Answer:
Step-by-step explanation:
n²+2n+1 = (n+1)(n+1)
n²-8n-9 = (n+1)(n-9)
the least common denominator for these two rational expressions is :
(n+1)(n-9)
for what value of a does (1/7)^(3a+3)=343^(a-1)
Answer:
a = 0Step-by-step explanation:
[tex]\left(\dfrac{1}{7}\right)^{3a+3}=343^{a-1}\qquad\text{use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\7^{-(3a+3)}=(7^3)^{a-1}\qquad\text{use the distributive property}\\\\7^{-3a-3}=7^{3a-3}\iff-3a-3=3a-3\qquad\text{add 3 to both sides}\\\\-3a=3a\qquad\text{subtract}\ 3a\ \text{from both sides}\\\\-6a=0\qquad\text{divide both sides by (-6)}\\\\a=0[/tex]
Answer quick please Points N, P, and R all lie on circle O. Arc PR measures 120° How does the measure of angle RNQ relate to the measure of arc PR?
A.Angle RNQ is equal in measure to arc PR.
B.Angle RNQ is half the measure of arc PR.
C.Angle RNQ is twice the measure of arc PR.
D.Angle RNQ is four times the measure of arc PR.
Answer:
Option A. Angle RNQ is equal in measure to arc PR.
Step-by-step explanation:
we know that
The triangle NOR is an equilateral triangle, because has three equal sides
NO=OR=RN ----> radius of the circle O
therefore
The interior angles of the triangle NOR measures 60 degrees each
so
∠RNO=60°
Find the measure of angle RNQ
we have that
∠RNO+∠RNQ=180° ------> by supplementary angles (linear pair)
substitute
60°+∠RNQ=180°
∠RNQ=180°-60°=120°
we know that
arc PR= 120° ----> see the graph
therefore
∠RNQ=arc PR
Angle RNQ is equal in measure to arc PR.
Answer:
it’s a
Step-by-step explanation:
Hal, Mark, and Frank are driving round-trip to a football game
that is 190 miles from their town. If each of them drives the same
distance, how far will each person drive?
Annabelle works in a deli and has been tracking the daily sales of different items over several months. Annabelle found that when there was an increase in the number of cups of hot chocolate sold, the number of cups of coffee sold also increased. Similarly, when there was a decrease in the number of cups of hot chocolate sold, the number of cups of coffee also decreased.
Which of the following is a valid conclusion?
A.
There is no correlation between the sale of hot chocolate and the sale of coffee.
B.
The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
C.
No conclusion can be drawn about the correlation or causation of the sale of hot chocolate and the sale of coffee.
D.
The increase in the sale of hot chocolate caused an increase in the sale of coffee.
Answer:
B. The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee
Step-by-step explanation:
Lets define correlation first:
Correlation is the connection or link between two things. We have to remember that both things or events being correlated doesn't mean that one is caused by the other.
By observing the given question we can conclude that the the increase in sale of hot chocolate is correlated to the sale of coffee but none of them is caused by each other.
Hence, the correct answer is:
B. The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee..
Answer:
The correct answer is B
Step-by-step explanation:
If F(x) = x^2+ 5x and G(x) = 2x + 1, find F(5) + G(6).
Answer:
The value of F(5) + G(6) is 63.
Step-by-step explanation:
[tex]F(x)=x^2+5x[/tex]
[tex]G(x)=2x+1[/tex]
Value of F(x) , x = 5
[tex]F(5)=5^2+5\times 5=50[/tex]
Value of G(x) , x = 6
[tex]G(6)=2\times 6+1=13[/tex]
F(5) + G(6) :
= 50 + 13 = 63
The value of F(5) + G(6) is 63.
Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?
He is correct because both solutions satisfy the equation.
He is not correct because he made a sign error.
He is not correct because there are no solutions.
He is not correct because there is only one solution: x = 5.
Answer:
He is not correct because he made a sign error.
