Evaluate -a^n when a=3 and n=2,3,4, and 5. Now evaluate (-a)^n when a=3 and n=2,3,4, and 5. Based on the sample, does it appear that -a^n = (-a)^n? If not, state the relationships,if any, between the two.

Y = 1/2 + 5 , the slope of this equation is 1/2

The equations of the parallel lines must also have a slope of 1/2.

This is because parallel lines have the same value of slope.

Answer:

Correct options are A and D

Step-by-step explanation:

According to the synthetic division in the diagram you can write down the result of division:

[tex]2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.[/tex]

Therefore,

When [tex]x= - 6,2{x^2} + 9x -7= 11[/tex] and when [tex]2{x^2} + 9x -7[/tex] is divided by [tex]\left( {x + 6} \right)[/tex], the remainder is 11.Option (A) is correct and option (D) is correct.

Further Explanation:

Given:

Explanation:

The synthetic division can be expressed as follows,

[tex]\begin{aligned}- 6\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,\,\,\,\,\,\, - 7} \,}} \right.  \hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,\,\,\,18}  \hfill\\\,\,\,\,\,\,\,\,2\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,11 \hfill \\\end{aligned}[/tex]

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is 11. Therefore, the remainder of the synthetic division is 11.

When [tex]x= - 6, 2{x^2} + 9x -7= 11[/tex] and when [tex]2{x^2} + 9x -7[/tex] is divided by [tex]\left( {x + 6} \right)[/tex], the remainder is 11. Option (A) is correct and option (D) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, factor (x+5), remainder 12, statements, true, apply, divided, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

given h = 600 - 16t ( add 16t to both sides )

16t + h = 600 ( subtract h from both sides )

16t = 600 - h ( divide both sides by 16 )

t = [tex]\frac{600-h}{16}[/tex]

when h = 400

t = [tex]\frac{600-400}{16}[/tex] = [tex]\frac{200}{16}[/tex] = 12.5 seconds

Answer:

The required time is 3.54 seconds approximately or [tex]\frac{5}{2}\sqrt{2}[/tex] seconds.

Step-by-step explanation:

Consider the provided function.

[tex]h(t) = 600-16t^2[/tex]

Where t represents the time in seconds and h represents the height.

It is given that we need to find the time to reach a height of 400 feet.

Substitute h(t)=400 in the above function.

[tex]400= 600-16t^2[/tex]

[tex]400- 600=-16t^2[/tex]

[tex]-200=-16t^2[/tex]

[tex]200=16t^2[/tex]

[tex]\frac{50}{4}=t^2[/tex]

[tex]t=\sqrt{\frac{50}{4}} \\t=\frac{5}{2}\sqrt{2}[/tex]

Neglect the negative value as time should be a positive number.

Or

[tex]t\approx 3.54[/tex]

Hence, the required time is 3.54 seconds approximately.

Answer:

<L = 50 degrees

Step-by-step explanation:

B and C are given. There should be a one to one Correspondence. <A should = <L

Since there are 180o in any triangle

<L = <A = 180 - 35 - 95

<L = <A = 50 degrees

If you need to, you can write and solve an equation for the factor you seek.

... 6×10^10 = factor × 2×10^-3

Divide by 2×10^-3 to find the value of the factor:

... (6×10^10)/(2×10^-3) = factor

... factor = (6/2)×10^(10-(-3))

... factor = 3×10^13

The first number is 3×10^13 times the second number.

_____

An exponent signifies repeated multiplication.

... 10×10×10 = 10³

Just as you cancel common factors when you do division, you can subtract exponents.

[tex]\dfrac{10\cdot 10\cdot 10}{10\cdot 10}=\dfrac{10}{1}=10\\\\\dfrac{10^3}{10^2}=10^{3-2}=10^1=10[/tex]

The same process works regardless of the signs of the exponents. When multiplying, we add exponents; when dividing we subtract the exponent of the denominator.

Answer:

f(x)=x-1

Step-by-step explanation:

replace y by f(x) to obtain functional notation

f(x) = x - 1

Expressed as a fraction 56 is 56/35 of 35. That fraction can be reduced, and expressed several ways.

56/35 = 8/5 = 1 3/5 = 1.6

56 is 1 3/5 of 35

56 is 1.6 times 35

Answer:

Step-by-step explanation:

Apparently, your periodic rate is that used to compute the interest accrued each period. It seems to be the compound (annual) rate divided by the number of periods in a year: quarterly, 4; monthly, 12; daily, 365; biweekly, 26; semimonthly, 24.

_____

If you want the effective annual rate to be 18% in each case, the numbers are different. For n periods per year, those are calculated as

[tex]\sqrt[n]{1.18}-1[/tex]

A periodic rate of 0.04224664 will give an effective annual rate of 18%.

Periodic rates for a 18% compound rate compounded quarterly, monthly, daily, biweekly, and semimonthly are calculated as follows :

Try this solution (all the details are in the attached picture, answers are underlined with colour).

The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]

Further explanation:

Given:

The measure of angle A is [tex]\angle A = {60^ \circ }.[/tex]

The measure of angle C is [tex]\angle C = {45^ \circ }.[/tex]

The length of side AB is [tex]AB = 8[/tex]

Calculation:

The sum of all angles of a triangle is [tex]{180^ \circ }.[/tex]

[tex]\begin{aligned}\angle A + \angle B + \angle C &= {180^ \circ }\\{60^ \circ } + \angle B + {45^ \circ } &= {180^ \circ }\\{105^ \circ } + \angle B &= {180^ \circ }\\\angle B&= {180^ \circ } - {105^ \circ }\\\angle B&= {75^ \circ }\\\end{aligned}[/tex]

The sine rule in triangle ABC can be expressed as,

[tex]\begin{aligned}\frac{{BC}}{{\sin {{60}^ \circ }}}&=\frac{8}{{\sin {{45}^ \circ }}}\\BC&=\frac{8}{{\frac{1}{{\sqrt2 }}}}\times\frac{{\sqrt 3 }}{2}\\BC&= 9.80\\\end{aligned}[/tex]

The length of AC can be calculated as follows,

[tex]\begin{aligned}\frac{{AB}}{{\sin {{45}^ \circ }}} &= \frac{{AC}}{{\sin {{75}^ \circ }}}\\\frac{8}{{\sin {{45}^ \circ }}} \times \sin {75^ \circ }&= AC\\10.93 &= AC\\\end{aligned}[/tex]

The perimeter of triangle ABC can be obtained as follows,

[tex]\begin{aligned}{\text{Perimeter}}&= AB + BC + AC\\&= 8 + 9.80 + 10.93\\&= 28.73\\\end{aligned}[/tex]

The area of triangle ABC can be obtained as follows,

[tex]\begin{aligned}{\text{Area}}&=\frac{1}{2} \times AB \times AC \times \sin \left( A \right)\\&= \frac{1}{2} \times 8 \times 10.93 \times \sin {60^ \circ }\\&= 4 \times 10.93 \times \frac{{\sqrt3 }}{2}\\&= 37.86\\\end{aligned}[/tex]

The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: angles, ABC, angle A=60 degree, perimeter, area of triangle, triangle ABC.

The answer to "What is the P(Gate 3 and Gate 4 are both open)?" is

B: 15%

It is because they state that the chance of both gates being open at the same time is 15% and that chance is indeed the probability.

point slope form

y-y1 = m (x-x1)

y- (-2) = 3(x-1)

y+2 = 3(x-1)

y + 2 = 3(x - 1)

the equation of a line in point-slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (1, - 2), hence

y + 2 = 3(x- 1) ← in point-slope form

Since the triangle is equilateral (you can tell by the tick on each side), all angles have the same measure as well.

The angles of a triangle sum up to 180 degress, so three equal angles must measure 60 degrees each.

