Patricia bought 4 apples and 9 bananas for $12. 70 Jose bought 8 apples and I bananas for $17. 70 at the same grocery store What is the cost of one apple?​

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The line on the graph showing the number of counters (c) for s students will have a slope of 20.

Answer:

91.26 ft2

Step-by-step explanation:

Given, length of side =.9 ft

The total surface area of a cube = 6× side 2

=6×3.9×3.9

=91.26ft

2

Answer:

Step-by-step explanation:

Given :

=> side length of cube = 12 feet

=> The surface area of cube = 6a²

=> 6×12×12

=> 864 ft ²

The answer is the lower bound theorem identifies -2 as a lower bound for the real zeros of f(x). The upper bound theorem does not specify any upper bound for the real zeros of (x)

The Lower bound theorem states that "If the terms of a polynomial are arranged in descending order of their degrees, then the absolute value of the quotient of the constant term and the coefficient of the term of the highest degree gives a lower bound for the absolute value of its zeros." Let's examine whether the lower bound theorem identifies -2 as a lower bound for the real zeros of f(x) and whether 3 is an upper bound for the real zeros of (x).

As f(x) = 56 = x + 17x² + 11x + 23Since f(x) is not arranged in descending order of their degrees, we have to rearrange it as follows. 17x² + 11x + x + 23 + 56 = 17x² + 12x + 79 on rearranging the equation we have: 17x² + 12x + 79 = 0Hence the constant term is 79 and the coefficient of the term of the highest degree is 17. Thus, using the lower bound theorem, we can evaluate that a lower bound for the absolute value of the zeros of the polynomial is 79/17 ≈ 4.65 Since -2 is less than the calculated lower bound of 4.65, it is indeed a lower bound for the real zeros of f(x). Now, for (x), the constant term is 0, and the coefficient of the term of the highest degree is 1. Thus, using the upper bound theorem, we can evaluate that an upper bound for the absolute value of the zeros of the polynomial is 1/0, which is equal to infinity. Since infinity is not a number, 3 cannot be an upper bound for the real zeros of (x).

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A statement of the equation could be as; "John bought y oranges which are 5 times the apples more than 3".

An equation is an expression that shows the relationship between two or more numbers and variables.

The information provided is that the real-world situation in which opposite quantities combine to make zero.

We have been given an equation as y = 5x + 3

A statement of equation could be as; "John bought y oranges which are 5 times the apples more than 3".

If the number of apple x is 6 then;

y = 5x + 3

y = 5(6) + 3

y = 33

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The temperature of a point \($(x,y)$\) in the plane is given by the expression \($x^2 y^2 - 4x 2y$\) . The coldest point in the plane is\($(0,1)$\) with a temperature of\($-4$\)

To find the coldest point in the plane, we need to minimize the given expression of temperature  \($T(x,y) = x^2 y^2 - 4x 2y$\) with respect to \($x$\) and \($y$\). We can do this by taking partial derivatives of \($T$\) with respect to \($x$\) and \($y$\), and setting them equal to zero:

\($\frac{\partial T}{\partial x}\)\( = 2xy^2 - 8y= 0$\)

\($\frac{\partial T}{\partial y}\)\( = 2x^2y - 8x = 0$\)

Solving these equations simultaneously, we get \($x=0$\) or \($x=2$\) and \($y=0$\) or \($y=1$\) . We can then evaluate the temperature at each of these four points:

\($T(0,0) = 0$\)

\($T(0,1) = -4$\)

\($T(2,0) = 0$\)

\($T(2,1) = 0$\)

This makes intuitive sense as the expression for temperature is symmetric about the \($x$\) and \($y$\) axes, and the point  \($(0,1)$\) corresponds to the "bottom" of the surface formed by the expression.

