d. x=11, y=-5, z= -71
To solve the given system of equations, we use the method of substitution. The solution is x = 11, y = -5, z = -71.
Explanation:To find the solution of the given system, we can use the method of substitution.
From the first equation, we have x = -3y - 4. Substituting this value for x in the second equation, we get -3y = 2(-3y - 4) - 7.
Solving this equation, we find y = -5. Substituting this value of y back into the first equation, we can solve for x. Plugging in y = -5, we get x = 11. Substituting these values for x and y in the third equation, we can find z. Plugging in x = 11 and y = -5, we get z = -71.
Therefore, the solution to the system is x = 11, y = -5, and z = -71.
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Help me with 1-8 please!
Answer:
Step-by-step explanation:
1) 144 x $12 = $1728.00
2) $10 x 2 = $20 $20 x 3 = $60 $30 x 2 = 60; $20+$60+$60 = $140
3) $350 - $234 = $116.00
4) $225 ÷ $15 = 15 lawns will need to be cut
5) 2/4 = 1/2 = .50 = 50% B
6) 0.99 + 1.19 + 1.50 + 0.99 = $4.67
7) B 90 seconds is = 1 minutes and 30 seconds (1 minute = 60 seconds)
8) 4 weeks x 5 nights = 20 nights of studying
20 nights x 30 minutes = 600 minutes
600 minutes ÷ 60 (minutes in an hour) = 10 hours of studying D
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]
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
Find the first four terms of the recursive sequence: a1 = 8 and an = an-1+n.
Answer:
a1 = 8
a2 =10
a3 = 13
a4 = 17
Step-by-step explanation:
The first term is a1 = 8
The second term is a2 = a1 + n
= 8+2
= 10
The third term is a3 = a2 + n
= 10+3
= 13
The fourth term is a4 = a3 + n
= 13+4
= 17
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).
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.
Twice the sum of a number and eleven is twenty-two less than three times the number. Find the number.
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.
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.
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)
Tickets for a choir concert cost $3 for students and $5 for adults. The choir director wants to sell at least $1500 worth of tickets to this concert. She knows that 226 students purchased a ticket. Enter the minimum number of adults that need to purchase a ticket to raise at least $1500.
Answer: 164.4 or 165
Step-by-step explanation: So, you do 226 x 3 and you get $678. So now that you know that you have $678 worth of student tickets, you want to find how much more you need for the adult tickets, so you do $1500-$678, and you get $822. Divide it by 5 and you get 164.4, so you wanna sell about 165 tickets. Check your work by multiplying 5 by 165 and you get $825, which meets your $1500 minimum
After calculating the revenue already obtained from the student tickets sold, the remaining revenue needed to reach $1500 is found. This amount is divided by $5 (the cost of an adult ticket) to find the minimum number of adult tickets needed. Since you can't sell fractions of tickets, we round up to the next whole number, which is 165 adult tickets.
Explanation:The first step to solve this problem is to calculate how much revenue has already been raised from the student tickets sold, which is $3 x 226 = $678. Then subtract this amount from the total revenue target of $1500, which gives $1500 - $678 = $822.
The choir director now needs to raise $822 from selling adult tickets. As each adult ticket costs $5, we can calculate the minimum number of adult tickets that need to be sold by dividing the amount of revenue needed by the price of an adult ticket. This is $822 / $5 = 164.4.
Since you can't sell .4 of a ticket, we'll need to round up to the next whole number, giving a minimum of 165 adult tickets that need to sell in order to reach the revenue target.
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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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16 less than a number equals -19. What is the number? PLS HELP (6TH GRADE MATH)
Answer:
-3
Step-by-step explanation:
-3-16=-19
-19+16=-3
Answer:
-3
Step-by-step explanation:
I really don't understand.
HELP QUICK IM GIVING 21 POINTS AND A BRAINLIEST AWARD
Peter had a 12:00 noon appointment that was 60 miles from his home. He drove from his home at an average rate of 40 miles per hour and arrived 15 mins late. At what time did Peter leave home
Answer:
10:45
Step-by-step explanation:
v...speed = 40 mph
s...distance = 60
t...time
if he was 15 min late he arrived at 12:15
v=s/t => t=s/v
t = 60/40 = 1.5 h = 1h and 30 min
if he arrived at 12:15 and he was driving for an hour and a half just substract
12:15 - 1:30 = 11:15 - 0:30 = 10:45
he left at 10 45
Find the measure of the angle
Answer:
? = 113
Step-by-step explanation:
The angles are alternate interior angles. Alternate interior angles are equal if the lines are parallel. Since the lines are parallel, the angles are equal.
? = 113
Can someone help me please
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
I also need help with this one
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]
Harold can buy 2 pounds of bananas for $7. Write and equation to represent the cost , c , for b bananas
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
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
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.
Write Y=3x^2+6x+8 In Vertex form
Ralph Kramer ingested $11,000 in a certificate of deposit for 1 year. The certificate earns interest at an annual rate of 5.75 percent compounded daily. The amount per $1.00 is 1.059180. What is the effective annual yield? Show work
Answer:
5.91%
Step-by-step explanation:
We are given an investment deposited fro 1 year compounded daily at an annual interest rate of 5.75%.
Compounding period per year, n: 365
The effective annual yield can be calculated by the following formula:
Effective Annual Yield = [tex] (1+\frac{r}{n})^{n}-1[/tex]
where n = 365
Interest rate, r= 5.75% = 0.0575
[tex]=(1+\frac{0.0575 }{365})^{365}-1[/tex]
= 0.059
The annual effective yield is 5.91%
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
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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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).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).