what is the gradient of the graph shown below. Give answer in simplest form

Answer:

x=7, -1 so the positive value is 7

Step-by-step explanation:

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = 7}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

[tex] \: ({x - 3})^{2} = 16[/tex]

➺[tex] \: (x - 3) = \sqrt{16} [/tex]

➺[tex] \: (x - 3) = \sqrt{4 \times 4} [/tex]

➺[tex] \: (x - 3) = \sqrt{( {4})^{2} } [/tex]

➺[tex] \: (x - 3) = ±4[/tex]

When [tex]x\:=\:+4[/tex], we have

➺[tex] \: x = 4 + 3[/tex]

➺[tex]\boxed{x\:=\:7}[/tex]

When [tex]x\:=\:-4[/tex], we have

➺ [tex]\:(x - 3) = - 4[/tex]

➺[tex] \: x = - 4 + 3[/tex]

➺ [tex]\boxed{x\:=\:-1}[/tex]

Therefore, the two values of [tex]x[/tex] are 7 and -1.

Hence, 7 is the positive value of [tex]x[/tex].

[tex]\sf \bf {\boxed {\mathbb {To\:verify:}}}[/tex]

➼[tex] \: ( {x - 3})^{2} = 16[/tex]

When [tex]x\:=\:7[/tex]

➼[tex] \: ({7 - 3)}^{2} = 16[/tex]

➼[tex] \: {4}^{2} = 16[/tex]

➼[tex] \: 16 = 16[/tex]

➼[tex] \: L.H.S.=R. H. S[/tex]

When [tex]x\:=\:-1[/tex]

[tex] \: ({x - 3})^{2} = 16[/tex]

➼[tex] \:( { - 1 - 3})^{2} = 16[/tex]

➼[tex]\: ({ - 4})^{2} = 16[/tex]

➼[tex] \: 16 = 16 [/tex]

➼[tex] \: L.H.S.=R. H. S[/tex]

[tex]\sf\purple{Hence\:verified. }[/tex] ✔

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{☂}}}}}[/tex]

Answer:

A 90

Step-by-step explanation:

multiple ways to prove this.

e.g. since the angle between the two lines from the center of the circle to the 2 tangent touching points is 90 degrees (that is the meaning of these 90 degrees here as the angle of the circle segment defined by the 2 tangent touching points and the circle center), the tangents have the same "behavior" as tan and cot = the tangents at the norm circle at 0 and 90 degrees. they hit each other outside of the circle again at 90 degrees.

another way

imagine the two right triangles of the tangents crossing point to the circle center and the tangent/circle touching points.

the Hypotenuse of each triangle is cutting the 90 degree angle of the circle segment exactly in half (due to the symmetry principle). so the angle between radius side and Hypotenuse is 90/2 = 45 degrees.

that means also the angle of such a right triangle at the tangent crossing point is 45 degrees (as the sum of all angles in a triangle must be 180, we have the remainder of 180 - 90 - 45 = 45 degrees).

the angles of both right triangles at that point are the same, and so we can add 45+45 = 90 degrees for the total angle at the tangent crossing point.

Answer:

9 feet

Step-by-step explanation:

The given is 30-60-90 special triangle with the side lengths as follows

x-x√(3- and 2x

The side length that sees 90 degrees (hypotenuse) is 18 which means x = 9

then the side length that sees 30 degrees is 9 as well

Answer:

642 miles

Step-by-step explanation:

Distance of Midville from their home = 214 miles

Walesburg is 3 times as far.

How far is Walesburg from their home?

Distance of Walesburg from their home = 3 × Distance of Midville from their home

= 3 × 214 miles

= 642 miles

Distance of Walesburg from their home = 642 miles

Given:

An item was sold at a loss of 20%.

If the item is sol for Rs. 50 more then, the profit would have been 5%.

To find:

The cost price of the item.

Solution:

Let x be the cost price of the item.

