the sum of three consecutive natural numbers is 156 find the number which is the multiple of 13 out of these numbers​

Final answer:

To estimate the product -12 4/9 · 5 7/8, round each number to the nearest whole number and multiply. The estimated product is -72.

Explanation:

To estimate the product -12 4/9 · 5 7/8, we can round each number to the nearest whole number and then multiply.

Rounding -12 4/9 to the nearest whole number gives -12.

Rounding 5 7/8 to the nearest whole number gives 6.

Now, we can multiply -12 and 6: -12 · 6 = -72.

So, the estimated product is -72.

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

Plug x = -5 into f(x)

f(x) = 2x-20

f(-5) = 2(-5) - 20

f(-5) = -10-20

f(-5) = -30

Then plug x = -5 into g(x)

g(x) = x-1

g(-5) = -5-1

g(-5) = -6

Divide the two results

(f/g)(-5) = f(-5)/g(-5)

(f/g)(-5) = (-30)/(-6)

(f/g)(-5) = -5

For this case we have the following functions:

[tex]f (x) = 2x-20\\g (x) = x-1[/tex]

We must find [tex]\frac {f (-5)} {g (-5)}[/tex], then:

We have in mind that:

[tex]+ * - = -[/tex]

Equal signs are added and the same sign is placed.

[tex]\frac {f (-5)} {g (-5)} = \frac {2 (-5) -20} {- 5-1} = \frac {-10-20} {- 6} = \frac {-30} {- 6} = 5[/tex]

Answer:

5

Answer:

[tex]y=19.7*10^{3}[/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](-200,-4.03*10^{4}), (50,9.7*10^{3})[/tex]

convert to

[tex](-200,-40.3*10^{3}), (50,9.7*10^{3})[/tex]

substitute in the formula

[tex]m=\frac{9.7*10^{3}+40.3*10^{3}}{50+200}[/tex]

[tex]m=\frac{50*10^{3}}{250}[/tex]

[tex]m=200[/tex]

step 2

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex](x1,y1)=(50,9.7*10^{3})[/tex]

[tex]m=200[/tex]

substitute

[tex]y-9.7*10^{3}=200(x-50)[/tex] ----> equation of the line into point slope form

step 3

Find the value of y when x=100

substitute in the equation the value of x

[tex]y-9.7*10^{3}=200(100-50)[/tex]

[tex]y=200(50)+9.7*10^{3}[/tex]

[tex]y=19,700[/tex]

[tex]y=19.7*10^{3}[/tex]

Answer:

[tex]Z=2.49[/tex] and this Z-score is “unusual.”

Step-by-step explanation:

To calculate the Z score use the following formula

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

Where

μ is the average

[tex]\sigma[/tex] is the standard deviation

x is the data to which we will calculate the z-score

In this case

[tex]\mu = 122.3\\\\\sigma= 18.5\\\\x =168.4[/tex]

So

[tex]Z=\frac{168.4-122.3}{18.5}[/tex]

[tex]Z=2.49[/tex]

A z-score is unusual if [tex]Z> 2[/tex] or [tex]Z < -2[/tex]

Finally

[tex]Z=2.49[/tex] and this Z-score is “unusual.”

Answer: 2.49 unusual

Step-by-step explanation:

Answer:

the slope intercept form is: y = x+2

Step-by-step explanation:

The general form of point slope form is : y-y₁ = m(x-x₁)

The given equation is: y – 3 = (x – 1)

comparing we get,

m = 1

and solving the equation;

y-3 = x-1

Adding +3 on both sides

y = x-1+3

y=x+2

The general formula of slope-intercept form is : y = mx+b

where m is the slope and b is the y-intercept

so, y = x+2

where m =1 and b=2

so, the slope intercept form is: y = x+2

Answer:

the answer is y = y= 1/2x+2

Step-by-step explanation:

let's recall that the vertical asymptotes for a rational expression occur when the denominator is at 0, so let's zero out this one and check.

