Piecewise defined function.

f(x) = {-x^2+2x+2 if
[tex]x \leqslant - 5[/tex]

{-3/4x+3 if
[tex]x > 1[/tex]

find what f(-5) = ​

Answer:

y = 2x + 4

Step-by-step explanation:

First, find the rate of change [slope], m = -y₁ + y₂\-x₁ + x₂. Next, you do either\or:

12 = 2(4) + b; 4 = b

8 = 2(2) + b; 4 = b

No matter which ordered pair you use, you will ALWAYS get the same answer, IF you put them in their correct places.

I am joyous to assist you anytime.

Answer:

40

Step-by-step explanation:

In this question, substitute the values of h and k in the expression

Given h=4 and k=6

The expression will be;

h(h+k)

4(4+6)

solve the brackets first

4+6=10

rewrite the expression as

4(10)

open the brackets by multiplication

4×10=40

Answer:

40

Step-by-step explanation:

We must substitute the values provided to us:

[tex]h=4[/tex] and [tex]k=6[/tex]

in the expression:

[tex]h(h+k)[/tex]

we get the following:

[tex]4(4+6)[/tex]

solving the sum inside the parentheses:

[tex]4(10)[/tex]

and finally solving the multiplication

[tex]4(10)=40[/tex]

the value of the expression is 40.

Answer:

[tex]\large\boxed{x=35^o}[/tex]

Step-by-step explanation:

We have the equation:

[tex]56^o+y+51^o=180^o\\\\(56^o+51^o)+y=180^o\\\\107^o+y=180^o\qquad\text{subtract}\ 107^o\ \text{from both sides}\\\\y=73^o\\\\\text{We know: the sum of the measures of the angles of the triangle}\\\text{is equal to}\ 180^o.\\\\\text{Therefore we have the equation:}\\\\x+y+72^o=180^o\qquad\text{put the value of}\ y\\\\x+73^o+72^o=180^o\\\\x+145^o=180^o\qquad\text{subtract}\ 145^o\ \text{from both sides}\\\\x=35^o[/tex]

Answer:

81

Step-by-step explanation:

We know the number is between 50 and 100.  The prime factorization consists of only one prime number, so the number must be a perfect square.  The possible numbers are 64 and 81.

The rectangles that can be made with 64 tiles are:

1×64, 2×32, 4×16, 8×8, 16×4, 32×2, 64×1

The rectangles that can be made with 81 tiles are:

1×81, 3×27, 9×9, 27×3, 81×1

There are 7 rectangles that can be made with 64 tiles.  There are only 5 rectangles that can be made with 81 tiles.  Therefore, the mystery number is 81.

Step-by-step explanation:

The mystery number is 64, sqare number of 8 , the only prime number contributing to it being 2

Being x the mystery number

[tex]50 < x < 100[/tex]

The only two sqare numbers that meet this request are 64 and 81.

Not knowing much about the above mentioned rectangles, 81 being the perfect square number of a perfect square number we would consider 64 the only posible answer

Answer:

we can use existing theorems to prove new theorems - true

It is true that we can use existing theorems to prove new theorems.

In geometry, new theorems are sometimes dependent on existing theorems.

This means that some new theorems would not exist, if not for the support and the existence of related existing theorems.

Hence, the statement is true

Read more about geometry at:

https://brainly.com/question/25306774

Answer:

h=x+1/x^3+4x^2

Step-by-step explanation:

hx^3+4hx^2=x+1

h^3+4x^2)=x+1

h(x^3+4x^2)/x^3+4x^2=x+1/x^3+4^2

h=x+1/x^3+4x^2

Answer:

hambger

Step-by-step explanation:ham de be gerf hamburger

Answer:

[tex]\large\boxed{r^2=(x+5)^2+(y-4)^2}[/tex]

Step-by-step explanation:

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have diameter endpoints.

Half the length of the diameter is the length of the radius.

