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vredina [299]
3 years ago
15

What is the solution of the ineuality 1/2x+1/4 > 3/2x+3/4 ?

Mathematics
1 answer:
Tpy6a [65]3 years ago
5 0

Answer:

x < - \frac{1}{2}

Step-by-step explanation:

Given

\frac{1}{2} x + \frac{1}{4} > \frac{3}{2} x + \frac{3}{4}

The lowest common multiple of 2 and 4 is 4

Multiply through by 4 to clear the fractions

2x + 1 > 6x + 3 ( subtract 2x from both sides )

1 > 4x + 3 ( subtract 3 from both sides )

- 2 > 4x ( divide both sides by 4 )

- \frac{2}{4} > x

- \frac{1}{2} > x , thus

x < - \frac{1}{2}

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Which is the first step in simplifying 4(3x-2)+6x(2-1)
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Answer:

The first step in simplifying this expression is to evaluate the terms within the parenthesis - starting with the multiplication and following the rules for operations in math.

8 0
3 years ago
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Kelsey, a marine biologist, has determined that the population (y) of Blue Whales off the coast of Antarctica varies with time,
Marrrta [24]

Answer: The answer is (A) [0,100].


Step-by-step explanation:  Given in the question that a marine biologist Kelsey determined that the population of Blue Whales off the coast of Antarctica varies with time as shown in the given graph.

The population of Blue Whales (y) is plotted on the Y-axis and the time in months (x) is plotted on the X-axis.

We need to find the range of the population of Blue Whales off the coast of Antarctica from 0 to 10 months.

We can see from the attached graph that

when x = 0, then y = 0,

when x = 10, then y = 100.

That is, when time varies between 0 to 10 months, then the population of Blue Whales varies between 0 and 100.

Thus, the correct option is (A) [0,100].

7 0
4 years ago
What are the major goals of America's foreign policy?
mafiozo [28]

Answer:

The State Department has four main foreign policy goals: Protect the United States and Americans; Advance democracy, human rights, and other global interests; Promote international understanding of American values and policies

Step-by-step explanation:

7 0
3 years ago
Evaluate the double integral.
Fynjy0 [20]

Answer:

\iint_D 8y^2 \ dA = \dfrac{88}{3}

Step-by-step explanation:

The equation of the line through the point (x_o,y_o) & (x_1,y_1) can be represented by:

y-y_o = m(x - x_o)

Making m the subject;

m = \dfrac{y_1 - y_0}{x_1-x_0}

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

m= \dfrac{2-1}{1-0}

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

m = \dfrac{1-2}{4-1}

m = \dfrac{-1}{3}

∴

y-2 = -\dfrac{1}{3}(x-1)

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy

\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg)   dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ([y^2(-4y+8)] \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( -4y^3+8y^2 \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1

\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1

\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [  \dfrac{-45+56}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [  \dfrac{11}{3}\bigg]

\iint_D 8y^2 \ dA = \dfrac{88}{3}

4 0
3 years ago
Ind the missing value. Hint: Use the number line to find the missing value.-3=blank-11
STatiana [176]

This math is just too much and makes little to no sense.

6 0
3 years ago
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