We have that:
[tex]\text{velocity}=\frac{\text{distance}}{\text{time}}[/tex]then, in this case, we have:
[tex]\begin{gathered} d=15.6m \\ t=17.2s \\ v=\frac{d}{t} \\ \Rightarrow v=\frac{15.6m}{17.2s}=0.90\frac{m}{s} \\ v=0.9\frac{m}{s} \end{gathered}[/tex]therefore, the velocity of the cart is 0.9 meters per second.
HELP ME PLEASE I NEED HELP I DONT KNOW HOW TO DO THIS
Answer:
convert miles to kilometers by multiply by 1.61 covert kilometers to miles by devide by 0.62(if am not wrong)
Sandra saves 12% of her salary for retirement. This year her salary was $1,000 more than in the previous
year, and she saved $4,920. What was her salary in the previous year?
Answer:
$32,000
Step-by-step explanation:
(8.59×10 4 )−(3.2×10 3 )
Answer:
The answer is 8.27×10^4
Answer: 8.27×10^4
Step-by-step explanation:
-15/2 = 3x solve for x and simplify your answer as much as possible
Answer:
x = -5/2
Step-by-step explanation:
-15/2 = 3x
multiply both sides by 2:
2(-15/2) = 2(3x)
-15 = 6x
divide both sides by 6:
-15/6 = 6x/6
x = -15/6
this can be reduced to:
x = -5/2
Chris and Sarah's dinner bill was $28.67. They want to leave an 18% tip. How much gratuity will they leave?
Please help me!
Answer:
Tip- $5.16
Total cost- $33.86
Step-by-step explanation:
To find a 18% tip, turn 18% into 0.18.
Multiply 28.67 by 0.18.
28.67x0.18=
5.16
If you add that to the bill, it would be 33.86
A triangle has side lengths of 10 inches, 11 inches, and 12 inches. What kind of triangle is it?
Answer:
Acute scalene triangle.
More Information:
Sides: a = 10 b = 11 c = 12
Area: T = 51.521
Perimeter: p = 33
Semiperimeter: s = 16.5
Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad
Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad
Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad
Height: ha = 10.304
Height: hb = 9.367
Height: hc = 8.587
Median: ma = 10.368
Median: mb = 9.579
Median: mc = 8.631
Inradius: r = 3.122
Circumradius: R = 6.405
Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]
Centroid: CG[5.708; 2.862]
Coordinates of the circumscribed circle: U[6; 2.242]
Coordinates of the inscribed circle: I[5.5; 3.122]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad
∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad
∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad
How to Solve:
The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).
1. Input data entered: sides a, b, and c.
a=10
b=11
c=12
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.
a=10
b=11
c=12
2. The triangle perimeter is the sum of the lengths of its three sides
3. Semiperimeter of the triangle
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.
4. The triangle area using Heron's formula
Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.
5. Calculate the heights of the triangle from its area.
There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.
6. Calculation of the inner angles of the triangle using a Law of Cosines
The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.
7. Inradius
An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.
8. Circumradius
The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.
9. Calculation of medians
A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.
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Evaluate log2 10 using the change of base formula. Round your answer to the nearest thousandth.
Take into account the following property:
[tex]\log _ab=\frac{\log b}{\log a}[/tex]Then, for the given expression you have:
[tex]\log _210=\frac{\log10}{\log2}=\frac{1}{\log }\approx3.322[/tex]Hence, the answer is approximately 3.322
Please Help :))
Given:
Prove: AABC = ACDA.
Step
-
2
try
Statement
ZB ZD
BC AD
AC
AC
Type of Statement
B
Reason
Given
Reflexive Property
D
3) [tex]\angle BCA \cong \angle CAD[/tex] (alternate interior angles theorem)
4) [tex]\triangle ABC \cong \triangle CDA[/tex] (AAS)
Luke receives an electric bill of \$84.21$84.21dollar sign, 84, point, 21 for the month of April. The electric company charges \$0.14$0.14dollar sign, 0, point, 14 per kilowatt-hour (\text{kWh})(kWh)left parenthesis, start text, k, W, h, end text, right parenthesis of electricity. Given that April has 303030 days, about how many kilowatt-hours did Luke use per day during the month of April?
Choose 1 answer:
Given that April has 30 days, Luke used, on average, 20.05 kilowatt-hours of electricity per day during April.
What is average?The average is the mean value obtained by dividing the total value of a data set by the number of items.
In this situation, we can divide the total electric bill for April by 30 to obtain the average daily charge.
In addition, we can divide the average charge per day by the cost per kilowatt-hour to obtain the number of kilowatt-hours used per day.
The total electric bill for April = $84.21
The charge per kilowatt-hour (kWh) = $0.14
The number of days in April = 30
The bill per day = $2.807 ($84.21/30)
The kilowatt-hours per day = 20.05 kWh ($2.807/$0.14)
Thus, Luke used an average of 20.05 kilowatt-hours per day in April.
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You have $1200 for your trip to the beach. You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare. Write an inequality that can be used to determine the maximum number of days you can stay at the beach. Clearly indicate what the variable represents. Then Solve the inequality, and interpret your answer in a complete sentence.
Explanation
Step 1
let x represents the numbers of days you can stay at the beach
then,
You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.
so
[tex]\text{total}=230+160x[/tex]but, you have only $1200, so the total needs to be smaller or equal than 1200
[tex]230+160x\leq1200\rightarrow Inequality[/tex]Step 2
solve the inequality
[tex]\begin{gathered} 230+160x\leq1200\rightarrow Inequality \\ subtract\text{ 230 in both sides} \\ 230+160x-230\leq1200-230 \\ 160x\leq970 \\ \text{divide both sides by 160} \\ \frac{160x}{160}\leq\frac{970}{160} \\ x\leq6.0625 \\ \text{rounded} \\ x\leq6 \end{gathered}[/tex]it means you can stay maximum 6 days
I hope this helps you
Y = 17x - 8, y = 24x +6 Parallel Perpendicular Neither
Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:
[tex]\begin{gathered} y_1=m_1x_1+b_1 \\ y_2=m_2x_2+b_2 \\ \text{Their slopes must be equal:} \\ m_1=m_2 \end{gathered}[/tex]For the given equations, the slopes are:
[tex]\begin{gathered} y=17x-8 \\ m=17 \end{gathered}[/tex][tex]\begin{gathered} y=24x+6 \\ m=24 \end{gathered}[/tex]The slopes are different, so this lines are not parallel.
Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:
[tex]\begin{gathered} y_1=m_1x_1+b_1 \\ y_2=m_2x_2+b_2 \\ m_2=-\frac{1}{m_1} \end{gathered}[/tex]For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:
[tex]m_{}=-\frac{1}{17}[/tex]The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.
The correct choice is Neither
iodinated (i 125) albumin injection contains 0.5 millicuries (18.5 mbq) of radioactivity per milliliter. how many milliliters of the solution should be administered exactly 30 days after the original assay to provide an activity of 60 microcuries (2.22 mbq) if the half life of i 125 is 60 days? round answer to the nearest hundredth (i.e. 0.xx). do not include units in your answer.
The decay constant of a radioactive nuclide exists its probability of decay per unit time.
The half life of i 125 is 60 days exists 0.169 ml.
What is meant by Decay constant?The decay constant of a radioactive nuclide exists its probability of decay per unit time. The number of parent nuclides P therefore decreases with time t as dP/P dt = −λ.
The ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.
The rate of decay is determined by the decay constant. The symbol for the decay constant is "lambda," or. The many diverse decay rates that have been seen may be caused by large variations in this constant probability among various types of nuclei.
Decay constant: [tex]$& \lambda=\frac{0.693}{t_{1 / 2}}[/tex]
Decay constant expressed in any unit of time
Such as reciprocal seconds, minutes, hours etc.
[tex]$\mathbf{N}=\mathrm{N}_o \mathrm{e}^{-\lambda t} \quad \lambda=\frac{0.693}{\mathrm{t}_{1 / 2}}$[/tex]
Half Life: [tex]$\quad t_{1 / 2}=\frac{0.693}{\lambda}$[/tex]
The half life of i 125 is 60 days exists 0.169 ml.
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In triangle ABC measure of angle A equals 45°. The altitude divides the side AB into two parts of 20 and 21 units. Find BC.
In triangle ABC, BC = 29 units.
Given,
In Δ ABC, ∠A = 45°.
A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.
Let altitude meet AB on D.
So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°
In ΔADC,
tan A = DC/AD
tan 45° = DC/20
1 = DC/20
DC = 20 units
In ΔBDC,
BC² = BD² + DC² (Pythagorean Theorem)
= 21² + 20²
= 441 + 400
= 841
BC = √841
= 29
Hence, BC = 29 units.
