in a school ,there are 150 students .out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for physics class . The students enrolled for English cannot attend any other class , but the students of mathematics and physics can take two course at times. find the number of students who have taken both physics and mathematics.

40

Step-by-step explanation:

First we need to subtract the 50 students enrolled in English class.

150 - 50 = 100

Next, let's add the mathematics students and the physics students.

80 + 60 = 140

Then we subtract the total amount of mathematics and physics students by the total number of students.

140 - 100 = 40

Therefore, there are 40 students who take both mathematics and physics.

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)