Which is the best description for the graph of a > 4?
O A vertical dotted line at (4,0) with the shading to the right of the line.
O A vertical solid line at (4,0) with the shading to the right of the line.
A vertical dotted line at (4,0) with the shading to the left of the line.
A vertical solid line at (4,0) with the shading to the left of the line.
Answers
Note that the best description for the graph is a > 4 is "A vertical solid line at (4,0) with the shading to the right of the line." (Option B)
What is the rationale for the above answer?Note that the inequality means that a is greater than 4. This means that the end value 4 is not included.
To graph the inequality " > " a dashed line is used. The inequality does not contain any y - value in it.
Hence, it has only one vertical line at a> 4 and is shaded for all values of a greater than 4.
Thus, the graph that fits the inequality is a vertical dashed line, shaded to the right of the line.
It is correct to state, therefore, that option B is the corect answer.
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Related Questions
The two rectangles above are similar. If b = 18 mm, and c = 24 mm, and d = 36 mm, what is the length of a?
Answers
Answer:
The length of a is 36 mm.
Step-by-step explanation:
Similar rectangles have the same shape, but can have different sizes. The ratio of the lengths of corresponding sides of similar rectangles is always the same.
Given that b = 18 mm, c = 24 mm, and d = 36 mm, the ratio of the lengths of corresponding sides of the two rectangles is c/d = 24/36 = 2/3.
So, the length of a is equal to b * (c/d) = 18 * (2/3) = 36 mm.
Find all the missing angles in the diagram below. Explain how you used at least two different angle theories to find some of these angles.
Answers
Answer:
Angle A is 90, angle B is 50, angle C is 90, and angle D is 40.
Answer:
<A = 90
<B = 50
<C = 90
<D = 40
Step-by-step explanation:
C:
vertical angles are congruent so the angle left of C is 40. The angle right to C is 50 because alternate interior angles are congruent
The three angles together are supplemental
180 - 50 - 40 = 90
A:
A = C vertical angles are congruent
A = 90
D:
A, D and 50 are supplemental
180 -90-50 = 40
B
The sum of the interior angles of a triangle are 180
180 - 40 - 90 = 50
Tracy bought a wristwatch for $845.00. She made a down-payment of $95.00 and financed the rest with six monthly payments of $128.75. Find the total installment price and total interest.
Answers
The total amount of the six monthly payments is 6 * $128.75 = $773.50
So, the total interest Tracy paid is $773.50 - $750.00 = $23.50
Therefore, the total installment price is $773.50 and the total interest is $23.50
Approximately how many downloads were there between 3 p.m. and 4 p.m.?
Answers
Answer: If you can explain the question a little bit more i would be happy to help!
Step-by-step explanation:
g(x) =8x²-5x³+7-12x total roots
Answers
The given cubic equation has no roots.
What are cubic equations?Traditionally, a cubic problem can be solved by converting it into a quadratic equation, which can then be solved by factoring or the quadratic formula. A cubic equation has three roots, just like a quadratic equation has two. Three real roots or one real root and two imaginary roots are both possible for a cubic equation. Cubic equations must also always be arranged in their standard form first.
The following strategies can be used to resolve a cubic equation:
Using Graphical Method to Find Integer Solutions with Factor Lists
Given that the cubic equation is: 8x²-5x³+7-12x
Regrouping the equation in standard form:
- 5x³ + 8x² - 12x + 7
Here, the constant is 7. Take the factors of the constant.
7 = 1, 7
Substitute the value of the factors as follows:
G(1) = - 5(1)³ + 8(1)² - 12(1) + 7 = -5 + 8 - 12 + 7 ≠ 0
G(7) = -5(7)³ + 8(7)² -12(7) + 7 = -1715 + 392 - 84 + 7 ≠ 0
Hence, the given cubic equation has no roots.
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Kate has a collection of 20 buttons. Each button has a diameter of either 2 or 3
centimeters. The combined diameters of all buttons is 48 cm. If x is the number of 2 cm
buttons, and y is 3 cm buttons, which system below represents the situation?
x+y=20
3x+2y=48
x+y=20
5xy=48
x+y=20
2x+3y=48
x+y=48
2x+3y=20
Answers
The solution is, the system represents the situation is, x+y= 20
and, 2x+3y = 48.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Each button has a diameter of either 2 or 3 centimeters.
The combined diameters of all buttons is 48 cm.
If x is the number of 2 cm buttons,
and y is 3 cm buttons.
Kate has a collection of 20 buttons.
So, the system represents the situation is,
x+y= 20
and, 2x+3y = 48.
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Natalia bought 3 boxes of pencils and 9 reams of paper for $75. Ronnie bought 8 boxes of pencils and 5 reams of paper for $67. Set up and solve a system of equations by elimination to determine the cost of a box of pencils and a ream of paper.
Answers
The cost of a box of pencils is $4.
The cost of a ream of paper is $7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 1 = 6 is an equation.
We have,
Pencils = x
Reams of paper = y
Now,
Natalie:
3x + 9y = 75 _____(1)
Ronnie:
8x + 5y = 67 _____(2)
From (1) and (2)
Multiply 8 on (1)
Multiply 3 on (2)
24x + 72y = 600
24x + 15y = 201
(-) (-) (-)
57y = 399
y = 7
Now,
3x + 9y = 75
3x + 9 x 7 = 75
3x + 63 = 75
3x = 75 - 63
3x = 12
x = 4
Thus,
The cost of a box of pencils and a ream of paper are $4 and $7.
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g (-9) if g(x) = -6x + 6
Answers
54 + 6 = 60
g(-9) = 60
A person invested $7500 for 1 year, part at 6%, part at 9%, and the remainder at 15%. The total annual income from these investments was $867. The amount of money invested at 15% was $100 more than the amounts invested at 6% and 9% combined. Find the amount invested at each rate.
Answers
Answer: The amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.
Step-by-step explanation:
Let's denote the amount invested at 6% as "x". Then, the amount invested at 9% would be "y", and the amount invested at 15% would be "z".
According to the problem, we have the following information:
x + y + z = $7500 (the total amount invested)
0.06x + 0.09y + 0.15z = $867 (the total annual income)
And,
z = x + y + $100 (the amount invested at 15% was $100 more than the amounts invested at 6% and 9% combined)
We can substitute the third equation into the first equation to get:
x + y + x + y + $100 = $7500
Simplifying:
2x + 2y + $100 = $7500
2x + 2y = $7400
Next, we can substitute "z = x + y + $100" into the second equation:
0.06x + 0.09y + 0.15(x + y + $100) = $867
Expanding:
0.06x + 0.09y + 0.15x + 0.15y + 0.15 * $100 = $867
0.21x + 0.24y + $15 = $867
0.21x + 0.24y = $852
Finally, we can solve for x and y using the equations "2x + 2y = $7400" and "0.21x + 0.24y = $852".
We can use elimination method to find x:
2x + 2y = $7400
0.21x + 0.24y = $852
Multiplying the first equation by 0.21:
0.42x + 0.42y = $1557.8
Subtracting the second equation from the first:
0.42x + 0.42y - 0.21x - 0.24y = $1557.8 - $852
0.21x - 0.03y = $705.8
Dividing both sides by 0.21:
x = $705.8 / 0.21 + 0.03y / 0.21
x = $3357.14 / 0.24 + y
Finally, substituting x back into the equation "2x + 2y = $7400":
2($3357.14 / 0.24 + y) + 2y = $7400
Expanding:
$6714.29 + 2.24y = $7400
Solving for y:
2.24y = $7400 - $6714.29
y = $685.71 / 2.24
y = $306.13
And finally, substituting y back into the equation "x = $3357.14 / 0.24 + y":
x = $3357.14 / 0.24 + $306.13
x = $1393.57
Therefore, the amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.
Cala rolls a biased dice 40 times. It comes up with a three 14 times. Calculate the relative frequency of rolling a three.
Answers
The relative frequency of rolling a three is 14/40 or 0.35.
Answer14/40 or 0.35
Step-by-step explanation:
Number of times dice is rolled= 40
Number of times three comes up= 14
Relative frequency(Probability) = 14/40 or 0.35
4. The sum of the first eight terms of an arithmetic sequence is 60. The sum of the 9th to 14th terms is 108. Find the 25th term.
Answers
Answer:
PLACEHOLDER SRRY BRB
Step-by-step explanation:
The formula for the sum of the first n terms of an arithmetic sequence is: Sn = n/2(2a + (n-1)d).
Using this formula, we can find the value of d:
For the first eight terms:
8/2(2a + (8-1)d) = 60
Solving for d:
d = (60 - 2a) / 14
For the next six terms:
6/2(2a + (9-1)d) = 108
Solving for a:
a = (108 - 6d) / 10
Now that we have the values of a and d, we can find the 25th term using the formula for the nth term of an arithmetic sequence: an = a + (n-1)d.
an = a + (25-1)d = a + 24d
Plugging in the values of a and d found above, we get the 25th term:
an = (108 - 6d) / 10 + 24 [(60 - 2a) / 14] = (108 - 6d) / 10 + 24 [(60 - 2(108 - 6d) / 10) / 14]
Simplifying further, we can find the 25th term
Last April, it rained in Danville on ten days. This graph shows how much rain fell on each day.
Answers
The difference in rainfall between the wettest and driest days is 3/8 inches.
3.0 inches of rain—is that a lot?The intensity of the rain is typically categorized as light, moderate, or heavy. Light precipitation is defined as less than 0.10 inches per hour. Rainfall that is considered moderate ranges from 0.10 to 0.30 inches per hour. More than 0.30 inches of rain per hour is considered heavy rainfall. under 0.5 mm per hour. Greater than 0.5 mm per hour but less than 4.0 mm per hour is considered moderate rain. Greater than 4 mm per hour but less than 8 mm per hour is considered heavy rain. greater than 8 mm per hour of extremely intense rain.
Rainfall in Rainiest day = 5/8
Rainfall in driest day = 2/8
So, The Difference = 5/8 - 2/8 = 3/8 inches
Hence, rainfall on the rainiest day 3/8 more than driest day
Proper fraction = 3/8
Mixed fraction = 8/2 inches.
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what is the answer for
−7x−y=0
Answers
Answer: y=-7x-0 if solving for literal y or x=y+0/-7 if solving for literal x.
Step-by-step explanation:
-7x-y=0
add (+) 7x to both sides
-y=7x+0
then divide by -1
y=-7x-0
-------------------------------------
for literal X
-7x-y=0
add y to both sides
-7x=y+0
then divide by -7\
x=y+0/-7
Another operation that can be defined on sets A and B is the difference of the sets, denoted by
A − B.
Here is the formal definition of the difference of sets A and B.
A − B = {x | x is in A and x not in B}
Thus
A − B
is the set of elements that belong to A but not to B. For instance, let
A = {1, 2, 3, 7, 8}
and
B = {2, 7, 11}.
Then
A − B = {1, 3, 8}.
Determine the difference, given that
U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {2, 4, 6, 8},
and
B = {1, 4, 6, 9}.
(Enter your answers as a comma-separated list.)
A − B'
Answers
Answer:
Step-by-step explanation:
To find the difference A - B', we need to first find the complement of B, denoted by B', which is the set of all elements in U that are not in B.
Given that U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
B = {1, 4, 6, 9},
then B' = {2, 3, 5, 7, 8}.
Next, we find A - B' by looking for the elements that belong to A and not to B':
A - B' = {2, 4, 6, 8} - {2, 3, 5, 7, 8} = {4, 6, 8}.
An game is on sale for $28, which is 30% off the original price. What was the original price?
a$19.60
b$40.00
c$84.00
d$98.33
Answers
The solution is the original price was 93.33.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
An game is on sale for $28, which is 30% off the original price.
let,
the original price was x
ATQ,
x*30% = 28
x = 280/3
x=93.33
Hence, The solution is the original price was 93.33.
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The sum of three numbers is 54. The difference of the largest and the smallest is 46, and the sum of the two smaller numbers is 13. Find the numbers?
Answers
These values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.
What is a three-variable linear equation?
When a, b, and c are constants, a linear equation in two variables has the form ax + by + c = 0. (real numbers). Similar to this, a three-variable linear equation has the form ax by c z plus d = 0, where a, b, c, and d are constants.
Let's call the three numbers x, y, and z, where x is the largest number and z is the smallest number. Then, we have the following information:
x + y + z = 54
x - z = 46
y + z = 13
From the second equation, we can find z:
z = x - 46
Substituting this into the third equation:
y + x - 46 = 13
y = 13 + 46 - x
Substituting both of these into the first equation:
x + (13 + 46 - x) + (x - 46) = 54
Expanding the parentheses:
2x = 154
Dividing both sides by 2:
x = 77
Substituting this value of x into the equation for z:
z = x - 46 = 77 - 46 = 31
And substituting it into the equation for y:
y = 13 + 46 - x = 13 + 46 - 77 = -18
Note that these values do not satisfy the requirement that x, y, and z be positive numbers, so the problem does not have a solution.
