Answer:
number line with open point at 10 with arrow pointing left
Step-by-step explanation:
Answer:a
Step-by-step explanation:
2(x+3)
2x+6
This is an example of the blank property.
4x-3
x=2
4(2)-3
The blank property is use here.
commutative property is an example of the blank property.
What in mathematics is a commutative property?
This law basically indicates that while adding and multiplying integers, you can rearrange the numbers in a problem without modifying the solution. Division and subtraction do not work commutative.What is a commutative property example?
Commutative characteristic of addition: The sum is unaffected by the arrangement of the addends. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4, plus 2, equals 2, plus 4. 4 + 2 = 2 + 44. Changes to the order of the addends have no effect on the sum, because of the associative property of addition.2(x+3) = 2x+6
Commutative Property used in this function.
4x-3
put x=2
4(2)-3 = Commutative Property used in this function.
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Solve the equation.
2x^2 = -128
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 8i[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 2 {x}^{2} = - 128[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{ 128}{2} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - 64[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 64} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{( - 1) \sdot(64)} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ 64} \sdot \sqrt{ - 1} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = 8 \sdot i[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: x = 8i[/tex]
[ i = iota, and i² = -1 ; (complex number) ]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]x=8i[/tex]
Step-by-step explanation:
Given equation:
[tex]2x^2=-128[/tex]
Divide both sides of the equation by 2:
[tex]\implies \dfrac{2x^2}{2}=\dfrac{-128}{2}[/tex]
[tex]\implies x^2=-64[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{-64}[/tex]
[tex]\implies x^2=\sqrt{-64}[/tex]
Rewrite -64 as 8² · -1:
[tex]\implies x=\sqrt{8^2 \cdot-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies x=\sqrt{8^2}\sqrt{-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies x=8\sqrt{-1}[/tex]
[tex]\textsf{Since $\sqrt{-1}=i$}[/tex]
[tex]\implies x=8i[/tex]
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.
An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].
What is the difference in
elevation between 3 feet above
sea level and 20 feet below sea
level?
Answer:
23
Step-by-step explanation:
3-(-20)
Assume AABC
ALMN. If AB = 41,
MN = 38, and LN = 25, what is the length
of AC?
1 Assume AFGH = APQR if FH = 3
QR = 4.5, what is the length of
FG:
, and
PQ
The missing lengths of the sides of the congruent triangles described are:
AC = 25 units.
PQ = 3 units.
What is the Side Lengths of Congruent Triangles?The corresponding side lengths of any two or more triangles that are congruent to each other are always equal in measure. That is, the three sides of one triangle have lengths that are equal to the corresponding three sides of the other triangle, if both triangles are congruent triangles.
We are told that triangles ABC and LMN are congruent to each other, therefore:
AB = LM = 41 units [corresponding sides]
AC = LN = 25 units [corresponding sides]
BC = MN = 38 units [corresponding sides].
Therefore, the length of AC is 25 units.
Also, it is assumed that triangles FGH and PQR are congruent triangles, therefore:
FG = PQ = 3 units [corresponding sides]
GH = QR = 4.5 units [corresponding sides]
Therefore, the length of PQ is 3 units.
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c) Calculate the percentage his peanuts. 2. Sipho's aunt sells her business and the new owner is not prepared to supply Sipho with free packaging. He now has to buy the packets and pays R50 for 1 000 packets. a) Calculate what one packet costs him. b) If Sipho continues to sell the packets at R1 each, calculate the percentage profit that he will make on his peanuts. c) If Sipho wants to make the same profit on the peanuts as before, calculate what he should charge for a 100 g of peanuts. d) What practical problem do you foresee in the case of Question 2. c)? e) Describe how you would advise Sipho to price his peanuts. lu huving a product and selling it at a profit. (2)
According to the given problem,
(i) It is given that,
The cost price of 1000 packets of peanuts = Rs. 50
We need to find the cost price of 1 packet of peanut = [tex]\frac{50}{1000}[/tex] = Rs. 0.05
(ii) Selling price at which Sipho continues to sell 1 packet = Rs. 1
Then Selling price of 1000 packets = 1000 x 1 = Rs. 1000
Then Profit made by sipho = Selling Price - Cost Price
= 1000 - 50
= Rs.950
Profit percentage gained by Sipho = [tex]\frac{Profit}{Cost Price}[/tex] x 1000
= [tex]\frac{950}{50}[/tex] x 1000
= 1900 %
(iii) The profit earned by sipho remains same, we nee to find the cost price at which Sipho should sell 100gm of her peanuts is Rs. 1
(iv) I would advice Sipho to sell peanuts at a selling price more than the cost price in order to gain profit
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What is the m∠QPT? Show work.
Answer:
m∠QPT = 32°
Step-by-step explanation:
∠QPT and ∠SPR are vertical angles, meaning that the measure of their angles are congruent (the same).
Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).
Step 1: Set the measure of the angles to equal each other.
[tex]\implies m \angle QPT = m \angle SPR[/tex]
[tex]\implies (2x+12) = (4x - 8)[/tex]
Step 2: Subtract 4x from both sides.
[tex]\implies 2x-4x+12 = 4x - 4x - 8[/tex]
[tex]\implies -2x+12 = - 8[/tex]
Step 3: Subtract 12 from both sides.
[tex]\implies -2x+12-12 = - 8-12[/tex]
[tex]\implies -2x = -20[/tex]
Step 4: Divide both sides by -2.
[tex]\implies \dfrac{-2x}{-2} = \dfrac{-20}{-2}[/tex]
[tex]\implies x = 10[/tex]
Step 5: Find the measure of ∠QPT by substituting 10 for x.
[tex]\implies [2(10)+12]^{\circ}[/tex]
[tex]\implies 32^{\circ}[/tex]
Therefore, the measure of ∠QPT is 32°.
Helena was curious if quadrilaterals QRSTQRSTQ, R, S, T and XYZWXYZWX, Y, Z, W were congruent, so she tried to map one figure onto the other using transformations:
Helena came to the right conclusion because the transition of quadrilaterals is accurately depicted.
Given,
Two quadrilaterals = QRST and XYZW
Helena came to the right conclusion because the transition of quadrilaterals is accurately depicted.
How should the facts be explained?
According to the information provided, Helena was interested to know whether the quadrilaterals were congruent.
The quadrilaterals in this instance cannot be mapped into one another via a series of stiff transformations, hence they are not congruent.
As a result, no mistakes are made.
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Question 17 of 25
What is the measure of BVD?
B
105⁰
V
D
A. 95°
B. 75°
C. 105°
D. 115°
C that's because the angles are vertically opposite
20 POINTS What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Length of major axis Length of minor axis
The lengths of the axes in the elipse are given as follows:
Major axes: [tex]8\sqrt{14}[/tex].Minor axes: [tex]4\sqrt{53}[/tex].Equation of an elipseThe equation of an elipse of center (x*, y*) is given according to the following rule:
(x - x*)²/a² + (y - y*)²/b² = 1.
The lengths of the axes are given as follows:
Major axes: 2 x greater of a or b.Minor axes: 2 x lesser of a or b.In this problem, the equation of the elipse is given as follows:
(x - 3)²/212 + (y + 4)²/224 = 1.
Hence the measures of a and b are calculated as follows:
Measure of a: a² = 212 -> a = sqrt(212) -> a = 2sqrt(53).Measure of a: b² = 224 -> b = sqrt(224) -> b = 4sqrt(14).Hence the lengths of the axes have numeric values given by:
Major axes: 2 x 4sqrt(14) = 8sqrt(14) = [tex]8\sqrt{14}[/tex].Minor axes: 2 x 2sqrt(53) = 4sqrt(53) = [tex]4\sqrt{53}[/tex].The difference in the measures is because I suppose there was a typo in the equation of the ellipse, but the procedure is as presented in this problem.
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A square play area has an area of 5625m2. How long is each side
Answer:[tex]75m^{2}[/tex]
Step-by-step explanation: Just have to square root 5625m2 to get each side length
Use the graph on the right to locate points D, E, and G
5. Locate D so that ABCD is a rectangle.
6. Locate E so that ABCE is a trapezoid
7. Locate G so that ACBG is a parallelogram that is not a rectangle
The graph on the right to locate points D, E, and G is, 5.D(0, 3), 6. E(0, 2), 7. G(0, -3).
What is graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
Here, for instance, we can plot a graph showing the type and quantity of school supplies used by pupils in a class based on the data provided below.
Rectangle: Rectangles have parallel opposite sides; therefore, D must be positioned such that CD is parallel to AB and AD is parallel to BC. This necessitates that point D be.
D(0, 3)
Trapezoid: A trapezoid has one set of parallel opposed sides. As a result, we must select point E such that either AE or CD are parallel to AB.
We have picked point E in the accompanying picture so that AE and BC are parallel.
E(0, 2)
Keep in mind that point E might be somewhere left of point C on line y=3 or above point A on line x=0. Point D and point E cannot be in the same place.
E(0, p) or E(q, 3) where p > 0, q < 8, and p≠3, q≠0
Parallelogram: The middle of each parallelogram is where its diagonals connect. As a result, the midway of AB and CG must coincide. We need to have... in order for that to occur.
A + B = C + G
G = A + B - C = (0, 0) +(8, 0) -(8, 3) = (0+8-8, 0+0-3) = (0, -3) (0, -3)
Point G is located where...
G(0, -3)
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Create an equation that is parallel to the line y = 2x + 3 and goes through the point (0, -2).
write each expression as the product of two factors h•3+6•3
Answer:
3(h + 6)
Step-by-step explanation:
Since we are starting with
h•3 + 6•3, try to see that there are two terms here h•3 and 6•3. In both of these terms is the factor 3. We can factor out the 3. This leaves behind (h + 6).
h•3 + 6•3
= 3(h + 6)
Its like "un-distributive" property. (this is not a technical term)
its any of this greater than 7.03 7.031 7.030 7.003 7.0
7.031 is greater than 7.03.
The given value is having a 2-digit decimal place.
The options which are provided are:
1)7.031
2)7.030
3)7.003
4)7.0
Comparing the first decimal placeholder of each option with the question, all options have the same digit which is zero.
Comparing the second decimal placeholder of each option with the question, only option 1)7.031 and option 2)7.030 is having .03 the rest of the options, option 3)7.0003 and 4)7.0 have .00 has their second digit hence both option 7.0003 and 7.0 are smaller than 7.03.
Out of the remaining options, when options 1)7.03 and 2)7.031 are compared it can be seen that 7.031 is greater because the third decimal placeholder of 7.031 is 1 and 7.03 is 0 hence 7.031 is greater than 7.03.
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21) Richard has 18 1/3 coins of the coins are dimes, of the coins are nickels, and the rest
are quarters. How many of the 18 coins are quarters?
The number of quarters, Richard have is 3 out of 198 coins he have.
What is termed as the fraction?Fractions are defined as a numerical value that represents a portion of a whole. A fraction is a portion as well as section of any quantity taken from the whole, which can be any amount, a specific value, or an item. Every fraction has a numerator and a denominator separated by a horizontal bar recognized as the fractional bar.For the given question,
The total number of coins Richard have is 18.
The fraction of dimes is 1/3.
1/3 of 18 = (1/3)×18 = 6
The number of dimes is 6.
The fraction of nickles is 1/2.
1/2 of 18 = (1/2)×18 = 9
Let the number of quarters be 'x'.
Total coin = dimes + nickles + quarters.
18 = 6 + 9 + x
x = 18 - 15
x = 3
Thus, the number of quarters, Richard have is 3.
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Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
[tex]f(x)=f(x)=\,\,-2(x-3)^2+5−2(x−3) 2 +5[/tex]
f(x) is maximum at x=3 and the maximum value of f(x) = 5.
The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of the maximum and minimum functions are maxima and minima, respectively.
The given quadratic function is [tex]f(x) = -2 (x-3)^{2} +5[/tex]
Comparing it with [tex]f(x) = a (x-h)^{2} +k[/tex]
Here, a= -2, h =3 and k = 5.
Since a is negative, so parabola is open downward.
Therefore, the quadratic function has a maximum value.
Here, the vertex is (h,k) =(3,5)
Therefore, f(x) is maximum at x=3 and the maximum value of f(x) = 5.
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Select the correct answer.
Which expression is equivalent to the given expression?
(6n-5) (3n-³)²
A. 301
36
OB. 547.30
367.30
O A.
O c.
O D. 511
54
Answer:
[tex] \frac{54}{n {}^{11} } [/tex]
Step-by-step explanation:
[tex](3n {}^{ - 3} ) \times (3 {n}^{ - 3} )[/tex]
[tex]6 {n}^{ - 5} \times 9n {}^{ - 6} [/tex]
[tex]54 {n}^{ - 11} [/tex]
[tex] \frac{54}{n {}^{11} } [/tex]
Amy, Ravi, and Bob have a total of $127 in their wallets. Bob has 4 times what Ravi has. Ravi has $7 less than Amy. How much do they have in their wallets?
I ONLY HAVE A FEW MINUTES LEFT TO TURN THIS IN!!
If Amy, Ravi, and Bob have a total of $127 in their wallets. Bob has 4 times what Ravi has. Ravi has $7 less than Amy. The amount they have have in their wallets is : Army has $22.33, Ravi $89.33, Henry $15.33.
How to determine wallet amount?Let Army represent x dollars
Let Ravi represent 4x
Let Bob represent x - 7
Hence,
x + x - 7 + 4x = 127
Simplify by combining like terms
6x - 7 = 127
Add 7 to both sides of the equation leaving 6x
6x = 127+7
6x = 134
x =134/6
x = 22.33
x = Army has $22.33
Ravi
4x where x = 22.33
4(22.33) = 89.33
Bob
x - 7 where x = 22.33
22.33 -7 = 15.33
Prove :
Ravi + Bob + Henry = 127
= 22.33 +89.33 + 15.33 = 126.99 ≅127 (Approximately)
Therefore the have $22.23, $89.33 and 15.33 respectively.
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Evaluate these expressions.
Type the correct answer in each box.
6² =
8²=
15² =
If h represents a number, which EQUATION is a correct translation of “Seventy less than 9 times a number is 375"?
Given the word exprssion:
Seventy less than 9 times a number is 375
Where h represents the number.
We have:
Seventy less than 9 times a number: 9h - 70
Seventy less than 9 times a number is 375: 9h - 70 = 375
Therefore, the equation that is a correct translation of Seventy less than 9 times a number is 375 is: 9h - 70 = 375
ANSWER:
9h - 70 = 375
What is an equation in point-slope
form of the line shown in the
graph, using the point (2, 2)?
8
6
4
2
OY
y
2
x^
X
Answer:
Step-by-step explanation:
Jan 15, 2020 — this line also pass through 0,8 and 2,2. slope is -3. the equation is y-2= -3(x-2). heart outlined. Thanks 10.
2 answers
·
10 votes:
Answer:this line also pass through 0,8 and 2,2. slope is -3. the equation is y-2= -3(x-2)
Missing: OY | Must include: OY
HELP PLEASE!! due at 8pm tonight.
Answer:
y=-1/3x+5
Step-by-step explanation:
Use rise/run
3. The boundary line on the graph represents the equation 6 = 5x + 2y.Write an inequality that is represented by the graph. **
Step 1. The expression we have for the graph is:
[tex]6=5x+2y[/tex]To find the inequality that represents the graph, we need to solve for y first.
Step 2. Solve for y in the equation:
[tex]6=5x+2y[/tex]We can also represent this as follows:
[tex]5x+2y=6[/tex]Move 5x to the right side as a -5x:
[tex]2y=-5x+6[/tex]Move the two that is multiplying on the left side, to divide on the right side:
[tex]y=\frac{-5x+6}{2}[/tex]Simplify:
[tex]\begin{gathered} y=-\frac{5}{2}x+\frac{6}{2} \\ \downarrow \\ y=-\frac{5}{2}x+3 \end{gathered}[/tex]This is the equation of the line.
Step 3. Find the inequality.
Since the shaded part is below the line, and it has a dotted line, the inequality that represents this is:
[tex]y<-\frac{5}{2}x+3[/tex]Which are the values below the dotted line.
Answer:
[tex]y<-\frac{5}{2}x+3[/tex]your balance is 89.75 and you deposit 156.90 and write a check for 34.79 and a withdrawal of 50.00 what is your new balance
I’m stuck on what equation I need to set up
The painting is a square, which means all its sides are equal.
If x is the length of one side, then, all the remaining 3 sides also have the same length: x.
The area of a square is the square if its side, then, for a square with sides x:
[tex]\text{Area}=x\cdot x=x^2[/tex]We know that the area of the painting will be 400 square inches, then:
a. The equation that can be set up to find the length of a side is:
[tex]x^2=400in^2[/tex]b. We can solve the equation by finding a number that multiplied by itself gives 400. For this case, we have two solutions. 20 and -20, since:
[tex]20^2=20\cdot20=400[/tex]And:
[tex](-20)^2=(-20)\cdot(-20)=400[/tex]-20 is also a solution because as a negative number, when multiplied by itself, gives a positive one. (A product between negative numbers gives always a positive number).
c. We have two solutions, however, only one of them makes sense: the 20. A negative length makes no sense, so we can discard the second solution (-20).
d. The length of the wood trim needed to go around the painting is then 20 inches. (we should not forget the units.)
Determine the value of y in the inequality.
18 + 6y < 42
Answer:
y<4
Steps:
18 + 6y < 42
6y < 42 - 18
y < 24/6
y < 4
Answer:
y<4
Step-by-step explanation:
18+6y<42
Subtract 18 from both sides.
6y<42−18
Subtract 18 from 42 to get 24.
6y<24
Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.
[tex]y < \frac{24}{6} [/tex]
Divide 24 by 6 to get 4.
y<4
Question 11
I just want the answer :)
The value of x is 4
The value of m ∠VUR = 126°
How to determine the valuesFrom the image shown, we have that;
A triangle is formedThe inscribed triangle is an equilateral triangleNote that all the sides of a equilateral triangle are equal.
Then, we have;
RV = SV = RSRV = 3x + 8SV = 6x - 4Now, equate the side lengths of the inscribed triangle, we have;
3x + 8 = 6x - 4
collect like terms
3x - 6x = -4 - 8
subtract the like terms
-3x = -12
Make 'x' the subject of formula
x = -12/-3
Find the quotient
x = 4
Note that m ∠VRS and m ∠VUR are on a straight line, we have;
m ∠VRS + m ∠VUR = 180
substitute the values
54° + m ∠VUR = 180
m ∠VUR = 180 - 54
m ∠VUR = 126°
Hence, the values are 4 and 126°
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How do I solve for number 4 and 5?
Answer:
i cant really see the words
Step-by-step explanation:
Evaluate the expression if a = 2 , b = − 3 , c = − 4 , h = 6 , y = 4 , and z = − 1 . | a − 5 | − 1
The solution to the expression | a − 5 | − 1 is 2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
| a − 5 | − 1
Also, we have the values to be
a = 2 , b = − 3 , c = − 4 , h = 6 , y = 4 , and z = − 1
Substitute these values in the given equation
So, we have the following equation
| a − 5 | − 1 = | 2 − 5 | − 1
Evaluate the difference
So, we have the following equation
| a − 5 | − 1 = | −3 | − 1
This gives
| a − 5 | − 1 = 3 − 1
Evaluate the difference
| a − 5 | − 1 = 2
Hence, the value is 2
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.