The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number. What is the original number?

Answer:

Step-by-step explanation:

Let the supplement = x

x + x +98 = 180                Equation

2x + 98 = 180                  Subtract 98    

2x = 180 - 98                   Combine

2x = 82                             Divide by 2

x = 82/2

x = 41

The two angles are

41

41 + 98 = 139

Step-by-step explanation:

From what you said, i would say that a line segment would be 1/3 od AB since AB is 300%

According to the question The graphs of the equations intersect at two points: (6, 8) and (-2, 0).

To find the total number of points of intersection between the graphs of the equations \($2x^2 - y^2 = 8$\) and \($y = x + 2$\) , we need to solve the system of equations.

Substituting \($y$\) from the second equation into the first equation, we get:

\(\[2x^2 - (x+2)^2 = 8\]\)

Expanding and simplifying:

\(\[2x^2 - (x^2 + 4x + 4) = 8\]\)

\(\[2x^2 - x^2 - 4x - 4 = 8\]\)

\(\[x^2 - 4x - 12 = 0\]\)

Factoring the quadratic equation, we have:

\(\[(x - 6)(x + 2) = 0\]\)

Setting each factor equal to zero:

\(\[x - 6 = 0 \quad \text{or} \quad x + 2 = 0\]\)

Solving for \($x$\) :

\(\[x = 6 \quad \text{or} \quad x = -2\]\)

Now, substituting these values of \($x$\) back into the equation \($y = x + 2$\)  to find the corresponding \($y$\) values:

When \(\\$x = 6$, $y = 6 + 2 = 8$\).

When \(\\$x = -2$, $y = -2 + 2 = 0$\).

Therefore, the graphs of the equations intersect at two points: (6, 8) and (-2, 0).

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The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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Answer:

She made a total of 50 dollars if you subtract the savings she saved she has a total of 40 dollars to spend but the total to this question is 50. The answer is 50 because 2 times 5 equals 10 so she needs to do 5 sessions of babysitting.

Your Final answer is 50

The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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Answer:

hey

Step-by-step explanation:

Answer:

down below

Step-by-step explanation:

we dont know what the number is

Answer:

Step-by-step explanation:

A pyramid is a solid shape that is made up of triangles, rectangles, squares and other polygons. A pyramid are classified based on the shape of its base. For example, the diagram given is a square based pyramid because of the shape of its base(which is a square). Other types includes the triangular based pyramid, triangular based pyramid and other polygon based pyramid.

If this square pyramid is cut with a plane that is parallel to the base of the pyramid, the shape of its cross section will be a triangle since the shapes that are parallel to the base are all triangles. So cutting the plane parallel to the base is similar to cutting out one side of the triangle making up the pyramid.

Answer:

C. Square

Step-by-step explanation:

When a pyramid is cut by a parallel plane that is parallel to the base, the cross section will be the shape of the base. The base of a square pyramid is a square. Thus, the shape of the cross section is a square.

Answer:

Step-by-step explanation:

We can find the distance between line l and point P by finding the distance between point P and the closest point on line l.The slope of line l is 0, since both points have the same y-coordinate. Therefore, line l is a horizontal line. The y-coordinate of any point on line l is 1.To find the closest point on line l to point P, we need to find the point on line l that has a y-coordinate of 7. Since line l is horizontal, any point on line l with a y-coordinate of 7 will work. Let's choose the point (5, 7), which is on the same horizontal line as line l.Now we can find the distance between point P and the point (5, 7):sqrt((5-(-2))^2 + (7-1)^2) = sqrt(49 + 36) = sqrt(85)Therefore, the distance between line l and point P is sqrt(85).

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The value of \( r_{2} \) is approximately 1.028 m. The moment or torque is calculated by multiplying the force applied by the distance from the point of rotation.

To find the value of \( r_{2} \), we need to use the concept of moments or torques in a system. The moment or torque is calculated by multiplying the force applied by the distance from the point of rotation.

In this case, if we assume that \( r_{1} \) and \( r_{2} \) are the distances of masses \( m_{1} \) and \( m_{2} \) from the point of rotation respectively, then the torques exerted by \( m_{1} \) and \( m_{2} \) should be equal since the system is in equilibrium.

Using the equation for torque:

Torque = Force × Distance

The torque exerted by \( m_{1} \) is given by:

\( \text{Torque}_{1} = m_{1} \cdot g \cdot r_{1} \)

where \( g \) is the acceleration due to gravity.

The torque exerted by \( m_{2} \) is given by:

\( \text{Torque}_{2} = m_{2} \cdot g \cdot r_{2} \)

Since the system is in equilibrium, \( \text{Torque}_{1} = \text{Torque}_{2} \), we can equate the two equations:

\( m_{1} \cdot g \cdot r_{1} = m_{2} \cdot g \cdot r_{2} \)

Now, let's substitute the given values into the equation and solve for \( r_{2} \):

\( 120 \, \text{lbs} \cdot 9.8 \, \text{m/s}^{2} \cdot 1.8 \, \text{m} = 210 \, \text{lbs} \cdot 9.8 \, \text{m/s}^{2} \cdot r_{2} \)

Simplifying the equation:

\( 2116.8 \, \text{N} \cdot \text{m} = 2058 \, \text{N} \cdot r_{2} \)

Dividing both sides of the equation by 2058 N:

\( r_{2} = \frac{2116.8 \, \text{N} \cdot \text{m}}{2058 \, \text{N}} \)

\( r_{2} \approx 1.028 \, \text{m} \)

Therefore, the value of \( r_{2} \) is approximately 1.028 m.

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Using fraction formula ,

The flour used by ramil and Carly for making bread is 33/40lb

Fraction: fraction is a number represented as a quotient, in which a numerator is divided by a denominator.

We have given that,

Ramil and Carly used 1/2 lb flour to make the bread.

They used 1/8lb less flour to make bread than to make cookies.

So, they used flour to make the cookies = 1/2+1/8

= 5/8lb

Therefore they used 5/8lb flour to make the cookies.

they used 1/5 lb more breads to make cookies than to make brownies. Mathematically, they used cookies for making the brownies is

= 1/5 + 5/8

=(8 + 25)/40 = 33/40lb

Therefore , they used 33/40lb flour to make the brownies.

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Complete question:

Ramil amd carly decided to make more baked goods for the bake sale. They used 1/8 lb less flour to make bread than to make cookies. She used 1/5 lb more to make cookies than to make brownies. If she used 1/2 lb of flour to make the bread, how much flour did she use to make the brownies

Answer:

yes

Step-by-step explanation:

Each time it is divided by three!

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

\( 40 \: {cm}^{2} \)

Step-by-step explanation:

Area of the figure = Area of rectangle with dimensions 6 cm by 5 cm + Area of triangle with base 5 cm and height 4 cm

\( = 6 \times 5 + \frac{1}{2} \times 5 \times 4 \\ \\ = 30 + 10 \\ \\ = 40 \: {cm}^{2} \)

Answer:

The scale factor is 3

Step-by-step explanation:

6/2=3 (one of the triangles sides)

If the polynomial p(x) is divided by (x-1) three times and has a remainder of 1 at the end, then -1 is a double root of p(x). This means that (x+1) is a factor of p(x) raised to the power of 2.

When a polynomial is divided by (x-1), the remainder represents the value of the polynomial at x=1. Since the remainder is 1, it implies that p(1) = 1. Dividing p(x) by (x-1) three times indicates that the polynomial has been factored by (x-1) three times. Consequently, the polynomial can be written as p(x) = (x-1)^3 * q(x) + 1, where q(x) is the quotient obtained after dividing p(x) by (x-1) three times. Since the remainder is 1, it means that when x=1, p(x) leaves a remainder of 1.

Thus, (1-1)^3 * q(1) + 1 = 1, which simplifies to q(1) = 0. This implies that (x-1) is a factor of q(x), meaning that q(x) can be written as q(x) = (x-1) * r(x), where r(x) is another polynomial.

Substituting this into the earlier expression for p(x), we get p(x) = (x-1)^3 * (x-1) * r(x) + 1. Simplifying further, p(x) = (x-1)^4 * r(x) + 1. Now, we can see that p(x) is divisible by (x+1) since (x+1) is a factor of (x-1)^4, and the remainder is 1. Therefore, -1 is a double root of p(x) because (x+1) appears twice in the factored form of p(x).

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No, this mechanism does not satisfy Dominant Strategy Incentive Compatibility (DSIC) no matter which random ordering is chosen by the mechanism.

DSIC requires that each agent has a dominant strategy, meaning that regardless of what other agents do, it is always in an agent's best interest to report their true preferences.

In this mechanism, the problem lies in the step where the ith agent is assigned her favorite room from the set R.

Since the rooms are assigned based on the agent's preferences, an agent has an incentive to misreport her preferences in order to increase her chances of getting her most preferred room.

For example, if an agent knows that her most preferred room is more likely to be available at a later stage, she may strategically misreport her preferences to increase the likelihood of getting that room.

This introduces the possibility of manipulation and strategic behavior, which violates the DSIC property.

Therefore, the mechanism described does not satisfy DSIC, regardless of the chosen random ordering.

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The sum of angle in a triangle is 180°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angle A, B and C is 180 i.e A+B +C = 180°

Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180

How do we prove that the sum of angle in a triangle is 180°?

Since triangle is 3 sided, n= 3, because n denote the number if sides

therefore the sum of angle = (n-2) 180 = (3-2)×180

= 180°

therefore the sum of angle In a triangle is 180°

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A  homogeneous linear differential equation with constant coefficients has the form a_

n y^{(n)} + a_{n-1} y^{(n-1)} + ... + a_1 y' + a_0 y = 0,

where a_n, a_{n-1}, etc. are all constants. The general solution of this equation is given by y = c_1 e^{\lambda_1 t} + c_2 e^{\lambda_2 t} + ... + c_n e^{\lambda_n t}, where c_1, c_2, etc. are constants and \lambda_1, \lambda_2, etc. are the roots of the characteristic equation a_n \lambda^n + a_{n-1} \lambda^{n-1} + ... + a_1 \lambda + a_0 = 0.

