Jose is driving to Denver. Suppose that the remaining distance to drive (in miles) is a linear function of his driving time (in
minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below.
Jose has 48 miles remaining after 50 minutes of driving. How many miles were remaining after 34 minutes of driving?

So you gotta break the trapezoid into 2 shapes, square and triangle.

Area of the square: 8 x 10 = 80 cm^2

Area of the triangle :  1/2 x base x height

base: 6

height: 8

therefore, 1/2 x 6 x 8 = 24 cm^2

24+80 = 104 cm^2

Therefore your answer is C

The area of the  trapezoid ABCD should be option c [tex]104\ cm^2[/tex]

Since

We know that  

Area of the square= [tex]8 \times 10 = 80\ cm^2[/tex]

And,

Area of the triangle:  [tex]1/2 \times base \times height[/tex]

Here

base =  6

height =  8

So, the area should be

[tex]= 1/2 \times 6 \times 8 \\\\= 24\ cm^2[/tex]

Now the area of trapezoid is

= 24+80

= 104

Hence, The area of the  trapezoid ABCD should be option c [tex]104\ cm^2[/tex]

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Answer:

7*x + y + 0.1*z

Step-by-step explanation:

An expression that satisfy what Ava said she wrote is the following:

7*x + y + 0.1*z

because

Answer:

The expression can be written as

7a + b + 0.1c

Step-by-step explanation:

Ava wrote an expression with three terms . According to the question each term involve a different variable. This means the term have different value. Since the term have different variable, each term can be represented as follow:

a , b and c

The first term which is a has a coefficient of 7. The second term which is b has a coefficient of 1 and the last term which is c has a coefficient of 0.1.

The coefficient of any value is usually the number in front of it.

The three terms and their coefficients can be expressed as follows:

First term and coefficient = 7a

Second term and coefficient = 1b

Third term and coefficient = 0.1c

The expression Ava wrote can be represented as follows

7a + b + 0.1c

Note an expression that contains variable , symbols( +, - )   and numbers is known as an algebraic expression. And

7a + b + 0.1c is an algebraic expression.

Answer:

The expression is equivalent to 12 + 3 + (negative 7) because of the commutative property.

Step-by-step explanation:

The expression should be 12- 7 +3 = 8

The associative property allows you to put parenthesis anywhere in the equation as long it just addition and multiplication. In this question, we have subtraction(minus 7) so we can't use the associative property.  

The commutative property allows you to move around a number as long as you didn't change its value or its group. Option C changes the value of the number so it's wrong. If you calculate it will give a different answer: 12-3+7=16

Option D didn't change the value so its the right answer.

Answer:

D is correct

Step-by-step explanation:

a. It will take 1.53 seconds for the rocket to reach its maximum height.

b. The rocket will reach a maximum height of 38.04 ft (rounded to the nearest tenth).

c. The range of the function h(t) is bounded below by h0 (0 ft) and above by h_max (38.04 ft). In mathematical notation, the range is:

Range = {h | h ∈ R, h0 ≤ h ≤ h_max}

d. The maximum point on the graph of the function exists because of the negative coefficient of the t^2 term (-16).

**a. Time to reach maximum height:**

The rocket's motion can be modeled by the formula:

h(t) = -16t^2 + vt + h0

where:

* h(t) is the height of the rocket at time t

* t is the time in seconds

* v is the initial upward velocity (49 ft/s)

* h0 is the initial height (0 ft)

We need to find the time t when the height h(t) is maximum. Since the acceleration due to gravity (-16 ft/s^2) is negative, the maximum height happens at the vertex of the parabola represented by the equation.

The time to reach the vertex can be found using the formula:

t_vertex = -v / (2a) = -49 / (2 * -16) = 1.53 seconds (rounded to the nearest hundredth)

Therefore, it will take 1.53 seconds for the rocket to reach its maximum height.

**b. Maximum height:**

Now, plug the t_vertex value back into the equation to find the maximum height:

h(1.53) = -16(1.53)^2 + 49(1.53) + 0 = 38.04 ft

Therefore, the rocket will reach a maximum height of 38.04 ft (rounded to the nearest tenth).

**c. Range of the function:**

The range of the function depends on the initial parameters (velocity and height) and the gravitational acceleration. Since the acceleration due to gravity is always negative, it acts as a downward force pulling the rocket back down. This means the highest point the rocket can reach is its initial height plus the maximum height achieved due to the initial velocity.

Therefore, the range of the function h(t) is bounded below by h0 (0 ft) and above by h_max (38.04 ft). In mathematical notation, the range is:

Range = {h | h ∈ R, h0 ≤ h ≤ h_max}

**d. Reason for the maximum point:**

The maximum point on the graph of the function exists because of the negative coefficient of the t^2 term (-16). This term represents the downward force due to gravity, which continuously slows down the rocket's upward motion. Eventually, the upward velocity becomes zero, and the rocket starts descending due to gravity. This point of zero velocity corresponds to the vertex of the parabola, which represents the maximum height achieved.

