Answers
Answer:
x = 46.2 (nearest tenth)KN = 34.5 (nearest tenth)KL = 41.1 (nearest tenth)x = 15.7 (nearest tenth)Step-by-step explanation:
To find the missing side lengths in the given right triangles, use trigonometric ratios.
[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 first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.
θ = 18°O = 15A = xTherefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:
[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]
[tex]\implies x\tan 18^{\circ}=15[/tex]
[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]
[tex]\implies x=46.165253...[/tex]
[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]
----------------------------------------------------------------------------------------
Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.
Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.
As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.
As KL is parallel to NM, then m∠K = 90°. Therefore, m∠KLN = 40°.
(Refer to the attached diagram).
For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:
[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]
[tex]\implies LN=45\tan 50^{\circ}[/tex]
LN is the hypotenuse of right triangle KLN.
If we use ∠KNL as θ, then side KN is adjacent to the angle.
Therefore, to find the KN use the cosine ratio:
[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]
[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]
[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]
[tex]\implies KN=34.471999...[/tex]
[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]
As KL is the side opposite ∠KNL, to find KL use the sine ratio:
[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]
[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]
[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]
[tex]\implies KL=41.0821297...[/tex]
[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]
----------------------------------------------------------------------------------------
From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.
θ = 70°A = xH = 46Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:
[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]
[tex]\implies x=46\cos 70^{\circ}[/tex]
[tex]\implies x=15.732926...[/tex]
[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]
Related Questions
I need a little help
Answers
Answer:
y=-2x+1
Explanation:
you can see that the x goes up by 1 every time. Y goes down by 2 every time, because 1-2=-1, -1-2=-3, etc. So the -2 goes in your m part of y=mx+b. Then you need to figure out what y is when x is 0, for your y-intercept, or your b part of y=mx+b. The picture makes it simpler, showing that when x is 0, y is 1. Therefore, 1 is your b part of y=mx+b. If you put it all together, it looks like this:
Y=-2x+1
Step-by-step explanation:
It looks Iike the equation is in slope intercept form
[tex]y = mx + b[/tex]
m is the slope
b is the y intercept
Finding B is easy, it's just where X = 0. On this table, Y is 1 when X is 0.
Finding the slope. We'll take two different (X,Y) coordinates. Let's do the first two rows (0,1) and (1,-1)
Next we apply the slope formula. That being
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
So plugging that in
[tex] = \frac{ - 1 - 1}{1 - 0} [/tex]
That gives you -2/1, also known as -2
Now that we have everything, we can put the forumla together
[tex]y = - 2x + 1[/tex]
Where -2 is the answer that belongs in the [?]
what is 3422.4 divided by 544
Answers
6.29117647059
This is the answer
Answer: 6.29117647059
Step-by-step explanation:
divide the problem :)
(6 + 12.5a) − (8 + 2.9a)
0.96a + (−14)
9.6a + (−2)
15.4a + (−2)
15.4a + (−14) PLS HELP
Answers
Answer:
9.6a + (-2)
Step-by-step explanation:
(6 + 12.5a) - (8 + 2.9a) Distribute the negative sign
6 + 12.5a - 8 - 2.9a Combine like terms
12.5a - 2.9a +6 - 8
9.6a + (-2)
A paperweight, the shape of a hemisphere, fits snugly inside a cylinder-shaped box with a radius of 9 cm. A cone fits snugly inside the paperweight hemisphere.
What is the volume of the cylinder in terms of
? Show all work.
What is the volume of the cone in terms of
? Show all work.
Estimate the volume of the hemisphere in terms of
by calculating the average of the volumes of the cylinder and cone. Show all work.
Answers
(a).The volume of the cylinder is 216π [tex]cm^{3}[/tex]
(b). The volume of the cone is 72π [tex]cm^{3}[/tex]
(c). The volume of the hemisphere is 144π [tex]cm^{3}[/tex]
(a). Volume of the cylinder:
The volume of the cylinder is 216π [tex]cm^{3}[/tex]
Since the hemisphere fits snugly inside the cylinder, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.
So, the volume of the cylinder V = [tex]\pi r^{2} h[/tex] where
r = radius of cylinder = 6 cm and
h = height of cylinder = radius of hemisphere = 6 cm
So, V = [tex]\pi r^{2} h[/tex]
=[tex]\pi r^{2}[/tex]× r
=[tex]\pi r^{3}[/tex]
= π(6 cm)³
= 216π [tex]cm^{3}[/tex]
So, the volume of the cylinder is 216π [tex]cm^{3}[/tex]
(b). Volume of the cone
The volume of the cone is 72π [tex]cm^{3}[/tex]
Since the cone fits snugly inside the same hemisphere, the radius and height of the cone equals the radius of the hemisphere.
So, the volume of the cone V' = [tex]\frac{\pi r^{2} h}{3}[/tex] where
r = radius of cone = 6 cm and
h = height of cone = radius of hemisphere = 6 cm
So, V' = [tex]\frac{\pi r^{2} h}{3}[/tex]
= [tex]\frac{\pi r^{2} *r}{3}[/tex]
= [tex]\frac{\pi r^{3} }{3}[/tex]
=[tex]\frac{ \pi(6 cm)^{3} }{3}[/tex]
[tex]= \frac{216 \pi}{3}cm^{3} = 72 \pi cm^{3}[/tex]
So, the volume of the cone is 72π [tex]cm^{3}[/tex]
(C). Volume of hemisphere
The volume of the hemisphere is 144π cm³
Since the volume of hemisphere, V" equals the averages of the volume of the cylinder, V and volume of the cone, V'
So, V" =[tex]\frac{ (V + V')}{2}[/tex]
V" =[tex]\frac{ (216\pi cm^{3} + 72\pi cm^{3})}{2}[/tex]
V" = [tex]\frac{288\pi cm^{3} }{2}[/tex]
V" = 144π [tex]cm^{3}[/tex]
So, the volume of the hemisphere is 144π [tex]cm^{3}[/tex].
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Find the value of the expression
s+2/5
for s = 8 .
Write your answer as a fraction or as a whole or mixed number.
Answers
8+2/5= we will multiply 8 with 5 and plus2
8•5+2= 42/5
The answer is 42/5 but for further simplification 42/5= 8.4
IT NOT EIGHT
Factor 56−16 using the GCF.
56−16=
Answers
Answer:
It should be 8...
Step-by-step explanation:
16 / 8 = 2 and there is no higher number 16 that can be divided by. 56 is dividable by 8 so it makes sense.
Also 56 isn't dividable by 16
2 A recipe uses 150 g butter, 500 g flour, 50 g su make 18 cakes. How much of each ingredient will be needed to make 72 cakes?
Answers
Answer:
600g Butter, 2000g Flour, 200g Sugar
Step-by-step explanation:
First we divide the final number of cakes by the initial
[tex]72 \div 18 = 4[/tex]
Then we multiply each of the ingredients by 4
[tex]150 \times 4 = 600[/tex]
[tex]500 \times 4 = 2000[/tex]
[tex]50 \times 4 = 200[/tex]
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.
The ratio for this problem is:
(Ingredients: number of cakes)
150, 500, 50: 18Therefore, we need to know how many times 18 can fit into 72.
72 ÷ 18 = 4Now, if we know that 18 can be multiplied by 4 to get 72, we need to multiply all of the ingredients by 4.
150 × 4 = 600 (butter)500 × 4 = 2000 (flour)50 × 4 = 200 (sugar)Therefore, if the recipe stays proportional, we will need 600g butter, 200g flour and 200g sugar to make 72 cakes.
What is the x-value of the solution to the system of equations shown
below?
