David is shoveling driveways to raise money for his Spring
Break trip. Each driveway he shovels, he earns $15. After shoveling 12 driveways, David has $243 saved for his trip.
Write an equation to represent the amount David has saved as a function of the number of driveways he has shoveled.

Final answer:

To translate the given statement into an inequality, it converts to 3x - 4 ≥ 2x + 8. Through simplification, we find that x must be at least 12. This showcases the application of basic algebra rules and solving inequalities.

Explanation:

The question asks to translate 'The sum of three times a number and -4 is at least twice the number plus 8' into an inequality. This can be put into mathematical terms as 3x - 4 ≥ 2x + 8, where 'x' represents the unknown number. To solve, we follow several steps:

Subtract 2x from both sides, resulting in x - 4 ≥ 8.

Add 4 to both sides to isolate the variable, giving x ≥ 12.

This inequality tells us that for the original statement to hold true, the number (x) must be 12 or greater. The process involves understanding operations with numbers, such as adding, subtracting, and applying the rules of inequality to solve for 'x'.

Answer:

The average speed of the first plane is 315 mph and that of the second plane is 105 mph.

Step-by-step explanation:

Let us assume that the first plane has speed x mph and that of the second plane is y mph.

So, as per given condition x = 3y ......... (1)

Now, given that after traveling in the same direction for 7.5 hours, they are 1575 miles apart.

So, we write the equation as  

7.5x - 7.5y = 1575

⇒ x - y = 210 ........ (2)

Now, solving equation (1) and (2) we get, 3y - y = 210

⇒ 2y = 210

⇒ y = 105 mph

So, from equation (1) we get, x = 3y = 315 mph.

So, the average speed of the first plane is 315 mph and that of the second plane is 105 mph. (Answer)

Answer:

[tex]1\dfrac{1}{4}a^6b^3[/tex]

Step-by-step explanation:

A square of a monomial is [tex]1\dfrac{9}{16}a^{12}b^6[/tex] that is [tex]\dfrac{25}{16}a^{12}b^{6}[/tex]

Use properties of exponents:

[tex](a^m)^n=a^{mn}\\ \\\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m\\ \\a^mb^m=(ab)^m[/tex]

Note that

[tex]\dfrac{25}{16}=\dfrac{5^2}{4^2}=\left(\dfrac{5}{4}\right)^2\\ \\a^{12}=a^{6\cdot 2}=(a^6)^2\\ \\b^6=b^{3\cdot 2}=(b^3)^2[/tex]

Then

[tex]\dfrac{25}{16}a^{12}b^{6}=\left(\dfrac{5}{4}\right)^2\cdot (a^6)^2\cdot (b^{3})^2=\left(\dfrac{5}{4}a^6b^3\right)^2[/tex]

So, the monomial is

[tex]\dfrac{5}{4}a^6b^3=1\dfrac{1}{4}a^6b^3[/tex]

Answer:

-1/2 = n

Step-by-step explanation:

2/3(1+n) = -1/2n

2/3 + 2/3n = -1/2n

2/3 + 2/3n - 2/3n = -1/2n

2/3 = -1/2n -2/3n

2/3 = -.5n -.66n

2/3 = -1.16n

2/3/-1.16 = n

.66 - 1.16 =n

-0.5=n

- 1/2 = n

For this case we must solve the following equation:

[tex]\frac {x} {4} + 2 = -12[/tex]

Subtracting 2 from both sides of the equation we have:

[tex]\frac {x} {4} = - 12-2[/tex]

Equal signs are added and the same sign is placed.

[tex]\frac {x} {4} = - 14[/tex]

Multiplying by 4 on both sides of the equation we have:

[tex]x = -14 * 4\\x = -56[/tex]

Thus, the solution of the equation is [tex]x = -56[/tex]

Answer:

[tex]x = -56[/tex]

So this is the answer...

Hope this can help :)

Answer:

The length of the diagonal measures 54.2 meters

Step-by-step explanation:

Pythagorean theorem,

a² + b² = c²

a = 21

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

√2941 = c

54.23098... = c

54.2 = c

The length of the diagonal measures 54.2 meters.

We have given that,

A rectangular swimming pool is 21 meters

wide and 50 meters long.

We have to determine the length of the diagonal.

a² + b² = c²

a and b are sides of the triangle and c is the hypotenuse

a = 21,

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

Taking square root on both side

√2941 = c

54.23098 = c

54.2 = c

Therefore the length of the diagonal measures 54.2 meters.

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√5 • √80

Combine the two using the product rule for radicals:

√(5 • 80)

Multiply:

√400

Rewrite 400 as 20^2

√20^2

= 20

The answer is 20

Step-by-step explanation:

speed= distance/time

time is meant to be in seconds

1mins = 60 secs

75mins =75 x 60 = 4500

distance is meant to be in metres

1metre= 0.001km

100 km = 100 x 1000= 100000

speed =distance/time

speed = 100000/4500

speed=22.22m/s

Answer:

[tex]\large\boxed{80\dfrac{km}{h}}[/tex]

Step-by-step explanation:

[tex]speed=\dfrac{distance}{times}\\\\\text{We have:}\\\\distance=100km,\ time=75min\\\\1h=60min\to1min=\dfrac{1}{60}h\\\\time=\dfrac{75}{60}h=\dfrac{5}{4}h=1.25h\\\\\text{Substitute:}\\\\speed=\dfrac{100km}{1.25h}=80\dfrac{km}{h}[/tex]

Answer:

x = 20

Step-by-step explanation:

-7 (2) = -14 so...

10 (2) = 20

Step-by-step explanation:

When a factor appears in both the numerator and denominator, that is a hole in the function.

Therefore, the domain of h(x) is (-∞, 4) (4, ∞).

Which means the range of h(x) is (-∞, 5) (5, ∞).

Graph: desmos.com/calculator/j58gdgugxy

Answer: 15

Step-by-step explanation:

Recall : if sin α = cos β , then α + β are complementary , that is

α + β = 90

Since  sin (2x+7) = cos(4x-7) , then (2x+7) and (4x-7)  are complementary , that is:

2x + 7 + 4x - 7 = 90

6x = 90

x = 90/6

x = 15

The missing value x is constituting the angles of both sin and cos trigonometric ratios.

By using complementary property, the value of x for given condition is evaluated as 15.

The missing value x is constituting the angles of both sin and cos trigonometric ratios.

Its known by trigonometry that  when [tex]sin(\alpha) = cos(\beta)[/tex], then [tex]\alpha + \beta = 90^{\circ}[/tex]

Thus, we have:

[tex]2x + 7 + 4x - 7 = 90\\\\6x = 90\\\\x = \dfrac{90}{6}\\\\x = 15[/tex]

Thus, value of x for given condition is 15.

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See the explanation

Since you haven't provided any options I'll face this problem in a general way. Linear functions are given of the form:

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

This is called the slope-intercept form of the equation of a line. When modeling a linear function we need to take into account that we will have a constant rate of change and that when plotting our model this will follow a line. In order to model a problem as a linear function we need to follow some tips:

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The quantity that is best modeled by a linear function must fit into y = mx + c

A model is a representation of reality. There are many different types of models such as;

A linear function is a function of the sort y =mx + c. The quantity is not shown in the question hence the question is incomplete.

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After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.

To find the height of the image after it has been scaled by 80% multiple times, we can use the formula for scaling:

[tex]\[ \text{New height} = \text{Original height} \times (\text{Scale factor})^{\text{Number of times scaled}} \][/tex]

Given that the original height is 150 mm and the scale factor is 80% (or 0.8), we can calculate:

a. After being scaled 3 times:

[tex]\[ \text{New height} = 150 \times (0.8)^3 = 150 \times 0.512 = 76.8 \, \text{mm} \][/tex]

b. After being scaled 6 times:

[tex]\[ \text{New height} = 150 \times (0.8)^6 = 150 \times 0.262 \approx 39.3 \, \text{mm} \][/tex]

As the image is scaled down by 80% each time, its height decreases significantly with each iteration.

After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.

These heights fall within the acceptable range for a U.S. passport photo (25-35 mm).

The probable question may be:

The distance from Elena's chin to the top of her head is 150 mm in an image. For a U.S. passport photo, this measurement needs to be between 25 mm and 35 mm. PASSPORT PHOTO 1. Find the height of the image after it has been scaled by 80% the following number of times. Explain or show your reasoning. a. 3 times b. 6 times

Answer:

Temperature of the ice for ice-skating = -5 °C

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Temperature of the ice for an ice hockey match = - 7 °C

Temperature for ice- skating is 2 degrees warmer.

2. What is the temperature of the ice for ice-skating?

For the correct calculation, we use this formula:

Temperature for ice-skating = Temperature of the ice for a hockey match + 2

Temperature for ice-skating = -7 + 2

Temperature of the ice for ice-skating = -5 °C

We add 2 to the temperature of the ice for a hockey match because the temperature for ice-skating is described as warmer. If it were described as colder, we should subtract.

Answer:

-5c

Step-by-step explanation:

because basically  you subtract because it is below normal

Answer: 12

Step-by-step explanation: To solve this equation, since x is being divided by 2, in order to get x by itself, we need to multiply by 2 on both sides of the equation.

On the left side of the equation, the 2's cancel and we have x and on the right side of the equation, 6 × 2 gives us 12 so we have x = 12 which is the solution for our equation.

To check our solution, we plug 12 in for x in the original equation.

Image provided.

Answer:

-4 = x

Explanation:

-11x +3x =-8x

24=-8x-8

+8= +8

--------------

32=-8x

--- -----

-8. -8

x= -4

To solve for x in the equation 24 =-11x-8+ 3x, combine like terms and isolate the variable by performing algebraic operations.

To solve for x in the equation 24 =-11x-8+ 3x, we can combine like terms:

Therefore, the solution for x is -4.

Answer:

6

Step-by-step explanation:

it's asking how much makes 10% of 60 and to find it we use this formula :

60 ÷ 100 × 10 = 6

Answer:

6 milkshakes

Step-by-step explanation:

All you need to do is multiply:

60 (0.10) = 6

Answer:

Andre has the correct answer. When simplified his answer is equivalent to the original equation.

Answer:

2pg1

Step-by-step explanation:

Hehe

Answer:

Speed of Carol is 78 mph and that of Steve is 84 mph.

Step-by-step explanation:

Let the speed of Carol is x mph and that of Steve is (x + 6) mph.

If they move towards each other with that speed, then the resultant speed will be (x + x + 6) = (2x + 6) mph

With this resultant speed, they cover 405 miles in 2.5 hours.

So, [tex]2x + 6 = \frac{405}{2.5} = 162[/tex]

⇒ 2x = 156

⇒ x = 78 mph

So, speed of Carol is 78 mph and that of Steve is (78 + 6) = 84 mph. (Answer)

The number is -9

Step-by-step explanation:

Let x be the number then according to given statement

[tex]4x+10 = x-17[/tex]

Subtracting 10 from both sides

[tex]4x+10-10 = x-17-10\\4x = x-27[/tex]

Subtracting x from both sides

[tex]4x-x = x-x-27\\3x = -27[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3} = \frac{-27}{3}\\ x = -9[/tex]

Verification:

[tex]4(-9)+10 = -9-17\\-36+10=-26\\-26=-26[/tex]

The number is -9

Keywords: Linear equation, variables

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Answer:

The approximate perimeter of the trapezoid is 31 units

Step-by-step explanation:

step 1

Plot the trapezoid

Let

A(-5, -3), B(-2, 5), C(2, 5), and D(5, -3)

see the attached figure

step 2

Find the perimeter of trapezoid

we know that

The perimeter of trapezoid is equal to

[tex]P=AB+BC+CD+AD[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

we have

[tex]A(-5, -3),B(-2, 5)[/tex]

substitute in the formula

[tex]d=\sqrt{(5+3)^{2}+(-2+5)^{2}}[/tex]

[tex]d=\sqrt{(8)^{2}+(3)^{2}}[/tex]

[tex]d_A_B=\sqrt{73}\ units[/tex]

Find the distance BC

we have

[tex]B(-2, 5),C(2, 5)[/tex]

substitute in the formula

[tex]d=\sqrt{(5-5)^{2}+(2+2)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]

[tex]d_B_C=4\ units[/tex]

Find the distance CD

we have

[tex]C(2, 5),D(5, -3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-5)^{2}+(5-2)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(3)^{2}}[/tex]

[tex]d_C_D=\sqrt{73}\ units[/tex]

Find the distance AD

we have

[tex]A(-5, -3),D(5, -3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3+3)^{2}+(5+5)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(10)^{2}}[/tex]

[tex]d_A_D=10\ units[/tex]

step 3

Find the perimeter

[tex]P=AB+BC+CD+AD[/tex]

substitute the values

[tex]P=\sqrt{73}+4+\sqrt{73}+10[/tex]

[tex]P=31\ units[/tex]

Answer:whole wheat

Step-by-step explanation:

Its whole wheat because when you divide the cost by the weight whole wheat is the best deal

Answer:

Step-by-step explanation:

20y - 60 = 5x

add 60 to both sides:

20y = 5x + 60

divide through by 20:

y = (1/4)x + 3

slope = 1/4

y-intercept = (0, 3)

Answer:

D) 0.0004

Step-by-step explanation:

(0.02)^2=0.02*0.02=0.0004

Answer:

Step-by-step explanation:

-8(k - 4)         use the distributive property: a(b + c) = ab + ac

= (-8)(k) + (-8)(-4) = -8k + 32

Answer:

-8k+32

Step-by-step explanation:

-8(k-4)=-8k+32

Answer:

7-c < 30

Step-by-step explanation:

its in your question.

Answer:

5

Step-by-step explanation:

(-3)(2)-7(-3)-10

-6+21-10

15-10

5