Answer:
y = -x + 7.
Step-by-step explanation:
General form:-
y = mx + c where m = slope. So:
y = x + 2 has a slope of 1.
The line perpendicular to it has slope -1/1 = -1
To find the required line we use the point-slope form with m = -1, x1 = 3 and y1 = 4.
y - y1 = m(x - x1)
y - 4 = -1(x - 3)
y - 4 = -x + 3
y = -x + 7.
factoris fully 2ab² + 8a²b
Answer:
2ab(b + 4a)
Step-by-step explanation:
2ab² + 8a²b
Factor Out the 2:
2(ab² + 4a²b)
Factor Out the a:
2a(b² + 4ab)
Factor Out the b:
2ab(b + 4a)
1. Solve.
2
The sides of a rectangle are represented by 4a-1 and 3a + 2. Find the expression for its perimeter.
Answer:
14a+2
Step-by-step explanation:
Perimeter of a rectangle: P=2(l+w) where l=length and w=width.
So P=2[(4a-1)+(3a+2)]=2(4a-1+3a+2)=2(4a+3a-1+2)=2(7a+1)=14a+2.
The expression to find the perimeter of the rectangle is 14a + 2.
What is Perimeter?Perimeter of a straight sided figures or objects is the total length of it's boundary.
Given that,
Sides of a rectangle is represented as 4a - 1 and 3a + 2.
Perimeter of a rectangle is represented as,
Perimeter = 2 (l + w)
Here l is the length and w is the width.
Substituting,
Perimeter = 2 (4a - 1 + 3a + 2)
= 2(7a + 1)
= 14a + 2
Hence the expression to find the perimeter is 14a + 2.
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what is 2(5+34-67/45*43)^2 equal to?
The value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Evaluating an ExpressionFrom the question, we are to determine the value of
2(5+34-67/45*43)^2
This can be written as
[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]
First, we will simplify the bracket
[tex]2 (\frac{-28}{1935 })^{2}[/tex]
Then, we get
[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]
= [tex]\frac{1568}{3744225}[/tex]
= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Hence, the value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
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The formula for the area of a rhombus is A = a equals StartFraction one-half EndFraction d 1 d 2.d1d2, where d1 and d2 are the lengths of the diagonals.
Which are equivalent equations? Select two correct answers.
The two equivalent equations are d₁= 2a/d₂ and d₂= 2a/d₁ , Option 2 and 5 is the right answer.
What is a Rhombus ?Rhombus is a quadrilateral with all the sides equal to each other.
It is given that d₁ and d₂ are the lengths of the diagonals.
and Area = a
a = (1/2) d₁ * d₂
2a = d₁ * d₂d₁ * d₂ = 2a
It can be written as
d₁= 2a/d₂
a = (1/2) d₁ * d₂
d₁ * d₂ = 2ad₂= 2a/d₁
Therefore Option 2 and 5 are the correct answer.
The options of this question are:
1. d₁=2Ad₂
2. d₁= 2A/d₂
3. d₂= d₁/2A
4. d₁= 2A/d₂
5. d₂= 2A/d₁
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The radius of a circle is 7 metres. What is the length of a 135° arc?
Answer:
16.5 meters
Step-by-step explanation:
The length of an arc of a circle = 2πr(C/360°) ;where:
C is the central angle of the arc,
R is the radius of the arc
Length of the arc = 2π(7)(135/360)
= 16.493
= 16.5 metres (approx.)
Answer:
Arc Length: 5.25π or [tex]\frac{21}{4} \pi[/tex]
Explanation:
An arc is the part of the circumference of a circle.
Formula:
[tex]\sf Arc \ Length = \dfrac{\theta}{360} \ \times \ 2\pi \ \times radius[/tex]
If applied:
[tex]\sf Arc \ Length = \dfrac{135}{360} \ \times \ 2\pi \ \times 7[/tex]
[tex]\sf Arc \ Length = \dfrac{3}{8} \ \times \ 14\pi[/tex]
[tex]\sf Arc \ Length = \dfrac{21}{4} \pi[/tex]
[tex]\sf Arc \ Length = 5.25 \pi[/tex]
PLEASE ANSWER ASAP!!!!!11
The nth term of a sequence is represented by 2n^3+25n^2+32n−15/ 6n^4+2n^3−11n^2−2n+17.
What is the limit of the the nth term as x becomes increasingly large?
A. 0
B. 1/3
C. 3
D. The limit does not exist
The limit of the nth term of a sequence does not exist option (D) is correct.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have an expression:
[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
Applying limit:
[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]
= ∞ = The limit does not exist
Thus, the limit of the nth term of a sequence does not exist option (D) is correct.
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Terrence is going on vacation and taking his dog Pickles along. Pickles eats 3 cups of Hungry Hound dog food each day. Terrence wants to know how many days he can feed Pickles from a 15-cup bag of Hungry Hound.
Answer:
Number of Days he can feed Pickles from a 15-cup bag of Hungry Hound = 5 Days
Step-by-step explanation:
this is question based on simple algebraic equations
Simple Algebraic equations - An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.
so in the question algebraic operation used to solve is simple division.
therefore, according to the question -
Total cups of Hungry Hound dog food pickles eats each day are - 3 cups
Total number of cups of Hungry Hound Terrence have = 15 cups
Number of days Terrence can feed pickles from these cups are =
15/3 = 5 days
so the correct answer is = 5 Days
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In triangle PQR, find the measure of angle Q.
P= 64 degrees
Q= X
R= 2x
Answer:
38.667°
Step-by-step explanation:
the total sum of 3 angles in a triangle is 180
in triangle PQR this means:
P+Q+R = 180
so:
64+x+2x=180
64+3x=180
3x=116
x=116/3=38.667
So Q=X=38.667
Please help!!!!!!!
picture below
Answer:
This would shift the equation to the right by 5
Step-by-step explanation:
They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.
If they decide to double the width to create the family-sized box, by what factor must they increase the height?
Answer:
Given that A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box. They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.
If original dimensions are l,w and h then volume = lwh
Volume of new box is= 3lwh
But here w becomes 2w and l remains the same. Let h' be the new height
Then we have
So by 1.5 factor height should be dilated.
Step-by-step explanation:
label the vertices and all the elements needed. find x
The value of x would be 30 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Let's consider an angle CAD be t.
In a triangle ABD
x + 90 + t = 180
t = 180 -x - 90
t = 90 - x ( by angle sum property)
Now, we know that the sum of the corresponding angle on a transversal is 180
So,
Angle A + angle D = 180
2x + t + x + x = 180
substitute the t value
2x + 90 - x + 2x = 180
3x + 90 = 180
3x = 90
x = 30 degree
Hence, the value of x would be 30 degrees.
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Evaluate − 5 x 2 + 4 y 3 when x = − 2 and y = 2
Answer:
hope this is helpful.
putting values of X and y in the equation
Answer is 12
Answer:
answer is 39
Step-by-step explanation:
So, we start with the original problem:
3
x
2
−
4
y
2
Then we substitute the given
x
and
y
values into the expression:
3
(
5
)
2
−
4
(
3
)
2
Now, according to the order of operations, we simplify the exponential powers first, thus, reducing the expression to this:
3
(
25
)
−
4
(
9
)
Then, we use the order of operations again and do the multiplication next:
75
−
36
We then use the order of operations a final time and finish off the expression with subtraction:
39
Find the minimum value of the following equation:
(Please provide detailed explanations, no links)
Answer:
×=11
Step-by-step explanation:
2×-4×+27-5=0
-2×+22=0
-2×=-22
×=11
PLEASE HELP ASAP!!!!
What is the rectangular equivalence to the parametric equations?
x(θ)=3cosθ+2,y(θ)=2sinθ−1 , where 0≤θ<2π .
Drag a term into each box to correctly complete the rectangular equation.
____ + ________ = 1, where the x is on the interval _______
options:
(x-2)^2/9
(x+2)^2/9
(x-1)^2/4
(x+1)^2/4
(y-2)^2/9
(y+2)^2/9
(y-1)^2/4
(y+1)^2/4
[-3,3]
[-3,1]
[-2,2]
[-1,5]
The correct answer is option A [tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2})^2=1[/tex] it will be an ellipse.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let's consider the following trigonometric identity:
Sin²[tex]\theta[/tex] + Cos²[tex]\theta[/tex] = 1
Each trigonometric function is cleared respectively in given parametric equations:
[tex]Cos \theta = \dfrac{x-2}{3}[/tex] and [tex]Sin\theta =\dfrac{y+1}{2}[/tex]
The equivalent expression in rectangular form is:
[tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2}^)^2 = 1[/tex]
Therefore the correct answer is option A [tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2})^2=1[/tex] it will be an ellipse.
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A, B, C and D are the four corners of a rectangular plot marked out on level ground. given that the bearing of B from A is 040 degree and the bearing of C from A is 090 degree, calculate the bearing of:
a. B from C
b. A from C
c. D from C
The bearing of B from C based on the information given will be 40°.
How to depict the bearing?A bearing is an angle measured from the North direction clockwise. Notice that the bearing of B from C is 40° because according to the problem, all four points are on level ground, which means they are coplanar, and the angle between the plane and the North is 40°.
The bearing of A from C is also 110° because it's the bearing of C from A and A from C are same-side internal angles between parallels which must sum 180°.
The bearing of D from C is 40° too because that setup is parallel to the bearing of B from C.
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Work out the sum of the interior angles of any quadrilateral
Answer:
The sum of the interior angles of any quadrilateral is 360°.
Answer:
360°Step-by-step explanation:
A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is 360°.
I'll give you an example with the square, it has 4 right angles, so the sum is 360 ° as in all quadrilaterals.
Express ratio 3.5:14 as 1:n
Answer:
1 : 4
Step-by-step explanation:
3.5 : 14 ( divide both parts by 3.5 )
= 1 : 4
Solve the equation.
7h-5(3h-8)= -72
7h-15h+40=-72
40+72=15h-7h
112=8h
h=14
the graph of F(x) can be stretched vertically and flipped over the x axis to produce the graph of G(x) if F(x)=x^2 which of the following could be the equation of G(x)
A. G(x)=-1/5x^2
B. G(x)=-5x^2
C. G(x)=5x^2
D. G(x)=1/5x^2
Answer:
g(x) = -5x²
(option B)
Step-by-step explanation:
we know that our original graph, f(x) = x² is a parabola.
So, we can consider what happens when we adjust the function/equation of a parabola.
when we "vertically stretch" a parabola, we are increasing the value of x.
think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.
Let's say our x = 5
if f(x)=x²
f(5) = 25
> y value / steepness is 25
f(x) = 3x²
f(5) = 75
> y value / steepness is 75
So, we are looking for an equation with an increase in x present.
When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative
suppose that x = 1
if y = x² ; y = 1² = 1
if y = -(x²) ; y = -(1²) ; y = -1
So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)
This means that we are looking for a function with a negative x value.
So, we are looking for a negative x-value that is multiplied by a number >1
The graph that fits our requirements is g(x) = -5x²
hope this helps!!
Currently,nova is 3 times as old as Damon. in 8 years, she will be as only 2 times as old as Damon. How old will Damon be in 8 years?
Answer:
16
Step-by-step explanation:
consider X = Damon's age
3x + 8 = 2x
x = 8
so Damon will be 16 in 8 years ( 8+8)
Answer:
16
Step-by-step explanation:
24/3 8
24+8=32
8+8=16
16/32=1/2
can anyone help me i beggg
Find the length of segment AC if AB = 7.8 cm and BC = 25 mm. How many solutions are there in each case? Point B lies on line AC .
Answer:
103mm or 53mm
Step-by-step explanation:
--A------B------C--
AB=78mm BC=25mm AC=AB+BC=103mm
--A----C---B---
AB=78mm BC=25mm AC=AB-BC=53mm
-B---A---C-
is impossible because BA<BC but 78mm>25mm
A running relay team ran a 400 meter race in a record-setting time of 36 seconds. What was their average speed to the nearest tenth of a meter per second?
please place the dot for me(20 points will give brainliest!!!)
Answer:
2,
Step-by-step explanation:
The vertex is the very highest or very lowest point. X coordinates are listed first, then Y.
A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win
Monica win 2 games.
What is Expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
According to the question,
First we look from the perspective of one player.
How many games does this person play? 5.
