Below are two different functions, f(x) and g(x). What can be determined about their slopes?
f(x)= 4x + 2
A) function f(x) has a larger slope
B) the function g(x) has a larger slope
C) they both have the same slope
D) the relationship between slopes cannot be determined

Answer/Step-by-step explanation:

Given:

Line equation => [tex] 2.1x + 9.9y - 9.2 = 0 [/tex]

Required:

x-intercept and y-intercept of the line.

SOLUTION:

The x-intercept is the point where the line intercepts the x-axis. To find the x-intercept of the line for which the equation is given above, set y = 0 and solve for x.

[tex] 2.1x + 9.9(0) - 9.2 = 0 [/tex]

[tex] 2.1x + 0 - 9.2 = 0 [/tex]

[tex] 2.1x - 9.2 = 0 [/tex]

[tex] 2.1x - 9.2 + 9.2 = 0 + 9.2 [/tex]

[tex] 2.1x = 9.2 [/tex]

[tex] \frac{2.1x}{2.1} = \frac{9.2}{2.1} [/tex]

[tex] x = 4.4 [/tex] (approximated)

The y-intercept is the point where the line intercepts the y-axis. At this point, x = 0. Set x = 0 and solve for y to find the y intercept.

[tex] 2.1(0) + 9.9y - 9.2 = 0 [/tex]

[tex] 9.9y - 9.2 = 0 [/tex]

[tex] 9.9y - 9.2 + 9.2 = 0 + 9.2 [/tex]

[tex] 9.9y = 9.2 [/tex]

[tex] y = \frac{9.2}{9.9} [/tex]

[tex] y = 0.9 [/tex] (approximated)

Answer:

125°

Step-by-step explanation:

Sum of angles of triangle equals 180°:

Answer:

x=125

Step-by-step explanation:

because sum of interior angles of a triangle is 180

Answer:

680,000

679,967 rounded to the nearest thousand is 680,000.

So, there are around 680,000 employees working for US Airlines. Hope it helps!

Answer:

680,000

Step-by-step explanation:

Look at the hundreds place if it's 5 or higher you round up the thousands place by one. Every place to the right of the hundreds place turns into a zero.

Answer:

0.875

Step-by-step explanation:

14÷16= 0.875

divide the mass value by 16

Answer:

Its learning how to read credit card statements

Step-by-step explanation:

Learn how to read your credit card statements and control the way you process them

Step-by-step explanation:

The approximate equation to convert from liters to quarts is : x • 1.056688.

We enter 65 for x and multiply.

65 • 1.056688 = 68.68472

We round that to the nearest 100th to get our final answer.

Our final answer: 68.68 liters

Hi there! :)

Answer:

[tex]\huge\boxed{-5.5q - 7}[/tex]

-(5.5q + 7)

Distribute:

-(5.5q) -(7)

-5.5q - 7

Answer:

Z≥0 = {0, 1, 2, .

Step-by-step explanation:

Just took test

Answer:

-b[a + (c-d)^2]

-(-8)[3/4 + (-2 -3)^2]

8 [3/4 + (-5)^2]

8 [3/4 + 25]

8 [25.75]

206

=======================================

Work Shown:

a = 3/4

b = -8

c = -2

d = 3

----------------

c-d = -2-3 = -5

(c-d)^2 = (-5)^2 = 25

a+(c-d)^2 = 3/4 + 25 = 3/4 + 100/4 = 103/4

-b * [ a + (c-d)^2 ] = -(-8)*103/4 = 8*103/4 = (8/4)*103 = 2*103 = 206

----------------

Another way to show the steps could be

[tex]-b[a+(c-d)^2]\\\\-(-8)\left[\frac{3}{4}+(-2-3)^2\right]\\\\8\left[\frac{3}{4}+(-5)^2\right]\\\\8\left(\frac{3}{4}+25\right)\\\\8\left(\frac{3}{4}+\frac{100}{4}\right)\\\\8\left(\frac{3+100}{4}\right)\\\\8\left(\frac{103}{4}\right)\\\\\frac{8}{4}*103\\\\2*103\\\\206\\\\[/tex]

Which is more or less the same thing as the previous section.

----------------

So ultimately,

[tex]-b[a+(c-d)^2] = 206[/tex]

when a = 3/4, b = -8, c = -2, and d = 3.

