Answer:
$780
Step-by-step explanation:
The initial sum of money borrowed was $750
at a simple interest rate of 8%
Dan pays the money back in 6 months
The amount of money Dan has to pay back his brother including the interest in 6 months' time.
The total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.
The total interest that is to be paid back can be calculated using the formula
where P is the prinicipal amount of money we begin with (in this case $750), r is the rate of interest (in this case 8%) and t is the time period (in this case, 6 months or 1/2 of a year).
(Note that we must take the value of t in years if the interest is annual interest and that is why we use t = 1/2 = 0.5 instead of t = 6).
So, by simple calculation we can find interest to be paid as
the interest accrued is $30
To find the total sum to be paid back, we add the initial sum or pricipal amount to the interest we have calculated above i.e.,
the total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.
If triangle XYZ’s points are X (-2, 1), Y (-4,-3), and Z (0,-2) what are the new coordinates of X’, Y’, and Z’ if the triangle is transformed using the rule (x - 1, y + 3) to form triangle X’Y’Z’.
Answer:
The coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).
Step-by-step explanation:
The vertices of triangle XYZ are X(-2,1), Y(-4,-3) and Z(0,-2).
It is given that the triangle translated by rule
[tex](x,y)\rightarrow (x-1,y+3)[/tex]
The coordinates of image of XYZ are
[tex]X(-2,1)\rightarrow X'(-2-1,1+3)[/tex]
[tex]X(-2,1)\rightarrow X'(-3,4)[/tex]
[tex]Y(-4,-3)\rightarrow Y'(-4-1,-3+3)[/tex]
[tex]Y(-4,-3)\rightarrow Y'(-5,0)[/tex]
[tex]Z(0,-2)\rightarrow Z'(0-1,-2+3)[/tex]
[tex]Z(0,-2)\rightarrow Z'(-1,1)[/tex]
Therefore coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).
What ordered pair doesn't belong in the solution set of y>2x+1? (1,4), (1,6), (3,8), (2,5)?
Put the coordinates of the points to the inequality and check.
y > 2x + 1
for (1, 4):
4 > 2(1) + 1
4 > 2 + 1
4 > 3 CORRECT
for (1, 6):
6 > 2(1) + 1
6 > 2 + 1
6 > 3 CORRECT
for (3, 8):
8 > 2(3) + 1
8 > 6 + 1
8 > 7 CORRECT
for (2, 5):
5 > 2(2) + 1
5 > 4 + 1
5 > 5 FALSE
Answer: (2, 5).Another math question because that’s my weak point 30 points
Answer:
4j-3 = j is an equation
2 + 66÷11 -3*2 is an expression
g+h>f is an inequality
Step-by-step explanation:
An equation has an equals sign =
An expression has no equals sign or greater or less than signs
An inequality has ( ≤,≥,<,>) greater than or equal to, less than or equal to, greater than, less than signs
Find (12x+12)−(−5x+8). step by step answers please.
Answer:
Step-by-step explanation:
First add 5x to 12x which becomes 17x and subtract 8 from 12 which becomes 4. So the answer is 17x+4!
graph the equation y=2x-3 using slope and y-intercept
Answer: The slope of the graph is 2x. In other words, rise over run: move up 2 and move to the right 1 because it is 2 over 1. The y-intercept is -3, which means you move down 3 on the y-axis.
Write Y=3x^2+6x+8 In Vertex form
5x + 3 < 3(x+2 need help
Answer:
x < [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
distribute the parenthesis on the right side
5x + 3 < 3x + 6 ( subtract 3x from both sides )
2x + 3 < 6 ( subtract 3 from both sides )
2x < 3 ( divide both sides by 2 )
x < [tex]\frac{3}{2}[/tex]
Answer:
x < [tex]\frac{3}{2} \\[/tex]
Determine the ratio in which the point (–6, m) divides the join of A(–3, –1) and B(–8, 9). Also, find the value of m.
Answer:
Ratio = 3 : 2 and value of m = 5.
Step-by-step explanation:
We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.
Let us assume that it cuts the line in k : 1 ratio.
