The pair of linear equations 2x-3y = 14 and 3x - 2y = 4 has solution(s).

answer plz....​

Step-by-step explanation:

by order pair we obtain:

[tex] \displaystyle \begin{cases} \displaystyle 3p = 2p - 1 \dots \dots i\\2q - p = 1 \dots \dots ii\end{cases}[/tex]

cancel 2p from the i equation to get a certain value of p:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q - p = 1 \end{cases}[/tex]

now substitute the value of p to the second equation:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q - ( - 1) = 1 \end{cases}[/tex]

simplify parentheses:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q + 1= 1 \end{cases}[/tex]

cancel 1 from both sides:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q = 0\end{cases}[/tex]

divide both sides by 2:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\q = 0\end{cases}[/tex]

by order pair we obtain:

[tex] \displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\3y= x + y \dots \dots ii\end{cases}[/tex]

cancel out y from the second equation:

[tex] \displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\ x = 2y \dots \dots ii\end{cases}[/tex]

substitute the value of x to the first equation:

[tex] \displaystyle \begin{cases} \displaystyle 2.2y-y= 3 \\ x = 2y \end{cases}[/tex]

simplify:

[tex] \displaystyle \begin{cases} \displaystyle 3y= 3 \\ x = 2y \end{cases}[/tex]

divide both sides by 3:

[tex] \displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2y \end{cases}[/tex]

substitute the value of y to the second equation which yields:

[tex] \displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2 \end{cases}[/tex]

by order pair we obtain;

[tex] \displaystyle \begin{cases} \displaystyle 2p + q = 2 \dots \dots i\\3q + 2p = 3 \dots \dots ii\end{cases}[/tex]

rearrange:

[tex] \displaystyle \begin{cases} \displaystyle 2p + q = 2 \\2p + 3q= 3 \end{cases}[/tex]

subtract and simplify

[tex] \displaystyle \begin{array}{ccc} \displaystyle 2p + q = 2 \\2p + 3q= 3 \\ \hline - 2q = - 1 \\ q = \dfrac{1}{2} \end{array}[/tex]

substitute the value of q to the first equation:

[tex] \displaystyle 2.p+ \frac{1}{2} = 2[/tex]

make q the subject of the equation:

[tex] \displaystyle p = \frac{3}{4} [/tex]

hence,

[tex] \displaystyle q = \frac{1}{2} \\ p = \frac{3}{4} [/tex]

Answer:

see above

............

Answer:

10

Step-by-step explanation:

We know there are 5 quarts.

There are 2 pints for each quart.

This can be though of as a ratio of:

2 : 1

There are 5 quarts, which is 5 times bigger than the ratio of 1.

So this means we need to mutliply both sides of the ratio by 5, to make the quarts equivelent to 5:

2*5 : 1*5

=

10 : 5

So for every 5 quarts there are 10 pints.

Hope this helps!

Answer:

96 oz.

Step-by-step explanation:

Mary drinks 24 ounces a day Lena drinks 3 times a much

24 x 3 = 72

72 + 24 = 96

Answer:

They dinks ounces of juice together = 96 ounces.

Step-by-step explanation:

Given that :-

To find :-

Solution :-

Mary drinks 24 ounces of juice a day = 24 ounces.

Lena drinks three times much than mary = 3 × 24 ounces = 72 ounces

They drinks ounces together = mary drinks ounces of juice + lena drinks ounces of juice

= 24 ounces + 72 ounces

Hence , They dinks ounces of juice together = 96 ounces.

Answer:

arc cosine (4/5)

(the third answer)

Step-by-step explanation:

Given:

1. 60 is the sum of 15 and Mabel's age.

2. Given equation is

[tex]-8(x+1)=-40[/tex]

To find:

1. The equation for the given situation.

2. Complete the two column proof.

Solution:

1.

60 is the sum of 15 and Mabel's age.

Let m be the Mabel's age. Then,

[tex]15+m=60[/tex]

Therefore, the required equation for the given situation is [tex]15+m=60[/tex].

2.

The complete two column proof is:

        Steps                                            Reasons

[tex]-8(x+1)=-40[/tex]                                   Given equation

[tex]\dfrac{-8(x+1)}{-8}=\dfrac{-40}{-8}[/tex]                                  Division Property of Equality

[tex]x+1=5[/tex]                                               Simplifying

[tex]x+1-1=5-1[/tex]                                   Subtraction Property of Equality

[tex]x=4[/tex]                                                     Simplifying

====================================================

Explanation:

Plug in the lower bound of the domain, which is x = -3

f(x) = 3x+2

f(-3) = 3(-3)+2

f(-3) = -9+2

f(-3) = -7

If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.

