Answers
Answer:
Step-by-step explanation:
The shapes have the same height, but the base of the rectangle is half the base of the triangle. They have the same area.
:::::
area of rectangle = base × height = 4 units × 6 units = 24 units²
:::::
area of triangle = ½×base×height = ½×8 units × 6 units = 25 units²
:::::
The triangle looks bigger, but isn't. Shape affects area.
Related Questions
Journal; 1.8.4, geometry
2. Looking at the Consecutive Interior Angles (9 points)
Look at the diagram of the scenario below. A steep downhill ski slope is intersected at an angle by a less steep ski slope. Safety fences need to be set up in the locations shown. The angles of the fences, angles 1 and 2, can be determined by finding the relationship between the angles a and b.
Draw a geometric diagram of this scenario using two parallel lines and one transversal. (Remember that a transversal is a line which cuts across parallel lines.) Label the angles, parallel lines, and transversal as indicated in the diagram above. (2 points)
Starting with the fact that angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, use a two column proof to prove that consecutive interior angles a and b are supplementary. (5 points)
Statement Reason
Explain what the result of your proof tells you about angles a and b. Specifically, if you measured one angle, what would you know about the other? (2 points)
3. The Exterior Angles (6 points)
The fences will be aligned with the exterior angles ∠1 and ∠2. What are some other relationships you can see between ∠1, ∠2, ∠a, and ∠b? (2 points)
Which of the relationships you listed above will be the most helpful in figuring out the measurements of the safety fences? (2 points)
What is the measure of ∠2? (2 points)
4. Reflections (2 points: 1 point each)
Can you think of any other real-life scenarios where parallel lines and transversals exist?
What are the limitations of the ski slope scenario as a real-life example?
Answers
The measurement of the angles formed between parallel lines having a common transversal are readily determined by the relationship between the angles
The measures of the angles in the figures are as follows;
2. The required two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
∠1 and ∠a are linear pair angles [tex]{}[/tex] Given
∠1 + ∠a = 180° [tex]{}[/tex] Linear pair ∠s are supplementary
∠2 and ∠b are linear pair angles [tex]{}[/tex] Given
∠2 + ∠b = 180° Linear pair ∠s are supplementary
∠a and ∠b are consecutive interior ∠s [tex]{}[/tex] Definition
x║y [tex]{}[/tex] Given
∠1 and ∠b are corresponding angles [tex]{}[/tex] Definition
∠1 ≅ ∠b [tex]{}[/tex] Corr. ∠s formed between║ lines
∠1 = ∠b [tex]{}[/tex] Definition of congruency
∠a + ∠b = 180° Substitution property
∠a and ∠b are supplementary [tex]{}[/tex] Definition
The information obtained from the proof is that given ∠1 and ∠b are located in corresponding locations relative to the common transversal of the parallel lines, they (∠1 and ∠b) are equal, and therefore, the the sum of ∠a and ∠b is 180°, given that the sum of ∠1 and ∠a is 180° by substitution property of equality. Which gives that ∠a and ∠b are supplementary angles. Therefore
If the measure of one of the angles ∠a or ∠b is known, the other angle is given by subtracting the known angle from 180°3. Some of the other relationships between ∠1, ∠2, ∠a, and ∠b, are;
∠1 and ∠b are corresponding angles, therefore, ∠1 ≅ ∠b, by corresponding angles formed between parallel lines∠2 and ∠a are corresponding angles, therefore, ∠2 ≅ ∠a, by corresponding angles formed between parallel lines ∠1 and ∠2 are same side exterior angles and they are therefore supplementary. ∠1 + ∠2 = 180°The relationship that will be most helpful in figuring the measurement of the safety fences is the relationship between ∠1 and ∠2; ∠1 + ∠2 = 180°The measure of ∠2 = 180° - ∠1
4. A real-life scenario where parallel lines and transversal exist are the handrail and baluster on railings of staircases
The limitations of the Ski slope scenario are;
The direction of the trail of the skier are usually along or parallel to the slopeThe slope is wide and usually lacks obstruction, and therefore, has few transversalsThe ski slope is usually located away from or follows a different direction from other ski slopesLearn more about parallel lines having a common transversal here:
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c. Explain what the result of your proof tells you about angles a and b.
Specifically, if you measured one angle, what would you know about the
other? (2 points)
Which is an equation of the line through (-8,-4) and (4, 5)?
Answers
Answer:
the right answer is A :)
The table shows the inputs and outputs for the function f(x) = -7x – 5.
Input
-10
Output
65
-5
?
-5
o
5
-40
When the input is –5, the output is
Answers
Answer:
30
Step-by-step explanation:
-7 times-5 minus 5=30
The missing value in the output is 30.
What is a Function ?A law that relates two variables is called Function.
The function given in the question is
f(x)= -7x - 5
For the input missing in the table
f(x)= - 7 *(-5) -5
f(x)= 30
Therefore the missing value in the output is 30.
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what is 3/12 as a precent
Answers
Answer: 25%
Step-by-step explanation:
Answer:
25% As a decimal its 0.25
Step-by-step explanation:
The sum of two trinomials is 4x3 + 3x
Answers
Answer:
it is 12+3x your welcome
The sum of two trinomials is 4x³ + 3x then one trinomial is x³ + 2 then the other is written as 3x³ + 3x.
Let's assume the two trinomials are A and B. We are given that the sum of these two trinomials is equal to 4x³ + 3x. Mathematically, we can represent this as:
A + B = 4x³ + 3x
Now, we are also given one of the trinomials, which is x³ + 2, and we need to find the other trinomial (B).
To find B, we need to isolate it on one side of the equation. Let's rearrange the equation:
B = 4x³ + 3x - A
Now, we need to determine the value of A. We can do this by comparing the given trinomial with the general form of a trinomial, which is ax³ + bx^2 + cx.
From the given trinomial x³ + 2, we can identify that a = 1 (coefficient of x³) and b = 0 (coefficient of x²), since there is no x² term. The coefficient of x is c = 0 (since 3x = 3x¹, there is no constant term in this expression).
Now, we can write A in terms of its coefficients:
A = 1x³ + 0x² + 0x
A = x³
Now, we can substitute the value of A back into the equation for B:
B = 4x³ + 3x - x³
B = 3x³ + 3x
So, the other trinomial (B) is 3x³ + 3x.
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Complete Question:
The sum of two trinomials is 4x³ + 3x then one trinomial is x³ + 2 then the other is
Please helppp I’m In desperate help
Answers
Answer:
330
Step-by-step explanation:
Hello There!
The shown figure is a trapezoid with the following dimensions:
Height - 11m
Base 1 - 41m
Base 2 - 19m
Given this information we need to find the area
Remember the formula for the area of a trapezoid is
[tex]A=\frac{a+b}{2} h[/tex]
where a and b are bases and h is the height
Because we are given all of the information needed to calculate the area all we have to do is plug in the values into the formula
So...
[tex]A=\frac{19+41}{2} 11\\19+41=60\\\frac{60}{2} =30\\30*11=330\\A=330[/tex]
In conclusion the area of the figure is 330 square units
Calcule (1/2)-² POR FAVOR RESPONDEM
Answers
Answer:
I think it's 1/4 or .25
Which statement is true?
A. All rectangles are squares.
B. Some trapezoids are parallelograms.
C. All squares are rhombuses.
D. No rhombuses are rectangles.
Answers
A square is a parallelogram with all congruent sides, which makes every square is a rhombus. Hope this helps :)
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.
Site 1: Solving Right
Triangles"
In addition to the trigonometric ratios, what other methods can be used to solve a right triangle? Give situations for when you might want to
use them. (Site 1)
Answers
Answer:
a
Step-by-step explanation:
In the morning, an outdoor thermometer shows a temperature of -8°C. Later that afternoon, the temperature drops an additional 4°C. What is the temperature in the afternoon?
Answers
Answer:
- 12°C
Step-by-step explanation:
Given :
Temperature in the morning = - 8°C
In the afternoon, temperature drops an additional 4°C
A temperature drop mean a reduction in the initial temperature :
Afternoon temperature = morning temperature - 4°C
Afternoon temperature = - 8°C - 4
After oon temperature = - 12°C
Write a cubic function whose graph goes through the points: (-5, 0) (1, 0) (2, -2) (4, 0)
Answers
Answer:
Step-by-step explanation:
From points (-5,0),(1,0),(4,0) we know it has the form
y=(x+5)(x-1)(x-4)
y=(x^2+4x-5)(x-4)
y=x^3-4x^2+4x^2-16x-5x+20
y=x^3-21x+20
Then it must pass through the point (2,-2) so
-2=[2^3-21(2)+20]b
-2=[8-42+20]b
-2=[-14]b
b=1/7 so the equation is
y=(x^3-21x+20)/7
encuentra el valor medio punto pendiente m=5 p(3,-2)
Answers
Answer:
y=5x−17
Step-by-step explanation:
Can someone plz correct me I got that wrong plz I beg u
Answers
Answer:
2400
Step-by-step explanation:
Write an equation that describes the function.
Answers
Answer:
y = xplus1 sorry, new keyboard and it doesn't have a plus sign
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
A.
x = 8, y = 4
B.
x = 6, y = 6
C.
x = 7, y = 5
D.
x = 9, y = 3
Answers
Answer:
c
Step-by-step explanation:
36-29=
[tex]36 - 29 = 3x - 2x + 3y - 3 \\ 7 = x \\ 12 = 7 + y \\ 12 - 7 = y \\ 5 = y[/tex]
Answer:
is is C
Step-by-step explanation:
i did the test
Help I'm not sure if this is the answer?
(This question is about trigonometric ratios)
Answers
9514 1404 393
Answer:
(b) 15.32
Step-by-step explanation:
You can use your triangle sense to answer this.
The side x will always be shorter than the hypotenuse, 20. This eliminates the last two choices.
If the angle is 45°, then the sides are equal at about 0.707 times the length of the hypotenuse. That would make them 0.707×20 = 14.14. Since the angle is greater than 45°, the opposite side will be greater than 14.14. Only one answer choice fits between 14 and 20: the second choice -- 15.32.
__
The mnemonic SOH CAH TOA reminds you of the relation ...
Sin = Opposite/Hypotenuse
sin(50°) = x/20
x = 20×sin(50°) . . . . multiply by 20 to find x
x ≈ 15.32 . . . . . . . . . use your calculator to evaluate
__
The attachment is intended to show how the triangle side lengths change with angle.
You buy a new video game for $60.
The sales tax is 8%.
What is the total cost for the game including sales tax?
Answers
Answer:
$64.8
Step-by-step explanation:
To determine the tax, you want to make the percent into a decimal by moving the decimal point over two times the the left, which means 8% would be 0.08. Then, multiply the new decimal by the price. 60 times 0.08 is 4.8. Now, add the tax to the original price. 60+4.8=64.8, so therefore the total cost is $64.8
what is -7 – 4 – (-6)
Answers
Answer:
-5
Step-by-step explanation:
Answer:
-7 - 4 -(-6)
-7 + - 4 - (-6)
-11 - (-6)
-11 + 6 = -5
Step-by-step explanation:
When looking at -7- 4, you can use the KCC rule, Keep, Change, Change. -7 would stay the same, but - would turn into a + and so would 4 to -4.
Now, -7 + - 4 would equal to -11. And bring down the -(-6).
When you look at two negative signs the become a positive sign, so it would now be +6.
Now, you subtract because 11 is the bigger number and you have to take it's sign, which is negative to the answer.
Therefore, your answer is -5. Hope this helps
A tree grows three-fourth feet per year. How long will it take the tree to grow from
a height of 17 3/4 feet to a height of 25 1/2 feet?
Answers
Answer:
9 years
Step-by-step explanation:
37-21.25 =15.75ft
1.75ft per year
15.75 / 1.75 = 9 years
6/12 + 6/24 + 1/4 =
I don't rember how to do this
Answers
Answer:
1
Step-by-step explanation:
6/12=1/2
6/24=1/4
1/2+1/4+1/4=1/2+2/4=2/4+2/4=4/4=1
Answer:
answer is 1
you divide and add them.
PEMDAS
Please help me!
----------------------------
Answers
Answer:
It should be D because you start off with the X coordinate then y
What is the slop of AB?????????????
Answers
Answer:
3 I am pretty sure
Step-by-step explanation:
Solve for x: three halves plus one half times x equals two x
x equals two thirds
x = 1
x = 2
x = 3
Answers
Answer:
b) x = 1
Step-by-step explanation:
Given statement,
→ three halves plus one half times x is equals two x.
