Please explain to me how to do this

Inequalities help us to compare two unequal expressions. For all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the inequality x²<4, whose solution can be calculated as shown below.

x² < 4

x² - 4 < 0

x² - 2² < 0

(x+2)(x-2)<0

x = (-2, 2)

Hence, for all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).

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Answer is below attached

Step by step. We know y = -3x -5

The first point on the graph is -5 on the y axis. It is your y intercept.

The second point is your slope, which is the number next to the x, stated as y/x, -3/1.

You will graph this from the y-intercept as shown in red.

Then you can connect the points, shown with the blue line.

The amount of cloth needed to make 1 headband is 10 meters.

Cloth needed to make 1 headband = Number of headbands Anne made / Total clothes used

= 6 ÷ 3/5

= 6 × 5/3

= (6 × 5) / 3

= 30/3

= 10 meters

Therefore, the amount of cloth needed to make 1 headband is 10 meters.

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Answer:

Step-by-step explanation:

To find:

Given:

[tex]\sf{7p+4=-p+9+2p+3p}[/tex]

Isolate the term of p, from one side of the equation.

Combine like terms.

[tex]\rightarrow \sf{7p+4=-p+2p+3p+9}[/tex]

Add the numbers from left to right.

-p+2p+3p=4p

7p+4=4p+9

Then, you subtract by 4 from both sides.

[tex]\sf{7p+4-4=4p+9-4}[/tex]

Solve.

7p=4p+5

Subtract by 4p from both sides.

7p-4p=4p+5-4p

Solve.

[tex]\boxed{\sf{3p=5}}[/tex]

Divide by 3 from both sides.

3p/3=5/3

Solve.

p=5/3

Divide is another option.

5/3=1.6666

So, the final answer is 3p=5.

I hope this helps, let me know if you have any questions.

Based on the average SAT Math score that the graduating classes got, the comparison is that this year's graduating class did better than last year's graduating class.

The average score is used to show the general trend of scores that students were able to attain.

The average score of 530 that this year's graduating class attained is higher than the average of the previous graduating year which is 520.

This means that on average, this year's graduating class did better than that of last year because their general trend was higher.

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Answer:

choice d

Step-by-step explanation:

I hand this question

A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.

In this context, we can logically deduce that the geometric shape which best models the object (cell phone tower) shown in the image attached above is a square pyramid.

Mathematically, the surface area of a square pyramid is given by this formula:

A = a² + 2a√(a²/4 + h²)

Where:

Given the following parameters:

Edge of the base = 50 feet.

Height = 200 feet.

Substituting the given parameters into the formula, we have;

A = 50² + 2(50)√(50²/4 + 200²)

A = 2,500 + 100√(2500/4 + 40,000)

A = 2,500 + 100√(625 + 40,000)

A = 2,500 + 100√(40,625)

A = 2,500 + 100(201.56)

A = 2,500 + 20,156

A = 22,656 ≈ 22,500 ft².

In conclusion, the best geometric shape for the model is a square pyramid and the approximate surface area is equal to 22,500 square feet.

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Answer:The best shape for the model is a square pyramid.

The approximate surface area is 22,500 square feet.

Step-by-step explanation: edmentum/plato answers

Given the:

ln(x + 6) - ln(2x - 1) = 1

Using the logarithm rule:

We know,

Simplifying we get,

By cross multiplication we get,

Therefore, the value of x is 1.97.

The correct option in the exercise ln (x + 6) - ln (2x - 1) = 1 is alternative "D".

Between 2 seconds and 2.5 seconds, the rock hits the ground after it is dropped.

What are distance and time?

As you can see at 2s the height of the rock is 0.4m and at 2.5s it is -10.6m, which tells us that in between these values the height would have been 0m, as the movement of the rock is uniform in direction and hence, the rock will hit the ground between 2s and 2.5s.

The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped.

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From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°

The lines ZY and ZW are tangents to the attached circle which is centered at x.

From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.

From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.

Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;

∠WZY = 360° - (90° + 90° + 109°)

∠WZY = 360° - 289°

∠WZY = 71°

Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°

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Answer:  B. 71°

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!! :)

I got it right!

The actual distance between the opposite corners of the school hall is; 10√34 m

The scale drawing showing the corners of the hall has been drawn and attached.

Now, from the attached scale drawing it was drawn with the scale;

1 cm to represent 5 m.

