This week, Marie trimmed 61% of the bushes in her yard. Katie trimmed 7/20 of the bushes in her yard. Who has trimmed a greater percentage of her bushes?

Answer:

D. [tex](x + 1)(x^2 + 3)[/tex]

Step-by-step explanation:

Hello!

We can group the first two terms and the last two terms.

Factoring by grouping is the process of breaking down larger polynomials to smaller ones to factor. We can then combine like factors.

In the second step, we can see that we can rewrite [tex]x^3 + x^2[/tex] as [tex]x^2(x + 1)[/tex], as both the two terms share a common factor of [tex]x^2[/tex]. We can pull out [tex]x^2[/tex] from that expression. Similarly, [tex]3x[/tex] and [tex]3[/tex] share a common factor of [tex]3[/tex], so we can pull that out.

=============================================================

Explanation:

a = 26 and b = 26 are the congruent legs

angle C = 60 degrees is between sides 'a' and b

c = unknown base which is opposite angle C

We'll use the law of cosines to find this missing side.

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 26^2 + 26^2 - 2*26*26*cos(60)

c^2 = 676

c = sqrt(676)

c = 26

It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.

---------------

Here's another way to see why we have an equilateral triangle.

The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180

x+x+60 = 180

2x+60 = 180

2x = 180-60

2x = 120

x = 120/2

x = 60

Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.

If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.

[tex] \textsf{let each of those angles measure ' x ' } [/tex]

[tex]\qquad \tt \rightarrow \:x + x + 60 = 180[/tex]

[ sum of all interior angles of a triangle ]

[tex]\qquad \tt \rightarrow \:2x + 60 = 180[/tex]

[tex]\qquad \tt \rightarrow \:2x = 180 - 60[/tex]

[tex]\qquad \tt \rightarrow \:2x = 120[/tex]

[tex]\qquad \tt \rightarrow \:x = \cfrac{120}{2} [/tex]

[tex]\qquad \tt \rightarrow \:x = 60 \degree[/tex]

Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.

henceforth, all its sides are equal to one another.

[tex]\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units[/tex]

Answer:

If the denominators are equal for all of the fractions, you can simply look at the numerator and order them. If the denominators aren't equal, you'll have to find the lcm (lowest common multiple), for example, if we have the fractions 3/6 and 1/4, we would find the lcm of 6 and 4, which is 12 and multiply the numerators accordingly. So the fractions would then become 6/12 and 3/12, this makes it easier for you to figure out their order from least to greatest.

Goodluck for your finals :)

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given information:

We can assume that 3 pupils play the flute only as we have also been told that 6 pupils play both instruments.

To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:

⇒ total number of pupils - pupils who play instruments

⇒ 20 - (3 + 6 + 6)

⇒ 20 - 15

⇒ 5

Therefore, 5 pupils do not play the piano and/or flute.

To calculate probability:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore:

[tex]\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}[/tex]

The answer is pretty simple but I put it in a picture below

Answer:

A

Step-by-step explanation:

Use the Pythagorean Theorem: a^2 + b^2 = c^2

The cable will be the hypotenuse, so c = 11.3 m

One leg is the distance of the anchor, so a = 4.2 m

(4.2)^2 + b^2 = (11.3)^2

17.64 + b^2 = 127.69

Subtract 17.64 from both sides

b^2 = 110.05

Square root both sides

b = ~10.5 m

The length of lake is 4500 feet.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as △PQR.

Here, In ΔABE and ΔDCE

          ∠ABE = ∠DCE         { each 90⁰ }

          ∠AEB = ∠CED         { vertically opposite angle}

By AA similarity, we get

          ΔABE ≈ ΔDCE

Now, AB/CD = BE/CE

       AB/500 = 1800/200

       AB/500 = 9

        AB = 9 X 500

       AB = 4500 feet.

Thus, the length of lake is 4500 feet.

Learn more about Triangle from:

https://brainly.com/question/2773823

#SPJ1

Answer:

the answer are A and Y , B and X.

 A and X are two independent events  , Option A is the correct answer.

Probability is the likelihood of an event to happen

A two way table is given

The two events will be independent when

If A is the first event and B is the second event , then

P(A) = P(A|B)

Here the P(A) = 30/100 = 0.3

P(B) = 20/100 = 0.2

P(A|X) = 15/50 = 0.3

P(A) = P(A|X)

Therefore A and X are two independent events , Option A is the correct answer.

To know more about Probability

https://brainly.com/question/11234923

#SPJ1

Answer:

50

Step-by-step explanation:

So you can think of this by grouping it like this:

(1-2) + (3-4) + (5-6) + ... + (97-98) + 99

which is equal to: (-1) + (-1) + (-1)... + (-1) + 99

(each group is equal to -1, and 99 won't have a pair since it's the last one)

then, find how many groups of -1 there are:

the groups start at 1 and end at 98, but there are two in each group, so 98/2 = 49. this means there are 49 groups.

so now, you know that there are 49 -1s, so 49 * (-1) = -49.

finally, you can't forget the extra 99 that didn't have a pair, so -49 + 99 = 50.

Answer:

Hence - 7 is the answer

Pls mark me brainliest plss

Answer:

Larger percentage of kids

Step-by-step explanation:

Kids: 32/40 = 4/5

Adults: 25/32 = 5/8

4/5 > 5/8

Answer:

[tex]|{\sf XY}| = 10\; {\rm cm}[/tex].

Step-by-step explanation:

Refer to the diagram attached. The dashed segment attached to [tex]\!{\sf Z}[/tex] points to the north. Rotating this segment clockwise with point [tex]{\sf Z}\!\![/tex] as the fixed center of rotation would eventually align this segment with the one between point [tex]\!\!{\sf Z}[/tex] and point [tex]\!\!{\sf X}[/tex]. The bearing of point [tex]{\sf X}[/tex] from point [tex]{\sf Z}[/tex] is the size of the angle between these two line segments when measured in the clockwise direction.

Subtract the bearing of [tex]{\sf Y}[/tex] from [tex]{\sf Z}[/tex] from the bearing of [tex]{\sf X}[/tex] from [tex]{\sf Z}[/tex] to find the measure of the angle [tex]\angle {\sf YZX}[/tex]:

[tex]\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}[/tex].

Thus, triangle [tex]\triangle {\sf YZX}[/tex] is a right triangle ([tex]90^{\circ}[/tex]) with segment [tex]{\sf YX}[/tex] as the hypotenuse. It is given that [tex]|{\sf XZ}| = 6\; {\rm cm}[/tex] whereas [tex]|{\sf ZY}| = 6\; {\rm cm}[/tex]. Thus, by Pythagorean's Theorem:

[tex]\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}[/tex].

Answer:

D

Hope this helps!

Answer:

x^4 - 3x^2 - 4.

Step-by-step explanation:

Imaginary roots  occur as conjugate pairs  so a 4th roots is -i.

So in factor form we have:

f(x) = (x - 2)(x + 2)(x - i)x + i)

     = (x^2 + 1)(x - 2)(x + 2)

     = (x^2 + 1)(x^2 - 4)

      = x^4 - 3x^2 - 4.

Answer:b.f(x) = x^4 – 3x^2 – 4

Step-by-step explanation:

In quadrilateral PQRS, ∠P and ∠S are opposite angles.

Answer:

x = -15

Step-by-step explanation:

the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

To do this, we can think on the situation as a right triangle, where the hypotenuse is 4 miles, the angle that we look at measures 10.5°, and the change in elevation (let's call it x) will be the opposite cathetus to that angle.

Then we can use the relation:

Sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know, we get:

sin(10.5°) = x/4mi

x = sin(10.5°)*4mi = 0.73mi

So the change in elevation is -0.73 miles (the negative sign is because the new elevation is smaller than the initial one).

If you want to learn more about right triangles:

https://brainly.com/question/2217700

#SPJ1

Based on the calculations, the equation for the curve of best fit is equal to y = -30.17x + 14.49.

From the table of data points, we have the following:

Mathematically, the standard equation of a straight line is given by:

y = ax + b       ....equation 1.

Thus, the equations that can be used to model the given data points are:

∑y = na + b∑x             ....equation 2.

∑xy = a∑x + b∑x²       ....equation 3.

Substituting the parameters into the equations, we have;

50.9 = 6a + 16b             ....equation 4.

24.6 = 16a + 35b       ....equation 5.

Solving eqn. 5 and 6 simultaneously, we have:

Substituting the value of a and b into eqn. 1, we have;

y = ax + b

y = -30.17x + 14.49.

Therefore, the equation for the curve of best fit is equal to y = -30.17x + 14.49.

Read more on curve of best fit here: brainly.com/question/9366563

#SPJ1

Answer:

C

Step-by-step explanation:

cos 30=12/x

[tex]x = 8 \sqrt{3} [/tex]

cos60=y/x

[tex]y =4 \sqrt{3} [/tex]

Answer:

x = [tex]8\sqrt{3}[/tex]

y = [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

• tan 60° = 12/ y         [tan θ = opposite/ adjacent]

y = 12/ tan 60°  

y = [tex]4\sqrt{3}[/tex]

• x² = y² + 12²             [Pythagoras's theorem]

x² = ( [tex]4\sqrt{3}[/tex] )² + 144

x = [tex]\sqrt{(4\sqrt{3})^{2} \space\ + \space\ 144}[/tex]

x = [tex]8\sqrt{3}[/tex]

Answer:

pm = 4

M is the mid point of PQ which means that pm = mq

so MQ = 4

PQ = PM + MQ

= 4 + 4

= 8

Answer:

the answer is C, 5a^6b

Step-by-step explanation:

ANSWER AT THE BOTTOM

Question:

There is a bag with 1 red pen, 4 black pens, and 3 blue pens. If 2 pens are chosen from the bag without replacement, what is the probability that you chose 2 black pens.

Explanation:

Right now there are a total of 8 pens. 4 of them are black. So, the probability of choosing a black pen right now is 4/8, or 1/2.

Lets assume we picked a pen and got black.

Now there are only 7 pens in the bag, and only 3 of them are black. The probability of choosing a black pen right now is 3/7.

So on the first draw, the probability is 1/2

And on the second draw, the probability is 3/7

To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.

For example, if we wanted to find the probability of rolling two 6's in a row on a dice, we would need to mutiply the individual probability together. The probability of rolling one 6 is 1/6, so the probability of rolling two 6's in a row is 1/6 MULTIPLIED BY 1/6, which is 1/36.

The probability of rolling two 6's in a row is 1/36.

Lets apply the same principle to our situation right now.

So on the first draw, the probability is 1/2

And on the second draw, the probability is 3/7

1/2 MULTIPLIED BY 3/7    =    3/14

3/14 in decimal form is 0.21

ANSWER:

0.21, OR 21%

Answer:

6 + (7 + 8) = 21

Step-by-step explanation:

the associative property of addition is: (a + b) + c = a + (b + c)

So the equivalent addition sentence would be:

(6 + 7) + 8 = 6 + (7 + 8) as they both equal 21

We can see that the area of the triangle is: 5.65in².

A triangle is actually known to be a shape that has three sides, three angles and three vertices. It's also known as a plane shape.

In order to find the area of the triangle, we will use Pythagorean Theorem: c² = a² + b².

Where c = hypotenuse = 6in.

b = 2in.

6² = a² + 2²

36 = a² + 4

a² = 36 - 4 = 32

a = √32

Area of the triangle = ½ × base × height.

Where base = √32

height = 2

Thus: A = ½ × √32 × 2

A = √32 = 5.65in².

Learn more about area of triangle on https://brainly.com/question/17335144

#SPJ1

Angle DAB will be equal to angle CAB

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

AC is a straight line and forms one of the sides of the triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ1

Answer:

  6/x²

Step-by-step explanation:

Rational expressions are added the same way numerical fractions are added. Their sum is the quotient of the sum of numerators, and the common denominator.

__

The given fractions already have the same denominator, so we simply add their numerators.

  [tex]\dfrac{2}{x^2}+\dfrac{4}{x^2}=\dfrac{2+4}{x^2}=\boxed{\dfrac{6}{x^2}}[/tex]

The true statements about ∠MJK and ∠MJL are

The statement is given as:

∠MJK and ∠MJL are a linear pair of angles and the angles are also supplementary

As a general rule, linear pair angles are adjacent angles that add up to 180 degrees. This means that:

The above means that, the following options are true:

(e), (f) and (h)

Also, the converse of the statement is:

∠MJK and ∠MJL are supplementary angles and the angles are also  linear pair of angles

This is false because not all supplementary angles are  linear pair angles

Read more about linear pair angles at:

https://brainly.com/question/1511741

#SPJ1

The substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an exponential function:

[tex]\rm N = N_oe^{-kt}[/tex]

Plug N = N⁰/2

[tex]\rm N_o/2 = N_oe^{-kt}[/tex]

[tex]\rm \dfrac{1}{2} = e^{-0.15t}[/tex]

Solving for t:

t = 4.62≈ 4.7 days

Thus, the substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15

Learn more about exponential decay here:

brainly.com/question/14355665

#SPJ1