Answers
Related Questions
Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length. What is the height of the pennant? Recall the formula A = 1/2bh.
A.) 12 inches
B.) 15 inches
C.) 30 inches
D.) 36 inches
Answers
A = 180
b = z
h = 2z + 6
180 = 1/2 * z * 2z + 6
180 = (2z^2 + 6z)/ 2
180 = z^2 + 3z)
z^2 + 3z - 180 = 0
(z - 12)(z + 15) = 0
z - 12 = 0
z = 12
z + 15 = 0
z = -15....not this one because it is negative
h = 2z + 6
h = 2(12) + 6
h = 24 + 6
h = 30 inches <====
In which the area = 180 square inches.
You can therefore make this formula:
180 = [2(2z+6)+6](2z+6) / 2
Now solve for z.
360 = [2(2z+6)+6](2z+6)
360 = (4z+12+6)(2z+6)
360 = (4z+18)(2z+6)
360 = 8z^2 + 24z + 36z + 108
360 = 8z^2 + 60z + 108
0 = 8z^2 + 60z - 252
Now we will use quadratic formula to get z = 3, -21/2
Substitute in now
2(2z+6) + 6
2(2(3)+6) + 6
2(6+6) + 6
2(12) + 6
24 + 6
30
or... (false)
2[2(-10.5)+6]+6
2(-21+6)+6
2(-15) + 6
-30 + 6
-24
Therefore, the height is 30 inches. I made some work errors but it is still true because of the property ab = ba
Identify the factors of x2 − 4x − 12. (1 point)
(x + 4)(x − 3)
(x − 4)(x + 3)
(x − 2)(x + 6)
(x + 2)(x − 6)
Answers
x² + 2x - 6x - 12 =
x(x + 2) - 6(x + 2) =
(x + 2)(x - 6)
Answer:
D. [tex](x-6)(x+2)[/tex]
Step-by-step explanation:
We have been given a polynomial [tex]x^2-4x-12[/tex]. We are asked to find the factors of our given polynomial.
We will use splitting the middle term format of factoring quadratic polynomial.
We need two numbers, whose product is [tex]-12[/tex] and whose sum is [tex]-4[/tex]. Such two numbers are [tex]-6\text{ and }2[/tex].
[tex]x^2-6x+2x-12[/tex]
[tex](x^2-6x)+(2x-12)[/tex]
Factor out GCF of each group:
[tex]x(x-6)+2(x-6)[/tex]
[tex](x-6)(x+2)[/tex]
Therefore, factors of our given expression are [tex](x-6)(x+2)[/tex] and option D is the correct choice.
Assume that you randomly select 6 cards from a deck of 52. what is the probability that all of the cards selected are hearts?
Answers
You can think about it like this:
P = (13/52)*(12/51)*(11/50)*(10/49)*(9/48)*(8/47) = 0.00008428903476
Can anyone help!? Points are high!
Answers
total was 49.10
mileage would be 49.10 = 2.10x +5.00
total miles =
49.10 = 2.10 +5.00
44.10 = 2.10x
x = 44.10/2.10 = 21 miles
Find the volume of the cylinder shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer: Volume of cylinder is 1846.32 cubic yd.
Step-by-step explanation:
Since we have given that
Height of a cylinder = 12 yard
Radius of a cylinder = 7 yard
As we know the formula of "Volume of cylinder":
[tex]Volume=\pi r^2h\\\\Volume=3.14\times 7\times 7\times 12\\\\Volume=1846.32\ yd^3[/tex]
Hence, Volume of cylinder is 1846.32 cubic yd.
Answer:
1846.32 cubic yards
Step-by-step explanation:
You make both rocking chairs and bar stools. You charge $100 for every rocking chair and $40 for every bar stool. Which expression represents your income if you sell r rocking chairs and b bar stools?
Answers
You have to multiply $100 per rocking chair and add it to $40 per bar stool to get our income.
Answer:
The answer is [tex]Income=100*r+40*b[/tex]
Step-by-step explanation:
In this case we have to construct an expression that describe the income of selling the rocking chairs ($100 each - r) and the bar stool ($40 each - b), so the total income will depend on the addition of this two variables multiplied by its individual price, this is:
[tex]Income=100*r+40*b[/tex]
The answer is [tex]Income=100*r+40*b[/tex]
In triangle ABC, m∠A=55 triangle ABC, m∠A=55°, c=11c=11, and m∠B=19m∠B=19°. Find the perimeter of the triangle
Answers
Since a triangle has a total of 180° in interior angles, then angle C can be solved by
180° = A + B + C
C = 180° - 55° - 19°
C = 106°
Next, we use the Law of Sines. This law can be used in any type of triangle. This law states that there is a fixed ratio of side to sine of the opposite angle. In equation, that would be written as
a/sin A = b/sin B = c/sin C
Since, we know already side c and angle C, the fixed ratio is then,
11/sin 106° = 11.443
The last step is to apply ratio and proportion:
11.433 = a/sin 55°
a = 9.37 units
11.433 = b/sin 19°
b = 3.73 units
Thus, the perimeter of the triangle is
P = a + b + c
P = 9.37 +3.73 +11
P = 24.1 units
Please help!!! Geometry.
