Answer:
Linear f(x) = 2·x + 3
Quadratic f(x) = x² + 2·x - 3
Exponential f(x) = 3ˣ - 2
Step-by-step explanation:
1) Linear function
The general form of the linear equation is of the form, f(x) = y = m·x + c
Where;
m = The slope
c = y-intercept (Constant)
The linear function is therefore, f(x) = 2·x + 3
2) Quadratic function
The general form of the quadratic function is f(x) = a·x² + b·x + c
Where;
a, and b are the coefficients of x² and x respectively and c is the constant term
Therefore, f(x) = x² + 2·x - 3, is a quadratic function, with a = 1, b = 2, and c = -3
3) Exponential function
The general form of the exponential function is f(x) = a·bˣ + k
Where;
a = The initial
b = The multiplier (growth or decay value)
k = vertical shift
Therefore, the function f(x) = 3ˣ - 2 is an exponential function with the initial = 1, b= 3, and k = -2
A silver chain has 100 links. Each link is made of thin silver wire and is in the shape of a circle of radius 2,5 cm. Find the value of the chain if the silver wire costs 6 cents per centimetre ( Use 3,14 for π )
Number of links = 100
Shape of each link = Circle
Radius = 2.5
Area = πr²
= 3.14×2.5×2.5
= 19.625
Now for 100 links
19.625×100
1962.5Cm²
Cost = 1962.5 × 0.06
= $117.75
Must click thanks and mark brainliest
If each link is made of thin silver wire and is in the shape of a circle of radius 2.5 cm, the value of the silver chain is $94.20.
To find the value of the silver chain, we need to calculate the total length of the silver wire used in making the chain and then multiply it by the cost per centimeter.
Each link in the chain is a circle with a radius of 2.5 cm. The circumference of a circle can be calculated using the formula 2πr, where r is the radius.
In this case, the circumference of each link is:
Circumference = 2 * 3.14 * 2.5 cm = 15.7 cm
Since there are 100 links in the chain, we multiply the circumference of each link by 100 to get the total length of the silver wire used:
Total length = 15.7 cm/link * 100 links = 1570 cm
Now, we can calculate the value of the chain by multiplying the total length of the silver wire by the cost per centimeter:
Value of the chain = 1570 cm * $0.06/cm = $94.20
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Picture Shown!
Find the image of the given point
under the given translation.
P(-5,7) T(x, y) = (x + 5, y - 4)
P' = ([?], [?])
Enter the number that belongs in
the green box.
Answer:
0'=(0,3)
Step-by-step explanation:
P'=(-5+5,7-5)=(0,3)
If a person invests $120 at 8% annual interest, find the approximate value of the investment at the end of 5 years. A. $164 B. $180 C. $401 D. $176
Answer:
[tex]\large \boxed{\sf \bf \ \ \ D. \ \$ 176 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
After 5 years, we will get
[tex]120*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)\\\\=120*(1+8\%)^5\\\\=120\cdot 1.08^5\\\\= 176.3193...[/tex]
Thank you
Find the Algebric Equation
The sum of the product of 5 and a number, and 8
Answer:
5x+8
Step-by-step explanation:
First find the product of 5 and a number
5x
Then sum it with 8
5x+8
Drag each tile to the correct box.
Answer:
The order is 4) → 5) → 6) → 7) → 2) → 1) → 3)
Please find diagram with the arrangements
Step-by-step explanation:
The horizontal width of an hyperbola
For
1) [tex]\dfrac{(y - 11)^2}{7^2} -\dfrac{(x - 2)^2}{6^2} = 1[/tex]
h = 2, k = 11
The widths are;
Horizontal (h - a, k) to (h + a, k) which is (2 - 7, 11) to (2 + 7, 11) = 14 units wide
(h, k - b) to (h, k + b) which is (2, 11 -6) to (2, 11 + 6) = 12 units wide
2)
[tex]\dfrac{(y - 1)^2}{5^2} -\dfrac{(x - 7)^2}{12^2} = 1[/tex]
h = 7, k = 1
(h - a, k) to (h + a, k) which is (7 - 5, 1) to (7 + 5, 1) = Horizontal width 10 units wide
(h, k - b) to (h, k + b) which is (7, 1 -12) to (7, 1 + 12) = 24 units wide
3) [tex]\dfrac{(x - 6)^2}{6^2} -\dfrac{(y + 1)^2}{3^2} = 1[/tex]
h = 6, k = -1
a = 8, b = 3
The widths are;
(6 - 8, -1) to (6 + 8, -1) Horizontal width = 16
(6, -1 - 3) to 6, -1 + 3) width = 6
4) [tex]\dfrac{(x - 4)^2}{2^2} -\dfrac{(y + 2)^2}{5^2} = 1[/tex]
h = 4, k = -2, a = 2, b = 5
(4 - 2, (-2)) to (4 + 2, (-2)) Horizontal width = 4
(4, -2 - 5) to (4, -2 + 5) width = 10
5) [tex]\dfrac{(y + 5)^2}{2^2} -\dfrac{(x + 4)^2}{3^2} = 1[/tex]
h = -4, k = -5, a = 2, b = 3
(-4 - 2, (-5)) to (-4 + 2, (-5)) Horizontal width = 4
(-4, -5 - 3) to (4, -5 + 3) width = 6
6) [tex]\dfrac{(y + 1)^2}{2^2} -\dfrac{(x - 1)^2}{9^2} = 1[/tex]
h = 1, k = -1, a = 2, b = 9
(1 - 2, (-1)) to (1 + 2, (-1)) Horizontal width = 4
(1, -1 - 9) to (1, -1 + 9) width = 18
7) [tex]\dfrac{(x + 7)^2}{4^2} -\dfrac{(y - 9)^2}{9^2} = 1[/tex]
h = -7, k = 9, a = 4, b = 9
(-7 - 4, 9) to (-7 + 4, 9) Horizontal width = 8
(-7, 9 -9) to (-7, 9 + 9) width = 18
the width of a rectangle is 3 less than twice length. the perimeter is 51 cm . what is the length and width of the rectangle.
Answer:
[tex]length = x[/tex]
[tex]width = 2x - 3[/tex]
[tex]perimeter = 2(x + (2x - 3))[/tex]
[tex]51 = 2(3x - 3)[/tex]
[tex]51 = 6(x - 1)[/tex]
[tex]x - 1 = 8.5[/tex]
[tex]x = 9.5cm[/tex]
[tex]length = 9.5[/tex]
[tex]width = 2x - 3 = 2(9.5) - 3 = 16cm[/tex]
WILL MARK BRAINLIEST!!!! PLZ HELP!!! A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds: Use the graph to determine the domain of f(x) for all viable x values, based on the context. x ≤ 6000 0 ≤ x ≤ 20 −20 ≤ x ≤ 20 All real numbers
Answer:
[tex]\large \boxed{\mathrm{All \ real \ numbers}}[/tex]
Step-by-step explanation:
The domain of a function is all possible values of x for which the function is real and defined.
[tex]f(x)=-15x^2 +6000[/tex]
The function has no undefined points nor any restrictions on the value of x.
[tex]- \infty < x < \infty[/tex]
The domain of the function is all real numbers.
Answer:
All real numbers
Step-by-step explanation:
The domain is the set of all possible values for x.
f(x) = -15x² + 6000
There are no restrictions on the value of x.
The domain is all real numbers.
+
50°
50°
PLEAE help
The answer will be 80 degrees
Step-by-step explanation:
50 +50 + x = 180 (Angle sum property of a triangle)
The angle sum property of a triangle:
The total measure of the three angles of a triangle is 180°[tex] \rm \large \rightarrow \: \: x \: + \: 50 \degree \: + \:50 \degree \: = \: 180 \degree[/tex]
[tex] \rm \large \rightarrow \: \: x \: + \: 100 \degree \: = \: 180 \degree[/tex]
[tex]\rm \large \rightarrow \: \: x \: = \: 180 \degree \: - \: 100 \degree[/tex]
[tex]\rm \large \rightarrow \: \: x \: = \: 80 \degree[/tex]
please help me Find DE.
Answer:
DE = 11
Step-by-step explanation:
DF = DF +EF
4x+2 = x+7 + 7
Combine like terms
4x+2 = x+14
Subtract x from each side
4x+2-x = x+14-x
3x+2 = 14
Subtract 2 from each side
3x+2-2 =14-2
3x=12
Divide by 3
3x/3 = 12/3
x = 4
DE = x+7 = 4+7 =11
Answer:
DE is 11
Step-by-step explanation:
[tex]DE = DF - EF \\ DE = (4x + 2) - 7 \\DE = 4x - 5 [/tex]
But for x:
[tex]4x + 2 = (x + 7) + 7 \\ 4x + 2 = x + 14 \\ 3x = 12 \\ x = 4[/tex]
Therefore:
[tex]DE = (4 \times 4) - 5 \\ = 16 - 5 \\ = 11[/tex]
please help!!!!!!!!!!!!! Select ALL the correct answers. Choose the statements that are true about a cube with side length 1 unit.
Answer:
i think it is 2
Step-by-step explanation:
Determine if the event described is independent or dependent. Two people are standing in line at a movie theater trying to decide on which movies to see. a independent b dependent c neither d both
Answer:
c as in neither.
Step-by-step explanation:
the question does not give enough info because there are not two variables to be dependant on
Given three consecutive even integers whose sum is 54, find the largest of the three integers.
Answer:
The largest of the three numbers is 20Step-by-step explanation:
16, 18, 20
(n) + n+2 + n+4
Note:We only took even numbers
Answer:
20
Step-by-step explanation:
Let the least integer = x. The three consecutive even integers can be denoted as:
x , x + 2 , x + 4
Set the equation:
(x) + (x + 2) + (x + 4) = 54
Simplify. Combine like terms:
(x + x + x) + (2 + 4) = 54
(3x) + (6) = 54
3x + 6 = 54
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract 6 from both sides of the equation:
3x + 6 (-6) = 54 (-6)
3x = 54 - 6
3x = 48
Next, divide 3 from both sides of the equation:
(3x)/3 = (48)/3
x = 48/3
x = 16
~
Next, find the largest of the three integers, which was denoted as x + 4:
x + 4
(16) + 4 = 20
20 is the largest integer.
Check:
x + (x + 2) + (x + 4) = 54
16 + (16 + 2) + (16 + 4) = 54
16 + 18 + 20 = 54
16 + 38 = 54
54 = 54 (True).
~
Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance
charge over the course of his loan?
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77
$30.88
$23.95
$19.80
7.5% $86.76 $45.00
$31.11
$24.18
$20.04
8.0% $86.99 $45.23
$31.34
$24.41
$20.28
8.5% $87.22 $45.46
$24.65
$24.65
$20.52
9.0% $87.45 $45.68
$31.80
$24.89
$20.76
A.
$355.65
O
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E. $17,071.20
Reset
Next
© 2020 Edmentum. All rights reserved.
Answer:
D. $2071.20
Step-by-step explanation:
The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...
48 × $23.71 = $1138.08
That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...
finance charge = 15 × $138.08 = $2071.20 . . . matches choice D
Does the equation |2x + 11| = 21 have 0, 1, 2, or 3 solutions? Explain your answer
Answer:
2x +11=21 and 2x+11=-21 it has 2 solutions because of the absolute value and to solve you would jist solve for X
What is the product? One-fourth times three and two-thirds
Answer:
11/12
Step-by-step explanation:
The product of One-fourth times three and two-thirds will be 1 / 2.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
Given that, the numbers are one-fourth times three and two-thirds. The product of the numbers will be calculated as,
Product = ( 1 / 4 ) x ( 3 ) x ( 2 / 3 )
Product = 6 / 12
Product = 1 / 2
Therefore, the product of One-fourth times three and two-thirds will be 1 / 2.
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I don’t really understand this
Answer
pretty sure its a or c, sorry I cant be more specific
Step-by-step explanation:
ABC is an equilateral triangle, solve y
Answer:
y is 60⁰
because all sides are equal
Answer:
60 degrees
Step-by-step explanation:
In an equilateral triangle, the angles are equiangluar and the sides are equal.
180 degrees in a triangle/3 sides =
= 60 degrees per side
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1.-4,-1,1,6
2.by substituting the values given, we get
32-|15+8|
32-|23|
32-23=9
3.-15+7=8
4..27-(-12)=27+12=39
5.-6.05+(-2.1)
-6.05-2.1=-8.15
6.-3/4-(-2/5)
-3/4+2/5
=-7/20
7.-9(-12)
=108
8.(3.8)(-4.1)
-15.58
9.(-8x)(-2y)+(-3y)(z)
(16xy)+(-3zy)
(16xy)-(3zy)
10.by substituting the value given,we get
2.5*(-3.2)+5
-8+5
-3
so here are the answers,mark as brainliest if u find it useful
thank you
prove that the line x-y=0 bisect the line segment joining the point (1,6) and (4, -1)
Step-by-step explanation:
x-y=0(l.6)-(4.-1)(6-4)-(1--1)2--2=03 cm
20 cm
4 cm
Find the volume of the rectangular prism.
[?] cm
Enter
Answer:
240cm^3
Step-by-step explanation:
3cmx20cmx4cm=240cm^3
Find the value of x. A. 74 B. 244 C. 52 D. 64
Answer:
Step-by-step explanation:
The formula you need to solve for angle x is:
∠x = 1/2(large arc - small arc)
We have enough info to find what we need to solve for the arcs. 58° is an inscribed angle. The rays of the angle cut off an arc on the circle and that arc measure is twice the measure of the angle. So the smaller arc is 58 * 2 = 116. Since around the outside of the circle measures 360°, then the larger arc measures 360 - 116 = 244. So the larger arc is 244. Filling in the formula to solve for the angle x:
∠x = 1/2(244 - 116) and
∠x = 1/2(128) so
∠x = 64
D is your answer.
Answer:
D.) 64
Step-by-step explanation:
I got it correct on founders edtell
Observe the figure drawn, in which a square of side 15cm is removed from one corner of the given rectangle. Find the perimeter of the shaded region. Pls answer, no other irrelevant answer. Pls solve this. I will follow you if you do it. It's urgent!!!
Step-by-step explanation:
Let's start by finding the area of figure 1
The square:
15cm×15cm=225cm²
Then we're going to find the area of figure 2
it's a rectangle (A=L×W)
L=60cm-15cm(because those cm have been cut off)=45cm
W=40cm
Area=45cm×40cm
=1800cm²
Then we add up the sum
Area of 1+Area of 2
=225cm²+1800cm²
=2025cm²
Answer:
140 cm is the perimeter of the unshaded shape.
Step-by-step explanation:
Perimeter of the rectangle in whole = 2l + 2w
Where length is 60 cm and width is 40 cm.
P = 2 × 60 + 2 × 40
= 120 + 80
= 200 cm
To find the perimeter of the unshaded square = 4l
Where the length is 15 cm.
P = 4× 15
= 60 cm
To find the perimeter of the shaded shape = Perimeter of rectangle - Perimeter of unshaded square.
P = 200 - 60
= 140 cm
140 cm is the perimeter of the unshaded shape.
solve the equation 2x + 4 > 16
Answer:
x > 6
Step-by-step explanation:
2x + 4 > 16
2x > 16 - 4
2x > 12
x > 12/2
x > 6
For the Parabolay = (x – 7)2 – 3. the equation for the Line Of Symmetry is
a) x
b) y
c) -7
d) 3
e) -3
Answer:
x = 7
Step-by-step explanation:
y = (x – 7)^2 – 3
This equation is in vertex form
y = a(x-h)^2 +k
where (h,k) is the vertex
For a vertical parabola, the line of symmetry is x=h
x = 7
In triangle ABC, ∠A is a right angle and m∠B = 45°. Find BC. If your answer is not an integer, leave it in the simplest radical form. The question is multiple choice and the choices are below. A. 20[tex]\sqrt{2}[/tex] ft B. 10 ft C. 20 ft D. 10 [tex]\sqrt{2}[/tex] ft
Answer: D [tex]10\sqrt{2}[/tex]
Step-by-step explanation:
It says that the measure of angle B is 45 degrees. So if we were to put in 45 degrees we could see that is is opposite AC and BC which we needs to find is the hypotenuse. So since we know the opposite of angle B is 10 ft we can using that to find the length of BC. Opposite hypotenuse is the sine function so we will use it to calculate the length of BC.
sin(45) = [tex]\frac{10}{BC}[/tex] multiply both sides by BC
BC sin(45) = 10 divide both sides by sin(45)
BC = [tex]\frac{10}{sin(45)}[/tex]
BC = [tex]10\sqrt{2}[/tex]
Answer:
[tex]\huge\boxed{Option\ D : \ BC = 10\sqrt{2}\ ft }[/tex]
Step-by-step explanation:
Since it's a right angled triangle, We'll use trigonometric rations.
Given that m∠B = 45°
So,
Sin B = opposite / hypotenuse
Where m∠B = 45°, opposite = 10 ft and hypotenuse = BC
Sin 45 = 10 / BC
[tex]\sf \frac{\sqrt{2} }{2} = \frac{10}{BC}[/tex]
BC = 20 / √2
Multiplying and Dividing by √2
BC = 20√2 / √(2)²
BC = 20 √2 / 2
BC = 10√2 ft
Geometry, please answer question ASAP
Answer:
XY = 24
Step-by-step explanation:
In similar triangles, the corresponding sides are in same ratio.
[tex]\frac{AC}{XZ}=\frac{AB}{XY}\\\\\frac{x+6}{30}=\frac{16}{2x-4}[/tex]
Cross multiply,
(x + 6 )(2x-4) = 16*30
Use FOIL method
x*2x + x*(-4) + 6*2x + 6*(-4) = 480
2x² - 4x + 12x - 24 = 480 {Combine like terms}
2x² + 8x - 24 = 480
2x² + 8x - 24 - 480 = 0
2x² + 8x - 504 = 0
Divide the entire equation by 2
x² + 4x - 252 = 0
Sum = 4
Product = -252
Factors = 18 , -14 {18 +(-14) = 4 & 18*(-14) = -254 }
x² + 4x - 252 = 0
x² + 18x - 14x - 252 = 0 {Rewrite middle term}
x(x + 18) - 14(x + 18) = 0
(x + 18)(x - 14) = 0
x - 14 = 0 {Ignore x + 18 = 0 as measurement will not come in negative}
x = 14
XY = 2x - 4
= 2*14 -4
= 28 - 4
= 24
AHHH PLEASE HELP MEH
Evaluate (cot90)(cos45) + sec45 exactly. No decimals allowed, rationalize if necessary
Answer: [tex]\sqrt{2}[/tex]
======================================================
Explanation:
Rewrite each trig function terms of sine and/or cosine. Then use the unit circle to find that,
[tex]\cot(90^{\circ})\cos(45^{\circ}) + \sec(45^{\circ})\\\\\frac{\cos(90^{\circ})}{\sin(90^{\circ})}\cos(45^{\circ}) + \frac{1}{\cos(45^{\circ})}\\\\\frac{0}{1}*\frac{\sqrt{2}}{2} + \frac{1}{(\sqrt{2})/2}\\\\\frac{2}{\sqrt{2}}\\\\[/tex]
Now rationalize the denominator
[tex]\frac{2}{\sqrt{2}}\\\\\frac{2\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{2\sqrt{2}}{\sqrt{2*2}}\\\\\frac{2\sqrt{2}}{\sqrt{4}}\\\\\frac{2\sqrt{2}}{2}\\\\\sqrt{2}[/tex]
Which is the exact value of [tex]\sec(45^{\circ})[/tex]
The portion [tex]\cot(90^{\circ})*\cot(45^{\circ})[/tex] evaluates to 0 and goes away.
A point is randomly chosen on a map of North America. Describe the probability of the point being in each location: North America: New York City: Europe:
Answer:
We know that the map is of North America:
The probabilities are:
1) North America:
As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1
or 100% in percentage form.
2) New York City.
Here we can think this as:
The map of North America is an extension of area, and New Yorck City has a given area.
As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:
New York City = 730km^2
North America = 24,709,000 km^2
So the probability of randomly pointing at New York City is:
P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%
3) Europe:
As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).
So the probaility is 0 or 0%.
Answer:
North America: certain
New York City: unlikely
Europe: impossible
Step-by-step explanation:
simply
What is the missing reason in the proof?
Statements
Reasons
1. AB / CD; BC // DA 1. given
2. Quadrilateral ABCD 2. definition of parallelogram
is a
3. AB CD; BC = DA 3. opposite sides of a
parallelogram are >
4. AC AC
4. reflexive property
5. AABC 2 ACDA 5. ?
perpendicular bisector theorem
Pythagorean theorem
HL theorem
SSS congruence theorem
Answer:
The correct option is;
SSS congruency theorem
Step-by-step explanation:
Given that opposite sides of a parallelogram are equal, whereby side AB is congruent to side CD and side BC is congruent to side DA and also that side AC is congruent to side CA, we have;
Triangle ABC with sides AB, BC, and AC is congruent to triangle CDA with corresponding sides CD, DA, and CA, by the Side-Side-Side (SSS) rule of congruency (two or more triangles that have all three sides of one triangle congruent to the three sides of the other triangle are congruent).
The missing reason in the proof is: SSS Congruence Theorem.
What is the SSS Congruence Theorem?SSS means side-side-side, meaning two triangles have three pairs of congruent sides.According to the SSS Congruence Theorem, two triangles with three pairs of congruent sides must be congruent to each other.Thus, ΔABC and ΔCDA has been shown to have three pairs of congruent sides, therefore, the missing reason in the proof is: SSS Congruence Theorem.
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solve the following: If 7a – 4b = 3, then b =
Answer:
D (7a-3)/4
Step-by-step explanation:
7a – 4b = 3
Subtract 7a from each side
7a-7a – 4b = 3-7a
-4b = 3 -7a
Divide by -4
-4b/-4 = (3-7a)/-4
b = (7a-3)/4
Answer:
b = (7a - 3)/4
Step-by-step explanation:
7a - 4b = 3
=> -4b = 3 - 7a
=> b = (3 - 7a)/(-4)
=> b = -(3 - 7a)/4
=> b = (-3 + 7a)/4
=> b = (7a - 3)/4