Frank weighs 160 pounds and is on a diet to gain 2 pounds a week so that he can make the football team. John weighs 208 pounds and is on a diet to lose 3 pounds a week so that he can be on the wrestling team in a lower weight class. If Frank and John can meet these goals with their diets, when will they weigh the same, and how much will they weigh at that time? (Hint: Solve for x and y and make sure you write a complete sentence for an answer)

Answer: 14-13i

Step-by-step explanation:

Answer:

14 - 13i

Step-by-step explanation:

We MUST do the work inside parentheses before anything else.

Step 1:  evaluate i^2:   (2i-1)(i^2-3i-7) =  (2i-1)(-1 -3i -7)

Step 2:  combine like terms inside the parentheses:  (2i-1)(-8 - 3i)

Step 3:  perform the indicated multiplication of binomials:

             -16i + 6 + 8 + 3i

Step 4:  combine like terms of the above expression:  14 - 13i

Answer:

Inequality to determine number of glass sets: 10x + 230 ≥ 498

Solved inequality: x ≥ 26.8 (She needs to buy at least 27 sets)

Step-by-step explanation:

In order to write an inequality to represent this situation, you must first identify the important information:

- The restaurant needs 498 glasses total at the least

- They already have 230 glasses

- Each set of glasses has 10 glasses

Now, you can write an inequality to represent this situation:

498 (needed glasses) ≤ 230 (glasses already owned) + 10x (number of glasses in one set (x))

You can rewrite it as 10x + 230 ≥ 498 so that x is on the left and it is ordered by variable exponential value. Now you have the inequality to represent the situation, so to find the number of sets of glasses Brooklyn could buy, you need to isolate x:

10x + 230 ≥ 498 (given)

10x ≥ 268 (subtract 230 from both sides)

x ≥ 26.8 (divide both sides by 10)

So, Brooklyn needs to buy at least 27 sets since she can't buy 4/5 of a set.

Answer:

10x + 230 ≥ 498

Step-by-step explanation:

Answer:

[tex]6x-6y-16=0[/tex]

Step-by-step explanation:

Consider the following system of equations:

[tex]a_1x+b_1y+c_1=0\\\\a_2x+b_2y+c_2=0[/tex]

The system of equations has infinite solutions if [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

One equation is [tex]3x-3y=8[/tex]

[tex]3x-3y-8=0[/tex]

Take another equation as [tex]6x-6y-16=0[/tex]

So, the two equations are [tex]3x-3y-8=0[/tex] and [tex]6x-6y-16=0[/tex]

[tex]a_1=3,b_1=-3,c_1=-8,a_2=6,b_2=-6,c_2=-16[/tex]

[tex]\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}\\ \frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\\ \frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}[/tex]

So,

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

Therefore, another equation can be [tex]6x-6y-16=0[/tex]

Answer:

D.115

Step-by-step explanation:

Use the exterior angle of a triangle theorem which states that the exterior angle of a triangle is equal to the sum of the opposite interior angles meaning D=C+B

Answer:

A. P = 3.3w

Step-by-step explanation:

A. P = 3.3w

B. P = 0.3w

C. P = 3.6w

D. P = 12w

P = price of the cereal

w = weight of the cereal

p = $3.60

w = 12-ounce

3.60p = 12w

Divide both sides by 3.60

3.60p / 3.60 = 12w / 3.60

P = 3.3w

The correct answer is A. P = 3.3w

Answer: 20 hrs

Step-by-step explanation:

Answer:

-3+7=4 is the answer if thats what you is looking for

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Scale factor is the ratio of the length of one side of a point/figure to a similar side in another point or figure.

The scale factor can either be less than one(1) or greater than one(1) depending on the figure/ point you begin from when finding the scale factor.

Hence you can find the scale factor for a point with 2 different scale factors

Answer: approximately 15

Step-by-step explanation:

Answer:

radius = 5.48ft

Step-by-step explanation:

The formula for the circumference of a circle is: C = πr² or pie times the radius squared.

Now that we know this, we can plug in the equation.

94.25 = πr²

÷π         ÷π

30 = r²

√30 = √r²

5.48 = r

So, the radius of the circle is 5.48 ft

Answer:

Step-by-step explanation:

Antonio’s rate is 1/6 while Emilia’s rate is 1/4 while working alone, together they will complete the job when.

t/6+t/4=1 making common denominators

(t/6)(2/2)+(t/4)(3/3)=1

(2t+3t)/12=1

5t=12

t=2.4 hours (or 2 hours and 24 minutes)

Answer:

On the sixth day (10 - 4), the worm was 2.5mm long.

Step-by-step explanation:

Giving the following information:

Future Value= 40mm

Present Value= 2.5mm

Number of periods (n)= ?

Growth rate= 100% per day

First, we need to calculate the number of days it will take to grow from 2.5mm (PV) to 40mm (FV):

n= ln(FV/PV) / ln(1+i)  

n= ln (40 / 2.5) / ln (2)

n= 4

It will take 4 days.

On the sixth day (10 - 4), the worm was 2.5mm long.

Answer:

14800 sq yd

Step-by-step explanation:

area of a trapeziod

Answer:

76+76=152

Step-by-step explanation:

Answer: Not a right-angled triangle

Step-by-step explanation:

Given

The sides of a triangle are [tex]7\ m, 8\ m, \text{and}\ 10\ m[/tex]

For a right-angle triangle, it must satisfy the Pythagoras theorem

[tex]a^2+b^2=c^2[/tex]

i.e. the square of the larger side must be equal to the sum of the square of the remaining two sides

Here,

[tex]\Rightarrow 7^2+8^2\ ?\ 10^2\\\Rightarrow 49+64\ ?\ 100\\\Rightarrow 113\neq 100[/tex]

Therefore, it is not a right-angle triangle

Answer:

A/C ≅ 2

Step-by-step explanation:

diameter of circle d = 8 in

Circumference of the circle C= 25 in

Let us assume we have to find the area of the circular lid  A = [tex]\frac{\pi}{4}d^2[/tex]

⇒ A= [tex]\frac{\pi}{4}\times8^2= 50.24 in^2[/tex]

Therefore ratio of area to circumference A/C = 50.24/25 = 2.0096≅2

Answer:

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Step-by-step explanation:

Answer:

John is currently 6 years old.  

You can find this by setting John's original age as x and Jose's original age as x + 6. Then we can set up an equation adding two to both.  

John's new age = x + 2

Jose's new age = x + 8

Now we can multiply John's new age by two and set equal to Jose's age, since Jose's new age is twice as much as John's.  

2(x + 2) = x + 8

2x + 4 = x + 8

x + 4 = 8

x = 4

This means John's original age is 4 and his new age is 6.  

Step-by-step explanation:

[tex]5x + x + y + 2x = 180 \\ y = 28 \\ 5x + x + 28 + 2x = 180 \\ 8x + 28 = 180 \\ 8x = 180 - 28 \\ 8x = 152 \\ x = 19[/tex]

Answer:

A D and E

Step-by-step explanation:

The statements true about the graph of the function are

a) The axis of symmetry is the line x = 6

b) The parabola opens down

c) The vertex of the graph is at (-6, -11)

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) = -3x² + 36x - 119

And , the vertex form of the function is

f ( x ) = -3 ( x - 6 )² - 11

Now , The axis of symmetry is the line x = 6. This is true because in vertex form, the equation of the axis of symmetry is given by x = h, where (h, k) is the vertex of the parabola. In this case, the vertex is (6, -11), so the axis of symmetry is x = 6.

The parabola has a minimum. This is also true because the coefficient of the x² term in the given equation is negative (-3), which means the parabola opens downward and has a minimum at the vertex.

Hence , the graph of the polynomial is solved

To learn more about equation of graph of polynomials click :

https://brainly.com/question/16957172

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Answer:

The expression is: (225 - (32 × 4))/0.15

Steps:

first we'll calculate the rental cost of 4 days without the miles driven

32 × 4 = $128.00

now we'll calculate the money that can be spent on miles

225 - 128 = $97.00

with $97.00 they can drive: 646.66 miles

97 / 0.15 = 646.66 miles

The expression is: (225 - (32 × 4))/0.15

Answer:

9.1 = a + 4

Step-by-step explanation:

Answer:

theres no numbers?

Step-by-step explanation:

Answer:

58.4197cm^2

Step-by-step explanation

cirlce area formula: [tex]\pi[/tex]r^2

r= 6.1

[tex]\pi[/tex]=3.14

Now plug numbers into the formula

area of circle:

= (3.14)(6.1^2)

=(3.14)(37.21)

= 116.8394cm^2  ------> area of full circle

now divide by 2, to find area of semi circle

116.8394/2= 58.4197cm^2

[tex] \huge\fbox\red{A}\fbox\pink{n}\fbox\purple{S}\fbox\green{w}\fbox\blue{E}\fbox\orange{r}[/tex]

area of semicircle is 58.572 m²

[tex] \huge \sf { \fcolorbox{green}{g}{Explanation :- }}[/tex]

[tex] \huge \underline{\large \fbox \red{Concept : }}[/tex]

We have to find the area of semicircle

So firstly we need to find the area of circle. because the semicircle of circle is the half of area of circle so first we find the area of circle then divide by 1 /2 then we get the area of semicircle.

We have given the radius of circle is 6.1 m

[tex]\huge\mathfrak\red{Solution : }[/tex]

[tex] \mathfrak \green{Area \: of \: circle = π × ( radius) ²}[/tex]

[tex]\mapsto \: \: \small \: \: \: \: \: \mathfrak \blue{ = \frac{22}{7} \: \times( 6.1 \: m)^{2} } \\ [/tex]

[tex]\mapsto \small \: \: \: \: \: \mathfrak \blue{ = \frac{22}{7} \: \times37.21 \: m {}^{2} } \\ [/tex]

[tex]\mapsto \: \small\: \: \: \: \: \: \mathfrak \blue{ = 116.94 \: m {}^{2} }[/tex]

Therefore,

[tex]\small \mathfrak \red{Area \: of \: semicircle = \frac{1}{2} \times area \: of \: circle}[/tex]

[tex] \small \mathfrak \green{ = \frac{1}{2} \times 116.94 \: cm \: {}^{2} } \\ [/tex]

[tex]\mapsto \: \small\: \: \: \: \: \: \mathfrak { = 58.472\: m {}^{2} }[/tex]

[tex] {\underline {\fbox\red{Hence, the area of semicircle is 58.572 m²}}}[/tex]

Answer:

[tex]x=49.16^{\circ}[/tex]

Step-by-step explanation:

We need to find the value of x in the given figure.

It is a right angled triangle, in which base is 19, height is 22.

We can use trigonometry to find x.

We know that,

[tex]\tan\theta=\dfrac{P}{B}[/tex]

Where

P is perpendicular and B is base

So,

[tex]\tan x=\dfrac{22}{19}\\\\x=\tan^{-1}(1.157)\\\\x=49.16^{\circ}[/tex]

So, the value of x is equal to [tex]49.16^{\circ}[/tex].

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Step-by-step explanation: