The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).

a. (1 - cos^2(x)) cot(-x)
b. (cos^2(x) - 1) cot(x)
c. (sin^(x) - 1) tan(x)
d. (cos^2(x) - 1) cot(-x)

Answer:

3 : 36 10: 120 6:72

Step-by-step explanation:

60 divided by 5 is 12

3 x 12 = 36

10 x 12 = 120

72/12= 6

3-36

5-60

6-72

10-120

One month equals 12$ saved

Answer:

(P, Q) = (-75, 57)

Step-by-step explanation:

The equation will have infinitely many solutions when it is a tautology.

Subtract the right side from the equation:

Px +57 -(-75x +Q) = 0

x(P+75) +(57 -Q) = 0

This will be a tautology (0=0) when ...

P+75 = 0

P = -75

and

57-Q = 0

57 = Q

_____

These values in the original equation make it ...

-75x +57 = -75x +57 . . . . . a tautology, always true

Answer:

10.153 years

Step-by-step explanation:

The future value of such an investment is given by ...

FV = P·(1 +r/12)^(12t)

where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.

Dividing by P and taking the log, we have ...

FV/P = (1 +r/12)^(12t)

log(FV/P) = 12t·log(1 +r/12)

Dividing by the coefficient of t gives ...

t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12

t ≈ 10.153 . . . years

Answer:

Step-by-step explanation:

Givens

V = 58 in^3

h = 5 inches

pi = 3.14

Formula

V = pi * r^2 * h

Solution

58 = 3.14 * r^2 * 5

58 = 15.7 * r^2

58/15.7 = r^2

3.6942 = r^2

sqrt(r^2) = sqrt(3.6942)

r = 1.922 which when rounded is

r = 1.92

Answer: r=1.92

given what we know about the equation i can determine what steps are needed to solve this :)

volume

1) V = 58 in^3

we know that h=5inches

2) h = 5 inches

heres what pi equals

3) pi = 3.14

then we use pi in the equation

4)= pi * r^2 * h

heres the solution steps

1)58 = 3.14 * r^2 * 5

2)58 = 15.7 * r^2

3)58/15.7 = r^2

4)3.6942 = r^2

5)sqrt(r^2) = sqrt(3.6942)

6)r = 1.922 then we round and get  r = 1.92

so final solution is r = 1.92

×║hope this helps║×

Final answer:

To solve the system of equations x + y = 6 and 12x + y = 5, substitute 6 - y for x in 12x + y = 5 and solve for y.

Explanation:

To solve the given system of equations x + y = 6 and 12x + y = 5, we need to substitute the value of x or y into the second equation. In this case, substituting 6 - y for x in 12x + y = 5 will allow us to solve for y.

Let's substitute 6 - y for x:

12(6 - y) + y = 5

After simplifying, we get:

72 - 12y + y = 5

Combining like terms:

-11y = -67

Dividing both sides by -11, we find that y = 67/11 or approximately 6.09.

So, option 1: 6 - y for x in 12x + y = 5 is the correct expression to substitute.

Answer:

i think it is the last one

Step-by-step explanation:

-2/25^3x^3

First find the slope of the given line:

4x +2y = 1

Subtract 4x from each side:

2y = -4x + 1

Divide both sides by 2:

y = -2x +1/2

The slope is -2.

Now use the slope to find the y-intercept. Because  the line is perpendicular, you need to use the negative inverse of the slope.

The negative inverse of -2 is 1/2

Now using the point-slope form y - y1 = m(x-x1)

Use the inverse slope for m, and the given point(-4,3) to get:

y - 3 = 1/2(x+4)

Simplify:

y - 3 = x/2 +2

Add 3 to each side:

y = x/2 + 5

Reorder the terms to get y = 1/2x +5

The answer is D.

All you have to do is treat the inequality like an equation and multiply both sides by 2.

[tex]-x<2 \\ \\ x>-2[/tex]

Answer: x> -2

Step-by-step explanation:

step 1 :take 2 to the other side ,and 1 will multiply by 2 which will give you 2

step 2 : take the negative or -1 to the other side ( you will divide 2 by -1 ) which will result to a -2

step 3: most important thing to remember once you multiply or divide by a negative number you will have to change the inequality sign ( in this case the smaller than sign changes to bigger than because you divided by -1 in step 3 )

hope this helped

Answer:

m∠1 = 92°

Step-by-step explanation:

∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that

m∠2 + m∠3 = 73° +107° = 180°

so, the angles are supplementary and lines a and b are parallel.

Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.

m∠1 = m∠4 = 92°

Answer:

It reduces the distance from the plotted points to the function curve.

Step-by-step explanation:

The goodness of fit of a model is measured by the "residuals", the differences between the given points and the modeled points. The smaller the residuals, the better the model. Any change to the model that will put it closer to the plotted points makes it a better model. The change proposed in your problem statement does that.

Answer:

1. all the right angles are congruent

2. opposite sides of a parallelogram are congruent

3. SAS congruent postulate

4. corresponding parts of a congruent triangle are congruent

Step-by-step explanation:

1. As all the right angles are congruent

          ∠JML≅∠KLM≅ ∠90°

2. As per the properties of a parallelogram, the opposite sides are congruent.

                  Hence the sides JM≅KL

3. SAS postulate is defined as Side-Angle-Side postulate. When the side, adjacent angle and the other other adjacent side of two triangle are congruent then the two triangles are said to be congruent. In the given case both the sides JM and ML of ΔJML are congruent to both the sides KL and ML of ΔKLM.

                            Hence ΔJML≅ΔKLM

4. As proven in part 3, ΔJML≅ΔKLM so the congruent parts of two congruent triangle are congruent.

                In given case the side JL(of ΔJML)≅MK(ΔKLM)

!

The completed proof is presented as follows;

Parallelogram JKLM is a rectangle and by definition of a rectangle, ∠JML

and ∠KLM are right angles, ∠JML ≅ ∠KLM because, all right angles are

congruent, [tex]\overline{JM}[/tex] ≅ [tex]\overline{KL}[/tex] because opposite sides of a parallelogram are

congruent, and [tex]\overline{ML}[/tex] ≅ [tex]\overline{ML}[/tex] by reflective property of congruence. By the SAS

congruence postulate, ΔJML ≅ ΔKLM. Because, congruent parts of

congruent triangles are congruent, [tex]\overline{JL}[/tex] ≅ [tex]\overline{MK}[/tex]

Reasons:

The given quadrilateral is a parallelogram, that have interior angles that are right angles, therefore, the figure has the properties of a rectangle, and

parallelogram including;

All right angles are congruent and equal to 90°

The length of a side is equal to itself by reflexive property, therefore,  [tex]\overline{ML}[/tex]

≅ [tex]\overline{ML}[/tex]

The Side-Angle-Side SAS postulate states that if two sides and an included

angle of one triangle are congruent to the corresponding two of sides and

included angle of another triangle, the two triangles are congruent.

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Answer:

Volume of the pyramid = 16m³ or 16 cubic meters.

Step-by-step explanation:

The equation for the volume of a pyramid is:

[tex]V=\frac{b*h}{3}[/tex]

where b = area of base and h = height.

In this case, the base is a square with a side length of 4m.

Area of the square base = (4m)² = b = 16m²

h = 3m

Insert b and a into the volume of a pyramid equation.

[tex]V=\frac{3m*16m}{3}[/tex]

= 16m³

Volume of the pyramid = 16m³ or 16 cubic meters.

Answer:

C

Step-by-step explanation:

Use such properties of logarithms:

[tex]\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa[/tex]

Thus,

[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]

Answer:

The answer is C

Step-by-step explanation:

Use such properties of logarithms:

\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa

Thus,

\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).

A)

Prime numbers and numbers with a multiple of four that are between 1 and 14 include: 1, 2, 3, 4, 5, 7, 8, 12, 13.

There are 9 numbers listed.

9/14 = ~0.64285... or roghly 65.3%

B) Numbers between 1 and 14 with the multiples of 2 or 3 include: 2, 4, 6, 8, 9, 10, 12, 14.

There are 8 numbers listed.

8/14 = ~0.5714... or, about 57.14%

C) 3 and 4 is a list of two numbers.

2/14 = 1/7 = ~0.1429, or about 14.9%

D) There is a total of  numbers equal to or less than 8 in a list of 1 and 14.

8/14 = ~0.5714... or, about 57.14%

Answer:

40

Step-by-step explanation:

The measure of the angle KJL is 40°.

Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point. A circle is a closed curve that has no corners or vertices.

Given is a circle O where m arc IVK = 120° and m arc KP = 2 × m arc IP,

We need to find the measure of the angle KJL,

So,

According to the question,

m arc IVK + m arc KPI = 360° [whole circumference of a circle is 360°]

m arc IVK + m arc KP + m arc IP = 360°

120° + m arc IP + 2 × m arc IP = 360°

3 m arc IP = 240°

m arc IP = 80°

Therefore,

m arc KP = 160°

Now, according to the property of a circle,

m ∠KJL = 1/2 × [m arc KP - m arc IP]

m ∠KJL = 1/2 × [160° - 80°]

m ∠KJL = 80°/2

m ∠KJL = 40°

Hence the measure of the angle KJL is 40°.

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Answer:

h = 7 + 6x

Step-by-step explanation:

Since we are trying to find the height of the tree, we put h on the left side of the equation. Since the tree is 7ft tall at the moment, we write 7ft on the right side of the equation. Knowing that the tree grows 6 inches each year (x) we write 6x on the right side of the equation.

Answer:

H=7+6x

Hope this helps

Answer:

Slope = -1/2

Y-intercept is y = -1

Equation of the line: [tex]y=-\frac{1}{2}x-1[/tex]

Step-by-step explanation:

The slope intercept form is  y = mx + b

Where, m is slope, and

b is y-intercept

We need 2 points to find these. One point is  (-2,0) and second point is (2,-2).

THe formula for slope, m, is m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Plugging the points, we get the slope to be:

[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-0}{2--2}\\=\frac{-2}{4}\\=-\frac{1}{2}[/tex]

y-intercept is the point where the line crosses the y axis. Looking at the graph, y-intercept is y = -1.

Now we plug slope and y-intercept into the slope-intercept form to get:

[tex]y=mx+b\\y=-\frac{1}{2}x-1[/tex]

ANSWER

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

EXPLANATION

The graph passes through (-2,0) and (0,-1).

The slope can be calculated using the formula,

[tex]m= \frac{rise}{run} [/tex]

[tex]m = \frac{0 - - 1}{ - 2 - 0} [/tex]

[tex]m = - \frac{1}{2} [/tex]

The y-intercept is -1.

The equation in slope-intercept form is

y=mx + c

We substitute the slope and y-intercept to obtain

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

Answer:

Sadly, it is still high in debate. Scientists are still in doubt of the Hypothesis, so no. Some may claim there is a solution, though.

Step-by-step explanation:

Final answer:

The Riemann Hypothesis is an unsolved mathematical problem, with no validated solution as of yet, and remains one of the Millennium Prize Problems in mathematics.

Explanation:

The Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the area of number theory. It postulates that all non-trivial zeros of the Riemann zeta function, a complex function important for understanding the distribution of prime numbers, have their real parts equal to 0.5. Despite significant efforts by mathematicians over the years, the solution to the Riemann Hypothesis remains elusive, and no proof or disproof has been universally accepted by the mathematics community.

As of my knowledge cutoff in 2023, researchers continue to explore various mathematical approaches and even computational methods to tackle this problem. However, no experiment or scientific test can validate the hypothesis since it is a purely mathematical conjecture. A resolution of the Riemann Hypothesis would have profound implications for number theory and related fields, yet it remains one of the seven Millennium Prize Problems, with a reward of one million dollars offered for a solution.

Answer:

B. Events H and C are dependent and P(H|C) < P(C|H)

Step-by-step explanation:

The ratios of groups with children to hiking groups on the trail are different for the two trails.

P(H|C) = 15/45 = 1/3

P(C|H) = 15/40 = 3/8

1/3 < 3/8 so the comparison of choice B is appropriate.

Answer:

26 terms

Step-by-step explanation:

The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...

an = -2 +5(n -1)

The sum of the first n terms is ...

(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573

n(5n -9) = 3146

5n^2 -9n -3146 = 0 . . . . . quadratic in standard form

Using the quadratic formula, we can find the positive solution for n to be ...

n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26

26 terms must be added to give the desired sum.

_____

Relevant formulas are ...

Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d

x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0

Answer: 9\20 or 45% hope this helps

The "odds" of picking a green are 9 to 11 .

