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MaRussiya [10]
2 years ago
13

Please help correct answer wins crowns

Mathematics
1 answer:
GrogVix [38]2 years ago
5 0

Answer:

Given equation: x + 2y = 7

Rearrange the given equation to make y the subject:

      \sf x + 2y = 7

\sf \implies 2y=7-x

\sf \implies y = \dfrac12(7-x)

Now input the given x-values into the equation to determine the y-values:

\sf x=-2\implies y = \dfrac12(7-(-2))=4.5

\sf x=-1\implies y = \dfrac12(7-(-1))=4

\sf x=0\implies y = \dfrac12(7-0)=3.5

\sf x=1\implies y = \dfrac12(7-1)=3

\sf x=2\implies y = \dfrac12(7-2)=2.5

\sf x=3\implies y = \dfrac12(7-3)=2

As ordered pairs: (-2, 4.5)  (-1, 4)  (0, 3.5)  (1, 3)  (2, 2.5)  (3, 2)

Plot the endpoints on the graph (-2, 4.5) and (3,2), then connect with a line segment.

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Suppose you are asked to find the area of a rectangle that is 2.1-cmcm wide by 5.6-cmcm long. Your calculator answer would be 11
Jlenok [28]

Answer:

12 square cm correct to 2 significant figures

Step-by-step explanation:

Area of a Rectangle = L X B = 2.1 X 5.6 = 11.76 square cm

To round your result to 2 significant figure, we start counting from the left from the first non-zero digit.

The first two digits are 11 but because the number after is 7 (greater than 4), we round up to 12.

11.76 square cm = 12 square cm correct to 2 significant figures

6 0
3 years ago
A hyperbola centered at the origin has verticies at (add or subtract square root of 61,0 and foci at (add or subtract square roo
deff fn [24]

Answer:

\frac{x^2}{61}-\frac{y^2}{37}  =1

Step-by-step explanation:

The standard equation of a hyperbola is given by:

\frac{(x-h)^2}{a^2} -\frac{(y-k)^2}{b^2} =1

where (h, k) is the center, the vertex is at (h ± a, k), the foci is at (h ± c, k) and c² = a² + b²

Since the hyperbola is centered at the origin, hence (h, k) = (0, 0)

The vertices is (h ± a, k) = (±√61, 0). Therefore a = √61

The foci is (h ± c, k) = (±√98, 0). Therefore c = √98

Hence:

c² = a² + b²

(√98)² = (√61)² + b²

98 = 61 + b²

b² = 37

b = √37

Hence the equation of the hyperbola is:

\frac{x^2}{61}-\frac{y^2}{37}  =1

6 0
3 years ago
I could use some help with this question?
slega [8]

Answer:

d

Step-by-step explanation:

if I divide the units of the scaled rectangle by the original you will get

18 \div 9 = 2 \\ 6 \div 3 = 2

3 0
2 years ago
Read 2 more answers
Given: ABCD is a rhombus. Prove: △AEB is a right triangle.
lukranit [14]

Answer:

Step-by-step explanation:

∵ ABCD is a rhombus

∴ AC is ⊥ on BD

∴ ΔAEB is right angled triangle

4 0
3 years ago
Write 2^8 * 8^2 * 4^-4 in the form 2^n
Eva8 [605]

The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.

<h3>What are exponential forms?</h3>

The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.

<u>For example:</u>

If we have a*a*a*a, it can be written in exponential form as:

=a^4

where

  • a is the base, and
  • 4 is the power.

The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power. 

From the information given:

We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:

\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }

\mathbf{= 2^8\times (2^6) \times (2^{-8}) }

\mathbf{= 2^{8+6+(-8)}}

\mathbf{= 2^{6}}

Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.

Learn more about exponential forms here:

brainly.com/question/8844911

#SPJ1

4 0
2 years ago
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