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3 years ago

20+25+65 using GCF and the distributive property

Mathematics

1 answer:

goldenfox [79]3 years ago

5 0

Answer: 110

Find the prime factors of each term in order to find the greatest common factor (GCF).

Find the GCF 20+25+65

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Is a triangle with angle measures 40,30,and 120 possible?

Schach [20]

No, it is nit possible to have any kind of triangle with these measurements.

5 0

3 years ago

Read 2 more answers

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

Olegator [25]

Answer:

The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is $y = \frac{1}{12}\cdot (x+5)^{2}+2$ .

Step-by-step explanation:

From statement we understand that parabola has its axis of symmetry in an axis parallel to y-axis. According to Analytical Geometry, the minimum distance between focus and directrix equals to twice the distance between vertex and any of endpoints.

If endpoints are (-5, 5) and (-5, -1), respectively, then such distance ( $r$ ), dimensionless, is calculated by means of the Pythagorean Theorem:

$r = \frac{1}{2}\cdot \sqrt{[-5-(-5)]^{2}+[5-(-1)]^{2}}$

$r = 3$

And the location of the vertex ( $V(x,y)$ ), dimensionless, which is below the focus, is:

$V(x,y) = F(x,y)-R(x,y)$ (1)

Where:

$F(x,y)$ - Focus, dimensionless.

$R(x,y)$ - Vector distance, dimensionless.

If we know that $F(x,y) = (-5,5)$ and $R(x,y) = (0,3)$ , then the location of the vertex is:

$V(x,y) = (-5,5)-(0,3)$

$V(x,y) =(-5,2)$

In addition, we define a parabola by the following expression:

$y-k = \frac{(x-h)^{2}}{4\cdot r}$ (2)

Where:

$h$ , $k$ - Coordinates of the vertex, dimensionless.

$r$ - Distance of the focus with respect to vertex, dimensionless.

If we know that $h = -5$ , $k = 2$ and $r = 3$ , then the equation of the parabola is:

$y = \frac{1}{12}\cdot (x+5)^{2}+2$

The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is $y = \frac{1}{12}\cdot (x+5)^{2}+2$ .

6 0

3 years ago

8. A right triangle has a perimeter of 60 cm. The legs have a ratio of 5:12. The hypotenuse is twice the

lakkis [162]

Answer:

a=24

b=10

c=26

Step-by-step explanation:

Perimeter is the sum of the sides ( $a+b+c=60$ )

The legs (a and b) have a ratio of 5:12, which means that $5a=12b$ , which can be simplified to $\frac{5}{12} a=b$ , where b will be the smaller leg.

The hypotenuse will be double the smallest leg, 2b, increased by 6 meters, giving us an equation of $c=2b+6$

Let's plug these in to get one variable:

$a+b+c=60\\a+b+2b+6=60\\a+\frac{5}{12}a+2(\frac{5}{12}a)+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a=54\\\frac{27a}{12}=54\\27a=648\\a=24$

Now that we have a, we can plug it in to our previous equations to find our other sides:

$5a=12b\\5(24)=12b\\120=12b\\10=b$

$c=2b+6\\c=2(10)+6\\c=20+6\\c=26$

Double-checking:

$a+b+c=60\\24+10+26=60\\60=60$

7 0

3 years ago

What’s the answer to this?

jeka57 [31]

Answer:

y=3/2x+0

Step-by-step explanation:

The formula for slope intercept form formula is y=mx+b where m is the slope and b is the y intercept and since the slope is rise over run ( or rise/run just put it into fraction form) we count from the y intercept up until we can see the line reach a point where it touches a actual cross point ( in this case from the y intercept we see it goes up three) Then we count over how many to that cross point ( the full point, not just a random place on the chart) (in this case 2) and that creates 3/2. Now for the y intercept. Where does the line intercept the vertical line? That's your y intercept. In this case it's 0. Now you can see where we count up from three ( for the slope) and over two. Right onto that point. Hope this makes sense! If not look up Khan academy for some extra tutoring that is free.

Hope this helps! If so please mark brainliest and rate/heart if it did.

8 0

3 years ago

A² + b² = 7b and b² + (2b-a)² = 7² find (a - b)².

Mamont248 [21]

Answer:

(a - b)^2 = 49 - 4b^2 +2ab

Step-by-step explanation:

Given: a^2 + b^2 = 7b (assuming A is really “a”)

b^2 + (2b - a)^2 = 7^2

Find; (a - b)^2

Plan: Use Algebraic Manipulation

Start with b^2 + (2b - a)^2 = 7^2 =>

b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.

a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms

a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>

a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2

(a - b)^2 = 49 - 4b^2 +2ab

Double Check: recalculated ✅ ✅

(a - b)^2 = 49 - 4b^2 +2ab

4 0

3 years ago