A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

y = x^2 + 3x + 2
y = x^2 + 3x - 2
y = x^2 - 3x + 2
y = x^2 - 3x - 2

Answer:

a₂ = 13

a₃ = 11

Step-by-step explanation:

Given a₁ = 15

The recursive formula is given as:  [tex]$ a_n = a_{n - 1} - 2 $[/tex]

This means that [tex]$ n^{th }[/tex] term is determined by subtracting 2 from the [tex]n -1^{th }[/tex] term.

Here, [tex]$ a_1 = 15 $[/tex]

Therefore, [tex]$ a_2 = a_1 - 2$[/tex]

= 15 - 2 = 13

Now, [tex]$ a_3 = a_2 - 2 $[/tex]

= 13 - 2 = 11

Therefore, a₂ = 13

a₃ = 11

Answer:

[tex]f(x)=20(2.5^x)[/tex]

Step-by-step explanation:

we know that

The function of the graph is a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

Looking at the graph

we have the points

(0,20) and (1,50)

Remember that if a point lie on the graph, then the point must satisfy the function

Verify each case

For x=1, f(x)=50

case 1) we have

[tex]f(x)=20(1.5^x)[/tex]

For x=1

[tex]f(1)=20(1.5^1)=30[/tex]

so

[tex]30\neq 50[/tex]

therefore

This function is not represented by the graph

case 2) we have

[tex]f(x)=20(1.4^x)[/tex]

For x=1

[tex]f(1)=20(1.4^1)=28[/tex]

so

[tex]28\neq 50[/tex]

therefore

This function is not represented by the graph

case 3) we have

[tex]f(x)=20(2.5^x)[/tex]

For x=1

[tex]f(1)=20(2.5^1)=50[/tex]

[tex]50=50[/tex]

For x=0

[tex]f(0)=20(2.5^0)=20[/tex]

[tex]20=20[/tex]

therefore

This function is represented by the graph

case 4) we have

[tex]f(x)=20(2.25^x)[/tex]

For x=1

[tex]f(1)=20(2.25^1)=45[/tex]

so

[tex]45\neq 50[/tex]

therefore

This function is not represented by the graph

Answer:

f(x)=20(2.5)x

Step-by-step explanation:

did the test and was correct

Answer:

3x^2 + 7x - 5 + 2x^2

= 5x^2 + 7x - 5 (a=5, b=7, c=-5)

x = (-b+/- √(b^2 - 4ac))/2a

= (-7+/- √(49+100))/10

= (-7+√149)/10, (-7-√149)/10

Hope this helps!

Answer:

68+28k

Step-by-step explanation:

Answer:

0.0008235

Step-by-step explanation:

8.235 x 10⁻⁴

10 to the exponent of a negative number means the decimal place is moved to the left to make the number smaller.

Move the decimal place 4 over the left.

0.0008235

Answer:

The number of student's tickets sold was 7

Step-by-step explanation:

Let

x ----> number of adult's tickets sold

y ----> number of student's tickets sold

we know that

[tex]x+y=23[/tex] ----> [tex]x=23-y[/tex] ---> equation A

[tex]13x+9y=271[/tex] ----> equation B

solve the system by substitution

substitute equation A in equation B

[tex]13(23-y)+9y=271[/tex]

solve for y

[tex]299-13y+9y=271[/tex]

[tex]13y-9y=299-271[/tex]

[tex]4y=28[/tex]

[tex]y=7[/tex]

therefore

The number of student's tickets sold was 7

Answer:

3x - 20 = 250

Step-by-step explanation:

Given,

The cost of cookies per dozen = $ 3,

Let x be the number of dozen cookies sold,

So, the cost of x dozen of cookies = x × cost of cookies per dozen

= 3x

Now, the amount of rent = $ 20,

Thus, total earning = cost of x dozen of cookies - rent

= 3x - 20

If $ 250 is needed to raise,

Then total earning = $ 250

⇒ 3x - 20 = 250

Which is the required equation.

Without further information or context like a diagram, it's not possible to accurately determine the measure of angle 1 based on the given measure of angle 7.

Without a diagram or additional information, it's impossible to definitively determine the measure of angle 1 (m∠1) based only on the measure of angle 7 (m∠7 = 50°). In geometry, the relationship between two angles can vary largely depending on their position relative to each other. For instance, if angle 1 and angle 7 are complementary angles, m∠1 would be 40°. However, if they're supplementary, m∠1 would be 130°. If they're vertical or corresponding angles, m∠1 would be equal to m∠7, which is 50°.

