Answer:
D) 15
Step-by-step explanation:
We know the formula for direct variation is
y=kx
Substituting y=5 and x=4 we can calculate k
5=k4
Divide each side by 4
5/4 =k
Now y= 5/4 x
If x =12
y =5/4*12
y = 15
Fifteen students taking a test the state assessment exam forgot their calculator. of the 250 students taking the exam, what percent forgot their calculator ?
Answer:
6%
Step-by-step explanation:
The percentage is the ratio 15/250 converted to a percent. That conversion can be accomplished by multiplying the ratio by 100%. (You can do this without a calculator.)
15/250 × 100% = (1500/250)% = 6%
6% of the students taking the state assessment exam forgot their calculator, as calculated by dividing the number of students who forgot the calculator (15) by the total number of students taking the exam (250) and then multiplying by 100%.
To calculate the percentage of students who forgot their calculator during the state assessment exam, we would use the formula for percentage, which is:
(Number of students who forgot their calculator / Total number of students taking the exam) × 100%
In this case, 15 students forgot their calculator out of a total of 250 students. By plugging these numbers into the formula, we get:
(15 / 250) × 100% = 6%
Therefore, 6% of the students taking the exam forgot their calculator.
Rashad baked a cake that was large enough for each of his friends to eat 1/6 of the cake. How many friends can have a piece of cake?
Answer:
He can have 6 friends eat cake
Step-by-step explanation:
If each friend can eat 1/6 of the cake, we need to find how many friend can have a piece
1/6 * f = 1 cake
Multiply each side by 6
6*1/6 * f = 1 *6
f = 6
He can have 6 friends eat cake
Answer:
6 friends can have a piece of cake.
Step-by-step explanation:
Each friend eats 1/6 of the cake.
There are six 1/6's in a unit.
6 friends can have a piece of cake.
If you have an equation of the form ax2 + c = 0, with a > 0, under what conditions will there be no real solutions?
Answer:
If c>0, then the solution is imaginary, which is not a real solution.
Step-by-step explanation:
ax^2 + c = 0, with a > 0
Subtract c from each side
ax^2 +c-c = 0-c
ax^2 = -c
Divide each side by a
ax^2/a = -c/a
x^2 = -c/a
Take the square root of each side
sqrt(x^2) = sqrt(-c/a)
AAAAAAAH
The only way to have real square roots is for -c/a to be positive.
We know that a>0, so -c >0
-c>0
Divide each side by -1, remembering to flip the inequality
c<0
If c<0 we have real solutions
If c=0 then x=0 which is a real solution
If c>0, then the solution is imaginary, which is not a real solution.
∠A and ∠B are vertical angles. ∠A = 65x − 12 and ∠B = 43x + 10 How many degrees are in ∠A?
Answer:
53 degrees
Step-by-step explanation:
Vertical angles are congruent so...
65x-12=43x+10
22x=22
x=1
Then add it into the equation of ∠A
m∠A= 65(1)-12
65-12
53
Vertical angles ∠A and ∠B are congruent, so their measures are set equal to each other to solve for x. Once x is found, it is substituted back into the expression for ∠A, resulting in a measure of 53 degrees for angle A.
Vertical angles are a pair of non-adjacent angles formed when two lines intersect. Since ∠A and ∠B are vertical angles, they are congruent, which means they have equal measures. We can set up an equation to solve for the variable x using the expressions for ∠A (65x − 12) and ∠B (43x + 10). Once x is found, we can substitute back into either expression to find the measure of ∠A in degrees.
To find the value of x, we set the expressions equal to each other: 65x − 12 = 43x + 10. Solving for x gives us: x = 22/22 = 1.
Now, substitute x back into the expression for ∠A: ∠A = 65(1) − 12 = 53°.
Therefore, ∠A measures 53 degrees.
A postal delivery service charges $3.40 per package and then an additional $0.50 per ounce the package weighs. The function can be modeled by f(x)= 0.5 +3.4. Tom ships 4 packages with the following weights: 2 ounces, 3.5 ounces, 15 ounces, and 21.3 ounces. Write four statements using function notation that evaluate the function given each of these weights. Interpret the results in terms of the context of the function.
The function you're to evaluate is
... f(x) = 0.5x +3.40
Using function notation, the value for x = 2 is ...
... f(2)
For x = 3.5, the value is ...
... f(3.5)
and so on.
To actually evaluate the function, you need to put the value where x is in the function definition and do the arithmetic:
... f(2) = 0.5·2 + 3.40 = 1.00 +3.40 = 4.40
_____
The function gives the charge for a package based on its weight in ounces. The result of evaluating the function for the given weights is that you find the charges for delivery of those packages.
I WILL GIVE THE BRAINLIEST
Answer:
[tex]a=6[/tex], [tex]b=6\sqrt{2}[/tex], [tex]c=2\sqrt{3}[/tex], and [tex]d=6[/tex]
Step-by-step explanation:
Looking at the left triangle, we can solve for [tex]a[/tex] and [tex]c[/tex].
a:
[tex]a[/tex] is to the opposite side of 60° angle, also we know the hypotenuse, [tex]4\sqrt{3}[/tex]. The ratio that relates opposite with hypotenuse is SINE. Thus we can write:
[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(60)=\frac{a}{4\sqrt{3}}\\[/tex]
Cross multiplying and solving for [tex]a[/tex]:
[tex]sin(60)=\frac{a}{4\sqrt{3} }\\a=sin(60)*4\sqrt{3}\\a=\frac{\sqrt{3}}{2}*4\sqrt{3}\\a=\frac{12}{2}=6[/tex]
( we know [tex]sin(60)=\frac{\sqrt{3}}{2}[/tex] and also [tex]\sqrt{a}*\sqrt{a}=a[/tex] )
c:
[tex]c[/tex] is to the adjacent side of 60° angle, also we know the hypotenuse, [tex]4\sqrt{3}[/tex]. The ratio that relates adjacent with hypotenuse is COS. Thus we can write:
[tex]cos(A)=\frac{adjacent}{hypotenuse}\\cos(60)=\frac{c}{4\sqrt{3}}[/tex]
Cross multiplying and solving for [tex]c[/tex]:
[tex]cos(60)=\frac{c}{4\sqrt{3}}\\c=cos(60)*4\sqrt{3}\\c=\frac{1}{2}*4\sqrt{3}\\c=2\sqrt{3}[/tex]
( we know [tex]cos(60)=\frac{1}{2}[/tex] )
Looking at the triangle to the right, we can solve for [tex]b[/tex] and [tex]d[/tex].
b:
[tex]a[/tex] is to the opposite side of 45° angle. We have figured out that [tex]a=6[/tex]. Also we know that [tex]b[/tex] is the hypotenuse.The ratio that relates opposite with hypotenuse is SINE. Thus we can write:
[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(45)=\frac{6}{b}\\b=\frac{6}{sin(45)}\\b=\frac{6}{\frac{1}{\sqrt{2}}}\\b=6*\frac{\sqrt{2}}{1}\\b=6\sqrt{2}[/tex]
( we know [tex]sin(45)=\frac{1}{\sqrt{2}}[/tex] )
d:
To solve for [tex]d[/tex], we can use the pythagorean theorem. Given by:
[tex]a^2+b^2=c^2[/tex]
Where,
[tex]a[/tex] and [tex]b[/tex] are two legs of the right triangle, and [tex]c[/tex] is the hypotenuse (side opposite 90 degree angle)In the triangle on the right, [tex]b[/tex] is the hypotenuse and [tex]a[/tex] and [tex]d[/tex] are the two legs. Using pythagorean theorem and solving for [tex]d[/tex], we get:
[tex]d^2+a^2=b^2\\d^2+(6)^2=(6\sqrt{2})^2\\d^2+36=72\\d^2=72-36\\d^2=36\\d=6[/tex]
( we know that [tex]\sqrt{a}*\sqrt{a}=a[/tex] )
Looking at the answers, 2nd answer choice is right.
Can you help me .....................?
Answer:
11/18
Step-by-step explanation:
The desired probability is the sum of ...
... (probability of choosing a coin) × (p(heads) on that coin)
Since the coins are chosen at random, we assume the probability of choosing a given coin is 1/3. Then ...
... p(heads) = (1/3)·(1/2) + (1/3)·1 + (1/3)·(1/3) = 1/6 + 1/3 + 1/9 = (3 +6 + 2)/18
... p(heads) = 11/18
which equation is best represented by the graph above (x+1)(x-3)(x+2). please explain why
y = (x +2)(x -1)(x -3) . . . . or . . . . y = x³ -2x² -5x +6
Step-by-step explanation:The graph shows y=0 at x=-2, x=1, and x=3. These are called the "zeros" or "roots" of the function, because the value of the function is zero there.
When "a" is a zero of a polynomial function, (x -a) is a factor. This means the factors of the graphed function are (x -(-2)), (x -1) and (x -3). The function can be written as the product of these factors:
... y = (x +2)(x -1)(x -3) . . . . . the equation represented by the graph
Or, the product can be multiplied out
... y = (x +2)(x² -4x +3)
... y = x³ -2x² -5x +6 . . . . . the equation represented by the graph
A recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flour you use. Write a direct variation equation to represent this.
Answer:
A direct variation equation to represent this ; [tex]y = \frac{2}{3}x[/tex]
Step-by-step explanation:
Direct Variation states that a relationship between two variables in which one is a constant multiple of the other one.
In other words, when one of the variable changes then the other changes in proportion to the first.
If b is directly proportional to a, then the equation is in the i.e,
form [tex]b = ka[/tex] where k is the constant of variation.
Let y represents the number of muffins and x represents the amount of flour.
It is given that the number of muffins varies directly with the amount of flour you use.
As per the given statement:
y = 2 dozen corn and x = 3 cups of flour.
Then, by definition of Direct variation;
y = kx
Substitute the given values to find k;
[tex]2 = 3k[/tex]
Divide both sides by 3 we get;
[tex]k = \frac{2}{3}[/tex]
then, equation is, [tex]y = \frac{2}{3}x[/tex]
Therefore, a direct variation equation to represent this situation is; [tex]y = \frac{2}{3}x[/tex]
Huilan is 15 years younger than Thomas. The sum of their ages is 33 . What is Thomas's age?
By using two equations, 'Thomas's age = Huilan's age + 15' and 'Thomas's age + Huilan's age = 33', and substituting Huilan's age, we find that Thomas is 24 years old.
Explanation:
To solve this problem, we use a system of linear equations. Based on the given information, we can create two equations:
Thomas's age = Huilan's age + 15 (because we know Huilan is 15 years younger than Thomas)Thomas's age + Huilan's age = 33 (because we know the sum of their ages is 33)Replacing Huilan's age in the second equation with '(Thomas's age - 15)', we get: Thomas's age + (Thomas's age - 15) = 33
This simplifies to 2 * Thomas's age = 48, meaning Thomas's age = 24 years.
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Josie took a road trip. She drove for 45 minutes at 70 miles per hour. Then she drove for 15 minutes at 20 miles per hour. How far did Josie drive? Round to the nearest mile.
A
3450 miles
B
150 miles
C
90 miles
D
58 miles
Answer:
D . 58 miles
Step-by-step explanation:
In order to find the distance travelled (d) in each stage, we will use the following expression.
d = v × t
where,
v: speed
t: time
First stage
v = 70 mi/h
t = 45 min × (1 h / 60 min) = 0.75 h
d = v × t = 70 mi/h × 0.75 h = 53 mi
Second stage
v = 20 mi/h
t = 15 min × (1 h / 60 min) = 0.25 h
d = v × t = 20 mi/h × 0.25 h = 5.0 mi
The total distance tyraveled is 53 mi + 5.0 mi = 58 mi
Josie drove 52.5 miles for the first part of her trip and 5 miles for the second part, totaling 57.5 miles. After rounding, it is approximately 58 miles, so the answer is D.
To calculate the total distance Josie drove, we need to find the distance for each segment of her journey and then sum them up. For the first part of her trip, she drove for 45 minutes at a speed of 70 miles per hour. Since time needs to be in hours to use the formula distance = speed × time, we convert 45 minutes to hours by dividing by 60, giving us 0.75 hours. So, the distance for the first part is 70 miles/hour × 0.75 hours, which equals 52.5 miles.
