For the following you need to do the following:
a. Name the slope
b. Name the starting value
c. Please draw figure 0, 4, and 5
d. Figure out how many blocks is in figure 100.
Answers
The slope, starting, values and number of blocks in the figures, found using arithmetic progression are;
1. Slope= 2
Starting value = 1
Figure 100 has 211 squares
2. Slope = 3
Starting value = ³
Figure 100 has 303 squares
3. Slope = 2
Starting value = 1
Figure 100 has 101 squares
4. Slope = 2•n + 1
Starting value = 1
Figure 100 has 10201 squares
5. Slope = 3
Starting value = 4
Figure 100 has 304 squares
6. Slope = 2
Starting value = 2 squares and 3 triangles
Figure 100 has 200 squares and 3 triangles
What is an arithmetic sequence?An arithmetic sequence is one that is formed by the addition of a constant to the value of a term, to get the value of the next term.
1. The difference between the number of squares in subsequent figure is 5 - 3 = 7 - 5 = 2
Which gives;
The equation that gives the number of blocks in each figure is a linear equation of the form, y = m•x + c
Where;
m = The slope = The rate of change of the number of blocks = 2 more squares each subsequent figure
c = The y–intercept = The number of blocks when the figure is Figure 0 = The number of blocks at the start (The starting value)
Subtracting 2 (the slope) from the number of blocks in Figure 1, gives;
c = The starting value = Number of squares in Figure 0 = 3 - 2 = 1
Figure 0 has one square
Figure 4 has (2 × 4 + 1) blocks = 9 Squares
Figure 5 has (2 × 5 + 1) blocks = 11 Squares
Figure 100 has (2 × 100 + 1) blocks = 201 Blocks
2. Here, the slope, m = The rate of change = 3
The starting value, c = 6 - 3 = 3 = Figure 0
The number of blocks in each of the required figures are;
Figure 0 = 3 Squares
Figure 4 = 3 + 4 × 3 = 15
Figure 5 = 3 × 5 + 3 = 18
Figure 100 has (3 × 100 + 3) squares = 303 Squares
3. The slope, c = 7 - 5 = 5 - 3 = 2
The starting value = 3 - 2 = 1
Figure 0 has 1 block
Figure 4 has (2 × 4 + 1) blocks = 9 squares
Figure 5 has (2 × 5 + 1) blocks = 11 squares
Figure 100 has (2 × 100 + 1) blocks = 101 blocks
4. The number of blocks is (n + 1)²
The number of blocks increases by 2•n + 1
The slope = 2•n + 1
The starting value = 2×0 + 1 = 1
Figure 0 has 1 block
Figure 4 has (4 + 1)² blocks = 25 blocks
Figure 5 has (5 + 1)² blocks = 36 blocks
Figure 100 has (100 + 1)² blocks = 10,201 blocks
5. Slope = 13 - 10 = 10 - 7 = 3
The starting value = 7 - 3 = 4
Figure 0 has 4 block
Figure 4 has (3 × 4 + 4) blocks = 16 blocks
Figure 5 has (3 × 5 + 4) blocks = 19 blocks
Figure 100 has (3 × 100 + 4) blocks = 304 blocks
6. The slope = 2
Starting value = 2 blocks and 3 triangles
Figure 0 has 2 blocks and 3 triangles
Figure 4 has (2 × 4) blocks + 3 triangles = 6 squares + 3 triangles
Figure 5 has 10 blocks and 3 triangles
The figure in question 6 shows only the block part
Figure 100 has (2 × 100 = 200) blocks and 3 triangles
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Related Questions
the temperature was 88°F at 2pm the temperature decreases 4° per hour what time will the temperature be 72°f
Answers
paula invited some friends to dinner, and she plans to make fajitas. at the grocery store, she spends $2.56 on red bell peppers and $1.92 on green bell peppers. if both types of bell peppers cost $1.60 per pound, how many total pounds of bell peppers does she buy?write your answer as a whole number or decimal. pounds
Answers
Answer:
2.8 pounds
Step-by-step explanation:
she spends on both types of bell peppers =
$2.56+$1.92=$4.48
$1.60 = 1 pound
$4.48 = ?
= 4.48/1.60
= 2.8 pounds
an executive in an engineering firm earns a monthly salary plus a christmas bonus of 5700 dollars. if she earns a total of 83500 dollars per year, what is her monthly salary in dollars?
Answers
The monthly salary of an executive is $6483.
What is monthly salary?
A salary is the amount of money that an employee receives from their employer each month, particularly when they work in a profession like education, law, or medical.
Given: An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 5700 dollars. She earns a total of 83500 dollars per year.
To find the salary for each month.
First to subtract the Christmas bonus from the total amount.
83500 - 5700 = 77800.
So, the salary from each month is, 77800/12 = 6483
Therefore, the salary for each month is, $6483.
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i need to multiply 11x0.08 how would i do it?
Answers
Answer:
just use calculator ,88 is answer and hi
Step-by-step explanation:
okay so basically you do it likr jormally but you drag the decimal down
1 1
×0.08
____
0.88
in a study by giacobbi et al. (2014), it was determined that about 60% of the participants found imagery very helpful in enhancing their physical activity, but 40% said they would no longer use imagery in their exercise. the implication from these results is that
Answers
Before offering imaging programs, practitioners need to be aware of the reasons why exercise participants are doing it.
Define imagery in sports.When we use imagery, we simulate an actual situation in our minds rather than actually going through it. It differs significantly from daydreaming or simply thinking about anything because it is a cognitive activity that is consciously used by an athlete or exerciser to accomplish a certain task.
In this study, an analysis of secondary data from a recently published randomized controlled trial. In a community-based, group-mediated physical activity intervention for sedentary people 50 and older, the Active Adult Mentoring Program (AAMP) tested the effectiveness of peer volunteers as delivery agents. The AAMP was built on the social-cognitive and self-determination theories, and mentors were trained to lead discussions in groups that would help reinforce key ideas from both theories.
The adaptability of images makes it useful at different times and in varied settings. Athletes employ imagery most frequently right before a competition or during practice, but they do so during the entire season, including the off-season. Similar to how it's reported by athletes, visualization is frequently used before an activity session. For example, it would be more effective for a swimmer to mentally practice her race start by adopting the proper position on the starting block at the swimming pool, as opposed to sitting on a chair at home. Both types of people will typically imagine within the sport and exercise environment where the benefits of this technique are maximized.
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i need help, what is 4x+14≤38
Answers
Answer:
x ≤ 6 I think!
Answer: [tex]x\leq 6[/tex]
Step-by-step explanation: [tex]4x\leq 38-14[/tex]. Move the 14 to the right side first.
Then you would get [tex]4x\leq 24[/tex]
Divide 4 on both side
[tex]x\leq 6[/tex]
Solve...........................................
Answers
The sum of 25 and 35 using their greatest common factor is 60.
What are factors?It should be noted that factors simply means the numbers that.van be multiplied with another number which is also a factor to get the original number.
In this case, it should be noted that the sum of 25 + 25 based on their factor will be:
= 5(5) + 5(7)
= 5(12)
= 60
The sum is 60.
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Vince took out a $500 loan to buy a new
couch. He paid back the loan in 2 years and
paid a total of $570. What was the simple
interest rate for his loan?
Answers
Answer:
Step-by-step explanation:
The requried, simple interest rate for Vince's loan was 7%.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Amount = Principal [1 + rate×time]
We can use the simple interest formula to solve this problem, where:
Simple interest = Principal x Rate x Time
In this case, the principal is $500, and the time is 2 years. We can rearrange the formula to solve for the rate:
Rate = Simple interest / (Principal x Time)
The total amount paid back, including the principal and the interest, is $570. So, the simple interest can be calculated as:
Simple interest = Total amount paid - Principal
Simple interest = $570 - $500
Simple interest = $70
Substituting these values into the formula, we get:
Rate = $70 / ($500 x 2)
Rate = $70 / $1000
Rate = 0.07 or 7%
Therefore, the simple interest rate for Vince's loan was 7%.
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(1) Solve x² + x + 2 = 0 by formula method.
Answers
The roots of the quadratic equation x² + x + 2 = 0 is [tex]-1+\sqrt{-7} /2[/tex] and[tex]-1-\sqrt{-7} /2[/tex]
What are roots?Roots: In mathematics, a solution to an equation, usually expressed as a number or an algebraic formula. The square root of a number is a value that can be multiplied by itself to give the original number. The square root of 9 is 3, because when 3 is multiplied by itself, you get 9.
given quadratic equation is, x² + x + 2 = 0
to find the roots we have formula method ,
x=[tex]-b+\sqrt{b^2-4ac}[/tex][tex]/2a[/tex]
x=[tex]-b-\sqrt{b^2-4ac}[/tex][tex]/2a[/tex]
a=1, b=1 and c=2
sub the values in the above equation
x=[tex]-1+[/tex][tex]\sqrt{1-4(1)(2)}[/tex][tex]/2[/tex]
x=[tex]-1-\sqrt{1-4(1)(2)} /2[/tex]
x= [tex]-1+\sqrt{-7}/2[/tex] and x=[tex]-1-\sqrt{-7} /2[/tex] are the roots of the quadratic equation
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if you finish these both ill give u a cookie
Answers
1. 135, 205, 330, 275, and 365 are divisible by 5.
2. 1, 4, and 7 can be filled in the blank space to make it divisible by 3.
3. 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.
4. 81 is the only composite number all the other nos. are prime.
What is the divisibility rule?Divisibility rules are methods for determining whether a number is divisible by a certain number or not without actually dividing.
We know numbers that are divisible by 5 are those numbers
having 5 or 0 in their unit place.
∴ 135, 205, 330, 275, and 365 are divisible by 5.
A number is divisible by 3 if the sum of all the digits is divisible by 3.
∴ 3,71_ has a digit sum of 11, so 1, 4, 7 can be filled in the blank space to make it divisible by 3.
A list of all the factors of 30 is those numbers that divide 30 completely.
∴ 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.
We know composite numbers are those numbers that are not prime.
∴ 81 is the only composite number all the other nos. are prime and they have only two factors 1 and the number itself.
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What is the constant of proportionality in the equation y = - 4.26x?
Answers
Answer:
im mexican im not good at math
Corey’s cat weighed 4 pounds. A year later, it weighed 175% of its previous weight
Answers
Answer:
7 lbs
Step-by-step explanation:
75 percent of 4 lbs is 3 lbs
4+3=7
Answer:7 pounds
Step-by-step explanation:khan
What values of x and y satisfy the system
y = −2x + 3
y = 5x - 4
Answers
The most appropriate choice for simultaneous linear equation will be given by -
x = 1, y = 1
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
y = −2x + 3
y = 5x - 4
So, -2x + 3 = 5x - 4
5x + 2x = 3 + 4
7x = 7
[tex]x = \frac{7}{7}\\x = 1[/tex]
Putting the value of x in the first equation'
y = [tex]- 2\times 1 +3[/tex]
y = 1
So, x = 1, y = 1
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x to the power of 7 divided by x to the power of 4
Answers
Using the product rule of power, the expression, x^7 / x^4 = x³.
How to Divide Numbers with Powers but the same Base?If the bases are the same for two numbers having powers, the product rule of power or exponent states that we are to subtract their powers.
For example, if we are given m³ divide by m², that is m³ / m², therefore we would have:
m³ / m² = m^(3 - 2)
m³ / m² = m [the power will now be 1]
In the same vein, we can simplify "x to the power of 7 divided by x to the power of 4" as shown below:
x^7 / x^4 = x^(7 - 4) [based on the product rule of powers or exponents]
x^7 / x^4 = x³
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model monster truck has a height of 3-inches tall. The model of the monster truck to
the actual monster truck is 1 inch: 38.4 inches. How many feet tall is the actual Monster
Truck?
Answers
Answer:38.4 times 3 divided by 2
Step-by-step explanation:
Which of the following is a geometric sequence?
O 0, 2, 6, 12, 72,
1 2 3 4 5
2'3'4'5'6'
O4, 9, 14, 19, 24,
O
O 1, 3, 9, 27, 81,
Answers
The geometric sequence is option(D) i.e, 1, 3, 9, 27, 81,..
What is Geometric sequence ?
A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
In this, the last option have the geometric sequence. since, there is a common ration between each term. If you multiplying the previous term in the sequence by 3 gives the next term.
Hence, The geometric sequence is 1, 3, 9, 27, 81,
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pls help it's very urgent !!
Answers
For given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]
In this question, we have been given a function f(x) = 3x² - 4
We need to write the rule obtained when finding f^(-1)
Le f(x) = y ........(1)
y = 3x² - 4
We find the value of x.
3x² = y + 4
x² = (y + 4)/3
x = ±√[(y + 4)/3]
From (1),
f^{-1}(y) = ±√[(y + 4)/3]
Since the choice of the variable is arbitrary, we can write this as ,
f^{-1}(x) = ±√[(x + 4)/3]
Therefore, for given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]
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a steamer sails 100 miles east and then 40 miles on a bearing of n60°e. how far is the steamer from its starting point, and at what angle has it traveled from its starting point? round your answer to the nearest thousandth.
Answers
how do i delete an answer?
Determine the range of f(x) = |x + 5|.
Answers
Answer:
f(x) ≥ 0
In interval notation Range: [0, ∞]
Step-by-step explanation:
Regardless of the value of x, |x+5| ≥ 0 and there is no upper bound on f(x)
Answer: C
Step-by-step explanation: Got it right for my test
how many solutions does the equation 7x+3-8=2(5x-4) have
Answers
The number of solutions in the equation where the equation is given as 7x + 3 - 8 = 2(5x - 4) is one solution
How to determine the number of solutions in the equation?The equation is given as
7x + 3 - 8 = 2(5x - 4)
The above equation is a linear function with one variable
So, we have
7x + 3 - 8 = 2(5x - 4)
Open the brackets
So, we have
7x + 3 - 8 = 10x - 8
Subtract 10x from both sides of the equation
So, we have
-3x + 3 - 8 = - 8
Subtract (3 - 8) from both sides of the equation
So, we have
-3x = - 3
Divide by -3
x = 1
The above equation is true because it has a definite solution
Hence, the number of solutions in the equation is one
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Plssss help plsssss it’s finding proofs
Answers
2) Supplementary Angles
3) Same-side Interior Angles Postulate
4) Substitution Property
5) Subtraction Property of Equality
Given: l || m
Prove:
∠4 = ∠6
2) m∠3 + m∠4 = 180
This is because angles 3 and 4 are supplementary as they lie on a straight line. If the total of two angles is 180 degrees, they are considered to be supplementary angles since they form a linear angle when combined.
3) m∠3 + m∠6 = 180
By the Same-side Interior Angles Postulate when a transversal connects two parallel lines, the interior angles on the same side are supplementary. Hence angles 3 and 6 are supplementary.
4) m∠3 + m∠4 = m∠3 + m∠6
Using Substitution Property we can replace angle 4 with angle 6, the value or sum will still remain the same i.e. 180.
5) m∠4 = m∠6
By the Subtraction Property of Equality, we can subtract the angle 3 from both sides of the equation in part(4) and the resultant equation will be m∠4 = m∠6.
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Convert this equation to slope intercept form y-4= 2(x+7)
Answers
Answer:
y=2x+18
Step-by-step explanation:
y=mx+c --> let's solve now:
y-4=2x+14
y=2x+18
the "m" aka slope is 2.
the "y int." is 18
help i don’t understand this question
Answers
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The correct statement are;
1. The radius of the circle is 3 units.
2. The center of the circle lies on the x-axis.
3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The equation of circle will be;
⇒ x² + y² - 2x - 8 = 0
The standard form of the equation of circle is;
⇒ x² + y² + 2gx + 2fy + c = 0
Where,
The center of circle = (-g , -f)
The radius of circle = √g² + f² - c
Since, The equation of circle will be;
⇒ x² + y² - 2x - 8 = 0
Compare with the standard form of circle, we get;
⇒ 2gx = - 2x
⇒ g = - 1
And, 2fy = 0
⇒ f = 0
Hence, The center = ( -g , -f) = (- (-1) , 0)
= (1, 0)
Clearly, This shows the center of circle is lies on x - axis.
Radius of circle = √g² + f² - c
Substitute all the values we get;
Radius of circle = √g² + f² - c = √(-1)² + 0 - (-8)
= √9
= 3
Thus, The radius of the circle is 3 units.
Now, For the equation of circle x² + y² = 9,
Radius = √9 = 3 units.
So, The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Therefore, The correct statement are;
1. The radius of the circle is 3 units.
2. The center of the circle lies on the x-axis.
3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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The distance to your cousin's house is 666 miles, and the distance to Chicago is 37 miles. If it took 18 hours to drive to your cousin's house. howlong would you estimate the drive to Chicago to take?
Answers
We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)
We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.
So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).
Answer:
666/18=37miles/hour
it would take 1 hour to drive 37 miles
as an avid fisherman, nick was curious if the advertised strength of fishing line is accurate. to investigate, he used "6 pound" fishing line to hang a bucket, which he then filled with weights until the line broke. then nick measured the total weight of the bucket and its contents to determine the breaking strength of that piece of fishing line. after trying this with many different sections of the fishing line, he estimated that the distribution of breaking strength for this type of line is approximately normal with a mean of 6.44 pounds and a standard deviation of 0.75 pound.
Answers
Using the normal distribution, it is found that this type of fishing line have a breaking strength less than the advertised 6 pounds 27.76% of the time.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The mean and the standard deviation for the breaking strengths are given as follows:
[tex]\mu = 6.44, \sigma = 0.75[/tex]
The proportion of times with breaking strength less than 6 inches is given by the p-value of Z when X = 6, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 6.44)/0.75
Z = -0.59
Z = -0.59 has a p-value of 0.2776.
Hence the percentage is of 27.76%.
What is the missing information?The question is:
How often will this type of fishing line have a breaking strength less than the advertised 6 pounds.
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thanks help bhjjjdjshshshsyshdh
Answers
Answer:
14.90 $ 527.86- 349.11 = 178.75 divided by 12 pta members is 14.89 rounded would be 14.90 the answer depends if u want to round it
Step-by-step explanation:
sub to imaginefn in utube
Help me please please
Answers
Answer:
second one . the ratio is 3/4 boys to girls and we have 175 girls . then you must put 175 in same level of 4. the same like answer 2 as it mention 3/4 = b/175.
Angle DEB is 71°. State the size of angle ABD, giving a reason for your answer.
Answers
Check the picture below.
sea level changes -73.5ft in 3minutes. what is the average change in the sea level each minute?
Answers
Answer
Average change in sea level per minute = -24.5 ft/minute
Explanation
The average change in sea level each minute is given as
[tex]\text{Average change in sea level per minute = }\frac{Sea\text{ level changes}}{Time\text{ Taken}}[/tex]For this question,
Sea level changes = -73.5 ft.
Time Taken = 3 minutes.
Average change in sea level per minute = (-73.5/3) = -24.5 ft/minute
Hope this Helps!!!
