Using proportions, considering the weight of each bar and the ratio, it is found that the ship is carrying 52 gold bars.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each bar weighs 5 kg, and the total weight is of 600 kg, hence the number of bars is given by:
n = 600/5 = 120.
The proportion of gold bars is given by:
p = 13/(13 + 17) = 13/30
Hence, out of 120 bars, the number of gold bars is given by:
nG = 120 x 13/30 = 4 x 13 = 52.
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Find the measure of x.
42°
X
17
x= [ ?
Round to the nearest hundredth.
Answer:
18.88
Step-by-step explanation:
tan 42° = 17/x
x= 17/(tan 42°)
x = 17/(0.9004)
x = 18.88
Unit 11: volume & surface area homework 6: surface area of pyramids and cones
The answer for the following part is
What is Volume?Surface area is the amount of space covering the outside of a three-dimensional shape.
Surface Area of Cone,
= πrl + πr²
=3.14*8*15.77 + 3.14* 8*8
= 597.61804 mm²
Surface Area of triangular pyramid,
= apothem * slant height * length
= 73.6 m²
Surface Area pentagonal pyramid
= B + LA
= 247.75 + 5 ( 1/2*12*19.5)
= 247.75 + 5 ( 117)
= 832.75 in²
Surface area of square pyramid
= P*l /2
= 2400 ft²
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simplify the mathematical expression to determine the appropriate india product or quotient in a scientific notation round round do the 1st fractor goes to the 10th place 3.3x10^3 7.8 3.7 2.1x10^-3
From the power rules, the matching of each expression with its result is:
[tex](8.6*10^7)(9.1*10^{-8})=7.8[/tex]
[tex](6.9*10^5)(4.8*10^{-3})=3.3*10^3[/tex]
[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =2.1*10^{-3}[/tex]
[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=3.7[/tex]
Power RulesThere are different power rules, see some them:
1. Multiplication with the same base: you should repeat the base and add the exponents.
2. Division with the same base: you should repeat the base and subctract the exponents.
3.Power. For this rule, you should repeat the base and multiply the exponents.
4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.
From this for your question, you have:
[tex](8.6*10^7)(9.1*10^{-8})[/tex] - From the distributive property of multiplication and power rules you can do:[tex](8.6*10^7)(9.1*10^{-8})=(8.6*9.1)*(10^7*10^{-8})=78.26*10^{-1}=7.8[/tex][tex](6.9*10^5)(4.8*10^{-3})[/tex] - From the distributive property of multiplication and power rules you can do:[tex](6.9*10^5)(4.8*10^{-3})=(6.9*4.8)*(10^5*10{-3})=33.12*10^2=3.3*10^3[/tex][tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})}[/tex] - From the distributive property of multiplication and power rules you can do:[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =\frac{(3.7*4.6)*(10^2*10^{-3})}{(1.4*5.7)*(10^{-6}*10^{8})} =\frac{17.02*10^{-1}}{7.98*10^2} =2.13*10^{-3}=2.1*10^{-3}[/tex]
[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}[/tex] - From the distributive property of multiplication and power rules you can do:[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=\frac{(3.1*5.3)*(10^{5}*10^{-9})}{(7.3*6.1)*(10^{2}*10^{-7})} =\frac{16.43*10^{-4}}{44.53*10^{-5}}=0.36896*10^1=3.7[/tex]
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In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.
On a coordinate plane, circle Q is centered at the origin with radius r. Triangle P Q S is shown. Point Q is at (0, 0) and points P is at (x, y). The length of Q P is r, the length of P S is y, and the length of Q S is x. Angle P S Q is a right angle.
If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?
(h + x)2 + (k + y)2 = r2
(x – h)2 + (y – k)2 = r2
(k + x)2 + (h + y)2 = r2
(x – k)2 + (y – h)2 = r2 7-foot radius.
Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²
The equation of a circle.Mathematically, the equation of a circle can be derived by using Pythagorean theorem;
x² + y² = r²
Where:
h and k represents the coordinates at the center.r is the radius of a circle.After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:
(x - h)² + (y - k)² = r²
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Answer: B) (x – h)2 + (y – k)2 = r2
Step-by-step explanation:
urgent please help with this function!!
Answer:
g(-2) = 0
g(4) = -4
Step-by-step explanation:
-2 works in the second equation because it is within the restrictions, therefore it is 0.
4 works in the third equation because it is within those restrictions, therefor it is -4.
Solve the following equations. 2x - y = 8 3x + y = 17
System of equations:
2x - y = 8
3x + y = 17
Solve for x:2x - y = 8
3x + y = 17
________ +
5x = 25
x = 5
Plug in x to one of the equations to solve for Y2(5) - y = 8
10 - y = 8
-y = -2
y = 2
The number of days to renovate a house, with 6 men, doing the job is 8 days. How many men need to work on the job if it takes 12 days to complete it ?
