In 25 years the account balance will be $38.51 if Jimmy Page puts $30 into a savings account that promises 1% interest compounded quarterly.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
P = $30
r = 1% = 0.01
n = 4
[tex]\rm A = 30(1+\dfrac{0.01}{4})^{4\times25}[/tex]
After calculating:
A = $38.51
Thus, in 25 years the account balance will be $38.51 if Jimmy Page puts $30 into a savings account that promises 1% interest compounded quarterly.
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can someone please help walk me through the steps to solve number 79? i’m lost
Answer: 70/29
Step-by-step explanation:
[tex]S=\theta r\\\\35=14.5 \theta\\\\\theta=\frac{35}{14.5}=\boxed{\frac{70}{29}}[/tex]
Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kite’s strings play out. He measures the angle of elevation from his hand to the kite to be 24∘. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
Answer: 46.0 ft
Step-by-step explanation:
[tex]\sin 24^{\circ}=\frac{x}{105}\\\\x=105\sin 24^{\circ}[/tex]
So, the distance above the ground is [tex]105\sin 24^{\circ}+3.25 \approx \boxed{46.0 \text{ ft}}[/tex]
A parallelogram ABCD is shown with DC equal to 8 feet and the perpendicular distance between AB and DC equal to 3 over 4 foot. Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)
Answer:
6,3
Step-by-step explanation:
hope this helps
the math section in part B shows the equation for the area of a triangle, but this math could be skipped with a similar problem if you just divide the parraellogram by 2. (logic section)
pls asap need it rn.
Similar triangles are those triangles whose corresponding sides are in the same ratio. The correct option is A.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
Since for the two of the given triangle, the measure of all the corresponding angles is the same. Also, all the corresponding sides are in a common ratio.
9/3 = 12/4 = 15/5 = 3
Therefore, the two of the given triangles are similar triangles.
Hence, the correct option is A.
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abcdefghijklmnopqrstuvwxyz
answer:
Now I know My ABC next time won't you sing with me.
Which model represents 2 . 36 ÷ 4 ?
A. Three groups each have three tens and 4 ones.
B. There are three groups of five tens and 9 ones in each group.
C. There are four groups of three tens and six ones.
D. There are three groups of five tens and nine ones in each group
Eve has two more marbles than Solene. Solene has twice as many marbles as Steve. Steve has 7 less marbles than eve. How many marbles do they have in all?
A. 27 B. 20 C. 34 D. 13
Using a system of equations, the total number of marbles that they have is given by:
A. 27.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Eve's marbles.Variable y: Solene's marbles.Variable z: Steve's marbles.Eve has two more marbles than Solene, hence:
x = y + 2.
Solene has twice as many marbles as Steve, hence:
y = 2z -> z = y/2.x = 2z + 2.Steve has 7 less marbles than eve, hence:
z = x - 7.
Hence:
[tex]\frac{y}{2} = x - 7[/tex]
y = 2(x - 7)
y = 2(y + 2 - 7)
y = 2y - 10
y = 10.
Then:
x = y + 2 = 10 + 2 = 12.z = x - 7 = 12 - 7 = 5.Hence the total is given by:
T = 12 + 10 + 5 = 27.
Which means that option A is correct.
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Select the graph that represents two quantities in a proportional relationship
The correct answer is option D.It is the graph that represents two quantities in a proportional relationship.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
As we can see graph D is showing the correct proportionality. We can also create an equation of proportionality as:-
Y = 2x
Put y = 0.5
0.5 = 2 x 0.5 = 1
As we put y=0.5 we get the value of x = 1 as shown in the graph.
Therefore the correct answer is option D.It is the graph that represents two quantities in a proportional relationship.
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Flying against the wind, an airplane travels 2520 kilometers in 4 hours. Flying with the wind, the same plane travels 9450 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Using the relation between velocity, distance and time, it is found that:
The rate of the plane is of 840 km/h.The rate of the wind is of 210 km/h.What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}[t}[/tex]
Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:
[tex]v - v_w = \frac{2520}{4}[/tex]
[tex]v - v_w = 630[/tex]
[tex]v = 630 + v_w[/tex]
Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:
[tex]v + v_w = \frac{9450}{9}[/tex]
[tex]v + v_w = 1050[/tex]
[tex]v = 1050 - v_w[/tex]
Hence, solving for the wind's speed:
[tex]630 + v_w = 1050 - v_w[/tex]
[tex]2v_w = 420[/tex]
[tex]v_w = \frac{420}{2}[/tex]
[tex]v_w = 210[/tex]
For the plane, we have that:
v = 1050 - 210 = 840.
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Find an angle between zero and 360 that is coterminal with 900°
Answer:
180
Step-by-step explanation:
Answer:
180
Step-by-step explanation:
To estimate the height of a totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which of the following is the best estimate of the height of the totem pole?
The height of the pole is 6.50 meters
How to calculate the height?To calculate the height of the pole, we will use of the following equivalent ratios.
By Pythagoras theorem, we have:
[tex]x ^2 = 2^2 + 3^2\\\\x ^2 = 4 + 9\\\\x = \sqrt{13}[/tex]
So, we have:
[tex]h = \dfrac{\sqrt{13}^2 }{2} \\\\h = \dfrac{13}{2}\\\\h = 6.5[/tex]
Hence, the height of the pole is 6.50 meters
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Find the longer and shorter lengths and hypotenuses
Answer:
Short leg: 9 in
Long leg: 40 in
Hypotenuse: 41 in
Step-by-step explanation:
This problem involves the Pythagorean Theorem, solving a system of equations, and solving a quadratic equation.
The Pythagorean Theorem applies because the question states this is a right triangle. That is one equation.
Two more equations come from descriptive relationships between various sides of the triangle.
Solving the system is done here with the Substitution Method, and solving the quadratic equation is done with factoring and the zero product property. Other methods could be used, but there is a character limit, so we can't dive into every way to solve this.
The Pythagorean TheoremPythagorean Theorem: [tex]a^2+b^2=c^2[/tex] where "c" is the hypotenuse of the right triangle.
"c" must be hypotenuse.
It doesn't matter which of the two legs' lengths is used for "a" & "b". However, because of other parts of the question, we'll need to know which one is which.
The question refers back multiple times to one specific leg (the short one). So, when we refer back to that leg in our equations, we need to make sure we're using the same leg each time.
Keeping track of which leg is which
Let's use "a" for the smaller leg, and "b" for the longer leg.
"c", as always, is the hypotenuse.
Setting up the relationships between the sidesNext, the question gives two statements relating the side lengths of the triangle to each other.
For the first statement, "the length of the longer leg of a right triangle" (that's "b") "...is 13 inches more than three times the length of the shorter leg ("a").
Translating the first sentence into math:
"the length of the longer leg of a right triangle" means "b""...is..." means "=""...13 inches more than..." means " +13 " (start with what's coming next, and then do the adding)"...three times..." means " 3* ""... the length of the shorter leg." means "a".[tex]b=3a+13[/tex]
Similarly from the second statement, we get: [tex]c=3a+14[/tex]
Combining this with the Pythagorean Theorem, we have a system of 3 equations, and 3 unknowns.
[tex]b=3a+13[/tex]
[tex]c=3a+14[/tex]
[tex]a^2+b^2=c^2[/tex]
Solving a system of equationsTo solve a system of equations, there are two main methods:
The substitution methodThe elimination methodEither method can be used, but the substitution method is the most intuitive.
Substitution method
To solve a system with the substitution method, isolate variable in an equation, written in terms of the other variables, and substitute them in to try to get a single equation with a single unknown.
Looking at our system, the first two equations already have "b" and "c" isolated in terms of "a". If we substitute both of these into the third equation, we'll have a single equation in terms of a, and can attempt to solve it.
[tex]b=3a+13[/tex]
[tex]c=3a+14[/tex]
[tex]a^2+b^2=c^2[/tex]
Substituting...
[tex]a^2+(3a+13)^2=(3a+14)^2[/tex]
Rewrite the square binomials as a product...
[tex]a^2+(3a+13)(3a+13)=(3a+14)(3a+14)[/tex]
Apply FOIL (a combination of the distributive property, the commutative properties of multiplication, and combining like terms)...
[tex]a^2+(9a^2+39a+39a+169)=(9a^2+42a+42a+196)\\a^2+(9a^2+78a+169)=(9a^2+84a+196)\\[/tex]
Observe that the equation is a degree-2 polynomial (polynomial with highest power of 2; aka quadratic). Move all terms to one side to get the equation equal to zero in preparation for solving:
[tex]a^2+(9a^2+78a+169)=(9a^2+84a+196)\\a^2+9a^2+78a+169-(9a^2+84a+196)=0\\a^2-6a-27=0\\[/tex]
There are a few ways to solve this, including the quadratic formula. However, factoring the polynomial and using the zero product property is quite efficient here:
Factoring to solve a Quadratic
Since the leading coefficient is 1, we can use the shortcut and find factors of -27 that add to make -6.
-27 has factor pairs of:
1 and -273 and -99 and -327 and -13 and -9 add to make -6, so factoring the polynomial is
[tex]a^2-6a-27=0\\(a+3)(a-9)=0[/tex]
Applying the zero product property...
[tex](a+3)=0[/tex] or [tex](a-9)=0[/tex]
So a=-3 or a=9. Given that this represents a length in a triangle, we discard the negative solution. So a=9.
Finding the other two unknowns
To finish up, substitute the "a" back into the two equations for "b" and "c".
[tex]b=3a+13\\b=3(9)+13\\b=27+13\\b=40[/tex]
[tex]c=3a+14\\c=3(9)+14\\c=27+14\\c=41[/tex]
The original problem set up our measurements in inches, so all three values are measured in inches.
Remember which length was which
"a": short leg
"b": longer leg
"c": hypotenuse
Short leg: 9 in
Long leg: 40 in
Hypotenuse: 41 in.
curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The cone below has a slant height of 23 cm and a
diameter of 6 cm.
Work out the curved surface area of the cone.
Give your answer to the nearest integer and remember
to give the correct units.
6 cm
23 cm
Not drawn accurately
The curved surface area of the cone is 144 cm².
What is the curved surface area?A cone is a three-dimensional object that consists of a circular base and an vertex.
curved surface area = πrl
Where:
r = radius = diameter / 2 = 6/2 = 3 cm l = slant heightπ = 3.143.14 x 3 x 23 = 144 cm²
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In the given figure, ABCD is a parallelogram. Find x, y and z.
Answer:
it is 18 by unknown number
3. Find how many numbers between 232 and 252.
Answer:
252-232=20-1=19
Step-by-step explanation:
the question said in between so you don't count the first and the last numbers
The function f(x) is shown in this graph.
The function g(x) = -7x-1.
Compare the slopes.
f(x)
(0.3)
A. The slope of f(x) is greater than the slope of g(x).
B. The slope of f(x) is less than the slope of g(x)..
C. The slope of f(x) is the same as the slope of g(x).
I need help
Answer:
A maybe?
Step-by-step explanation:
by looking at the graph you can see there are two points with one being at (0, 3) (given) and the other being at (1, 1) (by looking at the graph). You can use the slope formula (y2 - y1) / (x2 - x1) which gives you the slope.
Plug Values In:
(1-3) / (1-0) = -2/1 = -2
slope of f(x) = -2
slope of g(x) = -7 (slope-intercept form y=mx+b where m is the slope and b is the y-intercept)
I'm honestly not quite sure what it means by greater than since technically the slope of f(x) is greater than the slope of g(x) but does it mean how much it's changing by in which case the sign doesn't matter. Although I'm just going to assume it purely means the value in which case A is true.
Find the slope of the curve y=2/x at x=a.
Answer:
We are given:- y=2/xWe need to find the slope of the curve at x=a.Step-by-step explanation:
Solution,
We use the slope formula, setting x=a :
[tex] \displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }[/tex]
[tex] \displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}[/tex]
[tex] \displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}[/tex]
[tex] \displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }[/tex]
Therefore, The slope of the curve y=2/x at x=a is -2/a^2.
Find the average rate of change of the function f(x) - 2x² + 6x + 6, from x=-3 to x=-1. Note, the directions are equivalent to "Find the average rate of change over the interval [-3,-1]".
Answer: -2
Step-by-step explanation:
I will assume you meant [tex]f(x)=2x^{2}+6x+6[/tex].
[tex]f(-3)=2(-3)^2 + 6(-3)+6=6\\\\f(-1)=2(-1)^2 + 6(-1)+6=2\\\\\therefore \frac{f(-3)-f(-1)}{-3-(-1)}=\frac{6-2}{-2}=\boxed{-2}[/tex]
How can I find the three iterations of 3^(x)= 2^(-x)+4
After factorizing the given equation, we can find the three iterations by putting the consecutive values of x.
The given equation is 3∧x = 2∧(-x) + 4. We can modify it as shown below:
Take logarithm on both the sides
log(3∧x) = log[2∧(-x) + 4]
xlog3 = log[2∧(-x) + 4]
x = log[2∧(-x) + 4] / log3
For the first iteration, put x = 1
x = log[2∧(-1) + 4] / log3
x = log4.5 / log3
x = 0.477
For the second iteration, put x = 2
x = log[2∧(-2) + 4] / log3
x = log4.25 / log3
x = 0.477
For the third iteration, put x = 3
x = log[2∧(-3) + 4] / log3
x = log4.125 / log3
x = 0.477
So, this is how we can find three iterations.
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If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).
Answer:
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Step by step explanation:
Given that,
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = x - 1[/tex]
Solution:
Solving for (f•g)(x):
[tex] = f(x) \cdot g(x)[/tex]
Now substitute the given values.
[tex] = x {}^{2} \cdot(x - 1)[/tex]
[tex] = x {}^{2} (x - 1)[/tex]
Apply distributive property:
[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].
What would the following figure look like after a reflection in a horizontal mirror, followed by a rotation 90 degrees counterclockwise?
Answer:
Step-by-step explanation:
To rotate any figure we have to have the CENTER of rotation!!!!
You did not provide us (your helpers) with that point, so I chose point on the horizontal mirror.
A coin is flipped, and a number cube is rolled. What is the probability of getting heads on the coin and a number greater than 5 on the number cube?
HELPPP
Answer:
1/3
Step-by-step explanation:
factorise b^2 + 7b + 10
Step-by-step explanation:
b²+7b+10
Common factors are 5,2
b²+7b+10
b²+2b+5b+10
b(b+2)+5(b+2)
(b+2)(b+5)
Hope it helps.✨✨
Plss HELPP I neeed help on this question
Answer: 180 degrees
Step-by-step explanation:
The measure of the arc of a semicircle is 180 degrees.
find Y if AB bisects DAC and CB bisects ACE
Answer:
L1 and L2 are parallel
BAC = 58° as it is given in the question that AB bisects DAC
similarly BCE = y°
angle B = 90° ( from figure)
Y + 58° + 90° = 180 ( angle Sum property of a triangle).
Y + 148° = 180°
Y = 180 - 148
Y = 32°
Hi supreme turtle this is the question
Answer:
< $0 --------------$35------ $50>
Step-by-step explanation:
wait that's not the full question but uh I assume that's 30% off $50?
it would be 0.3x50 which is 15 and 50-15 is 35.
the range is 0 - $50 if I'm not mistaken
< $0 -------------------------- $50> scuffed number line
but 35 is somewhere around here?
< $0 --------------$35------ $50>
Which equation has a constant of proportionality equal to 1/2
Choose 1 answer:
Quadrilateral WXYZ has vertices W(2, 10), X(10, 10), (10,2), and Z(2, 2). Determine if quadrilateral WXYZ is a rhombus.
A. No, quadrilateral WXYZ is not a rhombus.
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
C. Yes, quadrilateral WXYZ is a rhombus because the slopes of the diagonals are perpendicular.
D. There is not enough information to determine.
Please select the best answer from the choices provided
Answer:
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
Step-by-step explanation:
1) according to the given coordinates the equations of the sides are:
YZ: y=2; WZ: x=2; WX: y=10; XY: x=10. It means
2) YZ⊥WZ; YZ⊥XY; WX⊥XY; WX⊥WZ. To the additional, WX=WZ=YZ=XY, then
3) the given quadrilateral is sqare (rhombus with angles m∠=90°).
4) finally, the correct answer is
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
Which compound inequality is represented by the graph?
-3≤x<1
-3 < x≤1
x≤-3 or x> 1
x<-3 or x ≥ 1
The inequality will be the negative 3 ≤ x < 1. Then the correct option is A.
The missing graph is attached below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Then the inequality will be
-3 ≤ x < 1
Then the correct option is A.
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Answer:
the answer is A
Step-by-step explanation:
An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the box as a function of the length of a side of the base, x.
The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
[tex]= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}[/tex]
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
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