Now, each or the 6 people in the tournament played 5 games,
SO,
[tex]^{6} C_{2} = \frac{6!}{2! * 4!} = \frac{6*5}{2} = 15[/tex]
Therefore,
We know that there were a total of 15 games played.
This means, there were 15 losses, and more importantly, 15 wins.
Not counting Monica, there were:
4 + 3 + 2 + 2 + 2 = 13 wins.
This leaves,
15 − 13 = 2 wins for Monica.
Hence, 2 games won by monica in a tournament.
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The area of a square is 256cm2. When each side of the square is increased by x cm, its area becomes 324 cm2.Find the value of x.
Answer: x = 2
Step-by-step explanation:
First, let's take the root of 256 to find the length of each side before the addition of x.
[tex]\sqrt{256} = 16[/tex]
This means 16 cm is the length of each side before the addition of x.
Then increase each side by X to get
[tex](16 + x)(16 + x) = 324[/tex]
[tex]256 + 16x + 16x + x^2=324[/tex]
[tex]x^2+32x -68=0[/tex]
[tex]x=2[/tex] or [tex]x=-34[/tex]
The value cannot be negative so x has to be 2
NEED SOME HELP ASAP PLEASE!!
Step-by-step explanation:
if it is cloudy, then it is snowing. False. This is obviously not true since sometimes it's just cloudy and it's also cloudy when it rains.
all quadrilaterals are rectangles. False. A quadrilateral has four straight sides which don't have to be parallel to each other unlike a rectangle which has four straight sides with all four sides being parallel to one other side.
All chocolates like students? False? Not sure if I'm writing the converse correctly for this one but if I am this isn't true because chocolate doesn't have feelings...
All triangles with two or more congruent angles are a right triangle. False. This is only true when those two congruent angles add up to 90 which is when they're both 45. But they could also both be 30, 29, 28, etc... which won't result in a right triangle.
Answer:
If it is cloudy, then it is snowing.
Counter-argument: It can be cloudy in the summer.
If a figure is a quadrilateral, then it is a rectangle.
Counter-argument: Trapezoids are not rectangles.
If someone likes chocolate, then they are a student.
Counter-argument: many people like chocolate who are not students.
If a triangle has 2 or more congruent angles, then it is a right triangle.
Counter-argument: Equilateral tr6iangles have 3 congruent angles.
None are right angles.
Step-by-step explanation:
Converse statements reverse the If Then in the original.
Solve the simultaneous equations below.
7x-6y = 30
2x+6y= 24
Answer:
(x,y)—>(6,2)
Step-by-step explanation:
Add both equations to eliminate y
9x=54
x=6
plug x=6 into either equation
2(6)+6y=24
6y=24-12
y=12/6=2
If triangle RST is within Quadrant 2 and csc T = 13/12, what is the value of cotT?
Answer:
[tex]\boxed {cot T = -\frac{5}{12}}[/tex]
Step-by-step explanation:
Finding the missing side :
x² = 13² - 12²x² = 169 - 144x = √25x = 5Taking the cot value :
cot T = adjacent / oppositecot T = -5/12 (As cot is negative in Quadrant 2)Answer:
csc T =13/12
(cot T)^2=csc^2T -1
Cot T)^2=(13/12)^2-1
(cot. T )^2=169/144-1
(cot T)^2=169-144/144
(cot T)^2=25/144
cot T =√ 25/144
cot T=5/12
where cot is negative in WE
so Cot T=-5/12
Step-by-step explanation:
please mark me as brainlest
Which function represents the inverse of function f?
Answer: Choice [B]
Step-by-step explanation:
Hii, I'd love to help you out! (:
This particular problem is all about finding inverse functions.
This can be done in 3 easy steps, which are shown below.
Replace f(x) with ySwitch x and y placesSolve for yThe process is shown below.
[tex]\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y[/tex]
[tex]\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y[/tex]
Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?
Ofc not! There's just one more thing that can be done to simplify our answer.
[tex]\tt \cfrac{x}{5}-\cfrac{5}{3}[/tex]
We're getting closer!
[tex]\tt \cfrac{1}{3}x-\cfrac{5}{3}[/tex]
Voila! There's our answer, cheers! (;
________________
Hope I helped!
Best wishes.
Reach far.
Aim high.
Dream big.
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