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The percent of change is approximately -15.5% (rounded to the nearest tenth).

To find the percent change between last year's enrollment and this year's enrollment, we can use the following formula

percent change = [(new value - old value) / old value] x 100%

where "new value" is the enrollment for this year, and "old value" is the enrollment for last year

Plugging in the numbers, we get:

percent change = [(87 - 103) / 103] x 100%

percent change = (-16 / 103) x 100%

percent change = -15.53%

Therefore, the percent of change is approximately -15.5% . This means that there was a decrease of about 15.5% in the enrollment for the drama club from last year to this year.

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Answer:

Then 1/2 or  30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.

Two hours after Tom began Tom would cover 12 miles and three hours after Linda started Linda would be 6 miles far away from the starting point

Step-by-step explanation:

Linda walks in a straight line at 2 miles/hour

then after t ( hours time) she is    2 (m/h) * t   = d (L)

for Tom running at 6 m/h starting one hour later to cover the same distance d(L)

d(L)  =  6 m/h * ( t - 1 )    then:

2 (m/h) * t   =   6 m/h * ( t - 1 )

2*t  =  6*t - 6

4*t = 6

t = 6/4

t =  1,5 h

Checking that result.

we see that in 1,5 hours Linda has covered  2* 1,5  = 3 miles

and  in 0.5 hours  Tom covered the same distance  0,5 * 6 = 3 miles

NOTE: Remember that tom started one hour later.

Then 1/2 or  30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.

b)  In this case

d(T) = 6* ( t - 1 )       must be equal  to  twice of the Linda distance

d(L)  = 2 * 2 * t

6*t - 6  =  4*t

2*t  =  6

t  = 3

To check it

in 3 hours   Linda had covered  3 * 2  =  6 miles

in 2 hours   Tom had covered   2 * 6  =  12 miles

The values of P and a that will make f(x)=Pa^x to be an exponential growth function is; A P = 1²; a = 2

The general formula for exponential growth function is;

y = a(b)ˣ

When a is a positive value and 'b' is the base greater than 1,

In order to represent exponential growth, a must be a positive number larger than 1.  If a is a fraction less than 1, we are basically taking a percent (less than 100) of the number and this will make it smaller, which would the become a decay function.  If a is a negative, the values would alternate between positive and negative.

The only option where a is a positive number larger than 1 is P = 1²; a = 2

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20% of a 400 liter tank is 80 liters.

Answer:

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

When two angles are complimentary, it means that, together, they make a 90 degree angle.

/_A + /_B must equal 90°

Step-by-step explanation:

your teacher has told you the first trick already : the figure is actually a combination of 2 simple figures.

so, we need to calculate these sub-areas and add them up for the total area.

the only second trick here is to know that the diameter of a circle is 2×radius. and as we can see on the graphic, the diameter of the half-circle is the width of the rectangle.

so, the area of the rectangle is

5 × (2×2) = 5 × 4 = 20

the area of the half-circle is

pi×r² / 2 = pi×2² / 2 = pi×2 = 6.283185307...

so, the total area of the figure is

20 + 6.283185307... = 26.283185307... ≈ 26.3

Plot the ordered pairs (0, -8), (1, -5), (2, -2), (3, 1) and (x, 3) on the graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given equation is y=3x-8.

Substitute x=0, 1, 2, 3, 4, 5,....in the given equation, we get

When x=0

y=-8

When x=1

y=-5

When x=2

y=-2

When x=3

y=1

When x=4

y=3

So, the ordered pairs are (0, -8), (1, -5), (2, -2), (3, 1) and (x, 3)

Thus, plot the ordered pairs (0, -8), (1, -5), (2, -2), (3, 1) and (x, 3) on the graph.

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well, profit equations are usually a parabolic path like a camel's hump, profit goes up up and reaches a maximum then back down, the issue is to settle at the maximum point, thus the maximum profit.

So for this equation, like any quadratic with a negative leading coefficient, the maximum will occur at its vertex, with x-price at y-profit.

\(\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-5}x^2\stackrel{\stackrel{b}{\downarrow }}{+209}x\stackrel{\stackrel{c}{\downarrow }}{-1090} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 209}{2(-5)}~~~~ ,~~~~ -1090-\cfrac{ (209)^2}{4(-5)}\right) \implies\left( - \cfrac{ 209 }{ -10 }~~,~~-1090 - \cfrac{ 43681 }{ -20 } \right)\)

\(\left( \cfrac{ 209 }{ 10 }~~,~~-1090 + \cfrac{ 43681 }{ 20 } \right)\implies \left( \cfrac{ 209 }{ 10 }~~,~~-1090 + 2184.05 \right) \\\\\\ ~\hfill~\stackrel{ \$price\qquad profit }{(~20.90~~,~~ 1094.05~)}~\hfill~\)