Answer:
x = -3
Step-by-step explanation:
When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....
x/3 - 1 = -2
x/3 = -1 ( add 1 on both side)
x = -3 (x3 on both side)
A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?
Answer:
the slope of the perpendicular bisector is -2/3
Step-by-step explanation:
The slope of the line joining the two points P1(0,3), P2(6,12) is given by
m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5
The slope m2 of a line perpendicular to the previous line is given by
m1*m2 = -1
solving
m2 = -1/m1 = -1/ (3/2) = -2/3
THerefore the slope of the perpendicular bisector is -2/3
The Vance family is saving money to buy a new car that costs $12,000. They plan to save $715 per month (m), and they have already saved $645. Which of the following inequalities show the number of months (m) the Vance family could save in order to buy the new car? Select all that apply. A. 715m≥11,355 B. 715m≤11,355 C. 12,000≤715m+645 D. 12,645≤715m
Answer:
C. 12,000≤715m+645
Step-by-step explanation:
You want to have either equal to or more than 12,000
Answecr:
C
Step-by-step explanation:
Of the 500 U.S. states, 4 have names that start with the letter W, What percentage of U.S. states have names that start with the lette W
Answer:
8%
Step-by-step explanation:
4/50 = 0.08, which is 8%
If 500 is not a typo, then 4/500 = 0.008, which would be 0.8%
Answer: 8%
Step-by-step explanation: 4/50 = 0.08 Convert the decimal to a percentage. 0.08 = 8%
Need help solving. Prefer you show each step in solving.
Answer:
AB║CD and AD║BC
Step-by-step explanation:
By the property of a parallelogram,
" Consecutive angles of a parallelogram are supplementary"
In the figure attached,
∠DCB and ∠CDA are the supplementary angles. Therefore ABCD will be a parallelogram.
[Given: m(∠DCB) + m(∠CDA) = 180°]
And the pair of opposite sides of the parallelogram ABCD will be parallel.
AD║BC and AB║CD
Which equation describes a parabola that opens left or right and whose
vertex is at the point (h, v)?
A. y = a(x - 1)2 + 1
B. x = aly - y)2 + h
C. x = aly - h)2 + V
O D. y = a(x - h)2 + V
Answer:
B. x = a(y - v)^2 + h
Step-by-step explanation:
The basic equation is ...
x = f(y)
x = y^2
To translate the vertex from (0, 0) to (h, v), we replace x with (x-h) and y with (y-v). Now, we have ...
x -h = (y -v)^2
To scale the graph horizontally by a factor of "a", we multiply the right side by "a":
x -h = a(y -v)^2
Adding h gives the form you want to compare to the answer list:
x = a(y -v)^2 +h
_____
The attachment shows an example for (h, v) = (4, 3).
Answer:
B
Step-by-step explanation:
Hopefully this helps :)
The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___
To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.
If you were to take a typical payday loan for $150, with an interest rate of 24.5% due in full after two weeks, what is the total amount you would have to repay?
Answer:
$186.75
Step-by-step explanation:
In order to solve this, we first need to convert the percentage into a decimal which can be done by dividing it by 100 like so
24.5 % 100 = 0.245
Now that we have the decimal form of the percentage we add a 1 to it and multiply that by $150 in order to get the total amount that is owed after two weeks .... without the 1 added it would only give us the amount of interest that needs to be paid.
$150 * 1.245 = $186.75
Therefore after two weeks you would need to pay a total of $186.75
A pack of 6 red pens costs £2.76. What is the price per pen?
Answer:
0.46 each
Step-by-step explanation:
Answer:
£0.46 per pen
Step-by-step explanation:
We need to find the unit rate, or price per pen.
Therefore, we can divide the price by the number of pens.
price / number of pens
It costs £2.76 for 6 pens.
price= £2.76
number of pens = 6 pens
£2.76 / 6 pens
Divide 2.76 by 6
£0.46 / pen
The price per pen is £ 0.46
It is given that trapezoid EFGH is an isosceles trapezoid. We know that FE ≅ GH by the definition of
. The base angle theorem of isosceles trapezoids verifies that angle
is congruent to angle
. We also see that EH ≅ EH by the
property. Therefore, by
, we see that ΔFHE ≅ ΔGEH.
The solution is ΔFHE ≅ ΔGEH. [SAS], i.e. triangle FHE is similar to triangle GEH, by SAS rule.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Given: An Isosceles trapezoid EFGH in which EF =GH
To prove: ΔFHE ≅ ΔGEH
Proof: In Isosceles trapezoid EFGH, Considering two triangles ΔFHE and ΔGEH
1. FE ≅ G H → [ Given]
2. ∠H = ∠E
→ Draw GM⊥HE and FN ⊥EH, and In Δ GMH and ΔFNE,
GH=FE [Given]
∠M+∠N=180°
so, GM║FN and GF║EH, So GFMN is a rectangle.]
