Answers
y amount earns 8% interest
The total investment is $1000, so the first equation is
x + y = 1000
x amount at 4% earns 0.04x interest
y amount at 8% earns 0.08y interest
The total interest earned is $50, so our second equation is
0.04x + 0.08y = 50
We have a system of two equations in two unknowns.
x + y = 1000
0.04x + 0.08y = 50
Multiply the first equation by -0.04 and add to the second equation.
-0.04x - 0.04y = -40
+ 0.04x + 0.08y = 50
-----------------------------------
0.04y = 10
Divide both sides by 0.04:
y = 250
Substitute y = 250 in the first equation to find x.
x + y = 1000
x + 250 = 1000
x = 750
Answer: x = 750, y = 250
Related Questions
What is the simplified form of (x – 2)(2x +3)? Use the Distributive Property. (1 point)
2x2 – x – 6
2x2 – 6
2x2 – 7x – 6
2x2 + x – 6
2. What is the simplified form of (3x + 2)(4x – 3)? Use a table. (1 point)
12x2 + 18x + 6
12x2 + x – 6
12x2 + 18x – 6
12x2 – x – 6
3. What is the simplified form of (4p – 2)(p – 4)? (1 point)
4p2 + 6p – 16
4p2 – 18p + 8
4p2 – 14p – 6
4p2 – 6p + 16
4. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.,
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2. 12x2 – x –6
3. 4p2 – 18p + 8
how fast is the water level rising in a rectangular fish tank whose base is 20 ft^2 if the tank is being filled at a rate of 0.5ft^3/min
Answers
0.5 ft^3 = (20 ft^2)h
h = (0.5 ft^3)/(20 ft^2) = 0.025 ft
The rate of change of water depth is 0.025 ft/min.
The water level is rising at a rate of 0.025 ft/min.
To determine how fast the water level is rising in the rectangular fish tank, you can use the formula for the volume of a rectangular prism:
V = base area × height
Given that the base area is 20 [tex]ft^2[/tex] and the tank is being filled at a rate of
0.5 cube ft/min, you want to find the rate at which the height (h) is changing [tex](\frac{dh}{dt} )[/tex].
V = base area × height
[tex]\frac{d V}{d t}=\text { base area } \times \frac{d h}{d t}[/tex]
Substitute the known values:
0.5 = 20 x [tex](\frac{dh}{dt} )[/tex]
Now, solve for [tex](\frac{dh}{dt} )[/tex]
[tex]\frac{d h}{d t}=\frac{0.5}{20}[/tex] = 0.025 ft/min
Thus, the required answer is 0.025 ft/min.
Jose owns 40 shares of stock A whose price increased by $0.75 per share. He also owns 100 shares of stock B whose price decreased by $0.20 per share. What is the total change in the value of Paul’s stock (A and B together)?
PLEASE HELP!
Answers
Paul's portfolio increased in value by $10.
The original value of a car is 18000, and it depreciates (loses value) by 15% each year. What is the value of the car after three years?
Answers
.. 18,000*0.85^3 = 11,054.25
If one angle of a triangle measures 32 degrees and another angle measures 71 degree, what is the measure of the third angle?
Answers
A circular piece of glass has a radius of 2.1 meters. The glass sells for $1.70 per square meter. What is the total cost of the circular piece of glass?
$23.54
$94.16
$3.57
$11.21
Answers
A rectangle is 7 feet long by 2 feet wide. If 2 feet are added to the length of the rectangle, what would be the area, in square feet, of the new rectangle?
Answers
If a rectangle is 7 feet long by 2 feet wide and 2 feet are added to the length of the rectangle then the area of rectangle is 18 square feet.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that a rectangle has a length of 7 feet.
The width of rectangle is 2 feet.
We have to find the area of rectangle when 2 feet is added to the length of rectangle
Initial length is 7 feet
When 2 feet is added the length will be 7+2, 9 feet.
Area of rectangle = Length × width
=9×2
Nine times two is eighteen.
=18 square feet.
Hence, if a rectangle is 7 feet long by 2 feet wide and 2 feet are added to the length of the rectangle then the area of rectangle is 18 square feet.
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Regard triangleTRI and the following facts:
Segment IR || Segment NA
TA= 12 cm, RA= 3 cm, NT= 18 cm, AN= 22
(a)What theorem or postulate proves Triangle ANT similar to RIT?(b)Solve for NI by using the Side-Splitting Theorem.Show all work.(c)What is the scale factor for similar triangles ANT and RIT?
(d)Calculate RI. Show your work.
(e)What is the ratio of the areas of the two triangles? Show your work.
Answers
B) NI = 4.5
C) 4:5
D) RI = 27.5
E) 16:25
Explanation
We will set up a proportion for b:
AT/RT = NI/TI
12/15 = 18/x
Cross multiply:
12*x = 18*15
12x = 270
Divide both sides by 12:
12x/12 = 270/12
x = 22.5
Since TI = TN + NI, we have
22.5 = 18 + NI
-18 -18
4.5 = NI
C) The ratio of the sides of the smaller triangle to the larger rectangle are given by the ratio AT/RT, or 12/15 = 4/5.
D) Setting up a proportion we have
AN/RI = AT/RT
22/RI = 12/15
Cross multiply:
22*15 = RI*12
330 = 12RI
Divide both sides by 12:
330/12 = 12RI/12
RI = 27.5
E) The ratio of the areas will be the square of the ratio of the side lengths, since area is a square measurement:
(4/5)² = 4²/5² = 16/25
Laila is having shirts made with a logo printed on them to promote her band. The total cost consists of a one-time fee of $75 to have the logo designed, plus $8 per shirt to print the logo. Write an equation that Laila can use to determine the total cost c, in dollars, to make x shirts
Answers
Is the mean always a more accurate measure of center than the median
Answers
PLS HELP ME ASAP ON THIS!! THANK YOU SO MUCH!!
BRAINLIEST WILL BE GIVEN
(RANDOM ANSWERS GETS MODERATED.)
Answers
The other two are
.. 0 fries + 1 shake + 1 burger = 4.20
.. 1 fries + 1 shake + 0 burger = 2.80
_____
Add any two orders and subtract the third to find the cost of one of the items.
For example add the two orders written above and subtract the one shown in the picture.
.. (1 fries + 2 shakes + 1 burger) - (1 fries + 1 burger) = (4.20 +2.80) -(3.40)
.. 2 shakes = 3.60
.. 1 shake = 1.80
Then the last equation tells you
.. 1 fries = 2.80 - 1 shake = 1.00
and the first equation tells you
.. 1 burger = 3.40 - 1 fries = 2.40
1 fries = $1.00
1 shake = $1.80
1 burger = $2.40
Factor completely: 9ab + 12ax - 6b - 8x (1 point)
1. Prime
2. (3b - 4x)(3a - 2)
3. (3b + 4x)(3a - 2)
4. (3b + 4x)(3a + 2)
Answers
Use FOIL to expand each factored form, only #3 will result in 9ab + 12ax - 6b - 8x
find the exact value of cos285 using the fact that 285=330-45
Answers
A horizontal line goes through the point (–7,10). Which statements are true about this line? Check all that apply. The slope of the line is zero. Another point on the line is (3,10). The y-intercept of the line is –7. The equation of the line is y = 10.
Answers
All horizontal lines have a slope of 0
B. Another point on this line is (3,10). True
All points on this line have a y coordinate of 10
C. The y intercept of the line is -7. False
The y intercept is 10 which is at the point (0,10)
D. The equation of the line is y = 10. True
The equation y = 10 indicates all y coordinates are 10 while the x coordinate is anything you want.
------------------------------------------------------------------------
Answers are: A, B, and D
The statement 1,2, and 4 are true and 3 is not true below given the reason behind it.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph is made up of some points and the distance between two It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.
The given statement is a line passing through ( -7, 10 ) so
Option 1 ⇒ the slope of that line will be zero because it is a horizontal line so it will be true.
Option 2 ⇒another point on this line will be (3,10) since it is a horizontal line so the y coordinate is the same and the x coordinate can vary so it is also true.
Option 3 ⇒ the y-intercept of this line will be 10 which is not true and can be confirmed by options 1 and 2.
Option 4 ⇒ the equation of the line will be y =10 which is true hence it is a horizontal line.
For more details about the graph
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Somebody help. I can’t figure this question out. thanks
Answers
.. (30 mm)/(21 mm) = (14 mm +x)/(14 mm)
.. (14 mm)*10/7 = 14 mm +x
.. (14 mm)*(10/7 -1) = x
.. (14 mm)*(3/7) = x = 6 mm
The value of x is 6 mm.
[tex]21 \div 30 = 14 \div 14 + x[/tex]
[tex]30 \times 14 = 420[/tex]
[tex]21 \times 14 + x = 294 + 21x[/tex]
[tex]420 = 294 + 21x[/tex]
[tex]420 - 294 = 126[/tex]
[tex]126 = 21x[/tex]
[tex]126 \div 21 = 6[/tex]
[tex]x = 6[/tex]
Find the ratio of the longest side to the perimeter of the right-triangular-shaped billboard. 20 feet 21 feet 29 feet
Answers
29/70
29 to 70
the ratio is 29 ft. to 70 ft.
Solution:
we have been asked to find the ratio of the longest side to the perimeter of the right-triangular-shaped billboard.
Sides of the right-triangular-shaped billboard are 20 feet 21 feet 29 feet.
As we know perimeter is just the sum of all the sides.
Perimeter[tex]=20+21+29=70\\[/tex]
And the longest side is 29 feet.
Hence the required ratio [tex]=\frac{29}{70}=29:70[/tex]
4) A mountain climber climbed up a cliff 1/4 mile at a time. he did this 5 times in one day. How many miles did he climb up? *
Answers
1/4+1/4+1/4+1/4+1/4= 1 1/4.
If arc XV = 68° and ∠YUV = 36°, what is the measure of arc VY?
Answers
we have
arc XV = 68°
∠YUV = 36°
we know that
The measure of the external angle is the semidifference of the arcs that it covers.
therefore
∠YUV =[arc VY-arc XV]/2
arc VY=[2*∠YUV]+arc XV----------> [2*36]+68---------> 140°
the answer is
the measure of arc VY is 140°
please help me thank you.
Answers
.. s = rθ . . . . . . . . . . . θ in radians
Your arc length is
.. s = (5 m)*(2π/3)
.. = 10π/3
.. ≈ 10.47 m
The 3rd selection is appropriate.
A cell phone weighs about 2.8X10^n pounds. Which value of n is most reasonable? A)-3 b)-1 c)0 d)1
please help im stuckk
Answers
2.8 * 10^-3 = 0.0028 - Much too light
2.8 * 10^-1 = 0.28 - Reasonable weight
2.8 * 10^0 = 2.8 - Too heavy
2.8 * 10^1 = Much too heavy
[tex]\sf 10^{-3}=0.001[/tex]
[tex]\sf 10^{-1}=0.1[/tex]
[tex]\sf 10^0=1[/tex]
[tex]\sf 10^1=10[/tex]
[tex]\sf 2.8\times 0.001=0.0028[/tex]
[tex]\sf 2.8\times 0.1=0.28[/tex]
[tex]\sf 2.8\times 1=2.8[/tex]
[tex]\sf 2.8\times 10=28[/tex]
So what is the most reasonable weight for a cell phone? 0.0028 pounds, 0.28 pounds, 2.8 pounds, or 28 pounds? I would definitely say 0.28 pounds.
Soon you will determine the right triangle connection the pythagorean theorem
Answers
Where is the centroid of any given triangle?
A. the point of concurrency of the altitudes of the triangle.
B. the point of concurrency of the medians of the triangle.
C. the point of concurrency of the perpendicular bisectors of the triangle.
D. the point of concurrency of the angle bisectors of the triangle.
Which of the following best describes the altitude of a triangle?
A. a segment perpendicular to a side of the triangle.
B. a segment that passes through the midpoint and is perpendicular to a side of a triangle.
C. a segment drawn from the ve
Answers
1. The centroid of any given triangle is at B. the point of concurrency of the medians of the triangle. It is a point is where the three points of the medians of the triangle meet.
2. B. a segment that passes through the midpoint and is perpendicular to a side of a triangle. It is line segment that is perpendicular to a line containing the base
Find the volume for the regular pyramid.
4 cu. units
6 cu. units
12 cu. units
Answers
Formula is V = lwh/3
v=volume
I=base length
w=base length
h=base height
Answer:
[tex]4\ cu.\ units[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of the pyramid
h is the height of the pyramid
Find the area of the base
[tex]B=2^{2}=4\ units^{2}[/tex]
[tex]h=3\ units[/tex]
Find the volume
[tex]V=\frac{1}{3}(4)(3)=4\ units^{3}[/tex]
Explain what needs to happen to the inequities sign when dividing or multiplying by a negative number
Answers
2 > 1
-2 < -1 . . . . . multiplied or divided by -1
___
A more "interesting" case is when a function is applied that has a negative slope.
0 < a < b < π
cos(0) > cos(a) > cos(b) > cos(π)
Given that the points (-3, 8), (2, 8), (2, -2), and (-3, -2) are vertices of a rectangle, what is the ratio of the rectangle's length to its width?
Answers
A ---> (-3, 8)
B ---> (2, 8)
C----> (2, -2)
D----> (-3, -2)
step 1
find the distance AB
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(8-8)²+(2+3)²]----> d=√25-----> d=5 units
step 2
find the distance BC
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(-2-8)²+(2-2)²]----> d=√100-----> d=10 units
step 3
find the ratio of the rectangle's length to its width
ratio=rectangle's length/rectangle's width
length=10 units
width=5 units
ratio=10/5-----> ratio=2
the answer is
the ratio of the rectangle's length to its width is 2
see the attached figure
Answer:
2:1
Step-by-step explanation:
Cheryl volunteers to mow the lawn at a retirement home.She can mow 1/4 of the lawn in 3/4 of an hour .At what rate ,how many hours will it take Cheryl to mow the entire lawn
Answers
Since she mows 1/4 in 3/4 hours, you can multiply 4 and 3/4 . . .
4 = 4/1
3/4 = 3/4
4 x 3 = 12
1 x 4 = 4
Simplifying 12/4 . . .
12/4 = 3 <---------
It will take 3 hours for Cheryl to mow the entire lawn.
Hope this helps you.
Have a great day!
can someone help me with this?
Answers
I did it by plugging the functions into a graphing calculator and seeing which one matched, but you could also plug in 2 or 3 values into each x position and see which one's results matched with the shown function.
Which ordered pair is a solution for this system of inequalities?
2x + 3y > 1 and y < 5/4 x - 1
A.(3, 9)
B.(-4, 2)
C.(8, -1)
D.(-2, -5),
Answers
For this problem, the easiest method is to simply try each of the 4 possible answers and see which one fits. So
A. (3, 9)
2x + 3y > 1
2*3 + 3*9 > 1 ; Obviously true, not going to finish calculation.
y < 5/4 x - 1
9 < 5/4 3 - 1
9 < 15/4 - 1 ; Obviously false, not going to finish calculation.
B. (-4, 2)
2x + 3y > 1
2*(-4) + 3*2 > 1
-8 + 6 > 1 ; Obviously false, not going to finish calculation.
No need to bother with 2nd inequality.
C. (8, -1)
2x + 3y > 1
2*8 + 3*(-1) > 1
16 - 3 > 1 ; Obviously true, not going to finish calculation.
y < 5/4 x - 1
-1 < 5/4 * 8 - 1
-1 < 40/4 - 1
-1 < 10 - 1 ; Obviously true, not going to finish calculation.
Both inequalities satisfied, this is the correct choice.
D. (-2, -5)
2x + 3y > 1
2*(-2) + 3*(-5) > 1; Left hand side is obviously negative, so obviously false,
not going to finish calculation.
No need to bother with 2nd inequality.
The triangles are congruent by SSS or HL. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation
Answers
Answer:- The sequence of the transformations for the given diagram must be reflection, then rotation, then translation.
Explanation:-
Given : Four triangles which are congruent by SSS postulate or HL theorem.
According to the given diagram , the rigid transformations are as follows
1. Reflection: ΔABC is flipped about BC to form ΔA'BC such that AC=A'C and its is already given that they are congruent thus the rigid transformation used here is reflection.
2. Rotation:- ΔA'BC is rotated about point A' at some angle to form ΔA'B'C' , and they are congruent (given). Thus the rigid transformation used here is rotation.
3.Translation:- ΔA'B'C' is translated exactly right by some factor to form ΔA"B"C" ∵ all the points have changed but as these triangles are congruent (given) then corresponding parts must be equal.Thus the rigid transformation used here is translation.
The sequence should be in the order for the given transformation as, reflection, then rotation, then translation. Thus the option D is the correct option.
How to rotate, reflect, and translation the figure?Rotation, reflection and translation is the way of transformation of an figure.
Rotation- Rotation of an object is rotating it about a fixed point without changing its shape and size.Reflection- Reflecting of an object is flipping it across a line without changing its shape and size.Translation- Translation of an object is the shifting of the object without changing its dimensions, without rotating it and without reflecting it.Given information-
In the given diagram the, triangle ABC is transformation into the three stages.
First the figure ABC is just flipped into the triangle A'BC by keeping the side BC fixed.Then the triangle A'BC is rotated around the point A' and to place of A'B'C'.Finally the figure is transact right from one place to another which is A"B"C".Hence the correct sequence of the transformations is reflection, then rotation, then translation. Thus the option D is the correct option.
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trevor needs to let his puppy outside every quarter (1 fourth) hour to potty train him. draw and label a number line from 0 hours to 1 hour to show every 1 fourth hour.