3g+5+3g+5+3g+5 Simplify!!!!!! PLZZ

Answer:

823.7 m²

Step-by-step explanation:

Given the ratio of sides = 5 : 6, then

the ratio of area = 5² : 6² = 25 : 36

let x be the area of the larger prism then by proportion

[tex]\frac{25}{572}[/tex] = [tex]\frac{36}{x}[/tex] ( cross- multiply )

25x = 36 × 572 ( divide both sides by 25 )

x = [tex]\frac{36(572)}{25}[/tex] ≈ 823.7

The surface area of the larger prism is 823.7 ( nearest tenth )

Answer: 823.7

Step-by-step explanation: (5/6)^2, cross multiply with 572/SA, 572*36/25 = 823.68, rounded to the nearest tenth is 823.7

Answer: Peter had 48 quarters and 11 dimes.

Step-by-step explanation:

Let be "q" the number of quarters and "d" the number of dimes.

We know that $13.10 in cents is 1,310 cents. Then, we can set up the following system of equations:

[tex]\left \{ {{25q+10d=1,310} \atop {q=3d+15}} \right.[/tex]

Applying the Substitution method, we can substitute the second equation into the first one and solve for "d":

[tex]25(3d+15)+10d=1,310\\\\75d+375+10d=1,310\\\\85d=1,310-375\\\\d=\frac{935}{85}\\\\d=11[/tex]

Finally, we must substitute the value of "d" into the second equation to find the value of "q". Then:

[tex]q=3(11)+15\\\\q=33+15\\\\q=48[/tex]

Peter had 48 quarters and 11 dimes

Simultaneous Linear Equations could be solved by using several methods such as :

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Number of quarters ( 25 cent coins ) = x

Number of dimes ( 10 cent coins ) = y

When he counted his quarters and dimes, he found they had a total value of $13.10.

The number of quarters was 15 more than 3 times the number of dimes.

If we would like to use the Substitution Method , then second equations above could be substituted into first equations.

0.25x + 0.10y = 13.10

0.25 (15 + 3y) + 0.10y = 13.10

3.75 + 0.75y + 0.10y = 13.10

0.85y = 13.10 - 3.75

0.85y = 9.35

y = 9.35 / 0.85

At last , we could find the value of x by substituting this y value into one of the two equations above :

x = 15 + 3y

x = 15 + 3(11)

x = 15 + 33

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

Answer:

In a part-to-whole ratio, one ratio compares a part to a whole.

In mathematics, a fraction is an example of a ratio that compares a part to a whole. Understanding this is crucial for analyzing parts and how they conform to the whole. Another practical illustration of this concept is through a pie graph, which represents the whole and its parts.

In a fraction, one ratio compares a part to a whole. This goes along with a concept in Mathematics where it's useful to take into consideration the parts that contribute to the totality of a whole. An example of this can be seen in numbers. If we look at the relationship between a part and a whole in a ratio, for example, the mass ratio of copper and chlorine in a certain compound, we can gain significant insights.

Another approach is to use a pie graph, which is a graphical representation showing how a whole is divided into parts. The whole circle showcases the entire group, while each slice or part shows the relative size or percentage it contributes to the whole. This visualization makes it easy to understand the relationship between parts and the whole.

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Answer:

Step-by-step explanation:

7. False.  Opposite angles of a rhombus are congruent, not necessarily supplementary unless it's a square.

8. False.  Parallelograms' consecutive angles must be supplementary.  168 and 22 do not add up to 180.

9. False.  Rhombuses are not the only quadrilateral with perpendicular diagonals.  Kites also have perpendicular diagonals.

10. Area of a regular polygon is:

A = 1/2 aP

where a is the apothem and P is the perimeter.

We're given a = 24.78, but we need to find the side length.

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a hexagon with 6 sides has an interior angle of:

θ = (6 - 2) × 180° / 6

θ = 120°

If we draw lines from the bottom corner to the center, we get a 30-60-90 triangle.  Therefore:

(s/2) × √3 = 24.78

s/2 = 14.307

s = 28.61

So the perimeter is:

P = 6s

P = 171.68

And the area is:

A = 1/2 aP

A = 1/2 (24.78) (171.68)

A = 2127.13 cm²

11. Area of a regular polygon is:

A = 1/2 aP

where a is the apothem and P is the perimeter.

