Simplify the expression

3a(3-a)+3(a^2-3)+3a

Answer:

Step-by-step explanation:

ΔNPM and ΔABM are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{NM}{AM}=\dfrac{PM}{BM}[/tex]

We have

[tex]NM=67.2m,\ AM=67.2m-32m=35.2m,\ PM=81.9m,\ BM=x[/tex]

Substitute:

[tex]\dfrac{67.2}{35.2}=\dfrac{81.9}{x}[/tex]          cross multiply

[tex]67.2x=(35.2)(81.9)[\tex]

[tex]67.2x=2882.88[/tex]              divide both sides by 67.2

[tex]x=42.9\ m[/tex]

Answer:

Square root of 21 + 4 = w

Step-by-step explanation:

Answer: [tex]x^2+4x-21=0[/tex]

Step-by-step explanation:

You need to remember that formula for calculate the area of a rectangle:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width.

You know that "x" represents the width of the doghouse, its rectangular base has an area of 21 square feet ([tex]A=21[/tex]) and its length is 4 feet more than its width ([tex]l=x+4[/tex])

Then, substituting into the formula, you get:

[tex]21=(x+4)(x)[/tex]

Simplifying, you get the following  that can be used to determine the possible dimensions of the base of the doghouse:

[tex]21=x^2+4x[/tex]

[tex]x^2+4x-21=0[/tex]

Answer:

[tex]\large\boxed{a=-\dfrac{1}{10}=0.1}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3=10a+b\\2=20a+b&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3=10a+b\\-2=-20a-b\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad1=-10a\qquad\text{divide both sides by (-10)}\\.\qquad-\dfrac{1}{10}=a\Rightarrow a=-\dfrac{1}{10}[/tex]

Answer:

this is in copy and paste form a = - 1/10 - 1.0

the answer is 3.5987

Answer:

where is the questions

Step-by-step explanation:

Answer:

1. 1/4

2. 1/2

Step-by-step explanation:

If there are equal numbers of males and females, we can simplify that by saying there's one male and one female for each coat color.

1. What's the probability that both are males?

Well, there's a 1/2 chances the light-colored coat bear is a male and there's also a 1/2 chances the dark-colored coat bear is a male.  So, we can make this reference table:

Light             Dark

Male             Male

Male             Female

Female         Male

Female         Female

As you can see, the probability that both of the spotted bears are males is 1/4 (1/2 * 1/2).

2. If the light-colored bear, what are the odds both are males?

If we know for sure the light-one is male, then there's 1/2 chances the other is too, refer to the table above to verify.

The answer is:

The solution to the equation is:

[tex]x=6[/tex]

To solve the problem, we must remember how to operate with fractions.

So, adding fractions we have:

[tex]\frac{a}{b}+-\frac{c}{d}=\frac{(a*d)+-(b*c)}{b*d}[/tex]

Now, we are given the expression:

[tex]\frac{3}{x} +\frac{1}{3}=\frac{5}{6}[/tex]

So, solving we have:

[tex]\frac{3}{x} +\frac{1}{3}=\frac{5}{6}\\\\\frac{3}{x}=\frac{5}{6}-\frac{1}{3}\\\\\frac{3}{x}=\frac{(5*3)-(6*1)}{6*3}\\\\\frac{3}{x}=\frac{15-6}{18}\\\\\frac{3}{x}=\frac{9}{18}\\\\\frac{3}{x}=\frac{1}{2} \\\\3*2=1*x\\\\x=6[/tex]

We have that the solution to the equation is:

[tex]x=6[/tex]

-1≤x≤3

i did that test

Good Luck

7.602 rounded to the nearest whole number would be 8.

Given is the number as -

7.602

We can round of the number to the nearest whole number as -

7.602

7.60

7.6

8

Therefore, 7.602 rounded to the nearest whole number would be 8.

To solve more questions on algebraic expressions, visit the link below-

brainly.com/question/1041084

#SPJ6

[tex]

(2y-z)^5=(2y-z)^2\cdot(2y-z)^3 \\

(4y^2-4yz+z^2)\cdot(8y^3-12y^2+6yz-(-z)^3) \\

(4y^2-4yz+z^2)\cdot(8y^3-12y^2+6yz-z) \\

\boxed{32y^5-48y^4+24y^3z-4y^2z-32y^4z+48y^3z-24y^2z^2+4yz^2+8y^3z^2-12y^2z^2+6yz^3-z^3} \\

[/tex]

Answer:

Final answer is 1/8.

Step-by-step explanation:

Total number cards in deck of cards = 52

Total number of cards with a letter = 16

Total number of cards with red King and letter both = 2

Then probability of getting card with letter P(L) = 16/52

Then probability of getting card with letter and king both  P(K and L) = 2/52

Then required compound probability P(K|L) is given by formula:

P(K and L)= P(L)*P(K|L)

2/52= 16/52*P(K|L)

(2/52)*(52/16)=P(K|L)

2/16=P(K|L)

1/8=P(K|L)

Hence final answer is 1/8.