Step-by-step explanation:

(i) 5 ≤ 2x − 4 ≤ 8 add 4 to all three expressions

9 ≤ 2x ≤ 12 divide by 2

9/2 ≤ x ≤ 6

(ii) −10 < (4 −3y)/− 5 ≤ 4 multiply all sides by -5

-20 ≤ 4 - 3y < 50 subtract 4

-24 ≤ -3y < 46 divide with -3

-46/3 < y ≤ 8

Answer:

[tex]\Large \boxed{0.40 < 0.430 < 0.480 < 0.489}[/tex]

Step-by-step explanation:

First you have to see the decimal places.

Than the number of digits there is.

So this is how we make it from least to greatest!

Since there is 3 numbers after the decimals in almost all of them...

Than let’s make ‘0.40’ into 3 numbers after the decimal too.

I am sure you have heard that if you add a ‘0’ to a decimal nothing will change right?

So let’s make 0.40 into 3 numbers after the decimal just like the other numbers!

Okay so first let’s add a zero to ‘0.40’... which now this turns into ‘0.400’

Now it will be more easier to compare least to greatest!

0.400 is the least, than comes 0.430, & than would be 0.480, & finally the greatest would be 0.489

Therefore the answer is 0.40 < 0.430 < 0.480 < 0.489.

Answer:

The answer of the question is 10.53%.

Answer:580

Step-by-step explanation:

Answer:

[tex]\huge \boxed{{m=6}}[/tex]

Step-by-step explanation:

Let's take two points,

(12, -4) and (13, 2).

slope = (difference of y) / (difference of x)

m = (2 - - 4) / (13 - 12)

m = (2 + 4) / 1

m = 6 / 1 = 6

The slope of the line is 6.

Answer:

6

Step-by-step explanation:

The slope is the change in y over the change in x

m = ( y2-y1)/(x2-x1)

    = (14-8)/(15-14)

   = 6/1

Answer:

ŷ = 6.69X - 706.18 ; 270.56; B. The predicted value is not close to the actual diastolic reading.

Step-by-step explanation:

Given the data below :

Systolic reading(x) :

117

134

150

113

138

113

144

145

Diastolic (y) :

85

74

86

55

75

80

106

841

A) Find the regression​ equation, letting the systolic reading be the independent​ (x) variable:

Using the online regression calculator :

The regression equation obtained is ;

ŷ = 6.69X - 706.18

Where ;

ŷ = dependent variable

6.69 is the gradient or slope

-706.18 is the intercept, where the line crosses the y - axis.

X - the independent variable (Systolic reading)

B.) Find the best predicted diastolic pressure for a person with a systolic reading of 146 .

ŷ = 6.69X - 706.18

ŷ = 6.69(146) - 706.18

ŷ = 270.56

Is the predicted value close to 91.0

B. The predicted value is not close to the actual diastolic reading.

Answer:

1 * 10 ^ -7

Step-by-step explanation:

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------

Calculate 36 to the power of [tex]\frac{1}{2}[/tex].

[tex]\frac{1}{2} = 0.5[/tex]

[tex]36^{0.5} = 6[/tex].

Answer:

[tex]\huge \boxed{f(-2)=6}[/tex]

Step-by-step explanation:

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

Switching x variable with -2.

[tex]\sf f(-2)=-1(-2)+4[/tex]

Evaluating.

[tex]\sf f(-2)=2+4[/tex]

[tex]\sf f(-2)=6[/tex]

Answer:

Step-by-step explanation:

[tex]f(x) = -1x + 4\\\\f(-2) =?\\\\f(-2) = -1(-2) +4\\f(-2) = 2+4\\f(-2) = 6[/tex]

Answer:

[tex]$\frac{51}{5}t$[/tex]

Step-by-step explanation:

Let W = [tex]$(p_0, p_1, p_2)$[/tex]  be orthogonal polynomials which is equal to [tex]$(4, 3t, t^2 -2)$[/tex], which defines the inner products as

[tex]$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$[/tex]

Now, we find the orthogonal projection of [tex]$p=3t^3$[/tex] on W.

So the projection is

[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]

[tex]$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$[/tex]

          [tex]$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$[/tex]

[tex]$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$[/tex]

            [tex]$=4(4)+4(4)+4(4)+4(4)+4(4)=80$[/tex]

[tex]$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$[/tex]

          [tex]$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$[/tex]

[tex]$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$[/tex]

            [tex]$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$[/tex]

[tex]$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$[/tex]

         [tex]$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$[/tex]

[tex]$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$[/tex]

            [tex]$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$[/tex]

Therefore,

[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]

              [tex]$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$[/tex]

              [tex]$=\frac{51}{5}t$[/tex]

Answer:

1.131,5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, I attached the graph.

