The table does not represent a direct variation as there is mismatch of k in three expressions.
We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.
What is direct variation?
A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.
For the first value of x and y, x=-4 and y=-8
Thus, it can be expressed as -8 = 2*-4, hence k=2
For the second value of x and y, x=-2 and y=-4
Thus, it can be expressed as -4 = 2*-2, hence again k=2
For the third value of x and y, x=6 and y=18
Thus, it can be expressed as 18 = 3*6, thus k here is 3 and not 2
Hence, this table does not represent a direct variation as there is mismatch of k in three expressions.
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Gonzalez Manufacturing borrowed $24000. Part of the money was borrowed at 8%, part at 10%, and part at 12%. The
total amount borrowed at 8% and 10% was twice the amount borrowed at 12%. Find the amount borrowed at each rate if
the annual interest was $2480.
How much money was borrowed at 8%?
The amount borrowed at 8% is $4000, at 10% is $12,000 and at 12% is $8000
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
let x be the amount borrowed at 8%
y be the amount borrowed at 10%
and z be the amount borrowed at 12%
total money borrowed = x+y+z = 24000 equation 1
also x+y = 2z equation 2
substitute 2z for x+y in equation 1
2z+ z = 24000
3z = 24000
z = 24000/3
z= $8000
the interest rate paid on z = 12/100× 8000 = $960
the interest paid on y = 10/100 × y
the interest paid on x = 8/100 × x
total interest paid = 960+10y/100+8x/100= 2480
10y/100+8x/100= 2480-960
10y/100+8x/100= 1520
multiply all terms by 100
8x+ 10y = 15200 equation 3
x+ y = 2z = 2× 8000
x+y = 16000 equation 4
using elimination method
8x+10y = 152000 equation 5
8x+8y = 128000 equation 6
subtract equation 6 from 5
2y = 24000
y = $12000
substitute 12000 for y in equation 4
x+12000= 16000
x = 16000-12000
x = $4000
therefore the amount borrowed at 8%, 10% and 12% are $4000, $12000, $8000 respectively.
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Penny has 4 books she wants to read. If she randomly chooses one to read at a time, in how many different
sequences could she read all the books?
Your answer is :
Answer:
24
Step-by-step explanation:
Evaluate the function below for x = 2.
F(x) = 2x³-x²-5x+6
OA. 56
OB. 16
OC. 4
O D. 8
Evaluating the function for x=2, F(x)= 8.
What is a linear equation?
Alternatively, a linear equation can be obtained by equating the linear polynomial over the field from which the coefficients are taken to zero.
The solution of such an equation is the value that makes the equation true when the unknowns are substituted.
If there is only one variable, there is only one solution. Often the term linear equation alludes to this special case where the variables are appropriately called unknowns.
With two variables, each solution can be interpreted as the Cartesian coordinates of a point on the Euclidean plane. The solutions of linear equations form lines in the Euclidean plane. Conversely, each line can be viewed as the set of all solutions to linear equations in two variables. This is the origin of the term linear for these types of equations. More generally, the solution of a linear equation in n variables forms a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n.
Therefore, Evaluating the function for x=2, F(x)= 8.
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Peter and Vivian each wrote a proof for the statement: if 22 23, then 21 is supplementary to 23.
1
Peter used
because
2
Peter's proof:
By the linear pair theorem, 21 is supplementary to 22. So, m/1 + m/2 = 180°. Since 2223, then 22 = 23. Applying the transitive property
of equality, m/1 + m/3 = 180°, which means 21 is supplementary to 23.
All rights recented
3
Vivian's proof:
Suppose 21 is not supplementary to 23. So, m/1 + m23 180°. By the linear pair theorem, 21 is supplementary to 22. By the definition of
supplementary angles, m/1 + m/2 = 180°. Applying the Transitive Property, m/1 + m23 # m/1 + m2. By the subtraction property of
equality, this implies that m/3 m/2. By definition of congruence, m/3 m/2. However, m/3 m/2 contradicts the given.
What type of proofs did they use?
e because
B. Vivian used
Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right.
How to carry out Congruence Proofs?
We are told that both peter and Vivian were trying to prove from the attached diagram the statement that;
If ∠2 ≅ ∠3, then ∠1 is supplementary to ∠3.
Now, from the proofs of both of them, we can see that peter used a direct proof because he knew he could get it directly but Vivian utilized another means which was by starting with contradiction to reprove that the answer was correct.
