The capture of the forts at Vincennes, Kaskaskia and Cahokia help end the war because it helped the Americans control the Appalachian Mountains.
What was the Siege of Fort Vincennes?It was the War frontier battle that was fought in present-day Vincennes in which the Indiana won by the militia led by George Rogers Clark over a British garrison led by Henry Hamilton.
What was the Siege of Fort Kaskaskia?The battle happened on 1778 where George Rogers Clark & his men reached Kaskaskia, seized it from the British men and bringing the colonies' battle for independence to the western edge of British territory in North America.
What was the Siege of Fort Cahokia?It was one of the battle that happened in the West as the leader of the secret expeditionary forces captured Kaskaskia, Cahokia and Vincennes in 1778 to 1779.
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1,-4,16 what is the 15th term
The sequence has its 15th term to be 268435456
What is the 15th term of the sequence?From the question, the given parameters are
1, -4, 16
The above sequence is a geometric sequence, with the following parameters
First term, a = 1Common ratio, r = -4/1Evaluate the quotient
So, we have
r = -4
The nth term of a geometric sequence is
Tn = a * r^(n-1)
Where
a = 1 and r = -4
Also, we have n = 15
Substitute a = 1 and r = -4 in the equation Tn = a * r^(n-1)
So, we have
Tn = 1 * (-4)^(n-1)
Substitute 15 for n
Tn = 1 * (-4)^(15-1)
Evaluate
Tn = 268435456
Hence, the 15th term of this sequence is 268435456
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Determine the value for m in the equation 1.4m = 0.42.
0.30
0.03
5.88
2.80
Determine the value for j in the equation 13 over 20 equals j plus 9 over 20.
4 over 20
4 over 40
2 over 20
22 over 40
Which statement correctly applies mathematical reasoning to find the possible values for x in the equation x − 1.3 = 1.5?
x is greater than 1.5
x is less than 1
x is between 0.1 and 1.5
x is less than 0.1
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
23.04
19.2
10.0
2.8
Determine the value for k in the equation k − 173.54 = 294.57.
121.03
589.14
347.08
468.11
Answer:
1. 0.30
2.4 over 20
3. x is greater than 1.5
4. 19.2
5. 468.11
Step-by-step explanation:
1) 1.4m = 0.42.
Divide both sides by 1.4
1.4m/1.4 = 0.42/1.4
m = 0.30
2) 13/20=j+9/20
Flip equation
j + 9/20 = 13/20
Substract 9/20 from both sides
j + 9/20 - 9/20 = 13/20 - 9/20
j = 13 - 9/20
j = 4/20
3) x − 1.3 = 1.5?
Add 1.3 to both sides
x - 1.3 + 1.3 = 1.5 + 1.3
x = 2.8
So, x is greater than 1.5
4) x/6 + 0.4 =3 + 0.6
Substract 0.4 from both sides
x/6 + 0.4 - 0.4 = 3 + 0.6 -0.4
x/6 = 3 + 0.2
x/6 = 3.2
Multiply both sides by 6
x/6 • 6 = 3.2 • 6
x = 19.2
5) k − 173.54 = 294.57.
Add 173.54 to both sides
k - 173.54 + 173.54 = 294.57 + 173.54
k = 468.11
The value of m from the given equation is 0.3.
The given equation is 1.4m = 0.42.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
1) 1.4m = 0.42
⇒ m = 0.42/1.4
⇒ m = 0.3
2) 13/20 = j+9/20
⇒ j = 13/20 - 9/20
⇒ j = 4/20
⇒ j = 1/5
3) x - 1.3 = 1.5
⇒ x = 1.5 + 1.3
⇒ x = 2.8
4) x/6 + 4/10 = 3 + 6/10
⇒ x/6+0.4=3.6
⇒ x/6 = 3.2
⇒ x = 19.2
5) k − 173.54 = 294.57
⇒ k = 294.57+173.54
⇒ k = 468.11
Therefore, the value of m from the given equation is 0.3.