∴ GM =FN [opposite sides of rectangle]
∠GMH = ∠FNE [ Each being 90°]
Δ GMH ≅ ΔFNE [ Right hand side congruency]
→∠H =∠E [CPCT]
→ Side EH is common i.e EH ≅ EH .
→ΔFHE ≅ ΔGEH. [SAS]
To learn more on triangle click:
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Which expression is equivalent to 2√98 x √2?
1) 14√2
2) 784
3) 4√98
4) 28
Answer: 28
Step-by-step explanation: √98 x √2 = √196
√196 = 14
2×14= 28
Answer:
4) 28. I don't know how to explain it...
WILL GIVE BRAINLIEST Jorge solves the equation 4x - (x + 20) + 6 = 2(3x + 8) using the steps below. Step 1: 4x - x + 2 + 6 = 6x + 16 Step 2: 3x + 8 = 6x + 16 Step 3: 8 - 16 = 6x - 3x Step 4: -8 = 3x Step 5: -8/3 = x Jorge verifies his solution by substituting -8/3 into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge’s error? A. Jorge distributed incorrectly. B. Jorge incorrectly combined like terms. C. Jorge incorrectly applied the addition and subtraction properties of equality. D. Jorge incorrectly applied the multiplication and division properties of equality.
Answer:
A. Jorge distributed incorrectly.
Step-by-step explanation:
4x - (x + 20) + 6 = 2(3x + 8)
4x - x - 20 + 6 = 6x + 16
3x - 14 = 6x + 16
3x - 6x = 16 + 14
-3x = 30
x = -10
For Step 1 of Jorge's work, he writes "4x - x + 2 + 6 = 6x + 16", instead of "4x - x - 20 + 6 = 6x + 16". That is the error that messes up the rest of his calculations.
What he did wrong does not apply to addition, subtraction, multiplication, or division, so we can eliminate choices C and D. Jorge isn't combining like terms, either, so we can eliminate choice B. What Jorge did wrong was that he distributed incorrectly, so that is your answer: A. Jorge distributed incorrectly.
Hope this helps!
Answer:
A is correct and thank you to the other person who answered i didn’t fail
Step-by-step explanation:
just took the quiz on edge
Factor this trinomial.
x² + 2x-3
A. (x + 3)(x + 1)
B. (x + 3)(x - 1)
C. (x-3)(x - 1)
D. (x-3)(x + 1)
Answer:
the answer is (x+3)(x-1).
hope u get it....
Answer:
B
Step-by-step explanation:
x^2 +3x -x -3 = x(x+3) -(x+3)=(x-1)(x+3)
What is an equation to a line parallel to the line on the graph that passes through (4,15)?
The equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3
How to find equation of a line?The equation of a line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
parallel line have the same slope
(5, 35)(10, 50)
m = 50 - 35 / 10 - 5 = 15 / 5 = 3
Hence,
(4, 15)
y = 3x + b
15 = 3(4) + b
15 - 12 = b
b = 3
Therefore, the equation to a line parallel to the line on the graph that passes through (4,15) is y = 3x + 3
learn more on equation of a line here: https://brainly.com/question/19043210
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Can someone help me please?
Answer:
336km^2
Step-by-step explanation:
There are 2 triangles and 3 squares in this 3D shape.
To find the surface area of this shape, you need to find the area add all the 5 shapes (height ✖️length) and add them.
area of the triangle: 8✖️9/2=36 +36<-- 2nd triangle=72km^2
area of a square: 11✖️8=88✖️3=264km^2
264+72=336km^2
The graph of a quadratic function is represented by the table.
Х
f(x)
6
-2
7
4
8
6
9
4
10
-2
What is the equation of the function in vertex form?
Substitute numerical values for a, h, and k.
Answer:
The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6
Step-by-step explanation:
The given values are
x, f(x)
6, -2
7, 4
8, 6
9, 4
10, -2
The equation of the function in vertex form is given as follows;
f(x) = a × (x - h)² + k
To find the values of a, h, and k, we proceed as follows;
When x = 6, f(x) = -2
We have;
-2 = a × (6 - h)² + k = (h²-12·h+36)·a + k.............(1)
When x = 7, f(x) = 4
We have;
4 = a × ( 7- h)² + k = (h²-14·h+49)·a + k...........(2)
When x = 8, f(x) = 6...........(3)
We have;
6 = a × ( 8- h)² + k
When x = 9, f(x) = 4.
