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The system of equations is graphed on the coordinate plane.


y=x−1

y=−2x−4


A graph with a blue line passing through coordinates (-2, 0), (-1, -2) and (0, -4) and a red line passing through coordinates (-1, -2), (0, -1) and (1, 0).

Answer:

30 students

Step-by-step explanation:

check the photo

Based on the , the counterexample to the statement "If two angles are congruent, then the angles are vertical angles" is:

B) Right Triangle with Two 45° Angles

Here's why:

The diagram shows a right triangle ABC.

Angles ∠ACB and ∠CAB are both 45 degrees, as indicated by the markings.

Therefore, ∠ACB and ∠CAB are congruent (they have the same measure).

However, these angles are not vertical angles. They are adjacent angles in the right triangle, sharing the vertex C but not formed by intersecting lines.

Therefore, diagram C provides a counterexample to the original statement. The other diagrams:

A) Doesn't show any congruent angles.

B) Shows vertical angles, but they are not marked as congruent.

D) Shows congruent corresponding angles in parallel lines, but not vertical angles.

Answer:

The width of the red tile would be [tex]2.25[/tex] inches.

Step-by-step explanation:

Given blue tile has a length of [tex]4.25[/tex] inches, and a width of [tex]6.75[/tex]inches.

Also, length of similar tile is [tex]12.75[/tex] inches.

Let us assume [tex]x[/tex] as the width of red tile.

It is given in the question that both tiles are similar.

So, their area will be the same.

Area of blue tile would be [tex]4.25\times 6.75=28.6875\ inch^2[/tex]

Area of red tile would be [tex]12.75\times x[/tex]

The area of blue tile would be equal to area of red tile.

[tex]28.6875=12.75\times x[/tex]

[tex]\frac{28.6875}{12.75}=x\\\\x=2.25[/tex]

So, the width of the red tile would be [tex]2.25[/tex] inches.

[tex]\bf \begin{cases} -2x+y=0\\ \boxed{y} = 2x\\[-0.5em] \hrulefill\\ 5x+3y=-11 \end{cases}\qquad \qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{5x+3\left( \boxed{2x} \right)=-11} \\\\\\ 5x+6x=-11\implies 11x=-11\implies x = \cfrac{-11}{11}\implies \blacktriangleright x = -1 \blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{y = 2x}\implies \blacktriangleright y = -2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-1~~,~~-2)~\hfill[/tex]

Answer:

The volume of the observatory is 497.43 [tex]feet^{3}[/tex]

Step-by-step explanation:

i) The diameter of the floor is 10 feet. The floor is circular and has a radius,          

    r =  [tex]\frac{10}{2}[/tex] = 5 feet.

   Therefore the area of the circular floor of the observatory

     = [tex]\pi r^{2}[/tex]      =   3.14159 × [tex]5^{2}[/tex]    =    78.54 [tex]feet^{2}[/tex]

ii) The observatory is made up of two parts

  a)  3 foot tall cylinder

      ∴ volume of cylinder = [tex]\pi r^{2}[/tex]   × h

                                         = 78.54 × 3

                                         = 235.62 [tex]feet^{3}[/tex]

   b)  hemisphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3} \pi r^{3}[/tex] = 0.6667 × 78.54 × 5   =  261.81 [tex]feet^{3}[/tex]

    c) Therefore the total volume of the observatory is = a) + b)

         = 235.62 + 261.81 =   497.43 [tex]feet^{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{2}}x\stackrel{\stackrel{b}{\downarrow }}{-2}[/tex]

Answer:

9.25

Step-by-step explanation:

An equation is formed of two equal expressions.The value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25. The correct option is C, 9.25.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of y in the equation 5x + 2y = 20, when x = 0.3 can be found by substituting the value in the equation.

5x + 2y = 20

Substitute the value of x,

5(0.3) + 2y = 20

1.5 + 2y = 20

Subtract 1.5 from both sides of the equation,

1.5 + 2y - 1.5 = 20 - 1.5

Divide both the sides of the equation by 2,

2y /2 = 18.5 /2

y = 9.25

Hence, the value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25.

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Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]

Step-by-step explanation:

Given,

Distance walked by Addie = [tex]2\frac{1}{2}=\frac{5}{2}\ miles[/tex]

Time taken by Addie = 45 minutes

Converting the time into hours;

1 hour = 60 minutes

45 minutes = [tex]\frac{45}{60}=\frac{3}{4}\ hour[/tex]

Distance = Speed * Time

Speed = Distance/Time

Speed = [tex]\frac{5}{2} / \frac{3}{4}[/tex]

Speed = [tex]\frac{5}{2}*\frac{4}{3} = \frac{10}{3}\ mph[/tex]

Speed = [tex]3\frac{1}{3}\ mph[/tex]

Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]

Keywords: speed, distance

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Answer:

c

Step-by-step explanation:

solve this equation 4/2.40

Answer:

c. 24 is a solution

Step-by-step explanation:

Given equation:

[tex]\frac{4}{3}=\frac{32}{d}[/tex]

To test the numbers 22, 23, 24, 25 for the solution.

