Write the numbers in ascending order

Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.

steposvetlana [31]

4(2 - x) > -2x - 3(4x + 1)
8 - 4x > -2x - 12x - 3
-4x + 2x + 12x > -3 - 8
10x > -11
x > -11/10
x > -1.1

Therefore, x = 0 and x = 10 zre solutions to the inequality.

4 0

2 years ago

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Lionel needs money quite frequently and doesn't need much interest at all. Which of these options for saving money is best for h

mestny [16]

Answer: Savings account - Apex

4 0

2 years ago

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Write the rational number as a decimal. −18/5

Angelina_Jolie [31]

Answer:

-3.6

Step-by-step explanation:

When plugged into a calculator, the answer turns out to be -3.6, which is a decimal.

6 0

2 years ago

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Terry invested money in a biotech stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of da

strojnjashka [21]

Answer:

The average rate of change is 1.275

Step-by-step explanation:

The average rate of change of f(x) from x=a to x=b is given by:

$\frac{f(b)-f(a)}{b-a}$

The money Terry invested is modeled by the function $f(x)=0.01(2)^x$ where x represents number of days.

The average rate of change from day 2 to day 10 is given by:

$\frac{f(10)-f(2)}{10-2}$

$f(10)=0.01(2)^{10}=10.24$

$f(2)=0.01(2)^{2}=0.04$

The average rate of change becomes:

$\frac{10.24-0.04}{8}$

$=\frac{10.2}{8}=1.275$

3 0

2 years ago

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In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .