The answer for math

All the correct options are:

The x-intercept of g(x) is (0.1, 0).

And the range is (-∞, ∞).

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given:

The functions,

f(x) = log x

And g(x) = 4logx + 4

The graph of g(x) is given in the attached image.

The x-intercept of g(x) is (0.1, 0).

And the domain is (0, ∞)

And the range is (-∞, ∞).

Therefore, all the features of function g(x) are given above.

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Claira must make fifteen payments of 334.44 each in equal amounts toward her new car, which she purchased for 5700.

For $5,700, Claire gets a brand-new vehicle. She made a 12% down payment. We must ascertain the fifteen equal monthly payments.

to find out the 15 equal monthly payment we shall use the formula,

for monthly installments =   [tex]\frac{P(1-D)}{m}[/tex]    

Where P stands for principal amount, D for down payment and m use for month.

we have P=5700

D=12%=0.12

m=15

Therefore, monthly payment = [tex]\frac{5700(1-0.12)}{15}[/tex]

=[tex]\frac{5700(0.88)}{15}[/tex][tex]= \frac{5016}{15} =334.44[/tex]

Thus, she has to make 15 payments of ∈ 344.44. for her new purchased car.

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h(t) and h-1(t) are inverses of each other.

Inverse is a function that is severs to undo another to the function.thag is produces y,then putting y and into the inverse of f of the produces the output x.

To find the inverse of h(t), we need to first solve for t in the equation h(t) = 16t^2 + 144. This can be done by finding the roots of the equation, which can be done by setting the equation equal to zero and using the quadratic formula,

t = ±√(h(t) - 144)/16

Since h(t) is a quadratic function, the inverse of h(t), h-1(t) will also be a quadratic function. Therefore, h-1(t) can be written as:

h-1(t) = ±√(t - 144)/16

To show that h(t) and h-1(t) are inverses, we can plug in a known value, such as t = 10, and check that the results of both equations are equal.

h(10) = 16(10)^2 + 144 = 272

h-1(272) = ±√(272 - 144)/16 = ±√(128)/16 = 10

Since the results of both equations are equal, it is clear that h(t) and h-1(t) are inverses of each other.

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The function can be written as - y = (7/3)x - (21.5/3).

Given is the equation as -

- 7x + 3y = - 21.5

The given equation is -

- 7x + 3y = - 21.5

3y = - 21.5 + 7x

y = - (21.5/3) + (7/3)x

y = (7/3)x - (21.5/3)

Therefore, the function can be written as -

y = (7/3)x - (21.5/3).

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The total cost for 5 pounds of apples, 2 pounds of grape and a pound of melon will be $10.42

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since the price of apples is $1.29/lb, the price of grapes is $0.79/lb and the price of melon is $2.39/lb, the total cost for 5 pounds of apples, 2 pounds of grape and a pound of melon will be:

= (5 × 1.29) + (0.79 × 2) + 2.39

= $10.42

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Complete question

The price of apples is $1.29/lb, the price of grapes is $0.79/lb and the price of melon is $2.39/lb. What is the total cost for 5 pounds of apples, 2 pounds of grape and a pound of melon.

Answer:I think its multiply

Step-by-step explanation: 90 x 2 = 180

The line with slope -2/3 that crosses the y -axis at the point (0,4) exists X = -2/3y + 4.

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

The values of the y-intercept and slope reveal details on the nature of the relationship between the two variables, x and y. According to a unit change in x, the slope shows how quickly y changes. When the x-value is 0, the y-intercept shows the value of the y-axis.

Vertical lines are described as having "unknown slope" because their slope seems to be an arbitrary, arbitrarily high amount. The four different slope types are represented in the graphs below.

Therefore, the correct answer is option d) X = -2/3y + 4.

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Answer: The slopes of the two equations are the same but the intercepts are different; therefore the lines are parallel and the system has no solutions. This is an inconsistent system.

Therefore , the solution of the given problem of quadrilateral comes out to be the centre of dilatation to produce a smaller polygon (0.9x, 0.9y).

In geometry, a four-sided object having four corners is referred to as a quadrilateral. The word comes from either the Latin quad or portfolio of innovative (meaning "side"). Four corners, four states, and four corners are the three dimensions of a rectangle. Concave and convex surfaces come in essentially two varieties. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, angles, rhombuses, and squares.

Here,

The rule that can describe this is (x, y). The polygon is expanded to use the beginning as the point of dilatation to generate a smaller polygon. (0.9x, 0.9y)

A point is transformed when it is moved from its original location to something like a new one. Reflection, rotation, translation, and dilation are examples of different transformations.

The term "dilation" refers to an alteration in a figure's size.

The clear element is A' if a position A(x, y) is stretched by a factor k. (kx, ky). It is a decrease if k 1 and an enlargement if k > 1.

The rule that can describe this is (x, y). The hexagon is dilated to use the beginning as the centre of dilatation to produce a smaller polygon.

(0.9x, 0.9y)

Therefore , the solution of the given problem of quadrilateral comes out to be the centre of dilatation to produce a smaller polygon (0.9x, 0.9y).

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The height of the given tree to the nearest foot is; 21 ft

If Carlos, mirror, and bottom of tree are points on the ground all on one line, then it means that the two right triangle are these:

LEFT Triangle: y and 31 as the legs and unknown hypotenuse.

RIGHT Triangle: 6 and 8.7 as legs and unknown hypotenuse.

The two angles at the mirror are of same measure; that is, the 31 and the hypotenuse of LEFT triangle makes same angle measure as the 8.7 and the hypotenuse of the RIGHT triangle.

Thus, using concept of similar triangles, we can say that;

y/31 = 6/8.7

y = (31 * 6)/8.7

y = 21 ft

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Answer:  To calculate the fee, we need to know the annual salary, the percentage fee and the number of weeks that the fee will be applied. In this case, the annual salary is $28,600, the fee is 23% and the number of weeks is 4.

First, we need to calculate the weekly pay by dividing the annual salary by 52 weeks in a year:

Weekly Pay = $28,600 / 52

Weekly Pay = $550

Then we can calculate the amount of money that the agency will charge for the first four weeks by multiplying the weekly pay by the number of weeks:

4 Weeks Pay = 4 x $550

4 Weeks Pay = $2200

Now, we can calculate the fee by multiplying the 4 weeks pay by 23%:

Fee = $2200 x (23 / 100)

Fee = $506

So, the agency will charge Greg a fee of $506 for the first four weeks of his job.

Step-by-step explanation:

The options that are true or false as regards the ratios are;

Options A & D are true

Options B & C are false

We are given;

Number of helium balloons ordered for every 5 people = 2

Number of  stuffed animals for every eight people = 3

Total number of people to attend = 120

A) The ratio of helium balloons to stuffed animals;

Number of helium balloons = 2/5 * 120 = 48

Number of stuffed animals = 3/8 * 120 = 45

Ratio = 48:45 = 16:15

This is true according to the option

B) The ratio of stuffed animals to  helium balloons;

Number of helium balloons = 2/5 * 120 = 48

Number of stuffed animals = 3/8 * 120 = 45

Ratio = 45:48 = 15:16

This is false according to the option

C) This is false according to the calculations above

D)  This is true according to the calculations above

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To begin solving a polynomial problem, express it in standard form. When it reaches zero, factor it and then set each variable factor to zero. The answers to the resultant equations are the original solutions. Factoring cannot solve all polynomial problems.

Polynomials are sums of terms of the form where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. A primer on polynomials. This video defines words such as degree, standard form, monomial, binomial, and trinomial.

A polynomial may be categorized into four categories based on its degree. There are four types of polynomials: zero polynomial, linear polynomial, quadratic polynomial, and cubic polynomial.

A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.

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To create the 90% confidence interval for the average speeds on his road journey, Keith should utilise t* 1.943.

To construct a confidence interval for the mean of a sample, Keith needs to use the t-distribution with a degree of freedom equal to one less than the sample size.

Since Keith has seven days of data, the degrees of freedom (df) is

= 7 - 1

= 6.

A 90% confidence interval corresponds to a 95% confidence level, as the remaining 5% is divided evenly between the two tails of the t-distribution.

The value of t* for a 90% confidence level and 6 degrees of freedom is 1.943.

So, Keith should use t* ≈ 1.943.

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1) The area of the shaded portion is; 63π

2) The area of the shaded portion is; 4π - 8√2

1) The formula for area of a circle is;

A = πr²

where r is radius

The radius here is 9cm and so;

A = π * 9²

A = 81π

The area of a sector is given by the formula;

(θ/360) * πr²

Thus;

A_sect = (80/360) * π * 9²

A_sect = 18π

Area of shaded region = 81π - 18π

Area of shaded region = 63π

2) Using trigonometric ratio, we can find the diameter LN as;

4/LN = cos 45

4/LN = 1/√2

LN = 4√2

Formula for area of semi circle is;

A = ¹/₂πr²

A = ¹/₂ * π * (¹/₂ * 4√2)²

A = ¹/₂ * π * 8

A = 4π

Area of triangle = ¹/₂ * 4 * 4√2

= 8√2

Area of shaded portion = 4π - 8√2

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The Round-off of 73 nearest to the 10th is 70. This process is called rounding off the numbers.

The process is used to simplify the numbers so that the number can easily be calculated, he Round-off process can take place to the nearest 10, 100,1000, and so on, this is called round-off. T It can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form.

For example: if the distance between the USA and Mexico is  1190 mi, what is the round-off distance? = 1200 mi.

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The inequality that represents the situation is 5h + 10 < 30.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Maria wants to rent a bicycle. The shop charges a $10 deposit and a $5 hourly fee.

Let, The number of hours be 'h'.

