Answer:
-x+4, 4+-x
Step-by-step explanation:
Obtain these answers by moving the X and 4 around and multiplying the equation by -1
4 kg 2 dag when converted in g gives you?
Answer:
4020 grams
Step-by-step explanation:
4kg=4000g
2 dag= 20g
Total: 4000g + 20g = 4020g
Answer:
4020 grams
Step-by-step explanation:
1 kg = 1000 g
1 dag = 10 g
4 x1000= 4000
2 x 10 = 20
4000 + 20
Maël mixes 15 milliliters (mL) of bleach with 3.75 liters (L) of water to make a sanitizing solution for a daycare. The amounts of bleach and water always have to be proportional when he makes sanitizing solution. Which of the following could be combinations of volumes of bleach and water for Maël's sanitizing solution?
A. 12 mL bleach and 3 L water
B. 6 mL bleach and 1.5 L water
C. 3 mL bleach and 0.75 L water
D. 20 mL bleach and 5.5 L water
E. 11 mL bleach and 3.75 L water
Answer: A,B,C
Step-by-step explanation: A,B,C is the answer
What is the range of the function?
-2
3
3
9
00
4
12
2
A. (3, 9, 12)
B. (-2, 2, 3, 4)
C. {3}
OD. (-2, 2, 3, 4, 9, 12)
Answer:
yeheheehejehejejejjejjejejejejje
What is the explicit formula for this sequence?
−7, −4, −1, 2, 5, …
The explicit formula for the sequence is 3n -10
What is an Arithmetic Sequence ?An arithmetic sequence is a series of terms which have common difference between its consecutive numbers.
The sequence given is
−7, −4, −1, 2, 5, …
The common difference between each term is d =3
-4-(-7) = 3
-1-(-4) =3
The nth term for a sequence is given by
[tex]\rm T_n = a +(n-1)d[/tex]
Here a is the first term = -7
n is the no. of terms = n
d is the common difference = 3
Therefore the equation will be
[tex]\rm T _n = -7 + (n-1) * 3[/tex]
[tex]\rm T _n[/tex] = -7 +3n -3
[tex]\rm T _n[/tex] = 3n -10
Therefore the explicit formula for the sequence is 3n -10 .
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A blueprint of a house shows a dining room with
an area of 7 square inches. If the blueprint's
scale is 1 inch: 6 feet, what would be the actual
area of the dining room?
A = 7 in.²
Actual Area = [?] ft²
Answer: The Actual area of the dining room is 252 square feet.
Explanation:
How to Find the Actual Area Using Scale?
Given that the area of the house on a blueprint = is 7 square inches.
The scale of the blueprint = is 1 inch: 6 feet.
Therefore, we would have the following proportion:
The area on the blueprint/actual area = square of the scale
7/actual area = 1²/6²
7/actual area = 1/36
Actual area = (7)(36)
Actual area = 252 square feet.
A teacher has a 2-gallon (32-cup) container of juice. She gives each student One-half cup of juice. Which equation represents the amount of juice that remains, y, after x students are served? a y = 32 x minus one-half b y = one-half x minus 32 c y = negative one-half x + 32 d y = negative 32 x + one-half
The equation represents the amount of juice that remains, y, after x students are served is y = negative one-half x + 32; option C
Equation of the unknownQuantity of juice = 2 gallon = 32 cupsQuantity given to each student = 1/2 cupNumber of juice remaining = yNumber of students served = xy = 32 - 1/2x
This can also be written as;
y = -1/2x + 32
Therefore, the correct answer is option C; y = -1/2x + 32
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Natalie works in a toy shop and earns $43 per day. she earns an extra $3 for each toy she sells. if natalie wants to earn at least $70 per day, which inequality shows the minimum number of toys, n, that she should sell?
A number written in scientific notation has a ________ that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
A number written in scientific notation has a Negative Exponent that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
The coefficient is always a number larger than or equal to one and less than ten in scientific notation. There is an integer exponent. When using scientific notation to write integers bigger than ten
The exponent is positive and equals the number of spaces to the left of the original decimal point. When expressed in scientific notation, a negative exponent. The exponent's value is equal to how many places to the right the decimal has been pushed.As a result, when a number is smaller than 1, it will have a negative exponent in scientific notation.
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What is true about anglemsr? it must be acute. it must be a right angle. it must be equal to anglemrh. it must be equal to anglerms.
From the given diagram <msr is a right angle (equal to 90 degrees) and <mrh is acute since it is less than 90degrees.
Properties ofa rhombusThe given diagram is a rhombus that has the following properties
Opposite side are equalAll the sides are congruentThe opposite angles are equalThe sum of the adjacent angles are supplementaryFrom the figure shown, we can see that;
<msr is a right angle (equal to 90 degrees)
<mrh is acute since it is less than 90degrees.
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Answer:
A (it must be acute)
Step-by-step explanation:
5 m
2m
6 m
2 m
Mrs Phillips is going to cover the floor with floor boards.
One pack of floor boards will cover 2.5 m².
How many packs of floor boards does she need?
You must show your working.
Diagram NOT
accurately drawn
Mrs. Phillips needs to buy 8 packs of floor boards
In contrast to a square, a rectangle is a planar figure having four equal neighboring sides, four straight sides, and four right angles. An enclosed 2-D form called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposing sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
As per the figure attached Mrs. Phillips floor plan can divided into two rectangles
The area of rectangle is as follow:
Area = length(l) x Width(w)
Area of part 1 will be:
A = 6 x 2 = 12 m²
Area of part 2 will be :
a = 3 x 2 = 6 m²
Total area of floor = A + a
Total area of floor = 12 + 6
Total area of floor = 18 m²
Given one pack of floor boards will cover 2.5 m².
So total pack of floor block needed will be as follow:
Total pack of floor block = Total area of floor/Area covered by one pack of floor boards
Total pack of floor block = 18/2.5
Total pack of floor block = 7.2 packs ≈ 8 packs
Hence Mrs. Phillips needs to buy 8 packs of floor boards
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Find all real numbers $a$ that satisfy \[\frac{1}{a^3 + 7} -7 = \frac{-a^3}{a^3 + 7}.\]
The real number of the given expression is a=-2.
Given that the expression is [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex]
Real numbers is known as the union of both rational and irrational numbers. Real numbers can be both positive or negative and are denoted by the symbol “R”.
To compute the value of a.
In the given expression multiply both sides with (a³+7) as
[tex]\frac{(a^3+7)}{a^3+7}-7=\frac{-a^3(a^3+7)}{a^3+7}[/tex]
Simplify the expression as,
1-7(a³+7)=-a³
Expand out terms of the left hand side
1-7a³-49=-a³
-7a³-48=-a³
Taking out minus common from both sides and cancel them
-(7a³+48)=-(a³)
7a³+48=a³
Add -a³-48 on both sides
7a³+48-a³-48=a³-a³-48
6a³=-48
Divide both sides with 6
(6÷6)a³=(-48÷6)
a³=-8
write -8 in the expansion form which is (-2)×(-2)×(-2)=-8
a³=(-2)³
From above it says that
a=-2
Hence, real number that satisfy [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex] is a=-2.
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A survey participant is randomly selected. Let F be the
event that the participant's first motor vehicle had four
cylinders and let C be the event that the participant's
first motor vehicle was a car. What is the value of PIF
The probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is:
Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table(please refer to the attached picture)
A survey participant is randomly selected. Let F be the event that the participant’s first motor vehicle had four cylinders and let C be the event that the participant’s first motor vehicle was a car. What is the value of P(F or C)?
A) 0.59B) 0.68C) 0.71D) 0.80We have to find the value of P(F or C):
[tex]\rm P( F \ or \ C) = \dfrac{118+6+18+16+2}{118+6+18+16+12+20+2+6+2}[/tex]
[tex]\rm P( F \ or \ C) = \dfrac{160}{200}[/tex]
P(F or C) = 0.80
Thus, the probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.
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4x²-12x+9 = 5
☐ A. x= -√√5 +
312
B. x= √√4-3
C. X = -√√4-3
O D. x = √5 + 2/
□ E. x= -√5 +3
2
OF. x = √5 +3
2
Answer:
x = 3/2 ± [tex]\sqrt{5}[/tex] /2
Step-by-step explanation:
4x²-12x+9 = 5
Rearrange:
4x²-12x+4 = 0
Solve using the quadratic equation:
x = 3/2 ± [tex]\sqrt{5}[/tex] /2
Having exactly the same shape and size
Answer:
If two things have the same shape and size then they are congruent to one another. If they are only the same shape but not size, then they are similar.
If two things have the same shape and size then they are congruent to one another.
If they are only the same shape but not size, then they are similar.
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If 9x+3=30, what is the value of 3x+1
9x + 3 = 30
9x = 27
x = 3
Then 3x + 1 = 3 * 3 + 1 = 10
[tex]9x + 3 = 30 \\ \\ 9x = 30 - 3 \\ \\ 9x = 27 \\ \\ x = \frac{27}{9} \\ \\ x = 3.[/tex]
putting x = 3 in 3x + 1
[tex]3x + 1 \\ \\ 3 \times 3 + 1 \\ \\ 9 + 1 \\ \\ 10.[/tex]
The value of 3x + 1 is 10.
The width of a certain rectangle is 2 m greater than half its length. Four times its length is 26 m greater than its perimeter. What are the dimensions of the rectangle?
Answer:
Length = 30
Width = 17
Step-by-step explanation:
Let L = length of rectangle and W = Width
The first sentence gives the equation
W = L/2 + 2 ==>
2W = L +4 ==>
L = 2W - 4 .... (1)
The perimeter of the rectangle is 2(L+W) = 2L +2W
Second sentence gives us the equation
4L = 2L + 2W + 26 ===>
2L = 2W + 26 ...... (2)
(2) - (1) ==> L = 30 (2W cancels out)
From (1), W = 30/2 + 2 = 15 + 2 = 17
Check:
Using these values and substituting in equation 2 gives us
2 * 30 = 2* 17 + 26
60 = 34 + 26
which matches
Hi everyone! I would be really glad if anyone could help me solve these step by step, I tried solving it on my own and viewing lessons, but I still don't understand. Thank you.
The equation of the function is f(x) = x(x + 2)(x -1)(x -3)
The function end behaviorFrom the graph, we have the following highlight:
As x increases, the function values increaseAs x decreases, the function values increaseThe above means that:
f(x) approaches positive infinity irrespective of the x value
Hence, the end behavior of the function is:
[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]
The sign of the leading coefficientSince, the function opens upward.
Then the sign of the leading coefficient is positive
The zeros of the functionThis is the point, where the graph crosses the x-axis.
From the graph, we have the zeros to be:
x = -2, x = 0, x = 1 and x = 3
Since the graph crosses the x-axis at this point, then the multiplicity of the zeros is 1
The equation of the functionIn (c), we have:
x = -2, x = 0, x = 1 and x = 3
Rewrite as:
x + 2= 0, x = 0, x - 1 = 0 and x - 3 = 0
Multiply these values
f(x) = x(x + 2)(x -1)(x -3)
Hence, the equation of the function is f(x) = x(x + 2)(x -1)(x -3)
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100 pints help would be greatly appreciated
Answer:
(4, -2) (see attached)
Step-by-step explanation:
Vector addition on a graph is accomplished by placing the tail of one vector on the nose of the one it is being added to. The negative of a vector is in the direction opposite to the original.
__
vector componentsThe components of the vectors are ...
u = (1, -2)
v = (-6, -6)
Then the components of the vector sum are ...
2u -1/3v = 2(1, -2) -1/3(-6, -6) = (2 +6/3, -4 +6/3)
2u -1/3v = (4, -2)
graphicallyThe sum is shown graphically in the attachment. Vector u is added to itself by putting a copy at the end of the original. Then the nose of the second vector is at 2u.
One-third of vector v is subtracted by adding a vector to 2u that is 1/3 the length of v, and in the opposite direction. The nose of this added vector is the resultant: 2u-1/3v.
The resultant is in red in the attachment.
The answer is (4, -2) hope this helps!
What is the equation of the line that is parallel to y=x+4 and that passes through (5,–4)?
Answer:
y = [tex]\frac{1}{5}[/tex] x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{5}[/tex] x + 4 ← is in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{1}{5}[/tex] x + c ← is the partial equation
to find c substitute (5, - 4 ) into the partial equation
- 4 = 1 + c ⇒ c = - 4 - 1 = - 5
y = [tex]\frac{1}{5}[/tex] x - 5 ← equation of parallel line
does y - x = 2 show direct variation
Answer:
no
Step-by-step explanation:
if I use any numbers too .the numbers can not be constant numbers so this equation is not a direct variation
7 - 5 = 2
6- 4 = 2
not contstant
Use the distance formula to find the perimeter of the triangle below. Round you answer to the nearest hundredth.
Answer: The perimeter of this triangle is 13.47.
Step-by-step explanation:
First you should choose your first two points on the triangle that are on the same line. In this case I'll start with C = (3,3) and B = (8,6)[tex]d = \sqrt{(3 - 8)^2 + (3-6)^2}[/tex]
*Note: Keep X and Y consistent in the distance equation.
The distance for CB = 5.831
After finding this distance continue onto a new set of points to find a new length of the triangle, my second set of points will be A = (5,7) and B = (8,6) to find the length of AB.
[tex]d = \sqrt{(5 - 8)^2 + (7-6)^2}[/tex]
The distance for AB = 3.162
Now you're going to need to use your final to points, in this case for me A and C, and find the length of your final segment. So, I'll use point A = (5,7) and point C = (3,3).
[tex]d = \sqrt{(5 - 3)^2 + (7-3)^2}[/tex]
The distance for AC =4.472
Then find the perimeter by adding up the three side lengths.
AB + CB + AC = P
[tex]5.831 +3.162+4.472=13.465[/tex]
Finally, round 13.465 to the nearest hundredth, 13.47.
*Note: Make sure not to round your answer until the end of the problem to avoid less accurate or even wrong answers.
5. The mapping f: xax² + bx + c defined on the set of real numbers is such that f(0) = -4,f(1)-1 and/(-1)= -5. Find a, b and c. 5 . The mapping f : xax² + bx + c defined on the set of real numbers is such that f ( 0 ) = -4 , f ( 1 ) -1 and / ( - 1 ) = -5 . Find a , b and c .
It looks like you're saying
[tex]f(x) = ax^2 + bx + c[/tex]
and you're asked to find [tex]a,b,c[/tex] given [tex]f(0)=-4[/tex], [tex]f(1)=-1[/tex], and [tex]f(-1)=-5[/tex].
Evaluate [tex]f[/tex] at the three given points:
[tex]x=0 \implies f(0) = \boxed{c = -4}[/tex]
[tex]x=1 \implies f(1) = -1 = a + b + c \implies a+b = 3[/tex]
[tex]x=-1 \implies f(-1) = -5 = a - b + c \implies a - b = -1[/tex]
[tex](a+b) + (a-b) = 3 + (-1) \implies 2a = 2 \implies \boxed{a=2}[/tex]
[tex]a-b = -1 \implies \boxed{b=3}[/tex]
and the mapping is [tex]f(x) = 2x^2 + 3x - 4[/tex].
please help!!!!!!!
picture below
A decagon with points labeled a through j clockwise. point a is the top left point. if this regular decagon is rotated counterclockwise by 3 times the smallest angle of rotation, which vertex will be in the top position?
The e vertex of the decagon will be in the top position after rotating it counterclockwise by 3 times the smallest angle of rotation.
Which vertex will be in the top position of the regular decagon?
A regular decagon has 10 sides of equal lengths with points labeled 'a' through 'j' clockwise. It is given that the point a is the top-left point. Hence, the the vertex which is in the the top position currently is 'b'.
Now, the smallest angle of rotation will be the angle between the two sides of the decagon.
In the first rotation by the smallest angle in counterclockwise direction, point 'c' will come to the top position. In the second rotation by the smallest angle in counterclockwise direction, point 'd' point will become the top most vertex. Finally, after the third similar rotation, 'e' vertex will be in the top position of the decagon. (Refer the attached diagram)
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The point (0, 0) is a solution to which of these inequalities?
O Ay+7<2x - 6
OB. y-7<2x-6
OC. y-6<2x-7
OD. y+7<2x+6
The point (0, 0) is a solution to which of these inequalities are satisfied. so option B. y-7<2x-6is the only correct answer.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
The point (0, 0) is a solution to which of these inequalities are satisfied.
A. y+7<2x - 6
7 < -6
So, it is incorrect.
B. y-7<2x-6
-7 < -6
So, it is correct.
C. y-6<2x-7
-6 < -7
So, it is incorrect.
D. y+7<2x+6
7 < 6
So, it is incorrect.
Hence, option B is the only correct answer.
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Micah is keeping track of how much he spends this month on gas. In the first week, he bought x gallons of gas at $2.39 per gallon. In the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. So far this month, he has spent a total $46.21 on gas.
In the first week, Micah bought
x gallons of gas.
In the second week, Micah bought
x gallons of gas.
Answer: In the first week, Micah bought 11 gallons of gas,
and in the second week, he bought 8 gallons of gas
Step-by-step explanation:
In the first week, Micah bought x gallons of fuel at $2.39/gallon
In the second week, he bought (x - 3) gallons at $2.49/gallon
Formulating an equation and solving for x gallons of fuel:
x × 2.39 + (x - 3) × 2.49 = 46.21
2.39x + x × 2.49 − 3 × 2.49 = 46.21
2.39x + 2.49x − 7.47 = 46.21
4.88x − 7.47 = 46.21
4.88x = 53.68
[tex]\frac{4.88x}{4.88} = \frac{53.68}{4.88}[/tex]
x = 11
Therefore,
In the first week, Micah bought 11 gallons of gas
In the second week, he bought (11 - 3) = 8 gallons of gas
question below
What matrix is the result of m*H?
Enter your answer by filling in the boxes. Enter any fractions as simplified fractions.
Answer:
[tex]m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right][/tex]
Step-by-step explanation:
Calculate the value of m
Given:
[tex]3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right][/tex]
Therefore:
[tex]\implies 3=\dfrac{2}{3}m[/tex]
[tex]\implies m=3 \times \dfrac{3}{2}[/tex]
[tex]\implies m=\dfrac{9}{2}[/tex]
Calculate the value of H
Given:
[tex]\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)[/tex]
Therefore:
[tex]\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]
Calculating m × H
[tex]\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]
[tex]\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right][/tex]
[tex]\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right][/tex]
What is the value of x in the equation 8x – 2y = 48, when y = 4?
Answer: x = 7
Step-by-step explanation:
First, we will plug 4 in for y. Then, to solve we will isolate the variable "x" in the equation.
Given:
8x – 2y = 48
Plug in the y value of 4:
8x – 2(4) = 48
Multiply -2 times 4:
8x – 8 = 48
Add 8 to both sides of the equation:
8x = 56
Divide both sides of the equation by 8:
x = 7
Answer:
x=7
Step-by-step explanation:
8x – 2y = 48
Let y=4
8x -2(4) = 48
8x - 8 = 48
Add 8 to each side
8x-8+8= 48+8
8x = 56
Divide by 8
8x/8 = 56/8
x = 7
Select Translation, Reflection, or Rotation to identify the single transformation that transforms ∆PQR to ∆P'Q'R'.
Translation Reflection Rotation
(The pictures of the graphs are in the file attached, please look at them to know which ones are for which option.
You have 200$ allocated for your gym membership. what is the maximum number of visits you can make with each membership??
The maximum number of visits you can make with each membership is 104.
What is gym membership?Gym membership refers to the cost to register, attend, and use a gym as a member for an agreed period.
Some gym memberships require one-time payments made monthly or annually.
Question Completion:Assume that the annual gym fee is $200 for Saturdays and Sundays only.
Thus, in this scenario, the maximum number of visits you can make with each membership is 104.
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