Liz is 36 years old. Liz's age is 3 years older than two times Rylan's age. Let x represent Rylan's age. Which equation can be used to solve for Rylan's age?
if someone does answer, could you write out the steps? >.

Answer:

6 weeks

Step-by-step explanation:

Let x represent the weeks

[tex]25=10+ (10x-7.5x = 2.5)[/tex]

[tex]25-10=2.5x = 15[/tex]

[tex]\frac{15}{2.5}=x \\(150/25)\\x=6[/tex]

Carol and Cathy will have same saved amount after 6 weeks.

What do you mean by algebraic expressions ?

Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.

It is given that Carol started with $25 and saved per week an amount of $7.50 whereas Cathy started with $10 and saved per week amount of $10.

Let's assume that after x no. of weeks they will have same saved amount.

So , we can write an algebraic expression which is :

25 + (7.5 × x) = 10 + (10 × x)

Now , reordering the like terms we get :

10x - 7.5 x = 25 - 10

Simplifying this we get :

2.5 x = 15

or

x = 15 ÷2.5

or

x = 6 weeks

Therefore , Carol and Cathy will have same saved amount after 6 weeks.

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Answer:

[tex]\frac{x-3w}{2}[/tex] = t

x < -2

x > 6

Step-by-step explanation:

For the first equation, let's solve for t.

Subtract 3w from both sides of the equation.

x - 3w = 2t

Now divide by 2.

[tex]\frac{x-3w}{2}[/tex] = t

t is equal to [tex]\frac{x-3w}{2}[/tex].

For the first inequality, let's solve for x.

First, subtract 1 from both sides, then divide by 3. The result is:

x < -2.

For the second inequality:

First add 5 to both sides, then divide by 2. The result is:

x > 6.

The compound inequality is as follows:

Solutions can be true if x is less than -2, or greater than 6.

We know that:

[tex]\large\tex\text{Circumference of circle} = 2\pi r = 35 \dfrac{13}{21} \ \tex\text{inches}[/tex]

[tex]\large \pi = \dfrac{22}{7}[/tex]

Somehow, we need to find the radius of the circle. To do that, we need to isolate 'r'.

Isolating 'r':

To isolate "r", we need to divide both sides by 2, then divide both sides by 22/7. You can also multiply 22/7 and 2 and then divide the result both sides to isolate "r".

Step-1: Divide both sides by 2.

[tex]2\pi r = 35 \dfrac{13}{21} \ \tex\text{inches} \\\\\\\ \dfrac{2\pi r}{2} = 35 \dfrac{13}{21} \div 2 \\\\\\ \pi r = \dfrac{35 \times 21 + 13}{21} \div 2 \\\\\\\pi r = \dfrac{748}{21} \times \dfrac{1}{2} \\\\\\\ \pi r = \dfrac{374}{21}[/tex]

Step-2: Divide π both sides.

[tex]\dfrac{\pi r}{\pi} = \dfrac{374}{21} \div \pi \\\\\\ r = \dfrac{374}{21} \div \dfrac{22}{7} \\\\\\ r = \dfrac{374}{21} \times \dfrac{7}{22} \\\\\\ r = \dfrac{17}{3}[/tex]

Now, let's multiply the radius by 2 to obtain the diameter.

Obtaining the diameter:

[tex]\tex\text{Diameter = 2(Radius)} \\\\\\ \tex\text{Diameter} = 2(\dfrac{17}{3} ) \\\\\\ \boxed{\bold{Diameter = \dfrac{34}{3}}}[/tex]

[tex]\\ \rm\rightarrowtail \pi d=35\dfrac{13}{21}[/tex]

[tex]\\ \rm\rightarrowtail \pi d=\dfrac{748}{21}[/tex]

[tex]\\ \rm\rightarrowtail d=748/21\pi[/tex]

[tex]\\ \rm\rightarrowtail d=11.34in[/tex]

Answer:

Sin theta= a/c

= 5/7.8

= 0.64

= 1

Step-by-step explanation:

Lets find the hypotenuse first by applying Pythagorean theorem.

a^2+b^2=c^2

(6)^2+(5)^2=c^2

36+25=c^2

61=c^2 (FIND SQUARE ROOT)

7.8=c

Sin theta= a/c

= 5/7.8

= 0.64

= 1

Cos theta= b/c

= 6/7.8

Tan theta= a/b

= 5/6

Answer:

   a = 0 makes the equation a linear equation, not quadratic

Step-by-step explanation:

A polynomial expression is quadratic if and only if its highest degree is 2. If the coefficient of the squared term is zero, then the polynomial does not contain a term of degree 2, so is not a quadratic. The coefficient of the squared term must be non-zero.

Answer:

7.5%

Step-by-step explanation:

one year has 12 months...and in one month the person saves 200

so in one year it will be 200×12 = 2400

%save=total saves/total earning×100

= (2400/32000)×100 = 7.5%

I hope this will help!

Answer:

the 2nd and last options

Step-by-step explanation:

Answer:

B and F

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

Vertex of function f(x)

From inspection of the graph, the vertex of f(x) is (2, 1)

Vertex of function g(x)

Given:  [tex]g(x)=2x^2-8x+1[/tex]

Standard form of a parabola is [tex]y=ax^2+bx+c[/tex]

Vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)

To convert from standard to vertex form, complete the square.

Set the equation to zero:

[tex]\implies 2x^2-8x+1=0[/tex]

Add 7 to both sides:

[tex]\implies 2x^2-8x+8=7[/tex]

Factor out common term 2 on left side:

[tex]\implies 2(x^2-4x+4)=7[/tex]

Factor expression inside brackets:

[tex]\implies 2(x-2)^2=7[/tex]

Subtract 7 from both sides:

[tex]\implies 2(x-2)^2-7=0[/tex]

Therefore:

[tex]g(x)=2(x-2)^2-7[/tex]

So the vertex of g(x) is (2, -7)

Solution

y-value of the vertex of f(x) = 1

y-value of the vertex of g(x) = -7

y-value of vertex of f(x) subtracted from the y-value of the vertex of g(x):

-7 - 1 = -8

Answer:

A

Step-by-step explanation:

so times it by two because there's two friends. Divide the numerator by 2 which is one there's Ur answer or u could just divide it by two which is basically timing the denominator

Answer:

3.349

Step-by-step explanation:

Answer:

Step-by-step explanation:

i honesty dont know if so i would help

Answer:

A, D, E are equivalent expressions.

Step-by-step explanation:

A)

[tex]\dfrac{2}{3}a+\dfrac{5}{3}b + ( 8 + 4) - 4 =\dfrac{2}{3}a +\dfrac{5}{3}b + 12 - 4\\\\=\dfrac{2}{3}a+\dfrac{5}{3}b + 8\\\\[/tex]

Here, 8+4 = 12 and when we subtract 4 from 12, we get 8.

[tex]D) 6*(\dfrac{2}{3}a+\dfrac{5}{3}b+8)*\dfrac{1}{6}=6*\dfrac{1}{6}(\dfrac{2}{3}a+\dfrac{5}{3}b+8)\\\\\\=\dfrac{2}{3}a+\dfrac{5}{3}b + 8[/tex]

Here, 6 and 1/6 will be cancelled and we get 1.

[tex]E) \dfrac{2}{3}a+\dfrac{5}{3}b+ 0*\dfrac{1}{3}c+8=\dfrac{2}{3}a+\dfrac{5}{3}b+0+8\\\\=\dfrac{2}{3}a+\dfrac{5}{3}b+8[/tex]

0 multiplied by any value is 0. So, term multiplied by 0 = 0

I had calculated and answer is jackson

Answer:

B. Faith

Step-by-step explanation:

Casey paid $2.75 per gallon

55/20= 2.75

Jackson: 33.60/12 = 2.80

Faith: 30.25/11 = 2.75

Xavier: 39/15 = 2.60

Dominic: 39.20/14 = 2.80

Answer:

10

Step-by-step explanation:

Answer:

1. C

2. X=8

3. The unknown number is what the bag of apples started out with

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

[tex]y = 65[/tex]

[tex]x + 65 = 180[/tex]

[tex]x = 180 - 65[/tex]

[tex]x = 115[/tex]

[tex]z = x = 115[/tex]

X+X^2= 132 6^2 then just divide your answer by the whole number

Answer:

c

Step-by-step explanation:

Answer:

x₁ > x₂

Step-by-step explanation:

Both actions imply a parable trajectories, since both are projectile shot cases.

Let´s call x₁ maximum distance in the first case

The maximum height is just in the middle of the curve, therefore x₁ the maximum horizontal distance is equal to 60 feet.

In the second case, the parable curve is modeled by:

y = x₂*( 0.08 - 0.002x₂)    or  y = 0.08*x₂ - 0.002*x₂²

A second degree equation, solving for x₂ and dismissing the value x₂ = 0

we get:

y = 0       ⇒    x₂*( 0.08 - 0.002x₂) = 0    x₂ = 0

And 0,08 - 0.002*x₂ = 0

- 0.002*x₂ = - 0.08

x₂ = 0.08/0.002

x₂ = 40 f

Then  x₁ > x₂

Answer:

164.5

Step-by-step explanation:

987/6

164.5

The Quotient when 987 is divided by 6 is 164.

The dividend is the number that is being divided, and the divisor is the number that is being divided. The quotient is the end result of division.

Since we need to find the quotient of 987 when it is divided by 6. Therefore, we can write the quotient as,

Quotient = 987 ÷ 6

               = 987 / 6

               = 164

Hence, When we divide 987 by the 6 we will get 164 as Quotient.

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Answer:

1234567890

Step-by-step explanation:

Answer:

1234567890

Step-by-step explanation:

Answer:

$4.07

Step-by-step explanation:

50-17.49=32.51

32.51/8=4.0637

round that up

Answer:

(0,-4)

Step-by-step explanation:

Just took the quiz

Using the t-distribution, as we have the standard deviation for the population, it is found that the confidence interval estimate is (4044.2, 4653.4).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 12 - 1 = 11 df, is t = 2.7181.

As for the other parameters, they are given by:

[tex]\overline{x} = 4348.8, s = 388.2, n = 12[/tex]

Hence:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 4348.8 - 2.7181\frac{388.2}{\sqrt{12}} = 4044.2[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 4348.8 + 2.7181\frac{388.2}{\sqrt{12}} = 4653.4[/tex]

The confidence interval estimate is (4044.2, 4653.4).

To learn more about the t-distribution, you can check https://brainly.com/question/16162795