Write as an algebraic expression

Answer:

Since the diagonals of a rhombus bisect each other, the diagonals are 5 * 2 = 10 and 12 * 2 = 24. To find the area of a rhombus we can divide the product of the diagonals by 2 which is 10 * 24 / 2 = 120 cm².

Answer:

[tex]x = 1 +/- \frac{i\sqrt{10} }{2}[/tex]

Step-by-step explanation:

The equation given is:

[tex]2x^2 = 4x - 7\\\\2x^2 - 4x + 7 = 0[/tex]

Using quadratic formula:

[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a}[/tex]

From the question:

a = 2, b = -4, c = 7

Therefore:

[tex]x = \frac{4 +/- \sqrt{(-4)^2 - 4 * 2 * 7} }{2 * 2}\\\\x = \frac{4 +/- \sqrt{(16 - 56)} }{4}\\\\x = \frac{4 +/- \sqrt{-40} }{4}\\[/tex]

=> [tex]x = 1 +/- \frac{i\sqrt{10} }{2}[/tex]

The solution of given quadratic equation is given as   [tex]x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex]

Given the quadratic equation:

[tex]2x^2 = 4x -7[/tex]

Formula for finding roots of quadratic equation [tex]ax^2 + bx + c = 0[/tex] is given by:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Here, we get a = 2, b = -4, and c = 7.

Thus, the roots can be found as:

[tex]x = \dfrac{4 \pm \sqrt{16 - 56}}{4} \\\\x = \dfrac{4 \pm \sqrt{-40}}{4} \\\\x = \dfrac{4 \pm 2i\sqrt{10}}{4} \\\\\\x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex]

Thus, the solution of the given quadratic equation is given as  [tex]x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex].

Learn here more:

https://brainly.com/question/4366363

Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

.116

Step-by-step explanation:

7 pink and 5 black balls. = 12 balls

P( pink) = pink balls/ total = 7/12

replace

P( pink) = pink balls/ total = 7/12

so  this is true for each case

P( pink, pink, pink, pink) = 7/12*7/12*7/12*7/12 = 2401/20736

                                        =.115788966

To 3 decimal places

.116

Answer:

Si

Step-by-step explanatio:

Answer:

idk

Step-by-step explanation:

hi

Answer:7678

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]answer = \\ triangle \: b \: and \: d \: does \: not \: seems \: to \\ be \: congruent \: to \: each \: other. \: \\ explanation \\ congruent \: triangles \: are \: those \: \\ which \: are \: exactly \: same \: copy \\ of \: each \: other.they \: have \: same \: side \\ lengths \: shape \: size \: and \: angles. \\ triangle \: a \: and \: e \: seems \: to \: be \: \\ congruent. \: triangle \: c \: and \: f \: seems \: \\ to \: be \: congruent.triangle \: b \: and \: d \: \\ doesnot \: match \: with \: any \: other \: triangles. \\ hope \: it \: helps[/tex]

Answer:

triangle b & d

(Apex)

Answer:

Step-by-step explanation:

30 mm = 3 cm

[tex]\\ height=\frac{Volume}{length*width}\\\\=\frac{675}{15*3}\\\\=15 cm[/tex]

Answer:

h = 15 cm

Step-by-step explanation:

V = l×w×h

h = V/l×w

= 675cm³/15cm×3cm

= 675cm³/45cm²

= 15 cm

Answer:

The correct option is;

Deductive

Step-by-step explanation:

Deductive reasoning or logic is the basic reasoning process that begins with a premise, hypothesis or general statement that is taken as being correct or true and continues with the consideration of the likelihoods or possibilities to come to a conclusion which is logically certain

In deductive reasoning a top to down reasoning approach is applied to link a premise with a conclusion.

Answer:

f(x)/g(x) = x - 6 + (2x+3)/(2x^2+5)

Quotient = x - 6

Remainder = (2x+3)/(2x^2+5)

Step-by-step explanation:

Getting x-6:

What number multiplies with 2x²+5 to get 2x³+...?

that number is x, so that's your first number. You multiply it with 2x²+5 and subtract it like how you would do divison by hand back in elementary school.

Now what number multiplies with 2x²+5 to get -12x²+ ...?

that number would be 6, so that's your second number. Multiply 2x²+5 with 6 and subtract it from -12x²+ ....

Now you have 2x+3. What number multiplies with 2x²+5 to get 2x+3? That number doesnt exist so 2x+3 is your remainder.

Answer:

n =3

Step-by-step explanation:

20 minutes to 1 hour can also be written as 20 minutes to 60 minutes.

when simplified, you get 1:3

Answer:

1:30

Step-by-step explanation:

minutes : hour
20           : 1
convert the hour into minutes
1 hr = 60 minds

20            : 60
it was simplified so that 20 = 1
so they did 20 divided by 20 to get it to equal to 1
1                 : _____
u need to equalise it and do the same to the other side so 60 divided by 20 as well ( this equals 30)
now the ratio is:
1                 : 30

Answer:

y = 1/3x - 1

Step-by-step explanation:

1. if the gradient is -3, then the gradient of the perpendicular line should be 1/3.

2. substitute the new gradient and points into y - y1 = m (x - x1)

3. rearrange/move everything to give you the equation in y = mx + c form

Answer:

8.4375

Step-by-step explanation:

multiply 2.5 times 2.25 times 1.5

lenght x width x height

Answer:

1) [tex]\frac{3}{7} = \frac{15}{35}[/tex]

2) [tex]\frac{64}{48}=\frac{4}{3}[/tex]

3) [tex]\frac{21}{56}=\frac{3}{8}[/tex]

Step-by-step explanation:

ESTAS SON FRACCIPONES EQUIVALENTES

1. 3(35)/7 = 15 ENTONCES 15/35

2. 48(4)/3 = 64 ENTONCES 64/48

3. 56(3)/21 = 8 ENTONCES 3/8

Answer:

The correct graph should have x values that have no more than one y value.

Step-by-step explanation:

A the inputs (x values) of a function can have no more than one y value. This is a "fact" for functions. So you should click on the graph until you see a graph where every x value has exactly 0 or 1 y value.

Answer:

The slope is the rise over run, so...

It  is 3/1 or just 3.

Step-by-step explanation:

Rise/run is slope

(2,1) is a point on the line, and so is (3,4)

[tex]answer \\ = £59.25 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps[/tex]

Answer:

b) 2 seconds

t=2 seconds will an object reach a height of 32 feet

Step-by-step explanation:

Explanation:-

Given  height  f =-16t+16t² ...(i)

Differentiating equation (i) with respective to 't'

[tex]\frac{df}{dt} = -16(t) +16(2t)[/tex]

Equating Zero

- 32 t + 16(2t) =0

 - 16 t = -32

        t = 2 seconds

Given height   f =-16t+16t²

                      f = - 16 (2) +16(4) = -32 +64= 32feet

Conclusion:-

t=2 seconds will an object reach a height of 32 feet

Answer:

y = 3x

where y is the plant height in cm and x is the time in months

at 12 months, height would be 36 cm

Step-by-step explanation:

Here, we want to model the data

let’s call the months x and the height y

What do you notice?

we can clearly see that the height is always 3 times the month

3 * 3 = 9

5 * 3 = 15

7 * 3 = 21

9 * 3 = 27

so we can say that;

Time in months * 3 = Plant height in cm

using the x and y notation;

x * 3 = y

or simply y = 3x

Now the height at 12 months can be calculated by substituting the value of x for 12

y = 3 * 12 = 36 cm

Answer:1/4

Step-by-step explanation:

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.

Answer: 2

Step-by-step explanation:

[tex](-3+5)^0=2[/tex]

Answer:

C. 68

Step-by-step explanation:

Explained in image attached

Answer:

Option (A). OB

Step-by-step explanation:

Angle bisector of any angle is a line segment that divides the angle into two equal parts.

From the given picture,

m∠MOB ≅ m∠NOB

(25 + 35)° ≅ (28 + 32)°

60° ≅ 60°

Therefore, OB is the line segment that divides ∠MON into two equal angles. (∠MOB and ∠NOB)

Option (A). will be the answer.

Answer:

3/4

Step-by-step explanation:

Let the unknown number be x.

Subtract 1/2 from the unknown number: x - 1/2

Multiply the result by 1/2: 1/2(x - 1/2)

You get 1/8: 1/2(x - 1/2) = 1/8

Now we solve the equation for x.

1/2(x - 1/2) = 1/8

Multiply both sides by 2.

2 * 1/2(x - 1/2) = 2 * 1/8

x - 1/2 = 1/4

Multiply both sides by 4

4x - 4 * 1/2 = 4 * 1/4

4x - 2 = 1

Add 2 to both sides.

4x = 3

Divide both sides by 4.

x = 3/4

Answer: The number is 3/4.

Answer:

15.33cm

Step-by-step explanation:

when you try to draw out this figure, satisfying the fact that Ad and Ac are both straight lines. you find the ultimately  it forms a right-angled triangle with sides AC and AD and hypotenuse CD.

Now, you may use Pythagoras theorem to solve:

AC^2 + AD^2 = CD^2

12.3^2 + 9.15^2 = CD^2

CD^2 = 235.0125

CD = square root of 235.0125 = 15.33cm

Hope this helps

Answer:

A solution to the system is (–1, –2).

One of the equations is y = x –1.

One of the equations is 3x + y = –5.

Step-by-step explanation:

Just took the assignment

Answer:

2, 4, and 5

Step-by-step explanation:

Got it right

Answer:

The numbers are closer to each other and the range will be smaller. The numbers will also be closer to the mean and median.

Step-by-step explanation:

Step-by-step explanation:

This question gives us a point on a line and the slope of that line. So, the easiest way to answer this question is to use point-slope form, which is written as:

y-y₁ = m(x-x₁)

So, first of all, we are trying to find y (y, not y₁ which is the y-coordinate of the point we were given). We can go ahead and add y₁ to both sides to get:

y = m(x-x₁) + y₁

We can now simplify the equation to:

y = m·x - m·x₁ + y₁

Now we just input the given information.

m = 5 (slope)

x = 21

x₁ = 5

y₁ = 6

Now we have all the information we need and we can solve.

y = 5·21 - 5·5 + 6

y = 105 - 25 + 6

y = 86

So y, when x = 21, is equal to 86.

Answer:

[tex]y= 500(1+0.15)^x[/tex]

Step-by-step explanation:

This problem can be solved using concept of compound interest

In compound interest

if p is the principal amount

and r is the interest rate

then value of principal amount(A) after n years time is given by

A = p(1+r)^n

=>[tex]A = p(1+r)^n[/tex]

__________________________________

in the problem

in place of n we have x years

y is the amount which is the total amount after n years

p is the principal money deposited = $500

r = 15%

substituting these value in the formula for amount after n years we have

[tex]y= 500(1+15/100)^x\\y= 500(1+0.15)^x[/tex]

Thus, function modeling the situation is [tex]y= 500(1+0.15)^x[/tex]