-3
-1
1
3
Answers
Answer:
-3
Step-by-step explanation:
you can use elimination to remove y from this equation
your first equation will be
4x+10y=-2; and you can multiply the other one by -10
30x-10y=-100
if you add the two equations, 10y and -10y will cancel out and you'll get
34x = -102
divide both sides by 34
x=-3
****
Identify the transformations that have been applied to the parent function
y=-1/(x-3)²-5.
Select all that apply.
Oshift 3 to the left
stretch
reflection over the x-axis
Oshift 5 up
Oshift 3 to the right
Oshift 5 down
O compression
Answers
Answer:
Step-by-step explanation:
The transformations that have been applied to the parent function y = 1/x^2 are:
shift 3 units to the right
shift 5 units down
reflection over the x-axis
So the correct options are:
shift 3 to the right
shift 5 down
reflection over the x-axis
On Monday, 5 painters took 7 hours and 36 minutes to paint an office.
On Tuesday, 8 painters are painting another office the same size.
a) Assuming the painters work at the same rate, how long will it take 8 painters to paint the office?
Give your answer in hours and minutes.
Answers
The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.
How to calculate working time for a certain number of workers?On Monday, 5 painters took 7 hours and 36 minutes to paint an office.On Tuesday, 8 painters are painting another office with the same size.If the they work at the same rate, find the time needed for the 8 painters to finish their job!
Let's say
w = number of workerst = time durationWe convert the unit of time in hours.
t₁ = 7 h 36 min
t₁ = (7 + 36/60) h
t₁ = (7 + 0.6) h
t₁ = 7.6 hours
If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,
w₁/w₂ = t₁/t₂
5/8 = 7.6/t₂
t₂ = 8/5 × 7.6
t₂ = 12.16 hours
In hours and minutes,
t₂ = 12 h + (0.16 × 60) min
t₂ = 12 h 9.6 min
Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.
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10. MGSE8.F.2, MGSE8.EE.5, MGSE8.F.3: A reporter collected data on y, the depreciation of a certain
car for various years, x, after it had been purchased new. The equation below was fit to the data.
y = 16,500 -1,500x
Part D Generate a table to show the depreciation over time show all your work
Answers
The table to show the depreciation over time for the first three years is:
Year (x) Depreciation (y)
1 $15,000
2 $13,500
3 $12,000
How to calculate the valueIt should be noted that in order to generate a table to show the depreciation over time for the first three years, we can use the given equation:
y = 16,500 - 1,500x
where y is the depreciation and x is the number of years since the car was purchased new.
Substituting x = 1, 2, and 3 into the equation, we get:
When x = 1, y = 16,500 - 1,500(1) = 15,000
When x = 2, y = 16,500 - 1,500(2) = 13,500
When x = 3, y = 16,500 - 1,500(3) = 12,000
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how many different ways are there to create a four-digit even number?
A. 2,000
B. 3,645
C. 4,500
D. 10,000
Answers
Explanation:-
There are ten numbers 0,1,2,3,4,5,6,7,8,9
So 10^4 = 10,000
What's the code and how do i solve this?
Answers
The code of the puzzle is 75.5 which is the sum of all the sides of the missing triangles.
What are Pythagorean Triples?Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as, a² + b² = c², where a, b, and c are positive integers.
1.
Substitute the known values in the Pythagorean theorem formula, and solve for a:
a² + 8² = 12²
a² + 64 = 144
a² = 144 - 64
a² = 80
a = √80
a = 8.9
Similarly, solve the length of the missing side of the other triangles.
2. The missing side b = 14.5
3. The missing side c = 10.3
4. The missing side a = 18.8
5. The missing side b = 8
6. The missing side c = 15
Now, the sum of all the sides of the missing triangles as:
8.9 + 14.5 + 10.3 + 18.8 + 8 + 15 = 75.5
Thus, the code of the puzzle is 75.5.
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Find a possible formula for the trigonometric function whose values are in the following table .
