At a skills competition, a target is being lifted into the air by a cable at a constant speed. an archer standing on the ground launches an arrow toward the target. the system of equations below models the height, in feet, of the target and the arrow t seconds after it was fired. which statement most likely describes the situation modeled by this system?

Answer:

PX = 10

Step-by-step explanation:

PR = 20

PX = PR/2 (diagonals of parallelogram bisect eachother)

or, PX = 20/2

so, PX = 10

The equations which have a leading coefficient of 3 and a constant term of –2 are 0 = 3x² +2x - 2 and 0=3x²-1x-2.

A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.

The standard form of the quadratic equation is,

[tex]ax^2+bx+c=0[/tex]

Here,(a,b, c) is the real numbers and (x) is the variable.In this equation, a is the coefficient of the highest term and c is the constant term.

The equations which has the leading coefficient of 3 and a constant term of –2 has to be find out.

The first equation given in the problem is,

[tex]0 = 3x^2 +2x - 2[/tex]

In this equation, the coefficient of the term which has the highest power is 3 and the constant term is -2. Thus, this option is correct.

The second equation given in the problem is,

[tex]0 = -2 - 3x^2 +3[/tex]

Rearrange the equation as,

[tex]0 = -2 - 3x^2 +3\\0=-3x^2+1[/tex]

In this equation, the coefficient of the term which has the highest power is -3 and the constant term is 1. Thus, this option is not correct.

The third equation given in the problem is,

[tex]0 = 3x^2 +x +2[/tex]

In this equation, the coefficient of the term which has the highest power is 3 and the constant term is 2. Thus, this option is not correct.

The fourth equation given in the problem is,

[tex]0 = -1x - 2 +3x^2[/tex]

Rearrange the equation as,

[tex]0=3x^2-1x-2[/tex]

In this equation, the coefficient of the term which has the highest power is 3 and the continuant term is -2. Thus, this option is correct.

Hence, the equations which have a leading coefficient of 3 and a constant term of –2 are 0 = 3x² +2x - 2 and 0=3x²-1x-2.

Learn more about the quadratic equation here;

https://brainly.com/question/1214333

Answer:

1875

Step-by-step explanation:

1335 + 0540 = 1875

Answer:

1,875

Step-by-step explanation:

[tex]1335 + 540 = 1,875[/tex]

Hope this helps! : )

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's see what's the domain and range for the given function ~

[tex]\qquad \tt \dashrightarrow \:domain \in [ -5 , 4 ] [/tex]

or

[tex]\qquad \tt \dashrightarrow \: - 5 \leqslant x \leqslant 4[/tex]

Because domain = all values of x between its maximum (4) and minimum (-5) value [ including them ]

[tex]\qquad \tt \dashrightarrow \:range \in[ -4 , 9 ][/tex]

or

[tex]\qquad \tt \dashrightarrow \: - 4 \leqslant y \leqslant 9[/tex]

Because range = all values of y between its maximum (9) and minimum (-4) value [ including them ]

Answer:

16% or 16.9492% I'm going to be honest I'm not 100% sure though

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

Answer:

x∈(-∞; 0).

Step-by-step explanation:

1) the given function is a parabola with its vertex in (0;0). Then

2) the increasing interval is (0:+∝), decreasing interval is (-∝;0).

Answer:

d

Step-by-step explanation:

god a 100 on edg

ΔABC cannot be congruent to ΔADC by SSS?l because D. No, because AB ≅ DA.

It should be noted that when the three corresponding sides of the figures have the same length, it can be concluded that the triangles are congruent by SSS.

In this case, ΔABC cannot be congruent to ΔADC by SSS?l because AB is not equal to DA.

Therefore, the correct option is D.

Learn more about congruent on:

brainly.com/question/2938476

#SPJ9

Answer:

[tex]\displaystyle (x,y) \longrightarrow (x+3, y+1)[/tex]

Step-by-step explanation:

We want to write a rule for the transformation shown.

We can see that ΔA'B'C' is the figure ΔABC shifted rightwards 3 units and upwards 1 unit.

In other words, all x-coordinates of ABC is increased by 3, and all y-coordiantes of ABC is increased by 1.

Therefore, the rule for the x-coordinate is:
[tex]\displaystyle x \longrightarrow x + 3[/tex]

And the rule for the y-coordinate is:

[tex]\displaystyle y \longrightarrow y + 1[/tex]

In conclusion, we have that:

[tex]\displaystyle (x,y) \longrightarrow (x+3, y+1)[/tex]

The inequality in both inequality expressions is the less than or equal to sign

Inequality 1

The inequality is given as:

[tex]-1 \le \frac x2[/tex]

Multiply both sides by 2

[tex]-2 \le x[/tex]

Rewrite as:

[tex]x \ge - 2[/tex]

The above means that the correct values of x are at least -2.

