Answer:
2.5 years
Step-by-step explanation:
The given amount invested, which is the principal, P = $16,800
The simple interest rate, R = 5% per annum
The intended total value of the investment, A = $18,900
The simple interest on the principal, I = A - P
∴ I = $18,900 - $16,800 = $2,100
The formula for the simple interest, I, is given as follows;
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Therefore, we have;
[tex]T = \dfrac{I \times 100}{P \times R}[/tex]
Plugging in the values, gives;
[tex]T = \dfrac{2,100 \times 100}{16,800 \times 5} =2.5[/tex]
The time it will take the investment to grow to $18,900 is T = 2.5 years
which kind of triangle is shown.
1. obtuse isosceles
2. acute equilateral
3. obtuse scalene
4. right scalene
Answer: 2, acute equilateral
Step-by-step explanation:
the image shows a triangle with all 3 sides congruent and 3 acute angles
change the following to grams only
a. 7kg 85g
b. 6kg 346g
c. 5kg 342g
Answer:
a) 7085g
b) 6346g
c) 5342g
Step-by-step explanation:
1kg = 1000g
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
A s= 3/ 10m
B s= 10/3m
C m=3/10s
D m=1/30s
Answer:
Step-by-step explanation:
I'm assuming that the length of the spring is s and the mass of the object is m. If that be the case, the direct variation equation, which a line btw, is
s = km where k is the constant of proportionality. We have to solve for k, the slope of the line, in order to determine the model for this situation.
9 = k(30) so
[tex]k=\frac{9}{30}=\frac{3}{10}[/tex] Now that we know, the slope of the line, we can rewrite the equation with the slope in place:
[tex]s=\frac{3}{10}m[/tex], choice A.
Find the height of the triangle
Answer:
The height is 12 cm
Step-by-step explanation:
Hi there!
We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).
This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.
One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.
Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:
a=15
b=20
c=25
Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle
15²+20²=25²
225+400=625
625=625
So we can safely say that the triangle is a right triangle
This makes the problem way easier, as there are 2 ways to find the area of a right triangle:
The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2
The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2
First, we need to figure out which sides are the legs, and which side is the hypotenuse
By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs
So let's find the area of the triangle using the legs
A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150
So the area of the triangle is 150 cm²
However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2
Which means that the area is also:
A=[tex]\frac{25x}{2}[/tex] cm²
As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)
[tex]\frac{25x}{2}=150[/tex]
Multiply both sides by 2
25x=300
Divide both sides by 25
x=12 cm
So the height of the triangle is 12 cm
Hope this helps!
Simplify 5 x 5^2 leaving your answer in index form.
Answer:
5^3
Step-by-step explanation:
5^1 x 5^2
indices rules when multiplying you add the powers to 1+2=3
5^3
3.) Find the measure of the missing angle X:
Xº
120°
70°
Answer:
x=50
Step-by-step explanation:
Let's look at the red angle. if a flat line makes the angle 180, and the outer angle is 120, subtract 120 from 180. This will give you 60. Now every angle of a triangle added together will give you the sum of 180. So you already have 60 and 70, which make 130 all together. Subract 130 from 180 - (180-130) - and you'll get the result of 50.
The solution is : the measure of the missing angle X is x=50.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
from the given diagram, we get,
Let's look at the red angle.
if a flat line makes the angle 180, and the outer angle is 120,
subtract 120 from 180.
This will give you 60.
Now every angle of a triangle added together will give you the sum of 180.
So you already have 60 and 70,
which make 130 all together.
Subtract 130 from 180
i.e. (180-130) = 50
and we get the result of 50.
Hence, The solution is : the measure of the missing angle X is x=50.
To learn more on angle click:
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……………….pls and thx——————-
Answer:
14 yards shorter
Step-by-step explanation:
Use Pythagoras' Theorem
a²+b²=c²
16²+63²=4225
√4225= 65yd
The diagonal line (c) is 65 yards long
16 + 63 = 79 yd
It would be 14 yards shorter (79-65)
Evaluate the line integral 2 + x2y ds where c is the upper half of the circle x2 + y2 = 1.
Parameterize C by
r(t) = 〈x(t), y(t)〉 = 〈cos(t), sin(t)〉
with 0 ≤ t ≤ π. Then the line integral is
[tex]\displaystyle \int_C (2+x^2y)\,\mathrm ds = \int_0^\pi (2+\cos^2(t)\sin(t))\left\|\mathbf r'(t)\right\|\,\mathrm dt \\\\ = \int_0^\pi (2+\cos^2(t)\sin(t)) \,\mathrm dt = \boxed{\frac23+2\pi}[/tex]
Will Mark Brainlest Help Please Please
Answer:
a=2
b=-3
c=2
d=0
Step-by-step explanation:
3a+b=3......1
3c-d=6.......2
a-b=5....... 3
a+b+d=2d-1
a+b=2d-d-1
a+b=d-1......4
taking equation 1 and 3 we get,
3a+b =3....... 1
a-b=5
a=5+b
substitute the value of a in equation 1 we get,
3*(5+b)+b=3
15+3b+b=3
4b=3-15
4b=-12
b=-12/4
b=-3
now putting the value of b in equation 3 we get,
a-b=5
a+3=5
a=5-3
a=2
substitute the value of a and b in equation 4 we get,
a+b=d-1
2-3=d-1
-1=d-1
d=-1+1
d=0
substitute the value of d in equation 2 we get,
3c-d=6
3c-0=6
3c=6
c=6/3
c=2
[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]
Now constructing equations
[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]
[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]
[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]
[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]
Adding eq(1) and (2)
[tex]\\ \sf\longmapsto 4a=8[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]
[tex]\\ \bf\longmapsto a=2[/tex]
Put the value in eq(2)
[tex]\\ \sf\longmapsto a-b=5[/tex]
[tex]\\ \sf\longmapsto b=a-5[/tex]
[tex]\\ \sf\longmapsto b=2-5[/tex]
[tex]\\ \bf\longmapsto b=-3[/tex]
put the values in eq(4)
[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]
[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]
[tex]\\ \sf\longmapsto d-1=2d-1[/tex]
[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]
[tex]\\ \sf\longmapsto -d=0[/tex]
[tex]\\ \bf\longmapsto d=0[/tex]
Put the value in eq(3)
[tex]\\ \sf\longmapsto 3c-d=6[/tex]
[tex]\\ \sf\longmapsto 3c-0=6[/tex]
[tex]\\ \sf\longmapsto 3c=6+0[/tex]
[tex]\\ \sf\longmapsto 3c=6[/tex]
[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]
[tex]\\ \sf\longmapsto c=2[/tex]
A candy jar contains several small pieces of candy:
• 5 miniature peanut butter cups
• 7 dark chocolate candy bars
• 8 gummy worms
Roger randomly selected one piece of candy from the jar.
Problem
Read aloude What is the probability in decimal form that the candy Roger selected was NOT a gummy worm?
Answer:
12/20 = 60%
Step-by-step explanation:
The probability that the candy Roger selected was NOT a gummy worm;
P(Not a gummy worm) = 0.6
We are told the quantity of candies in the jar is as follows;
Miniature peanut butter cups = 5
Dark Chocolate bars = 7
Gummy worms = 8
Total number of candy bars = 5 + 7 + 8
Total number of candy bars = 20
Probability is found as; number of possible outcomes/number of events.
P(randomly selected is a gummy worm) = 8/20
P(randomly selected is a gummy worm) = 0.4
Thus, probability that it was not a gummy worm = 1 - 0.4Probability that it was not a gummy worm = 0.6
Read more at; https://brainly.com/question/13160116
what is the answer ，and how do you solve it .please help
Answer:
10
Step-by-step explanation:
2000/ 2x = 10
Multiply each side by 2x
2000/ 2x = 10 *2x
2000 = 20x
Divide by 20
2000/20 = 20x/20
100 = x
Take the square root of each side
sqrt(100) = sqrt(x)
10 = sqrt(x)
can you help me to do this
Answer:
keep the pic clearly
Step-by-step explanation:
keep the pic clearly
Jason counted by 6's aloud and Lawton counted by 4's aloud. What is the first number they will both say?
Answer:
12
Step-by-step explanation:
The first number they will both say = L.C.M of (6,4)
=> L.C.M of (6,4) is 12
The first number they will both say is 12
solve this simultaneous linear equation=X+y=4and2x-y=5
From eq(1)
[tex]\\ \sf\longmapsto x+y=4[/tex]
[tex]\\ \sf\longmapsto x=4-y\dots(3)[/tex]
Put values in eq(2)[tex]\\ \sf\longmapsto 2x-y=5[/tex]
[tex]\\ \sf\longmapsto 2(4-y)-y=5[/tex]
[tex]\\ \sf\longmapsto 8-2y-y=5[/tex]
[tex]\\ \sf\longmapsto 8-3y=5[/tex]
[tex]\\ \sf\longmapsto 8-5=3y[/tex]
[tex]\\ \sf\longmapsto 3y=3[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{3}{3}[/tex]
[tex]\\ \sf\longmapsto y=1[/tex]
Put value in eq(3)
[tex]\\ \sf\longmapsto x=4-y[/tex]
[tex]\\ \sf\longmapsto x=4-1[/tex]
[tex]\\ \sf\longmapsto x=3[/tex]
A train travelling at 30km/hour reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel, how long is the train?
Answer: 111.1 m
Step-by-step explanation:
(30*2)/60 = 1 km ( the tunnel length is 1 Km.)
1 Km = 1000 m.
1000/9 = 111.1 m.
What is the largest number that has the factors of 3, 4 and 5 between 57 and 250?
I think the answer is 240
In the paper airplane shown, ABCD = EFGH, M
Answer:
it should be 90 I could be wrong
Solve for t in terms of q, r, and s.
r = sqt
t=
Answer:
t=r/(sq)
Step-by-step explanation:
r=sqt
=> r/(sq)=t
Answer:
T= r/(sq)
Step-by-step explanation:
r= sqt
=r/(sq) =t
Rewrite the expression (x2 – 3x – 18)/(x – 9) using the long division method.
Answer:
x + 3
Step-by-step explanation:
Image below
Is it the answer option D?
Answer:
D
Step-by-step explanation:
graph it
Circles in the Coordinate Plane
Acellus
Complete the equation of this circle:
A
1
Answer: [tex](x-3)^2 + (y-2)^2 = 16[/tex]
Explanation:
The center of this circle is point A(3,2). These coordinates are the (h,k) values.
The radius is r = 4
Plug those three items into the template [tex](x-h)^2 + (y-k)^2 = r^2[/tex] to arrive at the final answer shown above.
recurring decimals to fractions and give Convert the following she answer a simplest form 0•28 when 8 is recurring
Answer:
13/45
Step-by-step explanation:
x = .2888888888
100(x + .2888888)
100x + 28.8888
10x + 2.88888
90x = 26
x = 26/90 = 13/45
i need help this is the question.
A manufacturer determines that the cost of making a computer component is $.3.191919 Write the repeating decimal cost as a fraction and as a mixed number.
Let x = 3.191919…. Then 100x = 319.191919…, and we have
100x - x = 319.191919… - 3.191919…
99x = 316
x = 316/99
Next, we have
316 = 297 + 19 = 3 × 99 + 19
so
316/99 = (3 × 99 + 19)/99 = 3 + 19/99
in a right triangle the two sides are 10 and 5. find all possible values for the third side.
hint: there are two possibilities
Answer:
1. about 11.18
2. about 8.66
Step-by-step explanation:
1. 5^2 + 10^2= 125
square root of 125 equals about 11.18
2. 10^2-5^2=75
square root of 75 equals about 8.66
4 1
+
15
(Type a simplified fraction.)
5
Answer:
7/15
Step-by-step explanation:
hope the picture helps
A factory produces wrenches. The factory wants all of its
wrenches to weigh the same, but will accept a certain level of er-
ror. The inequality below describes the error they are willing to
accept, in pounds:
Answer:
b
Step-by-step explanation:
Zero is_______greater than any negative integer.
always
never
sometimes
Answer:
always
Step-by-step explanation:
Zero is always greater than any negative integer.
All the negative integers lie to the left of 0 on the number line. This implies that zero is always greater than any negative integer.can you help me? im so confused
Answer:
(AB) is longer than (AC)
Step-by-step explanation:
1. Approach
Use the distance formula to find the length of the segments (AC) and (AB); substitute their endpoints into the distance formula and simplifying to solve for the length. After finding the length of each segment, compare their lengths to find out which of the statements is true. The distance formula is as follows:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the endpoints of the segment.
2. Find the length of (AC)
Coordinates of point (A): [tex](-1,1)[/tex]
Coordinates of point (C): [tex](-4,4)[/tex]
Substitute these points into the distance formula,
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D=\sqrt{((-1)-(-4))^2+((1)-(4))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-1)-(-4))^2+((1)-(4))^2}[/tex]
[tex]D=\sqrt{(-1+4)^2+(1-4)^2}[/tex]
[tex]D=\sqrt{(3)^2+(-3)^2}[/tex]
[tex]D=\sqrt{9+9}[/tex]
[tex]D=\sqrt{18}[/tex]
3. Find the length of (AB)
Coordinates of point (A): [tex](-1,1)[/tex]
Coordinates of point (B): [tex](0,-4)[/tex]
Substitute these points into the distance formula,
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D=\sqrt{((-1)-(0))^2+((1)-(-4))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-1)-(0))^2+((1)-(-4))^2}[/tex]
[tex]D=\sqrt{(-1-0)^2+(1+4)^2}[/tex]
[tex]D=\sqrt{(-1)^2+(5)^2}[/tex]
[tex]D=\sqrt{1+25}[/tex]
[tex]D=\sqrt{26}[/tex]
4. Find the correct statement
(AB) is longer than (AC)
This statement is true for the following reason:
[tex]\sqrt{18}>\sqrt{26}[/tex]
0.008 x 2.5 in standard form is (A) 2 x 10-² (B) 2 x 10 (C) 2 x 10-¹ (D) 2 x 10²
Answer:
(D) 2 x 10²
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Hope it is helpful.....Answer:
2 × 10 ^2
Step-by-step explanation:
(d) option is correct
Find the measurement of the angle diagonal indicated in the following parallelogram
Answer:
24units
Step-by-step explanation:
From the parallelogram given, we can see that the line FH bisects EG at V. Hence;
GE = 2GV.
Given that
GV = 12
GE = 2(12)
GE = 24
Hence the measure of the length GE is 24units
