Solve the following equation for x.
15x^2 – 46x + 16 = 0

Answer:

Step-by-step explanation:

The first two steps are for the purpose of eliminating fractions.  Doing so results in 4(2x - 5) = 9(x - 2), which is to be solved for x.

Perform the indicated multiplication, obtaining:

8x - 20 = 9x - 18.

Then combine like terms:  -2 = x, or

x = -2.

To complete the formal check, substitute -2 for x in the first equation.  This results in:

(1/3)(-4 - 5) = (3/4)(-2 -2), or

        -3       =        -3

... which is obviously true.  

Answer:

Juanita dissolves 46 g of MgBr2 (molar mass: 184.11 g/mol) in 0.5 kg of distilled water. What is the molality of the solution?

Answer:

It will double in the year 2063

Step-by-step explanation:

Let the amount deposited be $x, when it doubles, the amount becomes $2x

we can use the compound interest formula to know when this will happen

The compound interest formula is as follows;

A = P(1+r/n)^nt

In this question,

A is the amount which is 2 times the principal and this is $2x

P is called the principal and it is the amount deposited which is $x

r is the interest rate which is 3.2% = 3.2/100 = 0.032

n is the number of times compounding takes place per year which is quarterly which equals to 4

t is the number of years which we want to calculate.

Substituting all these into the equation, we have;

2x = x(1+0.032/4)^4t

divide through by x

2 = (1+ 0.008)^4t

2 = (1.008)^4t

we use logarithm here

Take log of both sides

log 2 = log (1.008)^2t

log 2 = 2t log 1.008

2t = log 2/log 1.008

2t = 86.98

t = 86.98/2

t =43.49 which is 43 years approximately

Thus the year the money will double will be 2020 + 43 years = 2063

Answer:

probably a. metres

Step-by-step explanation:

hectometres are huge and the other two are super small so thats my guess lol

Answer:

Step-by-step explanation:

A square meters-

Millimeters are super small

And the other ones are to huge

Dats easy

Answer:

Henry=12, Bernard=18

Step-by-step explanation:

let Henry's age = x

let Bernard's age= 1.5x

according to d passage 6yrs ago x×2=1.5x

mathematically that is (x-6)2=1.5x-6

2x-12=1.5x-6

2x-1.5x=-6+12

0.5x=6

divide both sides by the co-efficient of x which is 0.5 can also be written as ½

there fore x=6÷½

x=Henry's age=12years

1.5x=Bernard's age=12×1.5=18years

Answer:

1). Surface area of the prism = 112 cm²

2). Area of the sphere = 615.8 cm²

Step-by-step explanation:

1). Surface area of the triangular prism = Area of the triangular bases + Area of three lateral (rectangular) sides

Area of a triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                          = [tex]\frac{1}{2}(3)(7)[/tex]

                                          = 10.5 cm²

Area of a rectangle = Length × width

Area of the rectangular lateral sides = (3 × 5) + (8 × 5) + (7 × 5)

                                                            = 15 + 40 + 35

                                                            = 90 cm²

Surface area of the prism = (2 × 10.5) + 90

                                           = 21 + 90

                                           = 112 cm²

2). Surface area of the sphere = 4πr²

                                                  = 4π(7)²

                                                  = 615.75

                                                  ≈ 615.8 cm²  

Answer:

3/5

Step-by-step explanation:

cos F = adjacent side/ hypotenuse

Cos F = 6/10

Cos F = 3/5

Answer:

6/10 which is 3/5

Step-by-step explanation:

Answer:

y < -2

Step-by-step explanation:

2y < -4

Divide both sides by 2.

y < -2

Answer:

y <-2. :::::::::::::::::::::::

Step-by-step explanation:

2y< -4 ==> y<-2

Answer:

0, 1

Step-by-step explanation:

The discriminant is b² - 4ac where we have ax² + bx + c, in this case a = -4, b = 12, c = -9 so D = 12² - 4(-4)(-9) = 0.

Because the discriminant is 0 that means that f(x) only has one solution for x meaning that it has only 1 x-intercept.

Answer:

D. - i

Step-by-step explanation:

i = √( - 1)

i³ = √( - 1)*√( - 1)*√( - 1) = √(-1)² *√(-1) = - 1*i = - i

Answer:

97

Step-by-step explanation:

y=mx+b

m= slope

y=97x+1

Answer:

250 g

Step-by-step explanation:

160 g after two bites

80% after 1 bite

[tex]\frac{80}{100} =.8[/tex]

160 ÷ .8=200

200 ÷ .8=250

Answer:

250

Step-by-step explanation:

We start with the 100% and if we take 20% from that we get 80% if we take 20% from that we have 64%. This means 160 is 64%. So if we do 160/64*100 we will get the answer!

Answer:

C. Decreasing

Step-by-step explanation:

Answer:

60 degrees

Step-by-step explanation:

Since the two lines are intersecting, the angles formed by them are vertical angles. Therefore:

2x+24=144

2x=144-24=120

x=120/2=60

Hope this helps!

Step-by-step explanation:

Therefore,

2x+24= 144° [ Vertically positive angles]

Or, 2x= 144-24

Or, 2x= 120

Or, x= 120/2

Therefore, x= 60°

Answer:

Step-by-step explanation:

Answer:

Solution set:  (3, 4) and (4, 3)

Step-by-step explanation:

Please, to indicate exponentiation, use " ^ ":  a^2 and b^2

Then you have:

a + b = 7 and a^2 + b^2 = 25.

Let's eliminate b:  Solve a + b = 7 for b, obtaining b = 7 - a.

Then we have:

a^2 + (7 - a)^2 = 25, or

a^2 + 49 - 14a + a^2 - 25 = 0, or

2a^2 - 14a + 24 = 0, or

a^2 - 7a + 12 = 0, which factors as follows:

(a - 3)(a - 4) = 0

This results in a = 3 and a = 4, in which case the equation a + b = 7 tells us that the b values are 4 and 3 respectively.

Solution set:  (3, 4) and (4, 3)

Answer:

rotation then translation

Based on the information given regarding the triangle, the transformations that can be used to map △RST onto △VWX is D. rotation, then translation.

It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.

Since Triangle RST can be rotated about point S and then shifted down and to the left to form triangle VWX, the transformations that can be used to map △RST onto △VWX is rotation, then translation.

Learn more about triangles on:

https://brainly.com/question/2644832

Answer:

(D) [tex]\angle CAB[/tex].

Step-by-step explanation:

The diagram is attached below:

Theorem: An exterior angle of a triangle is equal to the sum of the opposite interior angles.

The exterior angle is the angle formed by the third side and a straight line which forms a supplementary angle with the third interior angle.

In the diagram:

[tex]\angle ABF$ and \angle AFB[/tex] are opposite interior angles.

The third angle is [tex]\angle BAF[/tex]

The angle which forms a supplementary angle with [tex]\angle BAF[/tex] is [tex]\angle CAB[/tex].

Therefore, the exterior angle of triangle ABF is  [tex]\angle CAB[/tex].

Answer:

D

Step-by-step explanation:

Just took the test and got it right

Answer:

C) 3x

Step-by-step explanation:

There are three feet in a yard. Yards are represented by x in this problem and therefore the answer is 3x.

Answer: A. Triangle

Step-by-step explanation: Its A because its in order of number of sides starting from the left side. It goes 6 sides, 5 sides, 4 sides, then next should be 3 sides.

Answer:

A

I think A is the correct answer and this can only be true if we are following the sequence because the first shape has 6 sides followed by 5 and 4 so probably 3 should be the next.

Answer:

(-1,6)

Step-by-step explanation:

When you reflect over the y-axis, the x value becomes the opposite sign

Answer:

-1 6

Step-by-step explanation:

i copied the first answer

[tex]answer = 6 + 2b\\ solution \\ length = 3 \: m \\ breadth = b \: m \\ perimeter \: of \: rectangle = 2(l + b) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(3 + b) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 3 + 2 \times b \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6 + 2b \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

The perimeter of the rectangle is P = 6 + 2b, where b is the width.

Given data:

To find the perimeter of a rectangle, we add the lengths of all its sides. In this case, the rectangle is 3 meters long and b meters broad.

The perimeter is calculated as follows:

Perimeter = 2 × (length + breadth)

Given that the length is 3 meters and the breadth is b meters, substitute these values into the formula:

Perimeter = 2 × (3 + b)

Simplifying the expression,

Perimeter = 6 + 2b

Hence, the perimeter of the rectangle is 6 + 2b meters.

To learn more about perimeter of rectangle click :

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Answer:

32cm

Step-by-step explanation:

i think it is  symmetry of order 2 as it's rotational symmetry is 180°

Answer:

It has rotational symmetry of order 2 as it's rotational symmetry is 180°

<AED

Explanation:

B is the mid point of AD.( since AB=BD)

C is the mid point of AB( since AC=BC)

Therefore BC is parallel to DE.

Angle ACB= Angle AEB

Corresponding angles are equal.

And hence, they are congruent.

Hope it helps

Good luck on your assignment

The angle congruent to ∠ACB is B. ∠AED.

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

Congruent Angles have the same angle (in degrees or radians).

Now from the given figure,

In triangle  ABC and triangle AED

AC = CB

BC is parallel to DE

Thus, by law of congruent angles, interior angles are equal,

Thus, ∠ACB = ∠AED

this is the required congruent angle of ∠ACB.

Thus, the angle congruent to ∠ACB is B. ∠AED.

To learn more about congruent angles:

https://brainly.com/question/24887947

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Answer:

Step-by-step explanation:

Let the number be x

Take away 1: x -1

Then multiply the result by 3:  (x- 1) * 3 = (x-1)3 or 3x - 3

Answer:

Your answer is B.

Have a great day!

Step-by-step explanation:

I'm so sorry that I do not have an explanation for you. I truly am.

Answer:

B

Step-by-step explanation:

The correct answer is Pentagon 2 or B

Explanation:

In mathematics and related disciplines, a line of symmetry is a line that divides a figure, for example, a triangle, circle, or pentagon into two symmetrical or equal sides. This means you can fold the image following the line and both sides will be identical. This occurs in the second pentagon because the line that begins in the top of the figure divides it into two equal sides. Indeed each of the sides includes half of the base and two angles that coincide if you fold the figure following line.

Answer:

its b

Step-by-step explanation:

literally the only one you can fold in half

Answer: YES, Its correct.

[tex]M_x=\frac{-6+2}{2}=2\\\\M_y=\frac{-3+7}{2}=2\\\\M=(2,2)[/tex]

Answer:

(-2,2)

Step-by-step explanation:

The midpoint is the middle of the line. So, you can take it step-by-step and look at the individual numbers.

Between -6 and 2, that is 8 spaces. So, the middle would be four spaces from one of those numbers. Therefore, X-COORDINATE = -2

Between -3 and 7, that is 10 spaces. So the middle would be 5 spaces from one of those numbers, Therefore, Y-COORDINATE = 2

So, the midpoint would be (-2,2)

Answer:

Rational number

Step-by-step explanation:

Rational numbers repeat and terminate. The square root of 9 is 3, and 3 is a whole number as well as a number that terminates,  which makes it a rational number