Answer:
x = 2 or x = -4
Step-by-step explanation:
-5|x + 1| + 3 = -12
Add -3 to both sides.
-5|x + 1| = -15
Divide 5 into both sides.
|x+1| = 3
Possibility 1:
x + 1=3
x = 2
Possibility 2:
x + 1 = - 3
x = -4
Answer:
Step-by-step explanation:
This is our absolute value equation for which we want the values of x that make it true:
-5 | x + 1 | + 3 = -12. Subtracting 3 from both sides gives us
-5 | x + 1 | = = -15. Divide both sides by -5 to get
| x + 1 | = 3
This says, in words, "how many units from 3 is -1 on a number line?"
We have the following 2 equations:
x + 1 = 3 and x + 1 = -3
Solving the first one for x:
x = 2
Solving the second one for x:
x = -4
Both 2 and -4 are 3 units from -1 on a number line.
The points (0, 1), (7, 1), and (2, -3) represent the vertices of a triangle. What is the area, in square units, of the triangle?
Answer:
14 [tex]u^2[/tex]
Step-by-step explanation:
The attached image shows the diagram of the triangle drawn on the Cartesian plane.
We can see that it has the following measures:
base: [tex]b=7u[/tex]
height: [tex]h=4u[/tex]
the area of a triangle is given by the formula:
[tex]A=\frac{b*h}{2}[/tex]
substituting the values:
[tex]A=\frac{(7u)(4u)}{2}\\ \\A=\frac{28u^2}{2} \\\\A=14u^2[/tex]
the area, in square units, of the triangle is 14
Sandy borrowed 6709 R.O from a bank to buy a piece of land. If the bank charges 12 1/3 % compounded each two months, what amount will she have to pay after 2 years and half? Also find the interest paid by her.
Answer:
she is paying back 9112.5 R.O
Interest paid back is 2,403.95
Step-by-step explanation:
To find the amount, we use the compound interest formula.
This is given as;
A = I( 1 + r/n)^nt
where A is the amount we are trying to calculate
I is money borrowed = 6709
r is the interest rate = 12 1/3% = 37/3 = 12.33% which is same as 12.33/100 = 0.1233
n is the number of times interest is compounded. We have 15 2 months in 2 and a half years
t is the number of years = 2.5
Plugging these values, we have;
A = 6709(1 + 0.1233/15)^(15)(2.5)
A = 6709(1.0082)^(37.5)
A = 9112.95 R.O
Interest is amount - principal( money borrowed)
9112.95 - 6709 = 2403.95
Name the plane represented by the front of the box.
Answer:
FBC
Step-by-step explanation:
It's the only one at the front of the box
Answer:
FBC
Step-by-step explanation:
thats what it says on my sheet
Can someone please help me I’m stuck with this question I don’t know what’s the answer please help
Answer:
the SSS similarity theoremPlease see the attached picture...
Hope it helps...
Good luck on your assignment....
A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select all that apply.
A. a reflection over the y–axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2 B. a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5 2 C. a dilation about the origin by a scale factor of 2 3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left D. a dilation about the origin by a scale factor of 5 7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3 4
Answer:
C, D
Step-by-step explanation:
Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.
C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left
D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4
Answer:
c and something is not d
Step-by-step explanation:
Find the height of a cylinder of volume 200cm^3 and radius 4
Answer:
3.98 cm
Step-by-step explanation:
V= πr²h
V= 200 cm³, r= 4 cm, h=?
h= V/(πr²)= 200/(3.14*4²)= 3.98 cm
A circular pond has a radius of 6 feet. What is the area of that pond?
Answer:
radius x radius x pi = area of circle
6 x 6 = 36
36 x 3.14 = 113.04
113.04
Hope this helps
Step-by-step explanation:
What is the domain of the step function f(x) = ⌈2x⌉ – 1?
Answer:
believe its 2x cause 1 was wrong
What is the square root of 1/3
Answer: √3/3
Step-by-step explanation:
√1/3 = 1/√3 x √3 / √3
= √3/3
Answer:
±1/√3
Step-by-step explanation:
=> [tex]\sqrt{\frac{1}{3} }[/tex]
=> [tex]\frac{\sqrt{1} }{\sqrt{3} }[/tex]
√1 = ±1
=> ±1/√3
Simplify
(y + 1)
(y + 1)
Answer:
That is already at its simplest form.
Step-by-step explanation:
(y + 1)(y + 1) or (y + 1)² is the factored form of y² + 2y + 1. You cannot break it down any further after you reached binomials after you factor unless you are solving for x.
I WILL MAKE YOU THE BRAINLLEST
Which description matches the graph of the inequality y ≤ 2x – 1?
A.a shaded region below a solid boundary line
B.a shaded region above a dashed boundary line
C.a shaded region below a dashed boundary line
D.a shaded region above a solid boundary line
Answer:
The correct option is;
A. a shaded region below a solid boundary line
Step-by-step explanation:
The parameters given are;
The equation, y ≤ 2x - 1
We compare the above equation with the equation for a straight line, y = m·x + c to get
The slope m = 2
The y-intercept c = -1
Therefore, we have;
The graph of an inequality of a y value which is less than or equal to a function is represented by a solid line having the shaded region, which shows the area that satisfies the inequality, shaded below the line
Which gives the correct option as A. A shaded region below a solid boundary line.
The measures of both
Answer:
m<EAD=29°
m<CAB=119°
Solution,
< CAE+<EAD+90°=180°( angles on a straight line)
61+<EAD+90°=180°
<EAD=180-(90+61)
=180-151
=29°
<CAB+<FAB=180°( Linear pair)
<CAB+61°=180°
<CAB=180°-61°
<CAB=119°
hope this helps ..
Good luck on your assignment..
Alexi thinks of a number. he multiplies his number by 10 and then divides the answer by 100. he then multiples this answer by 1000 and gets a final answer of 67. What number does Alexi thinks of first ? please tell fast
Answer:
The number Alexis thinks of first is 6.7.
Step-by-step explanation:
Let the number Alexis thinks of be x and the first answer he got be y.
Since he multiplies the number by x and divides the answer by 100, the equation is
10x = y
10x = [tex]\frac{y}{100}[/tex]
Then, he multiplies this answer, [tex]\frac{y}{100}[/tex], by 1000 and gets a final answer of 67. The equation is
[tex]\frac{y}{100}[/tex] × 1000 = 67
To find y, you divide 1000y by 100 which gives 10y.
i.e. [tex]\frac{1000y}{1000} = 67[/tex]
10y = 67
Divide both sides of the equation by the coefficient of y (which is 10)
[tex]\frac{10y}{10} = \frac{67}{10}[/tex]
y = 6.7
Substituting 6.7 for y in 10x = y
10x = 6.7
Divide both sides of the equation by the coefficient of x (which is 10)
[tex]\frac{10x}{10} = \frac{6.7}{10}[/tex]
x = 0.67
∴ The number Alexis thinks of first is 0.67.
Hope this helps!!! :))
Answer:
0.67
Step-by-step explanation:
Solution 1
We can work out the initial number by going backwards from the end:
67/1000= 0.067
0.067*100= 6.7
6.7/10= 0.67
Solution 2
(x*10/100)*1000= 67
x/10*1000= 67
100x= 67
x=67/100
x=0.67
Probability of Tournament Winners
Try it
Which statements are true? Check all that apply.
A local chess tournament gives medals for first, second,
and third place. There are five students from Midland
High, three students from Leasburg High, and six
students from Cassville High competing in the
tournament.
Order matters in this scenario.
There are 2,184 ways to select a first-place,
second-place, and third-place winner.
The probability that all three winners are from
Midland High is 0.0275.
The probability that all three winners are from
Leasburg High is 0.0046.
The probability that all three winners are from
Cassville High is 0.0549
Answer:
The answer is A B C and E
Step-by-step explanation:
I just took it
The statements are true A, B, C, and E.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The given data in the problem is;
No of the students from Midland High = 5
No of the students from Leasburg High= 3
No the students from Cassville High = 6
The statements that are true will be;
A.Order matters in this scenario.