Then, the co-ordinates of P = [tex]( \frac{-8k-3}{k+1},\frac{9k-1}{k+1} )[/tex].
But, [tex]\frac{-8k-3}{k+1}[/tex] = -6
i.e. -8k-3 = -6k-6
i.e. -2k = -3
i.e. [tex]k = \frac{3}{2}[/tex]
So, the ratio is k : 1 i.e [tex]\frac{3}{2} : 1[/tex] i.e. 3 : 2.
Hence, the ratio in which P divides the line is 3 : 2.
Also, [tex]\frac{9k-1}{k+1}[/tex] = m where [tex]k = \frac{3}{2}[/tex]
i.e. m = [tex]\frac{\frac{9 \times 3}{2}-1}{\frac{3}{2}-1}[/tex]
i.e. m = [tex]\frac{27-2}{3+2}[/tex]
i.e. m = [tex]\frac{25}{5}[/tex]
i.e. m = 5.
Hence, the value of m is 5.
Answer:
m=5
Step-by-step explanation:
Given: Point [tex]C(x_3,y_3)=(-6,m)[/tex] divides the join of point [tex]A(x_1,y_1)=(-3,-1)[/tex] and point [tex]B(x_2,y_2)=(8,9)[/tex]
Let the line AB divides by Point C in a ratio m:n=k:1
Then, Using section formula [tex](x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}[/tex]
Applying formula,
[tex]x_3,y_3=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}[/tex]
[tex]x_3,y_3=\frac{-8k-3}{k+1},\frac{9k-1}{k+1}[/tex]
But, [tex]x_3=-6[/tex]
Therefore, [tex]x_3=\frac{-8k-3}{k+1}[/tex]
[tex]-6=\frac{-8k-3}{k+1}[/tex]
[tex]-6k-6=-8k-3[/tex]
[tex]2k-3=0[/tex]
[tex]k=\frac{3}{2}[/tex]
Therefore, C divides line AB in 3:2
Now, [tex]m=\frac{9k-1}{k+1}[/tex] where, k=3/2
[tex]m=\frac{9\frac{3}{2}-1}{\frac{3}{2}+1}[/tex]
[tex]m=\frac{\frac{25}{2}}{\frac{5}{2}}[/tex]
[tex]m=\frac{25\times2}{2\times5}[/tex]
[tex]m=5[/tex]
PLZ DO ASAP NEED LIKE NOW HELP ME PLZ
What is the equation of this graphed line? y = mx + b m is the slope b is the y intercept (where does the line cross the y - ordered pair) x and y can be a point on the line m = y2 - y1/x2 - x1 A graph with a line running through coordinates (-4, -6) and coordinates (2, 6) Enter your answer in slope-intercept form in the box.
Answer:
y = 2x+2
Step-by-step explanation:
When we have 2 points, we can find the slope from
m = (y2-y1)/(x2-x1)
= (6--6)/(2--4)
= (6+6)/(2+4)
= 12/6
= 2
The slope is 2
We can use the point slope form of the equation for a line
y-y1 = m(x-x1)
y-6 = 2(x-2)
We need to get this in slope intercept form
Distribute the 2
y-6 = 2x-4
Add 6 to each side
y-6+6 = 2x-4+6
y = 2x+2
Answer:
y = 2x + 2
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + b ( m is the slope and b the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 6) and (x₂, y₂ ) = (2, 6)
m = [tex]\frac{6+6}{2+4}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence
y = 2x + b is the partial equation
to find b substitute either of the 2 points into the partial equation
using (2, 6), then
6 = 4 + b ⇒ b = 6 - 4 = 2
y = 2x + 2 ← equation in slope-intercept form
A hot air balloon rose from ground level to 1000 feet in order to pass over a mountain. The balloon then descended 800 feet to a cruising height.
Answer:
200ft.
Step-by-step explanation:
It's 200ft because you just do 1000 - 800 = 200ft
Answer:
200
Step-by-step explanation:
As a clinical trials monitor, you recruit subjects for a new study. You want 175 subjects per group for 3 groups. How many subjects should you recruit for the whole study?
Answer:
You should recruit a total of 525 subjects for the whole study.
Step-by-step explanation:
The question states that you want 175 subjects per group for 3 groups. This indicates that we need to either multiply 175 times 3, or we can add 175 three times to get the total number of subjects we would need to recruit. Group 1 should have 175, Group 2 should have 175 and Group 3 should have 175. Whether we multiply 175 x 3 or add 175+175+175, we get a final anser of 525.
So far in math class, a student's quiz scores are 86%, 82%, 72%, and 69%. What score does the student need on the fifth quiz to have a mean quiz score of 79%? All the quizzes have equal weights. a 86% b 77.25% c 79% d 87%
Answer:
a
Step-by-step explanation:
the mean = [tex]\frac{total score}{count}[/tex]
let the fifth score be x and count = 5, hence
[tex]\frac{86+82+72+69+x}{5}[/tex] = 79 ( multiply both sides by 5 )
309 + x = 395 ( subtract 309 from both sides )
x = 86
the student requires a score of 86% → a
Harvey is finding the area that can be divided into 2 trapezoids.the basis of each trapezoid is 14 and 24. The height of each is 8. What is the area of the figure?
Answer:
Area of the figure is 304 sq. units
Step-by-step explanation:
The area is divided into two identical trapezoids of height 8 units and bases 14 and 24 units.
Area of a trapezoid = (1/2) * (Sum of base lengths) * height
So, area of 1 one trapezoid = (1/2)*(14+24)*8=152
The area of the figure is twice the area of the trapezoid.
So, area of figure = 2 * 152 = 304 sq. units
∴ Area of the figure is 304 sq. units
Twice the sum of a number and eleven is twenty-two less than three times the number. Find the number.
In which number is the value of the 7 ten times the value of the 7 in the number 1,273
Answer:
Your answer would require a 7 in the hundreds place
Step-by-step explanation:
1,273
The 1 is in the thousands place. 1 * 1000
The 2 is in the hundreds place. 2 * 100
The 7 in in the tens place. 7 * 10
The 3 is in the ones place. 1 * 1
To get from 10 to 100, we would multiply by 10, so to get from the tens place to the hundreds place is 10 times greater.
Your answer would require a 7 in the hundreds place
In the number system, each place to the left is ten times the place to its right. Therefore, for the value of the 7 to be ten times greater than the 7 in 1,273, it must be in the tens place, such as in numbers like 702, 770, or 170.
Explanation:The value of a digit in a number depends on its place or position. In the number system, each place is ten times the place to its right. Therefore, in the number 1,273, the value of the 7 is simply 7 (because it's in the units place). However, for the 7 in the new number to be ten times greater than the 7 in 1,273, it must be in tens place. Therefore, the new number could be 7x10 = 70 (with the 7 in the tens place). So, any number with 70 in the tens place (like 702, 770, or 170) has a 7 that's ten times the 7 in 1,273.
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Rafael's art class is 6 hours long. How long is his class in minutes?
Answer:
360 Minutes Long
Step-by-step explanation:
There are 60 minutes in an hour. Multiply 60*6, and you get 360 minutes.
Answer:
The art class would be 360 mins long.
Step-by-step explanation:
Find all the whole values of a for which the solution of the equation ax = 6 is a whole number.
Answer:
[tex]a=1,\ 2,\ 3,\ 6.[/tex]
Step-by-step explanation:
A whole number is any number of a set [tex]\{0,\ 1,\ 2,\ 3,...\}[/tex]
The equation [tex]ax=6[/tex] has a solution [tex]x=\dfrac{6}{a},\ a\neq 0.[/tex]
If [tex]a=1,[/tex] then [tex]x=\dfrac{6}{1}=6[/tex] is a whole number.
If [tex]a=2,[/tex] then [tex]x=\dfrac{6}{2}=3[/tex] is a whole number.
If [tex]a=3,[/tex] then [tex]x=\dfrac{6}{3}=2[/tex] is a whole number.
If [tex]a=6,[/tex] then [tex]x=\dfrac{6}{6}=1[/tex] is a whole number.
For all other values of [tex]a[/tex] equation [tex]ax=6[/tex] will have solution that is not a whole number.
