Answers
Given:-
A right angled triangle is given to us .Two angles are 45° , longest side is 5 and another side is "x" .To find:-
The value of x .Answer:-
In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is 5 which is hypotenuse and the measure of perpendicular needs to be find out .
We may use the ratio of sine here as , we know that in any right angled triangle,
[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]
And here , p = 5 and h = x , so on substituting the respective values, we have;
[tex]\implies \sin\theta = \dfrac{x}{5} \\[/tex]
Again here angle is 45° . So , we have;
[tex]\implies \sin45^o =\dfrac{x}{5} \\[/tex]
The measure of sin45° is 1/√2 . so on substituting this we have;
[tex]\implies \dfrac{1}{\sqrt2}=\dfrac{x}{5} \\[/tex]
[tex]\implies x =\dfrac{5}{\sqrt2}\\[/tex]
Value of √2 is approximately 1.414 . So we have;
[tex]\implies x =\dfrac{5}{1.414} \\[/tex]
[tex]\implies \underline{\underline{\red{\quad x = 3.53\quad }}}\\[/tex]
Hence the value of x is 3.53 .
and we are done!
Answer:
The length of side x to the nearest tenth is 3.5.
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 45°, 45° and 90°. Therefore, this triangle is a 45-45-90 triangle.
A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2. Therefore, the formula for the ratio of the sides is b: b : b√2 where:
b is the measure of the legs opposite the 45° angles.b√2 is the longest side (hypotenuse) opposite the right angle.We have been given the hypotenuse, so:
[tex]\implies b\sqrt{2}=5[/tex]
Solve for b:
[tex]\implies \dfrac{b\sqrt{2}}{\sqrt{2}}=\dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies b=\dfrac{5}{\sqrt{2}}[/tex]
The side labelled "x" is one of the sides opposite the 45° angles, so:
[tex]\implies x=b[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=\dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x=3.5355339...[/tex]
[tex]\implies x=3.5\;\sf(nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 3.5.
Related Questions
Can someone please help.
Answers
By circle , 15 is the length of x .
What is a circle, exactly?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by each line that traverses the circle.
Moreover, every angle has rotational symmetry around the center. With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.
AE² = EC . CD
10² = 5 * x
100 = 5 * x
100/5 = x
20 = x
ED = 20 - 5 = 15
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I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. Royalty would be great.
Answers
By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.
How many halves they need in total?Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.
So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:
3*(1/2) + 8*(1/2) + 7*(1/2)
3/2 + 8/2 + 7/2
All of these have the same denominator so we can directly add them up:
3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2
(3 + 8 + 7)/2 = 18/2
18/2 = 9
You need 9 cupcakes for you and your friends.
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Complete question:
"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"
Type the correct answer in the box.
The product of 2√3 and 3√12 in simplified form is
Answers
Answer: 36
Step-by-step explanation:
2root3 * 3root12
2*3*root3*root12
6root36
root36=6
6*6=36
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the angle has 4x and 6x what is the measurement of the angle
Answers
The sum of the measures of the two angles is 180 degrees, as they are angles of a straight line. The measure of the first angle is 4x = 72 degrees, and the measure of the second angle is 6x = 108 degrees.
What is angle ?
A measure of rotation of two crossing lines or planes in mathematics is called an angle. Angles are frequently defined as degrees or radians. Two lines or splines intersect at a location, known as the apex of the angle, to produce an angle. The edges of the angle are the two lines and line segments. According to its measurement, an angle can be categorized as: An acute angle is one that ranges from 0 to 90 degrees. Right arc: an angle that is 90 degrees in length. A measureable angle intermediate 90 and 180 degrees is referred to as an obtuse angle. 180 degree angle is referred to as a straight angle.
The sum of the measures of the two angles is 180 degrees, because they are angles of a straight line. Therefore:
4x + 6x = 180
Simplifying the left-hand side, we get:
10x = 180
Dividing both sides by 10, we obtain:
x = 18
So the measure of the first angle is:
4x = 4(18) = 72 degrees
And the measure of the second angle is:
6x = 6(18) = 108 degrees
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The complete question is: What is the measurement of an angle if its measure is 4x and another angle's measure is 6x?
Cyndi is making a mixture of cashews and peanuts the cashews are $7 per pound and $3 a pound for peanuts. Cyndi wants 20 pounds of the mixture which will cost $5.40 per pound .. what's the system and how much would she need to equal $108
Answers
The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:
Cashews: 12 pounds.Peanuts: 8 pounds.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: amount of cashews.Variable y: amount of peanuts.The mixture has a total of 20 pounds, hence:
x + y = 20.
y = 20 - x.
The total cost of the mixture is of $108, as 108/20 = 5.4, hence:
7x + 3y = 108
Replacing the second equation into the first, the value of x is given as follows:
7x + 3(20 - x) = 108
4x = 48
x = 12.
Then the value of y is given as follows:
y = 20 - 12
y = 8.
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Ella has an offer to buy an item with a sticker price of $12,300 by paying $420 a month for 36 months. What interest rate is Ella being offered?
Answers
Answer:
To calculate the interest rate, we can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r)^(-n)) / r]
where:
PV = present value
PMT = monthly payment
r = interest rate per period
n = number of periods
In this case, we have:
PV = $12,300 (the sticker price)
PMT = $420
n = 36 (36 months)
Substituting these values into the formula, we get:
12,300 = 420 x [(1 - (1 + r)^(-36)) / r]
Simplifying this equation algebraically is not possible, so we need to use numerical methods to solve for r. One way to do this is to use a financial calculator or spreadsheet program, which can find the interest rate that makes the equation true. Using Excel's RATE function, for example, we get:
=RATE(36,-420,12300)
This gives us an interest rate of approximately 3.33% per month or 39.96% per year.
Therefore, Ella is being offered an interest rate of 3.33% per month or 39.96% per year.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
Answer:
To determine which statements are true, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Using this form, we can rewrite the given equation as:
(x - 1)^2 + y^2 = 3^2 + 1^2 = 10
Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.
To find the radius, we can rearrange the equation as follows:
x^2 - 2x + y^2 = 8
Completing the square for x, we get:
(x - 1)^2 + y^2 = 9
This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Therefore, the three true statements are:
1.The radius of the circle is 3 units.
2.The center of the circle lies on the x-axis.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
hope its help <:
The perimeter of a rectangle is 343434 units. Its width is 6.56.56, point, 5 units.
Write an equation to determine the length (l)(l)left parenthesis, l, right parenthesis of the rectangle.
Answers
The length of the rectangle is 10.5 units.
What is perimeter?
Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.
The perimeter of a rectangle is given by the formula:
P = 2l + 2w
where P is the perimeter, l is the length, and w is the width.
In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:
34 = 2l + 2(6.5)
Simplifying, we get:
34 = 2l + 13
Subtracting 13 from both sides, we get:
21 = 2l
Dividing both sides by 2, we get:
l = 10.5
So the equation to determine the length of the rectangle is:
2l + 2w = P
Substituting the known values, we get:
2l + 2(6.5) = 34
Simplifying and solving for l, we get:
2l + 13 = 34
2l = 21
l = 10.5
Therefore, the length of the rectangle is 10.5 units.
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Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.
help and i give brbainlist
Answers
Answer:
Option C would likely produce the most representative sample of the population of smartphones made by the company. By testing every 500th smartphone off the production line, the manufacturer can ensure that they are selecting a random sample of smartphones from throughout the production process. This can help to account for any variations or changes that may occur in the manufacturing process over time.
Option A, testing the first smartphone off the production line each day, may not be representative of the entire production run since the first smartphone may not be representative of the rest of the batch. Similarly, option B, testing the last 1000 smartphones produced each month, may not be representative of the entire production run as there may be variations in quality and safety standards throughout the month.
Option D, testing every smartphone made on Wednesday, would likely not produce a representative sample as it may not account for any variations or changes that occur during other days of the week.
Please help
Find the surface area (show work)
Answers
Answer:
148 cm²
Step-by-step explanation:
You want the surface area of a cuboid with edge lengths 4 cm, 5 cm, and 6 cm.
AreaThe formula is shown in your problem statement.
