Answer:
Option C. [tex]\$34,252.67[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=18\ years\\ P=\$8,193\\ r=0.08\\n=6[/tex]
substitute in the formula above
[tex]A=\$8,193(1+\frac{0.08}{6})^{6*18}=\$34,252.67[/tex]
f(x)=2x an$ g(x)=2x+3,what is the value of f(g(-8))
First plug in g(x) into f(x)
F((g(x))=2(2x+3)
And now you plug in -8
F(g(-8))=2(-16+3)
F(g(-8))=2(-13)
F(g(-8))=-26
What is the measure of angle ABC?
Answer:
42.5
Step-by-step explanation:
110 - 25 divided by 2 because
angle ABC = (angle AC- angle DE)÷2
A jet travels 600 miles in 5 hours. At this rate, how far could the jet fly in 14 hours. What is the rate of speed of the jet?
Find the jets speed per hour by dividing distance by time:
600 miles / 5 hours = 120 miles per hour. ( Rate of speed)
Now multiply the speed by time:
120 miles per hour x 14 hours = 1,680 miles.
Answer:
120 miles per hour
Step-by-step explanation:
The rectangular prism has a volume of 93 cubic centimeters. Which equation can be used to find the height, h, of the prism? A.h = 93 × 15 . 5 B.ℎ=93.5×15.5×15.5 C.ℎ=93/15.5 D.h = 15 . 5/93
Answer: option C
Step-by-step explanation:
The volume of a rectangular prism can be calculated with this formula:
[tex]V=l*w*h[/tex]
Where "V" is the volume of the prism "l" is the lenght, "w" is the width and "h" is the height.
You know that the volume of this prism is 93 cubic centimeters and you need to find the height. Then, you have to solve for "h":
[tex]h=\frac{V}{l*w}[/tex]
You can observe that the volume is in the numerator and the product of the lenght and the width of the rectangular prism is in the denominator, then, the option that matches this form is the option C:
[tex]h=\frac{93}{15.5}[/tex]
Answer:
H= 93/15.5
Step-by-step explanation:
which of the following could be the system of nonlinear inequalities graphed below?
Answer:
Option A.
Step-by-step explanation:
step 1
we know that
The equation of the solid line is
[tex]y=5[/tex]
The solution is the shaded area above the solid line
so
The equation of the first inequality is
[tex]y\geq 5[/tex]
step 2
The equation of the dashed line is
[tex]y=x^{2} -5x+6[/tex]
The solution is the shaded area above the dashed line
so
The equation of the second inequality is
[tex]y>x^{2} -5x+6[/tex]
therefore
The system of inequalities could be
[tex]y\geq 5[/tex]
[tex]y>x^{2} -5x+6[/tex]
(3a ^3)^x = 27a^9
what’s the value of x?
Answer:
x = 3Step-by-step explanation:
[tex](3a^3)^x=27a^9\\\\(3a^3)^x=3^3a^{3\cdot3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(3a^3)^x=3^3(a^3)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\(3a^3)^x=(3a^3)^3\iff x=3[/tex]
If you have two dice and you roll one, what is the probability the second dice is less than or equal to the first dice number?
Answer:the probability is 0.5
Step-by-step explanation:
Iterations question two need help please :)
Answer:
option b
1 , 16, 121 , 13456
Step-by-step explanation:
Given in the question a function, f(x) = (x - 5)²
initial value [tex]x_{0}[/tex] = 4
First iteration
f(x0) = f(4) = (4 - 5)² = (-1)² = 1
x1 = 1
Second iteration
f(x1) = f(1) = (1 - 5)² = (-4)² = 16
x2 = 16
Third iteration
f(x2) = f(16) = ( 16 - 5)² = (11)² = 121
x3 = 121
Fourth iteration
f(x3) = f(121) = (121 - 5)² = (116)² = 13456
x4 = 13456
Which equation could be used to find the number of scarves, x, Syrilla needs to sell in order to earn $200? I don’t know the work
Answer:
Step-by-step explanation:
(1) 4x = 200
(2) 50
Answer:
4x = 200
50
Step-by-step explanation:
One scarf = $4
Number of scarves = x
Amount she needs to earn = $200
Equation
4x = 200
Number of scarves
= 200 ÷ 4
= 50
Please help! Thank you
Answer:
336 ft squared
Step-by-step explanation:
Looking for face area, not volume
So...
10*12=120
6*12=72
8*12=96
6*8/2=24
6*8/2=24
24+24+120+72+96=336ft squared
A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.
Answer:
The radius of circle is 5 cm
Step-by-step explanation:
Given a right triangle △ABC with right angle C is inscribed in a circle in which
m∠C = 90°, AC = 8 cm, BC = 6 cm
we have to find the radius of circle.
As ACB is right angles triangle where angle C is right angle.
⇒ side AB must be the diameter of circle as angle made at semi circle is 90°
[tex]Radius=AO=\frac{1}{2}AB[/tex]
By Pythagoras theorem
[tex]AB^2=AC^2+CB^2[/tex]
[tex]AB^2=8^2+6^2=64+36=100[/tex]
[tex]AB=10cm[/tex]
[tex]Radius=AO=\frac{1}{2}AB=\frac{1}{2}\times 10=5cm[/tex]
Hence, the radius of circle is 5 cm
Which of the following is true?
A.Perpendicular lines never intersect each other.
B.Parallel lines always intersect each other
.C.Parallel lines are always in the same plane.
D.Perpendicular lines are not in the same plane.
Answer:
C.
Step-by-step explanation:
A - Perpendicular lines always touch each other at least once.
B - Parallel lines never touch.
D- Not always true.
C is true. If they are not in the same plane they are skewed lines.
The true statement is C: Parallel lines are always in the same plane. Perpendicular lines do intersect, while parallel lines do not, and perpendicular lines can certainly be in the same plane. Hence, correct option C.
The question seeks to determine the accuracy of given statements about geometric relationships between. Perpendicular lines and parallel lines. Based on the provided theorems, the true statement is: C. Parallel lines are always in the same plane.
This is because if two lines are parallel, they will be equidistant from each other at all points, which can only occur if they are in the same plane. Statements A, B, and D are false.
Perpendicular lines do intersect at a 90-degree angle.
Parallel lines, by definition, never intersect as they are always equidistant.
Perpendicular lines can be in the same plane or in different planes, although a line that is perpendicular to a plane must lie in another plane.
Anybody know the answers to these 3?
Answer:
Part 1) The area of the shaded region is [tex]2.1\pi\ m^{2}[/tex]
Part 2) The length of the arc AB is [tex]2.5\pi\ in[/tex]
Part 3) The area of the shaded region is [tex]56.53\pi\ in^{2}[/tex]
Step-by-step explanation:
Part 1) Find the area of the shaded region
step 1
Find the area of the circle
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=3\ m[/tex]
substitute
[tex]A=\pi (3)^{2}[/tex]
[tex]A=9\pi\ m^{2}[/tex]
step 2
we know that
The area of complete circle subtends a central angle of 360 degrees
so
by proportion
calculate the area of the shaded region with a central angle of 84 degrees
[tex]\frac{9\pi }{360} =\frac{x }{84}\\ \\x=(9\pi)*84/360\\ \\x=2.1\pi\ m^{2}[/tex]
Part 2) What is the length of arc AB?
step 1
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=5\ in[/tex]
substitute
[tex]C=2\pi (5)[/tex]
[tex]C=10\pi\ in[/tex]
step 2
we know that
The length of complete circle subtends a central angle of 360 degrees
so
by proportion
calculate the length of the arc AB with a central angle of 90 degrees
[tex]\frac{10\pi }{360} =\frac{x }{90}\\ \\x=(10\pi)*90/360\\ \\x=2.5\pi\ in[/tex]
Part 3) Find the area of the shaded region given that XY measures 8 in
step 1
Find the area of the circle
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]XY=r=8\ in[/tex]
substitute
[tex]A=\pi (8)^{2}[/tex]
[tex]A=64\pi\ in^{2}[/tex]
step 2
we know that
The area of complete circle subtends a central angle of 360 degrees
so
by proportion
calculate the area of the shaded region with a central angle of (360-42)=318 degrees
[tex]\frac{64\pi }{360} =\frac{x }{318}\\ \\x=(64\pi)*318/360\\ \\x=56.53\pi\ in^{2}[/tex]
for v= 4i - 5j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vectors i and j.
Answer:
a. [tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]
Step-by-step explanation:
The given vector is v= 4i - 5j
The magnitude of this vector is;
[tex]|v|=\sqrt{(-4)^2+(-5)^2}[/tex]
[tex]|v|=\sqrt{16+25}[/tex]
[tex]|v|=\sqrt{41}[/tex]
The unit vector u in the direction of v is;
[tex]u=\frac{v}{|v|}[/tex]
[tex]u=\frac{4i - 5j}{\sqrt{41}}[/tex]
[tex]u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}[/tex]
We rationalize to get
[tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]
The area of a rhombus is 65 square units. The length of one diagonal is 13 units. What is the length of the other diagonal? 5 units 6 units 10 units 12 units
Answer:
The length of the other diagonal is 10 units
Step-by-step explanation:
we know that
The area of a Rhombus is equal to
[tex]A=\frac{1}{2}[D1D2][/tex]
where
D1 and D2 are the diagonals of the rhombus
we have
[tex]A=65\ units^{2}[/tex]
[tex]D1=13\ units[/tex]
substitute in the formula and solve for D2
[tex]65=\frac{1}{2}[(13)D2][/tex]
[tex]130=[(13)D2][/tex]
[tex]D2=130/13=10\ units[/tex]
Answer:
10
Step-by-step explanation:
Mustafa buys seed packets for a community garden. One packet of basil seeds costs $1.50. One packet of squash seeds costs $2.50. Let b represent the number of packets of basil seed. Let s represent the number of packets of squash seeds. Mustafa spent $38 on 18 packets of seeds. How many packets of each type of seeds did Mustafa buy?
Answer:
Step-by-step explanation:
b+s=18
s=18-b
1.50 b+2.50 s=38
multiply by 4
6.00 b+10.00 s=152
divide by 2
3 b+5 s=76
3 b+5(18-b)=76
3 b+90-5 b=76
-2b=76-90
-2b=-14
divide by -2
b=7
s=18-7=11
There are total 11 packets of squash seeds and 7 packets of basil seeds.
What is system of linear equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
What is substitution method?The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.
According to the given question.
Cost of one packet of basil seeds = $1.50
Cost of one packet of squash seeds = $2.50
Cost of 18 packets of seeds = 38
Also, b represents the number of packets of basil seeds and s represents of numbers of squash seeds.
Therefore, from the given conditions we get some system of equations
[tex]s + b = 18..(i)[/tex]
and [tex]b(1.50) + s(2.50) = 38...(ii)[/tex]
From equation (i)
[tex]s = 18-b[/tex]
Substitute the value of s in the equation (ii)
⇒[tex]1.50b+(18-b)2.50 =38[/tex]
⇒ [tex]1.50b + 45 - 2.50b = 38[/tex]
⇒[tex]-b = 38-45[/tex]
⇒ [tex]-1b =- 7[/tex]
⇒[tex]b = 7[/tex]
So, [tex]s = 18 - 7 =11[/tex]
Hence, there are total 11 packets of squash seeds and 7 packets of basil seeds.
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What is the solution to his equation 2x+6=20
2x+6=20
move 7 to the right side.
The sign changes from positive to negative. whenever moving a number to the other side the sign changes.
2x+6-6=20-6
2x= 14
Divide by 2 for both of the numbers
x=7
check answer:
Substitute x into the equation
2(7)+6=20
20= 20
Answer: x=7
The solution of the given linear equation in one variable is x = 7.
What are linear equations?The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.
Given is a linear equation in one variable, 2x+6 = 20,
We need to find its solution,
Since, the given linear equation has only one variable, so it will have only one solution.
The equation is =
2x+6 = 20
Solving for x,
2x = 20-6
2x = 14
x = 7
Hence, the solution of the given linear equation in one variable is x = 7.
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hugo must divide 5 apples among his 3 nephews. Each nephew receives the same amount, and there are no apples left over. How many apples did each nephew receive?
Answer:
D
Step-by-step explanation:
5 divided by 3 is 1.6666 which is the same as 1 and 2/3
The correct answer is D
Please solve and give answer
ANSWER
domain:
[tex]x \geqslant - 3[/tex]
Range
[tex]y \leqslant - 2[/tex]
EXPLANATION
The given function is
[tex]f( x) = - \sqrt{x + 3} - 2[/tex]
This base of this function is
[tex]y = \sqrt{x} [/tex]
This function has been shifted to the left 3 units and down 2 units.
This function is reflected in the x-axis.
Therefore graph starts at (-3,-2) and move down forever.
The domain is obtained using the expression under the radical sign.
It must be greater than or equal to zero.
[tex]x + 3 \geqslant 0[/tex]
[tex]x \geqslant - 3[/tex]
The range is
[tex]y \leqslant - 2[/tex]
Help! Ill mark you as brain! 15 points!
Answer:
35 in²
Step-by-step explanation:
The irregular shaped can be divided into two squares and one rectangle, so the area will be the additions of the area of the squares and the rectangle
area of square A = L *B = 3 *3 = 9in²
area of square B = L * B = 4*4 = 16in²
area of rectangle C = L * B = 5 *2 = 10in²
th area of the irregular shape = 9 in² + 16 in² + 10 in² = 35 in²
Write a function for the situation described and find the value after 7 yrs. A $16,800 car depreciates 11% each year
Answer:The starting value is 20,300, and the value is decreasing by 9.5% each year.
Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.
A decrease by 9.5% corresponds to multiplying by 91.5% each year.
We write . We plug in 11 years for t.
$7,671.18
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Step-by-step explanation:
Answer:
The starting value is 20,300, and the value is decreasing by 9.5% each year.
Step-by-step explanation:
Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.A decrease by 9.5% corresponds to multiplying by 91.5% each year.We write . We plug in 11 years for t.
The measures of the three angles of a triangle are (X)°,(2x)°and (3x)° what is the value of x
Help it’s due TOMORROW!!!!!!
Answer:
x=30
Step-by-step explanation:
Add up all of the values of the angles and set it equal to 180 degrees since a triangle is always made up of angles that have a sum of 180 degrees.
x+2x+3x=180
6x=180
x=30
Maggie’s bank has assigned her a temporary 3-digit PIN to use with her ATM card. Each digit is a number from 1 to 5, inclusive, and no digit can be used more than once in the PIN. Which multiplication problem can be used to determine the probability that the PIN she was assigned was 123?
A 1/5 1/5 1/5
B 1/5 1/4 1/3
C 4/5 3/4 2/3
D 4/5 4/5 4/5
Answer:
B 1/5 1/4 1/3
Step-by-step explanation:
The first digit Maggie's bank picked from the 5 digit available, so 1/5.
The second digit will be picked from the 4 remaining digits available, so 1/4.
For the final digit, the bank will have only 3 options to choose from, so 1/3.
So the possibility for the 3-digit assigned PIN to be 123 is
[tex]\frac{1}{5} * \frac{1}{4} *\frac{1}{3} =\frac{1}{60}[/tex]
1/60, so the formula is the one presented in the B option: 1/5 1/4 1/3
Which of these tables represents a non-linear function?
Answer:
The third table
Step-by-step explanation:
A linear function must increase or decrease at a constant rate. All the tables either add 1 or subtract 1 each time x increases except for the third one which at one point adds two. This is not a consistent increase and therefore is not linear
Answer:
3ed tabel
Step-by-step explanation:
adds 1 to both sides so its a non leirn
3x = 2* + 25
IF YOU HELP YOU GET BRAINLIEST PLEASE HELP FAST
Is the answer 25? Thats what I got.
The equation of a circle is x^2+y^2+18x+4y+49=0. What are the center and the radius of the circle?
please help I am failing math and have no idea what's :) going :) on :) in :) class :)
Answer:
Center: (-9, -2)
Radius = 6
Step-by-step explanation:
The general equation of the circle is:
[tex]x^{2} + y^{2}+2gx+2fy+c=0[/tex]
The center of the circle is given as (-g, -f) and the radius of this circle is calculated as:
[tex]r=\sqrt{g^{2}+f^{2}-c}[/tex]
The given equation is:
[tex]x^{2} +y^{2}+18x+4y+49=0[/tex]
Re-writing this equation in a form similar to general form:
[tex]x^{2} +y^{2}+2(9)(x)+2(2)(y)+49=0[/tex]
Comparing this equation with general equation we get:
g = 9
f = 2
c = 49
Thus center of the given circle is (-g, -f) = (-9, -2)
The radius of the circle will be:
[tex]r=\sqrt{9^{2}+2^{2}-49}=6[/tex]
Thus the radius of the given circle is 6.
I need help on number 19 ! Please for brainless answer !!
Answer:
Yes
Step-by-step explanation:
We need to determine the sides of the squares
Area = 9
A = s^2
9 = s^2
Taking the square root of each side
sqrt(9)= sqrt(s^2)
3 =s
Perimeter of a square = 16
P =4s
16 =4s
Divide each side by 4
16/4 =4s/4
4 =s
Side = 5 in
Right triangles obey the Pythagorean theorem
a^2 + b^2 = c^2
Putting the smaller sides in for a and b
3^2 +4^3 = 5^2
9+16=25
25=25
Since this is true, we can arrange the squares to make a right triangle
Answer:
Yes, due to the Pythagorean theorem.
Leg A would be 3
Leg B would be 4
Hypotenuse C would be 5
Explanation:
When making the right triangle, only one side length value is needed.
If the area of square one is 9, 9 divided by 2 is 3.
If the perimeter of square two is 16, 16 divided by 4 is 4.
The single side length for square three is given, which is 5.
The Pythagorean theorem consists of a^2 + b^2 = c^2.
Plug in the values.
3^2 + 4^2 = 5^2
9 + 16 = 25
Hope this helps! :)
ABC bank requires a 20% down payment on all of its home loans if a house is priced at 185000 what is the amount of the down payment required by the bank?
It would be 37’000 because 20% of 185000 is 37’000 which you get by 20 x 185000 and dividing the answer to 100.
Is the answer is b, please help
The correct answer is b
What is the equation of a circle with center (-3,-1) that contains the point (1,2)?
Answer:
(x + 3)^2 + (y + 1)^2 = 25
Step-by-step explanation:
Equation of a circle with center (h, k) and radius, r.
(x - h)^2 + (y - k)^2 = r^2
The center is (-3, -1), so h = 1, and k = 2.
(x - (-3))^2 + (y - (-1))^2 = r^2
(x + 3)^2 + (y + 1)^2 = r^2
Now we substitute x and y with the values of x and y from the given point, and we solve for r^2.
(1 + 3)^2 + (2 + 1)^2 = r^2
4^2 + 3^2 = r^2
16 + 9 = r^2
r^2 = 25
Now that we know r^2, we substitute it into the equation above.
(x + 3)^2 + (y + 1)^2 = 25
Answer:
The correct answer is,
(x + 3)² + (y +1)² = 25
Step-by-step explanation:
It is given that, What is the equation of a circle with center (-3,-1) that contains the point (1,2)
Formula;-
Equation of the circle passing through the point ( x₁,y₁) with radius r is given by,
(x - x₁)² + (y - y₁)² = r²
To find the radius of circle
r =√[ (1 --3)² + (2 --1)²]
=√(4² + 3²)
= √(16 + 9)
=√25 = 5
To find the equation of the circle
(x₁, x₁) = (-3, -1) and r = 5
(x - x₁)² + (y - y₁)² = r²
(x - -3)² + (y - -1)² = 5²
(x + 3)² + (y +1)² = 25