Answers
Related Questions
What is the value of h when the function is converted to vertex form? Note: Vertex form is p(x)=a(x−h)^
2+k . p(x)=x^2−14x+29
Answers
p(x)=a(x-h)^2+k
p(x)=x^2-14x+29
c=(b/2)^2=(-14/2)^2=49
hence:
x^2-14x+49=-29+49
(x-7)^2=20
hence:
p(x)=(x-7)^2-20
thus, h=7
the area of a rectangle is 20x^2-27x-8.the length is 4x+1. What is the width?
Answers
Explanation:
Let width be w
Then w(4x+1)=20x2−27x−8
So
(?x+?)(4x+1)=20x2−27x−8
Note that
5×4=20 and (−8)×(+1)=−8
⇒w(4x+1)
=(5x-8)(4x+1)=20x2+5x−32x−8
⇒w(5x−8)
find the roots of the equation x3-3x^2+x+5
Answers
(x+1)(x^2-4x+5)=0
x+1=0→x+1-1=0-1→x=-1
x^2-4x+5 different to zero
The root of the equation is x=-1
A support beam to be placed at a 28° angle of elevation so that the top meets a vertical beam 1.6 meters above the horizontal floor. Thanks vertical beam meets the floor at a 90° angle.
Law of sin: sin(A)/a=sin(B)/b=sin(C)/c
Approximately how far the vertical beam should the lower end of the support be placed along the horizontal floor
A)3.0 meters
B)3.4 meters
C)3.9 meters
D)4.4 meters
Answers
The answer is B
Answer:
B.
Step-by-step explanation:
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft2 . find the dimensions of the rectangle.
Answers
Then the length is 3w - 5.
The area = LW = 28
w(3w - 5) = 28
3w^2 - 5w = 28
3w^2 - 5w - 28 = 0
(3w + 7)(w - 4) = 0
3w + 7 = 0 or w - 4 = 0
w = -7/3 or w = 4
The width of a rectangle cannot be a negative number, so we discard w = -7/3.
The width is 4 ft.
The length is 3w - 5 = 3(4) - 5 = 12 - 5 = 7
The length is 7 ft
Answer: The dimensions are length 7 ft and width 4 ft.
The rectangle has a width of approximately 4.18ft and a length of approximately 7.55ft. These are obtained by setting up and solving a system of equations based on the given information.
Explanation:Let's start by setting up equations based on the problem statement. Let's denote the width of the rectangle as
w and the length as l. From the problem, we know two things: one is that the length is 5 feet less than three times the width, which can be written as l = 3w - 5. The second thing we know is that the area of the rectangle, which is obtained by multiplying the length by the width, is 28 square feet, written as l*w = 28 . By substituting the first equation into the second, we can solve for w: (3w - 5)*w = 28
. This simplifies to a quadratic equation 3w^2 - 5w - 28 = 0 which can be solved to give w=~4.18 ft and w=-2.02ft. Because the width cannot be negative, we discard the second solution. Substituting w=~4.18ft into l = 3w -5 gives
l=~7.55 ft . Therefore, the dimensions of the rectangle are approximately 4.18ft (width) and 7.55ft (length).
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What is the quotient of
13
÷
8
? Leave your answer as a mixed number
Answers
A waterfall has a height of 900 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 12 feet per second. The height, h, of the pebble after t seconds is given by the equation h equals negative 16 t squared plus 12 t plus 900. How long after the pebble is thrown will it hit the ground?
Answers
_____
The quadratic formula tells you the time is
.. t = (-12 -√(12^2 +4*16*900))/(-32) = (3/8)*(1 +√401) . . . seconds
Final answer:
To find when the pebble hits the ground, solve for time using the quadratic equation from the given height function, resulting in around 6 seconds.
Explanation:
To find how long the pebble takes to hit the ground, we need to find the time t when its height h becomes 0. This means we need to solve the equation for t when h = 0:
-16t² + 12t + 900 = 0
This is a quadratic equation, and we can solve it using various methods like factoring, the quadratic formula, or completing the square. Here, we'll use the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 12, and c = 900:
t = (-12 ± √(12² - 4 × -16 × 900)) / (2 × -16)
t = (-12 ± √(614400)) / -32
t ≈ (-12 ± 247.88) / -32
There are two possible solutions:
t1 ≈ 25.50 seconds
t2 ≈ -5.50 seconds (we can discard this since time cannot be negative)
The pebble will hit the ground approximately 6 seconds after it is thrown.
There are 6 speakers at a conference: Ms. Sally, Ms. Elaine, Ms. Boo-Koo, Mr. Adam, Mr. Jones, and Mr. Tall. In how many ways can we order the speakers so that Mr. Adam doesn’t speak first?
Answers
Even though there are 6 speakers, Mr. Adam cannot go first so there are 5 choices for who goes first. That leaves 5 speakers who can go second. As we already picked two people, there are 4 speakers who can go third and 3 who can go fourth. That leaves 2 that can go fifth and 1 that is left for the last slot.
The total number of ways is given by (5)(5)(4)(3)(2)(1) = 600
16. Which of the following are the measures of a right isosceles triangle?
a. 36°, 60°, 90°
b. 40°, 40°, 90°
c. 60°, 60°, 60°
d. 45°, 90°, 45°
17. Of the following triangles, which one is impossible to construct?
a. acute scalene
b. acute equilateral
c. obtuse scalene
d. obtuse equilateral
Answers
The angles of right isosceles triangle are such that there is the right angle, 90 degrees, and there are two identical angles that add up to 90.
17.
It is impossible to have an obtuse equilateral because and obtuse triangle has an angle that is more than 90 but less than 190. The equilateral triangle has all the angles equaling the same; 60 degrees. 60 degrees isn't obtuse so it is impossible to have an obtuse equilateral triangle.
Hope this helps :)
Which of the following is the solution of 5e^2x-4=11
Answers
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The population of a town is 6500 and is increasing at a rate of 4% per year.at this rate, approximately what will the towns population be in 4 years
Answers
End of 1st year = 1.04 x 6500 = 6760
End of 2nd year = 1.04 x 6760 = 7030
End of 3rd year = 1.04 x 7030 = 7312
End of 4th year = 1.04 x 7312 = 7604
To find the town's population in 4 years with an initial population of 6500 and a 4% annual growth rate, we use the exponential growth formula, resulting in an estimated population of approximately 7609.
The population of a town is 6500 and is increasing at a rate of 4% per year. To calculate the town's population in 4 years, we will use the formula for exponential growth:
P(t) = P0(1 + r)^t
Where:
P(t) is the future population
P0 is the initial population
r is the growth rate (as a decimal)
t is the number of years
Step-by-step calculation:
Convert the growth rate from a percentage to a decimal: r = 4% = 0.04
Use the formula with t = 4 years, P0 = 6500, and r = 0.04:
P(4) = 6500(1 + 0.04)⁴
Calculate P(4) = 6500 * 1.04⁴
Approximate the future population after 4 years.
By performing the calculation, the town's population in 4 years will be approximately 7609.
Find the area of the triangle. Round the answer to the nearest tenth.
A.
68.4 square units
B.
75.3 square units
C.
84.5 square units
D.
136.7 square units
Answers
Answer:
Option A. 68.4 square units.
Step-by-step explanation:
Since sides ED = EF = 13 units
So the given triangle is an isosceles triangle and in an isosceles triangle EFD, perpendicular drawn from E to DF, will be perpendicular bisector of DF.
Moreover, to this perpendicular bisector to DF will be the height of the triangle.
Now Area of a triangle of [tex]\frac{1}{2}[/tex] × base × height.
Sin 63 = [tex]\frac{Height}{Hypotenuse}[/tex] = [tex]\frac{h}{13}[/tex]
h = 13 sin 63 = 13 ( 0.891) = 11.583 units
Cos 63 = [tex]\frac{Base}{Hypotenuse}[/tex] = [tex]\frac{Base}{13}[/tex]
Base = 13 cos 63 = 13 × (0.454)
= 5.90 units
Since DF = 2 × base = 2 × 5.90
= 11.80 units
Now area of EDF = [tex]\frac{1}{2}[/tex] × 11.80 × 11.583
= 68.86 ≈ 68.40 square units.
Option A. 68.4 square units.
Makhaya is required to spend more than 300 minutes to complete assignments, and he can use at most 20 paper sheets. Let W denote the number of writing assignments he completes and M the number of math assignments he completes.
Write an inequality that represents the condition based on the number of minutes.
Write an inequality that represents the condition based on the number of paper sheets.
Answers
.. 75W +15M ≥ 300 . . . . . . . minutes
The constraint on paper is
.. 3W +M ≤ 20 . . . . . . . . . . . sheets of paper
Y varies directly as x and inversely as the square root of w; write the sentence as an equation.
Answers
y = kx
Y varies inversely as the square root of w
y = [tex] \frac{k}{ \sqrt{w} } [/tex]
The relationship where y varies directly as x and inversely as the square root of w can be represented by the equation y = k * (x / sqrt(w)). Here, k is a constant of proportionality.
Explanation:From the statement given, we can deduce an equation representing a direct proportionality to x and an inverse proportionality to the square root of w.
In mathematics, direct and inverse proportionality relationships are commonly depicted as y = kx and y = k/x respectively, where k is a constant. For direct proportionality, as x increases, y also increases. Contrastingly, for inverse proportionality, as x increases, y decreases.
Given the statement, we can represent the relationship as follows: y = k * (x / sqrt(w)).
Here, y varies directly as x and inversely as the square root of w. The constant k is the constant of proportionality which can be determined based on specific values of x, y and w.
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Write a real word problem that involves classifying a quadrilateral
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Maybe this helps or at least take ideas from this for me it wasn’t good but at least its something
Alice needs to classify her garden quadrilateral to determine if it is suitable for a specific species of flowers. She finds the sides equal in length and consecutive angles supplementary, which leads her to conclude the garden plot is a rhombus, meeting the criteria for her flowers.
Alice designs a garden plot in the shape of a quadrilateral. She knows that for a certain species of flower to grow optimally, her garden must have a specific shape: it needs to be a parallelogram with equal sides but not necessarily equal angles. In order to classify the quadrilateral of her garden, she begins by measuring the sides and finds that they are all of equal length. Then she measures the angles and finds that consecutive angles are supplementary, which means their measures add up to 180 degrees.
To determine if the quadrilateral meets the criteria for the species of flowers, she must classify her garden plot based on her measurements. Is Alice's garden a rectangle, a square, a rhombus, or a parallelogram with unequal angles?
Since the sides of the quadrilateral are all equal and the consecutive angles are supplementary, Alice can conclude that her garden plot is a rhombus, which is a type of parallelogram with all sides equal in length and opposite angles equal. Thus, it fulfills the requirements for her special species of flowers.
Help me ASAP!!! THANKS!
RANDOM ANSWERS WILL BE MODERATED!
Answers
Need help asap please.
Answers
axis of symmetry = x = 3/2
coordinates of the vertex = (2,-9)
vertex form = y = (x-7)^2-19
solution set = no real solution
Mia’s work to find the slope of a trend line through the points (3, 10) and (35, 91) is shown below.
Mia’s Work
Step 1: 3-35/10-91
Step 2: -32/-81
Step 3: 32/81
What was the first error that Mia made?
A: Mia simplified incorrectly and made the slope positive.
B: Mia subtracted in the wrong order.
C: Mia switched the numerator and the denominator.
D: Mia used subtraction instead of addition.
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m = (y2-y1) / (x2-x1)
Where we have two ordered pairs:
P1 = (x1, y1)
P2 = (x2, y2)
We observe then that according to the formula, the error of mine was to invert the numerator with the denominator.
Answer:
C: Mia switched the numerator and the denominator.
Answer:
Answer:
C: Mia switched the numerator and the denominator.
Step-by-step explanation:
just took the test
Mario bought a shirt priced at $ 24.99 and a pair of pants priced at $ 39.99. For these items, he paid a total of $ 69.53 , sales tax included. What was the sales tax rate?
Answers
24.99 + 39.99 = 64.98
69.53-64.98 = 4.55
4.55/69.53 = 0.0654 = 6.5% sales tax
Let A and B be two events in a sample space S such that
P(A)=.6 P(B)=.5 and P(A intersect B) =.2 Find
A) P(A|B)
B) P(B|A)
Please explain how to do this! Thank you
Answers
A) P(A intersect B) = P(A|B)*P(B)
Replacing the known vallues:
0.2=P(A|B)*0.5
Solving for P(A|B):
0.2/0.5=P(A|B)*0.5/0.5
0.4=P(A|B)
P(A|B)=0.4
B) P(B intersect A) = P(B|A)*P(A)
Replacing the known vallues:
0.2=P(B|A)*0.6
Solving for P(B|A):
0.2/0.6=P(B|A)*0.6/0.6
2/6=P(B|A)
1/3=P(B|A)
P(B|A)=1/3
Match the reasons with the statements in the proof.
1. j||k, m∠3 = m∠1
If alternate interior angles are =, then lines are ||.
2. m∠1 = m∠2
Substitution
3. m∠2 = m∠3
Given
4. l||m
If lines are ||, then corresponding angles are =.
Answers
Given
2. m∠1 = m∠2
If lines are ||, then corresponding angles are =.
3. m∠2 = m∠3
Substitution
4. l||m
If alternate interior angles are =, then lines are ||.
Answer:
1-given
2-if lines are parallel, then corresponding angles are equal
3-Substitution
4-if alternate interior angles are equal then lines are parallel.
Step-by-step explanation:
Given j is parallel to k,[tex]m\angle3 =m\angle 1[/tex]
We have to prove that line l is parallel to m
We have to match reason with its correct statement in given proof.
1.j is parallel to k,[tex] m\angle 3=m\angle 1[/tex]
Reason:given
2.[tex]m\angle 1=m\angle 2[/tex]
Reason:if the lines are parallel , then corresponding angles are equal.
3.[tex]m\angle 2=m\angle 3[/tex]
Reason: substitution
4.line l is parallel to m
Reason: If alternate interior angles are equal ,then lines are parallel.
What is the equation of the function y=3/x translated 4 units to the right and 5 units down
Answers
y = 3/(x -4) -5
Answer:
The required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].
Step-by-step explanation:
The given function is
[tex]y=\frac{3}{x}[/tex]
It can be written as
[tex]f(x)=\frac{3}{x}[/tex]
The transformation of a function is defined as
[tex]g(x)=f(x+a)+b[/tex]
Where, a represents the horizontal shift and b represents the vertical shift.
If a>0, then the function f(x) shifts a units left and a<0, then the function f(x) shifts a units right.
If b>0, then the function f(x) shifts b units up and b<0, then the function f(x) shifts b units down.
Since the function translated 4 units to the right and 5 units down, therefore the value of a is -4 and bis -5.
[tex]g(x)=f(x-4)-5[/tex]
[tex]g(x)=\frac{3}{x-4}-5[/tex] [tex][\because f(x)=\frac{3}{x}][/tex]
Therefore the required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].
How to find side of triangle if two sides and one angle is known?
Answers
If the given angle is opposite one of the given sides, the Law of Sines can be used.
Law of Cosines:
.. c^2 = a^2 +b^2 -2ab*cos(C) . . . . . for any permutation of sides a, b, c, and opposite angle C
Law of Sines:
.. a/sin(A) = b/sin(B) = c/sin(C)
Anslee is designing a doll house shaped like a rectangular prism. The doll house is 8 feet long, 2 feet wide and 3 feet high. What is the surface area of the doll house?
Answers
L=8 ft
W=2 ft
H=3 ft
[surface area of the doll house]=2*[W*H]+2*[L*H]+2*[W*L]
[surface area of the doll house]=2*[2*3]+2*[8*3]+2*[2*8]
[surface area of the doll house]=2*[6]+2*[24]+2*[16]
[surface area of the doll house]=12+48+32--------> 92 ft²
the answer is 92 ft²
what is the value of z so that -9 and 9 are both solutipns fo x^2+z=103
Answers
[tex]\bf \begin{cases} x=-9\implies &x+9=0\\ x=9\implies &x-9=0 \end{cases} \\\\\\ (x+9)(x-9)=\stackrel{original~polynomial}{0}\implies x^2+0x-81=0 \\\\\\ x^2\underline{-81}=0\qquad \textit{and we can write }-81=\underline{-103+22} \\\\\\ x^2\underline{-103+22}=0\implies x^2+22=103[/tex]
Solve the following inequality. 2x < 8
Answers
2x / 2 < 8/2
x < 4
hope it helps
The required solution of the given inequality 2x < 8 is x < 4.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given inequality is
2x < 8
According to given question we have
Write inequality
2x < 8
Divide both sides by 2 we get,
x < 4
Therefore, the required solution of the given inequality 2x < 8 is x < 4.
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what is 1000x - 1x?
A) 101x
B) 1001x
C) 99x
D) 999x
Answers
Let's think of what 1000x means.
We know that multiplication is repeated addition. For example, 5(5) = 5+5+5+5+5. It's 5 added five times.
It's no different here. That means we have x 1000 times. If we look at a simpler situation:
5x - 3x, we have (x + x + x + x + x) - (x + x + x)
That means we're getting rid of 3 x's, which means we have 2x. If we have different coefficients but the same variable, we can just subtract or add the coefficients but keep the variable. That means:
4x - 2x = 2x and 10x - 5x = 5x
Now, we can do this problem. We want:
(1000-1)x = 999x
Your answer is D.
Hope this helps!
The complement of an angle is 8 times as large as the angle. find the measure of the complement
Answers
Answer:
80⁰
Step-by-step explanation:
Angle = x
Complement = 90 - x
Given:
8x = 90 - x
9x = 90
x = 10⁰
Complement = 90 - 10 = 80⁰
The complement of an angle is 8 times as large as the angle. The measure of other angle is 80⁰.
What are complementary angles?The complement of an angle is the sum of angles which is equal to 90 degrees.
Let one Angle = x
Complement = 90 - x
The complement of an angle is 8 times as large as the angle.
so,
8x = 90 - x
9x = 90
x = 10⁰
Complement = 90 - 10
= 80⁰
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Let f(x)=x2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
Answers
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
f(7) is
[tex] {7}^{2} - 3(7) - 4[/tex]
[tex]49 - 21 - 4[/tex]
when x is 7, y=24
f(10) is
[tex] {10}^{2} - 3(10) - 4[/tex]
[tex]100 - 30 - 4[/tex]
when x is 10, y=66
the difference in the y values is 42 when the x values change by 3
[tex] \frac{66 - 24}{10 - 7} = \frac{42}{3} = 14[/tex]
the average rate of change is 14
What is the first step to be done when solving this equation: 3(x-2+3) + 5 = 25
Answers
3(x - 2 + 3) + 5 = 25
Ok, so the first step is to distribute the parentheses:
3(x - 2 + 3) = 3x - 6 + 9 <<< answer
Next step:
plug it in the equation
3x - 6 + 9 + 5 = 25
Simplify,
3x + 8 = 25
Then,
subtract 8 from both sides
3x = 25 - 8
so, 3x = 17
Divide both sides by 3
x = 17/3