Answer:
Step-by-step explanation:
(x+3)^2=35+1
(x+3)^2=36
(x+3)^2=6^2
taking squareroot
x+3=+-6
x+3=6,-6
x=6-3=3
or x=-6-3=-9
Lyle is camping at a campground. Lyle's cabin is represented by the point (-27,23). The dining hall is located 21 meters east and 20 meters south of Lyle's cabin and is represented by the point (-6,3).
The shortest distance from Lyle's cabin to the dining hall is_____meters.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{Lyle's cabin}}{(\stackrel{x_1}{-27}~,~\stackrel{y_1}{23})}\qquad \stackrel{\textit{dining hall}}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6-(-27)]^2+[3-23]^2}\implies d=\sqrt{(-6+27)^2+(3-23)^2} \\\\\\ d=\sqrt{21^2+(-20)^2}\implies d=\sqrt{841}\implies d=29[/tex]
The shortest distance from Lyle's cabin to the dining hall is 29 meters.
To calculate the shortest distance between Lyle's cabin and the dining hall, we can use the distance formula for two points in a coordinate plane. The distance formula is:
d = √[(x2 - x1)² + (y2 - y1)²]
Given:
Lyle's cabin coordinates: (-27, 23)
Dining hall coordinates: (-6, 3)
We use the following steps:
Calculate the difference in the x-coordinates: -6 - (-27) = -6 + 27 = 21
Calculate the difference in the y-coordinates: 3 - 23 = -20
Square these differences: 21² = 441 and (-20)² = 400
Add the squares: 441 + 400 = 841
Take the square root of the sum: √841 = 29
Thus, the shortest distance from Lyle's cabin to the dining hall is 29 meters.
I need help fast.
Number 18 and 19
Answer:
18.=400%
Step-by-step explanation:
80/20 we get 4 then we multiple 4 ×100 we get 400 and we check the answer 400% ×20 =80
Sabina makes $2,000 per month. She spends $150 on store credit and $250 on an auto loan each month. Does she have excessive debt?
A.)Yes, because her debt-to-income ratio is higher than 36 percent.
B.)No, because her debt-to-income ratio is lower than 36 percent.
C.)No, because her debt-to-income ratio lower than 42 percent.
D.)Yes, because her debt-to-income ratio is 50 percent.
Answer:
A or B
Step-by-step explanation:
Answer:
Should be B, No because her debt-to-income ratio is lower than 36 percent.
Step-by-step explanation:
Is 1/4 of a circle a polygon? Explain.
A polygon is a plane figure with at least three straight sides and angles, and typically five or more. In other words, a polygon is a 2 dimensional shape with straight sides. No curves!
A quarter of a circle has a curve on one side, and is therefore not a polygon.
In circle C, what is m?
I assume the 38º measurement refers to the measure of arc BE. Then
[tex]37^\circ=\dfrac{m\widehat{AJ}-38^\circ}2\implies m\widehat{AJ}=112^\circ[/tex]
and so
[tex]32^\circ=\dfrac{112^\circ-m\widehat{FH}}2\implies m\widehat{FH}=\boxed{48^\circ}[/tex]
(I think the theorem I used here is called "angle of intersecting secants")
what is the volume of the cylinder below?
972pi mm^3 as height is 12 mm radius is half of 18 mm ie 9mm
therefore volume=pi(r^2)h
ie 972pi mm ^3
Answer: [tex]972\pi\text{ mm}^3[/tex]
Step-by-step explanation:
We know that the volume of a cylinder is given by :-
[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.
Given: Diameter of cylinder = 18 mm
Then , radius of cylinder = [tex]\dfrac{18}{2}=9\ mm[/tex]
Height of cylinder = 12 mm
Then the volume of cylinder will be :-
[tex]\text{Volume}=\pi (9)^2 (12)\\\\\Rightarrow\text{Volume}=972\pi\text{ mm}^3[/tex]
Hence, the volume of the given cylinder = [tex]972\pi\text{ mm}^3[/tex]
PLEASE HELP!!!! The factored form of a quadratic expression is x (x – 4). The ordered pair (0, 0) represents one of the zeros of the associated quadratic function. Which ordered pair represents the other zero?
