If there are 100 postage stamps in a sheet of stamps, and each stamp cost 29 cents, how much will one sheet of stamps cost?

Answer:

[tex]\large\boxed{C.\ a=\dfrac{400}{21},\ b=\dfrac{580}{21}}[/tex]

Step-by-step explanation:

(LOOK AT THE PICTURE)

ΔABC, ΔDBA and ΔDAC are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{AB}{AD}=\dfrac{AC}{DC}[/tex]

We have AB = b, AD = 20, AC = 29 and DC = 21. Substitute:

[tex]\dfrac{b}{20}=\dfrac{29}{21}[/tex]             cross multiply

[tex]21b=(20)(29)[/tex]

[tex]21b=580[/tex]           divide both sides by 21

[tex]b=\dfrac{580}{21}[/tex]

and in proportion:

[tex]\dfrac{BD}{AD}=\dfrac{AD}{DC}[/tex]

We have BD = a, AD = 20 and DC = 21. Substitute:

[tex]\dfrac{a}{20}=\dfrac{20}{21}[/tex]           cross multiply

[tex]21a=(20)(20)[/tex]

[tex]21a=400[/tex]   divide both sides by 21

[tex]a=\dfrac{400}{21}[/tex]

Answer:

The number of coins Julia found is 5

Step-by-step explanation:

We know that the total number of gold coins collected divided by the number of people collecting is 6. So we can set up an equation:

[tex]\frac{6+5+6+8+x}{5}=6[/tex]

this simplifies to:

[tex]\frac{25+x}{5}=6[/tex]

Using the multiplication property of equality and multiplying both sides by we get:

25+x=30

Then finally, using the subtraction property of equality we get our answer:

x=5

Answer:

The answer is 176

Step-by-step explanation:

The answer is the square root of one hundred seventy-six feet.

The height of the antenna and the length of the wire form two sides of a right triangle. The distance from the base of the antenna to the point at which the wire is fixed to the ground forms the other leg.

The Pythagorean Theorem states that a squared plus b squared equals c squared, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.

Let g equal the length in feet of the unknown leg.

First, apply the Pythagorean Theorem, and substitute twenty-four feet for the length of the hypotenuse and twenty feet for one of the legs.

Next, we square twenty-four and twenty.

Then, subtract four hundred from both sides to get one hundred seventy-six equals g squared.

Finally, take the square root of both sides to get the square root of one hundred seventy-six equals g.

So the distance from the base of the antenna to the point at which the wire is fixed to the ground is the square root of one hundred seventy-six feet.

Answer:

(4x−3)(3x²+2)

Step-by-step explanation:

Factor 12x3−9x2+8x−6

12x3−9x2+8x−6

=(4x−3)(3x2+2)

The factored form of the expression 12x³ - 9x² + 8x - 6 by grouping is (3x² + 2)(4x - 3).

To factor the expression 12x³ - 9x² + 8x - 6 by grouping, we can group the terms in pairs and factor out the common factors.

Step 1: Group the terms in pairs

(12x³ - 9x²) + (8x - 6)

Step 2: Factor out the greatest common factor from each pair

3x²(4x - 3) + 2(4x - 3)

Step 3: Notice that both terms now have a common factor of (4x - 3)

(3x² + 2)(4x - 3)

Therefore, the factored form of the expression 12x³ - 9x² + 8x - 6 by grouping is (3x² + 2)(4x - 3).

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Answer:

[tex]\boxed{ a_{n} = 6a_{n-1}}[/tex]

Step-by-step explanation:

Step 1. Determine the common ratio

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

Data:

a₁ = 4

n = 6

a₆ =31 104

Calculation:

31 104 = 4r⁵

r⁵ = 7776

[tex]r = \sqrt [5]{7776}[/tex]

r = 6

aₙ = 4(6)ⁿ

Step 2. Determine the recursive formula.

aₙ = 4(6)ⁿ

aₙ₋₁ = 4(6)ⁿ⁻¹

[tex]\dfrac{a_{n}}{{a_{n-1}}} = \dfrac{4(6)^{n} }{4(6)^{n-1}} = 6\\\\a_{n} = 6a_{n-1}[/tex]

The recursive formula for the series is [tex]\boxed{ a_{n} = 6a_{n-1}}[/tex]

Answer: A. 370 cm2

Step by Step explanation:

10x15=150 The big rectangle

15x6=90x2=180 The small rectangles

20x2=40 the triangles

Add all up 150+180+40=370

Hope this helped

Answer:

See the graphic I made

Area of Section A = 4 *1 = 4 square centimeters

Section B = 4 * (3 + 4) = 28 sq cm

Section C = 3 * (2 + 3 + 4) = 27 sq cm

Total Area = 4 + 28 + 27 = 59 square centimeters

Step-by-step explanation:

To find the area of an octagon, you can use the formula 2 * (1 + √2) * s², where s is the length of one of the sides. If the area is given, you can solve for s and then use the formula to calculate the area.

