What value of x makes the equation 1+\sqrt{x-1=5} true?

Answer:

Step-by-step explanation:

I don’t understand this app how do I use it

Julie used direct proof because each statement is deduced from a previous statement. Samuel used indirect proof because the final statement contradicts the assumption.

What are direct and indirect proofs?

The complete question is given below.

Both Julie and Samuel are asked to prove m∠CBD  = 65°.

Let us look at Julie's proof.

She used the known facts which are given and finally proved that m∠CBD  = 65°. So Julie used direct proof.

Now let us observe Samuel's proof.

He started contradicting the statement when he wrote

 m∠CBD  + 65° ≠ 90°

So the last statement goes against what he was asked to prove.

Samuel used indirect proof.

Therefore Julie used direct proof because each statement is deduced from a previous statement. Samuel used indirect proof because the final statement contradicts the assumption.

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The inverse of the given functions are f⁻¹(x) = 3/4(x + 7) and f⁻¹(x) = x^2 + 10x + 25

The inverse of a function is a new function that undoes the effects of the original function.

In other words, if we have a function f(x) that maps x to y, then the inverse of f(x), denoted by f^-1(y), maps y back to x.

Given that:

f(x) = 4/3x - 7

Write as an equation

y = 4/3x - 7

Interchange the variables

x = 4/3y - 7

Solve for y

y = 3/4(x + 7)

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = 3/4(x + 7)

Also, the inverse of the function f(x) = √x -5 is computed as follows:

Interchange the variables and solve for y;

x = √y -5

y = x^2 + 10x +25

Replace y with f⁻¹(x) to show the final answer.

f⁻¹(x) = x^2 + 10x + 25

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Solution is in the attachment!! :)

The area of the image of the triangle under T is 5/9.

What is Triangle?

In geometry, a triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is characterized by its three vertices (points where two sides intersect) and three sides (line segments that connect the vertices). The sum of the interior angles of a triangle is always 180 degrees, and the length of each side is less than the sum of the lengths of the other two sides.

To show that T maps the given triangle to the domain D, we need to find the image of the three vertices of the triangle under T and then show that the image lies inside D.

Let's first consider the vertex (0,0) of the triangle. Applying T, we get T(0,0) = (0,0). So the image of the vertex (0,0) is the origin, which clearly lies inside D.

Now let's consider the vertex (1,1) of the triangle. Applying T, we get T(1,1) = (0,2), which lies on the y-axis and satisfies y²=4-4x, so it lies inside D.

Finally, let's consider the vertex (u,0) of the triangle, where 0≤u≤1. Applying T, we get T(u,0) = (u²,0). This lies on the x-axis and satisfies y²=4-4x only when x=1, which is outside D. Therefore, the image of this vertex is not inside D.

Hence, we can conclude that T maps the triangle to the domain D, except for the line segment {(u,0):0≤u≤1}.

To evaluate the area of the image, we can use the fact that the area of the image of a region under a transformation is equal to the absolute value of the determinant of the Jacobian matrix of the transformation, multiplied by the area of the original region.

The Jacobian matrix of T is given by

J(T) = [2u -2v]

[2v 2u]

The absolute value of the determinant of this matrix is 4u² + 4v², so the area of the image of the triangle is

∫∫R 4u²+4v² dA,

where R is the region in the uv-plane corresponding to the triangle.

Integrating over R, we get

∫0 ∫v 4u²+4v² dudv

= ∫0 (4/3) (1-v³+3v²) dv

= (4/3) (1/4 - 1/16 + 1/3 - 1/12)

= 5/9.

Therefore, the area of the image of the triangle under T is 5/9.

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The required real diameter of the tin is 250 mm.

Diameter is the length of a straight line drawn through the center of a circular object, such as a circle or sphere. It is the distance between two locations on the object's edge that are furthest apart and pass through the object's center.

Here,

If the diameter of the tin in the picture is 10 cm, then the actual diameter of the tin can be calculated as:

To convert the actual diameter to millimeters (mm), we can multiply by 10:

Therefore, the real diameter of the tin is 250 mm.

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Full Question:
See the attached.

The relation given is a function since each of the input value only maps to a single output value.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are set of coordinate values of a relation.

We have to determine whether the relation is function or not.

The points are,

{(-3, -8), (3, 6), (5, -5), (7,-6), (10, 6)}

Domain of the relation are {-3, 3, 5, 7, 10}

Range of the relation are {-8, 6, -5, -6, 6}

We can see that each of the input value only maps to a single output value.

So the relation is a function.

Hence the relation is a function.

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To solve this division problem, we can use the rule "division is the same as multiplication by the reciprocal".

So, 1/2 ÷ 7 is the same as 1/2 x 1/7.

Multiplying the numerators and denominators, we get:

1/2 x 1/7 = 1/14

Therefore, 1/2 divided by 7 is equal to 1/14.

Answer: 1/14

Step-by-step explanation:

To solve 1/2 divided by 7, you would first make 7 a fraction as well, which is 7/1. Then you do the inverse operation and fraction which is multiplying. So now, the question is 1/2 multiplied by 1/7. That equals 1/14

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

Mathematicians use the unitary method to tackle proportionality-related issues. Finding the value of one unit of a quantity and then using that value to determine the value of another quantity is what this process entails. The unitary technique, for instance, can be used to calculate how far a car will travel on 5 gallons of gas if it travels 40 miles on 2 gallons. We start by determining the price of one unit of gasoline: 2 gallons of fuel equals 20 miles per gallon, while 1 gallon of gasoline travels 40 miles. The distance the car will drive on 5 gallons of gasoline can then be calculated using this value:

given

The query does not include information on the typical wage of a professional basketball player. Let's say the average wage for a professional basketball player in the NBA is $5x106 per year.

We divide the salary of the basketball player by the salary of the worker to determine how many times higher the typical professional basketball player's salary is than the average American worker's salary:

$5x10^6 / $4x10^4 = $125000 / $1 = 125000

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

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There are 3.79 litres in 4 quarts.

Unit conversion is the conversion between different units and measurements of the same quantity through a process of multiplication or division. In mathematics, conversion is the process of changing values ​​in one form to another form like Inches to millimeters or liters to gallons.

Given in the table

1 quart = 0.9464 liter

4 quarts = 4 × 0.9464 litre

4 quarts = 3.7856 litres

hundredths means 2 digit right to the decimal point

3.7856 litres rounded to nearest hundredths

= 3.79 litres

Hence, 3.79 litres are there in 4 quarts.

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Answer:

DG = 12 , GC = 24

Step-by-step explanation:

DC is a median of Δ ABC

on each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, that is

GC = 2 DG , then

DG + GC = DC , that is

DG + 2 DG = 36

3 DG = 36 ( divide both sides by 3 )

DG = 12

thus

DG = 12 and GC = 2 × 12 = 24

Answer: 94%

Step-by-step explanation: there are 16 .4's in 6.4 and if he missed by .4 then he got 15/16 which equals 94%

The value of x in the figure and given in the task content is; x = 64.

As evident in the task content; the figure is a triangle with angle measures; 63°, 56° and (x - 3)°.

Since the sum of interior angles of a triangle is; 180°.

Therefore, we have;

63° + 56° + (x - 3 )= 180°

open parenthesis

63 + 56 + x - 3 = 180°

x = 180 + 3 - 63 - 56

x = 64°.

Ultimately, the value of variable, x from the triangle is; 64°.

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Answer:

10

Step-by-step explanation:

(-9,5) (-9,-5)

[tex]x_{1} = -9\\y_{1} =5\\x_{2} =-9\\y_{2} =-5[/tex]

[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2} -y_{1} )^{2} }[/tex]

[tex]\sqrt{(-9-(-9)^{2} +(-5-5)^{2} }[/tex]

[tex]\sqrt{(-9+9)^{2}+(-5-5)^{2} }[/tex]

[tex]\sqrt{(0)^{2}+(-10)^{2} }[/tex]

[tex]\sqrt{0+100}[/tex]

[tex]\sqrt{100} =[/tex] 10

(Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.

To find the height of an object in mathematics, you must first identify the shape of the object. Then, use the relevant formula for the shape to calculate the height. For example, if the object is a right triangle, the height can be found by using the Pythagorean Theorem. Additionally, if the object is a rectangle, you can use the formula for the area of a rectangle to calculate the height. Finally, if the object is a circle, you can use the formula for the circumference of a circle to find the height.

To solve this question, we will use the numerical approach. First, we need to subtract the number of saplings with a height greater than 27 1/4 inches from the total number of saplings. Then, we subtract the result from the total number of saplings. The result will be the number of saplings with a height of 27 1/4 inches or less.

Therefore, the equation is (Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.

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The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are;

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

The coordinates of the quadrilateral RSTU is

R = (1, -2)

S =(2, -4)

T = (4, -5)

U = (3, -3)

When the quadrilateral RSTU is rotated 90 degrees about the origin, it forms the quadrilateral MNPQ which has the coordinates

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

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Answer:

Aisha, Arsenio

Step-by-step explanation:

Because it adds up to a total of 180 degrees

Answer:

Raju spent a total of Rs 919.50. He bought 4 books at Rs 222.75 each, which cost Rs 891, and 2 books at Rs 14 each, costing Rs 28.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's first calculate the total cost of the 4 books that Raju bought:

Cost of 1 book = Rs 222.75

Cost of 4 books = 4 x Rs 222.75 = Rs 891

Now, let's calculate the amount of money Raju received by selling 2 books at Rs 14 each:

Amount received by selling 1 book = Rs 14

Amount received by selling 2 books = 2 x Rs 14 = Rs 28

Therefore, the total cost of 4 books is Rs 891 and the total amount received by selling 2 books is Rs 28. To find Raju's overall expenditure, we need to subtract the amount received from the total cost of 4 books:

Raju's overall expenditure = Total cost of 4 books - Amount received by selling 2 books

= Rs 891 - Rs 28

= Rs 863

Therefore, Raju's overall expenditure is Rs 863.

Answer:

Step-by-step explanation:

We can use the Pythagorean theorem to find the distance from second base to home plate, which is the diagonal of a right triangle with legs of 60 feet each:

d = sqrt(60^2 + 60^2) = sqrt(7200) ≈ 84.85 feet

So the total distance that you ran is:

60 + 60 + 84.85 ≈ 204.9 feet

Rounded to the nearest tenth, the answer is:

204.9 feet ≈ 204.9 feet

The equations of the relationship are

A: y = 1/4x

B: y = 2/5x

From the question, we have the following parameters that can be used in our computation:

The graph

We can see that the lines pass through the origin

This means that the equations can be represented as

y = mx

Where

m = slope

From the graph. we have

A = (8, 2)

B = (5, 2)

When these points are substituted, we have

A: 8m = 2

B: 5m = 2

When solved, we have

A: m = 1/4

B: m = 2/5

So, the equations are

A: y = 1/4x

B: y = 2/5x

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Therefore, the likelihood of a thunderstorm is roughly 0.2174, or a 21.74% chance that one will occur.

The study of random events or phenomena falls under the category of probability, which is a branch of mathematics. It is a way to quantify the possibility or likelihood of an event happening. A number between 0 and 1, where 0 denotes an improbable occurrence and 1 denotes a certain event, is used to express probability. By dividing the number of favorable outcomes by the total number of possible outcomes, one can determine the probability of an occurrence. In many disciplines, including statistics, economics, engineering, and science, probability is used to make predictions and well-informed choices in uncertain situations.

given

We must divide the amount of beneficial outcomes (chances of a thunderstorm) by the total number of possible outcomes in order to express the suggested degree of likelihood as a probability value between 0 and 1 inclusive.

When the likelihood of a thunderstorm is stated as "5 in 23," it indicates that out of a possible 23, 5 outcomes are likely to be favorable.

Therefore, the likelihood of a rainstorm is:

P (thunderstorm) is the ratio of the number of successful outcomes to all other possible outcomes.

Thunderstorm P(thunder) = 5 / 23

As a result, the probability value for the indicated degree of likelihood can be expressed as:

P(thunderstorm)= 5/230.2174

Therefore, the likelihood of a thunderstorm is roughly 0.2174, or a 21.74% chance that one will occur.

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Answer:

Step-by-step explanation:

he recives 8.52

Answer: $8.52

Step-by-step explanation:

First, you have to calculate how much Tommy spent, which is shown below:

2 x 3.99 = 7.98

7.98 + 3.5 = 11.48

Now that we know Tommy spent 11.48, we just subtract that from 20

$20.00 - $11.48 = $8.52

Answer:

Lamar claims that the weight of her cat is "almost 11 pounds".

Since Lamar is using the word "almost", we can assume that she means the weight of her cat is very close to 11 pounds, but not exactly 11 pounds.

Therefore, we can represent Lamar's claim with the inequality:

B) w < 11

This is because if the weight of Lamar's cat is almost 11 pounds, but not exactly 11 pounds, then the weight must be less than 11 pounds.

The population of 2 guppy fishes that grows at a rate of 1700% per month indicates;

A population growth formula is a formula of the form; A = P·(1 + r)^t, where, A is the amount after a period of t months, (or days or years), at a growth rate of r.