Step-by-step explanation:
-2 |8-x| - 6 = -12
-2 |8-x| = -12 + 6
-2 |8-x| = - 6
2 |8-x| = 6
|8-x| = 3
2 possible solutions:
8-x = 3 ----> x = 5
or
8-x = -3 ----> x = 11
Comparing the answer choices, we can see that Johan got the sign of x = 11 wrong.
Hence the correct answer is:
He is not correct because he made a sign error.
Answer: Just did it on ed, answer is "He is not correct because he made a sign error."
Step-by-step explanation:
A line has a slope of
Which ordered pairs could be points on a parallel line? Check all that apply.
(-8, 8) and (2, 2)
(-5, -1) and (0, 2)
(-3, 6) and (6.-9)
(-2, 1) and (3,-2)
(0, 2) and (5,5)
Answer:
B and D
Step-by-step explanation:
Given a line with slope m = - [tex]\frac{3}{5}[/tex]
Since the lines are parallel we require the points with the same slope
Using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = 8, 8) and (x₂, y₂ ) = (2, 2)
m = [tex]\frac{2-8}{2-8}[/tex] = 1 ← not parallel
Repeat with (x₁, y₁ ) = (5, - 1) and (x₂, y₂ ) = (0, 2)
m = [tex]\frac{2+1}{0-5}[/tex] = - [tex]\frac{3}{5}[/tex] ← Parallel
with (x₁, y₁ ) = (- 3, 6) and (x₂, y₂ ) = (6, - 9)
m = [tex]\frac{-9-6}{6+3}[/tex] = - [tex]\frac{5}{3}[/tex] ← not parallel
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (3, - 2)
m = [tex]\frac{-2-1}{3+2}[/tex] = - [tex]\frac{3}{5}[/tex] ← Parallel
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (5, 5)
m = [tex]\frac{5-2}{5-0}[/tex] = [tex]\frac{3}{5}[/tex] ← not parallel
The ordered pairs (-5, -1) and (0, 2); (0,2) and (5,5) could be points on a parallel line because they have the same slope according to the slope formula.
Explanation:In Mathematics, to find whether two points could be on a parallel line, we first need to understand the concept of slope. The slope of a line is determined by the ratio of the vertical change (delta y) to the horizontal change (delta x) between any two points on a line. It is often expressed as 'rise over run'.
If two lines are parallel, they have the same slope. Now, let's check the given ordered pairs. Using the slope formula (slope = (y₂-y₁) / (x₂-x₁)), you find the slope between each set of points:
(-8,8) and (2,2): slope = (2-8)/(2-(-8)) = -6/10 = -3/5 (-5, -1) and (0, 2): slope = (2-(-1))/(0-(-5)) = 3/5 (-3, 6) and (6,-9): slope = (-9-6)/(6-(-3)) = -15/9 = -5/3 (-2, 1) and (3,-2): slope = (-2-1)/(3-(-2)) = -3/5 (0,2) and (5,5): slope = (5-2)/(5-0) = 3/5
From the calculation, (-5, -1) and (0, 2) have the same slope with (0,2) and (5,5). Therefore, the lines passing through these pairs of points are parallel to each other.
Learn more about Parallel Lines and Slope here:https://brainly.com/question/35476105
#SPJ2
What system of equations is shown on the graph below?
x - 2y = -4 and 2x + y =4
x - 2y = 4 and 2x + y = 4
x - 2y = -2 and 2x + y = -4
x - 2y = 2 and 2x + y =4
Answer:
x - 2y = 4 and 2x + y = -4Step-by-step explanation:
Look at the picture.
Read the coordinates of intercepts of each line.
Put them to slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The blue line:
(4, 0), (0, -2) → b= -2
[tex]m=\dfrac{-2-0}{0-4}=\dfrac{-2}{-4}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}[/tex]
Substitute the values of a slope and an y-intercept to the equation of a line:
[tex]y=\dfrac{1}{2}x-2[/tex]
Convert to the standard form [tex]Ax+By=C[/tex]:
[tex]y=\dfrac{1}{2}x-2[/tex] multiply both sides by 2
[tex]2y=x-4[/tex] subtract x from both sides
[tex]-x+2y=-4[/tex] change the signs
[tex]x-2y=4[/tex]
The red line:
(-2, 0), (0, -4) → b= -4
[tex]m=\dfrac{-4-0}{0-(-2)}=\dfrac{-4}{2}=-2[/tex]
[tex]y=-2x-4[/tex] add 2x to both sides
[tex]2x+y=-4[/tex]
The answer is B.
Hope it helps
What is the Solution to the division problem v
Answer:
The answer is x^2-4x+1
Step-by-step explanation:
For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend, until reaching the remainder.
It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Answer:
Option C
See attached image
Evaluate the following expression.
(-6) 2
0 -36
0 -1/36
1/36
36
Answer:
36
Step-by-step explanation:
(-6)^ 2
-6*-6 = 36
5. Triangle MNO is an isosceles
triangle in which only one angle
measures 122.6°. What is the
angle measure of one of the two
congruent angles?
The measure of the congruent angle of the triangle MNO will be 28.7°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Triangle MNO is an isosceles triangle in which only one angle measures 122.6°.
Let the measure of the congruent angle be 'x'. Then the equation is given as,
x + x + 122.6° = 180°
2x = 180° - 122.6°
2x = 57.4°
x = 28.7°
The measure of the congruent angle of the triangle MNO will be 28.7°.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
solve the proportion 8/3=g/3 ... A.1/8 B.9/8 C.8 OR D.8/9
Answer:
g = 8. (Answer C)
Step-by-step explanation:
We are given 8/3 = g/3.
If we multiply both sides by 3, this will eliminate the fractions, and we will be left with g = 8. (Answer C).
The solution to the proportion 8/3 = g/3 is g = 8, corresponding to option C.
Explanation:In this proportion, the value of g can be found by solving the equation 8/3 = g/3. Because both sides of the equation are divided by 3, the 3's essentially cancel each other out, leaving you with g = 8.
Therefore, the solution to the proportion 8/3 = g/3 is g = 8. So, the correct answer is C. 8.
Learn more about solving proportions here:https://brainly.com/question/35507083
#SPJ2
samuel had some carnival tickets to sell. he sold 5/9 of them on monday and 1/8 of the remainder on tuesday. he sold the remaining 98 tickets on wednesday. each ticket was sold at $5 each. how many tickets were sold on tuesday?
Answer:
poooooooooooooooooop
Step-by-step explanation:
Perform the indicated operation. x+5/3 -x-3/2=
Step-by-step explanation:
to add or subtract in this case you have to the same common denominator. but what ever you do to the denominator you have to do to the numerator. top = numerator and bottom = denominator.
Answer:
[tex]-x+19/6[/tex]
Step-by-step explanation:
A newspaper advisor claims that an advertisement would increase sales by 35%. Sales are currently $500 per month. What will be the predicted sale in three years?
what is 1/2 divided by 74
Find the value of x.
A. 4 root 2/ 2
B. 4
C. 4 root 2
D. 4 root 3
Answer:
C. 4 root 2
Step-by-step explanation:
Total amount of angles = 45° + 45° = 90°
sin90 * 4 root 2 = 5.656854
Answer:
4
Step-by-step explanation:
You will either use cos or sin solve this problem
1. set up the problem like this
x/sin 45 x 4 root 2/sin 90
2. cross multiply (it will be useful to use calculator or if you know unit circle then you're good)
sin 90 = 1 and sin 45 = .7071067812 (don't really need to know this)
1x = (sin 45 x 4 root 2)
3. Solve for x like normal
1x = 4
1x/1 = 4/1
x = 4
Point A (7,3) is translated to A'(16,-9). Which rule describes the translation?
Answer:
(x + 9, y - 12)
Step-by-step explanation:
It's just telling the change from the pre image to the post image. Sorry for the lame explanation lol
Answer:
D (x.y) right arrow (x + 9, y - 12)
Step-by-step explanation:
hello this is the answer yw have a wonderful day!! :)
If f(x)=2x+2and g(x)=x^3, what is (g•f)(2)
Answer: 2x^3+4x+4 would be the answer.
Step-by-step explanation: x^2 can only be combines with another variable with the same exponent. Then you just multiply the whole equation by 2. Hope this helps!
Math Help It's appreciated. (Picture provided)
Answer:
Option 2
Step-by-step explanation:
As we can see, the old graph was:
y=x^2
And the new graph is:
y = -x^2 + 3
We can determine from the new graph that the minus sign with x^2 means the graph is reflected upon x-axis.
Now, there is 3 with the new graph. As 3 is separate from the function, this means there is vertical shift. Since the sign of the constant defines the direction of shift, the positive or plus sign means the shifting is upwards while the negative sign means downward shifting.
The given new function is obtained from reflecting the old function over the x-axis and shifting up 3.
So, option 2 is correct ..
Need help on inequality.
10 less than or equal to - 2/3 (9+12b)
Answer:
b less than or equal to -2.
Step-by-step explanation:
- 2/3 (9+12b) ≥ 10
-6 - 8b ≥ 10
-8b ≥ 16
b ≤ -2. ( Note the inequality sign flips as we are dividing by a negative).
- Dr. Watson combines 400 mL of detergent,
800 mL of alcohol, and 1,500 mL of water.
How many liters of solution does he have?
A 2.7 liters C 270 liters
B 27 liters D 2,700 liters.
Please give explanation on how you get the answer
Can (3,5 and square root 34) be sides on a right triangle?
Answer:
Yes, they are.
Step-by-step explanation:
Remember that a triangle is only a right triangle if its sides meet this mathematical requirement:
(leg)² + (leg)² = (hypotenuse)²
The hypotenuse of a right triangle is the longest side, while the legs are the two shorter sides. We can't say exactly where √34 is, but since √25 = 5 and √36 = 6, we know it must be at least bigger than 5, making it the triangle's longest side.
Using √34 as the "hypotenuse" and 3 and 5 as the "legs" of our triangle makes the equation 3² + 5² = (√34)², and simplifying gets us
9 + 25 = 34
34 = 34
The requirement's been met, so yes, this is a right triangle.
Use the properties of exponents to rewrite the expression.
5e•5e•5e•5e
Answer:
(5e)^4
Step-by-step explanation:
Please I need help I am stuck on this !!
Let's first find the slope
To find the slope you can use any two points in the table. The following are the two I picked:
(-3, 18) and (0, 12)
The formula for slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =12\\y_{1} =18\\x_{2} =0\\x_{1} =-3[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{12 - 18}{0 - (-3)}[/tex]
[tex]\frac{-6}{3}[/tex]
Simplify to...
-2
^^^This is your slope
Y-intercept is where the graph intersect with the y axis, which makes the x value 0. This means that the coordinate should look like so...
(0, y)
In this case the y-intercept is:
(0, 12)
Your answer is B!
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
B. The slope is -2, and the y-intercept is 12.
Step-by-step explanation:
Slope formula:
↓
[tex]\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
Slope-intercept formula:
↓
[tex]Y=MX+B[/tex]
[tex]\frac{12-18=-6}{0-(-3)=3}=\frac{-6\div3}{3\div3}=\frac{-2}{1}=-2[/tex]
Therefore, the answer is B.
write and simplify a multiplication expression to represent 5^4
Answer:
Step-by-step explanation:
5 * 5 * 5 * 5
= 625
ANSWER
[tex] {5}^{4} = 625[/tex]
EXPLANATION
We want to simplify the exponential expression 5⁴ by writing and simplifying a multiplication expression that represents it.
