Answer:
The slope would be 5/2.
Step-by-step explanation:
Use the formula Y=mx+b. m always represents the slope and the b is the intercept. Therefore the slope of this would be 5/2.
Draw a diagram of the archway modeled by the equation y = x^2 + 5x + 24. Fine and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25
The vertex of the parabola is at (-2.5, 17.75). And the y-intercept of the parabola is at (0, 24).
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation of the parabola is given as,
y = x² + 5x + 24
Convert the equation into a vertex form, then we have
y = x² + 5x + 25/4 - 25/4 + 24
y = (x + 5/2)² + 71/4
y = (x + 2.5)² + 17.75
The vertex of the parabola is at (-2.5, 17.75). The y-intercept of the parabola is given as,
y = (0)² + 5(0) + 24
y = 24
The y-intercept of the parabola is at (0, 24).
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Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He has 200 feet of fencing. The inequality that models the possible perimeter of the yard is 2l 2w ≤ 200. Which are possible dimensions for Mike’s backyard? Check all that apply. W = 50 ft; l = 10 ft w = 10 ft; l = 50 ft w = 20 ft; l = 60 ft w = 90 ft; l = 30 ft w = 50 ft; l = 40 ft.
The inequality that models the possible perimeter of the yard is 2(l + w) ≥ 200
The possible dimension of the width is 90 feet
The formula for calculating the perimeter of the fence is expressed as:
P = 2(l + w)l is the length of the fencew is the width of the fenceIf he has 200 feet of fencing, then:
2(l + w) ≥ 200
If the length of the fenced-in area to be at least 20 feet long, the equation becomes:
2(20 +w) ≥ 200
40 + 2w ≥ 200
2w ≥ 200 - 40
2w≥ 160
w≥ 80
Hence the possible dimension of the width is 90 feet
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when using the zero product rule you know at least one of the factors must equal *blank*
Answer:
The Principle of Zero Products states that if the product of two numbers is 0, then at least one of the factors is 0.
Step-by-step explanation:
Answer:
when using the zero product rule you know at least one of the factors must equal 0 because and most places anything that is put with zero equal zero because zero have no value
Step-by-step explanation:
((7,4),(6,3),(5,2)
Function?
Domain:
Range:
Answer:
see explanation
Step-by-step explanation:
For a function each value of x in the domain must map to exactly one unique value of y in the range.
This is the case here so it is a function.
The domain is the x- coordinates of the points
domain is { 5, 6, 7 }
The range is the y- coordinates of the points
range is { 2, 3, 4 }
The vertices of quadrilateral PQRS are listed.
P(3,7), Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS?
A.
Quadrilateral PQRS is a rectangle.
B.
Quadrilateral PQRS is a trapezoid.
C.
Quadrilateral PQRS is a square.
D.
Quadrilateral PQRS is a parallelogram.
Answer:
Rectangle
Step-by-step explanation:
Did it on
Option A is correct.
As, Quadrilateral PQRS is a rectangle because it has four right angles.
What is a rectangle?A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
here, we have,
Explanation:
Given:
The coordinate of vertices of quadrilateral PQRS are P(3,7), Q(6,-2), R(0,-4), S(-3,5).
Slope for two points (x1,y1) and (x2,y2) is given by:
m = y1-y2/ x1 - x2
.so, we get,
The slope of PQ is = -9/3 = -3
The slope of QR is = -2/-6 = 1/3
The slope of RS is = -3
The slope of SP is = 1/3
we know that,
The slopes of perpendicular lines are opposite reciprocals.
we get,
∴ all pair of sides has slopes that are negative reciprocals;
this means the figure has 4 right angle, so it is a rectangle.
Therefore, Quadrilateral PQRS is a rectangle because it has four right angles.
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A television set costs $4500 cash. When bought on hire-purchase, a deposit of $450 is
required, followed by 12 monthly payments of $400. How much is saved by paying cash?
Answer:
$750
Step-by-step explanation:
did the problem
Solve this question with Statements and reasoning.
Here
[tex]\\ \sf\longmapsto PD\cong PC[/tex]
As
P is the midpoint of AC and BD
[tex]\\ \sf\longmapsto AC=BD[/tex]
[tex]\\ \sf\longmapsto AP+PC=PD+BP[/tex]
Put PD=PC[tex]\\ \sf\longmapsto AP+PC=PC+PB[/tex]
Cancel PC[tex]\\ \sf\longmapsto AP=BP[/tex](Proved)
Evaluate
3
2
+
(
−
k
)
+
(
−
2
)
2
3
+(−k)+(−2)start fraction, 3, divided by, 2, end fraction, plus, left parenthesis, minus, k, right parenthesis, plus, left parenthesis, minus, 2, right parenthesis where
k
=
−
5
2
k=−
2
5
k, equals, minus, start fraction, 5, divided by, 2, end fraction.
Answer:
Iam very confused on this Answer please help me
Step-by-step explanation:
find the volume of this figure:
Answer:
= 5l. 66 in^3
Step-by-step explanation:
Area of cross section (A) = 1/2×b×h
=1/2 ×3.5×4.1
=7.175
Volume =AXH
= 7.175× 7.2
= 5l. 66 in^3
32 feet
8 feet
What will the new dimensions of the rectangle
be after a dilation with a scale factor of
7/8
Answer:
i do not know
Step-by-step explanation:
(I need these answered fast and with work and explanation)
A)What is the conditional probability of being on the marching band, given that you know
the student plays a team sport? Show your work.
b. What is the probability of being on the marching band, and how is this different from part
(a)? Explain completely.
C.
Are the two events, {on the marching band) and {on a team sport} associated? Use
probabilities to explain why or why not.
Answer:
most I know I don't know and I don't want to know
X
18. MODELING WITH MATHEMATICS The inequality
3x + 2y 2 93 represents the numbers x of multiple-
choice questions and the numbers y of matching
questions you can answer correctly to receive an A on
a test. You answer 20 multiple-choice questions and
18 matching questions correctly. Do you receive an A
on the test? Explain.
Answer:
yes
Step-by-step explanation:
Put the numbers into the inequality and see if it is true.
Given x = 20, y = 18, ...
3x + 2y = 3(20) +2(18) = 60 +36 = 96 ≥ 93 . . . . true
You have met the requirements for an A on the test.
Sally saved 65% of her pay check. If she made $500, how much did she save?
Answer: 325 dollars
Step-by-step explanation:
In order to find out a percentage of somethin, you can simply multiply and divide
[tex]500*65=32500[/tex]
32500÷100= 325
PLEASE HELP!!!!
ILL MARK AS BRAINIEST!!!!
ANSWER HOW MUCH U CAN!!!
Answer:
1) C
2) B
3) D
4) A
5) B
Step-by-step explanation:
Hope this helps
MAy I get braineist pls???????????
Answer:
MARK ME AS BRAINLIEST!!!
Step-by-step explanation:
1. A
2. B
3. D
4. A
5. B
HAVE A NICE DAY!!!
:)
2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles. On the Venn diagram, which region(s) represent the intersection of Set A and Set B (Aâ©B)? II I and III I, II, and III I, II, III, and IV.
The intersection of sets is the point that represents the common point of multiple sets.
The region that represents the intersection of sets A and B is region II.
From the question, we understand that sets A and B have a common set element at II.
This means that region II is the intersection of both sets.
Hence, the region that represents the intersection of sets A and B is II.
Read more about set intersection at:
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Answer:
II is the answer
Step-by-step explanation:
Edge 2022
simplify: 2x^2+15x-30
A= 2x^2
B= 15x
C= -30
(x-5)(x-6)
I dunno, its my question, just answering it for fun
Please help me with my math problem!! NO LINKS PLEASE!! IT IS DUE TONIGHT AT 11:59PM!! WILL GIVE BRAINLIEST!! :)
Step-by-step explanation:
Hi, i think this is how to do it. I'm sorry if I do it wrong!
For f(x) = -1/5x - 14 find x when f (x) = -8
Hi!
30 = x
f(x) = -1/5x - 14 find x when f (x) = -8
Set the equation equal to -8
-8 = -1/5x - 14
Add 14 to both sides.
6 = -1/5x
Multiply both sides by -5.
30 = x
Hope this helps! :D
write an algebraic expression for the word expression.
the sum of 9 and a number x
Answer:
9 + x
Step-by-step explanation:
i think this is what you meant
Answer:
Write each phrase as an algebraic expression. In Example 2, each algebraic expression consisted of one number, one operation and one variable.
...
Algebraic Expressions With Example Problems and Interactive Exercises.
Phrase Expression
the sum of nine and a number x 9 + x
Step-by-step explanation:
Hopes this helps\
Mark as brainliest
What is the probability for a bowler to score over 136? The mean for the set is 130, and the standard deviation is 3. So I know that it is Mean + 2(Standard Deviation), so is it 2.35% or 2.5%?
Answer:
135%
Step-by-step explanation:
A= 3x3x3x3x3x5x7x7x7
B= 2x2x2x3x7x7x7x7
Find the Lowest Common Multiple (LCM) of A and B.
Please help
Answer:
LCM(57624, 416745) = 23,337,720 or LCM = 23337720
Step-by-step explanation:
List all prime factors for each number.
Prime Factorization of 57624 is:
2 x 2 x 2 x 3 x 7 x 7 x 7 x 7 => 23 x 31 x 74
Prime Factorization of 416745 is:
3 x 3 x 3 x 3 x 3 x 5 x 7 x 7 x 7 => 35 x 51 x 73
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 3, 3, 3, 3, 3, 5, 7, 7, 7, 7
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 7 x 7 x 7 = 23337720
In exponential form:
LCM = 23 x 35 x 51 x 74 = 23337720
LCM = 23337720
Therefore,
LCM(57624, 416745) = 23,337,720
bryan has some 3 cent stamps and some 4 cent stamps. what is the least number of stamps he can combine so the value of the stamps is 33 cents?
Answer:
The least number of stamps required is [tex]9[/tex]
Step-by-step explanation:
Let the number of [tex]3[/tex] cent stamps be [tex]x[/tex] and [tex]4[/tex] cent stamps be [tex]y[/tex]
We have
[tex]3x+4y=33[/tex]
The minimum number is obtained when more [tex]4[/tex] cent stamps are used
Here [tex]y[/tex] cannot be greater than [tex]8[/tex] since [tex]\frac{33}{4} <9[/tex]
Substitute [tex]y=8[/tex]
[tex]3x+4\times 8=33\\\\3x=1\\\\x=\frac{1}{3}[/tex]
Not possible since [tex]x[/tex] is not a fraction
Substitute [tex]y=7[/tex]
[tex]3x+4\times 7=33\\\\3x=5\\\\x=\frac{5}{3}[/tex]
Not possible since [tex]x[/tex] is not a fraction
Substitute [tex]y=6[/tex]
[tex]3x+4\times 6=33\\\\3x=9\\\\x=\frac{9}{3}\\\\=3[/tex]
Possible
Hence minimum number of stamps is
[tex]=x+y\\\\=3+6\\\\=9[/tex]
Which equation represents the vertical line passing through (14,-16)?.
The vertical line shall have its x-coordinate equal to 14 because the points (14, -16) is on this vertical line.
Given the following data:
Points (x, y) = (14, -16)To find an equation of the vertical line that passes through the given points (14, -16):
The standard form of an equation of line is given by the formula;
[tex]y=mx+b[/tex]
Where:
x and y are the points.m is the slope.b is the intercept.For any equation of a straight line, the x-coordinate of a vertical line will always be the same irrespective of the point chosen on the vertical line. because a vertical line is perpendicular to the x-axis.
Deductively, the vertical line shall have its x-coordinate equal to 14 because the points (14, -16) is on this vertical line.
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4++++++++++++++++++++++++++++++++=4=
Answer:
is equal to 0
Step-by-step explanation:
points Lang habol
Help me solve for x. :>
Answer:
x = 9
Step-by-step explanation:
3 ㏒₄x = 2 ㏒₄27
㏒₄ x³ = ㏒₄ 27²
As ㏒₄ = ㏒₄
You can write this as,
x³ = 27²
x ³ = 27 × 27
x³ = 3³ × 3³
x ³ = 3⁶
x ³ = 729
x ³ = 9³
There fore,
x = 9
Hope this helps you :-)
y^2 - 19 = 0 find the sum and product
Answer: Sum of the roots: √19 - √19 = 0
Product of roots: (√19)(-√19) = -19
Step-by-step explanation:
y2 - 19 = 0
add 19 to both sides
y2 = 19
take square root of both sides
y = ±√19
So y = √19 or y = -√19
Trevor simplifies a linear equation
Answer:
C :3
Step-by-step explanation:
Whenever our simplification of a linear equation ends in a true statement, in this case 6=6, then our linear equation has infinitely many solutions.
Therefore, our answer is C.
even if we don’t know what x is we’ll still get an infinite amount of solutions
HOPE THIS HELPED :DDDD
Write an expression for the volume of the figure as a polynomial in standard form. (multiple choice)
Answer:
3.
2x^3+10x^2+14x+6
Step-by-step explanation:
according to figure,
v=w•l•h
(2x+2)(x+1)(x+3)
=(2x+2)x(x+1)+3(X+1)
=(2x+2)(x^2+4x+3)
=2x(x^2+4x+3)+2(x^2+4x+3)
=2x^3+10x^2+14x+6
The volume of the figure as a polynomial in standard form is
V = 2x³ + 10x² + 14x + 6.
What is a cuboid?A closed three-dimensional geometric shape called a cuboid is surrounded by six rectangular plane sections.
The given figure is a cuboid with dimensions (2x + 2), (x + 1), and (x + 3).
The volume of the cuboid is the multiplication of its dimension, therefore, the volume of the cuboid is:
V = (2x +2)(x + 1)(x + 3)
V = (2x² + 2x +2x + 2)(x + 3)
V = (2x² + 4x + 2)(x + 3)
V = 2x³ + 6x² + 4x² + 12x + 2x + 6
V = 2x³ + 10x² + 14x + 6
Hence, the volume of the figure as a polynomial in standard form is
V = 2x³ + 10x² + 14x + 6.
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What is the best estimate for this sum?
1/8+1/6
Options here:
The sum will be close to 1/4
The sum will be close to 1/2
The sum will be close to 1
*Disclaimer* show work
From the observation deck of a skyscraper, Jamal measures a 51° angle of depression
to a ship in the harbor below. If the observation deck is 1123 feet high, what is the
horizontal distance from the base of the skyscraper out to the ship? Round your
answer to the nearest hundredth of a foot if necessary.
Answer:
Your answer is 909.39 feet
Step-by-step explanation: