Write the equation in slope-intercept form.
- 4x – 10y = -7

Answer:

1.81 inches

Step-by-step explanation:

We are told that the sheet of metal to be used measures 12 inches by 10 inches.

Squares of equal sides x are cut out of each corner. Thus, it means total of 2x is cut of the 12 inches side and 10 inches side.

Thus;

Length; L = 12 - 2x

Width; W = 10 - 2x

Height; H = x

Volume of the box is;

V = LWH

V = (12 - 2x)(10 - 2x)x

Factorizing out, we have;

V = 4x[(6 - x)(5 - x)]

Equating V to zero, we can find the domain of the function;

At V = 0,

4x = 0; 6 - x = 0 ; 5 - x = 0

x = 0, x = 6, x = 5

The dimensions have to be positive. Thus;

0 ≤ x ≤ 5

Expanding the volume equation;

V = 4x[30 - 5x - 6x + x²]

V = 4x[30 - 11x + x²]

V = 4x³ - 44x² + 120x

dV/dx = 12x² - 88x + 120

Equating to zero to find the value of x that makes volume maximum;

12x² - 88x + 120 = 0

Using quadratic formula gives;

x = 1.81 or 5.52

From our domain, we have 0 ≤ x ≤ 5.

1.81 falls within the domain and therefore we will pick it as the height that makes the volume maximum.

Answer:1.81

Step-by-step explanation:

x=1.81

Answer:

How about you be nice and give it to us hardworkers for free?

Step-by-step explanation:

Answer: undefined

Step-by-step explanation: No value can be assigned to 0 to the power 0 without running into contradictions. Thus 0 to the power 0 is undefined :|

Answer:

We have the ration:

3:5:7

This means that, if they receive $15, then:

Person A will get $3

Person B will get $5

Person C will get $10

Let's then define the amount of money shared as:

Amount = K*$15

where we want to find the number K.

In this scenario, each they will get:

Person A : $3*K

Person B: $5*K

Person C: $7*K

Now, we know that one of them gets "10 more than the other"

(The problem here is that we do not know exactly who receives more than who, i will suppose that person B receives $10 more than person A)

then we can have:

$5*K = $10 + $3*K

solving this for K, we have:

$5*K - $3*K = $10

$2*K = $10

K = $10/$2 = 5

Then the amount shared, in this situation, is:

Amount = K*$15 = 5*$15 = $75.

Answer:

B

Step-by-step explanation:

First, let's rearrange the given equation into something more recognizable. If we add 13 to both sides, we now have the polynomial [tex]x^{2}-10x+13[/tex]. We can now use the quadratic formula to solve.

Remember that the quadratic formula is

[tex]\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Substitute the numbers from the equation into the formula.

[tex]\frac{-(-10)+/-\sqrt{(-10)^{2}-4(1)(13) } }{2(1)}[/tex]

Simplify:

[tex]\frac{10+/-\sqrt{100-52} }{2}[/tex]

[tex]\frac{10+/-\sqrt{48} }{2}[/tex]

Here, I'm going to assume that there was a mistype in option B because if we divide out the 2 we end up with [tex]5+/-\sqrt{48}[/tex].

Hope this helps!

Answer:

D) 14

Step-by-step explanation:

Absolute value |x| is defined as the distance x from 0.

Basically, whatever is in the absolute value sign cannot be negative

Answer:

The mean birth weight for the sampling distribution is

3,500 grams.

Step-by-step explanation:

The sample mean is the average of the sample values collected divided by the number of the samples, while the population mean is the average or mean of all the values in the population.  If the sample is random and the sample size is large enough, then the sample mean would be a good estimator of the population mean.  This implies that with a randomly distributed and unbiased sample size, the sample mean and population mean will be equal, according to the central limit theorem. Therefore, the mean of the sample means will always approximate the population mean.

Answer:

0

Step-by-step explanation:

A slope of a straight, horizontal line is 0 as it is not going up or down.

