Find the value of x.

"If the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent."

The given statement true.

When two angles become congruent, their degree measures are the same. The reverse of something like the Isosceles Triangle Theorem asserts that the sides of a triangle opposing congruent angles are also congruent.

If two two triangles are congruent, then perhaps the sides opposite the congruent angles are equal, in accordance with the isosceles triangle theorem converse.

Mathematics is defined by theorems. A theorem is a proposition that has been proven true by a rigorous proof, which is a type of logical argument.

To know more about Triangle Theorem  visit:

https://brainly.com/question/16888071

#SPJ4

The height of the flagstaff by suing trigonometric ratios is found to be 27 m.

Given,

Height of the ladder, AD = 18 m

The distance to the point below the top of a vertical flagstaff where the ladder reaches, CD = 18m

Angle of elevation of flagstaff from the foot of the ladder, ∠ CAB = 60 °

Δ ACD is isosceles triangle.(Image is attached)

∠ ACB = ∠ CAD = 30 °

In △ ABD, by using the trigonometric ratios, we get that:

Sin 30 ° =  BD / AD

1 / 2 = BD / 18

BD = 9 m

So, the height of the flagstaff will be:

BC = BD + DC =9 + 18 = 27 m

Therefore, we get that, the height of the flagstaff by using trigonometric ratios is found to be 27 m.

Learn more about trigonometric ratios here:

https://brainly.com/question/24349828

#SPJ1

A proportion is an equation stating that two ratios are equivalent.

Ratio is defined as the comparison of two quantities. The ratio between quantities a and b can be expressed as a : b or a/b.

example:

There are 3 girls for every 5 boys in a class. Then, the ratio of girls to boys is 3 : 5 or 3/5.

On the other hand, proportion is defined as the equality between two or more ratios.

a : b = c : d

Two ratios are equivalent if their cross-products are equal. Cross products are the products of the extremes and means.

If a : b = c : d, then ad = bc.

example:

2 : 3 = 6 : 9 is proportion since 2(9) = 3(6) ⇒ 18 = 18

3 : 5 and 4 : 6 is not a proportion since 3(6) ≠ 5(4) ⇒ 18 ≠ 20

To learn more about proportion: https://brainly.com/question/1496357

#SPJ4

[tex]\angle g=112^{\circ}[/tex] (vertical angles)

[tex]\angle h=68^{\circ}[/tex] (linear pair)

[tex]\angle k=92^{\circ}[/tex] (vertical angles)

[tex]\angle m=88^{\circ}[/tex] (linear pair)

The two-column proof are:

The angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

In this question, we are given;

X as the midpoint of line segment WY and line segment VZ

Therefore, it is correct for us to conclude that;

segment XZ is congruent to segment XV, segment XW is congruent to segment XY

Thus, angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

We then conclude that;

VW = ZY

To find more on midpoint, look into; brainly.com/question/17450762

#SPJ4

Answer:

Reflect back on a time when you did something you later were at least somewhat uncomfortable with. Maybe it was something you said or did, but upon reflection you knew it wasn't the right thing to do. If you can't think of a real situation, you can create a hypothetical one.

[tex]\pink{ \rule{2pt}{99999pt}}[/tex]

The required amount of weed killer is 48.6 quarts.

To find the amount of weed killer required, first we will find the total acres of land of two fields.

So, total area of land is -

Area of land = [tex]22\frac{1}{2} + 38\frac{1}{4}[/tex]

Converting mixed fraction to fraction

Area of land = ((2×22)+1)÷2 + ((4×38)+1)÷4

Solving the bracket -

Area of land = 45÷2 + 153÷4

Area of land = 22.5 + 38.25

Area of land = 60.75 acres

Now, for 1 acre of land the required amount of weed killer = 0.8 quarts

So, for 60.75 acres of land the required amount of weed killer = 0.8×60.75

Performing multiplication to find the amount of weed killer

Amount of weed killer required = 48.6 quarts

Hence, the amount of weed killer required is 48.6 quarts.

