Question 1 (Multiple Choice Worth 1 points)
A triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7. What a the length of third side of the triangle?
x+13
x-1
5 x-7
17 x-1

Answer:

Step-by-st(3 + x^3 + 3x^2) + (2x^3 - 2 - 4x^2)

= 3x^3 + x^2 + 3x^2 - 2 - 4x^2

= 3x^3 - x^2 - 2

So the final answer is 3x^3 - x^2 - 2ep explanation:

Answer:

75 teaspoons

Step-by-step explanation:

Due to the conversion, each fluid ounce= 6 teaspoons. Do 72 + 3, which equals 75. You get 72 by doing 12 fluid ounces by 6 teaspoons. <3 hope thi s helps, lovely !

Answer:

w = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

balls

Answer:

x ≥ 30

Step-by-step explanation:

The teacher wants to make at least 24 tutus. If each tutu requires 1.25 yards of tulle, then she will need to buy at least (1.25 × 24) yards of tulle. 1.25 yards × 24 is 30 yards.

The teacher will need at least 30 yards of tulle. In inequality form, this is x ≥ 30.

The volume comparison of the given data is written below:

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, A cone, cylinder, and Sphere all have the same radius with the height of the cone and cylinder being twice the radius.

The volume of the cone =  [tex]\frac{1}{3}[/tex] πr²h

Since, h = 2r

The volume of the cone =  [tex]\frac{1}{3}[/tex] πr² * 2r = 2/3 πr³

The volume of the Cylinder = πr²h

Since, h = 2r

The volume of the Cylinder = πr² * 2r = 2πr³

The volume of the sphere = 4 πr³

Thus, the volume of 3 cones = 2πr³

that is also equal to The volume of one Cylinder.

Thus, the volume of 2 cones = 4/3πr³

that is also equal to The 1/3 volume of the Cylinder.

Thus, the volume of 1 sphere = 4πr³

that is also equal to The volume of 2 cylinders.

Thus, the volume of 1 cone = 2/3πr³

that is also equal to The 1/6 volume of the cone.

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Answer:

The correct inequalities that could be solved to find the number of purchases that a customer needs to make in order to earn the first gift certificate are:

A) 12p+ 25 <100

C) 12p+ 25 ≥100

D) 12p-25 ≥100

F) 12p≥ 100-25

The inequality 12p+ 25 <100 represents the condition where the customer has fewer than 100 points, so they have not yet earned the first gift certificate.

The inequality 12p+ 25 ≥100 represents the condition where the customer has 100 points or more, so they have earned the first gift certificate.

The inequality 12p-25 ≥100 represents the condition where the customer has at least 100 points, so they have earned the first gift certificate.

The inequality 12p≥ 100-25 represents the condition where the customer has at least 100 points, so they have earned the first gift certificate.

From the table given the value of f(g(1)) = 3.

What is composite function?

Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.

From the given table we have to find the value of f(g(1)).

First to find the value of g(1).

From the table given g(1) = 3.

So, f(g(1)) becomes, f(3).

Now to find the value of f(3).

From the table given f(3) = 1.

So, f(g(1)) = 3.

Hence, from the table given the value of f(g(1)) = 3.

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2. In rectangle ABCD, DB = 12 cm AC = 12 cm and AB = √23 cm.

3. it is proven that ∠JMK = ∠LMK = ∠JMI = ∠IML = 90° and the diagonals of the rhombus are perpendicular.

Points to remember:

        Hypotenuse² = side² + side²

Problem - 2

ABCD is a rectangle

Give that DW = 6 cm and BC = 11

As we can see that DW is half of DB

=> Length of DB = 2(6) = 12 cm

Since the diagonals of a rectangle are equal

=> Diagonal DB = Diagonals AC

=> Length of AC = 12 cm

In the given figure, ABD will form right angle triangle

As we know in right angle triangle

Hypotenuse² = side² + side²

=> DB² = AB² + AD²

=> AB² = DB² - AD²

=> AB² = 12² - 11²

=> AB² = 144 -121

=> AB² = 23

=> AB = √23

Therefore,

In rectangle ABCD, DB = 12 cm AC = 12 cm and AB = √23 cm.

Problem - 3

Given that IJKL is a rhombus

IK and JL are diagonals of rhombus intersecting at M

To prove that the diagonals are perpendicular we need to prove that

∠JMK = ∠LMK = ∠JMI = ∠IML = 90°

As we know All Rhombus are parallelograms

IJ = JK = KL  = IL ---- (1)

In a parallelogram, diagonals bisect each other

Therefore, IM = KM and JM = LM ---- (2)

In ∆IML and ∆JMK

JM = ML [ From 2 ]

JK = KL  [ From 1 ]  

MK = MK  [ Common side ]

∆ IML ≅ ∆  JMK [ By SSS congruency criteria ]

=> ∠JMK = ∠LMK

=> ∠JMK + ∠LMK = 180° [ Linear pair ]

=> ∠JMK + ∠JMK = 180°

=> 2 ∠JMK = 180°

=> ∠JMK = 90°

=> ∠JMK = ∠LMK = 90°

Similarly, ∠JMI = ∠IML = 90°

Hence, it is proven that ∠JMK = ∠LMK = ∠JMI = ∠IML = 90° and the diagonals of the rhombus are perpendicular.

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Answer:

C. His labor is a chant.

Step-by-step explanation:

Metaphors are figures of speech where a word is applied to a noun or verb which is not literal. A person's labor cannot literally chant, as stated here, so this sentence is a metaphor.

The total value of the annuity in 26 years is $93,678.57.

An ordinary annuity is when a series of payments is made over a particular period at the end of each period.

The formula that can be used to determine the future value of the annuity is:

Future value = Quarterly deposit x annuity factor

Annuity factor = (1 + r)^n] - 1} / r

Where:

Annuity factor = [{(1 + 0.0175)^(104)} - 1 ] / 0.0175 = 290.02652

Future value = 290.02652 x 323 = $93,678.57

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Answer:

5/2

Step-by-step explanation:

Perpendicular lines are opposite reciprocals:

For example, -2 and 1/2 are opposite reciprocals:

Negate 1/2 to get -1/2. Then take the reciprocal of -1/2 to get -2.

In order to find the slope of an equation, isolate y:

4x + 10y = -140  ==> solve for y

10y = -4x - 140  ==> subtract 4x on both sides

y = (-4x - 140)/10  ==> divide both sides by 10 to isolate y

y = -4x/10 - 140/10  ==> divide each term by 10

y = -2x/5 - 14  ==> simplify

^^ In this equation, the slope is -2/5 since y increases by -2/5 every time x increases by 1.

Now take the opposite reciprocal of -2/5:

First, take the reciprocal of -2/5 by switching the numerator and denominator: -2/5  ==> -5/2

Now negate the result: -5/2 ==> -(-5/2) = 5/2

Hence, 5/2 is the slope of the line perpendicular to 4x + 10y = -140

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The length of arc FE, considering the dilation is given as follows:

4.42.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For the dilation, due to the multiplication of the side lengths by the scale factor, the side lengths are modified, meaning that the original triangle and the dilated triangle are not congruent.

The angle measures, conversely, remain constant, meaning that the original triangle and the dilated triangle are similar.

As the two circles in this problem are similar, we have that the central angle has the same measure.

The scale factor of the dilation is given as follows:

k = 2.5/5 = 0.5.

Then the length of arc EF is given as follows:

EF = 0.5 x 8.84 = 4.42.

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The double integral for this problem has the result given as follows:

[tex]\int_{0}^4 \int_0^1 \frac{4x}{1 + xy} dy dx = 20\ln{(5)} - 16[/tex]

Considering the variable y as the inner variable, the double integral is defined as follows:

[tex]\int_{0}^4 \int_0^1 \frac{4x}{1 + xy} dy dx[/tex]

We start calculating the inner integral, as follows:

[tex]I = \int_0^1 \frac{4x}{1 + xy} dy[/tex]

Using substitution, we have that:

u = 1 + xy

du = x dy.

dy = du/x

Hence:

[tex]I = \int \frac{4x}{u} \times \frac{du}{x}[/tex]

[tex]I = 4\int \frac{1}{u} du[/tex]

I = 4 ln(u).

Returning to x and y, we have that:

I = 4 ln(1 + xy), from y = 0 to y = 1.

Applying the Fundamental Theorem of Calculus for the definite integral, we have that:

I = 4 ln(1 + x) - 4 ln(1 + 0)

I = 4ln(1 + x).

Then the outer integral is given as follows:

[tex]O = \int_{0}^4 4 \ln{(1 + x)} dx[/tex]

Hence:

O = 4[ln(1 + x) + xln(1 + x) - 1 - x], from x = 0 to x = 4.

Applying the Fundamental Theorem again, now for the variable x, we have that:

O = 4[ln(5) + 4ln(5) - 1 - 4] - 4[ln(1) + 0ln(1) - 1 - 0]

O = 4[5ln(5) - 5] + 4

O = 20ln(5) - 20 + 4

O = 20ln(5) - 16.

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Ratio of lawns to hours is 6:5

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Frank mows the lawn constantly 6/5 per hour

But Rate is also equal to number of lawns mowed in a certain amount of time.

Since ratio should always be in terms of simple whole numbers.

If 6/5 lawns are mowed in 1 hour, then,

6 lawns will be mowed in:6/6/5

=5 hours

therefore, 6 laws will be mowed in 5 hours.

Hence, Ratio of lawns to hours is 6:5

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The Pythagorean theorem can be used to find the length of the third side of a triangle if the lengths of the other two sides are known. The formula for the Pythagorean theorem is: c^2 = a^2 + b^2, where c is the length of the third side, and a and b are the lengths of the other two sides.

3) 17

4) 32

Zach's response correctly shows combining the like terms, 2e's, and giving the remaining 2 as it is.

What is a simplification of an algebraic expression?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.

Zach simplifies the expression correctly because 2e + 2e + 2e = 6e with 2 left over.

The expression given "2+2+2+e+e+" is a mix of numerical constants and a variable, e. The correct simplification of this expression would be to combine like terms.

Like terms are terms that have the same variable raised to the same exponent.

In this case, 2's can be combined to give 6 and e's can be combined to give 2e. Adding 2 with 6 or 2e won't be correct as 6 and 2e are not like terms.

Hence, Zach's response correctly shows combining the like terms, 2e's, and giving the remaining 2 as it is.

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The mass of an object that is experiencing a net force of 200 N and an acceleration of 500 m/s² is 0.4kg.

We know that, according to newton's second law of motion

F = m×a

here, F: force, m: mass of the object, a: acceleration

200 N = m × 500 m/s²

m = 200/500 kg = 2/5 kg

or m = 0.4 kg

Therefore, the mass of an object that is experiencing a net force of 200 N and an acceleration of 500 m/s² is 0.4kg.

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Step-by-step explanation:

to solve this problem we use the growth exponential formula: A=P(1+r%)^t

3000×(1+(r/100))^39=6000

by dividing both sides by 3000

(1+(r/100))^39=2

1+r/100=2^(1/39)

r/100=2^(1/39)-1

r=100(-1+2^(1/39))

r=1.79318

by multiplying by 1,000,000

r=1,793,18 approximately

Answer:

3. 8÷ x² is the correct answer.

Answer:  3.0625

Step-by-step explanation:  math :}

The equation of the line as shown in the image above is: y = 3x.

Using the slope-intercept form we can write the equation of a line as y = mx + b, where we have:

To find the equation, use two points on the line, (0, 0) and (-2, -6) to find the slope:

Slope (m) = change in y / change in x = (-6 - 0) / (-2 - 0)

Slope (m) = -6/-2

Slope (m) = 3

The y-intercept (b) = 0

Substitute b = 0 and m = 3 into y = mx + b:

y = 3x + 0

y = 3x

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If weekday is true and miles is less than 10, then the Boolean variable available is set to true.

