Amy has $5000 to invest. She plans to invest part of the money at 10% and part at 13%. She wants her total interest to be $590. How much should she invest at each rate?
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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Taub went shopping for a new video game because of a sale. The price on the tag was $26, but Taub paid $23.40 before tax. Find the percent discount.
Answer:
10%
Step-by-step explanation:
(26-23.40)/26x100%
Answer:
10%
Step-by-step explanation:
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9 ft. Find the length of the ladder if the length is 3 ft more than its distance from the wall.
Answer:15
Step-by-step explanation:
A ladder is resting against a wall.The top of the ladder touches the wall at a height of 9 feet.Find the length of the ladder if the length is 3 feet more than its distance from the wall.
Let the distance of the ladder from the wall be x
The length of the ladder = x+3
The ladder touches the wall at a vertical height of 9 feet.
(x+3)^2 = x^2 + 9^2 ( using the pythagoras theorem
x^2 + 6x+ 9 = x^2 + 81
x^2- x^2 +6x = 81-9
6x= 72
x= 12
Therefore the length of the ladder will be x+3 = 12 + 3 =15 Answer.
30 points!!!
The dot plot below shows the hourly rate of some babysitters in a city:
A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollar per hour. There are 2 dots above 4 dollars, 3 dots above 5 dollars, 3 dots above 6 dollars, and 2 dots above 7 dollars. The title of the line plot is Babysitting Rates.
Which statement best describes the shape of the data?
A. It is symmetric and has no gaps.
B. It is not symmetric and has a peak at $7.00.
C. It is a cluster from $1.00 to $7.00 and has no gaps.
D. It is a cluster from $1.00 to $7.00 and has a peak at $6.00.
From the given choices, the answer is option A: It is symmetric and has no gaps.
How can we describe a number line?A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark.
The horizontal axis label is Dollar per hour.
There are 2 dots above 4 dollars, 3 dots above 5 dollars, 3 dots above 6 dollars, and 2 dots above 7 dollars.
The title of the line plot is Babysitting Rates.
A dot plot is the same as a histogram but it uses dots instead of bars.
The dot plot as described by the problem is shown in the picture.
A bell shape is drawn for symmetrical data.
From the given choices, the answer is option A: It is symmetric and has no gaps.
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Assuming that there are no hidden cubes, what is the front orthographic view of the diagram?
Answer:
the visible number of cubes is 7
Step-by-step explanation:
Assuming that there are no hidden cubes, the # of visible cubes is 7
Which linear inequality is graphed in the figure
Answer:
A) y < 1/3x - 2
Step-by-step explanation:
Please help me please
Answer:
4. false 1 is nor prime nor composite
Multi choice choose the rule for the table year 8 level maths
Answer:
second option, x + 2y = 3
Step-by-step explanation:
The slope intercept form is y = mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
The y - intercept is when x = 0
In the table its shown that (0, 3), y = 3 so b = 3
The slope (gradient) is a number that describes both the direction and the steepness of the line.
slope = rise / run = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
(x_1, y_1) = coordinates of first point in the line
(x_2, y_2) = coordinates of second point in the line
x is increasing by 1 (run)
y is decreasing by 2 (rise)
rise / run = -2 / 1 = -2
so the slope is -2
our slope intercept equation is, y = -2x + 3
Choice:
Some choice are in standard form so we need to convert to slope intercept
y = x + 3 is already in the correct form2x + y = 3 becomes y = -2x + 3subtract 2x from both sides, 2x - 2x + y = 3 - 2x
x + 2y = 3 becomes y = -1/2x - 3/2subtract x from both sides, x - x + 2y = 3 - x becomes 2y = 3 - x
divided both sides by 2, 2y / 2 = (3 - x) / 2
x - y = 0 becomes y = xsubtract x from both sides, x - x - y = 0 - x than switch signs
which option matches?!
THE SECOND ONE
8. Resuelve los siguientes problemas:
a) Cinco trabajadores de una empresa reci-
ben salarios de $1 200, $1 500, $1 600,
$1 300 y $2 500. ¿Cuál es el promedio
salarial?
see the attachment photo!
How many and what type of solutions does 5x^2-2x+6 have?
1 rational solution
2 rational solutions
2 irrational solutions
2 nonreal solution
Answer:
D) 2 nonreal solutionStep-by-step explanation:
GivenQuadratic trinomial
5x² - 2x + 6In order to determine what kind of roots it has, we need to find the value of the discriminant:
[tex]D= b^2-4ac[/tex][tex]D = (-2)^2-4*5*6 =4-120 =-116[/tex]Since the discriminant is negative, its square root is an imaginary number, hence there is no real solution.
Correct answer choice is D.
3 lines are shown. A line with points T, R, W intersects with a line with points S, R, V at point R. Another line extends from point R to point U in between angle V R W.
Which pair of angles are vertical angles?
Answer:
∠TRV and ∠WRS or ∠TRS and ∠WRV
Step-by-step explanation:
Vertical angles are angles that share a vertex and have sides that are opposite rays. That is, the opposites of the rays that form one of the angles are the rays that form the other angle.
__
Where lines cross, two pairs of vertical angles are formed. In your diagram, those pairs are ...
∠TRV and ∠WRS . . . . one vertical angle pair
∠TRS and ∠WRV . . . . another vertical angle pair
_____
Additional comment
In this diagram, the ray RU is of no consequence with respect to any vertical angles. It can be ignored.
The vertical angles will each have one red ray and one blue ray as sides. These rays have end point R. No sides are shared.
a store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. if he has 35 pounds of oolong tea that sells for 2.40 per pound, how much black tea worth 1.80 per pound must he mix with it so that he can sell the final mixture for 2.10 per pound
35 pounds of black tea is needed to be mixed to get the final mixture for 2.10 per pound
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of black tea worth 1.80 per pound to be mixed to get the final mixture for 2.10 per pound, hence:
2.4(35) + 1.8(x) = 2.1(x + 35)
x = 35 pounds
35 pounds of black tea is needed to be mixed to get the final mixture for 2.10 per pound
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Which operations can be applied to a matrix in the process of Gauss-Jordan elimination?
replacing a row with twice that row
replacing a row with the sum of that row and another row
replacing a row with three times another row
swapping rows
replacing a row with the absolute values of that row
Operations that can be applied to a matrix in the process of Gauss-Jordan elimination are options 1,2 and 4.
What is gauss Jordan's elimination?Gauss-Jordan Elimination is a matrix-based technique for solving linear equations or determining a matrix's inverse.
When using Gauss Jordan elimination, the following operations may be carried out on a matrix:
1. Replacing a row with twice that row
2. Replacing a row with the sum of that row and another row
3. Swapping row
The optional row(or column) procedures that can be employed are:
1. Alternate any two rows (or columns)
2. Scalar multiples of one row (column) are added or subtracted from another row (column) occurs when a row is substituted with the sum of another row and that row.
3. Multiply any row (or column) fully by a nonzero scalar, as seen below by substituting a row with two rows.
Hence, Gauss-Jordan elimination includes options 1,2, and 4.
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Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a
viable solution if x represents the number of days that a library book is late and y represents the total fee?
Answer:
y=0.30x
Step-by-step explanation:
because the amount of money (the fee) will keep increasing with the multiplication of the amount of days
(2.01)A polygon is shown on the graph:
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answer:
see picture for the coordinates
A’ = -2,-4
B’ = -3,-7
C’ = -1,-8
D’ = 1,-6
Step-by-step explanation:
add the translation coordinates to the original to get new coordinates
Answer:
Given translation:
4 units left3 units downTherefore,
To translate a point 4 units left, subtract 4 units from the x-value. To translate a point 3 units down, subtract 3 units from the y-value.⇒ (x, y) → (x - 4, y - 3)
Calculations
A (2, -1) ⇒ (2 - 4, -1 - 3) = A' (-2, -4)
B (1, -4) ⇒ (1 - 4, -4 - 3) = B' (-3, -7)
C (3, -5) ⇒ (3 - 4, -5 - 3) = C' (-1, -8)
D (5, -3) ⇒ (5 - 4, -3 - 3) = D' (1, -6)
Therefore, the new coordinates using prime notation are:
A' (-2, -4)B' (-3, -7)C' (-1, -8)D' (1, -6)A. Median
B. Perpendicular bisector
C. Angle bisector
D.altitude
Answer:
I belive c angle bisector
I need help asap please? and this is for the math question? what is the missing angle?
Answer:
the missing angle or the exterior angle is 120
Step-by-step explanation:
180-60=120
Answer:
90 degrees.
Step-by-step explanation:
The square symbol at the unlabeled angle means 90 degrees. Also, a triangle's interior angles equal 180. We already have 30 and 60, so 30+60=90. Now, subtract this from 180. 180-90=90. The answer is 90 degrees.
Hope this helps!
What is the slope of the line graphed below?
(-2,2)
(3, 1)
Answer:
-1/5
Step-by-step explanation:
To find the slope, the formula is y2-y1/x2-x1
1-2/3-(-2) = -1/5
Answer:
‐1/5Step-by-step explanation:
hope this helps!!!!
What is the domain of the function graphed below?
OA.{x\x = −2,1}
OB. (x | x-2,-1, 1)
OC. {x|x-1,}
OD. {x|x-1, 1}
From the graph, the domain of the function will be {x| x = −2,1}. Then the correct option is D.
What is an asymptote?An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.
From the graph, the domain of the function will be
The function is not defined for x = 2 and x = -1.
Then the domain will be
{x| x = −2,1}
Then the correct option is D.
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Which set represents the same relation as the graph below?
A coordinate plane has 7 points. The points are (negative 5, 4), (negative 3, negative 2), (negative 1, negative 2), (2, 0), (3, 3), (4, 5), (6, negative 4).
StartSet (4, negative 5), (negative 2, negative 3), (Negative 2, negative 1), (0, 2), (3, 3), (5, 4), (negative 4, 6) EndSet
StartSet (negative 5, 4), (negative 3, negative 2), (negative 1, negative 2), (2, 0), (3, 3), (4, 5), (6, negative 4) EndSet
StartSet (negative 5, 4), (negative 3, negative 1), (3, 3), (4, 5), (6, negative 4) EndSet
StartSet (4, negative 5), (negative 3, 2), (negative 1, 2), (2, 0), (4, 5), (6, 4) EndSet
The set that represents the same relation as the graph given is: B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).
What is a Relation?A relation is defined as a relationship between the input and output, which can be displayed on a graph on a coordinate plane.
From the graph as shown in the image attached below,
The set that has same coordinate points as indicated on the graph is:
B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).
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Which of the following is the equation of the quadratic function below?
The equation of the given quadratic function is y = x² -9x+18. The correct option is B. y = x² -9x+18
Quadratic equationFrom the question, we are to determine which equation represent the quadratic function
From the given graph,
The roots (zeros) of the function are
x = 3 and x = 6
Now, we will determine the equation of the function from its roots
x = 3 and x = 6
Then, we can write that
x -3 = 0 OR x - 6 = 0
Thus,
(x -3)(x -6) =0
Expanding
x² -6x -3x +18 =
x² -9x+18 = 0
∴ y = x² -9x+18
Hence, the equation of the given quadratic function is y = x² -9x+18. The correct option is B. y = x² -9x+18
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The total amount earned from a savings account is modeled by the expression p(1.015)^12t
where P represents the principal compounded monthly and t is the time in years. Which expression represents the approximate interest rate compounded quarterly?
Answer:
hope you can understand
Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles. 40 divided by (negative 10) 40 divided by 10 40 divided by 40 40 divided by 40
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is B.
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given 40 positive tiles are broken up into 10 groups of 4 positive tiles. The expression that represents this situation is 40 divided by 10.
Hence, the correct option is B.
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Answer:
b
Step-by-step explanation:
Amazing Gadget Corporation has determined a quadratic relationship between its selling price for its newest tablet and the company's daily profit. Which of the following would be a reasonable estimate of the rate of change for the interval 300 ≤ x ≤ 400?
A reasonable estimate of the rate of change for the interval
300 ≤ x ≤ 400 considering if the company is making a profit=2.
Consider the Quadratic relationship, between the selling price for its newest tablet and the company's daily profit is given,
f(x)= a x² + b x + c
Differentiating once
f'(x)= 2 a x + b
As we have to find the rate of change for the interval 200 ≤ x ≤ 300.
So,[tex]f(300)= 2 a \times 300 + b= 600a+b[/tex]
[tex]f(400)= 2 a \times 400 + b= 800 a + b[/tex]
Rate of change for the interval 300 ≤ x ≤ 400
What is the formula for the rate of change?[tex]=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]=\frac{800 a + b-(600 a + b)}{400-300} \\=\frac{800 a + b-600 a -b)}{100}\\\\=\frac{(200 a )}{100}\\\\=2a[/tex]
As considering, if the company is going through Profit, when the selling of the tablet is in the interval (300 ≤ x ≤ 400),
So, a Reasonable estimate of the rate of change for the interval 300 ≤ x ≤ 400 considering if the company is making a profit=2
Option (A).
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what is 250/100 as a whole number?
Answer:
Unless im being completely braindead right now there isn't a whole number that works with this. When simplified its 5/2 or 2.5 but because it isn't an actual whole number (like 2, 4 and 6) they don't count.
Answer:
between two whole numbers 2 and 3 or just 3.
Step-by-step explanation:
The answer to 250/100 would be 2.5 but that is a decimal and not a whole number. You couod round 2.5 to 3 to make it a whole nunber or you say that it is in between two whole nunbers which are 2 and 3 if you are allowed to. (since 2.5 alone is not a whole number)
Twenty Three more than a number is 68 . what is the number
Answer:
the answer is 45.
Step-by-step explanation:
45 + 23 = 68.
please help i’ll give brainliest
The missing length in triangle A given the similarity between the two triangles is 18.67
Solving triangles using ratioTriangle A is similar to triangle B
Triangle A:
Side 1 = (x + 2)Side 2 = 14Triangle B:
Side 1 = 8Side 2 = 6Ratio of side 1 to side 2 of the triangles respectively
(x + 2) : 8 = 14 : 6
(x + 2) / 8 = 14/6
cross product(x + 2) × 6 = 8 × 14
6x + 12 = 112
6x = 112 - 12
6x = 100
x = 100/6
x = 16.67
Therefore, Triangle A:
Side 1 = (x + 2)
= 16.67 + 2
= 18.67
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The graph of the fourth-degree polynomial function f (x) is shown in the coordinate plane below. Based on the graph, which of the following are linear factors of f (x). Select all that apply. A. (x - 2) B. (x - 3) C. (x + 2) D. (x - 5) E. (x + 1)
The linear factors of the function are the x-intercepts which are (x + 5), (x + 2), (x - 1) and (x - 6)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the graph of the function. The linear factors of the function are the x-intercepts which are (x + 5), (x + 2), (x - 1) and (x - 6)
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Find equivalent expressions of 3+2x−9−4x+11+5x−x.
The equivalent expression of the given expressions is 2x + 5.
What are Expressions?Expressions are statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is,
3 + 2x - 9 - 4x + 11 + 5x - x
There are like terms in the expression, which can be operated together.
Write terms with variables together and the constants together.
3 + 2x - 9 - 4x + 11 + 5x - x
= (2x - 4x + 5x - x) + (3 - 9 + 11)
= 2x + 5
Hence the given expression can be simplified to 2x + 5.
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Find the value of x.
Round to the nearest tenth.
34
A
B
26°
x = [? ]°
X
C
15
Answer: 83.5
Step-by-step explanation:
[tex]\frac{\sin x}{34}=\frac{\sin 26^{\circ}}{15} \\\\\sin x=\frac{34 \sin 26^{\circ}}{15}\\\\x=sin^{-1} \left(\frac{34 \sin 26^{\circ}}{15} \right) \approx \boxed{83.5}[/tex]
Answer:
x ≈ 83.5° or 96.5° (two possible values)
Step-by-step explanation:
The relationship between side lengths of a triangle and their opposite angles is given by the Law of Sines: side lengths are proportional to the sines of their opposite angles.
__
In this problem, the Law of Sines tells us ...
sin(A)/BC = sin(C)/AB
sin(C) = sin(A)·AB/BC
Using x for angle C, solving for x, and using the inverse sine function, we find ...
x = arcsin(sin(26°)·34/15) ≈ arcsin(0.993641)
The arcsine function returns a value in the range 0–90°, but the supplemental angle in the rangle 90°–180° can have the identical sine value.
x ≈ 83.5° or 96.5°
_____
Additional comment
For the graph in the attachment, we have set the angle mode to degrees. The solutions to f(x)=0 are solutions to the problem: 83.5° and 96.5°.
The triangle in the figure appears to be an acute triangle. The value of x for an acute triangle would be 83.5°. Often, we cannot take these figures at face value.