Learn more about calculation of amount of weed killer -

https://brainly.com/question/15240643

https://brainly.com/question/4617938

https://brainly.com/question/24653665

#SPJ4

The complete question is -

Alan is putting weed killer on a field to get it ready for planting. The directions on the container say to use 4/5 of a quart for each acre of land. How much weed killer will Alan need for two fields, one that is 22 1/2 acres and one that is 38 1/4 acres?

The system of equations  to represent the cost c for h hours of court use at each campus; c = 25h and c = 20h + 3.3.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

WE have been given that we can choose between two tennis courts at two university campuses to learn how to play tennis.

The system of equations  to represent the cost c for h hours of court use at each campus;

The first campus charges 25 per hour.

c = 25h

Similarly The other campus charges 20 per hour plus a one-time registration fee of 10 .

c = 20h + 1/3(10)

c = 20h + 3.3

Therefore, the system of equations  to represent the cost c for h hours of court use at each campus; c = 25h and c = 20h + 3.3.

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ1

The probability of the event P(A is on [tex]\bar{CD}[/tex]) is 6/13.

Probability:

The term probability defines the possibility of the favorable event across the total event.

Given,

Point A is chosen at random on [tex]\bar{BE}[/tex].

Here we need to find the the probability of the following event.

P(A is on [tex]\bar{CD}[/tex]).

Let us consider the following image, in order to solve this.

Based on the image we have identified that the probability of the event  P(A is on [tex]\bar{CD}[/tex]) is calculated by dividing the length of CD by the length of BE.

So, the probability of the event P(A is on [tex]\bar{CD}[/tex]) is,

P(A is on [tex]\bar{CD}[/tex]) =  (length of CD) / (length of BE)

Apply the values then we get,

P(A is on [tex]\bar{CD}[/tex]) = 12 / ( 5 + 12 + 9)

P(A is on [tex]\bar{CD}[/tex]) = 12 / 26

And it can be simplified as,

P(A is on [tex]\bar{CD}[/tex]) = 6/13

Therefore, the probability of the event P(A is on [tex]\bar{CD}[/tex]) is 6/13.

To know more about Probability here.

https://brainly.com/question/11034287

#SPJ4

The expression which represents the function evaluation (f -g)(x) according to the task content is; (f -g)(x) = 2x³ +5x² -8x -4.

It follows from the task content that the required function evaluation required is; (f -g)(x).

Given;

f(x) = 2x³ +5x² - 6x - 7

g(x)=2x-3

To find;

(f-g)(x).

Since; (f -g)(x) = f(x) - g(x), the resulting expression for (f -g)(x) is;

(f -g)(x) = 2x³ +5x² -6x -7 -2x +3

Collect like terms;

(f -g)(x) = 2x³ +5x² -6x -2x -7 +3

Hence, (f -g)(x) = 2x³ +5x² -8x -4

Read more on functions;

https://brainly.com/question/2284360

#SPJ1

The height of the candle after burning for 2 hours is 16.25 inches.

Given that, a candle is 16 inches tall after burning for 3 hours. after 5 hours, it is 15.5 inches tall.

We need to write a linear equation to model the relationship between the height h of the candle and time t.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent of more than 1. The graph of a linear equation always forms a straight line.

Let t be the time in hours and h be the height in inches.

Now, the ordered pair of the given situation is A(3, 16) and B(5, 15.5).

Find the slope m of the linear equation between points A and B

We know that the formula to calculate the slope between two points is equal to m=(y2-y1)/(x2-x1)

=(15.5-16)/(5-3)=-0.5/2

=-1/4

We know that the equation of the line in the point-slope form is (y-y1)=m(x-x1)

⇒y-16=(-1/4)(x-3

⇒4y-64=-x+3

⇒4y=-x+3+64

⇒4y=-x+67

We need to find how tall the candle will be after burning for 2 hours.

That is, put x=2

4y=-2+67

⇒4y=65

⇒y=16.25 inches

Therefore, the height of the candle after burning for 2 hours is 16.25 inches.

To learn more about a linear equation visit:

https://brainly.com/question/13738061.

#SPJ1

O( 0,0 ) A(9 , 0 ) D( 0,3 ) ( 9, 2) , ( 6 , 3 ) that are vertices of the feasible region.

What do math vertices mean?

The line 2x + 6y = 30

when x = 9 , 18 + 6y = 30

                     y = 2

So B = ( 9, 2)

So, C= ( b , 3 )

then , we can show O( 0,0 ) A(9 , 0 ) D( 0,3 )

Learn more about vertices

brainly.com/question/27029296

#SPJ9

Answer:

x = 7

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate variable by doing the inverse operation which is in this case subtracting 9 on both sides of the equation.

3x + 9 = 30

- 9 - 9

3x = 21

2. Divide both sides of the equation by 3 since this is the inverse operation.

3x = 21

--- ---- <-------- fraction bar, divide

3 3

x = 7

Check:

3(7) + 9 = 30

21 + 9 = 30

30 = 30 ✓

Using vectors, and the relation between velocity and position, it is found that:

a) The speed is given by: v(t) = 2i - 5j.

b) The position vector p at time t hours is: p(t) = (2t  + 8)i + (-5t + 3)j.

c) The ship is due north of the lighthouse at a time of 6 seconds.

d) The ship is 23 miles from the lighthouse at this point.

The position function is the integral of the velocity function.

As stated in the problem, the velocity is constant, hence:

The speed is given by: v(t) = 2i - 5j.

The position is the integral of the velocity, hence, integrating each component.

[tex]p(t) = \int v(t) dt[/tex]

[tex]p(t) = \int (2i - 5j) dt[/tex]

p(t) = (2t + k1)i + (-5t + k2)j.

Considering the initial position, we have that:

k1 = 8, k2 = 3.

Hence:

The position vector p at time t hours is: p(t) = (2t  + 8)i + (-5t + 3)j.

The ship is due north of the lighthouse(20i - 50j) when it has the same x-coordinate, hence:

2t + 8 = 20

2t = 12

t = 6.

Hence:

The ship is due north of the lighthouse at a time of 6 seconds.

The position of the ship at t = 6 seconds is:

(2(6) + 8)i + (-5(6) + 3)j = 20i -27j.

The distance is given by:

|-50 - (-27)| = |-23| = 23.

The ship is 23 miles from the lighthouse at this point.

More can be learned about vectors, velocity and position at https://brainly.com/question/15090827

#SPJ1

The equation of the line passing throigh the given points is given by y = x/7 + 3.

The slope of a line indicates its steepness and direction.

The slope of a line can be calculated using any two distinct points on it. The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.

Given: Point (28,7)

An equation of perpendicular line y = -7x.

We know if fwo lines are perpendicular then their slopes are negative inverse of each other.

i.e., [tex]m_{1} = \frac{1}{m_{2} }[/tex]

Therefore, y = -7x

Slope, [tex]m_{1}[/tex] = - 7x

Slope of other line will by be  [tex]$\frac{1}{m_1}$[/tex].

[tex]$$m_2=\frac{+1}{7}$$[/tex]

Slope of required equation = 1/7

Substitute [tex]\left(x_1, y_1\right)[/tex] = (28,7), m=1/7 in

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

(y -7) = 1/7 (x - 28)

(y - 7) = x/7 - 4

y = x/7 + 3

This is the required equation of line.

To know more about slope of a line visit:
https://brainly.com/question/2491620

#SPJ9

Answer:

Hello,

Step-by-step explanation:

P(x)=x^3-5x^2-7x+51

Since the coefficients are all reals,

4+i (conjugate of 4-i) is also a root.

The polynomial est divisible by (x-4-i)(x-4+i)=(x-4)²+1=x²-8x+17

If we divide P(x) by x²-8x+17 we find the quotient (x+3) and the remainder 0

P(x)=(x+4)(x-4-i(x-4+i)

Roots are -4,4+i and 4-i

Answer:

All the roots are -3, 4-i and 4+i.

Step-by-step explanation:

If oine root is 4 - i then another one is 4 + i as complex roots occur as conjugate pairs.

(4 - i)(4 + i)

= 16 - i^2

= 17.

As the last term = 51 = 3 * 17

looks like the other root is 3 or -3.

By the Factor theorem

If x = 3 then f(3) = 0

f(3) = 27 - 5(3)^2 - 7(3) + 51

     = 27 - 45 - 21 + 51 = 12 so 3 is not a root.

If x = -3:

f(-3) = -27 - 45 _ 21 + 51

      = 0

So,  x = -3 is a root.

Answer:

:D

Step-by-step explanation:

1.) One ticket out of eighty can be represented by a fractions, 1/80. To find the percentage, you can change 80 to 100 proportionally and then the difference (multiply/divide) to the 1 to find the percentage. You can also cross multiply to find the answer ("a")

[tex]\frac{1}{80} =\frac{x}{100}[/tex]

0.0125 is the chance of getting the ticket, and multiply by 100 to get percentage.

a = 1.25%

2.)
Same thing as #1, different equation :)

[tex]\frac{5}{80} =\frac{x}{100}[/tex]

x = 6.25%

3.)
Same thing as #2, but now, on the bottom is not 80, but instead 70.

[tex]\frac{5}{70} =\frac{m}{100}[/tex]

m = 7.14285714286%

m = 7.14%

Answer:

12a) 1/80=0.0125 = 1.25%

12b) 5/80=0.0625 = 6.25%

12c) 5/70=0.07142 = 7.14%

Step-by-step explanation:

Answer:

No 1.  3/31

No 2. 3/8

No3. 3/16

Step-by-step explanation:

you mainly just turn it into an improper fraction and then turn it upside down

Brainiest, please :) tysm

Answer:

a) 3/31

b) 3/8

c) 3/16

Step-by-step explanation:

You take the mixed number, turn it into an improper fraction (to do that, you multiply the whole number with the denominator on the fraction, and then you take that number and add it to the numerator of the fraction), and then you flip that improper fraction.

Answer:

x=2

angle 1= 27°

angle 2= 27°

Step-by-step explanation:

(x+6) =( 3x -36)

2x=42

x=21

In the account of Rodney's will have the higher ending balance after 1 year.

Given that:

Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly.

Gerald invests half that amount into an account that pays twice Rodney’s interest rate.

To find:

Which of the accounts will have the higher ending balance after 1 year?

So, according the question

We have,

For Rodney,

p = Principle = P

r = Interest rate = r

t = time expressed in year = 1 year

n = Number of periods in a year = 1

We, know that the formula to calculate the compound interest for new balance of Rodney ,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]

Now, putting the values,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]    

    B = [tex]P(1+\frac{r}{1} )^{1\times 1)[/tex]

    B = [tex]P (1 + r )[/tex]  

    B = P + Pr

Now, For Gerald,

p = Principle = P/2 ( Invest half of the money from Rodney )

r = Interest rate = 2r ( Twice the rate of Rodney's)

t = time expressed in year = 1 year

n = Number of periods in a year = 1

We know that the formula to calculate the compound interest for new balance of Gerald ,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]

Now, putting the values,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]    

    B = [tex]\frac{P}{2} (1+\frac{2r}{1} )^{1\times 1)[/tex]

    B = [tex]\frac{P}{2} (1+ 2r)[/tex]  

    B = [tex]\frac{P}{2}[/tex] + Pr

Now compare the amounts of their accounts, so we can say that the amount of Rodney's account will have the higher ending balance after 1 year.

So, In the account of Rodney's will have the higher ending balance after 1 year.

To learn more about compound interest, please click on the link;

https://brainly.com/question/14295570

#SPJ1

Answer:

2x²+10x+8

Step-by-step explanation:

you have to multiply the brackets first the multiply the 2 in

2(x+1)(x+4)

2(x²+4x+x+4)

2(x²+5x+4)

2x²+10x+8

Trent writes 10×6=60, then in multiplication equation 10 represents the quantity of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.

