Solve the inequality. –6 < 2 x – 4 < 4

Equations are separated by an equal sign. The value of x is given as -6/5

Given the equations below;

5(3x + 4) = 2

Expand

5(3x) + 5(4) = 2

15x +20 = 2

Subtract 2 from both sides

15x = 2 - 20

15x = -18

x = -18/15

x = -6/5

Hence the value of x is given as -6/5

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Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.

According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.

Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.

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Answer:

(10/3)π units

Step-by-step explanation:Mark if it is correct

Answer:

[tex]\frac{10\pi }{3}[/tex] inches

≈ 10.5 inches

Step-by-step explanation:

The formula for arc length is as follows:
Arc length = [tex]\frac{\theta}{360} * 2\pi[/tex]

[tex]\frac{120}{360} * 10\pi \\= \frac{1}{3} * 10\pi \\= \frac{10\pi}{3}[/tex]

Hope this helps and feel free to mark this as brainliest!

Answer:

  d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

Step-by-step explanation:

The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.

__

The law of sines applied to the top triangle is ...

  BC/sin(A) = AC/sin(θ)

Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...

  ∠A = 180° -θ -θ = 180° -2θ

A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...

  sin(A) = sin(180° -2θ) = sin(2θ)

and our above Law of Sines equation tells us ...

  BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)

__

The law of sines applied to the bottom triangle is ...

  DC/sin(B) = BC/sin(D)

  d/sin(α) = BC/sin(β)

Multiplying by sin(α) we have ...

  d = BC·sin(α)/sin(β)

__

Using our expression for BC gives the desired relation:

  d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

Answer:

[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)

Answer:

Systems of equations:

x=3

y=2

z=1

w=0

If the height of the triangle will be 6.28 meters. Then the value of x will be 8.46 meters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In the diagram shown, the area of the triangle is 44.3 m².

If b = 14.1 m and the angle at C = 48°.

Then the value of x will be

The height of the triangle will be

    A = 1/2 × B × H

44.3 = 1/2 × 14.1 × h

    h = 6.28 m

Then the value of x will be

sin 48° = 6.28 / x

x = 8.455 ≈ 8.46 m

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Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]

Factor out -1:

[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]

Divide both sides by -1:

[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]

Rearrange the terms:

[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]

[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]

Factor out the common term [tex](x^{98}-1)[/tex] :

[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]

Therefore, the solutions to the given equation are: x = 1 or x = -1

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Answer:

6

Step-by-step explanation:

Answer:

92 + ( -5 ) , 2+2

Step-by-step explanation:

1) 92 + ( -5 )

= 92 - 5

= 87

2) 2 + 2 = 4

According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons. Option D is correct.

The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure. The force involved vertically to the surface of an object per unit area is pressure.

It is denoted by P. The pressure relative to the ambient pressure is known as the gauge pressure.

The complete question is:

Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question. Which cylinder pressure will Jillian need if she plans to fill 90 balloons? Tank Pressure and Balloon Quantity Pressure in the helium cylinder (psi) Number of 9-inch balloons 100 30 150 ? 200? 250? 300?

According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons (PSI.)

Simply divide the number of balloons by the total PSI to arrive at this figure.

⇒990/300

⇒3.333333 psi each.

The no of the 90-inch balloon is found as;

⇒3.33333 × 90

⇒300

According to the typical Helium Cylinder/Balloon Chart, she will need 300 pounds of pressure to fill 90 balloons.

Hence option D is correct.

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Answer:

x = 9

Step-by-step explanation:

x/3 = 6/2

~Simplify

x/3 = 3

~Rewrite

1/3x = 3

~Multiply 3 to both sides

x = 9

Best of Luck!

Answer: x=9 ✅

Step-by-step explanation:

Hii student, I'd love to help you out! (:

In this problem, we need to solve a proportion. This is fun, right?

3,2,1 - start!

Solving proportions is easy as winking, if you are familiar with a skill that is known as "cross multiplying".

We have these two proportions:

(oh and by the way, proportions are just equivalent (equal) fractions. That's all proportions are. Nothing more)

Our proportions are:

[tex]\large\boldsymbol{\cfrac{x}{3}=\cfrac{6}{2}}[/tex]

We multiply x times 2 and 3 times 6; upon  doing that we obtain.

[tex]\multimap\quad \tt 2x=18[/tex]

Did you see that? 2 fractions turned into a little equation that we can solve within 5 seconds (or faster)!

To do that we simply divide both sides by 2, since x is multiplied by 2 and we need to get it all by itself on one side of the equal sign)

[tex]\multimap\quad \tt x=9[/tex]

Woohoo! We found the answer! ✨

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

If we put a=0 and b=-4.05 then the expression 4a+4b becomes -16.2 and when we put a=-4.05 and b=0 then the expression becomes -16.2.

Given  2 (a + b) = -8.1

Because no relationship between a and b is given so we can put any value of one variable to determine the value of another variable.

If we put a=0 in 2(a+b) =-8.1 then b=-4.05

If we put b=0 then a =-4.05.

We need to put these values in 4a+4b

when a=0 b=-4.05

4a+4b=4*0+4*-4.5

=-16.2

when b=0 and a=-4.05

4a+4b=4*-4.05+4*0

=-16.2

Hence for a=0,b=-4.5 the value of 4a+4b equals -16.2 and for a=-4.05 and b=0 the function equals -16.2.

