Vanessa purchased a used car on a payment plan. Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975.
Write an equation that models the balance y after t months.
y=___t+___

The sum of the interior angle measures of this polygon is 540 degrees

A convex polygon is simply described as closed figure having all its interior angles less than 180° and its vertices  pointing outwards.

The word 'convex' is used to described a shape that has a curve or a protruding surface.

Also, all the lines across the outline are straight and they all point outwards.

From the diagram shown, we have that;

Sum of the interior angles of a pentagon = (n - 2) 180

Substitute n as 5 in the equation

= (5 -2 ) 180

= 3(180)

= 540 degrees

Hence, the sum is 540 degrees

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Answer: y = ±√ 0.500 = ± 0.70711

Step-by-step explanation:

Solve  :    2y2-1 = 0  Add  1  to both sides of the equation :                       2y2 = 1 Divide both sides of the equation by 2:                     y2 = 1/2 = 0.500   When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:                        y  =  ± √ 1/2  

Answer:

Answer: y = ± √0.500 = ± 0.70711

Answer:

19/16 or 1 and 3/16 of an inch

Step-by-step explanation:

In order to add fractions, we must first find a common denominator, which in this case would be 16 because 8 times 2 = 16.

Whatever we do to the denominator must be done to the numerator, so we have to also multiply 7 by 2 to give us the fraction 14/16.

Now we can add the fractions: 5/16 + 14/16 = 19/16 or 1 3/16

Part 1

[tex]m=\frac{-7-(-5)}{8-0}=\boxed{-\frac{1}{4}}[/tex]

Part 2

[tex]y=-\frac{1}{4}x-5[/tex]

We must take into account the number of options for each PIN digit in order to get the total number of 4-digit personal identification numbers (PINs) that can exist. There are nine options available because the first digit must be 0. (1, 2, 3, 4, 5, 6, 7, 8, or 9). There are a total of 10 options available for each of the remaining 3 digits, which can all be any of the digits 0 through 9. Thus, there are a total of 9 * 10 * 10 * 10 = 9000 different 4-digit PIN combinations.

  However, since we're looking for 4-digit PINs that are odd, the last digit must be one of the following: 1, 3, 5, 7, or 9. This indicates that there are 5 options available for the final digit.

  As a result, there are 4500 4-digit PINs that are odd and cannot start with 0. This is calculated as 5 * 9 * 10 * 10. This is the right response, which goes with option b.

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The test statistic by the given values is t = -2.

Test statistic is a value calculated from a statistical test of hypothesis. It describes the closeness of the observed data with the expected distribution under the null hypothesis.

Test statistic can be calculated from the formula,

t = (xₐ - μ) / (s/√n)

where xₐ is the sample mean, μ is the population mean, s is the standard deviation and n is the sample size.

Given,

n = 49, xₐ = 50, s = 7

Since null and alternate hypothesis are given, μ = 52.

So the test statistic,

t = (50 - 52) / (7/√49)

 = -2 / (7/7)

 = -2

Hence the test statistic is -2.

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We can give the following two conclusions:

From the information provided:

Since GFH and HFJ are adjacent, they share a common side or vertex. This means that the two figures are not only congruent, but they also share at least one common angle.

Since GFH and HFJ are congruent, they have the same size and shape. This means that corresponding angles and sides are equal in measure. It also means that the two figures can be superimposed on each other exactly.

In conclusion, since they are congruent and adjacent, we can say that they are part of a larger geometric figure.

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The answer of addition & multiplication are,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

0.000000612 x 0.00031119 =

297,060 + 0.0004839 =

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

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Answer:

its b

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

$630.69

Step-by-step explanation:

Copnvert 93% into decimal format and multiply by $678.16:

(0.93)*($678.16) = $630.6888, whcih we will round to $630.69.

The linear function f(x) has a slope of -5 and intersects the y-axis at the point (0, 45).  The function g(x) intersects the x-axis closer to zero than the function f(x). Option D

Generally, To find the x-intercepts of a linear function, you can set the y-value equal to zero and solve for x.

For the function f(x), we have:

f(x) = -5x + 45

0 = -5x + 45

5x = 45

x = 9

So the x-intercept of f(x) is (9, 0).

For the function g(x), we have:

g(x) = -5x - 10

0 = -5x - 10

5x = 10

x = 2

So the x-intercept of g(x) is (2, 0).

Since the x-intercept of g(x) is closer to zero than the x-intercept of f(x), the correct answer is D. The function g(x) intersects the x-axis closer to zero than the function f(x).

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Find f when f"(x) = x^-2, x > 0, f(1) = 0, f(8) = 0

Integrate twice. Do not forget the constants of integration.

f'(x) = -1/x + C                    f(x) = - ln x + Cx + D

To find C and D, apply f(1) and f(2)

f(1) =  - ln (1) + C + D = 0    

C + D = 0     equation 1

f(8) = - ln 8 + 8C + D = 0  

8C + D = ln 8   equation 2

Solve for C and D from equations 1 and 2

C = ln 2/7   and D = - ln2/7

f(x) = - ln x  + (ln 2/7) x - ln 2/7

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals. Integration, along with differentiation, is a fundamental, crucial calculus operation.

It can be used to solve issues in mathematics and physics involving, among other things, the volume of a solid, the length of a curve, and the area of an arbitrary shape.

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At Marlins Park, the typical ticket cost during that season was $29.62. Operating the stadium for a single game costs about $300,000.

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Answer:

y = -5x/4 + 9

Step-by-step explanation:

Slope-intercept Form: y=mx+b where m=slope

In order to put the equation into slope-intercept form, solve for y:

10x + 8y = 72

8y = -10x + 72 ==> subtract 10x on both sides to isolate y

y = (-10x + 72)/8  ==> divide both sides by 8 to isolate y

y = -10x/8 + 72/8  ==> divide each term by 8

y = -5x/4 + 9  ==> simplify

The solution is : y = -5x/4 + 9, equation of a line into slope-intercept form, simplifying all fractions.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

we know that,

Slope-intercept Form:

y=mx+b

where m=slope

In order to put the equation into slope-intercept form, solve for y:

10x + 8y = 72

8y = -10x + 72 ==> subtract 10x on both sides to isolate y

y = (-10x + 72)/8  ==> divide both sides by 8 to isolate y

y = -10x/8 + 72/8  ==> divide each term by 8

y = -5x/4 + 9  ==> simplify

Hence, The solution is : y = -5x/4 + 9, equation of a line into slope-intercept form, simplifying all fractions.

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Answer:

Rectangle

Step-by-step explanation:

By putting the points in Desmos, it shows an image of a rectangle. It allows you to change the number of B and also A, and whatever number you change them to the image will still be a rectangle.

The quotient from the model of the number line is 0.05.

A quotient is an outcome of a division process carried out by two numbers in which one is a divisor and the other is a dividend. The divisor is the number that is being used to divide the dividend.

A quotient is the output of a division operation in more generic terms. It is the result of dividing one quantity by another. Aside from its mathematical use, the term "quotient" can also refer to the outcome of any division or separation process.

From the number line, we have 20 spaces between 0 to 1. So, it implies that 1 is the dividend and 20 is the divisor.

i.e.

[tex]\dfrac{1}{20}[/tex]

= 0.05  ... The result of this division process is known as the quotient.

Therefore, we can conclude that the quotient that models the division of the number line is 0.05.

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Answer: Y is 8

Step-by-step explanation:

Add 16 to both sides. y/4 = 2. Multiply both sides by 4 to get y=8.

Answer:

[tex]f^{-1}(x)=\sqrt{x+4}+1[/tex]

Step-by-step explanation:

[tex]f(x)=(x-1)^2-4\\y=(x-1)^2-4\\[/tex]

Swap x and y and solve for y:

[tex]x=(y-1)^2-4\\x+4=(y-1)^2\\\sqrt{x+4}=y-1\\\sqrt{x+4}+1=y\\f^{-1}(x)=\sqrt{x+4}+1[/tex]

Hence, the inverse function is [tex]f^{-1}(x)=\sqrt{x+4}+1[/tex]

Answer:

2 is correct answer.

Answer:

π/4

Step-by-step explanation:

(I cannot attach a unit circle here, sorry :)

Recall the function of the (x,y) values of the unit circle. X represents the cosine value, and y is the sine value.

If you look at a unit circle, π/2 has the coordinates (0,1), so the sine value of π/2 is 1.

To find arctangent, remember that the range of tangent is -π/2 < x < π/2. In terms of the unit circle, these are the minimum and maximum values, and we cannot use -π/2 and π/2 since x is 0, which means it'll be undefined. The angle where the coordinates can be found is the arctangent of the function.

So, find the coordinate where both x and y have the same value (√2/2, √2/2) at π/4. Therefore, the answer for the arctan(sin(π/2)) =  π/4.

The approximate probability that the proportion of individuals in the sample who favor capital punishment will exceed 0.41 is given as follows:

0.1093 = 10.93%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

p = 0.38, n = 400.

Hence the mean and the standard error for the approximation are given as follows:

The probability that the proportion exceeds 0.41 is one subtracted by the p-value of Z when X = 0.41, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.41 - 0.38}{0.0243}[/tex]

Z = 1.23

Z = 1.23 has a p-value of 0.8907.

Hence:

1 - 0.8907 = 0.1093 = 10.93%.

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The probability that a student likes either mathematics or social sciences, given the survey on the fourth - grade class is, 68 %.

The probability that a student would like either mathematics or social sciences in the fourth - grade class, is :

= Probability that student likes math + Probability that student likes social sciences - Probability that student likes both math and social sciences

Probability that student likes math = 64 %

Probability that student likes social sciences = 11 %

Probability that student likes both math and social sciences  = 7 %

The probability that a student likes either mathematics or social sciences is :
= 64 % + 11 % - 7 %

= 68 %

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Full question is :

A survey of a fourth-grade class, resulted in the following information:

64% liked mathematics, 11% liked social studies, and 7% liked both mathematics and social studies.

Find the probability that a student likes either mathematics or social sciences. (write the answer in percentage)

Triangle JKL is right. Triangle XYZ is acute.

To classify a triangle you need to know the measure of each angle.

For triangle JKL, if we measure the angles, we can see that angle JKL is 90 degrees, which makes it a right triangle.

For triangle XYZ, if we measure the angles, we can see that all angles are less than 90 degrees, which makes it an acute triangle.

Triangle JKL is a right triangle and triangle XYZ is an acute triangle.

Triangle JKL is right. Triangle XYZ is acute.

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Answer: b and a

Step-by-step explanation:

Douglas McGregor distinguished between these two techniques' fundamental assumptions about human motivation in his well-known "Theory X and Theory Y."

In his well-known "Theory X and Theory Y," Douglas McGregor distinguished between these two approaches' underlying assumptions about human motivation as follows: According to Theory X, employees must be forced, managed, and persuaded to work toward organizational objectives since they detest it.

Additionally, the majority of people prefer to be treated in this manner so they can evade accountability.

Theory Y, or the integration of aims, highlights the typical person's innate interest in his work, desire to be self-directing and seek responsibility, and the ability for originality in problem-solving for organizations.

Therefore, Douglas McGregor distinguished between these two techniques' fundamental assumptions about human motivation in his well-known "Theory X and Theory Y."

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Answer:

30.453

Step-by-step explanation:

n = (3000+45.3)/100

=     n = 3045.3/100

=     n = 30.453

Descartes's number is 30.453

Using simultaneous equations, Kieran and Louise's numbers are 20 and 8 respectively.

Kieran and Louise each think of a number. 4 less than Kieran's number is equal to 2 lots of Louise's number.

let's

x = Kieran's number

y = Louise's number.

x - 4 = 2y

x - 2y = 4

3 lots of Kieran's number added to Louise's number is 68.

Hence,

3x + y = 68

Hence, let's combine the system of equation.

x - 2y = 4

3x + y = 68

multiply equation(i) by 3

3x - 6y = 12

3x + y = 68

-7y = -56

y = -56 / -7

y = 8

Therefore, let's find x

x = 4 + 2y

x = 4 + 2(8)

x = 4 + 16

x = 20

Hence,

Kieran number = 20

Louise number = 8

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A triangle has three sides, three angles, and seven properties including sum of interior angles, exterior angle theorem, triangle inequality theorem, congruence, isosceles triangle theorem, right triangle theorem, and pythagorean theorem.

1. Sum of Interior Angles: The interior angles of a triangle always add up to 180°.

2. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.

3. Triangle Inequality Theorem: The sum of any two sides of a triangle must be greater than the measure of the third side.

4. Congruence: Triangles are congruent if their corresponding angles and sides are equal.

5. Isosceles Triangle Theorem: If two sides of a triangle are equal in length, then the angles opposite those sides are also equal in measure.

6. Right Triangle Theorem: A triangle with one 90-degree angle is called a right triangle.

7. Pythagorean Theorem: The sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.

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The seven properties of triangle is listed below.

Here we have to list down the seven properties of triangle.

The properties of the triangle are as follows:

1) Angle Sum Property states that the sum of the three interior angles of a triangle is always 180°.

2) Triangle Inequality Property states that the sum of the length of the two sides of a triangle is greater than the third side.

3) The difference property states that the difference between the two sides of a triangle is less than the length of the third side.

4) Pythagoras property states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

5) Exterior Angle Property states that the exterior angle of a triangle is always equal to the sum of the interior opposite angles

6) Similarity property states that if two triangles are said to be similar if their corresponding angles of both triangles are congruent and the lengths of their sides are proportional.

7) Congruence Property states that if two triangles are said to be congruent if all their corresponding sides and angles are equal.

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For the given equations the value of x is 3 and the value of y is -7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the system of equation is 5x + 7y = -34 and 10x + 17y = -89​. The value of x and y will be calculated as,

5x + 7y = -34   ........................(1)

10x + 17y = -89​ ........................(2)

Multiply the first equation by 2 and subtract the second equation from the first equation,

10x + 14y = -68

-10x - 17y = +89

____________

0    - 3y = 21

          y = -7

The value of x will be,

5x + (7 x -7 ) = -34

5x - 49 = -34

5x = -34 + 49

5x = 15

x =3

Hence, the values are x = 3 and y = -7.

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The Answer is 84, because 36 x 2 =72 and then 1/3 of 36 is 12 and 12+72=84.

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Answer:

9/5 ft/s

Step-by-step explanation:

v = v₀ + at

v = 2 f/s + (1.5 f/s²)(5 s) = 9.5 ft/s