Answer:
The ordered pair that represent the other zero is [tex](4,0)[/tex]
Step-by-step explanation:
we know that
The zeros or x-intercepts of the quadratic function, represent the value of x when the value of y is equal to zero
In this problem to find the other zero equate (x-4) to zero and solve for x
[tex](x-4)=0[/tex]
[tex]x=4[/tex]
therefore
The ordered pair that represent the other zero is [tex](4,0)[/tex]
Plz help with financial algebra !!
Answer: She will be there 8 years.
Step-by-step explanation:
If x = -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the
equation?
The discriminant is negative
The discriminant is -3.
The discriminant is 0.
The discriminant is positive
Answer:
The discriminant is 0
Step-by-step explanation:
Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.
If a quadratic equation has only one real root, then the discriminant is 0
If x = -3 is the only x-intercept of the graph of a quadratic equation then the discriminant is 0
help me with this one
Answer:
I think that a pair could be the second choice. MTS and PWQ.
Step-by-step explanation:
Please help! I'm am not that great at graphing like this...
Thanks a bunch! :)
Answer:
Step-by-step explanation:
If it's less than or greater than (<, >), then the circle is hollow.
If it's less than or equal to, or greater than or equal to (≤, ≥), then the circle is solid.
Less than points to the left, greater than points to the right.
Here we have less than (not equal to). So the circle is hollow, and the arrow points left. So the correct answer is the first one.
We can check our answer by picking a point and seeing if it's true. If we pick c=-6, is it true that -6 < -1? Yes.
How can you calculate the volume of a cylinder? Please help!
Step-by-step explanation:
Volume of a cylinder is the area of the circular cross section times the height:
V = πr²h
Answer:
V=(3.14)r^2×h
Step-by-step explanation:
(3.14)= pie
r^2= radius to the second power
h=height of cylinder
Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50. Question 1 Part A Ben has $172 to spend on a membership at the fitness club. How many months can Ben be a member of the fitness club?
Answer:
9 months
Step-by-step explanation:
Answer: 6 months
Step-by-step explanation: you take the initial membership fee of $49.50 and add it to the monthly for the first fee so it would be $67 and subtract that from the $172 he has. then divide the left over which is 105 and 17.50 you get 6
Given that EH is a median of EFG what can you say about HF and HG
Answer:
Option C.
Step-by-step explanation:
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side
therefore
In this problem
HF=HG
can two numbers have the same prime factorization
The prime factorization of a number is the set of prime numbers that can be multiplied together to give you that number. Therefore, two different numbers cannot have the same prime factorization, because if you multiply the same set of numbers together, you must get the same answer. For example, 2 × 3 × 5 will always give you 30.
Therefore, the answer will be no.
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
With the height of the rectangular box, the baton can fit diagonally in the box.
The length of the baton that Kylie needs to pack = 38 inches
The width of the rectangular box = 13 inches
The length of the rectangular box = 35 inches
The height of the rectangular box = 13 inches
Comparing the dimensions:
The baton is 38 inches long and longer than the length and width of the box.
The height of the box is 13 inches, making the box greater than the length of the baton diagonally.
Thus, the baton will fit in the box diagonally.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A six-sided die of unknown bias is rolled 20 times, and the number 3 comes up 6 times. In the next three rounds (the die is rolled 20 times in each round), the number 3 comes up 6 times, 5 times, and 7 times. The experimental probability of rolling a 3 is %, which is approximately % more than its theoretical probability. (Round off your answers to the nearest integer.)
Answer:
The experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).
Step-by-step explanation:
Theoretical probability of number 3 on a die:
Total no. of possibilities = 6
Probability of getting a 3 on a die each time it is rolled = 1/6
= 0.16667
= 17%
Experimental probability of number 3 on a die:
Total no. of rounds = 4
Rolls each round = 20
no. of 3s in round 1 = 6
no. of 3s in round 2 = 6
no. of 3s in round 3 = 5
no. of 3s in round 4 = 7
Total rolls = 20*4 = 80
no. of times 3 comes up = 6+6+5+7 = 24
Experimental probability of getting a 3 on a die
each time it is rolled = no. of 3s/total rolls
= 24/80
= 0.3
= 30%
Difference = 30% - 17% = 13%
Experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).