It can be made easier to compute using a little rearranging:
SA = 2LW +2LH +2WH
SA = 2(LW +LH +WH)
SA = 2(LW +H(L +W))
The choice of dimensions for L, W, and H doesn't matter.
SA = 2(4·6 +5(4+6)) = 2(24 +5(10)) = 2(74) = 148 . . . . cm²
The surface area is 148 cm².
Let’s first identify what shapes we have on the surface of the prism.
We have three pairs congruent rectangles. Congruent means exactly the same in every measurement, so the rectangles parallel from each other are congruent. Now, we know we are dealing with rectangles.
Recall the area of a rectangle formula:
A=L•W
So, using the definition of surface area and our observations of pairs of congruent rectangles, we can form the following formula to calculate surface area:
SA=2(L•W)+2(b•h)+2(L•h)
Now, let’s plug in the values into the formula:
SA=2(6•4)+2(6•5)+2(4•5)
Now, let’s simply using PEMDAS:
- Simplify parentheses first:
SA=2(24)+2(30)+2(20)
- Multiply all terms:
SA=48+60+40
- Add the terms:
SA=148
Therefore, the answer is:
The surface area is 148cm²
Write the letter of the definition next to the matching word as you work through the
lesson.
Answers
Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.
What is Hypotenuse?In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.
According to question:Altitude: In a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.Geometric mean: for two positive numbers, a and b, the positive number x that satisfies a/x = x/b.Hypotenuse: The side of a right triangle that is opposite the right angle and is always the longest side of the triangle.Leg: In a right triangle, either of the two sides forming the right angle.One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.
The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.
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2. The area of the triangle is 21 in². What is the
ngth of the base?
7in.
Answers
The length of the base is 6 inches.
What is triangle?
A triangle is a three-sided polygon, which is a flat shape with straight sides. It is a basic shape in geometry and has many interesting properties that are useful in mathematics and other fields.
The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle.
In this case, we know that the area of the triangle is 21 in² and the height is 7 in. So we can substitute these values into the formula and solve for the base:
21 = 1/2 * b * 7
Multiplying both sides by 2:
42 = b * 7
Dividing both sides by 7:
6 = b
Therefore, the length of the base is 6 inches.
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Complete question : The area of the triangle is 21 in² ad the height is 7 in. what is the length of the base?
Adam is finding 10 less than 708 mentally. He thinks the tens digit and the hundreds digit will change. He gets 698 for his answer. Is Adam's thinking correct? Explain.
Answers
Answer:
Adam's thinking is not correct.
When subtracting 10 from 708, we need to borrow 1 from the hundreds digit and add it to the tens digit. This will result in a new hundreds digit of 6 and a new tens digit of 9. The ones digit remains the same. Therefore, the correct answer would be 698.
Adam's answer is also 698, but his reasoning is incorrect. He thinks that both the tens and hundreds digits change, which is not the case. In reality, only the tens digit changes while the hundreds digit decreases by 1 due to the borrowing process.
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The perimeter of a rectangle is 34 units. Its width is 6.5 units.
Write an equation to determine the length of the rectangle
Answers
Given:
P = 34 [Perimeter]
W = 6.5 {let's use W and L to make it easy to read]
Also known:
P = W + L + W + L = 2(W+L)
Fill in values:
34 = 2(6.5+L) [NOTE: This is an equation to determine the length (L) of the rectangle."]
17 = 6.5 + L [NOTE: This is a simplified form of the above equation.]
10.5 = L [NOTE: This is the solution (the value of L)]
THE ANSWER IS D. You are designing a new product that requires the use of a stable, nonreactive gas. Which gas would be most suitable? O A. Oxygen, 0 O B. Bromine, Br OC. Sulfur, S O D. Argon, Ar SUBMIT
Answers
Argon is the gas who would work best for something that needs a steady, nonreactive gas. (Ar).
What are the uses of argon?When a neutral environment is required, argon is frequently used. In this manner, titanium and other volatile metals are produced. Additionally, it is used in the manufacture of incandescent bulbs to prevent air from corroding their filaments and by welders to safeguard the weld region.
