Given:
The slopr of line is m = -7.
The line passes through point (-6,8).
Explanation:
The equation of line in slope-intercept form is,
[tex]y=mx+c[/tex]Substitute the valus in the equation to determine the value of c.
[tex]\begin{gathered} 8=-7\cdot(-6)+c \\ c=8-42 \\ =-34 \end{gathered}[/tex]So equation of line is y = -7x - 34.
1. Angle AOC has what measurement according to the protractor?
In order to find the measure of angle AOC, let's start looking at point A.
Point A is in position 180, if we look in the upper numbers, and in position 0, if we look in the lower numbers.
Since it's easier to find the angle if one vertex is at position 0, let's consider position 0° for A.
Then, looking at point C, it is in position 130° in the upper numbers and 50° in the lower numbers.
Since we choose the lower numbers for A, we need to do the same for C.
Therefore A is in position 0° and C is in position 50°.
To find angle AOC, let's subtract both measurements/positions:
[tex]\text{AOC}=50\degree-0\degree=50\degree[/tex]Therefore angle AOC measures 50°, and the correct option is C.
write the equation Log 243 81= 4/5
Given
[tex]\log _{243}81=\frac{4}{5}[/tex]
Procedure
Exponential form
[tex]\begin{gathered} 243^{4/5}=81^{} \\ \end{gathered}[/tex]What’s the correct answer answer asap for brainlist
Answer:
I would say C but I'm really not sure hope this helps
Instructions: Find the measure of the indicated angle to thenearest degree.
Given:
• Length of side adjacent the indicated angle = 48
,• Length of hypotenuse = 56
Let's find the measure of the indicated angle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for cosine:
[tex]cos\theta=\frac{adjacent}{\text{ hypotenuse}}[/tex]Thus, we have:
[tex]\begin{gathered} cos\theta=\frac{48}{56} \\ \\ cos\theta=\frac{6}{7} \\ \\ \text{ Take the inverse cosine of both sides:} \\ \theta=cos^{-1}(\frac{6}{7}) \\ \\ \theta=31^o \end{gathered}[/tex]Therefore, the measure of the indicated angle is 31 degrees.
ANSWER
Use the distributive property to write an equivalent expression.
8(4n+ 3) =
12x-6=
5x+20=
3(x+6)=
7x-35=
20p + 16 =
The distributive property to write an equivalent expression.
8(4n+ 3) = 32n + 24
12x-6= 1/2
5x+20= 4
3(x+6)= 3x + 18
7x-35= 5
20p + 16 = 4/5
A distributive property in mathematics is defined:The distributive property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and combining the resulting products.
We use distributive property for what purposes?One of the most common properties in arithmetic is the distributive property. The multiplier is applied to each integer inside the parentheses, and the results are added to obtain the answer. This technique is used to simplify and solve multiplication problems.
According to the given data:the distributive property to write an equivalent .
8(4n+ 3)
= 8 * 4n + 3* 8
= 32n + 24
for 12x-6
12x-6 = 0
x = 6/12
x = 1/2
For 5x+20
5x+20 =
x = -4
For 3(x+6)
= 3 * x + 3 * 6
= 3x + 18
For 7x-35
= 35/7
= 5
For 20p + 16
= 20/16
= 5/4
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Question Use the Distributive Property to simplify the expression. 12(6−k) =
After simplifying and using the Distributive Property, the final solution would be [tex]72-12k[/tex].
Hope this helps!
Given the graph below write an equation of the form f(x) = Acos(w(x-c))+D
Amplitude = (Maximum + Minimum)/2 , = (1 + 1.8)/2= (2.8)/2= 1.4
Period = distance for the function to repeat. So, the distance is from -0.5 to 3.5, then it is 4, then it is smaller than 2 times pi number.
C is the distance from the Y axis to the function.
D is the horizontal line that passes through the middle of the distance between the maximum and minimum point, which is in that case the same one as the period has to use
Then, the formula is:
[tex]\begin{gathered} f(x)=Acos(w(x\text{ -c\rparen + D A is amplitude, C is horzontal distance and D}midpoint \\ \\ f(x)=1.4cos(4(x\text{ - 1.7\rparen+\lparen-0.4\rparen} \\ f(x)=1.4cos(4x\text{ - }6.8)\text{ - }0.4 \end{gathered}[/tex]Which graph is the solution of the system
x+2y≤16
4x+y>6
1 2 3 4
Graph 1 shows the correct representation the solution of the system.
What is solution of system of linear equation?The point that satisfies all of the equations in a system of linear equations is called the solution. A system of linear equations could be solved through graphing as well as identifying the intersection point, or by solving the variables algebraically.For the given question;
The system of linear equation are given as;
x + 2y ≤ 16 .......eq 1
4x + y > 6 ......eq 2
Consider equation 1;
x + 2y = 16
For x = 0; y = 8 , Point = (0, 8)
For y = 0, x = 16, Point = (16, 0)
As the inequality of the eq 1 is less than equal to, the shaded region will lies below the line with solid lines.
Consider equation 2;
4x + y = 6
For x = 0; y = 6 , Point = (0, 6)
For y = 0, x = 1.5, Point = (1.5, 0)
As the inequality of the eq 2 is greater than, the shaded region will lies above the line with doted lines.
Thus, graph 1 shows the correct representation the solution of the system.
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What values of b satisfy 4(3b+2)^2=64
solve for b:
take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{4(3b+2)^2}=\sqrt[]{64} \\ \sqrt[]{4}\cdot\sqrt[]{(3b+2)^2}=\pm8 \\ 2(3b+2)=\pm8 \\ 6b+4=\pm8 \\ so\colon \\ b=\frac{\pm8-4}{6} \end{gathered}[/tex]therefore:
[tex]\begin{gathered} b=\frac{2}{3} \\ or \\ b=-2 \end{gathered}[/tex]Answer: b=2/3 and b=-2
Step-by-step explanation:
) POLYNOMIAL AND RATIONAL FUNCTIONSVord problem involving the maximum or minimum of a quadrati.
SOLUTION:
Case: Minimum and Maximum functions
Given:
[tex]\begin{gathered} C(x)=0.8x^2-352x+58,583 \\ \end{gathered}[/tex]Required: To find the minimum Unit cost
Method: we apply completing square on the function
Step 1: First we find the square of half the coefficient of x
[tex]\begin{gathered} C(x)=\text{ 0.8x}^2-352x+58583 \\ C(x)=\text{ 0.8\lparen x}^2-440x+73228.75) \\ \frac{1}{2}(440)=\text{ 220}^2\Rightarrow\text{ 48400} \end{gathered}[/tex]Step 2: Add and subtract the value to the Right Hand Side
[tex]\begin{gathered} C(x)=\text{ 0.8\lparen x}^2-440x+48400-48400+73228.75) \\ Completing\text{ squares in the bracket} \\ C(x)=\text{ 0.8\lbrack\lparen x-220\rparen}^2+24828.75] \\ C(x)=0.8(x-220)^2+\text{ 19863} \end{gathered}[/tex]Step 3: From the equation
The quantity need to be produced to get the minimum unit cost is 220.
The value of the minimum cost therefore is obtained at C(220).
This would give:
C(220)= $19863
Final answer:
The minimum unit cost is $19863. Ignore the dollar sign($) when entering your answer.
8 Real life /
and are blue.
Rasheed and Kamal did a survey on car colours.
Problem-solving Approximately of cars in the UK are silver
a Rasheed found 120 people had silver cars.
How many people could he have asked?
b Kamal found 120 people had blue cars.
How many people could he have asked?
Using proportions, it is found that the number of people that each asked is given as follows:
a) Rasheed: 571 people.
b) Kamal: 667 people.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication and division, with the unit rates or percentages of the problem.
For Rasheed, since he was counting people with silver cars, we have that 21% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:
0.21n = 120
n = 120/0.21
n = 571 people. (rounding)
For Kamal, since he was counting people with blue cars, we have that 18% of the n people is equivalent to 120 people, hence the number of people n is calculated as follows:
0.18n = 120
n = 120/0.18
n = 667 people. (rounding)
Missing informationThe percentages of car colors in the UK are mussing and are given as follows:
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HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 50 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answer:
6 units13 units5 unitsStep-by-step explanation:
You want the lengths of the unknown sides in the given trapezoid figure, knowing that the perimeter is 18 units.
1.The side AB is a vertical line segment, so its length can be found by finding the difference of y-coordinates of its end points.
AB = (2) -(-4) = 2+4 = 6
The length of AB is 6 units.
2.The sum of the lengths of vertical and horizontal segments is ...
AB +BC +CD = 6 +4 +3 = 13
The total distance from A to D along vertical and horizontal segments is 13 units.
3.The perimeter is the sum of the lengths of all sides.
perimeter = AB +BC +CD +AD
18 = 13 + AD . . . . . . substitute known values
5 = AD . . . . . . . . . subtract 13
The length of segment AD is 5 units.
__
Additional comment
Finding the length of a vertical or horizontal line is no different than finding the distance between two points on a number line.
(3m + 5) - (6 - 5m) answer this for me
Answer: If you are simplifying the expression, 8m-1 is your answer.
If you are finding the roots of this polynomial, 1/8 is your answer. (Can also be written as 0.125, 2^-3)
If the point (2,-5) is reflected in the line y=x, then the image is:
Answer:
(-5, 2)
Explanation:
If a point (x,y) is reflected in the line y=x, the x-coordinate and y-coordinate change places.
That is:
[tex](x,y)\to(y,x)[/tex]Therefore, the image of (2, -5) when reflected in the line y=x is:
[tex](-5,2)[/tex]how do you use Congruence and similarity criteria to prove relationships in geometric figures?
Congruence and similarity criteria are used to determine congruence and proportional relationships respectively. That is, congruence criteria is used to establish a relationship of equivalence, and similarity criteria is used to establish a relationship of proportion with a common ratio between the figures.
Please help me solve question 6 on this algebra 1 worksheet
We have that one simply way to write that equation is
[tex]\frac{2}{3}(21q^2-3q+7)[/tex]Because we have that
[tex]undefined[/tex]Original price $27.00 Markdown 15%
Week 1: saves $ 35 Week 2 : saves $ 10 Week 3: spends $ 20 Week 4: spends $ 5 Week 5 saves $15 Week 6: saves $10 Susan wants to go on a vacation to the beach with her friends . For six weeks she keeps track of how much money she spends and saves . For the next six weeks she plans on increasing the amount she saves by $10 and decreasing the amount she spends by $5. How will this affect the MEAN amount of money that Susan has ? A) The mean will not change . B) The mean will increase by approximately $5. ) The mean will increase by approximately $ 8. D) The mean will increase by approximately $15. E) The mean will increase by approximately $30.
B) The mean will increase by $5
1) The first scenario has the following mean, adding all the spendings and savings:
[tex]x=\frac{35+10+20+5+15+10}{6}=\frac{95}{6}=15.83[/tex]2) Since for the following week there's an increase of $10 for her savings and a decrease of $ 5 we can write:
[tex]\begin{gathered} x=\frac{(35+10)+(10+10)+(20-5)+(5-5)+(15+10)+(10+10)}{6}= \\ =\frac{45+20+15+0+25+20}{6}=\frac{125}{6}=20.83 \end{gathered}[/tex]3) We can see that the mean changes, and examining the options we can state that:
the answer is B, the mean will increase by $5
Write +/99 +/44 in the form avb where a and b are integers.
