One side of a triangle is 6 cm shorter than the base x. The other side is 4 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 43cm?

first side is 7cm

second is 12cm

third is 14cm

The lengths of the sides are 7 cm, 12 cm, and 14 cm, respectively.

Let's denote the lengths of the sides as follows:

First side: x centimeters

Second side: y centimeters

Third side: z centimeters

According to the problem, we can set up a system of equations based on the given information:

The perimeter is the sum of all three sides, so:

x + y + z = 33

The first side is 5 centimeters shorter than the second:

x = y - 5

The third side is twice the first:

z = 2x

Now, we can use these equations to solve for the lengths of the sides. Substituting the second and third equations into the first, we get:

(y - 5) + y + 2(y - 5) = 33

y - 5 + y + 2y - 10 = 33

4y - 15 = 33

4y = 48

y = 12

Plugging y back into the second equation, we find:

x = 12 - 5

x = 7

And using the third equation:

z = 2x

z = 2(7)

z = 14

So, the lengths of the sides are:

x = 7 centimeters

y = 12 centimeters

z = 14 centimeters.

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Let the consecutive odd numbers be( x) and (x+2).

According to given condition.

(x)+(x+2) =284

solving  x+x+2 =284

2x+ 2 =284

subtracting 2 both sides

2x+ 2-2 =284-2

2x =282

dividing 2 both sides

x=141

as the second integer is (x+2) so

x+2 =141+2= 143

so integers are 141 and 143.

To estimate the difference between 17/18 and 3/7, one could use benchmark figures. These fractions are approximated as 1 and 1/2 respectively. Therefore, the estimated difference is typically around 1/2 or 0.5.

The student is asking for help to estimate the difference between the fractions 17/18 and 3/7. To estimate this, we first need to understand fractions and benchmark values. A benchmark value is a value that's easy to handle in calculations. For fractions, often 0, 1/2, and 1 are used as benchmarks.

Looking at the given fractions, 17/18 is close to 1 (our benchmark) and 3/7 is about 1/2 (another benchmark). Therefore, to estimate the difference, we subtract our rough approximation of 1/2 from 1, giving us an estimate of 1/2 or 0.5 as the difference.

This is a fairly quick way to estimate the difference between two fractions using benchmark values. It won't provide you with the exact answer, but it will give you a ballpark figure that's usually quite close to the actual result.

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QUESTION 1

Let [tex]n[/tex] represent the number of years.

Then each year the number of people added is given by the function

[tex]N(n)=8.7\times 10^5(n)[/tex]

Therefore after [tex]25[/tex] years,

[tex]N(25)=8.7\times 10^5(25)[/tex]

[tex]N(25)=21750000[/tex]

In scientific notation,

[tex]N(25)=2.175\times 10^7[/tex]

ANSWER TO QUESTION 2

The population after 25 years can be calculated by adding the increment in population to the initial population.

The initial population

[tex]P_0=9.7\times 10^7[/tex]

The population  after 25 years

[tex]P(25)=9.7\times 10^7+2.175\times 10^7[/tex]

[tex]P(25)=(9.7+2.175)\times 10^7[/tex]

[tex]P(25)=(11.875)\times 10^7[/tex]

[tex]P(25)=1.1875\times 10^1 \times 10^7[/tex]

[tex]P(25)=1.1875\times 10^1 \times 10^7[/tex]

[tex]P(25)=1.1875\times 10^8[/tex]

Answer:

1. [tex]2.175*10^{7}[/tex]

2. [tex]1.1875*10^{8}[/tex]

Step-by-step explanation:

We are given that population of a country is [tex]9.7*10^{7}[/tex] , and is increasing by [tex]8.7*10^{5}[/tex] people each year.

1. To find number of people added after 25 years we will multiply 25 by [tex]8.7*10^{5}[/tex].

[tex](2.5\cdot 10^{1})\cdot (8.7\cdot 10^{5})[/tex]

[tex](2.5\cdot 8.7)\cdot (10^{1+5})[/tex]

[tex](21.75)\cdot (10^{6})=(2.175)\cdot (10^{7})[/tex]

Therefore, [tex]2.175\cdot 10^{7}[/tex] will be added after 25 years.

2. To find out population after 25 years we will add population added in 25 years to initial population.

[tex]9.7*10^{7}+2.175\cdot 10^{7}[/tex]

[tex]11.875\cdot 10^{7}[/tex]

[tex]1.1875\cdot 10^{8}[/tex]

Therefore, population after 25 years will be [tex]1.1875\cdot 10^{8}[/tex].

A ray is a line with one end. It starts at a given point and goes off in a certain direction forever to infinity. The point where the ray starts is called the endpoint.

Answer:

any of a set of straight lines passing through one point.

Step-by-step explanation:

Answer: y = |x-3|

The point (1,1) has been moved 3 spots to the right to get to (4,1). The entire equation of the V shaped curve will also move 3 spots to the right. So that's how we go from |x| to |x-3|. Note how plugging in x = 4 leads to y = |x-3| = |4-3| = |1| = 1

Answer:

number x = 3.