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Rewrite one eighth times x cubed times y plus seven eighths times x times y squared using a common factor.
Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.
Given that,
Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.
This is how the equation can be rewritten:
The first equation is written as 1/8 x3y + 7/8 xy2.
It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.
Equation two:
1/4x.y.4x2 + 28y
1/4 .4 x³ .y + 28y
x3.y + 28y equation to be solved
Using the formula
y = (x3 + 28).
Third claim:
1/4. x. y. x2 + 7y
Fix the problem.
1/4 . x³ .y + 7y
Write y = (1/4x3 + 7) in a new way.
Fourth assertion:
1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x
After removing the common element x(1/8 x2y3+ 7), rewrite the equation.
Fifth Declaration
1/8 x. y. x² + 7y
1/8 x³. y + 7y
Equation y (1/8 x3 + 7) is rewritten.
Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.
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what proportion of american households has at least one television? group of answer choices virtually all american households have at least one tv. except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of american households have at least one tv. more than 50% of american households have at least one tv. virtually all middle-class and upper-class households have at least one tv; however, about 50% of lower-income families have a tv.
About 50% of Americans households have a tv except who live in low-income, single-parent, or disadvantaged homes
What is meant by Proportion?Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole
Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.
however, about 50% of Americans households have a tv
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a recipe calls for 40 ounces of rice. how many grams of rice dose the recipe require
Answer:
1133.98
almost 1134 grams :)
Step-by-step explanation:
multiply by 28.35 to get the answer :)
Answer:
1133.98
Step-by-step explanation:
Hope it helps and have a nice day!!!!! :)
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A poster is
than
25 cm taller
it is wide. It is
mounted on a piece
of cardboard so
that there is a 5
cm border on all
sides.
If the
area of the border
alone is 1350 cm²,
what are the
dimensions of the
poster
The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm
Define Dimension
A measurable extent of a particular kind, such as length, breadth, depth, or height.
Let,
T = how taller the poster is
W = how wide the poster is
According to question given,
T = W + 25 ---eq(i)
The total height is calculated by multiplying the top border by 5 and the bottom border by 5. The entire height is then multiplied by the border's width, 5, times 2, so there are two tall sides. then multiplying by 5 times 2 widths.The equation looks like that,
5 * (2 (T + 10)) + 5 * (2 * W) = 1350
Now substitute the eq(i) value,
5 * (2 ((W + 25) + 10)) + 5 * (2 * W) = 1350
Now, solve for W,
5 * (2W +50 + 20) + 10W = 1350
10W + 5(70)+ 10W = 1350
20W + 350 = 1350
20W = 1350 - 350
20W = 1000
W = 1000/20
W = 50
Now, put the W value in eq(i)
T = 50 + 25
T = 75
Therefore, The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm
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Which fraction is closest to 1/2?
a. 1/6
b.3/8
c.3/4
d.-1/2
Answer:
A. 1/6 would be the answer I think
Identify the rule for fg when f(x) = –3x – 6 and g(x) = x2 – x – 6.
The rule for the given function f /g when the function f(x) = -3x -6 and
g(x) = x² -x - 6 is identified as f(x) / g(x) = -3 / (x -3).
As given in the question,
Given function are:
f(x) = -3x -6
g(x) = x² -x - 6
Rule to identify for the function f(x) / g(x) we get,
Substitute the value of f(x) and g(x) in the required rule we have,
f(x) / g(x) = (-3x -6 ) / ( x² -x - 6 )
Now simplify the function to get the rule:
f(x) / g(x) = -3(x+2) / (x² -3x +2x -6)
⇒ f(x) / g(x) = -3(x+2) /(x-3)(x+2)
⇒ f(x) / g(x) = -3 / (x-3)
Therefore, the rule for the given function f /g when the function f(x) = -3x -6 and g(x) = x² -x - 6 is identified as f(x) / g(x) = -3 / (x -3).
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Point Mis a point of tangency.What is the value of x?446567111°230 x°88M
Answer:
The value of x is 65 degrees.
Explanation:
To solve for x, we use the formula for an angle formed by a tangent and a secant.
