Id : 688 737 6744<br>pas : c8SNRa

If Colorado Springs, Colorado, has 1.4 times more days of sunshine than Boston, Massachusetts, how many days of sunshine does ea

Rom4ik [11]

Days in boston=x
days in colorado=1.4x
boston+colorado=2.4x
475=2.4x
475/2.4=2.4x/2.4
198=x
198*1.4=277
days in boston=198
days in colorado=277
198+277=475

5 0

2 years ago

Find the measure of the the sides of DEF then classify it by it sides. <br> D(8,-6) E(-1,-3) F(-2,5)

Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

$d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}$

$d=\sqrt{(3)^{2}+(9)^{2}}$

$d_D_E=\sqrt{90}\ units$

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

$d=\sqrt{(5+3)^{2}+(-2+1)^{2}}$

$d=\sqrt{(8)^{2}+(-1)^{2}}$

$d_E_F=\sqrt{65}\ units$

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

$d=\sqrt{(5+6)^{2}+(-2-8)^{2}}$

$d=\sqrt{(11)^{2}+(-10)^{2}}$

$d_D_F=\sqrt{221}\ units$

step 4

Classify the triangle by the measure of its sides

we have

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

so

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

6 0

3 years ago

The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

kari74 [83]

The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or $2^6 = 64$ miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship $x * 2^6 = k$ , for some constant k.

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

$\dfrac{x}{2^6} = \dfrac{15x}{y^6} \\ (x)(y^6)=(2^6)(15x)$

Cancelling our x's (because we don't need to solve for them), we have

$y^6 = 15(2^6) = 15(64)=960$

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

$\sqrt[6]{y^6} = \sqrt[6]{960}$

Using a calculator, we see that $\sqrt[6]{960} = 3.14 \ miles \ per \ hour$ .

6 0

3 years ago

Plzzzzzzzzzzzzzzzzzzzzzzzz

lesantik [10]

Answer:

10x^2-11x-6

Step-by-step explanation:

To expand, we use the FOIL method. You do this by multiplying each number inside the parenthesis by the other numbers in the other set of the parenthesis. For example, on this problem, you would multiply 5x by 2x, and then 5x by -3.

Step by step, you would:

5x * 2x = 10x^2

5x * -3 = -15x

2 * 2x = 4x

2 * -3 = -6

In an equation, it would expand to 10x^2-15x+4x-6

To simplify, you add like terms (constants and those with the same variable). In this case, you would add together all the terms ending in x.

-15x+4x=-11x

Now, you have added like terms together, so your simplified answer is 10x^2-11x-6.

6 0

2 years ago

Possible solution for 4+x+2-2x=5

MrRissso [65]

Answer:

x=1

Step-by-step explanation:

For algebra always start by rewriting it.

4+x+2-2x=5

Then ask yourself is there any like terms we can combine, and here yes there is. 4 and 2 and x and -2x. Now lets combine them and rewrite.

6-x=5

Now lets get x alone and the quickest way is to subtract 6 to the other side

6-x=5

-6 -6

-x=-1

Now the two negatives cancel out as you would divide both sides by the coefficient -1 to get positive x alone. We can make this easier by just canceling out the negatives.

Your answer is

x=1

3 0

3 years ago

Id : 688 737 6744pas : c8SNRa​

Id : 688 737 6744pas : c8SNRa