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I don't know what any of this means for my son's homework please help
All we simply need to do is to apply the law of indices that states;
[tex](a^b)^c=a^{bc}[/tex]Hence;
[tex](\frac{x^2}{y^4})^3=\frac{x^6}{y^{12}}[/tex]The correct option is
The expression below is scientificnotation for what number?9.9x10^7
To change the number from scientific notation to normal number multiply 9.9 by 10^7
[tex]9.9\times10,000,000=99,000,000[/tex]The number is 99,000,000
Zachary has a container of worms for fishing. When empty, the mass of the container is 225 grams. With the worms in it, the container has a total mass of 751.4 grams. Each worm has a mass of 11.2 grams. How many worms are in the container? Write and solve an equation to model this equation.
Solving a linear equation we will see that there are 47 worms in the container
How many worms are in the container?We know that the mass of the container is 225 grams, and the mass of each worm is 11.2 grams.
Then if there are x worms on the containers, the total mass is:
M(x) = 225g + x*11.2g
In this case, we know that the total mass is 751.4 grams, then we can write:
751.4 g = 225g + x*11.2g
Solving this linear equation we get:
751.4g - 225g = x*11.2g
526.4g = x*11.2g
526.4g/11.2g = x = 47
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5. If c = -1 and d = -2, what is the value of the expression 2c²d-3cd?a. -10b. -24c. 2d. 10e. -2
Recall that to evaluate an expression at some given values, we substitute each variable with the corresponding given value.
Evaluating 2c²d-3cd at c=-1 and d=-2 we get:
[tex]2(-1)^2(-2)-3(-1)(-2).[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 2(1)(-2)-3(-1)(-2), \\ -4-6, \\ -10. \end{gathered}[/tex]Answer: Option a.
Answer:
-10
Step-by-step explanation:
Substitute variable values for variables.
[tex]2(-1)^2(-2) - 3(-1)(-2)[/tex]
Simplify
2(1)(-2) - 6
-4 - 6
-10
50 POINTS HELP PLEASE
Write the equation of the line given the following slope and y-intercept
m=4
b=−1
y=
(note for people answering and admins the y is supposed to be blank and its the answer box dont take it down pls,thank you)
Answer:
y = 4x - 1===========================
Given Slope m = 4,y-intercept b = - 1Equation of a line in slope-intercept formy = mx + bSubstitute the values to gety = 4x - 1Determine the intervals on which the function is strictly decreasing. Write your answer as an interval or a list of intervals. When writing a list of intervals make sure to separate it into roll with a comment to use his feet and triples as possible.
Given graph shown a function plotted.
The aim is to determine where the function is strictly decreasing.
The interval where the function is strictly decreasing is given by the union of intervals where the graph is descending from a point.
From the graph, it is clear that the function decreases from
[tex](-5,3)\text{ to (-2,-4)}[/tex]and again from
[tex](2,3)\text{ to (6,-1)}[/tex]Therefore, the intervals where the function is strictly decreasing is:
[tex](-5,-2)\cup(2,6)[/tex]Forever Flowers, the nursery that sells the peony plants, has an app that uses
equations to help customers order the correct number of plants. The function rule for
peony plants is P = 1.5n where P represents the number of plants needed for n yards.
a. What type of representation is a function rule?
b. State at least one reason why using this type of representation may be more useful
than other representations
a. A function rule is a representation of dependent variable, here n, in terms of the independent variable, here P, and is expressed as ƒ(P) = 1.5n.
b. This type of reason is useful because functions in an equation can take input from many variables, but always give the same result, which is unique to that function.
What is a function rule?The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.
f(x), where x is the input value, is how functions are expressed.
All functions have the general form y = f(x)
On any part of the function, a vertical line is drawn. It is a function if and only if it crosses the function at that single point. It is not a function if the line crosses itself more than once.
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A square swimming pool is surrounded by a cement sidewalk that is 3 feet wide. Enter two different function representations for the total area that the swimming pool and sidewalk enclose, A(x), if the length of the pool is x feet long
Step-by-step explanation:
the area function for the square pool itself is
A(x) = x² ft²
the area function for the pool and its sidewalk is
A(x) = (x + 6)² = x² + 12x + 36 ft²
simply because in this case the side length of the square is x+3+3 ft long (3ft added on both edges).
A ball is dropped from a height of 180 inches onto a level floor. After the second bounce it is still 5 inches off the ground. Presuming that the height the ball bounces is always the same fraction of the height reached on the previous bounce, what is that fraction?
The fraction which is a constant is equal to 1/6
How to find the fraction of the bouncing ballGiven data
A ball is dropped from a height of 180 inches
After the second bounce it is still 5 inches
the height the ball bounces is always the same fraction of the height reached on the previous bounce
Let the first height be x, this the initial drop height = 180
Let the second height be, the first bounce y
Let the third height be w, the second bounce = 5
the fraction is said to be:
height of y / height of x = height of w / height of y
y / x = w / y
y / 180 = 5 / y
y^2 = 180 * 5
y^2 = 900
y = √900
y = 30
the fraction is then 30 / 180 = 1 / 6
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URRGENT PLEASE HELP!!!! DOC ATTACHED
1. A conditional statement can be written as
If it is sunny then there is daylightThe hypothesis is: It is sunny
The conclusion is: there is daylight
2. The converse of the conditional statement
If there is daylight then it is sunny3. The inverse of the conditional statement
If it is not sunny then there is no daylight4. The contrapositive of the conditional statement
If there is no daylight then it is not sunny5. The biconditional statement and can be written because the statement and the converse are both true
6. The biconditional statement is
it is sunny if and only if there is daylightHow to identify a conditional statementA conditional statement is a term used in logic that refers to the type of statement that has "if-then". It is sometimes called if-then statements. Conditional statement are of two parts the hypothesis required to ensure that the conclusion. Other forms of conditional statements are
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Question 4c. Want to clarify something I want to ask right why does it become 3y square +6y-y-2
Answer:
Explanation:
Given the expression:
[tex]3y^2+5y-2[/tex]We want to write the given expression in the form:
[tex](ay-b)(y+c)[/tex]That is, to factorize the expression.
When an expression is to be factorized, follow the steps below:
Step 1: Multiply the coefficient of x² and the constant.
[tex]-2\times3y^2=-6y^2[/tex]Step 2: Find two terms that multiply to give the product -6y², and add to give the middle term, 5y. To do this, list the factors of -6: 1, 2,3, and 6
[tex]\begin{gathered} 6y\times-1y=-6y^2 \\ 6y+-y=5y \end{gathered}[/tex]Step 3: Rewrite the middle term, 5y with those numbers.
[tex]\begin{gathered} 3y^{2}+5y-2 \\ =3y^2+6y-y-2 \end{gathered}[/tex]Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =3y(y+2)-1(y+2) \\ =(3y-1)(y+2) \end{gathered}[/tex]Write an equation for the line point slope form and slope intercept formSlope= -6Passing through -3,-7
For this question, we recall the point-slope form of the equation of a line:
[tex]y-y_0=m(x-x_0)[/tex]and the slope-intercept form:
[tex]y=mx+b[/tex]Therefore for the given data, the point-slope form is:
[tex]\begin{gathered} y-(-7)=-6(x-(-3)) \\ y+7=-6(x+3) \end{gathered}[/tex]and the slope-intercept form is:
[tex]\begin{gathered} y=-6x-18-7 \\ y=-6x-25 \end{gathered}[/tex]The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The pressure is 672 pounds per square foot at a depth of 10.5 feet.
When a force is delivered to an object's surface perpendicularly to the region across which it is applied, the force is known as pressure (symbol: p or P).
The pressure in relation to the surrounding air is known as gauge pressure, also spelled gage pressure.Pressure is expressed using a variety of units. The standard unit of pressure in the imperial and U.S. customary systems is the pound-force per square inch (psi), which is equal to one newton per square meter (N/m²) in the SI. Some of these conclusions come up as a result of dividing a unit of force by a unit of area.a. The given formula is is P=64d
or , d = P ÷ 64
b. at a pressure of 672
d = 672 ÷ 64
or, d = 10.5 feet
Hence the water pressure on the submerged object is given by
d = P ÷ 64
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ONLY #11 please show work THANK YOU
The sketch of the given parametric equations is as appended.
Given parametric equations,
x(t) = 1+2t
y(t) = [tex]t^{2}[/tex]
y = [tex]\frac{(x-1)^{2}}{4}[/tex]
For bounding range of -2 ≤ t ≤ 2, corresponding values of x are as follows,
x = 2t + 1
For t = -2, x = 2(-2) + 1 = -3
For t = 2, x = 2(2) + 1 = 5
Hence the graph has been drawn with bounding limits of -3 ≤ x ≤ 5
The outcome is a parabola with vertex at (1,0) and open upwards. The curve moves towards infinity in upwards direction if there are no bounds / range.
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Which of the following could be a real-world description of the quantity three times x end quantity divided by 8?
A. The cost of a pizza split by 8 people plus a $3 tip
B. The cost of a pizza plus a $3 tip divided by 8 people
C. The cost per pizza for 3 pizzas divided by 8 people
D. The cost per pizza for 8 pizzas divided by 3 people
Sketch the graph of of the linear inequality: y<2x
Ive attached it on this photo. ur welcome :)
Answer:
Step-by-step explanation:
Solve for x. Below is the equation.
x = 110
Angle 4 is a vertical angle to the 115 degrees angle. Therefore, it must be the same in degree measure. So, we know angle 4 is 115 degrees.
Additionally, angle 4 and angle (x+5) are co-interior angles. This means that they should add up to 180 degrees.
Applying these concepts, we can create an equation:
115 + (x+5) = 180.
When we solve, we end up with x = 110
For the function f(x)=x2−9, find (a) f(x+h), (b) f(x+h)−f(x), and (c) f(x+h)−f(x) h.
Step-by-step explanation:
a)
[tex]f(x+h) = 2(x+h)-9[/tex]
[tex]f(x+h)=2x+2h-9[/tex]
b)
[tex]f(x+h)-f(x)=2x+2h-9-(2x-9)[/tex]
[tex]f(x+h)-f(x)=2x+2h-9-2x+9[/tex]
[tex]f(x+h)-f(x)=2h[/tex]
c)
[tex]f(x+h)-f(x)h=2x+2h-9-h(2x-9)[/tex]
[tex]f(x+h)-f(x)h=2x+2h-9-2hx+9h[/tex]
[tex]f(x+h)-f(x)h=-2hx+11h+2x-9[/tex]
in evaluating the expression 8+ 9/4 (-2) jenny found the volume to be 25/2. she thinks that the number is too great, but is not sure what she did wrong
In evaluating the expression 8+ 9/4 (-2) Jenny found the volume to be 25/2. The mistake she made was
volume = 8 1/4.
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
8+ 9/4 (-2) = ?
Hence we solve
(8 – 2) + (9/4 - 0)
6+9/4
The number four is the Least Common Multiple (LCM) of the number one. Multiply each fraction's numerator and denominator by whichever number will result in the denominator of each fraction being equal to the LCM, and then subtract that value from 1.
Subtract the numerators now that the fractions have the same denominators.
9 - 0/4 = 9/4
As we convert to whole numbers we have
9/4 = 2 1/4
Hence
=6 +2(1/4)
=8 1/4.
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Find the product. Write your answer as a mixed number in simplest form.
4 × 1 8/9
Answer: 68/9 which simplifies into 7 6/9
Use the Distributive Property and mental math to find the product.
5(88)
Please Explain how to do it. Everyone else is saying the answer is 440, which I know.
Eight billion eighty-one million, one hundred and one thousand, five hundred and thirty-one in figures
Answer:
8,081,101,531
Step-by-step explanation:
8,081,101,531
if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?
The location of the point B on the line with the endpoints is 63
How to determine the coordinates of the segment?On the segment, we have the following endpoints
A = -3
C = 8
Rewrite the endpoints of the line segment as
A = (-3,0) and C = (8,0)
The ratio of the line is given as
Ratio, A : B = 1 :5
This means that
Point C = A/A + B
So, we have
C = 1/1 + 5
Evaluate
C = 1/6
The coordinate of point C on the line segment is calculated using
Point C = C * (B - A) + A
So, we have
8 = 1/6 * (B + 3) - 3
This gives
1/6 * (B + 3) = 11
So, we have
B + 3 = 66
Subtract 3
B = 63
Hence, the coordinate of the point B on the line segment is 63
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Possible question
if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?
A = -3 and C = 8
Solve The Equation
-1.9 = 0.5(p +1.7)
Whoever answer first gets brainliest!
Answer:
p=-5.5Step-by-step explanation:
To solve this equation, use the distributive property. Isolate the difference between the numbers from one side of the equation.
Distributive property:
A(B+C)=AB+AC
-1.9 = 0.5(p +1.7)
First, switch sides.
0.5(p+1.7)=-1.9
Divide by 0.5 from both sides.
[tex]\sf{\dfrac{0.5\left(p+1.7\right)}{0.5}=\dfrac{-1.9}{0.5}}[/tex]
Solve.
-1.9/0.5=-3.8
p+1.7=-3.8
Then, you subtract by 1.7 from both sides.
p+1.7-1.7=-3.8-1.7
Solve.
Add or subtract the numbers from left to right.
-3.8-1.7=-5.5
[tex]\rightarrow \boxed{\sf{p=-5.5}}[/tex]
Therefore, the correct answer is p=-5.5.
I hope this helps, let me know if you have any questions.
The value of p on the equation - 1.9 = 0.5(p +1.7) is - 5.5.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, we have to solve for p in the equation - 1.9 = 0.5(p +1.7).
0.5(p + 1.7) = - 1.9
First, we'll distribute the terms.
0.5p + 0.85 = - 1.9.
0.5p = - 1.9 - 0.85.
0.5p = - 2.75.
p = - 2.75/0.5.
p = - 5.5
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Let 0 be an angle in quadrant
If angle theta is given as;
[tex]\cos \theta=-\frac{4}{5}[/tex]And angle theta is in the third quadrant, then we can find the value of y by using the pythagoras' theorem as follows;
[tex]\begin{gathered} r^2=x^2+y^2 \\ When\text{ cos}\theta=-\frac{4}{5},\text{ and cos}\theta=\frac{x}{r} \\ \text{Then,} \\ x=-4,r=5 \\ \text{Therefore,} \\ 5^2=-4^2+y^2 \\ 25=16+y^2 \\ \text{Subtract 16 from both sides;} \\ 9=y^2 \\ \text{Take the square root of both sides;} \\ y=3 \end{gathered}[/tex]Note also that;
[tex]\sin \theta=\frac{y}{r}[/tex]However, the angle theta is in the third quadrant where y is also negative. Therefore, sin theta would be;
[tex]\begin{gathered} \sin \theta=\frac{y}{r} \\ \sin \theta=-\frac{3}{5} \end{gathered}[/tex]Note also that cosec theta is given as;
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \csc \theta=\frac{1}{-\frac{3}{5}} \\ \csc \theta=-\frac{5}{3} \end{gathered}[/tex]Note also that, tan theta is given as;
[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]Therefore, we would have;
[tex]\begin{gathered} \tan \theta=-\frac{3}{5}\text{ / -}\frac{4}{5} \\ \tan \theta=-\frac{3}{5}\times-\frac{5}{4} \\ \tan \theta=\frac{3}{4} \end{gathered}[/tex]ANSWER:
[tex]undefined[/tex]What is the slope of the line on the graph
word problem for 4x - 3 = 17?????
Answer: My bill was 17 dollars. I gave four tokens of equal monetary value to the cashier who gave me in return 3 one dollar bills. How much was each token worth?
Step-by-step explanation: 4x - 3 = 17.
add 3 to both sides
4x = 20
x = 5. Each token was worth $5.
What is the surface area of the pyramid?
Answer:
d
Step-by-step explanation:
becuase you multiply leght times width then multiply height so it turns out to be
6x6=36
36x6=180