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3 years ago

What consecutive numbers have a sum of 133?

1 answer:

4 0

Two consecutive integers mean numbers like 2, 3 or -3, -2. Let x represent the first number. the next consecutive number will be x + 1. The equation becomes: x + (x + 1) = 133. Solve for x: x + (x + 1) = 133 x + x + 1 = 133 2x + 1 = 133 Subtract 1 from both sides: 2x = 132 Divide both sides by 2: x = 66 x + 1 = 67. Solution: The two consecutive numbers adding up to 133 are 66 and 67.

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At Maddison high school each student studies one foreign language is 3/5 take Spanish and one-fourth of the remaining take germa

Snezhnost [94]

Answer:

Step-by-step explanation:

3/5 = 0.6

1 - 0.6 = 0.4 students left

Multiply the amount of students remaining by the fractional amount that take German

0.4 x 1/4 = 0.1

1 - 0.6 - 0.1 = 0.3

0.3 x 100 = 30%

Therefore 30% of students take French

7 0

2 years ago

Write the equation of the line perpendicular to

r-ruslan [8.4K]

Solving for y, we add 5y to both sides and subtract 4, getting 9x-4=5y. Dividing both sides by 5, we get 9x/5-4/5=y. Since the slope is 9/5 (since 9/5*x=9x/5), we multiply it by -1 and find the reciprocal of it to get -5/9 as the perpendicular slope, so -5x/9+b=y. Plugging 1 in for x and -6 in for y, we get -5*1/9+b=-6 and by adding 5/9 to both sides we get -5-4/9=b , and since in y=mx+b y and x are variables, we end up with y=-5x/9+(-5-4/9) for slope intercept form.

To get it into standard form, we need it in ay+cx=b with a, b, and c being constants. Adding 5x/9 to both sides, we end up with y+5x/9=(-5-4/9) for standard form

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3 years ago

A concert sold general admission tickets for $47.50 and lower-level seating for $97.50. The 995 tickets sold took in $68,762.50.

BabaBlast [244]

Answer: 565 general admission and 430 lower-level seating tickets sold (Answer (D))

Steps:

Let x be the number of general admission tickets, and y be the number of lower level tickets.

Set up the two equations:

68762.5 = x * 47.50 + y * 97.50 (total price as a sum of individual volumes)

x + y = 995 (sum of individual count = total count of tickets sold)

solve for x, y:

x = 995 - y

plug into the first equation:

68762.5 = (995-y) * 47.50 + y * 97.50

solve for y:

y = 430

then x = 565

x = 565 and y = 430

8 0

3 years ago

Read 2 more answers

A cone has a volume of 5 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

DENIUS [597]

The answer is 15 in³.

The volume of the cone is:
$V_1= \pi r_1 ^{2} \frac{h_1}{3} = \frac{ \pi r_1^{2} h_1}{3}$
where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone

The volume of the cylinder is:
$V_2= \pi r_2h_2^{2}$
where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone

Since <span>the cone fits exactly inside of the cylinder, they have the same radius and the height:
r</span>₁ = r₂
h₁ = h₂

Also:
V₁ = 5

Now, let's write two volume formulas together:
$V_1= \frac{ \pi r^{2} h}{3}$
<span> $V_2= \pi rh^{2}$ </span>

We can include V₂ into V₁:
$V_1= \frac{V_2}{3}$

⇒ $V_2=3*V_1$
$V_2=3*5 in^{3}$
$V_2=15 in^{3}$

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3 years ago

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

vagabundo [1.1K]

Considering the vertex of the parabola, the correct statement is given by:

The range of the function is all real numbers less than or equal to 9.

<h3>What is the vertex of a quadratic equation?</h3>

A quadratic equation is modeled by:

$y = ax^2 + bx + c$