If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.

The range of f(x) is -7 < y < 17

Recall that the domain and range swap places when going from the original function f(x) to the inverse [tex]f^{-1}(x)[/tex]

This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.

-----------------------

In short, we found the range of f(x) is -7 < y < 17.

That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.

The domain of the resulting function exists on all real values that is the domain is -∞ < f-1(x) < ∞

The domain of a function are the independent values of the function for Which it exists.

Given the function f(x) = 3x + 2

Find its inverse

y = 3x + 2

Replace x with y

x = 3y + 2

Make y the subject of the formula:

3y = x - 2
y = (x-2)/3

The domain of the resulting function exists on all real values that is the domain is -∞ < f-1(x) < ∞
Learn more on domain here: https://brainly.com/question/26098895

a) [tex]\log \left(\dfrac{A^3B}{C} \right) = 3\log A + \log B - \log C[/tex]

b) [tex]\log \left(\dfrac{\sqrt{A}}{B^2} \right) = \frac{1}{2}\log A - 2\log B[/tex]

Answer:

√53

Step-by-step explanation:

Distance between two points =  

√(4−6)^2+(−2−5)^2

√(−2)^2+(−7)^2  

= √4+49

=√53

= 7.2801

Hope this helps uwu

9514 1404 393

Answer:

  option 2: √53

Step-by-step explanation:

The distance formula is useful for this:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((4-6)² +(-2-5)²) = √((-2)² +(-7)²) = √(4+49)

  d = √53

The distance between the given points is √53.

Answer:

[tex]471\:\mathrm{ft}[/tex]

Step-by-step explanation:

In one full rotation around the roundabout, the car is travelling a distance equal to the circumference, or the perimeter, of the circle. The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2r\pi[/tex]. In the diagram, the diameter is labelled 150 feet. By definition, the radius of a circle is exactly half of the diameter of the circle. Therefore, the radius must be [tex]\frac{150}{2}=75[/tex] feet. Thus, the car would travel [tex]2\cdot 75\cdot \pi=471.238898038=\boxed{471\:\mathrm{ft}}[/tex]

Answer:

<W=180 - (30+81)

<W=69°

Using Sine rule to evaluate x

x/sin30 = 19/sin69

x= 19sin30/sin69

x= 10.2m ( Nearest tenth)

Answer:

7.  Not enough information to determine congruency

8.congreunt by AAS

Step-by-step explanation:

7.  We know one side and the vertical angles between the triangles.  That is not enough to determine the triangles are congruent

8.  We know one angle and one side are congruent.  The angle between are vertical angles and they are congruent.    We know two angles and one side, so they are congruent by AAS

Answer:

perimeter of the rectangular ground floor

=2(length+width)

length=X+200

width=X

=2(X+200+X)

=4x+400

4x+400 =780

4x =780-400

4x =380

x =95

width=95 feet

length=95+200

=295 feet

Answer:

a= 250

b= 50

250 + 50 = 300

Step-by-step explanation:

There's many solutions but this was the first one I could come up with.

Answer:

my opinion is seince a+b=300 then the sqaure of 300= 17.3?

Step-by-step explanation:

Answer:

84 sq meters

Step-by-step explanation:

First, divide the shape in 2 or more parts so that you can find it step by step

Divide this shape in three parts:

One part (blue): 2 m and 3 m rectangle

Second part (orange): 5 m and 12 m rectangle

Third part (red): 6 m and 3 m rectangle

(you can also see this below: in the pic there are three parts so you figure out that which is the correct value for the sides)

Now, find area of each shape by multiplying its values:

1st shape: 3 x 2 = 6

2nd shape: 5 x 12 = 60

3rd shape: 6 x 3 = 18

As you have the area of all the different shapes,

add all of them:

6 + 60 + 18 = 84 sq meters

I hope this helps :)

Answer:

hey. pls complete your question.

Answer:

45 is answer I guess cuz my teacher taught me just like that

Answer:

The 10th term is 50

Step-by-step explanation:

5(10) = 50

Answer:

D

Step-by-step explanation:

Hi there!

We're given the equation y=-75x-50, which represents a submarine DESCENDING towards the ocean floor, where y is the depth in feet, and x is the number of minutes the submarine is descending

Since the submarine is DESCENDING, we can immediately eliminate A and C, which talk about the submarine ASCENDING

That leaves B and D

Looking at the given equation, y=-75x-50, -75 is the slope, or rate of change, and -50 is the y intercept, or the "beginning" (where the equation will "start")

Therefore, the submarine will start at -50 feet, or 50 feet below sea level

As x is the number of minutes the submarine is descending, that means that if the submarine travels 1 minute, it will descend 75 feet (-75*1=-75), at 2 minutes, it'll descend 150 feet (-75*2=-150), and so on

So that means the submarine must be descending at a rate of 75 feet per minute

Therefore D is the correct answer

Hope this helps! Good luck on your assignment :)

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the image of the polygon is not given.

I will answer this question with the attached image (similar to your question)

The attached polygon is a trapezoid of the following dimensions.

[tex]Height = 4ft[/tex]

Parallel sides

[tex]Side\ 1 = 4ft[/tex]

[tex]Side\ 2 = 4ft+1ft = 5ft[/tex]

So, the area is:

[tex]Area = \frac{1}{2} * (Side\ 1 + Side\ 2) * Height[/tex]

[tex]Area = \frac{1}{2} * (4ft + 5ft) * 4ft[/tex]

[tex]Area = \frac{1}{2} * 9ft * 4ft[/tex]

[tex]Area = 18ft^2[/tex]

Answer:

B

Step-by-step explanation:

Have a nice day :)

Answer:

A; 120 cubic inches

Step-by-step explanation:

Let us start with the formula of the volume of a rectangular prism,[tex]V=l*w*h[/tex], where l represents the length of the prism, w represents the width of the prism, and h represents the height of the prism. It is given to us that h =5 inches, w =3 inches, and l =8 inches. Let's plug the values in:

[tex]V= 8*3*5\\V=120[/tex]

A. The volume of the rectangular prism is 120 cubic inches.

I hope this helps! Let me know if you have any questions :)

using sin∆ = 5/13

= 0.3846

therefore ∆ = 22.62

Answer:

1 1/6

Step-by-step explanation:

5/6 + 3/9

Simplify 3/9 by dividing the top and bottom by 3

5/6 + 1/3

Get a common denominator of 6

5/6 + 1/3 *2/2

5/6 + 2/6

7/6

Rewriting

6/6 +1/6

1 1/6

The circumcenter is the center of the circle that contains the vertices of a triangle

When a triangle is inscribed in a circle, the vertices of the triangle touch the circumference of the circle

A line drawn through the center of the circle and passes through each of the triangle vertex is its circumcenter.

Hence, the name of the required point is the circumcenter

Read more about circumcenter at:

https://brainly.com/question/14368399

#SPJ2

Answer:

B. The point of intersection of the perpendicular bisectors of the side

Step-by-step explanation:

definition of circumcenter as the previos question answered

Answer:

The maximum volume of the box is:

[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]

Step-by-step explanation:

Given

[tex]Surface\ Area = 10m^2[/tex]

Required

The maximum volume of the box

Let

[tex]a \to base\ dimension[/tex]

[tex]b \to height[/tex]

The surface area of the box is:

[tex]Surface\ Area = 2(a*a + a*b + a*b)[/tex]

[tex]Surface\ Area = 2(a^2 + ab + ab)[/tex]

[tex]Surface\ Area = 2(a^2 + 2ab)[/tex]

So, we have:

[tex]2(a^2 + 2ab) = 10[/tex]

Divide both sides by 2

[tex]a^2 + 2ab = 5[/tex]

Make b the subject

[tex]2ab = 5 -a^2[/tex]

[tex]b = \frac{5 -a^2}{2a}[/tex]

The volume of the box is:

[tex]V = a*a*b[/tex]

[tex]V = a^2b[/tex]

Substitute: [tex]b = \frac{5 -a^2}{2a}[/tex]

[tex]V = a^2*\frac{5 - a^2}{2a}[/tex]

[tex]V = a*\frac{5 - a^2}{2}[/tex]

[tex]V = \frac{5a - a^3}{2}[/tex]

Spit

[tex]V = \frac{5a}{2} - \frac{a^3}{2}[/tex]

