Given statement 'The ₋Law of Sines can be used to find an angle measure when given three side lengths.' is False.
The correct statement is 'The ₋Law of cosines can be used to find an angle measure when given three side lengths.'
We know that an oblique triangle is a triangle which is either acute triangle or obtuse triangle but not a right triangle.
We know that the Law of Sines defines the relationship between the sides and angles of an oblique triangle.
And to use the Law of Sines we must know either two angles and one side of the triangle or two sides and one of the opposite angle to them (SSA).
But, the Law of Cosines is used to find the remaining parts of an oblique triangle.
This means, in case of the Law of Cosines when either the two sides and the angle included is given or the lengths of the three sides are given then we find the remaining angle measure.
Therefore, given statement 'The ₋Law of Sines can be used to find an angle measure when given three side lengths.' is False.
The correct statement is 'The ₋Law of cosines can be used to find an angle measure when given three side lengths.'
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Use your results from Exercise 13 to determine whether the given measures define 0,1, 2, or infinitely many obtuse triangles. Justify your answers.
a=13, b=17, m
When two sides are provided without an angle measurement, such as a = 13m and b = 17m , we can create an infinite number of obtuse triangles.
As an example:
How many different obtuse triangles can we make if our side lengths are 13m and 17m, and our angle value ranges from 90 to 360 degrees?
Make a triangle with sides of 13m and 17m metres, a 120 degree angle, and a third side that can be protractored to the length you desire. You've constructed a triangle.
We may create a whole different triangle that is identical to this one by altering the third side's length and angle.
You must always remember to select the side lengths and angles. It's hinted that you could choose another course of action. There are an infinite amount of distinct triangles that can be created by using the same angles.
Thus, we can make an infinite number of triangles by employing a single angle and a single side length.
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please help!!!!!!!!!!!!!! show your work and try to have the right answer
Answer:
Step-by-step explanation:
Jared has completed a controlled scientific experiment in which he found a strong
positive correlation between hours of daylight and pea plant growth. He calculates that
the correlation coefficient is 0.93. Does Jared's experiment suggest that sunlight causes
pea plant growth? Why or why not?
OYes; if the correlation coefficient is close to 1, then there is a cause-and-effect relationship.
Yes; finding a strong correlation in a controlled scientific experiment suggests a cause-and-effect
relationship.
O No; cause-and-effect relationships always have a correlation coefficient of 1 or -1.
No; cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
In Jared's experiment, we can conclude that; No, cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
How to Interpret Correlation Coefficient?
The correlation coefficient is simply the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis. It varies from -1 to 1.
Now, we are told that the correlation coefficient is 0.93. This means that it is close to 1. Now, we know that when the correlation coefficient is near 1 or −1, the linear relationship is strong; when it is near 0, the linear relationship is weak.
We also know that correlational studies allow researchers to detect the presence and strength of a relationship between variables, while experimental studies allow researchers to look for cause and effect relationships.
Thus, in Jared's experiment, we can conclude that; No, sunlight doesn't cause pea plant growth because cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
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determine whether the following graph represents a function
1. one to one function
2. Not a function
3. Function, but not one to one
Answer:
3. function, but not one to one
Step-by-step explanation:
If you do a vertical line test anywhere you draw a vertical line will only hit in one spot
If you do a horizontal line test to check If the line is one to one it hits in multiple spots therefore the line that is graphed is a function but not one to one
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
An equilateral triangle is always equiangular.
The given sentence about equilateral triangle is true.
A statement is given in the question.
We have to tell whether the statement is true or false.
What is an equilateral triangle ?
An equilateral triangle is a triangle in which all sides and all angles are equal.
As per the question ;
The statement given is , "An equilateral triangle is always equiangular."
Let's check whether it is true or false ;
We know that ,
Equiangular meant equal angles and we know that all the angles of equilateral triangle are equal.
Also ;
An equilateral triangle can also said as an isosceles triangle, that meant any two sides that are equal have equal opposite angles.
So ;
All three sides of an equilateral triangle are equal, all three angles are equal, too. We can conclude that every equilateral triangle is also equiangular.
Thus , the given statement about equilateral triangle is true.
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Is the distance from the center of a circle to a point in the interior of a circle sometimes, always, or never less than the radius of the circle? Explain.
The distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.
It is given that there is a point inside the circle.
We have to find that whether its distance from center of circle is sometimes, always, or never less than the radius of the circle.
What is the radius of a circle ?
The distance between the center of a circle and any point on the circle is called the radius of circle.
We know that ;
Radius is the distance between the center of a circle and any point on the circle.
Let's assume three points which are A, B, and C, where A is a point inside circle, B is a point on circle, and C is a point outside circle.
Also ;
O is the center of circle.
So ;
OA = the length of the line from center to point inside the circle.
OB = radius of the circle.
OC = the length of the line from center to the point outside the circle.
So ;
We can conclude that ;
OA<OB<OC.
or
The length of the line from the center of a circle to any point inside the circle will be always less than it's radius.
Thus , the distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.
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Natalie works as a playground supervisor for 8 weeks during the summer at a rate of
$15.27/h. She works a 40-hour week but averages 3 hours of overtime each week,
paid at time and a half. How much will she earn each week, and for the whole
summer?
Natalie will be paid $656.61 for a week and for summer $10505.76.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Natalie earns $15.27 per hour while working as a playground supervisor for 8 weeks throughout the summer. Although she works a 40-hour week, she typically puts in 3 hours of overtime.
For a week = ( 40 + 3 ) x 15.27 = $656.61
For a summer = 4 x 4 = 16 weeks
For a summer = 16 x $656.61 = $10505.76
Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.
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Given g(x)=-2x^(2)+1, find the indicated values. g(0)
Answer:
[tex]g(x) = 2 {x}^{2} + 1 \\ g(0) = 2 ({0})^{2} + 1 \\ = 2(0) + 1 \\ = 1[/tex]
help please
The cost of having a window fixed is $125 plus $25 per hour of labor. Using h for the number of hours of labor, write an expression that represents the total cost.
25 + 125h
125 + 25h
150h
125+25 over h
I believe the answer would be Y=125+25(h
Answer: 125 + 25h
Step-by-step explanation:
The total amount of money is the cost of the window plus the amount of hours.
A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
b. If A C=1300 meters, D C=550 meters, and D E=851.5 meters, what is AB? Explain your reasoning.
The value of line AB is 550 meters.
What do we presume by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
First, we'll prove that △BEA ≅ △DEC.
∠A = ∠C = (BA and CD is ⊥ AC)AE = CE = (E is the midpoint of AC)∠AEB = ∠DEC = (Inversely opposite angles)So, △BEA ≅ △DEC is under ASA condition.
Then, DC is identical to AB.Therefore, the value of AB is 550 meters.
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Y=-3x+6 and y=1/3x-8 determine if the equation are parallel, perpendicular, or neither
Answer:8
Step-by-step explanation:
1
Your phone is losing charge at a rate of 2%every 7 minutes. You check and see that you have 44% left. Write the function of total charge left where x is in minutes. Find the y-intercept, x-intercept and slope.
The y-intercept, x-intercept and slope are 100, 350 and 2 / 7, respectively.
How to describe the linear equation describing the discharge of a phone
In accordance with the statement, the phone charge decreases linearly in time based on the following linear model:
c(x) = 100 - (Δy / Δx) · x
Where:
c(t) - Current charge of the cell phone, in percentage.Δc - Current charge change, in percentage.Δx - Time change, in minutes.x - Time, in minutes.If we know that Δy = 2, Δx = 7, then the linear equation is:
c(x) = 100 - (2 / 7) · x
Then, the y-intercept, x-intercept and slope are, respectively:
y-intercept
b = 100
x-intercept
0 = 100 - (2 / 7) · x
(2 / 7) · x = 100
2 · x = 700
x = 350
Slope
m = 2 / 7
The y-intercept, x-intercept and slope are 100, 350 and 2 / 7, respectively.
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Solve by completing the square. Express answer in a simplified radical form when possible. When not possible, round to nearest hundredth.
x^2+6x+2=0
Answer:
[tex]{ \tt{ {x}^{2} + 6x + 2 = 0}} \\ { \tt{ {x}^{2} + 6x = - 2 }}[/tex]
- Add the square of the half of the sum on either sides:
[tex]{ \tt{ {x}^{2} + 6x + ( { \frac{6}{2}) }^{2} = - 2 + {( \frac{6}{2}) }^{2} }} \\ \\ { \tt{ {x}^{2} + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^{2} = 7}} \\ { \tt{x + 3 = \sqrt{7} }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm \sqrt{7} )}}[/tex]
please help
please good graph
You can see the graphs in the attached image. The order is the same as on page. Note that 7. and 8. give us an infinite number of solutions, and no solutions, respectively.
Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.Prove that the triangle with vertices (3,5),(-2,6) , and (1,3) is a right triangle.
Using the definition of slope, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
To prove that the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle, there should be a pair of adjacent lines perpendicular with each other(forms 90 degree angle). The slope of this pair of adjacent lines must be negative reciprocal of one another.
let A = (3 , 5)
B = (-2 , 6)
C = (1 , 3)
Determine the slope of each line of the triangle: AB, BC, AC.
AB : m = (6 - 5)/(-2 - 3) = 1/-5 = -1/5
BC : m = (3 - 6)/(1 - -2) = -3/3 = -1
AC : m = (3 - 5)/(1 - 3) = -2/-2 = 1
-1 is the negative reciprocal of 1. The slope of BC is the negative reciprocal of the slope of AC, hence, side BC is perpendicular with each other.
Therefore, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.
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A rectangular painting measures 13 inches by 20 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 98 inches. Determine the width of the frame.
The width of the frame is 8 inches.
We are given that:
The measures of the rectangular painting are:
Length = 13 inches
width = 20 inches
Now, the frame is of uniform with around the corner.
Let it be x inches.
So the new dimensions will be:
Length = 13 + x inches
Width = 20 + x inches.
Also, we are given that:
Perimeter = 98 inches
So, we get that:
P = 2(l + b)
Substituting the values, we get that:
98 = 2 (13 + x + 20 + x)
98 = 2( 33 + 2 x)
98 = 66 + 4 x
4 x = 98 - 66
4 x = 32
x = 32 / 4
x = 8 inches.
Therefore, the width of the frame is 8 inches.
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Write equations for the horizontal and vertical lines passing through the point (1,8)
Answer:
Vertical: x = 1
Horiz: y = 8
Step-by-step explanation:
The equation of a
vertical line is always:
x = anumber
The equation of a horizontal line is in the form:
y = anumber
In the question a point is given, the point (1,8) is in the form (x,y) So x is 1 and y is 8.
We can fill in this given information to complete the equations.
Vertical: x = 1
Horizontal: y = 8
Which expression has a value of -5?
A: (-3) -8
B: (-8) - (-3)
C:(-3) - (-8)
D: 8-(-3)
Points P, Q, R, and S are collinear Point Q is between P and R, R is between Q and S, and PQ congruent RS. If PS=23 and PR= 18, what is the value of QR?
The value of QR when points P, Q, R and S are collinear is .13
We are given that:
Points P, Q, R and S are collinear points.
Also,
PS = 23
PR = 18
We need to find the value for QR.
Now, we have that PQ is congruent to RS.
So, This means that PQ = RS
This can also be written as:
PR - QR = RS
18 - QR = RS
Also,
PR + RS = PS
Substituting the values, we get that:
18 + ( 18 - QR ) = 23
18 - QR = 23 - 18
18 - QR = 5
QR = 18 - 5
QR = 13
Therefore, we get that, the value of QR when points P, Q, R and S are collinear is .13
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In Exercises 1-16, solve the inequality. Graph the solution
1. 3y ≤ -9
By solving the inequality we get [tex]y\leq -3[/tex]
What is graphing the inequality?
The act of illustrating which area of the number line contains values that will "satisfy" the specified inequality is known as graphing the inequality. Take a look at the first inequality, "x > -5." The numbers that can be used to substitute x in our inequality to produce a true statement can be shown on a graph of our inequality.
[tex]3y\leq -9[/tex]
Dividing above equation by 3 we get,
[tex]\frac{3y}{3}\leq \frac{-9}{3}\\y\leq -3[/tex]
Graph of [tex]y\leq -3[/tex] is
Therefore by solving the inequality we get [tex]y\leq -3[/tex]
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Find two numbers whose sum is 52 and whose product is as large as possible? [Hint: Let x and 52-x be the two positive numbers. Their product can be
described by the function f(x)=x(52-x).]?
The two numbers whose sum is 52 and the product is maximum are 26 and 26.
How to find the sum of algebraic fractions?Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in the sum of fractions would give the sum of algebraic fractions.
We need to find the two numbers whose sum is 52 and the product is maximum.
So, the multiples of 52 are
2, 26, 4, 13,
So, here we can see that the sum of 26 to itself would be equal to 52.
26 + 26 = 52
The product is also maximum compared to others.
26 x 26 = 676
Therefore, the two numbers are 26 and 26.
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when slolved please show steps.
The expression for h in the information illustrated will be h = 2r.
How to illustrate the information?It should be noted that the expression is given as:
2πr³ = πr²h
In this situation, the information is that we should make h the subject of the formula.
This will be:
2πr³ = πr²h
Divide both side by πr²
2πr³/πr² = πr²h/πr²
2r = h
Therefore h = 2r
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m ebd = 29 bc bisects abd and be bisects cbd find m abc
We can conclude that in the question, angle m∠ABC = 58°.
What are angles?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner." Angles in geometry are classified according to their measurement. Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles.So,
∠EBD is 29° and line EB bisects ∠CBD.
Then, ∠CBD = ∠CBE + ∠EBD∠CBD = 29 + 29 = 58°Similarly, ∠CBD = 58° and line CB bisects ∠ABD
Then, ∠ABD = ∠ABC + ∠CBD ∠ABD = 58 + 58 = 116°Hence, ∠ABC = 58° as ∠CBD is also 58° because common line BC bisects the angle ∠ABD.
Therefore, angle m ∠ABD = 58°.
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Ana has 8 stamps. Together, Ricky and ana have 23 stamps. The equation 23 = r + 8 represents this situation,where r is the number of stamps Ricky has. Solve the equation to find the number of stamps ricky has
Ricky has the number of stamps in the number of 15 stamps.
According to the question, the given parameters can be used to form the expression by using simplification method and the parameters are as follows:
Stamps for Ana: 8
Stamps for Ricky and Ana: 23
Given equation: 23 = r + 8
The equation formed by the simplification method is: r + a = 23
Solving above two equations, we get a = 8 stamps and r = 15 stamps.
Hence, Ricky has the number of stamps in the number of 15 stamps.
What is simplification?
The word simplification is the procedure in which complicated expression can be written in a simpler form to make the calculation easy. This method is used to calculated the answers for the unknown quantity.
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Help Please
A woman has a total of $9,000to invest. She invests part of the money in an account that pays 7%per year and the rest in an account that pays 9%per year. If the interest earned in the first year is $710, how much did she invest in each account? She invested $ ____at 7%and $_____at 9%.
Answer:
5000.00 gives us 350
4000.00 gives us 360
Find the area
(Simplify your answer)
Answer:
why isnt there a backround base? it wouldnt be area if isnt so
Step-by-step explanation:
The area is 960 m
because 48*15=720
and 10*24=240
720+240= 960
Simplify the expression. Write your answers using integers or improper fractions.
− 3/2(1/2 n+2n−3)+4n
The expression is simplified to n - 16/ 4
What are algebraic expressions?
Algebraic expressions are expressions comprising of terms, variables, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
Given the expression;
− 3/2(1/2 n+2n−3)+4n
Solve the variables in the bracket, we have;
- 3/ 2 { n + 4n - 6 / 2} + 4n
-3/2 { 5n - 6/ 2 } + 4n
expand the bracket
- 15n - 18/ 4 + 4n
Fin the LCM
-15n - 16 + 16n /4
n - 16/ 4
Thus, the expression is simplified to n - 16/ 4
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Caroline rewrote a quadratic equation in vertex form by completing the square, but her work has errors.
f(x)
-2x² + 12x15
-2(x² - 6x) — 15
-2(x² - 6x + 9) - 9 - 15
-2(x - 3)²9 - 15
-2(x - 3)² - 24
Identify the first error in her work.
The required error in Caroline's quadratic equation in vertex form by completing the square is -2(x² - 6x + 9) - 9 - 15 is should be -18 in place of -9.
Given that,
To figure out the error made by Caroline in the calculation of a quadratic equation in vertex form by completing the square.
His calculation,
= -2x² + 12x - 15
= -2(x² - 6x) — 15
= -2(x² - 6x + 9) - 9 - 15-2(x - 3)²9 - 15
= -2(x - 3)² - 24
Correct calculation,
= -2x² + 12x - 15
= -2(x² - 6x) - 15
= -2(x² - 6x + 9) - 18 - 15
= -2(x - 3)² - 18 - 15
= -2(x - 3)² - 33
Thus, the required error in Caroline's quadratic equation in vertex form by completing the square is -2(x² - 6x + 9) - 9 - 15 is should be -18 in place of -9.
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Find the slope of the line passing through the
points (-3, 3) and (5, 9)
Answer: 3/4
Step-by-step explanation:
The slope of the line passing through the points (-3,3) and (5,9) is 3/4
The formula for calculating the slope of a line is expressed as:
Given the coordinate (-3,3) and (5,9), substitute the coordinates into the formula as shown below;
Hence the slope of the line passing through the points (-3,3) and (5,9) is 3/4
Write the equation of the line that is perpendicular to x + 4y = 12 and passes through the point (-8, 5) in slope-intercept form.
y = mx + b
m=
b=
The equation of the line is: y = 4x + 37
m = 4
b = 37
How to Write the Equation of a Line in Slope-intercept Form?The equation of the line that is perpendicular to x + 4y = 12, will have a slope that is the negative reciprocal of the its slope.
Rewrite the equation, x + 4y = 12 in slope-intercept form:
4y = -x + 12
y = -x/4 + 3
The slope is -1/4. Therefore, the slope of the perpendicular line would be 4.
Substitute m = 4 and (a, b) = (-8, 5) into y - b = m(x - a)
y - 5 = 4(x - (-8))
y - 5 = 4x + 32
y = 4x + 32 + 5
y = 4x + 37
The equation of the line is: y = 4x + 37
m = 4
b = 37
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