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Bumek [7]
3 years ago
9

If you have 30 spoons, according to the table below, how many forks will you have?

Mathematics
1 answer:
Marysya12 [62]3 years ago
3 0

\bf \begin{array}{|c|ll|} \cline{1-3} Forks&16&\stackrel{\downarrow }{8}\\ Spoons&10&\underset{\uparrow }{30}\\ \cline{1-3} \end{array}

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In this diagram, ABAC – AEDF. If the<br> area of ABAC = 6 in?, what is the<br> area of AEDF?
shepuryov [24]

Answer:

2.7 in²

Step-by-step explanation:

similar triangles have the same angles, and all side lengths (or other distances) of one triangle have the same scaling factor to the side lengths of the other triangle.

so, we know the relation between the 2 baselines is 2/3, as this is the factor to turn the baseline of the large triangle into the baseline of the smaller triangle.

in other words

EF = BC × 2/3

2 = 3 × 2/3

correct

how do we calculate the area of a triangle ?

Area = baseline × height / 2

from BAC we know

Area = 6

baseline = 3

height = ?

6 = 3 × height / 2

12 = 3 × height

height = 4

aha !

now, EDF has a height too that we need to calculate is Area. and this height has the same scaling factor compared to the larger triangle as the side lengths : 2/3

so, for EDF we know

Area = ?

baseline = 2

height = 4 × 2/3 = 8/3

therefore, the area is

Area = (2 × 8/3) / 2 = (16/3) / 2 = 8/3 = 2.66666... ≈ 2.7

the shirt answer would be :

we know from the 2 baselines that the scaling factor for each distance is 2/3.

for the area we need to multiply 2 distances, so that means we have to multiply both by 2/3. and so on the formula for the area we have to use 2/3 × 2/3.

2/3 × 2/3 = 4/9

=>

Area small = Area large × 4/9 = 6 × 4/9 = 24/9 = 8/3 ≈ 2.7

3 0
2 years ago
H^2+14h=-31 Solve by completing the square
matrenka [14]
Since the constant has been moved to the left side, you can move on to the next step which is adding (b/2)² to both sides of the equation.

h² + 14h + (14/2)² = -31 + (14/2)²

Simplify the parenthesis and exponent.

h² + 14h + 7² = -31 + 7²

h² + 14h + 49 = -31 + 49

h² + 14h + 49 = 18

Factor the expression of the left.

(h + 7)(h + 7) = 18

Take the square root of both sides.

√(h + 7)(h + 7) = ± √9 • 2

(h + 7) = ± 3√2

h + 7 = ± 3√2

Subtract 7 from both sides.

You solutions are:

h = -7 + 3√2 → -2.7573 → -2.76

h = -7 - 3√2 → -11.2426 → -11.24
5 0
3 years ago
Read 2 more answers
What Happens to the value of the expression 100 minus X as X increases
Marta_Voda [28]

Step-by-step explanation:

if f (x) = 100 - x;

as x increases, the value of f(x) will decrease

8 0
3 years ago
Read 2 more answers
What is the roots of the quadratic equation? 6x^2+5x-4=0
Rama09 [41]

x = \frac{1}{2} or x = - \frac{4}{3}

consider the factors of the product 6 × - 4 = - 24 which sum to the coefficient of the x- term ( + 5)

the factors are + 8 and - 3 ( split the middle term using these factors

6x² - 3x + 8x - 4 = 0 ( factor by grouping )

3x(2x - 1) + 4(2x - 1 ) ( take out common factor of (2x - 1) )

= (2x - 1)(3x + 4) = 0

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ x = \frac{1}{2}

3x + 4 = 0 ⇒ x = - \frac{4}{3}


4 0
3 years ago
Read 2 more answers
Determine the larger of two consecutive integers whose sum add to 85
Vesnalui [34]
N+(n+1) = 85. 2n+1=85, 2n=84. n=42. So the consecutive integers are 42 and 43, and the larger one is 43.
8 0
3 years ago
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