Answer:
x=-52/29
Step-by-step explanation:
-3(42x+46)=-15(-22-9x)
-126x-138=330+135x
-126x-135x-138=330
-261x-138=330
-261x=330+138
-261x=468
x=468/-261
x=-52/29
Answer: " m∠ACD = 40° " .
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Explanation:
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We are asked to find: "m∠ACD" ;
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Note: m∠ACD = m∠ABD ;
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So, given:
m∠ACD = (4x + 4)° ;
m∠ABD = <span>(6x - 14)° ;
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4x + 4 = 6x - 14 ;
Solve for "x" ; then solve for: "m</span>∠ACD" ;
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Add "14" to each side of the equation; and subtract "4x" from each side of the equation ;
4x + 4 + 14 - 4x = 6x - 14 + 14 - 4x ;
to get:
18 = 2x ;
↔ 2x = 18 ;
Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" ;
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2x / 2 = 18/2 ;
x = 9 .
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Now, to solve for: " m<span>∠ACD " :
</span>_________________________________________________________
m∠ACD = <span>(4x + 4)° ;
Substitute "9" for "x" ;
</span>
m∠ACD = (4*9) + 4 = 36 + 4 = 40° .
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Answer: " m∠ACD = 40° " .
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Let us check our answer:
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m∠ACD = 40 ; and m<span>∠ABD = (6x - 14) ;
</span>m∠ACD = ∠ABD ;
<span>
Since </span>m∠ABD = (6x - 14) ;
If x = 9; if we plug in "9" into the expression for "m∠ABD" ; will the value obtained be "40" ??
m∠ABD = (6x - 14) ; Let us plug in "9" for "x" ; to see if the value obtained is "40"
6x - 14 = ? (6*9) - 14 ??
6x - 14 = ? 54 - 14 ??
6x - 14 = ? 40 ?? Yes!
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Answer: Third
Step-by-step explanation:
We know that the HL theorem says that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of any other right triangle then the triangles are said to be congruent.
Among all the pairs of triangles in the picture , only first and third pair are right triangle.
The first pair of triangles can not be proven congruent by the HL theorem because it does not have one congruent legs.
The third pair of triangles can be proven congruent by the HL theorem as they have both hypotenuse and one leg congruent.
Hence, the third pair of triangles can be proven congruent by the HL theorem
The correct answer would be +13 since 90 is positive and the greatest number
