How to solve it and explain it

OPTION C is the correct answer.

The ΔAFE ≅ ΔBHG  by the angle, side and angle theorem are congruent. Option (A) is correct.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

The figure shows models of a roof truss. Based on the markings, there is enough information to prove that

ΔAFE ≅ ΔBHG

∠EFA=∠GHB  (90 degrees )

EF = GH  (equal side)

EAF = GBH (the side opposite to the angle is equal)

ΔAFE ≅ ΔBHG  (ASA )

Thus, ΔAFE ≅ ΔBHG  by the angle, side and angle theorem are congruent.

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Answer:

Hereeeeeeeeeeeeeeeee

Answer:

-9

Step-by-step explanation:

Since the threes are in parenthesis, you multiply them first then apply the negative sign.

I hope this helps!

Answer:

-9

Step-by-step explanation:

Multiplying 3 by -3 will get you -9. You know it's negative because only one number is negative and 3*3=9.

Step-by-step explanation:

Area of a square = s x s

(4x-7)x(4x-7)

Open brackets

4x(4x-7)-7(4x-7)

16x^2-28-28x+49

16x^2-28x+21

9514 1404 393

Answer:

  $4000

Step-by-step explanation:

The problem tells you the relation between commission (c) and stock value (v) is ...

  c = 10 + 0.025v . . . . $10 + .025 of the value traded

We want to find the value (v) for the given commission (c=110). We can put these numbers into the formula and solve for v:

  110 = 10 + 0.025v

  100 = 0.025v . . . . . . . subtract 10

  100/0.025 = v = 4000 . . . . divide by the coefficient of v

The value of stock traded was $4000.

_____

Additional comment

As always, you start by reading and comprehending the problem. You look for what is being asked for, what is being given, and any information that relates one to the other.

Here, the value of stock traded is asked for, the amount of commission is given, and a description of the relation of one to the other is provided. Translate that description to an equation, fill in the given value, and solve for the unknown. (That's what we did above.)

__

You can also work this in your head. The commission is $10 more than some fraction of the amount traded. Since the commission is $110, only $100 of that is the fraction of the amount traded. With a little experience, you can recognize the fraction 0.025 as being 1/40. That means $100 is 1/40 of the value traded, or the value traded is 40 × $100 = $4000.

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

[tex]h(t)=-16t^2+104t+56[/tex]

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

[tex]\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}[/tex]

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

[tex]\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}[/tex]

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

[tex]0=-16t^2+104t+56[/tex]

We can simplify a bit. Divide both sides by -8:

[tex]0=2t^2-13t-7[/tex]

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

[tex]\displaystyle 0=2t^2-14t+t-7[/tex]

Factor out a 2t from the first two terms and group the last two terms:

[tex]0=2t(t-7)+(t-7)[/tex]

Factor by grouping:

[tex]0=(2t+1)(t-7)[/tex]

Zero Product Property:

[tex]2t+1=0\text{ or } t-7=0[/tex]

Solve for each case:

[tex]\displaystyle t=-0.5\text{ or } t=7[/tex]

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

Answer:

40

Step-by-step explanation:

10/x = 25/100

Cross multiply 10 and 100 = 1000.

Then, divide 1000 by 25 = 40.

10/40 = 0.25 = 25%

Answer:

A = (2, 2)

B = (3, -1)

C = (-1, 0)

Step-by-step explanation:

To translate a point, you have to translate each individual point. At the bottom it shows <-2,3>, therefore you have to translate x 2 units to the left (because it's negative meaning the number is going away from 0, and 3 units to the right because 3 is a positive number.)

First Point A:

x: 4 - 2 = 2; y: -1 + 3 = 2

Second Point B:

x: 5 - 2 = 3; y: -4 + 3 = -1

Lastly, Point C:

x: 1 - 2 = -1, y: -3 + 3 = 0

I hope this helps!

Answer:

yeah u forgot to add the picture ig

Answer:

see image

Step-by-step explanation:

Answer: There are 16 Capulets and 6 Montaques.

Step-by-step explanation:Other choices were either less than or greater than 200 multiplied by each other. If we do 16x8 which is 128 for the Capulets. Also, if we do 12x6 which is 72 for the Montaques. 128+72=200 essays in total

Answer:

36 introverts

Step-by-step explanation:

Total number of adults in the survey = 120

Ratio of introverts to extroverts = 3:7

Number of introverts = ratio number of introverts / ratio total × 120

Ratio number of introverts = 3

Ratio total = 3 + 7 = 10

Number of introverts = 3/10 × 120

= 36

Answer:

X<-2551.5

Step-by-step explanation:

-2x<5112-9

-2x/-2<5103/-2

x<-2551.5

Answer:

For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.

For the proportion of smokers, mean = 0.167, standard deviation = 0.068

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.

This means that [tex]p = 0.184, n = 38[/tex]

What are the mean and standard deviation for the sampling distribution of p^?

Mean:

[tex]\mu = p = 0.184[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063[/tex]

Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.

This means that [tex]n = 30, p = 0.167[/tex]

What is the mean and the standard deviation of the sampling distribution of p^ ?

Mean:

[tex]\mu = p = 0.167[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068[/tex]

Answer:

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]P(1) = 2[/tex]

Required

The solution

We have:

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]

Split

[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]

Divide both sides by [tex]P^\frac{1}{2}[/tex]

[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]

Multiply both sides by dt

[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]

Integrate

[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Rewrite as:

[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the left hand side

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the right hand side

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)

To solve for c, we first make c the subject

[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]

[tex]P(1) = 2[/tex] means

[tex]t = 1; P =2[/tex]

So:

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]

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

So, we have:

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]

Divide through by 2

[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]

Square both sides

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Step-by-step explanation:

1) = Solution

(3x+2)(x-1) = 3x^2 - 3x+2x-2

= 3x^2 - x - 2

2) = (x-5)(2x+3)

= 2x^2 + 3x - 10x - 15

= 2x^2 - 7x - 15

3) = (2x+5)(3x-2)

= 6x^2 - 4x + 15x - 10

= 6x^2 + 11x - 10

i)50

Steps

30+20=50

ii)7

Steps

75-(30+20)-18

=75-(50)-18

=7

iii)20

Steps

From the available data from the question

iv)30

Steps

From the available data from the questionl

v)From the attcged image file

Answer:

5670272728262728227627

Answer:

Box dimensions:

x =  3.42 cm

y = 6.84 cm

C(min) = 14.04 $

Step-by-step explanation:

We need the surface area of the cube:

S(c)  =  2*S₁ ( surface area of top or base) +  4*S₂ ( surface lateral area)

S₁  = x²        2*S₁  = 2*x²

Surface lateral area is:

4*S₂  =  4*x*h                          V(c) =  80 cm³  =  x²*h          h  =  80/x²

4*S₂  = 4*80/x

4*S₂  = 320 / x

Costs

C (x)  =  0.2* 2*x²   +  0.1 * 320/x

Taking derivatives on both sides of the equation we get:

C´(x)  =    0.8*x   -  32/x²

C´(x)  =  0            0.8*x - 32/x²  = 0

0.8*x³  -  32  =  0            x³  =  32/0.8

x³  =  40  

x =  3.42 cm

h =  80/(3.42)²          h  = 6.84 cm

To find out if x = 3.42 brings a minimum value for C we go to the second derivative

C´´(x) =  64/x³       is always positive for  x > 0  

The C(min) = 0.4*(3.42)²  +  32/(3.42)

C(min)  =  4.68 +  9.36

C(min)  = 14.04 $

Answer:

300

Step-by-step explanation:

[tex] \frac{1.5}{100} = 20000 \\ 20000 \div 100 = 200 \\ 200 \times 1.5 = 300[/tex]

if A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression then 300 people clicked on the banner ad

percentage, a relative value indicating hundredth parts of any quantity.

A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression.

We need to find how many people clicked on the banner ad.

Let us find the value of  1.5%  of 20000

Convert 1.5 % to decimal

1.5/100=0.015

Now multiply 0.015 with 20000

0.015×20000

300

Hence, if A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression then 300 people clicked on the banner ad

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Answer:

C

Step-by-step explanation:

In ∆DEG, we are given that all the three angles are congruent.

This means that all the three angles have equal measure. Thus,

<D = <E = <F

An equilateral triangle has equal angle measure. ∆DEF is an equilateral triangle.

Since the sum of a triangle is 180°, therefore, each angle in ∆DEF = 60°

m<D = 60°

Answer:

f(n+1=-2f(n)

f(x)=-2f(n)

f(4)

f(4)=-2f(4)

Answer:

f(4) = - 1280

Step-by-step explanation:

Using the recursive rule and f(1) = 60 , then

f(2) = - 2f(1) = - 2 × 160 = - 320

f(3) = - 2f(2) = - 2 × - 320 = 640

f(4) = - 2f(3) = - 2 × 640 = - 1280

Step-by-step explanation:

It is Associative property, I have seen this somewhere

9514 1404 393

Answer:

  -∞ < y ≤ 12

Step-by-step explanation:

The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...

  -∞ < y ≤ 12

Answer:

(-2,3,10,8)

Step-by-step explanation:

eg

(x,y)=(domain,range)

x components are domain and y components are range in the given set of ordered pairs

Answer:

See attachment for graph

The height of the arch is: 120 m

The width to the nearest meter, at the base of the arch is 22 m

Step-by-step explanation:

Given

[tex]h = -0.06d^2 + 120[/tex]

Solving (a): The graph

See attachment for graph

Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.

Solving (b): The height

The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,

Hence:

[tex]height = 120[/tex]

Solving (c): The width

The curve touches the horizontal axis at two different points.

[tex]x_1 = -11[/tex]

[tex]x_2 = 11[/tex]

The absolute difference of both points represents the width.

So:

[tex]Width = |x_2 - x_1|[/tex]

[tex]Width = |11 - -11|[/tex]

[tex]Width = |11 +11|[/tex]

[tex]Width = |22|[/tex]

Hence:

[tex]Width = 22[/tex]

[tex](a^2 - b^2) = (a + b)(a - b)[/tex]

Answer:

The level of significance is the

b. maximum allowable probability of Type I error.

Step-by-step explanation:

The significance level provides the maximum probability of rejecting the null hypothesis when it is true.  It is the same as a type I error (also known as false-positive).  This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted.  It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.

Step-by-step explanation: