the sum of 2 numbers is 17 and there product is 66 what are the two numbers

Answer:

The numbers are -9 and -7 or 13 and 15

Step-by-step explanation:

Let

x and x+2 ----> two consecutive odd integers

we know that

[tex]x(x+2)=3[x+x+2]+111[/tex]  

Solve for x

[tex]x(x+2)=3[x+x+2]+111\\ \\x^{2}+2x=6x+6+111\\ \\x^{2}-4x-117=0[/tex]

Solve the quadratic equation by graphing

The solution is x=-9, x=13

see the attached figure

First solution

x=-9

x+2=-9+2=-7

The numbers are -9 and -7

Second solution

x=13

x+2=13+2=15

The numbers are 13 and 15

Answer:

(1,2)

Step-by-step explanation:

we know that

The rule of the transformation is equal to

(x, y)  ------> (x + 3, y + 1)

Pre-image -----> Image

(x, y)  ------> (4, 3)

so

x+3=4 ----> x=4-3=1

y+1=3 ---> y=3-1=2

therefore

The pre-image is the point (1,2)

Answer: f(x^-1) = x/5 - 3/5

Step-by-step explanation:

1. Replace f(x) with y

2. Swap the positions of x and y to make x = 5y + 3

3. Solve for y by subtracting 3 from both sides and dividing each side by 5

The inverse of the function is f(x) = (x-3)/5 if the function f(x) is 5x +3 by taking the subject as x in the parent function.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have a function:

f(x) = 5x+3

To find the inverse of the function, take the subject x and the value of x.

f(x) - 3 = 5x

x = (f(x) - 3)/5

Replace the f(x) →x and x →f(x)

f(x) = (x-3)/5

Thus, the inverse of the function is f(x) = (x-3)/5 if the function f(x) is 5x +3 by taking the subject as x in the parent function.

Learn more about the fraction here:

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ANSWER

{},{1},{3},{5},{7},{1,3},{1,5},{1,7},{3,5},{3,7},{5,7},{1,3,5},{1,3,7},{3,5,7},{1,5,7},{1,3,5,7}

EXPLANATION

The given set is {1,3,5,7}.

This set has

[tex] {2}^{n} = {2}^{4} = 16[/tex]

subsets.

Where n=4 is the number of elements in the set.

Recall that the null set is a subset of every set and every set is a subset of itself.

The subsets are:

{}

{1},{3},{5},{7}

{1,3},{1,5},{1,7},{3,5},{3,7},{5,7}

{1,3,5},{1,3,7},{3,5,7},{1,5,7}

{1,3,5,7}

To achieve 204 gallons of 5% butterfat milk, one would need 136 gallons of 6% butterfat milk and 68 gallons of 3% butterfat milk by solving a system of linear equations.

How to Mix Butterfat Percentages for Milk

To solve the problem of mixing two different butterfat percentages of milk to achieve a certain amount of milk with a desired fat content, we will use a system of equations.

Let x represent the gallons of 6% butterfat milk, and y represent the gallons of 3% butterfat milk.

To achieve 204 gallons of 5% butterfat milk, we have the following equations:

Equation 1: x + y = 204 (total gallons of milk)

Equation 2: 0.06x + 0.03y = 0.05(204) (total butterfat content)

Solving these equations simultaneously, we find:

From equation 1, we can express y as y = 204 - x.

Substituting this into equation 2 gives us 0.06x + 0.03(204 - x) = 10.2.

Simplifying this, we get 0.06x + 6.12 - 0.03x = 10.2, which leads to 0.03x = 4.08.

Hence, x = 136 gallons of 6% butterfat milk and y = 68 gallons of 3% butterfat milk.

For this case we must find the value of "b" of the following equation:

[tex]\frac {3} {2} + b = \frac {7} {4}[/tex]

Then, we subtract [tex]\frac {3} {2}[/tex] from both sides of the equation:

[tex]\frac {3} {2} - \frac {3} {2} + b = \frac {7} {4} - \frac {3} {2}\\b = \frac {7} {4} - \frac {3} {2}\\b = \frac {14-12} {8}\\b = \frac {2} {8}\\b=\frac{1}{4}[/tex]

Answer:

[tex]b = \frac {1} {4}[/tex]

Answer:

The answer is 1/4.

The smallest angle is a which is 35 and from 7 to 35 it X5 so times 18 and 11 by 5 as well which comes to the ratio 35:90:55 , you can tell this is right because angles in a triangle add up to 180 , 35+90+55 =180

What are you solving for?

ANSWER

B. 1

EXPLANATION

The given function is

[tex]f(x) =\left \{ {{x^{2} +3 (if) -5 \leq x< 1} \atop {x (if) 1 \leq x \leq 5 }} \right.[/tex]

This is a piece-wise defined function.

We want to find f(1)

We substitute x=1 into f(x)=x because, 1 belongs to the interval,

1≤x≤5

f(1)=1

The correct answer is B.

Answer:

3 minutes

Step-by-step explanation:

we know that

Pablo can put up a tent in 12 minutes

so

100% of the work Pablo can do in -------> 12 minutes

In one minute Pablo can do (100/12)%

His mom can put it up by herself in 4 minutes

so

100% of the work his Mon can do in -------> 4 minutes

In one minute his Mon can do (100/4)%

therefore

Pablo and his Mon together in one minute can do

(100/12)%+(100/4)%=(400/12)%

By proportion find how many minutes would they take to put up the tent working together

1/(400/12)%=x/100%

x=12*100/400=3 minutes

Use the vertex form, y=a(x−h)2+k y = a ( x - h ) 2 + k , to determine the values of a a , h h , and k k . Since the value of a a is positive, the parabola opens up. Find p p , the distance from the vertex to the focus. Find the distance from the vertex to a focus of the parabola by using the following formula.

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Answer:

Step-by-step explanation:

It is a first cousin to y=x^2. The only difference is the 2 in front of the x^2 which narrows x^2.

The vertex is at (0,0)

Answer:

b)0, yes

Step-by-step explanation:

Given:

Vectors (4,8) . (6,-3)

Finding inner product of vectors:

= 4x6 + 8x-3

=24-24

=0

Now to check the angle between them using formula a.b=|a|.|b|cosθ

|a|= [tex]\sqrt{4^{2} +8^{2} } \\\sqrt{16+64}[/tex]

   =8.9

|b|=[tex]\sqrt{6^{2} +(-3)^{2} } \\\sqrt{36+9}[/tex]

   =6.7

Putting values of a.b=0 and |a|=8.9, |b|=6.7 in a.b=|a|.|b|cosθ we get,

0= 8.9(6.7)cosθ

cosθ =0

θ=90 degrees

Hence the two vectors are perpendicular !

Answer:

A  Open circle at 6, line going to the right

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

We know the area is greater than 24

24 < l*w

One dimension is 4

24 < 4*w

Divide each side by 4

24/4 < 4w/4

6 < w

The other dimension must be greater than 6

Open circle at 6, line going to the right

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} n&a_n\\ \cline{1-2} 1&4\\ &\\ 2&\stackrel{4(-3)}{-12}\\ &\\ 3&\stackrel{-12(-3)}{36}\\ \cline{1-2} \end{array}\qquad \impliedby \textit{common ratio of "r" is -3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=-3\\ a_1=4\\ n=15 \end{cases} \\\\\\ S_{15}\implies \displaystyle\sum\limits_{i=4}^{15}~4(-3)^{i-1}[/tex]

Answer:

[tex]\sum_{n=4}^{15}4(-3)^{n-1}[/tex]

Step-by-step explanation:

The given sequence is 4, -12, 36

We can see there is a common ratio

[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-12}{4}=(-3)[/tex]

[tex]\frac{a_{2} }{a_{3} }[/tex] = [tex]\frac{36}{-12}=(-3)[/tex]

Therefore, the given sequence is a geometric sequence.

Now we have to determine the sigma notation of the sum for term 4 through term 15.

Since explicit formula of the sigma can be represented as

[tex]T_{n}=a(r)^{n-1}[/tex]

where [tex]T_{n}[/tex] = nth term

a = first term

n = number of term term

r = common ratio

and sum is denoted by [tex]\sum_{n=1}^{n}a(r)^{n-1}[/tex]

Now for the given sequence sigma notation will be

[tex]\sum_{n=4}^{15}4(-3)^{n-1}[/tex]

Find the difference vertically( North and South) and the difference horizontally ( East and West)

Then use  the Pythagorean Theorem.

600 North - 200 South = 400 m

400 West - 100 East = 300 m

Now using the Pythagorean Theorem;

400^2 + 300^2 = total displacement^2

Total displacement^2 = 160,000 + 90,000

Total displacement^2 = 250,000

Total displacement = √250,000

Total displacement = 500 m

Answer:

1.3 x 10^-5

Step-by-step explanation:

To convert 0.000013 to scientific notation, the decimal point is moved five places to the right, resulting in 1.3 × 10⁻⁵.

