Todd is 3 years older than his brother Jack. If Jack is x years old and Todd is y years old, write a rule that relates their ages over time. When Jack is 28 years old, how old will Todd be?

Answer:

(f-g)(x) = 7x+5

Step-by-step explanation:

Given that,

f(x)=2x+2 and g(x) =-5x-3

To Find:

Solution:

[tex](f - g)(x)[/tex]

Re-write as:

Now substitute the values on the polynomial/function:

Simplify using this order:BPEMDAS

Hence,(f-g)(x) = 7x+5.

Answer:

If the denominators are equal for all of the fractions, you can simply look at the numerator and order them. If the denominators aren't equal, you'll have to find the lcm (lowest common multiple), for example, if we have the fractions 3/6 and 1/4, we would find the lcm of 6 and 4, which is 12 and multiply the numerators accordingly. So the fractions would then become 6/12 and 3/12, this makes it easier for you to figure out their order from least to greatest.

Goodluck for your finals :)

The number of possible combinations of 7 objects taken 4 at a time is 35. Then the correct option is D.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The number of possible combinations of 7 objects taken 4 at a time.

so, the number of the combination is given as

[tex]^7C_4 = \dfrac{7!}{4!(7-4)!} \\\\\\^7C_4 = \dfrac{7!}{4!(3)!} \\\\\\^7C_4 = \dfrac{7 \times 6\times 5\times 4!}{4!(3\times 2)} \\\\\\^7C_4 = 35[/tex]

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Answer:

D. 35

Hope this helps!

Step-by-step explanation:

Answer:

d(v) =2.15v^/25.116

Step-by-step explanation:

Answer:

first 1  is .39
second one is C

Step-by-step explanation:

Answer:

6/12 or 1/2 or 50% or 0.5

Step-by-step explanation:

You have two 6-sided dice, and there are 3 odd numbers on each.

So, you put 6 on top, (the total number of odd outcomes) and 12 on the bottom. (12 total outcomes for both dice.) This simplifies to 1/2 or 50% or .5.

We need to prove

[tex]\frac{\tan A+\sin A}{\tan A-\sin A}=\frac{\sec A+1}{\sec A-1}[/tex]

[tex]\text{LHS}=\frac{\tan A+\sin A}{\tan A-\sin A}\\\\=\frac{\frac{\sin A}{\cos A}+\sin A}{\frac{\sin A}{\cos A}-\sin A}\\\\=\frac{\sin A+\sin A \cos A}{\sin A-\sin A \cos A}\\\\=\frac{\sin A(1+\cos A)}{\sin A(1-\cos A)}\\\\=\frac{1+\cos A}{1-\cos A}\\\\=\frac{1+\frac{1}{\sec A}}{1-\frac{1}{\sec A}}\\\\=\frac{\sec A+1}{\sec A-1}\\\\ =\text{RHS}[/tex]

The true statement is Peter walks at a rate of 13 over 4 miles per hour.

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases. When the hour Peter walks increases, the distance he walks also increases.

Here are the options:

Peter walks at a rate of StartFraction 4 over 13 EndFraction miles per hour.

Peter walks at a rate of 4 miles per hour.

Peter walks at a rate of StartFraction 13 over 4 EndFraction miles per hour.

Peter walks at a rate of 13 miles per hour.

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Answer:

24

Step-by-step explanation:

7 hours = 420 mins (7×60)

420-60=360 (time taken for lunch)

15mins=one ride

360÷15=24 rides

Answer:

opotion has not correct answer

answer is 15.

