2p+6a=$14
3p+9a=$21
3p+9a=21
Subtract 9a
3p=21-9a
divide all by 3
p=7-3a
plug it into start equations
2p+6a=14
2(7-3a)+6a=14
14-6a....+6a=14
this zeroes out...
Answer:
Step-by-step explanation:
Time taken to eat the pizza in seconds =28×60=1680 seconds
If it takes 20seconds to lift, bite and chew,
Then the total bites taken to finish the pizza =1680/20 =84 bites
If for each bite 9cm² disappeared, then area that disappeared for 84bites =84×9cm² = 756cm²
Total area of pizza =756cm²
If area =(πd²)/4,
Then d² =(4×A)/π
d²=4×756/3.14=963.06
d=√963.06 = 31.03cm
1 centimeter=0.394inches
31.03cm= 0.394×31.03=12.23 inches ≈ 12inches(to the nearest inch)
The diameter of the pizza is 12inches
Answer
a. 28˚
b. 76˚
c. 104˚
d. 56˚
Step-by-step explanation
Given,
∠BCE=28° ∠ACD=31° & line AB=AC .
According To the Question,
- a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°
- b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚
thus , ∠ABC=76° .
- c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,
Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°
Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)
∠DAB = 180° - 107° ⇔ 73°
& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°
Now, In Triangle ADC Sum of angles in a triangle is 180°
∠ADC = 180° - (31° + 45°) ⇔ 104˚
- d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre
For Diagram, Please Find in Attachment
Answer:
x = - 5, x = - 3
Step-by-step explanation:
Given
x² + 15 = - 8x ( add 8x to both sides )
x² + 8x + 15 = 0 ← in standard form
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are 5 and 3, since
5 × 3 = 15 and 5 + 3= 8, thus
(x + 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 3 = 0 ⇒ x = - 3
Answer:
1/2
Step-by-step explanation:
.5=1/2