We have;
4 = a × ( 9- h)² + k ..........(4)
When x = 10, f(x) = -2...........(5)
We have;
-2 = a × ( 10- h)² + k
Subtract equation (1) from (2)
4-2 = a × ( 7- h)² + k - (a × (6 - h)² + k ) = 13·a - 2·a·h........(6)
Subtract equation (4) from (2)
a × ( 9- h)² + k - a × ( 7- h)² + k
32a -4ah = 0
4h = 32
h = 32/4 = 8
From equation (6) we have;
13·a - 2·a·8 = 6
-3a = 6
a = -2
From equation (1), we have;
-2 = -2 × ( 10- 8)² + k
-2 = -8 + k
k = 6
The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6
Answer:
f(x) = -2(x - 8)² + 6
Step-by-step explanation:
I did the test.
5 3/4 divided by 1 1/2
Answer:
[tex] \frac{23}{6} [/tex]Solution,
[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{23}{4} \div \frac{3}{2} [/tex]
To divide by a fraction, multiply by the reciprocal of that fraction
[tex] \frac{23}{4} \times \frac{2}{3} [/tex]
Reduce the numbers with the GCF 2
[tex] \frac{23}{2} \times \frac{1}{3} [/tex]
Multiply the fraction
[tex] \frac{23}{6} [/tex]
Hope this helps...
Good luck on your assignment...
The cost of six hens and one duck at the university poultry farm is GH₵40. While four hens and three ducks cost GH₵36. What is the cost of each type of bird?
Answer:
Step-by-step explanation:
Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.
The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.
The system is
6h + 1d = 40
4h + 3d = 36
The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,
1d = 40 - 6h.
Now that we know what d equals, we can sub it into the second equation where we see a d. In order,
4h + 3d = 36 becomes
4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!
4h + 120 - 18h = 36 and
-14h = -84 so
h = 6.
That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:
1d = 40 - 6(6) and
d = 40 - 36 so
d = 4.
That means that each duck costs $4.
Calculate the slope of the line going through A(-4,3) and B(0,6) PLEASE ANSWER
Answer:
6-3/0-(-4)
=3/4
Step-by-step explanation:
Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3
Problem P(x)=x4−3x2+kx−2P(x)=x^4-3x^2+kx-2P(x)=x4−3x2+kx−2P, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 3, x, squared, plus, k, x, minus, 2 where kkkk is an unknown integer. P(x)P(x)P(x)P, left parenthesis, x, right parenthesis divided by (x−2)(x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis has a remainder of 10101010. What is the value of kkkk? K=k=k=
Answer: k = 4
Step-by-step explanation:
For this division, to determine the value of k, use the Remainder Theorem, which states that:
polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)
Knowing the degree of quotient is
degree of Q = degree of p(x) - degree of (x-a)
For this case, Q(x) is a third degree polynomial.
Using the theorem:
[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]
[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]
a = 1
b - 2a = 0 ⇒ b = 2
c - 2b = -3 ⇒ c = 1
-2d + 10 = -2 ⇒ d = 6
d - 2c = k ⇒ k = 4
Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]
find the time taken for rupees 12502 on an interest of rupees 1020 at the rate of 4% compounded annually
Answer:
t = 63.897 years
Step-by-step explanation:
Simple interest rate formula: A = P(1 + r)^t
Simply plug in what we know and solve:
12502 = 1020(1 + 0.04)^t
6251/510 = 1.04^t
log base 1.04 of (6251.510) = 63.897
help me again pleasee :(
I need help answering this so please help
Answer:
(2, f(2))
Step-by-step explanation:
f(x) = -3x^2
For point B, the y-coordinate is f(2).
Point B is (2, f(2))
2/3 - 5bx = bx + 1/3 In the equation shown above, b is a constant. For what value of b = NO SOLUTIONS? A. 5 B. 0 C. -5 D. 2/5
Answer:
B
Step-by-step explanation:
Here, we want to know at what values of b does the equation becomes not solvable
Now looking at the left hand side, we have;
2/(3-5bx) and also the right hand side bx + 1/3
For this expression if we insert b = 0, then automatically x cancels out on both sides of the equation and we shall be left with nothing to solve
Answer:
−5
Step-by-step explanation:
First, we observe that this is a linear equation.
A linear equation in one variable will have no solutions if the equation reduces to an equation of the form:
\blue a x+\red b=\blue c x + \red dax+b=cx+dstart color #6495ed, a, end color #6495ed, x, plus, start color #df0030, b, end color #df0030, equals, start color #6495ed, c, end color #6495ed, x, plus, start color #df0030, d, end color #df0030
where \blue a=\blue ca=cstart color #6495ed, a, end color #6495ed, equals, start color #6495ed, c, end color #6495ed and \red b\neq \red db
=dstart color #df0030, b, end color #df0030, does not equal, start color #df0030, d, end color #df0030.