For the second part of the trip, Josie drove for 15 minutes at 20 miles per hour. Converting 15 minutes to hours, we get 0.25 hours. Therefore, the distance for the second part is 20 miles/hour × 0.25 hours, giving us 5 miles. To find the total distance, we add the distances from both parts of the trip, resulting in 52.5 miles + 5 miles = 57.5 miles.
After rounding to the nearest mile, the total distance Josie drove was roughly 58 miles.
Therefore, the correct answer is D.
Eva left her home and drove for 4.3 hours due north at a rate of 60 miles per hour. After visiting a beach, she drove due south for 3.4 hours at 55 miles per hour.How far is Eva from her home?
Answer:
15
Step-by-step explanation:
Given: ΔАВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 30° AC = 6 cm. Find: BD
I NEED THIS ANSWER WITH FULL EXPLANATION STATEMENT REASON WOULD BE BEST AS MY TEACHER WANTS STAEMENT REASON PLZZZZZZZ HELP ASAP
Answer:
BD = 9 cm
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. That is, the longest side (hypotenuse) is twice the length of the shortest side.
All of the triangles in your geometry are 30°-60°-90° triangles. AC is the hypotenuse of ΔACD, and the short side of ΔABC.
The short side AD of ΔACD will be half the length of AC, so 3 cm. The hypotenuse AB of ΔABC will be twice the length of AC, so 12 cm. Segment BD is the difference of the lengths AB and AD, so is ...
... BD = AB -AD
... BD = 12 cm - 3 cm = 9 cm
_____
Comment on side length ratios
You can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. Or you can figure the length of the altitude of an equilateral triangle of side length 2 using the Pythagorean theorem.
Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door? Explain using approximations. (Pythagorean Theorem)
No
Step-by-step explanation:The diagonal of the door opening is given by the Pythagorean theorem as ...
... √(96² +42²) = √8820 ≈ 94
Even if the table had zero thickness, it would not fit through the door
To determine if the circular table will fit through Jill's front door, we can use the Pythagorean theorem to compare the diagonal distance of the door to the diameter of the table.
Explanation:To determine if the circular table will fit through Jill's front door, we can use the Pythagorean theorem. Assuming the door is rectangular, we can use the theorem to find the diagonal distance across the door and compare it to the diameter of the table. Let's calculate:
Find the length of the diagonal by using the formula d = sqrt(w^2 + h^2), where w is the width and h is the height of the door. In this case, w = 42 inches and h = 84 inches.Calculate the diagonal distance: d = sqrt(42² + 84²).Compare the diagonal distance to the diameter of the table (96 inches). If the diagonal distance is greater than or equal to the diameter, then the table will fit through the front door. Otherwise, it won't.Let's plug in the values and calculate. If the diagonal distance is greater than or equal to 96 inches, then the table will fit through the front door.
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Jaime wants to know how fast she can type, so she times herself as she types a paper. The paper has 410 words in it, and Jaime types it in 10 minutes. What is her typing rate, in words per minute?
Answer:
41 words per minute
Step-by-step explanation:
You just need to divide words by minutes and that will give you words per minute.
410 words / 10 minutes = 410 / 10 words per minute = 41 words per minute
A factory that manufactures basketballs spends $8 on each basketball that it produces. Which of the following describes the rate of cost growth at the factory? A. neither linear nor nonlinear B. nonlinear C. linear D. both linear and nonlinear
Answer:
C. linear
Step-by-step explanation:
Because they spend $8 to manufacture a basketball every time and stays constant, the rate of cost growth at the factor is linear.
If the factory manufactures basketball spends $8 on each basketball it produces, then the rate of cost growth at the factory will be neither linear nor nonlinear.
Step by Step SolutionStep 1: Find total amount.Let 'x' be the total number of basket ball produced by the factory.
The amount paid for the each ball is $8.
Let 'y' be the total amount spent on the manufacturing of the basketball.
Then,
y = 8x.
Step 2: Calculate the rate growth.As, the total manufacturing cost of the basketball depends upon the total production of the basketball.
Thus, total amount 'y' is the function of 'x'.
Differentiating 'y' with respect to 'x',
[tex]\frac{dy}{dx} =\frac{d(3x)}{dx}[/tex]
[tex]\frac{dy}{dx} =3\frac{dx}{dx} =3[/tex]
As, 3 is the constant value, it means change in the cost with respect to manufacturing of basketball is constant.