Answer:
The experimental probability of rolling a 3 is 30 %, which is approximately 13 % more than its theoretical probability.
Step-by-step explanation:
PLATO
What is the Greatest common factor of 18x^2 and 36x
For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.
So:
We look for the factors of 18 and 36:
18: 1,2,3,6,9,18
36: 1, 2,3,4, 6,9,18 ...
Thus, the GFC of both numbers is 18.
Then, the GFC of[tex]18x ^ 2[/tex] and [tex]36x[/tex] is:
[tex]18x[/tex]
Answer:
[tex]18x[/tex]
Final answer:
The Greatest Common Factor of 18x² and 36x is 18x, which is the product of shared prime factors to the lowest powers and includes the variable x.
Explanation:
Finding the Greatest Common Factor (GCF)
To find the Greatest Common Factor of 18x² and 36x, we need to break down each term into its prime factors and include the variable parts:
18x² can be factored into 2 × 3 × 3 × x × x (or 2 × 3² × x²)36x can be factored into 2 × 2 × 3 × 3 × x (or 2² × 3² × x)The GCF is the product of the lowest powers of common factors in both terms. Hence, the GCF of 18x² and 36x is 18x, which consists of 2 × 3 × 3 × x (or 2 × 3² × x).
Use the graph below to answer the question what is the slope of the weather is perpendicular to the line in the graph
Answer:
1
Step-by-step explanation:
Slopes of perpendicular lines are opposite reciprocal of one another i.e.
slope m1, of given line l1 = -1/slope m2, of its perpendicular line l2
slope m2, of its perpendicular line l2 = -1/slope m1, of given line l1
m2= -1/m1
Finding m1 from the given graph
m1= y2-y1/x2-x1
= -2-1/2+1
= -3/3
= -1
m2= -1/-1
= 1 !
Quadrilateral JKLM has vertices J(8,4)K(4,10)L(12,12) and M (14,10) . Match each quadrilateral,described by its vertices ,to sequence of transformation that will show it is congruent to quadrilateral JKLM
- A translation to 3 units left and 2 units up = E
- A translation to 2 units right and 3 units down = O
- A sequence of reflections across the x- and y-axes, in any order = A
- A translation to 3 units down and 3 units left = W
- Ouma
Translating 3 units left and 2 units right gives E(5,6), F(1, 12), G(9, 14) and H (11, 8)
Translating 2 units right and 3 units down gives O(10, 1), P(6, 7), Q(14, 9) and R(16, 7)
Reflecting across the x and y axis gives A(-8, -4), B(-4, -10), C(-12, -12) and D(-14, -10)
Translating 3 units down and 3 units left gives W(5, 1), X(1, 7), Y(9, 9) and Z(11, 7)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Quadrilateral JKLM has vertices J(8,4), K(4,10), L(12,12) and M (14,10) .
1) Translating 3 units left and 2 units right gives E(5,6), F(1, 12), G(9, 14) and H (11, 8)
2) Translating 2 units right and 3 units down gives O(10, 1), P(6, 7), Q(14, 9) and R(16, 7)
3) Reflecting across the x and y axis gives A(-8, -4), B(-4, -10), C(-12, -12) and D(-14, -10)
4) Translating 3 units down and 3 units left gives W(5, 1), X(1, 7), Y(9, 9) and Z(11, 7)
Find out more on transformation at: https://brainly.com/question/1620969
there are 21 marbles in a blue jar. the blue jars has 3 times as many marbles as a red jar. let m be the number of marbles in the red jar
Answer:
m=7
Step-by-step explanation:
1 blue jar = 21 marbles
1 blue jar = 3 red jars
Therefor
21 marbles= 3 red jars
(Now let m=1 red jar)
21= 3m
(Then sine we have 3m dived both sides by 3 to isolate the m)
21/3= 3m/3
7=m
There are 7 marbles in a red jar if there are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
There are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.
Let m be the number of marbles in the red jar
From the problem, we can make a linear equation in one variable:
3m = 21
m = 7
Thus, there are 7 marbles in a red jar if there are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.
Learn more about the linear equation here:
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During the Winter, you charged people $ 15 for going to their house to shovel then $11 for every hour you bag groceries. If you make $48 one day how many hours did you spend bagging groceries?
Answer:
you spent 3 hours bagging groceries.
Step-by-step explanation:
you can use a calculator and do 11 times 3 plus 15.
Final answer:
To find out how many hours were spent bagging groceries when making $48 in total, solve the given equation with the respective earnings from shoveling and bagging.
Explanation:
The question: During the Winter, you charged people $15 for shoveling snow and $11 for every hour bagging groceries. If you made $48 one day, how many hours did you spend bagging groceries?
Step-by-step explanation:
Let's denote the hours spent bagging groceries as x.
Write the equation: $15 (for shoveling) + $11x (for bagging) = $48.
Solve the equation to find x: $15 + $11x = $48, $11x = $33, x = 3 hours.
A diver who has a mass of 68 kg climbs to a diving platform that is 7.5 m above the surface of a pool. How much gravitational potential energy does the diver have in relation to the pool’s surface? 510 J 1912 J 3825 J 4998 J
Answer:
option D
4998 J
Step-by-step explanation:
Given in the question that,
mass of the diver = 68 kg
distance of the diver from the surface of a pool = 7.5 m
The gravitational potential energy of an object is given by
GPE = m(g)(h)
here,
m is the mass of the diver
g is the acceleration due to gravity = 9.81m/s²
h is the height from the surface
Plug values in the formula to calculate GPE
GPE = 68(9.8)(7.5)
= 4998 J
Therefore, the gravitational potential energy of the diver with respect to the surface of the pool is 4998 J
Final answer:
The diver has 4986 Joules of gravitational potential energy in relation to the pool's surface, with the closest answer choice being 4998 J, assuming rounding differences. Hence, the answer is D.
Explanation:
To calculate the gravitational potential energy (GPE) of the diver in relation to the pool's surface, we can use the formula GPE = mgh, where m is the mass of the diver, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the diving platform above the pool's surface.
Substituting the diver's mass (68 kg) and the height of the diving platform (7.5 m) into the equation, we get:
GPE = (68 kg) times (9.8 m/s2) times (7.5 m)
GPE = 4986 Joules
Therefore, the diver has 4986 Joules of gravitational potential energy in relation to the pool's surface. Since this value isn't exactly one of the choices, it's likely due to rounding differences, and the closest provided option is 4998 J, which we could assume is the intended answer.
Cuales son las dimensiones de un rectángulo con un perímetro igual a 578 pulgadas, si su largo es 6 pulgadas menos que 4 veces su ancho
Answer:
The dimensions of rectangle are 230 in by 59 in
Step-by-step explanation:
The question in English is
What are the dimensions of a rectangle with a perimeter equal to 578 inches, if its length is 6 inches less than 4 times its width?
Let
x-----> the length of rectangle
y----> the width of rectangle
we know that
The perimeter of rectangle is equal to
P=2(x+y)
P=578 in
so
578=2(x+y)
289=x+y -----> equation A
x=4y-6 -----> equation B
substitute equation B in equation A
289=(4y-6)+y
5y=295
y=59 in
Find the value of x
x=4y-6 -----> x=4(59)-6=230 in
therefore
The dimensions of rectangle are
230 in by 59 in
THIS I S EASY I JUST DON'T KNOW IT PLZZ ANYONE I REALLY NEED THIS ASP I PROMISE BRAIBLIEST ANYONE???????PLZZ HELP I DON'T KNOW WHAT TO DO !!!!!!!15PTS!!! WIL GIVE BRAINLIETS!!!!Which function rule represents the data in the table?
x –3 –2 –1 0 1
y –17 –14 –11 –8 –5
y = –3x – 8
y = 1/3x – 8
y = 3x – 8
y = 1/3x + 8
Answer: The answer is y=3x-8
Step-by-step explanation: All you have to do is plug in the x values and see what you get for y. For example: when you plug in -3 for x. y=3(-3)-8 than you multiply the -3 by 3 and that give you y=-9-8 which equals y=-17 so that shows you the equation works.
plugging in -2 for x
y=3(-2)-8
y=-6-8
y=-14
I hope this helps!!!
Answer:
y = 3x -8
Step-by-step explanation:
You can try a point in the function rules and see if it works. The first (x, y) pair is suitable for finding the right answer:
y = -3(-3) -8 = -1 ≠ -17 . . . . eliminates the first choice
y = 1/3(-3) -8 = -9 ≠ -17 . . . . eliminates the second choice
y = 3(-3) -8 = -17 . . . . . the third choice is viable
y = 1/3(-3) +8 = 7 ≠ -17 . . . . eliminates the last choice
__
Only the third choice is a possible solution. Checking other points from the table verifies this as the correct one.
Find (f-g)(x) when f(x) = 2x-3 and g(x) = -4x+8
Answer:
6x - 11
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x) = 2x - 3 - (- 4x + 8) = 2x - 3 + 4x - 8 = 6x - 11
Answer:
6x -11
Step-by-step explanation:
f(x) = 2x-3 and g(x) = -4x+8
f-g (x) =2x-3 - (-4x+8)
Distribute the minus sign
= 2x - 3 +4x -8
Combine like terms
= 6x -11
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line?
y = x – 12
y = x – 4
y = x + 2
y = x + 6
Answer:
y = x - 4
Step-by-step explanation:
Rewrite y – 4 = (x – 8) in slope-intercept form. To do this, solve the given equation for y:
y - 4 = x - 8 → y = 4 + x - 8, or y = x - 4
As the point-slope form is given, we will simplify it;
[tex]y-4=x-8[/tex]
By adding +4 on both the sides, we get:
⇒[tex]y=x-8+4[/tex]
⇒[tex]y=x-4[/tex]
The slope-intercept form of the equation for this line is y=x-4.
Hence, the correct answer is option (b).
What is slope y-intercept form?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
What is slope-intercept form example?Examples. y = 5x + 3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3. y = −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6.
Learn more about slope-intercept, refer to:
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a rectangle is graphed on the coordinate grid. which represents the equation of a that is perpendicular to side r?
Answer:
Fourth answer choice: y = x + 3
Step-by-step explanation:
Note that sides a and s are perpendicular to side r. Both sides a and s have positive slopes, so we can immediately eliminate answer choices 1 and 2.
If we extend side s up and to the left, it intersects the y-axis at (0, 3). Thus, the y-intercept is +3 and the desired equation is:
y = x + 3
Answer:
The answer is D
Step-by-step explanation:
Find the median of the following data set 6,2,59,12,11,9,9,54,54,46,2,32,43,11
By arranging the numbers in ascending order we get,
2, 2, 6, 9, 9, 11, 11, 12, 32, 43, 46, 54, 54, 59
The 2 middle numbers are:
11, 12
To find the median we have to add them and divide them by 2
So, (11+12)÷2
23÷2
11.5
For this case we have by definition that the median of a set of numbers is the average number in the set, after the numbers have been arranged from the lowest to the highest. If there is an even number of data, the median is the average of the two average numbers. So:
We order the numbers from least to greatest:
2,2,6,9,9,11,11,12,32,43,46,54,54,59
We have 14 numbers:
[tex]\frac {11 + 12} {2} = \frac {23} {2} = 11.5[/tex]
Answer:
11.5
What is 2x -4 ≤ 4x answer
Answer:
x ≥ -2
Step-by-step explanation:
2x - 4 ≤ 4x
Subtract 2x from both sides:
-4 ≤ 2x
Divide by 2:
-2 ≤ x
So -2 ≤ x, or x ≥ -2.
You can check your answer by picking a number greater than -2 and see if it works. For example, if x = 0:
0 - 4 ≤ 0
-4 ≤ 0