Jimmy needs to save at least $30 to buy a new video game. Write an inequality that representsthis situation.

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

For more such question Algebraic  expression visit:

https://brainly.com/question/2164351

#SPJ8

Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer: C

Step-by-step explanation:

The value inside the absolute value shifts the function on the x-axis, while the value outside shifts it on the y-axis.

Because it's at -5, this means the inside should be | x + 5 | while the outside should be -1 (as the function is shifted down one).

So, it is y = | x + 5 | - 1, which matches C.

Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

for more search question initially

https://brainly.com/question/28162977

#SPJ8

To calculate the average value of the cartridges, divide the overall total value (cell D14) by the total number of cartridge types (which is 8).

D16: =D14 / 8

To answer the questions, first create the table in Excel with the given values. Then, use the formulas mentioned below to answer each question.

Q.1.1: To determine the total value of each type of cartridge, multiply the purchase price by the quantity for each type of cartridge. Place these formulas in cells D2 - D9.

D2: =B2C2

D3: =B3C3

D4: =B4C4

D5: =B5C5

D6: =B6C6

D7: =B7C7

D8: =B8C8

D9: =B9C9

Q.1.2: Determine the overall total value of the various cartridges by summing the total values calculated in cells D2 - D9.

D10: =SUM(D2:D9)

Q.1.3: To calculate the inflation adjustment amount, multiply the overall total value (cell D10) by 10%.

D12: =D10 * 0.10

Q.1.4: Determine the overall total value of the cartridges, including the inflation adjustment amount, by adding the overall total value (cell D10) and the inflation adjustment amount (cell D12).

D14: =D10 + D12

Q.1.5: To calculate the average value of the cartridges, divide the overall total value (cell D14) by the total number of cartridge types (which is 8).

D16: =D14 / 8

Read more about business accounting here:

https://brainly.com/question/1033546
#SPJ1

Answer:

71% for the correct answers   and it would be 29% for the ones she missed

Step-by-step explanation:

Answer: She answered them 29% correctly.

Step-by-step explanation:

Divide number right by total number of questions:

58/200= .29

29%

Answer:

Your answer is 264

Step-by-step explanation:

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

For such more questions on  Circle Sector Area

https://brainly.com/question/30607726

#SPJ8

Part (a)

This sequence is convergent because all we care about are the leading terms for the numerator and denominator. As n gets really large, the leading terms dictate what happens.

The leading term up top is 9n

The leading term down below is 7n

Divide the two items to get (9n)/(7n) = 9/7

We don't have to worry about dividing by zero because n will go off to infinity, and as it does so, the sequence \(\{a_n\}\) converges to 9/7

========================================================

Part (b)

As n heads to infinity, the terms of the sequence are approaching 9/7 (they never quite hit the exact value though).

Note how 9/7 = 1.2857 approximately which is larger than 0

So effectively for very large values of n, we're adding on 1.2857 each time or close to it, meaning that this infinite series diverges.

------

For a series like this to converge, the answer to part (a) must be 0. This way at some point, we're effectively adding 0 to the series and we approach some fixed sum.

For example, consider the sequence 1/(7n+1)

As n goes to infinity, the terms of the sequence approach 0

This means that for some very large n, the 1/(7n+1) is basically 0 and we aren't adding much onto the sum to change it. So this sum will converge to a fixed value.

The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

To know more about Thale's theorem follow

brainly.com/question/14417137

#SPJ1

complete question;

Find the values of x and y. Find value of x.

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

so the limits are 2 and 9

We want to express  as a integral. To do this, we have to identify  as a Riemann Sum that approximates the integral. (taking the limit makes the approximation equal to the value of the integral)

In general, to find a Riemann sum that approximates the integral of a function f over an interval [a,b] we can the interval in n subintervals of equal length and approximate the area (integral) with rectangles in each subinterval and them sum the areas. This is equal to

, where  is a selected point of the subinterval.

In particular, if we select the ending point of each subinterval as the , the Riemann sum is:

.

Now, let's identify this in  .

The integrand is x² so this is our function f. When k=n, the summand should be  because the last selected point is b. The last summand is  thus b=9 and b-a=7, then 9-a=7 which implies that a=2.

To verify our answer, note that if we substitute a=2, b=9 and f(x)=x² in the general Riemann Sum, we obtain the sum inside the limit as required.

Answer:

17

Step-by-step explanation:

Given the data:

12, 18, x, 5

Average of the numbers = 13

The value of x will. Be

Sum of 12, 18, x and 5 divided by the number of data values.

