Describe how you know whether an equation will be true for all values of x or true for no values of x
Answer:
Step-by-step explanation:
Generally an equation which will be true for all values of x have some statement which can be simplified into another state which will always be true.
So for example: [tex]x+4=x+4[/tex], is kind of a bit obvious to tell it's going to be true for all values as the two expressions have the same exact terms, but we can subtract "x" from both sides leading us to the statement: [tex]4=4[/tex] which is always true.
One important thing to note is you must be cautious at times, for example: [tex]\frac{x-2}{x-2}=\frac{x-2}{x-2}[/tex] may seem to be true for all values, and x-2 over x-2 is the same thing, so it simplifies to one and same thing on the right side: [tex]1=1[/tex] thus the statement should be true for all values right? Not completely, it's true for most values, except for x=2, and this is because 1=1 isn't exactly the same expression. In the original fraction the denominator has an x-2, and if we plug in x=2, we get 2-2 resulting in division by one, which of course isn't definable. So that's just one important thing to note as simplifying expressions may result in expressions that look equal, but are slightly different in a way.
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answer: 39%
Step-by-step explanation:
using calculator
1 seat = 0.058%
1700 - 1037 = 663 seats are taken.
0.058% x 663 seats = 39%
what is the slope of this line?
Answer: -1/2
Step-by-step explanation: Down 1 over 2
Find the measure of the missing angles.
Answer:
F = 29
E= 151
D = 90
Step-by-step explanation:
For F:
The angle F is on a 180 degree angle with a degree next to it that is 151. To get the value F subtract 180-151 and you get 29.
For E: If F is 29 then the angle opposite of F is also 29. So again to find the measure of angle E, subtract 180 minus 29 and you get 151.
For D: D is also lying on a 180 degree angle. The angle next to it is 90. To get 180 add 90. 90 is the measure of angle d.
Answer:
d = 90°,e = 151°,f = 29°.-----------------------------------
Angle d is linear pair with a right angle, therefore:
d = 180° - 90°d = 90°Angle e is vertically opposite with 151° and therefore they are congruent:
e = 151°Angle f is adjacent with 151° and forming a linear pair, therefore:
f = 180° - 151°f = 29°find the length of AB
Answer:
8.5 cm
Step-by-step explanation:
You want to know the length of AB in rectangle ABCD with perimeter 26 cm if BC = PQ, QR = 10 cm, and the area of rectangle PQRS is 45 cm².
PQThe area of rectangle PQRS is ...
Area = PQ·QR
45 cm² = PQ·(10 cm)
PQ = (45 cm²)/(10 cm) = 4.5 cm
ABThe perimeter of rectangle ABCD is ...
Perimeter = 2(AB +BC)
26 cm = 2(AB +4.5 cm) . . . . . . . . BC = PQ = 4.5 cm
13 cm = AB +4.5 cm . . . . . divide by 2
8.5 cm = AB . . . . . . . . subtract 4.5 cm
The length of AB is 8.5 cm.
<95141404393>
angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive
The grades that Angie need to receive in her next test so that her average is 92 is 91.
What is average?The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:
Average = Sum of the observations / Total number of observations
Assume the marks that Angie needs in her next test is represented by x.
Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:
Average = Sum of the grades of all test / Total Number of test
92 = (88+96+92+93+x)/5
460 = 369+x
460 - 369 = x
x = 91
Hence, she needs 91 grades in her next test.
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The complete question is:
Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?
SOMEONE PLEASE HELP...............
A plane that passes through three edges of a cube produces a triangular cross section as shown.
In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.
A cross section of a cube that is a regular hexagon can only be obtained if the plane passes through the cube at a 60-degree angle with respect to its edges. If a plane is placed in this manner, it will intersect six of the cube's edges at their midpoints, producing a regular hexagon cross section.
What are True Statements about a Plane that Pass Through a Cube?The plane that passes through three edges of a cube to produce a regular hexagonal cross section must intersect the edges of the cube at 60 degree angles. This can be achieved if the plane is aligned with the diagonal of one of the faces of the cube, passing through the opposite vertices of the face.
This configuration of the plane will result in a regular hexagonal cross section of the cube as each vertex of the hexagon will correspond to one of the vertices of the cube, and each side of the hexagon will intersect two edges of the cube at 60 degree angles.
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If sin t= 7/9, and t is in quadrant I, find the exact value of sin(2t) , cos(2t) , and tan(2t) algebraically without solving for t .
Step-by-step explanation:
we know :
sin(2t) = 2×sin(t)×cos(t)
cos(2t) = cos²(t) – sin²(t) = 2×cos²(t) – 1 = 1 – 2×sin²(t)
tan(t) = sin(t)/cos(t)
tan(2t) = sin(2t)/cos(2t) = (2×tan(t))/(1 – tan²(t))
sin²(t) + cos²(t) = 1
as t is in quadrant I, 2t must be in either quadrant I or II.
sin(t) = 7/9
sin²(t) = (7/9)² = 49/81
cos²(t) = 1 - sin²(t) = 1 - 49/81 = 81/81 - 49/81 = 32/81
cos(t) = sqrt(32)/9
sin(2t) = 2×sin(t)×cos(t) = 2×7/9 × sqrt(32)/9 =
= 14×sqrt(32)/81 ≈ 0.98
cos(2t) = cos²(t) - sin²(t) = 32/81 - 49/81 = -17/81 ≈
≈ -0.21
tan(2t) = sin(2t)/cos(2t) =
= 14×sqrt(32)/81 / -17/81 =
= 14×sqrt(32)/81 × -81/17 =
= -14×sqrt(32)/17 ≈ -4.66
what’s the equation of the line graphed below i’ll give you brainlist pls help
y=3/2x+4
y=2/3x+4
y=2/3x-6
y=3/2x-6
Answer:
y = 2/3x + 4
Step-by-step explanation:
y-intercept (b) is 4
Use points (-6, 0) and (0, 4) to find the slope (m) = (4-0)/(0--6) = 4/6 = 2/3
y = mx + b = 2/3x + 4
Which of the following graphs matches the equation y=-4x+3
The equation of line is y = -4x + 3 , where the slope is m = -4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -4x + 3 be equation (1)
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -4
And , the y intercept is 3
The equation of line is plotted on the graph
Hence , the equation of line is y = -4x + 3
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The complete question is :
Which of the following graphs matches the equation y=-4x+3?
On a coordinate plane, a line goes through (0, 3)
On a coordinate plane, a line goes through (-2, 5) and (0, -3).
On a coordinate plane, a line goes through (0, 3) and (3, -1).
keeps saying ive gotten it wrong yet its an easy question.. help me? (probability)
Answer:
Pole Vault, Discus, 200m, Long Jump
Step-by-step explanation:
Once putting them all as decimals can’t you just sort it our from there? From what I can see, your answers are incorrect, but they might have reset.
What is the value of x in l-16l = x
Answer: |-16| =x
- (-16)= x
x = 16
Step-by-step explanation:
thank you
What is the completely factored form of 15a³bc³ – 6a²b²c³?
Answer:
The completely factored form of 15a³bc³ – 6a²b²c³ is 3a²bc³ × (5a - 2b).
Answer:
[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]
Step-by-step explanation:
[tex]15a^{3} bc^{3} - 6a^{2} b^{2} c^{3}[/tex]
[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]
The 8 red markers in a box account for 4% of all markers in the box. How many markers are in the box?.
Answer: 32
Step-by-step explanation: divide 8 into 4/100
Kcf
Keep change flip
Keep the 4/100 change the division sign to multiplication then flip the 8 to 8/1 then just multiply across.
Which of the following angles is in the solution set of (see picture)
Angles are measured in degrees, with a full circle being 360°, and can be thought of as the amount of rotation that two straight lines or planes undergo.
What best define about angle?The class definition of angle changed from a collection of ambiguous expressions, such as “the measurement of all the sides,” “the place where lines meet,” and “the corner of a shape or anything,” to
The equation below can be set up to calculate this.
Tan(angle) = 80 ft / (200 ft – 4 ft)
Solving for the angle, we get:
angle = tan-1(80 ft / 196 ft (ca. 60 m))
angle = tan-1(0.408163265)
Angle = 36.87 degrees (to the nearest hundredth of a degree).
Therefore, The law of tangents indicates that the angle between the subject's eyes and the top of the structure is roughly 36.87 degrees.
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Un capitalista tiene dos capitales que se diferencian en S/. 221 000, el mayor de ellos lo impone al 20% anual y el menor al 16% anual, así al cabo de 3 años, el monto producido por el mayor es el doble de lo que produce el menor. Hallar la suma de los capitales.
The sum of the capitals would be $530400.
What is the formula to calculate the simple interest?The formula to calculate the simple interest is -
I = PRT/100
Given is that a capitalist has two capitals that differ in $221,000. The largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces.
We can write the amount produced by largest as -
A = P(1 + rt)
A = 221000(1 + 0.2 x 3)
A = 221000 x 1.6
A = 353600
Amount generated by smallest -
a = 353600/2
a = 176800
Their sum would be -
A + a = 530400
Therefore, the sum of the capitals would be $530400.
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{Question in english -
A capitalist has two capitals that differ in S/. 221,000, the largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces. Find the sum of the capitals.}
Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Answer:
(a) 24%
Step-by-step explanation:
You want the percentage of people in the Decades slice of a circle graph if it represents 96 people. The other slices represent 128, 72, 52, 24, and 28 people.
PercentThe fraction in the second category is the ratio of the number in that category to the total number. The percent is the fraction multiplied by 100%.
96/(128 +96 +72 +52 +24 +28) × 100% = 96/400 × 100% = 24%
The Decades slice of the circle would be 24%, choice A.
<95141404393>
Quadrilateral ABCD has the following angle measures:
m∠A = ?°, m∠B = 97°, m∠C = 47°, m∠D = 90°
What is m∠A?
306°
234°
126°
54°
PLEASE HELP!
Answer:
126
Step-by-step explanation:
360-97-47-90=126
so 126
Answer: C) 126
Step-by-step explanation: first, you need to use this equation...
m∠A + m∠B + m∠C + m∠D = 360°
=> m∠A + 97° + 47° + 90° = 360° add all of the numbers...
=> m∠A + 234° = 360° subtract both sides by 234
=> m∠A = 360°- 234°
=> m∠A = 126°
Hope you've understood...
A mailer for posters is a triangular prism as shown. Determine the lateral surface area of the mailer. Draw a net if necessary.
The lateral surface area of the mailer is 234 In²
How to determine the lateral areaIt is important to note that the formula for the lateral area of a triangular prism is expressed as;
A = (a + b+ c) h
Given that the parameters are enumerated as;
A is the lateral area of the triangular prisma is the base sideb is the base sidec is the base sideNow, substitute the values into the equation, we have;
Lateral area, A = (4 + 4 + 5) 18
Add the values
Lateral area = (13)(18)
Multiply the values
Lateral area = 234 In²
Hence, the value is 234 In²
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Select the statement that correctly defines continuous and discrete quantitative variables. O A continuous variable has an infinite number of possible values, whereas a discrete variable always has a finite number of possible values. O A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units. O A continuous variable has a countable number of possible values, whereas a discrete variable has an uncountable number of possible values. O A continuous variable has numerical values, whereas a discrete variable serves to group items into categories.
The statement that correctly defines continuous and discrete quantitative variables is:
"A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units."
A variable is a quantity that may assume any one of a set of values.
This means that a continuous variable can take on any value within a certain range, which could be infinite, and that it can have decimal values. In contrast, a discrete variable has specific values that are separate and countable, such as integers or categories. For example, the height of individuals is a continuous variable, while the number of siblings someone has is a discrete variable.
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a student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d= days, r= raffle tickets, and h= hours, what function can he use to calculate his earnings?
The function can be used to calculate his earnings, 15d + 0.25r + 2h
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
The function that the student can use to calculate his earnings is:
Earnings = 15d + 0.25r + 2h
where:
d = number of days worked
r = number of raffle tickets sold
h = number of hours worked at the game
The first term, 15d, represents the base pay of $15 per day worked.
The second term, 0.25r, represents the additional earnings of $0.25 per raffle ticket sold.
The third term, 2h, represents the additional earnings of $2 per hour worked at the game.
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determine an equation of the line drawn on the right. The shapes under the line are squares
Answer:57.6^3
thats t
NISSAN NP300 Special deal at 2007 price! R 221,180 (incl. VAT) Features • Dual airbags Power steering • Air-conditioning • Radio CD 3.3 Central locking Roof rack Roll bar and tonneau ber Side steps 3 year90 000km Service Plan • 3 year/100 000km Warranty NISSAN DataDot Anti theft Identification system NP300 Special Offers Months Interest Vehicle rate Price Deposit Click here to book your test drive *Residual Monthly instalments Total Payment R303 007 80 180 *Residual is an amount that must be paid at the end of the term after all the monthly payments have been made. 3.1 What is the cash price of the NISSAN NP 300? 3.2 If a person decide to pay for the vehicle in instalments, determine the number of years it will take to pay for the vehicle. Calculate the amount of the deposit needed. (2) (2) (3)
3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).
3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.
A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit
How The answer was obtained3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).
3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:
Number of years = Number of months / 12
Number of years = 80 / 12
Number of years ≈ 6.67 years
So it would take approximately 6.67 years to pay off the vehicle through instalments.
To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:
Cash price = Total payment - Residual
Cash price = R303,007 - R80,180
Cash price = R222,827
So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:
Deposit = 0.1 x Cash price
Deposit = 0.1 x R222,827
Deposit = R22,282.70
So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.
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Examine the figure below, solve for a, round to the nearest whole number.
T
37
A
46⁰
28
D
The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.
By angle sum property,
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
sin46°/a=sin84°/37=sin50°/t
0.7193/a=0.9945/37=0.7660/t
0.7193/a=0.9945/37
0.9945a=0.7193×37
0.9945a=26.6141
a=26.6141/0.9945
a=26.76
≈27
0.9945/37=0.7660/t
0.9945t=0.7660×37
0.9945t=28.342
t=28.342/0.9945
t=28.5
Therefore, the option B is the correct answer.
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Which of the following is not an exponential function?
A y = 5x
By = 5x - 1
© y=5x-1
Dy = 3.5x
The correct answer would be an option (C) y = 5x - 1 is not an exponential function.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
As per option (A), we have
y = 5ˣ
This is an exponential function.
As per option (B), we have
y = 5ˣ - 1
This is an exponential function.
As per option (C), we have
y = 5x - 1
This is not an exponential function because it is a linear function.
As per option (D), we have
D. y = 3.5ˣ
This is an exponential function.
Thus, the correct answer would be an option (C) y = 5x - 1
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The complete question would be as:
Which of the following is not an exponential function?
A. y = 5ˣ
B. y = 5ˣ - 1
C. y = 5x - 1
D. y = 3.5ˣ
Solve for x, please!! I really need help!!
Answer:
x = 13
Step-by-step explanation:
You want to find x when one half of the diagonal of a parallelogram is 80 and the other half is 6x+2.
DiagonalsThe diagonals of a parallelogram bisect each other, so point Y is the midpoint of each. That means ...
VY = YX
80 = 6x +2 . . . . . substitute the given values
78 = 6x . . . . . . . subtract 2
13 = x . . . . . . . . divide by 6
The value of x is 13.
HELP ASAP TIMED!! hurry
Answer:
The solution is C. (x+8)² + (y-11)² = 4
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = -8
k = 11
r = 2
(x + 8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
The answer is C. (x+8)² + (y-11)² = 4
Word Problems
1. The sum of 21 and three times a number is 60. What is that number?
2. Three times the difference between a number and three is equal to four times the number.
That is that number?
3. The sum of three consecutive integers is 48. Once you find them, answer this question: What
is > times the 3m as minus z times the 1St ?
4. Twice the smallest of three consecutive odd integers is seven more than the largest. What is the middle number?
5. The length of a rectangle is 3 cm more than the width. The perimeter is 22 cm. What is the
AREA of this rectangle? Note: A = (L)(W)
6. The perimeter of a triangle is 43 in. Side b is 3 times the length of side a. Side c is 1 more than twice the length of side a. What is the SUM of sides a and b?
In the word problems given above, the results are:
The number is 13.The number is 12.The consecutive integers are 15, 16, 17. The answer to the question is 19.The middle number is 9.The width is 4 cm and the length is 7 cm. The area of the rectangle is 28 sq cm.The sum of sides a and b is 28 in. (a=7 in, b= 21 in, c= 15 in)What is the rationale for the above response?1) Let's call the number we're looking for "x". According to the problem, "three times a number" is the same as 60 minus 21, which is 39. So we can write the equation:
3x + 21 = 60
Subtract 21 from both sides:
3x = 39
Divide by 3:
x = 13
Therefore, the number we're looking for is 13.
2)
Let's call the number we're looking for "x" again. According to the problem, "three times the difference between a number and three" is the same as "four times the number". So we can write the equation:
3(x - 3) = 4x
Simplify:
3x - 9 = 4x
Subtract 3x from both sides:
-9 = x
Therefore, the number we're looking for is -9.
3)
Let's call the first of the three consecutive integers "x". The next two would be x+1 and x+2. According to the problem, their sum is 48, so we can write the equation: x + (x+1) + (x+2) = 48
Simplify:
3x + 3 = 48
Subtract 3 from both sides:
3x = 45
Divide by 3:
x = 15
So the three consecutive integers are 15, 16, and 17. To answer the second part of the question, we can substitute these values into the given expression:
3m - z(1st) = 3(16) - 15(15) = 48 - 225 = -177
4)
Let's call the smallest of the three consecutive odd integers "x". The next two would be x+2 and x+4. According to the problem, twice the smallest is seven more than the largest, so we can write the equation:
2x = (x+4) + 7
Simplify:
2x = x + 11
Subtract x from both sides:
x = 11
So the three consecutive odd integers are 11, 13, and 15. The middle number is 13.
5)
Let's call the width of the rectangle "w". According to the problem, the length is 3 cm more than the width, so the length is w + 3. The perimeter is the sum of all four sides, which is:
P = 2w + 2(w + 3) = 4w + 6
We know that the perimeter is 22 cm, so we can write the equation:
4w + 6 = 22
Subtract 6 from both sides:
4w = 16
Divide by 4:
w = 4
So the width is 4 cm, and the length is 7 cm (since it's 3 cm more than the width). To find the area, we use the formula:
A = (L)(W) = (7)(4) = 28 square cm
6)
Let's denote the length of side a as x. Then we know that side b is 3 times the length of side a, or 3x, and side c is 1 more than twice the length of side a, or 2x+1.
Since the perimeter of the triangle is 43 inches, we can write the equation:
a + b + c = 43
Substituting in our expressions for b and c, we get:
x + 3x + 2x + 1 = 43
Simplifying the left-hand side, we get:
6x + 1 = 43
Subtracting 1 from both sides, we get:
6x = 42
Dividing both sides by 6, we get:
x = 7
thus:
a = 7
b= 3x = 21; na d
c = 2x + 1 = 14+1
c = 15
Thus the sum of sides a and b =
21 + 7
= 28
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Line A (y = 3x + 1) is transformed into
Line B (y=2x-7). Which best describes
the new slope and y-intercept?
The slope is[ ? ],
and the line is shifted[ ? ]
steeper
flatter
Answer:
The new slope is 2,
New y-intercept is - 7
Line is flatter since slope has reduced
Step-by-step explanation:
Suppose you bought ares company 4 years ago at a price of $63.00 per share sold it at $71.50 per share. How much money die you make? $37750 $382.50 $387.50 $392.50
The amount you made per share is $8.50.
How to determine the amount you madeFrom the question, we have the following parameters that can be used in our computation:
Initial amount = $63.00
Final amount = $71.50
To calculate the profit made, we need to find the difference between the selling price and the buying price per share, and then multiply by the number of shares.
The difference in price per share is:
Difference = $71.50 - $63.00
Evaluate the difference
Difference = $8.50
Hence, the profit per share is $8.50.
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