10 points!

What is the most appropriate conclusion about the new drug to draw from this information?

Answer:

[tex]\large\boxed{y=-\dfrac{1}{2}x+\dfrac{3}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 2x-y=5.\\\\\text{Convert to the slope-intercept form y = mx + b:}\\\\2x-y=5\qquad\text{subtract 2x from both sides}\\\\-y=-2x+5\qquad\text{change the signs}\\\\y=2x-5\to m_1=2\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.[/tex]

[tex]\text{The equation of the searched line:}\ y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through }(3,\ 0).\\\\\text{Put the coordinates of the point to the equation.}\ x=3,\ y=0:\\\\0=-\dfrac{1}{2}(3)+b\\\\0=-\dfrac{3}{2}+b\qquad\text{add}\ \dfrac{3}{2} \text{to both sides}\\\\b=\dfrac{3}{2}[/tex]

f(x)= x[tex]x^2+x-30[/tex

    = [tex](x)^2+2*x*\frac{1}{2} +(\frac{1}{2} )^2-(\frac{1}{2} )^2-30[/tex]

    = [tex](x+\frac{1}{2} )^2-\frac{1}{4} -30[/tex]

    = [tex](x+\frac{1}{2} )^2-\frac{121}{4}[/tex]

    =[tex](x+\frac{1}{2} )^2-30\frac{1}{4}[/tex] (Answer)

Answer:

hypotenuse = 20

leg = x + 4

other leg = x

From the Pythagorean Theorem we know that

20^2 = (x + 4)^2 + x^2

400 = x^2 + 8x + 16 + x^2

2 x^2 + 8x -384 = 0

Solving the quadratic equation we get

x = 12 and x = -16

x = 12 and so the lengths of the 2 legs are:

12 and 16

Right Triangle Area = (leg1 * leg2) / 2

Right Triangle Area = (12 * 16) / 2

Area = 192 / 2

Area = 96 square centimeters

Step-by-step explanation:

To find the area of the triangle, we used the Pythagorean theorem to solve for the legs, obtaining lengths of 16 cm and 12 cm. The area is then calculated using the formula for the area of a right triangle (1/2 * base * height), resulting in an area of 96 cm².

We are given a right triangle with a hypotenuse of 20 cm and two legs where one leg (let's call it a) is 4 cm longer than the other leg (let's call it b). Using the Pythagorean theorem, we can express the relationship between the legs and the hypotenuse: a² + b² = 20². We know that a = b + 4, so if we substitute a into the equation, we get:

(b + 4)² + b² = 400

b² + 8b + 16 + b2 = 400

2b² + 8b - 384 = 0

Dividing everything by 2, we get:

b² + 4b - 192 = 0

Using the quadratic formula or factoring, we find that b = 12 (b can't be negative). Consequently, a = 16. The area of the triangle is given by 1/2 * base * height, which is:

Area = 1/2 * a * b

Area = 1/2 * 16 * 12

Area = 1/2 * 192

Area = 96 cm²

Answer:

[tex]g(x)=x^2-x[/tex]

Step-by-step explanation:

Given function is [tex]F\left(x\right)=x^2+3x+2[/tex].

Function [tex]F\left(x\right)=x^2+3x+2[/tex] is shifted 2 units right and gives result to a new function g(x).

Now we need to find about what is the equation of g(x).

We know that f(x-h) indicates right shift by "h" units.

So to get 2 units shift, replace x by (x-2) into given function

[tex]g(x)=F\left(x-2\right)[/tex]

[tex]g(x)=(x-2)^2+3(x-2)+2[/tex]

[tex]g(x)=x^2-4x+4+3x-6+2[/tex]

[tex]g(x)=x^2-x[/tex]

Hence final answer is [tex]g(x)=x^2-x[/tex].

ANSWER

[tex]b \geqslant - 18[/tex]

EXPLANATION

The given inequality is:

[tex] - 18 \leqslant b[/tex]

We can rewrite this as:

[tex]b \geqslant - 18[/tex]

The above two inequalities have the same meaning.

Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."

Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."

Therefore the two inequalities have the same meaning.

Step-by-step Answer:

Many inequalities are possible, for example:

Keeping the less than or equal to sign, we could write

-18-b<=0

or, switching sides,

b>= -18   (just by switching sides)

b+18>=0  (by transposing -18 to the left)

Then again, we can multiply both sides by -1, but we need to change the direction of the inequality:

18>=-b

or equivalently, by transposing 18 to the other side

0>=-b-18

and similarly

b+18>=0  (we already had this above)

Guess time to stop!

Answer:

the answer is 3

Step-by-step explanation:

21/8 simplify is 3

Yeah, The answer is 3

Answer:

Step-by-step explanation:

2x-10 is your answer

Answer:

D. 2x+5

Step-by-step explanation

All you have to do is put them all together and there you have it your answer of D 2x+5

No, two ordered pairs in this list have a repeated of the domain element.

We know that the definition of functions tells us that a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).

So here is important to know the term exactly one element, Why? because if you don't have this, you don't have a function. From the figure, two ordered pairs in this list have a repeated of the domain element. This can be proven by plotting these three points as indicated below. As you can see, the element 4 in the domain matches both 2 and -2 in the range. In conclusion, this relation is not a function.

Your answer is D. (4,3)

ANSWER

D(4,3)

EXPLANATION

The endpoints of AB have the coordinates A(9, 8) and B(-1, -2).

To calculate the coordinates of the midpoint of AB, we use the midpoint formula,

[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]

We substitute the coordinates of the endpoints into the formula to get,

[tex]( \frac{9+ - 1}{2},\frac{8+ - 2}{2} )[/tex]

[tex]( \frac{8}{2},\frac{6}{2} )[/tex]

We simplify further to obtain,

[tex]( 4,3)[/tex]

Answer:

2140

Step-by-step explanation:

Sofia paid a total of $7,440 over 24 months for a motorcycle with a sticker price of $5,300. The interest she paid can be found by subtracting the sticker price from the total amount paid, which comes to $2,140. Hence correct option C.

Sofia bought a motorcycle with a sticker price of $5300. If she paid $310 a month for 24 months, first we need to find out the total amount she paid over the 24 months. To do this, we multiply the monthly payment amount by the number of months:

$310 × 24 = $7,440

Now, to find the amount of interest paid, we subtract the original sticker price from the total amount paid:

$7,440 - $5,300 = $2,140

Therefore, Sofia paid $2,140 in interest.

Answer: [tex](f-g)(x)=-x+10[/tex]

Step-by-step explanation:

Given the function f(x):

[tex]f(x)=3x-1+4[/tex]

And given the function g(x):

[tex]g(x)=4x-7[/tex]

You must subtract both functions is order to find [tex](f-g)(x)[/tex].

You need to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]

Then:

[tex](f-g)(x)=3x-1+4-(4x-7)[/tex]

Now, you must distribute the negative sign:

[tex](f-g)(x)=3x-1+4-4x+7[/tex]

And finally, add the like terms. Then you get that  [tex](f-g)(x)[/tex] is:

[tex](f-g)(x)=-x+10[/tex]

Answer:

The range is 19

Step-by-step explanation:

First, you have to order the numbers from least to greatest:

-9.5, -3.1, 3.1, 3.2, 4.7, 4.9, 5.4, 6.3, 9.5

Then, you have to find the difference between the largest number and and smallest number. You do this by subtracting them:

9.5 - (-9.5)= 19

So, the range is 19

1/3 = 33%

33% * 390 = 118.8

Your answer 118.8 degrees

Answer: 120 degrees

Step-by-step explanation:

Just did it.

Answer:

See attachment

Step-by-step explanation:

The given function is [tex]y=\cos x +3[/tex]

The base function is [tex]y=\cos x[/tex]

The single transformation applied to this function is a vertical upward shift by 3 units.

Therefore the graph of  [tex]y=\cos x +3[/tex] is graph of  [tex]y=\cos x [/tex] shifted up 3 units.

See attachment

Answer: B

Step-by-step explanation:

Just did the test on edge

Answer:

Plan A:

C = $80

C = cost

Plan B:

C = 0.15t + 20

C = cost; t = amount of text messages

Step-by-step explanation:

Let C = cost.

Let t = amount of text messages.

Plan A:

C = $80

Plan B:

C = 0.15t + 20

If the next question asks for you to solve when Plan B will be equal to Plan A, set the two equations equal to each other.

80 = 0.15t + 20

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 20 from both sides.

80 (-20) = 0.15t + 20 (-20)

80 - 20 = 0.15t

60 = 0.15t

Divide 0.15 from both sides.

(60)/0.15 = (0.15t)/0.15

60/0.15 = t

t = 400

Those who use Plan B must send at least 400 text message to have the same price as Plan A.

~

(9 x 100) + (5 x 0.1)

OR

900 + .5

Nine hundred and five tenths

Hope this helped!

