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3 years ago

Work out the lengths of sides a and b. Give your answers to 1 decimal place.

Mathematics

1 answer:

torisob [31]3 years ago

3 0

Step-by-step explanation:

${a}^{2} = {8}^{2} + {5}^{2} \\ {a }^{2} = 64 + 25 \\ {a}^{2} = 89 \\ a = \sqrt{89} = 9.4 \: cm$

${17}^{2} = {12}^{2} + {b}^{2} \\ {b}^{2} = {17}^{2} - {12}^{2} \\ {b}^{2} = 289 - 144 \\ {b}^{2} = 145 \\ b = 12 \: cm$

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If ΔOPQ is dilated from point Q by a scale factor of 3, which of the following equations is true about segment R prime S prime?

Sergio [31]

Answer:

$\overline {R'S'} = 3 {\overline {RS} }$

Step-by-step explanation:

The scale factor of dilation of triangle ΔOPQ, S.F. = 3

The center of dilation = Point <em>Q</em>

Therefore;

The length of the segment, ${\overline {S'Q'} }$ = 3 × The length of the segment, ${\overline {SQ} }$

Similarly;

The length of the segment, ${\overline {R'Q'} }$ = 3 × The length of the segment, ${\overline {RQ} }$

By Pythagoras theorem, we have;

${\overline {R'Q'} }^2 = {\overline {R'S'} }^2 + {\overline {S'Q'} }^2$

Therefore;

${\overline {R'S'} }^2 = {\overline {R'Q'} }^2 - {\overline {S'Q'} }^2 = \left ({3 \times \overline {RQ} } \right) ^2 - \left (3 \times {\overline {SQ} } \right) ^2 = 9 \times \left (\overline {RQ} } ^2 - {\overline {SQ} } ^2 \right) = 9 \times {\overline {RS} }^2$

$\therefore \sqrt{ {\overline {R'S'} }^2} = \sqrt{ 9 \times {\overline {RS} }^2}= 3 \times {\overline {RS} }$

$\overline {R'S'} = 3 \times {\overline {RS} }$ .

6 0

3 years ago

I need help solving this equation: Solve x^2-4+1=0

Mamont248 [21]

Answer:

X=3/2 or 1.732

Step-by-step explanation:

X^2-4+1=0

Combine like terms

-4 + 1 = -3

X^2-3=0

add 3 to both sides

X^2= 3

X= 3/2

4 0

3 years ago

X² + 3x – 7=0<br> Solve<br> X= or x=

svetoff [14.1K]

Answer:

x = 2

Step-by-step explanation:

X² = 3x - 7 = 0

X² = 3x = 7

(x + 1) (x + 2) = 7

(x + 1) + x = 7 - 2

x + x = 7 - 3

2x = 4

x = 4/2

x = 2

8 0

3 years ago

I need help solving this!

blagie [28]

Answer:

miles hybrid car went = 9.80 gal × 54.1 miles/gal

= 530.18 miles

132km × 0.621 = 81.972 miles

530.18 miles = 9.80 gal

1 mile = 9.80/530.18

= 0.018 gal

81.972 miles = 0.018 × 81.972

= 1.515 gal

1.515 gal × 3.785 = 5.734 litres

3 0

3 years ago

A water tank is box shaped with a square base of side length 5 ft. The tank is fed by a pipe above and drains from its base. In

adell [148]

Answer:

dy/dt = - (1/5) ft/s = - 0.2 ft/s

Step-by-step explanation:

Given

L = 5 ft

Qin = 25 ft³/s

Qout = 30 ft³/s

h = 10 ft

dy/dt = ?

We can apply the relation

ΔQ = Qint - Qout = 25 ft³/s - 30 ft³/s

⇒ ΔQ = - 5 ft³/s

Then we use the formula

Q = v*A

where Q = ΔQ, A = L² is the area of square base and v = dy/dt is the rate of change in the depth of the solution in the tank

⇒ ΔQ = (dy/dt)*L²

⇒ dy/dt = ΔQ/L²

⇒ dy/dt = (- 5 ft³/s)/(5 ft)²

⇒ dy/dt = - (1/5) ft/s = - 0.2 ft/s

6 0

3 years ago