Answer:
The angles are 80° and 48°.==============================
Let the angles be x and y.
Their ratio is 5/3:
x/y = 5/3Their sum is 128:
x + y = 128Solve the system by substitution:
x = 5y/3x + y = 1285y/3 + y = 1288y/3 = 128y = 3*128/8y = 48Find x:
x = 128 - 48 = 80Betsy, a recent retiree, requires $6,000 per year in extra income. She has $60,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
$37,500 should be invested in B-rated bonds and $22,500 should be invested in a certificate of deposit in order to realize exactly $6,000 in interest per year.
The total amount to be invested is $60,000. We are given two options for investing the money.The money can be invested either in B-rated bonds, which pays 13% interest per year, or in a certificate of deposit (CD), which pays 5% interest per year.Let the amount to be invested in B-rated bonds be 'x'. The amount to be invested in a certificate of deposit equals 60,000-x. The requirement is to get an exact amount of interest that equals $6000. The total interest per year = 13% of 'x' + 5% of (60,000-x).6,000 = 13x/100 + 5(60,000-x)/100.6,00,000 = 13x + 5(60,000-x)6,00,000 = 13x + 300,000-5x6,00,000 = 8x + 300,0008x = 300,000x = 300,000/8x = 37,500Now calculate the value of 60,000-x.60,000-x = 60,000-37,50060,000-x = 22,500Thus, the amount to be invested in B-rated bonds is $37,500 and the amount to be invested in a certificate of deposit is $22,500.To learn more about interest, visit :
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In Ms. Block's class 8 students share a box of cherries equally. Each of them receives 9 cherries. There are
then 6 cherries left over. How many cherries were there altogether in the box?
Answer: 78
Step-by-step explanation:
first, you multiply 8 by 9 then you get 72, and then you can add the leftover cherries with 72 so 72 + 6 = 78
Answer:
Step-by-step explanation:
78
Find the equation of the line whose slope is -3 and which passes through the point (-5, 3).
y = 3x + 12
y=-3x - 12
y=-3x - 18
y=-3x + 8
27. If Q is the midpoint of PR, find the coordinates of R if
P (3,-5) and Q (-1,2)?
Answer: -5,9
Step-by-step explanation:
Tina Charlie and Amber have Matchbox cars each car has 4 wheels . how many wheels do their cars have altogether .
Answer:
I think its 12
Step-by-step explanation:
I think its 12 bc 4+4+4=12 Sorry if its wrong! ):)
A science class has a total of 47 students. The number of males is 11 more than the number of females. How many males and how many females are in the
class?
Number of males:
Number of females:
Answer:
number of males: 29
Number of females: 18
Step-by-step explanation:
X=number of females
X+11=number of males
X+X+11=47
2X+11=47
2X=47-11
2X=36
X=36/2
X=18
So number of females = 18
X+11=18+11=29
So number of males = 29
4.
Juan was competing in a 1000 meter
race. He had to pull out of the race after
running 3/4 of it. How many meters did
he run?
Answer:14
Step-by-step explanation:
Step-by-step explanation:
B is the midpoint of AC, in other words it is the halfway point.
So A to B should be equal to B to C
Our expression is:
2x + 9 = 37
Subtract 9
2x = 28
Divide by 2
x = 14
Answer:
750
Step-by-step explanation:
3/4 is 75%
Juan did 75% of the 1000 meters meaning he did 750
To get the answer u just do (3/4)*1000 and you get 750
If P=5+7+9+11+...+101 and Q=9+11+13+15+...+103 are sums of arithmetic sequences, determine which
is greater, P or Q, and by how much.
In the sequence, Q is greater by 115.
How to calculate the value?From the information, P=5+7+9+11+...+101 and Q=9+11+13+15+...+103.
It should be noted that by looking at the figures the greater value will be Q as it began with a higher number.
The difference will be:
= 5 + 7 + 103
= 115
Therefore, in the sequence, Q is greater by 115.
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C. describe how you could compare the corresponding sides and angles of figure STUV and its image, figure WXUY
Both the diagrams; figure STUV and its image, figure WXUY are congruent to each other.
What exactly is congruence?If two images are precisely the same in terms of length, width, and height, they are congruent.If one geometric figure can be superimposed on another so that their total area coincides, a certain geometric figure is considered to be congruent or to be situated in the reference of congruence.For the given two diagrams;
WXUY image to mirror STUV
If we rotate the STUV anticlockwise so that side UV coincides with side UY, then side ST≅ WX side TU ≅ side XU, side UY≅ side UV, side YW≅ side VS will be equal, as will angle S≅W, TUV≅XUV, X≅T, and Y≅V will be equal.
Therefore, the side corresponds to the area side ST≅ WX side of TU ≅ side XU, side UY≅ side UV, side YW≅ side VS, and the angle S≅W, TUV≅XUV, X≅T, and Y≅V".
Thus, the given two diagram figure STUV and image, figure WXUY are congruent to each other.
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Tony is hoping to find a job in management with an annual salary of $37,297. What will be his monthly pay rounded to the nearest cent?
Answer:
$3,108.08 per month
Step-by-step explanation:
Calculator shows the answer as 3,108.0833 with the 33 repeating. Rounding to the nearest cent (100ths place) gives $3,108.08
Three friends want to buy a DVD that costs $17.49, including tax. The friends agree to pay an equal amount. Each friend will pay??
help meee!!!!
Answer:
5.83
Step-by-step explanation:
You just divide the total amount by 3
Answer:
Each will pay $5.83
Step-by-step explanation:
What is:
2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11
Answer:
-44
Step-by-step explanation:
2 x 4 + 3 - 8 ÷ 1 x 6 + 4 - 11=-44
Hope this helps!
Answer:
-44
Step-by-step explanation:
evaluate the expression 3 to the third power multiplied by 12-2 divided by 2 iready
What is the product of 6+3i and its conjugate
Answer:
45
Step-by-step explanation:
You want the product of 6+3i and its conjugate.
ConjugateThe conjugate of a complex number is created by reversing the sign of the imaginary part.
(6 +3i)* = 6 -3i
Product of squaresThe product of a complex number and its conjugate is recognizable as the factored form of the difference of squares:
(6 +3i)(6 -3i) = (6)² -(3i)²
Of course, i² = -1, so this becomes ...
6² -(3i)² = 36 -(-9) = 36 +9 = 45
The product of 6+3i and its conjugate is 45.
__
Additional comment
The product of a complex number and its conjugate is the sum of the squares of the magnitudes of the real and imaginary parts. It is always a real number. This fact is used to simplify expressions involving complex numbers.
Carlos and Shawn are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Carlos sold 13 small boxes of oranges and 5 large boxes of oranges for a total of $133. Shawn sold 10 small boxes of oranges and 8 large boxes of oranges for a total of $148. Find the cost of each of one small box of oranges and one large box of oranges.
Answer: The cost of one small box of oranges is $6, while the cost of one large box of oranges is $11.
Step-by-step explanation:
First, set x for the cost of one small box of oranges in dollars, and y for the cost of one large box of oranges in dollars.
Hence, the equations will be:
[tex]13x+5y=133[/tex]
[tex]10x+8y=148[/tex]
Then solve for the equations using the method of elimination. In order to eliminate one of the variables, you need to make the coefficients the same. So, we can multiply the first equation by 8 and the second equation by 5. That would make the equations:
[tex]104x+40y=1064[/tex]
[tex]50x+40y=740[/tex]
Then you can eliminate the y by subtracting.
[tex]54x = 324[/tex]
Then divide by 54 on both sides.
[tex]x=6[/tex]
Now that x is solved, solve for y by substituting for x.
[tex]13(6) + 5y = 133[/tex]
[tex]5y+78=133[/tex]
[tex]5y=55[/tex]
[tex]y=11[/tex]
So, x=6 and y=11.
Stretch
1. John has 15 bills in his wallet that total $145. He has a mix of five-dollar bills, ten-dollar bills, and twenty-
dollar bills. The number of ten-dollar bills is one less than twice the number of twenty-dollar bills.
a. Write a system of three linear equations in three variables to represent this situation. Be sure to
define your variables.
b. How many of each denomination does John have in his wallet? Solve this system using Gaussian
elimination.
John has 7 five-dollar bills, 5 ten-dollar bills and 3 twenty-dollar bills.
Total number of bills with John = 15
Total money with John = $145
John has a mix of $5, $10 and $20 bills
Let the number of $5 bills be x, $10 bills are y and $20 bills be z
Formulating the equations:
5x + 10y + 20z = 145-------(1)
x + y + z = 15--------(2)
As per the question, the number of ten dollar bills is one less than twice the number of twenty dollar bills:
y = 2z - 1
Putting y = 2z-1 in equating (1) and (2) we get:
5x + 10(2z-1) + 20z = 145
5x + 20z - 10 + 20z = 145
5x + 40z = 155--------(3)
x + y + z = 15
x + 2z - 1 + z = 15
x + 3z = 16--------(4)
Multiplying equation (4) with 5 and using Gaussian Elimination to equate (3) and (4)
5x + 40z = 155
5x + 15z = 80
25z = 75
z = 3
Putting z=3 in (4) we get
x = 7 and y = 5
So, John has 7 five-dollar bills, 5 ten-dollar bills and 3 twenty-dollar bills.
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the points on the table are in a line what is the slope
Answer:
the slope of the table is -0.857
(a) Write a formula for the distance between the points (x,y) and (4,6)
(b) If the distance
between above points is 9 units, write an equation.
art sculpture composed of 3,880 craft sticks and 960 pieces of balsa wood. What is the ratio of craft sticks to balsa wood?
Answer:
3880 ÷ 960 = 4.041
ratio = 4:1
2/3x=6
a. x=9
b. x=4
c. x=18
d. x=12
option (a) x = 9
Step-by-step explanation:
2/3x = 6
2x = 18
x = 18/2
x = 9.
Given: Triangle ABC
Prove: mA = 64°
A
(4x)
B
(90)
C
(x+10)
For the given triangle ABC, the value of angle A = 64°.
What is defined as the triangle?A triangle is a two-dimensional closed shape. It has three sides and is a polygon. Straight lines make up all of the sides. The vertex is the intersection of two straight lines. As a result, the triangle does have three vertices. Each vertex creates an angle.A triangle is made up of three angles. These angles are made up of two triangle sides meeting at a main point recognized as the vertex. The total of all 3 interior angles is 180 degrees.For the given ΔABC;
∠A = 4x
∠B = 90
∠C = x + 10
By the sum of angles of triangle property;
∠A + ∠B +∠C = 180
Substitute the values;
4x + 90 + x + 10 = 180
Simplifying the equation;
5x = 180 - 100
5x = 80
x = 16
Put the value of x in angle A.
∠A = 4x
∠A = 4×16
∠A = 64°
Therefore, the value of angle A is found as 64°.
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The length of a rectangle is nine more than twice the width. Write a simplified expression that could be used to find the perimeter of the rectangle
The expression for the perimeter of the rectangle whose length of a rectangle is nine more than twice the width is 6x + 18.
Let the width of the rectangle be x units.
According to the given question.
The length of a rectangle is nine more than twice the width.
⇒ Length of the rectangle = 9 + 2x
As we know that, the perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width.
Therefore, the expression for the perimeter of the rectangle whose length of a rectangle is nine more than twice the width
= 2[x + (9 + 2x)]
= 2[ x + 2x + 9]
= 2[ 3x + 9]
= 6x + 18
Hence, the expression for the perimeter of the rectangle whose length of a rectangle is nine more than twice the width is 6x + 18.
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i need some help please help
3x + 1<10
The value of x from the inequality is x < 3
What is an inequality?An inequality is defined as a statement of an order relationship between two numbers or algebraic expressions.
Given the inequality;
3x + 1 < 10
To determine the solution, we take the followings steps;
collect like terms
3x < 10 - 1
Find the difference between the terms
3x < 9
Make 'x' the subject of formula
x < 9/ 3
x < 3
Thus, the value of x from the inequality is x < 3
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Acme Movers charges $105 plus $40 per hour to move household goods across town. Hank's Movers charges $55 per
Khour. For what lengths of time does it cost less to hire Hank's Movers?
It costs less to hire Hank's Movers for times less than
hours.
Incom
It costs less to hire Hank's Movers for times less than 7 hours.
What time would it cost less to hire Hank Movers?
The equation that can be used to represent the cost of hiring Acme movers is: $105 + $40t
The equation that can be used to represent the cost of hiring Hank's Movers : $55t
Where : t represent number of hours
The inequality sign that would be used is < less than or equal to
$55t < $105 + $40t
Combine similar terms
$55t - $40t < $105
$15t < $105
t < 105 / 15
t < 7 hours
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Helppppppppppppppppppppppppppp
A line passes through the point point (-6, -5) and has a slope of - 4/3. Write an equation in slope-intercept firm for this line.
The equation in slope-intercept firm for this line is y = -4/3x - 13
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the linear equation?The given parameters are
Slope, m = -4/3
Point (x1, y1) = (-6, -5)
The linear equation is calculated as
y = m(x - x1) + y1
So, we have
y = -4/3(x + 6) - 5
Open the bracket
y = -4/3x - 8 - 5
Evaluate the difference
y = -4/3x - 13
Hence, the equation in slope-intercept firm for this line is y = -4/3x - 13
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Describe the features of a Cartesian Plane in terms of its axes, the direction of the axes and its centre.
Answer:
A Cartesian Plane is a plane in Geometry which is an flat surface of infinite size. It has two number lines that intersect at right angles at their zeros. One number line is horizontal, and the other number line is vertical. The point of intersection is the zero of each line. In the horizontal line, the numbers increase to the right. In the vertical line, the numbers increase up. The horizontal line is called the x axis. The vertical line is called the y axis. The center of the Cartesian Plane is the intersection of the two axes, the two number lines, and is called the origin. Points on the Cartesian Plane are described with two numbers in parentheses separated by a comma. The position of the point in the Cartesian Plane is given by the first number, called the x-coordinate, telling us the number of units to the right (positive) or left (negative) of the origin and by the second number, called the y-coordinate, telling us the number of units up (positive) or down (negative) from the origin.
the question is on the screenshot
Answer:
I believe it's option 3, because you multiply 3 by 4, and get 12
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
List 5 questions you would ask if your conducting a parent teacher conference ik its not math but i need help i will mark brainlest
What is the sum of -1 + (-3)
Answer:
-4.
Step-by-step explanation:
When you add two negatives together it stays a negative. So the answer is -4.
