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NemiM [27]
3 years ago
5

HELP ASAP I WILL MARK BRAINLIEST please help on the last two

Mathematics
1 answer:
spin [16.1K]3 years ago
5 0

Answer:

the C one is 18in and the E one is 12in

Step-by-step explanation:

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Solve the exponential equation use a calculator to obtain a decimal approximation correct to two decimal place for the solution.
svetlana [45]
6^(8x) = 4
log 6^(8x) = log 4
8x log 6 = log 4
x = log 4 / 8log 6 = 0.10 to two decimal places.
3 0
3 years ago
Find the value of a if the line joining the points (3a,4) and (a,-3) has a gradient of 1
Otrada [13]

Recall that the slope or gradient of a line segment through two points is the ratio of the change in the <em>y</em> coordinate to the change in the <em>x</em> coordinate.

If the gradient is 1, then

1 = (-3 - 4) / (<em>a</em> - 3<em>a</em>)

Solve for <em>a</em> :

1 = -7 / (-2<em>a</em>)

1 = 7/(2<em>a</em>)

2<em>a</em> = 7

<em>a</em> = 7/2

6 0
3 years ago
Solve. if there is more than one solution, separate them with comas. (y-4)(y+7)=0
kogti [31]

Answer:

y= 4

Step-by-step explanation:

(y-4) (y+7)=0

(4-4) (4+7)=0

(0) (11)=0

11*0=0

3 0
2 years ago
Determine which of the indicated column vectors are eigenvectors of the given matrix
gladu [14]
]Eigenvectors are found by the equation (A-\lambda I) \vec{v} = 0$ implying that \det(A-\lambda I) = 0. We then can write:

A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ] 

And:

\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0 

Gives us the characteristic polynomial:

\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6

So, solving for each eigenvector subspace:

\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]

Gives us the system of equations:

4x + 2y = -x \newline 5x + y = - y 

Producing the subspace along the line y = -\frac{5}{2} x

We can see then that 3 is the answer. 



7 0
3 years ago
The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?
borishaifa [10]

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Substitute:

m=\dfrac{3-2}{4-2}=\dfrac{1}{2}

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}

We have the equation:

\dfrac{-3}{x-2}=\dfrac{1}{2}        <em>cross multiply</em>

(1)(x-2)=(-3)(2)

x-2=-6           <em>add 2 to both sides</em>

x=-4

<h3>Answer: x = -4.</h3>
7 0
3 years ago
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