Answer:
Part 1) The amount invested at 4% was $2,000
Part 2) The amount invested at 9% was $3,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x------> the amount invested at 4%
5,000-x ----> the amount invested at 9%
in this problem we have
[tex]t=1\ year\\ P=\$5,000\\I=\$350\\r1=0.04\\r2=0.09[/tex]
substitute in the formula above
[tex]350=x(0.04*1)+(5,000-x)(0.09*1)[/tex]
[tex]350=0.04x+450-0.09x[/tex]
[tex]0.05x=450-350[/tex]
[tex]0.05x=100[/tex]
[tex]x=2,000[/tex]
so
[tex]5,000-x=5,000-2,000=3,000[/tex]
therefore
The amount invested at 4% was $2,000
The amount invested at 9% was $3,000
15 points?Im just being lazy Lol
Answer:
38
Step-by-step explanation:
The 38-deg angle and <6 are vertical angles, so they are congruent.
m<6 = 38 deg
Answer:
38 degrees. Congruent inside angles. <3
Step-by-step explanation:
The distance between the points (3, 3) and (7, 3) is 4 √13 6
Answer:
4 units
Step-by-step explanation:
We have to calculate the distance between two points first to check the correct answer.
so,
The formula for distance is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\Here\\(x_{1},y_{1})=(3,3)\\(x_{2},y_{2})=(7,3)\\Putting\ Values\\d=\sqrt{(7-3)^{2}+(3-3)^{2}}\\d=\sqrt{(4)^{2}+(0)^{2}}\\d=\sqrt{16+0} \\d=\sqrt{16} \\Taking\ Square\ Root\ will\ give\ us:\\d=4 units\\So\ the\ distance\ between\ two\ points\ is\ 4\ units ..[/tex]
Could you Solve. 21r<7
Yes, I can solve that inequality.
Any value of ' r ' that's less than 1/3 is a solution.
Answer:
r < 1/3
Step-by-step explanation:
21r<7
Divide each side by 21
21r/21<7/21
r < 1/3
Does every line have a slope and a y-intercept? Explain
Answer:
the answer is yes because on a graph, even if it has a x intercept, it will eventually intercept the y intercept b/c the line will continue infinitely.
Step-by-step explanation:
Please mark brainliest and have a great day!
no
no becuase not every line acrosses along the whole graph and the y intercept gose up and down
the average height range if a golden retriever is 20-24 inches. Write the average height range as an absolute value inequality
Answer:
|x-22| < 2
The < has an underline below it
The absolute value inequality that represents the average height range of a golden retriever (20-24 inches) is |h - 22| <= 2, where h represents any height within the range. This means that the difference between any height in the range and the midpoint (22 inches) is at most 2 inches.
Explanation:To write the average height range of a golden retriever as an absolute value inequality, we need to first find the midpoint of the range and then use that to express the distance from any height in the range to that midpoint. In this case, the average height range for a golden retriever is 20-24 inches. The midpoint of the range is (20 + 24) / 2 = 22 inches. So, any height h in the range satisfies |h - 22| <= 2. This is because the maximum difference between any height in the range and the midpoint is 2 inches (24 - 22 or 22 - 20).
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Help please!........
Answer:
circumference is 21.99 and area is 47 and 2/35 unit squared sorry if its a little late
Determine the number of solutions for the equation shown below.
X = X-9
A. O
B. Infinitely many
c. 1
D. 2
Answer:
A. 0
Step-by-step explanation:
Nothing can be equal to itself if you subtract 9 from it.
Final answer:
The equation X = X - 9 yields a contradiction upon simplification (0 = -9), indicating that there are no solutions.
Explanation:
To determine the number of solutions for the given equation, we start by inspecting it closely:
X = X - 9
If we attempt to solve for X, we will subtract X from both sides of the equation:
0 = -9
This is a contradiction since 0 does not equal -9. Therefore, the given equation has no solution. Other examples of equations can have one solution, such as X = 1, or have two solutions, such as quadratic equations like x = 4.133 or 9.435. But in this case, the equation does not balance and therefore has no solutions.
The correct answer is:
A. 0
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a
tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds,
how far is the ball off the ground?
30 meters
40 meters
50 meters
60 meters
Answer: 50 meters
Step-by-step explanation: I just finished the pretest
Answer: The ball is 50 m off the ground after 2 seconds
Step-by-step explanation:
Given the function relating the height of an object off the ground to the time spent falling is a quadratic relationship.
Therefore if h=height and t=time then
[tex]h=a+bt+ct^{2}[/tex] ----------(A)
where a,b and c are constants
Apply given conditions
At t=0s h=90 m
=> 90 m = a+0+0
=>a=90 m
Also the ball has been just dropped at t=0 s
=>[tex]\frac{\partial h}{\partial t}=0=>\frac{\partial (a+bt+ct^{2})}{\partial t}=0[/tex]
=>[tex]b+2ct=0[/tex]
For t=0s b = 0
Thus equation (A) is reduced to [tex]h=90+ct^{2}[/tex]
At t= 3 s , h=0 m
[tex]\therefore 0= 90 +9c=>c=-10 \frac{m}{s^{2}}[/tex]
Finally we get [tex]h=90-10t^{2}[/tex]
Therefore at t= 2.0 s , [tex]h=(90-10\times 2^{2})m=50 m[/tex]
Thus the ball is 50 m off the ground after 2 seconds
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is {y|y < 16}. The domain is all real numbers. The range is {y|y ≤ 16}. The domain is {x|–5 < x < 3}. The range is {y|y < 16}. The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}-2x+15[/tex]
This is a the equation of a vertical parabola open downward
The vertex is a maximum
The vertex is the point (-1,16)
see the attached figure
therefore
The domain of the function is all real numbers ----> interval (-∞,∞)
Te range of the function is
[tex]y\leq 16[/tex]
All real numbers less than or equal to 16 ----> interval (-∞,16]
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}.
Step-by-step explanation:
B on edg
Writing about Translating Phras
Explain how to translate the phrase into an algebra
expression
a number squared decreased by ten
Answer:
Step-by-step explanation:
This can only be written one way.
Let the number = x
x^2 - 10
is how the statement translates.
x^2 = x*x
the 2 means that you need two xs.
The ^ means that you multiply the two xs.
Answer:
Hey there.. I will be more than happy to help you today.. :)
A Number squared decreased by ten
We will do this with steps:-
Step 1 - "A number ". So, Let's say any number be x
Step 2 - "A number squared". Our number x is squared i.e. x²
Step 3 - "A number squared" ( i.e. x² ) is decreased by ten
x² - 10
This is your answer.
Hope this helps you :)
Step-by-step explanation:
Hope you got helped
Find the value of k such that the quadratic polynomials x2-(k+6)x+2(2k+1) as sum of the zeroes as the half of their product
Answer:
k = 5
Step-by-step explanation:
The sum of the zeros is the opposite of the coefficient of x, so is (k+6).
The product of zeros is the constant term, 2(2k+1), so half their product is (2k+1).
The problem statement asks us to find k so that these values are the same:
k +6 = 2k +1
5 = k . . . . . . . . subtract k+1
The value of k is 5.
_____
The zeros are 5.5±√8.25. Their sum is 11; their product is 22.
WILL GIVE BRAINLIEST b. Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
Answer:
When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000
The slope of cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000
The slope of cost function over this part is 0
When 20000 < x <= 42000
The cost decreases when x increases from 20000 to 42000
The slope of cost function
[tex]m = \frac{y2 - y1}{x2 - x1} \\ = \frac{(0.83 - \frac{40000}{200000}) - (0.83 - \frac{20000}{200000})}{40000 - 20000} [/tex]
m= -5 × 10^-6
The letters that form the word ALGEBRA are
placed in a bowl. What is the probability, as a
percent, of choosing a letter other than A
and then choosing an A?
Answer:
Nearly 23.8%
Step-by-step explanation:
The word ALGEBRA consists of letters A, L, G, E, B, R and A (2 letters A and 5 letters other than A).
The probability that the first letter chosen will be other than A is
[tex]\dfrac{5}{7}[/tex]
Then 2 letters A and 4 letters other than A left (6 letters in total). The probabilty that the second letter chosen is A is
[tex]\dfrac{2}{6}=\dfrac{1}{3}[/tex]
Hence, the probability of choosing a letter other than A and then choosing an A is
[tex]\dfrac{5}{7}\cdot \dfrac{1}{3}=\dfrac{5}{21}\approx 23.8\%[/tex]
The probability of first drawing a letter other than 'A' and then drawing an 'A' from the word ALGEBRA is approximately 23.81%. This is determined by calculating the individual probabilities and then multiplying them together.
Explanation:The word ALGEBRA has 7 letters. The probability of choosing a letter other than 'A' means we are considering 5 valid letters out of the 7. Therefore, the probability is 5/7. Then, looking for an 'A' within the remaining 6 letters (after one letter is already taken), we see there are 2 'A' letters left, so the probability is 2/6 or simplified as 1/3.
Therefore, the combined probability of both these events happening is the product of their individual probabilities. We multiply the fractions: 5/7 * 1/3 = 5/21 = 0.238095. Translating that fraction into a percentage, we multiply by 100% to get approximately 23.81%.
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Which of the following is the quotient of the rational expressions shown below? 3x/2x+5 /2x/x+5
The quotient of the rational expressions given is obtained by converting the division to multiplication by the reciprocal leading to \((\frac{3x \times (x+5)}{2x \times (2x+5)})\). The final simplification depends on specific values of x.
Explanation:The question asks to find the quotient of the following rational expressions: \((\frac{3x}{2x+5}) \div (\frac{2x}{x+5})\). To solve this, we first recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, the problem becomes \((\frac{3x}{2x+5}) \times (\frac{x+5}{2x})\).
We simplify this further by multiplying the numerators together and the denominators together: \((\frac{3x \times (x+5)}{2x \times (2x+5)})\).
To solve the more difficult problem, as hinted, we might consider factoring or simplifying further. However, the key calculation here reveals that the certain factors in the numerator and denominator might not simplify directly in this expression, leading to a more nuanced understanding of rational expressions. As such, detailed simplification depends on the specific values of x and further factorization may not lead to a simpler form without more context.
The correct answer is: [tex]\text { B. } \frac{3 x+15}{4 x+10}[/tex].
To find the quotient of the given rational expressions, you divide the first rational expression by the second one.
[tex]\frac{\frac{3 x}{2 x+5}}{\frac{2 x}{x+5}}=\frac{3 x}{2 x+5} \cdot \frac{x+5}{2 x}[/tex]
Now, you can simplify this expression:
[tex]=\frac{3 x(x+5)}{2 x(2 x+5)}[/tex]
Cancel out x from both numerator and the denominator.
[tex]=\frac{3 (x+5)}{2 (2 x+5)}[/tex]
[tex]=\frac{3x+15}{4x+10}[/tex]
This value matches with the option B. Thus, B is the correct answer.
Complete Question:
Which of the following is the quotient of the rational expressions shown below?
[tex]\frac{3 x}{2 x+5} \div \frac{2 x}{x+5}[/tex]
[tex]\text { A. } \frac{4 x^2+10 x}{3 x^2+15 x}[/tex]
[tex]\text { B. } \frac{3 x+15}{4 x+10}[/tex]
[tex]\text { C. } \frac{6 x^2}{2 x^2+15 x+25}[/tex]
[tex]\text { D. } \frac{3}{4}[/tex]
The table represents a function. Which value is an output of the function? (A) –6 (b)–2(c) 4(d) 7
Answer:
Option B
Step-by-step explanation:
. If a function is given in the form of f(x) = ax² + bx + c, then value of x is "input" and the value ... Now from the given table output values of the function are 8, 3, -5, -2 and 12. ... Therefore Option B
Jim makes $10.35 per hour. Write an equation that Jim can use to calculate his pay.
Answer:
Step-by-step explanation:
Pay = 10.35 * h where h is the number of hours that he works. The other 2 questions should have been included with this one. I'll answer the second one here.
Distance = 65 * h
distance = 65 * h miles.
How is the graph of y=2x^2+3 different from the graph of y=x^2-9x+20 shown below?
Answer:
○ The graph of y = -2x² + 3 opens downward and is shifted up.
