Solve the equation.1/8+c=4/5

Answer:

1980.

Step-by-step explanation:

John was born in  1995 - 40 = 1955.

His father was born in 1995 - 65 = 1930.

Let x  be Johns age and his father 2x

1955 + x = 1930 + 2x

1955 - 1930 = 2x - x

x =  25

So the year is 1955 + 25 = 1980..

In that year John was 25 and his father was  50.

Answer:

The answer is B, given the module of a number has always a positive value

Answer:

Answer is B.

SECOND NUMBER LINE

Step-by-step explanation:

Answer:

[tex]3r^{4}s^{5}\\-r^{4}s^{6}[/tex]

Step-by-step explanation:

The standard form of a polynomial is when its term of highest degree is at first place.

In this case, we have two variables. The grade of each term is formed by the sum of its exponents. That means both given terms have a degree of six. So, the right answers must have a higher degree.

Therefore, the right answers are the second and third choice, because their degrees are 9 and 10 respectively.

Answer:

1) [tex]3 a^3 + 8 a^2 b - b^3[/tex]

2) 93 inches

Step-by-step explanation:

1) We know that the lenghts are given by these expressions:

[tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex]

Then, we need to add them in order to find the expression that represents the total length of the rope:

- Apply Distributive property.

- Add the like terms.

Then:

[tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex]

2) Knowing that:

[tex]a=2in\\\\b=3in[/tex]

We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is:

 [tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]

Answer:

[tex]\large\boxed{C.\ y=2+x^4}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of linear function:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

============================

[tex]A.\\\\9y+3=0\qquad\text{subtract 3 from both sides}\\\\9y=-3\qquad\text{divide both sides by 9}\\\\y=-\dfrac{3}{9}\\\\y=-\dfrac{1}{3}\to m=0,\ b=-\dfrac{1}{3}[/tex]

[tex]B.\\\\y-4x=1\qquad\text{add}\ 4x\ \text{to both sides}\\\\y=4x+1\to m=4,\ b=1[/tex]

[tex]C.\\\\y=2+x^4\qquad\text{nonlinear, because}\ x\ \text{is in fourth power}[/tex]

[tex]D.\\\\x-2y=7\qquad\text{subtract}\ x\ \text{from both sides}\\\\-2y=-x+7\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-\dfrac{7}{2}\to m=\dfrac{1}{2},\ b=-\dfrac{7}{2}[/tex]

[tex]E.\\\\\dfrac{x}{y}+1=2\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{y}=1\to y=x\to m=1,\ b=0[/tex]

Answer:

Equation of the parabola: [tex]y = 2x^{2} + 4x - 3[/tex].

Axis of symmetry: [tex]x= -1[/tex].

Coordinates of the vertex: [tex]\displaystyle \left(-1, -5\right)[/tex].

Step-by-step explanation:

The axis of symmetry and the coordinates of the vertex of a parabola can be read directly from its equation in vertex form.

[tex]y = a(x-h)^{2} +k[/tex].

The vertex of this parabola will be at [tex](h, k)[/tex]. The axis of symmetry will be [tex]x = h[/tex].

The equation in this question is in standard form. It will take some extra steps to find the vertex form of this equation before its vertex and axis of symmetry can be found. To find the vertex form, find its coefficients [tex]a[/tex], [tex]h[/tex], and[tex]k[/tex].

Expand the square in the vertex form using the binomial theorem.

[tex]y = a(x-h)^{2} +k[/tex].

[tex]y = a(x^{2} - 2hx + h^{2}) +k[/tex].

By the distributive property of multiplication,

[tex]y = (ax^{2} - 2ahx + ah^{2}) +k[/tex].

Collect the constant terms:

[tex]y = ax^{2} - 2ahx + (ah^{2} +k)[/tex].

The coefficients in front of powers of [tex]x[/tex] shall be the same in the two forms. For example, the coefficient of [tex]x^{2}[/tex] in the given equation is [tex]2[/tex]. The coefficient of [tex]x^{2}[/tex] in the equation [tex]y = ax^{2} - 2ahx + (ah^{2} +k)[/tex] is [tex]a[/tex]. The two coefficients need to be equal for the two equations to be equivalent. As a result, [tex]a = 2[/tex].

Similarly, for the term [tex]x[/tex]:

[tex]-2ah = 4[/tex].

[tex]\displaystyle h = -\frac{2}{a} = -1[/tex].

So is the case for the constant term:

[tex]ah^{2} + k = -3[/tex].

[tex]k = -3 - ah^{2} = -5[/tex].

The vertex form of this parabola will thus be:

[tex]y = 2(x -(-1))^{2} + (-5)[/tex].

The vertex of this parabola is at [tex](-1, -5)[/tex].

The axis of symmetry of a parabola is a vertical line that goes through its vertex. For this parabola, the axis of symmetry is the line [tex]x = -1[/tex].

Answer:

[tex]2*10^{9}[/tex]

Step-by-step explanation:

we know that

One billion is equal to  one thousand million

1 billion is equal to 1,000,000,000

so

Multiply by 2

2 billion is equal to  2,000,000,000

Remember that

In scientific notation, a number is rewritten as a simple decimal multiplied by 10  raised to some power, n

n is simply the number of zeroes in the  full written-out form of the number  

In this problem n=9  

so

[tex]2,000,000,000=2*10^{9}[/tex]

Answer:

7/20 m^2

Step-by-step explanation:

A = l*w

   =3/5 * 7/12

Multiplying the numerators

3*7 =21

Multiplying the denominators

5*12= 60

Putting the numerator over the denominator

21/60

Divide the top and bottom by 3

7/20

Answer:

7/20

Step-by-step explanation:

Answer:

(2,2)

Step-by-step explanation:

Answer:

385.5 USD

Step-by-step explanation:

If an average car is sold for 25,700 USD, and the sales person gets 1.5% commission of it, we can easily get to the amount of money that the sales person managed to get from each sale.

The 25,700 should be divided by 100, as that is number of total percentage:

25,700 / 100 = 257

So we have 1% being 257 USD, but we need 1.5%, so we should multiple the 257 USD by 1.5%:

257 x 1.5 = 385.5

So we get a result of 385.5 USD, which is the amount the sales person makes from commissions on average per sold car.

Answer:

The perimeter of the triangle is equal to 36 cm

Step-by-step explanation:

we know that

The inscribed circle contained in the triangle BCA is tangent to the three sides

we have that

BF=BH

CF=CG

AH=AG

step 1

Find CG

we know that

CF=CG

so

CF=7 cm

therefore

CG=7 cm

step 2

Find AG

we know that

CA=AG+CG

we have

CA=15 cm

CG=7 cm

substitute

15=AG+7

AG=15-7=8 cm

step 3

Find AH

Remember that

AG=AH

we have

AG=8 cm

therefore

AH=8 cm

step 4

Find BF

Remember that

BF=BH

BH=3 cm

therefore

BF=3 cm

step 5

Find the perimeter of the triangle

P=AH+BH+BF+CF+CG+AG

substitute the values

P=8+3+3+7+7+8=36 cm

The perimeter of  ΔBCA (triangle BCA) is 36 cm

The perimeter of a triangle is the sum of the length of the three sides.

The inscribed circle contained in the triangle BCA is tangent to the three sides

Therefore,

BF = BH = 3 cm

CF = CG = 7 cm

AH = AG = 15 - 7 = 8 cm

Therefore,

perimeter = CA + BC + BA

perimeter = 15 + 3 + 7 + 3 + 8

Therefore,

perimeter = 15 + 10 + 11

perimeter = 15 + 21

perimeter = 36 cm

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Answer:

Part A)

[tex]P=\$8,500\\ r=0.052\\n=4[/tex]  

Part B) [tex]S(7)=\$12,203.47[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]S(t)=P(1+\frac{r}{n})^{nt}[/tex]  

where  

S is the Future Value  

P is the Present Value  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

in this problem we have  

[tex]P=\$8,500\\ r=5.2\%=5.2/100=0.052\\n=4[/tex]  

Part B) How much money will Marcus have in the account in 7 years?

we have

[tex]t=7\ years\\ P=\$8,500\\ r=0.052\\n=4[/tex]  

substitute in the formula above  

[tex]S(7)=8,500(1+\frac{0.052}{4})^{4*7}[/tex]  

[tex]S(7)=8,500(1.013)^{28}[/tex]  

[tex]S(7)=\$12,203.47[/tex]  

In this problem, we find that Marcus should use the values P = $8,500, r = 0.052 and n = 4 for the given savings account. After calculating, we conclude that Marcus would have approximately $11,713.69 in the account after 7 years.

