WILL GIVE BRAINLIEST

The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

Given that,

f(x) = 1 + |2x - 5|

And,

f(x) = {f₁       x < a

         {f₂      x ≥ a

Now,

We have,

f(x) = 1 + |2x - 5|

And,

By definition of absolute value,

|x| = {x        x ≥ 0

       {-x       x < 0

And,

Given the absolute value,

|2x - 5|

Solve for x,

i.e.

2x - 5 = 0

We get,

x = 5/2 = 2.5

i.e.

a = 5/2

i.e.

For all values greater than x = 5/2, 2x - 5 is positive,

And,

For all values less than x = 5/2, 2x - 5 is negative.

So,

|x| = {x        x ≥ 5/2

       {-x       x < 5/2

i.e.

|2x - 5| = {2x - 5        x ≥ 5/2

              {-(2x - 5)       x < 5/2

Now,

f(1) = 1 + |2(1) - 5|

We get,

f₁ = 4

And,

f(2) = 1 + |2(2) - 5|

We get,

f₂ = 2

Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

To learn more about absolute values click here,

https://brainly.com/question/24734454

#SPJ1

If 75 grams of ice cream contains 10 grams of fat, then 150 grams of ice cream would contain 20 grams of fat. The amount of fat is directly proportional to the weight of the ice cream.


We can set up a proportion to solve the problem. Let x represent the unknown amount of fat in 150 grams of ice cream. According to the given information, we have the proportion:
10 grams of fat / 75 grams of ice cream = x grams of fat / 150 grams of ice cream
To solve for x, we can cross-multiply and then divide:
10 * 150 = 75 * x
1500 = 75x
X = 1500 / 75 = 20
Therefore, 150 grams of ice cream would contain 20 grams of fat. This is because the ratio of fat to ice cream remains constant, so we can use this proportion to find the missing value.

Learn more about Ratio here: brainly.com/question/13419413
#SPJ11

The percentage by which the number has to be decreased is 20%.

It represents a mathematical relationship or calculation. For example, the expression "2x + 3" is an algebraic expression that represents a linear equation with a variable x and constants 2 and 3. Algebraic expressions can be simplified, evaluated for specific values of the variables, and used to solve equations.

Given:

A number is increased by 25%

To find:

The percentage by which it has decreased

Solution:

The percentage by which the number has to be decreased is 20%.

We can find the percentage by following the given steps-

We know that a number increased by a percentage decreases by a different percentage.

Let us assume that the number is 100.

We know that this number has been increased by 25%.

So, the new number=100+25% of 100

=100+25/100×100

=100+25

=125

Now, the new number is 125.

Let us assume that this number has to be decreased by X% to obtain 100.

So, 125-X% of 125=100

125-X/100×125=100

125-1.25X=100

125-100=1.25X

25=1.25X

25×100/125=X

2500/125=X

X=20%

Therefore, the percentage by which the number has to be decreased is 20%.

To know more about expression visit:

https://brainly.com/question/27148036

#SPJ1

Binomial theorem allows us to expand expression (a + b)^n, where a and b are real numbers and n is a positive integer.Therefore, (root 3 - root 2)^5 can be expressed in form a√3 + b√2, a = 3 - 10 - 10√3 + 5√2 and b = -1.

Using the binomial theorem, we can expand this expression as follows:

(root 3 - root 2)^5 = C(5,0)(root 3)^5(-root 2)^0 + C(5,1)(root 3)^4(-root 2)^1 + C(5,2)(root 3)^3(-root 2)^2 + C(5,3)(root 3)^2(-root 2)^3 + C(5,4)(root 3)^1(-root 2)^4 + C(5,5)(root 3)^0(-root 2)^5

Simplifying each term, we get:

(root 3)^5 - 5(root 3)^4(root 2) + 10(root 3)^3(root 2)^2 - 10(root 3)^2(root 2)^3 + 5(root 3)(root 2)^4 - (root 2)^5

Further simplifying, we obtain:

3√3 - 10√6 + 15√2 - 10√(6√3) + 5√(2√3) - 2√32

Therefore, (root 3 - root 2)^5 can be expressed in the form a√3 + b√2, where a = 3 - 10 - 10√3 + 5√2 and b = -1.

To learn more about Binomial theorem click here : brainly.com/question/30095070

#SPJ11

If I were dealing with a data set that fluctuates quarterly, I would recommend using autoregressive models.

option (b) is correct

This is because autoregressive models take into account the pattern of the previous values to predict future values. Simple moving averages and exponential smoothing are better suited for data sets with more consistent trends, while the random walk is not an ideal method for forecasting as it assumes that future values will be equal to the previous value with no pattern or trend. Therefore, autoregressive models would be the most appropriate method for forecasting a quarterly fluctuating data set.

learn more about autoregressive models

https://brainly.com/question/31316715

#SPJ11

It's important to note that these characteristics are based on the assumption given in the question, and real-world flu distributions can vary.

In a distribution of flu symptoms that clusters at either the top or the bottom end of the age distribution, the following characteristics can be observed:

Bimodal Distribution: The distribution will exhibit two distinct peaks or modes, indicating the two groups of flu symptoms. One peak will be located at the top end of the age distribution, while the other peak will be located at the bottom end.

Age Divide: The distribution suggests a clear divide in terms of age groups affected by flu symptoms. One group, typically the older age group, will experience a higher number of flu symptoms, while the other group, typically the younger age group, will experience a lower number of flu symptoms.

Skewed Distribution: The distribution will be skewed towards one end, either the higher end or the lower end, depending on where the majority of flu symptoms cluster. If the symptoms cluster at the top end, the distribution will be positively skewed, with a longer tail towards the higher ages. Conversely, if the symptoms cluster at the bottom end, the distribution will be negatively skewed, with a longer tail towards the lower ages.

Difference in Symptom Severity: The severity of flu symptoms may differ between the two age groups. If the symptoms cluster at the top end, the older age group may experience more severe symptoms compared to the younger age group. Conversely, if the symptoms cluster at the bottom end, the younger age group may experience more severe symptoms compared to the older age group.

It's important to note that these characteristics are based on the assumption given in the question, and real-world flu distributions can vary. The exact nature of the distribution will depend on various factors, including the specific population studied and the underlying causes of the flu symptoms.

Learn more about Distribution  at

brainly.com/question/29664127

#SPJ4

Question :

The sales tax rate in New Mexico is 5.125%. Select all the equations that represent the sales tax, t, you

would pay in New Mexico for an item of cost c?

A. t = 5.125c

B. t = 0.5125c

C. t = 0.05125c

D. t = c = 0.05125

(E. t = 5.025 c

 Answer:

C. t = 0.05125c

Step-by-step explanation:

First we have to understand the meaning of % sign. It is called percent or percentage. Where cent means 100. Now all we know that 100 cents make one dollar, that is why these 100 smaller units are called as cents.

Now if sales tax is 5.125 percent, remember that if there is $100 capital amount, it will be $5.125 tax.

Now how much would it be for $1?

simply, it will be $0.05125

Now for equation in option C

t = 0.05125 x 1

t = 0.05125

here you can see that the equation is satisfied.

So from this we can establish the equation that for any cost, the relation between tax and cost will be:

t = 0.05125c

There are several resources where you can find free SAT practice tests, including:

1.Official SAT Practice Tests:

2.Khan Academy:

3.Ivy Global:

4.PrepScholar

5.CrackSAT

6.Peterson's

There are several resources where you can find free SAT practice tests, including:

1.Official SAT Practice Tests: The College Board, the organization that creates and administers the SAT, offers eight official practice tests for free on their website. These tests are the most accurate representation of the real exam.

2.Khan Academy: The College Board has partnered with Khan Academy to provide free SAT practice materials, including full-length practice tests and personalized study plans based on your performance.

3.Ivy Global: Ivy Global offers a free SAT practice test with answer explanations that mimic the actual test.

4.PrepScholar: Prep Scholar offers a free online SAT practice test that closely resembles the real exam.

5.CrackSAT :  CrackSAT offers a wide range of free practice tests, including SAT Subject Tests.

6.Peterson's: Peterson's offers a free online practice test that includes a score report with detailed feedback.

Remember, the more practice you have, the more prepared you'll be for the SAT. So take advantage of these free resources and practice as much as you can.

To learn more about  SAT:

https://brainly.com/question/16255571

#SPJ4

Answer:

we cant see it

Step-by-step explanation:

Answer:

Addition Property

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Combine like terms on both sides of the equation and simplify, isolating the variable on to one side of the equation:

6x + 18 = 90

6x = 72

x = 12

The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

To know more about the "variables": //brainly.com/question/25223322

#SPJ11

Considering the given values, initial point be (x1, y1) and terminal point be (x2, y2).