So, in particular, we have

[tex] 7x+4 = 60 \iff 7x = 56 \iff x=8[/tex]

x = 8 and y = 6

ΔRST is an equilateral triangle

with all 3 sides equal in length and all 3 angles = 60°, hence

7x + 4 = 60 ( subtract 4 from both sides )

7x = 56 ( divide both sides by 7 )

x = 8

similarly

8y + 12 = 60 ( subtract 12 from both sides )

8y = 48 ( divide both sides by 8 )

y = 6

f(x) = - [tex]\frac{6}{7}[/tex] x + [tex]\frac{53}{7}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = - [tex]\frac{6}{7}[/tex]

partial equation is y = - [tex]\frac{6}{7}[/tex] x + c

to find c substitute (3, 5 ) into the partial equation

5 = - [tex]\frac{18}{7}[/tex] + c ⇒ c = [tex]\frac{53}{7}[/tex]

f(x) = - [tex]\frac{6}{7}[/tex] x + [tex]\frac{53}{7}[/tex]

The point-slope form of a line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 6) and (3, 4). Substitute:

[tex]m=\dfrac{4-6}{3-5}=\dfrac{-2}{-2}=1\\\\y-6=1(x-5)\\\\y-6=x-5\qquad|\text{add 6 to both sides}\\\\y=x+1\qquad|\text{subtract x from both sides}\\\\-x+y=1\qquad|\text{change the signs}\\\\x-y=-1[/tex]

Answer:

slope-intercept form: y = x + 1

point-slope form: y - 6 = 1(x - 5)

standard form: x - y = -1

Hey there!

Given points:

...(5,6) and (3,4)

Slope-intercept form:

... y=mx+b

'm' is the slope and 'b' is the y-intercept.

Slope:

... (y₂-y₁)/(x₂-x₁)

... (4-6)/(3-5)

... -2/-2

...1

:

... y = x + b

... 4 = 3 + b

... b = 1

Slope-intercept form:

... y = x + 1

Hope helps!

Try this option:

x²+27=0;

[tex](x+\sqrt{-27})(x- \sqrt{-27})=0; \ => \ \left[\begin{array}{ccc}x=3 \sqrt{3}i\\x=-3 \sqrt{3}i \end{array}\right[/tex]

x = ± 3i√3

given x² + 27 = 0 (subtract 27 from both sides )

x² = - 27 ( take the square root of both sides )

x = ±[tex]\sqrt{-27}[/tex] = ± √(9 × 3 × -1 ) ← (i = √-1 )

  = ± (√9 × √3  ×√-1 ) = ±3i√3

"Enlargement" here implies that the two pentagons are similar.  Because of similarity, the following equation of ratios must be true:  7/15 = x/7.  Then 15x=49, and x = 49/15 = 3.27 cm, approximately.

Rounded to the nearest tenth, that comes to 3.3 cm.

Answer:

B

Step-by-step explanation:

ANSWER

The solution is

[tex](x=1,y=2),(x=2,y=3)[/tex]

EXPLANATION

We have

[tex]y=x+1---(1)[/tex]

and

[tex]y=x^2-1---(2)[/tex]

Let us substitute equation (1) in to equation (2). This gives us,

[tex]x+1=x^2-1(2)[/tex]

We rewrite this as a quadratic equation as the highest degree is 2.

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

This implies that

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

we factor to obtain,

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

[tex]x(x-1)-2(x-1)=0[/tex]

[tex](x-1)(x-2)=0[/tex]

This means,

[tex](x-1)=0\:\: or\:\:(x-2)=0[/tex]

[tex]x=1\:\: or\:\:x=2[/tex]

We substitute this values into any of the above equations, preferably equation (1)

When, [tex]x=1[/tex], [tex]y=1+1=2[/tex]

When, [tex]x=2[/tex], [tex]y=2+1=3[/tex]

The solution is

[tex](1,2),(2,3)[/tex]

Answer:

14

Step-by-step explanation:

(A) f(a + 2) = a² - 16

substitute x = a + 2 into f(x)

f(a + 2) = (a + 2)² - 4(a + 2) - 12

           = a² + 4a + 4 - 4a - 8 - 12

           = a² - 16

(B ) f(a + h) = a² + 2ah + h² - 4a - 4h - 12

substitute x = a + h into f(x)

f(a + h) = a² + 2ah + h² - 4a - 4h - 12

The answer would be 56 because 14X4 = 56

There were 56 girls who tried out for the volleyball team, found by dividing the number of girls on the team (14) by the percentage that made the team (25%), which equals 14 divided by 0.25.