Answer:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

Step-by-step explanation:

[tex]\left(\sqrt{3}\right)\left(\sqrt[5]{3}\right)=\sqrt[10]{3^7}\quad[/tex]

(√3)([tex]\sqrt[5]{3}[/tex]) = √3 · [tex]\sqrt[5]{3}[/tex]

{√3 = [tex]3^{\frac{1}{2}}[/tex]}                 {radical rule: [tex]\sqrt{x}=x^1^/^2[/tex]}

[tex]\sqrt3[/tex][tex]\sqrt[5]{3}[/tex] =  [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex]

{[tex]\sqrt[5]{3}[/tex] = [tex]3^{\frac{1}{5}}[/tex]}                  {radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex]}

 [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex] =   [tex]3^{\frac{1}{2}}[/tex] · [tex]3^{\frac{1}{5}}[/tex]     {exponent rule:  [tex]a^x*a^y=a^x^+^y[/tex]}

                (1/2 + 1/5 = 5/10 + 2/10 = 7/10)

              [tex]=3^\frac{7}{10}[/tex]        {opposite of radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex] ;  [tex]x^\frac{a}{b}=\sqrt[b]{x^a}[/tex]}

             = [tex]\sqrt[10]{3^7}[/tex]

so, the simplified version of this equation can either be written as:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

hope this helps!!

(I can't clearly see the last option, but if it's either of these, then it's correct)

Using the slope concept, it is found that the change of elevation for a car at the end of the 5 mile drive is of 0.3672 miles.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(4.2º) = h/5

h = 5 x tan(4.2º)

h = 0.3672.

The change of elevation for a car at the end of the 5 mile drive is of 0.3672 miles.

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Answer:

12 is the correct answer

The Correct Question is ......

Question :

Choose the simplified form of  the fifth term of  ⁶C₄ (2x)² (-y²)⁴

Answer: D. 60x²y⁸ is the simplified form of the fifth term of the

expansion ⁶C₄ (2x)² (-y²)⁴.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

According to the Given Expression,

⁶C₄ (2x)² (-y²)⁴

The value of the combination can be written as,

[tex]= [\frac{6!}{4!(6-4)!} ] (2x)^{2} (-y^{2})^{4}[/tex]

= 15 (4x²)  (-y²)⁴

The value of y can be written as,

= 15 (4x²)  y⁸

= 60 x²y⁸

Therefore,

The value of the expression ⁶C₄ (2x)² (-y²)⁴ is 60x²y⁸.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{First Inequality :} [/tex]

[tex]\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 2x - 10 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 10 + 4 > x + 2x[/tex]

[tex]\qquad \tt \rightarrow \: - 6 > 3x[/tex]

[tex]\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x[/tex]

[tex]\qquad \tt \rightarrow \: - 2 > x[/tex]

[tex]\qquad \tt \rightarrow \: \therefore x < - 2[/tex]

[tex] \textsf{Second Inequality :} [/tex]

[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)[/tex]

[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24[/tex]

[tex]\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 36 < 9x[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{36}{9} < x[/tex]

[tex]\qquad \tt \rightarrow \: 4 < x[/tex]

[tex]\qquad \tt \rightarrow \: \therefore x > 4[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

An equation is formed of two equal expressions. The given equation is not true.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The complete question is: Check whether the given equation is true or not?cos2pi/7+cos4pi/7+cos8pi/7=1/8.

To know if the given equation, [tex]cos\dfrac{2\pi}{7}+cos\dfrac{4\pi}{7}+cos\dfrac{8\pi}{7}=\dfrac18[/tex] is true or not, both the sides of the equation are needed to be solved separately.

The value of [tex]cos\dfrac{2\pi}{7}+cos\dfrac{4\pi}{7}+cos\dfrac{8\pi}{7}[/tex] when simplified is equal to -0.5, or the value can be written as -(1/2).

Since the right side of the equation is equal to -1/2, while the right side of the equation is 1/8. Thus, the given equation is not true.

Hence, the given equation is not true.

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If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get

[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]

Integrate both sides:

[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]

Use the initial condition to solve for [tex]C[/tex] :

[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]

Then the particular solution to the initial value problem is

[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]

(A)

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

Work Shown:

x = number of quarters

3x = number of dimes

0.25x = value of just the quarters, in dollars

0.10(3x) = 0.30x = value of just the dimes, in dollars

0.25x+0.30x = 0.55x = total value in dollars

0.55x = 9.35

x = (9.35)/(0.55)

x = 17

Alison has 17 quarters and 3x = 3*17 = 51 dimes

17 quarters = 17*0.25 = $4.25

51 dimes = 51*0.10 = $5.10

17 quarters + 51 dimes = $4.25 + $5.10 = $9.35

The answers are confirmed.

Answer: C: 5

Step-by-step explanation:

Answer:

Domain & Range are both all real numbers.

Step-by-step explanation:

i

If this was a traditional parabola, the range would be y<=4. However, the arrow on the left going back up means eventually y will go to both positive & negative infinity.

Answer:

Area = 168 cm²

Step-by-step explanation:

**Please note that there is an error in the drawing of the given parallelogram.  In order for the parallelogram to have the given shape, the diagonal AC is actually 22.5 cm in length, whereas diagonal DB is 15 cm in length (see attached diagram). Therefore, I shall be using the attached diagram for my calculations.  However, please note that due of the properties of a parallelogram, the final answer will be the same, regardless of which diagonal is used.**

To calculate the area of a parallelogram, we would usually multiply the base by the perpendicular height.  As the perpendicular height is unknown in the given parallelogram, use the following formula:

[tex]\textsf{Area of parallelogram} = ab \sin (x)[/tex]

where:

As the diagonal of the parallelogram is given, use the cosine rule to calculate the measure of the included angle ∠DCB.

Cosine Rule (for finding angles)

  [tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

From inspection of the given diagram:

Substitute the given values into the cosine rule formula and solve for ∠ABC:

[tex]\implies \sf \cos(DCB)=\dfrac{13^2+14^2-15^2}{2(13)(14)}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{140}{364}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{5}{13}[/tex]

[tex]\implies \sf \angle DCB=67.38013505...^{\circ}[/tex]

Substitute the found angle and the length of the parallel sides into the area formula:

[tex]\begin{aligned}\textsf{Area of parallelogram} & = ab \sin (x)\\\\\implies \textsf{Area} & = \sf (13)(14) \sin (DCB)\\& = \sf (13)(14) \left(\dfrac{12}{13}\right)\\& = \sf 168\:\:cm^2\end{aligned}[/tex]

Therefore, the area of the given parallelogram is 168 cm².

a) the correct expression for the perimeter of the shape is B

The inequality which represents the situation is; |x - 7| < 20 and the solution is; 27 > x > -13.

Since the number is less than 20 units away from.the number 7 on the number line, it follows.from interpretation that the inequality is;

|x - 7| < 20

Hence; x-7 < 20; x < 27

Or

-x + 7 < 20

-x < 13

x > -13

Hence, the solution of the inequality is; 27 > x > -13.

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Answer:

28 portraits

Step-by-step explanation:

Let's first figure out how many portraits Lamy can paint in 1 week, which is his unit rate. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.

In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is [tex]\frac{84 \text \: portraits}{6 \text \: weeks}[/tex] = 14 paintings per week.

Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a directly proportional relationship, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.

Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.

Hope this helps!

Answer:

a=10w +50

Step-by-step explanation:

a= amount

w= weeks

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Answer:

Adjacent sides are in the ratio 5 : 12

That means,

Let length = 12x and breadth = 5x

Perimeter = 34

2(l+b) = 34

12x + 5x = 17

17x = 17

x = 1

Lenth =12 cm

Breadth = 5 cm

By Pythagorean theorem

The length of the diagonal of rectangle = 13 cm

Step-by-step explanation:

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Answer:

-92/35

Step-by-step explanation:

-3 + 4/7 - 1/5 =

-21/7 + 4/7 - 1/5 =

-(21*5) / (7*5) + (4*5)/(7*5) - (1*7)/(5*7) =

-105/35 + 20/35 - 7/35 =

-105+20-7 / 35 = -92/35

Answer:

8/7

Step-by-step explanation:

-convert the mixed fractions into improper fractions

-find the LCD (least common denominator)

-solve!

-65/7-(-73/7)

8/7

mixed number form: 1 1/7

hope this helps!!

Answer:

8/7

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 is the intersecting point which states p intersect q giving both tennis and basketball players