Which angle in the image corresponds to ∠X in the pre-image?


∠L

∠M

∠N

Since angle LMN = angle PQR, angle M = angle Q

Since angle Q = 55 degrees, Angle M also = 55 degrees

We know that the three angles of a trainangle should be equal to 180 degrees

So, L + M + N = 180

Angle L is the unkown x

x + 55 + 39 = 180

x +94 =180

x = 180-94

x = 86 degrees

Answer:

The greatest possible number of red sweets is 28.

Explanation:

Let g represent the number of green sweets.  We know that the ratio of blue to green is 2:7; this means the number of blue sweets is 2/7 the number of green sweets, or 2/7g.

We also know that the number of green sweets to the number of red sweets is 3:1; this means the number of red sweets to the number of green sweets is 1:3, or that the number of red sweets is 1/3 the number of green sweets:

1/3g

We know that there are fewer than 140 total sweets; this gives us the inequality

g + 2/7g + 1/3g < 140

We must find a common denominator; 21 will work:

21/21g + 6/21g + 7/21g < 140

34/21g < 140

Divide both sides by 34/21:

(34/21g)÷(34/21) < 140÷(34/21)

g < 140÷(34/21)

To divide fractions, flip the second one and multiply:

g < 140×(21/34)

g < 2940/34

This means the number of red sweets will be 1/3 of this:

r < 2940/34 × 1/3

r < 2940/102

102 will go into 2940 28 times, so 28 is the largest number of red sweets.

     Greatest possible number of red sweets in the box will be 28.

 It's given in the question,

        [tex]\frac{b}{g}=\frac{2}{7}[/tex] ⇒ [tex]b=\frac{2}{7}g[/tex] ------(1)

        [tex]\frac{g}{r}=\frac{3}{1}[/tex] ⇒ [tex]r=\frac{1}{3}g[/tex] -------(2)

Since, total number of blue, green and red sweets in the box are less than 140,

[tex]b+g+r< 140[/tex]

Substitute the values of 'b' and 'r' from equations (1) and (2),

[tex]\frac{2}{7}g+g+\frac{1}{3}g< 140[/tex]

[tex]\frac{6g+21g+7g}{21}< 140[/tex]

[tex]\frac{34}{21}g< 140[/tex]

[tex]g< \frac{140\times 21}{34}[/tex]

Since, [tex]g=3r[/tex],

[tex]3r< \frac{140\times 21}{34}[/tex]

[tex]r< \frac{140\times 21}{34\times 3}[/tex]

[tex]r<28.82[/tex]

   Therefore, greatest possible number of red sweets will be 28.

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It is given Sally is making sun tea. Every hour the concentration of the tea doubles.Let the concentration of tea  at start is  nil.Then after  first hour concentration will be 2.After third hour concentration will be double of 2 that is 4.After fourth concentration will be 4(2)=8.After fifth hour concentration will be 8(2)=16.After sixth hour concentration will be 16(2)=32.

It is given:it takes 6 hours for the tea to be ready.WE need to find  how long would it take the tea to reach half of the final concentration.Half of final concentration is 32÷2=16.

Concentration of 16 is after fifth hour.

Answer:

Surface area of a square pyramid is:

112 cm²

Step-by-step explanation:

The surface area of square pyramid is given by:

S=2bs+b²

Where b is the length of base and s is the slant height.

and Area of base=b²

Here, s=12 cm

and Area of base=b²=16 cm²

⇒ b=4 cm

Hence, Surface Area=2×12×4+4×4

                                 = 112 cm²

Hence, surface area of a square pyramid is:

112 cm²

(-14)+2=(-12)

75-12=63

63/3=21

21-2=19     BASE=19

21+7=28  EACH LEG=28

28+28+19=75

new triangle 21+21+21

19+2=21

28-7=21

To find the original base length of the isosceles triangle, we set up equations based on the given perimeter and the condition for the triangle turning into an equilateral triangle after changes to its sides. Solving these equations, we find that the original base length is 19 cm.

The student is asking about solving a problem related to the perimeter of an isosceles triangle and finding the original base length given certain conditions that would turn it into an equilateral triangle.

In the original isosceles triangle, we'll denote the equal sides as 'a' and the base as 'b'. Since the perimeter is the sum of all sides, we have:

a + a + b = 75 cm

When altered, the base becomes 'b + 2 cm' and the equal sides become 'a - 7 cm'. To form an equilateral triangle, all sides must be equal:

b + 2 = a - 7

Simplifying gives us two equations:

Rearranging the second equation we get a = b + 9. Substituting 'a' in the first equation we get:

2(b + 9) + b = 75

Which simplifies to:

3b + 18 = 75
b = 19 cm

Therefore, the length of the base of the original isosceles triangle is 19 cm.

The table of contents for the equations is solved

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total number of people = 76

The number of people who opted for lunch = 28

The number of people who opted for dinner = 33

The number of males who opted for dinner = 19

The number of females who opted for lunch = 18

The total number of females = 36

Now , the table is created from the following equations

+-----------+-------+---------+-------+

|           | Males | Females | Total |

+-----------+-------+---------+-------+

| Breakfast | 11    | 4       | 15    |

+-----------+-------+---------+-------+

| Lunch     | 10    | 18      | 28    |

+-----------+-------+---------+-------+

| Dinner    | 19    | 14      | 33    |

+-----------+-------+---------+-------+

| Total     | 40    | 36      | 76    |

+-----------+-------+---------+-------+

Hence , the equations is solved

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a) The total responses recorded from the line plot is n = 28 responses

b) The number of students polled = 24 students

c) The fact that there were more responses than students polled suggests that one or more students engaged in more than one sport.

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

It displays information as a series of data points called 'markers' connected by straight line segments

Given data ,

Let the line plot be represented as A

Now , the total number of students in the class = 24 students

So , the total number of polls = 24 students

The total number of responses recorded from the points on the line plot is give by

The number of responses for football = 4

The number of responses for soccer = 8

The number of responses for baseball = 7

The number of responses for basketball = 5

The number of responses for football = 4

The total number of responses recorded from the points on the line plot is n = 28

Given that there were more replies than students asked, it is likely that some students participated in several sports.

Hence , the line plot is solved

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Answer:

The answer is D, and with the others you aren't experimenting with anything

Step-by-step explanation:

The trigonometric function gives the ratio of different sides of a right-angle triangle.The correct option is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Let the length of the line segement CD be represented by x.

In ΔABC, Using the pythgorus theorem, we can write,

AB² = BC² + AC²

AB² = 30² + 16²

AB = 34 units

In ΔABC, the measure of ∠A be written as,

tan(∠A) = BC/AC

tan(∠A) = 30/16

∠A = tan⁻¹ (30/16)

∠A = 61.9275°

Now, in ΔABD, the measure of ∠A can be written as,

Cos(∠A) = AB/AD

Cos(61.9275°) = 34/(AC+CD)

0.47 = 34/(16+CD)

16 + CD = 72.25

CD = 56.25 ≈ 56

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By isolating terms involving 't' and solving for 't', we manage to rearrange the provided equation to get t = (1-u+w)/(3v^2).

To rearrange the provided equation u=1-3v/vt-w with t as the subject, we can follow these steps:

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Answer:

Probability is smaller.

Step-by-step explanation:

To calculate future population growth, we use a formula incorporating the initial population, annual growth rate, and number of years. For growth, we add one to the growth rate and raise it to the power of elapsed years, then multiply by the initial population. For decline, we subtract the rate from one and then do similar exponentiation and multiplication.

Calculating Future Population Growth

To calculate the future population of deer given a starting population and a constant annual growth rate, we use the formula y = a(1+b)^x, where 'a' is the starting amount, 'b' is the growth rate, and 'x' is the number of years elapsed. For the deer population, from 2000 to 2020, there are 20 years of growth at 3.5% annually. Using a=3500, b=0.035, and x=20, the calculation is as follows:

Convert the percentage to a decimal: 3.5% becomes 0.035.

Add 1 to the growth rate: 1 + 0.035 = 1.035.

Raise this sum to the power of 20: (1.035)^20.

Multiply the result by the initial population: 3500 * (1.035)^20.

For the New Haven population, which is decreasing at 2.9% annually from 2004 to 2015 (11 years), the steps are similar. However, we subtract the percentage decline from 1 instead since the population is decreasing.

Convert the percentage to a decimal: 2.9% becomes 0.029.

Subtract this from 1: 1 - 0.029 = 0.971.

Raise this to the power of 11: (0.971)^11.

Multiply the result by the initial population of New Haven: 148220 * (0.971)^11.

After performing these calculations, we will get the estimated populations for both the deer and New Haven in the specified years.