Number of guppy fish bought = 2

Rate at which guppy populations grow = 1700% per month

The formula that models the population of guppies can be obtained as follows;

The population growth equation is an exponential formula that can be modeled using the following equation;

Where;

A = The number after the number of months

P = The initial population of the guppy fish = 2

r = The percentage growth rate = 1700%

t = The time of growth in months = 4

Therefore, after 4 months the population of guppy fish will be;

A = 2 × (1 + 17)^4 = 209952

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Answer: 15

Step-by-step explanation: to find a percent of a number you use the formula :  ( % x N )/100 where N is the number you are trying to find the percent of. So here 15x100= 1500 and this divided by 100 is 15

Answer:

15

Step-by-step explanation:

of means "x"

15% of which were well done

who is the which they refer here?

15% of 100 burgers were well done

15% x 100 burgers

15/100 x 100 burgers = ans

Answer:

26

Step-by-step explanation:

[tex] \sqrt{ {24}^{2} + {10}^{2} } = 26[/tex]

Answer:

----------------------------

Given is the right triangle with legs of 24 and 10.

Find the hypotenuse using Pythagorean theorem:

The inequality which represents the least number of days that Kelli needs to run to reach her goal is

2 1/4 + 1/3d ≥ 4.

The least number of days after Monday that Kelli needs to run to reach her goal is 5.25 days

Monday= 2 1/4 miles

Other days of the week = 1/3 miles

Her goal =™4 miles

Number of days = d

2 1/4 + 1/3d ≥ 4

subtract 2 1/4 from both sides

1/3d = 4 - 2 1/4

1/3d = 4 - 9/4

1/3d = 16-9 /4

1/3d = 7/4

divide both sides by 1/3

d = 7/4 ÷ 1/3

d = 7/4 × 3/1

= 21/4

d = 5.25 days

Hence, Kelli will reach her goal in at least 5.25 days.

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The answer of the question based on monthly installment is Anver's monthly installment is R6 253.27.

What is Formula?

In mathematics,  formula is  set of symbols or expressions representing mathematical relationship or the rule. Formulas are often used to describe and solve the problems in mathematics, science, engineering, and other fields.

To determine the amount of the loan, we can calculate 85% of the price of the van, which is the amount that Anver would have to borrow after paying the 15% deposit:

Amount of loan = 85% of R392 900

= 0.85 x R392 900

= R333 965

To determine the monthly installment, we need to use the formula for the present value of an annuity:

PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)

We can calculate the annual interest rate by adding 1% to the prime rate. According to the South African Reserve Bank, the prime rate in September 2013 was 9%.

Annual interest rate = prime rate + 1%

= 9% + 1%

= 10%

Therefore, we can substitute the given values into the formula:

PV = R333 965

r = 10% / 12 = 0.8333%

n = 12

t = 72 / 12 = 6

Rearranging the formula to solve for PMT, we get:

PMT = PV x (r/n) / (1 - (1 + r/n)^(-nt))

Substituting the values, we get:

PMT = R6 253.27 (rounded to two decimal places)

Therefore, Anver's monthly installment is R6 253.27.

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If the container is closed rectangular it has six faces - a top, a bottom, and four rectangular sides. If the container has an opening, it has five faces - a top, a bottom, and four rectangular sides.

The number of faces of any geometry can vary depending on its specific shape and design. In geometry, a face is a flat surface that forms part of the boundary of a solid object.

For example, a cube has six faces, a rectangular prism has six faces, and a sphere has no faces (because it is a curved surface with no edges or corners).

The number of faces in a container can vary depending on its shape and whether it has any openings. Here are some common types of containers and the number of faces they have:

Rectangular container: If the container is completely closed, it has six faces - a top, a bottom, and four rectangular sides. If the container has an opening, it has five faces - a top, a bottom, and four rectangular sides.

Circular container: If the container is completely closed, it has two faces - a top and a bottom. If the container has an opening, it has three faces - a top, a bottom, and a curved side.

Cylindrical container: If the container is completely closed, it has three faces - a top, a bottom, and a curved side. If the container has an opening, it has four faces - a top, a bottom, a curved side, and an additional flat side where the opening is located.

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Answer:

Step-by-step explanation:

Answer:

Base = 5inches

Step-by-step explanation:

2(x+2) + x
2x+4+x
3x+4=19
3x=15
x=5

Answer:x5

Step-by-step explanation: