The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
1 0 -1 -3
0 1 5
00 1
a.
X=-3
y--9
z-1
b. x-2
y=-9
N
I
T
C. X=-2
y--9
2-1
d. x-3
y=-9
2-1

Answer:

The probability that a student earns a grade of A is 1/7.

Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:

P(E) = n(E) / n(S)

As the total number of students = n(S) = 35

Students getting the grade A = n(E) = 5

So, the probability that a student earns a grade of A:

                     P(E) = n(E) / n(S)

                             = 5/35

                             = 1/7

Hence, the probability that a student earns a grade of A is 1/7.

Keywords: probability, sample space, event

Answer:

Slope =  - 1

Step-by-step explanation:

The equation is in form [tex]y=mx+c[/tex], [tex]m[/tex] s the slope and [tex]c[/tex]  is the intercept on [tex]y[/tex] axis.

Hence, in [tex]y=-x+3[/tex] , slope is -1  and intercept on [tex]y[/tex] axis is 3.

Answer: f(-2) = 8

Step-by-step explanation: On the graph there’s a point (-2,8), so f(-2), which just means -2’s y value on the graph, is 8.

Answer:

-12x²-25x+13

Step-by-step explanation:

First open parenthesis.

(3 − 13x − 7x²) − (5x² + 12x − 10)

3 − 13x − 7x² − 5x² - 12x + 10

Now combine like terms.

3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²

Now put into standard form, exponents greatest to least.

-12x²-25x+13

Hope this helps!

If not, I am sorry.

Answer:-12x²-25x+13

Step-by-step explanation:

Answer:

(i) x-intercepts: (2, 0), (6, 0)

(ii) vertex : (4, -4)

Explanation:

y = x² - 8x + 12

To find x intercepts, [set y = 0]

x-intercepts: (2, 0), (6, 0)

To find vertex:

x = -b/2a

  = -(-8)/2(1)

  = 4

y = x² - 8x + 12

  = 4² - 8(4) + 12

  = -4

Vertex : (4, -4)

Solve the equation for y=0

X inetercepts (2,0) and (6,0)

Vertex :-

x coordinate

Y coordinate

Verted at (4,-4)

Answer:

x=3.5

Step-by-step explanation:

x × 2 = 7

   ÷2     ÷2

    x=3.5

The figure is given in the below diagram.

The steps of constructing a square inside a circle are as follows:

Start from the middle O of the provided circle.

Finding the center of a circle's approach can be used to create the center of the circle's center point is not known.

1. Draw a circle and label point A. This will turn into one of the square's vertices.

2. Create point C by drawing a diameter line from point A through the center and back out to the outside of the circle.

3. Set the width of the compass to a little bit more than the distance to O.

4. Sketch an arc above and under O.

5. Repeat by moving the compass to C.

6. To create the new points B and D, draw a line across the intersection of the arc pairs that is long enough to touch the circle at both the top and bottom.

This diameter is perpendicular to the first AC.

7. Draw a line connecting each pair of points A, B, C, and D.

Done. The circle is circled by the square ABCD.

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The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.

An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.

Let the age of Kwaku is x

Let the age of Esi is y

From the given data

The age of Kojo is 2y

y = x +5

Sum of their age = 47

2y = 2x +10

therefore the equation formed is

x + y +2y = 47

x + x+5 + 2x +10 = 47

4x +15 = 47

4x = 32

x = 8

y = 13

2y = 26

Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.

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Answer:

Draw a line from one point A to B into the XY line in a angle

Draw a line parallel to the lines

Point a dot in the middle and name it O

Step-by-step explanation:

Hope it helps

Answer:

Distance between A and C = 16km

Bearing of A from C = 257°

Step-by-step explanation:

please see photo for detailed analysis

Answer:

B and D

Step-by-step explanation:

First take the equation and subtract 19 on both sides. You get x^2+8x-20=0

using the quadratic formula you get x= (-8 + or - root (8^2 -4(1)(-20)))/ 2(1)

simplify it and you get x= (-8 +or- 12) / 2  

Separate the equation into two and you get (-8 + 12) / 2    and (-8 - 12) / 2

first one gives: 4/2=2

second gives -20/2=-10

answer x=-10,2

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

A polynomial is a mathematical expression consisting of variables , constants and mathematical operators.

The standard form of a polynomial is

[tex]\rm a_1x^n +a_2x^{n-1}+............+a_0[/tex]

The only equation that is in its standard form or in other words

The only equation that is written in descending order is

2x³+4x²-7x+5 , Option D is the correct answer.

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Answer:

There are 8 possible answers for the value of m

Step-by-step explanation:

3025 (55^2), 3136 (56^2), 3249 (57^2)...., 3844(62^2)

The square of the numbers 55-62 could be a solution set for m.

Answer: x

Step-by-step explanation:

    For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.

Answer:

the cost price is Rs. 4500 and the sale price is Rs. 5040.