The item was sold at a loss of 20%. Then selling selling price is:

[tex]S.P.=x-\dfrac{20}{100}x[/tex]

[tex]S.P.=x-0.2x[/tex]

[tex]S.P.=0.8x[/tex]

If a the item is sold for 5% profit, then the selling price is:

[tex]S.P.=x+\dfrac{5}{100}x[/tex]

[tex]S.P.=x+0.05x[/tex]

[tex]S.P.=1.05x[/tex]

It is given that, if the item is sol for Rs. 50 more then, the profit would have been 5%. So,

[tex]0.8x+50=1.05x[/tex]

[tex]50=1.05x-0.8x[/tex]

[tex]50=0.25x[/tex]

Divide both sides by 0.25.

[tex]\dfrac{50}{0.25}=x[/tex]

[tex]200=x[/tex]

Therefore, the cost price of the item is Rs. 200.

Answer:

= 2 1/4 feet

Step-by-step explanation:

Length of chain Jesse needs = 10 1/4 feet

Length of chain Jesse has:

Two small pieces each measuring 2 1/8 feet

= 2 × 2 1/8 feet

= 2 × 17/8

= 34/8 feet

Third piece measuring 3 3/4 feet

Total Length of chain Jesse has = 34/8 feet + 3 3/4 feet

= 34/8 + 15/4

= 34+30/8

= 64/8

= 8 feet

Total Length of chain Jesse has = 8 feet

Length of chain Jesse needs to purchase = Length of chain Jesse needs - Total Length of chain Jesse has

= 10 1/4 feet - 8 feet

= 2 1/4 feet

Length of chain Jesse needs to purchase = 2 1/4 feet

Answer:

The answer is c

Step-by-step explanation:

2y=24

y=12

2x+3=29

x=13

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4 , then

y = - 4x + c ← is the partial equation

To find c substitute (- 2, - 5) into the partial equation

- 5 = 8 + c ⇒ c = - 5 - 8 = - 13

y = - 4x - 13 → B

Answer:

that he is trying to die

Step-by-step explanation:

i don't know just stating the obvious.

Answer:

i think it tells us that he jumped 16.5 meters down?

Step-by-step explanation: it’s pretty self explanatory

Answer:

More details are needed

Step-by-step explanation:

Given

[tex]l = 9.6cm[/tex] --- side length

[tex]a = 11cm[/tex] --- apothem

[tex]n = 5[/tex]

Required

The height of the prism

The apothem of a prism is:

[tex]a = \frac{l}{2\tan(\frac{180}{n})}[/tex]

There are no direct links between the apothem, the height and the side lengths of a prism.

To calculate the height, we will need to the base area and the volume of the prism.

Hence, more details are needed.

9514 1404 393

Answer:

  45 yd²

Step-by-step explanation:

The area of a rectangle is the product of its length and width. If your given measures are the length and with of a rectangle, the area is found by multiplying them.

  A = LW

  A = (9 yd)(5 yd) = 9·5 yd·yd = 45 yd²

The area of a 9 yd by 5 yd rectangle is 45 square yards.

Answer:

the slope, m, is 2/5

Step-by-step explanation:

y = (2/5)x - 7 may be compared to the standard slope-intercept equation

y = mx + b.  By comparison, we find that the slope, m, is 2/5 and the y-intercept, b, is -7.

Answer:

a+7b+12ab

Step-by-step explanation:

simplify simplify algebraic equation

Answer:

0.56

Step-by-step explanation:

The r-value that represents the most moderate correlation is 0.56

Correlation is represented with r.

And the range of values of r is:

-1 ≤ r ≤ 1

This means that r can take any value from -1 to 1

-1 and 1 are considered strong correlation

While values closer to 0.5 or - 0.5 are moderate

From the list of options,

0.56 is closer to 0.5 than others

Hence, the r-value that represents the most moderate correlation is 0.56

Read more about correlation at:

https://brainly.com/question/4219149

#SPJ9

Answer:

D) 2

Step-by-step explanation:

16 to the fourth root is what?

We need to find what number multiplied by itself 4 times is 16.

That number is TWO.

Answer:

Step-by-step explanation:

Answer:

f (g(x) = f (2x) = 2x + 1 (∵ f (x) = x + 1)

Answer:

2x+1=0 is the answer

(g(x) = f (2x) = 2x + 1 (∵ f (x) = x + 1)-

[tex] (x + 3)(x + 5)[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] {x}^{2} + 8x + 15 \\ ={x}^{2} + 5x + 3x + 15 [/tex]

Taking [tex]x[/tex] as common from first two terms and 3 from last two terms, we have

[tex] =x(x + 5) + 3(x + 5)[/tex]

Taking the factor [tex](x+5)[/tex] as common,

[tex] = (x + 3)(x + 5)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

a is the right answer

Step-by-step explanation:

becuse i took the text

Answer:

Step-by-step explanation:

angle C + Angle B= Angle A(sum of two interior oppposite angles are equal to the exterior angle formed)

61+B=143

B=143-61

B=82 degree

We know that,

→ C = 61°

[A = B + C]

→ 143° = B + 61°

→ B = 143° - 61°

→ B = 82°

[180° = A + B + C]

→ 180° = A + (82° + 61°)

→ A = 180° - 143°

→ A = 37°

Answer:

The last line is

[tex]x = 7 + - \sqrt{30} [/tex]

The roots of f(x) are 7+root 30 and 7 -root 30.

We have given that the quadratic equation is

[tex]f(x)=x^2-14x+19[/tex]

We have to find the zeros of the given f(x)

Compaire the given equation with the general form of quadratic equation

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

So we get,a=1,b=-14,c=19

We find the roots by using the quadratic formula method

[tex]x_{1,2}=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]

Use the value of a,b and c in above formula we get,

[tex]x_{1,2}=\frac{-(-14)\±\sqrt{(-14)^2-4(1)(19)} }{2(1)}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{30}}{2\cdot \:1}[/tex]

[tex]x_1=\frac{-\left(-14\right)+2\sqrt{30}}{2\cdot \:1}[/tex]

[tex]=\frac{14+2\sqrt{30}}{2}[/tex]

[tex]=\frac{14+2\sqrt{30}}{2}[/tex]

[tex]=\frac{2\left(7+\sqrt{30}\right)}{2}[/tex]

[tex]=7+\sqrt{30}[/tex]

Similarly, we get,

[tex]x_2=\frac{-\left(-14\right)-2\sqrt{30}}{2\cdot \:1}[/tex]

[tex]x_2=7-\sqrt{30}[/tex]

Therefore the roots of f(x) are 7+root 30 and 7 -root 30.

To learn more about the roots visit:

https://brainly.com/question/2833285

Answer:

A = 20

Step-by-step explanation:

Answer:A. 32 F

Step-by-step explanation:

im correct if I'm rwong

Answer:

12

Step-by-step explanation:

Ppopp

Answer:

Sam is  yeas old, and Dean is (x - 10) year's old, where 'x' is the age of their sister

Step-by-step explanation:

The relationship between the ages of the brothers are;

Sam's age + Dean's age = Their sister's age

Dean's age + 10 = Dean's age + Sam's age

Therefore, we have;

Sam's age = Dean's age + 10 - Dean's age = 10

Sam's age = 10 years

Let 'x' represent their sisters age, we get;

Sam's age + Dean's age = x

10 + Dean's age = x

Dean's age (in variable form) = x - 10

Answer:

r = 11.4 cm

Step-by-step explanation:

The question says that, "Spray will make a circle with a diameter of 22.8 cm how long a radius will measure."

Given that,

The diameter of the circle, d = 22.8 cm

We know that the relation between the diameter and the circle is given by :

d = 2r

Where

r is the radius of the circle

r = d/2

r = 22.8/2

r = 11.4 cm

So, the radius of the circle is equal to 11.4 cm.