Why are angles opposite each other when two lines cross called vertical angles?

1 answer:

3 0

They are called vertical angles because the definition of vertical is: <span>in a direction, or having an alignment, such that the top is directly above the bottom. The "angles opposite each other when two lines cross" match the definition.</span>

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What is the product of the fractions below?<br> 3/4•7/5

olasank [31]

Answer:

21/20 (1 1/20)

Step-by-step explanation:

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2 years ago

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Finding values or<br> k(x) = x - 2<br> h(x) = x2 +1<br> (h + k)(2) =

Serjik [45]

Answer:

Step-by-step explanation:

$(h+k)(x)=h(x)+k(x)\\\\\bold{METHOD\ 1:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(k+h)(2)=h(2)+k(2)\\\\\text{Calculate}\ h(2)\ \text{and}\ k(2).\\\text{Put}\ x=2\ \text{to the equations of the functions}\\\\h(2)=2^2+1=4+1=5\\k(2)=2-2=0\\\\\text\\\\\text{Substitute:}\\\\(h+k)(2)=5+0=5$

$\bold{METHOD\ 2:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(h+k)(x)=h(x)+k(x)=(x^2+1)+(x-2)=x^2+x-1\\\\(h+k)(2)-\text{put}\ x=2\\\\(h+k)(2)=2^2+2-1=4+2-1=6-1=5$

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3 years ago

You are playing a board game and your playing piece

SCORPION-xisa [38]

2 green spaces, 2 star spaces, 2 question mark spaces

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3 years ago

Solve The Equation <br> 4x×9y=7<br> 4x-9y=9

hoa [83]

Answer:

$\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}$

$4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}$

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3 years ago

Suppose that in a certain county 37% of voters are registered as Democrats, 29% as Republicans, 7% as Green party, and the rest

Fantom [35]

Answer:

$0.66$

Step-by-step explanation:

GIVEN: Suppose that in a certain county $37\%$ of voters are registered as Democrats, $29\%$ as Republicans, $7\%$ as Green party, and the rest are considered Independents. You conduct a poll by calling registered voters in the county at random.