This is a parabola, then a line and finally an horizontal line.

The vertex of the parabola is (0,0) and (2,4) is on the graph.

For the second part, draw a line which is passing by (2,4) and (0,4)

Finally, draw the line y = 4

You can see that f is continuous everywhere except in x = 4.

So, for any c real different from 4 the limit of f(x) exists.

Thank you

Answer:

a + (n-1)*4

Step-by-step explanation:

Day n could be any particular day located on the x-axis of the bar chart. Each bar represents the amount of cupcakes sold on each of the four days numbered from 1 to 4. The height of each bar marks the number of cupcakes sold. According to the chart attached, the number of cupcakes sold on each day is listed below:

Day 1 : 1 cupcake sold

Day 2 : 5 cupckaes sold

Day 3: 9 cupcakes sold

Day 4: 13 cupckaes sold

Studying the graph carefully fully, it will be observed that the number of cupcakes sold increases by a margin of 4 after day one.

As such the number of cupcakes sold in n days can be modeled by:

Using the Arithmetic progression formula:

Tn = a + (n-1)d

d = common difference, = 4

a = first term = 1

n = number of days

Hence, number sold in day n:

a + (n-1)*4

Arithmetic progressio

Answer:

3n−1  cupcakes

Step-by-step explanation:

Answer:

There are 15 more measles vaccines than polio vaccines

Step-by-step explanation:

Represent Polio with P and Measles with M

Given

5P + 3M = 225

P + M = 60

Required

How much is M greater than P; M - P

Make M the subject of formula in the second equation

[tex]M = 60 - P[/tex]

Substitute this in the first equation

[tex]5P + 3M = 225[/tex] becomes

[tex]5P + 3(60 - P) = 225[/tex]

Open the bracket

[tex]5P + 180 - 3P = 225[/tex]

Collect Like Terms

[tex]5P - 3P = 225 - 180[/tex]

[tex]2P = 45[/tex]

Divide both sides by 2

[tex]P = 22.5[/tex]

Substitute 22.5 for P in [tex]M = 60 - P[/tex]

[tex]M = 60 - 22.5[/tex]

[tex]M = 37.5[/tex]

Calculate the difference; M - P

[tex]M - P = 37.5 - 22.5[/tex]

[tex]M - P = 15[/tex]

Hence, there are 15 more measles vaccines than polio vaccines

Answer:

19

Step-by-step explanation:

first you would combine like terms to get 5x^2-3x-7. plug in -2 into the x's and you will get 19!

Answer:

Option (A) and Option (D)

Step-by-step explanation:

Point on the parabola is (x, y).

Focus given as (2, -4) and directrix of the parabola is y = -6

Therefore, distance of the point from the directrix will be,

d = |(y + 6)|

Similarly, distance of the point (x, y) from the focus will be,

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

  = [tex]\sqrt{(x-2)^2+(y+4)^2}[/tex]

Therefore, Option (A) and Option (D) will be the correct options.

Answer:

$540

Step-by-step explanation:

We know Damien earned $9 per hour, worked 30 hours a week and was paid every 2 weeks.

We can write an expression to something like this:

(9 x 30) x 2

Which would give us 540

The question asks for the Gross income (the total income, before any taxes or deductions)

Which means that his gross income was $540

Answer: $1.6

Step-by-step explanation:

price × percentage of tax=amount of tax

$20 × 8%=20 × 0.08= $1.6

Hope this helps!! :)

Answer:

a.   [tex]X(T) = 120 (1.058)^T[/tex]

b.   Population after 3 years is 142

c.   50 years

Step-by-step explanation:

Given

Type of growth: Exponential

Initial number of rats = 120

Number of rats (15months) = 280

Solving (a)

Since the growth type is exponential, we make use of the following exponential progression

[tex]X_T = X_0 (1 + R)^T[/tex]

Where Xo is the initial population;

Xo = 125

[tex]X_T[/tex] is the current population at T month

So;

[tex]X_T = 280[/tex]; when [tex]T = 15[/tex]