[tex]\bf \cfrac{5x+5}{x^2+x-2}\qquad \stackrel{\textit{zeroing out the denominator}~\hfill }{x^2+x-2=0\implies (x+2)(x-1)=0}\implies \stackrel{\textit{vertical asymptotes}}{ \begin{cases} x=-2\\ x=1 \end{cases}}[/tex]

Final answer:

The vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2) occur where the denominator equals zero. Factoring the denominator, we find the vertical asymptotes to be at x = -2 and x = 1.

Explanation:

The student is asking about the vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2). To find the vertical asymptotes of a function, we look for values of x where the denominator is equal to zero, because these are the points where the function is undefined and the graph of the function will approach infinity.

To find the vertical asymptotes, set the denominator equal to zero and solve for x:

x² + x - 2 = 0

Factoring the quadratic equation, we get:

(x+2)(x-1) = 0

Therefore, the vertical asymptotes are at x = -2 and x = 1, since these are the values of x for which the denominator becomes zero.

Check the picture below.

notice the alternate interior angles in the picture.

[tex]\bf tan(68^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{x}}\implies x=\cfrac{1.5}{tan(68^o)}\implies x\approx 0.61 \\\\[-0.35em] ~\dotfill\\\\ tan(56^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{w}}\implies w=\cfrac{1.5}{tan(56^o)}\implies w\approx 1.01 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{width of the crater}}{x+w\implies 1.62}~\hfill[/tex]

The width of the crater is 1.61 km.

Plane is flying at altitude of  1.5 km

The angle of depressions to point A = 68 degrees/

The angle of depression to point B = 56 degrees.

In the given diagram below, we can see:

Angle XPD is right angle and thus we have:

[tex]\angle APD + \angle APX = 90\\\angle APD = 180 - \angle APX = 90 - 68 = 22^\circ[/tex]

Similarly, Angle  YPD is right angle and thus:

[tex]\angle DPB + \angle BPY = 90\\\angle DPB = 90 - \angle BPY = 90 - 56 = 34^\circ[/tex]

Since the triangle ADP and triangle  PDB  are right angled triangles, thus we have by trigonometric ratios:

[tex]tan(22) = \dfrac{AD}{PD}\\\\0.404 \times 1.5 = AD\\\\AD = 0.606\: \rm km[/tex]

Similarly,

[tex]tan(34) = \dfrac{BD}{PD}\\\\0.674 \times 1.5 = BD\\\\BD = 1.01 \: \rm km[/tex]

The width of the crater = AD + DB = 1.01 km + 0.606 km  = 1.61 km

Thus, width of the crater is 1.61 km.

Learn more about angle of depression here:

https://brainly.com/question/10217662

I am going to assume that you mean:

x² < 49

To solve this you must do the opposite of squaring, which would be taking the square root. What you do to one side you must do to the other.

√x² < √49

x < 7

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

To solve the inequality x^2 < 49, we take the square root of both sides resulting in the solution -7 < x < 7, which means x can be any real number between -7 and 7.

Explanation:

The student's question is about solving an inequality involving a square of a variable, specifically x^2 < 49. To solve this inequality, we will first take the square root of both sides, keeping in mind that when we take the square root of a square inequality, we must consider both the positive and negative roots. Therefore, we can express the inequality as -7 < x < 7, since both positive and negative square roots of 49 are 7 and -7, respectively. This represents the range of values for x where the original inequality holds true.

The solution implies that x can take on any real value that is less than 7 and greater than -7. There's no need for tools like completing the square or the quadratic formula here, as the inequality is already in a solvable form.

Answer: 372in³

Step-by-step explanation:

All we have to do is find the volume of the two separate rectangular prisms and add them up.

First we will find the volume of the standing prism:

5in * 3in * 12in = 180in³

Now the other prism:

12in * 4in * 4in = 192in³

Now add them up:

180in³ + 192in³ = 372in³

Answer:

372 [tex]inches^{3}[/tex]

Step-by-step explanation:

Imagine the figures are each separate. The top figure's dimensions would be L=12 in, W=4 in, and H=4 in. The bottom figure's dimensions would be L=5 in, W=3 in, and H=12 in. So, do the volume formula for each: L x W x H and then add them together.

12 x 4 x 4 = 192 inches^3

5 x 3 x 12 = 180 inches^3

192 + 180 = 372 inches^3

Answer:

Infinitely many solutions.

Step-by-step explanation:

2 (n - 1) + 4n = 2 (3n - 1) Let's simplify this to solve it.

2n - 2 + 4n = 6n - 2 Distribute 2(n-1) and 2(3n-1)

2n + 4n - 2 = 6n - 2 Rearrange the left side of the equation.

6n - 2 = 6n - 2 Add 2n + 4n.

-6n        -6n Subtract 6n from both sides.

-2 = -2? Yes, -2 equals -2.

Therefore, the answer is infinitely many solutions, meaning that n can be any real number.

An equation can have no solution, one solution or infinitely many solutions.

The equation [tex]2(n -1) + 4n = 2(3n - 1)[/tex] has infinitely many solutions

Given that:

[tex]2(n -1) + 4n = 2(3n - 1)[/tex]

Open brackets

[tex]2n -2 + 4n = 6n - 2[/tex]

Collect like terms

[tex]2n + 4n - 6n= - 2+2[/tex]

[tex]0 = 0[/tex]

When the solution to an equation is 0 on both sides, the equation has infinitely many solutions

Read more about number of solutions at:

https://brainly.com/question/15272411

Answer:

[tex]g(x)=-x^{2}-4[/tex]

Step-by-step explanation:

we know that

The function g(x) is a vertical parabola open downward with vertex at (0,-4)

The equation of a vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

I assume that g(x) is a reflection of the function f(x) over the line y=-2

so

a=-1 ---> because in the function f(x) the value of a is equal to 1

therefore

[tex]g(x)=-x^{2}-4[/tex]

Answer:

B. Rectangle

Step-by-step explanation:

All rectangles are parallelograms.

Answer:

A. A translation right 2 units:

We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation right 2 units would be:

g(x) = f(x-2).

B. A translation left 2 units:

We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation left 2 units would be:

g(x) = f(x+2).

C. A translation up 2 units:

We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation up 2 units would be:

g(x) = f(x) + 2

D. A translation down 2 units:

We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation down 2 units would be:

g(x) = f(x) - 2

Final answer:

The function f(x) translated to g(x) via a translation right 2 units, which shifts the graph of the function 2 units to the right on the x-axis.

Explanation:

The transformation that transformed the parent function, f(x), to g(x) is a translation right 2 units. This is because when the argument of the function f(x) becomes f(x-2), the graph of f(x) is shifted to the right by 2 units along the x-axis. To understand this, let us consider the original function y = f(x).

The graph of the new function y = f(x-2) is the same as the original, but every point on the graph has been moved 2 units to the right. This can also be viewed as if the x-axis (and origin) has shifted 2 units to the left while the graph remains stationary.

Answer:

Paul's unmarried daughter, Candace, lived with him in his home for the entire year. Paul is divorced. He owns his own home and pays all of the costs of upkeep for the home. Paul paid over one-half of the cost of support for Candace. Paul may file as head of household if Candace is under the age of 19 or permanently disabled.

If none of the conditions statetd above are met, then Candance won't be considered a dependent. If Candance is not a dependant, Paul can still file as a head of household given that he paid over one-half of the cost of support for Candance.

When a line has a slope of zero it means that it is horizontal. This means that all the x values have the same y values. In this case it means that the y value is always -1.

The equation for this line is...

y = -1

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y= -1

Step-by-step explanation:

When we have a line with slope of 0, it means that the y value does not change, so our equation must be in the form y= something

The point has a y value of -1,

so  our equation is

y= -1

Answer:

figure 2

Step-by-step explanation:

Answer:

The answer is figure 4.

Answer:

The cost of the racquet is [tex]\$135[/tex]

Step-by-step explanation:

Let

x-----> the cost of the racquet

we know that

The racquet represent the 100%

so

using proportion

[tex]x/100\%=\$9.45/7\%[/tex]

[tex]x=100\%*(\$9.45)/7\%[/tex]

[tex]x=\$135[/tex]

Answer: d. 512

Step-by-step explanation:

You need to remember that:

[tex](\sqrt[3]{x})^3=x[/tex]

Then, given the equation:

[tex]\sqrt[3]{n}=8[/tex]

You can find the value of "n" that make the equation true, by solving for "n".

So, to solve for "n", you need to raise both side of the equation to power 3. Therefore, you get:

 [tex]\sqrt[3]{n}=8[/tex]

 [tex](\sqrt[3]{n})^3=(8)^3[/tex]

 [tex]n=512[/tex]

Then, the value of "n" that makes the equation [tex]\sqrt[3]{n}=8[/tex] true is: 512 (You can observe that this matches with the option d).

Answer:

the answer is D

Step-by-step explanation:

Answer:

(5y+3)(y-1)

Step-by-step explanation:

5y^2-2y-3

I don't know if you like trial factors or not... but we can try that way

notice we have 5y^2

that can be written as 5y * 1y

Notice at the end we have -3

that can be written as -3*1

So possible answers could be:

(5y-3)(1y+1)   =5y^2+5y-3y-3=5y^2+2y-3

So this was almost right.

If we just switch the signs the - and + there we will have got it

(5y+3)(1y-1)=5y^2-5y+3y-3=5y^2-2y-3 which is good

So the answer is (5y+3)(y-1)

To factor the quadratic equation 5y^2-2y-3 completely, find two numbers that multiply to -15 and add to -2, and use them to rewrite the middle term before factoring by grouping. The factors obtained are (5y - 3)(y + 1).

The given quadratic equation to factor completely is 5y^2-2y-3. To achieve this, we are finding two numbers that multiply to the product of the coefficient of y^2 (which is 5) and the constant term (which is -3), and at the same time add up to the coefficient of the y term (which is -2).

The required pair of numbers is -3 and -1, because (-3)*(1) = -3 (the product of coefficient of y^2 and the constant term) and (-3)+(1) = -2 (the coefficient of the y term).

We rewrite the middle term and then factor by grouping:

https://brainly.com/question/30398551

#SPJ2

Answer:

y = mx + b

Step-by-step explanation:

Since there is no illustration, that is all I can give you. I apologize.

Answer:

y=mx +b is the formula

Step-by-step explanation:

I think you are missing a part of the question.

The answer is C. (1, 12).

12 = 3 x [tex]4^{1}[/tex]

Answer:

Step-by-step explanation:

f(x)= 3 • 4^x

we can use the x coordinate of the points given in option to check what value do we get for y or f(x) .

so using the point from first option A :

x= 12

[tex]y=f(12)=3.4^{12}=50331648\neq 1[/tex]

for option B

x=0

[tex]y=f(0)=3.4^0=3[/tex]

option C

x=1

[tex]y = f(1)= 3.4^1=12[/tex]

so the correct option is C

Answer:

(6x5) • 8

Step-by-step explanation:

We’ll I find it’s 6 dollars a day and their are 5 days that would be 30 but this went in for 8 weeks so it would be 30 x 8 which equal 240

Answer:

Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240

Step-by-step explanation:

Given:

Amount spend on Breakfast using debit card = $6

Amount for breakfast spend for 5 mornings per week for past 8 weeks.

We need to write the multiplication expression for the given situation.

Amount spend on breakfast for a morning = $6

Amount spend on breakfast for 5 morning = 6 × 5

Amount spend on breakfast for 1 week = $ ( 6 × 5 )

Amount spend on breakfast for 8 week = ( 6 × 5 ) × 8

Required multiplication expression = ( 6 × 5 ) × 8

Answer of the multiplication = ( 6 × 5 ) × 8 = ( 30 ) × 8 = 240

Therefore, Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240

Answer:

The answer to this is 0.25

Step-by-step explanation:

7/12= 0.58333 repeating, and 1/3 is 0.3333 repeating. When you subtract 7/12 from 1/3 you get 0.25

Hope it helps

Answer:

0.25

Step-by-step explanation:

The answer is:

The equation is an example of the distributive property.

To determine which method/property is the equation example, we need to remember the distributive property.

We can state the distributive property with the following example:

[tex](a+b)(c+d)=a*c+a*d+b*c*+b*d[/tex]

So, we are given the expression:

[tex](2x^{2}-1)(3x+2)[/tex]

Then, apllying the distributive property we have:

[tex](2x^{2}-1)(3x+2)=(2x^{2})*(3x)+(2x^{2})*2+(-1)*(3x)+(-1)*(2)[/tex]

Hence, the equation is an example of the distributive property.

Have a nice day!

Answer:

x = 5 ± sqrt(35)

Step-by-step explanation:

X^2 - 10x+ 25 = 35.​

Factor the left hand side.  This is the difference of squares.  a^2 -2ab - b^2 = (a-b)^2  where a = x and b = 5

(x-5) ^2 = 35

Take the square root of each side

sqrt((x-5) ^2) =± sqrt(35)

x-5 = ± sqrt(35)

Add 5 to each side

x-5+5 = 5 ± sqrt(35)

x = 5 ± sqrt(35)

Answer:

c is the correct answer

Step-by-step explanation:

the way I study

Answer:

I only know how to do the first and second one i'm not sure about the rest:  V=Lwh

Step-by-step explanation:

so, (6)(6)(8)= 288ft^3

and (12)(16)(18)= 3456m^3

Hope i have helped you in some way!

Answer:

55 inches

Step-by-step explanation:

This question is on z-score for a sample

The general formula for finding z score for a sample is;

z=(x-μ)/δ...................where x is the sample is the height , μ is the mean and δ is the standard deviation

Given;

z=3       x=?      μ=49     δ=2

Substitute values above in the general formulae

z=(x-μ)/δ

3=(x-49)/2

[tex]3=\frac{x-49}{2} \\\\\\3*2=x-49\\\\\\6=x-49\\\\\\6+49=x\\\\\\55=x[/tex]

Answer:

Step-by-step explanation:

To solve this problem we need to use the following formula

[tex]Z=\frac{x- \mu}{\sigma}[/tex]

Where [tex]Z[/tex] is the z-value, [tex]\mu[/tex] is the mean, [tex]\sigma[/tex] is the standard deviation and [tex]x[/tex] is the height of the student.

In this case, we have

[tex]Z=3\\\mu=49\\\sigma=2[/tex]

Replacing all these values, we have

[tex]3=\frac{x- 49}{2}\\6=x-49\\x=6+49\\x=55[/tex]

Therefore, the student is 55 inches tall.

For this case we have a quadratic equation given by:

[tex]4x ^ 2 + 2x-1 = 0[/tex]

The roots are found by means of the quadratic formula below:

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

Where:

[tex]a = 4\\b = 2\\c = -1[/tex]

So, we have:

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

Or in an equivalent way we have:

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

Answer:

The correct option will be:

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

Answer:

a = 4, b = 2 and c= -1

Step-by-step explanation:

Quadratic formula: x =√[-b ± v(b² - 4ac)]/2a

Here quadratic equation is  4x2 + 2x – 1

a = 4, b = 2 and c= -1

x =[-b ± √(b² - 4ac)]/2a

 = [-2 ± √(2² - 4*4*-1)]/2*4

 = [-2 ± √(4  + 16)]/8

 = [-2 ± √20)]/8

 = [-2 ± 2√5)]/8

 =  [-1 ± √5)]/4

x = [-1 ± √5)]/4