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If an average-sized man with a parachute jumps from an airplane, he will fall
12.5(0.2t − 1) + 20t feet
in t seconds. How long will it take him to fall 130 feet? (Round your answer to two decimal places.)
Answers
It take the man 19.83 seconds to fall to 130 feet
How to determine how long will it take him to fall 130 feet?From the question, we have the following parameters that can be used in our computation:
h(t) = 12.5(0.2t − 1)^2 + 20
When the man reaches 130 feet, we have
h(t) = 130
Substitute the known values in the above equation, so, we have the following representation
12.5(0.2t − 1)^2 + 20 = 130
Using a graphing calculator, we have
t = 19.83
Hence, the time is 19.83 seconds
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In the diagram below of triangle CDE, F is the midpoint of CE and G is the midpoint of DE. If m∠ECD=12+9x, m∠EFG=−2x+111, what is the measure of ∠EFG?
Answers
The measure of m∠EFG in triangle CDE is equal to 93 units.
What is the midpoint theorem?In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.
By applying the midpoint theorem to triangle CDE, the measure of m∠EFG can be calculated as follows;
m∠ECD = m∠EFG
12 + 9x = −2x + 111
9x + 2x = 111 - 12
11x = 99
x = 99/11
x = 9.
For line segment m∠EFG, we have the following:
m∠EFG = −2x + 111
m∠EFG = −2(9) + 111
m∠EFG = −18 + 111
m∠EFG = 93 units.
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(100 POINTS!) In parallelogram JKLM if JL=32 find JN.
Answers
Answer:
JN = 16
Step-by-step explanation:
Since diagonals in parallelograms bisect each other, JN = [tex]\frac{1}{2}[/tex]JL
Answer:
To find JN in parallelogram JKLM when JL is 32, you can draw a line from J to L, and then extend the line to find JN. The length of JN will be equal to 32.
Express it to mathematical phrase:
Three added to four times a number
Answers
Answer:
4x + 3 = y
Step-by-step explanation:
Answer:
4x+3
there is no actual explanation
Three added= +3
four times a number= 4*x=4x
If
p
=
2
and
q
=
5
, evaluate the following expression:
40
2
q
−
p
Answers
Answer:
398
Step-by-step explanation:
40*2q-p
=40*2*5-2
=400-2
=398
Answer:
2008
Step-by-step explanation:
since p=2
q=5
therefore, 402(q)-p
=402(5)-2
=2,010-2
=2008
Which equation is more appropriate for modeling this DATA?
Answers
The equation which is more appropriate for modeling this DATA is y = 64 × (1.25)^x
The correct answer choice is option A.
Which equation is more appropriate for modeling this DATA?y = 64 × (1.25)^x
when,
x = 1
substitute into the equation
y = 64 × (1.25)¹
= 64 × 1.25
= 80
y = 79 × 1.25^x
when x = 1
= 79 × 1.25¹
= 79 × 1.25
y = 98.75
79 + 1.25x
when x = 1
= 79 + 1.25(1)
= 79 + 1.25
= 80.25
64 + 22x
when x = 1
= 64 + 22(1)
= 64 + 22
= 86
Therefore, y = 64 × (1.25)^x is the equation which is more appropriate to represent the data.
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10
Complete the equation for the line
shown in the graph.
6.67 y
-6.67
(0,2)
(1,-2)
10
y=[?]x + [ ]
Answers
Answer:
y= -4x+2
Step-by-step explanation:
diff in y / diff in x = slope
so the slope is (-2-2) /(1-0) = -4
intercept is whatever is on Y axis, it's 2
so y= -4x+2
Answer:
Step-by-step explanation:
Divide 100 by 16 and write the answer as a mixed number. Reduce the
fraction part of the mixed number. 6 1/4 here u go.
. Describe the graph of the function. Y=sqrt x-7 +8
Answers
-7 would be going left and +8 would be going up
sqrt is the radical and the one inside is radicand.
Hope this help
ngberg Company installs lawn sod in home yards. The company’s most recent monthly contribution format income statement follows:
Amount Percent of Sales
Sales $ 90,000 100%
Variable expenses 36,000 40%
Contribution margin 54,000 60%
Fixed expenses 40,500
Net operating income $ 13,500
Required:
1. What is the company’s degree of operating leverage?
2. Using the degree of operating leverage, estimate the impact on net operating income of a 7% increase in unit sales.
3. Construct a new contribution format income statement for the company assuming a 7% increase in unit sales.
Answers
1. The company’s degree of operating leverage is 4.
2. The degree of operating leverage is 3.34.
3. The new contribution is $17, 280.
What is degree of operating leverage?How much a company's operating income alters in reaction to a change in sales is measured by the level of operating leverage.
1. Degree of operating leverage = Contribution /Net Operating Income
and, Contribution = 54,000
Net Operating Income = $13,500
Thus, operating Leverage = 54000/ 13500 = 4
2. If Company's sales increase by 7% then contribution also increases by 7%,
Revised Contribution = $54000 + 7% = $57780
and, Revised net Operating income = $57780- $40500
= 17280
Degree of operating leverage = 57780 / 17280 = 3.34
3. Contribution format income statement:
Sales = $90000+ 7% = $96,300
Less: Variable Cost 36, 000 + 7% = $38520
So, New Contribution = 57780 - 40500 = $17, 280.
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Reid found 6 coins that totaled 61c in all. What coins did the find?
Answers
Reid found 1 quarter, 3 dimes, 1 nickel and 1 penny coins.
What is currency?Currency is anything that is generally accepted to have value as a medium of exchange so that it can be traded for goods and services.
Given that, Reid found 6 coins that totaled 61 cents in all.
Since, in total he got 6 coins that value 61 cents in total.
So, wd know that,
1 quarter = 25 cents
1 dime = 10 cents
1 nickel = 5 cents
1 penny = 1 cents,
Adding them = 25 + 10 + 5 + 1
= 41 cents
We need 20 cents and 2 coins more,
So, add 3 coins more in nickel, so, that,
3 nickels = 30 cents
Now, Reid in total will have 6 coins and that will value 61 c.
Hence, Reid found 1 quarter, 3 dimes, 1 nickel and 1 penny coins.
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i want my sparx to be done please help
Answers
(a) The perimeter of the rectangle in centimeter is 2,800 cm.
(b) The area of the rectangle is 450,000 cm².
What is the perimeter of the rectangle?The perimeter of the rectangle in centimeter is calculated as follows;
P = 2 ( L + B )
where;
L is the length of the perimeterB is the breadth of the perimeterThe length of the rectangle = 9 m = 900 cm
The breadth of the rectangle = 5 m = 500 cm
Perimeter = 2 ( 900 cm + 500 cm ) = 2,800 cm
The area of the rectangle is calculated as follows;
A = LB
A = 900 cm x 500 cm
A = 450,000 cm²
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Look at the figure. Find TW.
VIEW THE IMAGE ATTACHED.
Answers
Answer:
TW = 9
Step-by-step explanation:
WY is the perpendicular bisector of TZ with TY ≅ ZY , then
Δ TWZ is isosceles with ZW ≅ TW , that is
3x = x + 6 ( subtract x from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Then
TW = x + 6 = 3 + 6 = 9
What is the slope and y-intercept of this line?
y = –6x + 2
Answers
Answer:
the slope is -6
the y-intercept is 2
Step-by-step explanation:
y=mx+b where m is the slope and b is the y-intercept
a) Slope: -6;
b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).
Step-by-step explanation:Given equation: [tex]y = -6x + 2[/tex].
Here's a little tip that will help you quickly find the slope and y-intercept.
First, solve the equation for "y". This equation is already solved for "y", this is called "slope-intercept form". Now, take a look at the attached image and identify the values. As you can tell, for the given equation, values are:
a) Slope: -6;
b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).
You may verify this information using the algebraic methods (slope formula and substituting "x" by 0 and calculate "y"). It'll give you the same answer, this is just a faster way to find the values.
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Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180°.
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 28° more than the measure of the second angle.
What is themeasure of each angle?
Answers
Answer:
The first one is 76°, second one is 38°, third one is 66°
Step-by-step explanation:
Suppose the second one is x, given the first one is twice of the second one, so the first one is 2x.
2x+x+(28°+x)=180°
4x=152°
x=38
So, the first one is 76°, second one is 38°, third one is 66°