What is the equation for the line of reflection that maps the trapezoid onto itself?
A. x= -2
B. x=0
C. y=2.5
D. y=4
Answers
From the given trapezoid, the line of symmetry of the trapezoid is x = -2.
Therefore, the equation for the line of reflection that maps the trapezoid onto itself is x = -2.
Related Questions
Which of the following is a solution of x2 − 6x = –22?
A. -6-i√52
B. -6+i√13
C. 3-i√13
D. -3+i√52
Answers
For this problem, I'll be completing the square.
x² - 6x = -22
Since the constant has been moved to the right side already, we can move on to the next step which is adding (b/2)² to both sides of the equation.
x² - 6x + (-6/2)² = -22 + (-6/2)²
x² - 6x + 9 = -22 + 9
Factor the left side of the equation into a perfect square and simplify the right side.
(x - 3)(x - 3) = -13
Take the square of both sides.
x - 3 = ± √-13
Take out the negative from the square root as the letter "i"
x - 3 = ± i√13
Add 3 to both sides of the equation to let x be by itself.
x = 3 ± i√13
So your two roots will be:
x = 3 + i√13 and x = 3 - i√13
Solution: C. 3 - i√13
What is the product of −2 1/4 and 2 1/2?
Answers
product means multiply
-2 1/4 times 2 1/2:
-2 1/4 = -9/4
2 1/2 = 5/2
-9/4 x 5/2 = -45/8 = -5 5/8
~thanks for letting me answer your questions! x lots of love, lilly <3
H E L P PLEASE COME ON WHY WONT ANYONE HELP
Corey deposited $1,500 in a savings account that earns simple interest at 5.75%. What is the balance in his account at the beginning of the third quarter?
A. $1,556.78
B. $1,528.13
C. $1,543.13
D. $1,612.50
Please explain your answer CLEARLY so i can use the principles for future reference. Thanks!
Answers
At the beginning of the third quarter means at the end of two quarters which is 6 months
So the formula is
A=p (1+rt)
A future value?
P present value 1500
R interest rate 0.0575
T time 6 months/12
A=1,500×(1+0.0575×(6÷12))
A=1,543.13
The answer is c
Hope it helps!
Suppose △DEF≅△MNO. Which congruency statement is true?
EF¯¯¯¯¯≅MN¯¯¯¯¯¯¯DE¯¯¯¯¯≅MN¯¯¯¯¯¯¯DF¯¯¯¯¯≅NO¯¯¯¯¯¯EF¯¯¯¯¯≅MO¯¯¯¯¯¯
Answers
△DEF≅△MNO
answer
DE≅MN
Answer:
DE≅MN
Step-by-step explanation:
We know that corresponding parts of congruent triangles are congruent (CPCTC). Using the congruence statement we can match up the corresponding sides.
From the statement, ∠D matches ∠M, ∠E matches ∠N, and ∠F matches ∠O.
We also see that DE matches MN, EF matches NO, and DF matches MO.
Thus we have that DE≅MN.
Erica has found a pair of running sneakers that she likes, costing $150. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford the sneakers?
B) 18
C) 22
D) 14
Answers
HELP NEEDED
Which system of linear inequalities is graphed? See screenshot!
Answers
u have another line that has a y int of 2....it has a slope of -1/2....it has a solid line...so there is an equal sign in the problem...it is shaded below the line...so it is less then....
y < = -1/2x + 2
1/2x + y < = 2...multiply by 2
x + 2y < = 4
so ur answer is : y > = 3x - 2 and x + 2y < = 4...the 2nd one
1. State the domain of the rational function. (2 points)
f(x) = thirteen divided by quantity ten minus x.
a) All real numbers except -10 and 10
b) All real numbers except 13
c) All real numbers except 10
d) All real numbers except -13 and 13
2. State the vertical asymptote of the rational function. (2 points)
f(x) = quantity x minus six times quantity x plus six divided by quantity x squared minus nine.
a) x = 6, x = -6
b) x = 3, x = -3
c) x = -6, x = 6
d) None
3. State the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus four x minus seven divided by quantity x minus seven.
a) None
b) y = -4
c) y = 7
d) y = 6
4. State the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus eight x minus two divided by quantity x minus two.
a) None
b) y = 1
c) y = -8
d) y = 2
5. Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at
x = 2 and x = 1.
