of imaginary number/x\cdot (-y) = -x\cdot y/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

Step-by-step explanation:

Let be a rational complex number of the form z = \frac{a + i\,b}{c + i\,d}, we proceed to show the procedure of resolution by algebraic means:

1) \frac{a + i\,b}{c + i\,d}   Given.

2) \frac{a + i\,b}{c + i\,d} \cdot 1 Modulative property.

3) \left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)   Existence of additive inverse/Definition of division.

4) \frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}   \frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}  

5) \frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}  Distributive and commutative properties.

6) \frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)} Distributive property.

7) \frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}} Definition of power/Associative and commutative properties/x\cdot (-y) = -x\cdot y/Definition of subtraction.

8) \frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}} Definition of imaginary number/x\cdot (-y) = -x\cdot y/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

3 0
2 years ago
Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a nearby tree was 32 fee
dangina [55]

the height of the tree is 23 feet .

<u>Step-by-step explanation:</u>

Here we have , Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long. At the same time, the shadow of a nearby tree was 32 feet long. We need to find Find the height of the tree. Let's find out:

According to question , Tony is 5.75 feet tall. Late one afternoon, his shadow was 8 feet long . Let the angle made between Tony height and his shadow be x . Now , At the same time, the shadow of a nearby tree was 32 feet long. Since the tree is nearby so tree will subtend equal angle of x. Let height of tree be y , So

⇒ Tanx=\frac{y}{32}

But , From tony scenario

⇒ Tanx=\frac{5.75}{8}

Equating both we get :

⇒ \frac{y}{32}  = \frac{5.75}{8}

⇒ y=\frac{5.75(32)}{8}

⇒ y=23ft

Therefore , the height of the tree is 23 feet .

3 0
3 years ago
Suppose it takes 45 hours for robot A to construct a new robot. Working together with robot B, it takes 25 hours for both robots
Len [333]

Answer:

56 hours 25 minutes

Step-by-step explanation:

Given:

Suppose it takes 45 hours for robot A to construct a new robot

It takes 25 hours for both robots to construct a new robot.

Question asked:

How long would it take robot B to construct a new robot, working alone ?

Solution:

Let the time taken by robot B to construct new robot = x

<u>By robot A</u>

It takes 45 hours to construct = 1 new robot

It takes 1 hour to construct = \frac{1}{45} \ new\ robot

<u>By robot B</u>

It takes x hours to construct = 1 new robot

It takes 1 hour to construct = \frac{1}{x} new robot

<u>By working together</u>

It takes 25 hours to construct = 1 new robot

It takes 1 hour to construct = \frac{1}{25} \ new\ robot

\frac{1}{25} new robot is constructed in = 1 hour

<u><em>New robot is constructed by both working together in 1 hour = New robot is constructed by robot A in 1 hour + New robot is constructed by robot B in 1 hour </em></u>

\frac{1}{25} =\frac{1}{45} +\frac{1}{x} \\

Subtracting both sides by \frac{1}{45}

\frac{1}{25}-\frac{1}{45} =\frac{1}{45} -\frac{1}{45}+\frac{1}{x} \\\\\frac{1}{25}-\frac{1}{45} =\frac{1}{x}\\\\ Taking\ LCM \ of \ 25\ and\ 45,\ we\ got\ 225

\frac{9-5}{225} =\frac{1}{x} \\ \\ \frac{4}{225} =\frac{1}{x}\\\\ By\ cross \ multiplication\\4\times x=225\\Dividing\ both\ sides\ by\ 4\\x=56.25\ hours

Thus, robot B would take 56 hours 25 minutes to construct a new robot, working alone.

4 0
3 years ago
Read 2 more answers
1. Name of the missing segment.<br> 2.Length of the missing segment.
allochka39001 [22]

Answer:

Name: FE

Length: 13

Step-by-step explanation:

The total length is 34, so you would do 34-21, which equals 13.

6 0
3 years ago
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