Answers
A possible formula for the trigonometric function whose values are in the given table is u(x) = 3cos(πx/2)
What is the possible formula for the trigonometric function whose values are in the following table? .From the table, it is clear that the function has a period of 4 and its maximum value is 6 and minimum value is 0. These observations suggest that the function is a cosine function.The period of cosine function is 2π, so we need to find a constant that will make the period of the function 4, which is half of the period of cosine function. This constant is π/2.The amplitude of the function is 3, which is the difference between its maximum and minimum values. The amplitude of cosine function is 1, so we need to multiply the cosine function by 3 to get the correct amplitude.Putting these together, we get the formula:u(x) = 3cos(πx/2)To learn more about trigonometric function refer:
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Determine the value of x in the equation
5/7 x ( x + 2 ) - ( 3/7x ) = 2/7 x ( x + 5 )
A) Infinite solutions
B) No solution
C) x = 1
D) x = 3
Answers
Answer: x to the power of 0 is 1.
According to the zero property of exponents, any number other than 0 raised to the power of zero is always equal to 1.
H
Ex5: Solve for x.(1pt)
D
50°
8.x + 2
F
Em
Answers
So, on solving the provided question, we can say that the equation, we have been provided with is x = 48
Equation: What is it?The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.
A mathematical formula explains the connection between the two sentences on either side of a letter. There is typically just one variable, which also acts as the symbol. As an illustration, 2x - 4 = 2.
the equation, we have been provided with is
x + 2 = 50
x = 50-2
x = 48
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I need help with this question ASP
Answers
The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
In the given box it is given sides are 2, 3 and 4 ft.
So the volume of the rectangular prism is V = 2*3*4 = 24 ft².
So the greater surface area in the given description is 6ft, 2ft and 2ft.
Where the surface area will be 12ft ²
Hence The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.
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Given two vertices and the centroid of a triangle , how many possible locations are there for the third vertex?
Answers
Answer:i don't realy now so 5 point 3
Dr. Powell is a veterinarian. He gave Ruby, one of the cats he is treating, 40 micrograms of
medication. Based on Ruby's size, Dr. Powell expects there will be about 32 micrograms of
medication remaining in her body after one hour. Dr. Powell knows that the amount of
medication remaining in Ruby's body will continue decreasing each hour.
Write an exponential equation in the form y = a(b)* that can model the amount of medication
in Ruby's body, y, x hours after it was administered.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y = 40(31)*
ola
To the nearest whole number, how many micrograms of medication can Dr. Powell expect to
be remaining in Ruby's body after 4 hours?
micrograms
Submit
Answers
Answer: 8 micrograms, y=40-(8)4
Step-by-step explanation: after four hours, 8 (4) micorgrams will stil be in her body
Answer:
the answer is y=40(0.8)^x
16 micrograms
determine the probability that the first child of clara and charles will be a boy with both albinism and hemophilia.
Answers
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.
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evaluate xy- x 2 - 5x - 4 if x = -1 and y = 6
Answers
The value of the expression xy - x² - 5x - 4 when x = -1 and y = 6 is -6.
What is the value of xy - x² - 5x - 4 when x = -1 and y = 6?Given the expression in the question;
xy - x² - 5x - 4
x = -1y = 6To find the value of the expression; substitute in x = -1 and y = 6 for all occurrence of x and y in the expression and simplify.
xy - x² - 5x - 4
Plug in x = -1
(-1)y - (-1)² - 5(-1) - 4
Plug in y = 6
(-1)(6) - (-1)² - 5(-1) - 4
Simplify
-6 - 1 + 5 - 4
Add -6 and -1
-7 + 5 - 4
Add -7 and 5
-2 - 4
Add -2 and -4
-6
Therefore, the value of the expression is -6.
