What was Dimitri's mistake? He mixed up the coordinates of the ordered pair when Substituting it into the equations 7x+9y=-4 and 5x-2y=6

Answers

Answer 1

Answer:

He made a mistake in his calculations when simplifying 5x - 2y

Step-by-step explanation:

Given

The coordinate pair

[tex](x,y) = (2,-2)[/tex]

The equations

[tex]7x + 9y = ?[/tex]

[tex]5x - 2y = ?[/tex]

Dimitri's Solution

[tex]Equation\ 1: 7x + 9y = -4.[/tex]

[tex]7(2) + 9 (-2) = -4.[/tex]

[tex]14 + (-18) = -4.[/tex]

[tex]-4 = -4.[/tex]

[tex]Equation\ 2: 5x -2y = 6.[/tex]

[tex]5(2) - 2 (-2) = 6.[/tex]

[tex]10 - 4 = 6.[/tex]

[tex]6 = 6.[/tex]

Required

Identify Dimitri’s mistake

In the first equation, Dimitri made no mistake.

However, he made a mistake when simplifying the second equation.

We have:

[tex]5x - 2y[/tex]

and

[tex](x,y) = (2,-2)[/tex]

Substitute [tex]x = 2[/tex] and [tex]y = -2[/tex]

So, we have:

[tex]5(2) -2(-2)[/tex]

Open bracket

[tex]10 +4[/tex]

Finally, we have:

[tex]14[/tex]


Related Questions

Shannon participated in a national math contest by taking a math test. The test results followed a normal distribution with a mean score of 72.6 points out of 100 and a standard deviation of 8.7. Shannon received a score of 81 points. Shannon thinks she performed better than 68% of the students in the contest

Answers

Answer:

.

Step-by-step explanation:

find sin x/2 given that sin x=1/4 and 0

Answers

Answer:

Step-by-step explanation:

find sin x/2 in radians, given that sinx =1/4 and x terminates in 0 less than x less than pi/2

✓ sinx=1/4=opp side/hypotenuse adj side=√(4^2-1^2)=√(16-1)=√15 cosx=√15/4 sin x/2=√[(1-cosx)/2]=√[(1-√15/4)/2] .. calculator check: sinx=(1/4

The value of sin x/2 for sin x=1/4 and 0 is 0.124 and 0 respectively.

Given that, sin x=1/4 and 0.

We need to find sin x/2.

How to find the value of sin?

The sin formula is given as sin θ = Perpendicular / Hypotenuse.

Now, for sin x=1/4

sin 1/4/2=sin 1/8=0.124

=0.124

For sinx=0

sin 0/2=0

Hence, the value of sin x/2 for sin x=1/4 and 0 is 0.124 and 0 respectively.

To learn more about sine visit:

https://brainly.com/question/16853308.

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Find the Interquartile Range (IQR) of the data set.

5, 2, 3, 4, 7, 9, 8, 10, 12, 8, 7

Answers

Answer:

5

Step-by-step explanation:

show your work
B= 47, a = 20, c = 24

Answers

Answer:

Im lost what is this

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

a+b-c

20+47-24

67-24

43

Fernanda is filling a cylindrical pot with cans of vegetable soup. The pot has a diameter of 15 in. and a height of 11 in. The soup can has a diameter of 3 in. and a height of 6 in. How many cans of soup will it take to fill the pot? Round to the nearest can.

Answers

Answer:

45 cans

Step-by-step explanation:

To find the volume of a cylinder, we need to find the area of the cross section, which in this case is π(radius)², and multiply it with the height of the cylinder

This means the pot has a volume of:

- pot has radius of 7.5in. as diameter is 2 x radius

π x (15/2)² x 11 = 618.75π in.³

The soup can has a volume of:

- soup can has radius of 1.5in. as diameter is 2 x radius

π x (3/2))² x 6 = 13.5π in.³

Divide the volume of the pot by the volume of the can to get how many cans of soup will it take to fill the pot:

618.75π in.³ ÷ 13.5π in.³ = 45.833... cans

The question states you need to round to nearest can which would be 45 cans, but personally, I thought you would always round up as 45 cans won't fill up the whole pot, but it's up to the question.

if the polygon is a decagon, then it has ____sides?​

Answers

Answer:

10 sides

Step-by-step explanation:

Deca means 10 (decameter/decahedron/decagon)

Answer: 10 sides

Step-by-step explanation:

There are a list of suffixes for a "-gon"

- Pentagon=5 sides

- Hexagon=6 sides

- Heptagon=7 sides

- Octagon=8 sides

- Nonagon=9 sides

- Decagon=10 sides

- Hendecagon=11 sides

- Dodecagon=12 sides

Therefore, if the polygon is a decagon, then it has 10 sides

Hope this helps!! :)

Please let me know if you have any questions

What is 1.4. 106 written in standard notation?
O A. 140,000
B. 14,000,000
O C. 104,000
D. 1,400,000
E. 10,400,000
F. 1,040,000

Answers

The answer is D 1,400,000

To convert from scientific notation to standard notation you can just move the decimal point to the right how ever many times 10 is the the power of.

The following are the last 10 run scores Colin got in cricket:
18, 9, 7, 35, 30, 21, 33, 12, 30, 31
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 27 runs.
What is his new mean score?
Give your answers as decimals.

Answers

Answer:

a) 22.6

b) 23

Step-by-step explanation:

a)

Step 1: 18 + 9 + 7 + 35 + 30 + 21 + 33 + 12 + 30 + 31 = 226

Step 2: 226/10 = 22.6

b)

Step 1: 226+27 = 253

Step 2: 253/11 = 23

0. A hardware store sold h hammers in February. The hardware store sold 5 less than 2 times as
many hammers in June as it did in February. Write an expression the hardware store could use
to represent the number of hammers it sold in June.

Answers

Answer:

2h - 5

Step-by-step explanation:

Sold in February = hSold in June = 2h - 5

Answer:

solution given:

let hammers be H

now

an expression the hardware store could use to represent the number of hammers it sold in June is 2H-5

Which point does not pass through?
10 Points

Answers

Answer:

C  ( 9 , 15)

Step-by-step explanation:

The answer is c the point will not pass through the graph at points c(9,5)

Including the floor, how many faces are there?

Answers

6 because you count all of the sides

A square photograph has a side length of x + 8. It is
surrounded by a frame that is 2 inches wide all the way
around. Write a simplified expression for the area of
just the picture frame.

Answers

Answer:

(x + 10)^2

Step-by-step explanation:

*It helps to draw a diagram for these types of questions

Side length of photograph: x + 8

Width of frame: 2 in.

Area of a square: s^2

A = ((x + 8) + 2)^2

= (x + 10)^2

Therefore the area of the photograph with the frame is (x + 10)^2

Answer:

8(x + 10) or 8x + 80

Step-by-step explanation:

Area of the picture:

(x + 8)²

Side of the photograph with the frame:

(x + 8) + 2*2 = x + 12

Area of the frame:

(x + 12)² - (x + 8)² = (x + 12 + x + 8)(x + 12 - x - 8) = (2x + 20)(4) = 8(x + 10)

or

8x + 80

Find the area of the circle.
50.24 in?
803.84 in?
d= 8 in.
25.12 in?
12.56 in?
200.96 in?

Answers

Answer:

The answer is 50.24

Step-by-step explanation:

Equation is: 3.14 times 4²

Radius is 1/2 the diameter

find the area of each figure. Round your answers to the nearest hundredth 7-10​

Answers

Answer:

7.

area of parallelogram=base×height=19×7.8=148.2yd²

8.

area of semi circle=1/2[π(d/2)²]=

π×44²/8=760.265in²

9.

area of rectangle =length ×breadth

=16.4×11.8=193.52ft²

10.

area of triangle =1/2 ×base×height=1/2×20.4×14.6=148.92in²

Area of the given shapes are:

parallelogram: 148.2yd²Rectangle:  193.52 ft²Semicircle: 760.265 in²triangle: 148.92 in²

What is Area?

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, Four shapes and we need to calculate the area.

For parallelogram:

area of parallelogram = base×height

area of parallelogram = 19×7.8 = 148.2yd²

For, Semicircle:

area of semi circle= 1/2 [π(d/2)²]

area of semi circle= π×44²/8 = 760.265 in²

For Rectangle:

area of rectangle = length ×breadth

area of rectangle = 16.4×11.8 = 193.52 ft²

For triangle:

area of triangle = 1/2 ×base×height

area of triangle = 1/2×20.4×14.6 = 148.92in²

Learn more about Area here:

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Least to greatest 3 1/7 ,1.73,4 ,2.24

Answers

Answer:

1.73, 2.24, 3 1/7,4

Step-by-step explanation:

You do the whole numbers  first, and then the decimal or fraction.

funniest thing you'll see all day

Answers

Answer:

My dog getting smacked allot by my cat ( my cat was bullying my dog all day XD) 1 thanks = one less smack for the dog lol

Step-by-step explanation:

Me kat (cat) was mewing all day. Me go to market to buy his favourite food (fish).Me comes home. Me takes time to prepare fish. Me gives kat fish. He throw away fish and insult me with some more mews

500(x – 3) = 5,000

What’s the value of x?

Answers

Answer:

13

Step-by-step explanation:

500(x-3)=5000

500x-1500=5000

500x=5000+1500

500x=6500  /:500

x=13

Answer:

13

Step-by-step explanation:

cuz

13-3=10

10x500=5000

find the circumference of the pizza use 3.14 the pizza is 7 inches

Answers

Answer:

45 inches

Step-by-step explanation:

C = (pi)(diameter).

Assuming that the radius of the pizza in this case is 7 inches, the diameter is twice that, or 14 inches.

Thus, the circumference of the pizza is C = (3.14)(14 inches) = 45 inches

approximately.

21.99

Formula: C=2 pi r
First, turn the diameter to a radius by dividing 7 inches, the diameter, by 2. This turns out to be 3.5 inches.
Then, multiply 3.5 by pi(3.14), which would give you 10.99 inches.
Last, do the last step of the formula, which is multiplying 10.99 inches by 2.

Need more help guys :(

Answers

last one is correct
good luckkkkkkk

Step-by-step explanation:

Write a rule to describe the transition of a point from (-3,3) to (-2,2)

In the answers, we see that the rule must be formatted as:

(x,y) ⇾ (x _ 1, y _ 1)

Soo . .  we take the first x (-3) and the second x (-2) and try the 2 methods:

-3 - 1 = -4

-3 +1 = -2

So we see that the first one has to + 1

Here's the rule so far.

(x,y) ⇾ (x + 1, y _ 1)

Next, take the first y (3) and the second y (2) and repeat the 2 methods:

3 + 1 = 4

3 - 1 = 2

Here we get that we have to - 1

Therefore, the rule to describe the transition of a point from (-3,3) to (-2,2) is:

(x,y) ⇾ (x + 1, y - 1)

Which is option 4 or D.

Hope this helps you understand a bit better! =)

Prove or disprove that the point (51−−√, 7) lies on the circle centered at the origin and containing the point (6, 8).

Answers

Answer:

Yes, it lies on the circle.

Step-by-step explanation:

The actual question is:

"Prove or disprove that the point (√51, 7) lies on the circle centered at the origin and containing the point (6, 8)."

The equation of a circle of radius R and centered at the point (a, b) is:

(x - a)^2 + (y - b)^2  = R^2

In this case we have a circle centered at the origin, then: (a, b) = (0, 0)

And the equation becomes:

(x - 0)^2 + (y  - 0)^2 = R^2

x^2 + y^2 = R^2

We also know that this circle contains the point (6, 8), then we can find the radius of our circle if we replace x by 6 and y by 8.

6^2 + 8^2 = R^2

100 = R^2

√100 = 10 = R

Then the circle equation is:

x^2 + y^2 = 10^2

Now let's see if the point (√51, 7) is a solution of the above equation:

(√51)^2 + ( 7)^2 = 10^2 = 100

51 + 49 = 100

100 = 100

This is true, so we can conclude that (√51, 7) is a solution of the circle equation, so the point lies on the defined circle.

What is the lateral surface area?
7 A cylindrical pipe measures 18 inches and has a diameter of 1 inch. How many square inches of metal
are used to make the pipe, which is open on both ends? Round your answer to the nearest hundredth.

Answers

Answer:

56.556 square inches

Step-by-step explanation:

Surface area of an open cylindrical pipe is = πdh

3.142 × 1 × 18 = 56.556

Use the formula to find

Answers

Answer:

5525

Step-by-step explanation:

Using the formula with n = 25 , then

[tex]\frac{25(26)(50+1)}{6}[/tex]

= [tex]\frac{25(26)(51)}{6}[/tex]

= [tex]\frac{33150}{6}[/tex]

= 5525

Solve the system of equations. y = 3x + 2 y = -4 y = -4​

Answers

Answer:

y = x^2 i think

Step-by-step explanation:

graph{y=3x-2 [-10, 10, -5, 5]}

Explanation:

This equation is in the form

y

=

m

x

+

b

so the line is linear.

To graph this equation, all you have to do is figure out two things, the slope and the y-intercept.

The 3x is the slope and -2 is the y-intercept

Find the product of 0.25 x 16

Answers

The answer to this question is 4.

Answer:

4 is the answer

0.25*16 = 4

Step-by-step explanation:

product means multiplication..

what grade level is this?

Have a nice day!

Consider the following system of equations.

3x + 5y = 18
6x − 5y = 20

Decide which procedures eliminate the x variable and which eliminate the y variable. Drag and drop each procedure that will eliminate one of the variables into the appropriate category.

Subtract the second equation from the first equation.
Add the first and second equations. Multiply the first equation by −2; then add the two equations.
Divide the second equation by −2; then add the two equations. Subtract the first equation from the second equation.
Multiply the first equation by 2 then add the two equations.
Eliminate x Eliminate y

Answers

Answer:

Option B

On adding the first and second equations y can be eliminated

Step-by-step explanation:

The two equations are as follows

3x + 5y = 18 -- Eq (1)

6x − 5y = 20 -- Eq (2)

Adding equation 1 and 2, we get -

3x + 6x + 5y -5y = 18

9x = 18

x = 2

y = (18-3*2)/5

y = 12/5 = 2.4

What is the slope of the line passing through the points (-5, -4) and (-1, 6)?
A.2/5
B.-5/2
C.-2/5
D.5/2

Answers

Answer:

5/2

Step-by-step explanation:

Missy Diwater, the former platform diver for the Ringling Brothers’ Circus has a mass of 68kg jumps from a height of 8m. What is her potential energy

Answers

PE = mgh = 68 * 9.8 * 8

what is perimeter? what is area?​

Answers

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

Rotate 90° clockwise about the origin

E = (-3, 3)

F = (-2, -1)

D = (-2, 3)

C = (-1, 4)

Answers

Answer:

e

Step-by-step explanation:

Quelqu'un pourrais m’aider à faire cette exercice svp

Answers

Réponses:

1. pour calculer la distance OF on va utiliser tout simplement le théorème de pythagore

OF = √(68²+51²)

OF = √(4624+2601)

OF = √(7225)

OF = 85 mm

2. étant donné que la cible n'est pas atteinte si la pointe de la flèche est sur le bord, et on sait que le rayon de la cible est 100

donc la distance OF ne doit pas dépasser le nombre 100

OF < 100

3. la suite de la question trois n'est pas affichée malheureusement!

bonne journée ^^

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