For this case we have by definition, that the volume of a square base pyramid is given by:

[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]

Where:

L: It's the side of the base (square side)

h: It's the height of the pyramid

Substituting:

[tex]L = 6 \ ft\\h = 10 \ ft[/tex]

[tex]V = \frac {1} {3} * (6) ^ 2 * 10\\V = \frac {1} {3} * 36 * 10\\V = 120 \ ft ^ 3[/tex]

Answer:

[tex]V = 120 \ ft ^ 3[/tex]

Answer:

It is 2, 4, & 5.

Step-by-step explanation:

just got it right on edge.

Answer:

The correct answer option is f(x) = 3^(x+3).

Step-by-step explanation:

We are to determine whether which of the given answer options represent the given graph.

A graph which has a similar shape like that of the given graph here (big on the left and crawling along the x-axis on the right) represents the exponential growth or decay.

Therefore, the only correct option we have here is f(x) = 3^(x+3).

5(0)-5y=4

-5y=4

y=-4/5

the answer is 4/5

i hope this could help!!

Answer:

0=0

Step-by-step explanation:

When you  combine both expressions  you multiply the first one  by -3

As result all the terms in the second expression are cancelled when both expressions are added

-3x -6y = -30

3x  + 6y =30

0   +  0  = 0

Answer:yes that is the right answer

Step-by-step explanation:

Answer:

The measure of the central angle is 35° to the nearest degree

The area of the triangle formed is 28.7 inches²

Step-by-step explanation:

* Lets revise the cosine rule to solve the question

- In Δ ABC:

# AB² = BC² + AC² - 2(BC)(AC) cos∠C

- If you want to find m∠C, we can rearrange the rule

# cos∠C = BC² + AC² - AB²/2(BC)(AC)

* Now lets solve the problem

- The length of the radius of the circle is 10 inches

- The length of the chord is 6 inches

- The chord and the two radii drawn to the endpoints of the chord

 formed an isosceles triangle and the angle between the two radii

 is the central angle

- Lets use the cosine rule to find the measure of the central angle

- Let the name of the central angle is Ф

∵ cos Ф = r² + r² - (chord)²/2(r)(r)

∵ r = 10 inches and the chord = 6 inches

∴ cos Ф = (10)² + (10)² - (6)²/2(10)(10)

∴ cos Ф = (100+ 100 - 36)/200

∴ cos Ф = 164/200 = 41/50

- Find the measure of the Ф by using cos^-1 Ф

∴ m∠Ф = cos^-1 (41/50) ≅ 35°

* The measure of the central angle is 35° to the nearest degree

- To find the area of the triangle we will use the sine rule

# Area of any triangle by using the sine rule is

  A = 1/2 × (s1 × s2) × sin the included angle between them

∵ s1 = r , s2 = r and the angle between them is the central angle Ф

∴ Area of the triangle = 1/2 (r × r) × sin Ф

∵ r = 10 and Ф = 35°

∴ Area of the triangle = 1/2 × (10 × 10) × sin 35°

∴ Area of the triangle = 50(sin 35°) ≅ 28.7 inches²

* The area of the triangle formed is 28.7 inches²

Answer:

Step-by-step explanation:

This shows step by step

Hope this helps <3

1. The area of a circle is calculated using the formula:

[tex]Area = \frac{\pi \: {d}^{2} }{4} [/tex]

The diameter is d=11 feet.

This implies that,

[tex]Area = \frac{\pi \times {11}^{2} }{4} [/tex]

[tex]Area = \frac{121\pi}{4} = 95.03 {ft}^{2} [/tex]

2. For this second question the diameter is d=10.5 feet.

We substitute into the formula to get;

[tex]Area = \frac{\pi \times {10.5}^{2} }{4} [/tex]

[tex]Area = \frac{441\pi }{16} = 86.60 {in}^{2} [/tex]

3. The area of a circle is given by the formula,

[tex]Area =\pi \: {r}^{2} [/tex]

where the radius is r=6.3

This implies that,

[tex]Area =\pi \: {(6.3)}^{2} [/tex]

[tex]Area =36.69\pi = 124.69 {cm}^{2} [/tex]

4. The given circle has a radius of 3.25 yards.

[tex]Area =\pi \times {3.25}^{2} [/tex]

[tex]Area =10.5625 \pi = 33.18 {yd}^{2} [/tex]

Answer: [tex]x=11[/tex]

Step-by-step explanation:

Remembert that, by definition:

[tex]log_b(x)=y[/tex] → [tex]b^y=x[/tex]