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Each pound of jelly costs $2.5 and each pound of trail mix costs $1.25

Step-by-step explanation:

Let,

Cost of jelly beans = x

Cost of trail mix = y

According to given statement;

8x+4y=25   Eqn 1

3x+2y=10    Eqn 2

Multiplying Eqn 2 by 2;

[tex]2(3x+2y=10)\\6x+4y=20\ \ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1;

[tex](8x+4y)-(6x+4y)=25-20\\8x+4y-6x-4y=5\\2x=5[/tex]

Dividing both sides by 2;

[tex]\frac{2x}{2}=\frac{5}{2}\\x=2.5[/tex]

Putting x=2.5 in Eqn 1

[tex]8(2.5)+4y=25\\20+4y=25\\4y=25-20\\4y=5[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{5}{4}\\y=1.25[/tex]

Each pound of jelly costs $2.5 and each pound of trail mix costs $1.25

Keywords: linear equations, subtraction

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Answer:

All possible values for the number of tables that the store must sell in order to meet the requirements are 9, 10, 11, 12, 13.

Step-by-step explanation:

Let x be the number of chairs sold and y be the number of tables sold.

Chairs are sold for $50 each, then x chairs cost $50x.

Tables are sold for $250 each, then y tables cost $250y.

In total, x chairs and y tables cost $(50x+250y).

Every day, the store can ship no more than 36 pieces, then

[tex]x+y\le 36[/tex]

Every day, the store must sell at least $3,400 worth of chairs and tables, then

[tex]50x+250y\ge 3,400[/tex]

If 23 chairs were sold, then x = 23. Substitute it into the inequalities:

[tex]23+y\le 36\Rightarrow y\le 13\\ \\50\cdot 23+250y\ge 3,400\Rightarrow 250y \ge 2,250,\ \ \ y\ge 9[/tex]

Thus [tex]9\le y\le 13[/tex]

This means all possible values for the number of tables that the store must sell in order to meet the requirements are 9, 10, 11, 12, 13.

Answer:

9,10,11,12,13

Step-by-step explanation:

cuz

Answer:

Answer is (-5,1)

Step-by-step explanation:

Plug in the values and find the only one in the shaded region.

Answer:

I think it would be D, (1,2)

Answer:

5.4

Explanation:

a²+b²=c²

2²+5²= 4+25

4+25=29

Now we have to square root the 29 which would make the answer 5.4

5.4 is the slant height of the triangular prism.

The given figure is a triangular based pyramid and in order to determine the slant height, we will apply the pythagoras theorem as shown:

Hypotenuse = s

Opposite = 5

Adjacent = 4/2 = 2

According to the theorem:

hyp² = opp² + adj²

Substitute

s² = 5² + 2²

s² = 25 + 4

s² = 29

s = 5.4

Hence the slant height, s, of the triangular prism is 5.4

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Step-by-step explanation:

For any function,any point in the domain has a unique image in the codomain.

For set [tex]A[/tex]:

[tex]f(8)=-5[/tex] from the point [tex](8,-5)[/tex]

[tex]f(8)=7[/tex] from the point [tex](8,7)[/tex]

For a same point [tex]8[/tex],there are two images.

So,[tex]A[/tex] does not represent a function.

For set [tex]B[/tex]:

[tex]f(7)=-4[/tex] from the point [tex](7,-4)[/tex]

[tex]f(7)=-2[/tex] from the point [tex](7,-2)[/tex]

For a same point [tex]7[/tex],there are two images.

So,[tex]B[/tex] does not represent a function.

Answer:

Let the two nos. Be x and y

xy = -32

x - y = -12

(x-y)^2 = (x+y)^2 - 4xy

144 = (x+y)^2 + 128

16 = (x+y)^2

Therefore x+y = +4, -4

When x+y = +4, x-y = -12

x = -4, y = 8

When x+y = -4, x-y = -12

x= -8, y = 4

Hope this helps!

Answer:

Step-by-step explanation:

Numbers : 8 or -8       4, or -4

-8*4=-32             -4+8=  -32

-8-4= -12             -4-8 = -12

Answer:

1/6, 1/2, 7/8, 1/6

Step-by-step explanation:

1/6= .1666666667

1/2=.5

7/8=.875

5/2=2.5

1/6 is the smallest number than 1/2 than 7/8 and 5/2 is the greastest number.

Answer:

The statement is false

Step-by-step explanation:

we know that

If a system of equations has two equations with the same slope and the same y-intercept, then both equations represent the same line

so

we have a consistent dependent system

The system has has an infinite number of solutions

therefore

The statement is false

Answer:

Yes ,we can prove the two triangles are similar by angle angle test.

Step-by-step explanation:

Given:

∠ABE = 45°

∠EAB = 63° and

∠MNP= 72°

∠NMP = 63°

To Prove:

ΔABE  ~  ΔMPN

Proof:

In a Triangle sum of the angles of a triangle is 180°

In  ΔMPN

∴ ∠MNP +  ∠NMP  + ∠MPN = 180°

Substituting the given values we get,

[tex]72+63+\angle MPN = 180\\135 + \angle MPN = 180\\\angle MPN = 180-135\\\angle MPN = 45[/tex]

∠MPN = 45°  ..........................( 1 )

Now,for triangles to be similar

In  Δ ABE and Δ  MPN

∠ ABE ≅ ∠ MPN = 45°      ……….{From ( 1 ) and Given}

∠ EAB ≅ ∠ NMP = 63°     ………...{Given}

Δ ABE ~ Δ MPN ….{Angle-Angle test}

..........Proved

Answer:

The common denominator [tex]\frac{15}{20}[/tex] and [tex]\frac{8}{20}[/tex]

Step-by-step explanation:

To find the common denominator:

Here is the work:

LCD of [tex](4,5)[/tex] is [tex](4\times 5)=20[/tex].

So we will divide [tex]20[/tex] with [tex]4[/tex] and then with [tex]5[/tex] the quotient will further be put into the fraction.

So

[tex]\frac{20}{4}=5[/tex] will make the fraction [tex]\frac{3}{4}[/tex] as [tex]\frac{3\times 5}{4\times 5} =\frac{15}{20}[/tex].

Similarly

[tex]\frac{20}{5}=4[/tex] will make the fraction [tex]\frac{2}{5}[/tex] as [tex]\frac{2\times 4}{5\times 4} =\frac{8}{20}[/tex].

Hence with common denominators the fraction can be written as [tex](\frac{15}{20}),(\frac{8}{20})[/tex].

Answer:

see explanation

Step-by-step explanation:

Given

(bx + a)(ax + b) = (ax² + b)b ← distribute parenthesis on both sides

abx² + a²x + b²x + ab = abx² + b² ( subtract abx² from both sides )

a²x + b²x + ab = b² ( subtract ab from both sides )

a²x + b²x = b² - ab ← factor out x from each term on the left side

x(a² + b²) = b² - ab ← divide both sides by (a² + b²)

x = [tex]\frac{b^2-ab}{a^2+b^2}[/tex]

Answer:

x = -b/a

Step-by-step explanation:

(bx + a)(ax + b) = (ax^2 + b)(b) needs to be muliplied out as a first step to solving for x:

abx^2 + b^2 + a^2x + ab = abx^2 + b^2

Notice that abx^2 shows up on both sides of this equation, so we can cancel it out:

b^2 + a^2x + ab = b^2

Also, b^2 shows up on both sides, so we can also cancel the b^2 terms:

a^2x + ab = 0

Dividing both sides by a, we get ax + b = 0

and so ax = -b,

which means that x = -b/a

Answer:

[tex]\large\boxed{x=13\dfrac{79}{107}\approx13.74}[/tex]

Step-by-step explanation:

[tex]x(0.07)+x=14.70\qquad\text{combine like terms}\\\\(0.07+1)x=14.70\\\\1.07x=14.70\qquad\text{divide both sides by 1.07}\\\\x=\dfrac{14.70}{1.07}\\\\x=\dfrac{14.70\cdot100}{1.07\cdot100}\\\\x=\dfrac{1470}{107}\\\\x=13\dfrac{79}{107}\approx13.74[/tex]

To evaluate f(x)=3x3+x2−5x−14  when x=−2, use synthetic division to divide the polynomial by -2 and find the resulting value.

To evaluate f(x) = 3x^3 + x^2 - 5x - 14 when x = -2, we can use synthetic division. First, set up the synthetic division table with -2 as the divisor and the coefficients of the polynomial as the dividend.

Perform the synthetic division by bringing down the first coefficient, multiplying it by the divisor and adding it to the next coefficient, then continuing the process until you reach the last coefficient. The result in the last row of the table will be the evaluated value of the polynomial.

In this case, the evaluated value of f(x) when x = -2 is 0.

Final answer:

To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, use synthetic division to divide the polynomial by x + 2.

Explanation:

To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, we can use synthetic division. First, write the coefficients of the polynomial in order: 3, 1, -5, -14. The divisor will be x - (-2), which simplifies to x + 2. Set up the synthetic division table and perform the division. The result will be the quotient and the remainder. In this case, the quotient is 3x^2 - 5x - 7 and the remainder is -20.

Answer: 13/30 remaining

Step-by-step explanation:

well... 1 - 2/5 - 1/6 = 13/30 remaining

we use "1" to denote the money she began with

Answer:

(5,1)

Step-by-step explanation:

Equation of a straight ine in slope intercept form is [tex]y-y_{1} =m\times(x-x_{1} )[/tex]. from that calculate the both equations of straight lines sidewalks1 and sidewalks2 they are x+y=6 and 2x+y=11 on solving both of the equations we get the value of x to be 5 and the value of y to be 1.hence the system of linesr equations intersect at the point (5,1).

Answer:

$8 each

Step-by-step explanation:

Cost of the gift= $90- $42= $48

Each friend pays: $48 divided by 6= $8

The total cost of the gift is $48, which is calculated by subtracting the change received ($42) from the amount paid ($90). Divided by six friends, each friend pays $8 for the gift.

Calculating Individual Payments for a Gift

To determine how much each friend pays for the gift, we first need to calculate the total cost of the gift. The friends together paid $90, and they received $42 in change. This means that the actual cost of the gift is the amount paid minus the change received:

Total cost of the gift = $90 - $42 = $48

Since six friends are sharing the cost equally, we divide the total cost by the number of friends to find out how much each person pays. To find the amount each friend pays:

Cost per friend = Total cost of the gift / Number of friends

Cost per friend = $48 / 6 = $8 per friend.

Therefore, each friend pays $8 for the gift.

Answer:

x=0 and x=8

Step-by-step explanation:

The x-intercept is on the x-axis, so we must find x when y=0. f(x) is basically y and y=0, so 0=x^2-8x= x(x-8). For x(x-8) to equal  0, either x is equal to 0 (x=0) or x-8 is equal to 0 (so x is equal to 8). So the two intercepts are x = 0 and x = 8.

I hope this helped! :)

Answer:

Well, a parallelogram is a four-sided figure with opposite sides parallel. A rectangle is a figure with four straight sides and four right angles, and two of those sides are adjacent and unequal So, in short, all rectangles are parrolegrams but not all parrolelograms are rectangles. The answer would be: Yes, it is possible.

Yes, it is possible for Brooke to draw a parallelogram that is not a rectangle.

Yes, it is possible for Brooke to draw a parallelogram that is not a rectangle. A parallelogram is a quadrilateral with opposite sides that are parallel. While a rectangle is a specific type of parallelogram with four right angles, other parallelograms can have angles that are not right angles. For example, a rhombus is a parallelogram with all sides congruent, but its angles are not right angles.

Answer:

709

Step-by-step explanation:

Answer:

25:16 is the surface area of the cones.

Step-by-step explanation:

Given: The ratio of their radii and altitudes is 5:4.

Area of similar figures are proportional to the squares of their corresponding sides and this ratio is called scale factor.

Let z be the scale factor

∴z= [tex]\frac{5}{4}[/tex]

Now, let x be the surface area of the larger cone

     and let y be the surface are of smaller cone.

∴ [tex]z^{2} = \frac{x}{y}[/tex]

next substituting the value of z ,

⇒[tex](\frac{5}{4} )^{2} =\frac{x}{y}[/tex]

∴ [tex]\frac{x}{y} = \frac{25}{16}[/tex]

The ratio for the surface area of cones is 25:16

Answer:

The correct answer is 25:16

Step-by-step explanation:

Answer:

12.252, 12.26, 12.387, 12.4

Step-by-step explanation:

These are the only numbers in a series that are always increasing.

The first series (0.13, 0.31, 0.04, 0.5) and fourth series (6.009, 6.015, 6.241, 6.2) all have an area where they decrease (0.04 and 6.2 respectively).

The second series of numbers is in decreasing order, rather than increasing order. This can not be the answer.

Step-by-step explanation:

C. will be your answer.

Answer:

You are 48 inches

Step-by-step explanation:

You would just do the opposite of multiplication which is division so do 60/1.25 is 48 inches