The "probability" of picking a green is 9/20 or 45% .

Answer:

[tex](x-7)^2+(y-5)^2=16[/tex].

Step-by-step explanation:

The given circle has equation [tex]x^2+y^2=16[/tex].

This is the equation that has its center at the origin with radius 4 units.

When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).

The equation of a circle with center (h,k) and radius r units is [tex](x-h)^2+(y-k)^2=r^2[/tex].

This implies that, the translated circle will now have equation.

[tex](x-7)^2+(y-5)^2=4^2[/tex].

[tex](x-7)^2+(y-5)^2=16[/tex].

The correct equation for translating the circle x² + y² = 16 seven units to the right and five units up is (x - 7)² + (y - 5)² = 16. Therefore, option D is the correct answer.

The original equation for a circle with a radius of 4 units is x² + y² = 16. A translation of the circle seven units to the right and five units up would involve shifting the x-coordinate by +7 and the y-coordinate by +5. Therefore, the new equation would be (x - 7)² + (y - 5)² = 16.

This is due to the fact that a translation of a geometric figure does not alter its size, shape, or orientation; it simply shifts the figure in the plane. Keeping the radius the same, applying the translation to the circle's center (0,0) results in a new center at (7,5), which translates to the equation above.

Answer:

12.5

Step-by-step explanation:i did that problem before

Answer:

Step-by-step explanation:

r = a5/a4 = (81/4)/(-27/4) = -3

an = a1·r^(n-1)

-27/4 = a1·(-3)^3 = -27·a1 . . . . fill in the known numbers for n=4

(-27/4)/(-27) = a1 = 1/4

Answer:

Step-by-step explanation:

[tex]\text{The formula of a discriminant of}\ ax^2+bx+c=0:\\\\b^2-4ac\\\\================================\\\\\text{We have the equation:}\\\\3x^2-4x+2=0\to a=3,\ b=-4,\ c=2\\\\\text{Substitute:}\\\\b^2-4ac=(-4)^2-4(3)(2)=16-24=-8[/tex]

Answer:

$1214.19

Step-by-step explanation:

Let c and p represent the cost of the sofa and the original selling price, respectively. The original markup was 0.69·p, so we have ...

c + 0.69p = p . . . . . based on selling price, the original markup was 69%

c = p(1 -0.69) = 0.31p . . . . subtract the markup

p = c/0.31 . . . . . . . . . . . . . divide by the coefficient of c

So, the original selling price was ...

520/0.31 ≈ 1677.42

The first markdown decreased the selling price to ...

1677.42 - 0.13·1677.42 = 0.87·1677.42 ≈ 1459.36

The markup increased the selling price to ...

1459.36 +0.30·1459.36 ≈ 1897.17

And the final markdown decreased the selling price to ...

1897.17 -0.36·1897.17 ≈ 1214.19

The final sale price was $1214.19.

Answer:

• c = √89 ≈ 9.434

• A = arcsin(8/√89) ≈ 57.995°

• B = arcsin(5/√89) ≈ 32.005°

Step-by-step explanation:

By the law of cosines, ...

c² = a² + b² -2ab·cos(C)

Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.

c = √(8² +5²) = √89 ≈ 9.434

Then by the law of sines (or the definition of the sine of an angle), ...

sin(A) = a/c·sin(C) = a/c = 8/√89

A = arcsin(8/√89) ≈ 57.995°

sin(B) = b/c·sin(C) = b/c = 5/√89

B = arcsin(5/√89) ≈ 32.005°

Answer:

Step-by-step explanation:

3(4x+2)-6x=5x-5(2+x)

12x +6 -6x = 5x -10 -5x . . . . . eliminate parentheses using the distributive property

6x +6 = -10 . . . . . . . . . . . . . . . collect terms

x +1 = -10/6 . . . . . . . . . . . . . . . divide by 6

x = -1 - 5/3 . . . . . . . . . . . . . . . add -1

x = -8/3 . . . . . . . . . . . . . . . . . simplify

Answer:

b= -1

Step-by-step explanation:

y=3x+b

8=3(3)+b

8=9+b

b= -1

Answer:

y = 1/2x -8

Step-by-step explanation:

The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...

rise/run = 1/2

The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...

y = slope·x + y-intercept

y = 1/2x -8