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tekilochka [14]

3 years ago

13

The value of the expression StartFraction 2 x squared Over x EndFraction plus x (100 minus 15 x) when x = 5 is

1 answer:

Digiron [165]3 years ago

3 0

Answer:

135.

Step-by-step explanation:

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In May, Jim's lunch account has a balance of $58.19. If lunch costs 2.74 per day, how many days will Jim be able to buy lunch be

velikii [3]

He will be able to buy lunch for 21 days because 58.19 divided by 2.74 is 21. 237226

5 0

3 years ago

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

3 years ago

Polygons EFGH and E'F'G'H' are shown on the following coordinate grid:

vlabodo [156]

This would be modeled by a translation 1 unit down and a 270° clockwise rotation.

Each of these points has the x and y values switched, with the y value one less than that of the preimage and negated. Taking one off the y-value is a translation 1 down; negating the y and switching it and x is a 270° clockwise rotation.

5 0

3 years ago

Write an equation of each line with the given slope and y-intercept. slope =1/2 ; y-intercept = 0

CaHeK987 [17]

Answer:

y=1/2x

Step-by-step explanation:

Equations of lines are written in slope-intercept form:

y=mx+b

where m is the slope and b is the y intercept.

The slope is 1/2 and the y-intercept is 0. Therefore, we can substitute 1/2 for m and 0 for b.

y=1/2x+0

Adding 0 onto the end doesn't change the equation and doesn't serve a purpose, so it can be removed from the end of the equation.

y=1/2x

The equation is: y=1/2x

4 0

3 years ago

My friend recently proved 0=1 and i know something is wrong but i dont know what

konstantin123 [22]

Step-by-step explanation:

Remember when expanding radicals,

$\sqrt{ab} = \sqrt{a} \times \sqrt{b}$

When expanding radicals into two radicals, we don't let our radicand have two negative answers.

$i = \sqrt{ - 1}$

${i}^{2} = - 1$

We don't do this

$(\sqrt{ - 1} ) {}^{2} = \sqrt{ - 1 \times - 1}$

$- 1 = \sqrt{1}$

$- 1 = 1$

5 0

2 years ago

Read 2 more answers