Answer: Choice A) 9/45 and 8/40
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If you divide both top and bottom of 9/45 by the GCF 9, you get 1/5
If you divide top and bottom of 8/40 by the GCF 8, you also get 1/5
So the original fractions must be the same
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Another way to check is to use a calculator and see that 9/45 = 0.2 and 8/40 = 0.2, so 9/45 = 8/40
Or you can subtract the fractions and you should end up with 0, so, 9/45 - 8/40 = 0
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You can also set up a proportion and cross multiply
9/45 = 8/40
9*40 = 45*8
360 = 360
The last equation is true, so the first equation must be true
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?
You have just accepted a job at Wonders Day Camp for the summer. The camp will pay you $48.23 each day for 8 weeks. If you work 5 days each week, how much money will you make this summer?
Answer:
$192.20
Step-by-step explanation:
8 x 5=40 48.32x40=192.20
Answer:
You will make $1929.20 this summer.
Step-by-step explanation:
You have just accepted a jab at Wonders Day Camp for the summer.
The camp will pay for each day for 8 weeks = $48.23
You work 5 days each week.
So total days of work = 8 × 5 = 40 days
You earn $48.23 for one day.
For 40 days you will earn = 40 × 48.23 = $1,929.20
You will make $1929.20 this summer.
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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How many groups of 8 can you make out of 63
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).
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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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
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class? A. 72 + 78 + 70 + x 289 B. 72 + 78 + 70 + x > 289 C. 72 + 78 + 70 + x < 289 D. 72 + 78 + 70 + x 289
B. 72 + 78 + 70 + x > 289
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!! : )
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
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:
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 radio station have free tickets to 10% of the people attending a concert. The radio station gave 640 people free tickets. What is the total number of people who attended the concert?
Answer:
6400 people.
Step-by-step explanation:
If 640 is 10%. You multiply 640 by 10 to get 6400 or 100% of the people.
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:
Please show steps so I understand.
Rearrange the equation so X is the independent variable. 6x+y=4x+11
Y=______________
6x+y=4x+11
y=4x+11-6x
y=-2x+11
[tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.
To rearrange the equation [tex]\(6x + y = 4x + 11\)[/tex] so that (x\) is the independent variable and (y) is dependent, we need to isolate (y) on one side of the equation.
Start with the given equation: [tex]\(6x + y = 4x + 11\)[/tex].
Subtract (4x) from both sides to move all terms involving (y) to one side: [tex]\(6x - 4x + y = 11\).[/tex]
Simplify the left side by combining like terms: 2x + y = 11.
To isolate y, subtract 2x from both sides: 2x + y - 2x = 11 - 2x.
Simplify: [tex]\(y = 11 - 2x\)[/tex].
So, the rearranged equation with (x) as the independent variable is y = 11 - 2x.
Detailed calculation:
Starting equation: (6x + y = 4x + 11)
Subtract (4x) from both sides:
[tex]\(6x - 4x + y = 4x - 4x + 11\)[/tex]
[tex]\(2x + y = 11\)[/tex]
Subtract (2x) from both sides:
[tex]\(2x + y - 2x = 11 - 2x\)[/tex]
[tex]\(y = 11 - 2x\)[/tex]
Therefore, [tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.
fifty subtracted from a number equals eighty. find the number
Answer: hope this helps. it's 130.
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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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].
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]
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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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
a regular size chocolate bar is 5 4/9 inches long. the king size bar is 3 times as long as the regular size bar. how long is the king size bar
Answer:
15 4/9 inches long
Step-by-step explanation:
5 4/9 × 3
When lining them vertically the 3 ends up under 5 in which you multiply and transfer the 4/9 next to the product of 15. Hope that helped!
The king size chocolate bar is three times as long as the regular bar, so given that the regular bar is 5 4/9 inches long, the king size bar is 16 1/3 inches long.
Explanation:The problem involves a regular size chocolate bar that is 5 4/9 inches long and a king size bar that is three times as long. Given the length of the regular bar, our objective is to find out how long the king size bar is.
We start by converting the mixed number 5 4/9 into an improper fraction which gives us 49/9 inches. We then multiply 49/9 by 3 to get the length of the king size bar which is 147/9 inches. Converting this improper fraction back into a mixed number, we get 16 1/3 inches. Therefore, the king size bar is 16 1/3 inches long.
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what is the domain of f(x) = (1/3)^x ?
Answer:
B
Step-by-step explanation:
There isn't any number that x can't be. Start with a graph to show how this could be so.
It is easy to see that x > 0 gives a line that goes very near the x axis. It is not quite so easy to see that it never touches the x axis. But if you recreate the graph in Desmos, you will see that is true if you spread the x's out.
It is not quite so easy to see that when x<0 the graph tips upward very quickly but again if you move the values of the axis around you will see there is no value that x cannot be.
Answer:
B:All real numbers
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.
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 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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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]
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