Step-by-step explanation:
According to the Quadratic Equation, y = Ax² + Bx + C, C acts like a y-intercept, and in this case, since both graphs shift up [because both are positive values], we do not pay attention to those. Now, we come over to our A, which makes a BIG difference because both graphs open in opposite directions [one negative, one positive]. With this being stated, we have our answer.
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
** Extended information on Parabolas
Opens down → -A
Opens up → A
ZE and ZF are vertical angles with mZE= 9x + 12 and mZF= 3x + 24.
What is the value of x?
Answer:
x=2
Step-by-step explanation:
Vertical angles are equal
m ZE = m ZF
9x+12 = 3x+24
Subtract 3x from each side
9x -3x +12 = 3x-3x+24
6x+12 = 24
Subtract 12 from each side
6x+12 -12 = 24-12
6x = 12
Divide each side by 6
6x/6 =12/6
x = 2
simplify each of the following
a) 3a×9ac
b) 7de×3de²
Answer:
3a x 9ac
=(3a×9a)(c)
27a2 ×c
7de×3de2
=(7×3)(de ×de2)
= 21de3
Solve for y.
1. y= -1/4
2. 1/4.
3. y=41/4.
4.41/25
What is the correct answer?
Answer:
1. y= -1/4
Step-by-step explanation:
y/5 + 3/10 = (y+2)/7
Get a common denominator for the left hand side
2y/10 + 3/10 = (y+2)/7
(2y+3)/10 = (y+2)/7
Using cross products
(2y+3) *7 = 10*(y+2)
Distribute
14y+21 = 10y+20
Subtract 10y from each side
14y-10y +21 = 10y-10y+20
4y+21 =20
Subtract 21 from each side
4y+21-21 = 20-21
4y = -1
Divide by 4
4y/4 = -1/4
y = -1/4
f(x) = x + 8 and g(x) = -4x - 3, find (f-g)(x)
Answer:
5x + 11
Step-by-step explanation:
We are subtracting function g(x) from function f(x).
Write f(x) as is: f(x) = x + 8.
Then change all of the signs of g(x): -g(x) = 4x + 3.
Now combine like terms for the sum (f - g)(x) = x + 8 + 4x + 3. We get
(f - g)(x) = 5x + 11
Please help right now!!!!! Solve the system of equations below. x + y = 7 2x + 3y = 16
Answer:
[tex]x=5[/tex] and [tex]y=2[/tex].
Step-by-step explanation:
We have been given a system of equations. We are asked to solve our given system.
[tex]x+y=7...(1)[/tex]
[tex]2x+3y=16...(2)[/tex]
From equation (1), we will get:
[tex]x=7-y[/tex]
Upon substituting this value in equation (2), we will get:
[tex]2(7-y)+3y=16[/tex]
[tex]14-2y+3y=16[/tex]
[tex]14+y=16[/tex]
[tex]14-14+y=16-14[/tex]
[tex]y=2[/tex]
Now, we will substitute [tex]y=2[/tex] in equation (1).
[tex]x+2=7[/tex]
[tex]x+2-2=7-2[/tex]
[tex]x=5[/tex]
Therefore, the point [tex](5,2)[/tex] is solution for our given equation.
Answer:
The answer is (5,2)
Step-by-step explanation:
I took the test and got it correct.
If f(x)= -15x-5, then f^-1(x)=
Answer:
(x+5) /-15 = f^-1(x)
Step-by-step explanation:
f(x)= -15x-5
y = -15x-5
Exchange x and y
x = -15y -5
Solve for y
Add 5 to each side
x+5 = -15y -5+5
x+5 = -15y
Divide by -15
(x+5)/-15 = -15y/-15
(x+5) /-15 = y
(x+5) /-15 = f^-1(x)
Solve by using the given theorems of logarithms. log 5 + log 2 =
The expression log 5 + log 2 can be combined using the property that the logarithm of a product is equal to the sum of the logarithms, which simplifies to log 10. Since log 10 is equal to 1, the solution to the expression is 1.
To solve the expression log 5 + log 2 using the logarithmic theorems, we can apply one of the fundamental properties of logarithms. Specifically, the logarithm of a product of two numbers is equal to the sum of the logarithms of those two numbers (log xy = log x + log y). Applying this property to our expression, we can combine the two logarithms as follows:
log 5 + log 2 = log (5 x 2)
Now, we can easily calculate the combined term:
log (5 x 2) = log 10
Since the base of the logarithm is not specified, we can assume it is 10 (common logarithm). Therefore, we can simplify further:
log 10 = 1
Thus, the solution to the given expression is 1.
Please Answer I’m desperate
Answer:
B
Step-by-step explanation:
Given
f = c / λ ( multiply both sides by λ )
fλ = c
You simply have to multiply both sides by lambda:
[tex]f = \dfrac{C}{\lambda} \iff f\cdot \lambda = \dfrac{C}{\lambda}\cdot \lambda \iff C = f\lambda[/tex]
Find the equation for a parabola that has a vertex at (0, 4) and passes through the point (–1, 6).
Answer:
[tex]\large\boxed{y=2x^2+4}[/tex]
Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (0, 4) → h = 0 and k = 4.
Substitute:
[tex]y=a(x-0)^2+4=ax^2+4[/tex]
The point (-1, 6) is on the parabola. Put the coordinates of the point to the equation:
[tex]6=a(-1)^2+4[/tex] subtract 4 from both sides
[tex]2=a\to a=2[/tex]
Finally:
[tex]y=2x^2+4[/tex]
Please help me with this
Answer:
B, D
Step-by-step explanation:
Angles 1 and 2 combined form a right angle, so the sum of their measures is 90°. Therefore, they are complementary angles.
Since they share a common side and vertex and don't overlap, they are also adjacent angles.
the product of 3/4 and a number is 16
Answer:
21 1/3
Step-by-step explanation:
Write this as an expression
3/4 x = 16
Now it is a one step equation
divide 3/4 from its self and 16
3/4 divided by 16 = 21 1/3
x= 21 1/3
Answer:
[tex]21\frac{1}{3}[/tex] or 21.3
Step-by-step explanation:
We are given that the product of [tex] \frac { 3 } { 4 } [/tex] and a number is [tex] 1 6 [/tex].
Assuming that number to be [tex] x [/tex], we can write it as:
[tex] \frac { 3 } { 4 } \times x = 1 6 [/tex]
Taking the denominator to the other side of equation and multiplying it to get:
[tex] 3 x = 1 6 \times 4 [/tex]
[tex] 3 x = 6 4 [/tex]
Isolating the variable to get:
[tex] x = \frac { 6 4 } { 3 } [/tex]
[tex] x = 21\frac{1}{3}[/tex] or [tex] x = 21.3[/tex]
Convert this decimal into its fractional
form, simplified completely.
0.040
Hello There!
I Provided Steps In The Image Attached.
Have A Great Day!
A triangle has verticals at B(-3,0), C(2,-1), D(-1,2). Which transformation would produce an image with verticals B”(-2,1), C”(3,2), D”(0,-1)?
Answer:
The triangle is reflected across the x-axis and then translated 1 unite to the right , 1 unit up
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
then the new point = (x , -y)
- If point (x , y) reflected across the y-axis
then the new point = (-x , y)
- If the point (x , y) translated horizontally to the right by h units
then the new point = (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then the new point = (x - h , y)
- If the point (x , y) translated vertically up by k units
then the new point = (x , y + k)
- If the point (x , y) translated vertically down by k units
then the new point = (x , y - k)
* Now lets solve the problem
- A triangle has three vertices
- The vertices are B (-3 , 0) , C(2 , -1) , D (-1 , 2)
- The images of the vertices are B" (-2 , 1) , C" (3 , 2) , D" (0 , -1)
after two steps of transformations
- After comparing the points with their images we find
# The x-coordinates of the points are added by 1
∴ There is translation to the right
# The y-coordinates of the points not add or subtracted by the same
number, that means there is a transformation before the translation
for the y-coordinates
# The sign of y-coordinates of the points are changed , that means
there is a reflection across the x-axis
∴ B' is (-3 , 0) , C' is (2 , 1) , D' is (-1 , -2)
- After comparing the 1st image with the 2nd images we find
# The x-coordinates of the points are added by 1 and the
y-coordinates are add by 1
∴ B" is (-2 , 1) , C" is (3 , 2) , D" is (0 , -1)
- From all above
* The triangle is reflected across the x-axis and then translated 1 unite
to the right , 1 unit up