find the scale factor

Answer:

\((25x + 8)(x + 2)\)

Step-by-step explanation:

\(25x^{2} + 58x + 16 = 25x^{2} + 50x + 8x + 16 = 25x(x + 2) + 8(x + 2) = (25x + 8)(x + 2)\)

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

Step-by-step explanation:

This word problem involves solving a set of two equations for two unknowns: M (cost of 1 thin mint), and T (cost of 1 trefoil).

First customer: 3*M + 2*T = 1.35

Second customer: 5*M + 1*T = 1.55

Solving the second equation for T:     T = 1.55 - 5*M

Then, we can plug this into the first equation:

3*M + 2*(1.55 - 5*M) = 1.35

3*M + 3.1 - 10*M = 1.35

-7*M = 1.35 - 3.1

-7*M = -1.75

M = -1.75/-7

M = 0.25 --> one thin mint costs $0.25

Now that we have one price, we can solve for the other one.

T = 1.55 - 5*M = 1.55 - 5*(0.25)

T = 1.55 - 1.25 = 0.30 --> one trefoil costs $0.30

Answer:

0.9375

Step-by-step explanation:

\(\frac{15}{16}\) ( divide value on numerator by value on denominator , that is

15 ÷ 16 = 0.9375

Answer:

x≥5

Step-by-step explanation:

If x is the quantity of goats he wants x≥5

Answer:

80 degrees

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360 degrees. Adding up the known measures gives you 95 + 123 + 62 = 280. Then you can subtract that from 360. 360 - 280 = 80. So x has to be 80 degrees.

If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

Answer:

0

Step-by-step explanation:

•103n+26n = 131n

Combine 103 n and 26 n to get 129n

•129n=131n

Substract 131n from both sides

•129n-131n=0

Combine 129n and -131n to get 2n

•-2n=0

Product of two numbers is equal to 0 if atleast one of them is 0. Since -2 is not equal to 0, n must be 0.

•n=0

The congruency relationship which hold true after transformation is

YZ ≅ AB

What is congruent ?

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

Explanation:

A translation is known as a rigid transformation.  This is because it preserves congruence.  Since CAB is created from XYZ, this tells us that:

X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.

Since the triangles are congruent, the corresponding pieces are congruent as well.

Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.

Hence the answer is YZ≅AB.

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The rate of change of the area of the right triangle is given by dA/dt = 94.5 - 27t.

To find the rate of change of the area of a right triangle as the sides change, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

In this case, the legs of the right triangle are changing, and we need to find the rate of change of the area with respect to time.

Let's denote the short leg as x and the long leg as y. We are given that dx/dt (the rate of change of the short leg) is 9 in/sec (positive because it is increasing), and dy/dt (the rate of change of the long leg) is -3 in/sec (negative because it is shrinking).

We are interested in finding dA/dt, the rate of change of the area A with respect to time.

A = (1/2) * x * y [Area formula]

Taking the derivative of both sides with respect to time t:

dA/dt = (1/2) * (x * dy/dt + y * dx/dt) [Using the product rule]

Substituting the given values:

dA/dt = (1/2) * (x * (-3) + y * 9)

= (1/2) * (-3x + 9y)

Now, we need to find the values of x and y. Since the legs of the right triangle are changing, we can express x and y in terms of t.

Given:

x = 21 + 9t [Short leg is increasing by 9 in/sec, starting from 21 inches]

y = 28 - 3t [Long leg is shrinking at 3 in/sec, starting from 28 inches]

Substituting these expressions into the equation for dA/dt:

dA/dt = (1/2) * (-3(21 + 9t) + 9(28 - 3t))

= (1/2) * (-63 - 27t + 252 - 27t)

= (1/2) * (189 - 54t)

= 94.5 - 27t

Therefore, the rate of change of the area of the right triangle is given by dA/dt = 94.5 - 27t.

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The principal part at the isolated singular point -1 is not provided, so we cannot determine its nature or residue. And b) The principal part at the isolated singular point 1 is (x - 1)^2022 exp(-1). It is a pole of order 2022, and its residue is 0.

a) The principal part at the isolated singular point -1 is not provided, so we cannot determine its nature (removable singular point, essential singular point, or pole) or calculate its residue without additional information.

b) The given function is (x - 1)^2022 exp(-1). At the isolated singular point x = 1, the principal part of the function is (x - 1)^2022 exp(-1). Here, (x - 1)^2022 represents the pole part of the function, and exp(-1) represents the non-pole part.

Since the term (x - 1)^2022 dominates near x = 1, we can conclude that x = 1 is a pole. The order of the pole is determined by the exponent of (x - 1), which is 2022 in this case.