Step-by-step explanation:

Given : Three times the sum of a number and 4 is the same as 18 more than the number.

To find : what is the number.

Solution : We have given a statement

According to question :

Let the number= x

Sum of the number and 4 = x + 4

Three times the sum of the number and 4 = 3 ( x +4).

18 more than a number = 18 + x .

Three times the sum of a number and 4 is the same as 18 more than the number.

3 (x+4) = 18 + x

On distributing 3 over ( x+4)

3x + 12 = 18 + x

On subtracting both sides by 12

3x = 18 -12 +x

3x = 6+x

On On subtracting both sides by x

3x -x =6

2x = 6

On dividing both sides by 2

x = 3.

To verify plug x = 3 in 3x + 12 = 18 + x

3(3)+12 =18+3

9+12 = 18+ 3

21 =21

Therefore, number x = 3.

Answer: The point A is 26m above from the ground.

Explanation:

It is given that the maximum drop Is 65m over a horizontal distance of 65m in two sections. So, the maximum value is (65,65) and the value is (0,0) when it stops.

From the given information it is noticed that the first section has a gradient of 3 and the second section has a gradient of 1/2.

The equation of line passing through the point [tex](x_1,y_1)[/tex] with slope m is define as,

[tex]y-y_1=m(x-x_1)[/tex]

For first section the slope is 3 and the point is (65,65).

[tex]y-65=3(x-65)[/tex]

[tex]y=3x-130[/tex]    ..... (1)

For second section the slope is 1/2 and the point is (0,0).

[tex]y=\frac{1}{2}x[/tex]  .....(2)

Put [tex]y=\frac{1}{2}x[/tex] in equation (1), we get,

[tex]\frac{1}{2}x=3x-130[/tex]

[tex]\frac{5}{2}x=130[/tex]

[tex]x=52[/tex]

Put this value in equation (2)

[tex]y=26[/tex]

Therefore, the point A is 26m above the ground and the horizontal distance is 52m from the endpoint.

The t procedure can be used to construct a confidence interval for the mean of a population, even if the population is not normally distributed.

The correct statement is c. You may use the t procedure because it is robust to nonNormality.

The t procedure can be used to construct a confidence interval for the mean of a population, even if the population is not normally distributed. As long as the sample size is sufficiently large (usually considered to be at least 30), the t procedure provides reliable results. It is important to note that the t procedure assumes that the sample is random and that the observations are independent.

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Using the multiplication method, we find that 16 times 60 equals 960.

To find the product of 16 times 60, we can use the method of multiplication. The multiplication method is a straightforward way to find the product of two numbers by multiplying each digit separately and adding the results.

1. Write down the two numbers being multiplied: 16 and 60.

2. Start by multiplying the rightmost digit of the bottom number (60) with the top number (16). In this case, multiply 0 with 16, which equals 0.

3. Write down the result (0) below the line.

4. Now, multiply the next digit of the bottom number (6) with the top number (16). Multiply 6 with 16, which equals 96.

5. Write down the result (96) below the line, shifted one position to the left.

6. Finally, add the two results together: 0 + 96 = 96.

So, the product of 16 times 60 is 960.

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30 days. This is because everyday, the magician only climbs 1 foot since 3-2=1

5 x 2/3 = 5.333 repeatedly

There were 47 students on each bus.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that 386 students went on a field trip, eight buses were filled in 10 students traveled in cars.

Therefore,

386 total students - 10 riding in cars

386-10= 376 students riding in buses

Now,

376 students riding in buses dividied by 8 buses

376/8 = 47 students on each bus

Hence, there were 47 students on each bus.

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The sale price is $425

hope this helps

3445 divided by 13 is 265.

Answer:

[tex] {2}^{0} = 1[/tex]

[tex] {2}^{1} = 2[/tex]

[tex] {2}^{5} = 32[/tex]

[tex] {2}^{6} = 64[/tex]

It'd be c) g(x)=(x-4)2+9

Answer : C

The function [tex]f(x)= x^2[/tex] has been translated 9 units up and 4 units to the right to form the function g(x)

For 9 units up, we add 9 at the end of f(x)

f(x) + 9

so equation becomes [tex]f(x)= x^2 + 9[/tex]

For 4 units right , we subtract 4 from x  in f(x)

f(x-4)

So the equation becomes [tex]f(x) = (x-4)^2 + 9[/tex]

Hence [tex]g(x) = (x-4)^2 + 9[/tex]

The slope is the change in Y over the change in X

Label each point (x1,y1) and (x2,y2)

Slope = y2 - y1 / x2-x1

Slope = -7 - (-11) / -6 - (-1)

Slope = -7 +11 / -6 +1

Slope = 4 / -5

Move the negative sign in front:

Slope = -4/5

4.9 convert it fraction = 49/10

Answer:

Rational; irrational; irrational.

