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CONNECTING CONCEPTS You use 94 inches of plastic to frame the perimeter of a kite. One side of the kite has a
length of 18 inches. Find the length of each of the three remaining sides in order from least to greatest.
Length: in.,in., in

Answer:

m<a = 44°

Step-by-step explanation:

Left triangle:

95 + 39 + x = 180

x = 46

Right triangle:

46 + 90 + a = 180

a = 44

Step-by-step explanation:

ABC and ADE are similar triangles.

that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.

so, we see that AB = 2, AD = 2+1 = 3

the scaling factor f from AB to AD is then

AB × f = AD

2 × f = 3

f = 3/2

the same scaling factor now applies between BC and DE (= x).

BC × f = x

1 × 3/2 = x

x = 3/2 = 1.5

Answer:

[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]

Step-by-step explanation:

g(x) = 4x + 5

f(x) = -3x² - 3x

= 4x + 5 + (-3x² - 3x)

= 4x + 5 - 3x² - 3x

= 4x - 3x + 5 - 3x²

= x + 5 - 3x²

[tex]\rule[225]{225}{2}[/tex]

The correct option is a. The equation used to find Vanessa's age is v + 2 = 32.

A mathematical statement known as an equation utilises the equals sign to demonstrate the equality of two expressions. It may be used to address a variety of issues and can contain both numbers and variables. Algebraic operations including addition, subtraction, multiplication, division, and exponentiation are frequently used in equations.

In the given question, Vanessa's age may be calculated using the equation a. v+2=32. This equation shows that Vanessa's age plus 2 equals 32, implying that Vanessa's age is 30. We may solve this equation by removing 2 from both sides, yielding v=30. This equation is valid for determining Vanessa's age because it specifies that Vanessa's age plus Monique's age equals 32.

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The total amount y collected from x students is y = 10x.

The graph is given below.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The club is charging $10 per student that attends.

This means,

Number of students = x

The total amount y collected from x students.

y = 10x

The graph is given below.

Thus,

y = 10x is the total amount y collected from x students is

The graph is given below.

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There is no mode of the number of girl in the three classes.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode.

Given:

The data for boys: 15, 12, 12

The data for Girls: 14, 12, 16

As, mode is the most repeating data.

We can see that the data repeats in boys but not for the Girls.

So, number of boys have the mode but the number of girls do not have the mode.

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Answer:

18.84

Step-by-step explanation:

Answer:

Step-by-step explanation:

if the sum of two consecutive even numbers is 42 find the number

42 - 2 = 40                       remove the difference (2)

40 : 2 = 20                       find the smallest number

20 + 2 = 22                      find the largest number

------------------------------------

(20 + 22 = 42)                

In 1798, the first vaccination (for small pox) was discovered. The most notable achievement of these efforts has been the elimination of smallpox sickness from the world.

Hence, option (c) is correct choice.

In 1721, Lady Mary Wortley Montagu introduced smallpox vaccination to Europe by requesting that her two children be immunised against the disease, as she had seen done in Turkey. Dr. Edward Jenner developed the world's first effective vaccination. He discovered that those who had cowpox were resistant to smallpox.

Edward Jenner, a rural doctor from Berkeley (Gloucestershire), England, conducted the world's first vaccine in 1796. Jenner injected an eight-year-old kid, James Phipps, with pus from a cowpox lesion on a milkmaid's hand.

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The value of the shortest of the three side lengths is 3 inches.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The lengths of the three sides of a triangle (in inches) are consecutive integers.

The three sides are x, x+1 and x+2 which are consecutive.

We know that perimeter of a triangle is the sum of the three sides of a triangle.

Add the three Consecutive sides to find the perimeter.

Perimeter of triangle=x+x+1+x+2

The perimeter of triangle is 27 inhces.

27=3x+3

Substitute 3 from both sides

24=3x

Divide by 3 on both sides

8=x

Hence, the value of the shortest of the three side lengths is 3 inches.

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The perimeter of the rectangle in the given diagram is: D. 42 units.

In order to determine the perimeter of this rectangle, we would have to find the length of the third side of the right-angled triangle by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b = √144

b = 12 units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

P = 2(9 + 12)

P = 42 units.

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The probability of selecting a student who is wearing a yellow shirt is 36 %

The total number of students is 45 students and out of these, 3 / 7 are wearing blue shirts while 2 / 9 are wearing red shirts.

This means that the number of students wearing yellow is:

= 45 - ( 45 x 3 / 7 ) - ( 45 x 2 / 9 )

= 45 - 19 - 10

= 16 students

The probability of selecting a student who is wearing yellow is :

= 16 / 45

= 36 %

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The full question is:

A class has 45 students of the students are wearing 3/7 blue shirts, of

them are 2/9  wearing red shirts, and the rest are wearing yellow shirts.

What is the probability of selecting a student who is wearing a yellow

shirt?

Answer:

See below

Step-by-step explanation:

Sum of 18 and 6 = 24

1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4

In  a way you can think of it as a fractional question but the answer is a whole number

[tex]\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\[/tex]

The total length of the two welded together is 26ft.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. Division and multiplication are the other two fundamental mathematical operations. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

Given that the length of the two pieces of the pipe is 23ft and 3ft.

The total length of the two welded together is:

23 + 3 = 26ft

Hence, the total length of the two welded together is 26ft.

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Answer:

280

Step-by-step explanation:

Give me a moment, I am still gathering my explanation

Answer:

To find the number of courts with doubles matches, we need to determine the total number of players playing doubles. If each court with a doubles match has 4 players, then the total number of players playing doubles would be 4 times the number of courts playing doubles.

Since there are 28 players in total, and each court with a singles match has 2 players, the number of players playing singles would be 28 - 4x, where x is the number of courts playing doubles.

Since each court with a singles match has 2 players, the number of courts playing singles would be 28/2 = 14.

So, 28 - 4x = 14, and solving for x, we get x = 7.

Therefore, there are 7 courts with doubles matches and 14 courts with singles matches.

Answer:

7

Step-by-step explanation:

35-8-4-2=21

21/3=7

Answer:

7 pounds

Step-by-step explanation:

8+4+2=14

35-14=21

21/3=7

Answer:139.33 or 139 ft high

Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139

The number of crickets Great fed last week to Lizzy is 56.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Last week, Greta fed Draco 77 crickets.

Let the number of crickets Great fed last week be x.

Now, 11:8::77:x

11x=77×8

x=7×8

x=56

Therefore, the number of crickets Great fed last week to Lizzy is 56.

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"Your question is incomplete, probably the complete question/missing part is:"

Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets. How many crickets did Greta feed Lizzy?

Answer: 258 envelopes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

Let's call the number of purple counters "x". This means that the number of blue counters is x - 78, and the number of white counters is 18x.

According to the ratio, the sum of the number of purple and blue counters is 16x + (x - 78) = 17x - 78.

And the sum of all counters is 16x + 18x + 3x = 37x.

Knowing that the sum of all counters is the same, we can set the two sums equal to each other:

37x = 17x - 78 + 37x

So, we have:

74x = 17x - 78 + 37x

57x = -78

x = -78/57

Since x can't be negative, we have to reject this solution.

However, the number of white counters can be found by multiplying 18 by the number of purple counters:

18 * x = 18 * (x/57) = (18/57) * x = (18/57) * 78 = 72

Therefore, there are 72 white counters in the bag.

After finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.

What is meant by sine law?

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given,

 The distance between two observers = 600 ft

The angle of elevation of the first observer = 19°

The angle of elevation of the second observer = 21°

We are asked to find the height of the flagpole.

The figure is given below.

There are 2 right triangles, ΔABD and ΔCBD.

We will start with ΔABC.

∠B = 180 - (∠A+∠C) = 180 - (21+19) = 140

Now using sine law, we can find lengths a and b.

According to sine law,

b/sin21 = a/sin 19 = 600/sin 140

From this,

b/sin 21 = 600/sin 140

b/0.36 = 933.43

b = 336.03ft

Also,

a/sin 19 = 600/sin 140

a/0.33 = 933.43

a = 308.03ft

Now using ΔABD,

sin 21  =h/a

0.36 = h/308.03

h = 110.89 ft

Therefore after finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.

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The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.

Probability of dropouts next year being exactly 305: 0

Probability of dropouts next year being less than 305: 0.68

Probability of dropouts next year being greater than 305: 0.32

Probability of dropouts next year being within one standard deviation of 305: 0.95

The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.

The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.

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The money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.

Let us suppose the time period as x.

The simple interest is given as:

SI = PRT/100

Where,

SI = Simple Interest = 500

P = Principal = 2000

R = Rate = 5%

T = x

Substituting the values:

500 = (2000)(5)(x) / 100

500 = 100x

x = 5 years

Hence, the money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.

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A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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The equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m. The first option from the given options is

Algebraic expressions that produce the same final expression are said to be equivalent expressions. If the values of two algebraic expressions can be obtained by replacing the variables, then the expressions are equivalent. Using the equal symbol (=), equivalent phrases are represented or illustrated to one another.

From the information given;

= 7m - (2 + 4m)

= 7m - 2 - 4m

Therefore, we can conclude that the equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m.

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The amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.

Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.

Given that the interest is compounded continuously.

For the given situation the formula of compound interest is:

[tex]A = Pe^{rt}[/tex]

where, A is the amount = $12300

P is the principal amount

r is the rate = 4% = 0.04

t is the time = 8 years

Substituting the values we have:

[tex]12300 = Pe^{(0.04)(8)}\\\\P = \frac{12300}{e^{(0.04)(8)}} \\\\P =8932.461[/tex]

Hence, the amount that needs to be invested at the interest rate of 4% compounded continuously is P = $8932.461.

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Answer:

Step-by-step explanation:

To find the interest rate on an investment of $470 for seven years with an ending balance of $683.85, you can use the formula for simple interest:

I = P * r * t

Where I is the interest earned, P is the principal amount ($470), r is the interest rate, and t is the number of years (7).

Rearranging the formula to solve for r:

r = I / (P * t)

Substituting the given values:

r = (683.85 - 470) / (470 * 7)

r = 213.85 / 3290

r = 0.0649 or 6.49%

So, the interest rate on the investment of $470 for seven years with an ending balance of $683.85 is 6.49%.

Answer:

Step-by-step explanation:

you first take A15 and square it. Then you take B20 and square it also. Then you add them together and that is your answer. the hypotenuse of a triangle.

Answer: Side length C will be 25

Step-by-step explanation:

C^2 = A^2+B^2

15^2+20^2=C^2
225+400=625

Take square root of 625 to get side C