Answer:
12 and 14
Step-by-step explanation:
Let the even integers be x and x+2
three times the larger number is expressed as 3(x+2)
30 more than the smaller one is x + 30
Equating both expressions
3(x+2) = x +30
Find x
3x+6 = x+30
3x-x = 30-6
2x = 24
x = 12
The second integer is 12+2 = 14
Hence the required integers are 12 and 14
Answer:
134
Step-by-step explanation:
let me know if you need an explanation! :D
Those lines stand for the absolute value, or how far away it is from zero.
If you draw a number line from -3 to 3, and plot the points x = 2 and x = -2, what similarities do you see?
Although one is two units to the right of 0 and one is two units to the left of 0, both x = 2 and x = -2 are two units away from zero. Therefore, the absolute value of both 2 and -2 is 2.
Answer: a) BC = 1386.8 ft
b) CD = 565.8 ft
Step-by-step explanation:
Looking at the triangle,
AD = BD + 7600
BD = AD - 7600
Considering triangle BCD, we would apply the the tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan 24 = CD/BD = CD/(AD - 700)
0.445 = CD/(AD - 700)
CD = 0.445(AD - 700)
CD = 0.445AD - 311.5 - - - - - - - -1
Considering triangle ADC,
Tan 16 = CD/AD
CD = ADtan16 = 0.287AD
Substituting CD = 0.287AD into equation 1, it becomes
CD = 0.445AD - 311.5
0.287AD = 0.445AD - 311.5
0.445AD - 0.287AD = 311.5
0.158AD = 311.5
AD = 311.5/0.158
AD = 1971.52
CD = 0.287AD = 0.287 × 1971.52
CD = 565.8 ft
To determine BC, we would apply the Sine trigonometric ratio which is expressed as
Sin θ = opposite side/hypotenuse
Sin 24 = CD/BC
BC = CD/Sin24 = 565.8/0.408
BC = 1386.8 ft
Answer:
x = 5.13 yards to the nearest tenth
Step-by-step explanation:
The diagram is redrawn and labelled in the attached photo.
It is labelled as triangle ABC. Angle A is determined to be 25 degrees. This is because it is alternate to 25 degrees at the top.
To find x, we will apply trigonometric ratio
Tan # =opposite side / adjacent side
Where # = 25 degrees
Opposite side = x
Adjacent side = 11
Tan 25 = x/11
x = 11tan25
x = 11× 0.4663
x = 5.1293 yards
x = 5.13 yards to the nearest tenth.