Then, you can rewrite [tex]log_4(2x-6)=2[/tex] in exponential form:

[tex]4^2=2x-6[/tex]

Now you can solve for the variable "x":

Add 6 to both sides of the equation:

[tex]4^2+6=2x-6+6[/tex]

[tex]22=2x[/tex]

And finally you must divide both sides of the equation by 2, then:

[tex]\frac{22}{2}=\frac{2x}{2}\\\\x=11[/tex]

the easiest to solve for is y in the first equation

Answer:

the easiest to  for y in the first equation

Step-by-step explanation: -3

Answer:

[tex]\large\boxed{y-3=3(x+2)}\qquad\text{point-slope form}\\\boxed{y=3x+9}\qquad\text{slope-intercept form}\\\boxed{3x-y=-9}\qquad\text{standard form}\\\boxed{3x-y+9=0}\qquad\text{general form}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = 3 and the point (-2, 3). Substitute:

[tex]y-3=3(x-(-2))\\\\y-3=3(x+2)[/tex]

the point-slope form

[tex]y-3=3(x+2)[/tex]        use the distributive property

[tex]y-3=3x+6[/tex]           add 3 to both sides

[tex]y=3x+9[/tex]

the slope-intercept form

[tex]y=3x+9[/tex]           subtract 3x from both sides

[tex]-3x+y=9[/tex]         change the signs

[tex]3x-y=-9[/tex]

the standard form

[tex]3x-y=-9[/tex]              add 9 to both sides

[tex]3x-y+9=0[/tex]

the general form

Answer:

B) x + 1/y times h/g+1

Step-by-step explanation:

We need to divide [tex]\frac{x+1}{y}[/tex] by [tex]\frac{g+1}{h}[/tex] then match with given choices to find the correct equivalent result.

where given choices are:

A) x/y times h/g

B) x + 1/y times h/g+1

C) x+ 1/y divided h/g+1

D) y/x+1 divided g+1/h

So let's divide  [tex]\frac{x+1}{y}[/tex] by [tex]\frac{g+1}{h}[/tex]

[tex]\frac{\left(\frac{x+1}{y}\right)}{\left(\frac{g+1}{h}\right)}[/tex]

we are allowed to flip the bottom fraction and change division sign into multiplication. So we get:

[tex]=\left(\frac{x+1}{y}\right)\cdot\left(\frac{h}{g+1}\right)[/tex]

Hence correct choice is: B) x + 1/y times h/g+1

Let's start by simplifying the given expression step-by-step:
\[ \text{Given Expression:} \quad \frac{x + \frac{1}{y}}{g + \frac{1}{h}} \]
Firstly, we will find a common denominator for the numerator and denominator of the given fraction.
For the numerator, we already have a single term x and a fraction \( \frac{1}{y} \), which can be combined without altering the denominator.
For the denominator, we have term g and a fraction \( \frac{1}{h} \). To combine these, we need to multiply both terms by h to get a common denominator.
So, the expression becomes:
\[ \frac{x + \frac{1}{y}}{g + \frac{1}{h}} = \frac{xy + 1}{y} \cdot \frac{h}{gh + 1} \]
Next, we will multiply the separated fractions across the numerator and the denominator:
\[ \frac{xy + 1}{y} \cdot \frac{h}{gh + 1} = \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \]
Now, let's consider the given options and check which one is equivalent to our simplified expression:
Option A) \( \frac{x}{y} \times \frac{h}{g} \)
This option simplifies to \( \frac{xh}{yg} \), which is not equivalent to the expression we have because we have \( xy + 1 \) in the numerator, not just \( xh \).
Option B) \( (x + \frac{1}{y}) \times \frac{h}{g+1} \)
For this option, if we simplify, we do not obtain a single fraction with the term \( xy + 1 \) in the numerator and \( y(gh + 1) \) in the denominator, instead, this option gives us \( xh + \frac{h}{y(g+1)} \), which is different from our simplified expression.
Option C) \( \frac{x + \frac{1}{y}}{h/(g + 1)} \)
To simplify this option, we take the reciprocal of the denominator and multiply it with the numerator:
\[ \frac{x + \frac{1}{y}}{h/(g + 1)} = (x + \frac{1}{y}) \times \frac{g + 1}{h} \]
\[ = \frac{(x + \frac{1}{y})(g + 1)}{h} \]
\[ = \frac{xg + x + \frac{g}{y} + \frac{1}{y}}{h} \]
\[ = \frac{xg + x + \frac{g + 1}{y}}{h} \]
This is not equivalent to our simplified expression either because it involves terms like \( xg \) and \( x \), which do not appear in our expression and does not fit the form \( \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \).
Option D) \( \frac{y/(x+1)}{g + \frac{1}{h}} \)
To simplify this option, we multiply by the reciprocal of the denominator:
\[ \frac{y/(x+1)}{g + \frac{1}{h}} = \frac{y}{x+1} \times \frac{h}{gh + 1} \]
\[ = \frac{yh}{(x+1)(gh + 1)} \]
Again, this is not equivalent to our simplified expression, since the expressions \( y/(x+1) \) and \( (xy + 1)/y \) are different.
None of the options (A, B, C, or D) match the simplified form:
\[ \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \]
Therefore, none of the given options are equivalent to the original expression \( \frac{x + \frac{1}{y}}{g + \frac{1}{h}} \).