Answer:
9 men
Step-by-step explanation:
If 6 men are required to complete a job in 8, than 9 men would be required for a 12 day job.
12-8=4 which is half of 8
Half of 6 is 3
6+3=9
Answer:
4 men
Step-by-step explanation:
• Let x be the number of men needed to do the work I need 12 days.
•• it’s clear that the two variables (number of men and number of hours are in inverse proportion)
•• Which means their product is always equal to a constant.
Therefore
12 × x = 6 × 8 = 48
Then
x = 48 ÷ 12
= 4
complete the square to rewrite y=x^2+8x+3 in vertex form and then identify the minimum y-value of the function
The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.
In this problem, the equation is:
y = x² + 8x + 3.
Completing the squares, the function is:
y = (x + 4)² - 13
13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.
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The minimum y-value of the function for the parabolic equation is -13.
What is the vertex of a parabolic equation in quadratic form?The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]
From the given equation:
y = x² + 8x + 3
The parameters for the parabola are:
a = 1, b = 8, c = 3
[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]
[tex]\mathbf{x_v= -4}[/tex]
If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:
[tex]\mathbf{y_v = -13}[/tex]
Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.
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From one vertex of an n-sided polygon 5 different diagonals can be drawn which one of the following pairs of numbers are the number of sides (n) and the sum of measures of all interior angles of this polygon?
The number of diagonals drawn from the vertex of the polygon of n sides is (n−3).
The correct option is C)
⇒ A diagonal is a segment that connects two non-consecutive vertices in a polygon.
⇒ The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides.
What is the polygon?
A polygon is a plane figure enclosed by line segments called sides. Polygon is a 2d shape.
Regular polygons contain equal side lengths.
⇒ Let n be the number sides in the polygon.
⇒ So, the number of diagonals drawn from the vertex of the polygon of n sides is (n−3).
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are these right tell me yes or no
Answer:
Question 4: letter c
Question 3: letter c
Step-by-step explanation:
Which one is it? I need help
The statement that must be true about square WXYZ are as follows;
WX ≅ XYWX ≅ YZ∠W is a right angle.Properties of a Square.All sides are equal to each other.Opposite sides are parallel to each other.All the angles are right angle.The diagonals bisect each other and are perpendicular.Therefore, the statement that must be true about square WXYZ are as follows;
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Drag each tile to the correct location. These graphs are all rational functions. Classify the graphs based on how many vertical asymptotes they have.
Step-by-step explanation:
a vertical asymptote goes up and down.
the horizontal ones (like the horizon) go left and right.
A
1 vertical asymptote at x = 0
B
2 vertical asymptotes at x = -1 and x = +1
C
no vertical asymptote (whatever vertical line you can think of, it will always really cross the graph in finite space)
D
1 vertical asymptote at x = 3
E
like A
F
2 vertical asymptotes at x = -1 and x = +4
Which of the following sets of ordered pairs below represent a function?
{(0,0),(1,10),(10,4),(-1,-7)}
{(0,0),(4,1),(4,10),(7,1)}
{(0,0),(10,-1),(4,-10),(10,-2)}
{(0,0),(0,1),(0,10),(0,-1)}
The ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.
How to identify ordered pairs?A set of ordered pairs that defines a function will be the one that has exactly one y-value that assigned to every x-value. This means that none of its x-values can have two corresponding y-values.
All the sets of ordered pairs don't have exactly one y-value that corresponds to each of its x-value except {(0,0),(1,10),(10,4),(-1,-7)}.
Thus, we can say that the ordered pair that represents a function is {(0,0),(1,10),(10,4),(-1,-7)}.
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Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has
$658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m
years, Makayla has $613.04. What is the in approximate difference in the number of years that Calvin and Makayla have
their money invested?
O Makayla invests her money 1 year longer.
O Makayla invests her money 2 years longer.
O Calvin invests his money 1 year longer.
O Calvin invests his money 2 years longer.
Answer:
Dot number 2. Makayla invests her money 2 years longer.
Step-by-step explanation:
Calvin 400$ with 5% interest compounded monthly will get you to 666.0294029241$ after 13 months or 1 year and 1 month
Makayla 300$ with 6% interest quarterly
1st year 378.743088$(4 quarters)
2nd year 478.1544223592$(+4 quarters)
3rd year 603.6589415506$(+4 quarters)
3rd year and 1 quarter 639.8784780436$
Answer:
So the second option is the answer: Makayla invests her money 2 years longer.
Step-by-step explanation:
Formula for compound interest: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Calvin:
[tex]A=658.80[/tex]
[tex]P=400[/tex]
[tex]r=0.05[/tex]
[tex]n=12[/tex]
[tex]t=?[/tex]
Makayla:
[tex]A=613.04[/tex]
[tex]P=300[/tex]
[tex]r=0.06[/tex]
[tex]n=4[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex].
1) Divide both sides of the equation by [tex]P[/tex].
[tex]\frac{A}{P} =(1+\frac{r}{n})^{nt}[/tex]
2) Take the natural log of both sides.
[tex]ln(\frac{A}{P}) =ln((1+\frac{r}{n})^{nt})[/tex]
3) Rewrite the right side of the equation using properties of exponents.
[tex]ln(\frac{A}{P}) =nt*ln(1+\frac{r}{n})[/tex]
4) Divide each side of the equation by [tex]n*ln(1+\frac{r}{n})[/tex]
[tex]\frac{nt*ln(1+\frac{r}n)}{n*ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]
5) Cancel the common factor [tex]n[/tex] on the left side of the equation.
[tex]\frac{t*ln(1+\frac{r}n)}{ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]
6) Cancel the common factor of [tex]ln(1+\frac{r}{n})[/tex].
[tex]t=\frac{ln(\frac{A}{P)}}{n*ln(1+\frac{r}{n})}[/tex]
Now we have an equation for [tex]t[/tex] that we can use to answer your question.
For Calvin:
[tex]t=\frac{ln(\frac{658.80}{400)}}{12*ln(1+\frac{0.05}{12})}[/tex]
[tex]t=10[/tex]
For Makayla:
[tex]t=\frac{ln(\frac{613.04}{300)}}{3*ln(1+\frac{0.06}{3})}[/tex]
[tex]t=12[/tex]
So the second option is the answer: Makayla invests her money 2 years longer.
Note: This question took me 2 minutes to answer but typing it took 30. lol
The equation of a circle is (x-2)2+(y-6)2=25. What is the radius of the circle?
Answer:
radius = 5
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
(x - 2)² + (y - 6)² = 25 ← is in standard form
with r² = 25 ( take the square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5
help asap!!!!
Select the correct answer.
Which equation could represent the data in the table?
Answer:
A. y = 3x + 1
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Take two points: (0, 1), (1, 4)
[tex]\sf \rightarrow slope \ (m) : \dfrac{4-1}{1- 0 } = 3[/tex]
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 1 = 3(x - 0)[/tex]
[tex]\sf y = 3x + 1[/tex]
Find the nth term of this number sequence
1, 7, 13, 19, ...
Answer:
now we have to follow up with the formula n² - n¹
which is 7-1= 6
n³-n²
which is 13-7=6
so therefore the nth term=6
which function has a domain
Answer:
F(x) = - [tex]\sqrt[3]{x}[/tex]
Step-by-step explanation:
A square root can only have a positive input for the domain
(The domain is the input for the function)
The cube root can be either negative or positive as an input
F(x) = - [tex]\sqrt[3]{x}[/tex] can have inputs from negative infinity to infinity
one angle of a triangle measures 80° more than the smallest, while a third angle is twice the smallest. whats the measure of each angle?
Answer: The measure of each angle is 105°, 50°, and 25°.
Step-by-step explanation: The first step in solving this is writing down what you know.
In the phrase it tells you that "one angle of a triangle measures 80 more than the smallest", so we can say that one angle = 80 + smallest angle.
This can be simplified more to x = 80 + y
x = One Angle
y = Smallest Angle
Then if we continue with the phrase it says "a third angle is twice the smallest", so we can say that a third angle = 2(Smallest Angle).
This can be simplified more to z = 2(y)
z = Third Angle
We also know that a triangles angles add up to 180°, so we know x + y + z = 180.
So, with these equations we can now solve for x, y, and z.
The easiest way would be to simply just plug in x and z straight into the 180 equation as follows.
x = 80 + y
z = 2(y)
180 = x + y + z
180 = (80 + y) + y + (2y)
180 = 80 + 4y
100 = 4y
y = 25
Then we can use y to solve for the other two equations.
z = 2(25) x = 80 + 25
z = 50 x = 105
After completing that you are left with the three angles of the triangle, 25, 50, and 105.
please help me its math
Answer:
the answer is $62
Step-by-step explanation:
if you subtract 110 by 98 you get 12 and the same for the rest so if you subtract 74 by 12 you get 62
Hope that help :)
Answer:
62
Step-by-step explanation:
HURRRRYYY
Hurry pleaseee use elimination show your work
15y - 9x =-9 -8y+9x=12
Translate the following into algebraic expressions:
If a number is three less than five times m, what is the number
Answer:
5m-3
Step-by-step explanation:
Answer:
5m-3
Step-by-step explanation:
Which expression is equivalent to (startfraction x superscript negative 4 baseline y over x superscript negative 9 baseline y superscript 5 baseline endfraction) superscript negative 2? assume x not-equals 0, y not-equals 0.
The equivalent expression of [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex] is [tex]x^{-10}y^8[/tex]
Complete questionWhich expression is equivalent to [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]
Apply the exponent law of indices
[tex](\frac{x^{-9}y^5}{x^{-4}y})^{2}[/tex]
Next, we apply the common base law of indices
[tex](x^{4 -9}y^{5-1})^2[/tex]
Evaluate the difference
[tex](x^{-5}y^4)^2[/tex]
Remove bracket
[tex]x^{-10}y^8[/tex]
Hence, the equivalent expression of [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex] is [tex]x^{-10}y^8[/tex]
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Answer:
y^8/x^10
Step-by-step explanation:
The guy above me is right but just forgot to distribute the negative out of x. :)
(sec²0 + tan²0)(cosec²0+cot²0) = 1sec²5 sin 0
Answer:
865
Step-by-step explanation:
if minus than answer
HELP PLEASEEEE!!!!
If PQRS is a quadrilateral inscribed in a circle then the opposite angles of the quadrilateral are_____?
The values of x and y are _____ degrees and ______ degrees respectively.
Answer:
x: 98 y: 112
Step-by-step explanation:
Supplementary angles add up to 180 so:
x + 82 = 180
x = 98
And:
y + 68 = 180
y = 112
Answer:
supplementary, 98°, 112°
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.
∴ x° + 82° = 180°
x = 180° - 82°
x = 98°
y° + 68° = 180°
y = 180° - 68°
y = 112°
Which best explains the formula? the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector. the central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector. the central angle measure of the sector multiplied by the area of the circle will yield the area of the sector. the central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.
The sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
Area of a sectorThe coloured portion of the circle is known as a sector. The formula for calculating the area of a sector is given as:
Area of a sector = θ/360 * πr²
where
θ is the central angle
πr² represents the area of a circle.
Therefore the best statement that explains the formula is expressed as the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
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Answer:
Its A edge 2023
Step-by-step explanation:
What is the equation of the line that passes through the point (1,4) and has a slope of 4
Answer:
y = 4x
Step-by-step explanation:
Equation of line in point -y intercept form:
[tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]
[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]
y - 4 = 4(x -1)
y - 4 = 4*x - 4*1
y - 4 = 4x - 4
Add 4 to both sides
y = 4x - 4 + 4
y =4x
Hi 4 questions, about inequality’s and y intercepts and slope. Only 4 questions :)
The slope and y-intercept will be the negative 5/2 and 4.
The complete question is attached below.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The equation is given below.
y > -(5/2)x + 4
The slope and y-intercept will be the negative 5/2 and 4.
The graph is also attached below.
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Solve for x.
3x +1=7
6
Ox=12
O x = 4
x = 16
Answer:
x = 2
Step-by-step explanation:
3x + 1 = 7
3x = 7 – 1
3x = 6
x = 6/3
x = 2
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 2}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{3x + 1 = 7}[/tex]
Find: [tex]\textsf{Solve for x}[/tex]
Solution: In order to isolate x we need to subtract 1 from both sides and the divide both sides by 3.
Subtract 1 from both sides
[tex]\textsf{3x + 1 - 1 = 7 - 1}[/tex][tex]\textsf{3x = 7 - 1}[/tex][tex]\textsf{3x = 6}[/tex]Divide both sides by 3
[tex]\textsf{3x/3 = 6/3}[/tex][tex]\textsf{x = 6/3}[/tex][tex]\textsf{x = 2}[/tex]Therefore, the value of x is equal to 2.
If b = 7, then the value of c is...
7[tex]\sqrt{2}[/tex]
Step-by-step explanation:The triangle shown is a 45-45-90 triangle. This name comes from the fact the 3 angle measurements are 45, 45, and 90 degrees.
If needed, you could find the missing angle using the equation: 180 - (45 + 90) = x.
Special Right Triangles
Special right triangles allow us to use formulas and shortcuts to find missing sides easily. Another type of special right triangle is the 30-60-90 triangle. While both of these are special right triangles, they have different formulas.
Formulas
All 45-45-90 triangles have 2 types of sides: the legs (a and b) and the hypotenuse (c).
c = b[tex]\sqrt{2}[/tex]b = a a = bIn these triangles, both of the legs are congruent.
Solving for c
Since we are given b, we can just plug the b-value into the formula that solves for c.
c = 7[tex]\sqrt{2}[/tex]The answer cannot be simplified further, so this is the final answer.
Answer:
Second option
Step-by-step explanation:
It is a right triangle isosceles
a = b = 7
c = hypotenuse
[tex]c =\sqrt{7^{2}+7^{2} } =\sqrt{49+49} =\sqrt{2(49)}=7\sqrt{2}[/tex]
Hope this helps
