Answer:
5 15/22 hours
5.6818 hours
Step-by-step explanation:
Distance is equal to the rate times the time
D = rt
We know the rate = 88 km/hr and the distance = 500 km
Substitute these in
500 = 88 *t
Divide each side by 88
500/88 = 88t/88
5 15/22 hours
5.6818 hours
The endpoints of are A(1, 4) and B(6, -1). If point C divides in the ratio 2 : 3, the coordinates of C are
Answer
The answer is C=(4,2). Let me know if you need an explanation.
Step-by-step explanation:
I'm very confuesed where to start this problem:
Graph −18x+9y=72
Answer:
Plug in x=0 and plot the point, then plug in y = 0 and plot the point.
Answer:
y=-2x+8
Step-by-step explanation:
first you have to -18x on both sides because you want to get y by itself
9y=-18x+72
then divide 9 by both sides
9y/9=-18x+72/9.....-18/9=-2 and 72/9=8
y=-2x+8
-2x is your slope and 8 is your y intercept
PLEASE HELP!find the domain of the graphed function
Answer:
Domain is a set of all possible x values, so answer A is correct, as x is in [2,5].
Which function is undefined for x = 0? y=3√x-2 y=√x-2 y=3√x+2 y=√x=2
For this case, we have to:
By definition, we know:
The domain of [tex]f (x) = \sqrt [3] {x}[/tex] is given by all real numbers.
Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root. Thus, it will always be defined.
So, we have:
[tex]y = \sqrt [3] {x-2}[/tex] with[tex]x = 0[/tex]: [tex]y = \sqrt [3] {- 2}[/tex] is defined.
[tex]y = \sqrt [3] {x+2}[/tex]with [tex]x = 0:\ y = \sqrt [3] {2}[/tex] is also defined.
[tex]f (x) = \sqrt {x}[/tex]has a domain from 0 to ∞.
Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.
Thus, we observe that:
[tex]y = \sqrt {x-2}[/tex] is not defined, the term inside the root is negative when[tex]x = 0[/tex].
While [tex]y = \sqrt {x+2}[/tex] if it is defined for [tex]x = 0[/tex].
Answer:
[tex]y = \sqrt {x-2}[/tex]
Option b
Answer:
B on EDGE
Step-by-step explanation:
justin starts a bank account with $85 in his savings,and he puts in an additional 15 dollars a month towards his savings
Answer:
y = 15x + 85
Step-by-step explanation:
Let:
x = amount of months ; y = total amount
The constant is 85, meaning that this number will not change (for he would have at least 85 no matter how much time has passed).
15 is next to a variable, for depending on the amount of time passed, you will add a certain amount of "15" to the answer.
y is your total, and is also a variable, because it also depends on the amount of time that passes.
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Solve the system of equations by subtraction. What is the solution for x? 2x+y=1 4z+2y=-1
[tex]\left\{\begin{array}{ccc}2x+y=1&|\text{subtract 2x from both sides}\\4x+2y=-1\end{array}\right\\\\\left\{\begin{array}{ccc}y=-2x+1&(*)\\4x+2y=-1&(**)\end{array}\right\\\\\text{substitute}\ (*)\ \text{to}\ (**):\\\\4x+2(-2x+1)=-1\qquad\text{use distributive property}\\\\4x+(2)(-2x)+(2)(1)=-1\\\\4x-4x+2=-1\\\\2=-1\qquad\text{FALSE}\\\\Answer:\ \boxed{NO\ SOLUTION}[/tex]
Write the equation of a parabola with vertex at (0,0) and directrix of y=-3
Answer:
x^2=12y
**C on edge
The equation of a parabola with its vertex at (0,0) and directrix at y=-3 is y = 1/12 x².
Explanation:To write the equation of a parabola, we are given that its vertex is at (0,0) and its directrix is y=-3. The equation of a parabola with the vertex at (0,0) and the focus at (0,p) or a directrix at y=-p is given as y = 1/4p x². Considering the distance from the vertex to the directrix is the same as the distance from the vertex to the focus, the value of p in this case will be 3. Therefore, the equation of this parabola is y = 1/12 x².
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The following function represents the value of a house, in dollars, after x years:
f(x) = 242,000(1.04)x
What does 1.04 represent?
The present value of the house
The value of the house after x years
The increase in the value of the house per year, which is 4%
The value of the house after x years, which will be 4% of the present value
Answer:
the 1.04 represents the increase in the house value each year, which is 4%
Answer:
The correct option is 3.
Step-by-step explanation:
The general exponential growth model is
[tex]y=a(1+r)^x[/tex] .... (1)
where, a is the initial value, r is growth rate per period and x is number of periods. Here (1+r) is growth factor.
