An equation in terms of r which models the situation described is : 100r² = 10r² + 90r - 337.50
First investment :
Luke:
Total amount had = $100
Amount invested = $10
Amount left = $100 - $10 = $90
Return = r times the amount invested = (10 × r) = 10r
Owen:
Total amount had = $100
Amount invested = $100
Return = r times the amount invested = (100 × r) = 100r
Second investment :
Luke :
Amount invested = Return on first + amount left = 10r + 90
Return is r times the amount invested :
Return on second investment = (10r + 90) × r = (10r² + 90r)
Total amount earned after both investment = 10r² + 90r
Owen :
Amount invested = Return on first = 100r
Return is r times the amount invested :
Return on second investment = (100r × r) = 100r²
Total amount earned after both investment = 100r²
Owen made 337.50 more than Luke ; This means that :
Total earned by Owen = Total earned by Luke + 337.50
100r² = 10r² + 90r + 337.50
Hence, the equation in terms of r is : 100r² = 10r² + 90r - 337.50
Learn more : https://brainly.com/question/18796573
factorise [tex]x^{2} + 11x[/tex]
Answer:
x(x+11)
Step-by-step explanation:
x^2+11x
Factor out x
x*x+11x
x(x+11)
THIS IS TIMED! Find the equation of the graphed line.
On a coordinate plane, a line goes through (negative 6, 0) and (0, negative 7).
a.
y = negative 6 x minus 7
c.
y = negative StartFraction 6 Over 7 EndFraction x minus 6
b.
y = 6 x minus 7
d.
y = negative StartFraction 7 Over 6 EndFraction x minus 7
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
x/(-6)+y/(-7)=1
7x+6y=-42
7x+6y+42=0
y=(-7/6)x-7
Enter the missing values in the area model for multiplication below.
5 x 35
30
+
5
25
try
Solve for x.
5x + 3 – 2x = 24
X = [?]
[tex]\\ \sf \longmapsto 5x+3-2x=24[/tex]
[tex]\\ \sf \longmapsto 5x-2x+3=24[/tex]
[tex]\\ \sf \longmapsto 3x+3=24[/tex]
[tex]\\ \sf \longmapsto 3x=24-3[/tex]
[tex]\\ \sf \longmapsto 3x=21[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{21}{3}[/tex]
[tex]\\ \sf \longmapsto x=7[/tex]
(-8)^-2 / 3^-4 simplify the expression. Write your answer using only positiv exponents.
Answer:
3^4 / 8^2 or 81/64
Step-by-step explanation:
(-8)^-2 / 3^-4 =
= 3^4 / (-8)^2
= 3^4 / 8^2
= 81/64
multiply
12/18×10/18
lesson name fraction.
find me out this question for answer
Help anyone can help me do the question,I will mark brainlest.
Step-by-step explanation:
Ans 6 Use Pythagoras theorem...
Hypotneuse²=Base²+Height²
6²=4²+H²
36-16=H²
20=H²
√20=H
√2×2×5=H
2√5 = H....
hope it helps
Problem 4
Draw a diagonal to connect the opposite non-right angles as shown below. This forms two right triangles. As you can probably guess, we'll use the pythagorean theorem to find the length of this segment. We'll call it x.
a^2+b^2 = c^2
7^2+24^2 = x^2
49+576 = x^2
x^2 = 625
x = sqrt(625)
x = 25
The hypotenuse of each right triangle is 25 units long.
Move your focus to the upper right triangle. We can use the pythagorean theorem again in a slightly different way to find y.
a^2+b^2 = c^2
15^2+y^2 = 25^2
225+y^2 = 625
y^2 = 625-225
y^2 = 400
y = sqrt(400)
y = 20
Answer: y = 20====================================================
Problem 6
The largest triangle, ignore segment x for now, is isosceles because we have two congruent sides.
As with any isosceles triangle, the vertex angle is bisected by the perpendicular bisector as shown in the diagram. This produces two identical right triangles. Most importantly, it means that horizontal side 4 is cut in half to 4/2 = 2 units.
In short, each smaller right triangle has a horizontal leg of 2, vertical leg x, and hypotenuse 6. Let's focus on just one of those right triangles.
Like the previous problem, we'll use the pythagorean theorem to find x.
a^2+b^2 = c^2
x^2+2^2 = 6^2
x^2+4 = 36
x^2 = 36-4
x^2 = 32
x = sqrt(32)
x = sqrt(16*2)
x = sqrt(16)*sqrt(2)
x = 4*sqrt(2)
Answer: x = 4*sqrt(2)Write an algebraic expression for “three less than the sum of a number and a four”
Answer:
(x + 4) - 3
Step-by-step explanation:
Let the number be x
(x +4) - 3
1. Determine the measure of the unknown angles indicated by letters. Justify your answers with
the properties or theorems you used.