Step-by-step explanation:
[tex] \sqrt{99} = 3 \sqrt{11} \\ \sqrt{44} = 2 \sqrt{11} \\ 3 \sqrt{11} + 2 \sqrt{11} = 5 \sqrt{11} [/tex]
Answer:
[tex]3 \sqrt{11} [/tex]
[tex]4 \sqrt{11} [/tex]
because we rewrite it as integer statements
And also state the vertex and the axis of symmetry. I need help with number 2
In order to complete the square remember that
[tex](x\pm a)^2=x^2\pm2\cdot x\cdot a+a^2[/tex]first, equal the expression divide all the expressions by 2,
[tex]\begin{gathered} f(x)=2x^2+4x+7 \\ 2x^2+4x+7=0 \\ 2x^2+4x=-7 \\ x^2+2x=-\frac{7}{2} \end{gathered}[/tex]then, we can find "a" using the second portion of the definition
[tex]\begin{gathered} 2\cdot x\cdot a=2x \\ a=\frac{2x}{2x} \\ a=1 \end{gathered}[/tex]then,
[tex]a^2=1^2=1[/tex]add 1 on both sides
[tex]\begin{gathered} x^2+2x+1=-\frac{7}{2}+1 \\ x^2+2x+1=-\frac{5}{2} \end{gathered}[/tex]rewrite as a square expression on the left,
[tex](x+1)^2=-\frac{5}{2}[/tex]multiply both sides by 2
[tex]2(x+1)^2=-5[/tex]bring all to the left side and equal to f(x)
[tex]\begin{gathered} f(x)=2(x+1)^2+5 \\ \text{The vertex is at (-1,5)} \\ \text{the axis of symmetry is x=-1} \end{gathered}[/tex]2. The graph below shows the relationship between the number of pages printed (x) at a print shop and the total price (y), in dollars. Print Shop Prices у 9 Total Price ($) Based on the graph, what is the unit price at the print shop?
Let:
[tex]\begin{gathered} (x1,y1)=(2,1) \\ (x2,y2)=(4,2) \\ so\colon \\ m=\frac{y2-y1}{x2-x1}=\frac{2-1}{4-2}=\frac{1}{2}=0.5 \end{gathered}[/tex]Dave's wardrobe contains 25 T-shirts, of which 13 are gray. Dave selects a T-shirt at random.
What is the probability that Dave will select a gray T-shirt?
Enter a reduced fraction
What are the odds in favor of Dave selecting a gray T-shirt?
Enter the ratio in lowest terms
The probability that Dave will select a gray T-shirt is 13 / 25.
The odds in favor of picking a gray T-shirt is 13 : 25
What is the probability?
Probability is used to calculate the odds that are in favor or against a random event happening. The odds in favor or against a random event happening has a probability value that lies between 0 and 1. The higher the odds that are in favor of the event happening, the closer the probability value would be to 1.
The probability that Dave will select a gray T-shirt = number of gray T-shirts / total number of T-shirts
13 / 25
Ratio is used to compare two or more numbers together.
The odds in favor of picking a gray T-shirt = number of gray T-shirt : total number of T-shirts = 13 : 25
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Write a biconditional for the following conditional. Then state the truth value of the statement
If two lines intersect at right angles, then they are perpendicular.
The biconditional for the conditional statement is : Two line intersect each other at right angles . The two lines are perpendicular.
A conditional statements are part of mathematical reasoning, a fundamental ability that enables students to evaluate a given hypothesis without reference to a particular context or meaning.
Simply put, when a scientific research or allegation is studied, the logic is not reliant on an individual's viewpoint. Deductions and evidence must have factual and scientific foundations.Conditionals are programming language instructions used to manage judgments in the field of computer science. They are also referred to as conditional statements, conditional expressions, and conditional constructions.One needs to be capable of logical reasoning and critical thinking in mathematics in order to respond to questions involving mathematical reasoning and conditionals.The truth value for the conditional statement is true as we know that when two lines intersect at 90° then they are said to be perpendicular.
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Write an equation of the parabola that passes through the point (-9, 2) and has vertex (-3,1).
Answer:
[tex]\textsf{Vertex form}: \quad y=\dfrac{1}{36}(x+3)^2+1[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given:
Vertex = (-3, 1)Point = (-9, 2)Substitute the given vertex and point into the formula and solve for a:
[tex]\begin{aligned}y&=a(x-h)^2+k\\\\\implies 2&=a(-9-(-3))^2+1\\2&=a(-6)^2+1\\2&=36a+1\\36a&=1\\a&=\dfrac{1}{36}\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\boxed{y=\dfrac{1}{36}(x+3)^2+1}[/tex]
In standard form:
[tex]\implies y=\dfrac{1}{36}(x+3)(x+3)+1[/tex]
[tex]\implies y=\dfrac{1}{36}(x^2+6x+9)+1[/tex]
[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{6}{36}x+\dfrac{9}{36}+1[/tex]
[tex]\implies y=\dfrac{1}{36}x^2+\dfrac{1}{6}x+\dfrac{5}{4}[/tex]
If x = 9 and 4x + 7 = y
Then 4(9)+7 = y
This is an illustration of which property?
Answer: Substitution property
Step-by-step explanation:
It's substituting a variable into an equation.
what percentage increase from 9,620,000 to 9,980,000. Round to the earedt tenth of a percent.
Answer:
3.7%
Explanation:
Given
Original value = 9,620,000
New values = 9,980,000.
Increment = New - Original
Increment = 9,980,000 - 9,620,000
Increment = 360,000
%increae = 360,000/9,620,000 * 100
%increase = 3.7%
Hence the percentage increase is 3.7%
Determine whether the line that passes through points (-2, 1) and (6, 5) is parallel, perpendicular or neither to a line with a slope of -2.
We have a line with slope -2. A parallel line would have a slope of -2 too, and a line perpendicular to it will have a slope of 1/2.
If line A is perpendicular to B, the slope of B is the inverse multiplicative of the sloe of A. That is why a line perpendicular to the one with slope -2 is 1/2:
[tex]\text{Perpendicular Slope}=-\frac{1}{-2}=\frac{1}{2}[/tex]Now we know the slopes for both cases: parallel and perpendicular. If the slope is different to -2 or 1/2, we can say that is not parallel nor perpendicular to the line given.
Let's evaluate the slope of the line that passes through points (-2, 1) and (6,5).
The slope is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where x₁ and y₁ are the x and y-coordinates of the first point (-2 and 1), and x₂ and y₂ are the x and y coordinates of the second point (6 and 5, respectively).
Replacing values:
[tex]\begin{gathered} m=\frac{5-1}{6-(-2)}=\frac{4}{6+2}=\frac{4}{8} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]The slope of the line passing through the points given is 1/2, then, according to what was said above, that line is perpendicular to a line with slope -2.
The heights of ten-year-old males are normally distributed with a mean of 57.4 inches and a standard deviation of 5.1 inches. If a pediatrician selects a random sample of 46 ten-year-old males from his patient population, what is the probability that the mean height of this sample will be greater than 57 inches?Round your answer to at least three decimal places
Given:
[tex]Means,\text{ }\mu=57.4[/tex][tex]Standard\text{ deviation, }\sigma=5.1[/tex][tex]The\text{ sample size, n=46.}[/tex]Required:
We need to find the probability that the mean height of this sample will be greater than 57 inches,
[tex]P(x>57).[/tex]Explanation:
Consider the formula to find the z-score.
[tex]z=\frac{\mu-x}{\frac{\sigma}{\sqrt{n}}}[/tex][tex]Subst\text{itue }\mu=57.4\text{, }\sigma=5.1,\text{ n=46 and x=57 in the formula.}[/tex][tex]z=\frac{57-57.4}{\frac{5.1}{\sqrt{46}}}[/tex][tex]z=\frac{-0.4}{\frac{5.1}{\sqrt{46}}}[/tex][tex]z=-0.4\times\frac{\sqrt{46}}{5.1}[/tex][tex]z=-0.5319[/tex]From the z table, we get
[tex]P(x<57)=0.2974[/tex][tex]\text{We know that }P(x>57)=1-P(x<57).[/tex][tex]Substitut\text{e }P(x<57)=0.2974\text{ in the equation.}[/tex][tex]P(x>57)=1-0.2974.[/tex][tex]P(x>57)=0.7026.[/tex][tex]P(x>57)=0.703.[/tex]
Final answer:
The probability that the mean height of this sample will be greater than 57 inches is 0.703.
The product of two consecutive
odd positive integers is one hundred forty-three. Find the integers.
The integers are 71 and 72 respectively
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.
They are also known to be composed of mathematical operations such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given , we have;
x + 1 + x + 2 = 143
collect like terms
2x = 143 - 3
Subtract like terms
2x = 140
Make 'x' the subject
x = 140/2
x = 70
The numbers are;
x + 1 = 70 + 1 = 71
x + 2 = 70 + 2 = 72
Hence, the numbers are 71 and 72
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Three pencils are on sale for $0.45 at this rate what is the cost per pencil
1) Gathering the data
3 pencils ----------- $0.45