To calculate the residue, we need more information about the function, specifically the coefficients of the Laurent series expansion near the singular point. Without that information, we cannot determine the residue at x = 1.

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The graph that shows a unit rate of 3/4, which is the time Cindy reads while riding in the car is the graph attached below.

Unit rate can be described as a constant or exactly how much of one quantity is per 1 unit of another quantity.

Unite rate (k) = x/y.

In the graph attached below, when x (hours driving) = 3, y (hours reading) = 4.

Therefore, unit rate = 3/4. We can then conclude that the graph that shows that Cindy reads 3/4 of the time she rides in a car is the graph attached below.

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Answer:

To solve this problem, we need to calculate the change in temperature between noon and 3:30 p.m. and then divide that by the number of hours between noon and 3:30 p.m.

Let's say the temperature at noon was 70 degrees F and the temperature at 3:30 p.m. was 75 degrees F.

The change in temperature between noon and 3:30 p.m. is 75 - 70 = 5 degrees F.

The number of hours between noon and 3:30 p.m. is 3.5 hours.

Therefore, the rate of change in temperature between noon and 3:30 p.m. is 5 degrees F / 3.5 hours = 1.43 degrees F per hour.

Answer:

13

Step-by-step explanation:

I can't see the rest of the question but im assuming it's asking how many people there are so you add the 6 and 4 together which makes 10 and divide 130 by 10 because its 10 ounces all together for each person which makes 13. I'm really sorry of this is wrong but im assuming that is the answer because that is what the question looks like its asking

Answer:13

Step-by-step explanation:

not sure if correct but

Answer:

So we have an original figure with a value of 50 and then a scaled version or dilation

Hence we have a scale factor of

\( \frac{1}{5} \)

Answer:

formula for ratio: you can write a ratio with :, or, /

x axis is horizontal

0= x axis  6= y axis

Step-by-step explanation:

120 units are needed to complete the number of equivalent units if the ending work in the process contains 300 units.

Number of units =  300 units

Percentage of units completed  = 40%

To determine the number of equivalent units for a display operation, you need to view the teams that are fully satisfied as well as the partly finished units in the cessation outcome in the process.

Equivalent units = Number of fully completed units + Equivalent units in finishing work in process

Number of equivalent units = 0 + (300 units x 40%)

Number of equivalent units = 0 + 120 units

Number of equivalent units = 120 units

Therefore, we can conclude that the number of equivalent units is 120 units.

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The complete question is-

if the ending work in the process contains 300 units that are 40% complete the number of equivalent units is?

The location of point G on the given number line is 4.

Given that, partitions the directed line segment from F to D into an 8:5 ratio.

A measureable path between two points is referred to as a line segment. Line segments can make up the sides of any polygon because they have a set length.

Since, the line is 13 units and 8:5 is 13 parts each proportion is 1 unit.

Which means 8 parts and 5 parts are on the line.

So, 8+(-4)

= 8-4

= 4

Therefore, the location of point G on the given number line is 4.

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On the basis of birthday problem or scenario, the number of people should be selected to guarantee that at least 4 were born on the same day, not considering the year is equals to the 1096.

The worst case scenario is one of the many possible cases where the desired outcome comes after every other probable outcome has already occurred. The number of people who ensure that at least 7 people have a birthday on a single day of a non-leap year (365 days) can be determined by ensuring that in the number of people selected in each trial, two people do not have a birthday on a day. the same day. There are 365 days in a year.

Assuming everyone was born on a different day, then you could have 365 people where no one was born on the same day, but those 366 people would have to be born on the same day as someone else in the group. So the minimum number of people in a group would have to be 366 to guarantee that at least 2 people were born on the same day. But we wanted to guarantee that at least 4 people were born on the same day.

So, assuming we had 3 × 365 people together, with every 3 of them being born on the same day. Then would have a total of 365× 3 = 1095 people, with no more than 3 people being born on the same day. Now as we select one more person, the number of people born on a day for one of the days in the year will increase to 4. Hence the number of people that should be selected to guarantee that at least 4 were born on the same day are 1095 +1 = 1096. Hence, required value is 1096.

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Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).

The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.

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Answer:

8

Step-by-step explanation:

f(x) = 3x + x

Combine like terms

f(x) = 4x

Let x = 2

f(2) = 4(2)

f(2) = 8

Answer:

8

Step-by-step explanation:

f(x) = 3x + x

f(2) = 3(2) + 2

f(2) = 6 + 2

f(2) = 8

The required expression that includes the numbers 2,4, and 5, has a value of 50 is  5(4 + 2) + 5(4)

Expressions are mathematical statements having two or more variables and connected by mathematical signs. The mathematical signs can be +, - and *

According to the question, we are to form an expression with 2, 4, and 5 that will give 50.

Connecting the integers using the given signs, we will have:

5(4 + 2) + 5(4)

Checking:

Expand the expression using distributive law:

= 5(4) + 5(2) + 5(4)

= 20 + 10 + 20

= 30 + 20

= 50

This that one of the arrangement in parenthesis is 5(4 + 2) + 5(4)

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A . f(×)

IS POLYNOMIAL FUNCTION

or

E

the output of f(×) will remain greater than those of g(×) as input values continue to increase.

CORRECT ME IF I AM WHRONG.

THANK YOU.

Only option A, \(f(x)\) is a polynomial function is the correct answer based on the table given.

A polynomial is mathematical equation consisting of independent variables such that, for each value of the independent variable, the function have a unique value.

As for uniques values of the variable \(x\), the value of the function \(f(x)\) is unique so, \(f(x)\) is a polynomial function.

The function, \(g(x)\) is not a function as it have equal values for two different values of the variable \(x\).

Option E and F are incorrect as, we can see in the table that sometimes the value of \(f(x)\) is more and sometime the value of the function, \(g(x)\) is more.

Thus, only option A is the correct answer.

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Answer:

v=168

Step-by-step explanation:

The distance in the standard (x, y) coordinate plane between the given points (1, 0) and ( 0, 5) is equal to √26 units.

As given in the question,

In the coordinate plane :

The distance in the standard (x, y) coordinate plane is:

Distance between the given points (x₁ , y₁) = (1, 0) and (x₂ , y₂) = (0,5) is given by :

Standard distance formula :

d = √ ( x₂ - x₁)² + (y₂ - y₁)²

  = √ ( 0 -1)² + (5-0)²

  = √1 + 25

  = √26 units

Therefore, The distance in the standard (x, y) coordinate plane between the given points (1, 0) and ( 0, 5) is equal to √26 units.

The complete question is :

What is the distance in the standard (x, y) coordinate plane between the points (1,0) and (0,5)?

a. 4      b. 6                c. 16           d. 36          e. √26

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Answer:

3/10

Step-by-step explanation:

9/10 - 3/5

cross multiply and make denominators even

45-30/50

15/50

3/10

Answer:

14

Step-by-step explanation:

You can put it as a fraction like so:

2/1 divided by 1/7

Use the strategy KCF (Keep, Change, Flip)

2/1 x 7/1

=2x7

=14

Equation shows that Tom's indirect utility function V(p, w) is convex in p, as desired.

V(λ\(p1\) + (1-λ)\(p2\), w) ≤ λV(\(p1\), w) + (1-λ)V(\(p2\), w)

To prove that Tom's indirect utility function V(p, w) is convex in p, where p is the price vector and w is the wealth, we need to show that for any two price vectors p1 and p2, and for any λ ∈ [0,1], the following inequality holds:

V(λ\(p1\) + (1-λ)\(p2\), w) ≤ λV(\(p1\), w) + (1-λ)V(\(p2\), w)

To prove this, we can use the concept of homothetic preferences.

Homothetic preferences imply that the utility function is homogeneous of degree zero, meaning that multiplying prices and income by the same positive constant does not affect the consumer's preferences.

Let's assume Tom's utility function is U(x), where x represents the consumption bundle.

Tom's indirect utility function can be defined as:

V(p, w) = max { U(x) | px ≤ w }

Now, consider two price vectors p1 and p2, and let x1 and x2 be the optimal consumption bundles for p1 and p2, respectively.

Since U(x) is homogeneous of degree zero, we have:

U(λ\(x1\)+ (1-λ)\(x2\)) = U(x1 + λ(x2 - x1)) = U(x1) [using homogeneity]

From the definition of the indirect utility function, we know that V(p, w) = U(x), where x is the consumption bundle that maximizes U(x) subject to the budget constraint.

Therefore, we have:

V(λp1 + (1-λ)p2, w) = U(x1) [since λx1 + (1-λ)x2 is the optimal consumption bundle for λp1 + (1-λ)p2]

Now, let's consider the right-hand side of the inequality:

λV(p1, w) + (1-λ)V(p2, w) = λU(x1) + (1-λ)U(x2) [using the definition of the indirect utility function]

Since U(x1) = U(x2) (as shown above), we can simplify the right-hand side:

λV(p1, w) + (1-λ)V(p2, w) = U(x1)

Therefore, we have:

V(λp1 + (1-λ)p2, w) ≤ λV(p1, w) + (1-λ)V(p2, w)

This shows that Tom's indirect utility function V(p, w) is convex in p, as desired.

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