Thus, we can conclude that Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right
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police departments continue to control the sole statistical data available to measure homicide rates in the united states. true or false?
The given statement , police departments continue to control the sole statistical data available to measure homicide rates in the united states is false.
Domestic disagreements, interpersonal violence, violent fights over land resources, intergang violence over turf or control, and predatory violence and murders by armed organizations are all examples of intentional homicides.
Intentional homicide does not cover all intentional killing; the distinction is usually in the manner in which the killing is carried out.
Homicide is typically committed by individuals or small groups, but killing in armed conflict is typically performed by highly cohesive organisations of up to several hundred members and is thus typically omitted.
The 2020 murder/homicide rate in the United States was 6.52,
a 28.64% rise over 2019.
The murder/homicide rate in the United States in 2019 was 5.07,
up 1.19% from 2018.
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Sandy uses three and one half pounds of clay to make 7 small vases. Use a proportion to find how many pounds of clay she will use to make 21 small vases.
Answer: 10.5 pounds of clay
Step-by-step explanation:
We know she uses three and one-half pounds of clay to make seven small vases.
3 1/2 = 3.5
21 is 3 times 7
So We take 3.5 times 3 = 10.5 pounds of clay
she will use 10.5 pounds of clay to make 21 small vases.
a publisher reports that 52% of their readers own a personal computer. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 340 found that 49% of the readers owned a personal computer. is there sufficient evidence at the 0.02 level to support the executive's claim?
First, state the null and alternate hypothesis for the hypothesis test
H0:p=0.52
Ha:p≠0.52
z=pˆ−p/√p(1−p)/n
z= pˆ−p divided by the square root of p(1−p) divided by the sample (n)
z= 0.49^-0.52/ √0.52 ( 1- 0.52) / 340 = -2.24
z=-2.24
When using rejection regions, we reject the null hypothesis, H0, if:
z<−zα for a left-tailed test
z>zα for a right-tailed test
|z|>zα/2 for a two-tailed test
Thus the decision rule is: Reject the null hypothesis, H0, if |z|>2.33.
Since the absolute value of the z test statistic, 2.24, is less than the critical value, 2.33, we fail to reject the null hypothesis.
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Suppose Mr. Reed's class has 3 hours for presentations.
How many projects can be presented? Show your
solution by writing both a division equation and a
multiplication equation.
In 3 hour Mr. Reed can presents 15 presentations. The division equation and a multiplication equation are 3 ÷ 1/5 =15 and 3 × 5 = 15 respectively.
What is an equation of division?
Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety. The division operator and the numbers that are being divided will both be on one side. The other side displays the result of the division.
The 3 large rectangles represent the 3 hours.
Each presentation is 1/5 hour so each rectangle is divided into 5 equal sections.
From the model you can write the division equation: 3 ÷ 1/5 =15
You can also write the multiplication equation: 3 × 5 = 15
Both equations show 15 projects are presented in 2 hours.
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A) a wooden block is formed in a the shape shown by cutting a right rectangular solid from a larger one. What is the volume of the block
B) check your calculations by using a second method to solve the problem
The volume of the rectangular block in this problem is given as follows:
1300 cm³.
How to obtain the volume of the block?The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:
V = length x width x height.
The dimensions for this block are given as follows:
Length: 16 cm.Width: 10 cm.Height: 10 cm.However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:
Length: 6 cm.Width: 10 cm.Height: 5 cm.Hence the volume of the rectangular block can be calculated as follows:
V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.
(total volume subtracted by the removed volume from the empty space at the middle).
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PLEASE THIS IS SERIOUS
Solve for x
What is the process for doing the method of elimination for math systems?
Answer:
Elimination is the adding or subtracting of two equations used to solve them.
Step-by-step explanation:
Elimination is the adding or subtracting of two equations used to solve them.
Say you have this equation. [tex]\left \{ {{x + y=2} \atop {-x+y=6}} \right.[/tex]
Notice that the x in both equations are opposites. After adding together we get.
x + y - x + y = 2 + 6
2y = 8
y = 4
x + 4 = 2
x = - 2
(- 2,4)
Say you decide to subtract the equations.
[tex]\left \{ {{x+y=2} \atop {x+2y=8}} \right.[/tex]
x + y - x - 2y = 2 - 8
- y = - 6
y = 6
x + 6 = 2
x = - 4
(- 4, 6)
You can also multiply equations to make it easier to substitute.
[tex]\left \{ {{y+x=4} \atop {-2y+2x=8}} \right.[/tex]
[tex]\left \{ {{2y+2x=8} \atop {-2y+2x=8}} \right.[/tex]
2y + 2x - 2y + 2x = 8 + 8
4x = 16
x = 4
y + 4 = 4
y = 0
(4, 0)
I need help!! Please if you know how!!
Answer:
Step-by-step explanation:
Answer: 2
Answer:2
Step-by-step explanation:
A system of equations is shown.
\left\{\begin{array}{l}\ \ \ \ \ \ \ \ \ x=10\\3x+5y=20\end{array}\right.{
x=10
3x+5y=20
What is the solution \left(x,y\right)(x,y) of the system of equations?
Enter your answer in the box.
Value of y is -2.The variable mappings that satisfy all of the component equations in a system of equations.
How do you find system of equations?One or more equations involving a number of variables make up a system of equations. The variable mappings that satisfy all of the component equations in a system of equations, or the points where the components of this system of equations intersect, are the solutions to that system.
Explanation:
The equations are provided as follows:
x = 10
3x + 5y = 20
In the second equation, change x to 10
3 * 10 + 5y = 20
Evaluate
30 + 5y = 20
Take away 30 from both sides.
5y = -10
Multiply both sides by 5.
y = -2
Consequently, in the system of equations, y has a value of -2.
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Value of y is -2.The variable mappings that satisfy all of the component equations in a system of equations.
How do you locate an equation system?A system of equations is made up of one or more equations with numerous variables. A system of equations' solutions are either the variable mappings that satisfy each of its component equations or the locations where its component equations cross.
The equations are provided as follows:
x = 10
3x + 5y = 20
In the second equation, change x to 10
3 * 10 + 5y = 20
Evaluate
30 + 5y = 20
Take away 30 from both sides.
5y = -10
Multiply both sides by 5.
y = -2
Consequently, in the system of equations, y has a value of -2.
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Mabel is creating a mural on a building wall that is 40ft tall and 50ft wide. Her original drawing is 2ft tall and 2.5ft wide. What scale factor will Mabel use to enlarge the design?
Answer:
Mabel will use scale factor of 20 to enlarge the design.
{ If you do need explanation, Please inform me.}
please help me with math
Answer: C & D
Step-by-step explanation:
Remember when 2 same square roots are multiplied by one another, they cancel out.
√64 is equivalent to 8, so that is the answer as well.
One gallon of water is equivalent to 8.34 pounds. Write this value as a mixed number in simplest form
Answer:
8 17/50
Step-by-step explanation:
8.34
= 8 34/100
8 17/50
Answer: 8_17/50
Step-by-step explanation:
how do you solve this?
According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.
How to solve a variable in an isosceles triangle
In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.
According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:
m ∠ x = 74°
x = 74°
Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.
The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.
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Help me with this question please!!
Answer:
∠1 = 19°∠2 = 76°Step-by-step explanation:
You want to know the measure of angle 1 given that angle 2 is four times angle 1, and their sum is 95°.
Angle sum theoremThe angle sum theorem tells you the whole is equal to the sum of the parts.
∠1 +∠2 = ∠WXZ
Using the given information, we can write ...
∠1 + (4×∠1) = 95°
5×∠1 = 95° . . . . . . . . collect terms
∠1 = 19° . . . . . . . . . divide by 5
Then angle 2 is ...
∠2 = 4×∠1 = 4×19°
∠2 = 76°
What is the equation of a line, in slope-intercept form, which passes through (4, -1) and has a slope of 1/3
Answer:
The answer is y = 0.333x + -2.332
Step-by-step explanation:
All you have to do is put above values in equation, which should get you to:
-1 = 0.333 (4) + b
-1 = 1.332 + b
-2.332 = b
b = -2.332
y = 0.333x + -2.332
Which equation is parallel to the equation y = x + 1 and goes through the points (1, 5)
A. y=x+5
B. y=x-1
C. y=x+1
D. y=x+4
Answer: D. y=x+4
Step-by-step explanation:
1. The equation will have the same slope
2. Plug in the given point to find b, the y-intercept
what is the maximum width casket that will fit in a standard vault? 28 inches 32 inches 30 inches 26 inches
The maximum width Casket that will fit in a standard vault is 28 inches.
Standard measurements may vary significantly depending on the manufacturer.
Caskets normally measure 84 inches long, 28 inches broad, and 23 inches tall. Both wood and metal caskets often have the same proportions. Caskets are intended to fit into normal burial sites, which are generally 30-inches wide and may accommodate ordinary caskets as well as enlarged caskets of 28-inch and 29-inch dimensions.
Casket inside dimensions vary significantly; the metal caskets are typically 78 or 79 inches long and 23 or 24 inches broad.
A typical size casket/coffin is enough for the most majority of individuals. Standard caskets can typically (but not always) fit people up to 6'5" and 350 pounds, but we strongly advise you to speak with your funeral director to determine the precise casket size you require.
The maximum width Casket that will fit in a standard vault is 28 inches.
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pls help due tommaorw
(i also have other unanswered questions posted)
See the attached image.
The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.
Given that the rectangular box is made from cardboard the thickness is x.
The length of the box will be,
L = 4.5 - 3x
The width of the box will be,
W = 4 - 2x
The thickness of the box is,
H = x
The volume of the box will be calculated as,
V = ( 4.5 - 3x) ( 4 - 2x ) (x)
V = ( 4.5 - 3x) ( 4 - 2x ) (x)
V = ( 18 - 12x - 9x + 6x² ) x
V = 6x³ -21x² + 18x
For maximum volume differentiate the volume with respect to x and get the value of x,
dV / dx = d / dx ( 6x³ -21x² + 18x ) = 0
d / dx ( 6x³ -21x² + 18x ) = 0
18x² - 42x + 12 = 0
3x² - 7x + 6 = 0
Solve the above quadratic equation as,
x = [ -b ±√(b² - 4ac) ] / 2a
x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )
x = 1.17
The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,
V = 6x³ -21x² + 18x
V = 6(1.17)³ -21(1.17)² + 18(1.17)
V = 9.6 - 28.7 + 21.06
V = 1.96 cubic inches
The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.
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paige spends 1 hour on her homework she spends equal amount of time on all subjects, if paige spends 1/2 on spanish how much hours does she study
The number of subjects that Paige would study D. 2 subjects.
How to calculate the number of subject studiedIt should be noted that Paige would study for one hour. She spends 1/2 an hour, or 30 minutes, on a subject.
An hour is 60 minutes. If Paige studied 2 subjects, then she would of studied for 60 minutes.
30 + 30 = 60
So, if Paige spends 1/2 hour on Spanish, she would study 2 subjects to reach an hour.
Therefore, the correct option is D.
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Complete question
Paige spends 1 hour on her homework. She spends equal amounts of time on all subjects. If Paige spends 1/2 hour on Spanish, how many subjects does she study?
3 subjects
1 subject
4 subjects
2 subjects
1 - ? = 1/7 <- fraction
Fill in the missing value
6/7
Step-by-step explanation:
1 - x = 1/7
- x = 1/7 - 1
- x = 1/7 - 7/7
- x = -6/7
x = -(-6/7)
x = 6/7
thus,
1 - 6/7 = 1/7
If a is an odd number, b an even number, and c an odd number, which expression will always be equivalent to an odd number?
What i the value?
1/4 - 1/2 ( - 4/7)
Anwer
1) - 1 5/16
2) - 3/7
3) 3/7
4) 1 5/16
Answer:
None of these
Step-by-step explanation:
[tex]\frac{1}{4}+\frac{1}{2} \cdot \frac{4}{7}=\frac{1}{4}+\frac{4}{14}=\frac{1}{4}+\frac{2}{7}=\frac{7+8}{28}=\frac{15}{28}[/tex]
in triangle ABC, AB = 6 cm, BC = 13cm and angle ACB = 23 degrees. Calculate angle BÁC, which is obtuse.
Answer:
[tex]\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}[/tex]
Step-by-step explanation:
[tex]\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}[/tex]
which of the following statements is a proposition? (a) get me a glass of milk (b) god bless you! (c) what is the time now? (d) the only odd prime number is 2
The proposition ststement is: the only prime number that is odd is 2.
The correct answer is an option (d)
In this question we have been given some statements.
we need to identify the proposition statement.
We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.
a) get me a glass of milkshake.
It is a commanding statement.
b) god bless you!
It is a type of optative statement.
c) what is the time now?
It is a question sentence.
d) the only odd prime number is 2.
It is a false proposition statement.
Therefore, option (d) is a proposition statement.
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What number line represents the solution set for
Answer:
4th one
Step-by-step explanation:
Hope that helps.