Hello!

-EXPANDED FORM- To make the number 900.5 in expanded form, We use 900 and then add 0.5 which is also 1/2.

-WORD FORM- To make the number 900.5 in word form, the answer would be nine hundred and five tenths

0.5 as a percent is 50%

0.5 to a percent value is 50%

Answer:

374 miles

Step-by-step explanation:

To see how many miles each gallon gets, divide 102/3 which is 34 meaning there are 34 miles per gallon so if you multiply 34 x 11 gallons it equals 374 miles.

Hope this helps!

To solve this problem, we will use the concept of a unit rate, which in this scenario is the car's miles per gallon (mpg). A unit rate compares a quantity to one unit of another quantity. Here's how to do it step by step:
1. **Find the unit rate (mpg).**
  The car travels 102 miles on 3 gallons of gas. To find out how many miles it travels per gallon, we'd divide the total number of miles by the number of gallons of gas used:
  \[ \text{mpg} = \frac{\text{miles traveled}}{\text{gallons used}} \]
  \[ \text{mpg} = \frac{102 \text{ miles}}{3 \text{ gallons}} \]
  \[ \text{mpg} = 34 \text{ miles per gallon} \]
  So the car travels 34 miles per gallon of gas.
2. **Calculate the distance the car can travel on 11 gallons of gas.**
  Now that we know the car travels 34 miles on one gallon of gas, we can find out how far it travels on 11 gallons by multiplying the mpg by the number of gallons:
  \[ \text{distance} = \text{mpg} \times \text{gallons available} \]
  \[ \text{distance} = 34 \text{ miles/gallon} \times 11 \text{ gallons} \]
  \[ \text{distance} = 374 \text{ miles} \]
So, the car can travel 374 miles on 11 gallons of gas.

ANSWER

A.) The graph of f(x) is horizontally compressed.

EXPLANATION

The given absolute value function is

[tex]f(x) = - 6 |x + 5| - 2[/tex]

The parent function is

[tex]y = |x| [/tex]

Since the factor -6 has an absolute value greater than 1, the graph of the given function will be narrower than the graph of the base function.

Hence the graph is horizontally stretched by a factor of 6.

The graph opens downwards because of the negative sign.

It has vertex at (-5,-2)

Answer:

-5

Step-by-step explanation:

A line that is parallel to another line must have the same slope.

Answer:

-5

Step-by-step explanation:

Parallel lines all have the same slope (as each other). Both of the parallel lines you are describing have a slope of -5.

2, -1. I think, possibly.

Answer:

3, -1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Value of the function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] is zero.

Correct option is b.

Limits are defined as values ​​to which the function approximates the output for given input values. The limit is the unique real numbers. Given a real-valued function "f" and a real number "c", the limit is usually defined as [tex]\lim_{x \to c} f(x) = L[/tex]. We read that "the limit of f of x is equal to L as x approaches c". "lim" represents the limit, and the right arrow indicates that the function f(x) approaches the limit L as x approaches c.

Given functions,

[tex]\lim_{x \to 4} f(x) = 5 , \lim_{x \to 4} g(x) = 0, \lim_{x \to 4} h(x) = -2[/tex]

[tex]=\lim_{x \to 4} \dfrac {g}{h}(x)[/tex]

[tex]=\lim_{x \to 4} \dfrac {g(x)}{h(x)}[/tex]

[tex]=\dfrac{\lim_{x \to 4} g(x)} {\lim_{x \to 4} h(x)}[/tex]

= 0/-2

= 0

Hence, 0 is the value of function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] .

Learn more about limit here:

https://brainly.com/question/12207539

#SPJ2

The answer is 45, I believe so

Flying a plane through your own imagination. This implies how dominoes make you think and create, using your mind to make comparisons. The other option is like banging my head against the wall. It’s pointless and painful.

Answer:

writing answers to math questions

Step-by-step explanation:

writing a sentance

writing an add

writing a book

V = Bh

144 = (8 x 4)h

144 = 32h

4.5 = h

Final answer:

To calculate the height of the rectangular prism, we use the formula for volume and the given values to solve for height, resulting in a height of 4.5 inches.

Explanation:

To find the height of a rectangular prism with a given volume where the length is two times the width and the width is known, we use the formula for the volume of a rectangular prism: volume = length × width × height.

Given that the volume is 144 cubic inches, the width is 4 inches, and the length is two times the width, which is 2 × 4 inches = 8 inches, we can substitute these values into the formula:

144 in³ = 8 in × 4 in × height

Next, we need to isolate 'height' by dividing both sides of the equation by the length times the width of the prism:

144 in³ / (8 in × 4 in) = height

144 in³ / 32 in² = height

4.5 in = height

Therefore, the height of the rectangular prism is 4.5 inches.

Answer:

2/5

Step-by-step explanation:

There are 10 marbles and 4 of them are purple. That would give you the fraction 4/10. 4/10 can be simplified to 2/5. So, you have a 2/5ths chance of choosing a purple marble.

The probability of selecting a purple marble from a bag containing 10 marbles, 4 of which are purple, is 2/5.

The question asks: "A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag?" To find the probability, you divide the number of favorable outcomes (choosing a purple marble) by the total number of outcomes (all the marbles in the bag). Here, there are 4 purple marbles and 10 marbles in total.

The probability is therefore 4/10, which can be simplified to 2/5. So, the probability of choosing a purple marble from the bag is 2/5.

Answer:

Yes, i believe that the generalization about the measure of a point angle of a star polygon is true.

First we find sum of interior angle of an n-sided star polygon.

number of triangle in a polygon = n - 2

sum of interior angle of a triangle = 180°

sum of interior angle of an n-sided star polygon = ( n - 2 ) × 180°

To find measure of a point angle, we use:

[tex]\frac{|n-2(d)|}{n}[/tex] × 180°                                                            

To find a point angle we eliminate density by multiplying d by 2  in the formula for finding number of triangle, divide the whole by total number of sides and then multiply by the sum of interior angle of triangle(180°).  

Since all the angle of a regular star polygon are equal, we can calculate each pointy interior angle of a regular star polygon using the formula given below:

[tex]\frac{|n-2(d)|}{n}[/tex] × 180°    

Answer:

Step-by-step explanation:

First we calculate (-3)÷10 = -0.3

Then 12÷(-0.3) = -40

After that -4 + (-40) = -44

3(-2) = -6

Finally -44 + (-6) = -50

For this case we have that the order of algebraic operations is determined by PEMDAS:

P: Perform any calculation inside the parentheses, making the most internal ones first.

E: Simplify any exponential expressions.

MD: Do all the multiplications and divisions, from left to right, as they appear.

AS: Do all the addition and subtraction, from left to right, as they appear.

Then, we have the following expression:

-4 + 12 ÷ (-3) ÷ 10 + 3 (-2) =

-4-4 ÷ 10 + 3 (-2) =

-4-0.4 + 3 (-2) =

-4-0.4-6 =

-4.4-6 =

-10.4

Answer:

-10.4

Answer:

Step-by-step explanation:

Density is mass divided by volume:

ρ = M / V

So mass is density times volume:

M = ρV

If the density is 865 kg/m³ and the volume is 61.25 m³:

M = (865 kg/m³) (61.25 m³)

M = 52981.25 kg

Final answer:

To find the mass of oil in a tank, multiply the tank's volume (61.25 cubic meters) by the oil's density (865 kg/m³), resulting in 52,981.25 kilograms. The mass is not measured in kilometers, which suggests a typo in the original question.

Explanation:

The question concerns the calculation of the mass of oil if its density and the volume of the tank it fills are known. To find the mass, you would multiply the volume of the oil by its density:

Step-by-Step Calculation:

Determine the volume of the oil. In this case, the volume is already given as 61.25 cubic meters.

Identify the density of the oil. According to the question, it is 865 kilograms per cubic meter.

Multiply the volume by the density to get the mass. That is:

61.25 m³ × 865 kg/m³ = 52,981.25 kilograms.

In terms of mass in kilometers, there appears to be a typo, as mass is not measured in distances like kilometers. The correct unit should likely be kilograms.

Answer:

Step-by-step explanation:

We can first make y the subject of the formula by multiplying both sides of the equation by -1 ;

y = -x + 0

This is the equation of a line with a slope of -1, the coefficient of x, and passing through the origin.

In order to find three points that solve the equation, we can let x be;

0, 1, 2

then determine the corresponding values of y.

When x = 0, y = -(0) + 0 = 0

When x = 1, y = -(1) + 0 = -1

When x = 2, y = -2 + 0 = -2

Therefore, we have the following three sets of points that can be used to graph the linear equation;

(0,0)

(1,-1)

(2,-2)

Find the attached for the graph of the equation;

Answer: (-1,1) (0,0) (2,-2)

Step-by-step explanation: