Which statement correctly compares AB and FD?
AB and FD are the same length.
AB is longer than FD.
O
AB is shorter than FD
AB is shorter than or the same length as FD.

Answer:

[tex]k=\frac{-11}{2}[/tex].

Step-by-step explanation:

We are given [tex]\alpha[/tex] and [tex]\beta[/tex] are zeros of the polynomial [tex]x^2-(k+6)x+2(2k-1)[/tex].

We want to find the value of [tex]k[/tex] if [tex]\alpha+\beta=\frac{1}{2}[/tex].

Lets use veita's formula.

By that formula we have the following equations:

[tex]\alpha+\beta=\frac{-(-(k+6))}{1}[/tex]  (-b/a where the quadratic is ax^2+bx+c)

[tex]\alpha \cdot \beta=\frac{2(2k-1)}{1}[/tex] (c/a)

Let's simplify those equations:

[tex]\alpha+\beta=k+6[/tex]

[tex]\alpha \cdot \beta=4k-2[/tex]

If [tex]\alpha+\beta=k+6[/tex] and [tex]\alpha+\beta=\frac{1}{2}[/tex], then [tex]k+6=\frac{1}{2}[/tex].

Let's solve this for k:

Subtract 6 on both sides:

[tex]k=\frac{1}{2}-6[/tex]

Find a common denominator:

[tex]k=\frac{1}{2}-\frac{12}{2}[/tex]

Simplify:

[tex]k=\frac{-11}{2}[/tex].

Answer:

< 8, 4 >

Step-by-step explanation:

Consider the coordinates

x- coordinate A - 3 → A' 5 → that is + 8

y- coordinate A 1 → A' 5 → that is + 4

Hence T = < 8, 4 >

or (x, y) → (x + 8, y + 4)

The translation T is given by:

                        T(x,y)=(x+8,y+4)

i.e. it shifts the point 8 units to the right and 4 units up.

The translation is the transformation that changes the location of points of the figure but there is no change in the shape as well as size of the original figure.

It is given that:

The translation T maps point A(-3,1) onto point A'(5,5).

so, if the translation rule that is used is:

(x,y) → (x+h,y+k)

Here

(-3,1) → (5,5)

i.e.

-3+h=5    and  1+k=5

i.e.

h=5+3   and   k=5-1

i.e.

h=8   and   k=4

Hence, the translation is 8 units to the right and 4 units up.

Step-by-step explanation:

Just graph it and see if the descriptions fit the graph

(see attached)

A. We can see from the graph that the possible x-values are -∞ ≤ x ≤ +∞ . Hence limiting to domain to x≤ -2 this is obviously not true.

B. We can see from the graph that the vertex is y = 6 and that the entirety of the graph is under this point, hence range y<6 is true

C. We can see that the vertex is located at x=-2. Every part of the graph to the left of this point has a positive slope, hence the function is increasing for negative infinity to this point x=-2 is true

D) We can see that for the interval -4<x<∞, the graph actually increases between -4<x<-2, and then decreases after that. Hence this statement is not true.

E. it is obvious that the y intercept is y=2 which is positive. Hence this is true.

The graph of F(x)=-x^2-4x+2 is a downward-opening parabola with its vertex serving as the local and global maximum. There are no asymptotes for this quadratic function. The shape of the graph is best understood by examining its behavior over a range of x-values and by sketching it with the vertex and axis of symmetry.

The graph of the function F(x) = -x^2 - 4x + 2 represents a parabola opening downward because the coefficient of x^2 is negative. To understand the nature of the graph, we evaluate its characteristics by identifying the vertex, the axis of symmetry, and whether it has local or global extrema. The vertex of this parabola can be found using the formula -b/2a, which gives us the x-coordinate, and by substituting that back into the function for the y-coordinate. The axis of symmetry will be a vertical line passing through the vertex's x-coordinate.

Since this is a quadratic function, it does not have asymptotes because it extends indefinitely in both the positive and negative directions of the y-axis. Instead, the parabola will have a maximum point at the vertex, which is a local and global maximum because the parabola opens downward. Moreover, we should evaluate the function for a range of x-values to understand its behavior for large negative x, small negative x, small positive x, and large positive x.

Sketching the graph of this function would involve plotting the vertex, drawing the axis of symmetry, and selecting a few points around the vertex to determine the shape of the parabola.

To find the proportion of boys in the original class, divide the number of boys by the total number of students in the class.

To find the proportion of boys in the original class, we need to compare the number of boys in the original class to the total number of students in the original class.

The original class had 18 students, and it was joined by 6 boys from another class. This means there are now 18 + 6 = 24 boys on the field trip.

The overall ratio of boys to girls on the field trip is 2:3, which means for every 2 boys, there are 3 girls. If we have 24 boys, we can find the number of girls by dividing 24 by 2 and then multiplying by 3. This gives us (24/2) * 3 = 36 girls.

So, the original class had 24 boys and 36 girls. To find the proportion of boys in the original class, we divide the number of boys (24) by the total number of students (24 + 36 = 60). This gives us 24/60 = 0.4, or 40%.

do it

like this

i have done by coordinates of geometry

Answer:

Area = 24 square unit,

Fourth vertex = (-4, -3)

Step-by-step explanation:

Suppose we have a parallelogram ABCD,

Having vertex A(1, -2), B(2, 3), and C(-3, 2),

Let D(x,y) be the fourth vertex of the parallelogram,

∵ The diagonals of a parallelogram bisect each other,

Thus, the midpoint of AC = midpoint of  BD

[tex](\frac{1-3}{2}, \frac{-2+2}{2})=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]

[tex](\frac{-2}{2}, 0)=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]

By comparing,

[tex]-2=2+x\implies x=-4[/tex]

[tex]3+y=0\implies y = -3[/tex]

Thus, the fourth vertex is (-4, -3),

Now, the area of the parallelogram ABCD = 2 × area of triangle ABC (Because both diagonals divide the parallelogram in two equal triangles)

Area of a triangle having vertex [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,

[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

So, the area of triangle ABC

[tex]A=\frac{1}{2}|(1(3-2)+2(2+2)-3(-2-3)}|[/tex]

[tex]=\frac{1}{2}(1+8+15)[/tex]

[tex]=\frac{1}{2}\times 24[/tex]

[tex]=12\text{ square unit}[/tex]

Hence, the area of the parallelogram ABCD = 2 × 12 = 24 square unit.

Answer:

7

Step-by-step explanation:

0.3r = 2.1

r = 2.1 ÷ 0.3

r = 7

Answer:

9x²y¹⁴

Step-by-step explanation:

[tex]\tt (3xy^4)^2(y^2)^3\\\\=3^2x^2y^{4\cdot2}\cdot y^{2\cdot3}\\\\=9x^2y^{8}\cdot y^{6}\\\\= 9x^2y^{8+6}\\\\= 9x^2y^{14}[/tex]

Answer:

The length of the bold figure ABCDEFGH is 30.8 units

Step-by-step explanation:

* To solve the problem look to the attached figure

- There is a square of area 81 units²

∵ The area of the square = L² , where L is the length of the side of

   the square

∵ The area of the square = 81 units²

∴ L² = 81 ⇒ take √ for both sides

∴ L = 9 units

- Two points are drawn on each side of a square dividing it into 3

  congruent parts

∵ 9 ÷ 3 = 3

∴ The length of each part is 3 units

- Quarter-circle arcs connect the points on adjacent sides to create

 the attached figure

∵ The radius of each quarter circle is 3 units

∵ The length of each side joining the two quarter circle is 3 units

∵ The figure ABCDEFGH consists of 4 quarters circle and 4 lines

- The length of the 4 quarters circle = the length of one circle

∵ The length of the circle is 2πr

∴ The length of the 4 quarters circle = 2 π (3) = 6π units

∵ The length of each line = 3 units

∴ The length of the figure = 6π + 4 × 3 = 30.8 units

* The length of the bold figure ABCDEFGH is 30.8 units

Answer:

30.8

Step-by-step explanation:

Answer:

(4,0)

Step-by-step explanation:

Plug them into see:

Check (4,0)

In order for the lines to intersect at (4,0) it must be on both lines.

2(4)+0=8 is true because it is saying 8=8

4+0=4 is true because 4=4

So (4,0) is a intersection point.

Check (0,4)

2(0)+4=8 is not true because it is saying 4=8

0+4=4 is true so it's on this line while not on the other line.

So (0,4) is not an interestion point for the mentioned lines.

Well all points can't be on the line since (0,4) is not on both lines but just one of them.  

We could have solve this out instead plugging in but the problem gave us the option here with the choices.

The system of linear equations given intersects at the point (4, 0), and since these equations represent distinct lines, they only intersect at this single point.

The question involves solving a system of linear equations to find the point of intersection. The system given is:

Let's solve the equations step by step:

Therefore, the lines intersect at the point (4, 0).

To determine whether the lines intersect at all points on a line, note that these equations represent distinct lines with different slopes, meaning they only intersect at one point, facing the choice given, (4, 0) is correct.

Answer:

3000 pounds

Step-by-step explanation:

first sub in info to find k

2000=k/15 ; multiply both sides by 15 ; k=30000. if k is the constant, then to find the safe load (y) with the new beam (x), we input our new info into the equation.

y=30000/10 ; y=3000

Answer:

Safe load of the beam is 3000 pounds.

Step-by-step explanation:

If a horizontal beam of x feet length can hold y pounds safe load, the expression that represents the relation between load and length of the beam is

y = [tex]\frac{k}{x}[/tex]

If y = 2000 pounds and x = 15 feet

then 2000 = [tex]\frac{k}{15}[/tex]

k = 15×2000 = 30000

Now we will calculate the safe load when beam is 10 feet long.

From the formula,

y = [tex]\frac{30000}{10}=3000[/tex] pounds

Therefore, safe load of the beam is 3000 pounds.

Answer:

92

Step-by-step explanation:

87 + 91 + 92 = 270

270 / 3 = 90

Answer:

The x-coordinate of the solution is x=3

Step-by-step explanation:

we have

[tex]y=-x+5[/tex] ------> equation A

[tex]y=x-1[/tex] ------> equation B

Solve the system of equations by substitution

Substitute equation B in equation A and solve for x

[tex]x-1=-x+5[/tex]

[tex]x+x=5+1[/tex]

[tex]2x=6[/tex]

[tex]x=3[/tex]

Find the value of y

[tex]y=x-1[/tex]  ------> [tex]y=3-1=2[/tex]

The solution of the system of equations is the point (3,2)

therefore

The x-coordinate of the solution is x=3

Answer:

x = 3

Step-by-step explanation:

i did the same test and got it right

kinda.

x     = total of movies rented, INPUT

g(x) = total cost for all movies rented, OUTPUT.

the point of ( 6.5 , 17.50) means, that 6.5 movies were rented at a price of 17.50 total, that makes sense since 17.5 is more than 6.5 so the price is more than the quantity, however, whoever rents 6.5 movies?  I mean, unless the movie store clerk gives you 6 movies and then cuts another with a chainsaw and gives you half of another.

so, the input is not too feasible, since no one rents 6.5 movies.

Answer:

B. No the input is not feasible

because you cannot rent 6,5 movies  :p

Step-by-step explanation:

¼ pizza is to 5 dollars as x pizza is to 8 dollars.

¼ / 5 = x / 8

Cross multiply:

5x = 2

Divide:

x = ⅖

You can buy ⅖ of a pizza.

Answer:

A. Tina's favorite shade is more blue than Tyler's

Answer:  The correct option is

(A) Tina's favorite shade is more blue than Tyler's.

Step-by-step explanation:  Given that Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint.

Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.

We are to find how Tina's favorite shade of teal compare to Tyler's shade of teal.

The fraction of blue paint in Tina's  favorite shade of teal is given by

[tex]F_{ti}=\dfrac{7}{7+5}=\dfrac{7}{12}[/tex]

and the fraction of blue paint in Tyler's  favorite shade of teal is given by

[tex]F_{ty}=\dfrac{5}{7+5}=\dfrac{5}{12}[/tex]

We get

[tex]F_{ti}-F_{ty}=\dfrac{7}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}>0\\\\\\\Rightarrow F_{ti}>F_{ty}.[/tex]

That is, the fraction of blue paint in Tina's  favorite shade is more than the fraction of blue paint in Tyler's favorite shade.

Thus, Tina's  favorite shade is more blue than Tyler's.

(A) is the correct option.

Answer:

14.4

Step-by-step explanation:

72/5 in decimal form equals 14.4

[tex]\frac{72}{5}[/tex] in decimal form is 14.4

[tex]\frac{72}{5}[/tex] is the same as 72 ÷ 5

72 ÷ 5 = 14.4

All we have to do to turn this fraction into a decimal is divide the fractions numerator by its denominator and we will get our decimal.

Answer:

Trey earns a base pay of $47,300 plus 15% for each car sold.

The equation that represets Trey's total pay in dollars is:

y = $47,300 + 0.15x

Where $47,300 represents the base pay, and 0.15x represents the money he earn for the total cars sold.

Answer:

[tex]y=47,300+0.15x[/tex]

Step-by-step explanation:

Let x represent total sales in dollars.

We have been given that Trey earns base pay of $47,300 and was paid  commission of 15% for each car he sold.

Since Trey is paid 15% for each car he sold and total sales were x dollars, this means his commission would be 15% of x that is [tex]\frac{15}{100}x=0.15x[/tex].

The total salary of Trey would be base salary plus commission: [tex]y=47,300+0.15x[/tex]

Therefore, the equation [tex]y=47,300+0.15x[/tex] represents Trey's total pay in dollars.

Answer:

[tex]\boxed{(\frac{3}{2} ,-1)}[/tex]

Step-by-step explanation:

[tex]\left \{ {{2x-3y=6} \atop {4x+2y=4}} \right.[/tex]

It seems this system of equations would be solved easier using the elimination method (the x and y values are lined up).

Multiply everything in the first equation by -2 (we want the 4x to be able to cancel out with a -4x).

[tex]2x-3y=6 \rightarrow -4x+6y=-12[/tex]

Now line up the equations (they are already lined up - convenient) and add them from top to bottom.

[tex]\left \{ {{-4x+6y=-12} \atop {4x+2y=4}} \right.[/tex]

The -4x and 4x are opposites, so they cancel out.

Adding 6y and 2y gives you 8y, and adding -12 and 4 gives you -8.

[tex]8y=-8[/tex]

Divide both sides by 8.

[tex]y=-1[/tex]

Since you have the y-value you can substitute this in to the second (or first equation, it doesn't necessarily matter) equation.

[tex]4x +2(-1)=4[/tex]

Simplify.

[tex]4x -2=4[/tex]

Add 2 to both sides.

[tex]4x=6[/tex]

Divide both sides by 4.

[tex]x=\frac{6}{4} \rightarrow\frac{3}{2}[/tex]

The final answer is [tex]x=\frac{3}{2} ,~y=-1[/tex].

[tex](\frac{3}{2} ,-1)[/tex]

Answer:

D. if we are describing how to get from y=x^2 to y=x^2+8.

Step-by-step explanation:

If we are describing how to get from y=x^2 to y=x^2+8, then the transformation is just a translation of 8 units up.

