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3 years ago

Help me with this question below

Mathematics

1 answer:

lutik1710 [3]3 years ago

3 0

See attached picture for steps and answer:

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For what value(s) of k is the linear system consistent? (Enter your answers as a comma-separated list.)

AleksAgata [21]

Answer:

Step-by-step explanation:

Given

$6x_1-9x_2=8$

$9x_1+kx_2=-1$

The given system is $AX=B$ can be represented by

$\begin{bmatrix}6 &-9 \\ 9 & k\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}8\\ -1\end{bmatrix}$

The given system is consistent when determinant of A is not equal to zero

$|A|$

$|A|=6k-(-81)=6k+81$

$k\neq \frac{-27}{2}$

i.e. system is consistent for all value of k except $k=\frac{-27}{2}$

$R-\frac{-27}{2}$

4 0

4 years ago

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If x + 2 is a factor of x^2 +mx + 14 find m

jolli1 [7]

X² + mx + 14

If (x+2) one of the factors, we can write

14 = 2*7
m = 2+7= 9

x² +9x + 14 = (x+2)(x+7)

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4 years ago

If one bag of grass seed will cover 225 square feet, what is the minimum number of bags the haney family will need to cover thei

Veronika [31]

Answer:

9 bags

Step-by-step explanation:

First we will need to calculate the area of their entire backyard, which has a shape of trapezium.

So the formula for the area of a trapezium is $A=\frac{(a+b)*h}{2}$

a and b are the lenghts of the parallel sides and h is the height.

From the picture $a=10*5=50\\b=9*5=45\\h=8*5=40$

Then we plug into our formula

$A=\frac{(a+b)*h}{2} =\frac{(50+45)*40}{2} = 1200$ square feet

To get the number of bags required we just simply divide the aree of their entire yard by the space that 1 bag covers. We get:

$\frac{1900}{225} =8.444...$ bags

This is more than 8 bags so they will need 9 bags to cover their entire yard.

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3 years ago

Wym has a packet of 50 biscuits she gives half of them to her friend and then eats 8 how many are left

Zanzabum

Answer:

17 biscuits

Step-by-step explanation:

Since she starts with 50 and gives away half which is 25, that will leave her with 25 biscuits herself. If she then eats 8 of them, that will leave her with 17 since 25-8=17.

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2 years ago

What is the measure of Angle D F E? Triangle D E F. The exterior angle to angle F is 142 degrees. 38 degrees 52 degrees 118 degr

Eduardwww [97]

as the exterior angle is known

sum of that angle and f angle = 180

142 + f = 180

f = 180 - 142

f = 38

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3 years ago

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