To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that

Answer:

Gradient (slope) is 5.

Step-by-step explanation:

To find the gradient (slope) of a curve graph at x = x₁ can be done by steps following:

First, derive the given function which is:

[tex]\displaystyle{y = (\sqrt{x}+3)(3\sqrt{x}-5)[/tex]

Differentiation can be done two ways - go ahead and expand the expression then derive it or you can use the product rule where it states that [tex]\displaystyle{y'=u'v+uv'}[/tex]

I'll be using product rule:

[tex]\displaystyle{y' = (\sqrt{x}+3)'(3\sqrt{x}-5)+(\sqrt{x}+3)(3\sqrt{x}-5)'}[/tex]

Note that the following process will require you to have knowledge of Power Rules:

[tex]\displaystyle{y = ax^n \to y' = nax^{n-1}}[/tex]

Hence:

[tex]\displaystyle{y'=\dfrac{1}{2\sqrt{x}}(3\sqrt{x}-5) + (\sqrt{x}+3)\dfrac{3}{2\sqrt{x}}[/tex]

Now we know the derivative. Next, we find the slope at x = 1 which you substitute x = 1 in derived function:

[tex]\displaystyle{y'(1)=\dfrac{1}{2\sqrt{1}}(3\sqrt{1}-5) + (\sqrt{1}+3)\dfrac{3}{2\sqrt{1}}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(3-5) + (1+3)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(-2) + (4)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=-1 + 2(3)}\\\\\displaystyle{y'(1)=-1 + 6}\\\\\displaystyle{y'(1)=5}[/tex]

Finally, we have found the slope or gradient at x = 1 which is 5.

Please let me know if you have any questions!

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

and the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides opposite of their associated angles (A, B, C).

1)

17/sin(26) = 12/sin(C)

sin(C) = 12×sin(26)/17 = 0.309438457...

C = 18.02539254...° ≈ 18°

3)

180 = 27 + 115 + C

C = 38°

19/sin(38) = AC/sin(27)

AC = 19×sin(27)/sin(38) = 14.01065332... in ≈ 14 in

In first triangle side angle m∠C is 18° and in first triangle side AC is 14 in. This can be obtained by using the law of sine.

We know the law of sine which is,

If in a triangle, Δ ABC,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex], where a is the side opposite to the angle m∠A, b is the side opposite to the angle m∠B and c is the side opposite to the angle m∠C.

sine of the angle scan be found using calculator.

From the question,

1) In first triangle side,

AB = 12ft, BC = 17 ft and m∠A=26°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 26°/17 = sin B/AC = sin C/12

sin 26°/17 = sin C/12

12×sin 26° = 17×sin C

sin C = 5.26/17 = 0.3091

C = 18.023° ≈ 18°

3) In second triangle side,

m∠B = 27°, AB = 19 in and m∠A = 115°

m∠A + m∠B +m∠C = 180°

115° + 27° + m∠C = 180°

142° + m∠C = 180°

m∠C = 38°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 115°/BC = sin 27°/AC = sin 38°/19

sin 27°/AC = sin 38°/19

sin 27° × 19 = sin 38° × AC

8.63 = 0.62 × AC

AC = 13.91 in ≈ 14 in.

Hence in first triangle side angle m∠C is 18° and in first triangle side AC is 14 in.

Learn more about law of sine here:

brainly.com/question/17289163

#SPJ1

Proportionately, the total jelly beans in the world will be 115,703,826.

A proportion refers to a fraction of a whole.

A proportion is a ratio or a number relationship between two or more values or variables.

The proportion of a whole value can be represented as a fraction, decimal, or percent.

Red jelly beans in the world = 1/3

And 1/3 = 38,567,942

1/1 = 115,703,826 (38,567,942/1/3)

Thus, if 1/3 of the jelly beans in the world is 38,567,942, then the whole jelly beans will be 115,703,826.

Thus, proportionately, the total jelly beans in the world will be 115,703,826 because 1/3 of 115,703,826 is 38,567,942.

Learn more about proportions at https://brainly.com/question/1496357

#SPj1

The total number of 5 digit palindrome that we have is 900.

This is the term that is used to refer to a number or a word phrase that is the same way when it is written from the front and from the back.

Examples of palindrome numbers are

Read more on palindrome here:

https://brainly.com/question/14076732

#SPJ1

The ordered pairs of Nicole and Ian's sequence pattern are:(5,1),(17,3),(53,5),(161,10),(485,20).

Given that Nicole uses the  rule multiply by 3 then add 2 starting with it and Ian uses the rule add 1/2 then multiply by 2 starting from 0,

We ar rquired to find the ordered pairs of Nicole's and Ian's rules.

We are told that Nicole's pattern is multiply by 3 then add 2 starting with 1.

Thus Nicole's pattern is :5,17,53,161,485.

Ian's pattern is add 1/2 then multiply by 2 and starting with 0.Thus the  numbers are :1,3,5,10,20.

If we combine the numbers of both the person'rule then we will get the ordered pairs which can be written as under:

The ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).

Hence the ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).

Learn more about pattern at https://brainly.com/question/17386984

#SPJ1

Answer:

  8.  yes; 18

  9.  no

  10.  no

  11.  yes; -9

Step-by-step explanation:

The equation for inverse variation is y = k/x. The constant k will be the product of x and y: k = xy.

Products are (-3)(-6) = (2)(9) = (4.5)(4) = 18.

Inverse variation with k = 18.

Products are ...

  (5)(4) ≠ (10)(8).

Not inverse variation.

Products are ...

  (2)(25) ≠ (2.5)(16).

Not inverse variation.

Products are (3)(-3) = (9)(-1) = (12)(-.75) = -9.

Inverse variation with k = -9.

There are 20 $5 bills and 10 $2 coins.

He bought a radio for $120. He paid for it with 2 coins and $5 bills.

let

the number of $5 bills = x

the number of $2 coins = y

Therefore,

y = 1 / 2 x

2y + 5x = 120

2(1  /2 x) + 5x = 120

x + 5x = 120

6x = 120

x = 120 / 6

x = 20

y = 1 / 2 × 20

y = 10

Therefore, there are 20 $5 bills and 10 $2 coins.

learn more on equation here: https://brainly.com/question/2360540

#SPJ1

Step-by-step explanation:

is there something missing in the question ?

or is this meant to be a trick question ?

let me repeat :

pot1 contains 5 black and 7 white beads

pot2 contains 6 white beads (and nothing else, right ?)

then one bead is drawn from each pot.

so, 1 bead from pot1, and 1 bead from pot2.

the bead from pot1 is either white or black.

the bead from pot2 is white for sure.

so, the probability to get at least 1 white bead is 100% or 1, as there will be always the white bead taken from pot2.

Answer:

  (c)  (28/3)√6

Step-by-step explanation:

Side ratios of "special triangles" are used to solve this problem.

  30-60-90° triangle — 1 : √3 : 2

  45-45-90° triangle — 1 : 1 : √2

We need to apply these ratios a few times:

  CD : CE = √3 : 2   ⇒   CE = (7√3)(2/√3) = 14

  CE : BE = 1 : √2   ⇒   BE = 14(√2) = 14√2

  BE : AE = √3 : 2   ⇒   AE = (14√2)(2/√3) = (28√2)/√3

The fraction can be simplified by multiplying by (√3)/(√3):

  ((28√2)/√3)×(√3)/(√3) = (28√6)/3

  AE = (28/3)√6

Answer:

24 combinations

Step-by-step explanation:

To get to this answer, I multiplied 6 x 4, since there are 6 shirts and 4 pairs of jeans, there will be a total of 24 combinations. For combinations of two different things, you can just multiply the amount of each item by the other item. hope this helps :)

Answer: K

Step-by-step explanation:

I. Correct. When t=0, h=c, so if you alter the value of c, the h-intercept changes.

II. Correct, the maximum value of [tex]-at^2 +bt[/tex] will stay the same, but you are changing c, which is the amount you are always adding to it, meaning the maximum will change.

III. Correct. If you plug into the quadratic formula setting h=0, it is easy to see changing the value of c will change the solutions.

The correct statement regarding the quadratic function is:

K. I, II and III.

A quadratic function is given according to the following rule:

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

If a > 0, it has a maximum value, and if a < 0, it has a minimum value.

The extreme value is [tex](x_v,y_v)[/tex], in which:

The solutions are:

In this problem, we have a function h(t). Changing the coefficient c, the h-intercept h(0) changes. Looking at the formulas in the bullet point, the value of [tex]\Delta[/tex] changes, meaning that both the maximum value [tex]y_v[/tex] and the t-intercepts [tex]t_1[/tex] and [tex]t_2[/tex] will change, so option K is correct.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

Depending on the number of teams, the possible numbers of students per team are in the set:

{2, 3, 4, 6, 9, 12, 18}

We know that there are 36 students divided equally into N teams.

Such that the number of teams is larger than 1 and smaller than 20.

Then we could have 2 teams, such that the number of students in each team is given by the quotient between the total number of students and the number of teams.

36/2 = 18

There are 18 students in each team.

Notice that the numbers of teams can only be factors of 36, where:

36 = 6*6 = 2*2*3*3

So the factors are:

2, 3, 2*3, 3*3, etc...

If there are 3 teams we have:

36/3 = 12 students per team.

If there are 6 teams we have:

36/6 = 6 students per team.

if there are 9 teams:

36/9 = 4 students per team.

If there are 12 teams:

36/12 = 3 students per team.

If there are 18 teams:

36/18 = 2 students per team.

These are all the possibilities.

If you want to learn more about factors:

https://brainly.com/question/219464

#SPJ1

The entrance fee is proportional to the number of visitors at A)museum a.

In arithmetic, two sequences of numbers, often experimental statistics, are proportional or at once proportional if their corresponding factors have a regular ratio, that's called the coefficient of proportionality or proportionality consistent.

The definition of proportional is something that has an incredibly correct dating of length or that is appropriate. An example of something proportional is a woman's tiny toes to her quick stature. An instance of something proportional is the quantity of pay a worker receives for the hours that they installed.

While something is proportional to something else, it does no longer suggest the values are equal, simply that they trade with admiration for each other. The regular of proportionality serves as a multiplier.

Learn more about proportionality here: https://brainly.com/question/1496357

#SPJ4

Answer:

Museum C

Step-by-step explanation:

If you divide them all (like 3/4) you get .75

-8.(2a - 1) = 36

-16a + 8 = 36

-16a = 36 - 8 = 28

a = 28/(-16) = -7/4

The correct answer is -7/4 = -1.75

The solution to the given equation is [tex]\frac{-7}{4}[/tex].

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.

We have,

Expression -8(2a - 1) = 36

So,

Now,

To get the solution to this expression,

i.e.

-8(2a - 1) = 36

Rewrite it as,

i.e.

Opening Brackets,

We get,

-16a + 8 = 36

Now,

Taking variable terms on one side and other terms on another side,

We get,

-16a = 36 - 8

On solving we get,

-16a = 28

i.e.

a = [tex]\frac{-28}{16} = \frac{-7}{4}[/tex]

So,

The solution to the given equation is [tex]\frac{-7}{4}[/tex].

Hence, we can say that the solution to the given equation is [tex]\frac{-7}{4}[/tex].

To know more about expression click here

https://brainly.com/question/953809

#SPJ2

Answer:

f-¹(x) = (x + 6)/2

Step-by-step explanation:

Replace f(x) with y.

y = 2x – 6

Interchange x and y.

x = 2y – 6

Solve for y.

y = (x + 6)/2

Replace y with  f-¹(x)

f-¹(x) = (x + 6)/2

The sum of the angles, a, b and c is; 360° because, the sum measures 3 of all the equal angles in the regular hexagon.

It follows from the task content that the angle measures given in the task are a, b and c which are in a cyclic polygon (hexagon) in which case, the sum of all 6 angles in the hexagon is; 720.

Consequently, the sum of angle measures; a,b and c is; 720/2 = 360°.

Read more on hexagon;

https://brainly.com/question/10209400

#SPJ1

The probability that any given car will have a brake failure if it is make a is 0.0065%

The complete question is added as an attachment

From the table in the question, we have:

P(Brake failure|car a) = 0.0065%

The above represents the required conditional probability

Hence, the probability that any given car will have a brake failure if it is make a is 0.0065%

Read more about probability at:

https://brainly.com/question/2479210

#SPJ1

Answer: The probability that any given car will have a brake failure if it is making A, is 0.0065%.

Step-by-step explanation:

I got it right on Edmentum!

The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

Learn more about price on:

brainly.com/question/1153322

#SPJ1

Answer:

B

Step-by-step explanation:

Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.

This is equal to c(d+b), so:

(1/2)(c)(2d+a+b)=c(d+b)

(1/2)(2d+a+b)=d+b

d+0.5a+0.5b=d+b

0.5a+0.5b=b

0.5a=0.5b

a=b

Since the jet bomber arrived over its Target at the same time as its fighter jet escorted, it took the jet bomber 0.34 h to reach the target.

To find the number of hours, we need to solve simultaneous equations.

Simultaneous equations are pair of equations which contain two unknowns.

Let

So, D = vt

D = 500t  (1)

Also, D = VT

D = 60T  (2)

Since  jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off.

T = t + 2.5

So, D = 60(t + 2.5)  (3)

D = 500t  (1)

D = 60(t + 2.5)  (3)

Equating equations (1) and (3), we have

500t = 60(t + 2.5)

500t = 60t + 150

500t - 60t = 150

440t = 150

t = 150/440

t = 15/44

t = 0.34 h

So, it took the jet bomber 0.34 hours to reach the target.

Learn more about simultaneous equations here:

https://brainly.com/question/27829171

#SPJ1

Answer: the maximum is (-2,5 )and the equation for the axis of symmetry is  x = -2

Explanation if you want:

for the min and max:  when a quadratic has a maximum point, that is the largest point that it will ever be at.  When it has a minimum, that is the smallest.

for the axis of symmetry: basically, this is the line that splits the graph into two equal parts.

there u go

Answer:

4 square feet

Step-by-step explanation:

Answer: 7(8x + 6) = -1: Exact form: x = -43/56, decimal form: x = -0.76785714

Thats all i have because you can't solve for x for the second one!

Answer:

Given:

mu = 200 lb, the mean sigma = 25 the standard deviation

For the random variable x = 250 lb, the

z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2

From standard tables for the normal distribution, obtain

P(x < 250) = 0.977

Answer: 0.977

Answer:

900

Step-by-step explanation: