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dexar [7]
3 years ago
6

one negative number is 4.5 more than another number. the sum of the squares of these numbers is 46.25. Find both

Mathematics
1 answer:
evablogger [386]3 years ago
8 0

Answer:

y = -6.5 and x = 2

Step-by-step explanation:

Let one negative number be -y and another number be x

We are given that one negative number is 4.5 more than another number

So, -y=x+4.5

We are also given that The sum of the squares of these numbers is 46.25.

So,x^2+(-y)^2=46.25\\x^2+(x+4.5)^2=46.25\\x^2+x^2+20.25+18x=46.25\\2x^2+18x=26.25\\x^2+9x=13.125\\x^2+9x-13.125=0\\

x=-6.5,2

When x = -6.5

-y=x+4.5

-y=-6.5+4.5

-y=-2

y=2

When x = 2

-y=x+4.5

-y=2+4.5

-y=6.5

y=-6.5

So, y = -6.5 and x = 2

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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
PLEASE HELP!!! PLEASE DONT ANSWER IF U DONT KNOW!
timofeeve [1]

Answer:

x^2 - y^2) - (x^2 -3x +2)

Step-by-step explanation:

3 0
3 years ago
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If JL = 30, JK = 18, and LM = 6, then the value of LN is:
harina [27]

Answer:

LN = 15

Step-by-step explanation:

The arrows on the line segments indicate they are parallel.

\implies \overline{KM} \parallel \overline{JN}

<u>Triangle Proportionality Theorem</u>

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then it divides these two sides <u>proportionally</u>.

\textsf{If }\overline{KM} \parallel \overline{JN}, \textsf{ then }\dfrac{LK}{LJ}=\dfrac{LM}{LN}

Given:

  • LM = 6
  • JL = 30
  • JK = 18

⇒ LK = JL - JK = 30 - 18 = 12

Substituting the values into the equation and solving for LN:

\begin{aligned}\implies \dfrac{LK}{LJ} & = \dfrac{LM}{LN}\\\\\dfrac{12}{30} & = \dfrac{6}{LN}\\\\12LN & = 30 \cdot 6\\\\LN & = \dfrac{180}{12}\\\\LN & = 15\end{aligned}

7 0
2 years ago
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Rewrite the expression with a rational exponent as a radical expression.
telo118 [61]

Answer:

Step-by-step explanation:

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2 years ago
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According to national data, about 15% of American college students earn a graduate degree. Using this estimate, what is the prob
Sergio [31]

Using the binomial probability relation, the probability that exactly 27 graduates earn a college degree is 0.069

<u>Using the relation</u> :

<em>P(x = x) = nCx * p^x * q^(n-x) </em>

  • Probability of success, p = 0.15
  • q = 1 - p = 1 - 0.15 = 0.85
  • Number of trials, n = 200
  • X = 27

<u>Probability of exactly 27 graduates can be defined thus</u> :

P(x = 27) = 200C27 × 0.15^27 × 0.85^173

P(x = 27) = 0.0686264

Therefore, the probability of selecting <em>exactly 27 graduates</em> is 0.069

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