10
19 Solve the simultaneous equations.
You must show all your working.
x = 7 – 3y
x2 - y2 = 39

Answer:

DI = 38

Step-by-step explanation:

Δ EHC and Δ DIC are similar and ratios of corresponding sides are equal, that is

[tex]\frac{DI}{EH}[/tex] = [tex]\frac{DC}{EC}[/tex] , substitute values

[tex]\frac{DI}{76}[/tex] = [tex]\frac{1}{2}[/tex]  ( cross- multiply )

2DI = 76 ( divide both sides by 2 )

DI = 38

Answer:

The systems of equation satisfying the problem are

Y= 4x+9

Y= -3x-5

Y= 2x+5.

Y= 5x+11

Y= 3x+7

Y= -x-1

Step-by-step explanation:

From the graph in the figure

The point A ; x= -2,y=1

So the equations that will interest at point A are the equations that both pass through the point A.

To know the equations that pass through the point A we solve them simultaneously.

For

Y = 10x-1

Y= -3x-5

0= 13x +4

X= -4/13..... definitely not this one

For

Y= 4x+9

Y= -3x-5

0= 7x +14

-14= 7x

-2= x

Substituting the value of x into Y= 4x+9

Y= 4x+9

Y= 4(-2)+9

Y = -8+9

Y= 1

So it's definitely this one

Let's check to know if there is any more

Y = 2x+5

Y= x-1

0= x +6

Definitely not this one

For

Y= 2x+5.

Y= 5x+11

0 = 3x+6

-6= 3x

-2= x

Y= 2x+5.

Y=2(-2)+5

Y= 1

Definitely this one

For

Y= 3x+7

Y= -x-1

0 = 4x +8

-8= 4x

-2= x

Y= -x-1

Y= -(-2)-1

Y= +2-1

Y= 1

Definitely this one too

The correct options are system of equations shown by options (B)[tex]Y= 4x+9 \ and \ y = -3x-5[/tex]

(D) [tex]y= 2x+5 and \ y= 5x+11[/tex]

and (E) [tex]y= 3x+7 \ and\ y= -x-1[/tex].

Given, Coordinates of point A is (-2,1).

We have to find which systems of equations intersect at point A in this graph.

The system of equation which satisfy the point A(-2,1) will intersect at point A.

On putting the value of x=-2 and y= 1, in 1st pair

the equation doesn't satisfy.

similarly checking all the options, we find that the below system equations intersect at point A.

[tex]Y= 4x+9 \ and y = -3x-5 \\y= 2x+5 and \ y= 5x+11\\y= 3x+7 \ and y= -x-1[/tex]

Hence the correct options are system of equations shown by options (B), (D) and (E).

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Answer:

this is the answer of this question

hoping it will help u

Answer:

Jada drank less water than Elina.

Step-by-step explanation:

Water drunk by Elina = 3 liters

Jada drank the water [tex]\frac{3}{4}[/tex] times as much as water as Elina.

Therefore, water drunk by Jada = [tex]\frac{3}{4}\times 3[/tex]

                                                     = [tex]\frac{9}{4}[/tex]

                                                     = 2.25 liters

Lin drank water twice as much as Jada.

Therefore, Lin drank the amount of water = 2 × 2.25

                                                                   = 4.5 liters

Since Jada drank 2.25 liters of water and Elina drank 3 liters

Therefore, Jada drank less water than Elina.

Answer:

i dont know

Step-by-step explanation:

ask sssniperwelperer562

Answer:

she is saving in an exponential way, that is an amazing habit that will multiply her savings over time. At the end of the second week of July she will have 126 if she kept multiplying the amount every week from June into July but she will  have 38 if she starts over with saving 2 on the 1st week of the second month. I save money often, my way of saving is only spending the money i have on things I need rather than want. I also save in a linear way buy saving five dollars every month which is slower than aishas way in the long run but it is easy for me. There are so many different ways of saving money but some are slower than others and some are faster.

Step-by-step explanation:

Hope this helps, please give brainliest, i never got it before

Answer:

after discount sales price is rs 1997 which is 85 % of market price the market price = 1997/85×100 = 2350 ans.

Answer:

4

Step-by-step explanation:

8 ^ 2/3

Rewriting 8 as 2^3

( 2^3) ^ 2/3

We know that a^ b^c = a^ (b*c)

2 ^ ( 3 * 2/3)

2 ^ 2

4

Answer:

Quadrilateral

Step-by-step explanation:

Answer: 864.

Step-by-step explanation:

The volume of a rectangular prism has a volume equal to:

V = W*L*H

W = width

L = length

H = height

We know that the volume is equal to 864 cubic units.

This means that if we want to fill the prism such that there is no gap or overlap, we should use exactly 864 unit cubes.

Answer: Using width as diameter=32π Using length as diameter=72π

*I included both possibilities since I didn't see a picture of the way in which the semicircle and rectangle were joined.*

Step-by-step explanation:

In order to solve, you have to know the formula for area of a circle which is A=πr^2 (pi*radius to the 2nd power)

The problem does not give us the radius, but we know that radius is half of the diameter.

To find the diameter, we have to use the side measurement of the rectangle and divide it by 2 to find the radius.

Next, we increase the radius to the 2nd power, giving us the radius of a whole circle.

Finally, we have to divide that by 2 since it's a semi circle otherwise known as half of a circle.

I put the answer in terms of pi since that's the most accurate, but if the question specifically instructs it, you can calculate part of the irrational decimal and round to a certain place value.

Answer:

Option A

Step-by-step explanation:

Expression: y = 12h

If h = 15, then:

y = 12(15)

y =  $180

Option A

Answer:

2cm/present is the unit rate

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Harold used \underline{\underline{6 centimeters of tape}} to wrap}\\\huge\text{\underline{\underline{3 presents}}. \underline{\underline{\underline{What is the unit rate?}}}}[/tex]

[tex]\huge\boxed{\star \ Formula: \mathsf{\dfrac{a}{b}= unit\ rate \ }\star}[/tex]

[tex]\huge\boxed{\mathsf{Equation\boxed{\rightarrow}\ \dfrac{6}{3} = \boxed{unit\ rate}}}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{6}{3} = \boxed{\bf unit\ rate}}}\\\\\\\huge\boxed{\mathsf{ 6 \ \boxed{\div} \ 3\ \boxed{= } \ \bf\boxed{\bf unit\ rate}}}\\\\\\\\\huge\boxed{\boxed{=} \bf \ 2}[/tex]

[tex]\huge\boxed{\star\ \textsf{Therefore, the UNIT RATE IS: \bf \boxed{\bf 2}}\ \star}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: the unit rate is \bf \boxed{\underline{\underline{\underline{\underline{\bf 2}}}}}}}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

b-8=9

b=9+8

b=17

Step-by-step explanation:

hope it will help you mark me as a brilliant.

Answer:

b=17

Step-by-step explanation:

b-8=9

first isolate the variable by adding 8 to both sides

this gives us

b=17

Answer:

B = 135

Step-by-step explanation:

An octagon has 8 equal sides, and in total is 1080 degrees. Each angle is 135 degrees which adds up to 1080. Or:

135 × 8 = 1080.

Hope this helped.

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

[tex]pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

[tex]or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] 8[/tex]

Now,

again finding the distance between PR,

[tex] pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} } [/tex]

or,

[tex] \sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] = \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } [/tex]

now, finding the distance of QR,

[tex]qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} } [/tex]

or, by simplification we get,

[tex] \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

now, equating PR and QR,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

we cancelled the root ,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29[/tex]

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8} [/tex]

cancel the roots,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = 8[/tex]

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

Answer:

1,8.9

Step-by-step explanation:

Answer:

the slope is -3

Step-by-step explanation:

Answer:

the slope is 3

Step-by-step explanation:

Answer:

0.35 * 1000 = 350

1.2 * 1000 = 1200

Answer:

We know:

Covert the given l to ml:

(a)

(b)

Answer:

100 pages

Step-by-step explanation:

Yesterday, there were 400 pages left unread so you read 1/4 * 400 = 100 pages yesterday. Today, there are 400 - 100 = 300 pages left unread so today, you read 2/3 * 300 = 200 pages. This means that there are 300 - 200 =   100 pages left in the book.

Answer:

4

Step-by-step explanation:

4x4x4=64

Answer:

0.4193

Step-by-step explanation:

Root 64=8

Root 364=19.08...in 4 s.f

8÷19.08=0.4193...in 4 significant figures (4s.f)

Answer:

2000 milligrams —> 2 grams

6000 milligrams —> 6 grams

7000 milligrams —> 7 grams

10000 milligrams —> 10 grams

I hope I helped you^_^

Cheese required for 1 pizza = ½ pound

So, cheese required for 19 pizzas

= 19 × ½ pounds

= 19/2 pounds

= 9½ pounds

So, Hailey needs 9½ pounds of cheese to make 19 pizzas.

The solution is 9.5 pounds

The number of pounds of cheese Hailey need to make 19 pizzas is 9.5 pounds

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pounds of cheese for 19 pizzas be A

Now , the equation will be

The number of pounds of cheese for 1 pizza = 1/2 pounds

So , the number of pounds of cheese for 19 pizzas = 19 x number of pounds of cheese for 1 pizza

Substituting the values in the equation , we get

The number of pounds of cheese for 19 pizzas = 19 x ( 1/2 )

The number of pounds of cheese for 19 pizzas = 19/2

The number of pounds of cheese for 19 pizzas = 9.5 pounds

Therefore , the value of A is 9.5 pounds

Hence , the number of pounds of cheese is 9.5 pounds

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Answer:

  see the attached

Step-by-step explanation:

In the attachment, we will refer to the circles, bottom-to-top, as circles 1, 2 and 3. The black points of intersection, bottom-to-top, will be referred to by the letters A, B, C, D. The transversal line through the white point (W) and pink point (P) will be line q.

Step 1. Draw line q through point P so it intersects line m at some convenient point. Label that point W.

Step 2. Choose an arbitrary radius for your compass. Here, we have chosen it to be the length WB. It happens to be less than half the length of WP, but that is not a requirement.

Step 3. Draw an arc of the chosen radius centered at W and intersecting line q and line m. Label the intersection points A (on line m) and B (on line q). These intersection points are on circle 1.

Step 4. Draw an arc of the same radius centered at P. It should be a long enough arc that it would intersect the proposed line parallel to m. Label the intersection point on line q with label C. This intersection point is on circle 3.

Step 5. Adjust the compass width (radius) to the distance from A to B. This is the radius of circle 2.

Step 6. Draw an arc centered at C so that it intersects the arc of Step 4. This is circle 2, and you want it to intersect circle 3. Label that point of intersection D.

Step 7. Draw line PD parallel to m.

_____

The point of the construction is to create congruent alternate interior angles AWB and CPD, so that lines AW and PD are parallel.

Answer:

You can write in

Step-by-step explanation:

Lakhs

First write 100,203.

Put ones,tens,hundreds,thousands,ten thousands and lakh on top of each number from the extreme left.

This is how you can write 100,203 in another way. You can't write in any other way than this one.

Hope this helps....

Have a nice day!!!!

Answer:

8×k-3

Step-by-step explanation:

that would be the equation (:

Answer:

8k - 3 is the answer because they are not like terms.

Answer:

18/14 or 1 2/7

Step-by-step explanation:

13/14 - 2/14(1/7) = 11/14

11/14 + 7/14(1/2) = 18/14

[tex]\\ \sf\longmapsto \dfrac{13}{14}-\dfrac{1}{7}+\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{13-2+7}{14}[/tex]

[tex]\\ \sf\longmapsto \dfrac{11+7}{14}[/tex]

[tex]\\ \sf\longmapsto \dfrac{18}{14}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}[/tex]

Answer:

1. a. Greatest common factor: 4

b. Greatest common factor: x2

c. Greatest common factor: p2

d. Greatest common factor: x

2. a. (a2 + 1)(4a + 28)

b. (x + 3)(x2− 2)

c. (4x+ 1)(2x−y)

3. a. u2 – 100 = (u + 10)(u − 10)

b. 4a2 − 49 = (2a + 7)(2a − 7)

c. 81 − y2= (9 + y)(9 − y)

d. 16q4− 16 = 16(q4 − 1) 16 (q4 −1) = 16(q2 + 1) (q2− 1) = 16(q2 + 1) (q + 1) (q − 1)

e. 9c3− 9c = 9c (c2− 1) = 9c(c + 1)(c − 1)

f. 48a2b − 12b = 12b (4a2− 1) = 12b(2a + 1)(2a − 1)

Step-by-step explanation:

I got it at PennFoster

Answer:

AB is not a tangent to the circle

Step-by-step explanation:

The angle between a tangent and the radius at the point of contact = 90°

Using Pythagoras' identity to determine if the triangle is right at A

If the square of the longest side is equal to the sum of the squares on the other 2 sides then A is right.

longest side = 15 , then 15² = 225

8² + 9² = 64 + 81 = 145 ≠ 225

Then AB is not a tangent to the circle

Answer:

A= 5 8 11

     7 10 13

     11 14 17

x=3 y=2 z=-1 w=1/2

Step-by-step explanation:

Let matrix A= a11 12 13

                      a21 a22 a23

                      a31 a32 a33

aij=2^i+3j

When i=1 and j=1,

aij=2^1+3*1=2+3=5

Solve for all the elements and you'll get,

A= 5 8 11

     7 10 13

     11 14 17

For no 7,

x+y  0           =       5    2w-1

1       x-y               z+2      1

Equating,

x+y =5       z+2=1     2w-1=0    x-y=1

x=5-y         z=-1        w=1/2      From 1st 5-y-y=1   -2y=-4 y=2

x=5-2(from last)

x=3

Answer:

selling price; cost

Step-by-step explanation: