Melissa bought 3 bags of apples and 5 bags of pears. The pears cost $3 more per
bag than the apples. She pays a total of $55. Which of the following are true?
Choose all that apply. *
A: The cost p, in dollars, of 1 bag of pears is modeled by 5p + 3(D-3) = 55
B: One bag of apples plus one bag of pears costs $13
C: The cost, a, in dollars, of 1 bag of apples is modeled by 3(a - 3) + 5(a) = 55
D: Reducing the number of bags of apples by one would result in a total cost of $50
E: The pears cost twice as much as apples per bag.

The smallest possible area of a square which can be made from the three pieces is 11833.203125 cm².

To find the smallest possible area of a square, we need to make sure that we use the longest pieces to form the sides of the square. Therefore, we need to divide the 360 cm steel bar into equal parts first, then use the remaining parts to divide the other two steel bars.

Let's call the length of each part x.

The 360 cm steel bar can be divided into n parts of length x, where:

n = 360/x

Similarly, the 300 cm steel bar can be divided into m parts of length x, where:

m = 300/x

And the 210 cm steel bar can be divided into k parts of length x, where:

k = 210/x

To form a square, we need to use all the parts we cut from the steel bars. Therefore, the length of the sides of the square will be nx + mx + kx, which is equal to (n + m + k)x.

The area of the square will be (n + m + k)x²

To find the smallest possible area, we need to minimize (n + m + k)x². Since x can be any positive number, we can focus on minimizing n + m + k.

n + m + k = (360/x) + (300/x) + (210/x)

n + m + k = (870/x)

To minimize (n + m + k), we need to maximize x. However, x cannot be greater than the smallest steel bar, which is 210 cm long.

Therefore, x must be a factor of 210.

Let's try x = 1 cm. In this case, n + m + k = 870 cm, which means we can form a square with sides of length 870 cm/4 = 217.5 cm.

The area of this square is 217.5^2 = 47250.625 cm².

Let's try x = 2 cm. In this case, n + m + k = 435 cm, which means we can form a square with sides of length 435 cm/4 = 108.75 cm.

The area of this square is 108.75² = 11833.203125 cm².

Let's try x = 3 cm. In this case, n + m + k = 290 cm, which means we cannot form a square using all the parts we cut from the steel bars.

Therefore, the smallest possible area of a square which can be made from the three pieces is 11833.203125 cm², and this can be achieved by cutting the steel bars into parts of length 2 cm.

Learn more about area of square here: https://brainly.com/question/813881

#SPJ1

Answer:

Scalar is negative

Step-by-step explanation:

Answer:

Awesome I actually remember this haha

Step-by-step explanation:

So first, find -2 and go down to it and put a dot. Then I would go up 7 and over 2 to the left and put a dot. On number 2, I would go up 3 (because it's a positive) and then put a dot. And for -6x, make it into slope intercept form, or -6 over 1x. So it should look like this; -6/1x. Then I would go down -6 from the dot where you marked 3 at, and over to the right 1 because you already used your negative on the 6. And I always drew arrows, to make sure they wee straight lines. I really hope this helps and is right! Good luck!

Answer: 25

Step-by-step explanation: The number that is added to both sides is the number that is needed to create a perfect square trinomial.

The question is, what is that number?

Well, it comes from a formula. The number that is added to both sides always comes from half the coefficient of the middle term squared.

So half of -10 squared or -5 squared which is 25.

So 25 is added to both sides.

Answer:

6x^3-5x^2+9x+10

Step-by-step explanation:

Use the distributive property and multiply like terms.

Answer:

Pink, shiny cars were preferred by buyers at that time

Step-by-step explanation:

Rewriting the sentence, removing unnecessary words

It should be noted that QC = Q'C" and ACQ is a right angle.

Reflection is an isometric mapping from a Euclidean space to itself that has a set of fixed points called the axis or plane of reflection.

Given that a reflection is a transformation that maps point Q in a figure over a line, AB, such that for point C at the intersection of AB and QQ'.

We know that reflection creates a image equidistant from the line of reflection. Thus, QC = Q'C".

Also in reflection , a line drawn from the point is perpendicular to the line of reflection.

Therefore, ACQ is a right angle

Learn more about reflection on:

https://brainly.com/question/11930270

#SPJ1

The opposite sides of the rhombus are the same length. The opposite sides of the rhombus are the same length. Side AC is common to both triangles ABC and CDA. The two angles ABC and CDA are congruent by the SSS theorem congruent triangle

A rhombus is a quadrilateral with all sides equal. A rhombus is a special type of parallelogram with all sides equal because the opposite sides of a parallelogram are equal. Two angles are congruent only if they have the same dimensions. Two segments are congruent only if they have the same dimensions. These are the explanation for ABC being congruent to CDA

Learn more about the rhombus in

https://brainly.com/question/27870968

#SPJ4

Answer:

1) 8n-3

2) 3+(8-n)

3) 3(n-8)

4) 3(n+8)

Answer:

mention the other options or clip the pic of question

Answer:

what numbers represent the following? i'd take a wild guess and say that one of the right answers is 0/-6? idrk, I'd copy and paste the whole question so we can help you, Have a great day, good luck, and peace out! -Conner

Step-by-step explanation:

To find the probability that the student ONLY takes History Class, we need to divide the number of students taking only History (37) by the total number of students (150).

Probability is the measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability can be used to analyze and make predictions about a wide range of situations, including games of chance, weather patterns, financial markets, and more.

Here,

Using the given numbers, we can calculate the probabilities as follows:

To find the probability that the student ONLY takes History Class, we need to divide the number of students taking only History (37) by the total number of students (150):

P(ONLY History) = 37/150 = 0.2467 or approximately 24.67%

To find the probability that the student takes BOTH History and Biology, we need to divide the number of students taking both (25) by the total number of students (150):

P(History AND Biology) = 25/150 = 0.1667 or approximately 16.67%

To find the probability that the student does NOT take History or Biology, we need to add the number of students taking neither History nor Biology (21) to the number of students taking only Biology (17), and then divide by the total number of students:

P(Neither History nor Biology) = (21 + 17)/150 = 0.2533 or approximately 25.33%

The complement of this event (i.e., the probability of taking either History or Biology) is:

P(History or Biology) = 1 - P(Neither History nor Biology) = 1 - 0.2533 = 0.7467 or approximately 74.67%

To find the probability that the student takes Biology class, we need to add the number of students taking both History and Biology (25) to the number of students taking only Biology (17), and then divide by the total number of students:

P(Biology) = (25 + 17)/150 = 0.2133 or approximately 21.33%

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

Ok, so

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.

Answer:

Step-by-step explanation: First things first, you have to have the variables on one side. To do that, subtract 4x from each side.

4x + 6 = 8x - 10

-4x         -4x

Now you have your equation that is ready to graph.

6 = 4x - 10

Use a graphing calculator and put in the equation. You can also go to desmos.com

When you are done you will see your graph as well as the answer.

Answer:

\(23x-6y\)

Step-by-step explanation:

\(5(3x + 6y) + 4(2x - 9y)\\\\15x+30y+8x-36y\\\\15x+8x+30y-36y\\\\\boxed{23x-6y}\)

Hope this helps.

Answer:

23x-6y

Step-by-step explanation:

5(3x + 6y) + 4(2x - 9y)

15x + 30y + 8x - 36y

23x - 6y

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The magnitude of the net magnetic field at the square's center is \(= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\).

Using \(dB=\frac{u_0i}{4\pi} \frac{sin\theta}{r^2}\) the force on say, wire 1 (the wire at the upper left of the figure) is along the diagonal (pointing toward wire 3, which is at the lower right). Only the forces (or their components) along the diagonal direction contribute. With θ=45°, we find the force per unit meter on wire 1 to be

\(f_1 = |F_{12}+F_{13}+F_{14}|\\\\= 2F_{12}cos\theta+f_{13}\\\\=2(\frac{u_0i^2}{2\pi a} )cos45^0+\frac{u_0i^2}{2\sqrt{2}\pi a }\)

\(=\frac{3}{2\sqrt{2}\pi }(\frac{u_0i^2}{0})\\\\=\frac{3}{2\sqrt{2}\pi } \frac{(4\pi*10^{-7}T.m/A)(15.0A)^2} {(8.50*10^{-2}m)}\)

\(= 1.12 * 10^{-3}N/m\)

The direction of F1​ ​ is along r^=(i^=j^​)/sqrt2. In unit-vector notation, we have

\(F_1 = \frac{(1.12 * 10^{-3}N/m)}{\sqrt{2} }(i - j) \\\\= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\)

Hence the answer is the magnitude of the net magnetic field at the square's center is \(= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\).

To learn more about perpendicular click here https://brainly.com/question/28063031

#SPJ4

Answer:

1.25

Step-by-step explanation:

125/100 = 1.25

Answer:

it's 1.25

Step-by-step explanation:

125 ÷100 = 1.25

2. The exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

3. The exact value of tan 255° is (1/√3 - √3)/2.

The sine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.

We can use the difference identity for sine to find the exact value of sin (185° - 65°):

sin (185° - 65°) = sin 185° cos 65° - cos 185° sin 65°

Since sin (180° + x) = -sin x and cos (180° + x) = -cos x to simplify the expression:

sin (185° - 65°) = sin (120°) cos (65°) + cos (120°) sin (65°)

= (√3/2)(cos (65°)) + (-1/2)(sin (65°))

= (√3/2)(cos (65°)) - (1/2)(sin (65°))

Therefore, the exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

Here,

tan 255° = tan (225° + 30°)

Using the tangent sum identity, we get:

tan (225° + 30°) = (tan 225° + tan 30°)/(1 - tan 225° tan 30°)

Since tan 225° = tan (225° - 180°) = tan (-45°) = -1 and tan 30° = (√3)/3, we can substitute these values:

tan 255° = (-1 + (√3)/3)/(1 + 1/√3)

Simplifying the denominator by rationalizing the denominator, we get:

tan 255° = (-1 + (√3)/3)/(√3 + 1)

Multiplying the numerator and denominator by (√3 - 1), we get:

tan 255° = [(-1 + (√3)/3)(√3 - 1)]/[(√3 + 1)(√3 - 1)]

= [(√3 - 1 - 1 + 1/√3)]/(2)

= [√3 - 2 + 1/√3]/2

= (1/√3 - √3)/2

Therefore, the exact value of tan 255° is (1/√3 - √3)/2.

Learn more about Trigonometric functions here:

brainly.com/question/6904750

#SPJ1

Answer:

area= 452.39

circumference= 75.40

Step-by-step explanation:

circumference is equal to 2 * pi * r

area is equal to pi * r^2

circumference = 2 * pi * 12 = 75.40

area = pi * 12^2 = 452.39

hope this helps!

Total pounds of yogurt they buy (as a mixed number) : \(1\dfrac{5}{16}\)

Mass is one of the principal quantities, which is related to the matter in the object  

The main mass unit consists of 7 units of other than other units of mass such as quintals, tons, pounds, ounces:  

Kilogram, kg  

Hectogram, hg  

Decagram, dag  

gram, g  

Decigram, dg  

centigram, cg  

milligrams, mg  

Each unit descends then multiplied by 10, and if one unit increases then divided by 10  

Fraction numbers are known as numerator and denominator

On a number line, fractions are expressed in points that lie between two integers

The general form of fractions is

\(\dfrac{a}{b}\)

Mixed fractions consist of integers and ordinary fractions

A mixed number is a combination of a whole number and a fraction

Sara has 14 ounces of vanilla yogurt

Her father's yogurt weighs half of much, so her fathers have yogurt :

= 0.5 x 14 ounces

= 7 ounces

Total ounces of yogurt they buy

= 14 + 7 = 21 ounces

for 1 ounces (oz) the conversion = 0.0625 pounds(lbs)

So for 21 ounces there will be

= 21 x 0.0625

= 1.3125 pounds

if we express as a mixed number , it will be :

\(=\dfrac{13125}{10000}\)

\(=1\dfrac{5}{16}\)

Hence Total pounds of yogurt they buy (as a mixed number) : \(1\dfrac{5}{16}\)

To know more about Weight follow

https://brainly.com/question/2337612

#SPJ1

Answer: d. No, because the study was not taken from a random sample of scholarship athletes.

Step-by-step explanation:

Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.

The amount of the investment at the end of 12 years for the following compounding methods when $400 is invested at an interest rate of 5.5% per year will be as follows:

Annual compounding Interest = 5.5%

Investment = $400

Time = 12 years

The formula for annual compounding is,A = P(1 + r / n)^(n * t)  

Where,P = $400

r = 5.5%

= 0.055

n = 1

t = 12 years

Substituting the values in the formula,

A = 400(1 + 0.055 / 1)^(1 * 12)  

A = 400(1.055)^12  

A = $812.85  

Hence, the amount of the investment at the end of 12 years for the annual compounding method will be $812.85.

Rate = 5.5%

Compound Interest = 400 * (1 + 0.055)^12

= $813 (rounded to the nearest cent).  

To know more about intrest visit:

https://brainly.com/question/25720319

#SPJ11

Not a robot! I don't think.

Y in the beginning goes up to 3.

Y in the end goes down to -2 before shooting back up in an infinite sense.

Increasing: The beginning and the end the line on the graph. (Also the jump in the middle, the round part.)

Decreasing: The middle of the graph. (The jump, downward slope.)

Constant, Y at the near end going in a straight line from 9-12 at a -2.

End behavior: Decide for yourself. Is the line going up without fault at the end an appearing continuous or a discontinuous line?

Answer:

End Behavior:

x⇒-8,y⇒-∞

x⇒∞,y⇒∞

(-∞,1},{3,5},{12,∞)

{1,3},{5,9}

(9,12)

hope it helps...

have a great day

Answer:

Slope: -3/4

y-intercept: (0,-5)

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Answer and step-by-step explanation:

I am assuming the equation is:

\(y + 2 = -\frac{3}{4}(x + 4)\)

It will be easier if we convert the fraction to a decimal, for now.

\(y + 2 = -0.75(x + 4)\)

Then we can simplify a bit, using the distributive property.

\(y + 2 = -0.75x - 3\)

Now, we want to have the y all by its self. So, let's subtract 2 on both sides.

\(y + (2 - 2) = -0.75x + (-3 - 2)\)

\(y = -0.75x - 5\)

Let's convert the decimal back into a fraction.

\(y = -\frac{3}{4}x - 5\)

Now we have our equation. To start graphing, let's plot the y-intercept. Our y-intercept is -5. So we can plot the point (0, -5). Now, we need to find the slope. The slope is \(-\frac{3}{4}\). It's negative, which means that the line will start from the top right to the bottom left. That means that every time we move to the right one unit, we will move down 0.75 units. I hope this helps!

Answer:

To calculate a Pythagorean triple select any term of this progression and reduce it to an improper fraction. For example, take the term {\displaystyle 3{\tfrac {3}{7}}}3\tfrac{3}{7}. The improper fraction is {\displaystyle {\tfrac {24}{7}}}{\tfrac  {24}{7}}. The numbers 7 and 24 are the sides, a and b, of a right triangle, and the hypotenuse is one greater than the largest side. For example:

{\displaystyle 1{\tfrac {1}{3}}{\text{ }}{\xrightarrow {\text{yields}}}{\text{ }}[3,4,5],{\text{ 2}}{\tfrac {2}{5}}{\text{ }}{\xrightarrow {\text{yields}}}{\text{ }}[5,12,13],{\text{ 3}}{\tfrac {3}{7}}{\text{ }}{\xrightarrow {\text{yields}}}{\text{ }}[7,24,25],{\text{ 4}}{\tfrac {4}{9}}{\text{ }}{\xrightarrow {\text{yields}}}{\text{ }}[9,40,41],{\text{ }}\ldots }1{\tfrac  {1}{3}}{\text{ }}{\xrightarrow  {{\text{yields}}}}{\text{ }}[3,4,5],{\text{    2}}{\tfrac  {2}{5}}{\text{ }}{\xrightarrow  {{\text{yields}}}}{\text{ }}[5,12,13],{\text{    3}}{\tfrac  {3}{7}}{\text{ }}{\xrightarrow  {{\text{yields}}}}{\text{ }}[7,24,25],{\text{    4}}{\tfrac  {4}{9}}{\text{ }}{\xrightarrow  {{\text{yields}}}}{\text{ }}[9,40,41],{\text{ }}\ldots  

Jacques Ozanam[5] republished Stifel's sequence in 1694 and added the similar sequence {\displaystyle 1{\tfrac {7}{8}},{\text{ }}2{\tfrac {11}{12}},{\text{ }}3{\tfrac {15}{16}},{\text{ }}4{\tfrac {19}{20}},\ldots }1{\tfrac  {7}{8}},{\text{ }}2{\tfrac  {11}{12}},{\text{ }}3{\tfrac  {15}{16}},{\text{ }}4{\tfrac  {19}{20}},\ldots  with terms derived from {\displaystyle n+{\tfrac {4n+3}{4n+4}}}n+{\tfrac  {4n+3}{4n+4}}. As before, to produce a triple from this sequence, select any term and reduce it to an improper fraction. The numerator and denominator are the sides, a and b, of a right triangle. In this case, the hypotenuse of the triple(s) produced is 2 greater than the larger side. For example:

{\displaystyle 1{\tfrac {7}{8}}{\xrightarrow {\text{yields}}}[15,8,17],2{\tfrac {11}{12}}{\xrightarrow {\text{yields}}}[35,12,37],3{\tfrac {15}{16}}{\xrightarrow {\text{yields}}}[63,16,65],4{\tfrac {19}{20}}{\xrightarrow {\text{yields}}}[99,20,101],\ldots }1{\tfrac  {7}{8}}{\xrightarrow  {{\text{yields}}}}[15,8,17],2{\tfrac  {11}{12}}{\xrightarrow  {{\text{yields}}}}[35,12,37],3{\tfrac  {15}{16}}{\xrightarrow  {{\text{yields}}}}[63,16,65],4{\tfrac  {19}{20}}{\xrightarrow  {{\text{yields}}}}[99,20,101],\ldots  

Together, the Stifel and Ozanam sequences produce all primitive triples of the Plato and Pythagoras families respectively. The Fermat family must be found by other means.

With a the shorter and b the longer leg of the triangle:

{\displaystyle {\text{Plato: }}c-b=2,\quad \quad {\text{Pythagoras: }}c-b=1,\quad \quad {\text{Fermat: }}\left|a-b\right|=1}{\displaystyle {\text{Plato: }}c-b=2,\quad \quad {\text{Pythagoras: }}c-b=1,\quad \quad {\text{Fermat: }}\left|a-b\right|=1}

Dickson's method

Leonard Eugene Dickson (1920)[6] attributes to himself the following method for generating Pythagorean triples. To find integer solutions to {\displaystyle x^{2}+y^{2}=z^{2}}x^{2}+y^{2}=z^{2}, find positive integers r, s, and t such that {\displaystyle r^{2}=2st}r^{2}=2st is a perfect square.

Then:

{\displaystyle x=r+s\,,\,y=r+t\,,\,z=r+s+t.}x=r+s\,,\,y=r+t\,,\,z=r+s+t.

From this we see that {\displaystyle r}r is any even integer and that s and t are factors of {\displaystyle {\tfrac {r^{2}}{2}}}{\tfrac  {r^{2}}{2}}.  All Pythagorean triples may be found by this method.  When s and t are coprime, the triple will be primitive. A simple proof of Dickson's method has been presented by Josef Rukavicka (2013).[7]

Example: Choose r = 6. Then {\displaystyle {\tfrac {r^{2}}{2}}=18}{\tfrac  {r^{2}}{2}}=18. The three factor-pairs of 18 are: (1, 18), (2, 9), and (3, 6). All three factor pairs will produce triples using the above equations.

s = 1, t = 18 produces the triple [7, 24, 25] because x = 6 + 1 = 7,  y = 6 + 18 = 24,  z = 6 + 1 + 18 = 25.

s = 2, t =   9 produces the triple [8, 15, 17] because x = 6 + 2 = 8,  y = 6 +  9 = 15,  z = 6 + 2 + 9 = 17.

s = 3, t =   6 produces the triple [9, 12, 15] because x = 6 + 3 = 9,  y = 6 +  6 = 12,  z = 6 + 3 + 6 = 15. (Since s and t are not coprime, this triple is not primitive.)

1.b

2.refrection hope this helps may i have brainliest if not thats ok

Step-by-step explanation:

The correct answer is d. num1 = 4, num2 = 4.

After executing the method with arguments num1 and num2, the value of num2 is set to the value of num1 (which is 4) and num1 is set to 0 within the method. However, these changes are local to the method and do not affect the values of num1 and num2 in the client code. Therefore, num1 remains 4 and num2 becomes the returned value from the method, which is 4.

Here's the step-by-step explanation:

1. The method m() takes two parameters, x and y, and sets y equal to x and x equal to 0.
2. The method then returns the value of y.
3. In the client code, num1 is set to 4 and num2 is set to 9.
4. When calling m(num1, num2), x becomes 4 (value of num1) and y becomes 9 (value of num2).
5. Inside the method, y is set to the value of x, which is 4. Then x is set to 0.
6. The method returns the value of y, which is 4.
7. The returned value (4) is assigned to num2 in the client code.
8. The final values are num1 = 4 (unchanged) and num2 = 4 (updated).

To learn more about parameters : brainly.com/question/30757464

#SPJ11

Answer:

Perimeter

Step-by-step explanation:

perimeter is the sum of the whole sides of a figure

Answer:

30.84

Step-by-step explanation:

in order to find the perimeter you multiply 2 by pi (3.14) then multiply that answer by the radius which is 6. Then divide that answer by 2 since the shape is a semi circle then add the diameter (12) to that answer and you get 30.84.

2 * 3.14 * 6 / 2 + 12 = 30.84

The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches

The lateral surface area of the frustum is calculated using the given formula:

Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii²  + height²)

Lower base radius of frustum = 6 inches

Upper base radius of frustum = 3 inches

Height of frustum = 4 inches

Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]

                                                              = π × 9 × √[(9 + 16]

                                                              = 9π × 5

                                                              = 45π sq. inches

Hence, the lateral surface area of the given frustum is 45π sq. inches

To know more about lateral surface area here:

brainly.com/question/11385509

#SPJ4