Substitute these values in the above formula

[tex]280 =120 * (1 + R)^{15}[/tex]

Divide both sides by 120

[tex]\frac{280}{120} =(1 + R)^{15}[/tex]

[tex]2.3333 =(1 + R)^{15}[/tex]

Take 15th root of both sides

[tex]\sqrt[15]{2.3333} =1 + R[/tex]

[tex]1.05811235561 = 1 + R[/tex]

Subtract 1 from both sides

[tex]R = 1.05811235561 - 1[/tex]

[tex]R = 0.05811235561[/tex]

[tex]R = 0.058[/tex] (Approximated)

Plug in values of R and Xo in [tex]X_T = X_0 (1 + R)^T[/tex]

[tex]X_T = 120 (1 + 0.058)^T[/tex]

[tex]X_T = 120 (1.058)^T[/tex]

Write as a function

[tex]X(T) = 120 (1.058)^T[/tex]

Hence, the function is [tex]X(T) = 120 (1.058)^T[/tex]

Solving (b):

Population after 3 years

In this case, T = 3

So:

[tex]X(T) = 120 (1.058)^T[/tex]

[tex]X(3) = 120 (1.058)^3[/tex]

[tex]X(3) = 120 * 1.18466445254[/tex]

[tex]X(3) = 142.159734305[/tex]

[tex]X(3) = 142[/tex] (Approximated)

Solving (c): When population will reach 2000

Here: X(T) = 2000

So:

So:

[tex]2000 = 120 (1.058)^T[/tex]

Divide both sides by 120

[tex]\frac{2000}{120} = 1.058^T[/tex]

[tex]16.667 = 1.058^T[/tex]

Take Log of both sides

[tex]Log(16.667) = Log(1.058^T)[/tex]

Apply law of logarithm

[tex]Log(16.667) = TLog(1.058)[/tex]

Divide both sides by Log(1.058)

[tex]T = \frac{Log(16.667)}{Log(1.058)}[/tex]

[tex]T = 49.9009236926[/tex]

Approximate

[tex]T = 50\ years[/tex]

Answer: The Max fun is 9, and the Min fun is -3

Step-by-step explanation:

Please follow the steps carefully;

Let us consider the function f(x,y) = xy -------------- (1)

We will apply the Lagrange multipliers to maximize the function f(x,y) subject to the constraint  g(x,y) = x^2+y^2-xy = 9

By differentiating (1) w.r.t  x,   we get fx(x,y) = y

By differentiating (1) w.r.t  y,   we get fy(x,y) = x

By differentiating g(x,y) w.r.t  x,   we get gx(x,y) = 2x - y

Also By differentiating g(x,y) w.r.t  y,   we get gy(x,y) = 2y - x

let us take

fx = λgx

where y = λ(2x - y)

y/2x - y = λ  ----------- (2)

fy =  λgy

where x = λ(2y - x)

λ = x/2y -x ----------- (2)

Let us equate (2) and (3)

y/2x - y  = x/2y -x

2y² - xy = 2x² - xy

2y² = 2x² after cancelling like terms

y² = x²

So y = ±x

Now let us substitute y = x into the given constraint

x² + y² - xy = 9

x² + x² - x(x) = 9

x² = 9

therefore x = ± 3

We can conclude that when x = ±3, ⇒ y = ±3

The corresponding points are (3,3), (-3,-3)

Substitue y = -x in the given constraint gives

x² + y² - xy = 9

x² + (-x)² -x(-x) = 9

3x² = 9

x² = 3

x = ±√3

The corresponding points are (√3,-√3), (-√3,√3)

The function value is

f(x,y) = xy

f (√3,-√3) = (√3)(-√3) = -3

f (-√3,√3) = (-√3)(√3) = -3

we get;

f(3,3) = (3)(3) = 9

and

f (-3,-3) = (-3)(-3) = 9

We can conclusively say that ;

The Maximum value of the function is 9

The Minimum value of the function is -3

cheers i hope this helped

Answer:

1

Step-by-step explanation:

4^10/4^10 x 7^O =

= 4^(10 - 10) * 1

= 4^0 * 1

= 1 * 1

= 1

Answer:

1

Step-by-step explanation:

4^10/4^10 = 1

7^0 = 1

1 x 1 = 1

Answer:

The correct answer is B.

Explanation:

Putting it into your calculator as you see it gives you the correct answer.

Have a good day! :)