At the farmer’s market, Joan bought apples at $1.20 per pound, cherries for $2.00 per pound and pears for $0.80 per pound. She bought a total of 9 pounds of fruit for $11.00. Joan bought twice as many pounds of apples than cherries. Let A be the weight of the apples, C be the weight of the cherries, and P be the weight of the pears. Formulate a system of equations to determine how many pounds of each type of fruit were bought. Do Not Solve.
Answers
We have here a case in which we need to translate a problem into algebraic expressions to solve a problem, and we have the following information from the question:
• We have that Joan bought:
0. Apples at $1.20 per pound
,1. Cherries at $2.00 per pound
,2. Pears at $0.80 per pound
• We know that she bought a total of 9 pounds of fruit.
,• We also know that she spent $11.00 for the 9 pounds of fruit.
,• Joan bought twice as many pounds of apples than cherries.
We need to label weights as follows:
• Weight of apples ---> A
,• Weight of cherries ---> C
,• Weight of pears ---> P
Now to find a system of equations to determine the number of pounds of each type of fruit was bought, we can proceed as follows:
1. We know that if we multiply the price of the fruit per pound by the weight in pounds, we will obtain the amount of money Joan spent in total. Then we have:
[tex]1.20a+2.00c+0.80p=11.00\rightarrow\text{ \lparen First equation\rparen}[/tex]2. We also know that the total weight of the fruits was equal to 9 pounds. Then we can translate it into an algebraic expression as follows:
[tex]a+c+p=9\rightarrow(\text{ Second equation\rparen}[/tex]3. And we know that Joan bought twice as many pounds of apples than cherries, and we can translate it as follows too:
[tex]\begin{gathered} 2a=c \\ \\ \text{ If we subtract c from both sides of the equation, we have:} \\ \\ 2a-c=c-c \\ \\ 2a-c=0\text{ \lparen Third equation\rparen} \end{gathered}[/tex]Now we have the following equations:
[tex]\begin{gathered} 1.20a+2.00c+0.80p=11.00 \\ \\ \begin{equation*} a+c+p=9 \end{equation*} \\ \\ \begin{equation*} 2a-c=0 \end{equation*} \end{gathered}[/tex]Therefore, we have that the correct option is the first option:
• 1.20a + 2.00c + 0.80p = 11.00
• a + c + p = 9
,• 2a - c = 0
[First option].
Related Questions
Find the value or measure. assume all lines that appear to be tangent are tangent.JK=
Answers
In this problem we have that
mso
the formula to calculate the interior angle is equal to
msubstitute the given values
m
therefore
the answer is mNancy plans to take her cousins to an amusement park. She has a total of $100 to pay for 2 different charges. • $5 admission per person • $3 per ticket for rides Which inequality could Nancy use to determine y, the number of tickets for rides she can buy if she pays the admission for herself and x cousins? A. 5y + 3(x + 1) >= 100 B. 5(x + 1) + 3y > 100 C. 5(x + 1) + 3y =< 100 D. 5y + 3(x + 1) < 100
Answers
ANSWER
[tex]C.5(x\text{ + 1) + 3y }\leq100[/tex]EXPLANATION
Nancy has $100.
The charges are:
=> $5 admission per person. She has x cousins and herself to pay for, this means that she pays $5 for (x + 1) persons.
The admission charge is therefore:
$5 * (x + 1) = $5(x + 1)
=> $3 per ticket for rides. The number of rides she can pay for is y. So the charge for rides is:
$3 * y = $3y
Since she only has $100, everything she pays for can only be less than $100 or equal to $100.
This means that, if we add all the charges, they must be either less than or equal to $100.
That is:
[tex]5(x\text{ + 1) + 3y }\leq100[/tex]That is Option C.
Illustrate the ratio 7:3 using 'X' for 7 and 'y for 3
Answers
Given the ratio:
7:3
To illustrate the ratio above using x for 7 and y for 3, we have:
All you need to do is to replace 7 with x and replace 3 with y
7 : 3 ==> x : y
ANSWER:
x : y
A plumber charges $14 for transportation and $30 per hour for repairs. Complete the expression that can be used to find the cost in dollars for a repair that takes h hours.An expression that can be used to find the cost in dollars for a repair that takes h hours is ____ + ____h.
Answers
A plumber charges $14 for transportation and $30 per hour for repairs.
Complete the expression that can be used to find the cost in dollars for a repair that takes h hours.
An expression that can be used to find the cost in dollars for a repair that takes h hours is ____ + ____h.
_______________________________________________________________________
Charges
14 + 30* h
________________________________
Answer
An expression that can be used to find the cost in dollars for a repair that takes h hours is _14___ + _30___h.
____________________________________________
30 per hour, if it's two hours then 60 for example
Given that sin(0)= 10/ 13 and 0 is in Quadrant II, what is cos(20)? Give an exact answer in the form of a fraction. ,
Answers
SOLUTION
Given the image in the question tab, the following are the solution steps to the answer
Step 1: Write out the function
[tex]\begin{gathered} \sin \theta=\frac{10}{13} \\ \text{since }\sin \theta=\frac{opp}{hyp} \\ \therefore opp=10,\text{ hyp=13} \end{gathered}[/tex]Step 2: Solve for the adjacent using the pythagoras theorem
[tex]\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ 13^2=10^2+adj^2 \\ \text{adj}^2=13^2-10^2 \\ \text{adj}=\sqrt[]{169-100} \\ \text{adj}=\sqrt[]{69} \end{gathered}[/tex]Step 3: Calculate the value of cos2Ф
[tex]\begin{gathered} cos2\theta=\cos ^2\theta-\sin ^2\theta \\ \cos 2\theta=(\frac{\text{adj}}{\text{hyp}})^2-(\frac{opp}{hyp})^2 \\ \cos 2\theta=(\frac{\sqrt[]{69}}{13})^2-(\frac{10}{13})^2 \\ \cos 2\theta=\frac{69}{169}-\frac{100}{169} \\ \cos 2\theta=-\frac{31}{169} \end{gathered}[/tex]Hence, the value of cos2Ф is -31/169.
if the area of polygon A is 72 and Q is a scaled copy and the area of Q is 5 what scale factor got 72 to 5
Answers
A area= 72
Q area =5
So, if we multiply the A area by the square of the scale factor ( since they are areas) we obtain area Q:
72 x^2 = 5
Solving for x:
x^2 = 5/72
x = √(5/72)
x= 0.26
How would I write an equation in point- slope form with inequalities, slope-intercept form with inequalities and standard form with inequalities with these three sets of points(9,7) (8,5)(2,9) (2,7)(3,5) (5,4)
Answers
a. The point-slope equation is:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1,y1) are the coordinates of one point in the line. Also, you need to write the equation with inequalities, then you need to replace the = sign, for a <, > or <=, >= sign.
Let's start by finding the slope of the first set of points (9,7) (8,5).
The formula for the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]By replacing the values you obtain:
[tex]m=\frac{5-7_{}}{8_{}-9}=\frac{-2}{-1}=2[/tex]The slope is 2.
Now, replace this value into the slope-form equation and the values of the first point (9,7):
[tex]y-7_{}>2(x-9)[/tex]I choose the sign > (greater than), but you can choose anyone, the difference will be for the solution of the inequality. When you solve the inequality you will find that the x-values have to be greater than the solution you found, or less than... etc, it will depend on the sign you have in the inequality.
b. The slope-intercept equation is:
[tex]y=mx+b[/tex]Where m is the slope and b the y-intercept.
Let's use the second set of points (2,9) and (2,7)
Start by calculating the slope:
[tex]m=\frac{7-9}{2-2}=\frac{-2}{0}=\text{ undefined}[/tex]As there's no difference in the x-coordinates, the line is a vertical line at x=2.
Also, there's no y-intercept as the line never crosses the y-axis.
I will use the first set again, so you can understand the slope-intercept form.
From part a) you know that the slope is 2, let's replace it in the equation and use the first pair of coordinates to find b:
[tex]\begin{gathered} 7=2\times9+b \\ 7=18+b \\ 7-18=b \\ b=-11 \end{gathered}[/tex]Thus, the slope-intercept with inequality will be:
[tex]y<2x-11[/tex]c. The standard form equation of a line is:
[tex]ax+by=c[/tex]Let's use the third set of points (3,5) (5,4).