Answer: the answer Are 60,120,180

Step-by-step explanation:

Answer:

60,120,180

Step-by-step explanation:

Answer:

-2.5

Step-by-step explanation:

-2.5 is under 0 and 2.5 is positive so -2.5 is less

Hope this helps!

Answer: 6/3

Step-by-step explanation: The reason it's 6/3 is, if he's going to triple the amount of oil that means he multiplying 3 because triple = 3 and he normally uses 2/3 so mutliply that and you get 6/3 ! If you need it simplifty its 2! Hope this helps.

Answer:

[tex]\displaystyle x = \frac{h - 2}{4} - 3y[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle h = 4(x + 3y) + 2[/tex]

Step 2: Solve for x

Answer: It's B

Step-by-step explanation:

Answer:

d the anwser is d

Step-by-step explanation:

Answer:

6 action figures

Step-by-step explanation:

8 Comic books for every 3 action figures;

Ratio = 8:3

Monday =

32 Comic books: X

1 part = 32/8 = 4

X = 4 * 3 = 12

Therefore 12 action figures were sold on Monday.

Difference between Monday and Tuesday is 18-12 which is 6 action figures.

Final answer:

The answer provides a step-by-step explanation to find the difference in the number of action figures sold on Monday and Tuesday.

Explanation:

The difference between the number of action figures sold on Monday and Tuesday can be calculated as follows:

Given that the store sells 8 comic books for every 3 action figures, on Monday they sold 32 comic books, which is equivalent to 12 action figures (32 comic books ÷ (8 comic books/3 action figures)).

On Tuesday, the store sold 18 action figures directly. To find the difference, subtract the number of action figures sold on Monday from Tuesday's sales: 18 action figures - 12 action figures = 6 action figures.

Answer:

16r+8

Step-by-step explanation:

Answer:

[tex]Area= \frac{17 \sqrt{865} }{4} \: {units}^{2} [/tex]

Step-by-step explanation:

From Pythagoras theorem,

[tex] {h}^{2} = {12}^{2} + { (\frac{17}{2} )}^{2} [/tex]

[tex]{h}^{2} = \frac{865}{4} [/tex]

[tex]h = \frac{ \sqrt{865} }{2} [/tex]

The area of the isosceles triangle is

[tex]Area= \frac{1}{2} bh[/tex]

[tex]Area= \frac{1}{2} \times 17 \times \frac{ \sqrt{865} }{2} = \frac{17 \sqrt{865} }{4} [/tex]

Answer:

(2,√21)

Step-by-step explanation:

The circle centered at the origin has equation:

[tex] {x}^{2} + {y}^{2} = 25[/tex]

Any point that satisfies this equation lie on this circle.

When x=2, we substitute and solve for y.

[tex] {2}^{2} + {y}^{2} = 25 \\ 4 + {y}^{2} = 25 \\ {y}^{2} = 25 - 4 \\ {y}^{2} = 21[/tex]

Take square root to get:

[tex]y = \pm \sqrt{21} [/tex]

Therefore (2,-√21) and (2,√21) are on this circle.

From the options, (2,√21) is the correct answer

Answer:2, square root of 21 just took the test!

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Since the figure has 4 sides, the total of all of the angles add to 360 as:

180(n-2)=T

180(4-2)=T

180(2)=T

360=T

Now we can set up an equation and solve for x:

17x+8+74+110+66=360

17x+258=360

17x=102

x=6

So x=6

Answer:

The equivalent expression to 9(15) is 9(10+5).

Step-by-step explanation:

this is equivalent to 910 because 27 x 10 = 30 x 9 = 270.

this is also equal to 9(15) to 9(10+5)

An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to 9/10÷2/3 is (9×3)/(10×2).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression is equivalent to 9/10÷2/3, can be written as,

[tex]\dfrac9{10} \div \dfrac23\\\\\\= \dfrac{\frac{9}{10}}{\frac23}\\\\\\= \dfrac{9\times 3}{10 \times 2}[/tex]

Thus, the expression that is equivalent to 9/10÷2/3 is (9×3)/(10×2).

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Answer:

Perfect squares are whole numbers that are squared, so the two that are closest to 175 would be:

13*13=169 and

14*14=196

The two perfect squares closest to 175 are (13*13) and (14*14)

Hope this helps ;)

Answer: 14.7

Step-by-step explanation:

Data : 12,18    

Total Number of Values, N = 2

Step 1 : Find 1 / N

1 / N = 1 / 2 = 0.5

Step 2 : Find mean

GM = ( 12 * 18 )^ 0.5

       = 14.7

Step-by-step explanation:

The geometric mean between 12 and 18 =

[tex] \sqrt{12 \times 18} [/tex]

[tex]6 \sqrt{6} [/tex]

[tex]14.69[/tex]

14.7

Answer:

(a) Li and K belongs to the same group.

