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mr_godi [17]
3 years ago
6

Solve each system using substitution or elimination. Show all required work. Y=-5x^2+2x-3 Y=-3x-3

Mathematics
1 answer:
zubka84 [21]3 years ago
8 0

Step-by-step explanation:

y = -5x² + 2x - 3 and y = -3x - 3.

=> -5x² + 2x - 3 = -3x - 3

=> 5x² - 5x = 0

=> 5x(x - 1) = 0

=> x = 0 or x = 1.

When x = 0, y = -3(0) - 3 = -3.

When x = 1, y = -3(1) - 3 = -6.

The solutions are (0,-3) and (1,-6).

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O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°
andriy [413]

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  

4 0
3 years ago
I GIVEEEE BRAINLILSTT
Zigmanuir [339]
Alr bet x + 8 y - 9 :)
6 0
3 years ago
Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).
weeeeeb [17]

Answer:

\[y = (-1/2) * x + 6\]

Step-by-step explanation:

Equation of the given line: y=2x+2

Hence the slope of the line is given by 2

Any line which is perpendicular to the given line will have a slope m such that m*2 = -1

Or, \[m = \frac{-1}{2}\]

Only options 2 and 3 satisfy this condition.

The line is also supposed to pass through the point (6,3).

Substituting these values in the option 2:

\[3 = (-1/2) * 6 + 3\]

Or, \[ 3 =0 \] which is false . Hence option 2 is not valid.

Now substituting (6,3) in option 3:

\[3 = (-1/2) * 6 + 6\]

Or, \[ 3 =3 \] which is true . Hence option 3 is the required equation of the line.

5 0
3 years ago
The after school craft center has 15 boxes of 64 crayons each. In 12 of the boxes , 28 of the crayons have not been used. All th
Korolek [52]

The <em><u>correct answer</u></em> is:

624 crayons.

Explanation:

In 12 of the boxes, 28 crayons have not been used; this leaves 64-28=36 crayons that have been used. 12(36) = 432 crayons have been used in these boxes.

3 full boxes have been used; this is 3(64) = 192 crayons.

Together this makes 432+192 = 624 crayons that have been used.

5 0
3 years ago
Read 2 more answers
It is recommended that people have 1 g of calcium each day how many milligrams of calcium is that
ArbitrLikvidat [17]
There is 1000 milligrams in 1 gram
4 0
3 years ago
Read 2 more answers
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