Answer:
1. Protest
2. Thomas Jefferson
3. The natural rights everyone has
4. With a final statement that the Thirteen Colonies are now free from British rule
5. John Hancock
6. British troops
7. Britain controls who the colonies can trade with.
8. Ways King George III had violated colonists' rights
9. Being involved in activities that help decide how a town, state, or country is structured and runs
10. Talking about independence from Great Britain
Which scatterplot shows the weakest negative linear correlation?
On a graph, points are grouped closely together and increase.
On a graph, points are grouped closely together in a line and increase.
On a graph, points are grouped closely together and decrease.
On a graph, points are grouped closely together in a line and decrease.
The scatterplot shows the weakest negative linear correlation is On a graph points are grouped closely together and increase. Option A.
The scatterplot showing the weakest negative linear correlation is the following scatterplot. The dots are scattered along the decreasing trend line. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that an increase in one variable tends to increase the other variable.
A negative correlation means that as one variable increases the other tends to decrease. Plotted points indicate correlations between variables if any. The scatterplot above is an example of a weak negative correlation. In this graph, y values decrease as x values increase, but the pattern does not resemble a straight line.
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1. Write 250 metres as a fraction of a kilometre.
Answer:1/4 or 0.25/1
Step-by-step explanation:
In 1 kilometer there are a thousand meters. So 250 is a quarter of 1000 which makes the fraction 1/4 or 0.25/1 whichever you need.
AB bisects LDAC and
m/DAB = 37°. What is
m/DAC?
The value of the angle m∠DAC is 74° as AB bisects ∠DAC .
We know from the properties of angles that the angle bisector will bisect the angle into two equal parts.
∠DAC is bisected by the straight line AB. This forms two angles ∠DAB and ∠BAC .
∠DAC =∠DAB + ∠BAC
now, ∠DAB = ∠BAC
given that ∠DAB = 37
Hence m∠BAC = 37
now,
∠DAC = ∠DAB + ∠BAC
m∠DAC = 37° + 37°
m∠DAC = 74°
A line that divides an angle into two equal angles is known as an angle bisector in geometry. A device that splits an object or form into two equal halves is referred to as a "bisector." A ray that divides a given angle into two identical segments of the same length is called an angle bisector.
Therefore the value of m∠DAC is 74° .
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3(8 – 4x) < 6(х – 5)
the inequality equation is
3(8 - 4x) < 6(x -5)
open the parentheses
3*8 - 3*4x < 6*x - 6*5
24 - 12x < 6x - 30
collect the like terms
24 + 30 < 6x + 12x
54 < 18x
divide both sides by 18
54/18 < 18x/18
3 < x
x > 3
The answer is x > 3
what is the sum of the first five terms in this series?(picture of problem below)
Provided information:
We know the first 4th terms of the series:
[tex]6,-\frac{6}{3},\frac{6}{9},-\frac{6}{27}[/tex]We can express this series in summation notation as:
[tex]\sum_{i\mathop{=}1}^n\frac{6}{(-3)^{i-1}}[/tex]Therefore, the 5th term of the series is:
[tex]\frac{6}{(-3)^{5-1}}=\frac{6}{(-3)^4}=\frac{6}{81}[/tex]Now, we have to add the first five terms:
[tex]6+(-\frac{6}{3})+\frac{6}{9}+(-\frac{6}{27})+\frac{6}{81}[/tex]The next step is to convert all fractions to have the same denominator, so:
[tex]\begin{gathered} 1st:6*\frac{81}{81}=\frac{486}{81} \\ 2nd:-\frac{6}{3}*\frac{27}{27}=-\frac{162}{81} \\ 3rd:\frac{6}{9}*\frac{9}{9}=\frac{54}{81} \\ 4th:-\frac{6}{27}*\frac{3}{3}=-\frac{18}{81} \end{gathered}[/tex]Now, they have the same denominator, it remains the same and we just need to add the numerators:
[tex]\frac{486-162+54-18+6}{81}=\frac{366}{81}[/tex]And now, let's simplify the fraction by dividing the numerator and denominator by 3:
[tex]\frac{\frac{366}{3}}{\frac{81}{3}}=\frac{122}{27}[/tex]The answer is A. 122/27
The graph shows the function f(x). Which equation represents f(x). F(x)=-3 square root x. F(x) = -3 square root x - 1. F(x) = 3 square root -x - 1. F(x) = 3 square root - x
The graph given is has the cubic function as the parent function.
The cubic function is shown below:
Solve 5(4m + 1) − 2m = −13.
Answer:
Step-by-step explanation
5(4m+1)-2m=-13
20m+5-2m=-13
20m-2m=-13-5
18m=-18
m=-1
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{5(4m+1)-2m=-13 } \end{gathered}$}[/tex]
Apply the multiplicative law of distribution.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{20m+5-2m=-13 } \end{gathered}$}[/tex]
Combine as terms.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m+5=-13 } \end{gathered}$}[/tex]
Rearrange the unknown terms to the left side of the equation.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-13-5 } \end{gathered}$}[/tex]
Calculate the sum or difference.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-18 } \end{gathered}$}[/tex]
Divide both sides of the equation by the coefficient of the variable.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-\frac{18}{18} } \end{gathered}$}[/tex]
Solve for the common factor.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-1 \iff } \end{gathered}$}\boxed{\boxed{\bf{Answer}}}[/tex]
The rectangular floor of a classroom is 36 feet in length and 22 feet in width. a scale drawing of the floor has a length of 18 inches. what is the perimeter, in inches, of the floor in the scale drawing?
The perimeter of the floor in the scale drawing is 58 inches.
Define Perimeter of the rectangle.The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
The letter "p" stands for the perimeter, which is equal to twice the width plus twice the length of the rectangle.
Given, the length of rectangular classroom is 36 feet
and the width is 22 feet.
The scale drawing has a length of 18 inches.
Here we can see that two different units are used.
So, we need to convert feet to inches.
1 foot = 12 inches
Now we will convert the length in inches,
36 feet = 36*12 inches
= 432 inches
Now we will convert the width in inches,
22 feet = 22*12
= 264 inches
Now, we will calculate by how many times the length has been scaled down:
[tex]\frac{432}{18} = 24[/tex]
So, the length has been scaled down to 24 times.
Now, we will scale down the width 24 times:
[tex]\frac{264}{24} = 11[/tex]
So, the width of the scale drawing is 11 inches.
Now, we will find the perimeter of the scale drawing:
Perimeter = 2(scale down length + scale down width)
= 2(18+11)
=2*29
=58 inches
Therefore, the perimeter of the scale down drawing is 58 inches.
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Find the measures of the numbered angles in the isosceles trapezoid shown below.
First, notice that since we have an isosceles trapezoid, the base angles will be equal, then:
[tex]\measuredangle3=60\degree[/tex]next, we have that the angles adjacent to opposite bases are supplementary, then we can write the following equation:
[tex]\measuredangle2+\measuredangle3=180[/tex]using the fact that the measure of angle 3 is 60 degrees, we can find the measure of angle 2:
[tex]\begin{gathered} \measuredangle2+60=180 \\ \Rightarrow\measuredangle2=180-60=120 \\ \measuredangle2=120 \end{gathered}[/tex]then, since angles 1 and 2 are also base angles, they are equal. Therefore, the measure of the anlges is:
[tex]\begin{gathered} \measuredangle1=120 \\ \measuredangle2=120 \\ \measuredangle3=60 \end{gathered}[/tex]nearest thousandth in 67directions: use a calculator to approximate each to the nearest thousandth subject: 2.2C evaluating common and natural logarithms
EXPLANATION
Given the expression:
ln 67:
Solving the operation with a calculator gives us the following result:
ln 67 = 4.204692619...
Thus, rounding to the nearest thousandth will give us:
= 4.205
So, answer to point 1) is D) 4.205
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
Which of the following equations have odd products? Select all that apply.
A.4x3=?
B.6x8=?
C.3x7=?
D.3x9=?
E.1x9=?
c, d, and e. this is because c equals 21, d equals 27, and e equals 9
2. The scale from the real Eiffel Tower to the scale model is 15 ft to 3 in. What is the unit rate?
Ok, so
If the scale from the real Eiffel Tower to the scale model is 15 ft to 3 in, the unit rate will be:
[tex]\frac{15ft}{3in}=5\frac{ft}{in}[/tex]This means that, in the scale:
5 ft = 1 in.
