Each morning, John jogs at 6 miles per hour and rides a bike at 12 miles per hour. His goal is to jog and ride his bike a total of at least 9 miles in no more than 1 hour. If john jogs j miles and rides his bike b miles, which of the following systems of inequalities represents John's goal?
Answers
Answer:
4th Choice.
Step-by-step explanation:
.
Each morning, John jogs at 6 miles per hour and rides a bike at 12 miles per hour. His goal is to jog and ride his bike a total of at least 9 miles in no more than 1 hour. If john jogs j miles and rides his bike b miles, then the Inequalities representing John's goal is\(\[ \begin{cases} j + b \geq 9 \text{ (Total distance covered should be at least 9 miles)} \\ \frac{j}{6} + \frac{b}{12} \leq 1 \text{ (Total time taken should be no more than 1 hour)} \end{cases} \]\)
Inequalities are mathematical expressions that depict a relationship between two quantities, indicating whether one is less than, less than or equal to, greater than, or greater than or equal to the other. Unlike equations, which assert equality, inequalities allow for a range of values that satisfy the given conditions.
The symbols commonly used in inequalities include "<" (less than), "<=" (less than or equal to), ">" (greater than), and ">=" (greater than or equal to).
These mathematical statements are crucial in various fields, such as algebra, calculus, economics, and physics, as they provide a way to compare and analyze values within a range, making them an essential tool in problem-solving and decision-making processes.
John's goal is to jog and ride his bike a total of at least 9 miles within 1 hour.
Let's use the variables \(\( j \)\) and \(\( b \)\) to represent the distance John jogs and rides his bike, respectively.
1. Total Distance Constraint : The sum of the distances jogged and biked should be at least 9 miles. Therefore, the first inequality is \(\( j + b \geq 9 \).\) This ensures that John meets his minimum distance goal.
2. Time Constraint : The time taken to jog \(\( j \)\) miles at a speed of 6 miles per hour is \(\( \frac{j}{6} \)\) hours. Similarly, the time taken to ride \(\( b \)\) miles at a speed of 12 miles per hour is \(\( \frac{b}{12} \)\) hours. The total time taken to cover both distances should be no more than 1 hour. Therefore, the second inequality is \(\( \frac{j}{6} + \frac{b}{12} \leq 1 \)\).
By combining both inequalities, we ensure that John covers at least 9 miles in total while completing his jog and bike ride within the given time limit.
The system of inequalities captures John's goal in terms of distance and time, making sure he achieves his objective.
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Related Questions
Antonio is in a bowling league. His goal is to score an average of at least 100 points per game. His scores so far are 105,95,97,82, and 110. How many points can Antonio score in his next game to reach his goal? Show your work.
Please show work I need it so please have step by step I will give brainly thanks!
Answers
Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.
What are basic arithmetic operations?
Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.
To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:
Total points needed = (number of games + 1) × average score goal - total points scored so far
In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:
105 + 95 + 97 + 82 + 110 = 489
Substituting these values into the formula, we get:
Total points needed = (6) × (100) - 489
Total points needed = 600 - 489
Total points needed = 111
Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.
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Is anyone available to help with this?Find all solutions to the equation.7 sin^2x - 14 sin x + 2 = -5
Answers
We have the following trigonometric equation:
\(7sin^2x-14sinx+2=-5\)1. Now, we can rewrite the equation as follows:
\(\begin{gathered} 7sin^2x-14sinx=-5-2 \\ \\ 7sin^2x-14sinx=-7 \\ \\ \end{gathered}\)2. We have a common factor of 7 and sin(x). Then we have:
\(\begin{gathered} 7(sin^2x-2sinx)=-7 \\ \\ 7sinx(sinx-2)=-7 \end{gathered}\)3. Now, we have:
\(\begin{gathered} \frac{7sinx}{7}(sinx-2)=\frac{-7}{7} \\ \\ sinx(sinx-2)=-1 \\ \\ \end{gathered}\)4. Now, if we have:
\(\begin{gathered} sinx=1 \\ \\ sinx-2=-1\Rightarrow sinx=-1+2=1 \\ \\ sinx=1 \end{gathered}\)5. Then, the solutions for this equation will be - applying the inverse function of the sine function to both sides of the equation:
\(\begin{gathered} \sin^{-1}(sinx)=\sin^{-1}(1) \\ \\ x=\frac{\pi}{2}+2\pi n \end{gathered}\)Therefore, in summary, the values that are solutions for this equation are:
\(x=\frac{\pi}{2}+2\pi n\)Where n is the any integer value.
IIIKnowledge CheckA desk is on sale for 35% off. The sale price is $312.What is the regular price?Х5?
Answers
We know that
• The sale price is $312.
,• The desk is 35% off.
We just have to divide to find the regular price. Remember that 35% is equivalent to 0.35. It's important to notice that $312 represents 65% of the regular price since is 35% lower. Now, we use the rule of three: If $312 represents 65%, how much would represent 100%?
\(x=\frac{312}{0.65}=480\)Therefore, the regular price is $480.Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
Answers
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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Match the later drop-down
Answers
1) The expression 2⁻ˣ⁺³ = 3 is matched with graph B.
2 The expression 3ˣ⁺¹=3 is matched with graph C.
3) The expression 4ˣ = 3 is matched with graph
4 ) The expression 1ˣ/4 = 3 is matched with graph
What is the explanation for the above?1) The graph of the expression 2⁻ˣ⁺³ = 3 represents an exponential function where the y-coordinate is 3 when the base 2 raised to the power of (-x+3).
2) The graph of the expression 3ˣ⁺¹=3represents an exponential function where the y-coordinate is 3 when the base 3 raised to the power of (x+1). This graph is a straight line with a slope of 1.
3) The graph of the equation 4ˣ = 3 represents an exponential function where the base 4 raised to the power of x is equal to 3. This equation has a single solution, which can be determined using logarithms.
4) The graph of the expression 1ˣ/4 = 3 represents an exponential function where the base 1 raised to the power of (x/4) is equal to 3.
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Please help me with 10
Answers
Answer:
yes the answer is he does make sense
S={(3,p),(3,0),(4,q),(1,4)}
Answers
Answer:
S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:
(3,p): The first element is 3 and the second element is p.
(3,0): The first element is 3 and the second element is 0.
(4,q): The first element is 4 and the second element is q.
(1,4): The first element is 1 and the second element is 4.
Given that 2x + 3 > 9, the range of values of x is
Answers
Answer:
x>3
Step-by-step explanation:
2x+3>9
2x>6
x>3
So all values of x must be greater than 3 in order for the inequality to be true.
pls help me pls pls
Answers
x= -4
mark this as brainliest!!!
follow me!
Step-by-step explanation:
solution,or, 5x-3(x-2)=3x-2(x-1) or,5x-3x+6 =3x-2x+2 or,2x+6=x+2 or, 2x-x=6+2 ( therefore, x=-4)
A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals. What dimensions should
be used so that the enclosed area will be a maximum?
Answers
Length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
What is Area of Rectangle?The area of Rectangle is length times of width
Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.
Here, the dimensions of the rectangles are the same.
The width of the two rectangles is W=2W+2W=4W
The length of the two rectangles is L=L+L+L=3L
Because the adjacent side has a common length.
3L+4W=200
3L=200-4W
Divide both sides by 3
L=(200-4W)/3
Let us form an equation using the area of rectangle formula:
A=2LW
=2(200-4W)/3.W
A=400-8W²/3
Let us differentiate to get the area to be maximized dA/dW=0
1/3×(400-8W²)=0
1/3(400-16W)=0
400-16W=0
400=16W
Divide both sides by 16
W=25
The width is 25 feet.
Substitute W value in equation to get L value:
L=200-4×25/3
=200-100/3
=100/3
=33.33
The length is 33.33 feet.
Now let us find the maximum area
A=2LW
=2×33.33×25
=1666.66
Hence, length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
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Afiq. Bala and Chin played a game of marbles. Before the game, Bala had fewer marbles than Afig and Chinhad?
- as many marbles as Bala.
After the game, Balahad lost 20% of his marbles to Chinwhile Afig had lost
3
of his marbles to Chin. Chingained 105 marbles at the end of the
game.
(a)How many marbles didChinhave after the game?
(b)After the game, the 3 children each bought another 40 marbles. How manymarbles did the 3 children have altogether?
Answers
(a) Chin had 93.1 marbles after the game.
(b) The three children had a total of 271.44 marbles altogether.
Let's break down the problem step by step to find the answers:
Initial marbles
Before the game:
Let's assume Afiq had x marbles.
Bala had 1/6 fewer marbles than Afiq, so Bala had (x - 1/6x) marbles.
Chin had 3/5 as many marbles as Bala, so Chin had (3/5)(x - 1/6x) marbles.
After the game
After the game, Bala lost 20% of his marbles to Chin, so he has 80% (or 0.8) of his initial marbles remaining.
Afiq lost 2/3 of his marbles to Chin, so he has 1/3 (or 0.33) of his initial marbles remaining.
Calculating the marbles
(a) How many marbles did Chin have after the game?
To find Chin's marbles after the game, we add the marbles gained from Bala to Chin's initial marbles and the marbles gained from Afiq to Chin's initial marbles.
Chin's marbles = Initial marbles + Marbles gained from Bala + Marbles gained from Afiq
Chin's marbles = (3/5)(x - 1/6x) + 0.8(x - 1/6x) + 0.33x
Chin's marbles = (3/5)(5x/6) + 0.8(5x/6) + 0.33x
Chin's marbles = (3/6)x + (4/6)x + 0.33x
Chin's marbles = (7/6)x + 0.33x
We are given that Chin gained 105 marbles, so we can equate the equation above to 105 and solve for x:
(7/6)x + 0.33x = 105
(7x + 2x) / 6 = 105
9x / 6 = 105
9x = 105 * 6
x = (105 * 6) / 9
x = 70
Substituting the value of x back into the equation for Chin's marbles:
Chin's marbles = (7/6)(70) + 0.33(70)
Chin's marbles = 10(7) + 0.33(70)
Chin's marbles = 70 + 23.1
Chin's marbles ≈ 93.1
Therefore, Chin had approximately 93.1 marbles after the game.
(b) After the game, the 3 children each bought another 40 marbles. To find the total number of marbles the 3 children have altogether, we need to sum up their marbles after the game and the additional 40 marbles for each.
Total marbles = Afiq's marbles + Bala's marbles + Chin's marbles + Additional marbles
Total marbles = 0.33x + 0.8(x - 1/6x) + (7/6)x + 40 + 40 + 40
Total marbles = 0.33(70) + 0.8(70 - 1/6(70)) + (7/6)(70) + 120
Total marbles = 23.1 + 0.8(70 - 11.7) + 81.7 + 120
Total marbles = 23.1 + 0.8 × 58.3 + 201.7
Total marbles = 23.1 + 46.64 + 201.7
Total marbles = 271.44
The three children had a total of 271.44 marbles altogether.
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Question
Afiq. Bala and Chin played a game of marbles. Before the game, Bala had 1/ 6 fewer marbles than Afig and Chinhad 3/5 as many marbles as Bala.
After the game, Balahad lost 20% of his marbles to Chinwhile Afig had lost
2/3 of his marbles to Chin. Chingained 105 marbles at the end of the
game.
(a)How many marbles didChinhave after the game?
(b)After the game, the 3 children each bought another 40 marbles. How manymarbles did the 3 children have altogether?
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours After the leak is fixed, the height of the water is 4.75 feet The equation 4.75 = x +(-0.25) can be used to find x, the original height of the water in a pool. What was the original height of the water in the pool in feet?
Answers
Answer:
Step-by-step explanation:
5 feet
Since the height of the water is 4.75 feet, the equation is
4.75 = x + (-0.25)
To solve, add 0.25 to each side:
4.75+0.25 = x+(-0.25)+0.25
5.00 = x
Answer: B, 5.0
Step-by-step explanation:
Which of the following is the equation of the function f(x) graphed above? A. ƒ(x) = x(x − 2)²(x − 1)(x + 1) B. f(x) = (x - 2) (x − 1)(x + 1) c. f(x)= x(x - 2)²(x − 1)(x + 1) + 1)² D. f(x) = (x - 2)²(x - 1)(x - 1)^ E
Answers
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
Find the distance between the two points in simplest radical form.
(6,9) (9,6)
Answers
Answer:
3√2
Step-by-step explanation:
\( \sqrt{ {(6 - 9)}^{2} + {(9 - 6)}^{2} } \)
\( \sqrt{ {( - 3)}^{2} + {3}^{2} } \)
\( \sqrt{9 + 9} = \sqrt{2 \times 9} = \sqrt{2} \sqrt{9} = 3 \sqrt{2} \)
Anyone help please solve 4!
Answers
NEED HELP ASAP RIGHT ANSWER ONLY 69 POINTS
In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision.
(2,−1), (3,0.5), (6,1.5),
Answers
Answer:
A Least Square Regression Line is the best thing to use for this because there is inconsistencies and no direct equation to be able to fill all of these points. They may be outliers and therefore we should use a calculator for a Regression Line to be calculated to find the residual.
Step-by-step explanation:
What is the next step in the construction of an angle bisector of angle ABC?
