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Katen [24]
3 years ago
6

Y=6x/5 +27 find y-intercept and slope

Mathematics
1 answer:
mixas84 [53]3 years ago
5 0

Answer:

  1. General equation of a line is given by y = mx +c, where m is the gradient /slope, c is the intercept. To find for the intercept on y- axis, put x = 0.
  2. y =  \frac{6(0)}{5 }  + 27 \\ y =  \frac{0}{5}  + 27 \\ y = 27 \\ therefore \: the \: intercept \: on \: y \: is \: 27 \\
  3. By comparison,
  4. y =  mx +  \: c \\ y =  \frac{6}{5} x  \:  +27 \\ m =  \frac{6}{5 \: }  \: \\  hence \: slope \: is \:  \frac{6}{5}
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3 years ago
Help for number 10 please
tamaranim1 [39]

Start with

4(3^3-8) \div 2

Exponents have the highest priority, so we evaluate 3 cubed first:

4(27-8) \div 2

Next, we have to solve parenthesis first: we have 27-8 = 19, so the expression becomes

4 \times 19 \div 2

Multiplications and divisions have the same priority, so we perform them as they appear: 4 \times 19 = 76, so the expression becomes

76 \div 2 = 38

4 0
3 years ago
In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg
siniylev [52]

Answer:

\dfrac{AP}{PC}=\dfrac{3}{5}

\dfrac{BN}{CN}=\dfrac{3}{5}

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

  • angle A is the common angle, so \angle MAP\cong \angle DAC by reflexive property;
  • angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,

so

\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}

Consider triangles ACB and PCN. In these triangles,

  • angle C is the common angle, so \angle ACB\cong \angle PCN by reflexive property;
  • angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,

so

\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}

4 0
3 years ago
What is 9+9n=9 show work please
strojnjashka [21]
9 + 9n = 9

*subtract 9 from both sides

9n = 0

*divide both sides by 9

n = 0/9 = 0

n = 0
6 0
3 years ago
Read 2 more answers
Consider the following 8 numbers, where one labelled x is unknown.
In-s [12.5K]

Answer:

X = 65.

Step-by-step explanation:

The range is the greatest number - least, so we have:

X - 12 = 53

X = 53 + 12 = 65.

6 0
3 years ago
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