The area of an octagon can be calculated using the formula:

Area = 2 * (1 + √2) * s²,

where s is the length of one of the sides of the octagon.

In this case, since the area is given as 0.4 m², we can solve for s.

0.4 = 2 * (1 + √2) * s²

Dividing both sides by 2 * (1 + √2) gives:

s² ≈ 0.2

Taking the square root of both sides, the length of one side is approximately 0.45 m.

To find the area, use the formula:

Area = 2 * (1 + √2) * (0.45)² ≈ 0.4 m²

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There are 19 students in the class

The area of mathematics known as algebra deals with symbols and the formulas used to manipulate them. These symbols, which are currently expressed as Latin and Greek letters, are used in elementary algebra to represent variables or quantities without set values.

Given

If Stanley is the 10th tallest, then there are 9 shorter students

and if he is 10th shortest in the class, there are 9 taller students

9 + 1 + 9=19

so, there are 19 students in the class

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Answer:

Broker Q’s commission will be $13.56 less than Broker P’s

Step-by-step explanation:

Answer:

Broker Q will give Diana the better deal by $13.56.

Step-by-step explanation:

Diana wants to purchase a par value $1000 corporate bond. Broker P charges 4.4% of the market value, so the commission would be $46.06008 per bond. On the other hand, Broker Q would only charge $32.50 for each bond; due to this, the difference would be $13.56 in favor of Broker Q.

The height is 4.8. You can check it by substituting it into the formula.

Answer:

Therefore, Height = 4.8 inches.

Step-by-step explanation:

Given : A triangle whose base is 5 inches and area is 12 square inches.

To find : Find the height of a triangle.

Solution : we have given

Triangle base = 5 inches.

Area = 12 square in.

We need to find height of the triangle.

Area = [tex]\frac{1}{2}[/tex] * base * height .

Plugging the values .

12 =  [tex]\frac{1}{2}[/tex] * 5 * height .

On multiplying both sides by 2

24 = 5 * height .

On dividing both sides by 5.

Height = [tex]\frac{24}{5}[/tex].

Height = 4.8 inches.

Therefore, Height = 4.8 inches.

The number of students attending the camp that summer is 380 students

Step-by-step explanation:

There are four counselors for every fifty seven students

There are three teachers for every five counselors

Ms. Rifkin asked all 16 teachers present at the camp to attend a

teachers meeting

To solve this question we will use the ratio

The given is:

1. 4 counselors for every 57 students

2. 3 teachers for every 5 counselors

3. There are 16 teachers

At first let us find the 16 teachers are for how many counselors

∵ 3 teachers : 5 counselors

∵ 16 teachers : x counselors

∴ [tex]\frac{3}{5}=\frac{16}{x}[/tex]

By using cross multiplication

∴ 3x = 16 × 5

∴ 3x = 80

Divide both side by 3

∴ x = [tex]\frac{80}{3}[/tex]

Then let us find the [tex]\frac{80}{3}[/tex] counselors are for how many students

∵ 4 counselors : 57 students

∵ [tex]\frac{80}{3}[/tex] counselors : y students

∴ [tex]\frac{4}{57}=\frac{80/3}{y}[/tex]

By using cross multiplication

∴ 4y = 57 × [tex]\frac{80}{3}[/tex]

∴ 4y = 1520

Divide both sides by 4

∴ y = 380 students

The number of students attending the camp that summer is 380 students

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Answer:

No solution

Step-by-step explanation:

x² + 3 x + 40 = 0

Answer:

The answers for x^2+3x−40=0 are -8 and 5.

Step-by-step explanation:

For this problem, we are able to factor. Since 8 and 5 are both factors of 40, and since 8-5=3, we will use 8 and 5 in our binomial equation:

(x+8)(x−5)=40.

Just to prove that this is correct, let's multiply the two together: x^2−5x+8x−40=x^2+3x−40.

From here, we can use the zero product property to get our answers: x+8=0,x−5=0.

Subtract 8 from the first equation and subtract 5 from the second equation to get our answers, -8 and 5.

Hey there! :)

(13x + 7) = (8x + 27)

We're trying to find x, so we must isolate it.

We can start by subtracting 8x from both sides.

13x - 8x + 7 = 8x - 8x + 27

Then, subtract 7 from both sides.

13x - 8x + 7 - 7 = 8x - 8x + 27 - 7

Simplify!