B.There are 2,184 ways to select a first-place,second-place, and third-place winner.
C.The probability that all three winners are from Midland High is 0.0275.
E.The probability that all three winners are from Cassville High is 0.0549
Hence the statements are true A, B, C, and E.
To learn more about the probability refer to the link;
https://brainly.com/question/11234923
which of the following is the correct graph of the linear equation below? y+2=1/5(x-1)
Answer:
Step-by-step explanation:
f(x) = 4x^2 – 4x
Find f(-7)
Answer:
f(-7)=224
Step-by-step explanation:
[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]
What is the slope-intercept equation of this line
Answer:
y = -3x + 4
Step-by-step explanation:
Slope intercept form:
y = mx + b
Slope = y2 - y1/x2 - x1
-2 - 4/2-0 = slope
slope = -6/2 or -3
Equation:
y = -3x + 4
Answer:
[tex]y = 4x-3[/tex]
Step-by-step explanation:
y-intercept = b = 4 (because x becomes zero here)
Now, Finding the slope:
Slope = m = [tex]\frac{rise}{run}[/tex]
Slope = [tex]\frac{-2-4}{2-0}[/tex]
Slope = [tex]\frac{-6}{2}[/tex]
Slope = -3
Now putting m and b in the slope intercept equation to get the required form:
=> [tex]y = mx+b[/tex]
=> [tex]y = 4x-3[/tex]
please solve
thankyou in advance x
Answer:
For the first one,
x=6 and y=16
Step-by-step explanation:
If I think of any more then I will tell you
Which expression is equivalent to the following complex fraction? StartFraction x Over x minus 3 EndFraction divided by StartFraction x squared Over x squared minus 9 EndFraction StartFraction x minus 3 Over x EndFraction StartFraction x + 3 Over 1 EndFraction StartFraction x + 3 Over x EndFraction StartFraction x Over x + 3 EndFraction
Answer:
[tex](C) \dfrac{x+3}{x}[/tex]
Step-by-step explanation:
We want to determine an equivalent expression to:
[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]
Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.
[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]
Step 2: Change the division sign to multiplication
[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]
Step 3: Cancel out common terms and simplify
[tex]= \dfrac{x+3}{x}[/tex]
The correct option is C.
The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]
Given expression is,
[tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]
Use factorization, [tex]x^{2} -9=(x-3)(x+3)[/tex]
Now simplify the given expression.
[tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]
Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]
Learn more:
https://brainly.com/question/1280754
Pavel and Katie share some sweets in the ratio 3: 8.
Katie gets 32 sweets.
How many sweets does Pavel get?
Answer:
Step-by-step explanation:
Katie gets 32/8 = 4 lots of sweets
Pavel gets 4 lots x 3 = 12 sweets
please help me for the brainliest answer
Answer:
3, 12, 27 and 300
Step-by-step explanation:
Plug n as 1, 2, 3 and 10.
3(1)² = 3
3(2)² = 12
3(3)² = 27
3(10)² = 300
The numbers x, y and z are successive terms of the arithmetic sequence with a common difference of d=4. What is the sum of these numbers, if the numbers x, y and z+8 are successive terms of the geometric sequence?
Answer: The sum of the numbers is 3x + 12
Step-by-step explanation: A brief explanation of an arithmetic progression would be useful for a start.
An arithmetic progression (also known as arithmetic sequence) is series of consecutive numbers in which every term in the entire series is determined by adding a common difference to the previous term. In other words, if x and y are two successive numbers in an arithmetic term, y can be determined by adding the common difference to x. Similarly, the term that comes after y is determined by adding the same common difference to y.
As stated in the question, the numbers x, y and z are successive terms of an arithmetic progression, and the common difference is given as 4. This simply means;
y = x + 4
z = y + 4
z = (x + 4) + 4
z = x + 8
The terms x, y and z can now be re-written as follows,
x, x + 4, and x + 8
The sum of these numbers therefore is derived as,
Sum = x + x + 4 + x + 8
Sum = 3x + 12
Circle O is shown. Line segments A O and B O are radii. The length of O B is 16 inches. Angle A O B has a measure of StartFraction pi Over 4 EndFraction
In circle O, angle AOB measures radians.
What is the length of arc AB?
π in.
If you know the angle in radians, then the length of the arc is
(measure of the angle in radians) x (radius of the circle) .
In this circle, we know the angle and we know the radius.
Arc AB = ( π/4) x (16")
Arc AB = 4π inches
Arc AB = about 12.566... inches
Answer:
6 pie correct on edge
Step-by-step explanation:
The mean mass of a squad of 19 hockey players is 82 kg. A player of mass 93 kg joins the squad. work out the mean mass of the squad now
Answer:
82.55kg
Step-by-step explanation:
Calculate the total weight of the 19 hockey players: 19*82=1558kg.
Calculate the total weight of new players: 1558+93=1651kg.
The total number of players added is 19+1=20. Calculate the average weight: 1651/20=82.55kg.
anyone know how to do this?
Answer:
12.1 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos 30 = x/14
14 cos 30 = x
12.12435565 =x
12.1 =x
Which point gives the vertex of f(x) = x2 – 4x + 21? Question 1 options: (–2,–17) (2,17) (–2,17) (2,–17)
Answer:
[tex](2, 17)[/tex]
Step-by-step explanation:
A parabola has the general function: [tex]f(x)=ax^2+bx+c[/tex]
In this case we have: [tex]f(x) = x^2 - 4x + 21[/tex]
where
[tex]a=1[/tex]
[tex]b=-4[/tex]
[tex]c=21[/tex]
the vertex of a parabola is in the coordinates:
[tex](\frac{-b}{2a}, \frac{-b^2+4ac}{4a} )[/tex]
substituting all of the known values, we get the following:
[tex](\frac{-(-4)}{2(1)} ,\frac{-(-4)^2+4(1)(21)}{4(1)} )\\\\(\frac{4}{2} ,\frac{-16+84}{4} )\\\\\\(2 ,\frac{68}{4} )\\\\\\(2,17)[/tex]
the vertex of [tex]f(x) = x^2 - 4x + 21[/tex] is at the point (2,17) which is the second option.
Answer:
2,17
Step-by-step explanation:
A surveyor is 40m from the edge of a building. The angle of elevation from the surveyor to the top of the building is 55° . What is the height of the building?
Answer:
Height of building is 57.12 m.
Step-by-step explanation:
Let us try to understand the given dimensions as per the attached diagram.
Please refer to attached image (Right angled [tex]\triangle OBT[/tex])
with [tex]\angle B =90^\circ[/tex]
Let O be the point where the Surveyor is standing.
B be the point of the base of building.
T be the point of top of building.
As per question statement,
[tex]\angle O = 55^\circ[/tex]
Side OB = 40 m
To find: Side BT = ?
Using tangent trigonometric identity:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
[tex]tanO =\dfrac{BT}{BO}\\\Rightarrow tan55^\circ = \dfrac{BT}{40}\\\Rightarrow BT = tan55^\circ \times 40\\\Rightarrow BT = 1.43\times 40\\\Rightarrow BT = 57.12 m[/tex]
So, height of building is 57.12 m.
A family needs to build fencing around their rectangular home and square swimming pool, depicted below. A rectangle labeled home has its right side labeled (2 + 5 x) yards and its bottom side labeled (3 + 10 x) yards. The square, labeled pool, is smaller than the rectangle. One of its sides is labeled (2x) yards.
Answer:
1) 38
2) 160
3) 40
Step-by-step explanation:
Answer:
23, 42, 12
Step-by-step explanation:
The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. The point (8, -2) is on the circle. What is the equation of the line that is tangent to the circle at (8, -2)?
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
We know that the line which is tangent at a point on a circle is perpendicular to the line joining the center of the circle and that point.
please mark me as brainliest :)
Find the slope of a line passing through the points (-4,2) and (5,6)
Step-by-step explanation:
I hope you understand what I did