Solution:

In order to test the given number for the solution, we will plugin each number in the unknown variable [tex]d[/tex] and see if it satisfies the equation.

1) [tex]d=22[/tex]

[tex]\frac{4}{3}=\frac{32}{22}[/tex]

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

[tex]\frac{4}{3}=\frac{32\div 2}{22\div 2}[/tex]

[tex]\frac{4}{3}=\frac{16}{11}[/tex]

The above statement can never be true and hence 22 is not a solution.

2) [tex]d=23[/tex]

[tex]\frac{4}{3}=\frac{32}{23}[/tex]

The fractions can no further be reduced.

The statement can never be true and hence 23 is not a solution.

3) [tex]d=24[/tex]

[tex]\frac{4}{3}=\frac{32}{24}[/tex]

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

[tex]\frac{4}{3}=\frac{32\div 8}{24\div 8}[/tex]

[tex]\frac{4}{3}=\frac{4}{3}[/tex]

The above statement is always true and hence 24 is a solution.

4) [tex]d=25[/tex]

[tex]\frac{4}{3}=\frac{32}{25}[/tex]

The fractions can no further be reduced.

The statement can never be true and hence 25 is not a solution.

Answer:B

Step-by-step explanation:

Answer:

They both are the same.

Step-by-step explanation:

every day is 24 hours and that times three is 72

Answer: None of them is more. Both them are equal because 24 hours = 1 day.

1 day = 24 Hours

2 days = 48 hours

3 days = 72 hours

24 added to each one

Step-by-step explanation:

Answer:

x=3/8, y=-7/8. (3/8, -7/8).

Step-by-step explanation:

y=-5x+1

y=3x-2

----------

-5x+1=3x-2

-5x-3x+1=-2

-8x+1=-2

-8x=-2-1

-8x=-3

8x=3

x=3/8

y=3(3/8)-2=9/8-2=9/8-16/8=-7/8

Final answer:

A quadratic function with zeros at -5 and -6 can be written as f(x) = (x + 5)(x + 6), which expands to f(x) = x² + 11x + 30.

Explanation:

To write a quadratic function whose zeros are -5 and -6, you start by remembering that if α and β are the zeros of a quadratic function, the function can be written as f(x) = a(x - α)(x - β) where a is a nonzero coefficient. In this case, -5 and -6 are the zeros, so our function is f(x) = a(x + 5)(x + 6).

For simplicity, if we choose a to be 1, the quadratic function simplifies to

f(x) = (x + 5)(x + 6)

f(x) = x² + 11x + 30.

Therefore, the quadratic function with zeros at -5 and -6 is f(x) = x² + 11x + 30.

Answer:

see explanation

Step-by-step explanation:

P(head) = [tex]\frac{1}{2}[/tex]

P(4) = [tex]\frac{1}{6}[/tex]

P(head and 4 ) = P(head) × P(4) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

R=$1.75 B=$1.50

Step-by-step explanation:

35r+10b=X

b is 10

r is 5

X=3.25$

Answer:

Step-by-step explanation:

R=$1.75 B=$1.50  

35r+10b=X

b is 10

r is 5

X=3.25$

Answer:No

Step-by-step explanation:

Answer:

C.g(x) = 5x²

Step-by-step explanation:

To find the equation for the function g(x), use the format for a quadratic equation. Without any up/down and left/right shifts, the form is y = ax².

Substituting "x" and "y" into the equation tells you if a point is on the graph.

"a" tells you the vertical stretch (greater than 1) or compression (greater than 0, less than 1).

In f(x) = x², a = 1 even though it's not written.

Use the point (1, 5) on g(x) and substitute it into the form for a quadratic function. Remember points are (x, y), so x = 1 and y = 5.

g(x) = ax²    

y = ax²       In function notation, g(x) replaces the "y". Switch it back to "y".

5 = a(1)²     Substitute x = 1 and y = 5

5 = a(1)     Solve the exponent first. (1)² = 1

5 = a         When you multiply "a" by 1, the answer is just "a".

a = 5         Solved for "a". Put variable on left side for standard formatting.

With the quadratic form, substitute "a" into g(x).

y = ax²

g(x) = 5x²

Answer:

Step-by-step explanation: 72.1°

The circumference of the circle is given to be  = 20

The first thing to do here is to calculate the radius of the circle from the circumference given,

Formula for circumference  = 2πr or πd, where d is the diameter.

Make r the subject of the formula by equating it to 20

2πr = 20,

   r = 20/2π, π = ²²/₇ or 3.142

   r = 10/22/7

     = ( 10 x 7 )/22

     = 70/22

     = 3.18.

Now since the radius is known, we could now calculate the central angle of the arc.

