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2 years ago

Which value of a would make the expression 5 1/3 ÷ 4/a equivalent to a whole number?

Mathematics

1 answer:

nordsb [41]2 years ago

8 0

Answer:

a is any number that is multiples of 3

3, 6, 9, 12, etc...

Step-by-step explanation:

5 1/3 ÷ 4/a

16/3 * a/4

16a/12

$\frac{4}{3} a$

since denominator is 3, a can be any whole number that is a multiple of 3

$\frac{4}{3}(3) = 4$

$\frac{4}{3}(6) = 8$

$\frac{4}{3}(9) = 12$

so on and so on....

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Which products result in a perfect square trinomial? Select three options.

Kazeer [188]

Answer:

Second option: $(xy+x)(xy+x)$

Third option: $(2x-3)(-3+2x)$

Fifth option: $(4y^2+25)(25+4y^2)$

Step-by-step explanation:

By definition, a perfect square trinomial can be obtained by squaring binomials.

Then:

$(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2\\\\(a-b)^2=(a-b)(a-b)=a^2-2ab+b^2$

Knowing this, to obtain a perfect square trinomial, the binomials that you multiply must be equals.

Therefore, the products result in a perfect square trinomial are:

$(xy+x)(xy+x)=(xy+x)^2=(xy)^2+2(xy)(x)+x^2=x^2y^2+2x^2y+x^2$

$(2x-3)(-3+2x)=(2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9$

$(4y^2+25)(25+4y^2)=(4y^2+25)^2=(4y^2)^2+2(4y^2)(25)+25^2=16y^4+200y^2+625$

8 0

2 years ago

Read 2 more answers

Dorothy Wagner is currently selling 80 "I ♥ Calculus" T-shirts per day, but sales are dropping at a rate of 2 per day. She is cu

GrogVix [38]

Answer:

Increasing by $66 per day

Step-by-step explanation:

If sales are dropping at a rate of 2 per day, the sales function is:

$S = -2t +80$

If price is increasing by $1 per day, the daily price function is:

$P=1t+7$

Revenue is given by daily sales multiplied by daily price:

$R = S(t)*P(t) = (-2t+80)*(t+7)\\R(t) = -2t^2+66t+560$

The derivate of the revenue function gives us the daily rate of change in revenue:

$R(t) = -2t^2+66t+560\\R'(t) = -4t+66$

Currently (t=0) her daily revenue is changing by:

$R'(0) = -4*0+66\\R'(0) = \$66$

Her revenue is increasing by $66 per day.

3 0

2 years ago

Write or draw to explain a way to find each sum: 6+7, 8+4, 2+9

storchak [24]

Draw six dots then a plus sign then draw seven dots and the count them and put an equal sign and however many dots. Doe the same with the other numbers

6 0

2 years ago

Read 2 more answers

Select the angle that correctly completes the law of cosines for this triangle. 72 + 252 – 2(7)(25)cos ___ = 242 A. 180° B. 90°

meriva

Answer:

x =76.45 degrees

Step-by-step explanation:

72 + 252 – 2(7)(25)cos _x__=242

combine like terms

324-350cosx = 242

subtract 324 from each side

-350x = -82

divide by -350

cos x = -82/-350

cos x = 82/350

take the arccos of each side

arccos (cos x) = arccos (82/350)

x =76.45 degrees

7 0

2 years ago

What is the equation of a line in slope intercept form that contains the points (-4,3) and (2,-6)

Nataly_w [17]

Answer:

y = (-3/2)x - 3

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given two points, we can calculate the slope by dividing the change in y (or the difference in the y-coordinates) by the change in x (or the difference in the x-coordinates). Our two points are (-4, 3) and (2, -6):

m = (3 - (-6)) / (-4 - 2) = 9 / (-6) = -3/2

So, we can update our equation:

y = (-3/2)x + b

The y-intercept is where the graph crosses the y-axis, or the y-value where x = 0. Let's plug in 3 for y and -4 for x:

3 = (-3/2) * (-4) + b

3 = 6 + b

b = -3

So, our y-intercept is -3.

Our slope-intercept form is thus:

y = (-3/2)x - 3

<em>~ an aesthetics lover</em>

7 0

2 years ago