The center of the diameter is the center of the circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates of the given points (-8, 2) and (-2, 6):

[tex]d=\sqrt{(6-2)^2+(-2-(-8))^2}=\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}[/tex]

The radius:

[tex]r=\dfrac{d}{2}\to r=\dfrac{\sqrt{52}}{2}[/tex]

The formula of a midpoint:

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

Substitute:

[tex]x=\dfrac{-8+(-2)}{2}=\dfrac{-10}{2}=-5\\\\y=\dfrac{2+6}{2}=\dfrac{8}{2}=4[/tex]

[tex](-5,\ 4)\to h=-5,\ k=4[/tex]

Finally:

[tex](x-(-5))^2+(y-4)^2=\left(\dfrac{\sqrt{52}}{2}\right)^2\\\\(x+5)^2+(y-4)^2=\dfrac{52}{4}\\\\(x+5)^2+(y-4)^2=13[/tex]

Answer:

x = 4

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(x + 3)² + (4(x + 2))² = 25² ← expand parenthesis on left side

x² + 6x + 9 + 16(x+ 2)² = 625

x² + 6x + 9 + 16(x² + 4x + 4) = 625

x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side

17x² + 70x + 73 = 625 ( subtract 625 from both sides )

17x² + 70x - 552 = 0 ← in standard form

with a = 17, b = 70, c = - 552

Using the quadratic formula to solve for x

x = ( - 70 ± [tex]\sqrt{70^2-(4(17)(-552)}[/tex] ) / 34

  = ( - 70 ± [tex]\sqrt{4900+37536}[/tex] ) / 34

  = - 70 ± [tex]\sqrt{42436}[/tex] ) / 34

  = - 70 ± 206 ) / 34

x = [tex]\frac{-70-206}{34}[/tex] = - 8.1176....

or x = [tex]\frac{-70+206}{34}[/tex] = 4

However, x > 0 ⇒ x = 4

Hence

x + 3 = 4 + 3 = 7 and

4(4 + 2) = 24

The triangle is a 7- 24- 25 right triangle

Answer:

Elisondra and her three friends add up to four people, so the spinner should have 4 equal sized sections.

Answer:

D

Step-by-step explanation:

The given function [tex]f(x)=(2x+3)^2(3x+5)^2[/tex] is a polynomial function of degree 4, with a leading coefficient of 36 determined by multiplying the squares of the leading terms of the binomials.

The function[tex]f(x)=(2x+3)^2(3x+5)^2[/tex] is indeed polynomial. To determine the degree and the leading coefficient of a polynomial, we need to expand the given expression. However, without full expansion, we can deduce the degree by adding the exponents of the individual factors since the bases are polynomials of degree 1 (2x+3 and 3x+5).

Each factor is squared, so [tex](2x+3)^2[/tex] has degree 2 and ([tex]3x+5)^2[/tex]also has degree 2. By adding these, we find that the polynomial's degree is 2+2=4. To find the leading coefficient, we consider the leading terms of each binomial which are 2x and 3x. Squaring these and then multiplying them together [tex](2x)^2 * (3x)^2 = 4x^2 * 9x^2,[/tex]we get 36 as the leading coefficient when x is raised to the 4th power. Therefore, the correct answer is: This is a polynomial function of degree 4 with a leading coefficient of 36.

Answer:

C

Step-by-step explanation:

The nature of the solutions are determined by the value of the discriminant.

Given a quadratic equation in standard form ax² + bx + c = 0 : a ≠ 0

Then the discriminant is Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real and distinct solutions

• If b² - 4ac = 0 then solutions are real and equal

• If b² - 4ac < 0 then solutions are not real, 2 complex conjugate solutions

Here b² - 4ac = - 6 , hence 2 complex conjugate solutions → C

Answer:

The graph of g(x) = ㏑x translated 3 units to the right and then reflected

about the y-axis and then translated 2 units down to form the graph of

f(x) = ㏑(3 - x) - 2

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* lets solve the problem

∵ Graph of g(x) = ㏑x is transformed into graph of f(x) = ㏑(3 - x) - 2

- ㏑x becomes ㏑(3 - x)

∵ ㏑(3 - x) = ㏑(-x + 3)

- Take (-) as a common factor

∴ ㏑(-x + 3) = ㏑[-(x - 3)]

