Solve for x. 6/-4.5=8/4x
Answer: x = -3/2 , x = -1 1/2 , x = -1.5
Step-by-step explanation:
6/-4.5 = 8/4x
first determine the defined range --> x ≠ 0
cancel out the common factor 4 --> 6/-4.5 = 2/x
the convert the decimal into a fraction --> 6/-9/2 = 2/x
now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x
then simplify the complex fraction --> -4/3 = 2/x
simplify the equation using cross-multiplication --> -4x=6
divide both side of the equation by -4 --> x = -3/2 , x ≠ 0
lastly, check if the solution is in the defined range --> x = -3/2
solution : x = -3/2
Alternative form: x = -1 1/2 , x = -1.5 (simplified)
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 101° is added to the data, how does the mean change?
For the given scenario the mean changes from 80.42 to 82.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Given that, the average high temperatures in degrees for a city are 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57.
Now, average = (58+61+71+77+91+100+105+102+95+82+66+57)/12
= 965/12
= 80.42
If a value of 101° is added to the data, then the new average is
(965+101)/(12+1)
= 1066/13
= 82
Therefore, for the given scenario the mean changes from 80.42 to 82.
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Identify the missing species in each nuclear equation
the missing species in each nuclear equation are:
1. ¹⁰₄Be ---> ¹⁰₅B + ⁰₋₁β
2. ³⁴₁₄Be ---> ³⁴₁₅P + ⁰₋₁β
3. ¹⁹²₇₈Pt -----> ¹⁹⁰₇₆Os + ⁴₂α
4. ²⁸₁₂Mg ---> ²⁸₁₃Al + ⁰₋₁β
What is the nuclear equation?Nuclear equations represent the reactants and products in radioactive decay, nuclear fission, or nuclear fusion. Instead of chemical equations where it shows the different number of elements are conserved in a reaction, in a nuclear reaction the atomic mass and proton number are conserved.
1. In the first equation, the Beryllium-10 isotope undergoes beta decay, emitting a beta-particle to form the boron-10 isotope. The balanced nuclear equation is given below:
¹⁰₄Be ---> ¹⁰₅B + ⁰₋₁β
2. In this reaction, the silicon-34 isotope undergoes beta decay, emitting a beta-particle to form the phosphorus-34 isotope. The balanced nuclear equation is given below:
³⁴₁₄Be ---> ³⁴₁₅P + ⁰₋₁β
3. In this equation, the platinum-192 isotope undergoes alpha-particle decay emitting an alpha-particle to form the osmium-190 isotope. The balanced nuclear equation is given below:
¹⁹²₇₈Pt -----> ¹⁹⁰₇₆Os + ⁴₂α
4. In this equation, the magnesium-28 isotope undergoes beta decay, emitting a beta-particle to form the aluminum-28 isotope. The balanced nuclear equation is given below:
²⁸₁₂Mg ---> ²⁸₁₃Al + ⁰₋₁β
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A recipe for stir fry calls for 7 cups of rice for every 4 cups of veggies. Suppose a restaurant is making a large batch of stir fry using 20 cups of veggies. How much rice would they need?
Please helllppp
Answer:
They would need 35 cups of rice.
Step-by-step explanation:
4 x 5 = 20
7 x 5 = 35
Let x represent the number of water bottles and y represent
the number of pairs of socks that Malia buys.
Use the graph to determine if Malia can buy 75 water bottles
and 100 pairs of socks. Explain.
Malia can't buy 75 water bottles and 100 pairs of socks because it is not a solution to the system.
Can Malia buy 75 water bottles and 100 pairs of socks?Here we have a graph of inequalities, and we just need to see if the pair (75, 100) is a solution.
The solutions of the system are all the points in the intersection of the two shaded areas (in this case are all the points in the green area)
Now, clearly the point (75, 100) is not a solution
Even if you evaluate that in the first inequality:
x + y ≥ 200
we get:
75 + 100 ≥ 200
175 ≥ 200
which is false.
So no, Malia can't buy 75 water bottles and 100 pairs of socks.
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Prove that cosec (A+B) = sinA cosB - cosA sinB ÷ ( sinA + sinB ) ( sinA - sinB )
The formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) can be proven using the trigonometric identities.
How to prove this?Starting with the definition of cosecant:
cosec (A + B) = 1/sin (A + B)
Using the sum-to-product identity:
sin (A + B) = sinA cosB + cosA sinB
Substituting this expression into the definition of cosecant:
cosec (A + B) = 1 / (sinA cosB + cosA sinB)
Using the difference-to-product identity:
sinA - sinB = 2sin((A - B)/2)cos((A + B)/2)
Dividing both numerator and denominator by 2sin((A - B)/2)cos((A + B)/2), we get:
cosec (A + B) = (sinA cosB - cosA sinB) ÷ (sinA + sinB)(sinA - sinB)
Therefore, the formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) has been proven.
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Consider this right triangle.
Enter the measure of ZM to the nearest degree.
Answer:
21°
Step-by-step explanation:
For this right-angled triangle:
∠M = angle in question
Side LM = Hypotenuse
With respect to ∠M:
Side LN = Opposite side
Side MN = Adjacent side
Trigonometric function applied:
sin∠M = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{8}{22}[/tex]
∠M = [tex]sin^{-1} (\frac{8}{22})[/tex]
= 21.32°
∠M = 21° (Rounded to the nearest degree)
Answer:
∠M = 21°
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
The angle to be found is M ⇒ θ = MThe side opposite ∠M is LN ⇒ O = 8The hypotenuse is LM ⇒ H = 22Therefore, substitute the given values into the sine ratio and solve for ∠M:
[tex]\implies \sin(M)=\dfrac{8}{22}[/tex]
[tex]\implies M=\arcsin \left(\dfrac{8}{22}\right)[/tex]
[tex]\implies M=21.323686...^{\circ}[/tex]
[tex]\implies M=21^{\circ}\sf\;(nearest\;degree)[/tex]
Therefore, the measure of ∠M to the nearest degree is 21°.
Elizabeth has 10 mangoes eats 5 and gives 2 to Mary and throws 1 away how many mangoes are left
Answer:
2
Step-by-step explanation:
mangoes left=10-5-2-1=2
You are thinking of combining Designer Whey and Muscle Milk to obtain a 7-day supply that provides exactly 412 grams of protein and 108 grams of carbohydrates. How many servings of each supplement should you combine in order to meet your requirements?
Answer: Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk.
We know that:
x + y = 7 (because you want 7 days of supply)
And the protein content per serving of Designer Whey is 18g and the protein content per serving of Muscle Milk is 20g. So:
18x + 20y = 412 (because you want 412g of protein)
And the carbohydrate content per serving of Designer Whey is 4g and the carbohydrate content per serving of Muscle Milk is 8g. So:
4x + 8y = 108 (because you want 108g of carbohydrates)
We can now use the above two equations to solve for x and y. We'll start by solving for x in terms of y:
18x + 20y = 412
18x = 412 - 20y
x = (412 - 20y)/18
Now we can substitute this expression for x into the equation for the carbohydrates:
4x + 8y = 108
4((412 - 20y)/18) + 8y = 108
1664 - 80y + 8y = 1080
1664 = 1080 + 80y
584 = 80y
y = 7.3
Since y must be an integer, we'll round it down to 7. So y = 7. We can now use either equation to find x:
18x + 20y = 412
18x + 20 * 7 = 412
18x = 412 - 140
18x = 272
x = 15.1
Since x must be an integer, we'll round it up to 15. So x = 15.
Therefore, you should combine 15 servings of Designer Whey and 7 servings of Muscle Milk in order to meet your requirements.
Step-by-step explanation:
Express tan L as a fraction in simplest terms.
Answer:
Step-by-step explanation:
tan L = 8/15
Add write each sum in simplest form 5/12+1/4
Before solving for fractions, you must know what you're doing. This will list information you should know to solve fraction problems.
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters
Step by Step Answer Explanation[tex]\frac{5}{12} + \frac{1}{4}[/tex] is our equation, so let's solve this step by step,
Common Denominator
As you can see, the fractions have unlike denominators. An unlike denominator is when 2 or more fractions have different denominators. One of our denominators is 12 and the other is 4, so this shows we have unlike denominators. The way we get the denominators to be the same is multiplying. Its a quicker method to easily make them the same. We can also skip count until the numbers meet:
12: 12,
4: 4, 8, 12
The fraction denominator can be 12. We can also prove that it is 12 by showing the Least Common Denominator, or LCD. LCD (5/12, 1/4) = 12.
[tex]\frac{5}{12}[/tex] × [tex]\frac{1}{1}[/tex] = [tex]\frac{5}{12}[/tex] . We multiply this by [tex]\frac{1}{1}[/tex] because the denominator is already 12.
[tex]\frac{1}{4}[/tex] × [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{12}[/tex]. We multiply this by [tex]\frac{3}{3}[/tex] so we can make the denominator 12.
Adding the fractions
Now that we have our equation, [tex]\frac{5}{12}[/tex] + [tex]\frac{3}{12}[/tex], we can easily add the fractions.
We do not add the denominators, however, we do add the numerators. We can express this as [tex]\frac{5+3}{12}[/tex]. 5 + 3 = 8. So, the numerator is 8. This means our answer is [tex]\frac{8}{12}[/tex].
Reduce
As your question says the sum must be in simplest form, you must reduce the answer to get it in simplest form. To reduce, you must divide. [tex]\frac{8}{12}[/tex] can be reduced, or divided by 4 to get it to simplest form. [tex]\frac{8}{12}[/tex] ÷ [tex]\frac{4}{4}[/tex] = [tex]\frac{2}{3}[/tex].
Answer
Simplest form: [tex]\frac{2}{3}[/tex]
Not in its simplest form: [tex]\frac{8}{12}[/tex]
) The ratio of boys to girls on a softball team was 5:3. For every 35 girls how many ratio of boys will be there?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
If the ratio is 5: 3, (girls: boys) we can use this equation to figure out how many boys there are if there are 35 girls:
35 × 0.6 = 21Why do we multiply by 0.6?We can see that in the ratio 5: 3, 5 is being multiplied by 0.6 to get three. If the relationship between the numbers 5 and 35 stays proportional, we multiply 35 by 0.6.
Therefore, the ratio of girls to boys is 35: 21, meaning there are 21 boys.
Weights of newborn babies were gathered for a study last month at the local hospital. What is the level of measurement of the data?
The level of scale of measurements is the ratio scale for the data of the average weight of newborn babies in ounces.
What is level of Measurement of data?A ratio scale is a numerical scale with a genuine zero and uniform distances between adjacent points. A zero on a ratio scale, in contrast to an interval scale, indicates complete lack of the variable being measured. Examples of ratio scales include length, area, and population.
As, There are four scales of measurement: Nominal, Ordinal, Interval, and Ratio.
First, The categories in this scale are given names, hence the label "nominal." There is no innate hierarchy among the categories. Simply said, it is impossible to say that one category is superior to or better than another.
Ordinal scale: It is possible to rationally organise the various categories in a meaningful order. The distinction between the categories is not "meaningful," nevertheless.
Interval scale: Doubling has no significance, but values (not categories) can be arranged and have substantial differences. The lack of a "absolute zero" is the reason of this.
Scale of ratios: The values can be arranged in a way that makes a meaningful difference, and doubling also makes a difference. "Absolute zero" exists.
As a result, the ratio scale for the level of measurements is used to determine the average weight of newborn babies.
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y=30x+b what is b in this equation
solve the following inequality and graph the solution:
The solution will lie on the number line from (-∞ , 0)
An inequality is the representation of an algebraic statement with two non-equal values. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.
How is an inequality to be corrected?One of the following options is available for resolving an inequality: Add the same amount to each side, deduct the same amount from each side, multiply each side by the same positive number, or split each side in half. If you multiply or divide each side by a negative value, the inequality sign must be reversed.
Given,
(x-0)(x-6)<0
⇒ x < 0 and x < 6
the solution will lie on the number line from -∞ to 0.
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The linear system L has augmented matrix which is row equivalent to the following matrix. How many solutions does L have? 1 0 0 0 -1 0 1 0 0 -2 0 0 1 01-3 0 0 0 1-4 0 0 0 0 0 One. There is a unique solution. There is not enough information to determine how many solutions Lhas. Zero, the system is inconsistent Infinitely many solutions.
the system is inconsistent Infinitely many solutions.
What is matrix?
The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A' stands for "matrix," Aij.
The given matrix is [tex]\left[\begin{array}{ccccc}1&0&0&0&0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\\0&0&0&0&0\end{array}\right][/tex]
This is a linearly dependent matrix a row is 0.
Hence, the system is inconsistent Infinitely many solutions.
Hence the element s₂₃ of the given matrix is -2
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Hector manages Food Plaza, a small grocery store. Based on the previous year's sales data, he estimates that Food Plaza can sell
a = -2000p + 7540 lemons this year, where p is the price of a single lemon and a is the total amount of lemons sold at price p.
Walt supplies Food Plaza with all the fruits and vegetables they sell. Walt can sell Hector at most 5000 lemons in a single year.
If Food Plaza pays Walt $1.60 per lemon on average, how many lemons should Hector buy from Walt in order to maximize the
store's profit?
To maximize the store's profit, Hector should aim to sell as many lemons as possible while paying the lowest price possible for them. Since Hector estimates that he can sell a maximum of -2000p + 7540 lemons at price p, and Walt can supply at most 5000 lemons, Hector should buy all of the 5000 lemons from Walt.
To determine the price at which Hector should buy the lemons from Walt, we need to consider the average cost of the lemons. If Hector buys 5000 lemons at $1.60 per lemon, he will spend a total of 5000 x $1.60 = $8000 on lemons.
If he sells all 5000 lemons at the price p, his revenue will be (-2000p + 7540) x 5000 = -10,000,000p + 37,700,000.
His profit will be the difference between revenue and cost, which is given by:
Profit = -10,000,000p + 37,700,000 - $8000
To maximize profit, we need to take the derivative of the profit function with respect to p and set it equal to zero:
dProfit/dp = -10,000,000 = 0
Solving for p, we get:
p = $1.00
Therefore, Hector should buy 5000 lemons from Walt at $1.00 per lemon to maximize the store's profit.
Which multiplication equation best represents the figure?
The multiplication equation best represents the figure will be 6 x 0.32 = 1.92. Then the correct option is B.
What is Algebra?Algebra is the examination of ideational signs while reasoning the manipulation of all those thoughts.
The big square block represents the 1 unit. And each small block represents 0.01 units.
The number of small blocks which are marked by the color in one shot is 32 which means 0.32 units.
And these processes are done six times, then the expression that represents the condition is given as,
6 x 0.32 = 1.92
The multiplication equation best represents the figure will be 6 x 0.32 = 1.92. Then the correct option is B.
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into 12 squares. Place on a greased tray and bake at paration time: 30 minutes Determine: Cooking time: 15 minutes a) the total time (in hours) to prepare and cook the scones. b) the number of me all-purpose flour needed to bake 36 scones. c) The thickness of the dough in centimetres. Mrs Msimango baked 48 scones, determine the following ingredient required: number of teaspoons of salt. ml of butter. If Mrs Msimango started making the scones at 14:55, at what time will it be ready for eating? a) b) Express the baking temperature of 356 °F in °C Use the formula: °C (°F-32°) ÷ 1,8 ΤΟΥ
a) The total time taken in hours is 0.75 hours
b) The amount of all-purpose flour needed is not given in the question.
c) The thickness of the dough in centimetres is not given.
d) The amount of salt needed per scone is not given.
e) The amount of butter needed per scone is not given.
f) It will be ready for consumption by 15:30
g) 356°F in °C can be calculated using the formula:
°C = (356°F - 32°) / 1.8 = 180°C.
Step by step explanationa) Total preparation and cooking time = 30 minutes + 15 minutes = 45 minutes = 0.75 hours
b) To bake 36 scones, we need:
36 scones * all-purpose flour needed to bake 1 scone = all-purpose flour needed to bake 36 scones
The amount of all-purpose flour needed is not given.
c) The thickness of the dough in centimetres is not given.
d) Mrs. Msimango baked 48 scones, so the number of teaspoons of salt required would be:
48 scones * teaspoons of salt needed per scone = teaspoons of salt needed for 48 scones
The amount of salt needed per scone is not given.
e) Mrs. Msimango baked 48 scones, so the number of millilitres of butter required would be:
48 scones * ml of butter needed per scone = ml of butter needed for 48 scones
The amount of butter needed per scone is not given.
f) If Mrs. Msimango started making the scones at 14:55, they would be ready to eat at 14:55 + 0.75 hours = 15:30.
g) 356°F in °C can be calculated using the formula:
°C = (356°F - 32°) / 1.8 = 180°C
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If you collect 100 heights from around your school to get an average of 60.5
inches and you estimate that the population standard deviation is 5, what is your
confidence interval and margin of error (with a 95% level of confidence)?
A. Confidence interval: 60 to 61; margin of error: ± 0.5
B. Confidence interval: 59.5 to 61.5; margin of error: ± 1.0
C. Confidence interval: 59 to 62; margin of error: ± 1.5
D. Confidence interval: 58 to 63; margin of error: ± 1.0
The confidence interval: 59.5 to 61.5; margin of error: ± 1.0. Option B is the correct answer.
What is confidence interval?The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.
The confidence interval is given as:
x' ± 1.96 s/√n
Substituting the value of x' = 60.5, s = 5, and n = 100.
60.5 ± 1.96 (5/ √√100)
60.5 ± 1.96 (5/10)
60.5 ± 0.98
Hence, the confidence interval: 59.5 to 61.5; margin of error: ± 1.0. Option B is the correct answer.
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PLEASE HELP ME!
Anna is considering writing and publishing her own book She estimates her revenue equation as R = 6.56x and her cost equation as C = 10.063 + 1.09x where x is the number of books she sells. Find the minimum number of books she must sell to make a profit
Anna must sell atleast ? books to make a profit.
Step-by-step explanation:
In order to make a profit R > C
So let's make those equal first
R = C
[tex]6.56x = 10.063 + 1.09x[/tex]
Let's get X alone by subtracting 1.09x from both sides.
[tex]5.47x = 10.063[/tex]
Next we divide by 5.47
[tex]x = 1.83[/tex]
Rounding up to 2, looks like Anna needs to only sell 2 books to start making a profit
Please help due tonight
The missing side lengths are given as follows:
y = 6.93.x = 13.86.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.Considering the tangent of 30º, we can obtain the length y, as follows:
tan(30º) = y/12
y = 12 x tangent of 30 degrees
y = 6.93.
Applying the Pythagorean Theorem, we can obtain the length x, as follows:
x² = 6.93² + 12²
x = sqrt(6.93² + 12²)
x = 13.86.
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Anni traveled 2/7 of her trip in the first hour, and then 1/8 of her trip in the second hour. She plans to rest when she has completed half of her trip. What part of the trip does Annie still need to travel before she reaches her destination.
pleaseee i really need help with this
here is the picture
Find the difference in value between five in 14532 and five in 12754.
16=k/11
if you can please use this technic
I know its not many points but I need this,
thank you
Answer:
k = 176
Step-by-step explanation:
16 = k/11
16 * 11 = k/11 * 11
176 = k
Because k is being divided by 11 on the right-hand side of the equation, we would need to multiply both sides by 11 to undo the division operation done to k so we can isolate it.
Enlarge shape A by scale factor 2 with centre of enlargement (1, 5)
The coordinates of the vertices of the image include the following: (-1, 3), (-1, -1), (5, -1), and (7, 3).
How to enlarge shape A by a scale factor of 2?In this exercise, we would have to dilate (enlarge) the coordinates of the pre-image by using a scale factor of 2 centered at the point (1, 5) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate 1, we have;
Coordinate 1 = (2, 4) → (2(2 - 1) + 1, 2(4 - 5) + 5)
Coordinate 1 = (2, 4) → (2(-1) + 1, 2(-1) + 5)
Coordinate 1' = (-1, 3).
For coordinate 2, we have;
Coordinate 2 = (2, 2) → (2(2 - 1) + 1, 2(2 - 5) + 5)
Coordinate 2 = (2, 2) → (2(-1) + 1, 2(-3) + 5)
Coordinate 2' = (-1, -1).
For coordinate 3, we have;
Coordinate 3 = (3, 2) → (2(3 - 1) + 1, 2(2 - 5) + 5)
Coordinate 3 = (3, 2) → (2(2) + 1, 2(-3) + 5)
Coordinate 3' = (5, -1).
For coordinate 4, we have;
Coordinate 1 = (4, 4) → (2(4 - 1) + 1, 2(4 - 5) + 5)
Coordinate 1 = (4, 4) → (2(3) + 1, 2(-1) + 5)
Coordinate 1' = (7, 3).
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Solve the formula for the variable h.
F= 4gh
Answer:
h = F/4g
Step-by-step explanation:
Cand I get the answer to “Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3/4x + 1/3 = 1/2x +5”
Answer:
12
Step-by-step explanation:
6 - 3/4x + 1/3 = 1/2x + 5
6 - 9/12x + 4/12 = 6/12x + 5 If I multiply all the way through by 12 I will eliminate the fraction
72 - 9x + 4 = 6x+ 60
Help pls I need this quick thx :D
Only Euna successfully constructed an equilateral triangle inscribed in a a circle.
What is equilateral triangle?An equilateral triangle's sides are congruent, which indicates that they are all the same length. The inner angles are all equal (60°), as well. Equilateral is a compound word made up of the words "equi," which means equal, and "lateral," which means side. Thus, an equilateral triangle is one that has three sides of equal length. An equilateral triangle in geometry is a triangle whose three sides are equal in length. An equilateral triangle is also equiangular in the conventional Euclidean geometry, meaning that each of the three internal angles is 60 degrees and that all three are congruent with one another.
So, Euna successfully constructed an equilateral triangle inscribed in a a circle.
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