Arc length  = 2πr∅°/360°, reducing this to lowest term now becomes

                  = πr∅°/180°

Therefore equate the formula to 4 and solve for ∅°, since the arc length is 4

           πr∅°/180° = 4

Multiply through by 180°

                πr∅° = 4 x 180°

                πr∅°= 720

Divide through by πr to get ∅°

                   ∅° = 720/πr

                        =  720/3.142 x 3.18

                        = 720/9.99

                        =  72.07

                        = 72.1°

The angle substended by the arc  length 4 is 72.1°

Answer:

6.2

Step-by-step explanation:

sin 20 = x/18

solve for x

The value of p that makes the equation true is -20

Step-by-step explanation:

To solve an equation of one variable

∵ The equation is [tex]\frac{3}{5}p+\frac{1}{5}(40 - p)=0[/tex]

- Simplify the left hand side

∵ [tex]\frac{1}{5}(40-p)=\frac{1}{5}(40)-\frac{1}{5}(p)[/tex]

∴ [tex]\frac{1}{5}(40-p)=8-\frac{1}{5}p[/tex]

- Substitute [tex]\frac{1}{5}(40-p)[/tex] in the equation by [tex]8-\frac{1}{5}p[/tex]

∴ [tex]\frac{3}{5}p+8-\frac{1}{5}p=0[/tex]

- Add the like terms

∴ [tex](\frac{3}{5}p-\frac{1}{5}p)+8=0[/tex]

∴ [tex]\frac{2}{5}p+8=0[/tex]

- Subtract 8 from both sides

∴ [tex]\frac{2}{5}p=-8[/tex]

- Divide both sides by [tex]\frac{2}{5}[/tex]

∴ p = -20

To check the answer substitute p by -20 in the equation, the left hand side is equal to the right hand side, then the answer is right

∵ left hand side = [tex]\frac{3}{5}(-20)+\frac{1}{5}(40-(-20))[/tex]

∴ left hand side = [tex]\frac{-60}{5}+\frac{1}{5}(40+20)[/tex]

∴ left hand side = [tex]\frac{-60}{5}+\frac{60}{5}[/tex]

∴ left hand side = 0

∵ Right hand side = 0

∴ Left hand side = Right hand side

∴ The value of p makes the equation true

The value of p that makes the equation true is -20

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Answer:

-20

Step-by-step explanation:

Answer: Order if operations

Step-by-step explanation:

15-10n+12n

15+12n

Answer:

Option A    M<17   m is less than or equal to 17

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

5715x3=

Rs.17145

Step-by-step explanation:

The interest rate required for Rs.4500 to amount to Rs.5715 in 3 years is 9% per annum. This is obtained using the simple interest formula. Therefore, the annual rate is 9%.

To find the annual interest rate at which Rs.4500 amounts to Rs.5715 in 3 years, we use the formula for simple interest:

Final Amount (A) = Principal (P) + Interest (I)

Given:

First, we calculate the interest:

Next, we use the simple interest formula:

Rearranging for the rate (R), we get:

Substitute the known values:

Converting to a percentage:

Therefore, the rate per annum required for Rs.4500 to grow to Rs.5715 in 3 years is 9%.

Answer:

  12 pm noon

Step-by-step explanation:

The least common multiple of the two times is 240 minutes, or 4 hours. The buses will meet at the station again at noon.

__

60 = 20×3

80 = 20×4

The least common multiple is 20×3×4 = 240 minutes. There are 60 minutes in an hour, so this is 240/60 = 4 hours. 4 hours after 8 am is 12 pm, noon.

Answer:

vertex=?

Step-by-step explanation:

given data:

g(x)=-3x^2+18x+2

from the given equation

a=-3,b=18,c=2

x=-b/2a

x=-(18)/2(-3)

x=3

put value of x in the given equation

y=-3(3)^2+18(3)+2

y=-27+54+2

y=29

x=3    y=29

(3,29)

Answer:

Area of trapezoid = 144 cm²

Step-by-step explanation:

The length of parallel sides are,

a = 8 cm

b = 16 cm

h = 12 cm

Formula area of trapezoid:-

[tex]A=\dfrac{1}{2}(a+b)\times h[/tex]

[tex]A=\dfrac{1}{2}(8+16)\times 12[/tex]

[tex]A=144[/tex]

Hence, the area of trapezoid is 144 cm²

Answer:

Hence, the area of trapezoid is 12 cm²

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

10x-7x=12

3x=12

divide both sides by 3

x=4

Answer: x = 4

Step-by-step explanation: To solve this equation, we can first combine our like terms on the left side of the equation which are the x's.

10x - 7x = 3x so we now have the equation 3x = 12.

Now to solve for x, we want to get x by itself on the left side of the equation. Since x is being multiplied by 3, to get x by itself, we need to divide by 3 on the left side of the equation. Since we divided by 3 on the left side, we must also divide by 3 on the right side.

On the left side, notice that the 4's cancel out so we're simply left with x. On the right side we have 12 divided by 3 which is 4 so x = 4.

Finally, remember to check your answer by substituting a 4 back into the original equation.

So we have 10(4) - 7(4) = 12 or 40 - 28 = 12 or 12 = 12.

Since this a true statement, we know our answer is correct.

Remember to show all your work when solving equations.

Answer:

There are 24 gumballs, 6 of which are yellow.

P(yellow) = 6/24 = 1/4