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4 years ago

SURFACE AREA OF RECTANGULAR PRISMS

Mathematics

1 answer:

Sergeeva-Olga [200]4 years ago

7 0

Answer:

Lateral is 196

Step-by-step explanation:

7 cm times 10 cm times 2.8 cm

and for the surface it is length times width

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Using Cramer’s Rule, what is the value of y in the system of linear equations below?

Vadim26 [7]

for the system of equations

$a_1x+b_1y=c_1 \\a_2x+b_2y=c_2$

the three matrices needed to use Cramer's Rule are:

$D=\left[\begin{array}{cc}a_1&b_1\\a_2&b_2\end{array}\right] \\\\D_x=\left[\begin{array}{cc}c_1&b_1\\c_2&b_2\end{array}\right] \\\\D_y=\left[\begin{array}{cc}a_1&c_1\\a_2&c_2\end{array}\right]$ .

To use Cramer's Rule we have to calculate the three determinants listed below of the matrices listed below.

$D=\left[\begin{array}{cc}2&5\\-3&-2\end{array}\right] \\\\D_x=\left[\begin{array}{cc}-13&5\\3&-2\end{array}\right] \\\\D_y=\left[\begin{array}{cc}2&-13\\-3&3\end{array}\right]$ .

The value of the determinants are shown below.

$det(D)=(2)(-2)-(-3)(5)=-4+15=11\\det(D_x)=(-13)(-2)-(3)(5)=26-15=11\\det(D_y)=(2)(3)-(-3)(-13)=6-39=-33\\$

The value of y is $\frac{det(D_y)}{det(D)}=-\frac{33}{11} =-3.$ .

3 0

4 years ago

Solve for a and b. please help.

Pachacha [2.7K]

Answer:

a= 22.5

b= 37.5

Step-by-step explanation:

In △BCD:

Applying Pythagoras' Theorem,

a² +30²= b²

a² +900= b² -----(1)

In △ABC:

Applying Pythagoras' Theorem,

b² +50²= (40 +a)² -----(2)

Substitute (1) into (2):

a² +900 +50²= 40² +2(40)(a) +a² (expand bracket)

a² +900 +2500= 1600 +80a +a²

a² +3400= a² +80a +1600 (simplify)

a² +3400 -a² -80a -1600= 0 (bring everything to 1 side)

-80a +1800= 0

80a= 1800 (+80 on both sides)

a= 1800 ÷80

a= 22.5

Subst. a= 22.5 into (1):

22.5² +900= b²

b²= 506.25 +900

b²= 1406.25

b= √1406.25 (square root both sides)

b= 37.5 (reject negative value since b is a length)

☆(a +b)²= a² +2ab +b²

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3 years ago

Classify What type of number is the square root of 2

Amanda [17]

Answer:

The square root of 2, or the (1/2)th power of 2, written in mathematics as √2 or 21⁄2, is the positive algebraic number that, when multiplied by itself, equals the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property

Step-by-step explanation:

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4 years ago

If you know the rate of a water leak in gallons per hour, how can you find the number of hours it takes for 1 gallon to leak out

marusya05 [52]

You could make a small (easily repaired) leak and watch it for the amount of time you need to conclude what you need to.

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3 years ago

In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that

sveta [45]

Answer:

Step-by-step explanation:

$30 is your startup fee. You automatically pay that to join. When is is also $4 per month, you pay that much times however many months there are.

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3 years ago