Line AB passes through points A(–6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y = mx + b, then m = –1/6.
and b = ?
Put the value of slope to the equation of the function:
[tex]y=-\dfrac{1}{6}x+b[/tex]
Put the coordinates of the point B(12, 3) to the equation:
[tex]3=-\dfrac{1}{6}(12)+b[/tex]
[tex]3=-2+b[/tex] add 2 to both sides
[tex]5=b[/tex]
Answer: b = 5Answer:
The value of b is 5.
Step-by-step explanation:
Consider the provided information.
It is given that the slope intercept form is, y = mx + b
Where m is the slope and b is the y intercept.
Also, it is given that the slope of the line is -1/6.
Line AB passes through points A(–6, 6) and B(12, 3).
That means Point A and B must satisfy the equation of line.
Substitute [tex]m=\frac{-1}{6}, x=-6\ \text{and}\ y = 6[/tex] in slope intercept form:
[tex]6=\frac{-1}{6}\times(-6)+b[/tex]
[tex]6=1+b[/tex]
[tex]5=b[/tex]
Thus, the value of b is 5.
7y+44=12y+11, I need help!
Answer:
y = 33/5 or 6.6
Step-by-step explanation:
7y + 44 = 12y + 11
-11 -11
7y + 33 = 12y
-7y -7y
33 = 5y
Divide both sides by 5
= 33/5 or 6.6
Answer:
[tex]y=6\frac{3}{5}[/tex]
Step-by-step explanation:
We are given the following equation for which we have to solve for y:
[tex]7y+44=12y+11[/tex]
So first of all, we will rearrange the terms by putting the like terms together (variables on one side of the equation and constants on the other side) to get:
[tex]12y-7y=44-11[/tex]
Then solving for y:
[tex]5y=33\\\\y=\frac{33}{5}[/tex]
Therefore, the value of y is equal to [tex]y=6\frac{3}{5}[/tex] (rewriting y in a mixed fraction form).
9x-6a=-7,find x when a =-7
Answer:
Step-by-step explanation:
Plug in -7 for the variable a.
9x - 6(-7) = -7
Follow PEMDAS. Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x.
Multiply -6 with -7
9x - 6(-7) = -7
9x + 42 = -7
Isolate the variable x. Subtract 42 from both sides
9x + 42 (-42) = -7 (-42)
9x = -49
Divide 9 from both sides
(9x)/9 = (-49)/9
x = (-49)/9
x = ~5.44 (rounded)
~
Kameko bought a home in Homewood, Illinois, for $230,000. He put down 20% and obtained a mortgage for 25 years at 8%. What's the total interest cost of the loan?
Final answer:
The total interest cost of the loan is $28,999.
Explanation:
To find the total interest cost of the loan, we need to calculate the amount of interest paid over the 25-year period. First, we need to find the amount of the mortgage by subtracting the down payment from the purchase price. 20% of $230,000 is $46,000, so the mortgage is $230,000 - $46,000 = $184,000.
To calculate the interest cost, we can use the formula: Interest Cost = Total Repayment - Principal Amount.
Principal Amount = Mortgage Amount = $184,000.
Number of Payments = Number of years x Number of payments per year = 25 x 12 = 300.
Monthly Interest Rate = Annual Interest Rate / Number of payments per year = 8% / 12 = 0.00667.
Total Repayment = Monthly Payment x Number of Payments = [(Monthly Interest Rate x Principal Amount) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments)) ] x Number of Payments = [(0.00667 x $184,000) / (1 - (1 + 0.00667)^(-300))] x 300 = $526.67 x 300 = $157,001.
Interest Cost = Total Repayment - Principal Amount = $157,001 - $184,000 = $28,999.
Jack makes W dollars an hour. He will get a $2 an hour raise. Write an expression for his new hourly wage
Answer:
2w
Step-by-step explanation:
you multiply 2 by how many hours you have worked (w)
Is my answer correct
Answer:
yes
Step-by-step explanation:
the box would typically be closer to the left than in the middle
Answer:
Yes you are correct because the box plot's data is skewed left
Step-by-step explanation:
Your welcome and don't forget to say Thanks
Which method can you use to prove that the triangles are congruent?
