Answers
Answer:
p = 12+5n
Step-by-step explanation:
For every added triangle, the perimeter only increases by 5.
For n=1, the perimeter is 6+6+5 = 17
For n=2, the perimeter is 6+6+5+5 = 22
So in general, the perimeter is 12 + 5n
Answer:
Q12. p = 5n + 12
Q13. See below.
Q14. y-intercept = (0, -3); x-intercept = (-3/2, 0).
Step-by-step explanations:
Question 12. Perimeter
One triangle: p₁ = 2×6 + 1×5
Two triangles: p₂ = 2×6 + 2×5
Three triangles : p₃ = 2×6 + 3×5
n triangles: pₙ = 2×6 + n×5
General formula: p = 5n + 12
===============
Question 13. Modelling a function
Here's one possible table of values.
x y
-3 3
-2 1
-1 -1
0 -3
1 -5
You can see the graph of the function in Fig. 1 below.
===============
Question 14. x- and y-intercepts
y- intercept
y = -2x – 3 Set x = 0
y = -2×0 – 3
y = 0 – 3
y = -3
The y-intercept is at (0, -3).
=====
x-intercept
y = -2x – 3 Set y = 0
0 = -2x – 3 Add 3 to each side
3 = -2x Divide each side by -2
x = -3/2
The x-intercept is at (-3/2, 0).
Related Questions
Rectangle ABCD has vertices A(-3, 1), B(5, 7), C(9, 4), and D(1, -2). Calculate the
area of rectangle ABCD.
Answers
It's not a rectangle. Look at the picture.
It is a parallelogram.
The area of the red rectangle:
[tex]A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108[/tex]
The areas of the right triangles:
[tex]A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24[/tex]
The area of a parallelogram:
[tex]A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48[/tex]
job starting salary of 81,000 and gets a 2% raise every year.what is the expected salary after the eight year ? please explain how to do step by step. really need help.
Answers
Answer:
hell have 120,000
Step-by-step explanation:
Order each step and justification that is needed to solve the equation below. 2/3y+ 15=9
Answers
[ Answer ]
Y = -9
[ Explanation ]
Subtract 15 from both sides:
2/3y + 15 - 15 = 9 - 15
Simplify:
2/3y = -6
Multiply each side by 3:
3 * 2/3y = 3 (-6)
Simplify:
2y = -18
Divide both sides by 2:
2y / 2 = -18/2
y = -9
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Using the simplification, it is proven that the y = -9 from the equation 2/3y + 15 = 9.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given that 2/3y + 15 = 9
Subtract 15 from both sides;
2/3y + 15 - 15 = 9 - 15
Now Simplify,
2/3y = -6
Multiply each side by 3,
3 (2/3y) = 3 (-6)
2y = -18
y = -9
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Valerie and Robbie are playing a number game.
Valerie tells Robbie “I’m thinking of a number between 1 and 50. If I divide the number by 4, then add 5, that subtract 6, I get 6.”
What number is Valerie thinking of ?
Answers
In the number game that Valerie and Robbie are playing, based on Valerie's clues, the number she is thinking of can be determined using a mathematical equation: x/4 + 5 - 6 = 6. Solving this equation step-by-step, the number Valerie is thinking of is 28.
Explanation:In the given scenario, Valerie and Robbie are playing a number game. Valerie tells Robbie that she's thinking of a number which, when divided by 4, then added to 5, and subtracted by 6, equals to 6. This can be translated into a mathematical equation:
x/4 + 5 - 6 = 6
We can simplify this step-by-step. First, we can combine the constants:
x/4 -1 = 6
Next, add 1 to both sides to isolate x/4 on the left:
x/4 = 7
Finally, to find x, multiply both sides by 4:
x = 28
So, the number that Valerie is thinking of is 28.
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-x+2 > 3 whats the answer plz its urgent thanks
Answers
(03.02 LC)
Look at the figure below:
Triangle ABC with a segment joining vertex A to point D on side BC.
Which information is required to prove that angle ABD is congruent to angle ACD? (6 points)
Segment AC is congruent to segment AB.
Segment AD is congruent to segment AC.
Segment BD is congruent to segment AD.
Segment AB is congruent to segment BD.
Answers
Answer:
SEgment AC is congruent to segment AB
Step-by-step explanation:
given is a triangle ABC with a segment joining A to D on side BC.
To prove that ABD is congruent to ACD
Let us compare these two triangles.
AD = AD (reflexive) Thus one side is equal.
IF AB = AC, then by isosceles triangles property we have angle B = angle C
Thus we get two sides equal. But this is a necessary condition not sufficient.
Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB
Thus if either AD is angle bisector, or D is mid point besides AC = AB we get
the two triangles are congruent.
An airplane must clear a 60-foot pole at the end of a runway 500 yards long determine the angle of elevation at which the airplane must ascend to clear the pole.
Answers
Answer:
2.3 degrees.
Step-by-step explanation:
Please find the attachment.
We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.
Let us convert 500 yards to feet.
1 yard= 3 feet.
500 yards= 3*500 feet= 1500 feet.
We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.
Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.
[tex]tan(\theta)=\frac{60}{1500}[/tex]
[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]
[tex]\theta=\tan^{-1}(0.04)[/tex]
[tex]\theta=2.290610042639[/tex]
Therefore, the airplane must ascend 2.3 degrees to clear the pole.
which choice shows how to find the greatest common factor of 18 and 72 through prime factorization
Answers
[tex]\begin{array}{c|c}18&2\\9&3\\3&3\\1\end{array}\\\\18=\boxed2\cdot\boxed3\cdot\boxed3\\\\\begin{array}{c|c}72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\72=2\cdot2\cdot\boxed2\cdot\boxed3\cdot\boxed3\\\\GCF(18,\ 72)=\boxed2\cdot\boxed3\cdot\boxed3=\boxed{\boxed{18}}[/tex]
The greatest common factor of 18 and 72 can be found through prime factorization, by identifying the prime factors of each number, finding the common factors, and multiplying them together. In this case, the greatest common factor is 18.
Explanation:To find the greatest common factor (GCF) of 18 and 72 through prime factorization, follow these steps:
First, obtain the prime factors of each number. For 18, the prime factors are 2, 3, and 3. For 72, the prime factors are 2, 2, 2, 3, and 3. Next, identify the common prime factors. Both 18 and 72 have the prime factors 2, 3, and 3 in common. Then multiply these common factors together. This gives 2*3*3 = 18. So, the greatest common factor of 18 and 72 is 18.Learn more about Greatest Common Factor here:
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if y varies directly as x and y=8 when x=2, find y when x=6
Answers
Answer:
y = 8
Step-by-step explanation:
If y varies directly as x we can write y = kx where k is some constant.
Y = 8 when x = 2 so 8 = k*2
k = 8/2 = 4
so y = 4x
This is the equation of variation.
When x = 6, y = 4*6 = 24 (answer).
Answer:
y =24
Step-by-step explanation:
The equation for direct variation is
y =kx
If we know x and y we can solve for k
y=kx
8 =k*2
Divide each side by 2
8/2 = k2/2
4 =k
y =4x
We want to find y when x=6
y =4*6
y =24
-2/7 multiply by -5 2/3
Answers
Answer:
1.61904761905
Step-by-step explanation:
-5 2/3 is equal to -17/3. We then multiply the two fractions: -2/7 *-17/3, the answer is 1.61904761905 as a decimal or 34/21( or 1 13/21).
Hope this helps! <3
3x + 5 equals 19 - 4x what does x equals to
Answers
Answer:
x = 2Step-by-step explanation:
3x + 5 = 19 - 4x subtract 5 from both sides
3x = 14 - 4x add 4x to both sides
7x = 14 divide both sides by 7
x = 2
Answer:
x=2
Step-by-step explanation:
3x + 5 = 19 - 4x
Add 4x to each side
3x + 5 +4x= 19 - 4x+4x
7x+5 = 19
Subtract 5 from each side
7x+5-5 =19-5
7x =14
Divide each side by 7
7x/7 = 14/7
x = 2
A division of a ———ends?
Answers
The complete statement is a division of long form ends with zeroes as remainders
What is division and long division method? What is a expression? What is a mathematical equation?Division is the process of splitting a number or an amount into equal partsLong Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following statement -
A division of _____ ends?
The complete statement is -
A division of long division form ends with zeroes as remainders
Therefore, the complete statement is a division of long form ends with zeroes as remainders.
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5 pounds of chocolate cost $36.50. How much is each pound of Chocolate? (Please include Work)
Answers
Answer:
Each pound of chocolate costs $7.30
Step-by-step explanation:
if 5 pounds of chocolate costs $36.50 then you could simply divide the $36.50 by 5 to calculate the cost of 1 pound of chocolate.
So, 36.50 ÷ 5 = 7.30
Each pound of chocolate costs $7.30
To find the cost of each pound of chocolate, you divide the total cost by the total number of pounds. Given a total cost of $36.50 for 5 pounds of chocolate, the resulting calculation is $36.50 ÷ 5 = $7.30. Thus, each pound costs $7.30.
Explanation:If you have 5 pounds of chocolate that cost $36.50 in total, and you need to find the cost of each pound of chocolate, you can determine this by dividing the total cost by the number of pounds. This is similar to how in our reference material, to compute the cost of each piece of fruit, you divided the total expense by the quantity of fruit.
In this case, you need to divide the total cost, which is $36.50, by the quantity, which is 5 pounds. So the calculation is $36.50 ÷ 5 = $7.30. Therefore, each pound of chocolate costs $7.30.
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The velocity of a car increases from 2.0 m/s to 16.0 m/s in a time period of 3.5 s. What was the average acceleration?
Answers
The average acceleration of the car is 4 m/s²
The given parameters:
initial velocity of the car, u = 2 m/s
final velocity of the car, v = 16 m/s
time of motion of the car, t = 3.5 s
To find:
the average acceleration of the carThe average acceleration of the car is calculated as the change in velocity per change in time.
The formula for average acceleration is given below;
[tex]a = \frac{\Delta v}{\Delta t} = \frac{v- u}{t} = \frac{16 - 2}{3.5} = 4 \ m/s^2[/tex]
Thus, the average acceleration of the car is 4 m/s²
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which expression is equivalent to (7x^2-4)(5x+7)
Answers
Expand to get 35x^3+49x^2-20x-28
Answer:
3x(3x + 2)
Step-by-step explanation:
last year the attendance at the homecoming football game was 300.This year , 360 attended What was the percent increase from last year to this year ?
Answers
Answer:
20%
Step-by-step explanation:
Percent increase is difference/original
360-300) / 300
60/300 / 60/60 = 1/5 * 20/20 = 20/100
Percent is out of 100
WILL GIVE BRAINLIEST! THIS IS 20PTS! Which mathematical property is demonstrated? If x = –3 and –3 = z, then x = z. A.) symmetric property of equality B.) transitive property of equality C.) closure property of multiplication D.) closure property of addition
Answers
Answer:
B.) transitive property of equality
Step-by-step explanation:
x = –3 and –3 = z, then x = z.
Symmetric property of equality: if a = b then b = a
Transitive property of equality: if a = b and b = c, then a = c
Closure property of multiplication: the set is closed under multiplication
Closure property of addition: the set is closed under addition
In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find AC, if CD = 6 sqrt 3
Answers
Final answer:
Since ΔACD is an isosceles right triangle, the two legs AC and CD are equal. Given CD = 6 √ 3, AC is also 6 √ 3 units.
Explanation:
In triangle ΔABC, we are given that m∠ACB = 90°, meaning that ΔACB is a right-angled triangle. We are also given that CD is perpendicular to AB and that m∠ACD = 45°. Since CD is perpendicular to AB at D, triangle ΔACD is also a right-angled triangle with a 45° angle, which makes it an isosceles right triangle. In an isosceles right triangle, the lengths of the legs are equal. Therefore, AC will be equal to CD which is given as 6 √ 3.
The length of AC in triangle ΔACB can be found using Pythagoras' theorem, AC = √(AB² + BC²). But here we need only the length of AC in the right-angled ΔACD where AC equals CD.
Hence, AC = 6 √ 3 units.
Use the equation and type the ordered-pairs. y = 2^x {(-1, ), (0, ), (1, ), (2, ), (3, ), (4, )}
Answers
Put the values of x to the equation y = 2ˣ:
[tex]x=-1\to y=2^{-1}=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right)\\\\x=0\to y=2^0=1\to(0,\ 1)\\\\x=1\to y=2^1=2\to(1,\ 2)\\\\x=2\to y=2^2=4\to(2,\ 4)\\\\x=3\to y=2^3=8\to(3,\ 8)\\\\x=4\to y=2^4=16\to (4,\ 16)[/tex]
Answer:
[tex]\left\{\left(-1,\ \dfrac{1}{2}\right);\ (0,\ 1);\ (1,\ 2);\ (2,\ 4);\ (3,\ 8);\ (4,\ 16)\right\}[/tex]
abcd is not drawn to scale. based on the diagonal measures given abcd
Answers
Answer:
DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180
Answer: May or may not be
Step-by-step explanation:
check the picture and trust me
A coffee shop sold 1627 espressos, 2741 cappuccinos and 4226 lattes. how many cups of coffee were sold in total?
Answers
By using the simple addition operation, the total number of cups of coffee sold in the coffee shop, counting espressos, cappuccinos, and lattes, is 8,594 cups.
Explanation:To find the total number of cups of coffee sold, we should add up the number of espressos, cappuccinos, and lattes. This principle is known as simple summation or addition operation in mathematics. As per the numbers given:
Espressos sold: 1627Cappuccinos sold: 2741Lattes sold: 4226When we add these together, we get the total cups of coffee sold as:
1627 (Espressos) + 2741 (Cappuccinos) + 4226 (Lattes) = 8594 cups of coffee in total
So, the coffee shop has sold a total of 8594 cups of coffee.
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Write an explicit formula for the sequence given by the recursive definition a(1)=1 and a(n+1)=a(n)+7
Answers
Answer:
an = -6+n
or
an = 1 + 7(n-1)
Step-by-step explanation:
a(1)=1 and a(n+1)=a(n)+7
The explicit formula is
an = a1+ d (n-1)
we know a1 =1
Looking at a(n+1)=a(n)+7
We are adding 7 each time so the common difference is +7
an = 1 + 7(n-1)
We can simplify this
an = 1 + 7n -7
an = -6+n
You can use either formula
Please help me, ASAP!
A candy mixture is made from 6 pounds of sugar sticks of $10 per pound and 14 pounds of jelly beans of $8 per pound. Find the price of the candy mixture per pound.
Answers
Answer: The price per pound is $18
Find the area of rectangle PLUM
If entering your answer as a decimal, round your final answer to the nearest hundredth.
Answers
PL= sqrt(4^2+12^2)=4sqrt(1+9)=4sqrt(10)
Using similarity gives that AM=4/3.
ML=40/3
[PLMU]=40/3 * 4 = 160/3 (53.33)
Or
PM= sqrt(4^2+16/9)=sqrt(160/9)=4sqrt(10)/3
4sqrt(10)*4sqrt(10)/3=160/3 or approximately 53.33
Find the earnings for selling the same number of each type of sandwich use x to represent the number of each sandwich sold
Answers
The earnings for selling the same number of each type of sandwich, considering both Turkey and Ham with Pretzel Roll and Bagel options, amount to $48. This is derived from a simplified expression of $29.10x, factored by 11, indicating a total revenue of $4.30 per sandwich.
Earnings for Selling Sandwiches
1: Identify the Given Information
We have two types of sandwiches: Turkey and Ham.
Each type comes in two types of bread: Pretzel Roll and Bagel.
Prices are provided for each combination:
Turkey Pretzel: $2.25
Turkey Bagel: $2.00
Ham Pretzel: $1.55
Ham Bagel: $1.30
2: Represent the Number of Sandwiches with a Variable
Let x represent the number of each type of sandwich sold (both Turkey and Ham, regardless of bread).
3: Calculate Earnings for Each Type of Sandwich
Turkey Sandwich: $11 (given price) * x (number sold) = $11x
Ham Sandwich: $11 (given price) * x (number sold) = $11x
Step 4: Calculate Earnings for Each Bread Type (excluding overlapping information)
Pretzel Roll: (Earnings from Turkey Pretzel + Earnings from Ham Pretzel) = ($2.25 * x) + ($1.55 * x) = $3.80x
Bagel: (Earnings from Turkey Bagel + Earnings from Ham Bagel) = ($2.00 * x) + ($1.30 * x) = $3.30x
5: Combine Earnings for Total Revenue
Total Earnings = Earnings from Turkey Sandwiches + Earnings from Ham Sandwiches + Earnings from Pretzel Rolls + Earnings from Bagels
Total Earnings = $11x + $11x + $3.80x + $3.30x = $29.10x
6: Simplify the Expression
Total Earnings = $29.10x
Since we are selling the same number of each type of sandwich, 11 is a common factor in all four terms.
We can factor out 11 to obtain:
Total Earnings = 11 * ($2.65 + $1 + $0.35 + $0.30) = 11 * $4.30 = $48
Therefore, the earnings for selling the same number of each type of sandwich are $48.
251,589 divided by 252
Answers
Answer:
The answer would be 998.4
Step-by-step explanation:
251,589 divided by 252 = 998.36
round it to 998.4
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is {y|y < 16}. The domain is all real numbers. The range is {y|y ≤ 16}. The domain is {x|–5 < x < 3}. The range is {y|y < 16}. The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}. Mark this and return Save and Exit Next
Answers
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}.
Step-by-step explanation:
The vertex of a parabola is given by
[tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex].
As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).
As a is negative, it opens downward, so the range is {y|y ≤ 16}.
Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].
Mrs hawk assigns her students an average of no more than 15 questions on each assignment mrs. hawks students had 11,10,13,14 and 14 questions write amd solve amd inequality that Mrs hawk can use to determine the number of questions she can have in the sixth assignment
Answers
Answer:
The number of questions in sixth assignment must be less than or equal to 28.
Step-by-step explanation:
The number of questions in first five assignments are 11,10,13,14 and 14.
It is given that Mrs hawk assigns her students an average of no more than 15 questions on each assignment. Therefore the average of six assignments is less than or equal to 15 questions.
Let the number of questions in sixth assignment be x
[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
Average of six assignments are
[tex]A=\frac{11+10+13+14+14+x}{6}[/tex]
[tex]A=\frac{62+x}{6}[/tex]
Since the average of questions is no more than 15, therefore
[tex]A\leq 15[/tex]
[tex]\frac{62+x}{6}\leq 15[/tex]
[tex]62+x\leq 90[/tex]
[tex]x\leq 28[/tex]
Therefore the number of questions in sixth assignment must be less than or equal to 28.
X+2=x+4
A.The equation has no solution
B.The equation has one solution
C.The equation has infinitely many solutions
Answers
Answer:
A. The equation has no solution
The unchanging value of the ratio between two proportional quantities is
Answers
Answer:
The proportional
Step-by-step explanation: