o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex .
What is vertex?In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.Vertex is a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet. The plural of a vertex is vertices.A line segment is a part of a line. A ray is a line segment that we can extend indefinitely. When two line segments or rays meet, they form an angle.To learn more about polygons refer to:
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The cost of a cake is twice that of a cup of tea.
1 cake and 5 cups of tea cost £21.
How much does a cake cost?
Answer:
The cake cost $6.00
Step-by-step explanation:
Let c = the cost of the cake
Let t = the cost of the tea
c = 2t
c + 5t = 21 Substitute 2t for c
2t + 5t = 21 Combine like terms
7t = 21 Divide both sides by 7
[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]
t = 3
A cup of tea costs $3.00
c = 2t Substitute 3 for t
c = 2(3)
c = 6
A cake costs $6.00
Answer:
Cake: £6
Step-by-step explanation:
1c = 2t Eq. 1
1c + 5t = 21 Eq. 2
c = cost of a cake
t = cost of a cup of tea
Replacing Eq. 1 in Eq 2:
2t + 5t = 21
7t = 21
t = 21/7
t = 3
From Eq. 1:
c = 2t
c = 2*3
c = 6
Check:
From Eq. 2:
c + 5t = 21
6 + 5*3 = 21
6 + 15 = 21
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]51.4^{\circ}[/tex]
Step-by-step explanation:
Since this is a right triangle, the cosine formula says
[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]
[tex]\longrightarrow cos(x) = 0.6235[/tex]
[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]
Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]
due now pls help!!!!!!!!!!!
Answer:
A and D
Step-by-step explanation:
so sorry im in school
x+y=4
-y. -y
x=4-y
4-y-y=2
4-2y=2
-4 -4
-2y= -2
/-2. /-2
y=1
x+1=4
-1 -1
x=3
so A and D is correct
a population of adult wildebeests in a certain region of africa have weights that are normally distributed with a standard deviation of 579 lbs. how large of a sample is needed to estimate the mean weight to within 135 lbs with a 99% confidence level?
Sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
What is confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.
Z(α/2) at 99% confidence level = 2.576
λ = 579
margin of error = ( Z(α/2) * λ ) / √n = 135
(2.576 * 579) / √n = 135
On simplifying, n ≈ 123
So, sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
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(3 points) assume she has brought 5 shirts and 3 jackets. for her 3-day trip (where the days are ordered), she wants to wear a different shirt and a different jacket each day. in how many ways can this be done? g
Answer:3-4 times but im not sure but here my logic
use it to your needs
Step-by-step explanation:
she has 5 shirts and 3 jackets right
so take the first shirt the third jacket then the fourth shirt the 2nd jacket
that 2 outfits then take the second shirt and the last remaining jacket then on the weekend wear one of the non-used shirts no jacket or the first jacket
-ElectricWolfieOnYT
14. Between a pair of points on the line y = 5x-2, suppose that the rise is 15.
Then the run is...
(A) 3
(B) 4
(C) 5
(D) 10
Answer:
Below
Step-by-step explanation:
m = slope = rise / run
m = 5 for this equation
rise /run = 5
15 / run = 5
run = 3
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.
What are angle bisectors?Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.
According to the angle bisector theorem;
An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.
a point is equally far from both sides of an angle if it is on the angle's bisector.
According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.
The explanation with diagram is given in the image.
Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
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2 ^ (x + 3) * 3 ^ (x + 4) = 18
The value of the variable x is -2
What is an algebraic expression?An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.
These expressions are also made up of arithmetic or mathematical operations, which includes;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 18
Now, let's find the factors of 18 in 2's and 3's, we have;
2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2
Collect the common factors, we get;
x+ 3 + x + 4 = 1 + 2
collect like terms
2x = 3 - 7
2x = -4
make 'x' the subject of formula
x = - 2
Hence, the value is -2
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solve the question attached
Answer:
B) y = 4a------------------------------
Given:
[tex]log_2 \ y = 2+ log_2\ x[/tex]Find y if x = a:
[tex]log_2 \ y = 2+ log_2\ a[/tex][tex]log_2 \ y =2 log_2\ 2+ log_2\ a[/tex][tex]log_2 \ y = log_2\ 2^2+ log_2\ a[/tex][tex]log_2 \ y = log_2\ 4+ log_2\ a[/tex][tex]log_2 \ y = log_2\ (4*a)[/tex][tex]log_2 \ y = log_2\ (4a)[/tex][tex]y=4a[/tex]Correct choice is B.
If EF = 71, FD = 80, ED = 74, IG = 40, and HG = 37, find the perimeter
of AGHI. Round your answer to the nearest tenth if necessary.
The perimeter of the object is the sum of the lengths of all the sides
which is 302 units.
What is the perimeter?Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.
In the case of a circle, we call it perimeter circumference it is the distance around the circle.
Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and
HG = 37.
Now the perimeter of this figure is the sum of the lengths of all the sides which is,
= (EF + FD + ED + IG + HG).
= (71 + 80 + 74 + 40 + 37).
= 302 units.
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Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness,
extrema, asymptotes, and end behavior.
f(x)=3•e^2x
A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.
What are the values of the terminologies of the graph ?The given function is f (x ) = [tex]3e^{2x}[/tex]
1. Domain :
The function has no undefined points or domain constraints . Therefore the domain is -∞ < x < ∞ .2.Range :
The range of the exponential function is of the form f(x) > kSince k = 0, f(x) > 03.Continuity:
The graph is a single, continuous curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We can observe that the function is basically continuous.4.Behaviour that is either increasing or decreasing:
For any x in the domain, as x grows, f(x) shrinks. This indicates that the function behaves in a diminishing manner.5.Symmetry:
It is clear to see the graph of f(x) has no symmetry.6.Boundedness:
When we choose negative values, the graph of f(x) expands upward exponentially, showing that it is unbounded above.7.Extrema:
There are no extreme points for the function.8.Asymptotes:
This curve does not have any vertical asymptotes, despite the way it seems. Simply put, the curve's negative-x region is expanding so swiftly that it resembles an asymptote. For any x < 0, there is a value for f(x). However, a horizontal asymptote exists , y = 0.9.End behaviour :
As [tex]\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty[/tex] As,[tex]\:x\to \:-\infty \:,\:f\left(x\right)\to \:0[/tex]Refer image for graph.To learn more about Asymptotes , refer:
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Write an equation that passes through the point (4,-3) and is perpendicular to the line 4x+y=3
Answer:
y = 1/4x - 4
Step-by-step explanation:
4x + y = 3
y = -4x + 3
Perpendicular slope = 1/4
y = 1/4x + b
-3 = 1/4(4) + b
-3 = 1 + b
b = -4
y = 1/4x - 4
Pamela is 9 years younger than jiri. The sim of their ages is 49. What is jiri’s age ?
Answer: 40
Step-by-step explanation:
all you have to to is subtract
9 from 49 = 40
Answer:40
Step-by-step explanation:49-9=40
What is sin(60) in degrees?
Answer:
(sqrt3)/2
Step-by-step explanation:
Sin(x)=opposite/hypotenuse
30, 60, 90 right triangle.
ratio of sides are 1, sqrt3, and 2.
Locate the 60 degree angle on the triangle
The opposite side is sqrt3
The hypotenuse is 2
so its (sqrt3)/2
Answer:
√3/2 or 0.866
Step-by-step explanation:
Help please i can’t do the math right I’m not getting any of those 4 options right
Answer:
B
Step-by-step explanation:
970 + 2436 = 3406
Question 2
What is the length of the line segment with endpoints P(2, 1,-4) and Q(-1,5,3)?
The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units
How to find the length of a line segment?To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:
length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Substituting the coordinates of P and Q into the formula, we get:
length = √((-1 - 2))² + (5 - 1))² + (3 - (-4)))² )
= √((-3))² + (4))² + (7))² )
= √(9 + 16 + 49)
= √(74)
= 8.60 units
Therefore, the length of the line segment is 8.60 units
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find X giving Brainly show work
Answer:
[tex]b = 6\sqrt{2}[/tex]
Step-by-step explanation:
Don't say giving brainiest for work, I will still help you.
Use the Pythagorean Theorem to solve:
[tex]a^2+b^2=c^2[/tex]
A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.
Plug in what you know:
[tex](7)^2+b^2=(11)^2[/tex]
[tex]49 + b^2 = 121[/tex]
Subtract 49 on both sides.
[tex]49 - 49 + b^2 = 121-49[/tex]
[tex]b^2=72[/tex]
Find the square root of both sides.
[tex]\sqrt{b^2} = \sqrt{72}[/tex]
b = [tex]6\sqrt{2}[/tex]
x = 4
Graph the linear equation
Answer:
Step-by-step explanation:
A linear equation has only more than one additional, that may be expressed as , and the further discussion can be defined as follows:
In this, No factor has been raised the power which is greater than one or utilized as the denominator of a fraction.
When we discover pairs of values that satisfy a linear model and plot them on a coordinate grid, all the points fall on the same line.
Please find the attached file of the graph.
need help now i need to finish this delta
Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.
What do you mean by transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
What is reflection in mathematics?In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.
Figure H
Mapped onto figure I
The required transformation:
reflection along y=x.
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I will give brainliest to whoever ANSWERS THESE 2 QUESTIONS
100 POINTS!!!
Answer:
2. 43 degrees
3. 35 degrees
Step-by-step explanation:
Srr the attached worksheet.
Graph the line that has a slope of -4/3 and includes the point ( -6,2)
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
Slope intercept form:The slope-intercept form a line is given by
y = mx + c,where m is the slope of a line and c is the y-intercept.
Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line
Here we have
Slope of line = -4/3
The point of the line
As we know y = mx + c is the line Here m is the slope of the line
From the given data, m = -4/3
=> y = (-4/3)x + c
=> 3y = -4x + 3c
Given that the point on the line is (-6, 2)
=> 3(2) = -4(-6) + 3c
=> 6 = 24 + 3c
=> 3c = 18
=> c = 6
Therefore,
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
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"the time since dinosaurs became extinct is roughly equal to _____ average human lifespans"
average human lifespan: 2.4 x 10^4
time since dinosaurs became extinct: 2.4 x 10^10
The time since dinosaurs became extinct is roughly equal to 10⁶ average human lifespans
How to complete the blanks in the statementFrom the question, we have the following parameters that can be used in our computation:
Average human lifespan = 2.4 x 10^4Time since dinosaurs became extinct = 2.4 x 10^10Rewrite the exponents properly
So, we have the following representation
Average human lifespan = 2.4 x 10⁴Time since dinosaurs became extinct = 2.4 x 10¹⁰This means that
Number of times = Time since dinosaurs became extinct/Average human lifespan
Substitute the known values in the above equation, so, we have the following representation
Number of times = 2.4 x 10¹⁰/2.4 x 10⁴
Evaluate the quotient
Number of times = 10⁶
Hence, the number of times is 10⁶
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Solve each equation by factoring. Check your answers. To start, factor the quadratic expression.
1.x²2 - x - 30 = 0
4. x – 5x =0
2. x² - 10x = -21
5. 10x 24 = x²
3.x²= 10x - 9
6. x² = -12x
the factor of the quadratic expression are:
1) x² - x - 30 = 0 : (x - 5)(x + 6) = 0
2) x² - 10x = -21 : (x - 7)(x + 3) = 0
3) x²= 10x - 9 : (x - 3)(x + 3) = 0
4) x – 5x =0 : x = 0
5) 10x - 24 = x² : (x - 6)(x - 4) = 0
6) x² = -12x : (x + 6)(x - 2) = 0
What is the factor of the quadratic expression?
Factorization of quadratic equations is the part of finding the roots of a quadratic equation. Factoring quadratic equations means converting the given quadratic expression into the product of two linear factors.
1) x² - x - 30 = 0
To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (-30) and add to give us the coefficient of the x term (-1). The two integers that fit this criterion are -6 and 5, so we can factor the expression as:
(x - 5)(x + 6) = 0
2) x² - 10x = -21
To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (-21) and add to give us the coefficient of the x term (-10). The two integers that fit these criteria are -7 and 3, so we can factor the expression as:
(x - 7)(x + 3) = 0
3) x²= 10x - 9
To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (-9) and add to give us the coefficient of the x term (10). The two integers that fit this criteria are -3 and 3, so we can factor the expression as:
(x - 3)(x + 3) = 0
4) x – 5x =0
To solve this equation, we can first combine like terms to get:
-4x = 0
Then, we can divide both sides by -4 to get:
x = 0
5) 10x - 24 = x²
To solve this equation, we can first move the x² term to the left side and the constant term to the right side to get:
x² - 10x + 24 = 0
To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (24) and add to give us the coefficient of the x term (-10). The two integers that fit this criteria are -6 and 4, so we can factor the expression as:
(x - 6)(x - 4) = 0
6) x² = -12x
To solve this equation, we can first move the constant term to the right side to get:
x² + 12x = 0
To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the coefficient of the x term (12) and add to give us 0. The two integers that fit this criteria are -6 and 2, so we can factor the expression as:
(x + 6)(x - 2) = 0
Hence, the factor of the quadratic expression are:
1) x² - x - 30 = 0 : (x - 5)(x + 6) = 0
2) x² - 10x = -21 : (x - 7)(x + 3) = 0
3) x²= 10x - 9 : (x - 3)(x + 3) = 0
4) x – 5x =0 : x = 0
5) 10x - 24 = x² : (x - 6)(x - 4) = 0
6) x² = -12x : (x + 6)(x - 2) = 0
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What property is this the rule for?
a +b= b+a
one leg of a right triangle has length 24 inches; the hypotenuse is 26.7 inches. what is the length of the other leg of the triangle?
The length of the other leg of the triangle is 11.7 inches
Now, According to the question:
We have the right triangle
The length of the right triangle is 24 inches
The length of the hypotenuse is 26.7 inches
To find the length of the other leg of the triangle
We know that the Pythagorean theorem.
The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.
Let the length of the other leg of the triangle be 'x'
According to the information:
[tex]24^2 + x^2 = 26.7^2[/tex]
576 + [tex]x^{2}[/tex] = 712.89
[tex]x^{2}[/tex] = 712.89 - 576
[tex]x^{2}[/tex] = 136.89
x = [tex]\sqrt{136.89}[/tex]
x = 11.7
Hence, The length of the other leg of the triangle is 11.7 inches.
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A right triangle is shown, where the horizontal leg has a measure of 48 centimeters (cm), and the hypotenuse has a measure of 73 cm.
Answer:
55
Step-by-step explanation:
Using the Pythagorean theorm:
a^2+b^2=c^2
48^2+b^2=73^2
b^2=73^2-48^2
b^2=3025
b=55
4. 8 friends are lining up to get in to see the Hunger Games: Catching Fire movie,
including Bob and Sam
A) What is the probability that Bob and Sam will be next to each other.
Answer:
1/64
Step-by-step explanation:
1/8 x 1/8 = 1/64
Hello this is the question
Answer:
A. 36/5
Step-by-step explanation:
cross multiply
6/5 = x/6
5x = 36
x = 36/5
Answer:
A) [tex]\frac{36}{5}[/tex]
Step-by-step explanation:
[tex]\frac{6}{5}[/tex] = [tex]\frac{x}{6}[/tex] Cross multiply and solve for x
36 = 5x Divide both sides by 5
[tex]\frac{36}5}[/tex] = [tex]\frac{5x}{5}[/tex]
[tex]\frac{36}{5}[/tex] = x
please help with 4 and 6 its my 4th time asking with no response
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
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Need to turn this in today help!!
The angle 2 is 149° , angle 3 is 31° , angle 4 is 149°
What is the name for two opposing angles?
Angles where two lines cross that are directly opposite one another are known as opposing angles. The vertex, where the lines come together to produce the angle, is the location of the junction. Vertical angles are another name for opposite angles.
Given that :
Angle 1 is = 31°
Angle 2 is = 180 - 31 = 149° (As in a line total angle is 180°)
Angle 3 is = 31° (As equal opposite angle with angle 1)
Angle 4 is = 149° (As equal opposite angle with angle 2)
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