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Answer:

Step-by-step explanation:

Answer:

3 months

Step-by-step explanation:

G1= 10 m +45

G2=25

10 m + 45= 25 m

10 m - 25 m = -45

-15 m/-15=-45/-15

m=3

∴ it's 3 months

The other name for angle 2 is ∠DBC

The correct option is (D)

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

We know that while naming the angle we have to consider the point where the angle is made should be at center.

Hence, the angle 2 can also be written as ∠DCB.

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The equation of the line in point-slope form is: C. y − 5 = −(x − 2).

A line with a slope (m) and a point (a, b) is represented in point-slope form as, y - b = m(x - a).

Slopes of perpendicular lines are negative reciprocals of each other. Find the slope of the line in the graph given as follows:

Slope (m) = rise/run = 3 units/3 units = 1

Negative reciprocal of 1 is -1.

The slope of the line would be m = -1.

Substitute m = -1 and (a, b) = (2, 5) into y - b = m(x - a) to wrote the equation:

y - 5 = -1(x - 2)

y − 5 = −(x − 2)

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Answer:

C

Step-by-step explanation:

Use the equation [tex]a^2 + b^2 = c^2[/tex]

Input the numbers----> [tex](2865)^2 +(4550)^2=c^2[/tex]

Simplify ----> [tex]28910725=c^2[/tex]

Find the square root------->[tex]5376.9=c[/tex]

AC is equal to BC by the corresponding side of a congruent triangle.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

The midpoint of a line segment means a point that lies in the mid of the given line segment.

If D is the midpoint of segment AB, then AD = BD.

So in a triangle ACD and BCD

AD = BD (by midpoint D)

angle ADC = angle BDC = 90

CD = CD (common)

Therefore, triangle ACD and BCD are congruent.

Hence, AC = BC by the corresponding side of a congruent triangle.

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Answer:

x = ± [tex]\sqrt{2}[/tex] , x = ± i

Step-by-step explanation:

f(x) = [tex]x^{4}[/tex] - x² - 2

to find the zeros , equate f(x) to zero , that is

[tex]x^{4}[/tex] - x² - 2 = 0

using the substitution u = x² , then

u² - u - 2 = 0 ← in standard form

(u - 2)(u + 1) = 0 ← in factored form

equate each factor to zero and solve for u

u - 2 = 0 ⇒ u = 2

u + 1 = 0 ⇒ u = - 1

convert u back into terms of x

x² = 2 ( take square root of both sides )

x = ± [tex]\sqrt{2}[/tex]

x² = - 1 ( take square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i

Answer: Positive or negative square root of 2, ±i

Proof o fvalidity is shown below.

Answer: y = 2x - 6

Step-by-step explanation:

   Let us turn the second given equation into slope-intercept form to match the first equation.

8x - 4y = 12

8x - 12 = 4y

4y = 8x - 12

y = 2x - 3

   Now, parallel lines have the same slope. This is the m value.

y = 2x - 3

   \/

y = mx - 6

y = 2x - 6

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Answer:

please see photo attached for detailed analysis.

The value ∠y is 40⁰. So the correct option is option B

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Here,  given that;   ΔUVW ≅ ΔXYZ

∠u = ∠x = 70⁰

∠v = ∠y = a⁰

∠w = ∠z = 70⁰

We know that,

Sum of angles of a triangle is 180⁰.

∠x + ∠y + ∠z = 180⁰

70⁰ + a⁰ + 70⁰ = 180⁰

a⁰ + 140⁰ = 180⁰

a⁰ = 180⁰ - 140⁰

a⁰ = 40⁰

Thus, the value ∠y is 40⁰.

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Answer:

The value of the expression will be "392.79".

Step-by-step explanation:

~ The technique of dividing a quantities into equivalent portions as well as    determining however many equal components may be formed, is determined as a division.

~ It is denoted by "/".

According to the equation, the expression is:

→ 196/0.499

By applying the division, we get

→ 392.79

Answer:

392

Explanation:

Note that we are estimating, not finding the actual value. 0.499 is very close to 0.5, so to estimate this expression, we can do 196 ÷ 0.5. Dividing a number by 0.5 is the same as doubling it, so this can also be seen as
196 · 2, which is 392.

Hope this helps !! :D
The actual answer is the other one, but again, you're finding an estimate!

x = 2/3 , 0 .

Question :

[tex] {3x}^{2} - 2x = 0[/tex]

use quadratic formula :

[tex]x = \frac{( - b)± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

Solution :

[tex]a {x}^{2} + bx + c = 0 \\ a = 3 \\ b = - 2 \\ c = 0[/tex]

[tex]x = \frac{ - ( - 2)± \sqrt{ { (- 2)}^{2} - 4 \times 3 \times 0} }{2 \times 3} \\ \\ x = \frac{2± \sqrt{4 - 0} }{6} \\ \\ x = \frac{2± \sqrt{4} }{6} \\ \\ x = \frac{2± 2}{6} [/tex]

separate into two equations :

[tex]x = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} .[/tex]

[tex]x = \frac{2 - 2}{6} = \frac{0}{6} = 0.[/tex]

the values of x are 2/3 and 0 .

The area of ABCD is 104 units²

The area of rectangle is the product of its length to its breadth.

i.e., Area of rectangle= length * breadth

As, ABCD is in the shape of rectangle.

Using distance formula,

AB = √(1-(-5)² + (6-2)²

AB = √36+16

AB = √52

AB= 2√13

BC= √(9-1)² + (-6-6)²

BC= √64+144

BC =√208

BC= 4√13

Now, area of rectangle

=length *  breadth

= 2√13 * 4√13

= 8*13

=104  units²

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Hang on ,it is already proven through given .

So The proof is of one line only

Hence proved .