5. Read the problem carefully, then choose the inequality that best represents this real life situation. Explain your thinking. Lydia spent $2.50 per pound on apples and $1.80 per pound on oranges. She spent at most $22. Which inequality represents this situation?
(Let a = pounds of apples, and r = pounds of oranges)
a) 2.50 + 1.80 = 22
b) 2.50a + 1.80r = 22
c) 2.50a + 1.80r ≤ 22
d) 2.50a + 1.80r ≥ 22 ​

Answer:

y = - x + 9

Step-by-step explanation:

Because the line is perpendicular, the slope with be the opposite reciprocal. So, if the slope is 1 as in the equation y = x - 1, the opposite reciprocal is -1.

So the equation that is perpendicular will look like this so far:

y = -x + b   (b represents our y-intercept that we have not found yet)

Now we will find the y-intercept. We can find it by substituting the coordinates (5,4) as x and y into the equation right above ^^.

So,  4 = -(5) +b     or     4 = -5 + b

Add 5 to both sides to isolate b on the right side. b = 9

Therefore, the y-intercept is 9.

Now we have found everything we need for the equation, which is

y = - x + 9

The variables in the equations are aligned as follows:   2x - 3y = 9 and

2x - 3y = 8/3

When we talk about aligning a system of linear equations, we mean rearranging the equations so that the variables are in the same order and have the same coefficients. This is done to make it easier to apply methods for solving systems of equations, such as substitution or elimination.

In a system of linear equations, each equation typically involves two or more variables. The variables may have different coefficients in each equation, and they may appear in a different order. Aligning the system involves rearranging the equations in a way that puts the variables in the same order, with the same coefficients.

Align the variables in given the system of linear equations :

To align the variables in the given equations, we need to rearrange the second equation so that the coefficients of  and  are the same as in the first equation.

To align the variables in the equations, we need to rearrange the terms so that the x, y, and constant terms are all grouped together.

Starting with the first equation:

2x - 3y = 9

We can rearrange this as:

2x = 3y + 9

Now we can divide both sides by 2 to get x by itself:

x = (3/2)y + 4.5

Now let's move on to the second equation:

1-6x +9y = -7

We can rearrange this as:

-6x + 9y = -8

Next, we'll divide both sides by -3 to get x by itself:

2x - 3y = 8/3

Now both equations are in the form of:

ax + by = c

where a, b, and c are constants. The aligned equations are:

2x - 3y = 9

2x - 3y = 8/3

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Step-by-step explanation:

(21 - 3) ÷ 32

BIDMAS

Brackets: 21 - 3 = 18

Division: 18 ÷ 32 = (0.5625)

Answer:

3.1.1.  A(-4, 0)   B(0, -2)   E(4, 0)

3.1.2.  k = -16

3.1.3.  (-∞, ∞)

3.1.4.  [-16, ∞)

3.1.5.  [-6, 4]

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=x^2+k\\g(x)=-2x+8\\h(x)=\dfrac{6}{x-2}+1\end{cases}\)

Points A and B are the x-intercept and y-intercept of function h(x).

Point E is the x-intercept of function g(x).

The x-intercept of function h(x) is when h(x) = 0:

\(\begin{aligned}h(x) & = 0\\\implies \dfrac{6}{x-2}+1 & = 0\\\dfrac{6}{x-2} & = -1\\6 & = -1(x-2)\\6 & = -x+2\\4 & = -x\\x & = -4\end{aligned}\)

Therefore, the coordinates of point A are (-4, 0).

The y-intercept of function h(x) is when x = 0:

\(\begin{aligned}h(x) & = \dfrac{6}{x-2}+1\\\implies h(0) & = \dfrac{6}{0-2}+1\\ & = -3+1\\& = -2\end{aligned}\)

Therefore, the coordinates of point B are (0, -2).

The x-intercept of function g(x) is when g(x) = 0:

\(\begin{aligned}g(x) & = 0\\\implies -2x+8 & = 0\\-2x & = -8\\x & = 4\end{aligned}\)

Therefore, the coordinates of point E are (4, 0).

As function f(x) passes through point C (-6, 20), substitute the point into the equation of the function to find the value of k:

\(\begin{aligned}f(-6) & = 20\\\implies (-6)^2 + k & = 20\\36 + k & = 20\\k & = 20 - 36\\k & = -16\end{aligned}\)

Hence, proving that the value of k is -16.

The domain is the set of all possible input values (x-values).

The domain of function f(x) is unrestricted, therefore its domain is:

The range is the set of all possible output values (y-values).

The range of function f(x) is restricted, since the minimum point of the parabola is at (0, -16).  Therefore its range is:

\(\begin{aligned}g(x) - f(x) & \geq 0\\\implies g(x) &\geq 0+f(x)\\ \implies g(x) & \geq f(x)\end{aligned}\)

Therefore, find the interval for which g(x) is greater than or equal to f(x).

From inspection of the given graph this is between points C and E:

D (2,-3)

Just look where the lines meet

Answer: D IS CORRECT

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Now, the numbers are 6⁄10 and 8⁄12, so the required rational number can be in between these numbers. The numerator and denominator of the required number should be between the given number, i.e., numerator can be 7 and denominator can be 11. Hence, the rational between 3⁄5 and 2⁄3 is 7⁄11.

Answer:

m'n' equals 13

Step-by-step explanation:

39 divided by 1/3 equals 13

Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

Answer:

1 day

Step-by-step explanation:

none of the answers shown are correct,it is 1 day,is the question worded diffrently?

Answer:3/5

Step-by-step explanation:when he takes one marble it’s 7/11 and when he takes another it’s 6/10 so simplify and you get 3/5

Answer:

Step-by-step explanation:

Answer:3/5

Answer:

y = 1x - 5

Step-by-step explanation:

We will use the slope equation for this: y = mx + b

y is our output/answer

m is our slope, or the rate of change

x is our x coordinate. For example, in (3,2) x would be 3.

b is our y intercept, or where the line passes through the y axis.

Knowing this, we can fill out the blanks.

when we look at one point on the grid, and then find the next closest number from the point we chose, we can see that the slope is 1 so we now have: y = 1x + b

to find b, we find where the line passes over the y axis which on our grid is -5. Normally we would write: y = 1x + 5 Since we have a negative 5 or -5, we will change the + to a -

This means we write y = 1x -5.

I hope this helps you and have a great day :D

The sοlutiοns οf the quadratic equatiοn \(x^2 + 8x + 3 = 0\) are:

\(x = -4 + \sqrt{(13)\) and \(x = -4 - \sqrt{(13)\)

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x.

Tο find the sοlutiοns οf the quadratic equatiοn \(x^2 + 8x + 3 = 0\), we can use the quadratic fοrmula:

\(x = (-b \± \sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 8, and c = 3.

Substituting these values intο the fοrmula, we get:

\(x = (-8 \± \sqrt{(8^2 - 4(1)(3))}) / 2(1)\)

\(x = (-8\± \sqrt{(64 - 12)}) / 2\)

\(x = (-8 \± \sqrt{(52)}) / 2\)

\(x = (-8 \± 2\sqrt{(13)}) / 2\)

\(x = -4 \± \sqrt{(13)\)

Therefοre, the sοlutiοns οf the quadratic equatiοn \(x^2 + 8x + 3 = 0\)are:

\(x = -4 + \sqrt{(13)\) and\(x = -4 - \sqrt{(13)\)

Sο the answer is οptiοn C.

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Complete Question:

What are the solutions of this quadratic equation?

x² + 8x + 3 = 0 A. B. C. D.

In a sample of 26 days from the desert, the average of the high daily temperature is 114 degrees F, and the sample standard deviation is 5 degrees F.

To determine the 90% confidence interval for the average temperature, we can use the t-distribution as follows:To find the critical value of t, we can use the t-table. Since our sample has n = 26, the degrees of freedom (df) are n - 1 = 25. At a confidence level of 90%, with 25 degrees of freedom, the critical t-value is 1.708.The standard error of the mean is calculated as s / sqrt(n), where s is the sample standard deviation and n is the sample size. Therefore, the 90% confidence interval for the average temperature is (114 - 1.67, 114 + 1.67), or (112.33, 115.67) degrees F.