Hello!

Answer:

x = 7

Step-by-step explanation:

Substitute y = 4 into the equation and solve for x

8x - (2 × 4) = 48

8x - 8 = 48 ( add 8 to both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Answer with explanation:

Volume of a solid right pyramid with a square base = V (units)³

                            -------------------------------------(1)

The Solid right pyramid will be in the shape of Cube.

Length of edge of Right Pyramid = y units

So,Volume of Right Pyramid which is in the shape of Cube

= (Side)³

=y³ (Units)³

                           ---------------------------------(2)

   Equating (1) and (2)

[tex]\Rightarrow y^3=V[/tex]

Answer:

B

Step-by-step explanation:

A translation of 3 units up, means adding 3 to the y- coordinate of the original points while the x- coordinates remain unchanged, that is

S(1, 1) → S'(1, 1 + 3) → S'(1, 4)

T(2, - 3) → T'(2, - 3 + 3) → T'(2, 0)

U(4, 0) → U'(4, 0 + 3) → U'(4, 3)

x=3,y=2

lkajsdfvnkkkkkk

It's a system of linear equations; let me write it out more neatly for you:

[tex]\left \{ {x + 2y = 7} \atop {x - 2y = -1}} \right.[/tex]  

Good. In order to solve a system of equations with two variables, we can find one variable and then use that variable to find the other. This wouldn't be the case if we just had one equation, note.  

Let's work on the top one first. There's multiple ways of solving this one, but here's the most simple way: isolating a single variable. The goal is to get either just x or just y on one side.  

[tex]x + 2y=7\\x = 7-2y[/tex]  

Nice. Now that we have a value of x, we can just plug it into the other equation -- since we know that x is equal to another expression, we can replace x in the other equation with the expression.  

[tex]x - 2y = -1\\(7-2y)-2y = -1\\7 - 2y - 2y = -1\\7 - 4y = -1 \\-4y = -8\\y = 2[/tex]  

Now that we have y, we can do the same thing for x. This time, however, we have the actual value of y, meaning we can just plug that in.  

[tex]x = 7 - 2y\\x = 7 - 2(2)\\x = 7 - 4 \\x = 3[/tex]  

Our solution is  

[tex]\left \{ {{x=3} \atop {y=2}} \right.[/tex]  

We can check this by plugging the values back into the equation.  

[tex]3 + 2(2) = 7\\3 + 4 = 7[/tex]  

and  

[tex]3 - 2(2) = -1\\3 - 4 = -1\\[/tex]  

That's it. There's another (easier) way to handle this specific equation, but this is the simplest way to do it.

Esther should save $125 each month to reach her goal of $3,000 in 2 years.

Esther wants to save $3,000 in 2 years and is determining the fixed monthly amount she should contribute to her savings. To find the monthly savings amount, we must divide the total savings goal by the total number of months in 2 years.

Total amount to save: $3,000
Total number of months: 2 years x 12 months/year = 24 months

Fixed monthly saving amount = Total savings goal / Total number of months
Fixed monthly saving amount = $3,000 / 24
Fixed monthly saving amount = $125

Answer:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

Solution fixed: [tex]m=17[/tex]

Micaela is 17 years old now.

Step-by-step explanation:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

To fix the error, you can set up these equations based on the information given:

[tex]m=s+2[/tex]  

[tex](m+4)+(s+4)=40[/tex]  

Solve for "s" from the first equation:

[tex]s=m-2[/tex]

Substitute this equation into the second equation:

[tex](m+4)+((m-2)+4)=40[/tex]  

Now you need to solve for "m":

[tex]m+4+(m-2+4)=40\\m+4+m+2=40\\m+m=40-4-2\\2m=34\\m=\frac{34}{2}\\\\m=17[/tex]

Micaela is 17 years old now.

Answer:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

Solution fixed: m=17

Micaela is 17 years old now.

Step-by-step explanation:

brainliest please?

Answer:

two distinct real roots

Step-by-step explanation:

The coefficients of the equation are ...

a = 1

b = -5

c = -3

So, the discriminant, b^2-4ac, has the value ...

(-5)^2 -4(1)(-3) = 25 +12 = 37

This number is positive, so the square root of it is non-zero and real. This means the two roots are real and distinct.