∵ x changed to x - 3

∴ The function g(x) translated 3 units to the right

∵ There is (-) out the bracket (x - 3) that means we change the sign

  of x then we will reflect the function about the y-axis

∴ g(x) translated 3 units to the right and then reflected about the

   y-axis

∵ g(x) changed to f(x) = ㏑(3 - x) - 2

∵ We subtract 2 from g(x) after horizontal translation and reflection

  about y-axis

∴ We translate g(x) 2 units down

∴ g(x) translated 3 units to the right and then reflected about the

   y-axis and then translated 2 units down

* The graph of g(x) = ㏑x translated 3 units to the right and then

  reflected about the y-axis and then translated 2 units down to

  form the graph of f(x) = ㏑(3 - x) - 2

Answer:

c edge

Step-by-step explanation:

Answer:

The coordinates of point P are (3 , 13)

Step-by-step explanation:

* Lets explain how to solve the problem

- Point P divides the segment AB in the ratio 1 : 1

- The ratio 1 : 1 means divide the segment into two equal parts

- Then P is the mid-point of segment AB

- If (x , y) are the coordinates of the mid-point of a segments whose

 endpoints are (x1 , y1) and (x2 , y2) then;

 [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]

∵ The coordinates of point A is (-4 , 15)

∵ The coordinates of point B is 10 , 11)

- Let point A is (x1 , y1) , point B is (x2 , y2) and point P is (x , y)

∵ x1 = -4 , x2 = 10 and y1 = 15 , y2 = 11

∴ [tex]x=\frac{-4+10}{2}=\frac{6}{2}=3[/tex]

∴ [tex]y=\frac{15+11}{2}=\frac{26}{2}=13[/tex]

∴ The coordinates of point P are (3 , 13)

Answer:

(3,13)

Step-by-step explanation:

I got it correct on founders edtell

Answer:

A. 0.80

Step-by-step explanation:

First, you need to find the mean of the cost of Sara's lunches the first week. The mean is the 'average,' and to find the average, add all of your terms and divide by the amount of terms.

[tex]11.52+6.48+5.99+14+9.5\\18+5.99+14+9.5\\23.99+14+9.5\\37.99+9.5\\47.49[/tex]

Sarah's total cost for the first week was $47.49. Divide by your number of terms (5) for your average daily cost.

[tex]\frac{47.49}{5} =9.498[/tex]

This can be rounded to $9.50.

For the next week, Sara spent $4 more in total than the first week. So, add $4 to your total.

[tex]47.49+4=51.49[/tex]

Now, divide $51.49 by your number of terms (5) again to find your average for the second week.

[tex]\frac{51.49}{5} =10.298[/tex]

This can be rounded to $10.30.

Find the difference.

[tex]10.30-9.50=0.80[/tex]

Sara spent $0.80 more on average.

Answer:

-10 4/64, -.3125, 1/16, 10 51/80, 10 45/48

Step-by-step explanation:

negatives, the larger the number the smaller it is, opposite for positives. 10 45/48 is closer to 11 than 10 51/80

Answer:

Option C. Shape

Step-by-step explanation:

How the data set rises and drops can best be summarized by the shape of the data set.

For example look at the graph attached: Just by looking at the graph you know at which points the graph increases or decreases and how fast it does. To know exact values, working with the equation/data set is better.

Answer:

C. Shape

Step-by-step explanation:

Answer:

a. 2 and 50

b. 10 and 10

Step-by-step explanation:

Let's denote the side lengths by x and y.

The area is 100 which means that x*y=100.

The only whole numbers which satisfy this are the following:

2,50

4,25

5,20

10,10

Just go through them one by one and find your answer.

The rectangle with an area of 100 square units and whole number side lengths with the largest perimeter is 50 by 2 with a perimeter of 104 units. The smallest perimeter rectangle possible for the same area is a square measuring 10 by 10, which has a perimeter of 40 units.

We are tasked with finding the dimensions of a rectangle with an area of 100 square units and whole number side lengths that will result in either the largest perimeter or the smallest perimeter.

Largest Perimeter Rectangle

To find the rectangle with the largest perimeter, we should aim for the rectangle to have the longest possible length and the shortest possible width while still maintaining an area of 100 square units. In the extreme case, this could be a rectangle with a length that approaches infinity and a width that is infinitely small, but we are limited to whole numbers. Therefore, the rectangle with the largest perimeter in this scenario would be 50 by 2, resulting in a perimeter of (50+2)*2 = 104 units.

Smallest Perimeter Rectangle

To find the rectangle with the smallest perimeter, we need to look for the most square-like dimensions, as a square has the smallest possible perimeter for a given area. For an area of 100 square units, the side lengths would be 10 by 10, so the perimeter would be 10*4 = 40 units.

Answer:

the answer to your question is the fourth one listed on your multiple choice, where it shows it curving at the lowest point out of all the others , in the 4th quadrant

Answer:

B. 5.2%

Step-by-step explanation:

Total number of tables = 20

Number of tables next to window = 5

Number of tables next to salad bar = 5

Probability that the first customer chooses the window table = 5 out of 20 = [tex]\frac{5}{20}[/tex]

When this table is chosen, the total remaining tables are 19 out of which 4 tables are next to windows.

So, now the probability that a customer will choose a window table = 4 out of 19 = [tex]\frac{4}{19}[/tex]

Since the selection of two customers is independent of each other, the probability that two customers will chose the window table will be the product of probabilities of their individual selections.

Therefore, the probability that the next two customers will choose to sit at the window = [tex]\frac{5}{20} \times \frac{4}{19} = 0.052[/tex]

Thus, the probability that the next two customers will choose to sit at the window is 0.052 or 5.2%

Answer:

25 bananas.

Step-by-step explanation:

The cost of one banana = 84/15 =  rs 28/5 = rs 5.60.

So the number of bananas costing rs 140

= 140 / 5.60

= 25 bananas.

Answer:

Step-by-step explanation:

[tex]5^{7x-3}=625\\\\5^{7x-3}=5^4\iff7x-3=4\qquad\text{add 3 to both sides}\\\\7x=7\qquad\text{divide both sides by 7}\\\\x=1[/tex]

Answer:

X = 1

Step-by-step explanation:

Answer:

a bouquet of 18 flowers, 12 pink and 6 blue is correct.

Step-by-step explanation:

Step 1: Find the total number of children.

Number of boys = 2

Total number of children = 3 x number of boys

Total number of children = 3 x 2 = 6

Step 2: Find the ratio of girls to boys

Number of girls = total number of children - total number of boys

Number of girls = 6 - 2 = 4

Girls : Boys

4 : 2

2 : 1

Step 3: Find the ratio of pink and blue flowers

Pink : Blue = Girls : Boys = 2 : 1

Step 4: Check the statements. The ratio of Pink : Blue should be 2 : 1.

1) a bouquet of 12 flowers, 4 pink and 8 blue. Incorrect because in this statement the ratio of pink : blue is 4 : 8 = 1 : 2 instead of 2 : 1.

2) a bouquet of 14 flowers, 8 pink and 6 blue. Incorrect because in this statement the ratio of Pink : Blue 8 : 6 = 4 : 3.

3) a bouquet of 15 flowers, 6 pink and 9 blue  Incorrect because in this statement the ratio of pink : blue is 6 : 9 = 2 : 3.

4) a bouquet of 18 flowers, 12 pink and 6 blue. This is correct because the ratio of pink : blue is 12 : 6 = 2 : 1.

!!                        

Answer:

A bouquet of 12 flowers, 4 pink and 8 blue

Step-by-step explanation:

Let

x----> the number of boys

y ---> the number of girls

z ---> the number of children

we know that

x=2 boys----> equation A

z=3x-----> z=3(2)=6 children ----> equation B

z=x+y ----> equation C

substitute the value of x and the value of z in the equation C and solve for y

6=2+y

y=6-2=4 girls

so

The ratio of girls to boys is equal to

2/4=1/2

therefore

The ratio of pink flowers to blue flowers is equal to 1/2

Let

a -----> the number of pink flowers

b -----> the number of blue flowers

so

For b=9  blue carnations -----> Find the value of a

1/2=a/b

1/2=a/9

a=4.5 pink carnations ----> It doesn't make sense (must be a integer)

For b=8  blue carnations -----> Find the value of a

1/2=a/b

1/2=a/8

a=4 pink carnations ----> It makes sense

therefore

A bouquet of 12 flowers, 4 pink and 8 blue

Answer:

probability is 50 percent

Step-by-step explanation:

total area= 30000

area of secknd ring=15000

therefore 15000/30000 times 100

equals 50 percent

Answer:

Option D.

Step-by-step explanation:

From he given information, we get

Total area of a dartboard = 30,000 mm²

The area of the second ring = 15,000 mm²

We need to find the probability of landing in that second ring.

[tex]Probability=\dfrac{\text{The area of the second ring }}{\text{Total area of a dartboard}}[/tex]

[tex]Probability=\dfrac{15000}{30000}[/tex]

[tex]Probability=0.5[/tex]

Multiply the probability by 100 to find the percentage.

[tex]Probability=0.5\times 100[/tex]

[tex]Probability=50[/tex]

Hence the correct option is D.

Answer:

1/6

Step-by-step explanation:

To find slope here, I'm going to use that slope is rise/run.

I'm going to start at the left dot. How much would I need to go to be on same level as the right point? Up 3.

Now that we are on the same level, how many units right would I need to travel to get to the right point? Right 18.

The slope is 3/18.

You can reduce this to 1/6.

Answer:

A. 1/6

The slope is 1/6.

Step-by-step explanation:

The slope formula is  [tex]\Rightarrow\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex].

[tex]y_2=6\\y_1=3\\x_2=12\\x_1=(-6)\\[/tex]

[tex]\displaystyle\frac{6-3}{12-(-6)}=\frac{3}{18}=\frac{3\div3}{18\div3}=\frac{1}{6}[/tex]

[tex]\large\textnormal{Therefore, the slope is 1/6.}[/tex]

In other words, what is y if x is 0.

Look on the graph, a line passes through point, [tex]A(x,y)\longrightarrow A(0,-3)[/tex]

So we can conclude that at that very point the input x was 0 and the output y was -3 therefore,

[tex]\boxed{f(-3)=0}[/tex]

Hope this helps.

r3t40

Answer:

(2y-1/y_2)(3y_2/7)

= 2y*(3y_2/7) - (1/y_2)(3y_2/7)

= 6y*y_2/7 - 3/7 = (6y*y_2 - 3)/7

Note: I'm not sure if the 2y-1 was written correctly. If it were intended as the entire thing being a numerator or as 2y_1, this answer is inaccurate.

Answer:

(6y-3)/7

please give me brainliest

Step-by-step explanation:

(2y-1/y²)(3y²/7) first simplify 3y²/y² =3

(2y-1)(3/7) =

(6y-3)/7

Answer:

5x³

Step-by-step explanation:

As discussed in one of my videos, whenever you divide, you subtract the exponents.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

214....

Step-by-step explanation:

If the question is : solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to minus 3 by 4 + 2 by 243 raise to minus 1 by 5​

The given expression can be written as:

4/(216)-2/3+1/(256)-3/4+2/(243)-1/5

This expression has three terms.

Notice that the exponents are negative:

We will change the division into multiplication so that the exponents will become positive;

4*(216)^2/3+ 1*(256)^3/4+ 2*(243)^1/5

If we multiply 6 three times it will give us 6^3=6*6*6=216

If we multiply 4 four  times it will give us 4^4=4*4*4*4=256

If we multiply 3 five times it will give us 3^5=3*3*3*3*3=243

So we will write it as:

=4*(6^3)^2/3+ 1(4^4)3/4 +2(3^5)^1/5

=4(6)^2+(4)^3+2(3)

=4*36+64+6

=144+64+6

=214

The answer is 214....

The expression 9 / 3[(18 - 6) - 22] evaluates to -0.3, following the order of operations: first compute the parentheses, then multiply, and finally divide.

To evaluate the expression 9 / 3[(18 - 6) - 22], we need to follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's solve it step-by-step:

Next, multiply by 3. Since there are no explicit parentheses around the 3 and the expression, we interpret it as 3 times the result from step 1, 3 * (-10), which equals -30.

Finally, divide 9 by the result from step 2, 9 / -30. That gives us -0.3.

The final answer, after doing the calculations in the correct order, is -0.3.

[tex]\huge{\boxed{y=\bf{5x+11}}}[/tex]

Distribute the 5. [tex]y-1=5x+10[/tex]

Add 1 on each side. [tex]y=5x+11[/tex]

y−1=5(x+2)

Step 1: Add 1 to both sides.

y−1+1=5x+10+1

y=5x+11

Answer:

y=5x+11