To express the number 0.000013 in scientific notation, follow these steps:

Therefore, the scientific notation for 0.000013 is 1.3 × 10⁻⁵. This notation is particularly useful for representing very small numbers in a compact and readable form.

Answer:

45pairs

Step-by-step explanation:

15x3=45

Answer:

It’s B

6x log (4)

The statements about the functions that are true include:

A. f(x) and g(x) intersect at exactly two points.

B. The x-intercepts of f(x) are common to g(x).

In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).

By critically observing the table of values and graph shown in the image attached above, we can reasonably and logically deduce the following x-intercepts for both f(x) and g(x):

x-intercepts of f(x) = (-1, 0) and (1, 0).

x-intercepts of g(x) = (-1, 0) and (1, 0).

Therefore, the x-intercepts of f(x) are common to g(x), which means they intersect at exactly two points.

For the minimum value of f(x) and g(x), we have;

Minimum value of f(x) = -1

Minimum value of g(x) = -3

Therefore, the minimum value of f(x) is greater than the minimum value of g(x).

For the y-intercept of f(x) and g(x), we have;

y-intercept of f(x) = (0, -1).

x-intercepts of g(x) = (0, 1).

In conclusion, we can logically deduce that f(x) and g(x) have different y-intercept.

Answer:

One of the many reasons of this is because the diet soda is less dense than the normal soda, therefor, it will float even though there's the same amount of liquid in each can, and the cans weigh the same amount

I hope this helps

Step-by-step explanation:

Answer:

The options in the question are missing, but the answer is "The can of diet soda will float due to the Archimedes principle.

Step-by-step explanation:

Now, Archimedes Principle can be defined as,

when a body is partially or completely immersed in a fluid, the body losses its weight in the fluid equal to the amount of fluid displaced by this body.

Notice that the phenomena of floating and sinking is based on Archimedes principle. If, the weight of body is higher than the amount of liquid it displaced, body will sink and if the weight of body is lower than the amount of liquid it displaced, then it will float. Now, in comparison of regular can with diet can, one needs to notice that diet can is slightly lighter due to absence of sugar in the liquid it contained. But the volume of both regular and diet can are same. When immersed, both displace same amount of water, but the weight of diet can is slightly lesser than the amount of water it displaced, so it floats, while on the other hand, the weight of normal can is slightly higher than the amount of water it displaced, so it sinks.

Answer:

D) The relationship between y-intercepts cannot be determined.

Step-by-step explanation:

We have been given two different functions f(x) and g(x). Now we need to find about what can be determined about their y-intercepts. Then match with the correct choice from the given choices:

A) The function f(x) has a higher y-intercept.

B) The function g(x) has a higher y-intercept.

C) They both have the same y-intercept.

D) The relationship between y-intercepts cannot be determined.

We know that y-intercept is the y of function value when x=0.

In the table of g(x), we don't see any point that has x=0

So we can't find the y-intercept for g(x)

Hence correct choice is :

D) The relationship between y-intercepts cannot be determined.

The answer is:

C) They both have the same y-intercept.

In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.

So,

- Finding the equation of the g(x):

Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4[/tex]

Now, calculating the value of "b" using the first point (-1,8)  and the slope of the function, we have:

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

[tex]y=-x+b[/tex]

[tex]8=-4(-1)+b[/tex]

[tex]b=4[/tex]

So, the equation of g(x) is:

[tex]y=-4x+4[/tex]

- Comparing the y-intercepts of f(x) and g(x):

Finding the y-intercept of f(x),  by making "x" equal to 0, we have:

[tex]y=x+4\\\\y=4[/tex]

We have that the function f(x) has its y-intercept at "y" equal to 4.

Finding the y-intercept of g(x), by making "x" equal to 0, we have:

[tex]y=-4x+4[/tex]

[tex]y=-4*(0)+4[/tex]

[tex]y=4[/tex]

We have that the function g(x) has its y-intercept at "y" equal to 4.

Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:

C) They both have the same y-intercept.

Have a nice day!

I know the first 3 are c. I'm pretty sure the last one is a or d

Answer: 7. 2n + 162 = 424

              8. 3 hours

              9. K ≥ 18

7. The number of Delicious apples sold is represented by n. Because they  sold 162 more Empire apples than Delicious apples, the number of Empire apples sold can be represented by (n + 162). The total number of apples sold was 424, so the equation is Delicious apples + Empire apples = 424.

