What are the points of intersection between the graphs of the functions
f(x) = (x+3)(x − 1) and g(x) = (x + 1)(x − 3)

Answer:

If a stand can hold 157.5kg

x stand can hold 1.25kg

1=

Answer:

126 bags.

Step-by-step explanation:

157.5 / 1.25

= 126.

The measure of x, that is, the angle OBA is equal to 22.5°.

Herein we find a geometric system formed by a circle, a diameter and a chord. In the image attached below we present all the possible angles of the geometric system, formed by two isosceles triangles.

According to Euclidean geometry, an isosceles triangle has two sides and two angles of equal length. Then, the sum of the internal angles of the triangle AOB is equal to:

m ∠ AOB + m ∠ OBA + m ∠ OAB = 180°

135° + 2 · m ∠ OBA = 180°

2 · m ∠ OBA = 45°

m ∠ OBA = 22.5°

By taking advantage of the properties of isosceles triangles, the measure of x, that is, the angle OBA is equal to 22.5°.

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Answer:

118 .........................

The length and width of the rectangular garden is estimated as-

A rectangle's perimeter is the total length and distance of its border across all sides. The perimeter of a rectangular box is a linear measurement that is expressed in meters, feet, cm, or yards. Let us first examine the two primary characteristics of a rectangle.

The perimeter of the rectangle is given as-

Perimeter = 2(length + width)

perimeter= 256

Let the width of the rectangle be x.

Length is 8 feet longer than width, Thus,

length = x+8

Substitute the values in the formula of perimeter;

256 = 2( x+ 8+ x)

256 = 2( 2x + 8)

128= 2x + 8

120= 2x

x=60

Thus, width = 60 ft.

Length = 60 + 8 = 68 ft.

Therefore, the length and width of the rectangular garden is estimated.

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The complete question is -

A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8feet longer than it is wide. Find the length and width of the garden.

The value of the longest side of the triangle is 31 feet

The perimeter of the triangle is the sum of all its sides.

The formula for perimeter where a, b and c are the three sides of the triangle is given as:

Perimeter = a + b + c

It is given that the sides are consecutive integers and the perimeter is 90 feet, therefore

Let sides be x, x+1 and x+2

Perimeter = x + x+1 + x+2

90 = x + x+1 + x+2

90 = 3 + 3x

87 = 3x

x = 29 feet

The value of the longest side will be x+2, which will be 29+2 = 31 feet

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Answer:

The arrow indicates that the angle terminates in the second quadrant, meaning that its more than 270 deg

Answer:12/8y

Step-by-step explanation:

i took the test

The spam of the sets of vector of all linear combination is 0,

The span of the set {(2, 5, 3), (1, 1, 1)} is the subspace of R 3 consisting of all linear combinations of the vectors v 1 = (2, 5, 3) and,

v 2 = (1, 1, 1).

this defines a plane in R 3.

Since a normal vector to this plane in n = v 1 x v 2 = (2, 1, −3),

the equation of this plane has the form 2 x + y − 3 z = d for some constant d. the plane must contain the origin—it's a subspace— d must be 0.

No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line

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The probability would be zero that both the pirate and the captain hit each other's ships.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Captain Ashley has probability 1/2 of hitting the pirate ship.

Dread pirate Umaima has a 1/3 probability of attacking the Captain's ship if it hasn't already.

The captain must miss if the pirate hits, and the requirement that both hits are not satisfied. The requirement that both hits cannot be satisfied if the pirate misses.

Therefore, the probability would be zero that both the pirate and the Captain hit each other's ships.

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Answer:

Step-by-step explanation: Hello! My name is Madison and I will being helping you how to go about doing these problems! First things first.

1) 50,000 divided by 12 would be 4166.6 repeating.

2)

Answer:

2x+1>3

2x>4

x=2

3x-4≤17

3x≤21

x=7

Answer:

Step-by-step explanation:

A and C

Answer:

-25+27k

Step-by-step explanation:

-5(1-5k)-4(2k+5)

= -5+35k-8k-20

=-5-20+35k-8k

= -25+27k

TX IS THE OVERALL MAGNITUDE OF THE LINE

TX IS THE OVERALL MAGNITUDE OF THE LINE WHICH IS MADE BY TW+WX

MATHEMATICALLY

TX=TW+WX

[tex](5x - 9) = (3x + 5) + 10 \\ 5x - 9 = 3x + 5 + 10 \\ 5x - 3x = 5 + 10 + 9 \\ 2x =24 \\ \frac{2x}{2} = \frac{24}{2} \\ x = 12[/tex]

HOPE THIS HELPS!!!

PLEASE DO NOT HATE MATHS I'M HERE FOR YOU TO MAKE SURE YOU ENJOY IT.

Answer: 10

Step-by-step explanation:

Distance formula = (x2-x1)^2 + (y2-y1)^2

In this circumstance, we have (0,0) and (6,8) as our two points.

(6-0)^2 + (8-0)^2

(6^2) + (8^2)

36 + 64 = 100

Square root the 100.

SQRT of 100 is 10 (perfect square) so your answer is, again, 10.

I hope I managed to help.

Answer:

Step-by-step explanation:

Make the following operations:

and

The required value is:

Answer:

[tex]\dfrac{a+b}{a-b}=-\sqrt{2}[/tex]

Step-by-step explanation:

Given:

[tex]a^2+b^2=6ab[/tex]

[tex]0 < a < b[/tex]

Add 2ab to both sides of the given equation:

[tex]\implies a^2+b^2+2ab=6ab+2ab[/tex]

[tex]\implies a^2+2ab+b^2=8ab[/tex]

Factor the left side:

[tex]\implies (a+b)^2=8ab[/tex]

Subtract 2ab from both sides of the given equation:

[tex]\implies a^2+b^2-2ab=6ab-2ab[/tex]

[tex]\implies a^2-2ab+b^2=4ab[/tex]

Factor the left side:

[tex]\implies (a-b)^2=4ab[/tex]

Therefore:

[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=\dfrac{8ab}{4ab}[/tex]

[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=2[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]

[tex]\implies \left(\dfrac{a+b}{a-b}\right)^2=2[/tex]

Square root both sides:

[tex]\implies \sqrt{\left(\dfrac{a+b}{a-b}\right)^2}=\sqrt{2}[/tex]

[tex]\implies \dfrac{a+b}{a-b}=\pm\sqrt{2}[/tex]

As 0 < a < b then:

Therefore:

[tex]\implies \dfrac{a+b}{a-b}=\dfrac{+}{-}=-[/tex]

So:

[tex]\implies \dfrac{a+b}{a-b}=-\sqrt{2}[/tex]

The inequality for the number of cups of lemonade she can buy is :

             0 < c < 5.

Marilyn has $40 to spend in the amusement park.

Admission price = $20

So money left = 40 - 20 = $20

Now she plans to buy a sandwich for $5.

So the money left now will be = 20 - 5 = $15

Price of a cup of lemonade = $3

Marilyn can buy at most $15/3 = 5 cups of lemonade.

She can either choose to not buy a cup of lemonade or can buy at most 5 cups of lemonade.

So the inequality for the number of cups of lemonade she can buy will be

0 < c < 5 , where 'c' denotes the number of cups of lemonade.

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The three ways that the problem that Ernie has written can  be solved are:

This is the term that is sued to refer to the topic in mathematics that has to do with the ways that numbers can be broken down into smaller units. The number that is being divided is often done with the aid of a divisor.

In this question, the number that is to be divided is 525 and the number that is to do the division is 1500. This can be written as 525 / 1500 for us to see clearly.

When written, we can write this out in the different ways that have been stated above. Hence we would have The three ways that the problem that Ernie has written can  be solved are:

The solution is 0.35

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The rate of change/slope of the ramp’s incline is found to be 3.

A line's slope is defined as the change in y coordinate in relation to a change in x coordinate.

m = Δy/Δx

where, m is the slope

And, tan θ = Δy/Δx

Such an tan θ is also known as the line's slope.

The slope of a line could be determined by calculating using only two straight line points. The slope of line formula could then be used with two point coordinates.

Now, in response to the question;

To link a driveway to a front door, a ramp with a constant incline is built.

The ramp's height  y₁ is 12 inches at a point 4 feet from of the driveway x₁.

The height y₂ of the ramp is 18 inches at a point 6 feet from of the driveway x₂.

The incline of the ramp's rate of change is given by:

Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)

The values given in the question;

(x₁, y₁) = (4, 12) and,

(x₂, y₂) = (6, 18)

Put the values in the formula of the slope;

Slope = m = (18 - 12)/(6 - 4)

m = 6/2

m = 3

Therefore the rate of change also called as ramp’s incline is calculated as 3.

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Answer:

Step-by-step explanation:

Spherical geometry would be use in the real world practical applications to navigation. Professions that would need to make it use is astronomy.

These professions make use of spherical geometry for making Spherical conic, Spherical distance, Spherical polyhedron, Half-side formula.

Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2 dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.

An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere.

Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable, or one-sided, and unlike the sphere it cannot be drawn as a surface in 3-dimensional space without intersecting itself.

Spherical geometry would be use in the real world practical applications to navigation. Professions that would need to make it use is astronomy.

These professions make use of spherical geometry for making Spherical conic, Spherical distance, Spherical polyhedron, Half-side formula.

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The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. AB and CD are not congruent

Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. For instance, create two circles with the same radius, cut them out, and stack them.

We'll see that they'll be placed entirely on top of one another and will superimpose one another. This demonstrates that the two circles are similar. Given that they have an equal radius and can be positioned exactly over one another, the circles below are considered to be congruent. "≅" is the sign used to represent the congruence of figures. Since circle A and circle B are similar, we may say the following: Circle B ≅ Circle A.

Lets assume AB and CD are congruent

Then according to Pythagoras theorem

Hypotenuse of AB of right-angled triangle AOB is equal to Hypotenuse of CD of right-angled triangle COD

Hypotenuse AB = Hypotenuse CD

Hypotenuse AB

a² + b² = c²

(-7)² + 9² = c²

49 + 81 = c²

130 = c²

Hypotenuse CD

a² + b² = c²

(-4)² + 12² = c²

16 + 144 = c²

160 = c²

Here, 130 ≠ 160

So, The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. AB and CD are not congruent

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Answer: The answer is -5

Step-by-step explanation: According to the question it stated that the temperature was 7 degrees at 3pm and by 9pm it dropped 12 degrees so  from my answer it would -5 degrees

Answer: x=1

Step-by-step explanation:

Answer:

IMS (Infinitely Many Solutions)

Step-by-step explanation:

1. Combine like terms (2/3x + 1/3x) Equation: 1x = x

2. 1x is just x, so the final equation is x = x. When you get an answer like this, it means there are infinitely many solutions.

The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 )

critical value at 0.01 significance level with 17 df = 2.898

x = mean;

99% confidence interval for μ is

(x - t * S) /√n  <  μ <( x + t * S) /√n;

(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;

14.74<  μ< 48.89;

99% CI is ( 14.74, 48.89 ) ;

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Answer:

y = -3(2)+7

y= -6+7

y= 1

(2,1)

y=-3(5)+7

y= -15+7

y= -8

(5,-8)

y= -3(3)+7

y=-9+7

y=-2

(3,-2)

y=-3(0)+7

y=0+7

y=7

0,7)

Step-by-step explanation:

substitute the values of x in the equation

The locations of the vertices of the dilated figures are (48,16), (32,40), and (8,24).

This problem can be solved by using the concept of scale factor. Scale factor is useful in finding proportional measurements.

Proportion implies having the same ratio.

Scale factor can be defined as the ratio of the measurement of the model to the measurement of the actual form in the simplest form. In other words, the ratio of any two corresponding lengths in two similar geometric figures is called a scale factor.

If the scale factor is more than 1, that is, scale factor > 1,

then it is an enlargement,

If the scale factor is less than 1, that is, scale factor < 1,

then it is a reduction.

We can obtain the answer by multiplying the given coordinates, first by a scale factor of 4 and then by a scale factor of 2/3.

(18,6) => (18x4, 6x4) => (72,24) => (72x2/3, 24x2/3) => (48,16)

(12,15) => (12x4, 15x4) => (48,60) => (48x2/3, 60x2/3) => (32,40)

(3,9) => (3x4, 9x4) => (12,36) => (12x2/3, 36x2/3) => (8,24)

Therefore, using the concept of scale factor, we get the locations of the vertices of the dilated figures as (48,16), (32,40), and (8,24).

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Answer:

-0.5

Step-by-step explanation:

[tex]\frac{f}{g} =\frac{f(n)}{g(n)} = \frac{4n}{n^2-3n}[/tex]

[tex]\frac{4(-5)}{(-5)^2-3(-5)} =\frac{-20}{40} =\frac{-1}{2}[/tex]

Segment PS in the scaled copy corresponds to segment AD in polygon ABCD in polygon PQRS. They are similar in appearance and appear in the same location.

A polygon is a two-dimensional flat shape with straight, fully closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.

Polygon is derived from the Greek word "polugonos." It has evolved into the term "polygon" over time. The term "polygon" means "many" and "gon" means "angled." This is due to the fact that a polygon has numerous angles and corners within its shape.

The Greeks may have been the first to recognize polygons, as there are numerous examples of them recognizing polygons such as the pentagram in their ancient art and writings.

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The value of the expression [tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex] is [tex]cot(A)+\frac{A}{sin^{2}A}[/tex].

The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine derivatives, continuity, and integrals.

Mathematical expressions consist of at least two variables or numbers, at least one arithmetic operation, and a statement. It's possible to divide, multiply, add, or subtract with this mathematical operation.

Consider the expression,

[tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex]

Adding and subtracting Acot(A) and A common in the numerator,

[tex]\lim_{x \to A} \frac{xcot(A)-Acot(A)+Acot(A)-Acot(x)}{x-A}[/tex]

Taking cot(A) common,

[tex]\lim_{x \to A} \frac{cot(A)(x-A)+A(cot(A)-cot(x))}{x-A}[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A(cot(A)-cot(x)}{x-A}[/tex]

Now, using the identity:

cot x = cos x / sin x

[tex]\lim_{x \to A} cot(A) + \frac{A(\frac{cos(A)}{sin(A)} -\frac{cos(x)}{sin(x)}) }{x-A}[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{cos(A)sin(x)-cos(x)sin(A) }{sin(A)sin(x)})[/tex]

By using the identity, sin ( a - b ) = sin(a)cos(b) - sin(b)cos(a)

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=\lim_{x \to A} cot(A) +\lim_{x \to A} \frac{sin(x-A)}{(x-A)}\frac{A}{sin^{2}A}[/tex]

[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=cot(A)+1 \cdot \frac{A}{sin^{2}A}[/tex]

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