We're given s = 11, but we need to find the apothem.

The interior angle of a regular polygon is:

θ = (n - 2) × 180° / n

So a polygon with 11 sides has an interior angle of:

θ = (11 - 2) × 180° / 11

θ = 1620/11 °

If we draw lines from the bottom corner to the center, we get a right triangle with a base angle of θ/2.  Therefore:

tan (θ/2) = a / (s/2)

a = s/2 tan(θ/2)

a = 11/2 tan(810/11 °)

a = 18.73

The perimeter is:

P = 11s

P = 121

And the area is:

A = 1/2 aP

A = 1/2 (18.73) (121)

A = 1133.24 in²

2 as what he said above

Answer:

Step-by-step explanation:

We have three pairs of rectangles:

4cm × 5cm

4cm × 7cm

5cm × 7cm

The formula of an area of a rectangle l × w:

A = l × w

l - length

w - width

Substitute:

A₁ = (4)(5) = 20 cm²

A₂ = (4)(7) = 28 cm²

A₃ = (5)(7) = 35 cm²

The Surface Area:

SA = 2A₁ + 2A₂ + 2A₃

Substitute:

SA = 2(20) + 2(28) + 2(35) = 40 + 56 + 70 = 166 cm²

Answer:

Last option: 4

Step-by-step explanation:

The quadratic equation simplified: [tex]x^2-4x=-\frac{7}{2}[/tex] has the form:

[tex]ax^2+bx=c[/tex]

In this case, you can identify that "a", "b" and "c" are:

[tex]a=1\\b=-4\\c=-\frac{7}{2}[/tex]

To solve this quadratic equation  by completing the square, Carlos should add [tex](\frac{b}{2})^2[/tex] to both sides of the equation. This is:

[tex](\frac{-4}{2})^2=(-2)^2=4[/tex]

Then:

[tex]x^2-4x+4=-\frac{7}{2}+4[/tex]

Therefore you can observe that the number he should add to both sides of the equation is: 4

Answer:

Step-by-step explanation:

b) 1- scale factor from the first map to the second map:

[tex]\frac{8}{6}[/tex]  = 1.33

   2- landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm.

Side lengths of the landmark on the second map

Divide the length by scale factor:

side lengths of 3 mm:  [tex]\frac{3}{1.33}[/tex] = 2.25 mm

side lengths of 4 mm:  [tex]\frac{4}{1.33}[/tex] = 3.007 mm

side lengths of 5 mm:  [tex]\frac{5}{1.33}[/tex] = 3.75 mm

Answer:

A. Being above 180 centimeters and having black hair are independent of each other.

Step-by-step explanation:

These are instinctively two characteristics that are not related and the table data proves it.

If they were dependent, you would have only people with black hair above 180 cm, and all people with black hair would be above 180 cm.

You can be above 180 cm and have black, brown or blonde hair. The table shows a proportion of people > 180 cm about equal (around 30% of the sampling) for each hair color.

And people above 180 cm only represent 30% of the people with black hair.

Option: A is the correct answer.

     A. Being above 180 centimeters and having black hair are independent of each other.

Height :         Less than  175 cm  175-180 cm Above 180 cm     Total

Hair  Color

   Black                    38                        32                  30               100

  Brown                    27                        24                  19                70

  Blonde                    21                        33                  26                80

  Total                    86                89                  75                250

Two events A and B are said to be independent if:

     [tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

else they are dependent.

A)

Being above 180 centimeters and having black hair are independent of each other.

Let A denote Black hair

and B denote above 180 cm.

[tex]P(A)=\dfrac{100}{250}=\dfrac{10}{25}[/tex]

and [tex]P(B)=\dfrac{75}{250}=\dfrac{3}{10}[/tex]

This means that:

 [tex]P(A)\times P(B)=\dfrac{10}{25}\times \dfrac{3}{10}=\dfrac{3}{25}[/tex]

Also,

[tex]P(A\bigcap B)=\dfrac{30}{250}=\dfrac{3}{25}[/tex]

Since,

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

Hence, events A and events B are independent.

        Hence, option: A is correct.

2. First you need to know about the pythagorean theorem which is

a^2 + b^2 = c^2. Look at the first picture below for more reference.

Next you use the pythagorean theorem to find out the right triangle sides to then know the length and width of the rectangle.

a = 8

b = unknown

c = 10

Now use algebraic steps. 8^2 + b^2 = 10^2 --) 64 + b^2 = 100 --) b^2 = 36 --)

b = 6 .

Finally you know the length which is 8 + 8 = 16 and the width which is 6, so the area of the rectangle is 16 x 6 = 96. And to look apporpriate 96in.^2 .

Check the picture below.

so then, let's use the pythagorean theorem to find "x" and "y", and the distance is just x+y.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{9}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ x=\sqrt{9^2+5^2}\implies x=\sqrt{81+25}\implies x=\sqrt{106} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{17}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ y=\sqrt{17^2+5^2}\implies y=\sqrt{289+25}\implies y=\sqrt{314} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total distance}}{x+y}\implies \sqrt{106}+\sqrt{314}\qquad \approx 10.296+17.72\qquad \approx 28.016[/tex]

Final answer:

To find the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we use the Pythagorean theorem. Adding together the two legs of a right triangle formed by the given distances and solving for the hypotenuse, we find it is approximately 26.48 miles.

Explanation:

To determine the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we need to create a diagram and use the Pythagorean theorem. First, we know that Salemburg is 17 miles south of Linbrooke, Linbrooke is 5 miles west of Pueblo, and Carson lives 9 miles north of Linbrooke. Therefore, the distance directly north from Carson's to Pueblo is 9 miles (since he is directly north of Linbrooke), and from Pueblo to Salemburg the direct line would consist of 5 miles west and 17 miles south, which forms a right triangle.

Using the Pythagorean theorem to find the length of the hypotenuse (direct line from Carson's past Pueblo to Salemburg), we have:

Calculate the total distance north-south by adding Carson's 9 miles north to Salemburg's 17 miles south, which gives us 26 miles.

Since we already have the west-east distance as 5 miles, we can set up the equation a^2 + b^2 = c^2, where 'a' is 5 miles, 'b' is 26 miles, and 'c' is the hypotenuse we are looking for.

Plugging in the values gives: 5^2 + 26^2 = c^2, or 25 + 676 = c^2, resulting in c^2 = 701.

Take the square root to find 'c': c ≈ 26.48 miles.

Therefore, the distance from Carson's house to Salemburg 'as the crow flies' passing through Pueblo is approximately 26.48 miles.

Answer:

y = -x + 4

Step-by-step explanation:

Step 1: Use the subtraction property of equality

6y = -6x + 24

Step 2: Use the division property of equality

y = -x + 4

Answer:

y = -x +4

Step-by-step explanation:

6x+6y= 24

Subtract 6x from each side

6x-6x+6y=-6x+ 24

6y = -6x+24

Divide by 6 on each side

6y/6 = -6x/6 +24/6

y = -x +4

The answer is:

The correct option is the second option:

[tex]\frac{5}{2},\frac{-1}{2}[/tex]

We are given the following expression:

[tex]\frac{2+-\sqrt{9}}{2}[/tex]

Now, solving we have:

First solution:

[tex]\frac{2+\sqrt{9}}{2}=\frac{2+3}{3}=\frac{5}{2}[/tex]

Second solution:

[tex]\frac{2-\sqrt{9}}{2}=\frac{2-3}{3}=\frac{-1}{2}[/tex]

Hence, we have that the correct option is the second option:

[tex]\frac{5}{2},\frac{-1}{2}[/tex]

Have a nice day!

Answer:

The correct answer is second option

5/2, -1/2

Step-by-step explanation:

From the attached figure we can see that,

(2 ± √9 )/2

To find the simplified form of (2 ± √9 )/2

(2 ± √9 )/2 = (2 + √9 )/2 or (2 - √9 )/2

(2 + √9 )/2 = (2 + 3)/2 = 5/2

(2 - √9 )/2 =  (2 - 3)/2 = -1/2

Therefore simplified form of (2 ± √9 )/2 are

5/2 and -1/2

The correct answer is option 2

Answer:

8 ft and 14 ft

Step-by-step explanation:

Let one diagonal be x then the other diagonal is 2x - 2

The area (A) of the rhombus is calculated using

A = [tex]\frac{1}{2}[/tex] product of the diagonals, that is

A = [tex]\frac{1}{2}[/tex] x(2x - 2) = 56

Multiply both sides by 2

x(2x - 2) = 112 ← distribute left side

2x² - 2x = 112 ( subtract 112 from both sides )

2x² - 2x - 112 = 0 ← in standard form ( divide through by 2 )

x² - x - 56 = 0

To factor the quadratic

Consider the factors of the constant term (- 56) which sum to give the coefficient of the x- term (- 1)

The factors are - 8 and + 7, since

- 8 × 7 = - 56 and - 8 + 7 = - 1, thus

(x - 8)(x + 7) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 7 = 0 ⇒ x = - 7

However, x > 0 ⇒ x = 8

One diagonal = 8 ft and the other = 2x - 2 = (2 × 8) - 2 = 16 - 2 = 14 ft

Answer:

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

Answer is B. -4,-2,1,3

A quadratic function is graphically represented by a parabola with a vertex located at the origin, below the x-axis, or above the x-axis. .

The points at which the graph crosses or touches the x-axis, give the real roots of the function(or zeros of the function) represented by the graph.

If the graph touches the x-axis and turns back, then it would be a double root at that point. Roots are also called x-intercepts or zeros.

The roots of the graph are Option B -4, -2, 1, and 3.

The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1. y = x^2.

The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠0)

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Answer:

[tex]10^{-6}=7[/tex]

Step-by-step explanation:

Remember that according to the laws of logarithms if [tex]log_ay=x[/tex], then [tex]a^x=y[/tex],

In other words to convert a logarithm to an exponential equation we just need to raise the base of the logarithm to the result and equate that to the argument of the logarithm.

Since our logarithm does not have a base, its base is 10; therefore [tex]a=10[/tex]. The argument of our logarithm is 7, so [tex]y=7[/tex]. The result of our logarithm is -6, so [tex]x=-6[/tex].

Replacing values

[tex]log_ay=x[/tex] ⇔ [tex]a^x=y[/tex]

[tex]log_{10}7=-6[/tex] ⇔ [tex]10^{-6}=7[/tex]

By the way [tex]log_{10}7=-6[/tex] is not a true equation since [tex]10^{-6}\neq 7[/tex].

Answer:

(15 km/2 days)(5 days) = 37.5 km/week

(37.5 km/week)(4 weeks) = 150 km

The correct answer is A.

Answer: hey! sorry if very late :(

it's A).

Step-by-step explanation:

d

Answer:

D

Step-by-step explanation:

Answer:

D.-$21

Step-by-step explanation:

Answer:  b

Step-by-step explanation:

15% of the $96.6 clothes only is $14.49

in order to get over 100 dollars kelly would have to purchase 5 packages of gum

5 times .79 = $3.95

With the gum the total would be $100.55 divided by 20% = $20.11

$20.11 - $14.49 = $5.62  however you need to subtract the price of the gum also

$5.62 - $3.95 = $1.67

B....

Its right trust!

Answer:

The graph is included in the attached pictures

Step-by-step explanation:

The graph for y=4-|x| is shown in the attached picture, the inequality tell us that the region is located below that particular graph including the function, hence you have the second attached picture

Answer:

b=3:25 and b:c=105 3:25/105

Step-by-step explanation:

{3}{25}}{105}={1}{875}=0.00114

{3}{25.105}

{3}{2625}

=1/875

Hope this helps

Answer:

A. 1.2 yd

Step-by-step explanation:

We are informed that Mr.Reddrick has a 74 total yards of red and blue felt to distribute to students in his art class. Moreover, we also have the information that each of his 20 students gets 2.5 yards of blue felt for the project. This implies that the total blue felt distributed is;

20*2.5 = 50 yards

The remainder is the total red felt left for distribution;

74 - 50 = 24 yards

Since we have 20 students, each one of them receives;

24/20 = 1.2 yd

Answer:

A 1.2

Step-by-step explanation:

Answer:

the answer would be 90

Step-by-step explanation:

100 giants fills 5/8 (100/160) of the theater leaving 3/8 of the theater for the elves.

3/8 times 240 elves is 90 elves.

If there were 150 elves that would also be 5/8 filled plus the original 5/8 filled with 100 giants! Some elves might suffer!!!

Answer:

(5,6)

Step-by-step explanation:

First, count how many units are between b and c, that is 10, half of that is 5 units because they want the mid point so we divided by 2 but now you are going to count 5 units from point b so the y value isn't isn't 5. So from b, count 5 units upwards which lands at 6 so that is the y value. Now you move from their to the right to touch the line (if you understand what i mean) and that would fall at the value of 5. so x is equal 5. Coordinate: (x,y)=(5,6). Hopefully that helped.

The midpoint of the line BC is (5,6).

The midpoint of a line segment is the point equidistant from its endpoints. It is calculated as the average of the x-coordinates and y-coordinates of the endpoints.

Midpoints are crucial in geometry for construction, line segment division, and coordinate geometry. They play roles in physics, engineering, and bisection problems, contributing to spatial reasoning and problem-solving.

The midpoint M of a line segment with endpoints B(x₁, y₁) and C(x₂, y₂) is calculated as:

M = (x₁ + x₂)/2, (y₁ + y₂)/2.

So, for points B(2, 1) and C(8, 11) the midpoint is:

M(2 + 8)2, (1 + 11)/2

= 10/2, 12/2

= (5, 6).

The midpoint of the line BC is (5,6).

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This is the area of a triangle

Answer:

Use the formula Area=1/2bh

Step-by-step explanation:

[tex]\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}-sin(\theta ) \right)~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&3\\ \theta =&\stackrel{radians}{\frac{2\pi }{3}}\\ &\stackrel{degrees}{120} \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left(\cfrac{\pi (120) }{180}-sin(120^o) \right)\implies A=\cfrac{9}{2}\left(\cfrac{2\pi }{3}-\cfrac{\sqrt{3}}{2} \right) \\\\\\ A \approx \cfrac{9}{2}(1.23)\implies A\approx 5.535[/tex]

Answer:

87380

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{16}{4}[/tex] = 4 and a = 4, hence

[tex]S_{8}[/tex] = [tex]\frac{4(4^8-1)}{4-1}[/tex] = [tex]\frac{4(65535)}{4}[/tex] = 87380

As we can see on the picture we have a rectangle and half of circle.

The areas for half circle and rectangle are:

[tex]

A_{rectangle}=a\cdot b \\

A_{halfcircle}=\frac{A_{circle}}{2}=\frac{\pi r^2}{2}

[/tex]

The area of the figure is the sum of the area of half circle and rectangle. Also the height of a rectangle (6ft) is a diameter of a half circle therefore the radius of half circle is 6ft ÷ 2 = 3ft.

Now we calculate the areas.

[tex]

A_{rectangle}=10\cdot 6=\underline{60} \\

A_{halfcircle}=\frac{3.14\cdot3^2}{2}=\underline{14.13} \\

A_{total}=A_{rectangle}+A_{halfcircle} =60+14.13=\boxed{74.13\approx74}

[/tex]

The area of the figure is approximately 74ft squared.

Hope this helps.

r3t40

Answer:

B

Step-by-step explanation:

Answer:

113 beats per minute.

Step-by-step explanation:

904 / 8 = 113

The pulse rate in Salvador is 113 beats per minute.

calculation:

    ⇒number pf heartbeat count = 904

    ⇒time of count= 8 minutes

    ⇒pulse rate= 904/8

                  =113 beats per minute.

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