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3 years ago

Find the missing length . Leave your answers in simplest radical form

Mathematics

1 answer:

Eddi Din [679]3 years ago

4 0

Use Pythagorean theorem:

$x^2+5^2=(\sqrt{122})^2\\\\x^2+25=122\qquad\text{subtract 25 from both sides}\\\\x^2=97\to x=\sqrt{97}$

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ABC is an isosceles triangle with BA=BC

melomori [17]

Explanation:

1. ∠BAC≅∠BCA, ∠ABD≅∠ADB; Reason: definition of isosceles triangles

2. ∠ABD +∠BAC +∠ADB = 180°; Reason: sum of internal angles is 180°

3. ∠BAC = 180° -2(∠ABD) = 36°; Reason: Subtraction and substitution properties of equality

4. ∠BAC +∠BCA +∠ABC = 180°; Reason: sum of internal angles is 180°

5. ∠BCA = 180° -2(∠BAC) = 108°; Reason: Subtraction and substitution properties of equality

6. ∠ABD +∠DBC = ∠ABC; Reason: Angle sum theorem

7. ∠DBC = ∠ABC -∠ABD = 108° -72° = 36°; Reason: Subtraction and substitution properties of equality

8. ∠BCA = ∠BAC = 36°; Reason: Substitution property of congruence

9. ΔBCD is isosceles; Reason: Base angles DBC and BCA are congruent.

_____

There may be extra steps involved if you separately use subtraction and substitution properties of equality, or if you separately claim congruence of angles and equality of their measures. We have assumed that the definition of "isosceles triangle" includes the fact of equal side lengths <u>and</u> equal base angles.

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3 years ago

Who wan na ta lk? im bo red

olga_2 [115]

Answer:

So this is what hello means :):):):):):):)

Step-by-step explanation:

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2 years ago

1. Describe how transformations can affect a parent function and then describe the transformation of f(x) = -2/x - 7 - 3 from f(

ss7ja [257]

я не знаю что тут написано поэтаму я русский ::3

5 0

3 years ago

Four less than the product of two and a number

Zinaida [17]

Answer:

2x - 4

Step-by-step explanation:

Product means to multiply and four is less than it so you minus it.

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3 years ago

In rectangle WXYZ, A is on side WX such that AX = 4, B is on side YZ such that BY = 18, and C is on side XY such that angle ACB=

Lemur [1.5K]

Answer:2*sqrt(130)

Step-by-step explanation: $From right triangle $AXC$, we have $\angle XAC = 90^\circ - \angle XCA$. We also must have $\angle YCB + \angle ACB + \angle XCA = 180^\circ$, so $\angle YCB = 180^\circ - 90^\circ - \angle XCA = 90^\circ - \angle XCA$, which means $\angle YCB = \angle XAC$. Combining this with $\angle X = \angle Y$, we have $\triangle XCA \sim \triangle YBC$ by AA Similarity, and\[\frac{CX}{AX} = \frac{BY}{CY},\]so\[\frac{CX}{4} = \frac{18}{2CX}.\]\\\\This gives us $2CX^2 = 72$, so $CX^2 =36$ and $CX=6$. \\\\\\\\$ $Therefore, $CY = 12$.Applying the Pythagorean Theorem to right triangles $XCA$ and $CYB$ gives us\begin{align*}CA^2 &= XA^2 + XC^2 = 16 + 36 = 52,\\BC^2 &= CY^2 + BY^2 = 144 + 324 = 468.\end{align*}Applying the Pythagorean Theorem to right triangle $ABC$ gives\[AB = \sqrt{AC^2 + BC^2} = \sqrt{52 + 468} = \sqrt{520} = \boxed{2\sqrt{130}}.\](We can also compute $AB$ by dropping a perpendicular from $A$ to $\overline{YZ}$, which creates a right triangle.)$

3 0

4 years ago