[tex]23=\frac{1}{2}(111-x)[/tex]Next, solve the equation for x:
[tex]\begin{gathered} 23\times2=111-x \\ 46=111-x \\ x=111-46 \\ x=65\degree \end{gathered}[/tex]The value of x is 65 degrees.
A soldier walked from his base for 3 km on a bearing of 050° to a point A. He then walked a further 4 km due east to a point B.
Find:
1. How far east of the base is point B
2. The bearing of B, as measured from the base
3. The bearing of the base as measured from B
The east of the base is 6.3 km far from B.
The bearing of B, as measured from the base is 73°.
The base is 73° south vest of the B.
What is sin?
Sin is a periodic function with a period of 2π, and the domain of the function is (−∞, ∞) and the range is [−1,1]. Sin formula is used to find sides of a triangle.
Given, the distance between soldier and base is 3 km. and the bearing is 50°.
He then walked a further 4 km due east to point B.
1) the east of the base to point B = 3 sin 50° +4
= 6.3 km
2) The bearing of B is solved as
3(cos 50°) = 1.9km
then, bearing is 6.3/1.9
= 73°
3) the base is 73° south vest of the B
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Math
classify each polynomial below as monomial, binomial or trinomial
Answer:
1) trinomial
2) binomial
3) binomial
4) trinomial
5) monomial
Step-by-step explanation:
Monomial: 1 term
Binomial: 2 terms
Trinomial: 3 terms
Terms are separated by plus and minus signs.
1) trinomial
2) binomial
3) binomial
4) trinomial
5) monomial
Please help asap
this is an assignment due today please help real quick
no fake answers
Answer:
where???????????????
A school is arranging a field trip to the zoo. The school spends 564.16
I need this answered please
The rate of the slowest car is 86 km/hr using the concept of relative velocity.
What is Relative velocity?Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.
Let the speed of 1st car is v₁.
Let the speed of 2nd car is v₂.
v₁- v₂ = 18 km/hr --- (1)
And using the concept of relativity.
S(rel) = D(rel)/time
S(rel) = 360 / 2
S(rel) = 190
v₁ + v₂ = 190 --- (2)
Adding equations 1 and 2 we get
v₁ = 104 km/hr
v₂ = 86 km/hr
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Which of the following is the correct factorization of the polynomial below?p3 - 21603O A. (0-360)(p? + 36pq + 692)O B. (p2 + 129) (03 + 36pq + 50%)O C. (2-6)(p2 + 6pq + 3602)O D. The polynomial is irreducible.
We have the polynomial:
[tex]p^3-216q^3[/tex]We have to factorize it.
We know that 216 is the cube of 6.
We then applied the property for the difference of cubes.
[tex]\begin{gathered} p^3-(6q)^3 \\ (p-6q)(p^2+p\cdot6q+(6q)^2) \\ (p-6q)(p^2+6pq+36q^2) \end{gathered}[/tex]The answer is Option C.
Difference of cubes property:
x^3-y^3 = (x-y)(x^2+xy+y^2)
Rewrite 20 − 4x3 using a common factor.
Using a common factor, 20 - 4x³ can be rewritten as 4(5 - x³).
What is a Common Factor?A common factor of two or more numbers is any number that the two numbers can be divided by and will leave no remainder.
For example, a common factor of 4 and 8 is 2. This is because:
2 into 4 will give us 2 without a remainder.
2 into 8 will give us 4 without a remainder.
To rewrite the expression, 20 - 4x³ using a common factor, find the factor that will go into each of the terms without a remainder.
4 into 20 will give us 5 without a remainder.
4 into 4x³ will give us x³ without a remainder.
Therefore, we can factor out the common factor from the expression to rewrite 20 - 4x³ as 4(5 - x³).
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Explain each step in the space provided below.
Answer:
1) multiply and divide by 2 on right hand side
2) multiply by 24 on both sides ( LHS and RHS)
3) divide by -1 on both sides so that negative sign on RHS will be cancelled
2The shape shown is made up of three similar right-angled triangles.22The smallest triangle has two sides of side-length 2, as shown.What is the area of the shape?1412 + 12V22824 + 20V56Erase
The triangles are similar. The smaller is isosceles, so the 3 of them are as well.
Let's Start by finding the hypotenuse of the smaller one:
a² = 2
This question has two parts. First, answer Part A. Then, answer Part B.
part A:
The length of the incline of the ramp will be [h] = 12.0415 ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft
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[This question also has part B. Visit the following link for part B -
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