Solve simultaneously. 2x + 3y=4, 3x

Triangle A’B’C’ is a dilation of triangle ABC about point P with a scale factor of 1/2 . Is the dilation a reduction or an enlar

alex41 [277]

This is a reduction because the scale factor is in between 0 and 1.

3 0

4 years ago

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You must buy cupcakes and pizza for a party. Each cupcake costs $2, and each pizza pie costs $10

saul85 [17]

Answer:

$20

Step-by-step explanation:

so you take 10 and times it by 2 and their is your answer all so have a great day your welcome

7 0

3 years ago

Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equatio

lina2011 [118]

Answer:

The point of intersection is:

$\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)$

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

$y=0.5x+5$

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

$(x-h)^2+(y-k)^2=r^2$

Where (h, k) is the center and r is the radius.

Since our center is (0, 5), h = 0 and k = 5. The radius is 3. So, r = 3. Substitute:

$(x-0)^2+(y-5)^2=(3)^2$

Simplify:

$x^2+(y-5)^2=9$

At the point where the two equations intersect, its x-coordinate and y-coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for x. So:

$x^2+((0.5x+5)-5)^2=9$

Simplify:

$x^2+(0.5x)^2=9$

Square:

$x^2+0.25x^2=9$

Combine like terms:

$\displaystyle 1.25x^2=\frac{5}{4}x^2=9$

Solve for x:

$\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}$

Note that since we are looking for the point of intersection in QI, x should be positive. So, we can ignore the negative answer.

To find the y-coordinate, substitute the x-value back into either equation. Using the linear equation:

$\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34$

So, the point of intersection in QI is:

$\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)$

6 0

3 years ago

Construct a line from A perpendicular to the x-axis, determine the distance from A to the x-axis along this perpendicular line,

Vaselesa [24]

Step-by-step explanation:

To determine distances, we need to use this formula: $d=\sqrt{(y_{2}-y_{1} ) ^{2} +(x_{2}-x_{1}) ^{2} }$

To apply that formula we need to use the coordinates of point, but in this case will be calculated generally, due to the lack of specific values.

So, Point A have the coordinates $(x_{1};y_{1})$

Let's call Point P the one that's on the x-axis, its coordinates are $(p_{1};q_{1})$

Applying the formula, the distance between this two points will be:

$d=\sqrt{(q_{1}-y_{1} ) ^{2} +(p_{1}-x_{1}) ^{2} }$

To find an opposite and equidistant point, we only need to use opposite values. So, let's call Point B, the opposite point, its coordinates will be:

$(-x_{1};-y_{1})$

And the distance will be the same, because squared values will always results positive.

3 0

3 years ago

What should be added to -5/7 to get -2/3

Brums [2.3K]

Answer:

This is basic algebra

$\frac{-5}{7} + x =\frac{-2}{3} \\x=\frac{-2}{3} + \frac{5}{7} \\x = \frac{-14 + 15}{21} \\x = \frac{1}{21}$

Hope that answers your question

Step-by-step explanation:

3 0

3 years ago

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Solve simultaneously.2x + 3y=4, 3x - 2y= -7​

Solve simultaneously.2x + 3y=4, 3x - 2y= -7