A. HL
B. ASA
C. SAS
D. SSS
E. AAS
Answer:
The answer is ASA.
Step-by-step explanation:
There is one other angle in the middle which is congruent to its self.
ASA (Angle-Side- Angle) method can we use to prove that the triangles are congruent
Two triangles are called to be congruent if their sides have the equal length and angles have equal measure.
Thus, two triangles can be superimposed side to side and angle to angle.
If any two angles and the side of the angles of triangle are equivalent to the corresponding, then the two triangles are said to be congruent by ASA rule.
There is one other angle in the middle which is congruent to its self
ASA (Angle-Side- Angle)
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2 Emma buys 33 yards of blue fabric and some yellow fabric at a store. She buys a total of 53 yards of fabric. The equation 1 2 5333can be used to represent this situation, where y is the number of yards of yellow fabric she buys. How much yellow fabric does she buy?
Step-by-step explanation:
your answer is 99
Which is the graph of f(x)= 4[1/2]^x ?
Answer:
B
Step-by-step explanation:
A
f(1) = 4*(1/2)^1 = 4/2 = 2
(1,1) is not the same thing.
B
B is the answer.
C
f(0)=4 not 2 C is incorrect. C is not the answer
D
Same problem as C
1. find the product and write it in simplest form: 1 1/3 x 3/8 =
a. 1/2
b. 3 5/9
c. 7/24
d. 1 1/3
2. find the quotient and write it in simplest form: 1 2/3 ÷ 2 1/2
a. 4 1/6
b. 2/3
c. 3 2/6
d. 10/15
3. find the quotient and write it in simplest form: 4/9 ÷ 9/4
a. 1
b. 8/9
c. 4/9
d. 16/81
4. the number 7 is the multiplicative inverse of which number?
a. 1/7
b. 7
c. - 1/7
d. - 7
5. simplify using the order of operations 3 x 7² + 4
a. 151
b. 445
c. 625
d. 159
6. using the order of operations, which operation should be performed first? 3(7+2²) - 5
a. 7 + 2
b. 2²
c. 3 x 7 and 3 x 2
d. 11 - 5
7. which operation should be performed immediately after evaluating exponents using the order of operations?
a. addition & subtraction in order from left to right
b. multiplication & division in order from left to right
c. parentheses
d. powers
Answer:
The answer to number 1 is A.
Step-by-step explanation:
To find this answer, I made 1 1/3 into one big fraction. I multiplied the denominator by the whole number (3x1) and then added that product to the numerator. (3+1). The new fraction is now 4/3 (you keep the denominator the same). The next step is to multiply 4/3 by 3/8. When multiplying fractions, you multiply straight across (the numerator by the numerator, and the denominator by the denominator). Your answer is now 12/24. The final step is to simplify the answer. Since 12 is half of 24, the answer is 1/2.
van someone please help me with this i dont need an explaination i just need a. b. c. or d. please and thank you
Answer:
option C
[tex]f(x)=-\sqrt{x+3}+8[/tex]
Step-by-step explanation:
we have
[tex]f(x)=-2\sqrt{x-3}+8[/tex]
using a graphing tool
see the attached figure N[tex]1[/tex]
The range is the interval--------> (-∞,8]
[tex]y\leq 8[/tex]
case A) [tex]f(x)=\sqrt{x-3}-8[/tex]
using a graphing tool
The range is the interval--------> [-8,∞)
[tex]y\geq -8[/tex]
case B) [tex]f(x)=\sqrt{x-3}+8[/tex]
using a graphing tool
The range is the interval--------> [8,∞)
[tex]y\geq 8[/tex]
case C) [tex]f(x)=-\sqrt{x+3}+8[/tex]
using a graphing tool
The range is the interval--------> (-∞,8]
[tex]y\leq 8[/tex]
case D) [tex]f(x)=-\sqrt{x-3}-8[/tex]
using a graphing tool
The range is the interval--------> (-∞,-8]
[tex]y\leq -8[/tex]
Can someone help me please
Harold can buy 2 pounds of bananas for $7. Write and equation to represent the cost , c , for b bananas