Answer:
$165.62
Step-by-step explanation:
Multiply principle(910) by rate (0.052) and time (3.5)= interest(165.62)
Answer:
His ending balance is $1075.62
Step-by-step explanation:
To solve this question, we will simply use this formula;
Simple Interest = P × R × T / 100
where p is the principal amount
R is the rate and T is the time
From the above question, principal p=$910 Rate r=5.2 and Time t = 3 1/2
We first change 3 1/2 from mixed number to either improper fraction or decimal fraction ;
3 1/2 = 7/2 = 3.5
We can now go ahead and substitute all our variables in the formula;
Simple Interest = P × R × T / 100
= $910 × 5.2 × 3.5 / 100
= $ 16562 / 100
=$165.62
Simple interest is $165.62
But what we are ask to look for is the ending balance, to get the ending balance, jut add the principal and the interest altogether;
Ending balance = $910 + $165.62
Ending balance = $1075.62
Find all the zeros of the quadratic function:
y=x^2+15x+36
Answer:
x=-12 and -3
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. We will substitute a=1, b=15 and c=36.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-15+/-\sqrt{(15)^2-4(1)(36)} }{2(1)}\\x=\frac{-15+/-\sqrt{225-144} }{2}[/tex]
We will now simplify and solve.
[tex]x=\frac{-15+/-\sqrt{81}}{2}\\x=\frac{-15+/-9}{2}[/tex]
x=-12 and x=-3
"If a - 7 = b(x + 2), then x = ?"
Please help!!!!
I need a step by step explanation too.
Answer: choice (3), x = (2b+7)/(a-b)
==============================
Explanation:
The idea is to get all the x terms to one side (after distributing), then factoring out the common term x, finally divide both sides by (a-b) as shown below
ax-7 = b(x+2)
ax-7 = bx+2b .... distribute
ax-7+7 = bx+2b+7 ... add 7 to both sides
ax = bx+2b+7
ax-bx = bx+2b+7-bx ... subtract bx from both sides
ax-bx = 2b+7
(a-b)x = 2b+7 .... factor out the GCF x
x = (2b+7)/(a-b) ... divide both sides by (a-b)
We have all of "2b+7" over "a-b" as one big fraction. This is what choice (3) is showing.
Wells college Aurora New York Was previously an all girls college.In 2005 the college began to allow boys to enroll.By 2012 The ratio of boys to girls was 3 to 7. If there were 200 more girls than boys in 2012 how many boys in enrolled that year
Answer:
150
Step-by-step explanation:
The ratio of boys to girls is 3 to 7.
We don't know the number of boys or girls. The number of boys and the number of girls are multiples of 3 and 7, respectively. Since they are in the ratio of 3 to 7, then by multiplying both 3 and 7 by the same number, you will get the number of boys and the number of girls. We need to find that number. Call that number x.
The ratio of boys to girls is:
3x to 7x
There are 3x boys and 7x girls.
The number of girls is 200 more than the number of boys.
7x = 3x + 200
Subtract 3x from both sides.
4x = 200
Divide both sides by 4.
x = 50
The number of boys is 3x, so
3x = 3(50) = 150
150 boys and 350 girls were enrolled that year.
Since a college was previously an all girls college, and then it began to allow boys to enroll, and by 2012 the ratio of boys to girls was 3 to 7, to determine, if there were 200 more girls than boys in 2012, how many boys were enrolled that year, the following cross multiplication calculation must be performed:
7 - 3 = 200 3 = X 4 = 200 3 = X 3 x 200/4 = X 600/4 = X 150 = X 150/3 = 50 (150 + 200) / 3 = 50
Therefore, 150 boys and 350 girls were enrolled that year.
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In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.
Answer:
[tex]AC=14\sqrt{2}m[/tex]
Step-by-step explanation:
we are given trapezoid ABCD
AC is a diagonal
∠ABC ≅ ∠ACD
we know that
BC and AD are parallel
so, <DAC = <ACB
so, ΔABC ≅ΔACD
Since, both triangles are similar
so, their ratios must be equal
we get
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now, we can plug values
[tex]\frac{14}{AC} =\frac{AC}{28}[/tex]
[tex]AC^2=14\times 28[/tex]
[tex]AC^2=14^2\times 2[/tex]
[tex]AC=14\sqrt{2}m[/tex]
To find the length of AC, the diagonal in trapezoid ABCD, we can use the fact that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD. By setting up a proportion using the corresponding sides of the similar triangles ABC and ACD, we can find that AB/AC = 1/2. Multiplying the length of AB by 2 gives us AC = 28m.
Explanation:Given that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD are 14m and 28m respectively, we can find the length of AC, which is a diagonal in trapezoid ABCD.
Because the two angles are congruent, triangle ABC is similar to triangle ACD. This means their corresponding sides are proportional.We can set up a proportion using the corresponding sides of the triangles:The length of a rectangular garden is represented by 3x-4 and the width is represented by 2x-5. Which of the following represents the total area of the garden
The options are
a.) 5x - 9
b.) 6x + 20
c.) 6x²- 23x + 20
d.) 6x²-14x - 9
Answer:
c.) 6x²- 23x + 20
Step-by-step explanation:
Rectangle area can be computed as length × width . The garden is a rectangle so the area can be computed by multiplying the length and the width.
Area= L × W
Length = 3x - 4
width = 2x - 5
Area = (3x - 4)(2x - 5)
Area = 3x(2x) + 3x(-5) -4(2x) -4(-5)
Note : - × - = +
Area = 6x² -15x - 8x + 20
Area = 6x² - 23x + 20
Use the diagram to answer the question
Line m is parallel to line p. M angle HEF IS 39 degrees. And m IGF is 13 degrees. Find the m EFG. Explain in detail how you know you are correct. I WILL MARK THE BRAINLIEST
Answer:
[tex]m\angle EFG=52^{o}[/tex]
Step-by-step explanation:
We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].
Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.
We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.
We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.
[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]
Upon substituting our given values we will get,
[tex]m\angle EFG=13^{o}+39^{o}[/tex]
[tex]m\angle EFG=52^{o}[/tex]
Therefore, measure of angle EFG is 52 degrees.
How to write 21/6 as a mixed number
The calculated fraction 21/6 to a mixed number is 3 1/2
How to change the fraction 21/6 to a mixed numberFrom the question, we have the following parameters that can be used in our computation:
Number = 21/6
Divide 21 by 6
So, we have
Quotient = 3
Next, we have
Remainder = 21 - 6 * 3
Evaluate the products
Remainder = 3
So, we have
Fraction = 3 3/6
Simplify
Fraction = 3 1/2
Hence, the fraction to a mixed number is 3 1/2
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Consider the steps to simplify the expression. Which property is used to reach Step 3?
Expression: -4
3
7
+ 7 + (-3
4
7
)
Step 1: = -4
3
7
+ (-3
4
7
) + 7
Step 2: = -4 + (-
3
7
) + (-3) + (-
4
7
) + 7
Step 3: = -4 + (-
3
7
) + (-
4
7
) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
A) The associate property of addition.
B) The commutative property of addition.
C) The opposite of a sum is the sum of its opposites.
D) Subtracting a number is the same as adding its inverse.
NOTE: I ACCIDENTALLY clicked one star. That DOES NOT count as a real rating, and this DOES NOT mean my answer is bad!
Answer:
Commutative Property of Addition
Step-by-step explanation:
Step 2: -4 + (-37) + (-3) + (-47) + 7
Step 3: -4 + (-37) + (-47) + (-3) + 7
Because the order was changed, it is the Commutative Property.
Jack's pancakes recipe calls for 2 teaspoons baking powder and 3 cups of flour. How how much baking powder is needed if Jack uses 9 cups of flour
Answer:
6
Step-by-step explanation:
Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.
To determine how much baking powder is needed if Jack uses 9 cups of flour instead of 3, you can set up a proportional relationship because the quantity of baking powder required is directly proportional to the amount of flour used.
If the original recipe calls for 2 teaspoons of baking powder for every 3 cups of flour, for 9 cups of flour (which is 3 times as much), you would need 3 times as much baking powder. Hence, the calculation would be as follows:
2 teaspoons baking powder / 3 cups flour = x teaspoons baking powder / 9 cups flour
By cross-multiplication, we can find the value of x:
2/3 * 9 = x
x = 2 * 3 = 6 teaspoons of baking powder
Therefore, Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.
Marshall Earns a salary of 36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise. How many years will it take before Marshall and Jim earn the same salary
Answer:
It will take 6 years
Step-by-step explanation:
Marshall starts at 36,000 dollars and Jim starts at 51,000, multiply the pay raises by 6 and for Jim you get $9,000 and Marshall gets $24,000 pay raise in 6 years.
Sorry If It Is a bit confusing, I'm not really good with words. :/
Both of them will get the same salary after 6 year.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Marshall Earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise.
Let x be the year in which they will get the same salary
Establishing the equation, we get
36000+4000x = 51000+1500x
Simplifying the equation,
36+4x = 51+1.5x
2.5x = 15
x = 6
Hence, Both of them will get the same salary after 6 year.
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Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply. (x + 1) (2x + 1) (x + 2) (5x + 1) (5x – 2) Mark this and return Save and Exit
Answer:
(5x-2) and (x+2)
Step-by-step explanation:
Answer:
the factors are (5x-2) and (x+2)
Step-by-step explanation:
5x^2 + 8x – 4
first we multiply 5 and -4= -20
product is -20 and sum is +8
find out two factors whose product is -20 and add upto +8
10 * (-2) = 20
10 +(-2)= 8
5x^2 +10x-2x – 4
group the terms and factor out GCF
(5x^2 +10x)+(-2x – 4)
5(x+2) -2(x+2)
(5x-2)(x+2)
the factors are (5x-2) and (x+2)
Question 3(Multiple Choice Worth 5 points) (06.08A) Simplify negative 15.5 divided by 5 .. −3.1 3.1 −3.3 3.3
A negative divided by a positive gives a negative result
So the answer is -3.1
Hope this helps!
this was correct on my test, hope it helps! ;)
(Brainliest would help a lot btw)
Find the slip of the line that passes through each pair of point (-6,1), (4,8).
X1 = -6
Y1= 1
X2= 4
Y2 = 8
8 - 1
____
4 + 6
7
_ is your answer
10
If there’s a negative before brackets you do the opposite terms right?
Answer:Yes
Step-by-step explanation:
When the negative is on the outside of the bracket you distribute the negative to each term inside the parentheses.
Answer:
yes you would change the signs that are inside the parenthesis
Step-by-step explanation:
you do so because the negative outside the parenthesis mean you are distributing the negative to the terms.
If you roll 2 dice, what is the probability that the sum is 9?
thanks :) will give brainliest!
Answer:
0.1111%
Step-by-step explanation:
2 dice, each with 6 sides. 36 possible outcomes.
Possible sums for 9 are 1,8 2,7 3,6 4,5
That means there is only 4 possible ways to get 9 out of 36 possible outcomes. 4/36 is your probability
Ashley is the utilities manager at a paper mill. She's watching over one of her holding tanks. It takes of an hour to fill the tank. At this rate, how many holding tanks will she fill in 1 hour?
Answer: 5/8
Step-by-step explanation:
I do not get this. Evaluate.
Simplify your answer as much as possible.
3!6!/5!2!
Answer:
18
Step-by-step explanation:
[tex]\frac{3!6!}{5!2!}[/tex]
n! = n * (n-1)!
For example 7! can be written as 7 * 6!
3! is 3* 2!
6! is 6 * 5!
[tex]\frac{3!6!}{5!2!}[/tex]
[tex]\frac{3*2!6*5!}{5!2!}[/tex]
Cancel out 5! from the top and bottom . Also cancel out 2! from top and bottom.
[tex]\frac{3*2!6*5!}{5!2!}[/tex]
3*6= 18
The perimeter of a rectangle is 34 units. Its width is 6.5 units. Write an equation to determine the length of the rectangle.
Answer:
The length for a rectangle with a perimeter of 34 units and a width of 6.5 units would be 10.5 units.
Step-by-step explanation:
To find the length, you can use the equation [34 - (6.5 x 2) ÷ 2 = the length]. So, 6.5 x 2 = 13, then 34 - 13 = 21, finally, 21 ÷ 2 = 10.5 . So the length of the rectangle is 10.5 . To double check, (6.5 x 2) + (10.5 x 2) (=) 34. So this answer is correct.
A kite, flying 50 feet high in the air is attached by a string to a stake in the sand. How long is the string to the nearest tenth of a foot? A) 50.0 feet B) 70.7 feet C) 77.9 feet D) 88.6 feet
Answer:
Hello, the answer tho this question is C.) 70.7 feet.
20 Points!! Will give Brainliest!!! Need Help ASAP!!! PLzz!!
Ray knows that the m<3 = m<6.
Which of the following conclusions can Ray make based on the given information?
A. Lines l and m are parallel because alternate interior angles are equal.
B. Lines l and m are parallel because alternate exterior angles are equal.
C. Lines l and m are parallel because corresponding angles are equal.
D. No conclusion can be made about the lines.
Answer:
The answer is B
Step-by-step explanation:
3 and 6 are alternate exterior angles which make lines l and m parallel.