Step-by-step explanation:

a/3b is a rational number, as it is represented by a fraction and b ≠ 0.  This means the first blank is "rational."

√5 is an irrational number.  This means the second blank is "irrational."

Since we have an irrational number set equal to a rational number, this is a contradiction.  This means our original assumption is wrong, and the number is irrational.  This is the third blank.

There are Rational, irrational, and irrational are the correct options respectively.

A rational number is defined as a numerical representation of a part of a whole that represents a fraction number.

It can be a/b of two integers, a numerator a, and a non-zero denominator b.

Given Number = 3√5

We have to prove that 3√5 is an irrational number.  

Let us assume 3√5 is a rational number.

Because it is represented as a fraction and b ≠ 0, a/3b is a rational number. This implies that the first blank is "reasonable."

The number √5 is irrational. This indicates that the second blank is "irrational."

This is a contradiction since we have an irrational number set equal to a rational number. This signifies that our initial assumption was incorrect, and the number is irrational.

Therefore, the assumption is wrong, and the product is irrational.

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x = 4 and x = - 9

In both cases the angles inside the parallel lines are same sided interior angles

24x - 1 + 20x + 5 = 180

44x + 4 = 180 (subtract 4 from both sides )

44x = 176 ( divide both sides by 44 )

x = [tex]\frac{176}{44}[/tex] = 4

Similarly

x + 109 + x + 89 = 180

2x + 198 = 180 ( subtract 198 from both sides )

2x = - 18

x = [tex]\frac{-18}{2}[/tex] = - 9

let the wigth =x

then the length =2x

You can get

2·(2x+x)=60

2·(2x+x)÷2=60÷2

2x+x=30

3x=30

x=10

So 2x=2×10=20

The width of the garden is 10 feet, the length is 20 feet and the area is 200 square feet.

Final answer:

To find the dimensions of the garden, set up equations based on the perimeter formula and the given relationship between length and width. Solve to find that the width is 10 feet, and therefore the length is 20 feet.

Explanation:

To find the dimensions of a rectangular garden with a perimeter of 60 feet where the length is twice the width, we first need to set up two equations based on what we know about perimeters and the relationship between the garden's length and width. The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that P = 60 feet and the length is twice the width (l = 2w), we can substitute the latter into the perimeter formula and get 60 = 2(2w) + 2w, simplifying to 60 = 4w + 2w, which further simplifies to 60 = 6w. Dividing both sides by 6 gives us w = 10 feet. Therefore, the width is 10 feet and since the length is twice the width, the length is 20 feet.

The opposite of 4 is -4 for additivity and 1/4 for multiplicity.

In mathematical language, opposite of a number means inverse of a number and 2 inverses of the number are possible. One is additive inverse, while the other is multiplicative inverse.

To calculate an additive inverse of 4:

Let x be an additive inverse of 4, then

4+x=0

On transposing,

x=-4

Let y be multiplicative inverse of 4, then

4 x y=1

On transposing,

y=1/4

Thus, additive opposite of 4 is -4 and multiplicative opposite of 4 is 1/4.

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X= cost of each bracelet

9x+9=72

9x+9-9=72-9

9x=63

9x/9=63/9

X=7

The answer to the first part is $7 / each bracelet.

Answer:

Step-by-step explanation:

Factor 125[tex]x^{3}[/tex]-64

5³ₓ³ -  64

2.1      Factoring: 125[tex]x^{3}[/tex]-64

Theory : A difference of two perfect cubes [tex]a^3 - b^3[/tex] ,can be factored into

(a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =

           [tex]a^3+a^2b+ab^2-ba^2-b^2a-b^3 =[/tex]

           [tex]a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3 =[/tex]

           [tex]a^3+0+0-b^3 =[/tex]

           [tex]a^3-b^3[/tex]

Check :  125  is the cube of  5

Check :  64  is the cube of   4

Check :  x³ is the cube of   x¹

Factorization is :

(5[tex]x[/tex] - 4)  •  (25[tex]x^{2}[/tex] + 20[tex]x[/tex] + 16)

2.2     Factoring  25[tex]x^{2}[/tex] + 20[tex]x[/tex] + 16

The first term is,  25[tex]x^{2}[/tex]  its coefficient is  25 .

The middle term is,  +20[tex]x[/tex]  its coefficient is  20 .

The last term, "the constant", is  +16

Step-1 :

Multiply the coefficient of the first term by the constant   25 • 16 = 400

Step-2 :

Find two factors of  400  whose sum equals the coefficient of the middle term, which is 20 .

                       -400     +     -1    =     -401

                     -200     +     -2    =     -202

                     -100      +     -4    =      -104

                      -80      +     -5    =      -85

                      -50      +     -8    =      -58

                      -40      +    -10   =      -50

For tidiness, printing of 24 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

[tex](5x - 4) • (25x^2 + 20x + 16)[/tex]