[tex]n + (n + 162) = 424\\\\n + n + 162 = 424\\\\2n + 162 = 424[/tex]

8. The equation is given for this problem. Simply solve for h in the equation.

[tex]55h + 275 = 440\\\\55h = 165\\\\h = 3[/tex]

9. The term "at least" generally means greater than or equal to. Thus, since Suzy scored at least 18 points, she scored 18 or more points.

[tex]K \geq 18[/tex]

4.02, 5, 7.3, 19, 23, 23, 34, 35, 41, 42

(Numbers are organized in ascending order from smallest to largest)

Answer:

sin 40/x =sin 60/12

Step-by-step explanation:

The question is on law of sines

Given a triangle with sides a, b, c and angles A, B, C respectively, the sine law states that; a/sin A = b/sin B = c/sin C

In the question x=a, b=12 feet, A=40° , B=60° and C=80°

Finding value of x;

x/sin 40° = 12/sin 60°

x sin 60° =12 sin 40°

x=12 sin 40 / sin 60

x=29.33 ft

Answer:

The length of the pole is 9.90 feet.

Step-by-step explanation:

From the figure, it is given that x is the length of the pole and the pole casts a shadow when the sun is at 40 degree angle.

Thus, using the sine law, we have

[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Substituting the given values, we get

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}=\frac{c}{sin80^{\circ}}[/tex]

Taking the first two equalities, we have

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}[/tex]

[tex]x=\frac{12sin40^{\circ}}{sin60^{\circ}}[/tex]

[tex]x=\frac{12{\times}0.642}{0.866}[/tex]

[tex]x=8.90 feet[/tex]

Therefore, the length of the pole is 9.90 feet.

Answer:

Its the first one

Step-by-step explanation:

Final answer:

The rational expression[tex](r^2 - 4r + 5)/(r - 4)[/tex] is already in its simplest form, as the numerator cannot be factored to cancel out any terms with the denominator.

Explanation:

The question asks for the simplified rational expression for the quadratic equation [tex]r2 - 4r + 5[/tex] divided by the linear expression r - 4. Simplifying rational expressions often involves factoring the numerator and the denominator and then canceling out common factors. However, in this case, the numerator cannot be factored in a way that will cancel out terms with the denominator. Simplifying further requires either polynomial division or realization that the expression is already in its simplest form because there are no common factors. Therefore, the rational expression[tex]r2 - 4r + 5[/tex] over r - 4 is already simplified as no further reduction is possible.

For this case we have a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Rewriting the equation we have:

[tex]3k ^ 2-4k-7 = 0[/tex]

So we have to:

[tex]a = 3\\b = -4\\c = -7[/tex]

The solutions will come from:

[tex]k = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Thus, the value of "b" is -4

Answer:

[tex]b = -4[/tex]

can the answer not being an integer?

The angle of elevation is at angle D

So the answer would be 13.8

Answer:

x<2

Step-by-step explanation:

-x+8>6

-x>6-8

-x>-2 (flip the sign)

x<2

Answer:

x < 2

Step-by-step explanation:

-x+8>6

Subtract 8 from each side

-x+8-8>6-8

-x > -2

Divide each side by -1.  Remember to flip the inequality

-x/-1 < -2/-1

x < 2

Answer:

maximum value of the given function is = 3

Step-by-step explanation:

Given function is [tex]F(x)=-4(x-6)^2+3[/tex].

Now we need to find about what is the maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] and explain the method about how did you find the maximum value.

Given function [tex]F(x)=-4(x-6)^2+3[/tex] looks similar to the quadratic function of the form [tex]f(x)=a(x-h)^2+k[/tex].

Comparing both we get: h=6, k=3

We know that maximum value occurs at the vertex where maximum value is given by "k"

Hence maximum value of the given function is = 3

Answer:

Final answer is [tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex].

Step-by-step explanation:

given functions are [tex]f(x)=x-6[/tex] and [tex]g\left(x\right)=\frac{1}{2x\left(x+3\right)}[/tex].

Now we need to find about what is the value of [tex]g\left(x\right)*f\left(x\right)[/tex].

[tex]g\left(x\right)*f\left(x\right)[/tex] simply means we need to multiply the value of  [tex]f(x)=x-6[/tex] and [tex]g\left(x\right)=\frac{1}{2x\left(x+3\right)}[/tex].

[tex]g\left(x\right)\cdot f\left(x\right)=\frac{1}{2x\left(x+3\right)}\cdot\left(x-6\right)[/tex]

[tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex]

Hence final answer is [tex]g\left(x\right)\cdot f\left(x\right)=\frac{\left(x-6\right)}{2x\left(x+3\right)}[/tex].