In this case, the equation will reduce to the statement \red b=\red db=dstart color #df0030, b, end color #df0030, equals, start color #df0030, d, end color #df0030, which is not true for any value of xxx.
Hint #2
Since \red {\dfrac23}\neq \red {\dfrac13}
3
2
=
3
1
start color #df0030, start fraction, 2, divided by, 3, end fraction, end color #df0030, does not equal, start color #df0030, start fraction, 1, divided by, 3, end fraction, end color #df0030 , the equation will have no solutions if \blue b=\blue {-5}b=−5start color #6495ed, b, end color #6495ed, equals, start color #6495ed, minus, 5, end color #6495ed.
Let's check that this is the case. If we add \blue {5}{x}5xstart color #6495ed, 5, end color #6495ed, x to both sides, we get
\begin{aligned} \red{\dfrac23}\blue{-5}x&= \blue{-5} x+\red{\dfrac13}\\\\ \red{\dfrac23}\blue{-5}x+\blue5x&= \blue{-5}x+\blue{-5}x+\red{\dfrac13} \\\\ \red{\dfrac23}&=\red{\dfrac13} \end{aligned}
3
2
−5x
3
2
−5x+5x
3
2
=−5x+
3
1
=−5x+−5x+
3
1
=
3
1
which is not true for any value of xxx, so there are no solutions.
For all other values of b,b,b, comma there will be one solution.
Hint #3
If b=-5b=−5b, equals, minus, 5, the equation will have no solutions.
Help ASAP please .
Which expression represents the volume of the sphere,
in cubic units?
3/4pi(6)^2
4/3pi(6)^3
3/4pi(12)^2
4/3pi(12)^3
Answer:
second option
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )
Here r = 6 , thus
V = [tex]\frac{4}{3}[/tex]π(6)³
Answer:
Second option
Step-by-step explanation:
Volume of a sphere = [tex]\frac{4}{3}*\pi *r^{3}[/tex]
→ Substitute in the value of radius
Volume of a sphere = [tex]\frac{4}{3}*\pi *6^{3}[/tex]
Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common
tangent, what is AB?
Answer:
[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]
Step-by-step explanation:
In the attached diagram
CA=CO+OA
CO=DB
Therefore:
5=2+OA
OA=3 Units
The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:
OB=12 units
OA=3 units
Using Pythagoras theorem
[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]
What is 25% of 84.
Help ASAP
Answer:
21
Step-by-step explanation:
[tex] \frac{25}{100} \times 84[/tex]
Answer:
21
Step-by-step explanation:
if y=2x+7 were changed to y=5x+7, how would the graph of the new function compare with the origial
Answer:
The new line is steeper than the original, but still crossing the y=axis at 7 .
Step-by-step explanation:
Since what has changed from y = 2 x + 7 going into y = 5 x + 7 is the slope of the linear function, (from 2 to 5) what one would notice is that the new line is steeper - raising 5 units every one unit ste to the right- but would still be intersecting the y-axis at the point (0, 7), since the y-intercept has not changed.
Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each. If she pays with a £20 note, how much change would she get in pounds, £?
Answer: £2.4
Step-by-step explanation:
From the question, Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each.
Total cost of potatoes = 3 × £2 = £6
Total cost of carrots = 4 × £2 = £8
Total cost of turnips = 4 × 90p = £360p = £3.6
The total cost of things bought by Erin will now be:
= £6 + £8 + £3.6
= £17.6
If she pays with a £20 note, she will collect a change of:
= £20 - £17.6
= £2.4
= 2 pounds, 40 pennies.
A marble is randomly selected from a bag. The probability of selecting a marble with dots on it is 0.2. The probability of selecting a marble that is both purple and has dots on it is 0.1. What is the probability of selecting a purple marble given that the marble has dots on it? Enter your answer as a decimal in the box.
Answer:
0.5
Step-by-step explanation:
Let D be the event of selecting a marble with dots.
Let P be the event of selecting a purple marble.
The probability of selecting a marble with dots, P(D)=0.2
The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]
We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)
By the definition of conditional probability:
[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]
The probability of selecting a purple marble given that the marble has dots on it is 0.5.
what is 25 (10 + 50) - 25?
Answer:
Hey there!
25(10+50)-25
25(60)-25
1500-25
1475
Hope this helps :)
Answer:
The answer is
1475Step-by-step explanation:
25 (10 + 50) - 25
Expand
250 + 1250 - 25
Simplify
We have the final answer as
1475
Hope this helps you