According to the statement

We have to find that the multiplication equation.

So, For this purpose, we know that the

The linear equation is defined as an equation that is written in the form of Ax+By=C.

From the given information:

Given,

Trent writes 10×6=60,

Here,

10 represents the quantity of muffin boxes

And

6 represents the numbers of muffins in each box

Then

60 represents the overall numbers of muffins

Hence, Trent writes 10×6=60, then within the multiplication equation 10 represents the amount of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.

Learn more about multiplication equation here

https://brainly.com/question/23724600

#SPJ1

Answer:

Hello,

Step-by-step explanation:

In the triangle ABG, using  law of sin

[tex]\dfrac{sin(121^o)}{7} =\dfrac{sin(41^o)}{AG} =\dfrac{sin(18^o)}{BG} \\\\AG=\dfrac{sin(41^o)*7}{sin(121^o)} =5.358(km)\\\\BG=\dfrac{sin(18^o)*7}{sin(121^o)} =2.526(km)\\\\CG=5+BG=7.526(km)\\\\GD=CG*sin(31^o)=3.875(km)\\\\AD=AG+GD=9.233(km)\\\\CD=CG*cos(31^o)=6.451(km)\\\\AC=\sqrt{AD^2+CD^2} =11.263(km)\\[/tex]

The translation vector will be as follows:

(x, y) → (x - 3, y + 5)

Regina travelled 3 blocks west and 5 blocks north.

The interpretation vector is the distance through which a particle should be moved (made an interpretation of) to be in the following unit cell. The image for an interpretation vector is television. The television ought to be indicated toward the finish of the math.

The distance that an atom must travel in order to transfer to the following unit cell is known as the translation vector. A translation vector is denoted by the letter Tv. At the conclusion of the geometry, the Tv should be provided. Real or fake atoms shouldn't follow a Tv, but symmetry information and other things are acceptable.

Let us consider the direction similar to map where north is positive y-axis , east is positive x-axis , west is negative x-axis and south is negative y-axis.

Therefore the translation vector will be as follows:

(x, y) → (x - 3, y + 5)

To learn more about translation vector refer to:

https://brainly.com/question/23158623

#SPJ4

Answer:

(a): 26.1

(b): 27.9

Please see below for the steps.

Step-by-step explanation:

(a):

Use points (0,0) and (3, 78.3)

Use slope formula. The slope formula is also used to find average rate of change (just so you know).

y2-y1/x2-x1

78.3-0/3-0=78.3/3=26.1

Answer for (a) is 26.1

(b):

Use points (4, 147.6) and (9, 287.1)

Use slope formula.

y2-y1/x2-x1

287.1-147.6/9-4=139.5/5=27.9

The answer for (b) is 27.9

Hope this helps!

Please mark as brainliest if correct!

Have a great day!

Answer: 18 Days

Step-by-step explanation: 30x18=540

Answer:

Proportion says that two ratios (or fractions) are equal.

La proporción dice que dos razones (o fracciones) son iguales.

( translated )

Answer:

-9/7

Step-by-step explanation:

Distribute

2x + 8 = -5x - 1

Get variables on left; constants on right

2x + 5x = -1 -8

Gather like terms and do the math

7x = -9

x = -9/7

By elimination, the solution of the system of equations, 5x - 2y = -19 and 2x + 3y = 0, is (-3 , 2).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 3 and the second equation by 2.

5x - 2y = -19 ⇒ 15x - 6y = -57     (equation 1)

2x + 3y = 0 ⇒ 4x + 6y = 0     (equation 2)

Adding the two equations will eliminate the variable y.

15x - 6y = -57     (equation 1)

4x + 6y = 0     (equation 2)

19x        = -57

x = -3

Substitute the value of x to any of the two equation and solve for y.

2x + 3y = 0     (equation 2)

2(-3) + 3y = 0

3y = 6

y = 2

Hence, the solution of the system of equations is (-3 , 2).

Learn more about solving systems of equations by elimination here: brainly.com/question/28405823

#SPJ4