Write “$4,915 for 72 shares of stock” as a unit rate. Round to the nearest hundredth if necessary.
divide
4915/72 = 68.2638
so $68.26 per stock is the unit rate
Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
Determine the standard variation of the data below. (1, 2, 3, 4, 5)
Answer:
So basically sqrt of 2...
Step-by-step explanation:
The sum of the digits of a certain number is 12. When you reverse its digits you decrease the number by 36. Find the number
x+y=12
x*y =36
8+4=12, so make the digits 84, reverse to make it 48
84-48=36
the numbers are 8 & 4
A farmer had 17 sheep. all but 9 died. how many live sheep were left
70 decreased by twice a number
Use The variable n to represent the unknown number
The required expression of the given statement is 70-2n.
Given that,
To determine the expression for the given statement 70 decreased by twice a number.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the number be n,
According to the question,
Number = n
70 decreased by twice the number,
So
= 70 - 2n
Thus, the required expression of the given statement is 70-2n.
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For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Let
x-------> the pressure in PSI
y------> the volume of the gas in cubic inches
In this problem we have the point [tex](30,600)[/tex]
so
[tex]x=30\ psi\\y=600\ in^{3}[/tex]
Find the constant k
[tex]y*x=k[/tex]
substitute the values of x and y
[tex]600*30=k[/tex]
[tex]k=18,000\ lb*in[/tex]
the equation is
[tex]y=18,000/x[/tex]
therefore
the answer is
[tex]y=18,000/x[/tex]
Answer:
[tex]y=\frac{18000}{x}[/tex]
Step-by-step explanation:
Let the volume of gas be y
Let the pressure be x
Since we are given that the volume of the gas is inversely proportional to its pressure.
⇒[tex]y \propto \frac{1}{x}[/tex]
Let the proportionality be k
So, [tex]y=\frac{k}{x}[/tex] ---A
Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches
So, substitute x = 30
y = 600
[tex]600=\frac{k}{30}[/tex]
[tex]600 \times 30=k[/tex]
[tex]18000 =k[/tex]
Substitute the value of k in A
So, [tex]y=\frac{18000}{x}[/tex]
Hence function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is [tex]y=\frac{18000}{x}[/tex]
Identify a semicircle that contains C.
A.ABC
B.AC
C.CB
D. ACB
Answer: The correct option is (D). ACB.
Step-by-step explanation: We are given to identify a semi-circle that contains the point 'C'.
As shown in the figure, AB is the diameter of the circle with center 'O'.
So, there are two congruent semi-circles made by the diameter AB.
The point 'C' lies on the upper semi-circle made by the diameter AB.
Since the upper semi-circle contains the point 'C', so it is named as the semi-circle ACB.
Thus, the semi-circle ACB contains the point 'C'.
Option (D) is correct.
What is the value of 64? 60 = 1 61 = 6 62 = 36 63 = 216
State the Midpoint formula?
How are the midpoint formula and the Distance formula alike? How are they different?
Give a real-world example that could be addressed using the distance formula.
Give a real-world example that could be addressed using the midpoint formula.
Find the value of angle M
opposite angels = 180
so 6m+13 +4m+7 =180
combine like terms
10m+20=180
10m =160
m=160/10 = 16
Angle M = 6m = 6(16) = 96 degrees
Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
HELPPP Plzzzzzzzzzz ASAP
Use Addition of Composite Figures to find the total shaded regions.
1) Find the shaded area. Round your answer to the nearest tenth, if necessary.
Solve for 4/x+2 = 2/x x and determine if the solution is extraneous or not.
x = −2, extraneous
x = −2, non-extraneous
x = 2, extraneous
x = 2, non-extraneous
The given equation is:
4/(x + 2) = 2/x
First we get the value of x by doing cross multiplication so that all variables are in the numerator side:
4 x = 2 (x + 2)
4 x = 2 x + 4
2 x = 4
x = 2
An extraneous solution is one in which if we plug in the value of x back into the equation, the resulting values would be wrong.
Plug x = 2 back into the original equation:
4 / (2 + 2) = 2 / 2
4 / 4 = 2 / 2
1 = 1 (TRUE!)
Since the value of x = 2 satisfies the equation, then the solution is non-extraneous.
Answer:
x = 2, non-extraneous
The sum of three consecutive odd integers is 18 less than 5 times the middle number. Find the 3 integers. Use an algebraic solution
X +(x+2) + (x+4) = 5(x+2)-18
3x+6 = 5x+10-18
3x+6 = 5x-8
3x=5x-14
-2x=-14
x=7
(x+2) =9
(x+4) =11
7 + 9+ 11 =27
5(9)-18 =45-18 =27
3 numbers are 7, 9 & 11
Solve the equation: h/9 = 7. A. h = 1 2/7 B. h = 63 C. h = –63 D. h = 7/9
Ryan spent $3.25 on lunch every day, Monday through Friday. If he had $20 at the start of the week, how much money will he have left after Friday?
The amount of money left after Friday is $3.75.
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
According to the given question.
Amount of money spent for the lunch every day is $3.25.
Total amount of money Ryan have is $20.
Now, number of total days from Monday to Friday is 5.
So,
The amount spent for lunch for 5 days by Ryan
= 5 × $ 3.25 = $16.25 (by unitary method)
Therefore,
The amount of money left after Friday
[tex]\$20 - \$16.25\\= \$3.75[/tex]
Hence, the amount of money left after Friday is $3.75.
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30 POINTS!!!!!!!
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 99m long and 72m wide.
Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
1273 hola aaaaa oigan busco novia
In triangle PQR, C is the centroid.
A. If CY = 10, find PC and PY
B. If QC = 10, find ZC and ZQ
C. If PX = 20, find PQ
Because point C is the centroid of the triangle, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:
PC = 20
PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:
ZC = 5
ZQ = 15
C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:
PQ = 40
How do you get rid of an exponent on a variable?
To get rid of an exponent on a variable, apply the inverse operation of the exponent such as division or root operations.
Explanation:To get rid of an exponent on a variable, you need to apply the inverse operation of the exponent. If the exponent is multiplication, you use division, and if the exponent is an exponentiation, you use a root operation. For example, to get rid of a squared variable, you take the square root of the variable. If you have a variable raised to the third power, you take the cube root of the variable.
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What is the missing step in this proof?
The missing step in the proof is;
Statement: ∠1 ≅ ∠4 and ∠3 ≅ ∠5Reason: Alternate interior angle theorem.The correct answer choice is option C.
What is alternate interior angles theorem?Alternate angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior or exterior angles are congruent.
It is used to prove that alternate interior angles are equal if two parallel lines are cut by a transversal,
Hence, angle 1 is congruent to angle 4 and angle 3 is congruent to angle 5.
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Use the following graph of the function f(x) = 2x^3 + x^2 - 3x + 1
What is the average rate of change from x = -1 to x = 1
A) -1
B) 1
C) 2
D) 4
Which is a sum of cubes? a3 + 18 a6 + 9 a9 + 16 a12 + 8
a3 + 18
a6 + 9
a9 + 16
a12 + 8
Answer: [tex]a^{12}+8[/tex]
Step-by-step explanation:
let's check all the expressions
1. [tex]a^3+18[/tex]
here 18 is not a perfect cube.
2. [tex]a^6+9[/tex]
here 9 is not a perfect cube.
3.[tex]a^9+16[/tex]
here 16 is not a perfect cube.
4.[tex]a^{12}+8[/tex]
here 8 is a perfect cube, thus we can write above expression by using laws of exponents as
[tex](a^4)^3+2^3[/tex]
Thus, [tex]a^{12}+8[/tex] is a sum of cubes.
a line perpendicular to a plane, would intersect the plane at one what
A line perpendicular to a plane, would intersect the plane at one point.
Perpendicular linesWhen a line is perpendicular directly away from the plane, the line will tend to intersect the plane at one points or single points.
The reason why the line intersect the plane is because the line cannot point to other places except directly away from the plane.
Therefore a line perpendicular to a plane, would intersect the plane at one point.
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a triangle has two sides of the lengths 8 and 10 what value could the length of the third side be
Given that WXYZ is a rhombus, find the value of x. A. 15 B. 20 C. 30 D. 45
In this problem, we are given the equations of the two sides of a rhombus.
Equation 1 is 4 x – 10
Equation 2 is 2 x + 20
Since the given shape is a rhombus, therefore the two sides have equal sides. Hence, we can simply equate equation 1 and equation 2:
4 x – 10 = 2 x + 20
2 x = 30
x = 15
Therefore the answer is:
A. 15
4 x – 10 = 2 x + 20
2 x = 30
x = 15
An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.
To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula: inradius = (area of the triangle) / (semiperimeter of the triangle). First, we need to find the area and semiperimeter of the triangle. Then, we can calculate the inradius and find the radius of the circle.
Explanation:To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula:
inradius = (area of the triangle) / (semiperimeter of the triangle)
First, we need to find the area of the triangle. Since it is an isosceles triangle with equal sides of 5 inches, we can split it into two congruent right triangles. The height of each right triangle can be found using the Pythagorean theorem:
height = sqrt(5^2 - (6/2)^2) = sqrt(25 - 9) = sqrt(16) = 4 inches
Now, we can find the area of the triangle:
area = (1/2) * base * height = (1/2) * 6 * 4 = 12 square inches
Next, we need to find the semiperimeter of the triangle:
semiperimeter = (5 + 5 + 6) / 2 = 16 inches
Finally, we can calculate the inradius:
inradius = 12 / 16 = 3/4 inches
Therefore, the radius of the circle is 3/4 inches.
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If measure B= 60 degrees and a = 10 meters, find b.
Answer: A. 17.32m
Step-by-step explanation:
Just took edge test
Answer:A
Step-by-step explanation:
If the solution to 4 - 2x > x + 16 is x < a, what is the value of a?
A) 6
B) 4
C) 2
D) -4
E) -6
In which case would it be best to use the “Factoring Method” to solve the trinomial equation?
x^2 + 4x = -5
4.3x^2 + 2.4x - 3 = 0
x^2 - 4x + 3 = 0