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Answer:

hiiiiii girlyyy

Step-by-step explanation:

i think the answer is

a/b like a divided by b is the answer

cuz 8 ÷ 3 = 2.7

and 24 ÷ 9 = 2.7

and 40 ÷ 15 = 2.7

so maybe like

b · 2.7 = a

hope this helpsss

Answer:

well on side A, it starts off on 8 (as you can see) and adds 16, which gives you 24, then add another 16 and that gives you 40. Then on side B, it starts with 3, adds 6 which gives you 6, then add another 6 and you'll have 15.

Step-by-step explanation:

The x-intercept of the function  is -3

One example of an intercept is the X-intercept, which is when a line crosses the x-axis.

Where a line crosses the y-axis is known as the y-intercept.

One play in numerous football formats is the interception.

Donald Hamilton's 1980 thriller The Mona Intercept

Nixon announced Operation Intercept as a drug-prevention initiative.

Telephone monitoring, often known as third-party eavesdropping on phone and online talks

Android smartphone Samsung Intercept (SPH-M910) Visual Intercept, a Microsoft Windows-based software defect monitoring tool

A measurement of the linearity of an electrical device is the intermodulation intercept point.

A telephone recording known as the intercept message informs the caller that the call cannot be finished.

The Intercept is an online news source run by Jeremy Scahill, Laura Poitras, and Glenn Greenwald.

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Answer:

To find the x-intercept of the function, we need to find the value of x where the function h(x) is equal to zero.

Setting h(x) = 0, we have:

0 = 3∛(x - 5) + 6

Subtracting 6 from both sides, we get:

-6 = 3∛(x - 5)

Dividing both sides by 3, we get:

-2 = ∛(x - 5)

Cubing both sides, we get:

-8 = x - 5

Adding 5 to both sides, we get:

x = -3

Therefore, the x-intercept of the function is -3.

The answer is: -3.

If the product of the terms of the fraction is 162 and the fraction is equivalent to 2/9 then the fraction is 6/27.

Let's assume the two terms of the fraction are x and y. We are given that xy = 162. Also, we know that the fraction is equivalent to 2/9. So, we can write,

x/y = 2/9

Cross-multiplying, we get,

9x = 2y

Solving for y, we get,

y = (9/2)x

Substituting this value of y in the equation xy = 162, we get,

x(9/2)x = 162

Simplifying, we get,

(9/2)x² = 162

x² = 36

x = 6 (taking the positive square root as x and y are positive)

Substituting this value of x in the equation y = (9/2)x, we get,

y = (9/2)(6) = 27

So, the fraction is 6/27, which simplifies to 2/9.

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Complete question - The product of two terms of a fraction is 162, find the fraction if it is equivalent to 2/9.

A standard normal random variable probability is 0.0250.

The probability P(Z > 1.96)  found by subtracting the cumulative probability from 1.

Using a standard normal distribution table or calculator, find the cumulative probability corresponding to 1.96, which is approximately 0.9750.

P(Z > 1.96) = 1 - P(Z ≤ 1.96) = 1 - 0.9750 = 0.0250.

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The number of ways that Grant can arrange 3 of his 10 plants on a window ledge is 120 ways

The number of ways that Grant can arrange 3 of his 10 plants on a window ledge will be:

= 10!/(10! - 3!)3!

= 10!/7!3!

= (10 × 9 × 8)/(3 × 2)

= 120

When the parade organizer received 8 entries for floats, the number of ways that he can arrange 4 floats out of the 8 entries will be:

= 8!/(8! - 4!)4!.

= 8!/4!4!

= (8 × 7 × 6 × 5)/(4 × 3 × 2)

= 70

4! in expanded form will be:

= 4 × 3 × 2

= 24

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Answer:12 pints of milk

Step-by-step explanation:

4x6=24cups

2cups = 1 pint

24 divided by 2 = 12

your answer is 12 pints of milk

The largest subset of ℝ³ on which the vector field is differentiable is ℝ³ - {(0, 0, 0)

How to determine largest subset?

To determine largest subset where the given vector field is differentiable, we need to check that all partial derivatives of each component of the vector field exist and are continuous.