Therefore, The inequality that represents the number of hours Maria can rent the bicycle if she wants to pay less than $30 is,

5h + 10 < 30.

5h < 25.

h < 25/5.

h < 5.

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Answer: Circle 2

Step-by-step explanation:

If you show that angle 2 is equal to angle 3, then since angle 1 is equal to angle 2, angle 1 is equal to angle 3, which proves that the 2 lines are parallel.

(The wording is a bit weird sorry)

The ink will diffuse one micrometer in 5 x 10⁻⁴ seconds

From the problem it can be deduced that

time, t in seconds it takes t diffuse 1 centimeters

t = x² / 2D

The diffusion coefficient for a drop of ink in water is about 10⁻⁵ square centimeters per second

D = 10⁻⁵ cm²/s

time to for the ink to diffuse 1 micrometer

1 micrometer =  10⁻⁴ centimeter = x

t = x² / 2D

t = (10⁻⁴)² / 2 * 10⁻⁵

t = 5 x 10⁻⁴ seconds

In 5 x 10⁻⁴ seconds the ink will diffuse 1 micrometer

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Slope 1 is the blue line.

Slope 2 is the yellow line.

Slope 1/5 is the black line.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Take two coordinates from each line.

Yellow line.

(0, 3) and (1, 5)

m = (5 - 3) / (1 - 0) = 2/1 = 2

Slope = 2

Blue line.

(0, 8) and (1, 9)

m = (9 - 8) / (1 - 0) = 1/1 = 1

Slope = 1

Black line.

(0, 5) and (5, 6)

m = (6 - 5)/(5 - 0) = 1/5

Slope = 1/5

Thus,

The blue line has slope 1.

The yellow line has slope 2.

The black line has slope 1/5.

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The only value of x that is in the domain of F(x)=√x5 is x≥0. This means that the answer to the question is option D: x=1.

The domain of the function F(x)=√x5 is all values of x greater than or equal to zero (x≥0). This is because when a number is raised to the fifth power, it can never be negative; so the square root of a negative number is undefined. The calculation to prove this is as follows:

Let x=−5.

F(x)=√(−5)5=√(−25)=undefined

Therefore, the only value of x that is in the domain of F(x)=√x5 is x≥0. This means that the answer to the question is option D: x=1.

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The distance 60ft when converted to miles is 1/88 mi or 0.0114 mi

Distance can be measured in various units such as miles, kilometers, feet, meters, etc.

To convert a distance from one unit to another, you need to know the conversion factor between the units.

In this case, the conversion factor is 5280. Therefore, to convert 60 feet to miles, divide it by 5280 (since 5280 ft = 1 mi). Therefore, based on the information given above, the calculation will be done thus:

60ft = 60/5280 mi

= 1/88 mi = 0.0114 mi

Therefore, the calculation shows that the conversion will be 0.0114 miles.

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Answer: y=x/3-6

Step-by-step explanation:  ✨Math sucks doesn’t it darling✨

Answer:

x=-27/11

Step-by-step explanation:

This answer is x=-27/11

A parabola's vertex, which is its maximum or minimum, and focus, which is a fixed point inside the parabola, are both mathematical terms. The parabola's axis is parallel to the directrix, which lies outside the parabola.

Y=ax2+bx+c is a parabola; hence,

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ZMOP must have a measure of 60°.

A triangle is a three-sided polygon that is one of the most basic shapes in geometry. It is defined by three points, known as its vertices, and the straight lines connecting them. Triangles come in many different shapes and sizes, and can be classified by their angles, sides, and area. Triangles have many uses in mathematics, for example, to calculate interior angles, calculate area and perimeter, or to prove certain geometric theorems.

In order to find the measure of ZMOP, we must first look at the structure of triangle NOP. Since it is formed by connecting the midpoints of the sides of triangle KLM, it can be classified as an equilateral triangle. This means that all three of its interior angles are equal in measure. Therefore, ZMOP must have a measure of 60°. This is because the sum of all three interior angles of an equilateral triangle is 180°, and since the other two angles have measures of 34° and 74°, the third angle must have a measure of 180° - (34° + 74°) = 60°.

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Answer: just graph it on the y-axis

Step-by-step explanation:

Yes, x² is a quadratic equation.

A polynomial equation is an equation that can be written as the sum of a finite number of non-negative integer powers of x.

A polynomial equation of degree 2 is also called a quadratic equation. It can be represented in the standard form as f(x) = ax² + bx + c, where a, b, and c are real numbers and a is not equal to 0.

Quadratic equations have a specific shape of parabola, with the vertex being the point that is the lowest or highest point of the parabola depending on the sign of the leading term.

Hence, x² is a quadratic equation.

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Answer:

are you allowed to repeat numbers?

if so, the first one will be 2/5 + 2/5

if not, the first one will be 1/5 + 3/5

for the second one, the only possible combination would be 1/5 + 2/5 + 1/5

Step-by-step explanation: