Answers
Question 8
1) [tex]\triangle ACE[/tex] with [tex]\overline{AC} \cong \overline{EC}[/tex], [tex]\overline{BC} \cong \overline{DC}[/tex] (given)
2) [tex]\angle C \cong \angle C[/tex] (reflexive property)
3) [tex]\triangle ACD \cong \triangle ECB[/tex] (SAS)
Question 9
1) [tex]\overline{PQ}[/tex] and [tex]\overline{PR}[/tex] are the legs of isosceles [tex]\triangle PQR[/tex], [tex]\overline{PS} \cong \overline{QR}[/tex] (given)
2) [tex]\angle PSQ[/tex] and [tex]\angle PSR[/tex] are right angles (definition of perpendicular lines)
3) [tex]\angle Q \cong \angle R[/tex] (angles opposite the legs of an isosceles triangle are congruent)
4) [tex]\overline{PS} \cong \overline{PS}[/tex] (reflexive property)
5) [tex]\angle PSQ \cong \angle PSR[/tex] (all right angles are congruent)
6) [tex]\triangle PSQ \cong \triangle PSR[/tex] (AAS)
Question 10
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AB} \perp \overline{BC}[/tex], [tex]\overline{CD} \perp \overline{AD}[/tex] (given)
2) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
3) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle ABC[/tex] and [tex]\triangle ADC[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle ABC \cong \triangle CDA[/tex] (HL)
6) [tex]\overline{AD} \cong \overline{CB}[/tex] (CPCTC)
Related Questions
Solve 3[-x + (2 x +1)]=x-1
Answers
The result of the evaluation of the equation given in the task content is; x =-2.
What is the solution of the equation?It follows from the task content that the equation given whose solution is to be determined is;
3[-x + (2 x +1)]=x-1
The equation can be solved as follows;
-3x + 6x +3 = x-1
2x = -4
x = -2
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A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the test was 84. The juniors all received the same score, and the average score of the seniors was 83. What score did each of the juniors receive on the test
Answers
Each junior receives 93 score on the test. It is also the average score of the juniors.
Given Information
It is given that 10% of the strength of the class consists of juniors and 90% consists of seniors.
Let us assume the total strength of the class is 100, then,
Number of seniors = 90
Number of juniors = 10
It is also given that the average score of the class = 84
And, average score of the seniors = 83
Another given information is that all the juniors all received the same score, which is their average score. Let it be x.
Average Score of Juniors
Total marks obtained by the seniors = Number of seniors × Average score of seniors
= 90 × 83
= 7470
Total marks obtained by the juniors = Number of juniors × Average score of juniors
= 10x
Average marks on the test = Total marks / Total number of students
⇒ 84 = (7470 + 10x)/100
⇒ 84 × 100 = 7470 + 10x
⇒ 10x + 7470 = 8400
⇒ 10x = 8400-7470
⇒ 10x = 930
⇒ x = 930/10
⇒ x = 93
Thus, each junior scores 93 on the test.
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From points a and b on level ground the angles of elevation of the top of a building are 25degree and 37 degree respectively. if [ab] =57m, calculate to the nearest metre, the distances of the top of the building from a and b if they are both on the same side of the building
Answers
The distance of the top of the building from a is 163m and that from b is 115m .
Calculating the Perpendicular Distance of the Top From Ground
It is given that the angle of elevations of the building top from a and b are 25° and 37° respectively.
ab = 57m
Let the top of the building be point c and the distance between the building and the point b be x. Then, from the figure, we can deduce the following,
In Δacd, tan 25° = cd/ad
⇒ 0.4663 = cd /(x+57)
⇒ cd = 0.4663(x+57) ......................... (1)
In Δbcd, tan 37° = cd/x
⇒ 0.7536 = cd/x
⇒ x =cd / 0.7536 .......................... (2)
Solving for the Distance cd
Substitute the value of in equation (2) to equation (1) to get,
cd = 0.4663 ((cd/0.7536)+57)
cd = 0.4663(cd+42.9552)/0.7536
0.7536cd = 0.4663cd + 20.03
0.7536cd - 0.4663cd = 20.03
0.2906cd = 20.03
cd = 20.03/0.2906
Thus, the distance cd ≈ 68.93m
Finding the Distance cb and Distance ca
In Δacd, sin25° = cd/ca
⇒ 0.4226 = 68.93/ca
ca = 68.93/0.4226
ca = 163.10
∴ The distance ca ≈ 163m
Similarly, in Δbcd, sin37° = cd/cb
⇒ 0.6018 = 68.93/cb
cb = 68.93/0.6018
cb =114.54m
∴ The distance cb ≈ 115m
Therefore, the points a and b are at a distance of 163m and 115m respectively from the top of the building.
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d) Arrange 8/9,7/18,10/16 in ascending order of magnitude
Answers
8/9 = 0.888888....
7/18 = 0.388888888889
10/16 = 0.625
Ascending order - means going up, smallest to largest. (Imagine climbing a ladder, where you start of low, then, go higher up the ladder.)
Thus, answer is 7/18, 10/16, 8/9
Hope this helps!
PLEASE HELP (the picture has the problem)
Answers
Explanation:
12/18 = x/13.5
12(13.5) = 18x
162/18 =18x/18
9= x
Find the missing side length of the triangle.
Answers
Answer:
c = 10
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)
Here given: a = 8 cm, b = 6 cm, c = ?
Substituting values:
8² + 6² = c²
c² = 64 + 36
c² = 100
c = √100
c = 10
Answer:
10 cm
Step-by-step explanation:
[tex]a^2=b^2+c^2[/tex]
[tex]a^2=6^2+8^2[/tex]
[tex]a^2=100[/tex]
[tex]\sqrt{a^2}=\sqrt{100[/tex]
a=10
250-{(135+34)÷(46-33)}-15 simplify
Answers
Answer:
222
Step-by-step explanation:
Hey there!
250 - {(135 + 34) ÷ (46 - 33)} - 15
= 250 - 169/(46 - 44) - 15
= 250 - 169/13 - 15
= 250 - 13 - 15
= 237 - 15
= 222
Therefore, your answer should be:
222
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
successor of -501 is
Answers
Answer:
-500
Step-by-step explanation:
since 501 has a negative sign,add 1 to to the number,the next number will be -500
-501 +1 = -500
successor in this case means a number that succeeds another
Apply the distributive property to factor out the greatest common factor. 24j-16=
Answers
Answer:
8(3j - 2).
Step-by-step explanation:
24j-16
GCF = 8
so the answer is
8(3j - 2).
find the slope of a line parallel to the line through the given points. E(5, 7), F(3, 1) •-3
•-1/3
•1/3
Answers
Answer:
3
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (1 - 7)/(3 - 5)
slope = -6/(-2)
slope = 3
Parallel lines have equal slopes.
Answer: 3
True or false: the mayans wrote the digits in their numerals in a vertical format
Answers
Answer:
True
Step-by-step explanation:
Find all solutions to 2w^4 - 5w^2 + 2 = 0
asap please
Answers
Answer:
w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]
Step-by-step explanation:
if we say some variable y = w^2, we can rewrite the equation to:
2y^2 - 5y + 2 = 0
this can be factored into (2y-1)(y-2) = 0
putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0
The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.
If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots
the four solutions are ±√1/2 and ±√2
(because the positive counts as one solution and the negative another solution)
23. Which equation translates y = | x | by 8 units to the left?
y = |x-81
y = |x + 81
y = |x|-8
y = |x | +8
Answers
Answer:
y = |x + 8|
Explanation:
Please see the table attached below.
Answer:y=|x+8|
Step-by-step explanation:
Help with these two problems and show work please !!
Answers
Answer:
1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]
2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]
Step-by-step explanation:
[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
Given quadratic equations:
1. [tex]x^2+2x-7=0[/tex]
2. [tex]4x^2-3=x^2-5x-4[/tex]
1. x² + 2x - 7 = 0
[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]
Step 1: Substitute the given values into the formula and simplify.
[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]
Step 2: Simplify the radicand (under the square root).
[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]
Step 3: Separate into two solutions and simplify them.
[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]
[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]
----------------------------------------------------------------------------------------------------------------
2. 4x² - 3 = x² - 5x - 4
Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).
4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]
3x² + 5x + 4 = 0
[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]
Step 2: Substitute the given values into the formula and simplify.
[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]
Step 3: Separate into two solutions.
[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]
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Given the parent cosine function f(x) = cos x , find the function g(x) after the parent function undergoes a horizontal shift right 7 units, and up 4 units.
Answers
By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.
How to find the resulting function by transformation rules
Transformation rules are rules that makes changes on charateristics and behavior of a function to create a new one. Rigid transformations like horizontal and vertical translations are examples of transformation rules. In this question we must apply the following transformation rules to the parent cosine function f(x) = cos x:
Horizontal translation: f'(x) = f(x - 7) (1)Vertical translation: g(x) = f'(x) + 4 (2)Now we proceed to derive the resulting function by applying the rules defined above:
Horizontal translation
f'(x) = cos (x - 7) (3)
Vertical translation
g(x) = cos (x - 7) + 4 (4)
By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.
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Analyze the diagram below and complete the instructions that follow. (7x - 3) (12x -7) Solve for x.
Answers
Answer:
Step-by-step explanation:
(7x-3)(12x-7)
we are solving for x and we are multiplying.
we start with the x's 7x*12x= 84x
-3*-7=21
so now we have
84x+21=0
the 0 is a placer for answering the question
we minus 21 to both sides
84x=-21
now we divide
84/-21= -4
x=-4
Find the center and radius of the circle with the equation: (x-0^2 + (y+1)^2 = 4
a.
center: (-5, 1)
radius: 4
c.
center: (-5, 1)
radius: 2
b.
center: (5, -1)
radius: 4
d.
center: (5, -1)
radius: 2
Answers
The center and radius of the circle is (b) center: (-5, 1) radius: 2
How to determine the center and the radius?The circle equation is given as:
(x-5)^2 + (y+1)^2 = 4
The circle equation is represented as:
(x-a)^2 + (y-b)^2 = r^2
Where:
Center = (a,b)
Radius = 4
By comparison, we have:
(a, b) = (-5, 1)
r^2 = 4
This gives
(a, b) = (-5, 1)
r = 2
Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2
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Can someone help me with the first question please
Answers
Answer:
(c) 5y -17x +99 = 0
Step-by-step explanation:
The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.
MidpointThe midpoint of XZ is the average of the coordinates of X and Z.
M = (X +Z)/2
M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)
Line through two pointsThe slope of the median can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
The slope of line YM is ...
m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The line with slope 17/5 through point Y(7, 4) is ...
y -4 = 17/5(x -7)
Subtracting the right side, and multiplying by 5 gives ...
5(y -4) -17(x -7) = 0
5y -17x +99 = 0 . . . . equation of the median through Y
Derrick had a 0.250 batting average at the end of his last baseball season, which means he got a hit 25% of the times he was up to bat. if derrick had 47 hits last season, how many times did he bat?
Answers
The number of times that Derrick batted last season is 188 times.
How many times did Derrick bat?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.
A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.
Number of times Derrick bat last season = Number of hits last season / percentage of his batting average
47 / 25%
47 / 0.25 = 188
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Solve 5x=125 using the one-to-one property of exponents.
A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5
Answers
Answer:
C) x = 3
Step-by-step explanation:
Given equation:
[tex]5^x=125[/tex]
Rewrite 125 with base 5: 125 = 5³
[tex]\implies 5^x=5^3[/tex]
[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]
[tex]\implies x=3[/tex]
What is the relation between the variables in the equation
a. varies inversely as y
b.xvaries directly as y
Please select the best answer from the choices provided
O
O
A
B
C
O
y
-7?
c. y varies directly as x¹
d. y varies inversely as ¹
Answers
The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y
How to determine the relation between the variables in the equation?The complete question is added as an attachment
From the attached figure, we have the following equation
x^4/y = 7
Multiply both sides of the equation by y
x^4 = 7y
The above represents a direct variation from x^4 to y.
Where 7 represents the variation constant
Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y
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22. If 1 m,m/19 - 118°, and m/16 - 48°, calculate m/12.
0 0
103"
98
109⁰
110"
18
17
19 20
14
16
13
15
11
10
12
9
63
5
m
Answers
Answer: [tex]110^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle 20=62^{\circ}[/tex] (linear pair)
[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)
[tex]m\angle 12=110^{\circ}[/tex] (linear pair)
Melissa is planning a rectangular vegetable garden with a square patch for tomatoes
Answers
The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.
A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.
In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.
The side of the square is given to be x feet.
We are asked to write expressions for the length and width of the rectangular garden.
For the length of the rectangle:-
We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.
Thus, the length of the garden can be shown as the expression 3x + 2 feet.
For the width of the rectangle:-
We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.
Thus, the width of the garden can be shown as the expression x + 5 feet.
Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.
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The provided question is incomplete. The complete question is:
"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.
Enter the correct answer in the box."
explain how the following problem could be solved. then, solve the problem. a full-grown dog is about one-eighth as heavy as a cow. together, they weigh 360 kg.
Answers
The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
The weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
We assume the weight of the cow to be x kg.
The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.
Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.
But, we are given that together, they weigh 360 kg.
This can be shown as the linear equation in the one variable:
x/8 + x = 360.
Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
To solve the problem, we solve the equation as follows:
x/8 + x = 360,
or, (9/8)x = 360 {Simplifying},
or, x = 360*8/9 {Cross-Multiplying},
or, = 320.
Thus, the weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
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Help, please. I just need an answer, so if anyone is bored, for the love of god please...
Answers
Answer:B & E
Step-by-step explanation:
We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.
[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]
Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.
For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]
[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]
The first line is found in option E, so option E is one of the correct options.
We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).
[tex]-\frac{3}{4}x+y=1[/tex]
If we multiply the whole equation by -4, we can get rid of the fraction.
[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]
Hence, option B is also correct.
a cone has a height of 16 centimeters and a radius of 12 centimeters. what is the exact lateral and surface area of the cone? type the correct answer in each box. use numerals instead of words.
Answers
The lateral and total surface areas of the given cone are 753.98 cm² and 1206.31 cm² respectively.
What are the formulae for lateral and total surface areas of a cone?A cone has a height 'h', radius 'r', and slant height 'l'.
The slant height of the cone is obtained by the Pythagorean theorem. I.e.,
l² = h² + r²
Then,
Its lateral surface area(LSA) = πr([tex]\sqrt{h^2+r^2}[/tex]) square units and
Its total surface area(TSA) = πr(r + l) square units
Calculation:It is given that,
A cone has a height h = 16 cm and radius r = 12 cm
Then, the slant height is calculated by
l² = h² + r²
l = [tex]\sqrt{h^2+r^2}[/tex]
On substituting,
l = [tex]\sqrt{16^2+12^2}[/tex]
= [tex]\sqrt{400}[/tex]
= 20 cm
So,
LSA = πr([tex]\sqrt{h^2+r^2}[/tex])
= π × 12 × ([tex]\sqrt{16^2+12^2}[/tex])
= π × 12 × 20
= 753.98 cm²
and
TSA = πr(r + l)
= π × 12 × (12 + 20)
= π × 12 × 32
= 1206.37 cm²
Therefore, the lateral and total surface areas of the cone with a height of 16 cm and a radius of 12 cm are 753.98 cm² and 1206.37 cm².
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Answer: The lateral area is 240π square centimeters. The total surface area is 384π square centimeters.
Step-by-step explanation:
(03.01 MC)
Simplify
the square root of 4 divided by 3 to the third power , the square root of 4
Answers
Answer: [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{4} }{3^{3} }[/tex]
The square root of 4 can be written as 2
3 to the third power can be written as 9
So, the answer is [tex]\frac{2}{9}[/tex]
Hi I don't know how to do this
Answers
Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:
B. 1147 gm.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Weight of an apple.Variable y: Weight of an orange.Variable z: Weight of a banana.Considering the data given, the equations are:
3x + 5y = 928.4y + 6z = 1088.5x + 3z = 799.From the first equation:
3x = 928 - 5y.
x = 309.33 - 1.667y.
From the second equation:
6z = 1088 - 4y
z = 181.33 - 0.667y
Replacing in the third equation:
5x + 3z = 799
5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799
10.336y = 12961.64
y = 1291.64/10.336
y = 125 gm.
The other weights are:
x = 309.33 - 1.667y = 309.33 - 1.667 x 125 = 101 gm.z = 181.33 - 0.667y = 181.33 - 0.667 x 125 = 98gm.The weight of 5 apples, 2 oranges are 4 bananas is:
5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.
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The perimeter of a parallelogram is 180 cm. One side exceeds the other by 10 cm.
What are the lengths of adjacent sides of the parallelogram?
Answers
Answer:
One side is 40 cm and the adjacent side is 50 cm
Step-by-step explanation:
We can use a rectangle because a rectangle is a parallelogram. Draw a rectangle. Write the width as x and the length as x + 10. We find the perimeter by adding all 4 side lengths.
Two side lengths are x and two side lengths are x + 10. If we add all of this together we get 180
x +x +x+10+x+10 = 180
4x + 20 = 180 Combine the like terms. There are 4 x's and 10+10 is 20
4x = 160 Subtract 20 from both sides
x = 40 Divide both sides by 4
So, two sides are 40 and two sides are 50, this will add up to 180
Answer:
40 cm & 50 cm
Step-by-step explanation:
one side = X cm (??)
the other side =X+10 cm
Solve
2(x+x+10)=180
x+x+10=90
2x=80
x = 80/2
x=40
therefore
x+10=50cm
Find the equation of the line that passes through the given points. (1, 4.5) and (3, 6)
Answers
Answer:
y=0.75x+3.75
Step-by-step explanation:
The slope is
[tex] \frac{6 - 4.5}{3 - 1} = \frac{3}{4} [/tex]
Substituting into point-slope form,
y - 6 = 0.75(x - 3)
y - 6 = 0.75x - 2.25
y = 0.75x + 3.75