Start by finding the slope:
[tex]m=\frac{4-5}{5-3}=\frac{-1}{2}=-0.5[/tex]Now, you can start with the point-slope form and then convert it into the standard form:
[tex]\begin{gathered} y-5\ge-0.5(x-3) \\ Apply\text{ the distributive property} \\ y-5\ge-0.5x+1.5 \\ y\ge-0.5x+1.5+5 \\ y\ge-0.5x+6.5 \\ 0.5x+y\ge6.5 \end{gathered}[/tex]Where a=0.5, b=1 and c=6.5
FIVE STAR®
The cost associated with a school dance is $300 for a venue rental and $24 for each couple
that attends. This can be represented by the expression 300 + 24x.
a. Define all the variables and terms is this scenario. That means tell us what x, 24x, and
300 represent
Answers
Answer:
300 -- venue cost24 -- cost for each couplex -- the number of couples24x the cost associated with all couple300+24x -- the total cost for the danceStep-by-step explanation:
Given the scenario that cost is $300 for the venue and $24 for each couple attending a dance at that venue, you want to know the meaning of the variables and terms in 300 +24x.
ComparisonYou can compare the terms, coefficients, and variables in the given expression with the parts of the problem statement.
300 is a constant term that corresponds to "$300 for a venue rental'24 is a coefficient that corresponds to "$24 for each couple"x is a variable representing the number of "couple that attends"24x is a term representing the cost associated with "$24 for each couple that attends"That is, the cost associated with the number of people attending is $24 times the number of couples: 24x. The expression 300+24x is the total of the fixed venue cost and the per-couple costs
subtract (7u^2+10u+6) from (3u^2_5u+4).
Answers
Given:
[tex]\mleft(3u^2-5u+4\mright)-(7u^2+10u+6)[/tex]The objective is to subtract both the terms.
[tex]\begin{gathered} \mleft(3u^2-5u+4\mright)-(7u^2+10u+6) \\ 3u^2-5u+4-7u^2-10u-6 \\ -4u^2-15u-2 \end{gathered}[/tex]Hence the subtraction of the given term is,
[tex]-4u^2-15u-2[/tex]y 4 7(x-6)
x-intercept:
y-intercept:
PLEASE ANSWER FAST.
Answers
Answer: y-4=7(x-6)
x-intercept(s): (38/7,0)
y-intercept(s): (0,−38)
I believe this is right hope this helps
Step-by-step explanation:
Explain how to find the point equidistant from all three vertices in the given triangle. Choose the correct answer below. A. Find the intersection of the perpendicular bisectors of each side of the triangle B. Find the intersection of all of the midsegments of the triangle, C. Find the intersection of the angle bisectors of each angle of the triangle, D. Find the midpoint of the line segment that bisects Angle B.
Answers
ANSWER:
The correct option is the following:
C. Find the intersection of the angle bisectors of each angle of the triangle,
EXPLANATION:
The point that equidistant is the point at which the three bisectors of the internal angles of the triangle intersect, and it is the center of the circumference inscribed in the triangle and equidistant from its three sides.
IMPORTANT NOTE:
Any point on the bisector of an angle of a triangle equidistant from the sides that define that angle.
I need help to do these composition of functions. I have a photo if needed.h(a)=4a+1g(a)=2a-5Find (h×g)(-9)
Answers
The composition of two functions is defined as follows:
[tex](h\circ g)(x)=h(g(x))[/tex]Use the given rules of correspondence of h and g to find the composition of those two functions. Then, evaluate the composition at -9:
[tex]\begin{gathered} h(a)=4a+1 \\ \Rightarrow h(g(a))=4\cdot g(a)+1 \end{gathered}[/tex][tex]\begin{gathered} g(a)=2a-5 \\ \Rightarrow4\cdot g(a)+1=4\cdot(2a-5)+1 \\ =8a-20+1 \\ =8a-19 \end{gathered}[/tex]Then:
[tex]\begin{gathered} (h\circ g)(a)=h(g(a)) \\ =4\cdot g(a)+1 \\ =8a-19 \\ \\ \therefore(h\circ g)(a)=8a-19 \end{gathered}[/tex]Evaluate the composition of h and g at a=-9:
[tex]\begin{gathered} (h\circ g)(-9)=8(-9)-19 \\ =-72-19 \\ =-91 \end{gathered}[/tex]Therefore:
[tex](h\circ g)(-9)=-91[/tex]Hello, I had a question on how to find the leading coefficient and the degree.
Answers
Given:
given polynomial is
[tex]23v^5-2v+4v^8-18v^4[/tex]Find:
we have to find the leading coefficient and degree of the polynomial.
Explanation:
The lewading coefficient is the coefficient of highest power term of the polynomial.
Highest power of v is 8 and its coefficient is 4.
Therfore, leading coefficient is 4.
and the degree of the polynomial is equal to the highest power of v in the polynomial, which is 8.
Therefore, the leading coefficient of polynomial is 4 and degree is 8.
STRUCTURE Quadrilateral DEFG has vertices D(-1, 2), E(-2, 0), F(-1,-1) and G(1, 3). A translation maps quadrilateral DEFG to
quadrilateral D'EFG. The image of D is D'(-2,-2). What are the coordinates of E, F, and G'?
E (
FD
G' (
Answers
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Given,
Quadrilateral DEFG with vertices;
D = (-1, 2)E = (-2, 0)F = (-1,-1) G = (1, 3)We have to find the coordinates of E', F', G'.
A figure is translated when it is moved to the left, right, up, or down.
The original figure's points are all translated (moved) by the same amount and in the same direction.
Here,
Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.
D = (-1, 2)
D' = (-2, -2)
The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Then,
The mapping rule is:
(x, y) → (x-1, y-4)
To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
That is,
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Learn more about translation maps here;
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24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.
Answers
The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the ladder reach 12 feet up the side of the house
10. Find the area of ABC. (A) 84 (B) 168 (C) 170 (D) 48 (E) 56A: 10B: 17C: 21Right angle: 8
Answers
we know that
the area of triangle ABC is equal to the area of two right triangles
so
triangle ABD and triangle BDC
D is a point between point A and point C
step 1
Find the length of segment AD
Applying Pythagorean Theorem in the right triangle ABD
10^2=AD^2+8^2
100=AD^2+64
AD^2=100-64
AD^2=36
AD=6
Find teh area of triangle ABD
A=AD*BD/2
A=6*8/2
A=24 units^2
step 2
Find the area of triangle BDC
A=DC*DB/2
DC=21-6=15 units
A=15*8/2
A=60 units^2
step 3
Find teh area of triangle ABC
Adds the areas
A=24+60=84 units^2
therefore
the answer is the option A 84 units^2The population of a country dropped from 52.5 million in 1995 to 44.2 million in 2007. Assume that P(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model.a) Find the value of k, and write the equation.b) Estimate the population of the country in 2018.c) After how many years will the population of the country be million, according to this model?
Answers
we have the exponential decay function
[tex]P(t)=52.5(e)^{-0.0143t}[/tex]Part b
Estimate the population of the country in 2018
Remember that
t=0 -----> year 1995
so
t=2018-1995=23 years
substitute in the function above
[tex]\begin{gathered} P(t)=52.5(e)^{-0.0143\cdot23} \\ P(t)=37.8\text{ million} \end{gathered}[/tex]Part c
After how many years will the population of the country be 2 million, according to this model?
For P(t)=2
substitute
[tex]2=52.5(e)^{-0.0143t}[/tex]Solve for t
[tex]\frac{2}{52.5}=(e)^{-0.0143t}[/tex]Apply ln on both sides
[tex]\begin{gathered} \ln (\frac{2}{52.5})=\ln (e)^{-0.0143t} \\ \\ \ln (\frac{2}{52.5})=(-0.0143t)\ln (e)^{} \end{gathered}[/tex][tex]\ln (\frac{2}{52.5})=(-0.0143t)[/tex]t=229 years
Solve the system of two linear inequalities graphically,4x + 6y < 24(x22Step 1 of 3 : Graph the solution set of the first linear inequality.AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (--)Enter two points on the boundary line:10-5Select the region you wish to be shaded:
Answers
Answer:
To solve the system of two linear inequalities graphically,
[tex]\begin{gathered} 4x+6y<24 \\ x\ge2 \end{gathered}[/tex]For step 1,
Draw a line 4x+6y=24
Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.
Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,
Similarly for the inequality,
[tex]x\ge2[/tex]It covers the region right side of the line x=2,
we get the siolution region as the intersecting region of both inequality which defined in the graph as,
Dark blue shaded region is the required solution set for the given inequalities.
Harold Hill borrowed $16,400 to pay for his child's education at Riverside Community College. Harold must repay the loan at the end of 15 months in one payment with 3 3/4 % of interest.
A. How much interest must Harold pay? (Round answer to the nearest cent.)
B. What is the maturity value? (Round answer to the nearest cent.)
Answers
The interest that Harold pay is $768.75 and his maturity value is $17168.75.
Harold Hill borrowed $16,400
Harold must repay the loan at the end of 15 months in one payment with 3 3/4 % of interest
First we need to calculate the interest amount
= loan amount x rate of interest x number of months
interest = (16400 x 3 3/4 x 15/12)/100
interest = $768.75
The maturity value = loan amount + interest
= 16400 + 768.75
= 17168.75
Therefore, the interest that Harold pay is $768.75 and his maturity value is $17168.75.
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A bug is moving along a straight path with velocity v(t)= t^2-6t+8 for t ≥0. Find the total distance traveled by the bug over interval [0,6].
Answers
Answer
Explanation
Given:
A bug is moving along a straight path with velocity
[tex]V(t)=t^2-6t+8\text{ }for\text{ }t>0[/tex]What to find:
The total distance traveled by the bug over interval [0, 6].
Solution:
To find the total distance traveled by the bug over interval [0, 6], you first integrate v(t)= t² - 6t + 8
[tex]\begin{gathered} \int_0^6t^2-6t+8 \\ \\ [\frac{t^3}{3}-\frac{6t^2}{2}+8t]^6_0 \\ \\ (\frac{t^3}{3}-3t^2+8t)^6-(\frac{t^{3}}{3}-3t^2+8t)^0 \\ \\ (\frac{6^3}{3}-3(6)^2+8(6))-(\frac{0^3}{3}-3(0)^2+8(0)) \\ \\ (\frac{216}{3}-3(36)+48)-(0-0+0) \\ \\ 72-108+48-0 \\ \\ =12\text{ }units \end{gathered}[/tex]Solve the following system of linear equations by graphing.{5x - 2y = 10 {x - y = -1 Graph the equations on the same set of axes.Note: Use different points on each line when plotting the graphs.The solution point is: (_, _)
Answers
Kindly Check below
1) The first thing we need to do in this question, is to pick the method we are going to use to solve this system. Let's use the Elimination Method.
2) So, let's solve this system analytically (algebraically):
[tex]\begin{gathered} 5x-2y=10 \\ x-y=-1\:\:(\times-2) \\ \\ 5x-2y=10 \\ -2x+2y=2 \\ ------- \\ 3x=12 \\ \\ \frac{3x}{3}=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Now, let's plug into the 2nd original equation x=4 and solve it for y:
[tex]\begin{gathered} x-y=-1 \\ \\ 4-y=-1 \\ \\ -y=-1-4 \\ \\ y=5 \end{gathered}[/tex]So we know the solution is (4,5).
3) Now, let's graph these equations by setting two t-tables. Let's rewrite those equations from the Standard form to the Slope-intercept form.
5x-2y=10 -2y=10-5x, y=-5+5/2x
x-y=-1,-y=-1-x, y=x+1
4) Now, let's plot those points and trace the lines through them
(-2,-10), (-1,-7.5), (0,-5), (1,-2.5), (2,0)
(-2,-1), (-1,0), (0,1), (1,2), (2,3)
Just do all 25 points If can show how it works it will be better thanks
Answers
a) Given:
The length of the side of a square is,
[tex]\frac{1}{5}cm[/tex]To find:
The area of the square.