If the equation was y=x^2-8, it would have been down 8 units.

If the equation was y=(x-8)^2, it would have been right 8 units.

If the equation was y=(x+8)^2, it would have been left 8 units.

Answer:

Vertices of hyperbola: (2,0) and (-2,0)

Foci of hyperbola: (8,0) and (-8,0)

Step-by-step explanation:

The given equation is:

[tex]\frac{x^2}{4}-\frac{y^2}{60}=1[/tex]

The standard form of equation of hyperbola is:

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

Center of hyperbola is (h,k)

Comparing given equation with standard equation

h=0, k=0

so, Center of hyperbola is (0,0)

Vertices of Hyperbola

Vertices of hyperbola can be found as:

The first vertex can be found by adding h to a

a^2 - 4 => a=2, h=0 and k=0

So, first vertex is (h+a,k) = (2,0)

The second vertex can be found by subtracting a from h

so, second vertex is ( h-a,k) = (-2,0)

Foci of Hyperbola

Foci of hyperbola can be found as

The first focus of hyperbola can be found by adding c to h

Finding c (distance from center to focus):

[tex]c=\sqrt{a^2+b^2}  \\c=\sqrt{(2)^2+(2\sqrt{15})^2}\\c=8[/tex]

So, c=8 , h=0 and k=0

The first focus is (h+c,k) = (8,0)

The second focus is (h-c,k) = (-8,0)

Answer:

[tex]g(x)=x+6[/tex] is the answer

given

[tex]h(x)=4\sqrt{x+7}[/tex] and [tex]f(x)=4\sqrt{x+1}[/tex].

Step-by-step explanation:

[tex]h(x)=(f \circ g)(x)[/tex]

[tex]h(x)=f(g(x))[/tex]

Inputting the given function for h(x)  into the above:

[tex]4\sqrt{x+7}=f(g(x))[/tex]

Now we are plugging in g(x) for x in the expression for f which is [tex]4\sqrt{x+1}[/tex] which gives us [tex]4\sqrt{g(x)+1}[/tex]:

[tex]4\sqrt{x+7}=4\sqrt{g(x)+1}[/tex]

We want to solve this for g(x).

If you don't like the looks of g(x) (if you think it is too daunting to look at), replace it with u and solve for u.

[tex]4\sqrt{x+7}=4\sqrt{u+1}[/tex]

Divide both sides by 4:

[tex]\sqrt{x+7}=\sqrt{u+1}[/tex]

Square both sides:

[tex]x+7=u+1[/tex]

Subtract 1 on both sides:

[tex]x+7-1=u[/tex]

Simplify left hand side:

[tex]x+6=u[/tex]

[tex]u=x+6[/tex]

Remember u was g(x) so you just found g(x) so congratulations.

[tex]g(x)=x+6[/tex].

Let's check it:

[tex](f \circ g)(x)[/tex]

[tex]f(g(x))[/tex]

[tex]f(x+6)[/tex] I replace g(x) with x+6 since g(x)=x+6.

[tex]4\sqrt{(x+6)+1}[/tex] I replace x in f with (x+6).

[tex]4\sqrt{x+6+1}[/tex]

[tex]4\sqrt{x+7}[/tex]

[tex]h(x)[/tex]

The check is done. We have that [tex](f \circ g)(x)=h(x)[/tex].

Answer:

50.5 km

Step-by-step explanation:

If speed=distance/time, then distance=time*speed.

So we have the time and the speed to find the distance.

