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Lubov Fominskaja [6]
3 years ago
10

Find the value of the variable if P is between J & K. A) JP = 8z - 17 B) PK = 5z + 37 C) JK = 17z - 4

Mathematics
2 answers:
Daniel [21]3 years ago
3 0
<span>We cannot deduce about the exact location of P between J and K. But we can conclude: segment JP + segment PK = line JK.
</span><span>JP + PK = JK.
</span><span>Substitute first each.
(8z - 17) + (5z + 37) = 17z - 4
Combine like terms.
13z + 20 = 17z - 4
Isolate the variable z.
4z = 24
z = 6
The value of the variable z is then 6 units.</span>
Reptile [31]3 years ago
3 0
<span>From the problem statement, we can say that the sum of segment JP and segment PK is equal to the line JK.

</span><span>JP + PK = JK.

</span><span>First, we substitute the equations to each term.
(8z - 17) + (5z + 37) = 17z - 4 

Combining like terms.
13z + 20 = 17z - 4

Solving for z,
4z = 24 
z = 6

</span>
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8. For circle A, the circumference is 31.4 ft. What is the area? Use 3.14 for pi
telo118 [61]

Answer:

\huge\boxed{\sf A = 78.5\ ft\²}

Step-by-step explanation:

Circumference = C = 31.4 ft

We know that,

<h3>C = 2πr</h3>

Where, r is the radius

31.4 = 2(3.14)r

31.4 = 6.28(r)

Divide 6.28 to both sides

31.4/6.28 = r

5 ft. = r

<h3>r = 5 ft.</h3>

Now,

<h3><u>Finding area:</u></h3>

A = πr²

A = (3.14)(5)²

A = (3.14)(25)

<h3>A = 78.5 ft²</h3>

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7 0
2 years ago
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8 0
3 years ago
MATH HELP!!! 100PTS!!!
Lostsunrise [7]

Answer:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Step-by-step explanation:

<u>Given functions</u>:

  p(x)=2x-4

  r(x)=\dfrac{6x-1}{9x+1}

Solve for p(x) = r(x):

\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

Therefore:

a=18, \quad b=-40, \quad c=-3

Substitute the values of a, b and c into the <u>quadratic formula</u> and solve for x:

\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}

Therefore, the solutions are:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

6 0
2 years ago
Need help asap please
Rzqust [24]

Answer:

Option 3

Step-by-step explanation:

The number on the inside is the dividend and the number on the outside is the divisor. So we just have to place the dividend on the top and the divisor on the bottom.

7 0
3 years ago
Find an equation of the line that has undefined slope and contains the point left parenthesis negative 1 comma 6 right parenthes
Rudiy27

When the slope isn't defined, it's not possible to write the line in slope-intercept form. No slope means a vertical line, which here must be


x= -1


The ordered pair (-1,6) obviously satisfies the above equation so is on the vertical line x=-1.



6 0
3 years ago
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