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2 years ago

5

Which expression is equivalent to |8| + |-7|?

2 answers:

mrs_skeptik [129]2 years ago

8 0

The answer is 15

explained: since the absolute value of 8 is 8 and the absolute value of -7 is 7, that means the expression is now 8+7 which gives you 15

enot [183]2 years ago

4 0

Answer: The answer would be 15

Step-by-step explanation:

Hope this helps.

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Solve the system using the elimination method.

spayn [35]

Answer:

(x, y, z) = (-22/13, 29/13, 6/13)

Step-by-step explanation:

Adding the first and second equations, we get ...

(3x +2y -3z) +(7x -2y +5z) = (-2) +(-14)

10x +2z = -16 . . . . collect terms

5x + z = -8 . . . . . . divide by 2 . . . [eq4]

Adding twice the second equation to the third, we get ...

2(7x -2y +5z) +(2x +4y +z) = 2(-14) +(6)

16x +11z = -22 . . . . . . [eq5]

Now, we have two equations with the variable y eliminated. We can subtract [eq5] from 11 times [eq4] to eliminate z:

11(5x +z) -(16x +11z) = 11(-8) -(-22)

39x = -66

x = -66/39 = -22/13

From [eq4], we can find z as ...

z = -8 -5x = -8 -5(-22/13) = 6/13

And from the second equation, we get ...

y = (1/2)(7x +5z +14) = (1/2)(7(-22/13) +5(6/13) +14) = 29/13

The solution is (x, y, z) = (-22/13, 29/13, 6/13).

6 0

3 years ago

Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

<em><u>Solution:</u></em>

<em><u>The slope intercept form is given as:</u></em>

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

8 0

3 years ago

A plane flying overhead at night is located by two

Gemiola [76]

Answer:

Step-by-step explanation:

B

2

3

Let the distance of two consecutive stones are x, x+1.

In ΔBCD, we have

tan60

o

=

x

h

⇒x=

3

h

.....(i)

In ΔABC, we have

tan30

o

=

x+1

h

⇒

3

1

=

x+1

h

⇒

3

h

+1=

3

h ......[from equation (i)]

⇒

3

2h

=1

⇒h=

2

3

km

solution

6 0

3 years ago

A man earned x pesos in 10 days and spent y pesos during each of those days. Write an expression to determine how many pesos he

Vsevolod [243]

Answer: $\dfrac{x}{10}-y$

Step-by-step explanation:

Given : A man earned x pesos in 10 days and spent y pesos during each of those days.

i.e. Total earning in 10 days = x

Earning per day = $\dfrac{x}{10}$ [By unitary method] (1)

Money spent per day =y (2)

We know that

$\text{Savings = Money earned - Money spent}$

i.e. Subtract (2) from (1), we get

$\text{Savings = }\dfrac{x}{10}-y$

Hence, the expression to determine how many pesos he saved per day will be:-

$\dfrac{x}{10}-y$

3 0

3 years ago

100^a x 1000^b can be written in the form 10^w <br><br> Show that w = 2a + 3b

Elena L [17]

$100^a \time 1000^b = 10^{2a} \times 10^{3b} = 10^{2a + 3b}$

$10^{w} = 10^{2a + 3b}$

$w = 2a + 3b \text { (shown)}$

3 0

3 years ago