Therefore, the rate of cost growth at the factory is neither linear nor nonlinear.
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Find the measure of the numbered angles in each rhombus.
Answer:
∠1 = ∠2 = ∠3 = ∠4 = 28°
Step-by-step explanation:
A rhombus is a parallelogram with congruent sides. As with any parallelogram, the sum of adjacent interior angles is 180°. The figure is symmetrical, so either diagonal is also an angle bisector.
By any of various rules related to parallel lines and/or angle bisectors and/or isosceles trianges, all of the numbered angles are congruent (= α). Each of them is the complement of half the angle measure shown.
... α = (1/2)(180° -124°) = 90° -62° = 28°
The measure of the numbered angles in each rhombus is [tex]28^\circ[/tex] and this can be determined by using the properties of a rhombus.
Given :
A rhombus ABCD whose [tex]\rm \angle C = 124^\circ[/tex].
A rhombus is a quadrilateral whose all the sides are equal, opposite angles are equal, and opposite sides are parallel.
Line BD is the angle bisector and triangle BCD is the isosceles triangle and therefore, all the numbered angles 1, 2, 3, and 4 are equal.
[tex]\angle 1 = \angle 2 = \angle 3 = \angle 4[/tex]
[tex]\angle 1 = \angle 2 = \angle 3 = \angle 4 = \dfrac{1}{2}(180^\circ-124^\circ)[/tex]
[tex]\angle 1 = \angle 2 = \angle 3 = \angle 4 = \dfrac{1}{2}(56^\circ)[/tex]
[tex]\angle 1 = \angle 2 = \angle 3 = \angle 4 = (28^\circ)[/tex]
The measure of the numbered angles in each rhombus is [tex]28^\circ[/tex].
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the ratio for the number of people that use an android phone to the number of people that use an iphone is 4:5 if 56 people in the movie theater use and android phone, how many people would you expect to use an iphone show all work including labels and write a therefore statement
Answer:
70
Step-by-step explanation:
If 56 people correspond to 4 ratio units, then each of those units stands for 56/4 = 14 phone users.
Therefore 5 ratio units stands for 5·14 = 70 phone users.
70 people are expected to be using an iPhone.
In a parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is the ratio of BE:EC?
Answer:
[tex]\frac{BE}{EC} =\frac{1}{3}[/tex]
Step-by-step explanation:
In the diagram below we have
ABCD is a parallelogram. K is the point on diagonal BD, such that
[tex]\frac{BK}{CK} =\frac{1}{4}[/tex]
And AK meets BC at E
now in Δ AKD and Δ BKE
∠AKD =∠BKE ( vertically opposite angles are equal)
since BC ║ AD and BD is transversal
∠ADK = ∠KBE ( alternate interior angles are equal )
By angle angle (AA) similarity theorem
Δ ADK and Δ EBK are similar
so we have
[tex]\frac{AD}{BE} =\frac{DK}{BK}[/tex]
[tex]\frac{AD}{BE} =\frac{4}{1}[/tex]
[tex]\frac{BC}{BE}=\frac{4}{1}[/tex] ( ABCD is parallelogram so AD=BC)
[tex]\frac{BE+EC}{BE}=\frac{4}{1}[/tex] ( BC= BE+EC)
[tex]\frac{BE}{BE} +\frac{EC}{BE}=\frac{4}{1}[/tex]
[tex]1+\frac{EC}{BE}=4[/tex]
[tex]\frac{EC}{BE}=3[/tex] ( subtracting 1 from both side )
[tex]\frac{EC}{BE}=\frac{3}{1}[/tex]
taking reciprocal both side
[tex]\frac{BE}{EC} =\frac{1}{3}[/tex]
Please help and fast
Answer:
216 in squared
Step-by-step explanation:
using the formula, a cube has six sides so 6 squared is 36 times 6 equals to 216
please help me asap!
Answer:
c) G= (4,0)
Step-by-step explanation:
Point A (-5,0) and point E is (7,4)
Point A (-5,0) and point E is (7,4)
A is on x axis so F is also on x axis. So F is (7,0)
AE is divided into 4 equal parts
First we find the distance between A and F. Then divide it by 4
A is (-5,0) and F is (7,0)
Distance = 7 -(-5) = 12
Now divide it by 4 so 12/ 4= 3
We subtract 3 from point F(7,0) to get point G
G= (7-3,0)
G= (4,0)
Solve the linear equation.
8x+32=15(25x−15)−4x
Enter your answer in the box.
x =
Answer:
"x = -5"
Step-by-step explanation:
i took test
For the linear equation, the value of x is 257/363.
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The linear equation is,
⇒ 8x + 32 = 15 (25x - 15) - 4x
Now, Solve the linear equation for value of x.
⇒ 8x + 32 = 15 (25x - 15) - 4x
⇒ 8x + 32 = 375x - 225 - 4x
⇒ 32 + 225 = 375x - 8x - 4x
⇒ 257 = 363x
⇒ x = 257 / 363
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SHOW YOUR WORK
PLZ PLZ PLZ PLZ PLZ
HELP ME ASAP I NEED HELP!!!
Without loss of generosity, let x equal the number of sandwiches bought and y be the number of bottles of water bought. Since Eric bought 9 items,
x+y=9.
Also,
5x+2y=30.
This is because 5 is the price for the sandwiches and 2 is the price for the bottle of water.
Answer:
x + y = 95x +2y = 30Step-by-step explanation:
You are given two bits of information that relate to the numbers of items:
the total number of items purchasedthe total cost of items purchasedThese two relations let you write two equations in the two unknowns, one for each relation.
Of course, the total cost is the cost of each multiplied by the number purchased. The variables are defined as the number purchased.
_____
Though the question doesn't ask for it, the solution can be found by elimination. Subtract twice the first equation from the second:
... (5x +2y) -2(x +y) = (30) -2(9)
... 3x = 12 . . . . . simplify
... x = 4 . . . . . . . divide by 3
... 4 + y = 9 . . . . substitute the value of x into the first equation
... y = 5 . . . . . . . subtract 4
The solution is (x, y) = (4, 5).
The mass of a sewing needle is 0.585 gram.Round the mass to the nearest hundredth of a gram.
Solve. 3(3x+10)=50−x
Answer:
x=2
Step-by-step explanation:
3(3x+10)=50−x
The first step is to distribute the 3
3*3x + 3*10 = 50-x
9x+30 = 50-x
Add x to each side
9x+x+30 = 50-x+x
10x+30 = 50
Subtract 30 from each side
10x+30-30 = 50-30
10x= 20
Divide each side by 10
10x/10=20/10
x =2
Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not?
a)Yes, they both partition the segment into a 1:3 ratio.
b)Yes, they are both the distance from one endpoint to the other.
c)No, P is the distance from A to B, and Q is the distance from B to A.
d)No, Q is closer to A and P is closer to B.
Answer:
c)No, P is the distance from A to B, and Q is the distance from B to A.
Step-by-step explanation:
Point P partitions the directed segment from A to B into a 1:3 ratio.
Ratio is 1:3
So AP is 1 and PB is 3
Q partitions the directed segment from B to A into a 1:3 ratio.
Ratio is 1:3
So BQ is 1 and QA is 3.
That is AQ= 3 and BQ= 1
The ratio of Q and P varies
AP =1 and AQ=3
So P and Q are not at the same point.
Because P is the distance from A to B and Q is the distance from B to A
Answer:
c
Step-by-step explanation:
bc
a candy factory made 54 boxes of chocolate each box weigh 2 pounds they pack the boxes and 6 cases with the same number of vodkas in each how many pounds of chocolate were in each case
Answer:
18 pounds of chocolate
Step-by-step explanation:
54 boxes divided among 6 cases means each case held 54/6 = 9 boxes.
Each box weighs 2 pounds, so 9 boxes (in 1 case) weigh 9·2 = 18 pounds.
Mr. black class has a female student to male student ratio of 3:2. If Mr. Black's class has 18 girls, how many boys does he have? explain in writing how you determined your answer.
Answer:
12
Step-by-step explanation: Well if you do 18 divided by 3 you will get 6 now take that 6 multiply it by 2 and you will get you answer 12.
Which point on the unit circle corresponds to -(π/6)?
Answer:
The point [tex](\frac{\sqrt{3}}{2},-\frac{1}{2})[/tex]
Step-by-step explanation:
I added a graphic to the explanation.
Given the unit circle (the circle with radius equal to 1 unit centered at the point (0,0) ) we can represent its points only with an angle.
The point [tex]-(\frac{\pi}{6})[/tex] corresponds to the point that forms an angle of -30° respect to the positive axis-x (we measure the positive angles counterclockwise respect to the positive x-axis and the negative angles clockwise) because [tex]-(\frac{\pi}{6})[/tex] it is in radians and 180° = π radians ⇒
-(π/6) = - (180°/6) = - 30°
Given that we identify the point on the graph, we can find it coordinates using sine and cosine function :
[tex]sin(-30)=\frac{y1}{1} \\y1=-0.5=-\frac{1}{2}[/tex]
[tex]cos(-30)=\frac{x1}{1} \\x1=\frac{\sqrt{3}}{2}[/tex]
It is important to note that the hypotenuse of the right triangle which we used to apply sine and cosine is equal to 1 because is the radius of the unit circle.
The coordinates of the point are [tex](x1,y1)=(\frac{\sqrt{3}}{2},-\frac{1}{2})[/tex]
The point on the unit circle has the coordinates (√3/2, -1/2)
Which point on the unit circle corresponds to the given angle?For a given angle a in an unit circle, the rectangular coordiantes of the point located in the circle are:
x = cos(a)
y = sin(a)
Here the angle is -(π/6), using the above relations, we will get the rectangular coordinates:
x = cos(-(π/6))
y = sin(-(π/6))
Simplify that:
x = √3/2
y = -1/2
The point is (√3/2, -1/2)
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Which pairs of triangles can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of triangles.
Answer:
Congruent; Not Congruent; Congruent; Not Congruent; Not Congruent; Congruent
Step-by-step explanation:
We will use the distance formula to find the length of each segment:
[tex]AB=\sqrt{(-4--3)^2+(4-2)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\BC=\sqrt{(-3--1)^2+(4-1)^2}=\sqrt{(-2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\AC=\sqrt{(2-1)^2+(-4--1)^2}=\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
In order for ABC to be congruent to DEF, AB must be congruent to DE, BC must be congruent to EF, and AC must be congruent to DF:
[tex]DE=\sqrt{(4-3)^2+(-2--4)^2}=\sqrt{(1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\EF=\sqrt{(3-1)^2+(-4--1)^2}=\sqrt{(2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}\\\\DF=\sqrt{(4-1)^2+(-2--1)^2}=\sqrt{(3)^2+(-1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
Since AB is congruent to DE, BC is congruent to EF and AC is congruent to DF, the two triangles are congruent.
In order for ABC to be congruent to JKL, AB must be congruent to JK, BC must be congruent to KL, and AC must be congruent to JL. We know the measurements of AB, BC and AC;
[tex]JK=\sqrt{(-4--2)^2+(-1--3)^2}=\sqrt{(-2)^2+(2)^2}=\sqrt{4+4}=\sqrt{8}\\\\KL=\sqrt{(-2--1)^2+(-3-0)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}\\\\JL=\sqrt{(-1--4)^2+(0--1)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
While AC is congruent to JL, the other two corresponding pairs of sides are not congruent. Therefore the triangles are not congruent.
In order for ABC to be congruent to QRS, AB must be congruent to QR, BC must be congruent to RS, and AC must be congruent to QS. We know the measurements of AB, BC and AC;
[tex]QR=\sqrt{(3-4)^2+(3-1)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\RS=\sqrt{(3-1)^2+(3-0)^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\QS=\sqrt{(4-1)^2+(1-0)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}[/tex]
Since AB is congruent to QR, BC is congruent to RS, and AC is congruent to QS, this means that the two triangles are congruent.
Since ABC is congruent to DEF, and ABC is not congruent to JKL, this means that triangle DEF is not congruent to triangle JKL.
Since ABC is congruent to QRS, and QRS is not congruent to JKL, this means that triangle QRS is not congruent to JKL.
Since ABC is congruent to DEF and ABC is congruent to QRS, this means that DEF is congruent to QRS by the transitive property.