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3 years ago

Q3. a. Simplify the following ratios. 360:120:60

Mathematics

1 answer:

Maslowich3 years ago

4 0

Answer:

6：2：1

Step-by-step explanation:

360÷60=6

120÷60=2

60÷60=1

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What is the answer to this equation using the quadratic formula? 3x^2+2x+4x=0

o-na [289]

$~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+4}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(4)}}{2(3)}\implies x=\cfrac{-2\pm \sqrt{4-48}}{6}$

$x=\cfrac{-2\pm \sqrt{-44}}{6}\implies x=\cfrac{-2\pm \sqrt{(-1)(2^2)(11)}}{6}\implies x=\cfrac{-2\pm 2~i\sqrt{11}}{6} \\\\\\ x=\cfrac{2(-1\pm i\sqrt{11})}{6}\implies x=\cfrac{-1\pm i \sqrt{11}}{3}$

mind you that it has two complex roots, or imaginary values.

3 0

2 years ago

(a) Are triangles the congruent? Write the congruency statement.

Maru [420]

Answer:

Part A) Yes , the triangles are congruent

Part B) The side-angle-side (SAS) theorem

Part C) The perimeter of ∆PQR is $17\ ft$

Step-by-step explanation:

Step 1

we know that

The side-angle-side (SAS) theorem, states that: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

so in this problem

Traingle PQR and Triangle STU are congruent by the SAS Theorem

because

m<PQR=m<STU -------> included angle

PQ=TS

QR=TU

Step 2

Find the value of y

we know that

If the triangles are congruent

then

The corresponding sides are equal

$PR=SU$

substitute

$(3y-2)=(y+4)$

$(3y-y)=(2+4)$

$(2y)=(6)$

$y=3\ ft$

$PR=3y-2=3(3)-2=7\ ft$

$SU=y+4=(3)+4=7\ ft$

$PR=SU$

Step 3

Find the perimeter ∆PQR

Remember that

The perimeter of ∆PQR is equal to the perimeter ∆STU

The perimeter is equal to

$P=PQ+QR+PR$

substitute the values

$P=4+6+7=17\ ft$

6 0

3 years ago

Please help with this question thank you see attached image

maw [93]

The area of a triangle can be determined as half the product of two sides multiplied by the sine of the angle between them. In this case,
A = (1/2)(AB)(AC)(sin A) = (1/2)(6)(15)(sin 48) = 33.44 square units.

8 0

3 years ago

What is the value of x? Enter your answer, as a decimal, in the box.

iragen [17]

Answer:

x = 67.50 ft

Step-by-step explanation:

Consider, ΔMAB and ΔMNP,

∠M = ∠M (Common)

Given AB║NP and let MN as transversal,

∠MAB = ∠MNP (alternate angle)

Also, Given AB║NP and let MP as transversal,

∠MBA = ∠MPN (alternate angle)

Therefore, ΔMAB ≅ ΔMNP (By AAA similarity )

Thus, by CPCT,

$\frac{MA}{MN}=\frac{MB}{MP}=\frac{AB}{NP}$

consider first two ratios,

$\frac{MA}{MN}=\frac{MB}{MP}$

Substitute the values, MA = MN - AN = 49.5 ft

$\frac{49.5}{71.5}=\frac{x}{97.5}$

On solving for x , we get, x = 67.50 ft

Thus, value of x is 67.50 ft

3 0

3 years ago

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Sally is analyzing a circle, y2 + x2 = 9, and a linear function g(x). Will they intersect?

Mamont248 [21]

This ones kinda hard I'm not really sure, but looking at the table, when f(x) = 1, g(x) = 1. So therefore it is yes, and Im guessing you know the negative and positive x coordinates/zero thing, so I think you should be correct. Sorry if this is wrong, not too sure, but hopefully it gives you a better idea.

4 0

3 years ago

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