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2 years ago

Averi was trying to factor 4x2 + 20x - 16. She found

Mathematics

1 answer:

hichkok12 [17]2 years ago

7 0

Answer:

The width will be $x^{2} +5x-4$

Step-by-step explanation:

Thinking process:

Let the model be:

$4x^{2} +20x-16$

factoring out 4 gives:

$4(x^{2} +5x-4)$

Factorizing the expression in the parentheses gives:

$4(x^{2} +5x-4)$

Therefore, since the expression in the parentheses cannot be factorized further, the expression is:

$length = 4 units\\width = x^{2} +5x-4$

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Draw a pair of vertical angles with a given measure

Veseljchak [2.6K]

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

Vertical Angles are the congruent angles opposite each other when two lines cross

see the attached figure to better understand the problem

m<ACD=m<BCE ------> by vertical angles

m<ACB=m<DCE ----> by vertical angles

8 0

3 years ago

Applying the the properties of Congruence.

kolbaska11 [484]

Answer:

$LM = 35cm$ and $m \angle H = 98^o$

Step-by-step explanation:

For this problem, it is critical to understand what the opening statement means.

$Quadrilateral GHJK \cong quadrilateral LMNP$ means that each pair of corresponding sides between shapes are congruent (they have equal length), and each pair of corresponding angles between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).

So, it's important to be able to determine which pairs are the corresponding parts. When the congruence is given like $Quadrilateral GHJK \cong quadrilateral LMNP$ the letters are in a particular order. That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.

So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc

In other words, point G and L correspond, point H and K correspond, etc.

To find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).

$\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}$

While all of that is true, we only have a few sides with any information in them. Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written. So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent sides above, we see that $\overline{GH} \cong \overline{LM}$

Since the sides (line segments) are congruent, their lengths are equal

$GH = LM$

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"

$GH = LM\\(4x+3)=(6x-13)$

$(4x+3)+13=(6x-13)+13\\4x+16=6x$

$(4x+16)-4x=(6x)-4x\\16=2x$

divide both sides by 2

$\frac{16}{2}=\frac{2x}{2}\\8=x$

So, to find the length, LM, we just need to look back at the expression for LM:

$LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35$

remembering that the lengths are measured in centimeters (as indicated on the diagram): $LM = 35cm$

To find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.

$\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P$

While all of that is true, we only have a few angles with any information in them. Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written. So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent angles above, we see that

$\angle H \cong \angle M$

Since the angles are congruent, their measures are equal

$m\angle H = m\angle M$

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"

$m\angle H = m\angle M\\(9y+17)=(11y-1)$

subtract 1 from both sides

$(9y+17)+1=(11y-1)+1\\9y+18=11y$

subtract 9y from both sides

$\\(9y+18)-9y=(11y)-9y\\18=2y$

divide both sides by 2

$\frac{18}{2}=\frac{2y}{2}\\9=y$

So, to find angle H, we just need to look back at the expression for the measure of angle H:

$m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98$

remembering that the angle is measured in degrees (as indicated on the diagram): $m \angle H = 98^o$

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1 year ago

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icang [17]

Answer:

yes

Step-by-step explanation:

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3 years ago

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If an item is 30% off and 350 how much is the original price

alisha [4.7K]

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3 years ago

Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new wall

Gekata [30.6K]

The relationship between the length & the width of the closet and the length of the wall is an illustration of a linear equation.

The equation for f(l) is: $f(l) = 1.5l$ .
The desired length and width are 8m and 4m