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Nadusha1986 [10]
3 years ago
6

Maria has $5.00 more than José. Together they have. $37.50.

Mathematics
2 answers:
Soloha48 [4]3 years ago
8 0

Answer:

Step-by-step explanation:

32.50 dollar

Yuri [45]3 years ago
6 0

Answer:

B

Step-by-step explanation:

Maria has $5.00 more than José

Maria, M

Jose, j

M = j + $5

j + M = $37.50

j + j + $5 = $37.50

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Cheyenne drove 3000 miles in 75 hours. At this rate, how long will it take her to drive 4000 miles?
lyudmila [28]
Set up a proportion:
\frac{3000}{75}=\frac{4000}{x}
To solve cross multiply:
3000x=300000
divide both sides by 3000:
3000x/3000=300000/3000
x=100

It will take her 100 hours to drive 4000 miles assuming she continues to travel at this rate.

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3 years ago
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Two angles are complementary. mZT is (3x + 17)° and mZW is 19°<br> Solve for x and for mZT.
natima [27]

Answer:

x = 18

mZT = 71º

Step-by-step explanation:

Complementary angles total 90º

(3x + 17) + 19 = 90

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mZT = 71º

Subtract 17 from both sides

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3 years ago
Let T:ℝ2→ℝ2 be the linear transformation that first rotates points clockwise through 45∘ (????/4 radians) and then reflects poin
Alisiya [41]

Answer:

T = \left[\begin{array}{ccc}-\frac{1}{\sqrt{2} } &\frac{1}{\sqrt{2} }\\\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\end{array}\right]

Step-by-step explanation:

Let General Transformation matrix be denoted as T

Step 1: Clockwise rotation of 45 degrees

General counterclockwise rotation matrix in 2-dimension is given as

                                        R(\theta)=\left[\begin{array}{ccc}cos\theta & - sin\theta\\sin\theta&cos\theta\\\end{array}\right]

For clockwise rotation we need to insert θ as negative in the above matrix. Therefore, the resulting matrix is

                                        R(-\theta)=\left[\begin{array}{ccc}cos\theta & sin\theta\\-sin\theta&cos\theta\\\end{array}\right]

as sin(-θ) = -sin (θ) and cos(-θ) = cos (θ)

For 45 degrees

sin(45)  = \frac{1}{\sqrt{2} }   and   cos(45)  = \frac{1}{\sqrt{2} }

                                       R(-45)=\left[\begin{array}{ccc}\frac{1}{\sqrt{2} }  & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]

Step 2: Reflection through line y = x

This type of reflection maps (x,y)→(y,x)

Therefore the general matrix is

                                           R(x,y)=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]

Step 3: General Transformation Matrix

T = R(x,y) R(-θ)

                                    T=\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }  & \frac{1}{\sqrt{2} }\\-\frac{1}{\sqrt{2} }&\frac{1}{\sqrt{2} }\\\end{array}\right]

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