Let's start by finding the partial derivatives of each component:

∂/∂x (−x² − y² − z²- 1)4/3 = −4/3(x² + y² + z² + 1)1/3 × 2x = -8x(x² + y² + z² + 1)1/3/3

∂/∂y (−x² − y² − z²- 1)4/3 = −4/3(x² + y² + z² + 1)1/3 × 2y = -8y(x² + y² + z² + 1)1/3/3

∂/∂z (−x² − y² − z²- 1)4/3 = −4/3(x² + y² + z² + 1)1/3 × 2z = -8z(x² + y² + z² + 1)1/3/3

∂/∂x (x cos(yz)) = cos(yz)

∂/∂y (x cos(yz)) = -xz sin(yz)

∂/∂z (x cos(yz)) = -xy sin(yz)

∂/∂x (xy⁴−z²) = y⁴

∂/∂y (xy⁴−z²) = 4xy³

∂/∂z (xy⁴−z²) = -2z

Now we need to check the continuity of all these partial derivatives. We can see that all of them are continuous except for the partial derivatives involving the expressions (x² + y² + z² + 1)1/3 and (yz).

The expression (x² + y² + z² + 1)1/3 involves a cube root, which is not continuous at (0, 0, 0). Therefore, the partial derivatives involving this expression are not continuous at the origin, which means that the vector field is not differentiable at the origin.

The expression yz involves the product of y and z, which is also not continuous at (0, 0, 0). Therefore, the partial derivatives involving this expression are also not continuous at the origin, which means that the vector field is not differentiable at the origin.

Therefore, the largest subset of ℝ³ on which the vector field is differentiable is ℝ³ - {(0, 0, 0).

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Correct question is "determine the largest subset of double-struck ℝ³ on which the given vector field is differentiable. f = (−x² − y² − z²- 1)4/3, x cos(yz), xy ⁴− z²".

Answer: The largest subset of ℝ³ on which the vector field is differentiable is ℝ³ itself. In summary, the given vector field is differentiable on the entire ℝ³ space.

Answer:

(0, 170) (5, 150) (60, -170)

Step-by-step explanation:

Plug each x value into the equation. The point is located on the line if the y values match.

Ex. -4 (170) + 170 = -510 this point is not on the line

-4 (0) + 170 = 170 this point is on the line because it is a "true" statement

Answer:

(0, 170) (5, 150) (60, -170)

Step-by-step explanation:

Answer:

B,C,E

Step-by-step explanation:

Add the first number with itself and it will need to equal the second one

So 5+5 would equal 10, 5/10 is basically this

Answer:

8/16, 1/2, 6/3, 5/10

Step-by-step explanation:

Two months would pass before they received the same sum of money.

In mathematics, equivalence is a relationship that states that two quantities have the same value or that two mathematical expressions reflect the same mathematical object. A = B is the symbol for the equality of A and B, and it is also pronounced as A = B.

Total amount saved = amount started with + (amount deposited per month x number of months)

Amount saved by Tonya = $60 + $20m

Amount saved by Jull = $20 + $40m

The two aforementioned equations would be equivalent if they both saved the same amount of money:

60 + 20m = 20 + 40m

Take the below actions to find the value of m:

60 - 20 = 40m - 20m

40 = 20m

m = 40 / 20

m = 2

In the calculation that shows how much money Tonya has overall saved, replace m with:

$60 + $20(2)

$60 + $40 = $100

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Answer:

$8.8

Step-by-step explanation:

\(8*0.10=0.8\)

\(8+0.8=8.8\)

Based on the given information, if the observed price (p) exceeds the price expected by the producers (pe), then we can infer the following:

Demand exceeds supply: When the observed price is higher than the price expected by the producers, it suggests that there is greater demand for the product than initially anticipated. This could be due to various factors such as increased consumer demand, scarcity of supply, or other market dynamics.

Potential increase in profitability: If the observed price is higher than the expected price, it implies that producers can potentially generate higher profits. This situation may incentivize producers to increase production to meet the higher demand and take advantage of the higher prices.

Market equilibrium may shift: When the observed price surpasses the price expected by the producers, it indicates an imbalance between supply and demand. This could lead to a new market equilibrium where the price adjusts to reflect the increased demand and potentially influence the producers' pricing strategies in the future.

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Answer:

x = 7 km

Step-by-step explanation:

Perimeter of a polygon is  P = sum of the sides of a polygon

In this figure we are given all the sides except one designated as x and the perimeter

We can add up all the sides and solve for x

Sum of sides = 4 + 3 + 12 + 9 + x

Perimeter = 35

=> 4 + 3 + 12 + 9 + x = 35

=> 28 + x = 35

=> x = 35 - 38 = 7