Answer:
13
Step-by-step explanation:
The longest side must be less than the sum of the shorter sides:
c < a + b
c < 6 + 8
c < 14
So the largest whole number length is 13.
You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds? 121.862 years 12.1862 years 10.155 years 1.0155 years
Answer:
10.153 years
Step-by-step explanation:
The future value of such an investment is given by ...
FV = P·(1 +r/12)^(12t)
where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.
Dividing by P and taking the log, we have ...
FV/P = (1 +r/12)^(12t)
log(FV/P) = 12t·log(1 +r/12)
Dividing by the coefficient of t gives ...
t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12
t ≈ 10.153 . . . years
Which equations have the variable term in the equation –6 + 2x = 6x – 9 isolated to one side of the equals sign, and the constant isolated to the other side? Select all that apply.
–6 = 4x – 9
3 – 4x= 0
–4x = –3
3 = 4x
2x= 6x - 3
Answer:
-4x=-3
3= 4x
Step-by-step explanation:
The equation –4x = –3 fulfills the condition of variable isolation. Options C and D are correct
Given that,
To determine the expression consist of the isolation of the variable and constant.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
-6 + 2x = 6x - 9
-4x = -3 or 4x = 3
Thus, the equation –4x = –3 fulfills the condition of variable isolation. Options C and D are correct.
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PLEASE HELP!!!
Multiply the following using the vertical multiplication method 3x^2-5x+1 x^2+2x+4
Answer:
3x⁴ + x³ + 3 x² - 18 x + 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
3x^4+x^3+3x^2-18+4
PLEASE HELP WILL GIVE BRAINLIEST
Life expectancy in the U.S. is steadily increasing due to medical advancements and the increased awareness of maintaining a healthy lifestyle. The life expectancies for men and women in the U.S. can be modeled by the following functions:
W(x)=0.126x+76.74
M(x)=0.169x+69.11
where W(x) represents the life expectancy for women and M(x) represents the life expectancy for men, and x represents the number of years since 1975. (x = 0 corresponds to the year 1975, x = 5 corresponds to the year 1980 and so on.)
Write an inequality that represents in what years the life expectancy of men is greater than that of women.
a.0.169x+69.11 > 0.126x+76.74
b.0.169+69.11 < 0.126x+76.74
c.0.169x+69.11<0.126x+76.74
d.0.169x+69.11 = 0.126x+76.74
Answer:
a. 0.169x+69.11 > 0.126x+76.74
Step-by-step explanation:
So, there's a lot of talk in the question statement. Of course, it presents some important data... but it's also meant to confuse you.
We can boil it down to the following life expectancies :
Men = 0.169x+69.11
Women = 0.126x+76.74
Then they ask you to write with that men have a greater life expectancy than woman using the models above.
Start by writing the goal:
men > women
Then replace "men" by the model and "women" by the model:
0.169x+69.11 > 0.126x+76.74
And you have your answer.
Answer:
A
Step-by-step explanation:
maybe, maybe not
Any assistance would be great!
The domain is the input values, which would also be X values.
{ x |x= -5, -3, 1, 2,6}
For this case we have by definition that the domain of a function y = f (x) is the set of all the values that the variable x takes, for which the function is defined. They are also represented by the starting set.
It is observed in the figure, that the domain is:
[tex]{x | x = -3,2, -5,1,6}\\{x | x = -5, -3,1,2,6}[/tex]
Answer:
Option A
What is the equation for the translation of x2 + y2 = 16 seven units to the right and five units up?
(x + 7)2 + (y – 5)2 = 16
(x - 7)2 + (y + 5)2 = 16
(x + 7)2 + (y + 5)2 - 16
(x - 72 + (y – 5)2 = 16
Answer:
[tex](x-7)^2+(y-5)^2=16[/tex].
Step-by-step explanation:
The given circle has equation [tex]x^2+y^2=16[/tex].
This is the equation that has its center at the origin with radius 4 units.
When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).
The equation of a circle with center (h,k) and radius r units is [tex](x-h)^2+(y-k)^2=r^2[/tex].
This implies that, the translated circle will now have equation.
[tex](x-7)^2+(y-5)^2=4^2[/tex].
[tex](x-7)^2+(y-5)^2=16[/tex].
The correct equation for translating the circle x² + y² = 16 seven units to the right and five units up is (x - 7)² + (y - 5)² = 16. Therefore, option D is the correct answer.
The original equation for a circle with a radius of 4 units is x² + y² = 16. A translation of the circle seven units to the right and five units up would involve shifting the x-coordinate by +7 and the y-coordinate by +5. Therefore, the new equation would be (x - 7)² + (y - 5)² = 16.
This is due to the fact that a translation of a geometric figure does not alter its size, shape, or orientation; it simply shifts the figure in the plane. Keeping the radius the same, applying the translation to the circle's center (0,0) results in a new center at (7,5), which translates to the equation above.
Given: m arc KP=2m arc IP
, m arc IVK=120°
Find: m∠KJL.
Answer:
40
Step-by-step explanation:
The measure of the angle KJL is 40°.
What is a circle?Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point. A circle is a closed curve that has no corners or vertices.
Given is a circle O where m arc IVK = 120° and m arc KP = 2 × m arc IP,
We need to find the measure of the angle KJL,
So,
According to the question,
m arc IVK + m arc KPI = 360° [whole circumference of a circle is 360°]
m arc IVK + m arc KP + m arc IP = 360°
120° + m arc IP + 2 × m arc IP = 360°
3 m arc IP = 240°
m arc IP = 80°
Therefore,
m arc KP = 160°
Now, according to the property of a circle,
m ∠KJL = 1/2 × [m arc KP - m arc IP]
m ∠KJL = 1/2 × [160° - 80°]
m ∠KJL = 80°/2
m ∠KJL = 40°
Hence the measure of the angle KJL is 40°.
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....Help Please.......
Answer:
The first two tables show y as a function of x.
Step-by-step explanation:
A relation is not a function if the same x-value shows up more than once in the table. That will be the case for the last two tables, each of which has x=2 show up twice.
Which of the following is the measure of an exterior angle of a 15-sided regular polygon?
A) 24
B) 12
C) 40
D) 36
Answer:
24 ˚
Step-by-step explanation:
Exterior angle of a regular -sided polygon:
360 ˚/ n ⇒ 360 ˚/15 = 24 ˚
Answer:
A) 24
Step-by-step explanation:
Since the sum of the exterior angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equal exterior angles and therefore 15 vertices and sides to the polygon.
What is the solution to the Reimann Hypothesis (If there is one)?
Answer:
Sadly, it is still high in debate. Scientists are still in doubt of the Hypothesis, so no. Some may claim there is a solution, though.
Step-by-step explanation:
Final answer:
The Riemann Hypothesis is an unsolved mathematical problem, with no validated solution as of yet, and remains one of the Millennium Prize Problems in mathematics.
Explanation:
The Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the area of number theory. It postulates that all non-trivial zeros of the Riemann zeta function, a complex function important for understanding the distribution of prime numbers, have their real parts equal to 0.5. Despite significant efforts by mathematicians over the years, the solution to the Riemann Hypothesis remains elusive, and no proof or disproof has been universally accepted by the mathematics community.
As of my knowledge cutoff in 2023, researchers continue to explore various mathematical approaches and even computational methods to tackle this problem. However, no experiment or scientific test can validate the hypothesis since it is a purely mathematical conjecture. A resolution of the Riemann Hypothesis would have profound implications for number theory and related fields, yet it remains one of the seven Millennium Prize Problems, with a reward of one million dollars offered for a solution.
The owner of a catering company wants to select a random sample of clients to find out about their food preferences. Select Yes or No to tell whether each method results in a random sample of the population.
Yes or No, The owner uses a database to print the names of all clients on slips of paper. The owner chooses 20 of the slips of paper without looking.
Yes or No, The owner sends a survey to every client who spent more than $500 with the catering company in the past year.
Yes or No, The owner sends a survey to all clients whose phone number ends in 5.
Yes or No, The owner sends a survey to the last 20 clients who used the catering company's services.
Answer:
1. Yes
2. No
3. Yes
4. No
Step-by-step explanation:
When you say a random sample, this means that every member of the population will have a chance to be part of the sample. If you consider the scenarios, only the 1st and 3rd option will come up with a random sample because the respondents of the sample is not predetermined. If you take the other options into consideration, you can see that not everyone would have had a chance to be part of the sample.
50 POINTS ANSWER ASAP
What is an equation of the line that passes through the point (−1,8) and is parallel to the line x+y=4?
Answer:
y = -x+7
Step-by-step explanation:
We need to get x+y=4 in slope intercept from to determine the slope
x+t=4
Subtract x from each side
x-xy = -x+4
y= -x+4
The slope is -1
Parallel lines have the same slope
We have the slope and a point of the new line.
We can use the point slope form
y-y1 = m(x-x1)
y-8 = -1(x--1)
y-8 = -1(x+1)
Distribute the negative sign
y-8 = -x-1
Add 8 to each side
y-8+8 = -x-1+8
y = -x+7
A gardener determines the cost of planting daffodil bulbs to be $2.40 per square foot. How much will it cost to plant daffodil bulbs in a rectangular garden that is 12 feet long and 5 feet wide? (show your work)
a) $40.80
b) $60
c) $81.60
d) $144
Answer: 144$
Step-by-step explanation: multiply 5 by 12 and then multiply that answer by 2.40
What is the distance between the y-intercepts of the lines? Adding a picture please help
The equation of a line is:
y = mx + c
The m is the gradient of the line, and the c is the y-intercept of the line
That means that the y-intercept of [y = -4x + 3] is 3
and the y-intercept of [y = -4x + 4] is 4
So the distance between the two y-intercepts is:
4 - 3 = 1
Drag and drop an answer to each box to correctly complete the proof.
Given: Parallelogram JKLM is a rectangle.
Prove: JL¯¯¯¯¯≅MK¯¯¯¯¯¯¯
Answer:
1. all the right angles are congruent
2. opposite sides of a parallelogram are congruent
3. SAS congruent postulate
4. corresponding parts of a congruent triangle are congruent
Step-by-step explanation:
1. As all the right angles are congruent
∠JML≅∠KLM≅ ∠90°
2. As per the properties of a parallelogram, the opposite sides are congruent.
Hence the sides JM≅KL
3. SAS postulate is defined as Side-Angle-Side postulate. When the side, adjacent angle and the other other adjacent side of two triangle are congruent then the two triangles are said to be congruent. In the given case both the sides JM and ML of ΔJML are congruent to both the sides KL and ML of ΔKLM.
Hence ΔJML≅ΔKLM
4. As proven in part 3, ΔJML≅ΔKLM so the congruent parts of two congruent triangle are congruent.
In given case the side JL(of ΔJML)≅MK(ΔKLM)
!
The completed proof is presented as follows;
Parallelogram JKLM is a rectangle and by definition of a rectangle, ∠JML
and ∠KLM are right angles, ∠JML ≅ ∠KLM because, all right angles are
congruent, [tex]\overline{JM}[/tex] ≅ [tex]\overline{KL}[/tex] because opposite sides of a parallelogram are
congruent, and [tex]\overline{ML}[/tex] ≅ [tex]\overline{ML}[/tex] by reflective property of congruence. By the SAS
congruence postulate, ΔJML ≅ ΔKLM. Because, congruent parts of
congruent triangles are congruent, [tex]\overline{JL}[/tex] ≅ [tex]\overline{MK}[/tex]
Reasons:
The given quadrilateral is a parallelogram, that have interior angles that are right angles, therefore, the figure has the properties of a rectangle, and
parallelogram including;
The length of opposite sides are equalAll right angles are congruent and equal to 90°
The length of a side is equal to itself by reflexive property, therefore, [tex]\overline{ML}[/tex]
≅ [tex]\overline{ML}[/tex]
The Side-Angle-Side SAS postulate states that if two sides and an included
angle of one triangle are congruent to the corresponding two of sides and
included angle of another triangle, the two triangles are congruent.
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Find the equation of the line that is perpendicular to the line 4x+2y=1 and passes through the point (-4,3)
A) y=2x+5
B) y=2x+2
C) y=1/2x+2
D) y=1/2x+5
First find the slope of the given line:
4x +2y = 1
Subtract 4x from each side:
2y = -4x + 1
Divide both sides by 2:
y = -2x +1/2
The slope is -2.
Now use the slope to find the y-intercept. Because the line is perpendicular, you need to use the negative inverse of the slope.
The negative inverse of -2 is 1/2
Now using the point-slope form y - y1 = m(x-x1)
Use the inverse slope for m, and the given point(-4,3) to get:
y - 3 = 1/2(x+4)
Simplify:
y - 3 = x/2 +2
Add 3 to each side:
y = x/2 + 5
Reorder the terms to get y = 1/2x +5
The answer is D.
Green River State Park has two popular hiking trails: Overlook Trail and High Ridge Trail. On one particular day, 80 hiking groups used the trails: 40 groups used Overlook Trail and 40 groups used High Ridge Trail. Of the 40 groups that used Overlook Trail, 30 groups had children and 10 groups had no children. Of the 40 groups that used High Ridge Trail, 15 groups had children and 25 groups had no children. Consider the following events.
H: A hiking group uses High Ridge Trail.
C: A hiking group has children.
Which statement is true about events H and C?
A. Events H and C are independent and P(H|C) < P(C|H).
B. Events H and C are dependent and P(H|C) < P(C|H).
C. Events H and C are independent and P(H|C) = P(C|H).
D. Events H and C are dependent and P(H|C) = P(C|H).
Answer:
B. Events H and C are dependent and P(H|C) < P(C|H)
Step-by-step explanation:
The ratios of groups with children to hiking groups on the trail are different for the two trails.
P(H|C) = 15/45 = 1/3
P(C|H) = 15/40 = 3/8
1/3 < 3/8 so the comparison of choice B is appropriate.
I need help ASAP.
Laura flicks the spinner below one time. What is the probability that the flicker will land on BLUE?
Question 3 options:
1/6
1/8
1/2
1/4
Answer:
1/4
Step-by-step explanation:
The are 8 different sections that the spinner can land on
2 of them are labeled blue
P(blue) = spots labeled blue/ total spots
= 2/8
= 1/4
3(4x+2)-6x=5x-5(2+x) please solve show your work do not solve for x
Answer:
simplifies to 6x+6=-10x = -8/3 = -2 2/3Step-by-step explanation:
3(4x+2)-6x=5x-5(2+x)
12x +6 -6x = 5x -10 -5x . . . . . eliminate parentheses using the distributive property
6x +6 = -10 . . . . . . . . . . . . . . . collect terms
x +1 = -10/6 . . . . . . . . . . . . . . . divide by 6
x = -1 - 5/3 . . . . . . . . . . . . . . . add -1
x = -8/3 . . . . . . . . . . . . . . . . . simplify
If the fourth term of a gwometric progression is -27/4 and the fifth term is 81/4 find a1 and r
Answer:
a1 = 1/4r = -3Step-by-step explanation:
r = a5/a4 = (81/4)/(-27/4) = -3
an = a1·r^(n-1)
-27/4 = a1·(-3)^3 = -27·a1 . . . . fill in the known numbers for n=4
(-27/4)/(-27) = a1 = 1/4
The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6. The estimated value of is 3.14. The measure of the angle subtended by the arc is ?
Answer:
The measure of the angle is [tex]68.79\°[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=78.5\ cm^{2}[/tex]
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]78.5=(3.14)r^{2}[/tex]
[tex]r^{2}=78.5/(3.14)[/tex]
[tex]r=5\ cm[/tex]
step 2
Find the circumference of the circle
The circumference of the circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=5\ cm[/tex]
[tex]\pi =3.14[/tex]
Substitute
[tex]C=2(3.14)(5)[/tex]
[tex]C=31.4\ cm[/tex]
step 3
Find the measure of the angle by an arc length of 6 cm
we know that
The circumference of a circle subtends a central angle of 360 degrees
So
by proportion
[tex]\frac{31.4}{360}=\frac{6}{x}\\ \\x=360*6/31.4\\ \\x=68.79\°[/tex]
Answer:
The measure of the angle subtended by the arc is 68.8°
Step-by-step explanation:
Formula for calculating length of an arc is expressed as:
Length of an arc = theta/360×2πr
Where theta is the angle subtended by the arc
r is the radius of the circle
To get the radius r;
Given Area of the circle to be 78.5cm²
Since area = πr²
78.5 = πr²
78.5 = 3.14r²
r² = 78.5/3.14
r² = 25
r =√25
r = 5cm
This radius of the circle is 5cm
Remember that
Length of an arc = theta/360° × 2πr
6 = theta/360 × 2(3.14)(5)
6 = 31.4theta/360
2160 = 31.4theta
theta = 2160/31.4
theta = 68.8°
the service tip for the waiter is 20%. The total cost of a meal is calculated as c + 0.20c. How much would you have to pay if you have a meal that costs $21.00?
Answer:
$25.20
Step-by-step explanation:
Cost of the meal = $21
Total cost
= c + 0.20c
= 21 + 0.20(21)
= $25.20
For this case we have the following function, to calculate the total cost of the meal, including 20% of the tip:
[tex]f (c) = c + 0.20c[/tex]
They tell us that a meal costs $ 21.00. That is,[tex]c = 21[/tex]
[tex]f (21) = 21 + 0.20 (21)\\f (21) = 21 + 4.2\\f (21) = 25.2[/tex]
Thus, the total cost of the meal is 25.2
Answer:
$ 25.2
use the quadratic formula to solve the equation 9x^2 - 2=0
Answer:
x = ±(√2)/3
Step-by-step explanation:
For the quadratic ...
ax^2 +bx +c = 0
the quadratic formula gives solutions as ...
x = (-b ±√(b^2-4ac))/(2a)
Comparing your quadratic to the general form above, we find ...
a = 9; b = 0, c = -2
Filling these values into the formula gives ...
x = (-0 ±√(0^2 -4(9)(-2)))/(2·9)
x = ±(√72)/18 = ±(6√2)/18
x = ±(√2)/3
Which graph matches y=x?
Answer:
see below
Step-by-step explanation:
Of your remaining answer choices, the only one that shows a reflection (not a translation) is the one below. It has the orientation of the figure reversed (side lengths shortest-to-longest are CCW instead of CW).
The reflection over y=x reverses the coordinates: (x, y) ⇒ (y, x), so the vertices become ...
(1, -3) ⇒ (-3, 1)(3, -2) ⇒ (-2, 3)(4, -5) ⇒ (-5, 4)i need some help on this question please
Answer:
36, 32, 28, 24
Step-by-step explanation:
Fill in the values of n and do the arithmetic.
a1 = 36 -4(1 -1) = 36
a2 = 36 -4(2 -1) = 32
a3 = 36 -4(3 -1) = 28
a4 = 36 -4(4 -1) = 24
_____
You could recognize the formula as the specific case of the explicit formula for an arithmetic sequence with first term 36 and common difference -4. That tells you the second term is 36 -4 = 32, and each successive term is 4 less than the one before.
A tree 7ft y’all grows an average 6 in each year which equation models the trees height h after x years
Answer:
h = 7 + 6x
Step-by-step explanation:
Since we are trying to find the height of the tree, we put h on the left side of the equation. Since the tree is 7ft tall at the moment, we write 7ft on the right side of the equation. Knowing that the tree grows 6 inches each year (x) we write 6x on the right side of the equation.
Answer:
H=7+6x
Hope this helps
Use the graph to find the slope and y-intercept to write
the equation in slope-intercept form.
The graph shown is y=
x+
Answer:
Slope = -1/2
Y-intercept is y = -1
Equation of the line: [tex]y=-\frac{1}{2}x-1[/tex]
Step-by-step explanation:
The slope intercept form is y = mx + b
Where, m is slope, and
b is y-intercept
We need 2 points to find these. One point is (-2,0) and second point is (2,-2).
THe formula for slope, m, is m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging the points, we get the slope to be:
[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-0}{2--2}\\=\frac{-2}{4}\\=-\frac{1}{2}[/tex]
y-intercept is the point where the line crosses the y axis. Looking at the graph, y-intercept is y = -1.
Now we plug slope and y-intercept into the slope-intercept form to get:
[tex]y=mx+b\\y=-\frac{1}{2}x-1[/tex]
ANSWER
[tex]y = - \frac{1}{2} x - 1[/tex]
EXPLANATION
The graph passes through (-2,0) and (0,-1).
The slope can be calculated using the formula,
[tex]m= \frac{rise}{run} [/tex]
[tex]m = \frac{0 - - 1}{ - 2 - 0} [/tex]
[tex]m = - \frac{1}{2} [/tex]
The y-intercept is -1.
The equation in slope-intercept form is
y=mx + c
We substitute the slope and y-intercept to obtain
[tex]y = - \frac{1}{2} x - 1[/tex]
Given: ΔPSQ, PS = SQ Perimeter of ΔPSQ = 50 SQ – PQ = 1 Find: Area of ΔPSQ
Answer:
120 units²
Step-by-step explanation:
Perimeter = PS + SQ + PQ
50 = SQ + SQ + (SQ -1)
51 = 3SQ
17 = SQ
17 -1 = 16 = PQ
The midpoint of the base is one leg of the right triangle whose other leg is the height of this isosceles triangle. That height is ...
h = √(17² -(16/2)²) = √225 = 15
Then the area is ...
A = (1/2)bh = (1/2)(16)(15) = 120 . . . . . square units
What is the volume of the square pyramid with base edges 4 m and height 3 m?
Answer:
Volume of the pyramid = 16m³ or 16 cubic meters.
Step-by-step explanation:
The equation for the volume of a pyramid is:
[tex]V=\frac{b*h}{3}[/tex]
where b = area of base and h = height.
In this case, the base is a square with a side length of 4m.
Area of the square base = (4m)² = b = 16m²
h = 3m
Insert b and a into the volume of a pyramid equation.
[tex]V=\frac{3m*16m}{3}[/tex]
= 16m³
Volume of the pyramid = 16m³ or 16 cubic meters.
A bag contains 9 green marbles and 11 white marbles. You select a marble at random. What are the odds in favor of picking a green marble?
Help pls
Answer: 9\20 or 45% hope this helps
The "odds" of picking a green are 9 to 11 .
The "probability" of picking a green is 9/20 or 45% .