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notsponge [240]
3 years ago
9

Please answer quickly, more might be coming soon. 50 Points!

Mathematics
1 answer:
Brut [27]3 years ago
5 0

Answer:

2) ∠SDH and ∠SDT are right angles because SD ⊥ HT.

3) \bar{SH}\cong \bar{ST} as it is given in the question.

4) \bar{SD}\cong \bar{SD}  is the reflexive property.

5) ΔSHD ≅ ΔSTD by RHS congruency.

Step-by-step explanation:

Given in the question:

\bar{SH}\cong \bar{ST}\\\bar{SD}\perp \bar{HT}

In ΔSHD and ΔSTD

\bar{SH}\cong \bar{ST}   (Given)

\angle SDH\cong \angle SDT=90^o    (SD ⊥ HT)

\bar{SD}\cong \bar{SD} (Common)

Therefore, \Delta SHD\cong \Delta STD   (By RHS rule)

Reflexive property of congruency is defined as the property in which something is equal to itself. Hence, the reflexive property of these two triangles is \bar{SD}\cong \bar{SD}

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the axis of symmetry for the graph of the function is f(x) = 1/4x2 bx 10 is x = 6. what is the value of b?
Lady bird [3.3K]

we have

f(x)=\frac{1}{4} x^{2} +bx+10

This is a vertical parabola open upward

The axis of symmetry is equal to the x-coordinate of the vertex

The vertex is the point (h,k)

the equation of the axis of symmetry is x=h

In this problem

x=6

so the x-coordinate of the vertex is h=6

<u>Convert the quadratic equation in vertex form</u>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-10=\frac{1}{4} x^{2} +bx

Factor the leading coefficient

f(x)-10=\frac{1}{4}(x^{2} +4bx)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)-10+b^{2}=\frac{1}{4}(x^{2} +4bx+4b^{2})

Rewrite as perfect squares

f(x)+(b^{2}-10)=\frac{1}{4}(x+2b)^{2}

f(x)=\frac{1}{4}(x+2b)^{2}-(b^{2}-10)

remember that

h=6

so

(x+2b)=(x-6)

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substitute in the equation

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f(x)=\frac{1}{4}(x-6)^{2}+1

therefore

<u>the answer is</u>

b=-3


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