Answers
f(x) = 13 / (10-x)
The only x value that would not produce a real number for f(x) is 10, since you
cannot divide a number by zero. Answer is C
2)
F(x)
=(x-6)(x+6)/(x2 - 9)
The vertical asymptotes are x=3 and x=-3. Graph the function on a graphing
calculator to observe the behavior of the function at these points. There is
both a positive and negative vertical asymptote a both x=3 and x=-3. Keep in
mind that the denominator approaches zero at these points, and thus f(x) approaches
either positive or negative infinite, depending on whether the denominator, however small, is a positive or
negative number. Answer is B) 3, -3
3)
F(x) = (x2
+ 4x-7) / (x-7)
Although there is a vertical asymptote as x=7, there is no horizontal asymptote.
This makes sense. As X gets bigger, there is nothing to hold y back from
getting greater and greater. X2 is the dominant term, and it’s only
in the numerator. A) none
4)
(x2 +
8x -2) / (x-2)
This function is very similar in structure to the previous one. Same rules
apply. Dominant term only in the numerator means no horizontal asymptote.
A)None
5)
Our
function approaches 0 as x approaches infinite, and has a vertical asymptote at
x=2 and x=1.
Here’s an easy example: 10 / ((x-2)*(x-1)). At x=2 and x=1, there is both a
positive and negative vertical asymptote. As x approaches infinite, the
numerator is dominated by the denominator, which contains x (actually x2 ),
and thus y approaches zero.
c) All real numbers except 10
Compare the denominator to zero and it will give you the point where there is no f(x) because it is impossible to divide anything by 0.
10-x=0 ⇔ x=10
The function has a domain containing all real numbers except 10 → x<10 or x<10.
2. Considering f(x)=[tex] \frac{(x-6)(x+6)}{x^{2}-9 } [/tex]
b) x = 3, x = -3
Once more, compare the denominator to zero and it will give you the point/points where there is no f(x) because it is impossible to divide anything by 0, and there is where you can find the vertical asymptotes.
x²-9=0 ⇔ x=-3, x=3
The vertical asymptotes are x=3 and x=-3.
3. Considering [tex] \frac{x^{2}+4x-7}{x-7} [/tex]
a) None (of those presented)
Apply long division on the function.
The horizontal asymptote is y=x+11.
4. Considering [tex] \frac{x^{2}+8x-2}{x-2} [/tex]
a) None (of those presented)
Once more, apply long division on the function.
The horizontal asymptote is y=x+10.
5. The polynomial in the numerator has to have a smaller degree than the polynomial in the denominator. The polynomial in the denominator needs to have factors of x-1 and x-2. This factors should not be part of the polynomial in the numerator. An example of such a function could be: f(x)=[tex] \frac{8x-2}{ x^{2} -3x+2} [/tex]
2. The coordinates of the vertices of are P(-2,5), Q(-1,1) and R(7,3) . Determine whether PQR is a right triangle. Show your work.
Answers
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 5}})\quad % (c,d) &({{ -1}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-5}{-1-(-2)}\implies \cfrac{1-5}{-1+2} \\\\\\ \cfrac{-4}{1}\impliedby\stackrel{slope~of}{PQ}[/tex]
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 1}})\quad % (c,d) &({{ 7}}\quad ,&{{ 3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-1}{7-(-1)}\implies \cfrac{3-1}{7+1} \\\\\\ \cfrac{2}{8}\implies \cfrac{1}{4}\impliedby \stackrel{slope~of}{QR}[/tex]
now, two lines who meet at a perpendicular angle, have a negative reciprocal slope of each other, to make it short, if you multiply their slopes, you should get -1 as the product, if they're indeed perpendicular.
[tex]\bf \stackrel{PQ}{-\cfrac{4}{1}}\cdot \stackrel{QR}{\cfrac{1}{4}}\implies -1[/tex]
low and behold, they're indeed perpendicular, thus that angle is indeed a right-angle.
6+ 4/a + b/3 a=4 b=3
Answers
6+1+1=
The answer is 8.
I hope this helped! :))
Nellie is buying bird seed to put in her bird feeders. She uses about 10 pounds of bird seed each week, but has room to store any extra that she purchases.The bird seed comes in 3 different sizes as given below: 3.5 pounds for $2.52 7.5 pounds for $5.40 11 pounds for $7.92 Nellie is trying to be a smart shopper and get the best deal on the bird seed. Which size bag of bird seed should Nellie buy? a. Nellie should buy the 3.5 pound bags because they have the cheapest unit price b. Nellie should buy the 7.5 pound bags because they have the cheapest unit price c. Nellie should buy the 11 pound bags because they have the cheapest unit price. d. Nellie should buy any size she wishes because they all have the same unit price..
Answers
Given: Nellie has to buy bird seed and the prices are as follows
3.5 pounds for $2.527.5 pounds for $5.4011 pounds for $7.92To Find: which size bag should Nellie buy (which one would have the cheapest unit price)
Solution: D. Nellie should buy any size because they all have the same unit price.
Explanation:
We begin by finding the unit price, i.e., price per pound for each of the three bags.
This is done by using the Unitary Method. We must divide the price by the volume of the bag to find the price per pound.
price per unit of the smallest (3.5 pound) bag is [tex]\frac{2.52}{3.5} =0.72 $ per pound[/tex]price per unit of the medium (7.5 pound) bag is [tex]\frac{5.40}{7.5} =0.72 $ per pound[/tex]price per unit of the biggest (11 pound) bag is [tex]\frac{7.92}{11} =0.72 $ per pound[/tex]Answer:
D
Step-by-step explanation:
Nellie should buy any size she wishes because they all have the same unit price..
The community center has a pottery class each month. Each student pays $15 for the class and $27 for materials. This month the pottery class brought in a total of $714. How many students are in the class this month?
Answers
42x=714
X=17
BRAINLIEST!!!!
8. Find the glide reflection image of the black triangle where the translation is (x,y) -> (x,y - 7) and the line of reflection is x = 1.
Am I correct?
Answers
Answer:
Option D is correct.
Explanation:
From the given figure,
Labelled the black triangle as A, B and C
The coordinates of triangle ABC are;
A= (2,8) , B= (2,5) and C=(6,5)
To find the glide reflection image of the triangle ABC.
Glide Reflection: It is a composition of transformations.
In glide reflection, a translation is first performed on the figure then it is reflected over a line.
Given: The rule of translation is: [tex](x,y) \rightarrow (x, y-7)[/tex] and line of reflection is x= 1.
Now, apply the rule of translation on black triangle, we get;
[tex]A (2,8) \rightarrow (2, 8-7)[/tex] = A' (2,1)
[tex]B (2,5) \rightarrow (2, 5-7)[/tex] =B' (2,-2)
[tex]C (6,5) \rightarrow (6, 5-7)[/tex] = C' (6,-2)
Next,
Apply the rule of reflection over the line x =1,
i.e, [tex](x,y) \rightarrow (-x+2, y)[/tex]
[tex]A' (2,1) \rightarrow (-2+2, 1)[/tex] =A" (0,1)
[tex]B' (2,-2) \rightarrow (-2+2, -2)[/tex] =B" (0,-2) and
[tex]C' (6,-2) \rightarrow (-6+2, -2)[/tex] =C" (-4,-2)
You can see the graph of Glide reflection as shown below in the attachment.
If x + b > c and x > 0 have the same solutions, what is the relationship between b and c
Answers
An apple pie uses 4 cups of apples and 3 cups of flour. An apple cobbler uses 2 cups of apples and 3 cups of flour. You have 16 cups of apples and 15 cups of flour. When you sell these at the farmers market you make $3.00 profit per apple pie and $2.00 profit per apple cobbler. Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize your profit.
1. let ×= the number of apple pies you make and y= the number of apple cobblers you make. Write an inequality to show the constraint on the amount of apples you have?
2. Write an inequality to show the constraint on the amount of flour you have .
3. Write any non negativity contraints on x and y
Answers
Given that x represents the number of apple pies that can be made and y represents the number of apple cobblers that can be made.
Given that an apple pie uses 4 cups of apples and an apple cobbler uses 2 cups of apples and there are 16 cups of apples available.
An inequality to show the constraint on the amount of apples available is given by:
4x + 2y ≤ 16
Part 2:
Given that an apple pie uses 3 cups of flour and an apple cobbler uses 3 cups of flour and there are 15 cups of flour available.
An inequality to show the constraint on the amount of flour available is given by:
3x + 3y ≤ 15
Part C:
The non negativity contraints on x and y are:
x ≥ 0 and y ≥ 0
A culture of 2.4×1011 bacteria is in petri dish A. A culture of 8×109 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
Answers
2.4/8=0.3
10^11-9=10^2
0.3•10^2
(This is not in scientific notation 1 or 1 to 9)
Move the decimal right once and subtract one from the exponent.
3•10^1
Standard notation is 30.
Hoped I helped!
The number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
What is bacteria?Bacteria are small single-celled organisms. Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems.
Given is a culture of 2.4 × 10¹¹ bacteria is in petri dish 'A' and a culture of
8 × 10⁹ bacteria is in petri dish B.
Number of bacteria's in petri dish A = n[A] = 2.4 × 10¹¹ bacteria
Number of bacteria's in petri dish B = n[B] = 8 × 10⁹ bacteria
For comparison, lets assume that -
k = n[A]/n[B]
k = 2.4 × 10¹¹ / 8 × 10⁹
k = 240 / 8
k = 30
n[A] = 30 n[B]
Therefore, the number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
To solve more questions on Number comparison, visit the link below-
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to find the weight of the golden 22 karat gold object
Answers
i hope this helped and have a wonderful day filled with joy!
A round cookie cake, divided into 8 equal pieces, has a diameter of 16 inches. Marty eats one piece of cake. What is the area of the piece of cake that Marty eats? Leave your answer in terms of pi. A)4π in2 B) 8π in2 C)16π in2 D) 64π in2
Answers
What is the area of the entire cookie cake?
The area of a circle is π*r²
The diameter is 16 inches, so the radius is 8 inches.
Area = π * 8²
Area = 64 π in²
The entire cookie has an area of 64 π in².
To find the area of Marty's piece, divide this number by 8:
64 π in² ÷ 8 = 8 π in²
Answer is B
Answer:
8
Step-by-step explanation:
What is the maximum product of two numbers whose sum is 13? what numbers yield this product?
Answers
The substitution property of equality allows you to say that if 7j + 14k = 28 And j = 2 then
Answers
The bedroom of a house is 1,200 cubic meters. We know that there are 3.4 x 109 particles of dust per cubic meter. How many particles of dust are present in the bedroom of the house
Answers
To find the number of dust particles in a 1200 cubic meter bedroom with 3.4 x 10⁹ particles per cubic meter, multiply the volume by the number of particles per volume, resulting in approximately 4.08 trillion dust particles.
To calculate the number of dust particles in the bedroom, we need to multiply the volume of the bedroom by the number of dust particles per cubic meter. Given that the bedroom is 1200 cubic meters and that there are 3.4 x 10⁹ particles of dust per cubic meter, we can use the following calculation:
Number of particles = Volume of the bedroom x Number of particles per cubic meter
Number of particles = 1200 m³ x 3.4 x 10⁹ particles/m3
Number of particles = 4.08 x 10¹² particles
Therefore, there are approximately 4.08 trillion dust particles in the bedroom of the house.
what is the union of the two sets R= {10, 11, 13, 15, 17} T= {5, 7}?
Answers
union is { 5,7,10,11,13,15,17 }...and if they repeat, u would only have to write them once...although that doesn't apply in this situation...I am just letting u know
Select Repeating or Nonrepeating to correctly classify each decimal. 1.01011 2.23¯¯ 3.426¯ 4.321321… the minus signs mean like a line over the number
Answers
Answer:
2.23 3.426 4.32321... are repeating and 1.01011 is not repeating
The decimal 1.01011 is a non-repeating decimal. For the others, 2.23, 3.426, and 4.321321... are all repeating decimals because they have digits or group of digits that repeat indefinitely.
Explanation:In mathematics, decimals are either repeating or nonrepeating. A repeating decimal is a decimal that has a digit or group of digits that repeats infinitely. A non-repeating decimal doesn't have a pattern of digits that repeats infinitely.
The decimal 1.01011 is non-repeating because there's no group of digits that repeats infinitely. The decimal 2.23¯¯ is a repeating decimal. The notation with two bars above the 23 indicates that 23 is the repeating part. The decimal 3.426¯ is also a repeating decimal. The bar above the 6 indicates that the digit 6 repeats indefinitely. Lastly, the decimal 4.321321... is a repeating decimal where the group of digits 321 repeats infinitely.Learn more about Repeating and Non-Repeating Decimals here:
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What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 42 and the two congruent sides each measure 21 units?
Answers
Answer:
69 degrees
Step-by-step explanation:
Which of the following values would complete the ordered pair if the point is on the graph of ƒ(x) = -2x + 3?
(-1, ___)
-4
0
1
5
PLZ HELP ASAP
Answers
Erica had 6 coins in her coin collection. she goes to a coin show and buys some coins. how many dose she have now?
Answers
Susan divides the fraction 5/8 by 1/16 . Her friend Robyn divides 5/8 by 1/32 predict which person will get the greater quotient . Explain and check your prediction
Answers
So 5/8 times 16/1. 80/8. Simply to 10.
Now do the same with 5/8 and 1/32
5/8 times 32/1. 160/8. Simplify to 20.
So I good prediction would be 1/32 since you have to flip the divisor and multiply.
Answer:
Robyn will get the greater quotient
Step-by-step explanation:
Prediction: Since 1/16 >1/32
So, it will prove the smaller quotient
Susan divides the fraction 5/8 by 1/16 .
Calculation : [tex]\frac{5}{8} \div \frac{1}{16}[/tex]
[tex]\frac{\frac{5}{8}}{\frac{1}{16}}[/tex]
[tex]\frac{5}{8} \times 16[/tex]
[tex]10[/tex]
Robyn divides 5/8 by 1/32
Calculation : [tex]\frac{5}{8} \div \frac{1}{32}[/tex]
[tex]\frac{\frac{5}{8}}{\frac{1}{32}}[/tex]
[tex]\frac{5}{8} \times 32[/tex]
[tex]20[/tex]
So, The prediction is true.
Robyn will get the greater quotient
What is the value of the expression when n=3?
–2n(5 + n – 8 – 3n)
Answers
When n=3, the value of the expression is 54.
Explanation:To find the value of the expression when n=3, we substitute n=3 into the expression: –2n(5 + n – 8 – 3n).
First, we simplify the expression:
–2n(5 + n – 8 – 3n) = –2(3)(5 + 3 – 8 – 3(3))
= –2(3)(5 + 3 – 8 – 9)
= –2(3)(-9)
= –2(-27)
= 54.
Therefore, when n=3, the value of the expression is 54.
If ABC XYZ, mA = 50°, and mY = 70°, find mC
Answers
Final answer:
Using the properties of congruent triangles and the fact that the sum of the angles in a triangle is 180°, the measure of angle C (mC) is found to be 60°.
Explanation:
Given that triangle ABC is congruent to triangle XYZ, we know that corresponding angles of congruent triangles are equal. Since the measure of angle A (mA) is given as 50°, and in triangle XYZ, the measure of angle Y (mY) is 70°, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C (mC).
The sum of the angles in triangle ABC would be:
mA + mB + mC = 180°
50° + mB + mC = 180°
Since triangle ABC is congruent to triangle XYZ, mB will be equal to mX, which is the same as mY, that is 70°:
50° + 70° + mC = 180°
Now, we just need to subtract the sum of mA and mB from 180° to find mC:
mC = 180° - (50° + 70°)
mC = 180° - 120°
mC = 60°
How are hourly and salaried gross pay calculated?
Answers
The perimeter of an isosceles triangle is 15.6m. Find the lengths of its sides, if: The base is 3m smaller than a leg ____m, ___m, _____m
Answers
we know that
An isosceles triangle is a triangle with two equal sides and two equal angles
Let
x-------> the length of the equal sides
y-----> the length of the base
[tex]y=x-3[/tex] -----> equation A
The perimeter of an isosceles triangle is equal to
[tex]P=2x+y[/tex]
[tex]P=15.6\ m[/tex]
so
[tex]15.6=2x+y[/tex] ------> equation B
substitute equation A in equation B
[tex]15.6=2x+[x-3][/tex]
[tex]15.6=3x-3[/tex]
[tex]3x=18.6[/tex]
[tex]x=6.2\ m[/tex]
Find the value of y
[tex]y=x-3[/tex]
[tex]y=6.2-3=3.2\ m[/tex]
therefore
the answer is
The dimensions of the triangle are
[tex]leg1=6.2\ m[/tex]
[tex]leg2=6.2\ m[/tex]
[tex]base=3.2\ m[/tex]