The measure of angle m<2 for the given linear pair is found as 109°.
What is meant by the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair has always been 180°.For the given question;
<1 and <2 form a linear pair.
m<1 = (18r - 1)° and m<2 = (23r + 17)°
Thus, from the property of the linear pair;
m<1 +m<2 = 180
Put the values;
(18r - 1)° + (23r + 17)° = 180
Simplify the expression.
18r - 1 + 23r + 17 = 180
41r = 180 - 16
r = 4
m<2 = (23r + 17)°
m<2 = (23×4 + 17)°
m<2 = 109°
Thus, the measure of angle m<2 for the given linear pair is found as 109°.
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what is the answer to 24+12x=-12
If Z has a standard normal probability distribution, find P(Z > −0.75).
Given that Z has a standard normal probability distribution, you need to find the following Probability:
[tex]P(Z>-0.75)[/tex]Therefore, you can find it using the Standard Normal Distribution Table.
By symmetry, you can determine that:
[tex]P(Z>-0.75)=1-P(Z<-0.75)[/tex]Using the Standard Normal Distribution Table (Left Tail), you get that:
[tex]P(Z<-0.75)\approx0.2266[/tex]Therefore:
[tex]P(Z>-0.75)=1-0.2266\approx0.7734[/tex]Hence, the answer is:
[tex]P(Z>-0.75)\approx0.7734[/tex]Niko uses 1212marshmallows and 88graham crackers to make 44s'mores. Drag marshmallows and graham crackers into the box to show how many Niko needs to make 33s'mores.
Write the fraction 27/72 in simplest form
Therefore, 27/72 simplified to lowest terms is 3/8.
what is the value of f(-9) to the nearst hundredth
For this problem, we are given the expression for a function, f(x), and we need to determine the value of f(-9) to the nearest hundredth.
The expression is:
[tex]f(x)=2^{8+x}+7[/tex]We need to replace "x" with the value "-9", and simplify the expression.
[tex]\begin{gathered} f(-9)=2^{8-9}+7 \\ f\mleft(-9\mright)=2^{-1}+7 \\ f\mleft(-9\mright)=\frac{1}{2}+7 \\ f\mleft(-9\mright)=0.5+7=7.5 \end{gathered}[/tex]The value of f(-9) is 7.5
If f(x) = |x – 1] + 2 is changed to g(x) = -2f(x) + 8, how is the graph of the function transformed?
we have
f(x) = |x – 1] + 2
g(x) = -2f(x) + 8
substitute the value of f(x) in g(x)
so
g(x)=2(|x – 1] + 2) +8
g(x)=2|x – 1] + 4 +8
g(x)=2|x – 1] + 12
Using a graphing tool
see the attached image
Find the slope of the line that passes through (2, 7) and (-4, 19).
m =
The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.
According to the question,
We have the following information:
A line is passing through two points (2,7) and (-4,19).
We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:
m = (y2-y1)/(x2-x1)
(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)
In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.
m = (19-7)/(-4-2)
m = 12/(-6)
m = -2
Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.
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Priya creates a scatter plot showing the relationship between the number of steps she takes and her heart rate. The correlation coefficient of the line of best fit is 0.88.Are they correlated? Explain your reasoning.
Correlation coefficient: statistical measure of the strength of the relationship between the relative movements of two variables.
• If a correlation coefficient has an exact value of one, it has a perfect positive relationship between the two variables
,• If a correlation coefficient has an exact value of minus one, there is a perfect negative relationship between the two variables.
,• Analysts in some fields of study do not consider correlations important until the value surpasses at least 0.8. However, a correlation coefficient with an absolute value of 0.9 or greater would represent a very strong relationship.
Thus, they have a weak correlation.
Solve p3 = −343.
p = ±18
p = −18
p = ±7
p = −7
Answer:
p = -7
Step-by-step explanation:
[tex] {p}^{3} = - 343[/tex]
[tex]p = \sqrt[3]{ - 343} = - 7[/tex]
25.10.2 Test (CST): Polynomial FunctionsQuestion 9 of 25Which of the two functions below has the smallest minimum .y-value?f(x) = x5-2g(x) = 3x² + 1O A. g(x)OB. There is not enough information to determineC. The y-values for f(x)and g(x) both go to -O D. f(x)SUBMIT
Solution
- To find the minimum values of the functions, we need to find the x-value of the vertex of the quadratic function, and then subsitute this x-value into the function to get its minimum value, while for the quintic equation, we simply apply the fact that it is an odd function. Because of this, the tails of the function move in opposite directions; one towards positive infinity, while the other moves towards negative infinity.
- The formula for finding the x-value of the vertex of a quadratic function is:
[tex]x=-\frac{b}{2a},\text{ Given, }ax^2+bx+c=f(x)[/tex]- Thus, we can find the x-value of the vertex for the quadratic equation as follows:
[tex]\begin{gathered} f(x)=3x^2+1 \\ a=3,b=0,c=1 \\ \\ \therefore x=-\frac{b}{2a}=-\frac{0}{2(3)}=0 \end{gathered}[/tex]- Now that we have the x-value of the vertex of the quadratic equation, we can find its minimum value as follows:
[tex]\begin{gathered} f(x)=3x^2+1 \\ put\text{ }x=0 \\ f(x)=3(0)^2+1 \\ f(x)=1 \end{gathered}[/tex]- Thus, the minimum value of the quadratic equation is 1.
- Next, we already know that the quintic equation moves down towards negative infinity. Thus f(x), the quintic equation, has a smaller minimum value
Final Answer
f(x), the quintic equation, has a smaller minimum value
Jacob invests $8,634 in a savings account with a fixed annual interest rate of 2.67% compounded continuously. What will be the account balance be after 6 years?
Answer:
$10134.12
Step-by-step explanation:
Pe^(rt)
8634e^(0.0267)(6)
8634e^(0.1602)
= 10134.12
I hope this helps!
3024 divided by 42 with remainder
Answer:
72 Remainder: 0
Step-by-step explanation:
3024 / 42 = 72
Remainder of 0!
Answer:
Step-by-step explanation:
72 Remainder 0
don’t need an explanation just the answer. Community takes too long lol
SOLUTION
Step 1: Find the area of the wall.
[tex]\begin{gathered} A=l\times b \\ A=42\times25.5 \\ A=1071ft^2 \end{gathered}[/tex]Step 2: Find the cost of wallpaper per square foot
[tex]=\frac{total\text{ cost of wallpaper}}{Area\text{ of the wall}}[/tex][tex]\begin{gathered} =\frac{771.12}{1071} \\ =0.72\text{ dollars} \end{gathered}[/tex]The correct answer is B: $0.72
What is the length in units of segment cd
Answer: 7.2
Step-by-step explanation: I took the test and got it correct, I'm just trying to spread the correct answer around.
i need help with the question where I wrote +1 and +2. to find the slope do I just do 2/1
To find out the slope we need two points
from the table
we take
(0,1) and (1,3)
so
m=(3-1)/(1-0)
m=2/1
m=2if i have 12 cupcakes and i have to take away 80% how many cupcakes do you have
You have remains 2.4 cupcakes when taking away 80% of the cupcakes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that
The total number of cupcakes was 12
Then take away 80% of cupcakes
The number of cupcakes you have = 12 - (80% of 12)
The number of cupcakes you have = 12 - (80/100) × 12
The number of cupcakes you have = 12 - 0.80 × 12
The number of cupcakes you have = 12 - 9.6
Apply the subtraction operation,
The number of cupcakes you have = 2.4
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Solving Linear Inequalities
HELP PLEASE(┬┬﹏┬┬)
In Step 2 have a mistake in student solution so the option B is correct answer.
In the given question,
A student solved the inequality [tex]\frac{-x+4}{3} > \frac{x+1}{2}[/tex].
We have to find the error in the student solution.
To find the mistake we first solve the give inequality.
The equality is [tex]\frac{-x+4}{3} > \frac{x+1}{2}[/tex]
To solve this equality we firstly equal the denominator by multiplying and divide 2 on left side and 3 on right side.
So [tex]\frac{2}{2}\times\frac{-x+4}{3} > \frac{x+1}{2}\times\frac{3}{3}[/tex]
Now simplifying
[tex]\frac{2(-x+4)}{6} > \frac{3(x+1)}{6}[/tex]
Now simplifying the brackets of numerator ob both side using distributive property.
In Distributive Property: a(b+c)=ab+bc
[tex]\frac{2\times(-x)+2\times4}{6} > \frac{3\times x+3\times1}{6}[/tex]
[tex]\frac{-2x+8}{6} > \frac{3x+3}{6}[/tex]
Since the both side have same numerator. So we can write the inequality as
-2x+8 > 3x+3
Subtract 8 on both side
-2x+8-8 > 3x+3-8
-2x > 3x-5
Subtract 3x on both side
-2x-3x > 3x-5-3x
-5x > -5
Divide by -5 on both side
-5/-5 x > -5/-5
x > 1
Hence the value of x is greater than 1.
Now we see the step on student.
We can see that in step 2 has mistake. In step 2 student doesn't use distributive property to solve the bracket.
Hence, we can say that option 2 is correct.
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PLEASEEEEEEEEEEE HELP!!!!!!!
Answer:
answer y=-5/3x+5
Step-by-step explanation:
The slope is decreasing so the slope is negative
Rise is 5 run is 3 so its 5/3 but the slope is negative so its -5/3
Y intercept is located at 0,5 so it equals 5
y=-5/3x+5
The equation of line will be;
⇒ y = - 5/3x + 5
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line is decreasing.
The rise will be 5.
The run will be 3.
Now,
Since, The equation of line is decreasing.
Hence, The slope of the line is negative.
Here, The rise will be 5.
The run will be 3.
So, The slope = Rise / Run
= 5/3
Thus, The slope = - 5/3
So, The equation of line in point-slope form will be;
⇒ y = mx + b
⇒ y = - 5/3x + 5
Thus, The equation of line will be;
⇒ y = - 5/3x + 5
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write parallel and perpendicular equation thru (-3,5) y=2/3x + 1
Answer:
Step-by-step explanation:
1 Simplify (-3,5)y(−3,5)y to -3,5y−3,5y.
-3,5y=\frac{2}{3}x+1
−3,5y=
3
2
x+1
2 Simplify \frac{2}{3}x
3
2
x to \frac{2x}{3}
3
2x
.
-3,5y=\frac{2x}{3}+1
−3,5y=
3
2x
+1
3 Switch sides.
\frac{2x}{3}+1=-3,5y
3
2x
+1=−3,5y
4 Break down the problem into these 2 equations.
\frac{2x}{3}+1=-3
3
2x
+1=−3
\frac{2x}{3}+1=5y
3
2x
+1=5y
5 Solve the 1st equation: \frac{2x}{3}+1=-3
3
2x
+1=−3.
x=-6
x=−6
6 Solve the 2nd equation: \frac{2x}{3}+1=5y
3
2x
+1=5y.
x=\frac{3(5y-1)}{2}
x=
2
3(5y−1)
7 Collect all solutions.
x=-6,\frac{3(5y-1)}{2}
x=−6,
2
3(5y−1)
(6×10 to the ninth power)divided by (2.4×10 to the third power)
Answer:
2.5×10 to the sixth power
Step-by-step explanation:
6÷2.4=2.5
10^9÷10^3=6
A carpenter is using a lathe to shaper the final leg of a handcrafted table. In order for the leg to fit, it needs to be 150 mm wide allowing for a margin of error of 2.5mm. Find the range of widths for the table leg can be.
Simplify the expression positive exponents only 17C^9d^4 - 2c^3d^9 (times) 3C^6d^5
The value of the expression, [tex]17c^{9} d^{4} -2c^{3} d^{9} .3c^{6} d^{-5}[/tex], after simplification with only positive exponents is [tex]11c^{9} d^{4}[/tex].
According to the question,
We have the following expression:
[tex]17c^{9} d^{4} -2c^{3} d^{9} .3c^{6} d^{-5}[/tex]
Now, we know that we will first solve terms in multiplication and we also that if numbers with same base are in multiplication then their powers are added.
So, we will have the following expression:
[tex]17c^{9} d^{4} -6c^{3+6} d^{9-5\\}\\17c^{9} d^{4} -6c^{9} d^{4}[/tex]
Now, they have the same variables so the terms can be easily subtracted.
(More to know: if the variables would have been different in these two terms then they could not have been subtracted.)
[tex]11c^{9} d^{4}[/tex]
Hence, the value of the expression, [tex]17c^{9} d^{4} -2c^{3} d^{9} .3c^{6} d^{-5}[/tex], after simplification with only positive exponents is [tex]11c^{9} d^{4}[/tex].
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The difference of the digits of a 2-digit number is 3. If the digits are interchanged and the new number is added
to the original number, the result is 77. Find the original number.
Answer:
Original number = 10x + y = 52
Step-by-step explanation:
Please answer this question!
Answer: 1/4
Step-by-step explanation: 1/2 turned into decimal form is 0.5 but halved equals 0.25 which in fraction form is 1/4
A building security code has 2 numeric digits, 0 through 9, followed by 2 letters. What is the probability that the first digit is nine and the last letter is a?.
The probability of the event that the first digit is nine and the last letter is a is 1/260.
