Answer:
1/4h
Step-by-step explanation:
The car trip is 1/2h shorter than the bus trip.
The bus trip is 3/4h long.
Therefore, the length of the car trip is:
3/4h - 1/2h = 1/4h
The car trip is 1/4h long.
The arithmetic sequences 1, 5, 9, 13,... and 1, 8, 15, 22,... have infinitely many terms in common. Calculate the sum of the first three common terms.
Answer:
87
Step-by-step explanation:
Sequence 1 has common difference of 4 and sequence 2 has 7
The first terms are common
We need a new sequence with common difference of:
LCM(4,7)= 4*7=28So the next common term is 1+28= 29 and the following one is 29+28= 57
Sum of 3 terms:
1+29+57= 87Answer:
87
Step-by-step explanation:
The first sequence:
1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61...
The second sequence:
1, 8, 15, 22, 29, 36, 43, 50, 57, 63...
The first three common terms are 1, 29, 57.
The sum of the first three common terms:
1 + 29 + 57
= 87
a line segment has the endpoint (2,-3) (-6,-1) Describe theOff the line that through the points ex and Y
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
where the slope m is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (2, -3) and (-6, -1).
Substitute:
[tex]m=\dfrac{-1-(-3)}{-6-2}=\dfrac{2}{-8}=-\dfrac{1}{4}[/tex]
[tex]y-(-3)=-\dfrac{1}{4}(x-2)\\\\y+3=-\dfrac{1}{4}(x-2)\to\text{point-slope form}[/tex]
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
[tex]y+3=-\dfrac{1}{4}(x-2)[/tex]
[tex]y+3=-\dfrac{1}{4}x+\dfrac{1}{2}[/tex] subtract 3 from both sides
[tex]y=-\dfrac{1}{4}x-2\dfrac{1}{2}\to\text{slope-intercept form}[/tex]
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
[tex]y+3=-\dfrac{1}{4}(x-2)[/tex] multiply both sides by 4
[tex]4y+12=-(x-2)[/tex]
[tex]4y+12=-x+2[/tex] subtract 12 from both sides
[tex]4y=-x-10[/tex] add x to both sides
[tex]x+4y=-10\to\text{standard form}[/tex]
Piravena must make a trip from A to B then from B to C, then from C to A. Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle as shown, with C a distance of 3000 km from A and with B a distance of 3250 km from A. To take a bus, it costs Piravena $0.15 per kilometer. To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometer. Determine the distance she travels for her complete trip. URGENT! I Will mark brainiest if it is correct
Answer:
a) Cost of flying from A to B = $425
b) Total distance travelled by Piravena during the complete trip = 7,500 km
c) To minimize cost and arrive at the final cost given, she must have travelled by bus from B to C and then travelled by taking an airplane from C to A.
Step-by-step explanation:
The complete question is presented in the attached image to this question.
Full Question
a) To begin her trip she flew from A to B. Determine the cost of flying from A to B.
b) Determine the distance she travels for her complete trip.
c) Piravena chose the least expensive way to travel between cities and her total cost was $1012.50. Given that she flew from A to B, determine her method of transportation from B to C and her method of transportation from C to A.
Solution
a) The distance from A to B is given as 3250 km.
To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometer.
So, to fly 3250 km, she will pay
100 + (0.10×3250) = $425
b) For her complete journey, she is to make a trip from A to B then from B to C, then from C to A.
Her complete distance travelled = AB + BC + CA
But it is given that the three cities form a right angled triangle as given in the question with AB serving as the hypotenuse side.
Pythagoras theorem gives that the square of the hypotenuse side is equal to the sum of the respective squares of the other two sides
AB² = BC² + CA²
3250² = BC² + 3000²
BC² = 3250² - 3000² = 1,562,500
BC = √1,562,500 = 1,250 km
Total distance covered by Piravena during the entire trip = AB + BC + CA = 3250 + 1250 + 3000 = 7,500 km
c) Her total cost of travel = $1012.50
But she definitely flew from A to B at a cost of $425
This means she spent (1012.50 - 425) on the rest of the journey, that is, $587.5
Note that to travel by bus, it is $0.15 per kilometre and to travel by airplane is $100 + $0.10 per kilometre. Indicating that the airplane saves cost on long distance travels while the bus saves cost on short distance travels.
To confirm this, we calculate the two options (bus or airplane) for each route.
If she travels B to C by bus, cost = 0.15 × 1250 = $187.5
If she travels B to C by airplane, cost = 100 + (0.10×1250) = $225
Hence, the bus obviously minimizes cost here.
If she travels from C to A by bus, cost = 0.15 × 3000 = $450
If she travels from C to A by airplane, cost = 100 + (0.10×3000) = $400
Here, travelling by airplane minimizes the cost.
So, if we confirm now that she travelled from B to C by bus and then from C to A by airplane, total cost = 187.5 + 400 = $587.5
which is the remaining part of her total cost is she minimized expenses!
Hope this Helps!!!
Answer:
The distance is 7500 kilometers
Step-by-step explanation:
I got the answer wrong myself and the website told me that it’s 7500 kilometers
please help me out here :’(
Answer:
Step-by-step explanation:
We are going to use the areas given to find the lengths of the sides of each of their respective squares. For the purple square, the area is 35 units squared. Because the formula for the area is A = s * s, then we can fill in the value for the area and solve for s, the side length, of the purple square.
[tex]35=s^2[/tex] and
[tex]s=\sqrt{35}[/tex]. That side length also serves as the height of the right triangle. Now on to the blue square on the bottom. It has an area of 50 units squared, so
[tex]50=s^2[/tex] and
[tex]s=\sqrt{50}[/tex]. We could feasibly simplify that, but it's not necessary, really. That side serves as the base of the right triangle. Now we can use Pythagorean's Theorem to find the length of the hypotenuse of the right triangle, which also serves as the side of the big blue square. We will call the side of the big blue square x.
[tex]x^2=(\sqrt{35})^2+(\sqrt{50})^2[/tex] and
[tex]x^2=35+50[/tex] and
[tex]x^2=85[/tex] and
[tex]x=\sqrt{85}[/tex]. That is the side length of the large blue square. The area for the square is s * s, and since we know the side length to be √85:
[tex]A=(\sqrt{85})(\sqrt{85})[/tex] so
A = 85 units squared
In need of an answer (giving brainliest)
Answer:
The answer is D.
Step-by-step explanation:
The lateral surface area of a 3-D figure is the area of each face that is NOT a base.
Explain why the graphs of reciprocals of linear functions (except horizontal ones) always have vertical asymptotes,
but the graphs of reciprocals of quadratic functions sometimes do not.
Answer:
The reason is because linear functions always have real solutions while some quadratic functions have only imaginary solutions
Step-by-step explanation:
An asymptote of a curve (function) is the line to which the curve is converging or to which the curve to line distance decreases progressively towards zero as the x and y coordinates of points on the line approaches infinity such that the line and its asymptote do not meet.
The reciprocals of linear function f(x) are the number 1 divided by function that is 1/f(x) such that there always exist a value of x for which the function f(x) which is the denominator of the reciprocal equals zero (f(x) = 0) and the value of the reciprocal of the function at that point (y' = 1/(f(x)=0) = 1/0 = ∞) is infinity.
Therefore, because a linear function always has a real solution there always exist a value of x for which the reciprocal of a linear function approaches infinity that is have a vertical asymptote.
However a quadratic function does not always have a real solution as from the general formula of solving quadratic equations, which are put in the form, a·x² + b·x + c = 0 is [tex]\dfrac{-b \pm \sqrt{b^{2} - 4\cdot a\cdot c}}{2\cdot a}[/tex], and when 4·a·c > b² we have;
b² - 4·a·c < 0 = -ve value hence;
√(-ve value) = Imaginary number
Hence the reciprocal of the quadratic function f(x) = a·x² + b·x + c = 0, where 4·a·c > b² does not have a real solution when the function is equal to zero hence the reciprocal of the quadratic function which is 1/(a·x² + b·x + c = 0) has imaginary values, and therefore does not have vertical asymptotes.
You wish to make a snack mixes from peanuts and almonds to sell in your health-food store. Mix A is half peanuts and half almonds. Mix B is one fourth peanuts and three-fourths almonds. If you have 15 pounds of peanuts and 20 pounds of almonds, how many pounds of each mix should you make to exactly use all of your ingredients?
Answer:
25 pounds of mix A
10 pounds of mix B
Step-by-step explanation:
Each pound of mix A takes half a pound of peanuts and each pound of mix B takes one fourth of a pound of peanuts. Total peanuts consumption is:
[tex]0.5A+0.25B=15[/tex]
Each pound of mix A takes half a pound of almonds and each pound of mix B takes three fourths of a pound of almonds. Total almonds consumption is:
[tex]0.5A+0.75B=20[/tex]
Solving the linear system:
[tex]0.5A+0.25B=15\\0.5A+0.75B=20\\0.5B=5\\B=10\ pounds\\0.5A=15-0.25*10\\A=25\ pounds[/tex]
In order to exactly use all of your ingredients, you should make 25 pounds of mix A and 10 pounds of mix B
What is the prime factorization of 97?
Answer:
97 is a prime number.
Prime[25] = 97
The radius of the circle shown below is 17 yards. What is the length
of the 300 degree arc?
Round your answer to the nearest whole number.
17 yd
300°
Answer:
The length of the arc is 89 yards
Step-by-step explanation:
Mathematically, to find the length of an arc, we use the formula below;
Length of an arc = Theta/360 * 2 * pi * r
In this case, Theta = 300 and r = 17 yards
Length of the arc = 300/360 * 2 * 22/7 * 17 = 89.047619047583 which is 89 yards to the nearest yard
I am very confused in this question. Please Help!!!
Answer:
32
Step-by-step explanation:
A : B : C: total
2 3 4 2+3+4 = 9
Take the number of rolls received 72 and divide by 9
72/9 = 8
Multiply each number by 8
A : B : C : total
2*8 3*8 4*8 9*8
16 24 32 72
C received 32 rolls
Rain trees are planted every 15 metres apart along a road pavement, Bougainvillea
bushes are planted every 1.6 metres apart along the same pavement,
A rain tree and bougainvillea bush are planted at a common point A along the
pavement. Find the distance from A to the next point where a rain tree and
bougainvillea bush are planted together.
Please help with this question.
Answer:
120 m
Step-by-step explanation:
LCM of 1.6 and 15 will give us the distance
Put 1,6 and 15 in same format:
16/10= 2*2*2*2/10150/10= 2*3*5*5/10LCM= 2*2*2*2*3*5*5/10= 120 m
So the next point is 120 m apart
I need help ASAP psnnsndjsjajasj
Answer:
16pi
Step-by-step explanation:
Answer:
50.24 cm^2
Step-by-step explanation:
The formula of the area of a circle is πr².
by substituting each values as π=3.14, r²=4², we get, 3.14×4²=3.14×16
= 50.24cm²
Please answer this question now in two minutes
Answer:
the correct answer is (b).........
Answer:
ABC = 140
Step-by-step explanation:
ABD = 70
ABD = DBC since it is bisected
ABC = ABD + DBC
= 70+70
ABC = 140
Q3. A student plans a method to prepare pure crystals of copper sulfate.
The student's method is
1. Add one spatula of calcium carbonate to dilute hydrochloric acid in a beaker.
2. When the fizzing stops, heat the solution with a bunsen burner until all the liquid is gone.
The method contains several errors and does not produce copper sulfate crystals.
5
Explain the improvements the student should make to the method so that pure crystals of
copper sulfate are produced. (6) * S
Answer:
1) The student didn't add copper sulfate but instead he added calcium carbonate.
2) The heated solution should be left to get bigger crystals and should not be instantly allowed to evaporate.
3) He should use copper carbonate not calcium carbonate.
4) Sulfuric acid was added instead of hydrochloric acid.
5) Add solid excessively so that all of the acid is retained.
6) Filter the solution to remove unreacted solid.
7) Heat gently, so the crystals will start to appear.
The reactants in this reaction ought to have been copper carbonate and sulfuric acid.
The student is trying to carry out a reaction that would produce copper sulfate using two starting materials. The process is also expected to involve the evolution if a gas. However the process failed to produce the desired product. The following adjustments should be made to the process;
The student should use copper carbonate instead of calcium carbonate The student should use sulfuric acid instead of hydrochloric acid.If these two adjustments are made, the equation of the reaction occurs as follows; CuCO3(s) + H2SO(aq) → CuSO4(aq) + CO2(g) + H2O(l).