We just need to multiply 5 hours and 10.1 km/hour.

distance=(5 hours)(10.1 km/hour)

The time unit cancels and you are just left with the distance unit.

distance=50.5 km

Answer:50.5 km

Step-by-step explanation:

Answer:

This graph is a not a Function because it doesn't pass the vertical line test. The opened and closed circles are not  in relation to the y-value and the x-value. This function also doesn't corresponds to one another, which messes up the domain and range.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x^m=(x^{13})^5x(x^{-8})^{-5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\x^m=(x^{(13)(5)})x(x^{(-8)(-5)})\\\\x^m=(x^{65})x^1(x^{40})\qquad\text{use} \ a^na^m=a^{n+m}\\\\x^m=x^{65+1+40}\\\\x^m=x^{106}\Rightarrow m=106[/tex]

Answer:

Step-by-step explanation:

2+(-2+23)-/8-9/=

2+ 21- /-1/=

2+21-1=

2+20=

22

Please mark as brianliest! Hope this helps!

Answer:

Solution of the expression is 22.

Step-by-step explanation:

The given expression is 2 + (-2 + 23) – Ӏ 8 - 9 Ӏ

We have to solve this expression

2 + (-2 + 23) - | 8-9 |

= 2 + (21) - |-1 |

= 2 + 21 - 1    [Since absolute value of (-x) is x or |-x | = x ]

= 23 - 1

= 22

Solution of the expression is 22.

For this case we have:

[tex]x <2[/tex]Represents the solution of all strict minor numbers to 2.

[tex]x \geq2[/tex] Represents the solution of all numbers greater than or equal to 2.

The solution set, according to the figure, is given by the union of [tex]x <2[/tex] and [tex]x\geq2[/tex]. Thus, the complete solution is given by all the real numbers.

Answer:

Option D

Answer:

Tan A = 3/4

Step-by-step explanation:

sin A = y/r

Cos A = x/r

Tan A = y/x

Answer:

3/4

Step-by-step explanation:

sin A = 3/5

cosA =4/5

We know that tan A = sin A / cos A

                                   = 3/5  /   4/5

                                    = 3/5 * 5/4

                                    = 3/4

Answer:

F. 10

Step-by-step explanation:

She had 15 flowers today

So if she had 5 more than yesterday

You subtract the 5 to get how much she had yesterday

15-5=10

Answer:

F. 10

Step-by-step explanation:

Today: 15 flowers

          : 5 more than yesterday

more than means add

15 = 5+ yesterday

Subtract 5 from each side

15-5 = 5+ yesterday -5

10 = yesterday

[tex]\huge{\boxed{36}}[/tex]

Substitute the values. [tex]48 - 18 \div 3 * 2[/tex]

Follow PEMDAS and multiply and divide first. [tex]48 - 6 * 2[/tex]

[tex]48 - 12[/tex]

Continue following PEMDAS and subtract. [tex]\boxed{36}[/tex]

Answer:

C.

Step-by-step explanation:

Let's identify some points here that are on the graph:

(0,0), (pi/2,-1), (pi,0).

Let's see if this is enough.

We want to see which equation holds for these points.

Let's try A.

(0,0)?

y=cos(x-pi/2)

0=cos(0-pi/2)

0=cos(-pi/2)

0=0 is true so (0,0) is on A.

(pi/2,-1)?

y=cos(x-pi/2)

-1=cos(pi/2-pi/2)

-1=cos(0)

-1=1 is false so (pi/2,-1) is not on A.

The answer is not A.

Let's try B.

(0,0)?

y=cos(x)

0=cos(0)

0=1 is false so (0,0) is not on B.

The answer is not B.

Let's try C.

(0,0)?

y=sin(-x)

0=sin(-0)

0=sin(0)

0=0 is true so (0,0) is on C.

(pi/2,-1)?

y=sin(-x)

-1=sin(-pi/2)

-1=-1 is true so (pi/2,-1) is on C.

(pi,0)?

y=sin(-x)

0=sin(-pi)

0=0 is true so (pi,0) is on C.

So far C is winning!

Let's try D.

(0,0)?

y=-cos(x)

0=-cos(0)

0=-(1)

0=-1 is not true so (0,0) is not on D.

So D is wrong.

Okay if you do look at the curve it does appear to be a reflection of the sine function.