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2 years ago

How do i factor 2x^2+11x+5

2 answers:

7 0

For simple integer factors as this one has, you want to find two values for the quadratic in the form ax^2+bx+c. Let the two values be j and k. These two values must satisfy two conditions.

jk=ac=10 and j+k=b=11, so j and k must be 1 and 10.

Now replace bx with jx and kx...

2x^2+x+10x+5 now factor 1st and 2nd pair of terms.

x(2x+1)+5(2x+1)

(x+5)(2x+1)

pantera1 [17]2 years ago

6 0

Factor by grouping.Tap for fewer steps...For a polynomial of the form ax2+bx+cax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅5=10a⋅c=2⋅5=10 and whose sum is b=−11b=-11.Tap for fewer steps...Factor −11-11 out of −11x-11x.2x2−11x+5=02x2-11x+5=0Rewrite −11-11 as −10-10 plus −1-12x2+(−10−1)x+5=02x2+-10-1x+5=0Apply the distributive property.2x2+(−10x−1x)+5=02x2+-10x-1x+5=0Remove parentheses.2x2−10x−1x+5=02x2-10x-1x+5=0Factor out the greatest common factor from each group.Tap for fewer steps...Group the first two terms and the last two terms.(2x2−10x)+(−1x+5)=02x2-10x+-1x+5=0Factor out the greatest common factor (GCF) from each group.2x(x−5)−1(x−5)=02xx-5-1x-5=0Factor the polynomial by factoring out the greatest common factor, x−5x-5.(x−5)(2x−1)=0x-52x-1=0Set x−5x-5 equal to 00 and solve for xx.Tap for fewer steps...Set the factor equal to 00.x−5=0x-5=0Since −5-5 does not contain the variable to solve for, move it to the right side of the equation by adding 55 to both sides.x=5x=5Set 2x−12x-1 equal to 00 and solve for xx.Tap for fewer steps...Set the factor equal to 00.2x−1=02x-1=0Since −1-1 does not contain the variable to solve for, move it to the right side of the equation by adding 11 to both sides.2x=12x=1Divide each term by 22 and simplify.Tap for more steps...x=12x=12The solution is the result of x−5=0x-5=0 and 2x−1=02x-1=0.x=5,12x=5,12

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3 years ago

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3 years ago

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Gary made 5 baskets than Susan this season bill made 3 less then twice as many baskets as Susan. Together, all three made 42 bas

Nezavi [6.7K]

Answer:Gary made 15 baskets.

Susan made 10 baskets.

Bill made 17 baskets.

Step-by-step explanation:

Let x represent the number of baskets that Gary made.

Let y represent the number of baskets that Susan made.

Let z represent the number of baskets that Bill made.

Gary made 5 baskets than Susan this season. This means that

x = y + 5

Bill made 3 less than twice as many baskets as Susan. This means that

z = 2y - 3

Together, all three made 42 baskets. This means that

x + y + z = 42 - - - - - - - - - - 1

Substituting x = y + 5 and z = 2y - 3 into equation 1, it becomes

y + 5 + y + 2y - 3 = 42

4y + 2 = 42

4y = 42 - 2 = 40

y = 40/4 = 10

x = y + 5 = 10 + 5

x = 15

z = 2y - 3 = 2 × 10 - 3

z = 20 - 3 = 17

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2 years ago

Find the length between (1, 3) and (5, 6)

ipn [44]

Answer:

Step-by-step explanation:

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2 years ago

What is the area of the shape below

Bad White [126]

Answer:

The area of the shape is $A=886 \:cm^2$ .

Step-by-step explanation:

The shape in the graph is a composite figure is made up of several simple geometric figures such as triangles, and rectangles.

Area is the space inside of a two-dimensional shape. We can also think of area as the amount of space a shape covers.

To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.

First separate the composite shape into three simpler shapes, in this case two rectangles and a triangle. Then find the area of each figure.

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The area of the first rectangle is $A=34\cdot 16=544\:cm^2$

The area of the second rectangle is $A=11\cdot19=209\: cm^2$

The area of a triangle is given by the formula $A=\frac{1}{2} bh$ where b is the base and h is the height of the triangle.

The area of the triangle is $A=\frac{1}{2} \cdot 14\cdot19=133\:cm^2$

Finally, add the areas of the simpler figures together to find the total area of the composite figure.

$A_{composite\:shape}=544+209+133=886 \:cm^2$

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3 years ago