Learn more: https://brainly.com/question/731147
Subtracting Fractions
13 minus 12/40 equals
Answer:
12 7/10
Step-by-step explanation:
13 - 12/40
Simplify the fraction
13 - 3/10
Borrow 1 from 13 in the form of 10/10
12 + 10/10 - 3/10
12 7/10
I am really struggling with this question. please help.
Answer:
y = -2/3x + 1
Step-by-step explanation:
Step 1: Find slope
m = (-1 - 3)/(3 + 3)
m = -2/3
y = -2/3x + b
Step 2: Find b
-1 = -2/3(3) + b
-1 = -2 + b
b = 1
Step 3: Write equation
y = -2/3x + 1
porfavor alguien que me ayude con la siguiente operación,
(1/3√3 ×5/4√3) +7/4
Answer:
17/6
Step-by-step explanation:
El único problema aquí es conocer las operaciones con el surd por favor note que;
√a * √a = a Así;
√3 * √3 = 3
Entonces, la otra cosa a tener en cuenta es el orden de las ecuaciones.
Resolvemos los corchetes antes de proceder con cualquier otra cosa.
1 / 3√3 * 5 / 4√3 = 5/12 (3) = 5/36
Es esto lo que agregamos a 7/4
5/36 + 7/4 = (5 + 63) / 36 = 68/36 = 17/6
Will give Brainliest if u help me solve this problem
Answer:
31
Step-by-step explanation:
Median is the middle number when you order them ascending.
Answer:
40 million acres.
Step-by-step explanation:
15 ,27, 31, 40, 44. The median number is the middle number(arranged from least to greatest). In 5 numbers, the middle number is the 3rd number(arranged from least to greatest), therefore; the answer is 31.
Triangles ABC and CDE are mathematically similar.
a) Work out the length of DE.
b) Work out the length of AB.
Answer:
Step-by-step explanation:
The trick here is to notice that :
[tex]\frac{AB}{DC}[/tex]=[tex]\frac{BC}{DE}[/tex]=[tex]\frac{AC}{CE}[/tex]Now let's replace by the values we khow :
[tex]\frac{AB}{18}[/tex]=[tex]\frac{8}{24}[/tex]=[tex]\frac{5}{DE}[/tex] 8/24 is 1/3 to make it simple Now AB= 18*(1/3)=6 AND DE= 5*(3/1)=15So AB=6 cm and DE=15 cm
From the given information in the diagram
a) The length of DE is 15cm and
b) The length of AB is 6cm
From the question,
Triangles ABC and CDE are mathematically similar.
a) To determine the length of DE
Since ΔABC is similar to ΔCDE
By similar triangles theorem, we can write that
[tex]\frac{/BC/}{/DE/}=\frac{/CA/}{/EC/}[/tex]
From the diagram
/BC/ = 5cm
/CA/ = 8cm
/EC/ = 24 cm
/DE/ = ?
Putting these values into
[tex]\frac{/BC/}{/DE/}=\frac{/CA/}{/EC/}[/tex]
We get
[tex]\frac{5}{/DE/}=\frac{8}{24}[/tex]
∴ [tex]8 \times /DE/ = 5 \times 24[/tex]
Now, divide both sides by 8
[tex]\frac{8 \times /DE/}{8}= \frac{5 \times 24}{8}[/tex]
[tex]/DE/ = \frac{120}{8}[/tex]
/DE/ = 15cm
b) To work out the length of AB
Also, by similar triangles theorem, we can write that
[tex]\frac{/AB/}{/CD/}=\frac{/CA/}{/EC/}[/tex]
From the diagram
/AB/ = ?
/CD/ = 18cm
/CA/ = 8cm
/EC/ = 24 cm
Putting these values into
[tex]\frac{/AB/}{/CD/}=\frac{/CA/}{/EC/}[/tex]
We get
[tex]\frac{/AB/}{18}=\frac{8}{24}[/tex]
Now, multiply both sides by 18, that is
[tex]18 \times \frac{/AB/}{18}=\frac{8}{24} \times 18[/tex]
[tex]/AB/ = \frac{144}{24}[/tex]
/AB/ = 6cm
Hence,
a) The length of DE is 15cm and
b) The length of AB is 6cm
Learn more here: https://brainly.com/question/14106654
If you invest $1,000 in an account paying 4% interest compounded quarterly,lhow much money will you have after 3 years? A.)$1,500 B.)$1,005 C.)$1,220 D.)$1,225
Answer:
C is closest to the actual result, $1126.03.
Step-by-step explanation:
Use the Compound Amount formula: A = P(1 + r/n)^(nt), where:
P is the original principal; r is the interest rate as a decimal fraction; n is the number of compounding periods per year, and t is the number of years.
Then we have A = $1000(1 + 0.04/4)^(4*3), or
= $1000(1.01)^12 = $1126.03
In circle A, angle BAE is congruent to angle DAE.
What is the length of BE?
You need to give us answer choices.
However, I looked back to previous questions posted on Brainly, and I found one that was similar to yours.
The length of BE could possibly be 27 units.
- I hope this helps. Next time, please use the search feature :)))
What is the value of f(4), if f(x) = x2 + 9x + 8?
Find using synthetic division.
Answer:
x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]
Step-by-step explanation:
Using Synthetic division
divisor is (x - 5) , thus evaluate at h = 5
5 | 1 8 - 25 - 193
5 65 250
-----------------------------
1 13 50 57 ← remainder = 57
The coefficients of the quotient are 1, 13, 50 , that is
x² + 13x + 50
Thus
[tex]\frac{x^3+8x^2-25x-193}{x-5}[/tex] = x² + 13x + 50 + [tex]\frac{57}{x-5}[/tex]
A. Fill in the boxes :
8 tens + 19 ones = 9 tens +
ones
8 tens + 2 ones = 7 tens +
ones
7 tens + 25 ones = 9 tens +
ones
70 + 11 = 80 +
50 +
= 60 + 3
90 + 13 =
+ 3
Step-by-step explanation:
it's simple:
8 tens + 19ones = 9 tens + 9 ones8 tens + 2 ones =7 tens+12 ones7 tens +25 ones = 9 tens + 5 ones70+11=80+150+13=60+390+13=100+3find a polynomial with a degree of 3 and the zeros 1, 7 & -4 with no other zeros
Answer:
x³ - 4x² - 25x + 28
Step-by-step explanation:
Step 1: Write out binomial linear factors
(x - 1)(x - 7)(x + 4)
Step 2: Expand
(x² - 8x + 7)(x + 4)
Step 3: Expand
x³ - 4x² - 25x + 28
The following quadrilateral is a parallelogram.
J
M
115°
?
K
L
The measure of angle Lis — degrees.
Answer:
65
Step-by-step explanation:
Angle M and angle L are supplementary angles, so they add up to 180°.
180 - 115
= 65
The measure of angle L is 65 degrees.
Find the solutions to the equation below.
Check all that apply.
x2 - 25 = 0
O A. X=-3
OB. x = 3
O c. x= -1
O D. x= 1
E. x = -5
O F. X = 5
Answer:
[tex]\boxed{\sf \ \ \ x = 5 \ or \ x=-5 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-25=0\\<=> x^2-5^2=0\\<=> (x-5)(x+5)=0\\<=> x-5 = 0 \ or \ x+5=0\\<=> x = 5 \ or \ x=-5[/tex]
hope this helps
If ε= {x: x is an integer such that 1
2 < x < 12,
4 < x < 21,
-1 < x < 9
0 < x < 8
x<6
From above: 4 < x < 6 --> x = 5.
Answer: B.
Kaitlin paid $16.60 for 33.2 centimeters of wire.
Find the unit price in dollars per centimeter.
If necessary, round your answer to the nearest cent.
Answer:
Step-by-step explanation:
$0.50 per centimeters i think
Ally and Beth are at the grocery store. Ally buys a container of milk for $4 and 4.75 pounds of apples. Beth buys a box of cereal for $3 and 5.5 pounds of apples. If the two shoppers spend the same amount, how much does 1 pound of apples cost?
Answer:
$1.33
Step-by-step explanation:
let the cost of apple be $x .
now according to question the two shoppers spend the same amount
4.75x+4=5.5x+3
0.75x=1
x= 4/3= $1.33
therefore, pound of apples cost = $1.33