Answer:
1/4(12x-28)
Step-by-step explanation:
1/4(12x-28)=3x-7
Answer:
This equation has infinite solutions.
Step-by-step explanation:
5h - 7 = 5(h - 2) + 3
Distributive property.
5h - 7 = 5h - 10 + 3
Combine like terms.
5h - 7 = 5h - 7
Cancel like terms.
0 = 0
The angle opposite of the 27° one would also be 27° because vertically opposite angles are congruent
The other two angles would be 180°-27° which =153°
This is because co-interior angles (allied angles) are supplementary.
Supplementary means that they add up to 180°.
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Answer:
247 yd²
Step-by-step explanation:
this figure can be "split" into 3 sub-figures.
2 rectangles and one triangle "at the top".
these 3 areas can be easily calculated, and the we simply sum them all up, and that is the total area.
my approach is to pick the first rectangle to be the one extruding one to the right.
R1 = 11×5 = 55 yd²
the second rectangle is then the rest of the"straight" area up to the beginning of the triangle top
R2 = 8 × (13+5) = 8×18 = 144 yd²
and the area of a triangle is
baseline × height / 2
we can clearly see in our example, it is a right-angled triangle, so the left side is also the height, which is the remainder of the long side of the original figure, when we deduct all the other parts we used for the rectangles.
so, we have
T = 8 × (30 - 5 - 13) / 2 = 8×12/2 = 8×6 = 48 yd²
so, in total we have
F = 55 + 144 + 48 = 247 yd²
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is
<h3>How to determine the equation of the hyperbola?</h3>
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
So, we have:
Evaluate
Hence, the equation of the hyperbola is
Read more about hyperbola at:
brainly.com/question/3405939
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