The building security code has 2 numeric digits in between 0-9 and 2 letters.
The choices for letters is 26 each and the choices for digits is 10 each.
So, the total possible security code can be,
Total security codes possible = 10 × 10 × 26 × 26
Total security codes possible = 67600
Now, the number of codes that starts with 9 and end with a are,
= 1 × 10 × 26 × 1
= 260
The probability that the first digit is nine and the last letter is a is,
P(E) = 260/67600
P(E) = 1/260
So, the probability that the first digit is nine and the last letter is a is 1/260.
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Answer the questions below about the quadratic function.f(x) = -2x² - 4x
We are given the function below;
[tex]f(x)=-2x^2-4x[/tex]PART A
We then proceed to find if the function has a minimum or maximum value. To find if the function has a minimum or maximum value. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.
ANSWER: From the above, we can see that x^2 is negative, hence the function has a maximum
PART B and C
To find the minimum or maximum value, we would plot the graph of the f(x). The graph can be seen below.
From the graph, the black point helps answer part A and part B.
ANSWER: The function's maximum value is f(x)=2.
This is the point where the slope of the graph is equal to zero
ANSWER: The maximum value then occurs at x= -1
We can also solve this by differentiating the function.
[tex]\begin{gathered} f(x)=-2x^2-4x \\ f^{\prime}(x)=-4x-4 \\ At\xi maxmum\text{ }f^{\prime}(x)=0 \\ -4x-4=0 \\ -4x=4 \\ x=-\frac{4}{4} \\ x=-1 \\ \therefore\text{The max}imum\text{ value occurs at x=-1} \\ \text{Inserting the value of x into the function, we have} \\ f(x)=-2(-1)^2-4(-1) \\ f(x)=-2+4 \\ f(x)=2 \\ \therefore\text{The function max}imum\text{ value is 2} \end{gathered}[/tex]what is the gcf for 18x^3 y^2, 9xyz
Given,
[tex]18x^3y^2,9xyz[/tex]To find GCF we will factor constant and variable terms individually,
First factorize 18:
[tex]18=1,2,3,6,9,18[/tex]Factors of 9:
[tex]9=1\times3\times9[/tex]Now,
[tex]\begin{gathered} 18=1,2,3,6,9,18 \\ 9=1,3,9 \end{gathered}[/tex]Now GCF of 18,9 is 9.
GCF of
[tex]x^3=x,x,x[/tex]GCF of
A class board with edge lengths of √80 dm and √150 dm has a square with an edge length of √3 dm how many pieces of cardboard can be placed in such a way that they do not overlap?
A) 48
B) 42
C) 35
D) 30
The total number of square cardboards that can be placed is 35 square pieces.
Length of the class board = √150dm
Length of the square side = √3 dm
Number of cardboards that can be cut = √150 ÷ √3 = 7.07 ≈ 7
Width of the square = √80 dm
Number of cardboard pieces = √80 ÷ √3 = 5.16 ≈ 5
Total number of cardboard squares = 7 × 5 = 35 pieces
A square is just a normal quadrilateral because it has four equal sides and four equal 90-degree, /2 radian, or right angles angles.
An alternative explanation is that it is a rectangle with two adjacent sides that are equal in length. It is the only uniform polygon with equal-length diagonals and identically 90° internal, central, and external angles.
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find thevsurface area of a square pyramid wuth side length 3 km and slant height 5 km
The Total Surface Area = 4 triangles + 1 square
The TSA of the Pyramid = 4(1/2 bh) + LxL
[tex]\begin{gathered} d^2=3^2+3^2 \\ d^2=9+9 \\ d=\sqrt[]{18}\text{ =}\sqrt[]{9\times2}=\sqrt[]{9}\text{ }\times\sqrt[]{2}\text{ =3 }\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} 5^2=h^2+(\frac{3}{2})^2 \\ 25-\frac{9}{4}=h^2 \\ 25-2.25=h^2 \\ h=\sqrt[]{22.5}\text{ =1.5km} \end{gathered}[/tex]TSA of the pyramid =
[tex]4(\frac{1}{2}\times5\times3)+(3^2)=(2\times15)+9=30+9=39km^2[/tex]Find the volume and surface area of the hexagonal pyramid.
Solution
A hexagonal pyramid is a three-dimensional object with a hexagon-shaped (6 sides) base and six triangular faces originating from each side to a common vertex.
The distance between the center of the hexagonal base and the common vertex is the altitude or height (h) of the pyramid.
The length of the base's side is the base edge or base length (a) of the pyramid.