Answer:
110
Step-by-step explanation:
we use the sum of 3 angles in a triangle is 180
and sum of 2 adjacent angles is 180 too
180= (180-d)+)+(180-85)+(180-165)
so d=110
Step-by-step explanation:
video do oo so do to go do go to
Relaciona la columna de la izquierda con los elementos asociados al polígono
a) centro
b) lado
c) vértice
d) ángulo interno
e) radio
f) ángulo central
g) apotema
h) ángulo exterior
Answer:
i dont know
Step-by-step explanation:
bu bu bu
8x+4=3(x-1) +7 solve
Answer:
x = 0
Step-by-step explanation:
8x + 4 = 3(x − 1) + 7
Simplify both sides of the equation:
8x + 4 = (3)(x)+ (3)(−1) + 7
8x + 4 = 3x + (−3) +7
Combine like terms:
8x + 4 = (3x) + (−3+7)
8x + 4 = 3x + 4
Subtract 3x from both sides:
8x + 4 − 3x = 3x + 4 − 3x
5x + 4 = 4
Subtract 4 from both sides:
5x + 4 − 4 = 4 − 4
5x =0
Divide both sides by 5:
5x/5 = 0/5
x = 0
The pair of shoe cost 2500,On the ocation of Dashain its cost 2000,how much discount does buyer get?
plz help
Total Cost Of Shoe=2500
Totall discount Cost=2000
= 2500-2000
=500
Find the number in which 9 has greater value.
0.5689
5.6890
56.89
569.80
Answer:
569.80Step-by-step explanation:
Among all the choices, the digit 9 has the greatest value in number 569.80. For the reason that 9 got ones value - which are greatest than other.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Find the measure of angle A.
probably i think it is 22.5°
I really need these answered!
Answer:
Step-by-step explanation:
#1) [tex]\arcsin \left(0.64958\right)=0.70703\dots \quad \begin{pmatrix}\mathrm{Degrees:}&40.51^{\circ \:}\end{pmatrix}[/tex]
∡C =62.49
[tex]\frac{\left(\sin \left(27^{\circ \:}\right)\right)}{3}=\frac{\sin \left(54^{\circ \:}\right)}{x}\quad :\quad x=\frac{3\left(\sqrt{5}+1\right)}{\sin \left(27^{\circ \:}\right)\cdot \:4}\quad \left(\mathrm{Decimal}:\quad x=5.34603\dots \right)[/tex]
Find the distance between the origin and the points (-8,4)
Hi, I'm happy to help!
To solve this, we need to find the distance from the origin to the y coordinate value, x coordinate value, then use the Pythagorean Theorem.
The origin of a graph (center) has the coordinates (0,0), so this will be our other coordinates.
First, let's find the x coordinate distance change. We move from the x coordinate 0, to the x coordinate -8, so we move 8 x units.
Next, let's find the y coordinate distance change. We move from the y coordinate 0, to the y coordinate 4, so we move 4 y units.
Now that we have these two leg lengths, let's imagine this as a right triangle. Moving from the origin, we draw a line from (0,0), to (-8,0). Then, we draw a line from (-8,0) to (-8,4). Now, draw a direct line from (0,0), to (-8,4). We have the length of the first(8) and second(4) lines, and we need to find the third line length to find our answer. To do this, we use the Pythagorean Theorem, which states that a²+b²=c². This says that, in a right triangle, the square of the two shorter lengths equals the square of the longest length. The longest length is what we are solving for.
Let's say x distance is a, and y distance is b. Now, apply the values:
8²+4²=c²
64+16=c²
80=c²
Now, we need to find the value of c, so we need to find the square root of 80.
√80=c
8.9442...=c
Since the number goes on forever, we need to round it. For this example, let's round it to the nearest tenth, which would be 8.9.
To summarize the distance between the origin and the coordinates (-8,4), is about 8.9.
I hope this was helpful, keep learning! :D
Answer these questions about finding the missing
angle measures.
What is the measure of
What is the measure of
What can be concluded about these triangles?
Answer choices/:
what can be concluded?
1.corresponding angles are proportional
2.The triangles are congruent
3.The triangles are similar
Answer:
Answer number one the
Step-by-step explanation:
the unequal triangles. If measured by angle, they are equivalent.
PLEASE HELP ASAP!!
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
A. 146.85 units²
B. 45+9√3 units²
C. 36+9√3 units²
D. 36+3√3 units²
The total surface area of the pyramid is 52 square units
The formula for calculating the area of the triangular based pyramid is expressed as;
[tex]TSA=Base \ Area+\frac{1}{2}ps[/tex] where;
p is the perimeter of the base
s is the slant height
Get the Base area
[tex]Base \ Area = \frac{1}{2}bh\\Base \ Area = \frac{1}{2}*6*\sqrt{5^2-3^2} \\ Base \ Area = \frac{1}{2}*6*\sqrt{25-9} \\ Base \ Area = \frac{1}{2}*6*\sqrt{16} \\ Base \ Area = \frac{1}{2}*6*4 \\ Base \ Area = \frac{24}{2} \\Base \ Area = 12 units^2[/tex]
Get the perimeter
Perimeter = 5 + 5 + 6
Perimeter = 16 units
Slant height = 5units
Substitute the given values into the formula above as shown;
[tex]TSA=12+\frac{1}{2}*16*5\\TSA=12+(8*5)\\\\TSA = 12 + 40\\TSA = 52 units ^2[/tex]
Hence the total surface area of the pyramid is 52 square units
Learn more here: https://brainly.com/question/23353623
Answer:
52squnits
Step-by-step explanation:
Rodney and their roommates are making homemade pizza for dinner. Rodney tells his roommates that he would like for his slice to be cut at a 100 degree angle. The pizza has a diameter of 20 inches. To the nearest tenth of an inch, find the area of Rodney's slice of pizza. Approximate pi at 3.14.
Answer:
Area of pizza slice = 87 inches² (Approx.)
Step-by-step explanation:
Given:
Angle cut of pizza = 100°
Diameter of pizza = 20 inches
Find:
Area of pizza slice
Computation:
Area of sector = [Ф / 360][π][r²]
Area of pizza slice = [100/360][3.14][(20/2)²]
Area of pizza slice = [100/360][3.14][(10)²]
Area of pizza slice = [100/360][3.14][100]
Area of pizza slice = [0.2778][3.14][100]
Area of pizza slice = 87.2292
Area of pizza slice = 87 inches² (Approx.)
The path from the subway station to the art museum is three blocks to the north then four blocks to the west.
What is the straight-line distance in blocks from the subway station to the art museum?
Answer:
7 block s
Step-by-step explanation:
3 from North plus
4 from West
4+3=7
If the order of two matrices are different, then the addition of matrices does not exists true or false
Answer:
true
Step-by-step explanation:
A matrix can only be added/subtracted with another matrix if the two matrices have the same dimensions
Put the steps In order
Indicate all the possible values for the variable in each of the
expressions:
13–2x + V1-x
Answer: -3
Step-by-step explanation:
13−2x+V1−x
Combine −2x and −x to get −3x.
13−3x+V
1
The 1 is supposed to be under the V
5. There are 5,280 feet in a mile. What part of a mile, in decimal form, will you drive until you reach the exit? I NEED THIS QUICK PLZ HELP I’LL GIVE YOU 30
Answer:
5.280
Step-by-step explanation:
i did this question and got it
True or False: The function y = (x2 – 4)/(x2 – 4) is continuous for all values of x
Answer:
False
Step-by-step explanation:
The function isn't continuous at x=±2 as a function isn't continuous at the point where the function becomes undefined, this function becomes undefined when the denominator is equal to 0. So x^2-4=0 => x=±2.
Please help im stuck on this pls help ( i have to sort the cubes some how) i will give brainliest to who gets it right
Answer:
see image
three groups of 4 means 12 / 4 = 3
Step-by-step explanation:
Which figure is described below?
The locus of points in a plane
equidistant between
(-5, -6) and (-5, 7).
Answer:
A.Line
Step-by-step explanation:
The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
We know that the graph of x = 5 is the vertical line through 5 on the x-axis. Two points on this line are (-5, -6) and (-5, 7).
We form a horizontal line through (0,1) and (1,1). This is the locus of points equidistant between (-5, -6) and (-5, 7)
We have parallel lines like this, the locus of points equidistant from the two lines is always one single line, and it's the middle line as described above.
This applies to diagonal parallel lines as well, and vertical parallel lines.
Hence, The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.
Learn more about a point dividing a line segment in a ratio here:
https://brainly.com/question/14186383
#SPJ2
A real estate agent receives a 3%
commission for selling a house. Find the
commission that the agent earned for
selling a house for $131,000.
you just have to divide the value by 100 and then multiply by 3 (the order doesn't matter tho) so,
131000/100 = 1310 x 3 = 3930
the commission is $3930.00
hope it helps :)
A cylindrical paint can has a diameter of 12 centimeters and height of centimetrs which is closest to the volume of the paint can in cubic centimeters
Answer:
The correct answer is "1808.64 cm³".
Step-by-step explanation:
Seems that the given query is incomplete. Below find the attachment of the complete problem.
Given:
Diameter,
d = 12 cm
Radius,
r = [tex]\frac{d}{2}[/tex]
= [tex]\frac{12}{2}[/tex]
= [tex]6 \ cm[/tex]
Height,
h = 16 cm
As we know,
The volume of cylinder is:
= [tex]\pi r^2 h[/tex]
By substituting the values, we get
= [tex]3.16\times (6)^2\times 16[/tex]
= [tex]3.14\times 36\times 16[/tex]
= [tex]1808.64 \ cm^3[/tex]
state the following true or false
Answer:
c. false (it should always be neg.)
d. false
Step-by-step explanation:
Answer:
(c) True, (d) False
Step-by-step explanation:
