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3 years ago

What is the constant of proportionality in the equation y=2/3x

Mathematics

2 answers:

Elina [12.6K]3 years ago

7 0

Answer:

$\frac{2}{3}$ .

Step-by-step explanation:

We have been given an equation $y=\frac{2}{3}x$ . We are asked to find the constant of proportionality.

We know that two directly proportional quantities are in form $y=kx$ , where y is directly proportional to x and k is the constant of proportionality.

Upon looking at our given equation, we can see that $k=\frac{2}{3}$ , therefore, the constant of proportionality is $\frac{2}{3}$ for our given equation.

Alexandra [31]3 years ago

6 0

2/3x no y intercept

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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

Identify the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in.

Galina-37 [17]

Note that a squared pyramid has a square base & 4 equal triangles.
To find the lateral the lateral area you calculate the area of the 4 equal triangles and to find the surface area (total Area) you add the area of the base:

Area of each triangle = side (5) x slant (9) and you divide by 2

==>Aera of 1 triangle = (9x5)/2 = 45/2 & for the 4 triangles

Lateral area = (45/2) x 4 = 90 in²

Now the base area (square) = 5 x 5= 25 in²

so the surface area = 90+25 = 115 in² (answer a)

7 0

2 years ago

Factor the expression. 35x-28xy=

zalisa [80]

Answer:

7x(5-4y)

Step-by-step explanation:

35x-28xy

7x(5-4y)

4 0

2 years ago

Read 2 more answers

Help asap please!! Find the measure of y. A. 43 B. 53 C. 90 D. 47

Amiraneli [1.4K]

Answer:

$y=43$

Step-by-step explanation:

$y=2(90-46)/2$

$y=43$

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5 0

2 years ago

Please help me with number 1 please help ???

stira [4]

Answer:

mean: 26

median: 28

mode: 28

range:19

Step-by-step explanation:

hipe this helped hun

3 0

2 years ago