There were 15 red apples and
6 green apples in a bowl,
Eric ate 2 of the apples,
How many apples are
in the bowl now?

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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Answer:

4/3 is the fraction / the denomonator would then be 3

Step-by-step explanation:

4 shaded on the top and 3 shaded on the bottom. The numerator is on the top and the denomonator is on the bottom.

The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

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Answer:

The resultant polynomial is: \(6x^2-6x+5\)

Step-by-step explanation:

We need to subtract \((x+1)^{2}\) from \(7x^2-4x+6\)

so, we start by performing the multiplication involved in the perfect square of the binomial \((x+1)\), and obtain its expression in separate terms that can be combined:

\((x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1\)

Now we can subtract this trinomial from  \(7x^2-4x+6\), and  combining like terms to get the resultant polynomial expression:

\(7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5\)

Then the resultant polynomial is: \(6x^2-6x+5\)

The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

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Answer:

5, 25, 28, 35, 56, 75 80 are not the factors of 42

Answer:

x=−7

Step-by-step explanation:

Answer:

x=-7

Step-by-step explanation:

-5(x-2)-(x+2)=50

-5x+10-x-2=50

-6x+8=50

-6x=42

x=-7

The fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example -  5/9. Here, (5) is called numerator and (9) is called denominator.

Given is Melinda who ate 3/5 of the cookies and left the rest for Suzanne.

Assume that the fraction of cookies left for Suzanne is represented by [x].

Fraction of cookies ate by Melinda = [y] = 3/5

The sum of the fractions representing the cookies eaten by both Suzanne and Melinda will be equal to 1. Mathematically -

x + y = 1

x + 3/5 = 1

x = 1 - 3/5

x = (5 - 3)/5

x = 2/5

Therefore, the fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.

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Answer:

it is the answer number 1

To solve this equation:

We can proceed as follows:

Subtract 3 from both sides of the equation:

Divide both sides by -6:

So, the solution for the equation is x = -3.

Given:

Invest Amount = 13000

Time = 1 year

Compound daily = 10%

Compound continuously = 9.86%

Sol:

The compound interest formula is:

Where,

So the amount is 14367.025

(b)

When compounded continuously.

So the amount is 34846.38

Answer:14m

Step-by-step explanation:

3 1/2 x 4= 14

Answer:

-1

Step-by-step explanation:

It hits the y-axis at -1, so the answer is -1.

Answer:

Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.

In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

The possible value of the side length of the plot of land that Abby owns, which is between 2200 and 2400 square meters is A. 48 meters.

The length is the quantitative measurement of a distance from one point to another position.

Length can also refer to the size of an object that has width or/and height.

The square of 2,200m² = 46.9 meters (√2,200)

The square of 2,400m² = 48.99 meters (√2,400)

The square of the median value of 2,200m² and 2,400m², which is 2,300m² is 48 meters approximateluy.

Thus, the possible value of the side length of the plot of land is A. 48 meters.

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A. 48 meters

B. 46 meters

C. 44 meters

D. 50 meters

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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The possible values of x are 51% < x < 59%.

When you are given various values, the range of those values is how big the difference is between the largest value and the smallest value. In other words, the range is what you get when you subtract the smallest value in the group from the largest value in the group.

Its possible values are 1, 2, 3, 4, 5, and 6; each of these possible values has a probability of 1/6. 4. The word “random” in the term “random variable” does not necessarily imply that the outcome is completely random in the sense that all values are equally likely.

Let K represent Kofi

1st paper = 45/100

2nd paper = x / 100

Mean score = ( 45 + x ) % / 2

The possible range of x = 48% < (45+X)/2 < 52%

Cross multiplying

96% < 45 + x < 104%

Subtract 45 from both sides

Range = 51% < x < 59%

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The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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A) The polynomial with the given roots and multiplicity is; P(x) = -0.3(x - 3)²(x + 1)

B) The function after the given transformations is; g(x) = [2√(x - 5)] - 2

A) We are told that the polynomial is of degree 3 and as such, the general form is;

y = a(x + b)(x + c)(x + d)

We are told that it has a root multiplicity of 2 at x = 3.

Thus, (x - 3)² is a factor

We are now told that it has a root of multiplicity 1 at x = -1. Thus;

(x + 1) is a factor.

Thus, the polynomial is;

P(x) = a(x - 3)²(x + 1)

y-intercept is at y = -2.7. Thus;

P(0) = a(0 - 3)²(0 + 1) = -2.7

9a = -2.7

a = -0.3

Thus, the polynomial is; P(x) = -0.3(x - 3)²(x + 1)

2) We are given the function;

f(x) = 2√x

When we shift a function by a units up, we are adding a units to the function. Thus, shifting f(x) 2 units down is the opposite and we subtract 2 from the function to get;

f'(x) = (2√x) - 2

Now, shifting the function by 5 units right means we subtract 5 from the x value to get; g(x) = [2√(x - 5)] - 2

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P = principal = 8400

r = interest rate in decimal form = 0.0775

t = time in years = 10/12 = 5/6

i = simple interest

i = P*r*t

i = 8400*0.0775*(5/6)

i = 542.50 dollars is the answer

Answer: x = $1.75

Step-by-step explanation:

Let's assume that the cost of each sparking plug is x dollars. Then, the cost of the fan belt is x + $1.75 since it costs $1.75 more than each sparking plug.

According to the problem, the total cost of four sparking plugs and a fan belt is $10.50. We can express this as an equation:

4x + (x + $1.75) = $10.50

Simplifying and solving for x, we get:

5x + $1.75 = $10.50

5x = $8.75

x = $1.75

Therefore, each sparking plug costs $1.75 and the fan belt costs $3.50 ($1.75 + $1.75).