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Answer:

51 feet

Step-by-step explanation:

Since it's an isosceles triangle, the only side that would be unequal to the other two would be the base, so the base would be the side of 60 feet. Subtract that 60 feet from the given perimeter to get 102. Divide that number by two to get 51 feet as the lengths of the other two sides.

Answer:

Each of the other two sides are 51 feet.

Step-by-step explanation:

Take the perimeter, 162, minus one side, 60.

162 - 60 = 102

Divide 102 by 2 to find the length of each of the other two sides

102/2 = 51 feet

Answer:

B)3 = 5x2 – 10x

D)8 = 5(x2 – 2x + 1)

G)  = (x – 1)2

Step-by-step explanation:

Given quadratic : 3 - 4x = 5x2 - 14x

We need to apply completing the square to solve the equation.

First step is to get rid 4x from left side.

We can add 4x on right side to get rid from left side.

3 = 5x^2-14x+4x

On simplifying this step, we get

3 = 5x^2-10x

Now, we need to factor out 5 from right side to get the coefficient of x^2 as 1.

We get,

3 = 5(x^2-2x)

Now, coefficient of x is -2. So, we need to add half of the square of -2.

-2/2 = -1.

And square of -1 is 1.

Therefore, adding 1 inside parenthesis and 5×1 = 5 on left side, we get

3+5 = 5(x^2 -2x+1)

8 = 5(x^2 -2x+1)

Let us find the perfect square of (x^2 -2x+1).

(x^2 -2x+1) = (x-1)^2

Therefore, we get

8 = 5(x-1)^2.

So, the above highlighted are steps in the process of completing the square.

Answer:

2nd 4th and 7th on edg

Step-by-step explanation:

Answer: 27.44 % decrease in gas prices

Step-by-step explanation: First subtract 2.15 by 1.56 to get 0.59

then divide it by the starting value which is 2.15

0.59 divided by 2.15 is  approximately 0.2744

then multiply times 100 to get 27.44 %

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Answer:

B

Step-by-step explanation:

If you unfold it you get shape B

Answer:

B.

Step-by-step explanation:

The nth term rule of the given linear sequence is -8n + 23. It follows the pattern of subtracting 8 from the previous term. So, each term in the sequence is obtained by -8n + 23.

The nth term rule of the given linear sequence is -8n + 23.

To find the nth term rule, we can observe that each term is obtained by subtracting 8 from the previous term. Therefore, the sequence follows the pattern:

So, we can generalize the sequence as -8n + 23, where n represents the position of the term in the sequence.

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To solve this problem, we can set up a system of equations and use elimination to find the values of x and y. After solving, we find that 40 pounds of chocolate are used to make the 30-pound mixture.

To solve this problem, we can set up a system of equations. Let's call the amount of chocolate used x pounds and the amount of nuts used y pounds. We know that the total amount of candy is 30 pounds, so we can write the equation x + y = 30. We also know that the cost per pound of chocolate is $4 and the cost per pound of nuts is $2.50, and the cost per pound of the candy is $3.50, so we can write the equation 4x + 2.50y = 3.50(30).

To solve this system of equations, we can use substitution or elimination. Let's use elimination. Multiply the first equation by 2.50 to match the coefficients of y. We get 2.50x + 2.50y = 75. Subtract this equation from the second equation: (4x + 2.50y) - (2.50x + 2.50y) = (3.50(30)) - 75. Simplify the equation to get 1.5x = 60. Divide both sides by 1.5 to find that x = 40. Now substitute this value of x into the first equation to find y. 40 + y = 30, so y = -10.

Since we can't have a negative amount of nuts, we know that our solution for y is extraneous. Therefore, 40 pounds of chocolate are used to make the 30-pound mixture.

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We don't really have to put this in slope intercept form; it would clearly end up as

y = -4x + something

so we know the slope is -4.

Answer:  C)   -4

Answer:

5

Step-by-step explanation:

3x = 2x + 5

3x - 2x = 2x - 2x +5

1x = 5

x = 5

That number is 5

By letting the unknown number be x, we solve the equation 3x = 2x + 5 and find that x equals 5.

Let's denote the unknown number as x. According to the problem, triple a number is the same as double the number increased by five. This can be expressed using the equation:

⇒ 3x = 2x + 5

To isolate x, we can subtract 2x from both sides of the equation:

⇒ 3x - 2x = 2x + 5 - 2x

Which simplifies to:

⇒ x = 5

This means the unknown number is 5. Triple of 5 is 15, and double of 5 plus 5, which is also 15, confirming that the solution is correct.

Therefore, the number that triples to become the same as double the number increased by five is 5.

Answer:

Step-by-step explanation:

The answer is A, just got it wrong because I selected b. Answer is A.

Final answer:

For large populations, taking every possible sample of a certain size becomes unfeasible due to the rapidly increasing number of combinations. Hence, random sampling methods are used to capture the population characteristics in a practical way, with larger samples providing more reliable statistics.

Explanation:

When a population size is large, it becomes impractical to take every sample of a certain size due to the combinatorial explosion in the number of potential samples. For instance, with a population of size 4, there are 6 possible samples of size 2, which is manageable. However, as the population size increases, the number of possible samples grows astronomically, making it unfeasible to examine them all. This is why sampling is a vital technique.

Random sampling methods like simple random sampling, stratified sampling, cluster sampling, and systematic sampling are employed to ensure each individual has an equal chance of being selected, which helps in capturing the characteristics of the entire population in the sample. Larger sample sizes are generally preferred as they reduce sampling variability and provide more reliable statistics.

Answer:

X is equal to 37

Step-by-step explanation:

The angle between lines a and b in image is 37 degrees.

The image shows a line segment with a label `37` above it and two arrows pointing in opposite directions. The arrows represent the two lines, a and b, which intersect at the midpoint of the line segment. The angle between the two lines is marked with an arc.

To find the angle between two lines, we can use the following formula:

tan(θ) = (m2 - m1) / (1 + m1m2)

where: θ is the angle between the two lines

m1 and m2 are the slopes of the two lines

In this case, the slopes of the two lines are equal, so the angle between them is 90 degrees. Therefore, the answer is 37 degrees.

For such more questions on angle

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[tex] \qquad \qquad\large\rm{Together \: We \: Go \: Far!} \\ \qquad \qquad \sf \small{\red{♡}\:Swifties\:\red{♡}}[/tex]

Question :-

Answer :-

[tex] \rule{180pt}{3pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{2 \: cm}}\put(9,17.5){\sf{8.2 \: cm}}\end{picture}[/tex]

Solution :-

As per the provided information in the given question, we have been given that the diameter of the cylinder is 4 cm. Thus, the radius of the cylinder is 2 cm. The height of the cylinder is 8.2 cm. We have been asked to find or calculate the surface area of the cylinder.

To calculate the surface area of the cylinder, we will use the formula below :-

[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Cylinder)} = 2\pi r^2 + 2\pi rh \:\:}}[/tex]

Substitute the given values into the above formula and solve for surface area:

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = 2\pi r^2 + 2\pi rh[/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(3.14)(2 \: cm)^2 + (2)(3.14)(2 \: cm)(8.2\:cm) [/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(3.14)(4 \: cm^2) + (2)(3.14)(16.4\:cm^2) [/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = (2)(12.56 \: cm^2) + (2)(51.496 \: cm^2) [/tex]

[tex]\sf:\implies Surface \: Area_{(Cylinder)} = 25.12 \: cm^2 + 102.992 \: cm^2 [/tex]

[tex]\sf:\implies \bf{Surface \: Area_{(Cylinder)} = 128.112 \: cm^2}[/tex]

Therefore :-

[tex]\\[/tex]

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Answer:

954.56 in²

Step-by-step explanation:

A = 2×π·r² + 2·π·r·h

= 2×3.14×64 + 2×3.14×8·11

= 401.92 + 552.64

= 954.56 in²

Answer:

The answer to your question is C. 3.2

Step-by-step explanation:

 | 3.2 |

lines |  |  mean absolute value, and absolute value means the distance of a number to the origin (0,0) it does not matter the sign.

Then to answer your question just do not write the |  |  and consider it as a positive sign.

If your question had a negative number  ex. | -3.2 | the answer would also be 3.2.

Step-by-step explanation:

Answer:

The three angles of the right-angled triangle are

a = 35°

b = 90°

c = 55°

Step-by-step explanation:

We are given the ratio of angles of a right-angled triangle

a:b:c = 7:18:11

Recall that the sum of interior angles in a right-angled triangle is always 180°

7x + 18x + 11x = 180

36x = 180

x = 180/36

x = 5

a:b:c = 7x:18x:11x

a:b:c = 7(5):18(5):11(5)

a:b:c = 35:90:55

a = 35°

b = 90°

c = 55°

Alternatively:

We are given that the smallest angle is 35°

a = 7x = 35

x = 35/7

x = 5

b = 18x

b = 18(5)

b = 90°

c = 11x

c = 11(5)

c = 55°

Answer:

Step-by-step explanation:

solution

sum of angles on a triangle=180

total ratio=7+18+11=36

for angle a: (7/36)x180=35°

for angle c: (11/36)x180=55°

for angle b: (18/36)x180=90°

therefore: the 3 angles are 35°, 90°, 55°.

Answer:

gold and silver

Step-by-step explanation:

Answer:

(4, -1)

Step-by-step explanation:

3 x minus 4 y = 16

2 x + 3 y = 5

3x - 4y = 16

2x + 3y = 5

x = 2.5 - 1.5y

3(2.5 - 1.5y) - 4y = 16

7.5 - 4.5y - 4y = 16

-8.5 = 8.5y

y = -1

x = 2.5 - 1.5(-1)

x = 2.5 + 1.5

x = 4

(4, -1)

The solution to the system of equations 3x - 4y = 16 and 2x + 3y = 5

is (4, - 1).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of linear equations 3x - 4y = 16 and 2x + 3y = 5.

Multiplying equation (i) by 2 and equation (ii) by 3 we have,

6x - 8y = 32 and 6x + 9y = 15.

Subtracting equation (iii) from (iv) we have,

9y + 8y = 15 - 32.

17y = - 17.

y = -1 and, 6x - 8(-1) = 32 ⇒ 6x + 8 = 32 ⇒ 6x = 24 ⇒ x = 4.

So, The solution to the system of equations is (4, - 1).

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Answer:

The 1st one, the 3rd one, and the 4th one.

Step-by-step explanation:

Final answer:

To find the unknown side lengths of a rectangle with a perimeter of 14 units and one known side length of 4 units, use the perimeter formula, resulting in the unknown sides being 3 units each.

Explanation:

To find the unknown lengths of the sides of a rectangle when one side length is 4 units and the perimeter is 14 units, first understand that the perimeter of a rectangle is calculated using the formula 2(length + width). Since the perimeter is 14 units, we can set up the equation 2(l + 4) = 14, where l represents the unknown length.

Dividing both sides by 2, we get l + 4 = 7. Subtracting 4 from both sides yields l = 3 units. Therefore, the lengths of the two unknown sides are 3 units each, as a rectangle has two pairs of sides of equal length, indicating the width in this case is 3 units.

Answer: A. x- 8x= 70

Step-by-step explanation: if x equals 10 then subsitute x for 10 in the equation this gets you 8(10) - 10 = 80

and 80 - 10 = 70 so

8(10) = 80

so 80 - 10 = 70

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Answer:

19.32

Step-by-step explanation:

The amount Chrissy spent on food for the party is determined by subtracting the cost of the fruit bars, $3.22, from her total amount spent, $22.54. This leads to a result of $19.32.

The subject of this question is Mathematics, specifically subtraction. To figure out how much Chrissy spent on food for the party, you have to deduct the cost of the three fruit bars from the total amount she spent that day.

Given:
Total amount spent by Chrissy = $22.54
Cost of three fruit bars = $3.22

By subtracting the amount she spent on the fruit bars from the total amount:
Amount spent on the party = Total amount spent - Cost of the fruit bars
Thus, Amount spent for the party = $22.54 - $3.22 = $19.32

Therefore, Chrissy spent $19.32 on food for the party.

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Answer:

9w(2w+3)

Step-by-step explanation:

18 w^2 = =2*9*w*w=2*3*3*w*w

27w = 3*9*w=3*3*3*w

We can factor out 3*3*w = 9w

3*3*w(2*w+3)

9w(2w+3)

Answer:

9w(2w+3)

Step-by-step explanation:

just trust

Seven less than a number is the same as [ n - 7 ]

Is at most twenty-three [ = 23 ]

Put the expression together:

n - 7 = 23

Solve for n if needed:

n - 7 = 23

~Add 7 to both sides

n - 7 + 7 = 23 + 7

~Simplify

n = 30

Best of Luck!

Final answer:

The student's question is about solving an inequality in mathematics. The inequality '7 less than a number is at most 23' is written as x - 7 ≤ 23 and solved to find that x can be any number up to and including 30.

Explanation:

The student is dealing with an inequality problem in mathematics. The phrase '7 less than a number is at most 23' translates to the inequality x - 7 ≤ 23, where x represents the unknown number. To solve for x, you would perform the following steps:

Add 7 to both sides of the inequality to isolate x on one side: x - 7 + 7 ≤ 23 + 7, which simplifies to x ≤ 30.

Therefore, the number x can be any number up to 30, including 30 itself, to satisfy the inequality.

This inequality demonstrates an important concept in mathematics: understanding and solving equations and inequalities.

Answer:

  No

Step-by-step explanation:

You want to know if (x, y) = (3, -3) is a solution to y ≤ -5x +3y.

Put the value where the variables are and see if the statement is true:

  -3 ≤ -5(3) +3(-3)

  -3 ≤ -15 -9

  -3 ≤ -24 . . . . . . False. Therefore, (3, -3) is NOT a solution.

__

Additional comment

We can rearrange the inequality to make comparison easier:

  5x ≤ 2y . . . . . . . add 5x-y to both sides

Since x is positive and y is negative, this cannot possibly be true.

Answer:

he needs to catch up by 5 pages

Step-by-step explanation:

Answer:

1. y = 35x

2. y = 30x + 1

3. y = 35x

   y = 30 x + 1

4. Its more convenient to substitute y because It's easier.

    35x = 30(x + 1)

5.  35x = 30x + 1

    35x = 30x + 30

    35x -30x = 30

    5x = 30

    x = 6    (30/5 = 6)

    35 x 6 = 210 (y)

6. Both people have read 210 pages and it takes amir 6 days to catch up.

Step-by-step explanation:

Answer: -4y + 4

Step-by-step explanation: 12 + 3y - 8 - 7y

                                              12 + 3y + -8 + -7y

                                             (3y + -7y) + (12 + -8)

                                             = -4y + 4

Answer:

Length: x + 5

Step-by-step explanation:

x² + 8x + 15 = length × width

x² + 8x + 15

x² + 5x + 3x + 15

x(x + 5) + 3(x + 5)

(x + 5)(x + 3)

Width: (x + 3)

Length: (x + 5)

Answer:

A. Line AB is parallel to, is equal to Line DC

Step-by-step explanation:

A rhombus is a quadrilateral whose four sides have the same length. It is similar to a square in the sense that it has all its four sides having equal length. It is basically a square which is tilted at an angle. It is also called an equilateral quadrilateral.

Line AB is equivalent to Line DC & both lines are parallel one to another; the same is the relationship between Line BC & Line AD (You can check the attached image for more clarity)

Hence, option A is the answer - Lines AB & DC are parallel & equal to one another

Answer:

is parallel to, is equal to

Step-by-step explanation:

A rhombus has two sets of parallel sides. All four sides are equal in length.