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find each sum by graphing on the complex plane. (-4-4i)+(4+2i)
Answers
Answer:
To find the sum of two complex numbers on the complex plane, we can simply add their real and imaginary parts separately. The real part of a complex number is the x-coordinate on the complex plane, while the imaginary part is the y-coordinate.
In this case, the two complex numbers are (-4-4i) and (4+2i). To find their sum, we add their real and imaginary parts separately:
Real part: -4 + 4 = 0
Imaginary part: -4 + 2 = -2
So, the sum of (-4-4i) and (4+2i) is 0 - 2i, which can be represented as a point on the complex plane with x-coordinate 0 and y-coordinate -2.
Step-by-step explanation:
What is the factored form of 25b²-60b + 36?
O A. (6b-5)²
O B. (5b-6)²
O C. (5b-4)(5b - 9)
OD. (5b-12)(5b - 3)
Answers
Answer: B. (5b-6)2
Step-by-step explanation:
If 9x^2 – 6x + 5 is rewritten as p2 – 2p + 5, what is p in terms of x?
Answers
By applying the algebra concept, it can be concluded that p = 3x or p = 2 - 3x.
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.
We want to express p in terms of x of this equation:
9x² – 6x + 5 = p² – 2p + 5
First, we have to eliminate 5, so we have:
9x² – 6x = p² – 2p
Then we add 1 on each side, so we have:
9x² – 6x + 1 = p² – 2p + 1
(3x - 1)² = (p - 1)²
p - 1 = √(3x - 1)²
Thus the solutions are:
p - 1 = 3x - 1 ⇔ p = 3x
or
p - 1 = -(3x - 1) ⇔ p = 2 - 3x
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Need help trying to get at least a 80
Answers
Answer:
B
Step-by-step explanation:
cause the premeter is way around the area
Answer:
B. V = pi*r^2*H/6
Step-by-step explanation:
The formula for the volume of a cone is V=pi*r^2*h/3, where h is the height of the cone, and r is the radius of the base. In this case, the hieght of the cone is equal to half the height of the cylinder, so it's h=H/2
If we substitute, we get
V = pi * r^2 * h / 3 = pi * r^2 * (H / 2) / 3 = pi * r^2 * H / 6
Given ABCD is a parallelogram.From B draw a line meets CD at M ; from D draw a line meets BC at N such that BM = DN . Intersection of DN and BM is point I. Prove that IA is a bisector of ∠BID
Answers
Given a parallelogram ABCD with points B and D, we draw two lines such that line BM intersects CD at point M and line DN intersects BC at point N, and BM = DN. The intersection of these lines is point I. Our goal is to prove that IA is a bisector of angle BID.
To prove this, we first note that since ABCD is a parallelogram, AB is parallel to CD and AD is parallel to BC. This means that ∠BAD and ∠CDA are congruent, and ∠BAC and ∠DCB are congruent.
Next, we consider triangle ABM. Since BM is perpendicular to AB, we have ∠BAM = 90°. By the same reasoning, we have ∠BID = 90°. This means that IA is perpendicular to both AB and BD.
Since IA is perpendicular to AB and BD, it follows that IA bisects ∠BAD and ∠BDC. Additionally, we know that AB = BD and ∠BAD = ∠BDC, so it follows that IA bisects ∠BID.
This completes the proof that IA is a bisector of ∠BID. The key idea here is that a line perpendicular to two parallel lines bisects the angles formed by the intersection of the two parallel lines with a third line.
In conclusion, given a parallelogram ABCD with points B and D, the intersection of lines BM and DN, point I, is the bisector of angle BID. This result can be used to prove various geometric theorems and helps to understand the properties of parallelograms and their related figures.
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PLS HELP DUE TODAY
i need this done asap
Answers
Answer:
1. 4
2. $52
3. $20
4. 58
5. 30
6. 2
7. 132
8. 24
Step-by-step explanation:
1. If he needs 10 feet all together, and only has 6, you can put it in an equation as “6+x=10” because 10 would be the final amount, and he already had 6 feet, so he needs x feet. Then you need to get the x alone in the equation, so you would subtract 6 from both sides. 10-6 is 4, which means x=4. So Phil needs 4 more feet of lumber.
