The statement 'All squares are rectangles' written as a conditional is 'If a shape is a square, then it is a rectangle.' This forms a strict conditional that states the sufficiency of the condition of being a square for the necessity of being a rectangle.
When we are asked to write the statement 'All squares are rectangles' as a conditional, we are forming what is called a strict conditional. This type of conditional states that if the antecedent (the 'if' part) is true, then the consequent (the 'then' part) must also be true without any exceptions. In our example, the antecedent is the condition of being a square, and the consequent is the condition of being a rectangle.
Strict Conditional Example
If a shape is a square, then it is a rectangle. This expresses a clear relationship between two properties: being a square and being a rectangle. This conditional is considered strict because there are no exceptions to the rule; every square is, by definition, a rectangle.
PLEASE YOU CAN ANSWER NUMBER 1 OR 2 OR BOTH PLEASE I JUST NEED HELP WITH BOTH AND NO ONE WILL ANSWER MY QUESTIONS!!!!!!!! :(
1.)In two or more complete sentences, explain how to find the time it takes for a rocket following the path, h(x) = -4x 2 + 16x, to hit the ground.
2.)A ball is thrown straight up from the top of a building that is 280ft high with an initial velocity of 48ft/s. The height of the object can be modeled by the equation s(t) = -16t 2 + 48t + 280.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.
1.) You plug a number into the variable x. Then you will solve the equation for h(x) to find the time it takes for the rocket to travel the path given.
Answer:
Step-by-step explanation:
Given that a rocket path is given by
[tex]h(x) = -4x^2 + 16x[/tex]
When it hits the ground h(x) =0
Hence we get
[tex]-4x^2 + 16x=0\\x=0, 4[/tex]
i.e. after 4 minutes the rocket hits the ground
2) Given that
[tex]s(t) = -16t^2 + 48t + 280.[/tex]
We have to find time t when height >280
[tex]s(t) = -16t^2 + 48t + 280>280\\\\t=0, 3[/tex]
Between 0 and 3 seconds the object would be above the building.
a football team gains 8 yards in one play, then loses 5 yards in the next.How many yards did the team gain in these two plays
going down the river a boat went 13 km/h. going up the river it only 1 km/h. Find the speed of the boat in still water and the speed of the current.
The speed of boat is 7 km/h and speed of stream is 6 km/h.
What is speed ?
In unit time the distance covered by any object is called speed.
In mathematical term, Speed is express as S=D/T,
where S=speed, D=distance, T= time .
Let the speed of boat in N, and the speed of current is D,
Given that,
The speed in downward stream of a boat N+D= 13 km/h, (1)
And the speed in upward stream of a boat N-D= 1 km/h. (2)
To Find speed of boat in still water, add equation (1) and (2),
2N=14 ⇒ N=7 km/h
To Find speed of current, substract equation (1) and (2),
2D=12 ⇒ D=6 km/h.
The speed of boat is 7 km/h and speed of stream is 6 km/h.
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Show how 10 - 4 helps you solve 30 - 4
[tex]\boxed{ \ 30 - 4 = \ ? \ }[/tex]
30 - 4 = ...
/ \
20 + 10
[tex]\boxed{ \ 10 - 4 = 6 \ }[/tex]
[tex]\boxed{ \ 20 + 6 = 26 \ }[/tex]
[tex]\boxed{ \ \boxed{ 30 - 4 = 26} \ }[/tex]
Further explanation
This material is part of the common core mathematics curriculum.
Show how 10 - 4 helps you solve 30 - 4.
We know 10 - 6 = 4.
Furthermore, we can take out 10 from 30 and subtract 6 from 10.
[tex]\boxed{ \ 10 - 4 = 6 \ }[/tex]
Then we can add what is left, which is 20 to add to 6.
20 + 6 = 26
So, results from 30 - 4 are 26.
Let's review the steps again.
[tex]\boxed{ \ 10 - 4 = 6 \ }[/tex]
[tex]\boxed{ \ 20 + 6 = 26 \ }[/tex]
[tex]\boxed{ \ \boxed{ 30 - 4 = 26} \ }[/tex]
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With the help of 10 - 4, the solution of 30 - 4 is 26.
Using 30 - 4 to solve 10 - 4
Since the subtracted value from 30 and 10 are the same (4) ;
Therefore,
The sum of the difference between :
(10 and 4) and (30 and 10)
(10 - 4) + (30 - 10)
6 + 20 = 26
Hence, from 10 - 4; 30 - 4 gives 26
Subtracting directly also gives :
30 - 4 = 6.
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Dave has a 32-ounce energy drink. He drinks 10 ounces. Enter the percentage of ounces Dave had left from his energy drink. Round your answer to the nearest hundredth
Answer:
Step-by-step explanation:
Dave has a 32-ounce energy drink and he drinks 10 ounces then 68.75% of the energy drink has been left by Dave.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Dave has a 32-ounce energy drink.
Dave drinks 10 ounces of energy drink.
We need to find the percentage of ounces Dave had left from his energy drink.
To find this first we have to subtract 10 from 32
32-10 = 22.
Now let us find 22 is what percentage of 32.
x/100 × 32 = 22
0.32x=22
Divide both sides by 0.32
x=22/0.32
x=68.75 %
Hence, 68.75% of the energy drink has been left by Dave.
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Please help!
Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures.
Write a problem involving how much more Than and solve it. Explain how drawing a diagram helped you solve the problem
Use a bar model to find the unknown value: 3/6 = ?/7
I can't figure this out... Can someone please help me?
a table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of each rectangular leaf is 3 feet. The extended table is rectangular with an area of (18+6x) square feet. a) write an algebraic expression that represents the length of the extended table b) what does your variable represent?
a. The algebraic expression that represents the length of the extended table is 6 + 2x
b. The variable 'x' represents the length added by inserting each identical table leaf.
How to write an algebraic expression
a) To write an algebraic expression representing the length of the extended table, consider the original length of the table (6 feet) and the length added by inserting two identical table leaves (each with a longest side length of 3 feet).
Let's denote the length added by inserting the table leaves as 'x'.
Since we're inserting two identical leaves, the total length added would be 2x.
The length of the extended table can be expressed as the sum of the original length (6 feet) and the length added by the table leaves (2x):
Length of the extended table = 6 + 2x
b) The variable 'x' represents the length added by inserting each identical table leaf. It quantifies the extra length that extends the original table when the leaves are inserted.
Write each mixed number as a percent 2 1/2
What is the value of the underlined digit 53
Evaluate c-2 when c =7
Answer:
The value of given expression c-2 is 5 when c=7.
Step-by-step explanation:
The given expression
[tex]c-2[/tex]
We have to find the value of given expression c-2 when c=7.
Substitute c=7 in the given expression.
[tex]c-2=7-2[/tex]
[tex]c-2=5[/tex]
Therefore the value of given expression c-2 is 5 when c=7.
You have $ 2 0 $20dollar sign, 20 to spend on taxi fare. The ride costs $ 5 $5dollar sign, 5 plus $ 2 . 5 0 $2.50dollar sign, 2, point, 50 per mile. Let m mm represent the number of miles ridden. Write an inequality to determine how many miles you can ride for $ 2 0 $20dollar sign, 20.
Answer:
6 x $2.5 = $15
$15 + $5 = $20
−p(d+z)=−2z+59. solve for z.
we have
[tex]-p(d+z)=-2z+59[/tex]
Solve for z
[tex]-p(d+z)=-2z+59\\-pd-pz=-2z+59[/tex]
Group terms that contain the variable z, and move the other terms to the opposite side of the equation
[tex]-pz+2z=59+pd\\z(2-p)=59+pd[/tex]
Divide by [tex](2-p)[/tex] both sides
[tex]z=\frac{(59+pd)}{(2-p)}[/tex]
therefore
the answer is
[tex]z=\frac{(59+pd)}{(2-p)}[/tex]
Final answer:
The equation −p(d+z)=−2z+59 was solved for z by distributing the negative sign, combining like terms, and dividing by the coefficient of z, resulting in z = (59 + pd)/(2 - p).
Explanation:
The student asked to solve the equation −p(d+z)=−2z+59 for z. To solve for z, we need to isolate z on one side of the equation, following these steps:
Distribute the negative sign through the parentheses on the left side of the equation: −pd − pz = −2z + 59.
Move the terms containing z to one side of the equation: −pz + 2z = 59 + pd.
Combine like terms by adding pz to both sides: 2z + pz = 59 + pd or z(2 - p) = 59 + pd.
Divide both sides by (2 - p) to solve for z: z = (59 + pd)/(2 - p).
Now, z is isolated and the solution is given in terms of p and d.
What is the acceleration of a wagon of mass 20 kg if a horizontal force of 64 N is applied to it? (Ignore friction)
The acceleration of the wagon is 3.2 m/s².
Explanation:To find the acceleration of the wagon, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force applied to it divided by its mass. In this case, the net force is 64 N (the horizontal force applied) and the mass of the wagon is 20 kg. So the acceleration can be calculated as follows:
A = F/M = 64 N / 20 kg = 3.2 m/s²
Therefore, the acceleration of the wagon is 3.2 m/s².
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Which of the following measurements could be the side lengths of a right triangle? A. 66 in, 88 in, 110 in
B. 66 in, 88 in, 132 in
C. 66 in, 99 in, 110 in
D. 55 in, 88 in, 110 in
please dont answer if not 100 % sure.
Answer:
Step-by-step explanation:
The cable is 50 yards long, viewing post is 40 yard high , how far is the bottom cable from the base of the viewing post
12x+28y=84 how do I graph it
on a tour of an old gold mine, you find a gold nugget containing .82 ounces of gold. gold is worth $1566.80 per ounce. how much is your gold worth?
The value of a gold nugget containing 0.82 ounces of gold at $1566.80 per ounce is $1284.776.
The value of a gold nugget containing 0.82 ounces of gold, given that gold is worth $1566.80 per ounce, can be calculated through a simple multiplication. The value of the gold nugget is found by multiplying the amount of gold in the nugget by the price per ounce of gold.
To calculate:
Multiply the weight of the gold nugget (0.82 ounces) by the value per ounce ($1566.80).0.82 ounces imes $1566.80/ounce = $1284.776Therefore, the gold nugget is worth $1284.776.
Find the difference. 632
-274
Solve for S.
3s + 2 = 12 - 2s
3s+2=12-2s
(3s-3s)+2=12(-2s-3s)
2=12-5s
2-12=(12-12)-5s
-10=-5s
-10/-5=-5s/-5
2=s
Check
(3*2)+2=12-(2*20
6+2=12-4
8=8
S=2
What is the fraction of 35%
Which statements about opposites are true?
Select each correct answer.
A.The product of a number and its opposite is always 1.
B.A number and its opposite are located the same distance from zero on a number line.
C.The opposite of zero is zero.
The opposite of a negative number is always a positive number.
D.
B is true
D as well
Write words to match the expression of 4x(10 -2)
How many times larger is 9 x 10-8 than 3 x 10-12?
[tex]9\times10^{-8}[/tex] is [tex]3\times10^{4}[/tex] times larger than [tex]3\times10^{-12}[/tex].
The given number is [tex]9\times10^{-8}[/tex] and [tex]3\times10^{-12}[/tex].
We need to find how many times larger is [tex]9\times10^{-8}[/tex] than [tex]3\times10^{-12}[/tex].
What is scientific notation?To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.
If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.If the given number is smaller than 1, then the decimal point has to move to the right, so the power of 10 will be negative.Now, [tex]\frac{9\times10^{-8}}{3\times10^{-12}}[/tex]
[tex]=3\times\frac{10^{-8}}{10^{-12}}[/tex]
[tex]=3\times10^{-8+12}[/tex] (∵[tex]\frac{a^{m}}{a^{n}} =a^{m-n}[/tex])
[tex]=3\times10^{4}[/tex]
Therefore, [tex]9\times10^{-8}[/tex] is [tex]3\times10^{4}[/tex] times larger than [tex]3\times10^{-12}[/tex].
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A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top of the mountain. She then walked 3,972 feet in 7 minutes. In that time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.
The average rate of change in altitude of the hiker from her starting point to her ending point is -63.5 feet per minute.
The following can be deduced based on the information provided in the question:
During the first walk, she descended 1024 feet and during the second walk, she descended 500 feet. Therefore, the total will be:
= 1024 feet + 500 feet = 1524 feet
During the first walk, the time taken was 17 minutes while for the second walk, the time taken was 7 minutes. Therefore, the total time taken will be:
= 17 minutes + 7 minutes
= 24 minutes.
Therefore, the average rate will be:
= 1524 / 24
= 63.5 feet per minute
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a school has a goal of getting at least 2000 boxtops. they have 872 so far.
they have 8 days left to get it.at least how many do they need to collect each day to meet or exceed their goal.
The Ortiz family will travel round-trip from Indianapolis to Denver this summer. The driving distance between the two cities is 1,058 miles. They need to find out about how much the gas will cost round trip. Their car gets about 20 miles per gallon. They usually spend about $2.89 per gallon.
47% of $118 estimate
Mark put his dog on a diet. The dog's total weight change for the first 2 weeks was −3/4 pound. The dog lost the same amount of weight each week. What was the change in the dog's weight after the first week of the diet? Enter your answer in the box.