5x = 20

Divide both sides by 5.

5x ÷ 5 = 20 ÷ 5

Simplify.x = 4

~Hope I helped!~

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

[tex]13x + 7 = 8x + 27[/tex]

Take 8x to the left side and 7 to the right.

[tex]13x - 8x = 27 - 7[/tex]

Combine like terms.

[tex]5x = 20[/tex]

Divide both sides by 5.

[tex]x = 4[/tex]

Answer:

D)4x + 6/(x + 1)(x - 1)

Step-by-step explanation:

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

[tex]p=2(l+w)[/tex]

where

[tex]p[/tex] is the perimeter

[tex]l[/tex] is the length

[tex]w[/tex] is the width

We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so [tex]l=\frac{2}{x+1}[/tex] and [tex]w=\frac{5}{x^2-1}[/tex].

Replacing values:

[tex]p=2(l+w)[/tex]

[tex]p=2(\frac{2}{x+1} +\frac{5}{x^2-1})[/tex]

Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a[/tex] is the first term and [tex]b[/tex] is the second term. We can infer that [tex]a=x^2[/tex] and [tex]b=1^2[/tex]. So, [tex]x^2-1=(x+1)(x-1)[/tex]. Replacing that:

[tex]p=2(\frac{2}{x+1} +\frac{5}{x^2-1})[/tex]

[tex]p=2(\frac{2}{x+1} +\frac{5}{(x+1)(x-1})[/tex]

We can see that the common denominator of our fractions is [tex](x+1)(x-1)[/tex]. Now we can simplify our fraction using the common denominator:

[tex]p=2(\frac{2(x-1)+5}{(x+1)(x-1)} )[/tex]

[tex]p=2(\frac{2x-2+5}{(x+1)(x-1)} )[/tex]

[tex]p=2(\frac{2x+3}{(x+1)(x-1)} )[/tex]

[tex]p=\frac{4x+6}{(x+1)(x-1)} [/tex]

We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).

Answer:

I believe n equals 13.

Step-by-step explanation:

Answer:

The answer to your question is n=13

Step-by-step explanation:

n-26= -13

Add 26 on both sides

n-26+26=-13+26

n=13

Answer:

bench:  $416; table:  $325.

Step-by-step explanation:

Let t and b represent the costs of the table and bench respectively.  Then:

t + b = $741, and t = b + $91.

Substituting b + $91 for t in the first equation, we get:

b + $91 + b = $741

Then 2b = $741 - $91, or 2b = $650

Then the bench costs $325 and the table ($325 + $91), or $416.

Answer:

[tex]\frac{circumference\ }{diameter}=\pi[/tex]

Step-by-step explanation:

Given that radius of the circle = 10

Using π, we need to find about which equation expresses the ratio of the circumference of the circle to the circle's diameter.

diameter of the circle = 2(radius) = 2(10)=20

circumference of the circle = 2 π r = 2 π (10)  = 20 π

then ratio of the circumference of the circle to the circle's diameter is given by: [tex]\frac{circumference\ }{diameter}=\frac{20\pi}{20}=\pi[/tex].

Hence required equation is [tex]\frac{circumference\ }{diameter}=\pi[/tex]

Answer:

P = 21%

Step-by-step explanation:

We look for the percentage of employees who are not more than 30 years old.

This is:

[tex]P = \frac{x}{n} *100\%[/tex]

Where x is the number of new employees who are not over 30 years old and n is the total number of new employees.

We do not know the value of x or n. However, the probability of randomly selecting an employee that is not more than 30 years old is equal to [tex]P = \frac{x}{n}[/tex]

Then we can solve this problem by looking for the probability that a new employee is not more than 30 years old.

This is:

[tex]P(X< 30)[/tex]

Then we find the z-score

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

We know that:

μ = 38 years

[tex]\sigma = 10[/tex] years

So

[tex]Z = -0.8[/tex]

Then

[tex]P (X<30) = P (\frac{X- \mu}{\sigma} < \frac{30-38}{10})\\\\P (X<30) = P(Z<-0.8)[/tex]

By symmetry of the distribution

[tex]P(Z<-0.8)=P(Z>0.8)[/tex]

Looking in the normal standard tables

[tex]P(Z>0.8)=0.211[/tex]

Finally P = 21%

Substitute

4x+2=x-4

Then solve

3x=-6

x=-2

Substitute answer into an equation to find y

y=-2-4

y=-6

So you solution is:

(-2,-6)

Answer:

D. [tex]F(x)=(x+4)^2-5[/tex]

Step-by-step explanation:

The parent function is [tex]G(x)=x^2[/tex].

This function has its vertex at the origin (0,0).

When this function is shifted down 5 units and to the left 4 units, then its new vertex will be at (-4,-5)

The vertex form of the equation is given by;

[tex]F(x)=a(x-h)^2+k[/tex] where (h,k)=(-4,-5) is the vertex and a=1 because of the parent function.

Hence its equation is

[tex]F(x)=(x+4)^2-5[/tex]

Answer:

Option C

Step-by-step explanation:

A function g(x) = x² has been given as the parent function.

This function then shifted 5 units down.

Translated  function formed will be f(x) = x² - 5

Further this graph has been shifted 4 units to the left then the function will become

f(x) = [x - (-4)]² - 5

f(x) = (x + 4)² - 5

Therefore, option C is the answer.

Answer:

The answer is 131 you have to add the two angles together

Answer:

40

Step-by-step explanation:

Find the smallest multiple number shared by the two numbers.

10: 10, 20, 30, 40

8: 8, 16, 24, 32, 40

40 is the smallest multiple shared by the two numbers, and is your answer.

~

Answer:

40

Step-by-step explanation:

have a nice day

Answer:

Part B: [tex]\displaystyle [1, 2][/tex]

Part A: Set both equation equal to each other by Substitution, since our y-values are already given to us.

Step-by-step explanation:

6x - 4 = 5x - 3

- 6x + 3 - 6x + 3

____________

[tex]\displaystyle -1 = -x; 1 = x[/tex]

Plug this coordinate back into the above equations to get the y-coordinate of 2.

y = mx + b [where b is the y-intercept and the rate of change (slope) is represented by m]

[tex]\displaystyle y = 5x - 3; [0, -3]; 5 = m \\ y = 6x - 4; [0, -4]; 6 = m[/tex]

I am joyous to assist you at any time.

Answer:

Step-by-step expla5+7x12+75-94x347+7 2/9​nation:

Answer:

Step-by-step explanation:

[tex]f(x)=2x;\ g(x)=?\\\\(g\circ f)(x)=6x+2=3(2x)+2=3\bigg(f(x)\bigg)+2\to g(x)=3x+2\\\\Check:\\\\f(x)=2x,\ g(x)=3x+2\\\\(g\circ f)(x)\to\text{instead of x in g (x), put}\ 2x:\\\\(g\circ f)(x)=3(2x)+2=6x+2\qquad\bold{CORRECT :)}[/tex]

Answer:

the first question is B

and I am very sorry i don't know the second question

Answer:

C, B

Step-by-step explanation:

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a pentagon with 5 sides has an interior angle of:

θ = (5 - 2) × 180° / 5

θ = 108°

If we draw a line from the bottom left corner to the center, we get a right triangle.  Using tangent, we can say:

tan (108°/2) = a / (7.6/2)

tan (54°) = a / 3.8

a = 3.8 tan (54°)

a = 5.2

Answer C

If the interior angle is 144, then the number of sides is:

144 = (n - 2) × 180 / n

144n = 180n - 360

360 = 36n

n = 10

Answer B.

Answer:

[tex]y-1=3(x-2)[/tex]

Or

[tex]y-4=3(x-3)[/tex]

Step-by-step explanation:

The slope formula is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The line containing (2, 1) and (3, 4)  has slope;

[tex]m=\frac{4-1}{3-2}=3[/tex]

The point-slope form is given by:

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

We substitute the point and slope to get:

[tex]y-1=3(x-2)[/tex]

Or

[tex]y-4=3(x-3)[/tex]

ANSWER

[tex]<8,4> \bullet< - 3,5> = - 4[/tex]

EXPLANATION

The dot product of two vectors:

[tex] < a,b > [/tex]

and

[tex]< c,d> [/tex]

is

[tex] < a,b > \bullet< c,d> = ac + bd[/tex]

The given vectors are:

[tex]<8,4> [/tex]

and

[tex]< - 3,5> [/tex]

The dot product of these vectors is

[tex]<8,4> \bullet< - 3,5> = 8 \times - 3 + 4 \times 5[/tex]

[tex]<8,4> \bullet< - 3,5> = - 24 + 20[/tex]

[tex]<8,4> \bullet< - 3,5> = - 4[/tex]

Answer:

-4

Step-by-step explanation:

a p e x

Answer:

I think that the answer is D. CB ║DE

To find the answer, all we need to is to calculate all the missing one.

So: ∠CBD = 180° - 60° - 40° = 80°

     ∠BDE = 180° - 60° - 40° = 80°

     ∠DEF = 180° - 60° - 45° = 75°

Since we have ∠CBD ≅ ∠BDE ( = 80°) and they are alternate interior angles, we can conlcude that CB ║ DE.