This implies that
[tex] {5}^{4} = 5 \times 5 \times 5 \times 5[/tex]
This simplifies to
[tex]{5}^{4} = 25 \times 2 5[/tex]
We finally obtain:
[tex] {5}^{4} = 625[/tex]
Which of the following expressions are equivalent to -(-5/3)
a. -5/-3
b. 5-/-3
c. None of the above
Answer:
A; [tex]\frac{-5}{-3}[/tex]
Step-by-step explanation:
[tex]-(-\frac{5}{3}) = \frac{5}{3}[/tex]
[tex]\frac{-5}{-3} = \frac{5}{3}[/tex]
[tex]\frac{5}{3} = \frac{5}{3}[/tex]
The mathematical expression -(-5/3) translates to positive 5/3 due to the fact that two negative signs cancel each other out. The expressions equivalent to this is -5/-3, while 5-(-3) is not equivalent.
Explanation:In mathematics, negative signs can change the sign of the operand they are applied to. Essentially, the expression -(-5/3) means the negative of negative 5/3. In mathematics, multiplying or dividing two negative numbers yields a positive result, hence two negative signs cancel each other out. So, -(-5/3) becomes positive (5/3).
Now, let's look at the options provided:
a. -5/-3: As stated before, two negative signs cancel each other, so the result is positive 5/3 which is the same as -(-5/3).
b. 5-(-3): According to the order of operation rules (PEMDAS/BODMAS), subtraction and division operations aren't equivalent. Therefore, this expression is not equivalent to -(-5/3).
So, the answer is a. -5/-3.
Learn more about Equivalent Expressions here:https://brainly.com/question/34744290
#SPJ2
Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and in
exponential form by filling in the boxes for exponents.)
please help me
the greatest common factor of 270 and 360 is 90.
because 2 x 3 x 3 x 5 = 90
the factors of each number is:
270: 1, 270, 2, 135, 3, 90, 5, 54, 6, 45, 9, 30, 10, 27, 15, 18
360: 1, 360, 2, 180, 3, 120, 4, 90, 5, 72, 6, 60, 8, 45, 9, 40, 10, 36, 12, 30, 15, 24, 18, 20
In the figure below what is the value of x
Answer:
127
Step-by-step explanation:
As we know that the sum of all angles of a triangle is 180°.
So, here we will apply this knowledge.
[tex]115\°+12\°+x\°=180\°[/tex]
[tex]127\°+x\°=180\°[/tex]
Now, we will subtract 127° from both sides of the equation, and we get;
[tex]x\°=180\°-127\°[/tex]
[tex]x\°=53\°[/tex]
Therefore,[tex]x=53.[/tex]
The value of x° is 53°.
Hence, the third angle in the given triangle is 53°.
What is a triangle?A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same.
What is called triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC. Examples of Triangles. Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.
What are the parts of a triangle?All triangles have three sides and three corners (angles). The point where two sides of a triangle meet is called a vertex. The base of a triangle can be any one of its three sides, but it is usually the bottom one.
To learn more about triangles, refer to:
https://brainly.com/question/2772128
#SPJ2
On a DVD, information is stored on bumps that spiral around the disk. There are 73,000 ridges (with bumps) and 73,000 valleys (without bumps) across the diameter of the DVD. What is the diameter of the DVD in centimeters? Round your answer to the nearest whole number.
Answer:18542
Step-by-step explanation:simplemath
The diameter of the circular DVD is d = 12 cm
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the diameter of the circular DVD be d
The total number of ridges = 73,000
The total number of valleys = 73,000
The width of each ridge = 0.000032 cm
The width of each valley = 0.000074 cm
The length of center portion c = 4.26 cm
And , the diameter of circular DVD = total width of ridges + total width of valleys + center portion
The total width of ridges = ( 0.000032 cm ) x 73,000
The total width of valleys = ( 0.000074 cm ) x 73,000
So , the total width of ridges and valleys = 73,000 ( 0.000106 ) = 7.738 cm
On simplifying , we get
The diameter of circular DVD d = 7.738 cm + 4.26 cm
The diameter of circular DVD d = 11.998 cm
The diameter of circular DVD d ≈ 12 cm
Hence , the diameter of the circular DVD is 12 cm
To learn more about circle click :
https://brainly.com/question/28391204
#SPJ3