Step 1: Check if weekday is true

Step 2: Check if miles is less than 10

Step 3: If both conditions are true, then set the Boolean variable available to true

Step 1: Check if weekday is true. This is done by checking if the Boolean variable weekday is set to true. If it is, then proceed to the next step.

Step 2: Check if miles is less than 10. This is done by using the integer variable miles and checking if it is less than 10. If it is, then proceed to the next step.

Step 3: If both conditions are true, then set the Boolean variable available to true. This is done by setting the Boolean variable available to true if the conditions from the previous steps are both true. If not, then the Boolean variable available is set to false.

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It looks like you are trying to find the values of a, b, c, d, e, and f in the matrix [-3x+3y] given the matrices X and Y.

To find the values of a, b, c, d, e, and f, you will need to perform matrix multiplication. Here is how you would do this:

[-3x+3y] = [-3X+3Y]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [[-21 21] [9 -3]]

Therefore, the matrix [-3x+3y] is equal to [[-21 21] [9 -3]].

Answer:

what

Step-by-step explanation:

Answer: 9.2

Explanation: The value of the square root of 85 lies between the whole numbers 9 and 10.

Answer:

the LCM of 105, 126, and 147 is 18420.

Since the fruit boxes need to be equally packed and no fruit is left, the largest possible number of fruit boxes needed is 18420/105 = 176 fruit boxes.

Step-by-step explanation:

To find the largest number of fruit boxes needed, we need to find the least common multiple (LCM) of 105, 126, and 147.

[The least common multiple is the smallest number that is a multiple of all the given numbers. One way to find the LCM of three numbers is to first find the LCM of two of the numbers, and then find the LCM of the result with the third number.]

To find the LCM of 105 and 126, we can list the multiples of each number and look for the smallest number that is a multiple of both:

Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, ...

Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, 1386, 1512, ...

The smallest multiple that both 105 and 126 share is 1260. Therefore, the LCM of 105 and 126 is 1260.

Now we can find the LCM of 1260 and 147 by finding the smallest multiple of 1260 that is also a multiple of 147:

Multiples of 1260: 1260, 2520, 3780, 5040, 6300, 7560, 8820, 10080, 11340, 12600, 13860, 15120, ...

Multiples of 147: 147, 294, 441, 588, 735, 882, 1029, 1176, 1323, 1470, 1617, 1764, ...

The smallest multiple that both 1260 and 147 share is 18420. Therefore, the LCM of 105, 126, and 147 is 18420.

Since the fruit boxes need to be equally packed and no fruit is left, the largest possible number of fruit boxes needed is 18420/105 = 176 fruit boxes.

Answer:

the correct answer is 27.5 feet

Step-by-step explanation:

The scale of a blueprint is a ratio that represents the relationship between the size of an object on the blueprint and the size of the actual object. In this case, the scale is 1:55, which means that for every 1 unit of length on the blueprint, the actual object is 55 units long.

If a wall on the blueprint is 6 inches long, then the actual wall is 55 times longer, or 6 inches * 55 = 330 inches. Since there are 12 inches in a foot, the actual wall is 330 inches / 12 inches/foot = 27.5 feet long. Therefore, the correct answer is 27.5 feet

Answer:

47.5% of the mixture is sugar.

Step-by-step explanation:

To find the percent of the mixture that is sugar, we need to first find the total weight of the mixture. We can do this by adding the weight of the sugar to the weight of the flour: 2.85 kg + 3.15 kg = 6.00 kg.

Next, we need to divide the weight of the sugar by the total weight of the mixture and multiply the result by 100% to express the answer as a percentage: (2.85 kg / 6.00 kg) * 100% = 47.5%.

Therefore, 47.5% of the mixture is sugar.