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3 years ago

What is the distance between -4.5 and 3.5

Mathematics

2 answers:

Aloiza [94]3 years ago

7 0

8 because 4.5 plus 3.5 is 8

iVinArrow [24]3 years ago

4 0

-8 hope this helps u :)

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A father and his son can clean the house together in 9 hours. When the son works alone, it takes him an hour longer to clean th

leonid [27]

Answer:

It will take the son 18.55 hours

Step-by-step explanation:

It takes 9 hours for the father and son to clean the house if they work together. This means that their unit rate of working together will be 1/9

When the son works alone, it takes him an hour longer to clean than it takes his dad alone.

Let x = the time it takes the father to clean the house. This means that it takes the son (x+1) hours to clean the house alone.

The unit rate if working of the son will be 1/+1

The unit rate of working of the father will be 1/x

Since they are working simultaneously, their unit rates are additive. Therefore

1/(x+1) + 1/x = 1/9

(x + x + 1)/x(x+1) = 1/9

(2x+1)/(x^2 + x)= 1/9

18x + 9 = x^2 + x

x^2 + x - 18x-9

x°2 - 17x - 9 = 0

Applying the general formula for quadratic equations,

x = [-b+-√b^2-4ac)]/2a

x =[ - -17 +-√-17^2-4(2×1)]/2×1

x = (17+-18.03)/2

x = (17 + 18.03)/2 or x = (17 - 18.03)/2

x = 17.55 or x = -0.515.

The time cannot be negative so it is 17.55

It takes the father 17.55 hours if he works alone.

It will take the son 17.55 + 1 = 18.55 hours

4 0

3 years ago

Find a 2 × 2 matrix b ≠ o and b ≠ i2 such that ab = ba, where a = 1 7 0 1 . b =

riadik2000 [5.3K]

If $\mathbf A$ is invertible, then we can simply choose $\mathbf B=\mathbf A^{-1}$ because for any invertible matrix $\mathbf X$ by definition we must have $\mathbf{XX}^{-1}=\mathbf X^{-1}\mathbf X=\mathbf I$ .

We have $\det\mathbf A\neq0$ , as

$\det\mathbf A=\begin{vmatrix}1&7\\0&1\end{vmatrix}=1\times1-0\times7=1$

which means $\mathbf A$ is non-singular and has an inverse. The inverse itself would be

$\mathbf A^{-1}=\dfrac1{\det\mathbf A}\begin{bmatrix}1&0\\-7&1\end{bmatrix}^\top=\begin{bmatrix}1&-7\\0&1\end{bmatrix}$

6 0

3 years ago

I need help ASAP please ant thank you <br> what is x

Marizza181 [45]

Answer:

(3x-17)°+(x+40)°+(2x-5)°=180°[sum of angle of triangle]

6x°+18°=180°

6x°=180°-18°

x°=162°÷6°

x°=27°

Again,

=3x-17. 2x-5. x+40°

=3×27-17. =2×27-5. =27+40

=64°. =49°. =67°

6 0

2 years ago

Consider the two triangles.

GuDViN [60]

Answer:

(A)Show that the ratios StartFraction U V Over X Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over Z Y EndFraction are equivalent.

$\dfrac{UW}{XZ}=\dfrac{WV}{ZY}=\dfrac{UV}{XY}$