Answer: c
Step-by-step explanation:
what is the midpoint between -9 and 15 on the number line? A. 3
B. 12
C. 6
D. 2
Answer:
A. 3
Step-by-step explanation:
To find the midpoint between two numbers, we add the two numbers and divide by 2
midpoint = (x1+x2)/2
midpoint = (-9+15)/2
midpoint = (6)/2
midpoint =3
which is greater .513 or .5129
Answer:
.513 is larger
Step-by-step explanation:
1st method is the thousandths place larger or smaller
.1 tenths
.01 hundredths
.001 thousandths
In this case the thousandths is larger for .513
2nd method
subtract the two number
.513 - .5129 = .0001
Since the number recieved is positive this means .513 is larger
In a triangle the sides has 82 degrees ,2x+10 degrees and x degrees what is x
Answer:
x = 29 1/3 degrees
Step-by-step explanation:
A triangle has 3 angle that total 180 degrees.
The three angles given are 82 degrees ,2x+10 degrees and x degrees.
So,
82+ (2x+10) + x = 180
Combine like terms.
92 + 3x = 180
Subtract 92 from each side
3x = 180 -92
3x = 88
divide each side by 3
3x/3 = 88/3
Change 88/ 3 to a mixed number
3 goes in to 88 29 times with 1 left over.
x = 29 1/3 degrees
Plz I need by tonight
Answer: Yes
Step-by-step explanation: 4x5 is 20 + 2 is 22 then when you multiply that by 9 you get 198
36x5 is 180 + 18 is 198
Both answers equal each other
Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces. what is true about the length of each piece of fabric. I need the answer as a fraction.
Answer:
The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]
Step-by-step explanation:
Given : Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces.
To find : What is true about the length of each piece of fabric ?
Solution :
Dai has 3 meters of fabric.
He cuts the fabric into 5 equal sized pieces.
So, The length of each piece is defined as
[tex]L=\frac{3}{5}[/tex]
Therefore, The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]
6a. Suppose you need to find a box that you can fit your cube-shaped gift into. You know that you will need to find a box that is 4 inches longer than the cube’s length, 3 inches wider than the cube’s width, and 7 inches taller than the cube’s height. Create a polynomial that represents the gift box’s volume in terms of the cube’s length/width/height, in factored and standard form
Answer:
( l + 4) * ( w + 3 ) * ( h + 7)
let l represent the length, w represent the width, and h represent the height of your cub-shaped gift.
Though, if your gift is in the shape of a cube, that would mean all the sides are the same length.
( 2 + 4 ) * ( 2 + 3 ) * ( 2 + 7 )
6 * 5 * 9 = 270
(I haven't done geometry in awhile though, so this may be incorrect unless it actually makes sense.)
Answer:
V = (x+ 4)(x + 3)(x + 7); V = x³ + 14x² + 61x + 84
Step-by-step explanation:
Let x = the side of the cube
Then the dimensions of the gift box are
l = x + 4
w = x + 3
h = x+ 7
V = lwh
V = (x+ 4)(x + 3)(x + 7) Multiply the first two terms
V = (x² + 7x + 12)(x+ 7) Remove parentheses
V = x³ + 14x² + 61x + 84
the ratio of 6th graders to 7th graders at a basketball game is 4:1. if there are eight 6th 7th graders how many 6th graders are there
Answer:
if there are 8 7th graders there are 32 6th graders. 4*8=32
Step-by-step explanation:
Which of the following could be the equation of the function below?
Answer:
Option C is the correct option.
Step-by-step explanation:
In the given cosine graph we can draw some parameters of the equation as below
y = a cos(bx + c) + d
1) amplitude a = (1+3)/2=2
2) Period = π
3) phase shift = -π ( to the left)
4) Vertical shift = -1 ( downwards on y-axis)
Therefore the equation of the graph will be
y = -2cos[2(x + π)] - 1
Option C is the correct answer.
What Is the Slope And Y Intercept Of This Line?
Y = X -5
Answer:
slope = 1 , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = x - 5 is in this form
with slope m = 1 and y- intercept c = - 5
Can I please get someone who is good at Geometry to help me? PLEASE AND THANK YOU!!!! (You just have to do problem A. Thanks again)
Answer:
x=6
Step-by-step explanation:
We can find < PMN by using the law of triangles.
The sum of the angles of a triangle adds to 180
<M + <N + < PMN = 180
32 + 64+ < PMN = 180
96 + < PMN = 180
Subtract 96 from each side
96 -96 < PMN = 180-96
< PMN =84
<PMN + <NPQ forms a straight line so it equals 180
<PMN + <NPQ=180
84 + <NPQ=180
Subtract 84 from each side
84-84 + <NPQ=180-84
<NPQ=96
<NPQ = 6x
96 = 6x
Divide each side by 6
96/6 = 6x/6
16 =x