See attachment for the complete table is as follows:

Inequality 2

The inequality is given as:

[tex]1 \le \frac {-x}2[/tex]

Multiply both sides by 2

[tex]2 \le -x[/tex]

Rewrite as:

[tex]-x \ge 2[/tex]

Multiply both sides by -1

[tex]x \le -2[/tex]

The above means that the correct values of x are at most -2.

See attachment for the complete table is as follows:

Read more about inequalities at:

https://brainly.com/question/11234618

The means of samples 1 and 2 is 3.45. The mean of sample 3 is 3.8. Based on the data, the average diner would visit the restaurant 3 or 4 times.

The mean of a sample is the average of all the data sets given in the sample. The mean of a sample is useful in calculating population averages, central tendency, standard deviation, etc.

Mathematically, the mean of a sample can be expressed as:

[tex]\mathbf{\overline X =\dfrac{sum \ of \ the \ terms }{no \ of \ terms } }[/tex]

[tex]\mathbf{\overline X =\dfrac{\sum X}{N} }[/tex]

Thus, the means of samples 1 and 2 is:

[tex]\mathbf{\overline X =\dfrac{36+33}{20} }[/tex]

[tex]\mathbf{\overline X =3.45}[/tex]

The mean of sample 3 is:

[tex]\mathbf{\overline X =\dfrac{3+3+6+4+1+5+3+4+4+5}{10} }[/tex]

[tex]\mathbf{\overline X =3.8}[/tex]

Based on the data, the average diner would visit the restaurant 3 or 4 times, because the mean of the samples lies between 3 to 4.

Learn more about the mean of a sample here:

https://brainly.com/question/12892403

Answer:

The radius is 3 and it is the same all around

Step-by-step explanation:

Since The hypotenuse equals the two other sides squared, let's find out what those are.

[tex]\sqrt{9} + \sqrt{9} = \sqrt{18}[/tex]

Now, let's find the square root of those 9s.

[tex]\sqrt{9} = 3[/tex]

Those other sides we talked about (more specifically the base of the triangle) are the radius of the circle because of how they extend to the exterior of the circle, which means since their length is 3, the radius is also 3.

The radius is always constant so it is supposed to be the same all around.

Answer:

B) -2

Step-by-step explanation:

[tex]log_{6} \frac{1}{36}[/tex]                           ORIGINAL

[tex]log_{6} 6^{-2}[/tex]                          REWRITE  1/36

-2                                  LOG RULE - 6's CANCEL

Hope this helsp!

Answer:

$1350

Step-by-step explanation:

Simple Interest = Deposit ×Rate/100×Time

SI=5000×9/100×3

=$1350

Answer:

a club has 2 dollar down payment and 4 $ per week how much money is owed after 2 weeks

Step-by-step explanation:

Answer:

r= 0.402

Step-by-step explanation:

The approximate area of the decagon with a side of 8cm is 492.37 cm².

Given side of the regular decagon = 8cm

A decagon is a polygon with 10 equal sides.

We know that area of a regular decagon with side a is given by:

[tex]A=\frac{5}{2} a^{2} \sqrt{5+2\sqrt{5} }[/tex]

So, the area A of the regular decagon with a side of 8cm=[tex]\frac{5}{2} 8^{2} \sqrt{5+2\sqrt{5} }[/tex]

[tex]A=160\sqrt{5+2\sqrt{5} }[/tex]

A=492.37 cm²

Therefore, the approximate area of the decagon is 492.37 cm².

To get more about the decagon visit:

https://brainly.com/question/19899848

The final answer of the solution is x∈ (-13,1) ∪ [1, 15 ] or, x∈(-13, 15] and x∈ (-∞ , 1) ∪ [1, ∞) or, x∈ (-∞, ∞) or x∈ R.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

For |x - 1 | + 1 < 15 , we should first break the modulus function .

Two cases are possible for this inequality ,

case 1 - when x ≥ 1

x - 1 + 1 < 15 ⇒ x < 15

putting the number line both x ≥ 1 and x≤ 15

Then, x∈ [1, 15)

case 2 - when x < 1

-x + 1 + 1 < 15

⇒ -x + 2 < 15

⇒ -x < 13 ⇒ x > -13

putting the number line both x > -13 and x < 1

then, x∈ (-13, 1)

now, answer is x∈ (-13,1) ∪ [1, 15 ] or, x∈(-13, 15]

Again, for |x - 1| + 1 > 15

Similarly z there are two cases possible for this

case 1 :- when x ≥ 1

x - 1 + 1 > 15 ⇒ x > 15

Putting the number line both x ≥ 1 and x > 15

then, x ∈ [1, ∞)

case 2 - when x < 1

-x + 1 + 1 > 15 ⇒ x < -13

putting the number line both x < 1 and x < -13

Then, x∈ (-∞, 1)

hence, final answer is x∈ (-∞ , 1) ∪ [1, ∞) or, x∈ (-∞, ∞) or x∈ R

Learn more about Inequality :

https://brainly.com/question/20383699

The package which the company should choose if it costs the same to produce the two products is the cylinder because it has about 27.5 in.3 less wasted space than the prism.

The term "cost of production" refers to all the costs that are involved when a company offers a service or manufactures a product.

Costs of production relate to the different expenses that a firm faces in producing a good or service.

This refers to the amount which is used to produce a good.

With this in mind, we can see that there are the given dimensions for the square prism and cylinder from the complete question.

Hence, because they cost the same, choosing the cylinder is the best choice because of the less wasted space than the prism.

Read more about the cost of production here:

brainly.com/question/19569102

Answer:

It's A

Step-by-step explanation:

Total money Tammy has = $70

Money she is left with now = $19.54

Therefore, the money she used on coffee =

70 - 19.54 = $50.46

Now,

1 pound coffee costs $8.41

Pounds of coffee she bought = 50.46 ÷ 8.41

= 6 pounds

The 3 rules that we need to use to simplify the expression are:

As I understand, the expression that we have is:

[tex]\frac{((-8)^4)^{-5}}{(-8)^6}[/tex]

The first rule we need to use, is the exponent of an exponent rule, it says that:

[tex](a^n)^m = a^{n*m}[/tex]

If we apply that to the denominator, we get:

[tex]\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6}[/tex]

Now we need to use the quotient of powers:

[tex]\frac{a^m}{a^n} = a^{m - n}[/tex]

Using that we get:

[tex]\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-20 - 6} = (-8)^{-26}[/tex]

Finally, we use the rule for a negative exponent:

[tex]a^{-n} = \frac{1}{a^n}[/tex]

So we get the simplified form:

[tex]\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-26} = \frac{1}{(-8)^{26}}[/tex]

If you want to learn more about exponents, you can read:

https://brainly.com/question/8952483

Answer:

B, C, and E

Step-by-step explanation:

option 3

center (-1,-5)

radious √41

hope this helped!

Answer:

[tex] \frac{25}{100} \times 1.20[/tex]

Answer:

Option A :- if finding lateral surface area

Other information

radius r = 6 m

height h = 8 m

slant height s = 10 m

volume V = 301.592895 m3

lateral surface area L = 188.495559 m2

base surface area B = 113.097336 m2

total surface area A = 301.592895 m2

Step-by-step explanation:

Using the formulas

A=πrl+πr²

l=√r²+h²

Solving forA

A=πr(r+√h²+r²)=π · 6 · (6+√8²+6²)≈301.59289

Answer:

41%

Step-by-step explanation:

step one to determine what the fraction would be you just read the question: first you have to see what they want to calculate the percentage of. In this case it's students who like traveling out of state but don't like camping. 88 students like traveling out of state and 36 of those students don't like camping so the fraction you have to use is 36/88 step two next you multiply your fraction by 100 to calculate your percentage 36/88×100= 40.9% step three since you have to round to the nearest whole percent your answer would be 41%

The railroad crew repair 1500 km in 25 days if the railroad crew can replace 360 meters of rails in 6 days

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

A railroad crew can replace 360 meters of rails in 6 days.

Let's suppose the x kilometers of rail they can repair in 25v days

Per day they repair = 360/6 = 60 km/day

Then the x can be found:

x = 60×25

x = 1500 km

Thus, the railroad crew repair 1500 km in 25 days if the railroad crew can replace 360 meters of rails in 6 days.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ1

The best measure of centre is the mean , don't take median as we need average of marks here.

Mean of Lamar

Mean of Mimi

Mimi has been better

The equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y = x + 2 is y = -1/2 - 3

The equation of a line in slope intercept form is expressed as:

y = mx + c

m is the slope

c is the intercept

Given the equation of a line y = x + 2, the slope of the line perpendicular is -1/2. If this line pass through the point (2, -2), the required equation will be

y - (-2) = -1/2(x+2)
2(y+2) = -(x+2)
2y + 4 = -x - 2

2y = -x - 6
y = -1/2 - 3

Hence the equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y = x + 2 is y = -1/2 - 3

Learn more on equation of a line here: https://brainly.com/question/13763238

Answer:

  52°

Step-by-step explanation:

The sum of an angle and its complement is 90°.

__

The sum of 38° and its complement, x, is 90°:

  38 +x = 90 . . . . . an equation to find the complement of 38°

  x = 90 -38 . . . . subtract 38 from both sides

  x = 52 . . . . degrees

The measure of x is 52°.