&
B
E
A. Use a straightedge to draw a line passing through points D and C.
O
B. Use a straightedge to draw a line passing through points Eard A.
C. Use a straightedge to draw a line passing through points D and E.
о
D. Use a straightedge to draw a line passing through points A and C.
Answers
Option (4) is correct. Draw a line with a straight edge through points A and C.
What does the angle bisector theorem say?
The angle bisector of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle. By the angle bisector theorem, BDDC=ABAC.
The next step in constructing the angle bisector of angle ABC is:
D. Draw a line with a straight edge through points A and C.
For the angle bisector, we must find a point D on side AB, which is equidistant from point A and the apex of angle B. We have already constructed the radius BO that bisects the angle ABC. Now a line must be drawn that passes through point A and is parallel to ray BO. To do this, we draw a straight line through points A and C. The point where this line intersects the ray BO is point E. Finally, a line is drawn through points D and E. That line bisects angle ABC at O.
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Please see screenshot.
Answers
Answer:
See below
Step-by-step explanation:
Convert 41 divided by 2 day.
to an
hour
Answers
41/2 days is equivalent tο 492 hοurs.
What is divisiοn?Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.
We knοw that there are 24 hοurs in day therefοre,
Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:
41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs
Therefοre, 41/2 days is equal tο 492 hοurs.
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Which of the following statements is false?
If a number is divisible by 8, it must be divisible by 4.
If a number is divisible by both 9 and 10, it is divisible by 90.
The sum of two consecutive odd numbers is always divisible by 4.
If a number is not divisible by both 3 and 4, it is divisible by 12.
Answers
Answer:
The last one
Step-by-step explanation:
It doesn't make sense for that to be true
Solve by using substitution.
a =5b-4
-2a +10b = 5
Answers
Answer:
Step-by-step explanation:
step 1
(a =5b-4)(-2a +10b = 5) equation
step 2
a=5b-4 solve for a
-2a+10b=5
-2(5b−4)+10b=5
8=5
step 3
8=5 simplify
step 4
8+(-8)=5+(-8) add -8
0=-3
There are no solutions
ridgette brings a bag of 100 assorted candies in different flavors to her swim meet. She randomly grabs some candies out of the bag and hands them out to her teammates. The table below shows the flavors she has handed out. Flavor Number of candies lemon 6 orange 5 grape 8 cherry 13 Based on the data, estimate how many lemon candies were in the bag of 100 candies
Answers
Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.
What is proportion?In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.
In the given question,
We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:
6/total candies = number of lemon candies/100
We can cross-multiply to solve for the number of lemon candies:
number of lemon candies = 6 x 100 / total candies
We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:
total candies = lemon + orange + grape + cherry
Using the information from the table, we can estimate the total number of candies:
total candies = 6 + 5 + 8 + 13 = 32
Therefore, the estimated number of lemon candies in the bag is:
number of lemon candies = 6 x 100 / 32 = 18.75
We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.
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can someone please help I pay £100
Answers
Answer:
The new points to the triangle will be:
\(A(1,4)\\ B(1,1)\\ C(-1,1)\)
Step-by-step explanation:
Because the reflection point is at \(x=2\), all x values will subtract their distances from \(x=2\) to get their new values. The y values remain the same.
The starting values are:
\(A(3,4)\\ B(3,1)\\ C(5 ,1)\)
Point \(A\) is 1 unit away from \(x=2\), so we'll subtract 1 from 2 to get the new x value: \(2 - 1 = 1\), so \(A(1,4)\).
Point \(B\) is also 1 unit away from \(x=2\), so we'll subtract 1 from 2 to get the new x value: \(2 - 1 = 1\), so \(B(1,1)\).
Point \(C\) is 3 units away from \(x=2\), so we'll subtract 3 from 2 to get the new x value: \(2 - 3 = -1\), so \(C(-1,1)\).
What is the factored form of x2 - 6x – 16?
O (x – 4)(x - 2)
O (x + 4)(x - 2)
O (x-2)(x + 8)
O (x-8)(x + 2)
Answers
(x - 8)(x + 2)
x^2 + 2x - 8x - 16
x^2 - 6x - 16
The factored form of equation x² - 6x - 16 is,
⇒ (x - 8) (x + 2)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The equation is,
⇒ x² - 6x - 16
Now, We can simplify as;
⇒ x² - 6x - 16
⇒ x² - 8x + 2x - 16
⇒ x (x - 8) + 2(x - 8)
⇒ (x - 8) (x + 2)
⇒ (x - 8) (x + 2)
Thus, The factored form of equation x² - 6x - 16 is,
⇒ (x - 8) (x + 2)
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The two-way table shows the type of lunches ordered by teachers and students in the cafeteria yesterday. Of the total people who ordered in the cafeteria yesterday, find the relative frequency of teachers to the nearest percent. Record your answer
on the grid.
Answers
The two - way frequency table is solved and the relative frequency of the teachers to cafeteria is A = 5.7 %
Given data ,
Let the relative frequency of teachers to total in the cafeteria be represented as A
Now , from the table of values , we get
The total number of teachers is = 29
Now , the total of the cafeteria is = 508
So , the relative frequency A = 29 / 508
On simplifying , we get
A = 0.05708
On rounding to the nearest percentage , we get
A = 5.708 %
Hence , the relative frequency is A = 5.7 % and the table is plotted
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Which of these descriptions best suits a pyramid?
A.
Pyramids have polygonal faces and a triangular base.
B.
Pyramids have triangular faces and a polygonal base.
C.
Pyramids have triangular faces and a circular base.
D.
Pyramids have polygonal faces and a polygonal base.
E.
Pyramids have curved faces and a polygonal base.
Answers
Answer:
The correct option is B. Pyramids have triangular faces and a polygonal base.
Answer:B. Pyramids have triangular faces and a polygonal base.
Step-by-step explanation:
A pyramid is a three-dimensional shape that has a polygonal base and triangular faces that meet at a single point called the apex. Here's how to identify which of the given descriptions best suits a pyramid:
A. Pyramids have polygonal faces and a triangular base.
This description is incorrect because pyramids have a polygonal base, not a triangular base.
B. Pyramids have triangular faces and a polygonal base.
This description is correct because it correctly identifies that pyramids have triangular faces and a polygonal (meaning multi-sided) base.
C. Pyramids have triangular faces and a circular base.
This description is incorrect because pyramids have a polygonal base, not a circular base.
D. Pyramids have polygonal faces and a polygonal base.
This description is partly correct because pyramids do have a polygonal base, but their faces are always triangular.
E. Pyramids have curved faces and a polygonal base.
This description is incorrect because pyramids have flat, triangular faces, not curved faces.
So, in summary, option B, "Pyramids have triangular faces and a polygonal base," is the description that best suits a pyramid.
6d. Write an equation to represent the dollar amount in her savingsaccount and the number of weeks of saving. Be sure to specify what eachvariable represents.
Answers
Answer:
y = 24x + 80
Where x is the number of weeks of saving and y is the dollar amount in her savings
Explanation:
We need to find the equation of the line. If x is the number of weeks of saving and y is the amount in her savings, the equation has the following form
y = mx + b
Where m is the slope and b is the y-intercept.
The slope can be calculated using two points in the line (x1, y1) and (x2, y2) as follows
\(m=\frac{y_2-y_1}{x_2-x_1}\)Then, replacing (x1, y1) = (0, 80) and (x2, y2) = (5, 200), we get:
\(m=\frac{200-80}{5-0}=\frac{120}{5}=24\)Additionally, the y-intercept is the point where the graph crosses the y-axis. In this case, the point is (0, 80), so the value of b is 80.
Therefore, the equation of the line is
y = 24x + 80
Where x is the number of weeks of saving and y is the dollar amount in her savings
Tim invest $5,000 in an account with a bank that offers an annual interest rate of 5%, compounded quarterly. Write the function that models the growth of a deposit of $5,000.
A(t)= __(__+(__\__)) ^__t
Answers
9514 1404 393
Answer:
A(t) = 5000(1 +.05/4)^(4t)
Step-by-step explanation:
The compound interest formula is ...
A = P(1 +r/n)^(nt)
where principal P earns interest at annual rate r compounded n times per year for t years. The problem statement tells you P=5000, r=0.05, n=4. Putting these values into the formula gives ...
A(t) = 5000(1 +0.05/4)^(4t)
ASAP NEDDDD HELPPPPPP
Answers
By translation, the image of the triangle X is equivalent to the triangle E.
How to determine the image of a figure by rigid transformations
Herein we find the representation of a triangle, whose vertices are described below:
A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)
Whose image must be determined by a rigid transformation known as translation:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Image of the point.T(x, y) - Translation vector.Now we proceed to determine the images of the vertices of the triangle:
A'(x, y) = (5, 5) + (4, - 3)
A'(x, y) = (9, 2)
B'(x, y) = (5, 6) + (4, - 3)
B'(x, y) = (9, 3)
C'(x, y) = (7, 5) + (4, - 3)
C'(x, y) = (11, 2)
Therefore, the triangle E is the image of the triangle X.
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