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A polynomial function f is equal to x^3- 11x^2+41x- 51 of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

The degree of this polynomial is 3 and the leading coefficient is 1. Three zeros are 3, 4+i, 4-i bc, and a-bi if a+bi is zero, also known as the conjugate postulate. With this information, we can say that the factors are (x-3)(x-(4+i) )(x-(4-i)).

When we start multiplying, we group like this

(x-3)( (x-4) + i )( (x-4) -i )

Multiply the second two factors first.

(x-4)^2 - (i)^2 [This is the difference of squares (a+b)(a-b)].

We know that

i^2 = -1

= x^2 -4x -4x +16 - (-1)

= x^2-8x+16+1

= x^2 -8x +17

Don't forget (x-3).

Solving complete factors

(x-3)(x2-8x+17)

= x^3 -8x^2 +17x -3x^2 +24x -51

= x^3-11x^2+41x-51

This is the final equation of the polynomial.

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Answer:

x = 24, y = 19

Step-by-step explanation:

Form the question,

Note: opposite side of a parallelogram are equal.

From the diagram,

2x-8 = x+16

Solve for x.

Collect like terms

2x-x = 16+8

x = 24.

Also,

2y = y+19

Solve for y

Collect like terms

2y-y = 19

y = 19.

Hence, x = 24, y = 19.

The first option is correct

The relative extrema of the function  f(x) = x³ + 4x² - x - 4 is at

( \(-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27}\) )and the graph of the function is attached below.

The given function is f(x) = x³ + 4x² - x - 4

For the relative extrema we will first have to find the first derivative of the function:

f'(x)  = 3x² + 8x - 1

Now for4 the function to have an extremum, f'(x) = 0

3x² + 8x - 1 = 0

Solving we get :

the values of x using the quadratic formula  are \((-\frac{4-\sqrt{19}}{3} , -\frac{4+\sqrt{19}}{3} )\) .

Now we will substitute the values of x in the function f(x) to get the local extremum.

The maximum value of f(x) is \(\frac{56+38\sqrt19}{27}\).

The minimum value of f(x) is \(\frac{56-38\sqrt19}{27}\) .

Now we will use various points to find the values of f in the function.

At x = -3 , y = 8

At x = 0 , y = -4

At x =-1 , y = 0

Hence the relative extremum of the function is at \((-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27})\) .

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Answer:

1.x^2+5x-24

2.-12x^2-7x+10

3.x^2-16

4.x^2+10x+25

5.4x^2+28x+49

6.x^2-49

7.10x^3+18x^2-19x+3

8. 3x^3-5x^2+3x-10

Step-by-step explanation:

Answer: 225 adult tickets, 375 student tickets

Step-by-step explanation:

a = adult tickets

s = student tickets

a + s = 600 (the adult and student ticket added together should equal 600)

6.00a + 4.50s = 3,037.50 ($6 multiply by the adult ticket plus $4.50 multiply by the student ticket should equal to 3,037.50)

a = -s + 600 (get one of the variable by itself by subtracting it from one side)

6 (-s + 600) + 4.5s = 3,037.5 (substitute the a for -s + 600)

-6s + 3600 + 4.5s = 3,037.5 (combine like terms)

-1.5s + 3600 = 3,037.5 (subtract 3600 from each side)

-1.5s = - 562.5 (divide -1.5 from each side)

s = 375

600 = 375 + a (substitute s for 375)

a = 225

To calculate the length of the curve defined by r(t) = 〈2 cos(t), 2 sin(t)〉 with the domain -π/2 ≤ t ≤ π/2, we need to find the arc length using the following formula:

Arc length = ∫(from a to b) ||r'(t)|| dt

First, let's find the derivative r'(t) of the given vector function r(t):

r(t) = 〈2 cos(t), 2 sin(t)〉
r'(t) = 〈-2 sin(t), 2 cos(t)〉

Next, find the magnitude ||r'(t)|| of the derivative vector:

||r'(t)|| = √((-2 sin(t))^2 + (2 cos(t))^2)
||r'(t)|| = √(4 sin^2(t) + 4 cos^2(t))

Factor out 4:

||r'(t)|| = √(4(sin^2(t) + cos^2(t)))

Since sin^2(t) + cos^2(t) = 1:

||r'(t)|| = √(4) = 2

Now, we can find the arc length by integrating ||r'(t)|| over the given domain:

Arc length = ∫(from -π/2 to π/2) 2 dt

To integrate, simply multiply the constant by the difference in t:

Arc length = 2(π/2 - (-π/2)) = 2(π) = 2π

So, the length of the curve is 2π.

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False. An n × n matrix that is orthogonally diagonalizable does not necessarily have to be symmetric. A matrix is said to be orthogonally diagonalizable if it can be expressed as PDP^T, where P is an orthogonal matrix and D is a diagonal matrix.

For a matrix to be symmetric, it must satisfy the condition A = A^T, where A^T denotes the transpose of A. While it is true that symmetric matrices are always orthogonally diagonalizable, the converse is not necessarily true. There exist non-symmetric matrices that can still be orthogonally diagonalized. An example of such a matrix is the following:

  [1  2]

A = [3 4]

This matrix is not symmetric, as A^T is:

  [1  3]

A^T = [2 4]

However, it is still orthogonally diagonalizable. The matrix A can be diagonalized as:

A = PDP^T, where P = [0.8507 -0.5257]

[0.5257 0.8507]

          and D = [-0.3723   0     ]

                    [ 0      5.3723]

Therefore, it is not necessary for an n × n matrix that is orthogonally diagonalizable to be symmetric.

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Answer:

Step-by-step explanation:

Given,

Area of square ground = 42025

Now, let's find the length of square ground

Area of square = \( = {l}^{2} \)

plug the values

\(42025 = {l}^{2} \)

Swipe the sides of the equation

\( {l}^{2} = 42025\)

Squaring on both sides

\( \sqrt{ {l}^{2} } = \sqrt{42025} \)

Calculate

\(l = 205\) meters

The length of square ground = 205 meters

Now,Let's find the perimeter of square

Perimeter of square \( = 4l\)

plug the value of length

\( = 4 \times 205\)

Multiply the numbers

\( = 820\) meters

Hope I helped.

Best regards!!

Answer:

X=11

Step-by-step explanation:

Vertical angles equal each other.

5x+10 = 7x -12

Then solve for x by placing all the X values on one side and the number values on the other side.

5x+10=7x-12

5x-7x=-12-10

-2x=-22

x=11

Step-by-step explanation:

8

a. total cost ($)

→ 25 = 25×2.5 = $62.5

→ 50 = 50 × 2.5 = $125

→ 75 = 75 × 2.5 = $187.5

b. 2.5n

c. $400/2.5 = 160

therefore, she can make 160 crafts by $400.

9. 7x + 12 = 18

→ 7x = 18 - 12 = 6

→ x = 6/7

therefore value of x is 6/7.

hope this answer helps you dear...take care

Answer:

The difference between the bonus is £2.6

Step-by-step explanation:

First, you have to calculate the amount that Tom get for his bonus. So you have to multiply 30% to £96 :

\( \frac{30}{100} \times 96 = 28.8\)

Next, you have to subtract Tom's amount from Sally's amount because Sally has the higher amount of bonus than Tom :

\(31.4 - 28.8 = 2.6\)

Answer:

13.5 pounds.

Step-by-step explanation:

9.18 divided by .68

= 13.5

Answer:

13.5

$0.68 times 13.5 = $9.18

Answer:

-7.8(x+6.5)=-25.74

x+6.5 = 3.3

x=-3.2

Let me know if this helps!

Answer:

a = 16

Step-by-step explanation:

The median is the middle value of the data arranged in ascending order.