Argon is it a vapour or a metal?A chemical substance in the periodic table's 18th group is argon. It is an expensive gas and the third most common gas in the atmosphere of the planet. Aside from nitrogen and oxygen, argon is the most prevalent gas in the atmosphere.
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In a survey on supernatural experiences, 718 of 4,005 adult Americans surveyed reported that they had seen a ghost. Assume that this sample is representative of the population of adult Americans.
Answers
The survey results, it can be estimated that approximately 17.93% of adult Americans have seen a ghost at some point in their lives[tex] (718/4,005 = 0.1793)[/tex].
However, it is important to note that this estimate is based on a sample and there may be some degree of error or variability.
Additionally, the term "supernatural experiences" may encompass a wide range of phenomena beyond just seeing ghosts, so the estimate may not accurately reflect the prevalence of all types of supernatural experiences in the population.
In the given survey on supernatural experiences, 718 out of 4,005 adult Americans reported having seen a ghost. Assuming this sample is representative of the adult American population, you can calculate the proportion of adults who have seen a ghost.
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What is the tangent ratio for angle FFDF is 6DE is eight and EF is 10?
Answers
The tangent ratio for angle F is [tex]\frac{4}{3}[/tex] . The solution has been obtained by using trigonometry.
What is trigonometry?
In the area of mathematics known as trigonometry, right-angled triangles, including their sides, angles, and connections, are studied.
We are given a right angled triangle. The sides of the triangle are given as DF is 6, DE is 8 and EF is 10.
This means that the perpendicular is 8 and base is 6.
We know by trigonometry that tan θ is the ratio of triangle's perpendicular and base.
So, from this we get
⇒ tan F = [tex]\frac{8}{6}[/tex]
⇒ tan F = [tex]\frac{4}{3}[/tex]
Hence, the tangent ratio for angle F is [tex]\frac{4}{3}[/tex] .
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Question: What is the tangent ratio for angle F, if DF is 6, DE is 8 and EF is 10?
please please i’m begging someone help
Answers
Using ratios, we can find the average weight of the adult bear to be 250 pounds and the angles of the triangles are 10°, 75° and 95°.
What are ratios?Comparing two amounts of the same unit and calculating the ratio allows us to determine how much of one quantity is included in the other. Two categories of ratios exist. The part to whole ratio is one, and the part-to-part ratio is another. The part-to-part ratio illustrates the relationship between two separate entities or groupings.
In the question given,
Ratio between birth weight and adult weight of a bear is 3:1000.
The average birth weight as given here is = 12 ounces.
Now let the average adult weight be = x
According to the ratio,
12/x = 3/1000
⇒ 3x = 12000
⇒ x = 4000 ounces.
Now 16 ounces = 1 pounds
4000 ounces
= 4000/16
= 250 pounds.
The angles are in the ratio 2:15:19
Now we know all the angles sum up to 180°
Let the angle be = x.
The equation is as follows:
2x + 15x + 19x = 180
⇒ 36x = 180
⇒ x = 180/36
⇒ x = 5
So, all the angles of the triangles are, 10°, 75° and 95°.
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If
f
(
x
)
=
3
5
−
x
+
6
f(x)=3
5−x
+6, what is the value of
f(5), to the nearest tenth (if necessary)?
Answers
Answer:
the answer is f-1(x) = 5 - ln (x - 6)/ln (3) (I guess?)
Find a fraction that is equivalent to 5/7 and its denominator is 9 less than twice its numerator.
5/7=
Answers
The fraction that is equivalent to 5/7 is 15/21
How to determine the fraction?It is important to note that fractions are simply described as part of a whole number or element.
Also, equivalent expressions are defined as expressions that have the same solution but differ in the mode of arrangement of the values.
From the information given, we have;
The numerator be x
The denominator is 9 less than twice the numerator
This is represented as;
x/2x - 9 = 5/7
Cross multiply the values, we have;
7(x) = 5(2x - 9)
expand the bracket
7x = 10x - 45
collect the like terms, we have;
7x - 10x = -45
-3x = -45
Make 'x' the subject
x = 15
Then, the fraction = 15/21
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Find a1 in the geometric series Sn=3045, r=2/5, and an=120 Please help this is due at 11:59 pm TONIGHT! Remember to show work!
Answers
Answer:
a1 = 1875
Step-by-step explanation:
You want a1 for the geometric series that has r = 2/5, an = 120, and Sn = 3045.
Series relationsThe n-th term of the geometric series with first term a1 and common ratio r is ...
an = a1·r^(n-1)
The sum of the first n terms of the geometric series is ...
Sn = a1·(r^n -1)/(r -1)
ApplicationWe can use the expression for an to substitute for r^n in the sum equation:
[tex]a_n=a_1(r^n)(r^{-1})\\\\r^n=\dfrac{a_n}{a_1r^{-1}}=\dfrac{a_nr}{a_1}\\\\S_n=a_1\dfrac{r_n-1}{r-1}=a1\dfrac{\dfrac{a_nr}{a_1}-1}{r-1}\\\\S_n=\dfrac{a_nr-a_1}{r-1}\\\\a_1=a_nr-S_n(r-1)=a_nr+(1-r)S_n\\\\a_1=(120)\dfrac{2}{5}+(1-\dfrac{2}{5})(3045)=\dfrac{2\cdot120+3\cdot3045}{5}\\\\\boxed{a_1=1875}[/tex]
__
Additional comment
The sum is of the first four terms:
1875 +750 +300 +120 = 3045
We can also find this by working backward. The previous term is 5/2 times the current term. We need to find the terms that have a sum of 3045.
120 +300 +750 +1875 +4687.5 +...
Clearly, 5 terms is too many. The sum of the first 4 terms of the backward series is 3045, so we know n=4 and the first term is 1875—the last term of our 4-term backward series.
Benjamin invests money in a bank account which gathers compound interest each year. After 2years there is $658.20 in the account. After 5years there is $710.89 in the account. Work out the annual interest rate of the bank account. Give your answer as a percentage to 1 d.p.
Answers
The compound interest rate of the given information for which the annual rate of the bank account is = 3.9%.
What about compound interest?
Compound interest refers to the interest that is earned not only on the principal amount of a loan or investment but also on any interest that has been previously earned. In other words, it is the interest calculated on the initial principal and on the accumulated interest of previous periods. This compounding effect can result in significant growth over time, as the interest earned in each period is added to the principal, and the interest earned in subsequent periods is calculated on the new, larger principal amount. Compound interest is often used in long-term savings and investment accounts, such as retirement funds or fixed deposits, as it can result in a higher return than simple interest over time.
According to the given information:
In this case we know that;
⇒ A = [tex]P(1 + r)^n[/tex]
⇒ A = amount
⇒ P = principal
⇒ r = rate
⇒ n = number of years
⇒ 710.89 = 658.20[tex](1 + r)^2[/tex]
⇒ 710.89/658.20 = [tex](1 + r)^2[/tex]
⇒ 1.08 = [tex](1 + r)^2[/tex]
⇒ ln(1.08) =ln [tex](1 + r)^2[/tex]
⇒ 0.077 = 2ln[tex](1 + r)[/tex]
⇒ 0.077/2 = ln(1 + r)
⇒ ln[tex](1 + r)[/tex] = 0.0385
⇒ 1 + r = 1.039
⇒ r = 1.039 - 1
⇒ r = 0.039
⇒ r = 3.9%
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there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
Answers
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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Mar 09, 1:56:27 PM
In a certain Algebra 2 class of 28 students, 11 of them play basketball and 13 of them
play baseball. There are 11 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
Answer:
Submit Answer
attempt 1 out of
Answers
The probability of choosing a student who plays both basketball and baseball is approximately 0.4643.
What is probability?It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
According to question:We can use the inclusion-exclusion principle to find the number of students who play both basketball and baseball.
Number of students who play both = Number of basketball players + Number of baseball players - Number of students who play neither
= 11 + 13 - 11
= 13
Therefore, out of 28 students, 13 play both basketball and baseball.
The probability of choosing a student who plays both sports can be calculated as follows:
P(plays both) = Number of students who play both / Total number of students
= 13/28
= 0.4643 (rounded to 4 decimal places)
So the probability of choosing a student who plays both basketball and baseball is approximately 0.4643.
