What’s the slope of (-2,1) and (3,-3)

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:

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:

68+28k

Step-by-step explanation:

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:

4

Step-by-step explanation:

The simple interest per year is 3% times $5000 which is 150 dollars.

Now, we have the equation 150x = 600.

We solve and get x = 4

Answer:

There will be [tex]243[/tex] billion messages sent or received in November.

Step-by-step explanation:

Given.

Number of text messages sent or received [tex]=215[/tex] billion.

Increment on the very next month [tex]=13\%=\frac{13}{100}=0.13[/tex]

Lets find what is [tex]13\%\ of\ 215[/tex]

 ⇒[tex]13\%\ of\ 215[/tex]

 ⇒[tex]0.13\times 215=27.95[/tex]

So we will add this value to our previous months data.

Now

Number of text messages sent in the month of November [tex]=(27.5+215)=242.95[/tex] billion.

Rounding to the nearest tenth the answer will be [tex]243[/tex] billion.

So [tex]243[/tex] billion text messages were sent or received in November.

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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Answer:

There was 40% decrease in the mass of the pumpkin.

Step-by-step explanation:

Given:

Mass of pumpkin before carving = 6.5 kg

Mass of pumpkin after carving = 3.9 kg

Decrease in mass = Mass of pumpkin before carving - Mass of pumpkin after carving = 6.5 kg - 3.9 kg = 2.6 kg

Now to find the percentage decrease in mass we need to divide Decrease in mass with the total mass of pumpkin before carving and then multiply by 100

% Decrease in mass = [tex]\frac{\textrm{Decrese in mass}}{\textrm{Mass of Pumpkin before carving}}\times100 = 40\%[/tex]

Hence, there was 40% decrease in the mass of the pumpkin.

Answer:

40%

Step-by-step explanation:

I had this problem

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:

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:

[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:

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:

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: 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

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:

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:

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.

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:

709

Step-by-step explanation:

If the question is (4+D)/2 the answer is 6 but if the question is 4+(D/2) the answer is 8. It depends on which way the question is written.

Answer:

the answer is 8

Step-by-step explanation:

If the question is (4+D)/2 the answer is 6 but if the question is 4+(D/2) the answer is 8. It depends on which way the question is written.

The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis between the ordered pairs (-7,0) and (-6,0), and between (-2,0) and (-1,0).

The graph of the quadratic function f(x) = 0.5x² + x - 9 crosses the negative x-axis at those x-values that make the function equal to zero. To find these, we solve for x in the equation 0.5x² + x - 9 = 0 using the quadratic formula x = -b ± √(b² - 4ac) / 2a.

Here, a = 0.5, b = 1 and c = -9. Substituting these into the formula gives x = -1 ± √(1 + 36) / 1 = -1 ± √(37) / 1. The two possible solutions are approximately -7.06 and +5.06. Therefore, the ranges of x-values crossing the negative x-axis are between the ordered pairs (-7,0) and (-6,0), as well as between (-2,0) and (-1,0).

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The function f(x) = one-halfx2 + x - 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0) when solved using the quadratic formula.

The question concerned is a quadratic function, specifically, it wants to know where f(x) = one-halfx2 + x – 9 intersects with the negative x-axis. The x-axis is the line where y = 0, so we need to solve the equation 0.5x² + x - 9 = 0 to locate the roots. By applying the quadratic formula, x = [-b ± sqrt(b² - 4ac)] / (2a), we substitute our coefficients into the equation to get: x = [-1 ± sqrt((1)² - 4*0.5*(-9))] / (2*0.5). This will lead to two solutions, x = -2 and x = -3. Hence, the function f(x) = one-halfx2 + x – 9 intersects the negative x-axis between the ordered pairs (-4, 0) and (-3, 0) and also between (-3, 0) and (-2, 0).

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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:

[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]

Answer:

total sum is called perimwter

the perimeter will be the outer border, and in this case we have three semi-circles and one square, well, the semi-circles have a diameter of 7, we can just get the circumference of all 3 semi-circles add them and append the 7 ft at the bottom, Check picture below.

[tex]\bf \textit{circumference of a semicircle}\\\\ C=\cfrac{\pi d}{2}~~ \begin{cases} d = diameter\\[-0.5em] \hrulefill\\ d=7 \end{cases}\qquad \implies \stackrel{\textit{circumference of all 3 semi-circles}}{3\left( \cfrac{\pi 7}{2} \right)\implies \cfrac{21\pi }{2}} \\\\\\ \stackrel{\textit{sum of all borders}}{\cfrac{21\pi }{2}~~+~~7}~~\approx ~~32.99+7~~\approx~~ 39.99[/tex]

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:

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:

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:

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:

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:

Yes then no

Step-by-step explanation:

A linear function is of the form y=mx+b, where b and m are constants(not variables). Since the input is the radius, we make that x. The circumference is πd, or 2πr, so if we plug in 2π for m, circumference for y, and 0 for b, this works. The area is πr², which would mean that m would have to be πr. Since r is not a constant, this does not work.