Find the value of x. Round the length to the nearest tenth.

Answer:

  -5x = 8

Step-by-step explanation:

The result is shown here. The y-terms cancel.

  [tex]\begin{array}{rccc}& -2x+7y &= &10 \\-&(\ \,3x+7y &= &2)\\\cline{1-4}&-5x+0y&=&8 \end{array}[/tex]

The simplified result is ...

  -5x = 8

Answer:

The result is that 5x = -8

Step-by-step explanation:

Here, we want to subtract 3x + 7y = 2 from -2x + 7y = 10

Mathematically that would be;

(-2x+7y)-(3x+7y) = 10-2

-2x + 7y -3x -7y = 8

-2x -3x + 0 = 8

-5x = 8 or 5x = -8

Answer:

x=-5

Step-by-step explanation:

The answer is x = -5. The explanation and answer is in the image below.

Answer:   [tex]t_9=\dfrac{1}{2^8}[/tex]

Step-by-step explanation:

[tex]t_n=t_1\times r^{n-1}\\\\Given: t_1=1,\quad r=\dfrac{1}{2}\\\\\\t_9=1\times\bigg(\dfrac{1}{2}\bigg)^{9-1}\\\\\\.\quad =\large\boxed{\dfrac{1}{2^8}}[/tex]

Answer:

144 units²

Step-by-step explanation:

Surface area of a traingular prism is given as:

Area = 2(B.A) + P*L

Where,

B.A = base area of the triangular prism = ½*b*h

b = base of the triangular base = 4 units

h = height of the triangular base = 3 units

Base Area (B.A) = ½*4*3 = 2*3 = 6 units²

P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units

L = length or height of prism = 11 units

Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L

[tex] Area = 2(6) + 12*11 [/tex]

[tex] = 12 + 132 [/tex]

[tex] Surface Area = 144 [/tex]

Surface area of the triangular prism = 144 units²

C. A line has one dimension, length.

E. A plane consists of an infinite set of lines.

Answer:

Step-by-step explanation:

let the plane intersects the join of points in the ratio k:1

let (x,y,z) be the point of intersection.

[tex]x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}[/tex]

point of intersection is (8/3,14/3,8/3)

and ratio of division is 2:1

Answer:

Andy's house to Billy's hometown 15 ways

Andy's house to Willie's hometown 2 ways.

Step-by-step explanation:

Andy's house to Billy's hometown there are 3 roads. There 5 road from billy's hometown to Willie's house . In total there will be 15 ways to travel which is calculated by 3 * 5. For traveling to Willie's hometown there will be two ways. There are two roads that are built to get to Willie's house.

Answer:

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

Answer:

6 km

Step-by-step explanation:

Let us assume the following items

the Point at Train depot = T

The Point at Main gate =  M

The Point at Bird sanctuary =  B

The Point at Elephant house = E

The Point at manatee Springs =  S

As we can see that there are two triangles namely TMB and TSE.

Mentioned that

MTB = ∠STE

∠TMB = ∠TSE

∠TBM = ∠TES.

According to the Angle-angle-angle (AAA similarity)

So, the triangles TMB and TSE are the same.

[tex]\frac{TM}{TS} = \frac{TB}{TE} \\\\ \frac{TM}{4,200} = \frac{2,000}{3,500}[/tex]

So, the TM is 2400 yds

Now the Distance between Main gate M and manatee Spring S is

MS = MT + TS

= 2,400 + 4200

= 6600 yds

Now the MS is

= 6600 × 0.0009144 km

= 6.035 km

≅ 6 km

Answer:

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°

Answer:

500[tex]\pi[/tex] or around 1570

Step-by-step explanation:

The formula for a volume of a cylinder is [tex]r^{2}h\pi[/tex]

The cylindrical garbage pain has a volume of 15700 cm².

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

The given cylindrical garbage has a radius(r) = 10 cm and a height(h) of

50 cm.

∴ The volume of the cylindrical garbage is = π(10)²×50 cm².

= 5000π cm².

= 15700 cm².

learn more about cylinders here :

https://brainly.com/question/16134180

#SPJ2

[tex](-a+3)(a+4)=-a^2-a+12[/tex].

Hope this helps.

Answer:

-a²-a+12

Step-by-step explanation:

-a²+3a-4a+12

-a²-a+12

Answer:

86.55 ft

Step-by-step explanation:

First find the perimeter for 3 sides of the rectangle that are solid

24+15+24 = 63

The we find the circumference for 1/2 of the circle

C = pi d

The diameter is 15 and pi = 3.14

But we only want 1/2

1/2 C = 1/2 pi d

        = 1/2 ( 3.14) * 15

       =23.55

Add the lengths together

23.55+63 =86.55 ft

Answer:

  all real numbers

Step-by-step explanation:

There is nothing on the graph to indicate the function is undefined for any values of x. The domain is all real numbers.

Answer:

Domain is all real numbers.

Step-by-step explanation:

The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x.

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.

Answer:

x=3

Step-by-step explanation:

To solve for x, we will follow the steps below:

First note that exterior angle =two  opposite interior angle

From the diagram below

(25x) ° + (57 + x)°   = (45x)°

25x° + 57° + x° = 45x°

next step is to collect the like term

45x° - 25 x°  - x°  =  57°

19x° = 57°

Divide both-side of the equation by 19

19x°/ 19 = 57° /19

On the left-hand side of the equation 19 will cancel out 19 leaving us with just x°  while on the right-hand side of the equation 57 will be divided by 19

x  =   3

Answer:

Step-by-step explanation:

First we must know that the sum of all the exterior angle of all polygons is 360°.

Measure of each angle of a polygon = 360°/total sides of the polygon

Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;

Measure of each angle of a polygon  = 360°/9

Measure of each angle of a polygon  = 40°

Hence the measure of an exterior angle x of a nonagon is 40°

Answer:

B in Edg

Step-by-step explanation:

Answer:

288π

Step-by-step explanation:

V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.

Answer:

Total number of animals in the group = 170

Step-by-step explanation:

Let the number of sheep = a

Number of dragons in the group = 75

Number of dragons opposite dragons = 37

Number of sheep opposite to the dragon = 1

Number of sheep left = a - 1

Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]

Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,

[tex]\frac{(a-1)}{2}[/tex] = 37 + 10

[tex]\frac{(a-1)}{2}=47[/tex]

a - 1 = 94

a = 95

Then total number of animals in the group = Total number of sheep + Total number of dragons

= 95 + 75

= 170

Therefore, total number of animals in the group are 170.

Answer:

Step-by-step explanation:

Given the coordinates P(-2, -3). Q(2, - 6). R(6. - 3). S(2, 1), to determine the type of shape the quadrilateral is, we need to find the measure of the sides. To get the measure of each sides, we will take the distance between the adjacent coordinates using the formula to formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²-(y₂-y₁)²

For the side PQ with the coordinate P(-2, -3). Q(2, - 6)

PQ = √(2-(-2))²-(-6-(-3))²

PQ = √(2+2)²-(-6+3)²

PQ = √4²-(-3)²

PQ = √16-9

PQ = √7

For the side QR with the coordinate Q(2, - 6) and R(6, -3)

QR = √(6-2))²-(-3-(-6))²

QR = √(4)²-(3)²

QR = √16-9

QR = √7

For the side RS with the coordinate R(6. - 3) and S(2, 1)

RS = √(2-6)²-(1-(-3))²

RS = √(-4)²-(1+3)²

RS = √16-(4)²

RS = √16-16

RS = 0

For the side PS with the coordinate P(-2, -3) and S(2, 1)

PS = √(2-(-2))²-(1-(-3))²

PS = √(4)²-(1+3)²

PS = √16-(4)²

PS = √16-16

PS = 0

For the quadrilateral to be a rectangle, then two of its sides must be equal and parallel to each other. A rectangle is a plane shape that has two of its adjacent sides equal and parallel to each other. Since two of he sides are equal i.e RS = PS and PQ = QR then the quadrilateral PQRS is a rectangle. Both rhombus and square has all of its sides equal thereby making them wrong.

Answer:

A square.

Step-by-step explanation:

Answer:

shape AREA= 35cm^2

Step-by-step explanation:

you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.

A=h/2(b1 + b2) for trapezoid

A=2/2((4+4)+4)

A=1*12

A=12cm^2

A=bh/2. for TRIANGLE

A=1/2((4+4)*5.75)

A=1/2(46)

A=23cm^2

shape AREA= triangle AREA + trapezoid AREA

shape AREA=12cm^2 + 23cm^2

shape AREA= 35cm^2

Answer:

a=-5

Step-by-step explanation:

When you do this every time the slope will go down 2 and over 1 which is rise over run or slope. You can see the y coordinates go down 4 points and every time is should go down 2 so you will know that it would have gone down 2 times so a+2 should equal -3 so if we subtract 2 from both sides we would get a=-5 and that is our answer.

Answer:

a = - 5

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 2

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (a, 3)

m = [tex]\frac{3+1}{a+3}[/tex] = [tex]\frac{4}{a+3}[/tex] = - 2 ( multiply both sides by a + 3 )

- 2(a + 3) = 4 ( divide both sides by - 2 )

a + 3 = - 2 ( subtract 3 from both sides )

a = - 5

Answer:

x = 60

Step-by-step explanation:

In a circle, the sum of the angles that meet at a point is 360 degrees. So now that we have the total, we can subtract all the given information in the picture. We have 84, 75, 68, and x + 73. Now let us set up and equation for this problem.

360 = 84 + 75 + 68 + x + 73

Now combine like terms.

360 = x + 300

Now subtract 300 on both sides.

x = 60

And this is the value of x.

Answer:

50 degrees

Step-by-step explanation:

84 + 75 + 68 = 227

227 - 360 = 133

133 - 73 = 50

The answer is 50 degrees.

Answer:

9*((2-1)/9)

or

2 -1

9

2-9 =-7

9. 9

9× -7

9

=-7

2- 3

9. -3

=(1.22222222222)

or

11/9

or

1*(2/9)

Answer:

Sister is 70

Step-by-step explanation:

John is 39.

8 less than twice his age is

39*2-8 = 70

Answer:

70 years old.

Step-by-step explanation:

Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.

Hope this helps!! <3

from the above picture

2,3 = 1 quadrant

5,-6 = 4 quadrant

2,0 = on x axis

-5,2 = 2 quadrant

-2,-4 =3 quadrant

0,-2 = on y axis

Answer:

[tex]\large \boxed{87.5 \, \%}[/tex]

Step-by-step explanation:

            Let x = the original number of books

Then 0.375x = the total number of biographies

 and 0.20  x = the original number of biographies

[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]