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german
3 years ago
11

Type the correct answer in the box. Use numerals instead of words.

Mathematics
1 answer:
Nitella [24]3 years ago
4 0

Answer:

35cm²

Step-by-step explanation:

Area = trapezium + triangle

Trapezium = ½×(8+4)×2 = 12

Triangle = ½×8×5.75 = 23

Area = 12+23 = 35 cm²

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Hi, can someone please give me a detailed explanation on how to solve this problem?
Dovator [93]

Answer:

Step-by-step explanation:

log3^(2x+3) = log243

(2x+3)log3 = log243

2x+3 = log243/log3

2x = (log243/log3)-3

x = [(log243/log3)-3]/2

x = (5-3)/2

x = 2/2

x = 1

Check:

3^2(1)+3 = 243

3^2+3 = 243

3^5 = 243

3×3×3×3×3 = 243

9×9×3 = 243

81×3 = 243

243 = 243

5 0
3 years ago
In a multiple regression equation, two independent variables are considered, and the sample size is 30. The regression coefficie
MAXImum [283]

Answer:

Both the variables are important for the regression analysis and cannot be deleted.

Step-by-step explanation:

(1)

The hypothesis for for the testing of coefficient β₁ are:

<em>H</em>₀: β₁ = 0 vs. <em>H</em>ₐ: β₁ ≠ 0

The test statistic is:

t=\frac{b_{1}}{S_{b_{1}}} =\frac{2.815}{0.75}= 3.753

It is provided that H₀ is rejected if <em>t</em> > 2.042.

The test statistic value, <em>t</em> = 3.753 > 2.042.

Thus, the null hypothesis is rejected.

<u>Conclusion:</u>

There is a significant relationship between the regression variable and the dependent variable.

(2)

The hypothesis for for the testing of coefficient β₂ are:

<em>H</em>₀: β₂ = 0 vs. <em>H</em>ₐ: β₂ ≠ 0

The test statistic is:

t=\frac{b_{2}}{S_{b_{2}}} =\frac{-1.249}{0.41}= -3.046

It is provided that H₀ is rejected if <em>t</em> < -2.042.

The test statistic value, <em>t</em> = -3.046 < -2.042.

Thus, the null hypothesis is rejected.

<u>Conclusion:</u>

There is a significant relationship between the regression variable and the dependent variable.

Thus, both the variables are important for the regression analysis and cannot be deleted.

7 0
3 years ago
If (6^2)^x equals 1, what is the value of x
ValentinkaMS [17]

Answer:

x = 0

Step-by-step explanation:

If p is a number other than zero, then

p^x=1

only if x=0.

8 0
3 years ago
How many sixths are in 3 and 1 third ??
lorasvet [3.4K]
1 whole thing = 6 sixths
3 whole things = 18 sixths

1 third of a whole thing = 2 sixths of it

3 wholes plus 1 third = 18 sixths plus 2 sixths = 20 sixths
6 0
3 years ago
Read 2 more answers
A 4 meter long ladder leans against a 90 degree wall at a 68 degree angle.
Alenkinab [10]

Answer:

Step-by-step explanation:

We use trig to answer these questions:

sin x = opposite side of a triangle / hypotenuse

cos x = adjacent side / hypotenuse

Construct a right triangle with hypotenuse 4 m and lower angle 68 degrees.

The height of the top of the ladder  is then defined by:

sin 68 degrees = height / 4 m, which yields (4 m)(sin 68) = height =

3.71 m

and the distance of the bottom of the ladder from the wall as follows:

cos 68 degrees = horizontal distance / hypotenuse =

1.50 m

3 0
2 years ago
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