Answer:

B) 0

Step-by-step explanation:

When it is a straight horizontal line the slope is 0, and when it is a straight vertical line the slope is undefined.

y= ___ is slope of 0

x= ___ is slope of undefined

Answer:

The correct answer is B

Answer:

523.3ft³

Step-by-step explanation:

Given

Diameter, D = 10ft

Required

Determine the volume of helium it can hold.

To solve this, we simply calculate the volume of a sphere, which is:

V = 4/3πr³

Where

r = ½D

r = ½ * 10ft

r = 5ft

Substitute 5 for r in the stated formula and take π as 3.14

V = 4/3 * 3.14 * 5³

V = 4/3 * 3.14 * 125

V = ⅓(4 * 3.14 * 125)

V = ⅓ * 1570

V = 523.3 ft³

Hence, the sphere can contain 523.3ft³ of helium

Answer:

K=4

Step-by-step explanation:

4(K+2)=32-2k

4k+8=32-2k

+2k          +2k

6k+8=32

     -8  -8

6k=24

divide 6 from both sides

k=6

Answer:

k=4

Step-by-step explanation:

4(k+2)=32-2k

You would use distributive property with the 4 and the numbers in the parenthesis.

4k+8=32-2k

Next, you add 2k to both sides

6k+8=32

Then, you subtract 8 from each side

6k=24

Lastly, you divide by 6 on both sides

k=4

Answer:

The area of a triangle is:

Step-by-step explanation:

Given the points of a triangle

A(1, 1)

B(2, 3)

C(4, 5)

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

Distance between AB:

[tex]AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}[/tex]

     [tex]=\sqrt{1+4}[/tex]

     [tex]=\sqrt{5}[/tex]

so

Distance between BC:

[tex]BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}[/tex]

     [tex]=\sqrt{2^2+2^2}[/tex]

     [tex]=\sqrt{2^3}[/tex]

     [tex]=2\sqrt{2}[/tex]

so

Distance between AC:

[tex]AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}[/tex]

    [tex]=\sqrt{3^2+4^2}[/tex]

   [tex]=\sqrt{5^2}[/tex]

    [tex]=5[/tex]

so

Semiperimeter = sum of sides ÷ 2            

                       [tex]s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224[/tex]

Area of the triangle:

[tex]A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}[/tex]

[tex]A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}[/tex]

[tex]A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}[/tex]

[tex]A=1[/tex]

Therefore, the area of a triangle is:

Step-by-step explanation:

3x+6+4x-20=10

7x-14=10

7x=24

x=24/7

Answer:

x=3.43

Step-by-step explanation:

3(x-2)+4(x-5)=10

3x+6+4x-20=10

7x-14=10

7x=24

x=24/7

24/7=3.428571428571429(round to nearest hundredths)

x=3.43

Answer:

The total cost for  each health club will be the same after 4 months.

Step-by-step explanation:

We want to when the total cost at each health studio is the same.

In other words, when A = B.

Therefore, the expression becomes

[tex]A = B[/tex]

[tex]22\:+\:24.5x=47.00\:+\:18.25x[/tex]

Step 1: Simplify both sides of the equation.

[tex]24.5x+22=18.25x+47[/tex]

Step 2: Subtract 18.25x from both sides.

[tex]24.5x+22-18.25x=18.25x+47-18.25x[/tex]

[tex]6.25x+22=47[/tex]

Step 3: Subtract 22 from both sides.

[tex]6.25x+22-22=47-22[/tex]

[tex]6.25x=25[/tex]

Step 4: Divide both sides by 6.25

[tex]\frac{6.25x}{6.25}=\frac{25}{6.25}[/tex]

[tex]x=4[/tex]

Therefore, the total cost for  each health club will be the same after 4 months.

Answer:

66m

Step-by-step explanation:

perimeter is the distance all round a figure

perimeter(p)= 2( length(l) + width(w))  or  perimeter= 2 length + 2 width

p= 2(l + w)                                                 or      p =  2l  + 2w

p= 2(16.3 +16.7)                                        or      p=  2(16.3) + 2(16.7)

p=2(33)                                                      or     p=   32.6  +  33.4

p=66m                                                        or     p=  66m

Answer:

Number 4. 83

Answer:

83

Step-by-step explanation:

(2x+ 1 ) +(x+15)+x=180

4x+16=180

4x=164

x=41

Largest angle -2x+1

2(41)+1=83

Answer:

m = 34 ; n = 17√3

Step-by-step explanation:

m = 17 × 2 = 34

n² = 34² - 17² = 867 = 17² × 3 ⇒ n = 17√3

Repost your question. Unclear as typed.

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given that the profit function is

[tex]P(x) = -0.5x^2 +200x - 14000[/tex]

let us find the profit when sale x=122

[tex]P(x) = -0.5(122)^2 +200(122) - 14000\\\\P(x)=-7442+24400-14000\\\\P(x)=2958[/tex]

Step two:

let us find the profit when sale x=150

[tex]P(x) = -0.5(150)^2 +200(150) - 14000\\\\P(x)=-11250+30000-14000\\\\P(x)=4750[/tex]

Hence the change is 4750-2958= $1792

Answer:

1 1/5 miles per hour

Step-by-step explanation:

3/5 = 0.60

1/2= 0.5 hr

0.60 * 2 = 1.2

1.2 mph = 1 1/5

Answer:

Yes, they are equalent

Step-by-step explanation:

12:14 = 6:7

60:70 =6:7

both can be simplified to 6:7

Answer:

11 7/15 (Not listed on paper!)

Step-by-step explanation:

6 12 /15  +  4 4 /6  =

(6 + 4) + (  12 /15  +  4/ 6 )

=  10 +  12 × 2

15 × 2

+  

4 × 5

6 × 5

=  10 +  

24 /30

+  

20 /30

=  10 +  

24 + 20 /30

=  10 +  

44 /30

=  10 +  

44 ÷ 2

30 ÷ 2

=  10 +  

22 /15

=  10 +  

1 7 /15

=  

11 7 /15

(Eleven and seven fifteenths)

[Sorry but all of the answers you gave are all wrong!]

Answer:

25%

Step-by-step explanation:

Looking at the attached diagram, we can see that the box plot is divided into 3 sections,

Q1 = First Quartile (1/4 the players) = 25%

Q2 = Second Quartile (2/4 = 1/2 of the players) = 50%

Q3 = Third Quartile (3/4 of the players) = 75%

From the attached diagram, the weight of 242 pounds is on the Third Quartile, this means , 75% of the players weigh 242 pounds and below

The percentage of players weighing greater than or equal to 242 pounds is calculated as: 100 - 75%

= 25%

The percentage of players weighing greater than or equal to 242 pounds is 25 %.

From the attached diagram, the weight of 242 pounds is comes on the Third Quartile.

It means that 75% of the players weigh 242 pounds and below

Hence, The percentage of players weighing greater than or equal to 242 pounds is,

                 [tex]100-75=25[/tex]

Learn more about the Quartile here:

https://brainly.com/question/10005803

Answer:

2/28

Step-by-step explanation:

Answer:

By the use of algebra.

Step-by-step explanation:

You wish to break the quantity '12' into parts (number of parts not specified) and multiply each part by 6.

If you didn't want to break 12 into parts, the straight method would be to simply multiply 12 by 6.    12 × 6 = 72

Breaking 12 into 12 parts, you have

X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂

In this case, X₁ represents the first unit of the number 12.  X₂ represents the second unit of the number 12.   X₁₂ represents the last unit of the number 12.

Hence, X₁ + X₂ + X₃ + X₄ + X₅ + X₆ + X₇ + X₈ + X₉ + X₁₀ + X₁₁ + X₁₂ = 12

Each X value is the number 1; just that it's in 12 places and each case has a separate identity.

Each X value can then be multiplied by 6 and the sum of all would be 72.

ANSWER:

distance when starting her walk/ when time is 0

Step-by-step explanation:

y axis will be distance and x intercept is the point where y is 0

so represents when distance is 0.

Answer:

the time it takes to walk from her house to school

Step-by-step explanation: