Answers
Answer:
It would take [tex]2.7[/tex] seconds, correct to 1 decimal place/nearest tenth.
Step-by-step explanation:
Step 1: Understanding the formula
The formula is given as [tex]h=16t^{2}[/tex], where [tex]h[/tex] represents the height, and [tex]t[/tex] represents the time.
Step 2: Substituting and solving
The question asks for the time that would take when the height is [tex]117~\text{feet}[/tex].
So, substitute [tex]117[/tex] for [tex]h[/tex] in the formula, since [tex]h[/tex] denotes the height:
[tex]h=16t^{2}\\117=16t^{2}[/tex]
Now, let's solve the equation to find the time, [tex]t[/tex]:
[tex]117=16t^{2}\\\\\text{Divide by 16 on both sides of the equation:}\\\frac{117}{16}=\frac{16t^{2}}{16}\\\\\text{Simplify:}\\7.3125=t^{2}\\\\\text{Square root both sides of the equation:}\\\sqrt{7.3125}=\sqrt{t^{2}}\\\\\text{Calculate:}\\2.7 \approx t\\\\\text{Rearrange the equation:}\\t\approx2.7[/tex]
So, it takes about [tex]2.7[/tex] seconds to travel [tex]117[/tex] feet, according to the formula.
Related Questions
write 2 quadratic equations (of any form) that are not equivalent, each with a vertex of (4,5)
Answers
Answer:
[tex]g(x)=-x^2+8x-11\\\\f(x)=x^2-8x+21[/tex]
Step-by-step explanation:
Generally when you're given the vertex of a quadratic, you can express it in vertex form: [tex]f(x)=a(x-h)^2+k[/tex], where (h, k) is the vertex, and "a" is some constant value that determines the stretch/compression and the direction (up or down)
So we know that: (h, k) = (4, 5), meaning we can plug those values into the equation: [tex]f(x)=a(x-4)^2+5[/tex]
we can change the function by changing the value of the constant "a".
we can use two arbitrary values, but in this example I'll use -1 and 1.
this gives us the following functions: [tex]f(x)=(x-4)^2+5\\g(x)=-(x-4)^2+5[/tex]
these two functions are actually very similar, the only different is they're reflected across the x-axis (and some vertical shift) since the y-value is being negated, or at least part of it.
In your question it states (of any form), so I'm assuming we can leave it in vertex form, but just in case I'll expand them further into standard form
[tex]f(x)=(x-4)^2+5\\\\f(x)=(x-4)(x-4)+5\\\\f(x)=x(x-4)-4(x-4)+5\\\\f(x)=x^2-4x-4x+16+5\\\\f(x)=x^2-8x+21[/tex]
We can also expand the other function similarly.
[tex]g(x)=-(x-4)^2+5\\\\g(x)=-[(x-4)(x-4)]+5\\\\g(x)=-[x(x-4)-4(x-4)]+5\\\\g(x)=-[x^2-4x-4x+16]+5\\\\g(x)=-[x^2-8x+16]+5\\\\g(x)=-x^2+8x-16+5\\\\g(x)=-x^2+8x-11[/tex]
simplify the following: [tex]\frac{(7^2.3^-1)^4.7^5}{(3^2.7^-6)^3}[/tex]
(. means multiply)
Answers
The simplification of the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex] is 2453.5.
How to simplify the equation?
Consider the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex]
Solve for Numarator [tex](7^{2} .3-1)^{4}[/tex]= [tex](7^{2} .3-1)^{2} (7^{2} .3-1)^{2}[/tex]
= [tex](147-1)^{2}[/tex][tex](147-1)^{2}[/tex]
= (21316) (21316)
Solve for Denominator [tex](3^{2}.7-1)^{3\\}[/tex]
= [tex](63-6)^{3}[/tex]
= 57³
Solve both, and simplify the equation.
= [tex]\frac{(21316) (21316)}{185193}[/tex]
= 2453.5
∴ Simplification is 2453.5
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9t + 5(t + 3) = -(t + 13) + t
Answers
If we solve the given equation for t we get that t=-2
The equation given,
9t+5(t+3) = -(t+13) +t
⇒9t + 5t + 15 = -t -13 +t
⇒14t + 15 = -13 (∵-t+t=0)
⇒14t = -13-15 (bringing 15 from left hand side to right hand side the sign is flipped and 15 becomes -15)
⇒14t = -28
⇒[tex]t=\frac{-28}{14}[/tex] (dividing both sides by 14)
⇒t = -2
Thus on solving the equation we get t = -2
Your question was incomplete but most probably your full question was
Solve for t when this equation is given, 9t+5(t+3) = -(t+13) +t
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5x/6 = 30 solve for x simplify your answer as much as possible
Answers
Answer:
x = 36
Step-by-step explanation:
Simplify:To find the value of 'x', isolate 'x'.
[tex]\sf \dfrac{5}{6}x = 30\\\\ \text{Multiply both sides by 6,}\\\\ 5x = 30*6\\\\\text{Divide both sides by 5,}\\\\ x = \dfrac{30*6}{5}\\[/tex]
x = 6 * 6
x = 36
The midpoint of AB is M(1, 1). If the coordinates of A are (-2,5), what are the
coordinates of B?
Answers
The coordinates of B are (4 , -3) .
A cartesian coordinate system, which uses signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.
The origin of each reference coordinate line, known as an axis of the system or simply an axis (plural axes), is the intersection of the ordered pairs (0, 0). The coordinates can also be determined by looking at the locations of the perpendicular projections of the point onto the two axes, which are shown as signed distances from the origin.Let the coordinates of B be (x, y)
As M is the mid point of AB , we know from the distance formula that the coordinates of M will be:
abscissae of M = (-2 + x) /2
or, 1 = (-2 + x) /2
or, x = 4
Ordinate of M = (5 + y)/2
or , 1 = (5 + y)/2
or, y = -3
Therefore the coordinates of B are (4 , -3)
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Can someone answer this! Its due in 34 minutes!!!!
Answers
I WILL BE USING LAWSOF EXPONENTS.
[tex] = {3}^{3} \times (3^{2})^{3x} \\ = {3}^{3} \times 3^{2 \times3 x} \\ = {3}^{3} \times {3}^{6x} \\ = 3^{3 + 6x} [/tex]
IF IT SAID THAT K IS THE IS THE EXPRESSION IN TERMS OF K THEN THE EXPRESSION NOW IS
[tex]3 +6 x[/tex]
HOPE THIS HELPS
a local salesman receives a base salary of $875 monthly. he also receives a commission of 10% on all sales over $1800. how much would he have to sell in a month if he needed to have a monthly income of $1500?
Answers
The total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.
What is termed as the sales commission?Sales commission is indeed the amount of cash as well as money paid to salespeople for exceeding a predetermined sales target. For instance, a company may agree to pay it's own salespeople a 4% commission on monthly sales exceeding Y.The total monthly earnings for salespeople can be calculated as follows:
Monthly salary = base salary + sales commission
Given that what a local salesman generates a base salary of $875 and a 10% sales commission on any and all sales above $1,800, the salesman must make the following sales in order to earn $1500 in a given month:
Let the sales done by 'x'.
Then,
875 + 7% (x - 1800) = 1500
875 + (7/100) (x - 1800) = 1500
7(x - 1800) = 62500
x - 1800 = 8928.7
x = 894657.14
Thus, the total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.
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♾️ How is the infinite possible? Has anyone ever counted numbers their whole life?
Answers
Answer: False, not possible.
The human was never meant to calculate or go beyond their fingers in search of great numbers, taking count for themselves, giving them names, appropriating. If you wanted to go higher for a laugh, it was called guessing. "Give me ZERO of this, give me 14,739,628,837 of that" are words that nobody says and words that stand behind delusion.
The only "anyone" to be counting their whole life is a divine. Keep math, numbers, and geometry sacred.
2. Write ONE algebraic rule that represents triangle JKL being translated to triangle J"K"L".
Answers
The original coordinates of JKL:
J(-3, -3), K(-4, 2) and L(2,1)
First, it is translated by the algebraic rule (x,y)->(x+2, y-3):
J(-3, -3)-> J'(-3+2, -3-3)=J'(-1, -6)
K(-4, 2) -> K'(-4+2, 2-3)= K'(-2, -1)
L(2,1) -> L'(2+2, 1-3)= L'(4, -2)
Then, this image is translated by (x,y)-> (x-2, y-1)
J'(-1, -6) -> J''(-1-2, -6-1) = J''(-3, -7)
K'(-2, -1) -> K''(-2-2, -1-1)= K''(-4, -2)
L'(4, -2) -> L''(4-2, -2-1)= L''( 2, -3)
Coordinates for triangle J''K''L'':
J''(-3, -7), K''(-4, -2) and L''( 2, -3)
2. To find algebraic rule that represents JKL to J''K''L'':
[tex]\begin{gathered} J^{\doubleprime}(-3,-7)\text{ and J(-3, -3)} \\ (x,y)\rightarrow(x,\text{ y+4)} \end{gathered}[/tex]How long is the hypotenuse?
Answers
The sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The hypotenuse exists c = 50.
How to determine hypotenuse?To determine the hypotenuse from the sides of a right triangle, use the Pythagorean theorem. Sum of squares is squared as c = √(a² + b²).
The longest side of a right-angled triangle, or the side opposite the right angle, exists comprehended as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
a² + b² = c²
⇒ c = √(a² + b²)
Where, a = 30 and b = 40, then
substitute the values in the above equation, we get
30² + 40² = c²
900 + 1600 = c²
2500 = c²
50 = c
Therefore, the hypotenuse exists c = 50.
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James sells 6 cupcakes for £5
Maddie sells 4 cupcakes for £3.50
Which is better value?
You must show all your working.
Answers
6 = 5
1 = ? Crisi cross
6? = 5. Divide both side by 6
? = 5/6 = 0.966
Maddie
4 = 3.5
1 = ?
4? = 3.5
? = 0.875
0.966 > 0.875 so James is selling with bigger price
Oscar
and maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles one entry in the table paired 152 km with 95 miles if k represents the number of kilometers and m represents the number of miles who wrote the correct equation that would relate kilometers to miles
Answers
The answer to the given question is Oscar wrote the correct equation that would relate kilometers to miles.
Calculation and Parameters1. Table
km miles
152 95
2. Set the proportion with / and solve for k
/ = 152 km / 95 miles
/ = 1.6 km / 1 miles
= 1.6 , where 1.6 / 1 represents kilometers per mile.
So, Oscar is right.
Maria is wrong because:
If we solve the proportionality:
/ = 152 km / 95 miles
/ = 95 miles / 152 km
= 0.625 , where 0.625 represents miles per kilometer
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The complete question is:
"Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If represents the number of kilometers and represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.
Oscar wrote the equation = 1.6, and he said that the unit rate 1.6 / 1
represents kilometers per mile.
Maria wrote the equation = 0.625 as her equation, and she said that 0.625 represents kilometers per mile."
What is the slope of the line that passes through the points (2, 8) and
(-3, 14)? Write your answer in simplest form.
Answers
Answer:
-6/5
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (14 - 8)/(-3 - 2)
slope = 6/(-5)
slope = -6/5
The solution is -6/5
The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the first point be A
Now , the value of A is A ( 2 , 8 )
Let the second point be B
The value of B is B ( -3 , 14 )
And , the slope of the line between 2 points is given by the formula,
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 14 - 8 ) / ( -3 - 2 )
On simplifying the equation , we get
Slope m = 6 / ( -5 )
Slope m = -6/5
Therefore , the slope of the line is m = -6/5
Hence , The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5
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Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per
gigabyte. She wants to keep her bill under $60 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Ella
can use while staying within her budget.
> ≤ >
Inequality: 5g +37.5 < 59
9 4.3
Submit Answer
attempt 2 out of 2
Answers
The gigabyte needed will be g<2.2 as per the given condition that is- " Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per gigabyte. She wants to keep her bill under $60 per month."
What is inequality?A mathematical statement of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things. The five inequality symbols in Maths are greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
How to solve inequality?Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the numbers on the other by adding or subtracting quantities.
Here,
Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.
So the inequality will be,
49+5g<60
5g<11
g<2.2
The required gigabyte will be g<2.2 under the following circumstances: "Ella's cell phone plan has a fixed monthly fee of $49 and a per-gigabyte charge of $5. She wants to keep her monthly bill under $60."
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Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=6(x-6)
Answers
The question wants us to represent your the equation y - 4 = 6()
Please help me with this math problem!! Will give brainliest!! :)
Answers
Answer: 1/2
Step-by-step explanation:
Answer:
The correct answer seems to be 1/2
What kind of transformation converts the graph of f(x)=3x+9 into the graph of g(x)=3x–10?
Answers
The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up
How to determine the transformation?The equations of the functions are given as
f(x) = 3x + 9
g(x) = 3x - 10
Let the translations from f(x) to g(x) be h and k
So, we have
g(x) = f(x + h) + k
This gives
f(x + h) = 3(x + h) + 9 + k
Open the brackets
f(x + h) = 3x + 3h + 9 + k
Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k
g(x) = 3x + 3h + 9 + k
This means that
3x + 3h + 9 + k = 3x - 10
Evaluate the like terms
3h + 9 + k = - 10
This gives
3h + k = - 19
Express -19 as -21 + 2
3h + k = -21 + 2
Express 21 as 3 * 7
3h + k = -3 * 7 + 2
By comparison, we have
h = -7 and k = 2
This means that the transformation is 7 units right and 2 units up
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Find the circumference of the circle. Use 3.14 for x
17 ft
Answers
The circumference of the circle with a radius of 7 ft is 106.76 ft
What is circumference?The circumference of a circle is the perimeter of the circle
How to calculate the circumference?The given parameters are
Radius = 17 ft
As a general rule, radius are represented by the variable r
So, we have the following representation equation
r = 17
The circumference of the circle is then calculated as
C = 2πr
Next, we substitute the value of the variable r in the above equation
i.e. r = 17
So, we have the following equation
C = 2π * 17
From the question, we have
π = 3.14
So, we have the following equation
C = 2 * 3.14 * 17
Evaluate the products
So, we have the following equation
C = 6.28 * 17
Evaluate the products
So, we have the following equation
C = 106.76
Hence, the circumference is 106.76 ft
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Given f(x)=3x2−5x−2.
What is the value of f(−2/3)?
Answers
Answer:
[tex]2\frac23[/tex]
Step-by-step explanation:
Hello!
Evaluate the function for -2/3, by plugging it in for x in the equation.
Evaluate[tex]f(x) = 3x^2 - 5x - 2[/tex][tex]f(-\frac23) = 3(-\frac23)^2-5(-\frac23)-2[/tex][tex]f(-\frac23) = 3(\frac49) + \frac{10}{3} - 2[/tex][tex]f(-\frac23) = \frac{4}3 + \frac{10}3 - 2[/tex][tex]f(-\frac23) = 4 \frac23 - 2[/tex][tex]f(-\frac23) = 2\frac23[/tex]The evaluated value is [tex]2\frac23[/tex].
Answer:
Step-by-step explanation:
The absolute value of negative two third is really 2/3 but if your trying to reduce it to the lowest term its 0.66 or 0.67 However I would just put only 2/3 in the box, confidently knowing it would be scored correct.
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 4500 pounds on Planet A, find the elephant's weight on Planet B.
Answers
Based on the ratio of the weights of objects in Planet A to Planet B, an elephants weighing 4,500 pounds on Planet A would weigh 135 pounds on Planet B
How to find the weight?The ratio of the weight of an object in Planet A is 100 to 3 on Planet B. This means that every 100 pounds on Planet A is 3 pounds on Planet B.
If an elephant on Planet A is 4,500 pounds, on Planet B it would weigh:
Weight on Planet B = (4,500 x 3) / 100
Weight on Planet B = 13,500 / 100
Weight on Planet B = 135 pounds
In conclusion, the weight of the elephant on Planet B would be 135 pounds.
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write the equation of the line that is perpendicular to 5x-4y=4 and passes through the point (-8, 2)
Answers
The linear equation perpendicular to 5x-4y=4 is:
y = (-4/5)*x + 42/5
How to get the linear equation?We want to find a line perpendicular to:
5x - 4y = 4
Solving this for y, we get:
y = 4 - 5x
y = (4 - 5x)/-4 = -1 + (5/4)*x
We can see that the slope of this line is 5/4, the slope of a perpendicular line will be the inverse of the opposite, so we get:
slope = -4/5.
Then the line is something like:
y = (-4/5)*x + b
To find the value of b, we use the fact that the line passes through (-8, 2)
2 = (-4/5)*-8 + b
2 = (-32/5) + b
2 + 32/5 = b
10/5 + 32/5 = b
42/5 = b
The linear equation is:
y = (-4/5)*x + 42/5
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3. (02.02)
Angle ABC is formed by segments AB and BC on the coordinate grid:
90 degree
m/ABC 180 degrees
Angle ABC is rotated 90 degrees counterclockwise about the origin to form angle AB'C'. Which statement shows the measure of angle A'B'C' (4 points)
OmzABC 90
m/ABC= mzABC
5-
OmzABC-2 m/ABC
8
Answers
The statement that shows the correct measure of ∠A'B'C' is
m∠ABC = m∠A'B'C'.
What type of transformation does rotation do?
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point. A rotation produces a new figure known as the image. The picture matches the original figure exactly.
The rotation will typically be at a similar angle, even if a figure can be rotated by any number of degrees. Positive degrees will cause the figure to revolve counterclockwise. The graphic will turn clockwise if the degree value is negative. Any point on the figure can be rotated.
Given, ΔABC with co-ordinates (3, 4), (5, 3) and (3, 2); also ∠ABC = 53.13°
Again, ΔABC is rotated counter-clockwise by 90° to make the ΔA'B'C'.
Thus, new triangle having co-ordinates (-4, 3), (-3, 5) and (-2, 3) is obtained.
Rotation retains congruence since it is a transformation that does not alter side length or angle measure.
Thus, we have ∠A'B'C' = 53.13°
Therefore, ∠ABC = ∠A'B'C' = 53.13° i.e. m∠ABC = m∠A'B'C'.
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Logan is having his dog professionally groomed and wants to tip the groomer 15%. What equation can Logan use to calculate the tip, y, if his total bill is x dollars?
Answers
Answer:
y = 1.15x
Step-by-step explanation:
15% = 0.15
100% = total bill
Total bill + 15% = 115% or 1.15
x × 1.15 = y
Three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes. Which of the following statements is true regarding Rick's votes?
Answers
The statement that is true regarding Rick's votes is D. Rick has 32 more votes than Jami.
How to calculate the value?From the information, three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes
Rick = h + 10
Jami = h - 22
In this case, it's important to note that the difference between Jami and Rick will be:
= 10 - (-22)
= 10 + 22
= 32
Therefore, Rick will have 32 more votes.
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Three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes. Which of the following statements is true regarding Rick's votes?
A. Rick has 10 more votes that Jami
B. Rick has 22 more votes that Jami
C. Rick has 5 more votes than Helen
D. Rick has 32 more votes than Jami.
Simplify the complex rational expression. Type your answer in simplest form, multiplying any factors you may have in the numerator or denominator. When typing your answers, type your terms with variables in descending power and in alphabetical order without any spaces between your characters. If needed use the carrot key ^ (press shift and 6) to indicate an exponent.\frac{\left(\frac{2c}{c+2}+\frac{c-1}{c+1}\right)}{\frac{\left(2c+1\right)}{c+1}}
Answers
We will simplify the complex expression shown below:
[tex]\frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}}[/tex]The simplification process is shown below >>>>
[tex]\begin{gathered} \frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{2c(c+1)+(c-1)(c+2)}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{2c^2+2c+c^2+2c-c-2}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{3c^2+3c-2}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{3c^2+3c-2}{(c+2)(c+1)}\times\frac{c+1}{2c+1} \\ =\frac{3c^2+3c-2}{(c+2)\cancel{c+1}}\times\frac{\cancel{c+1}}{2c+1} \\ =\frac{3c^2+3c-2}{(c+2)(2c+1)} \end{gathered}[/tex]If we multiply out the denominator, we have:
[tex]\begin{gathered} \frac{3c^2+3c-2}{(c+2)(2c+1)} \\ =\frac{3c^2+3c-2}{2c^2+c+4c+2} \\ =\frac{3c^2+3c-2}{2c^2+5c+2} \end{gathered}[/tex]AnswerThe numerator is
[tex]3c^2+3c-2[/tex]The denominator is
[tex]2c^2+5c+2[/tex]Consider the following definite integral.sxex²+1d'dx0Identify the definite integral that will result after making a u-substitution.
Answers
The first choice is the correct result
I need help asap!!!!
Answers
The answer is -1 and 5
At the beginning of baseball season, the
concession stand had inventory of
4,250 bags of popcorn. At the end of the
season, 1,250 bags remain. What is the
percent of decrease in the number of
bags of popcorn? Round to the nearest
tenth if necessary.
Answers
Answer:
70.6% decrease
Step-by-step explanation:
4250-1250 = 3000
4250x = 3000
x=70.6%
70.6% decrease
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Items 11-15. Lines a, b, c, and d
intersect as shown.
11. Which pairs of lines are parallel?
(a) a and b
(b) a and c
(c) c and d
(d) b and d
12. What is x?
13. What is y?
(a) 37
(b) 84
(c) 88
(d) 92
14. What is z?
(a) 84
(b) 92
(c) 96
(d) 109
15. If the slope of line d is given, the slope of which other line is known?
LEFT SIDE OF PAPER!!
Answers
Answer:
11. (c) c and d
12. x = 109°
13. (b) 84
14. (c) 96
15. C
Step-by-step explanation:
11. Parallel means that if the lines continued on forever, the lines will never cross. They have the same slope.
12. x is an alternate exterior angle to the angle labeled 109°. this means that the angles are equivalent.
13. y is the last unknown angle in the triangle. The interior angles of a triangle always add up to 180°. So 180° = 55° + 41° + y.
y = 180° - 55° - 41° = 84°
14. z is a supplementary angle to y, meaning that y + z = 180°.
180° - 84° = 96° = z
15. Lines d and c are parallel meaning they have the same slope, therefore if you know the slope of one, you know the slope of the other.
3) Identify the following by using the given figure
a) Two pairs of adjacent angles
b) Two pairs of supplementary angles
c) Linear pairs
Answers
Step-by-step explanation:
a) angles that share 1 side and are next to each other
<DBA, <ABE
<ABE, <EBC
b) two angles whose measures add to 180°
<ABE, <EBC
<ABD, <DBC
c) two adjacent angles whose noncommon sides lie on a line
<ABE, <EBC
<ABD, <DBC