(b) Mg has the tendency to lose two electrons.

(c) C prefers sharing of electrons to complete its octet.

(d) K is the most metallic element.

(e) S forms acidic oxide.

(f) Al belongs to group 13.

_______________________

(a) Li and K belongs to the same group. (Group 1)

(b) Mg has the tendency to lose two electrons because it has 2 ions in it's outermost shell

(c) C prefers sharing of electrons to complete its octet because it has 6 ions in it's outermost shell need 2 ions to complete octet

(d) K is the most metallic element.

(e) S forms acidic oxide.

(f) Al belongs to group 13.

Answer:110 in 2 hours

Step-by-step explanation:

440/80 = 55/1 (55/1x2)

Answer:

I am confused with the question

Step-by-step explanation:

can you correct your spelling

Answer:

10% Decrease

Step-by-step explanation:

Let the number is 100.

Now, if we increase the number by 20%, the new number will be -

100 + (100 × 20%) = 100 + 20 = 120

The new number is 120.

Again, if we decrease the new number by 25%, the number will be -

120 - (120 × 25%) = 120 - 30 = 90

The new number is 90.

The change will be decreased by = (100 - 90) = 10

Percentage change = (10 ÷ 100) × 100 = 10%

¹/24

Step-by-step explanation:

The number of favorable outcomes (rolling a 5) is 3

The total number of possible outcomes is 12 * 6 = 72

Therefore;

P(5) = 3/72

= 1/24

Answer: Yes, if both are the same length width and height, then they would have the same volume.

Answer: 320 , 112, 432

Step-by-step explanation:

Volume of Rectangular Prism= 4 * 8 * 10

= 32*10

= 320 ft cubed

Volume of triangular prism= 4 * 7 * 8

= 28 * 8

= 224

= 224 divided by 2

= 112

Volume of composite= 112 + 320

=  432

The exponential e is used when modeling continuous growth that occurs naturally such as populations, bacteria, radioactive decay, etc.

Explanation

We can think of e like a universal constant representing how fast we could possibly grow using a continuous process. And, the beauty of e is that not only is it used to represent continuous growth, but it can also represent growth measured periodically across time.

The exponential e will be used in situations of continuous growth or decay. The following formula is used to illustrate continuous growth and decay. If a quantity grows continuously by a fixed percent, the pattern can be depicted by this function.

                                                  [tex]A = Ao e^k^t[/tex]

In case of exponential decay, k is less than 0.

Answer:38

Step-by-step explanation:he has 38 cupcakes leftover

or it could be 47 as it states he has ate 47

The coordinates of P are (12, 2).

Solution:

Given data:

A = (4, 2) and B = (22, 2)

P(x, y) is the point on the line segment AB.

AP : PB = 4 : 5.

Section formula:

[tex]$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)[/tex]

Here, [tex]x_1=4, y_1=2, x_2=22, y_2=2[/tex] and m =4, n =5.

[tex]$P(x, y)=\left(\frac{4\times 22 + 5\times 4}{4+5}, \frac{4\times 2 + 5\times 2}{4+5}\right)[/tex]

[tex]$P(x, y)=\left(\frac{88 + 20}{9}, \frac{8+10}{9}\right)[/tex]

[tex]$P(x, y)=\left(\frac{108}{9}, \frac{18}{9}\right)[/tex]

P(x, y) = (12, 2)

Hence the coordinates of P are (12, 2).

Answer:

11/15 I think cause it's a pretty easy fraction

Final answer:

To determine the probability that a student randomly selected from a class likes sports but not music, calculate the difference between those who like sports and those who like both sports and music, then divide by the total students, resulting in a 50% probability.

Explanation:

The question asks for the probability that a student selected at random from a class likes sports but not music. To solve this, we first understand the problem as a set problem in mathematics. Given that 60 students like music, 110 like sports, and 35 like both music and sports, we can find the number of students who like only sports by subtracting those who like both sports and music from the total number of students who like sports. This calculation is 110 (students who like sports) - 35 (students who like both sports and music) = 75 (students who like only sports).

To find the probability, we divide the number of students who like only sports by the total number of students in the class. So, the probability is 75 (students who like only sports) / 150 (total students) = 0.5 or 50%.

Therefore, the probability that a student selected at random likes sports but not music is 50%.

Width of the rectangle is 13 cm and length is 29 cm.

Step-by-step explanation:

Step 1:

Given perimeter of the rectangle = 84 cm. Let the width be x, then the length of the rectangle = 2x + 3. Use the formula for perimeter of a rectangle = 2(length + width) to find the dimensions.

84 = 2(2x + 3 + x) = 2(3x + 3) = 6(x + 1) [taking 3 as common factor outside)

⇒ 84 = 6x + 6

⇒ 78 = 6x

∴ x = 13

⇒ Width of the rectangle = 13 cm

∴ Length of the rectangle = 2x + 3 = 29 cm