The vector AB is represented as-3i - 6j.

Then we have the following vector AB whose initial point is A(x1, y1) and terminal point is B (x2, y2).

Let's find out the vector AB:

AB(arrow over on top) = OB - OA

Where OA represents the vector whose initial point is O and terminal point is A(x1, y1) and similarly OB represents the vector whose initial point is O and terminal point is B(x2, y2).

Note: O represents the origin point or (0, 0).

Here is the graphical representation of vector AB.

We are given that,

initial point = (2, 2)

terminal point = (-1, -4)

So, here,  

x1 = 2,

y1 = 2,

x2 = -1

y2 = -4O

A= (x1, y1)

    = (2, 2)

OB= (x2, y2)

    = (-1, -4)

AB = OB - OA

     = (-1, -4) - (2, 2)

     =-1i - 4j - 2i - 2j

      = (-1 - 2)i + (-4 - 2)j

      = -3i - 6j

So, the vector AB is represented as-3i - 6j.

To know more about initial point, visit:

https://brainly.com/question/31405084

#SPJ11

Answer: y=4 or y= 4 over 3

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

If the linear trend remained constant, the tuition cost at Ivy Tech in 2017 would have been approximately $3256.40.

To calculate the slope of the line, we will use the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

where y₂ is the tuition cost in 2015 ($3196), y₁ is the tuition cost in 2010 ($3090), x₂ is the year 2015, and x₁ is the year 2010. Plugging these values into the formula, we get:

slope = (3196 - 3090)/(2015 - 2010) = 106/5

Therefore, the slope of the line is 21.2.

Now that we have determined the slope, we can create a linear model that would predict tuition for any year after 2010. The formula for a linear model is:

y = mx + b

where y is the predicted tuition cost, m is the slope of the line, x is the year (with 2010 being 0), and b is the y-intercept (the tuition cost in 2010). Plugging in the values we have, we get:

y = 21.2x + 3090

This is the equation of the line that represents the linear relationship between year and tuition cost at Ivy Tech.

Finally, we can use this linear model to predict what the tuition cost would be in 2017. To do this, we simply plug in x = 7 (since 2017 is 7 years after 2010) and solve for y:

y = 21.2(7) + 3090 = 3256.4

To know more about linear model here

https://brainly.com/question/29757372

#SPJ4

Answer:

p(2) = 0

Step-by-step explanation:

p(2) = 3(2)(2-2)

p(2) = 6(2-2)

p(2) = 6(0)

p(2) = 0

Answer:

19 cents because 2.85/15=0.19ct   and now we round it up its 20cents!

Step-by-step explanation:

Hope this helps!

Answer:

The answer is $0.19

Step-by-step explanation:

Divide 2.85 by 15.

2.85 ÷ 15 = 0.19

The solutions of the equation sin(4x) in the interval [0,2pi) are x = 0, pi/4, pi/2, 3pi/4, pi.

To solve the equation sin(4x) in the interval [0,2pi), we need to find all the values of x that satisfy the equation.

The equation sin(4x) = 0 has solutions when 4x is equal to 0, pi, or any multiple of pi.

Solving for x, we get:
4x = 0, pi, 2pi, 3pi, 4pi, ...

Dividing each solution by 4, we find the corresponding values of x:
x = 0, pi/4, pi/2, 3pi/4, pi, ...

So, the solutions of the equation sin(4x) in the interval [0,2pi) are x = 0, pi/4, pi/2, 3pi/4, pi.

Know more about interval here:

https://brainly.com/question/11051767

#SPJ11

Answer:

5 meters.

Step-by-step explanation:

The side of the building and the ground makes an angle of 90°. This means that we don't need to use sine or cosine law to find for the other side.

We can just simply use the Pythagorean Theorem which is

\({a}^{2} = {b}^{2} + {c}^{2} \\ {a}^{2} = {3}^{2} + {4}^{2} \\ a = \sqrt{9 + 16 } \\ = \sqrt{25} \\ a = 5\)

The volume of a solid is found using the curve y = (1/9)x² and the line x=5.  And the volume is found to be 625π/18 cubic units.

