What system of equations can be used to ring s, the cost in dollars of each standard photo and w, the cost in dollars of each wallet photo ?

Answer:

-12.73

Step-by-step explanation:

since you are adding a negative, it is the same as subtracting. subtract -7.1 from -5.63 to get -12.73. hope this helps

Answer:

chidori or fire ball jutsu

Step-by-step explanation:

Answer:

nice i like naruto

Step-by-step explanation:

The correct formula to calculate the number of tires, t, needed for c cars per day is t = c/4, which is option b).


The formula that shows how to calculate the number of tires, t, needed for c cars per day is option b) t = c/4.

To understand this formula, let's break it down step by step:

1. Each car needs four regular tires and one spare tire for the trunk. So, the total number of tires needed for one car is 4 + 1 = 5.

2. If we want to calculate the total number of tires needed for c cars, we can multiply the number of cars by the number of tires needed per car, which is 5. So, the formula becomes t = 5c.

3. However, we need to find the number of tires needed, which is represented by t. Since we have t on the left side of the equation, we can rearrange the formula by dividing both sides by 5: t/5 = c.

4. Now, we have the number of tires needed (t) expressed in terms of the number of cars (c), but we want to find the number of cars needed given the number of tires (t).


To do this, we can rearrange the formula again by dividing both sides by 4: t/4 = c/4.

Therefore, the correct formula to calculate the number of tires, t, needed for c cars per day is t = c/4, which is option b).

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The max value and min value can then be determined from these critical points.

To find the extreme values of a function subject to a constraint, we can use Lagrange multipliers. First, we set up the Lagrangian equation by multiplying the constraint by a scalar λ and adding it to the original function.

Then, we take the partial derivatives of the Lagrangian equation with respect to each variable and set them equal to zero. This will give us a system of equations to solve for the critical points.

Once we have the critical points, we need to determine which ones are maximums and which are minimums.

To do this, we can use the second derivative test. If the second derivative is positive at a critical point, it is a minimum. If the second derivative is negative, it is a maximum.

In summary, to find the extreme values of a function subject to a constraint using Lagrange multipliers, we set up the Lagrangian equation, solve for the critical points, and then use the second derivative test to determine which ones are maximums and which are minimums.

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The maximum value of f(x, y, z) is 26.5, and the minimum value is -29.

To find the extreme values of the function f(x, y, z) = 6x + 6y + 5z subject to the constraint 3x² + 3y² + 5z² = 29 using Lagrange multipliers, set up the following system of equations:

1. ∇ f = λ∇g

2. g(x, y, z) = 3x² + 3y² + 5z² - 29

where ∇f and ∇g are the gradients of f and g respectively, and λ is the Lagrange multiplier.

Taking the partial derivatives, we have:

∇ f = (6, 6, 5)

∇g = (6x, 6y, 10z)

Setting these two gradients equal to each other, we get:

6 = 6λx

6 = 6λy

5 = 10λz

Dividing the first two equations by 6\(\lambda\), we obtain:

x = ¹/λ

y = ¹/λ

Substituting these values into the third equation, we have:

5 = 10λz

z = ¹/2λ

Now, substitute x, y, and z back into the constraint equation to find the value of λ:

3(¹/λ)² + 3(¹/λ)² + 5(1/2λ)² = 29

6(¹/λ²) + 5(⁴/λ²) = 29

24 + 5 = 116λ²

116λ² = 29

λ² = ²⁹/₁₁₆

λ = ±√²⁹/₁₁₆

λ = ± √²⁹/2√29

λ = ± ¹/₂

We have two possible values for λ, λ = ¹/₂ and λ = ¹/₂

Case 1: λ = ¹/₂

Using this value of λ, we can find the corresponding values of x, y, and z:

x = ¹/λ = 2

y =¹/λ = 2

z = 1/2 λ = ¹/₂

Case 2: λ = -1/2

Using this value of λ, find the corresponding values of x, y, and z:

x = 1/λ = -2

y = 1/λ = -2

z = 1/(2λ) = -1

Now that we have the values of x, y, and z for both cases, substitute them into the objective function f(x, y, z) to find the extreme values.

For Case 1:

f(x, y, z) = 6x + 6y + 5z

= 6(2) + 6(2) + 5(1/2)

= 12 + 12 + 2.5

= 26.5

For Case 2:

f(x, y, z) = 6x + 6y + 5z

= 6(-2) + 6(-2) + 5(-1)

= -12 - 12 - 5

= -29

Therefore, the maximum value of f(x, y, z) is 26.5, and the minimum value is -29.

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Divide each term by  

4

and simplify.

Inequality Form:

r ≤ 3

Interval Notation:

( − ∞ , 3 ]

the amount of coins stacked t frets is 10

x^3 - a^3

The above expression represent differnt of 2 cubes

This can be re- written as

(x - a)^3

(x - a) ( x ^2 + ax + a^2)

expand the bracket

x * x^2 + ax*x + x *a^2 - a * x^2 - a * ax - a * a^2

= x^3 + ax^2 + a^2x - ax^2 - a^2x - a^3

collecting the like terms

= x^3 + ax^2 - ax^2 + a^2x -a^2x - a^3

ax^2 - ax^2 = 0

a^2x - a^2x = 0

Therefore

= x^3 + 0 + 0 - a^3

= x^3 - a^3

Given equation: x² - 14x + 40 = 0We need to rewrite the equation by completing the square.Now, we will follow these steps to complete the square.

Step 1: Write the equation in the form of ax² + bx = c. x² - 14x = -40Step 2: Divide both sides of the equation by the coefficient of x². x² - 14x + (49) = -40 + 49 + (49)Step 3: Write the left-hand side of the equation as a perfect square trinomial. (x - 7)² = 9The equation is now in the form of (x - 7)² = 9.

We can write this equation in the form of (x + a)² = b by making some changes. (x - 7)² = 9 ⇒ (x + (-7))² = 3²Hence, the rewritten equation by completing the square is (x - 7)² = 9 which can also be written in the form of (x + (-7))² = 3².

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Answer:

24/b-3 + 24/b+3

Step-by-step explanation:

For PLATO users!!!!

This expression represents the total time, Time = \(\frac{24}{b-3} + \frac{24}{b+3}\)

Distance is defined as the product of the speed and time.

Given,

b = the speed of the boat in miles/hour

let,  effective speed upstream = (b+3)

effective speed downstream = (b-3)

∵Time = distance/ speed

Given that, upstream a distance of 24 miles

Time = \(\frac{24}{b-3} + \frac{24}{b+3}\)

This expression represents the total time it takes to complete a round-trip up and back.

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Answer:

Rachel

Step-by-step explanation:

Rachel has the greater representation; if the students are in the lunch line, they are buying food (this does not account for students who bring lunch from home).

The last number in an ID has nothing to do with lunch choice.

Answer:

n= 10

Step-by-step explanation:

You can cross multiply, set each side equal to each other, and solve from there. 6.3n=63. divide 63 by 6.3 to get 10.

\(\frac{7}{n}=\frac{6.3}{9}\\6.3n=63\\n=10\)

Answer:

n = 10

Step-by-step explanation:

You would have to cross multiply.

7 * 9 = 63

6.3 * n = 6.3n

63 = 6.3n

63/6.3 = 10

I hope that helps! :)

Triangle ABC is congruent to Triangle CDA using the SSS rule.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

SSS rule states that,

If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

To prove:

ΔABC ≅ ΔCDA.

AB = DC ( given)

AD = BC (given)

AC = AC (common to both the triangles)

ΔABC ≅ ΔCDA ( By SSS rule )

Thus,

ΔABC ≅ ΔCDA by SSS rule.

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Answer:

The measure of the 2 angles are 90° and 35°.

Step-by-step explanation:

The sum of angles in a triangle is 180°.

2x + x - 10 + 55 = 180

Simplify.

3x + 45 = 180

Find 3x.

3x = 180 - 45

    = 135

Find x.

x = 135 ÷ 3

x = 45

2x° = 45° × 2

     = 90°

(x-10)° = 45° - 10°

          = 35°

Answer: x=45

Step-by-step explanation:

2 times 45 is equal to 90

45-10 is equal to 35

55+90+35=180

Step-by-step explanation:

do 1/2 x 4/2 x 3/2 = your answer :)

Answer:

12m8n16 = 1536mn

But i think you wrong to write a problem

Answer

1,536

Step-by-step explanation:

(3m2n4)4

\(multiply \: both \: sides \: by \: 4 \\ 3m \times 4 \times 2m \times 4 \: 4 \times 4 \\ 12m \: 8m \: 16 \: \\1,536 \)

Answer:

40 units^2

Step-by-step explanation:

The area of the triangle is

A = 1/2 bh

A = 1/2 ( 8 * 10)

   = 1/2 (80)

  = 40 units^2

Step-by-step explanation:

a=1/2*b*h

a=1/2*8*10

a=40

The statement is true. If the two nonadjacent angles are formed by two intersecting lines, then the  angles are congruent

When two non-adjacent angles are formed with two intersecting lines then they are called​ opposite angles.

There are some properties of nonadjacent angles:

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Answer:

The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = 10 pounds

The number of pounds of the farmers cheese she bought = 5 pounds

The number of pounds of peaches she bought = 6 pounds

Step-by-step explanation:

The given information are;

The amount that Samantha's mother spent in the market = $78

The number of pounds of apples she bought = The number of pounds of tomatoes she bought

The number of pounds of the farmers cheese she bought = 1/2 of the  number of pounds of apples she bought

The number of pounds of peaches she bought = 1 + 1/2 of the number of pounds of apples she bought

The price of the apples = $1.50

The price of the tomatoes = $2.50

The price of the farmers cheese = $4.00

The price of the peaches = $3.00

If we put the number of pounds of the apples she bought = X, we have

X×$1.50 + X×$2.50 + 1/2×X×$4.00 + (1 + 1/2×X)×$3.00 = $78.00

Which gives;

X×$1.50 + X×$2.50 + 1/2×X×$4.00 + $3.00+ 1/2×X×$3.00 = $78.00

\(\dfrac{X \times \$15.00 + \$ 6.00}{2} = \$ 78\)

X × $15.00 + $6.00 = $78 × 2 = $156.00

X × $15.00 + $6.00 = $156.00

X × $15.00 = $156.00 - $6.00 = $150.00

X = $150.00/($15.00) = 10 pounds

Therefore;

The number of pounds of the apples she bought = X = 10 pounds

The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = 10 pounds

The number of pounds of the farmers cheese she bought = 1/2 of the  number of pounds of apples she bought = 1/2 of 10 = 1/2×10 = 5 pounds

The number of pounds of the farmers cheese she bought = 5 pounds

The number of pounds of peaches she bought = 1 +The number of pounds of the farmers cheese she bought = 1 pound + 5 pounds = 6 pounds

The number of pounds of peaches she bought = 6 pounds.

The solution is: Samantha´s mother bought:

As the question of the problem is" How many pounds of each product Samantha´s mother bought" it is convenient to call:

According to that:

Spent

She spent 78 $ buying

1.50× x + 2.50×x + 4× y + 3 × z = 78      (1)

Now y = x/2       and   z = y + 1

By substitution in equation (1) we get

3.50× x + 4×(x/2) + 3× [( x/2 ) + 1 ] = 78

Solving for x

5.50×x + (3/2)×x + 3 = 78

11×x + 3×x + 6 = 156

14×x = 150

x = 10.71 Lbs

y = 10.71/2         y  = 5.36 Lbs  

and    z  =  5.36  +  1  = 6.36 Lbs

z = 6.36 Lbs

Answer:

Y=-2/3+4

Step-by-step explanation:

The slope of the equation can be solved with

2-4/3-0 y2-y1 divide by x2-x1 which gives 3/2 and the y intercept the point at which the slope hits the y intercept which is 4. Also the slope is negative as it’s pointed downwards.

Getting the slope:

m=\((y_1 - y_2 )/(x_1 - x_2)\)

Using this formula, the slope is calculated to be -2/3

To find intercept, plug in a point value into equation and solve.

Intercept = 4

Total equation: y=-2/3x + 4

​  

​  

​

Answer:

$400

Step-by-step explanation:

450-50=400

Answer:325

Step-by-step explanation: Start off with 150, 150-225=-75   -75-50=-125   -125+450=324 Positive

-

Answer:

m∠A + m∠B = 130°

Step-by-step explanation:

the interior angle measures of a triangle always add up to 180°. using this information along with the fact that a straight line is also 180°, we can infer that the measure of angle C is 50°. to find the sum of angle A and angle B, we will subtract 50 from 180. this gives us 130. so this means that the answer to your question is 130°. hope this helps you

Answer:

Step-by-step explanation:

∠C+130=180°

∠A+∠B+∠C=180

∠A+∠B+∠C=∠C+130

∠A+∠B=130°

Answer:

-10 and 10

Step-by-step explanation:

subtracting what is to the right of the equal sign from both sides of the equation :  x^2-10-(90)=0

step 1 - A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

(at the end of step 1 it should look like this) =  (x + 10)  •  (x - 10)

solve as many equations as there are terms in the product

any solution of term = 0 solves product = 0 as well.

Answer:

x = 5 ±√115

Step-by-step explanation:

x² - 10x - 90 = 0

You can solve for x by doing it in 2 ways: Completing the square and by using the quadratic formula

Completing the Square

(x² - 10x + 25) - 25 - 90 = 0

(x - 5)² - 115 = 0

(x - 5)² = 115

x - 5 = ±√115

x = 5 ±√115

Quadratic Formula

√460 = √4 X √115

Hence 2√115

Answer:

78

Step-by-step explanation:

A 45-45-90 triangle has sides like..

So the height of the parallelogram is 6.5

6.5 x 12 = 78

Answer:

78 in^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = ( 12) * h

We can find the height  from using trig functions

tan 45 = h /6.5

6.5 tan 45 = h

A = ( 12) * 6.5 tan 45

   =12 ( 6.5) * 1

   =78

Assume that q≥3. If p+q and p−q are both squares, then p−q and p+q are both even squares, which means both are divisible by 4, which means then that p+q−(p−q)=2q must be divisible by 4. But this cannot be i.e., 2q=(p+q)−(p−q) cannot be divisible by 4, as q is an odd number as q is a prime at least 3.

[Note that I only used that p and q are odd.]

As for q=2, note that with the exception of the pairs 1,4, the absolute value of the difference between every two integral squares is at least 5. So with q=2, note that p+2 and p−2 cannot both be squares as they differ by only 4<5.

Answer:

(D) \(\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}\)

Step-by-step explanation:

The quadratic formula is:

\(\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}\)

Assuming that a is our x² term, b is our x term, and c is the constant, we can substitute inside the equation.

\(\begin{array}{*{20}c} {\frac{{ - (-5) \pm \sqrt {5^2 - 4\cdot1\cdot3} }}{{2\cdot1}}} \end{array}\)

\(\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 12} }}{{2}}} \end{array}\)

\(\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}\)

So the answer is D, \(\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}\).

Hope this helped!

Answer:

5. The numerator is the top number in a fraction, while the denominator is the bottom number in a fraction.

6. \(\frac{5}{7}\) bottle

Step-by-step explanation:

Answer:

I CANT SEE THE IMAGE BUT I NEEED POINTS xD

Step-by-step explanation:

PERIODDDDDDDDD

Answer:

Laptops, 82 is the largest number when you look at the totals.

Step-by-step explanation:

gender|    electronic tablet | Laptop | Both | Neither | Total

----------|----------------------------|------------|---------|-------------|--------

girl       |      13                       |    51      |   8     |      17      |   89

boy      |      12                       |    31      |   5     |      13      |   61

total     |      25                      |    82     |   13    |     30     |    150

LMK If I have to explain but I basically just got the 150 students from the directions and went from there.

The measure of angles are:

3. <1 = 63, <2= 49, <3= 87, <4= 44

4. <1= 52, <2= 79, <3= 38

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle. A closed shape with both inner and exterior angles, a triangle is created by three line segments. When the values of the other two angles are known, one can utilise the angle sum property to determine the measure of an unknown interior angle.

3. <3 + 93=1 80 (linear pair)

<3 = 87

<2 = 49 (Vertical opposite angle)

<3 + <4 + 49= 180  (Angle sum property)

87 + <4 + 49= 180

<4 = 44

and, <2 + <1 + 68= 180  (Angle sum property)

49+ <1 + 68= 180

<1 = 63

4. <3 = 38 (alternate interior angle)

<2 + <3 + 63= 180  (Angle sum property)

38+ <2 + 63= 180

<2 = 79

and, <1 + 90 + 38= 180  (Angle sum property)

<1= 52

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The first four nonzero terms of the Taylor series for the function (1+12x⁹) centered at 0 are: 1, 12x⁹, 0x², and 0x³. Since the last two terms are zero, the Taylor series is simply: 1 + 12x⁹.

To find the first four nonzero terms of the Taylor series for the function (1+12x⁹) centered at 0, follow these steps:
1. Identify the function: f(x) = (1+12x⁹)
2. Since the function is already a polynomial, the Taylor series will be the same as the original function
3. The first four nonzero terms will be the terms with the lowest powers of x.
So, the first four nonzero terms of the Taylor series for the function (1+12x⁹) centered at 0 are: 1, 12x⁹, 0x², and 0x³. Since the last two terms are zero, the Taylor series is simply: 1 + 12x⁹.

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