Mean(average) = Σ(X) / n

n = number of values

13 = (12 + 18 + x + 5) / 4

13 = (35 + x) / 4

13 * 4 = 35 + x

52 = 35 + x

x = 52 - 35

x = 17

Answer:

To solve the quadratic equation 9×^2-15×-6=0, we can use the quadratic formula, which is given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 9, b = -15, and c = -6, so we can substitute these values into the quadratic formula:

x = (-(-15) ± sqrt((-15)^2 - 4(9)(-6))) / 2(9)

Simplifying this expression gives:

x = (15 ± sqrt(225 + 216)) / 18

x = (15 ± sqrt(441)) / 18

x = (15 ± 21) / 18

So the two solutions to the quadratic equation are:

x = (15 + 21) / 18 = 2

x = (15 - 21) / 18 = -1/3

Therefore, the solutions to the quadratic equation 9×^2-15×-6=0 are x = 2 and x = -1/3.

If D be a region bounded by a simple closed path C in the xy-plane, then the centroid of the quarter circle is  (4a/3π , 4a/3π)   .

In the question ,

it is given that D is the region bounded by a simple closed path C in the xy-plane .

the radius of the circle is = "a" ,

let the equation of the circle be x² + y² = a² ,

So , the area of the quarter circle is (A)  = (1/4)*πa²

The coordinate of the centroid x will be :

x = \(\frac{1}{2A} \int\limits x^{2} dy\)

x = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -y^{2} } \, dy\)

Simplifying further ,

we get ,

x = 2/πa² [{a²(a) - a³/3} - 0 ]

x = 2/πa² [a³ - a³/3 ]

x = 4a/3π

The coordinate of the centroid y will be :

y = \(\frac{1}{2A} \int\limits y^{2} dx\)

y = \(\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -x^{2} } \, dx\)

Simplifying further ,

we get ,

y = 2/πa² [{a²(a) - a³/3} - 0 ]

y = 2/πa² [a³ - a³/3 ]

y = 4a/3π

Therefore , the coordinates of the centroid is (4a/3π , 4a/3π) .

The given question is incomplete , the complete question is

Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = \(\frac{1}{2A} \int\limits x^{2} dy\)  ,  y = \(\frac{1}{2A} \int\limits y^{2} dx\) ?  

Find the centroid of a quarter-circular region of radius a.

Learn more about Centroid here

https://brainly.com/question/5872501

#SPJ4

Answer:

Step-by-step explanation:

uhh

Given data,

digits are 0, 1, 2, 3

Test simple operation,

Take 2.103 value,

Then,

Take 2.130 value,

Then,       

Take 2.301 value,

Then,      

Take 2.310 value,

Then,     

Take 2.013 value,

Then,

Take 2.031 value,

Then,    

Take 1.230 value,

Then,     

Take 1.320 value,

Then,    

Therefore,

See the parsing

Learn more about event correlation here: brainly.com/question/15687135

#SPJ9

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

Learn more about the angle bisector of an equilateral triangle here:

https://brainly.com/question/30341397

#SPJ1

Answer:

B.   3x = 90

Step-by-step explanation:

m<QPS + m<RPS = m<QPR

Let m<RPS = x

Then m<QPS = 2x

2x + x = 90

3x = 90

Answer: B.   3x = 90

When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.

Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.

The equation is given as y = 1/2(x) - 25

When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25

This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)

On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.

Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.

In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).

For more questions on intersection

https://brainly.com/question/30429663

#SPJ8

Answer:

C 38.1 ft hope this helps

The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.

The critical value is the value of x for which the double derivative of the function f(x) becomes zero.

When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either

a maxima or a minima.

Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.

To learn more about critical value visit:

https://brainly.com/question/36886

#SPJ1

Answer:

The measure of angle 8 is 54 degrees

Step-by-step explanation:

We know that angles 4 and 2 are linear pairs. Linear pairs add up to 180. Write an equation. (10x+6)+(5x-6). Now solve. 15x=180. x=12. With this, we can find the value of angle 8 by using angle 4's measure because 8 and 4 are congruent because they are corresponding angles. So, plug it in. 5(12)-6=60-6= 54. Therefore, angle 8 is 54 degrees

The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

For more such questions on maximum, click on:

https://brainly.com/question/29795588

#SPJ8

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

Learn more on Pythagorean theorem here;

https://brainly.com/question/343682

#SPJ1

Answer:

Jane earns 8 dollars for every hour that she babysits

Step-by-step explanation:

If you look the bottom of the graph and see 1 hour.  Then go up until you hit the line and the look left.  You will see that is $8

The correct answer that is an example of a permutation is; D: The number of ways 7 books can be selected from 50.

Formula for permutation is;

nPr = n!/(n - r)!

Now, permutation is defined as the arrangement of objects in a definite order. Thus, looking at the given options, the only one that depicts permutation is Option D.

Thus, the correct answer is the number of ways 7 books can be selected from 50.

Read more about Permutation at; https://brainly.com/question/12468032

#SPJ1

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

More can be learned about the mean of a data-set at brainly.com/question/1156334

#SPJ1