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3 years ago

Simplify the expression 4x+3(5y−x)

2 answers:

5 0

4x+3(5y-x)
Start by multiplying out the brackets
4x+15y-3x
Collect like terms
4x-3x+15y
Subtract the x's
X+15y
Hope this helps!

kipiarov [429]3 years ago

3 0

4x+3 (5y-x)

4x+15y-3x
X+15y

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Pick the expression that matches this description:

Katen [24]

Option C is correct because it is a trinomial with a leading coefficient of 3 and a constant term of -5

Step-by-step explanation:

We need to pick the expression that matches this description:

A trinomial with a leading coefficient of 3 and a constant term of -5

First lets explain the terms:

Trinomial: a polynomial having 3 terms

Leading coefficient: The constant value of variable having highest power

Constant term: Having no variable and value cannot be changed.

Now using these definitions, we can choose the correct option

Option A is incorrect because the expression has 2 terms

Option B is incorrect because it is a trinomial but the leading coefficient is -5 and not 3 constant term is 3 and not -5.

Option C is correct because it is a trinomial with a leading coefficient of 3 and a constant term of -5

Option D is incorrect because it is a trinomial but the leading coefficient is 3 but constant term is 1 and not -5.

So, Option C is correct.

Keywords: Algebra

Learn more about Algebra at:

#learnwithBrainly

6 0

3 years ago

Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

3 0

3 years ago

(3x+4)-(-8-2x) simplified

goldenfox [79]

Answer:

5x+12

Step-by-step explanation:

7 0

3 years ago

Translate each of the following research questions into appropriate H0 and Ha.

Mandarinka [93]

Answer:

$H_{0}: \mu = 62500\text{ dollars per year}\\H_A: \mu > 62500\text{ dollars per year}$

$H_{0}: \mu = 2.6\text{ hours}\\H_A: \mu \neq 2.6\text{ hours}$

Step-by-step explanation:

We have to build appropriate null and alternate hypothesis for the given scenarios.

a) Population mean, μ = $62,500 per year

The market research wants to find whether the mean household income of mall shoppers is higher than that of the general population.

$H_{0}: \mu = 62500\text{ dollars per year}\\H_A: \mu > 62500\text{ dollars per year}$

We would use one-tail(right) test to perform this hypothesis.

b) Population mean, μ = 2.6 hours

The company want to know the average time to respond to trouble calls is different or not.

$H_{0}: \mu = 2.6\text{ hours}\\H_A: \mu \neq 2.6\text{ hours}$

We would use two-tail test to perform this hypothesis.

7 0

3 years ago

you pick a card at random without getting the first card back you pick a second card at random what is the probability of pickin

Keith_Richards [23]

We have to calculate the probability of picking a 4 and then a 5 without replacement.

We can express this as the product of the probabilities of two events:

• The probability of picking a 4

• The probability of picking a 5, given that a 4 has been retired from the deck.

We have one card in the deck out of fouor cards that is a "4".

Then, the probability of picking a "4" will be:

$P(4)=\frac{1}{4}$

The probability of picking a "5" will be now equal to one card (the number of 5's in the deck) divided by the number of remaining cards (3 cards):

$P(5|4)=\frac{1}{3}$

We then calculate the probabilities of this two events happening in sequence as:

$\begin{gathered} P(4,5)=P(4)\cdot P(5|4) \\ P(4,5)=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12} \end{gathered}$

Answer: 1/12

8 0

1 year ago