This problem involves the concept of compound interest in mathematics. Let's break it down:

We use the formula S(t)=P(1+rn)^(nt):

S(7) = 8500(1 + 0.052/4)^(4*7)

By calculating the above, we find the balance after seven years to be approximately $11,713.69 when rounded to the nearest penny.

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Answer:

100/9

Step-by-step explanation:

(7*5*2/7*3)² * (5^0/2^-3)³ * 2^-9

Solution:

We know that any number with power 0 = 1

(7*5*2/7*3)² * (1/2^-3)³ * 2^-9

Now cancel out 2 by 2

= (7*5*2/7*3)² * (1/1^-3)³ * 1^-9

=(70/21)² * (1)³/(1^-3)³ * 1^-9

=(10/3)^2 * 1/1^-1 * 1/1^9

=100/9 *1 *1

=100/9....

Answer:

C

step-by-step explanation:

you just have to subtract them 9/16-1/4=8/12

Answer:

8 yards

Step-by-step explanation:

This can be illustrated from drawing it. (Attachment)

Scale-  Real : Map

          10 yard : 1 cm

        150 yard : 15 cm

        145 yard : 14.5 cm

Step 1: Draw a 7.5 cm line from origin to Point A

Step 2: Form a 2 degree angle from the origin

Step 3: Draw a 7.25 cm line 2 degree angle from the origin to Point B

Step 4: Measure the distance in cm from Point A to Point B

Step 5: Convert the distance from Point A to Point B in yards.

Therefore, the ball is 8 yards far from the goal.

!!

Answer:

The ball is 7.176 yards away from the center of the goal.

Step-by-step explanation:

Given distance between the center goal and Mark is AB = 150 yards

Distance traveled by ball at angle 2 degree off to the right from Mark is

AC = 145 yards

We have to find the distance BC in triangle ABC

Using cosine rule

[tex]BC^{2}=AB^{2}+AC^{2}-2AB\times AC\times \cos \Theta[/tex]

=>[tex]BC^{2}=[150^{2}+145^{2}-2\times 150\times 145\times \cos (2^{\circ})] yards^{2}[/tex]

=>BC^{2}=51.5 yards^{2}

=>[tex]BC=\sqrt{(51.5 yards^{2})}=7.176yards[/tex]

Thus the ball is 7.176 yards away from the center of the goal.

[tex]13 - |3x-9| = 2\\|3x-9|=11\\3x-9=11\vee 3x-9=-11\\3x=20 \vee 3x=-2\\x=\dfrac{20}{3} \vee x=-\dfrac{2}{3}[/tex]

TWO

Answer:

2

Step-by-step explanation:

[tex]13-|3x-9|=2[/tex]

Subtract 13 on both sides.

[tex]-|3x-9|=2-13[/tex]

Simplify right hand side.

[tex]-|3x-9|=-11[/tex]

Take the opposite of both sides (also known as multiply both sides by -1).

[tex]|3x-9|=11[/tex].

Let u=3x-9.

Since we have |u|=positive, we will have two solutions for x.

If we had |u|=negative, we will have no solutions for x.

If we had |u|=0, we would have one solution for x.

Answer:

[tex]\large\boxed{y=-\dfrac{8}{5}x+\dfrac{31}{5}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept[/tex]

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\--------------------------[/tex]

[tex]\text{We have:}\\\\y=\dfrac{5}{8}x-4\to m_1=\dfrac{5}{8}\\\\\text{The slope of a perpendicular line:}\ m_2=-\dfrac{1}{\frac{5}{8}}=-\dfrac{8}{5}\\\\\text{The equation:}\\\\y=-\dfrac{8}{5}x+b\\\\\text{Put the coordinates of the point (2, 3) to the equation:}\\\\3=-\dfrac{8}{5}(2)+b\qquad\text{solve for}\ b\\\\3=-\dfrac{16}{5}+b\qquad\text{add}\ \dfrac{16}{5}\ \text{to both sides}\\\\\dfrac{15}{5}+\dfrac{16}{5}=b\to b=\dfrac{31}{3}\\\\\text{Finally:}\\\\y=-\dfrac{8}{5}x+\dfrac{31}{5}[/tex]

Answer:

[tex]2(x-1)^{2}=4[/tex]

Step-by-step explanation:

we have

[tex]2x^{2} -4x-2=0[/tex]

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

Group terms that contain the same variable and move the constant to the other side

[tex]2x^{2} -4x=2[/tex]

Factor the leading coefficient

[tex]2(x^{2} -2x)=2[/tex]

[tex]2(x^{2} -2x+1)=2+2[/tex]

[tex]2(x^{2} -2x+1)=4[/tex]

Rewrite as perfect squares

[tex]2(x-1)^{2}=4[/tex] -----> this is the answer

The vertex is the point (1,-4)

(9 - 4i)(2 + 5i)

To solve this question you must FOIL (First, Outside, Inside, Last) like so

First:

(9 - 4i)(2 + 5i)

9 * 2

18

Outside:

(9 - 4i)(2 + 5i)

9 * 5i

45i

Inside:

(9 - 4i)(2 + 5i)

-4i * 2

-8i

Last:

(9 - 4i)(2 + 5i)

-4i * 5i

-20i²

Now combine all the products of the FOIL together like so...

18 + 45i - 8i - 20i²

***Note that i² = -1; In this case that means -20i² = 20

18 + 45i - 8i + 20

Combine like terms:

38 - 37i

^^^This is your answer

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

10,000 m/square

Step-by-step explanation:

we know that

A hectare is a unit of area equal to [tex]10,000\ m^{2}[/tex]

The symbol is Ha

Verify each case

case 1) 10,000 m/square

The option is true

case 2) 100 m/square

The option is false

case 3) 100,000 m/square​

The option is false

Answer:

f(8) = 8.25(1.1)^7; f(8) = 16.077

Step-by-step explanation:

In order to calculate the explicit formula we need to look at the y coordinates. All the options list the formula of a Geometric Sequence, so we will find which sequence defines the given coordinates:

The sequence is:

8.25, 9.075, 9.9825, 10.98075

f(1) = First term of the Sequence = 8.25

r = Common Ratio = Ratio of two consecutive terms = [tex]\frac{9.075}{8.25}[/tex] = 1.1

The explicit formula for a geometric sequence is:

[tex]f(n)=f(1)(r)^{n-1}[/tex]

Using the values, we get:

[tex]f(n)=8.25(1.1)^{n-1}[/tex]

For 8th term, we have to replace n by 8:

[tex]f(8)=8.25(1.1)^{8-1}\\\\ f(8)=8.25(1.1)^{7} \\\\ f(8)=16.077[/tex]

So, second option gives the correct answer: f(8) = 8.25(1.1)^7; f(8) = 16.077

Answer:

B // f(8) = 8.25(1.1)^7; f(8) = 16.077

Step-by-step explanation:

I'm Pretty Sure She's Got It ^^^

Answer:

[tex]f^{-1}(x)=-2x+6[/tex].

Step-by-step explanation:

[tex]y=f(x)[/tex]

[tex]y=3-\frac{1}{2}x[/tex]

The biggest thing about finding the inverse is swapping x and y.  The inverse comes from switching all the points on the graph of the original.  So a point (x,y) on the original becomes (y,x) on the original's inverse.

Sway x and y in:

[tex]y=3-\frac{1}{2}x[/tex]

[tex]x=3-\frac{1}{2}y[/tex]

Now we want to remake y the subject (that is solve for y):

Subtract 3 on both sides:

[tex]x-3=-\frac{1}{2}y[/tex]

Multiply both sides by -2:

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

We could leave as this or we could distribute:

[tex]-2x+6=y[/tex]

The inverse equations is [tex]y=-2x+6[/tex].

Now some people rename this [tex]f^{-1}[/tex] or just call it another name like [tex]g[/tex].

[tex]f^{-1}(x)=-2x+6[/tex].

Let's verify this is the inverse.

If they are inverses then you will have that:

[tex]f(f^{-1}(x))=x \text{ and } f^{-1}(f(x))=x[/tex]

Let's try the first:

[tex]f(f^{-1}(x))[/tex]

[tex]f(-2x+6)[/tex]  (Replace inverse f with -2x+6 since we had [tex]f^{-1})(x)=-2x+6[/tex]

[tex]3-\frac{1}{2}(-2x+6)[/tex]  (Replace old output, x, in f with new input, -2x+6)

[tex]3+x-3[/tex]  (I distributed)

[tex]x[/tex]

Bingo!

Let's try the other way.

[tex]f^{-1}(f(x))[/tex]

[tex]f^{-1}(3-\frac{1}{2}x)[/tex] (Replace f(x) with 3-(1/2)x since [tex]f(x)=3-\frac{1}{2}x[/tex])

[tex]-2(3-\frac{1}{2}x)+6[/tex] (Replace old input, x, in -2x+6 with 3-(1/2)x since [tex]f(x)=3-\frac{1}{2}x[/tex])

[tex]-6+x+6[/tex] (I distributed)

[tex]x[/tex]

So both ways we got x.

We have confirmed what we found is the inverse of the original function.

Answer:

[tex]\laege\boxed{f^{-1}(x)=-2x+6}[/tex]

Step-by-step explanation:

[tex]f(x)=3-\dfrac{1}{2}x\to y=3-\dfrac{1}{2}x\\\\\text{Exchange x to y and vice versa:}\\\\x=3-\dfrac{1}{2}y\\\\\text{Solve for}\ y:\\\\3-\dfrac{1}{2}y=x\qquad\text{subtract 3 from both sides}\\\\-\dfrac{1}{2}y=x-3\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\cdot\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=-2x-3(-2)\\\\y=-2x+6[/tex]

Answer:

[tex]\large\boxed{\dfrac{1}{36a^4b^{10}}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{\left(2a^{-3}b^4\right)^2}{\left(3a^5b\right)^{-2}}\right)^{-1}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\dfrac{\left(3a^5b\right)^{-2}}{\left(2a^{-3}b^4\right)^2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\dfrac{3^{-2}(a^5)^{-2}b^{-2}}{2^2(a^{-3})^2(b^4)^2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{3^{-2}a^{(5)(-2)}b^{-2}}{4a^{(-3)(2)}b^{(4)(2)}}=\dfrac{3^{-2}a^{-10}b^{-2}}{4a^{-6}b^8}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]

[tex]=\dfrac{3^{-2}}{4}a^{-10-(-6)}b^{-2-8}=\dfrac{3^{-2}}{4}a^{-4}b^{-10}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{3^2}\cdot\dfrac{1}{4}\cdot\dfrac{1}{a^4}\cdot\dfrac{1}{b^{10}}=\dfrac{1}{36a^4b^{10}}[/tex]

Answer:

1 / 36a^4 b^10

Step-by-step explanation:

Neither of those two graphs do the trick, but if I saw the rest of the answer choices, then I would be happy to assist you.

Answer:

[tex]\large\boxed{(2x^4y^3)(6x^3y^2)=6x^7y^5}[/tex]

Step-by-step explanation:

[tex](2x^4y^3)(6x^3y^2)\\\\=(2)(3)(x^4x^3)(y^3y^2)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=6x^{4+3}y^{3+2}\\\\=6x^7y^5[/tex]

Answer:

60 nickles and 30 dimes

Step-by-step explanation:

60 $0.05=3.00

30 $.10=3.00

60+30=90

In the box, there are 30 dimes and 60 nickels, as determined by solving a system of equations based on the total number of coins and their value.

The box contains both dimes and nickels, totaling an amount of money of $6.00. Because a dime is worth $0.10 and a nickel is worth $0.05, we can set up a system of equations to solve this problem.

Let's denote the number of dimes as x and the number of nickels as y. Thus, our equations are x + y = 90 (since the total number of coins is 90) and 0.10x + 0.05y = 6 (since the total value of the coins is $6.00).

Solving these equations will give us the number of dimes and nickels in the box. Doubling the second equation gives us 0.20x + 0.10y = 12. We can subtract the first equation from this to solve for x, giving us x = 30. Substituting x=30 into the first equation, y = 90 - 30, so y = 60. So, there are 30 dimes and 60 nickels in the box.

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Step-by-step explanation:

I have answered ur question

To make y the subject, distribute and simplify the equation, then isolate y on one side by performing the necessary operations.

To make y the subject of the equation X = 5y + 4/2y - 3, we need to isolate y on one side of the equation.

Therefore, y = (X + 1)/5 is the solution.

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Answer:

=6√3 the third option.

Step-by-step explanation:

We can use the Pythagoras theorem to find the value of y. We need two equations that include y.

a²+b²=c²

c=9+3=12

x²+y²=12²

x²=144 - y².........i (This is the first equation)

We can also express it in another way but let us find the perpendicular dropped to c.

perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.

y²=(x²-9)+9²

y²=x²+72

x²=y²-72....ii( this is the second equation

Let us equate the two.

y²-72=144-y²

2y²=144+72

2y²=216

y²=108

y=√108

In Surd form √108=√(36×3)=6√3

y=6√3