If there is no exact middle then the median is the average of the 2 values either side of the middle

a + 1 , 2a - 1 ,  a + 7 ,  3a + 4

                   ↑ middle

Then

\(\frac{2a-1+a+7}{2}\) = 27 ( multiply both sides by 2 to clear the fraction )

3a + 6 = 54 ( subtract 6 from both sides )

3a = 48 ( divide both sides by 3 )

a = 16

Answer:

b=2.5a

Step-by-step explanation:

a=2, b=5

a=3, b=7.5

a=4, b=10

a=6, b=15

a=22, b=55

Let the event D be that a person has the disease.

Now Let T be positive test and T' be a negative test result.

So the probability that the person has the disease given that the test is positive is given by:

So only 0.46% of the people who tested positive will have the disease.

if we have a class of 15 students and we want to choose a committee of 5 students, their order and position don't matter, 3003 many different ways are there of creating a 5-person committee among the 15 students.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Since order and position doesn't matter in this problem, use the combination formula.

The combination formula is: n! / (n-r)! r!

where n is the total number of items (15 in this case) and r is the number of items being selected at once (5 in this case)

Plugging our numbers into the formula:

= 15! / (15-5)! 5!

= 3003 ways.

So, there are 3003 ways of picking 5 people from a group of 15.

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To determine which sunflower field has plants with more consistent heights, we need to look at the variability in the heights of the plants in each field as shown in the box plot.

The more consistent the heights, the smaller the range and the less spread out the box plot will be. So, we should look for the field with the smallest range and the narrowest box plot. This indicates that the majority of the plants in that field have similar heights.

Therefore, we need to compare the box plots or IQRs of the different sunflower fields to determine which field has plants with more consistent heights.  please follow these steps:

1. Look for the Interquartile Range (IQR) of each sunflower field. IQR is the range within which the middle 50% of the data lies. In a box plot, it is represented by the width of the box, which is the distance between the first quartile (Q1) and the third quartile (Q3).

2. Compare the IQRs of the sunflower fields. The field with the smaller IQR has plants with more consistent heights, as it indicates that the middle 50% of the plant heights are closer together.

In summary, check the box plots of the sunflower fields for their IQRs, and the field with the smaller IQR has more consistent plant heights.

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Answer: Field A typically has plants with more consistent heights. You can tell because the IQR of its samples is less than that of the other field.

Step-by-step explanation:

I just took the test on Iready, trust me.

Let's first find the constant speed of the freight train using the provided information:

Time (in hours) | Distance (in miles)
      3        |        120
To find the constant speed, we can use the formula:
Speed = Distance ÷ Time
Using the information from the table:
Speed = 120 miles ÷ 3 hours = 40 miles per hour
Now that we have the constant speed, we can complete the table:
1. Time = 2 hours:
Distance = Speed × Time = 40 miles/hour × 2 hours = 80 miles
2. Time = 200 hours:
Distance = Speed × Time = 40 miles/hour × 200 hours = 8000 miles
3. Time = 8 hours:
Distance = Speed × Time = 40 miles/hour × 8 hours = 320 miles
So the completed table is:
Time (in hours) | Distance (in miles)
      2        |         80
      3        |        120
    200        |       8000
      8        |        320

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Answer:

16777216

Step-by-step explanation:

64 times 64 equals 4096. 4096 to the power of 2 is 16777216.

Answer:

B.

Step-by-step explanation:

The quickest and most fool-proof way to do this is to using a graphing calc to graph the given equations. When you do so, you should see that B is the right choice. You can also tell from the asymptotes. x cannot equal 1 or -1, so B.

From the decimal theory 10 has no decimal places, as it is a whole number.

As per the data given in the above question are as bellow,

The provided details are as bellow,

We have given the number as 10.

we have to find the decimal in the given number.

Thus we have to know about decimal value.

The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal. Up until there are no more digits, the remaining ones keep the place values filled in.

Here don't have any decimal value in the given number 10.

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Answer:

its c, the minus makes the positive 3 negative and the neg 2 positive