Now, the distance between the opposite corners of the hall measuring 50 m and 30 m is indicated as D on the scale drawing. Thus, to find the distance between the opposite corners, we will use Pythagoras theorem to get;

D² = 30² + 50²

D² = 900 + 3500

D² = 4400

D = √4400

D = 10√34 m

Thus, the actual distance between the opposite corners of the school hall is; 10√34 m

Complete question is;

Make a scale drawing of a rectangular school hall which is 50 m long and 30 m wide using a scale of 1 cm to 5 m. From your scale drawing, find the actual distance between the opposite corners of the hall.

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The complete proofs are:

Proof 1

Proof 2

Proof 1

Lines a & b and c and d are given as parallel lines.

So, we have

a || b; c || d ⇒ Given

From the question, we have:

∠5 is supplementary to ∠4

So, we have

∠5 + ∠4 = 180

This is so because supplementary angles add up to 180

Corresponding angles are equal.

So, we have:

∠2 = ∠4

By the substituting ∠2 for ∠4 in ∠5 + ∠4 = 180, we have

∠5 + ∠2 = 180

Hence, angles ∠5 and ∠2 are supplementary angles

Proof 2

Line BD bisects angle ABC; lines AD & BC and AB & CD are given as parallel lines.

So, we have

BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given

From the question, we have:

∠3 ≅ ∠4 ⇒ Definition of congruent angles

∠1 ≅ ∠3 ⇒ Definition of corresponding angles

Substitute ∠1 ≅ ∠3 in ∠3 ≅ ∠4

∠1 ≅ ∠4

Hence, the angles 1 and 4 are congruent

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The maximum value of P = x + 6y subject to the constraints is 9

The objective function is given as:

P = x + 6y

The constraints are given as:

2x + 4y ≤ 10

x + 9y ≤ 12

x≥0 y≥0

Rewrite 2x + 4y ≤ 10 and x + 9y ≤ 12 as equations

2x + 4y = 10

x + 9y = 12

Divide 2x + 4y = 10  through by 2

x + 2y = 5

Subtract x + 2y = 5 from x + 9y = 12

x - x + 9y - 2y = 12 - 5

Evaluate the difference

7y = 7

Divide by 7

y = 1

Substitute y = 1 in x + 2y = 5

x + 2(1) = 5

Solve for x

x = 3

So, we have

(x, y) = (3, 1)

Substitute (x, y) = (3, 1) in P = x + 6y

P = 3 + 6 * 1

Evaluate

P = 9

Hence, the maximum value of P = x + 6y subject to the constraints is 9

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The time it will take the thermometer to hit the ground is 22 seconds

From the question, we are to determine the how long it would take the thermometer to hit the ground

From the given information,

The equation for the height as a function of time is

h(t) = -16t² + initial height

From the given information,

The thermometer falls from a weather balloon at a height of 7744 ft

∴ Initial height = 7744 ft

When the thermometer hits the ground, h(t) = 0

Thus, we get

0 = -16t² + 7744

16t² = 7744

t² = 7744/16

t² = 484

t = √484

t = 22 seconds

Hence, the time it will take the thermometer to hit the ground is 22 seconds

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Answer:

334 in^2.

Step-by-step explanation:

The surface area = area of the top prism + area of the bottom - 2 * area of the base of the  top smaller prism

= 2(5*3 + 5*3 + 3*3) + 2(9*7 + 9*5 + 7*5) -  2* 3*5

= 2* 39 + 2*143 - 30

= 334

The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.

Given;

Location of the tree = The other side of the river from the surveyor

Length of the line measured along the river, L = 125 feet

Angle to the tree from the start of the line = 65°10'

1° = 60'

10' = ((1/60)×10)° = (1/6)°

65°10' = (65 + 10/60)° = (65 + 1/6)°

Angle measured at the end of the line, E = 60°10'

Similarly;

E = 60°10' = (60 + 1/6)°

The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;

Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)

S = (114+5/6)°

From the angle sum property of a triangle, angle formed at the tree, T, is therefore;

T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°

According to the rule of sines, we have;

l/(sin T) = b/(sin E)

Where;

b = The length of the bridge

Which gives;

124/(sin 5°) = b/(sin (60 + 1/6)°)

b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2

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Answer:

Step-by-step explanation:

As per the same approach I answered in a similar problem:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate theRise/Run:

RISE = (-11 - 9) = -20

RUN = (3 - (-2)) = 5

Rise/Run, or slope, is = -20/5 or -4

I graphed this line and the two points (attached).

Answer:

-20/5 or -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per the same approach I answered in a similar problem:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate theRise/Run:

RISE = (-11 - 9) = -20

RUN = (3 - (-2)) = 5

Rise/Run, or slope, is = -20/5 or -4

Answer:

200,075

Step-by-step explanation:

90 times 2.5 = 225

225 divided by 3 = 75

75 + 200,000 = 200,075

Answer: 200075

Step-by-step explanation:

90 * 2.5 = 225

225 / 3 = 75

75 + 200,000 = 200,075

I believe that its easier to understand the multiplication of a radical than that of a polynomial.

In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.

A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.

When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:

= 3✓2 × 4✓2

= 12✓4

= 12 × 2

= 24

The multiplication of a radical is easier.

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The value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and                    f(x) = (h ° g) (x). This can be obtained by finding composite of (h ° g) (x) using the formula for composition.

Composition of a function : A composite function is created when one function is substituted into another.

f composite of g is denoted as (f ° g)

The formula to find the composite of a function,

For example,

f(x) = x + 2, and g(x) = 3x

In the question,  

Given that, f(x) = (8x³ - 1)³, h(x) = x³

f(x) = (h ° g) (x)

⇒ (8x³ - 1)³ = h(g(x))

⇒ (8x³ - 1)³ = (g(x))³

Taking cube roots on both sides,

⇒ ∛(8x³ - 1)³ = ∛(g(x))³

⇒ (8x³ - 1) = (g(x))

⇒ g(x) = 8x³ - 1

Hence the value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and                    f(x) = (h ° g) (x).

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Answer:

its the 4th one i think

Step-by-step explanation:

Answer: x = 0 ; y = -7

Step-by-step explanation:

Given equation:

1) 3x + 8y = -56

2) 2x - y = 7

Subtract 2x on both sides of 2) equation to isolate y-value

2x - y - 2x = 7 -2x

-y = 7 - 2x

Divide -1 on both sides of 2) equation

-y / -1 = (7 - 2x) / -1

y = 2x - 7

Current system

1) 3x + 8y = -56

2) y = 2x - 7

Substitute 2) equation into the y-value of 1) equation

3x + 8 (2x - 7) = -56

Simplify by distributive property

3x + 8 × 2x - 8 × 7 = -56

3x + 16x - 56 = -56

Combine like terms

19x - 56 = -56

Add 56 on both sides

19x - 56 + 56 = -56 + 56

19x = 0

Divide 19 on both sides

19x / 19 = 0 / 19

[tex]\Large\boxed{x=0}[/tex]

Substitute the x-value into one of the equations to find the y-value

2x - y = 7

2 (0) - y = 7

0 - y = 7

-y = 7

[tex]\Large\boxed{y=-7}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

To form an equation from a word problem, we can recognize variables and operations from keywords.

Let the number of weeks be a.

We're given:

Because $200 is the minimum account required, we know that the amount earned must be greater than or equal to 200.

[tex]200\leq[/tex]

Our current savings and money can be calculated by adding 15a and 32:

[tex]200\leq15a+32[/tex]

[tex]200\leq15a+32[/tex]

Answer:

-3

Step-by-step explanation:

(h o k)(2) means

h( k(2)).

Remember when you have a function like f(x) or g(x) or h(x) or k(x), whatever number (or expression) is inside of the parenthesis, they're telling you to use that in place of x.

What h( k(2) ) means is we're going to put k(2) into h.

Well, what's k(2)? We need to find that first. k(x) is given as the oval and arrows thing going on there. If we're looking for k(2) then 2 is being the x. Find 2 in the first oval, follow the arrow to the output which is k(2).

If x = 2, the k(2)= -2

So back to

(h o k)(2):

(h o k)(2)

= h( k(2) )

= h(-2)

Since h(x)= 3/x+1

and x is -2, we'll put -2 in place of x.

h(-2) = 3/-2+1

= 3/-1

= -3

Step-by-step explanation:

Greetings !

Given expression

[tex] \frac{10}{n} = \frac{15}{6} [/tex]

cross multiply

apply fraction cross multiply

[tex]if \: \: \frac{a}{b} = \frac{c}{d} \: \: then \: \: a.d = b.c[/tex]

10.6=n.15

simplify:

Thus, 60=n.15

switch sides

[tex]n.15 = 60[/tex]

divide both sides by 15

[tex] \frac{n.15}{15} = \frac{60}{15} [/tex]

simplify

[tex]n = 4[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

The minimum is at the vertex of this parabola because it opens up.

Now if (-4, 2) is the minimum then  all the y values on the parabola must be > 2,

But we are given that  y = -3 is on the graph ( the point (6,-3) - that is y < 2 here,

Therefore (-4, 2)  cannot be the vertex .

The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

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