What is the sum of the first five prime numbers?

A triangle with angles that measure 120°, 39°, and 21° is an obtuse triangle.

The student has asked about the classification of a triangle with angles that measure 120°, 39°, and 21°. Based on Euclidean geometry, the sum of the angles in any plane triangle is 180°. A triangle with one angle that measures more than 90° is an obtuse triangle, as it has one obtuse angle. Therefore, this triangle, with a 120° angle, is classified as an obtuse triangle.

145 -19 = 126

 she needs to learn 126 more words

 divide 126 by 6 to find number of days

126 / 6 = 21

 it will take 21 days, Answer is B

Answer: More than 40 students

Step-by-step explanation:

Let x be the number of students .

Given : Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student.

i.e. Total cost : [tex]80+5x[/tex]          (1)

The Dino Discovery Museum simply charges $7 per student.

i.e. Total cost : [tex]7x[/tex]              (2)

The inequality that shows Science Center charge less than the Dino Discovery Museum charges will be :-

[tex]80+5x<7x[/tex]  

Subtract 5x on both sides , we get

[tex]80<2x[/tex]

Divide both sides by 2 , we get

[tex]40<x[/tex]

Hence, for more than 40 students the Science Center charge will less than the Dino Discovery Museum charges.

Answer:

n+11=30

n = 19

Step-by-step explanation:

You have 30 CDs and you friend had n amount of CDs. We also know that you have 11 more CDs than your friends. Therefore we can write expression as:

[tex]n+11=30[/tex] and simplify

[tex]n =30 -11[/tex]

[tex]n=19[/tex]

Therefore you friend will have 11 CDs which is 11 less than what you have.

Answer:

C) $1412.79; D) monthly salary of $2995; B) $18.94; C) $573.75

Step-by-step explanation:

Getting paid semimonthly means there will be two paychecks a month.  There are 12 months in the year, so this is 24 checks per year.  To find the gross pay on each check, divide the salary by 24:

33907/24 = 1412.79

There are 52 weeks per year.  This means a weekly salary of 781 would be an annual income of 781(52) = 40,612.

A biweekly salary means getting paid every two weeks.  This means there will be 52/2 = 26 paychecks per year; this gives an annual income of 26(1430) = 37,180.

Semimonthly pay means there will be 24 paychecks per year; this gives us an annual income of 24(1550) = 37,200

There are 12 months in the year; this gives us an annual salary of 12(2995) = 35,940.  This is the smallest amount in our given choices.

25% = 25/100 = 0.25; this makes the tip 0.25(75.77) = 18.9425 ≈ 18.94.

11.25 per hour for 35 hours is 11.25(35) = 393.75.  4.5% commission is 4.5/100(4000) = 0.045(4000) = 180.  Together this gives us

393.75+180 = 573.75

The opposite angles of a parallelogram are congruent this can be proved by the fact that;

To prove opposite angles in a parallelogram are congruent, it's necessary to recognize that opposite sides are congruent and use the property that corresponding parts of congruent triangles are congruent.

To prove that the opposite angles of a parallelogram are congruent, it's not necessary that opposite sides be perpendicular. Instead, let's consider the properties that are relevant to this proof:

In this case:

The proper proof would rely on establishing congruent triangles within the parallelogram and then using the property that corresponding parts of congruent triangles are congruent to show that the opposite angles are congruent.

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Answer: -6.

Step-by-step explanation: Given geometric series is-

[tex]-3,~-\dfrac{3}{2}, ~-\dfrac{3}{4}, ~-\dfrac{3}{8},~-\dfrac{3}{16},...[/tex]

Here, the first term of the series, [tex]a=-3[/tex]

and the common ratio, [tex]r=\dfrac{1}{2}.[/tex]

Since it is an infinite series, so sum is given by

[tex]S=\dfrac{a}{1-r}\\\\\\\Rightarrow S=\dfrac{-3}{1-\frac{1}{2}}\\\\\\\Rightarrow S=\dfrac{-6}{2-1}\\\\\\\Rightarrow S=-6.[/tex]

Thus, the sum of the series is -6.

Answer:

The value of x is [tex]\frac{k+9}{4}[/tex]

Step-by-step explanation:

 Given : equation 4x - 9 = k

We have to find the value of x.

Consider the given equation  4x - 9 = k

Adding 9 both sides, we have,

4x = k + 9

Divide both side by 4, we have,

[tex]x=\frac{k+9}{4}[/tex]

Thus, The value of x is [tex]\frac{k+9}{4}[/tex]

Answer:

∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.

∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.

∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.

Step-by-step explanation:

Vertical angles are the angles made by two intersecting lines and they are equal

So,

∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.

Straight angles are angles that are 180°

So,

∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.

The angles less than 90° are called acute angles

So,

∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.

∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.

∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.

∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.

Vertical angles are the angles made by two intersecting lines and they are equal, ∠GEN and ∠FED, ∠GEF and ∠DEN are few of the vertical angles.

Straight angles are angles that are 180° ∠ENM and ∠NKP, ∠HKC and ∠ADE are few of the straight angles.

The angles less than 90° are called acute angles∠GEN and ∠FED, ∠JNM and ∠EHK are few of the acute angles.

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the answer would be A because if you graph those equations they are perpindicular. They cross eachother like a t

Answer:

Step-by-step explanation:

Answer:

Real part: -6

Imaginary part: -1

Step-by-step explanation:

A complex number is a number that has a real part and an imaginary part. These numbers usually are represented in the form a + bi where a and b are real numbers and b is the imaginary part (i is actually the solution to the equation [tex]x^{2} +1=0[/tex] or x²=-1 which has no roots in the real numbers and therefore we call the solution √-1=i)

Now, proceeding to the complex number you wrote, if we write it as a + bi we would have a = -6 b = -1

Therefore the real part is a = -6 and the imaginary part would be -1.

Final answer:

By using the given lengths of AE and BC, along with the equality of AB, DB, and DC, we can solve for CE to be 14.67cm.

Explanation:

The lengths of AE, BC, AB, DB, and DC are given or can be determined with the information provided. Since AB = DB = DC and BC is given as 10 cm, we can deduce that AB + BC + CE = AE. Given AE is 28cm and BC is 10cm, we can find the length of AB by realizing that AB + AB + AB (which is AB + DB + DC) is the same as BC or 10cm. This makes each section AB, DB, and DC equal to 10cm / 3.

With AB, DB, and DC all being equal to 10cm / 3, and knowing AE is 28cm, we can then calculate the length of CE:

AE = AB + BE (and BE = BC + CE)

28cm = (10cm/3) + (10cm + CE)

To find CE, rearrange the equation:

CE = 28cm - 10cm - (10cm/3)

CE = 28cm - 10cm - 3.33cm

CE = 18cm - 3.33cm

CE = 14.67cm

To solve for the length of CE in a line segment configuration, we calculate CE = AE - BC - DC after determining the lengths of AB, BC, and DC. The solution reveals that CE is 9cm.

The student has a geometry problem, which involves calculating the length of segment CE on a line segment AE. We know that AE = 28cm and BC = 10cm, with AB, DB, and DC being equal in lengths.

Since B is between A and C, and D is between B and C, and C is between B and E, we can write the entire length AE as AB + BC + CE. Because AB = DB = DC, we can substitute DB and DC for AB in the sums to get 2(DB) + BC = 28cm.

We are given that BC = 10cm, so we can set up an equation: 2(DB) + 10cm = 28cm. Solving for DB, we find that DB = 9cm. Since DC is equal to DB, DC is also 9cm. CE can be found by subtracting BC and DC from the total length of AE: CE = AE - BC - DC, so CE = 28cm - 10cm - 9cm, resulting in CE = 9cm.

the number inside the parenthesis includes the interest rate ( annual percentage

looking at the possible functions, if you raise the interest rate to the power of 12, you would need to divide the number of years (t) by 12 as well

 so the function could be rewritten as A=1000(1.023^12)^t/12

 since the annual percentage rate is 2.3% ( 0.023)

 divide 0.023/12*100 = 0.19% per month interest

Answer:

C

Step-by-step explanation:

Area = 338

Width = X

Length = 2x

2x * x = 338

3x = 338

x = 112.7

The value of x from the rectangular shaped canvas box is x = 13 inches

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of rectangle canvas be A = 338 inches²

Let the width of the canvas = x inches

And , length = 2 x ( width )

Now , the length of the canvas = 2x inches

So , Area of Rectangle = Length x Width

On simplifying , we get

Area of Rectangle = 2x ( x )

Area of Rectangle = 2x²

338 = 2x²

Divide by 2 on both sides , we get

x² = 169

Taking square roots on both sides , we get

x = 13 inches

Hence , the value of x of the canvas is 13 inches

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A reasonable conjecture for Mei is the Alternate Interior Angles Theorem, which states if a transversal intersects parallel lines, the alternate interior angles are equal.

Based on the scenario, a reasonable conjecture for Mei to make would be, if a transversal intersects parallel lines, then the alternate interior angles are congruent. This statement is known as the Alternate Interior Angles Theorem. In other words, in each of Mei's figures, if the angles she measured are alternate interior angles, they should have the same measurement.

For example, if three pairs of parallel lines are intersected by a third line (called a transversal), a pattern that consistently appears is the equality of the alternate interior angles (angles that are on opposite sides of the transversal and inside the parallel lines). This implies, if the two lines are parallel, then any alternate pair of interior angles are equal.

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