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There are 3 questions please try to show work
1.Batman started the month with $57 in his bank account and accidentally over spend his money, so he ended the month with -$42. How much money did Batman spend this month? Show all organized work.
2. Barbie a scuba diving. Her position changes from -2.1 m ti -38.6 m in 5 minutes.b what is the average change in barbies position each minute? Show all organize work.
3. Ms.Blue went on a diet. She stocked her meal plan and successfully lost 4 pounds every month what was the change in Ms.Blue’s weight after on year of dieting? (include the sign in your answer)
Answers
1. Batman spent $99 this month after starting with $57 and ending with a balance of -$42.
2. The average change in Barbie's position each minute in the scuba diving is -7.3 meters.
3. The change in Ms. Blue's weight after one year of dieting and losing 4 pounds monthly is -48 pounds.
How the values are determined:1) Batman's Bank Account:Initial balance in the bank account = $57
Final balance at month-end = $-42
The total amount spent = $99 ($57 + $42)
Thus, when $99 is taken away from $57, the balance is $-42.
2) Barbie's Scuba Diving:Initial position = -2.1 m
Final position = -38.6 m
Change in position = -36.5 m (-38.6 - -2.1)
The number of minutes used to change position = 5 minutes
The average change per minute = -7.3 m (-36.5 ÷ 5)
3) Ms. Blue's Weight Loss:The quantity of pounds lost per month = 4 pounds
The period of dieting = 1 year = 12 months
The total change in weight after one year of dieting = -48 pounds (-4 x 12)
Thus, these three problems are solved using mathematical operations.
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If 720,000 is the result when 7__1,846 is rounded to the nearest ten thousand, what could be the missing digit?
Answers
Answer: the missing digit would be 2
721,846 rounded to the nearest ten thousand is 720,000
A rental car cost $45 a day and $0.20 a mile. How many miles can you drive in one day on a budget
of $100
Set up your inequality
Answers
275 miles can be driven in one day on a budget of $100.
Definition of Inequalitiesan inequality is defines as a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on either sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The rental car costs $45 a day and $0.20 a mile. So, for a budget of $100, the inequalities can be written as
45+.20m≤ 100
Where m= no.of miles
No.of miles can be travelled in 100
.2m=100-45
m=55/.2
m=275miles
Hence,275 miles can be driven in one day on a budget of $100.
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100 points and brainliest
Find all the missing angles:
Answers
Answer:
<AOB = 112
<AOD = 68
<DOC = 112
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Solve the following quadratic by completing the square
f(x) = x^2 + 2x-12
Answers
The quadratic equation f(x) = x² + 2x - 12 can be rewritten as f(x) = (x + 1)²- 13 using the completing square method.
What is completing squares method?Completing the square is a strategy used in algebra to solve quadratic equations of the type ax² + bx + c = 0, where a, b, and c are constants and x is the variable. By converting the quadratic equation into a perfect square trinomial, the square roots of both sides of the equation may be used to quickly solve the problem. This is the core notion behind the completion of the square. The quadratic expression becomes a perfect square when we add and subtract a specific number from it to complete the square. Half of the x-term squared coefficient is equal to the sum of the numbers we add and remove.
The given function is f(x) = x² + 2x-12.
Now, group the x terms together:
f(x) = (x² + 2x) - 12
Between the parenthesis, add and remove the square of the x-half-coefficient: term's:
f(x) = (x² + 2x + (2/2)² - (2/2)²) - 12
f(x) = (x + 1)² - 1 - 12
f(x) = (x + 1)² - 13
Hence, the quadratic equation f(x) = x² + 2x - 12 can be rewritten as f(x) = (x + 1)² - 13.
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Quelle est l’explication de la puissance de 10
Answers
Answer:
Step-by-step explanation:
Lorsque l'exposant (a) est positif, alors la puissance de dix 10a correspond au nombre 1 suivi d'un nombre de zéros correspondant au chiffre a. Quelques exemples : 103 correspond au nombre 1 suivi de 3 zéros donc 103 = 1 000.