Then, the unit rate is 5.
Which of the following equations does the graph below represent?
Answer:
The answer is -3x + 6y = 36
Step-by-step explanation:
In a circle with radius 0.9, an angle intercepts an arc of length 3.6. Find the angle inradians to the nearest tenth.
SOLUTION
Given the question on the question tab;
[tex]\begin{gathered} radius\text{ r=0.9} \\ angle\text{ }\theta=? \\ Length\text{ of arc=3.6} \end{gathered}[/tex][tex]\begin{gathered} Length\text{ of arc =}\theta r \\ 3.6=0.9\theta \\ \theta=\frac{3.6}{0.9} \\ \theta=4.0 \end{gathered}[/tex]
The angle is 4.0
what is the converted fraction of 110/17
Answer:
6 8/17
Step-by-step explanation:
17 x 6 is 102 so that can go into 110
Then you do 110-102 to find how many are left over 110-102= 8 so there are 8 left over so that goes into the numerator so the answer is 6 8/17 The denominator stays the same unless you can simply but in this case you can’t.
Use the expression x^2 + 10x − 13 to answer the following questions.Part A: What numeric expression should be added in order to complete the square for the given expression?Part B: What expression is equivalent to the given expression after completing the square?Select two answers: one for Part A and one for Part B.
Given the expression below
[tex]x^2+10x-13=0[/tex]The general form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]Using the completing the square method,
[tex]\begin{gathered} x^2+10x-13=0 \\ x^2+10x=13 \end{gathered}[/tex]Where b =10 from the given equation
[tex]\begin{gathered} \text{Addding (}\frac{b}{2})^2\text{ to both sides} \\ ie\text{ (}\frac{10}{2})^2=5^2=25 \\ \text{Add 25 to both sides} \end{gathered}[/tex][tex]x^2+10x+25=13+25[/tex]For part A, the numerical value to be added is 25
Hence, for part A, the answer is 25-25
By completing the square
[tex]\begin{gathered} x^2+10x+25=13+25 \\ (x+5)^2=38 \\ (x+5)^2-38=0 \end{gathered}[/tex]Hence, for part B, the answer is (x+5)²-38
Which expressions are equivalent to the one below? Check all that apply.log(103)A.3 • log 10B.1C.3 • 10D.3
We are given log ( 10^3)
We can use one of the properties of logs
log u^n = n log u
Rewriting log ( 10^3) using this property
log ( 10^3) = 3 log 10
log has an implied base of 10
log 10 = 1
3 log 10 = 3 *1 =3
The two correct choices are
A. 3 * log 10
D. 3
1. What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.(a) Show your work.(b) is the product of 3x-4 and 5x² - 2x + 6 equal to the product of 4 - 3x and 5x² - 2x + 6? Explain
SOLUTIONS
(a) What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.
[tex](3x-4)(5x^2-2x+6)[/tex][tex]\begin{gathered} 3x(5x^2-2x+6)-4(5x^2-2x+6) \\ 15x^3-6x^2+18x-20x^2+8x-24 \\ collect\text{ like terms} \end{gathered}[/tex][tex]15x^3-26x^2+26x-24[/tex]The product is
[tex]15x^3-26x^2+26x-24[/tex][tex](4-3x)(5x^2-2x+6)[/tex]The product will be
[tex]\begin{gathered} 4(5x^2-2x+6)-3x(5x^2-2x+6) \\ 20x^2-8x+24-15x^3+6x^2-18x \\ -15x^3+26x^2-26x+24 \end{gathered}[/tex]The product of 4 - 3x and 5x² - 2x + 6 will be equal to the -1 multiply be the product of 3x - 4 and 5x² - 2x + 6, thus the two product are same
Checking
[tex]\begin{gathered} -1(-15x^3+26x^2-26x+24) \\ 15x^3-26x^2+26x-24 \end{gathered}[/tex]Hence the two answer are the same.
what 93 by the power of 7
The value of the expression ''93 to the power of 7'' will be;
⇒ 60,170,087,060,757
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 expression is,
''93 to the power of 7''
Now,
Solve the expression as;
93 to the power of 7 = 93⁷
= 93 × 93 × 93 × 93 × 93 × 93 × 93
= 60,170,087,060,757
Thus, The value of the expression ''93 to the power of 7'' will be;
⇒ 60,170,087,060,757
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I need help
What is 15% off of 10$
Answer: $8.50
hope this helps :)
im not the nest at math but im pretty sure that is what is is.
Step-by-step explanation:
help please which one is it
The function B has a greater rate of change.
What is rate of change?
How quickly something changes over time is referred to as its rate of change, or ROC. Therefore, rather than the size of each change individually, it is the rate—or the acceleration or deceleration of changes. In finance, rate of change is employed to comprehend price returns and spot trend momentum.
First to find the rate of change for function A.
Rate of change = [tex]\frac{0-5}{2.5-1.5} = \frac{-5}{1}=-5[/tex]
Function A has rate of change is -5.
Now consider, the second equation
y = -4.5x + 15
Since, the slope is rate of change for the equation.
So, function B has rate of change of -4.5
Now compare the rate of change for both the functions A and B
-5 < -4.5
Therefore, function B have greater rate of change.
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Page 5.26, Problem 3: A baseball team had 80 players show up last year and this year had 96 players show up for tryouts. Find increase in players from last year to this year. Your answer.
In order to determne the increse in the number of players, estimate the percentage increase. Proceed as follow:
First, calculate the difference in the number of player:
96 - 80 = 16
next, determine what is the associated percentage of such difference:
(16/80)(100) = 20%
Hence, the percentage increase was of 20%
penelope had 1/2 of her birthday cake leftover so she decided to take it to work. she shared her birthday cake equally among herself and four of her co workers. what fraction of the cake did each person get?
A telephone plan consists of a monthly fee of $15 plus 20 cents per minute for long distance calls are made. Write an equation for the total monthly cost C, when n minutes are used for long distance calls.
a)Using the given information we can set the following equation:
[tex]C=0.20n+15[/tex]b) The graph of the linear equation above for up to and including 200 minutes is as follows:
Which corresponds to option B.
c) If n=40 then:
[tex]C=0.20\cdot40+15=8+15=23[/tex]Then the total monthly cost is $23.
d) If C=30, solving the first equation on the board for n we get:
[tex]\begin{gathered} 30=0.20n+15 \\ 0.20n=15 \\ n=75 \end{gathered}[/tex]Then the number of minutes is 75.
Simplify four fourths over nine
The simplification of four fourths over nine written as 4/4 ÷ 9 is given by 1/9
How to simplify fraction?Fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
Given: four fourths over nine
= 4/4 ÷ 9
= 1 ÷ 9
= 1/9
Or alternatively
4/4 ÷ 9
multiply by the reciprocal of 9= 4/4 × 1/9
= (4 × 1) / (4 × 9)
= 4/36
= 1/9
In conclusion, the fraction four fourths over nine is simplified as 1/9
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Write the equation of the line that passes through the points `(1,\ -2)` and `(4,\ 4)`.
1. What is the x intercept of the graph y=x-32. What is the y intercept of the graph y=x-33. What is the x intercept of the graph y=4x+24. What is the y intercept of the graph y=4x+2
1. The x-intercept of a function is the point where the line crosses the x-axis. At this point, the y-coordinate is equal to zero.
You can identify the point from the graph or calculate the coordinates by replacing the equation of the linear function with y=0 and determine the corresponding value of x.
-Looking at the graph, the red line, that corresponds to the equation y=x-3, crosses the x-axis at point (3,0)
-Replacing the equation of the function by y=0:
[tex]\begin{gathered} y=x-3 \\ 0=x-3 \\ 0+3=x-3+3 \\ 3=x \end{gathered}[/tex]The x-intercept has coordinates at (3,0)
2. The y-coordinate is the point where the red line crosses the y-axis. At this point, the x-coordinate is equal to zero.
You can identify this point directly from the graph, or calculate it by replacing the equation of the line with x=0 and calculate the corresponding value of y.
-Looking at the graph, the red line crosses the y-axis at the point (0,-3)
-Replace the equation with x=0
[tex]\begin{gathered} y=x-3 \\ y=0-3 \\ y=-3 \end{gathered}[/tex]The y-intercept is (0,-3)
3. The equation y=4x+2 is represented in the graph by the blue line
As before, you have to identify the point where the line crosses the x-axis.
-From the graph:
-Replace the equation with y=0 and calculate the corresponding value of x:
[tex]\begin{gathered} y=4x+2 \\ 0=4x+2 \\ 0-2=4x+2-2 \\ -2=4x \\ -\frac{2}{4}=\frac{4x}{4} \\ -\frac{1}{2}=x \end{gathered}[/tex]The x-intercept is (-1/2,0)
4. The y-intercept is the point where the blue line crosses the y-axis.
-You can identify it from the graph:
-Or replace the equation with x=0 and determine the corresponding value of y
[tex]\begin{gathered} y=4x+2 \\ y=4\cdot0+2 \\ y=2 \end{gathered}[/tex]The coordinates of the y-intercept are (0,2)
What is the value of -175-15- (-204)?
O-394
O-14
O 14
O 29
The value of -175-15- (-204) is 14
Mathematical operations, Addition, and Subtraction:We learn to add and subtract two or more integers or any other mathematical values using the two basic arithmetic operations of addition and subtraction. The plus sign (+) stands for addition, whereas the negative sign (-) stands for subtraction (minus sign). The opposite of addition is subtraction and vice versa.
The following are rules for addition and subtraction:
=> [tex]+ \times + = +[/tex]
=> [tex]- \times - = +[/tex]
=> [tex]+ \times - = -[/tex]
=> [tex]- \times + = -[/tex]
Here we have
-175-15- (-204)
=> - 175 - 15 + 204
=> - 190 + 204
=> 14
Therefore,
The value of -175-15- (-204) is 14
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PLEASE HELP ITS URGENT
Solve for the roots in simplest form using the quadratic formula:
x²-16x = -100
Answer:
[tex] \rm x = 8 \pm 6i [/tex]
Step-by-step explanation:
Given equation: x² - 16x = -100
x² - 16x + 100 = 0
By comparing given equation with standard quadratic equation i.e. ax² + bx + c = 0 we get:
a = 1
b = -16
c = 100
Quadratic formula:
[tex] \boxed{ \rm x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} } [/tex]
Now, substituting the values in the quadratic formula:
[tex] \rm \implies x = \dfrac{ - ( - 16) \pm \sqrt{ {( - 16)}^{2} - 4(1)( 100) } }{2(1)} \\ \\ \rm \implies x = \dfrac{ 16 \pm \sqrt{ 256 - 400} }{2} \\ \\ \rm \implies x = \dfrac{ 16 \pm \sqrt{-144 } }{2} \\ \\ \rm \implies x = \dfrac{ 16 \pm 12i }{2} \\ \\ \rm \implies x = 8 \pm 6i [/tex]
Answer:
x has no real solutions.
x = 8 + 6i, x = 8 - 6i
Step-by-step explanation:
First, move the all the terms to one side of the equation.
x^2 - 16x + 100 = -100 + 100
x^2 - 16x + 100 = 0
Then, based on our knowledge of the standard form of a quadratic equation: ax^2 + by + c = 0, we can plug the coefficients in front of the variables into the formula, which looks like [tex]x=\frac{-b+or-\sqrt{b^2-4ac} }{2a}[/tex].
Our a here is 1,
The b is -16,
The c is 100.
plugging it in:
[tex]\frac{-(-16)+or-\sqrt{(-16)^2-4*1*100} }{2*1}[/tex]
simplifies down to:
16/2 + or - (√(256 - 400))/2
= 8 + or - √(-36)
Here, we have a negative square root, meaning there will be no roots for this equation in the real number system.
If you include imaginary/complex numbers, this equation will have roots.
x = 8 + or - √(-36)
x = 8 + or - 6√(-1)
x = 8 + or - 6i
so the final answer:
x = 8 + 6i, x = 8 - 6i