The question asks us to find the total number of girls who tried out for the volleyball team if 14 girls (making up 25% of those who tried) made the team. To calculate the total number of girls who tried out, we can set up the equation based on the percentage:

25% of total girls = 14

We can rewrite 25% as 0.25 in decimal form:

0.25 × total girls = 14

To find the total number of girls, we divide both sides of the equation by 0.25:

total girls = 14 ÷ 0.25

total girls = 56

Therefore, 56 girls tried out for the volleyball team.

The percent change is given by ...

... (percent change) = (new amount - old amount)/(old amount) × 100%

This can be rearranged to give a formula for the new amount. First, we'll rewrite it to a slightly different form.

... (percent change) = ((new amount)/(old amount) -1) × 100%

... (percent change)/100% = (new amount)/(old amount) -1 . . . . divide by 100%

... (percent change)/100% + 1 = (new amount)/(old amount) . . . add 1

... (old amount) × ((percent change)/100%) +1) = new amount . . . . multiply by old amount

We can now use this formula to find the new amount in each case.

13. 25 × (300%/100% +1) = 25 × 4 = 100 . . . . dollars

14. 160 × (-20%/100% +1) = 160 × 0.8 = 128 . . . . bananas

15. 56 × (-75%/100% +1) = 56 × .25 = 14 . . . . books

16. 52 × (25%/100% +1) = 52 × 1.25 = 65 . . . . companies

17. 12000 × (5%/100% +1) = 12000 × 1.05 = 12,600 . . . . miles

18. 710 × (-10%/100% +1) = 710 × 0.90 = 639 . . . . points

_____

Considering the above formula for percent change (or its "slightly different form"), you may want to reconsider your answers for problems 7–12.

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = [tex]\frac{2}{5}[/tex] x - 6 is in this form with slope m = [tex]\frac{2}{5}[/tex]

Parallel lines have equal slopes, thus

y = [tex]\frac{2}{5}[/tex] x + c is the partial equation of parallel line

to find c , substitute (- 1, 5 ) into the partial equation

5 = - [tex]\frac{2}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex] ← equation of parallel line

Answer:

B. 80 km/h

Step-by-step explanation:

The graph is linear and goes through the origin, so distance is proportional to time, and the constant of proportionality is speed. The desired answer can be read from the point on the graph at time = 1 hour: 80 km.

Julian's speed is 80 kilometers per hour.

B

speed = [tex]\frac{distance}{time}[/tex]

From the graph the distance travelled = 480 Km

and time taken = 6 hours

speed = [tex]\frac{480}{6}[/tex] = 80 Km / hour

(1)

take out the common factor (y - 4 )

= (y - 4)(3x - 2)

(2)

factor by grouping (1/2 terms and 3/4 terms )

4y(5x - 1) + 7(5x - 1)

take out the common factor (5x - 1)

= (5x - 1)(4y + 7)

1.  Factor out the (y-4)

(y-4) (3x-2)

2.Factor by grouping

20xy -4y    +35x -7

4y(5x-1) +7(5x-1)

then factor out 5x-1

(5x-1)(4y+7)

Yes this is a Law of Detachment.

Using Pythagorean's Theorem we know that a^2 + b^2 = c^2

C is the length of the ladder, and we are given one of the sides, let's call that side b

                                                                                          _________

we have a^2 + b^2 = c^2, and a^2 = c^2 - b^2, so a = √ c^2 - b^2

       _________      ______     ____

a = √12^2-3^2 = √ 144-9 = √ 135 = 11.61895 

so the top of the ladder is 11.6 feet above the ground

here u go hope this helps

Answer:

12 sin60°

Remember SOHCAHTOA.

sinθ =

opposite

hypotenuse

sin60° =

x

12

x = 12 sin60°