A tv costs £800. Work out the price after a 3% discount.

Answer:

The correct option is SSS (Side-Side-Side) Theorem

Step-by-step explanation:

The question is incomplete because the diagrams of ΔLON and ΔLMN are not given. I have attached the diagram of both triangles below for better understanding of the question.

Consider the diagram attached below. We have to find the congruence theorem which can be used to prove that ΔLON ≅ ΔLMN

We can see in the diagram that both triangle have a common side that is LN. It means 1 side of both triangles is congruent because LN≅LN

Consider the sides ON and MN. Both side have a single bar on them, which means that it is given that both of these side are congruent. Hence ON≅MN

Consider the sides LO and LM. Both side have a double bars on them, which means that it is given that both of these side are also congruent. Hence LO≅LM

SSS theorem states that if all sides of the triangles are congruent, then the triangles themselves are also congruent, which is the same case in this question

Answer:

D. SSS

Step-by-step explanation:

I hope this helps.

Answer:

y=x+ 3

Step-by-step explanation:

The given equation is y = x, which is parallel to y = x + 3

Also, the equation I chose has an x-intercept of -3.

The equation of the line that is parallel to the given line and has an x - intercept of - 3 is,

⇒ y = 2/3x - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (3, 1) and (0, -1).

Now,

Since, The equation of line passes through the points (3, 1) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 1) / (0 - 3)

m = - 2 / - 3

m = 2/3

Thus, The equation of line with slope 2/3 is,

⇒ y - 1 = 2/3 (x - 3)

⇒ y - 1 = 2/3x - 2

⇒ y = 2/3x - 1

Therefore, The equation of the line that is parallel to the given line and has an x - intercept of - 3 is,

⇒ y = 2/3x - 1

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Answer:

12-y------------> 9

3x-y------------>21

4y-10----------->2

1/4 xy-----------> 6

Solution,

Given,

X=8

y=3

Now,

[tex]1. \: \: 12 - y \\ \: \: \: = 12 - 3 \\ \: \: = 9 \\ 2. \: \: 3x - y \\ \: \: = 3 \times 8 - 3 \\ \: \: = 21 \\ 3. \: \: 4y - 10 \\ \: \: = 4 \times 3 - 10 \\ \: = 12 - 10 \\ \: \: = 2 \\ 4. \: \: \frac{1}{4} xy \\ \: \: = \frac{1}{4} \times 8 \times 3 \\ = 6[/tex]

hope this helps...

Good luck on your assignment...

Answer:

6 1/6 ft

Step-by-step explanation:

12 inches = 1 ft

So 2 inches is 2/12 of a foot

2/12 = 1/6

6 ft 2 inches = 6  1/6 ft

[tex]42 \times 48=2016[/tex]

[tex]24 \times 84 = 2016[/tex]

The answer is 42 × 48 because even when we switch the digits, the product remains the same.

Answer:

[tex]x = 4[/tex]

[tex]2x + 2(x + 4) \times \frac{1}{2} = 2(x + 4) \\ 2x + x + 4 = 2(x + 4) \\ 3x + 4 = 2(x + 4) \\ 3x + 4 = 2x + 8 \\ 3x + 4 - 2x = 8 \\ x + 4 = 8 \\ x = 8 - 4 \\ x = 4[/tex]

Answer:

A reflection across the y axis

Step-by-step explanation:

think about it, if you reflect some point across the y-axis it will have a negative x value.  For example, if you reflect (1,2) across the y-axis you will get (-1,2)

Answer:

This type of transformation is called mirroring in the y-axis.

Step-by-step explanation:

By mirroring in the y-axis, you can find the new value, by multiplying the x-coordinate by -1.

Any point (a , b) will be transformed after mirroring in the y-axis, to (-a , b), which is the question here.

This type of transformation is called mirroring in the y-axis.

Answer:

Converges

Sum = 20.8333

Step-by-step explanation:

A geometric series has a general formula of:

[tex]\sum ar^n[/tex]

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:

[tex]\sum 25*(-0.2)^n[/tex]

Since 0.2 < 1.0, the series converges.

The sum of the series is given by:

[tex]S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333[/tex]

The sum is 20.8333.

The geometric series converges and the sum is equal to 20.83.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .

A geometric series has a general formula of:

∑arⁿ

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25 and each term is divided by -5 or multiplied by (-0.2)

Therefore r = -0.2 and as it is <1 therefore the series converges

The sum of a convergent series is

S = a/(1-r)

S = 25/(1-(-0.2))

S= 25/1.2

S = 20.83

Therefore the sum of the series is 20.83

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Answer:

100

Step-by-step explanation:

Since the inscribed angle of a circle is always half of its corresponding, the measure of this angle is 200/2=100 degrees. Hope this helps!

Answer:

100

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

f(x)= 2x^2 + 5x - 17,

f(-1)

Let x = -1

f(-1)= 2 *(-1)^2 + 5(-1) - 17

     = 2 *1   -5 -17

    = 2 -22

   = -20

Answer:

-20

Step-by-step explanation:

f(x)= 2x² + 5x - 17

Put x as -1.

f(-1)= 2(-1)² + 5(-1) - 17

Solve for the powers.

f(-1)= 2(1) + 5(-1) - 17

Multiply the terms.

f(-1)= 2 + -5 - 17

Add or subtract the terms.

f(-1)= -20

Answer:

The maximum height the projectile reaches is 100 feet

Step-by-step explanation:

Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.

therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:

[tex]f(x)=ax^2+bx+c[/tex]

with x-position of the vertex given by:

[tex]x_v=\frac{-b}{2a}[/tex]

Then in our case  ([tex]H(t)=-16t^2+16t+96[/tex])  we have:

Horizontal position of the vertex given by:

[tex]t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}[/tex]

and now we can find the maximum height plugging this value into the height expression:

[tex]H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft[/tex]

Answer:

37.7 ft²

Step-by-step explanation:

2×3.14×r=30.77

Divide both sides by 2

3.14×r=15.385

Divide both sides by 3.14

r≈4.9

3.14×r²

3.14×4.9²=

24.01×3.14≈

75.4

75.4÷2=

37.7

Answer:

AB=6 Units

Step-by-step explanation:

Given the following lengths of rectangle ABCD and its dilation A'B'C'D' respectively

We are to determine the length of AB. To do this, we first determine the dilation factor.

[tex]D$ilation Factor =\dfrac{B'C'}{BC} =\dfrac{9.5}{3.8} =2.5[/tex]

Therefore:

[tex]\dfrac{A'B'}{AB} =2.5\\\\\dfrac{15}{AB} =2.5\\$Cross multiply \\ 2.5 AB =15 \\AB=15 \div 2.5\\$Therefore, AB=6 Units[/tex]

Answer:

6 units

Step-by-step explanation:

edge 2022

Answer:

V = 1072.3 cm³

Step-by-step explanation:

Volume of a hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] [Because it's half of a sphere's volume]

V = [tex]\frac{2}{3} (3.14)(8)^3[/tex]

V = [tex]\frac{2}{3} (3.14)(512)[/tex]

V = [tex]\frac{3216.99}{3}[/tex]

V = 1072.3 cm³

See attached graph: v is on the y-axis and t is on the x-axis

Answer:

D

Step-by-step explanation:

subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.

Answer:

x = 2, y= -1

Step-by-step explanation:

12x - y = 25

9x + y = 17

add both equations to eliminate y

21x = 42

divide by 21

x = 42/21

x = 2

sub x in equation i to find y

12(2) - y = 25

24 - y = 25

-y = 1

therefore y = -1, x = 2

Answer:

$6.89

Step-by-step explanation:

To find unit price divide the dollar by the amount. The dollar is 20.67. The amount of socks are 3. The equation would then be 20.67/3. Then solve and the answer would be $6.89.

Answer:

Step-by-step explanation:

An x value of 0 can only be plugged into the equation that has a domain that includes 0. The first function's domain is between -2 and -4, so 0 is not included in that domain. In the third function, the domain is between 1 and 3, so 0 is not included in that domain, either. The middle function's domain does include 0 (0 falls between -2 and 1) so we can only evaluate this function at an x value of 0.

g(0) = -0 - 1 so

g(0) = -1

Answer:

B

Step-by-step explanation:

-1

Answer:

The lines are parallel

Step-by-step explanation:

x - y = 2

Solving for y

-y = -x+2

y = x -2

And the other equation is

y = x+1

These are both in slope intercept form

We notice that the slopes are both 1, but the y intercepts are different

That means the lines are parallel, but have different y intercepts

Answer:

option D

Step-by-step explanation:

x/-3≤3

multiply by (-1) on both sides

x/3≥-3

x>=-9

Answer:

Letter D

Step-by-step explanation:

Answer:

-40*h+280

Step-by-step explanation:

Let s define the function f which represents Emily's distance from home

at h = 0 Emily is 280 miles away from home

so f(0)=280

as she is traveling back at a rate of 40 miles per hour

f(h)=-40*h+280

the graph is below

The required equation for the distance is y = 280 - 40h and graph is shown below.

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

Distance of Emily from her home = 280 miles,

The speed of Emily of coming back = 40 miles per hour.

In h hours, the distance covered by Emily = 40h

Let the remaining distance is y,

So the equation can be written as,

y = 280 - 40h.

The graph of the equation represented below.

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Answer:

21,845

Step-by-step explanation:

The sum of geometric sequence:

S n = a 1 * ( q^n - 1 ) / ( q - 1 )

where:  a 1 = 1,

q = a 2 : a 1 = 4 : 1 = 4

S 8 = 1 * ( 4^(8) - 1 ) / ( 4 - 1 ) =

= ( 65,536 - 1 ) / ( 4 - 1 ) = 65,535 / 3 = 21,845

Answer:

1. A letter, A, added to a letter, B, equals ten.

2. A letter, x, which is multiplied by 4, then has a number, y, subtracted from it to equal a letter, a.

If you try write these out, I'm sure you'd get the algebraic expression given.

Answer:

in total she would spend 27.90 so she should bring C i got this by doing 7.80 x 3 because she is buying 3 medium pizzas then i did 0.75 x 6 and got 27.90 so at least bring 25-30 dollars with her

Step-by-step explanation:

Answer:

Hi there!

The correct answer is: True

Step-by-step explanation:

If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .

Answer:

Step-by-step explanation:

The integer is 45, since integers are only whole numbers and they're negative counterparts, so even if the fraction or decimal is negative, it is not an integer because it's not a whole number. Hope that helps!

Answer:

[tex]45/9\\45\\14/2[/tex]

Step-by-step explanation:

An integer is a number that can be written without a fractional component.

[tex]-92.67=-278/3[/tex]

[tex]-6/7=-6/7[/tex]

[tex]45/9=5[/tex]

[tex]45=45[/tex]

[tex]14/2=7[/tex]

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared ​(units are in​ meters).

Also, v Subscript x is constant at 10.0 ​m/s.

The water from a fire hose follows a path described by the following equation below;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

The velocity of the [tex]x[/tex] component is constant at =  [tex]v_x=10.0 \text{ m/s}[/tex]

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

[tex]v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}[/tex]

Now, differentiating the above equation with respect to t, we get;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

[tex]\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}[/tex]

[tex]v_y = 0.9v_x -0.2v_x[/tex]

[tex]v_y = 0.7v_x[/tex]

Now, putting [tex]v_x=10.0 \text{ m/s}[/tex] in the above equation;

[tex]v_y = 0.7 \times 10.0[/tex] = 7 m/s

Now, the resultant velocity is given by = [tex]v=\sqrt{v_x^{2}+v_y^{2} }[/tex]

                            [tex]v=\sqrt{10^{2}+7^{2} }[/tex]

                               = [tex]\sqrt{149}[/tex] = 12.21 m/s

Answer:

a) 0.68

b) 0.08

c) 0.74

Step-by-step explanation:

Given that:

Probability of hitting bulls eye, P(B) = 0.26

Probability of an inner, P(I) = 0.42

Probability of an outer, P(O) = 0.24

a) Probability of hitting an inner or better (inner or bulls eye):

P(I or B) = P(I [tex]\cup[/tex] B)

Formula for P(P [tex]\cup[/tex] Q)  where P(P) and P(Q) are the probabilities of two mutually exclusive events i.e. having nothing in common:

P(P [tex]\cup[/tex] Q)  = P(P) + P(Q)

P(I [tex]\cup[/tex] B)  = P(I) + P(B) = 0.26 + 0.42 = 0.68

b) Probability of failing to hit the target:

P(F) = 1 - (P(B)+P(I)+P(O))

P(F) = 1 - (0.26 + 0.42 + 0.24)) = 1 - 0.92 = 0.08

c) Probability of failing to score a bulls eye:

P(B)' = 1 - P(B) = 1 - 0.26  = 0.74

So, the answers are:

a) 0.68

b) 0.08

c) 0.74

Answer: The vertex form is h(x)=(x-3)^2-6

Step-by-step explanation:

Using the complete the square method, first complete any squares

X^2-6x+(-3)^2-(-3)^2+3

Use the binomial formula

(x-3)^2 - (-3)^2 +3

Simplify

(x-3)^2-6