Answers
make sure your calculator is in Degree mode.
Given the arithmetic sequence an = −1 + 7(n − 1), what is the domain for n?
All integers
All integers where n ≥ 0
All integers where n ≥ 1
All integers where n > 1
Answers
The domain for n in the arithmetic sequence is all integers where n ≥ 1.
Explanation:The domain for n in the arithmetic sequence is all integers where n ≥ 1. In this sequence, the value of n represents the position of the term in the sequence. Since the first term of the sequence is represented by n=1, n can't be less than 1 because there is no zeroth term in the sequence. Therefore, the domain for n is all integers where n ≥ 1.
A piece of rope 94.2 inches long will enclose a circular child’s wading pool. What is the diameter of the pool?
Answers
The sine function is an odd function
Answers
Example: sin (- 30°) = - sin (30°) = -1/2
Answer:
The given statement is true.
Step-by-step explanation:
We have been given a statement and we are supposed to determine whether our given statement is even or odd.
Statement: The sine function is an odd function.
We know that sine is symmetric about origin and [tex]\text{sin}(-x)=-\text{sin}(x)[/tex]. Therefore, sine is an odd function and our given statement is true.
Which best explains if quadrilateral WXYZ can be a parallelogram?
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.
WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.
WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.
Answers
"WXYZ can be a parallelogram with one pair of sides measuring 15mm and the other pair measuring 9mm"
To find this, you first have to solve for x. Assuming WXYZ is a parallelogram, then the side (x + 8) must equal 15, which means we can subtract 8 and get x as 7.
Now we substitute 7 into the other side's, (7 + 2) = 9mm, and (7 × 2) - 5 = 14 - 5 = 9mm.
I hope this helps!
If quadrilateral WXYZ is a parallelogram, the opposite sides will be equal, in length from which the value of x will satisfy the two equations.
Response:
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.How can the option that best indicates if WXYZ can be a parallelogram be obtained?Properties of a parallelogram
The length of the opposite sides of a parallelogram are equal, which gives;
2·x - 5 = x + 2
2·x - x = 2 + 5
x = 7Similarly, we have;
x + 8 = 15
x = 15 - 8 = 7
The lengths of the opposite sides are therefore;
2·x - 5 = 2 × 7 - 5 = 9 and x + 8 = 15
The option that indicates if WXYZ is a parallelogram is therefore;
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.Learn more about parallelograms here;
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What is the quotient and remainder when x2 + x − 12 is divided by x − 2?
Answers
Factor: x - 2;
We equate this factor to zero to be able to find the value of x. That is,
x - 2= 0;
x = 2
Substitute 2 to the x's of the quadratic equation.
R = (2)² + 2 - 12 = -6
ANSWER: Remainder = -6
A cube has side lengths of 8 inches. What is the volume of the cube
Answers
V=a³
V=512 in³
a=Edge
A 7.5 kg block is placed on a table. If it's bottom surface area is 0.6m2, how much pressure does the block exert on the tabletop?
Answers
Pressure = Force / Area
Force = Mass * Gravity = 7.5 kg * 9.81 m/s² = 73.575 N
P = 73.575 N / 0.6 m² = 122.625 N/m² = 122.625 Pa
Answer: The block exerts the pressure of 122.625 N/m² or 122.625 Pa.
Final answer:
The pressure exerted by a 7.5 kg block on a tabletop is calculated as the force due to its weight divided by the surface area. This results in a pressure of 122.5 Pascals (Pa).
Explanation:
The pressure exerted by an object on a surface is calculated by dividing the force it applies, which is its weight (a result of gravity), by the area over which the force is distributed. In this case, to find the pressure exerted by a 7.5 kg block on a tabletop with a bottom surface area of 0.6m2, we use the formula for pressure (P), which is P = Force (F) / Area (A).
To calculate the force, we need to know that the weight of the block is the product of its mass (m) and the acceleration due to gravity (g), where g is approximately 9.8 m/s2. So, the weight (F) is:
F = m × g = 7.5 kg × 9.8 m/s2 = 73.5 N
To calculate pressure (P), we then divide the force by the area:
P = F / A = 73.5 N / 0.6 m2 = 122.5 Pa
Therefore, the pressure exerted by the block on the tabletop is 122.5 Pascals (Pa).
ILL GIVE BRAINLIEST !!!1 A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
Step 1: m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle)
Step 2: m∠w − m∠z = 90 degrees (corresponding angles)
Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z
Step 4: So, m∠x + m∠y = m∠w
In which step did the student first make a mistake and how can it be corrected?
Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of corresponding angles)
Step 2; it should be m∠w + m∠z = 180 degrees (supplementary angles)
Step 1; it should be m∠x + m∠y + m∠z = 90 degrees (corresponding angles)
Step 2; it should be m∠w + m∠z = 90 degrees (alternate exterior angle)
Answers
What is 180 as product of prime factors and 180 as a Square root?
Answers
90 = 2*45
45 = 3*15
15 = 3*5
The prime factors are 2, 2, 3, 3, 5
Alternatively, you can draw up a factor tree like what you see in the attached image. The prime numbers are in the red boxes.
Either way, the prime factorization is
180 = 2*2*3*3*5
which can be written as
180 = 2^2*3^2*5
---------------------------------------------------------------------------
As for your second question, are you looking to simplify the square root of 180? If so, then follow these steps
sqrt(180) = sqrt(2*2*3*3*5)
sqrt(180) = sqrt(2^2*3^2*5)
sqrt(180) = sqrt((2*3)^2*5)
sqrt(180) = sqrt((2*3)^2)*sqrt(5)
sqrt(180) = 2*3*sqrt(5)
sqrt(180) = 6*sqrt(5)
sqrt stands for "square root"
what is .00463 in fraction form
Answers
After the decimal point starts the negative powers of ten in those columns...
. 10^-1, 10^-2, 10^-3, 10^-4, 10^-5
1/10s, 1/100s, 1/1000s, 1/10,000s, 1/100,000s
so .00463 is equal to
463/100000
What are the two equations that need to be solved to find the solutions for the absolute value equation |2x-3|=x+6?
2x – 3 = x + 6 and 2x – 3 = –x – 6
2x – 3 = x + 6 and 2x + 3 = –x + 6
2x – 3 = x + 6 and 2x – 3 = x – 6
2x – 3 = x + 6 and 2x + 3 = x + 6
Answers
The equations to solve for [tex]\( |2x-3|=x+6 \)[/tex] are [tex]\( 2x - 3 = x + 6 \)[/tex] and [tex]\( 2x - 3 = -(x + 6) \).[/tex]
Let's solve the absolute value equation |2x-3|=x+6 step by step.
We'll start by writing down the equation:
|2x - 3| = x + 6
Since the absolute value expression |2x - 3| can be either positive or negative, we'll split the equation into two cases:
Case 1: 2x - 3 = x + 6
Case 2: 2x - 3 = -(x + 6)
Let's solve Case 1:
2x - 3 = x + 6
Subtract x from both sides:
2x - x - 3 = 6
Simplify:
x - 3 = 6
Add 3 to both sides:
x = 9
Now, let's solve Case 2:
2x - 3 = -(x + 6)
Distribute the negative sign:
2x - 3 = -x - 6
Add x to both sides:
2x + x - 3 = -6
Simplify:
3x - 3 = -6
Add 3 to both sides:
3x = -3
Divide both sides by 3:
x = -1
So, the solutions to the equation |2x-3|=x+6 are x = 9 and x = -1.
(05.01)
Which statement best explains if the graph correctly represents the proportional relationship y = −2x?
No, the points shown would not be part of y = −2x
No, proportions cannot be represented on a graph
Yes, all proportions can be shown on a graph of this line
Yes, the points shown on the line would be part of y = −2x
Answers
So yes, the points shown on the line would be a part of y=-2x
The best statement which is true for the graph y=-2x is that Yes, the points shown on the line would be a part of y=-2x.
What is line?A line is collection of various points on a surface which together joins two points on a surface. Equation of a line looks like y=a +b x where b is the slope of line.
How to make graph?We have been given an equation y=-2x and we have to find the graph of equation and for that we need to find points and for this we have to put the values of x which gives the values of y.
At x=0 ,y=0
At x=1 ,y=-2*1=-2
At x=2 ,y=-2*2=-4
At x=-1 ,y=-2*-1=2
Coordinates will be (0,0),(1,-2),(2,-4),(-1,2)
If we find these points on this line then will surely be able to find these points.
Hence the statement which is true is that Yes, the points shown on the line would be part of y = −2x.
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the ratio of boys to girls are 8 to 7. if there was a total of 195 students, how many boys and girls are there?
Answers
8+7= 15
Boys: 195/15= 13(8)=104
Girls: 195/15= 13(7)= 91
There are 104 boys and 91 girls. Hope this helps!
P(A∩B)=1150,P(A|B)=1120,P(B)=?
Answers
For the given probabilities P(A∩B) = 1150 and P(A|B) = 1120, using Bayes' theorem for conditional probability, the probability of event B, P(B), is found to be approximately 1.027.
Explanation:The topic of this question is probability, specifically concurrent events in probability theory. Here, we use Bayes' theorem for conditional probability which states that P(A|B) = P(A ∩ B) / P(B).
Given that P(A∩B) = 1150 and P(A|B) = 1120, we can plug these values into the formula to find P(B). Hence, P(B) = P(A ∩ B) / P(A|B), substituting the given numbers, we get P(B) = 1150 / 1120 = 1.027 approximately.
So P(B), the probability of event B occurring, we would expect to be approximately 1.027 (or 102.7% assuming the probabilities were in decimal form to start with).
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Alright, let's solve the problem with these given values.
The formula for calculating the probability of B in the context of A and B both happening is:
`P(A and B) / P(A|B)`.
In this case, the probability of A and B occurring is 1150, while the likelihood of A given that B has occurred is 1120. We can substitute these values into the formula:
So, P(B) = P(A and B) / P(A|B)
Substitute the given into the formula:
P(B) = 1150 / 1120 = 1.0267857142857142
Therefore, the Probability of event B (P(B)) is approximately 1.027 when rounded to three decimal places.
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What is the slope of the line whose equation is 3x-5y=10?
Answers
m=slope
3x-5y=10
minus 3x from both sides
-5y=-3x+10
divide both sides by -5
y=-3/-5x+10/-5
y=3/5x-2
the slope is 3/5
Marion is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 18 km/h. After four hours, the velocity of the cyclist is 4 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points) Part B: How can you graph the equations obtained in Part A for the first 8 hours? (5 points)
Answers
v(t) = a + bt
where
v = velocity (km/h) at time t (hours),
a and b are constants.
When t = 2 hours, v = 18 km/h, therefore
a + 2b = 18 (1)
When t = 4 hours, v = 4 km/h, therefore
a + 4b = 4 (2)
Subtract (1) from (2) to obtain
a + 4b - (a + 2b) = 4 - 18
2b = -14
b = -7
From (1), obtain
a = 18 - 2b = 18 - 2*(-7) = 32
Part A.
The equation is
v = 32 - 7t
Part B
To graph the equation for the first 8 hours, create a table as shown below.
t, hours: 0 1 2 3 4 5 6 7 8
v, km/h: 32 25 18 11 4 -3 -10 -17 -24
We can see from the table that the velocity becomes negative between t=4 and t=5. Therefore, we shall change all negative velocities to zero, and assume that the cyclist comes to rest.
TNote that when the velocity is zero,
32 - 7t = 0
7t = 32
t = 4.57
The new table becomes
t: 0 1 2 3 4 4.57 5 6 7 8
v: 32 25 18 11 4 0 0 0 0 0
The graph is shown below.
Which number is irrational, an integer, and a real number?
A)there are no such numbers
B) 0
C) sq root of 4
D) -4/2
Answers
Integers are rational numbers, so there can't be a number that is irrational and integer at the same time.
Answer:
Option A is the correct answer.
Step-by-step explanation:
An Irrational Number is a real number that cannot be written as a simple fraction. All the integers can be written as a simple fraction. So an integer is not an Irrational Number. So there is no number is irrational, an integer, and a real number.
Option A is the correct answer.
Given the following geometric sequence, find the common ratio. {0.1,-0.9,8.1,...}
Answers
-0.9/0.1=8.1/-0.9=-9
The common ration is negative 9.
Answer:
Common ratio, r = -9
Step-by-step explanation:
If we have geometric progression, the common ratio is the ratio of (n+1)th term and nth term.
Here geometric progression is
0.1,-0.9,8.1,.................
Common ratio
[tex]r=\frac{-0.9}{0.1}=-9\\\\r=\frac{8.1}{-0.9}=-9[/tex]
Common ratio, r = -9
the question is.......... ASAP
Answers
The population of snakes at a wildlife park over the course of six months is modeled by the equation y = x5 − 5x4 + 2x3 − 10x2 + 100x + 5, where x is the number of months. If the park officials count 505 snakes, how many months have passed since the initial count was taken?
Answers
505 = x5 − 5x4 + 2x3 − 10x2 + 100x + 5
x = 5 months
This must be true because it is within the specified time bracket of 6 months.
Ten children are to be divided into an a team and a b team of 5 each. the a team will play in one league and the b team in another. how many different divisions are possible?
Answers
n = size of the selection
r = number of items being picked
In the case of the question, there is a selection of 10 people of which 5 will be chosen to be in team a so:
n = 10
r = 5
The number of combinations is 10C5 = 252
This means there are 252 possible different a teams that could be made from the 10 people.
Team b will be another of the 252 combinations.
Note: scientific calculators, e.g. Casio ones, have a button for the nCr formula.
Find the congruence transformation that maps ∆ABC to ∆A’B’C’. Explain your reasoning
Answers
-So your answer to this question would be that only a Reflection over the y-axis will allow the two shapes to map over each other correctly.