The given function is
[tex]f(x)=242,000(1.04)^x[/tex]
It can be written as
[tex]f(x)=242,000(1+0.04)^x[/tex] .... (2)
From (1) and (2) we get
[tex]r=0.04=4\%[/tex]
In the given function 1.04 is growth factor. It means it represents increase in the value of the house per year which is 4%.
Therefore the correct option is 3.
In a rectangle the length is 2 cm longer than the width. If its length and width are both increase by 4 cm it's area is increased by 56 cm. Find the original length and width.
Answer:
Length = 6 cm and width = 4 cm.
Step-by-step explanation:
Let the width be x, then the length is x + 2 cm and its area = x(x + 2).
The new width and length are x + 4 and x + 6, and the new area is
(x + 4)(x + 6).
So we have the equation:-
(x + 6)(x + 4) = x(x + 2) + 56
x^2 + 10x + 24 = x^2 + 2x + 56
10x - 2x = 56 - 24
8x = 32
x = 4 cm = width
and length = 4 + 2 = 6 cm
The area of a rectangular dog pen is 8 1/2 square feet.if the width is 3 2/5 feet,what's is the length,in feet ?
Answer:
l = 2.5 feet
Step-by-step explanation:
A = lb
8.5 = l * 3 2/5
8.5 = l * 3.4
l = 8.5 / 3.4
l = 2.5 feet (Always remember to put the units, otherwise you may not get points.)
Please give a rating and a thanks.
Thank you.
Answer:
l = 2 1/2 ft
Step-by-step explanation:
Area is given by the formula
A = l*w
We know the area is 8 1/2
Changing this to an improper fraction 8 1/2 = (2*8 +1)/2 = 17/2
The width is 3 2/5 as an improper fraction = (5*3+2)/5 = 17/5
A = l*w
17/2 = l* 17/5
Multiply each side by 5/17
17/2 * 5/17 = l* 17/5 * 5/17
5/2 = l
2 1/2 = l
Doreen is flipping two fair coins. What is the probability that both coins land on heads?
Answer:
There are four different possible outcomes: both coins are heads, the red coin is heads and the blue coin is tails, the red coin is tails and the blue coin is heads, or both coins are tails. Each outcome has equal probability. So the probability of both being heads is 1/4.
Step-by-step explanation:
Why do interest rates on loans tend to be lower in a weak economy than in a strong one?
Why do interest rates on loans tend to be lower in a weak economy than in a strong one?
The interest rates on loans tend to be lower in a weak economy than in a strong one because in a weak economy there is less demand for credit so the rates are lesser. In a stronger economy, the credit market demand is higher so as the demand increases the rate also increases.
Answer:
C
Step-by-step explanation:
took test
HELP ASAP PLEASEE!! a metal alloy weighing 4 mg and containing 20% iron is melted and mixed with 12 mg of a different alloy which contains 40% iron. which percent of the resulting alloy is iron?
A)12%
B)20%
C)35%
D)55%
Answer:
35 percent
Step-by-step explanation:
To solve this problem we multiply the amount by the percent and add them up to get the total amount times the percent
amount * percent + amount * percent = total amount * percent
4 * .20 + 12 * .40 = (4+12) * x
.8 + 4.8 = 16 x
Combine like terms
5.6 = 16x
Divide by 16
5.6/16 = 16x/16
.35 =x
35 percent
Solve the system of equations below by graphing. 2.4x-y=-3.5 x^2+x+y=6 What are the approximate solutions rounded to the nearest tenth? (–6.2, –4) and (5, 0.6) (–4, –6.2) and (0.6, 5) (–2.4, 2.4) and (3.7, –12.8) (2.4, –2.4) and (–12.8, 3.7)
Answer:
(-4.0,-6.2) and (0.6,5)
Step-by-step explanation:
We have been given the system of equations
[tex]
2.4x-y=-3.5........(1)\\x^2+x+y=6 .....(2)[/tex]
Let us graph these equation on the xy-plane.
The intersection point of these two curves will give us the solution of the system of equations.
Equation 1 represents a parabola and equation (2) represents a straight line.
The graph is shown in the attached file.
The intersection points of the parabola and the line are (0.622,4.992) and (-4.022, -6.152)
Therefore, the solutions rounded to nearest tenth are
(-4.0,-6.2) and (0.6,5)
Answer:
B. (–4, –6.2) and (0.6, 5)
Step-by-step explanation:
Hope this helps!! Have a great day!! : )
An ice cream cone that is 4cm across the top is topped with a single scoop of ice cream (spherical) that is 4cm in diameter. What is the minimum height of the cone so that when the ice cream melts, the ice cream does not overflow out of the cone? Justify your answer.
Answer:
8 cm.
Step-by-step explanation:
We have been given that an ice cream cone that is 4 cm across the top is topped with a single scoop of ice cream (spherical) that is 4 cm in diameter.
To find the minimum height of cone we will use volume of cone formula and volume of sphere as we are told that when the ice cream melts, the ice cream does not overflow out of the cone. This means that volume of sphere will be equal to volume of cone.
[tex]\text{Volume of cone}=\frac{1}{3} \pi r^2h[/tex]
[tex]\text{Volume of sphere}=\frac{4}{3} \pi r^3[/tex]
Since diameter of both cone and sphere is 4 cm, so radius will be half the diameter, that is 2 cm.
Let us substitute r=2 in both equations and equate the volumes of cone and sphere to find the height of cone.
[tex]\frac{4}{3} \pi\times 2^3=\frac{1}{3} \pi\times 2^2\times h[/tex]
[tex]\frac{4}{3} \pi\times 8=\frac{1}{3} \pi\times 4\times h[/tex]
Multiply both sides of equation by 3.
[tex]3\times \frac{4}{3} \pi\times 8=3\times \frac{1}{3} \pi\times 4\times h[/tex]
[tex]4 \pi\times 8= \pi\times 4\times h[/tex]
[tex]32 \pi= 4\pi\times h[/tex]
[tex]h=\frac{32 \pi}{4\pi}[/tex]
[tex]h=8[/tex]
Therefore, the minimum height of cone must be 8 cm.
Is 2/4 equal to 1/2 cup?
Answer:
yes
Step-by-step explanation:
if you reduce 2/4 and divid both sides by u get 1/2
and 1/2 = 1/2
can someone please help n fast
Answer: 1. D) Exponents 2. A) Addition and subtraction from left to right
Step-by-step explanation: PEMDAS will help you to understand! Remember, first, its parentheses, then exponents (Answer for Question 1), then multiply and divide from left to right, then add and subtract from left to right (Answer for Question 2).
Hope this helped!
Plz mark brainliest!
The area of a square is (4x + 3)^2 square inches. The perimeter of the square is 172 inches. What is the value of x?
Answer:
x = 10
Step-by-step explanation:
the area of a square = s² ( s is the side length )
s² = (4x + 3)² ( take the square root of both sides )
s = [tex]\sqrt{(4x+3)^2}[/tex] = 4x + 3
perimeter = 4s = 172, that is
4(4x + 3) = 172 ( distribute left side )
16x + 12 = 172 ( subtract 12 from both sides )
16x = 160 ( divide both sides by 16 )
x = 10
Write a real-world situation for 7.50y + 9
Johnny needs to buy an amount of small bags of flour at the store for making cookies. One bag of flour is $7.50. Y represents the amount of bags he buys.
At the checkout, the cashier asks if he wants to donate 9 dollars to charity, and he says yes.
How much money did Johnny spend?
how do you simplify 27 over 20
Answer:
1 7/20
Step-by-step explanation:
well 27/20 is 1 and 7/20
make it to a improper fraction
Answer:
1 7/20
Step-by-step explanation:
The fraction given to us (27/20) is called an improper fraction, because the numerator (top number) is greater than the denominator (bottom number).
In this case, break it down. You know that when the numerator & denominator have the same number, it will equal 1. And so change the number.
27/20 = (20 + 7)/20
20/20 = 1
7/20 is left over
1 7/20 is your answer
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there is $3080 in the math department fund. They need to deposit enough money in the fund to pay for a shipment work $2800, and still have $500 left for future shipments. Write an inequality to describe (d), the amount of money that needs to be deposited?
Answer:
3080+d > = 3300
Step-by-step explanation:
The first question to ask is how much money do they need in the fund?
They need the shipment costs plus the future shipment costs
2800+500 = 3300
They have 3080
Let d = how much they need to deposit
How much they have plus how much they need to deposit must be greater than or equal to how much they need.
3080+d > = 3300
Which decimal is between 0.6 and 0.7
Answer:
You can recognize that .25 is 1/4, so 0.625 is 1/4 of the way
from 0.6 to 0.7
Answer: I agree with Sauske. Sorry If I'm saying your name wrong.
Step-by-step explanation:
Solve the equation for b. b/2q=h+7
[tex]\dfrac{b}{2q}=h+7\qquad\text{multiply both sides by 2q}\neq0\\\\b=2q(h+7)\qquad\text{use distributive property}\\\\b=(2q)(h)+(2q)(7)\\\\\boxed{b=2hq+14q}[/tex]
Which is the definition of an acute triangle?
Answer:
A triangle with angles less than 90°
Step-by-step explanation:
An acute triangle is a triangle where all its interior angles are less than 90 degrees, distinguishing it from other types of triangles.
Explanation:In mathematics, an acute triangle is a type of triangle where all three of its interior angles are less than 90 degrees. This is what distinguishes it from other types of triangles such as right triangles, which have one angle of exactly 90 degrees, or obtuse triangles, where one angle is larger than 90 degrees. For example, a triangle with angles of 30, 60, and 90 degrees would be considered an acute triangle because all the angles are less than 90 degrees.
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Rohan invested in a precious mineral. The value of the mineral tends to increase by about 9% per year. He invests $12,000 in 2018.
How much more will his investment be worth by 2025?
Enter your answer in the box.
Round to the nearest whole dollar.
Answer:
$9,936.47
Step-by-step explanation:
Similarly to the other problem I helped you with we have:
[tex]A_{final}=A_{initial}(1+r)^t[/tex]
Where A is amount, r is rate and t is time.
In this case A=12000, r=9%=0.09 and 9% in decimals is 0.09 (9÷100=0.09), and t=7 since 2025 -2018 = 7 years. So how much is this investment worth in 7 years? Let's plug those values in and we obtain:
[tex]A_{final}=12000(1+0.09)^7=12000(1.09)^7=21936.47[/tex]
So the investment will be worth $21,936.47. Now we must calculate how much more will this precious mineral be worth so we get the difference of the final amount and the initial amount the mineral was worth and so:
[tex]A_{final}-A_{initial}=21936.47-12000=9936.47[/tex]
And so the mineral will be worth $9,936.47 more than it originally was worth after 7 years.
fifty subtracted from a number equals eighty. find the number
Answer: hope this helps. it's 130.
m<KGH=x+161,m<FGK=x+41,and m<FGH=180° Find x
Answer: x = -11 ∠FGK = 30° ∠KGH = 150°
Step-by-step explanation:
∠FGK + ∠KGH = ∠FGH Segment Addition Postulate
x + 41 + x + 161 = 180 Substitution
2x + 202 = 180 Simplify (added like terms)
2x = -22 Subtraction Property of Equality
x = -11 Division Property of Equality
∠FGK = x + 41 = (-11) + 41 = 30
∠KGH = x + 161 = (-11) + 161 = 150
A lit house worker is tracking a boat that is 2.1 km south from her. She is also tracking a boat that is 3.5 km from the tower located 70 degrees east of north. To the nearest tenth of a kilometer, how far apart are the two boats?
Answer:
21.5 km
Step-by-step explanation:
We have to find the distance between two boat
We are given that
AC=2.1 km
BC=3.5 km
We have to find BC
The angle between two boat =110 degrees
Using cosine law
BC=[tex]\sqrt{(2.1)^2+(3.5)^2-2\cdot(2.1)\cdot(3.5)cos 110}[/tex]
BC=[tex]\sqrt{4.41+12.25+ 2\cdot2.1\times3.5cos 70[/tex]
BC=[tex]\sqrt{4.41+12.25+9.3051}[/tex]
BC=21.507 km
Hence, the distance between two boat is 21.5 km
The distance between the two boats can be determined using the law of cosines. Inserting the provided values into the formula yields a distance of approximately 3.9 kilometers.
Explanation:To solve this problem, we can apply the law of cosines, which states that c² = a² + b² - 2ab(cos Θ), where a and b are lengths of two sides of a triangle, c is the length of the third side, and Θ is the angle between sides a and b. Let's consider our light house worker as a starting point. The boat at 2.1 km south constitutes one side of the triangle (a = 2.1 km). The other boat, at 3.5 km 70° east of north, constitutes the second side (b = 3.5 km). The angle Θ between side a and side b is 70°. Therefore, the distance between the two boats (c) can be calculated as follows:
c² = a² + b² - 2ab(cos Θ) = (2.1 km)² + (3.5 km)² - 2 *(2.1 km)*(3.5 km) cos(70°)
Computing the above gives a distance of approximately 3.9 km.
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What integer represents saving $65?
Answer:
+$65
Step-by-step explanation:
We are asked to determine the integer that represents saving $65.
We know that savings represent a positive number. Savings stands for the amount saved by a person.
We know that loss, withdraw and spend represent negative quantities, while the savings, profit and deposit represent positive quantities, therefore, saving of $65 would be +$65.
which expression represents a circle with a center at (2, -8) and a radius of 11?
Answer:
(x - 2)² + (y + 8)² = 121
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (2, - 8) and r = 11, hence
(x - 2)² + (y + 8)² = 121
The equation [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex] represents a circle with a center at (2, -8) and a radius of 11. This is derived from the general circle equation [tex]\((x - h)^2 + (y - k)^2 = r^2\).[/tex]
The correct equation representing a circle with a center at (2, -8) and a radius of 11 is option (b) [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex].
The general equation of a circle is [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where (h, k) is the center and r is the radius.
In option (b), [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex], the values match the given center (2, -8) and radius of 11. The squared terms with (x-2) and (y+8) are in the correct form, and the radius squared [tex](\(11^2 = 121\))[/tex] is on the right side.
Options (a), (c), and (d) do not represent the given circle because they have incorrect signs, centers, or radius values. Therefore, the correct equation is option (b).