Which additional facts prove that RST and
WXY are congruent? (Geometry)

Answer:

[tex]{ \bf{r(t) = 7e {}^{0.6t} }} \\ { \tt{r(2) = 7 {e}^{0.6 \times 2} }} \\ = { \tt{7 {e}^{1.2} }} \\ = 23.241 \: thiusand bacteria \: per \: hour[/tex]

Answer:

8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz

Step-by-step explanation:

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Step-by-step explanation:

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Answer:

y = -3x + 13

Step-by-step explanation:

First, find the slope:

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]

Finally, find the equation:

[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]

let the number be b

62.5/100 x b = 25

0.625 x b = 25

b =25/0.625

b=40

half of b= 40/2 = 20

Answer:

[tex]cos \theta = \frac{11}{12}[/tex]

Step-by-step explanation:

[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]

Answer:

Sister's house is 7.5 feet high

Step-by-step explanation:

Given :

     My house = 5  feet

     Sisters house = [tex]1\frac{2}{4}[/tex]  [tex]times[/tex]  [tex]my \ house[/tex]

                           = [tex]\frac{6}{4} \times 5[/tex]

                           [tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]

Answer:

a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons  

b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons

Step-by-step explanation:

Given the data in the question;

We know that the weight of a body varies inversely as the square of its distance from the center of the earth.

⇒F(x) = c / x²

given that; F(x) = five-ton = 5 tons

we know that the radius of earth is approximately 4000 miles

so we substitute

5 = c / (4000)²

c = 5 × ( 4000 )²

c = 8 × 10⁷

∴ Increment of work is;

Δw =  [ ( 8 × 10⁷ ) / x² ] Δx

a) For 100 miles above Earth;

W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]

= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]

= 487.8 mile-tons  

Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons  

b) For 300 miles above Earth.

W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]

= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]

= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]

= 1395.3 mile-tons

Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons

Answer:

a.) 15 feet

b.) 3.25 seconds

c.) 17.1125 feet

d.) 12.5 seconds

Step-by-step explanation:

a

This is just asking for the y intercept

to get this just do h(0)= 15

b

This is asking for the x value of the vertex

solve that through -b/2a

-1.3/(2*-.2)= 3.25

c

This is asking for the y value of the vertex

to solve this plug in the x value from b

-.2*3.25²+1.3*3.25+15= 17.1125

d

This is asking for an x intercept

using the quadratic formula...

[tex]\frac{-b(+-)\sqrt{b^2-4*a*c}}{2a}=\frac{-1.3(+-)\sqrt{1.3^2-4*-.2*15}}{2*-.2}= -6, 12.5[/tex]

*note the (+-) before the radical is ± *

logic will tell us that a negative x intercept doesn't make any sense so we only take the positive value, 12.5

Answer:

$30.21

Step-by-step explanation:

100% -25%= 75%

Discounted price of the book

= 75% ×$38

= $28.50

Since the customer must pay an additional 6% of the discounted price,

percentage of discounted price paid

= 100% +6%

= 106%

Total amount paid

= 106% × $28.50

= $30.21

_________________________________

Alternative working:

Original selling price= $38

Since the book is discounted 25%,

100% ----- $38

1% ----- $0.38

75% ----- 75 ×$0.38= $28.50

Since the sales tax is based on the discounted price, we let the discounted price be 100%.

100% ----- $28.50

1% ----- $0.285

106% ----- 106 ×$0.285= $30.21

∴ The total amount the customer pays for the discounted book is $30.21.

Answer:

x=2

Step-by-step explanation:

the sides are proportional due the angles being equal

since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference

so 4÷2=x

x=2

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that [tex]\mu = 14, \sigma = 2[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{14.2 - 14}{0.2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Answe

SI Si olla amigo lel just spammin here

Step-by-step explanation:

Answer:

37.68 in.^3

Step-by-step explanation:

diameter = 4 in.

radius = diameter/2 = 2 in.

height = 9 in.

[tex] V = \dfrac{1}{3}\pi r^2 h [/tex]

[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]

[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]

[tex] V = \blue{37.68~in.^3} [/tex]

9514 1404 393

Answer:

  (c)  2440

Step-by-step explanation:

The sum of the squares of numbers 1 .. n is ...

  s(n) = n(n +1)(2n +1)/6

You want the sum of squares from 5 to 19. We can compute that from ...

  s(19) -s(4) = (19(20)(39) -4(5)(9))/6 = (14820 -180)/6 = 2440

Answer:

Step-by-step explanation:

hope it helps u too

Answer:

Espanol la vecsu

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

The diagonals of a rectangle bisect each other , so

DE = EB , that is

7x - 1 = 2x + 4 ( subtract 2x from both sides )

5x - 1 = 4 ( add 1 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

11%

Hope this helps! :)

______________

Answer:

[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]

Answer:

30 hour

Step-by-step explanation:

girls time

12 20 hour

8 x(let)

now,

12/8=x/20

12×20=8×x

240=8x

x=240/8

x=30,,

Answer:

216

Step-by-step explanation:

=>log   36 = -2/3

        m

=>36=(m)^-2/3

=>(root(-36))^3=m

=>m=(root(36))^3

=>m=6^3

=>m=216

Answer:

Your options are not clear

Step-by-step explanation:

[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]

Step-by-step explanation:

2³×2^n+2=32

2^3+n+2=2⁵

n+5=5

n=0

[tex]_____________________________________[/tex]

[tex]\sf\huge\underline\red{ANSWER:}[/tex]

[tex]\tt n = 0[/tex]

[tex]\sf\huge\underline\red{SOLUTION:}[/tex]

[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]

[tex]_____________________________________[/tex]

[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]

[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]

[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]

Answer:

14.5%

Step-by-step explanation:

Use the number 100 as an example to find the single discount.

Take a 10% discount off of this:

100(0.9)

= 90

Take a 5% discount:

90(0.95)

= 85.5

So, after the successive discounts, $14.5 was discounted.

This means that the single discount is 14.5%.

So, the answer is 14.5%

Answer:

third option

Step-by-step explanation:

m(n(x)) =

[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]

the domain of this is R/(4)

so as the third option

The function that has the same domain as (m o n)(x) is

h(x) = 11 / (x - 3)

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,

Now,

(m o n)(x)

= m (n(x)

= m (x - 3)

= (x - 3 + 5) / (x - 3 - 1)

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

We can not have x = 3.

So,

The domain can not have x = 3.

From the options,

h(x) = 11 / (x - 3) can not have x = 3.

Thus,

The function that has the same domain as (m o n)(x) is

h(x) = 11 / (x - 3)

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ7

Answer:

It will take him 5.85 seconds.

Step-by-step explanation:

12.5 (0.2t - 1) + 21t = 150

Use Distributive Property:

2.5t - 12.5 + 21t = 150

Combine like terms:

23.5t - 12.5 = 150

Subtract 12.5 from both sides:

23.5t = 137.5

Divide both sides by 23.5 to isolate variable t:

5.851063.....

Round to two decimal places (hundredths place):

5.85

Answer:

x ≥ 12

Step-by-step explanation:

-3/4x +2 ≤ -7

Subtract 2 from each side

-3/4x +2-2 ≤ -7-2

-3/4x  ≤ -9

Multiply each side by -4/3, remembering to flip the inequality

-3/4x * -4/3 ≥ - 9 *(-4/3)

x ≥ 12

Answer:

x>=12

Step-by-step explanation:

-3/4x + 2<=-7

-3/4x <= -7 -2

-3/4x<=-9

cross multiply

-3x<=-36

dividing throughout by -3

x>=12

Answer:

x^2+2x-5 - 1/x

Step-by-step explanation:

f(x)=1/x

g(x)=x^2+2x-5

(g-f)(x) = x^2+2x-5 - 1/x

Answer:

c. x² + 2x - 5 - 1 / x

Step-by-step explanation:

f ( x) = 1 / x.

g ( x) = x² + 2x - 5

so,

( g - f) ( x) = x² + 2x - 5 - 1 / x

Answer:

The last one!

Step-by-step explanation:

Answer:

last step is (2x + 5)(2x + 1)

Step-by-step explanation:

4x^2 + 12x + 5

4x^2 + (10 + 2)x + 5

4x^2 + 10x + 2x + 5

2x(2x + 5) +1(2x + 5)

(2x + 5)(2x + 1)

Answer:

we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm

The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8

The function is given as:

[tex]f(x) = -2x + 8[/tex]

The above function is a linear function.

A linear function is represented as:

[tex]y =mx + c[/tex]

Where:

m represents the slope, and c represents the y-intercept.

So, by comparison;

[tex]m =-2[/tex]

[tex]c = 8[/tex]

This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8

See attachment for the graph of the function

Read more about linear functions at:

https://brainly.com/question/15602982

Answer:

Correct answers= 18

Incorrect answers=30-18= 12 answers

Step-by-step explanation:

total questions=30

correct answers= x

incorrect answers= 30-x

given: 5 marks for each correct answer

therefore, marks for correct answers = 5*x = 5x

Given: 1 mark deducted for every incorrect answer

therefore, marks deducted = 1(30-x) = 30-x

Total marks scored= 78

★  The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78

5x- (30-x) =78

5x-30+x=78

5x+x=78+30

6x= 108

x=108/6 = 18

Correct answers= 18

Incorrect answers=30-18= 12 answers