Forming the equation,
→ (1/2) + (1/2) + (1/2) + (1/2)x = 2x
Now the value of x will be,
→ (1/2) + (1/2) + (1/2) + (1/2)x = 2x
→ (1 + 1 + 1)/2 = 2x - (1/2)x
→ 3/2 = ((4 - 1)/2)x
→ 3/2 = (3/2)x
→ (3/2)x = 3/2
→ x = (3/2) × (2/3)
→ x = (3 × 2)/(2 × 3)
→ x = 6/6
→ [ x = 1 ]
Hence, the value of x is 1.
what is 10/20 as a percent
Answers
Answer:
answer would be 50%.
Step-by-step explanation:
How you get it: Always divide the numerator and denominator to get your answer to these kind of questions. small number goes out and bigger number goes in when doing long division
Out of a total of 125 students surveyed, 48 said they did not like ice cream. Out of the total number of students surveyed, what percent said they did like ice cream?
Answers
Answer:
62% said they like ice cream
The percentage of students who liked the ice cream is given by the equation A = 61.6 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the percentage of students who liked ice cream be A
Now , the equation will be
The total number of students = 125 students
The number of students who didn't like ice cream = 48 students
The number of students who liked ice cream = 125 - 48
The number of students who liked ice cream = 77 students
So ,
The percentage of students who liked ice cream A = ( number of students who liked ice cream / total number of students ) x 100
Substituting the values in the equation , we get
The percentage of students who liked ice cream A = ( 77/125 ) x 100
On simplifying the equation , we get
The percentage of students who liked ice cream A = 0.616 x 100
The percentage of students who liked ice cream A = 61.6 %
Therefore , the value of A is 61.6 %
Hence , the percentage is A = 61.6 %
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when doing a surgery for her friends Fernanda asked 12 friends what their favorite soda is 75% of her friends said Sprite. Determine how many friends voted for sprite
Answers
Answer:
the answer is 9
Step-by-step explanation:
12-75%=3
12-3=9
The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = -5 and x = 1. Use the line segment to determine the average rate
of change of the function f(x) on the interval –5 < x < 1?
Answers
Answer:
no not really
Step-by-step explanation:
the values dont match up
Angel uses 1/8 cup of sugar for 1/3 of a recipe. How much sugar is needed if Angel makes the entire recipe twice?
Answers
Answer:
3/4 cups of sugar
Step-by-step explanation:
So we know that 1/8 cup of sugar is for 1/3 OF a recipe.
So if we want the full recipe we jsut have to multiply 1/8 by 3 since its only worth 1/3 of the recipe.
You’ll get 3/8 cups of sugar for a whole recipe. The question asks for 2 full recipes and since we already know it takes 3/8 cups for one we can multiply that by 2 to find the amount of sugar needed for 2 full recipes.
You’d get 6/8 cups of sugar.
Simplified: 3/4
can anyone help on this question?
Answers
Answer:
volume = 262.14 yd³
Step-by-step explanation:
volume = 6.4³ = 6.4 x 6.4 x 6.4 = 262.14 yd³
Answer:262.144
Step-by-step explanation:you will have to round it.
Andres y Jorge fueron a una dulcería, Andrés compró 5 chocolates y 1 paleta por lo que pagó $26 y Jorge compró 2 chocolates y 1 paleta y pagó $14, ¿Cuál es el precio de cada chocolate y cada paleta?
Answers
Answer:
Precio del chocolate = x = $ 4
Precio de la paleta = y = $ 6
Step-by-step explanation:
Vamos a representar
Precio del chocolate = x
Precio de la paleta = y
Andrés y Jorge fueron a una tienda de dulces, Andrés compró 5 chocolates y 1 paleta por la que pagó $ 26
= 5x + y = 26 ...... Ecuación 1
Jorge compró 2 chocolates y 1 paleta y pagó $ 14.
2x + y = 14 ....... Ecuación 2
Combinando ambas ecuaciones juntos resolvemos usando el método de eliminación
Restamos la Ecuación 2 de la Ecuación 1
5x + y = 26 ...... Ecuación 1
2x + y = 14 ....... Ecuación 2
3 veces = 12
x = 12/3
x = $ 4
Resolver para y usando la Ecuación 1
5x + y = 26 ...... Ecuación 1
5 (4) + y = 26
20 + y = 26
y = 26 - 20
y = $ 6
Por lo tanto, el precio de cada chocolate y cada paleta:
Precio del chocolate = x = $ 4
Precio de la paleta = y = $ 6