The amount invested in the account that earns 10% interest is $2000.
The amount invested in the account that earns 13% interest is $3000.
What are the linear equations that represent the question?a + b = 5000 equation 1
0.1a + 0.13b = 590 equation 2
Where:
a = amount invested in the account that earns 10% interest b = amount invested in the account that earns 13% interest How much was invested in the account that earns 13% interest ?Multiply equation 1 by 0.1
0.1a + 0.1b = 500 equation 3
Subtract equation 3 from equation 1
90 = 0.03b
Divide both sides by 0,03
b = $3000
How much was invested in the account that earns 10% interest ?
Subtract $3000 from $5000: 5000 - 3000 = $2000
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the radius of the bigger circle is 9cm and the area of the shaded region is twice that of the smaller circle then how long is the radius of the smaller circle ?
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
How to determine the radius of the smaller circle
In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:
[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]
2 · r² = (9-r)²
2 · r² = 81 - 18 · r + r²
r² + 18 · r - 81 = 0
The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
Remark
The image is missing and is thus included in the figure attached below.
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30-60-90 Triangle Practice
I need help with this, I do not understand anything.
(Teacher just give us hw expecting to know it already.)
Answer:
When there are numbers like that next to the radical it means multiply. like this: 2√9. You would first figure out the square root. Square root of 9 is 3. 2 times 3 is 6.
After you figure out those problems, you just need to put the number, x, and y in an equation with 2 unknowns.
Step-by-step explanation:
Answer:
When there are numbers like that next to the radical it means multiply. like this: 2√9. You would first figure out the square root. Square root of 9 is 3. 2times 3 is 6.
Step-by-step explanation:
Consider the expression below.
9 + 4(x + 2) – 3x
Select the term that best describes "3" in the given expression.
A.
exponent
B.
variable
C.
coefficient
D.
constant
Answer:
the term that best describes 3 is a coefficient because a
Step-by-step explanation:
Coefficient is a number that is being multiplied by the variable.
Pre Calc question, thanks for the help! Question linked in photo below.
The valid solution for the positive demand is (6,3)
How to determine the valid solutions?The equation of the function is given as:
[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]
Next, we test the options::
Option (a): (t, C(t)) = (2,3)
This gives
[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)
Option (b): (t, C(t)) = (6,3)
This gives
[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{0} + 3 = 3[/tex]
Evaluate the root
0 + 3 = 3
Evaluate the sum
3 = 3 ---- this is true
Hence, the valid solution for the positive demand is (6,3)
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Find the midpoint of the line segment with end coordinates of:
(-4,-4) and (-4,-8)
Answer:
(-4, -6)
Step-by-step explanation:
(x,y) = ((x1+x2)/2 , (y1+y2)/2)
[substitute the values given]
(x,y) = ((-4+-4)/2 , (-4+-8)/2)
[solve]
(x,y) = (-8/2 , -12/2)
[simplify]
(x,y) = (-4, -6)
THE ANSWER IS (-4, -6) HOPE IT HALP'S MARK IT AS BRAILY.
Please help, i need right answers and be help if it with proof, ty! Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.
Which sequence of transformations will produce the same results?
a reflection over the y-axis and then a rotation 90degree clockwise about the origin
a reflection over the x-axis and then a rotation 90degree clockwise about the origin
a 180degree rotation about the origin
a reflection over the y-axis and then a reflection over the x-axis
Answer:
A. A reflection over the y-axis and then a rotation 90 degree clockwise about the origin.
Step-by-step explanation:
Given information: Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.
This means Figure H is made by G rotated CLOCKWISE and reflected over the X-AXIS.A sequence of transformations to produce the same results could be the opposite of this, wherein Figure H undergoes a series of transformations to form Figure G.
A reflection over the y-axis flips figure H like folding a piece of paper in half vertically. To help visualize, the point (5, -2) becomes (-5, -2). A 90 degree clockwise turn about the origin makes the point (-5, -2) on figure H to become (-2, 5). Figure G has the same point at (-2, 5).so, a reflection of figure H over the y-axis and then a rotation 90 degree clockwise about the origin will form figure G, thus producing the same results.The length of a reclangle can be represented by the expression 2x - 1. The width of the same rectangle can be represented by the expression x^2 - x + 3. Which of the following expressions can represent the area of the rectangle?
Answer:
2x^3 - 3x^2 + 7x - 3
Step-by-step explanation:
Area = length * width
= (2x - 1)(x^2 - x + 3)
= 2x(x^2 - x + 3) - 1(x^2 - x + 3)
= 2x^3 - 2x^2 + 6x - x^2 + x - 3
= 2x^3 - 3x^2 + 7x - 3
Which number produces a rational answer when added to 0.85
The number that produces a rational answer when added to 0.85 is; 193/180
How to identify rational numbers?A rational number is an algebraic term expressed as a fraction. The fraction can also be in decimals but only if the decimal places are not repeating or not infinitely long. If they aren't, then these are called irrational numbers.
Now, let us convert 0.85 to a fraction. Thus;
0.85 = 85/100 = 17/20
From the given options, the only one that when added to 0.85 will yield a rational number is 2/9. This is because;
17/20 + 2/9 = 193/180
193/180 is a rational number.
The missing options are;
A. 2/9
B. 0.2645751311...
C. √2
D.
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A comparson of two or more quantities of the same kind is called a
Bob's family pays $50.37 at the pizzeria. This included a 19% tip. What was the cost of the bill without the tip percentage. (Please include how to solve it)
Answer:
$43.33
Step-by-step explanation:
50.37/119 = ?/100
cross multiply,
? = 43.3277
Give brainliest, please!
Hope this helps :)
What is startfraction 3 pi over 4 endfraction radians converted to degrees? if necessary, round your answer to the nearest degree.
Unit conversion is a way of converting some common units into another without changing their real value. The value of (3π/4) radian converted to a degree is 135°.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
Since π radian is equal to 180°. Therefore, the value of (3π/4) radian is equal to,
1 radian = 180°/π
(3π/4) radian = (3π/4) × (180°/π) = 135°
Hence, the value of (3π/4) radian converted to a degree is 135°.
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Answer:
option 2
Step-by-step explanation:
If $3840 is deposited into a bank account at a 5% interest rate how long will it take the account to make $960 in interest?
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]
The number of slugs in a garden t days from now is p, where
Po = 100
P1+1= 1.06pt
Work out the number of slugs in the garden 3 days from now.
The number of slugs in the garden 3 days from now is 119
How to determine the number of slugs?The function is given as:
Po = 100
[tex]P_{t+1} = 1.06P_t[/tex]
When t = 0, we have:
[tex]P_{0+1} = 1.06P_0[/tex]
[tex]P_1 = 1.06 * 100\\[/tex]
[tex]P_1 =106[/tex]
When t = 1, we have:
[tex]P_2 = 1.06 * 106[/tex]
[tex]P_2 = 112.36[/tex]
When t = 2, we have:
[tex]P_3 = 1.06 * 112.36[/tex]
[tex]P_3 = 119.1016[/tex]
Approximate
[tex]P_3 = 119[/tex]
Hence, the number of slugs in the garden 3 days from now is 119
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The table below represents the closing prices of stock ABC for the last five
days. Using your calculator, what is the equation of linear regression that fits
these data?
Day
Value
1
20.71
2
19.69
3
19.61
4
19.64
5
19.26
OA. y = 0.289x + 21.459
OB. y=-0.311x + 19.213
O C. y=-0.295x+20.667
D. y=-0.272x+22.319
Using a calculator, it is found that the equation of linear regression that fits the data is given by:
C. y=-0.295x+20.667
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are given as follows: (1, 20.71), (2, 19.69), (3, 19.61), (4, 19.64), (5, 19.26). Hence the equation is:
Doing this, the equation is:
y = -0.295x + 20.667.
Hence option C is correct.
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Find Measure of angle B (m18. a = 7 m, b = 5 m, m∠A = 45°
Answer:
30.34 degree
Step-by-step explanation:
Apply sine formula
[tex]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}[/tex]
[tex]\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}[/tex]
->simplify
[tex]\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}[/tex]
you will get
[tex]\sin \left(b\right)=\frac{5\sqrt{2}}{14}[/tex]
which
sin b is about 0.50507
[tex]sin^{-1}\left(0.50507\right)[/tex]
->arc sine in degree mode
the answer is 30.34
This graph talks about supply and demand can I get some help with it?
well that's Economics not Mathematics
Mary O’Connell is earning a weekly salary of $521.60 as a payroll clerk. She has accepted a new assignment in the tax processing department. In her new position, she will be paid an annual salary of $30,534. How much more will she earn per week in her new position
Answer:
$ 65.59 more per week
Step-by-step explanation:
Assuming she worked 52 weeks a year as a clerk :
30534 - 52 * 521.6 = $ 3410.80 more per year
now each WEEK that is 3410.80 / 52 = 65.59
This chart shows the result of an experiment conducted to see the effect of different brands of fertilizers on the growth of a bean plant.
Which of the following ranges would be appropriate to use in order to represent the numerical data in centimeters on the vertical axis of a Line Graph?
A. 0.0 to 26.0
B. 0.0 to 25.0
C. 14.0 to 25.2
D. 0.0 to 20.0
The range that is appropriate to use to represent the numerical data is 0.0 to 26.0.
What is a line graph?
A line graph is a graph that is used to represent numerical data. It shows the changes in the data with the passage of time. There are two axes on a line graph, the vertical axis and the horizontal axis. The range of the vertical axis should start from 0 and end at the largest number of data set.
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pls help me answer thiss. I really really need help! thank u
Answer:
see explanation
Step-by-step explanation:
the centroid is where the medians intersect.
On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.
(3)
GF = [tex]\frac{1}{2}[/tex] CG = [tex]\frac{1}{2}[/tex] × 14 = 7
CF = CG + GF = 14 + 7 = 21
(4)
GD = [tex]\frac{1}{3}[/tex] AD = [tex]\frac{1}{3}[/tex] × 45 = 15
AG = 2 × GD = 2 × 15 = 30
(5)
GE = 2 × BG , that is
9x = 2(3x + 6) = 6x + 12 ( subtract 6x from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
5 feet to 31 inches write the ratio of the first measurement to the second measurement compare in inches
Answer:
60:31
Step-by-step explanation:
6x - 5y = 8
-12x + 2y = 0
Answer:
the answer is in picture
Step-by-step explanation:
hope it will help you
Solve for the h in the triangle below. Round to the nearest tenth. 90⁰ 6.0 Oh-13.3 Oh 5.5 Oh 8.0 53%
Answer:
h=8.0
Step-by-step explanation:
law of sines
sinA/a=sinB/b
b/a=sinB/sinA
b = a times sinB/sinA
b = 10 times sin53/sin90
on a calculator type sin53 in degrees
b = 10 times 0.7986/1
b = 7.986
Rational and irrational numbers
Answer:
Rational numbers is a ratio (i.e., P/Q and Q≠0)
Irrational numbers cannot be expressed as a fraction.
so a
Rational numbers can show a Fraction
Irrational numbers can not show a Fraction
Hope This Helped
Answer:
Rational numbers are any infinite number or ratio that goes on and on and represents such mathematical values, e.g five-over-twelve is a rational number because it is a fraction.
Irrational numbers are squares of a number or any number that does not include a comparison(e.g division, fraction, ratio, etcetera) of a value. For instance, the square root of 2 is an irrational number because it does not go on indefinitely.
asap need help quick
Answer:
Answer:11
Step-by-Step Answer:
When we multiply 11 with 1\2 then thier answer will be 11\2
(c) If f(x) = a^x , then show that f(m +n + p) = f(m). f(x). f(p)
[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]
ACTIVITY #1
Try It!
A. Write the definition, property, postulate or theorem that will prove each of the given statements.
What completes the proof are:
1. LC ≅ CU; CU ≅ UK
2. Given
3. Unequal angle theorem (Aa → Ss)
What is the Unequal Angle Theorem?The unequal angle theorem states that the longer side of a triangle will always be directly opposite the largest angle measure. This implies that, if an angle that is opposite a side is greater than another another, the side it is opposite will also be longer than the side opposite the other angle (Aa → Ss).
From the image given, statement 1 was given as well as statement 2.
Statement 1 would be: LC ≅ CU; CU ≅ UK.
The reason for statement 2 will also be "given".
Then, UL > CK using the unequal angle theorem (Aa → Ss).
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The equation of line A is y = 5 - 2x Line B is parallel to line A. Line B passes through the point (-3,7)
Work out the coordinates of the point where line B intersects the x-axis.
Answer:
The answer is (0.5, 0)
Step-by-step explanation:
- Write the inequality that shows how much money you can spend on the booth.
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if you have $1000 and need to buy 10 chairs worth $5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:
x + 10(5) ≤ 1000
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.
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(3x+43)^((2)/(3))+22=38
Answer:
X = 7 and -35.6666
Step-by-step explanation:
A ser of esta consists of four scores…
Answer:
x4 = 8
Step-by-step explanation:
To find the mean, add the values and divide by the number of values.
mean = (x1 + x2 + x3 + x4)/4
(3 + 12 + 7 + x4)/4 = 8
x4 + 22 = 32
x4 = 10
Answer:
x4 = 8
Step-by-step explanation: