Translate this sentence into an equation.
The difference of Goran's height and 10 is 57
Use the variable g to represent Goran's height.

Answer:

37.9 units (nearest tenth)

Step-by-step explanation:

As ABCD is a rectangle, AD = BC and AB = DC.

Find the length of AD and AB using the distance formula.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}}[/tex]

From inspection of the given diagram:

Therefore:

[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(-7-(-5))^2+(-3-(-9))^2}\\& =\sqrt{(-2)^2+(6)^2}\\& =\sqrt{4+36}\\& =\sqrt{40}\end{aligned}[/tex]

[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(7-(-5))^2+(-5-(-9))^2}\\& =\sqrt{(12)^2+(4)^2}\\& =\sqrt{144+16}\\& =\sqrt{160}\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = \sf 2(length + width)\\& = 2(AB+AD)\\& = 2(\sqrt{160}+\sqrt{40})\\& = 2(18.97366596...)\\& = 37.94733192...\\& = 37.9\: \sf units\:(nearest\:tenth)\end{aligned}[/tex]

Therefore, the perimeter of the rectangle ABCD is 37.9 units (nearest tenth).

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450c > 900 + 250c;

For business to be profitable;

Selling price of daycare services > Cost price;

Payment for daycare of 1 child =  $450

Payment for daycare of 'c' children = $450 × c;

                                                       = $450c;

Operating cost for 1 child = $250;

Operating cost for 'c' children = $250c;

Total daily operating cost = $900 + $250c;

Therefore;

450c > 900 + 250c;

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Answer:

x = 2.4

Step-by-step explanation:

see image for explanation.

Hope it helps

The coordinates of the image of the reflection of the parallelogram, HIJK, over the y-axis are;

H'(1, 3), I'(1, - 1), J'( -2, -2), K'( -2, 2)

The reflection of a pre-image, (x, y), over the y-axis gives an image at the point (-x, y), on the coordinate plane.

The given vertices of the parallelogram HIJK are;

H(-1, 3), I(-1, -1), J(2, -2), and K(2, 2)

The coordinates of the image are therefore;

[tex]H(-1, 3) \: \underrightarrow{ R_{ y-axis}} \: H ' (1, 3)[/tex]

[tex] I (-1, - 1) \: \underrightarrow{ R_{ y-axis}} \: I ' (1, - 1)[/tex]

[tex] J (2, -2) \: \underrightarrow{ R_{ y-axis}} \: J'( -2, -2)[/tex]

[tex] K (2, 2) \: \underrightarrow{ R_{ y-axis}} \: K'( -2, 2)[/tex]

The coordinates of the image, H'I'J'K' are therefore;

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Answer:

(7.5, -2)

Step-by-step explanation:

Label the coordinates(x₁,y₁) and (x₂,y₂)

Input the values into the formula  (x₁ + x₂)/2, (y₁ + y₂)/2

Add the values in the parentheses and divide each result by 2

Answer:

Step-by-step explanation:

Find the area of the figure. (Sides meet at right angles.)

1 rettangle on a square

Area Rectangle

(2+2+5)*5=

9*5=

45in²

Area of the Square

5*5=

25in²

sum

45+25=

70in²

Answer: DE = CE

Step-by-step explanation: AB is a continuous line so the distance from A to E could be different than the distance from D to E.

DE = CE is true.

A perpendicular bisector is a line that divides another line into two equal parts and is also perpendicular to it.

Here, we are given that AB is the perpendicular bisector of DC and DC is a perpendicular bisector of AB.

This means that AB and DC are the perpendicular bisectors of each other at the point of intersection, that is, E.

Now, since AB bisects DC at point E

⇒ DE = CE

and similarly, DC bisects AB

⇒ AE = BE

Apart from these two equalities, we cannot infer anything else from the given information.

Thus, out of the given options, we can see that only option 3, that is, DE = CE is true.

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The number of cats the nemesis have is 4

A fraction is defined as the part of a whole.

Types of fractions;

From the information given, we have that the Nemesis number of cats is ' Five-sixths of my cats plus three

This is expressed as;

Number of cats =  1 - 5/ 6 + 3

Number of cats = 1/ 6 + 3

Number of cats = 6 + 18 /6

Number of cats = 24/6 = 4

Thus, the number of cats the nemesis have is 4

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Step-by-step explanation:

Technically what you have to do is find what changed in the table charts

find the difference between the output values

find the difference between the input values

then calculate the ratio between the change in the Y and X values

Answer:

the nearest thousand is 63000

Answer:

I believe R is congruent to U

Step-by-step explanation:

I don't exactly remember much about these types of problems but I hope it helps! =D

Answer:

∠VS is congruent to ∠UR

Step-by-step explanation:

congruent means same size or shape and the markings are the little lines

the little curves over the angles are congruent as well

Answer:

12 ×13.5 y 13.5

Step-by-step explanation:

es igual a 400

Answer:

y=4x

Step-by-step explanation:

Answer:

  288 miles

Step-by-step explanation:

Kevin's trip took 9 hours one way, and 4 hours the other way, driving 40 mph faster. You want to know the one-way length of Kevin's trip to the mountains.

The relation between time, speed, and distance is ...

  speed = distance/time

Using d to represent the one-way distance Kevin drove, we can relate his speeds with ...

  d/4 = 40 +d/9 . . . . . . speed coming home was 40 mph more than going

Multiplying by 36 to clear fractions, we have ...

  9d = 1440 +4d

  5d = 1440 . . . . . . . subtract 4d

  d = 288 . . . . . . . divide by 5

Kevin lived 288 miles from the mountains.

The ordered pairs are;

A (2, 4)

B ( -1, 2 ) ,

C (-3, -2) ,

D (2, 0) ,

E ( 0, -4 )

F ( 5, -4 )

What is Coordinate?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Now, To find ordered pairs we can count the number of intervals on horizontal and vertical lines.

Horizontal line gives the coordinate of x - axis and vertical line gives the coordinate of y - axis.

So, To find ordered pairs as;

We start at the origin ( where the axis cross).

The point A move 2 units to the right and 4 units up.

So, The ordered pair of A is;

⇒ A (2, 4)

The point B move 1 units to the left and 2 units up.

So, The ordered pair of B is;

B ( -1, 2 ) ,

The point C move 3 units to the left and 2 units down.

So, The ordered pair of C is;

C (-3, -2) ,

The point D move 2 units to the right and on x - axis.

So, The ordered pair of D is;

D (2, 0) ,

The point E on y- axis and move 4 down.

So, The ordered pair of E is;

E ( 0, -4 )

The point F move 5 units to the right and 4 units down.

So, The ordered pair of F is;

F ( 5, -4 )

Therefore, The ordered pairs are;

A = (2, 4)

B = ( -1, 2 ) ,

C = (-3, -2) ,

D = (2, 0) ,

E = ( 0, -4 )

F = ( 5, -4 )

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The smaller number is 1389. We get this by using the technique of subtracting the bigger from the smaller number and equate it to the difference product.

Given the difference between two numbers is 2811.

The bigger number is 4200.

The smaller number is = ?

let the smaller number be 'x'

as the statement says difference between two numbers = 2811

Subtract the largest number from the smallest number to determine the difference between two integers. This sum is a product, and the difference between the two values is the product.

⇒ bigger number ₋ smaller number = 2811

⇒ 4200 ₋ x = 2811

⇒ ₋ x = 2811 ₋ 4200

⇒ ₋ x = ₋ 1389

cancel the negative sign from both sides.

x = 1389

hence we get the smaller number as 1389.

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Answer:

Step-by-step explanation: bnnnnnnnnnnnnnnm

The value of AB that is 5x is equal to 30.

It is given that the points A, B and C are collinear. Collinear points may be defined as three or more points which lie on a straight line.

Here B lies between A and C and the three points A, B and C are collinear. Thus, according to property of collinear points:

AB+BC=AC

Now, according to question AB=5x, BC= 4x+12 and AC= 10x+6.

So, 5x+4x+12=10x+6

Taking the like terms on one side;

12-6 = 10x+9x

=> x=6

Now, AB=5x, thus AB= 5×5=30

Therefore, the value of AB is 30.

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Complete question:

Three points A, B and C are collinear. Point B is between points A and C. AC=10x+6, AB=5x, and BC=4x+12, Find AB.

The left over sand is a 3/10 bag of the colored sand.

According to the statement

We have to find that the how much sand does she use for the project.

So, For this purpose, we know that the

Left over is a something that remains unused or unconsumed

From the given information:

amber has a 4/5 pound bag of colored sand she use 1/2 of the bag for an art project

then it means

Total sand is = 4/5 pound bag of colored sand

Used sand is = 1/2 of the bag of colored sand

Then

Left over sand is = Total sand - Used sand

Left over sand is = 4/5 - 1/2

Left over sand is = 8 - 5/10

Left over sand is = 3/10.

So, The left over sand is a 3/10 bag of the colored sand.

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Answer:

27.5 years old

Step-by-step explanation:

We are given the formula: [tex]P=0.006A^{2} -0.02A+120[/tex] relating a patient's pressure to age.

We are also given the value for pressure (P) as 124 mmHg and need to find age (A). In order to do this, we can substitute the value 124 for P in the equation and solve the quadratic equation to obtain A:

[tex]124=0.006A^{2} -0.02A+120[/tex]

1. Set equation to 0 by subtracting 124 from both sides:

[tex]124-124=0.006A^{2} -0.02A+120-124\\= > 0.006A^{2} -0.02A-4=0[/tex]

2. Solve equation using a calculator:

It should give the solutions: [tex]A= 27.54, -24.2[/tex]

It doesn't really make sense for someone's age to be negative, therefore we can accept the positive solution as our answer.

The man whose normal blood pressure measures 124 mmHg is 27.5 years old.

Hope this helped!

The speed of the fox should be 35/t + 40 to catch up to the rabbit.

Speed is the ratio of distance and time.

Speed = Distance / Time

We have,

The distance between the rabbit and fox = 35 feets

The rabbit's speed = 40 feet per second

Let fox's speed = F

Let the time taken to catch up to the rabbit = t

Now,

Rabbit's distance from fox after time t will be:

= 35 + (40 × t)

= 35 + 40t

Fox's distance after time t:

= F × t

Fox and rabbit distance must be the same in order for the fox to catch up with the rabbit.

35+40t = Ft

Dividing both sides by t.

35/t + 40 = F

Therefore the fox's speed must be 35/t + 40 in order to catch up with the rabbit.

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Step-by-step explanation:

it seems there is some trick question involved.

we find such answers by putting a horizontal line through the y points and see, where the horizontal line is intersecting the function graph and go straight down to the x-axis to see the value of x for that y value.

the horizontal line through y = -1.5 does not intersect at all.

so, in one hand the answer is "no solution".

but on the other hand, we could assume that the function graph continues further to the right (and down).

and then the intersection point would be

(7.5, -1.5),

and the corresponding x = 7.5.

for y = 0 the horizontal line is the x-axis itself. so, for what values of x does the x-axis intersect the function curve ?

at x = -3, and at x = 6.

for y = 2 the corresponding horizontal line is intersecting the function curve at

x = -2.125 (it looks like it is at the half of the half of the half unit as the grid unit left of -2, so it is -2 - 1/2³ = -2 1/8 = -2.125)

x = 0.5

x = 4 (it just touches the tip of the curve there)

for y = 2.5 there is truly no solution. that horizontal line does not intersect the function curve at any point.

Answer:

The sides are 62, 69, and 49

Step-by-step explanation:

x + (x + 7) + (x - 13) = 180

3x - 6 = 180

3x = 186

x = 62

8 + x / 3 = 75

Minus 8 on both sides

x / 3 = 67

Multiply by 3 on both sides.

x = 201

Answer:

15. x<-2 or x>1

16. -5<=x<=-1

17. -0.5<=x<0.25

18. x<=-1.2 or x>=-0.4

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Use the distance formula to determine the distance between two points.
√[(x₂ - x₁)² + (y₂ - y₁)²]

hi  

2* 5/8  =   10/8  =  5*2 /4*2 = 5/4

and  2*1/4 =  1/2

so :   2*5/8   /  2/4   =    5/4   / 1/2  =  5/4 * 2/1  =   5*2 / 2*2*1 =  5/2

Answer:

[tex]=1\frac{1}{6}[/tex] or 7/6

Step-by-step explanation:

[tex]=\frac{21}{8}\div \frac{9}{4}[/tex] <- Convert to improper fraction
[tex]=\frac{21}{8}\times \frac{4}{9}[/tex] <- Fraction Rule
[tex]=\frac{84}{72}[/tex]
[tex]=\frac{7}{6}[/tex]
[tex]=1\frac{1}{6}[/tex]