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3 years ago

What is an equation of the line that passes through the point (−2,−3) and is parallel to the line 4x-y=14

Mathematics

1 answer:

liraira [26]3 years ago

5 0

Answer:

4x - y = -5

Step-by-step explanation:

The equation of a new line which is parallel to old line 4x - y = 14 looks exactly the same as that of the old line EXCEPT that we replace the constant, 14, with C and find C for the line that passes through (-2, -3).

4x - y = 14 becomes 4x - y = C

Now substitutte -2 for x, -3 for y and calculate C:

4(-2) - (-3) = C, or

-8 + 3 = C = - 5

Thus, the new equation is 4x - y = -5

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The table gives the relative frequencies of recipes that contains sugar and salt, contain at least one of those ingredients, or

tigry1 [53]

Answer-

The probability that a randomly selected recipe does not contain sugar, given that it contains salt is 22.4%

Solution-

The given table in the link shows the relative frequencies of recipes that contains sugar and salt, or contains at least one of those ingredients, or contains neither of those ingredients.

We have to find the conditional probability that the recipe doesn't contain sugar, given that it contains salt.

We know that, the conditional probability of occurrence of A given that B occurs is,

$P(A|B)=\frac{P(A\ and\ B)}{P(B)} =\frac{P(A\bigcap B)}{P(B)}$

$P(\text{Doesn't contain sugar}\ |\ \text{Contains salt})=\frac{P(\text{Doesn't contain sugar}\ and\ \text{Contains salt})}{P(\text{Contains salt})}$

$P(\text{Doesn't contain sugar}\ and\ \text{Contains salt})=\frac{0.15}{1} =0.15\\P(\text{Contains salt})=\frac{0.67}{1}=0.67$

Putting these values,

$P(\text{Doesn't contain sugar}\ |\ \text{Contains salt})=\frac{0.15}{0.67} =0.224=22.4\%$

5 0

4 years ago

Janet is drawing the path formed by the parametric equations x=2+3 sin t and y=1-1/2cos t. Which curve did she draw??

irakobra [83]

Sin²t +cos²t =1

 x=2+3 sin t
sin t=(x-2)/3

y=1-1/2cos t
y-1= - (cos t)/2
cos t =-(y-1)/(1/2)

(x-2)²/3² + (y-1)²/(1/2)² = 1
Ellipse

5 0

3 years ago

Tristan is working on dilating rectangles. Rectangle ABCD is dilated by a factor of 3. The resulting rectangle WXYZ has an area

zloy xaker [14]

Answer:

Tristan is correct, because he needs to find the possible dimensions for rectangle WXYZ and then divide each dimension by 3.

Step-by-step explanation:

The rectangle ABCD is dilated by a factor of 3 to get the rectangle WXYZ whose area is found to be 72 cm².

Let the dimensions of the dilated rectangle WXYZ are a cm by b cm.

So, ab = 72 ........... (1)

Now, the dimensions of the original rectangle are 3 times lesser than the dimensions of rectangle WXYZ.

So, the area of rectangle ABCD will be $(\frac{a}{3} \times \frac{b}{3}) = \frac{ab}{9} = \frac{72}{9} = 8$ cm² {from equation (1)}

Therefore, Tristan is correct, because he needs to find the possible dimensions for rectangle WXYZ and then divide each dimension by 3. (Answer)

8 0

3 years ago

Which statement is true about every rectangular pyramid?

Ratling [72]

Answer:

At least two of the lateral faces are congruent.

Step-by-step explanation:

Because the words "at least" are used this means that at a minimum 2 of the faces are congruent. Because the base is in the shape of a triangle, this will definitely be true.

hope this helps:)

3 0

3 years ago

Read 2 more answers

A liquid mixture of 56 ounces contains 14 ounces of sugar and the rest is water. What is the ratio of swar to water

Pachacha [2.7K]

Step-by-step explanation:

Ounces of water = 56 - 14 = 42 ounces

Ratio of sugar to water

56 : 42

8 : 6

4 : 3