Differentiate V with respect to a

[tex]V' = \frac{5}{2} -3 * \frac{a^2}{2}[/tex]

[tex]V' = \frac{5}{2} -\frac{3a^2}{2}[/tex]

Set [tex]V' =0[/tex] to calculate a

[tex]0 = \frac{5}{2} -\frac{3a^2}{2}[/tex]

Collect like terms

[tex]\frac{3a^2}{2} = \frac{5}{2}[/tex]

Multiply both sides by 2

[tex]3a^2= 5[/tex]

Solve for a

[tex]a^2= \frac{5}{3}[/tex]

[tex]a= \sqrt{\frac{5}{3}}[/tex]

Recall that:

[tex]b = \frac{5 -a^2}{2a}[/tex]

[tex]b = \frac{5 -(\sqrt{\frac{5}{3}})^2}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{5 -\frac{5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{\frac{15 - 5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{\frac{10}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{\frac{5}{3}}{\sqrt{\frac{5}{3}}}[/tex]

Apply law of indices

[tex]b = (\frac{5}{3})^{1 - \frac{1}{2}}[/tex]

[tex]b = (\frac{5}{3})^{\frac{1}{2}}[/tex]

[tex]b = \sqrt{\frac{5}{3}}[/tex]

So:

[tex]V = a^2b[/tex]

[tex]V =\sqrt{(\frac{5}{3})^2} * \sqrt{\frac{5}{3}}[/tex]

[tex]V =\frac{5}{3} * \sqrt{\frac{5}{3}}[/tex]

[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]

The maximum volume of the box which has a 10 m² surface area is given below.

[tex]\rm V_{max} = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

We want to construct a box with a square base and we currently only have 10 m² of material to use in the construction of the box.

The surface area = 10 m²

Let a be the base length and b be the height of the box.

Surface area = 2(a² + 2ab)

  2(a² + 2ab) = 10

      a² + 2ab = 5

Then the value of b will be

[tex]\rm b = \dfrac{5-a^2}{2a}[/tex]

The volume of the box is given as

V = a²b

Then we have

[tex]\rm V = \dfrac{5-a^2 }{2a}* a^2\\\\V = \dfrac{5a - a^3}{2}\\\\V = \dfrac{5a}{2} - \dfrac{a^3}{2}[/tex]

Differentiate the equation with respect to a, and put it equal to zero for the volume to be maximum.

[tex]\begin{aligned} \dfrac{dV}{da} &= \dfrac{d}{da} ( \dfrac{5a}{2} - \dfrac{a^3}{2} ) \\\\\dfrac{dV}{da} &= 0 \\\\\dfrac{5}{2} - \dfrac{3a^2 }{2} &= 0\\\\a &= \sqrt{\dfrac{5}{2}} \end{aligned}[/tex]

Then the value of b will be

[tex]b = \dfrac{5-\sqrt{\dfrac{5}{2}} }{2*\sqrt{\dfrac{5}{2}} }\\\\\\b = \sqrt{\dfrac{5}{2}}[/tex]

Then the volume will be

[tex]\rm V = (\sqrt{\dfrac{5}{2}} )^2*\sqrt{\dfrac{5}{2}} \\\\V = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]

More about the differentiation link is given below.

https://brainly.com/question/24062595

9514 1404 393

Answer:

  10

Step-by-step explanation:

Possible tower heights using 3 blocks are ...

  {9, 10, 11, 12, 14, 15, 16, 19, 20, 24}

There are 10 different heights possible.

_____

Each block can be used 1, 2, or 3 times.

Using a 3 in block as the smallest, we have ...

  3+3+3 = 9

  3+3+4 = 10

  3+3+8 = 14

  3+4+4 = 11

  3+4+8 = 15

  3+8+8 = 19

Using a 4-in block as the smallest, we have ...

  4+4+4 =12

  4+4+8 = 16

  4+8+8 = 20

And ...

  8+8+8 = 24

Since ABCD ~ QRST

AB/QR = AD/QT

=>6/m= 9/6

=> m = (6×6)/9 = 36/9 = 4

Answer:

m=4

Step-by-step explanation

since they are similar triangle .use these ratios

given:AB=6  , AD=9 , QR=m , QT=6

AB/QR=AD/QT

6/m=9/6

do cross multiplication

m*9=6*6

9m=36

m=36/9

m=4

therefore the value of m is 4