2. Emmet paid $64 in total. Within that total, $12 is for the case. You can set up an equation as either 12+x=64 or 64-12=x, both get the same answer, as shown in the first problem. 64-12 is 52, so that would be your answer.
3. So if he paid $x, 6+14=x. 6 from how much money was spent, 14 from how much was returned. 6+14=20. In total, brandy gave the cashier $20.
4. If the temprature dropped 15 degrees, and it is now 43, all you need to do is undo the dropping. If it didnt drop, it rose. To you need to add 15 to 43, giving you 58. The starting temperature was 58.
5. Her rate per hour is $12. That means if she worked x hours, you would set it up as 12x=m, m being the amount of money she earns. If she earns $360, you plug that in, making it look like 12x=360. Then you do the opposite of multiplication, on both sides, so you decide both sides by 12. On the left it cancels out, on the right 360/12 is 30. That means that Cindy worked for 30 hours.
6. If she used 32 cups and there is 16 cups in a gallon, all you need to do is divide 32 by 16. 32/16 is 2. So Mary used 2 gallons of juice.
7. You can write an equation for this one that looks like x/12=11. X is the total number. From there, you multiply 12 on both sides, giving you 132. That means there are 132 students in the gym class.
8. If there are 4 ping-pong balls in each package and there are 6 packages, all you need to do it multiply 6 by 4. 6 times 4 is 24. So Matthew has 24 ping-pong balls.
Angela has a collection of nickels and quarters worth 8.80 if she has 68 total buckles and quarters how many quarters does she have
Answers
Answer:
Step-by-step explanation:
We got two equations.
First modeling the total money using x for nickels and y for quarters.
0.05x + 0.25y = $8.80
Our second equation is modeling the total coins.
x + y = 68
Which we can change to substitute for x.
x = 68 - y
Substitute for x to find the answer.
0.05(68 - y) + 0.25y = 8.80
3.4 - 0.05y + 0.25y = 8.80
3.4 + 0.20y = 8.80
0.20y = 5.4
y = 27.
So, there is 27 quarters and 41 nickels.
How many terms are there in the expression?
-11 - 7c + 5 - 2x - 13b - 7
Answers
The number of terms in the expression -11 - 7c + 5 - 2x - 13b - 7 is 6
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed with coefficients, terms, factors, constants and variables.
They are also known to consist of mathematical operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesfloor divisionFrom the information given, we have the algebraic expression as;
-11 - 7c + 5 - 2x - 13b - 7
The terms are either single number or variables in the expression. They are six
Hence, the number is 6
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You and your best friend are picking apples at a local orchard. If there were already 12 bushels of apples on the tractor when you began at 8:00am and you picked apples until noon, what was your rate of change if there were 44 bushels filling the tractor when you stopped?
Answers
The rate of change picking the apples is 8 bushels of apples per hour.
What is rate of change?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, the formula for rate of change is: R = (D2 - D1)/T. where: R = rate of change.
Given that, you and your best friend are picking apples at a local orchard. there were already 12 bushels of apples on the tractor when you began at 8:00 am and you picked apples until noon, we are asked to find, what was your rate of change if there were 44 bushels filling the tractor when you stopped,
So, the rate change = total apples picked in 8 am to noon / number of hours.
Therefore, the total apples picked in 8 am to noon =
Since, it was 44 bushels at the end and when they started there were already 12 bushels, so the number of bushels of apples filled between given hours = 44 - 12 = 32 bushels.
The number of hours in picking 32 bushels of apples = 12 noon - 8 am
= 4 hours
Therefore,
The rate of change = 32 / 4
= 8
Hence, the rate of change picking the apples is 8 bushels of apples per hour.
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