Step-by-step explanation:

Let the cost price of the compute be Rs. x.

The profit earned is, Rs. 540.

The profit percentage is, 12%.

The formula to compute profit is:

Profit = SP - CP

\begin{gathered}540=x[1+\frac{12}{100}]-x\\540=1.12x-x\\540=0.12x\\x=\frac{540}{0.12}\\x=4500\end{gathered}540=x[1+10012]−x540=1.12x−x540=0.12xx=0.12540x=4500

Compute the selling price as follows:

SP = CP + profit

     = 4500 + 540

     = 5040

Thus, the cost price is Rs. 4500 and the sale price is Rs. 5040.

Answer:

D. 0 < x < 20

Explanation:

Domain is in the x axis, Range lies in the y axis.

Here it is seen that function's domain lies between 0 to 20.

Here, as the circle's are open. Domain: 0 < x < 20

Additionally,

Considering the given histogram, the mean of the data-set is closest to:

B. 5.

An histogram is a graph that shows the number of times each element of x was observed.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

Hence, considering the histogram, the mean is given by:

M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.

Which is closest to 5, hence option B is correct.

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Answer:

The dog is 16 years old.

Step-by-step explanation:

X/4 + 6 = X/8 + 8

X/4-X/8 = 8-6

0.125X = 2

X = 2/0.125

X = 16

Answer:

16 years old

Step-by-step explanation

Dividing the dog’s age by 4 and adding 6

D÷4  + 6

dividing the dog’s age by 8 and adding 8

D÷8  + 8

equating both

D÷4  + 6 = D÷8 + 8

=> D÷4 - D÷8  = 2

multiplying by 8 both sides

=> 2D - D = 16

=> D = 16

hence, the dog is 16 years old

Answer:

The ratio of sides of triangle = 13:14:15

perimeter = 84 CM

perimeter of a triangle = Sum of all sides

let the sides of a triangle be 13x, 14x and 15x

84 = 13x + 14x + 15x

84 = 42x

x = 2

13x = 13* 2 = 26 CM

14x = 14*2 = 28 CM

15x = 15*2 = 30 CM

Answer:

3) r = 1.5

7) y = 18

11) x = -10

Step-by-step explanation:

3) Isolate the variable by dividing each side by factors that don't contain the variable.

7) Solve for y by simplifying both sides of the equation, then isolating the variable.

11) Move all terms that don't contain x to the right side and solve.

Answer:

d=8t

Step-by-step explanation:

Step-by-step explanation:

[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]

Hope it helps

Z – 6 < 3

Z < 3 + 6

Z < 9

(i) The area of the cross section ABCDEFG is 1771.6cm³

(ii) The volume of the concrete lab is 212592 cm³

(iii) the total surface area of the concrete slab is 30284 cm²

(iv) The mass of the concrete slab is 40746.8 kg/m³.

Given, dimensions are 120 cm by 60 cm by

40 cm.

(i) area of cross section = 40 × 60 ₋ π(60 ₋10 ₋ 10)/2 . 1/2

                                     = 1771.6 cm³

(ii) the volume of the concrete slab = 40 × 60 × 120 ₋ 1/2 π((60 ₋ 10   ₋10)/2)² . 120

= 212592 cm³

(iii) The total surface area is:

=40 × 120 × 2 ₊ 60 × 120 ₊ 1771.6 × 2 ₊ 10 × 120 × 2 ₊ 1/2 π(60 ₋ 10 ₋10) × 120

= 30284 cm²

(iv) Mass of the concrete slab given density is 2300 kg/m³

Mass = Volume × density

Mass = 17.716 m³ ×  2300

         = 40746.8 kg/m³

Hence we get the mass as 40746.8 kg/m³.

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I assume you meant r(x) = |x-2| -1.

Answer:

All answers are correct.

Step-by-step explanation:

A. 1.84 is between 1.74 and 1.84.

B. 1.84 < 1.85. Lower values go to the left.

C. 1.84 > 1.83. Higher values go to the right.

D. 1.84 is between 1.0 and 2.0.

Answer: (2,9)

Step-by-step explanation:

It lies in the region that is shaded both red and blue (representing the fact that it satisfies both inequalities).

Answer:

x > 9

Step-by-step explanation:

for this inequality, we want to isolate x, so that we know the inequality of x

5x + 3 > 48

     - 3      -3        {subtract 3 from both sides to get x alone}

5x > 45

/5      /5                {divide both sides by 5 to find 1x}

x > 9

So , x > 9 is the inequality in terms of x {is the solution}

hope this helps! :)

Answer:

[tex]\huge\boxed{\sf x > 9}[/tex]

Step-by-step explanation:

5x + 3 > 48

Subtract 3 to both sides

5x > 48 - 3

5x > 45

Divide 5 to both sides

x > 9

[tex]\rule[225]{225}{2}[/tex]