Four times the sum of a number and 15 is at least 120 let x represent the number

Mathematics

2 answers:

alexira [117]3 years ago

6 0

Answer:

Step-by-step explanation:

4(x+15)=120

4x+60=120 Subtract 60 and 120

4x=60 then divide

X=15

Dvinal [7]3 years ago

3 0

Answer:

x > 15

Step-by-step explanation:

4(x + 15) > 120

Divide by 4

x + 15 > 30

Subtract 15

x > 15

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Anyone who knows how to do this right please

Elan Coil [88]

Answer:

13. 9.77 inches (rounded to 3 s.f.)

14. 249m² (rounded to 3 s.f.)

Step-by-step explanation:

13. To find the arc length, the formula is the angle of the arc out of 360° multiplied by the circumference of the full circle. Circumference of circle: pi × r × 2

$\frac{80}{360}$ × pi × 7 × 2 = 3 $\frac{1}{9}$ pi

= 9.77 inches (rounded to 3 s.f.)

14. To find the sector area, the formula is the angle of the sector out of 360° multiplied by the area of the full circle. Area of circle: pi × r × r

$\frac{285}{360}$ × pi × 10 × 10 = 79 $\frac{1}{6}$ pi

= 249m² (rounded to 3 s.f.)

5 0

2 years ago

Polygon ABCD is dilated, rotated, and translated to form polygon A′B′C′D′. The endpoints of AB are at (0, -7) and (8, 8), and th

Anton [14]

Rotation and translation are rigid transformations, they don't change figure sizes. Dilation change figure sizes increasing or decreasing them by scale factor.

First, find AB and A'B' by the formula:

$AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}= \sqrt{(8-0)^2+(8-(-7))^2}=\sqrt{8^2+15^2}=\sqrt{64+225}=\sqrt{289}=17,\\ \\A'B'=\sqrt{(x_{B'}-x_{A'})^2+(y_{B'}-y_{A'})^2}= \sqrt{(2-6)^2+(1.5-(-6))^2}=\sqrt{4^2+7.5^2}=\sqrt{16+56.25}=\sqrt{72.25}=8.5.$