Explanation:
Using the formula of the area of the square,
[tex]\begin{gathered} A=a^2 \\ A=(\frac{1}{5})^2 \\ A=\frac{1}{25}cm^2 \\ A=0.04cm^2 \end{gathered}[/tex]Final answer:
The area of the square is,
[tex]0.04cm^2[/tex]13. Puppies have 28 teeth and most adult dogs have 42 teeth. Find the primefactorization of each number. Write the result using exponents. (Example 5)
Answers
To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.
So let's calculate our first prime factorization:
As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).
Now, for the second number we have:
And both prime factorizations are our final answers.
Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?
Answers
We have to find how far is the bird from Amanda.
With the information given, we can draw:
We can start by finding the third angle.
The sum of the angles have to be equal to 180°, so we can find it as:
[tex]\begin{gathered} \alpha+55\degree+63\degree=180\degree \\ \alpha=180-55-63 \\ \alpha=62\degree \end{gathered}[/tex]Now, we can apply the Law of Sines to find the distance between Amanda (A) and the bird (B):
[tex]\frac{AB}{\sin J}=\frac{AJ}{\sin B}[/tex]where AJ is the distance between Amanda and Jamie and AB is the distance between the bird and Amanda.
We then can solve for AB as:
[tex]\begin{gathered} AB=AJ\cdot\frac{\sin J}{\sin B} \\ AB=25\cdot\frac{\sin63\degree}{\sin62\degree} \\ AB\approx25\cdot\frac{0.891}{0.883} \\ AB\approx25.23 \end{gathered}[/tex]Answer: 25.23 [Option A]
Identify the postulate illustrated by the statement: Line ST connects pointS and point T
Answers
We have two points known to be ( S ) and ( T ). A line connects two points.
The minimum number of points that are required to form a straight line in a cartesian coordinate system are ( two ).
The minimum number of points that are required to form a plane in a cartesian coordinate system are ( three ) which will form two vectors i.e it requires two lines formed with a common point.
Two planes always intersect at exactly one point with direction normal to the two plane normal vectors.
Hence, the only possible postulate that relates two points is the formation of a line between two points; hence, the correct postulate for the given statement is:
[tex]\text{\textcolor{#FF7968}{Through any two points there is exactly one line}}[/tex]
Find the measure of each angle in the triangle. F R 6x 15x 15x O 02
Answers
Answer:
R = 75
O = 75
F = 30
Step-by-step explanation:
15x + 15x + 6x = 180
add like terms
36x = 180
divide
x = 5
The measure of angle P is 30°, angle R is 75° and angle O is 75° in triangle POR.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
From the given triangle POR, ∠R=15x, ∠O=15x and ∠P=6x.
By using angle sum property, we get
∠P+∠O+∠R=180°
6x+15x+15x=180
36x=180
x=180/36
x=5
So, ∠R=15x=75°, ∠O=15x=75° and ∠P=6x=30°
Therefore, the measure of angle P is 30°, angle R is 75° and angle O is 75° in triangle POR.
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Put the following equation of a line into slope-intercept form, simplifying allfractions.2x + 8y = 24
Answers
“Use the properties to rewrite this expression with the fewest terms possible:3+7(x - y) + 2x - 5y”
Answers
Expanding 7(x - y) in the above expression gives
[tex]-5y^{}+2x+7x-7y+3[/tex]adding the like terms (2x+ 7x) and (-5y-7y) gives
[tex](-5y-7y)+(2x+7x)+3[/tex][tex]\rightarrow\textcolor{#FF7968}{-12y+8x+3.}[/tex]The last expression is the simplest form we can convert our expression into.
Find the measure of Zx in the figure.
The measure of Zx isº.
57°
X
90°
...
Please help me with this
Answers
The whole angle = 147 degrees
find a slope of the line that passes through (8,8) and (1,9)
Answers
The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we can use this formula by introducing the values of the given points. In our case
[tex]\begin{gathered} (x_1,y_1)=(8,8) \\ (x_2,y_2)=(1,9) \end{gathered}[/tex]Hence, we have
[tex]m=\frac{9-8}{1-8}[/tex]It yields,
[tex]m=\frac{1}{-7}[/tex]hence, the answer is
[tex]m=-\frac{1}{7}[/tex]