A volume of a solid is used to determine how much space a particular object will take. It tells the amount of space that is present in an object. For example, if we consider a cylinder and fill it with water, the amount of water it can hold is the cylinder's volume.

Given the equation is y = (1/9)x² and x=5, y=0; about the y-axis. From the graph, the larger radius R = 5 and the smaller radius r=x=√(9y). Then, the limit is written as follows,

when x=0, y=0

when x= 5,  y = 1/9×(5)²=25/9

Now, the volume is calculated by using the integral as follows,

\(\begin{aligned}V&=\int^{25/9}_0 (\pi R^2-\pi r^2)\;dy\\&=\pi \int^{25/9}_0 ((5^2-(\sqrt{9y})^2)\;dy\\&=\pi \int^{25/9}_0 (25-9y)\;dy\\&=\pi\left[25y-\frac{9y^2}{2}\right]^{25/9}_{0}\\&=\pi\left[25\left(\frac{25}{9}-0\right)-\frac{9}{2}\left(\left(\frac{25}{9}\right)^2-0^2\right)\right]\\&=\pi \left[\frac{625}{9}-\frac{625}{18}\right]\\&=\frac{625 \pi}{18}\end{aligned}\)

The required answer is 625π/18 cubic units.

To know more about the volume of solids:

https://brainly.com/question/23705404

#SPJ4

Answer:

9

Step-by-step explanation:

I'M TELLING U THE ANSWER IS 9

Integral setup The following equation can be used to determine the volume of a solid of revolution:

V = ∫[a, b] A(x) dx where A(x) is the area of the cross-sections and dx is the thickness of each cross-section.

To determine the volume V generated by rotating the region bounded by y = x³, y = 0, and x = 4 around the y-axis,

For the region bounded by y = x³, y = 0, and x = 4, the cross-sections are perpendicular to the y-axis and they take the shape of washers.  

The washer's area can be determined by taking the difference between the area of the larger circle (with radius 4) and the area of the smaller circle (with radius x³) which is:

A(x) = π(4² - x⁶) dx

To determine V, integrate A(x) over the limits of x = 0 to x = 4 which gives:

V = ∫[0,4] π(4² - x⁶) dx = π[4³x - 1/7x⁷][0,4]V = π[(64 × 4) - (1/7 × 4⁷)] = π[256 - (16384/7)] = 780.189 cubic units

Therefore, the integral set up to determine the volume V generated by rotating the region bounded by y = x³, y = 0, and x = 4 around the y-axis is:

V = ∫[0,4] π(4² - x⁶) dx where A(x) is the area of the cross-sections and dx is the thickness of each cross-section.

To know more about volume visit:

brainly.com/question/30707291

#SPJ11

No, [1 -2 1] is not an eigenvector of [3 3 5; 6 3 6; 7 7 5].

To determine if [1 -2 1] is an eigenvector of [3 3 5; 6 3 6; 7 7 5], we need to check if the given matrix multiplied by the vector is equal to a scalar multiple of the vector.

Let's perform the calculation:

[3 3 5; 6 3 6; 7 7 5] * [1; -2; 1] = [3 + (-6) + 5; 6 + (-6) + 6; 7 + (-14) + 5] = [2; 6; -2].

Since the result is not equal to a scalar multiple of [1 -2 1], we can conclude that [1 -2 1] is not an eigenvector of [3 3 5; 6 3 6; 7 7 5].

There is no corresponding eigenvalue for [1 -2 1] in this case.

For more questions like Vector click the link below:

https://brainly.com/question/29740341

#SPJ11

Answer:

4

Step-by-step explanation: i guessed and got it right

sorry if youre looking for an actual education!!

Answer:$13.15/thirteen USD and fifteen cents

Step-by-step explanation: 50.00-36.85= 13.15

Answer:

0.6 then calculate which expression is equal to that

Step-by-step explanation:

arccos = cos^-1

Put that in calculator

Answer:

5x² + 2x - 3 - px - p

= 5x² + 5x - 3x - 3 - p(x + 1)

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

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

The linear function for the cost is given as follows:

C(t) = 10 + 3t.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

We have that each hour, the cost increases by $3, hence the slope m is given as follows:

m = 3.

For a time of 0 hours, the cost is of $10, hence the intercept b is given as follows:

b = 10.

Thus the function is given as follows:

C(t) = 10 + 3t.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1