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3 years ago

What is the equation of a line that has a slope of 2, and contains the point (4,6)?

Mathematics

1 answer:

Tems11 [23]3 years ago

3 0

Answer:

y= 2x -2

Step-by-step explanation:

You would use point- slope formula. y-y = m(x-x). With your numbers it would end up looking like this ----> y-6 = 2(x-4), then do the distributive property which then gives you ----> y-6 = 2x - 8, then subtract 6 on both sides and you get ---> y = 2x - 2. Hope this helped!!!!

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PLEASE HELP!!!

Aliun [14]

Answer:

a. 8.75 M NaOH

b. 0.425 M CuCl₂ or 0.43 M CuCl₂

c. 0.067 M CaCO₃ or 0.07 M CaCO₃

Step-by-step explanation:

Molality is computed using the formula:

$M = \dfrac{Moles\:of\:solute}{Liters\:of\:solution}$

So first thing you need to do is determine how many moles of solute there are and divide it by the solution in liters.

Converting mass to moles, you need to get the mass of each solute per mole. You can use the periodic table to get the atomic mass (which is the grams per mole of each atom) of each of the elements involved. Then add them up and you will have how many grams per mole of each compound.

1. 35.0g of NaOH in 100ml H₂O

Element number of atoms atomic mass TOTAL

Na 1 x 22.99g/mol = 22.99g/mol

O 1 x 16.00g/mol = 16.00g/mol

H 1 x 1.01g/mol =<u> 1.01g/mol</u>

40.00g/mol

This means that the molecular mass of NaOH is 40.00 g/mol

Then we use this to convert 35.0g of NaOH to moles:

$35.0g \:of\:NaOH \times \dfrac{1\:mole\:of\:NaOH}{40.00g\:of\:NaOH} = \dfrac{35.0\:moles\:of\:NaOH}{40.00}=0.875\:moles\:of\:NaOH$

Now that you have the number of moles we divide it by the solution in liters. Before we can do that you have to conver 100ml to L.

$100ml\times\dfrac{1L}{1000ml} = 0.1 L$

Then we divide it:

$\dfrac{0.875\:moles\:of\:NaOH}{0.1L of solution} = 8.75M\: NaOH$

2. 20.0g CuCl₂ in 350ml H₂O

Element number of atoms atomic mass TOTAL

Cu 1 x 63.55g/mol = 63.55g/mol

Cl 2 x 34.45g/mol = <u>70.90g/mol</u>

134.45g/mol

$20.g\:of\:CuCl_2\times\dfrac{1\:mole\:of\:CuCl_2}{134.45\:g\:of\:CuCl_2}=0.1488\:moles\:of\:CuCl_2$

350ml = 0.350L

$\dfrac{0.1488\:moles\:of\:CuCl_2}{0.350L\:of\:solution}=0.425M\:CuCl_2$

3. 3.35g CaCO₃ in 500ml

Element number of atoms atomic mass TOTAL

Ca 1 x 40.08g/mol = 40.08g/mol

C 1 x 12.01g/mol = 12.01g/mol

O 3 x 16.00g/mol =<u> 48.00g/mol</u>

100.09g/mol

$3.35g\:of\:CaCO_3\times\dfrac{1\:mole\:of\:CaCO_3}{100.09\:g\:of\:CaCO_3}=0.0335\:moles\:of\:CaCO_3$

500ml = 0.5L

$\dfrac{0.0335\:moles\:of\:CaCO_3}{0.5L}=0.067M\:CaCo_3$

4 0

3 years ago

What is the length of AA' , rounded to the nearest hundredth? Type a numerical answer is the space provided. Do not type spaces

inna [77]

Coordinate of A are (0,0)
Coordinates of A' are (5,2)

We can find the distance from A to A' using the distance formula:

$AA'= \sqrt{(5-0)^{2}+ (2-0)^{2} } \\ \\ 
AA'= \sqrt{25+4} \\ \\ 
AA'= \sqrt{29} \\ \\ 
AA'=5.39$

Thus, rounded to nearest hundredth, AA' is equal to 5.39

3 0

3 years ago

In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1

svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements: Reasons:

$1)\, XY=XZ$ Given

$2) \text{ $ m\angle Y= m\angle Z$}$ Isosceles Triangle Theorem

$\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}$ Angle Addition

$\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}$ Given

$5) \text{ $m\angle XYQ=m\angle QYZ$}$ Definition of Bisector

$\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}$ Substitution

$7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}$ Angle Addition

$8)\text{ $ZP$ bisects $\angle XZY$}$ Given

$\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }$ Definition of Bisector

$\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}$ Substitution

$11)\text{ } 2m\angle QYZ=2m\angle PZY$ Substitution

$12)\text{ }m\angle QYZ=m\angle PZY$ Division Property of Equality

$13)\text{ } YZ=YZ$ Reflexive Property

$14)\text{ } \Delta YZP\cong\Delta ZYQ$ Angle-Side-Angle Congruence*

$15)\text{ } YQ=ZP$ CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0

3 years ago

Read 2 more answers

(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

A T-shirt launcher can launch 105 shirts in 20 minutes. What is the rate in shirts per hour?

Margarita [4]

The T-shirt launcher can launch 315 shirts per hour.

4 0

4 years ago

Read 2 more answers