Answer:
B
a. down payment: $31,500b. amount of mortgage: $178,500c. points paid at closing: $1785d. total cost of interest over 30 years: $227,667Step-by-step explanation:
You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.
Look at the Answer ChoicesThe answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...
1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C
The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.
Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.
Answer choice B is the only one that makes sense.
Work the problemIf you like, you can work the problem.
down payment = 15% × $210,000 = $31,500
loan amount = $210,000 -31,500 = $178,500
one point = 0.01 × $178,500 = $1785
The monthly payment is found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24
The monthly payment amount is about $1128.
So, the total repaid is 360 payments of $1128.24, or $406,167.
The interest paid is this amount less the principal:
interest paid = $406,167 -178,500 = $227,667
A patient is using a bicycle as part of their physiotherapy routine. The diameter of the bicycle’s wheel is 590 mm. While in session, the wheel is rotating at a speed of 82 rpm (revolutions per minute). If the patient is riding the bicycle for 1 h and 10 minutes, determine the number of kilometres the patient has travelled. Round to the nearest tenth.
The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.
What is the distance?The distance is the length from one point to the end.
For our purpose, distance represents the product of speed and time.
Diameter of the bicycle's wheel = 590 mm
Speed (Revolutions) per minute = 82 rpm
Time riding the bicycle = 1 hr and 10 minutes = 70 minutes
1 Kilometer = 1,000,000 Millimeters
Distance per rotation = pi x diameter
= 3.14 x 590
= 1,852.6 mm/minute
Total distance traveled in kilometers = (1,852.6 x 82 x 70) ÷ 1,000,000
= 10,633,924 ÷ 1,000,000
= 10.6 kilometers
Thus, we can conclude that the patient traveled 10.6 kilometers by bicycling for one hour and 10 minutes.
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NO LINKS!! Please help me with this probability question Part 3j
Answer:
b) 64 to 76 inches.
Step-by-step explanation:
In a normal distribution, 95% of the population is within 2 standard deviations of the mean.
Given values:
[tex]\textsf{Mean}\; \mu=70\; \sf inches[/tex][tex]\textsf{Standard deviation}\; \sigma=3\; \sf inches[/tex]Given that the mean height is 70 inches and the standard deviation is 3 inches:
[tex]\implies \mu -2 \sigma = 70-2(3)=64[/tex]
[tex]\implies \mu+2 \sigma = 70+2(3)=76[/tex]
Therefore, an appropriate height range for 95% of all people in the sample would be:
64 to 76 inches.A rectangular playground is enclosed by 440 feet of fencing. If the length of the playground is 20 feet less than 3 times the width, find the dimensions of the playground.
The dimensions of the playground are;
Width = 60 feet
Length = 160 feet
How to determine the dimensionsThe formula for calculating perimeter of a rectangle is expressed as;
Perimeter = 2( l + w)
Where;
l is the length of the rectanglew is the width of the rectangleWe have the values as;
Perimeter = 440 feet
Length = 3w - 20
Width = w
Now, substitute the values into the formula, we have;
440 = 2( 3w - 20 + w)
expand the bracket
440 = 2( 4w - 20)
440 = 8w - 40
collect like terms
8w = 480
Make 'w' the subject of formula
w = 60 feet
Length = 3(60) - 20
Length = 180 - 20
Length = 160 feet
Hence, the values are 60feet and 160 feet
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Suppose 57% of the doctors in a hospital are surgeons.
If a sample of 465 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 6%? Round your answer to four decimal places.
The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%
How to solve for the probabilityP of 6%
= P (p > 0.06)
we would have to use the formula that is given below
[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]
where we have n = 465
p = 6%
P = 0.57
Q = 1 - 0.57 = 0.43
We would have to put the values into the equation that we have here as:
0.06 - 0.057 = -0.51
0.57 x 0.43 / 465 = 0.000527
√0.000527 = 0.022956
The probability = -0.51 / 0.022956
= -22.22%
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solve the expression when a= 0.25 and b = -1
36a + 42b - 18a +6
The solution to the expression is -31.5
Algebraic expression
An algebraic expression in mathematical is statement that comprises of numbers, variables, symbols and mathematical operators.
Given, when a= 0.25 and b = -1
Step 1: Substitute the given into the expression 36a + 42b - 18a +6
we have; 36(0.25) + 42(-1) - 18(0.25) +6
= 9 - 42 - 4.5 +6
Step 2; use BODMAS to evaluate
we have; 9 - 42 - 4.5 +6= -31.5
Therefore the solution to the expression is -31.5
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Approximate the following square root to the nearest integer.
√10~
The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V= 70 cm^3 when T = 420 kelvin and P = 18 kg/cm^2 . Find the pressure when T = 140 kelvin and V = 60 cm^3.
In a case where the expression is give as volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P, then the pressure will be 7kg/cm^2.
How can the pressure be calculated?V = k T/ P
and V= 70 cm^3
T = 420 kelvin
P = 18 kg/cm^2
where K is constant of proportionality,
70 =( k * 420) / 18
k = (70 * 18) / 420
k= 3
Then we were given that the pressure=?
T = 140 kelvin
V = 60 cm^3
then V = k T/ P
P= kT/V
P= (3*140)/60
=7
Then the pressure is 7kg/cm^2
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A baseball team has three different pitchers. Randy allowed
2
22 runs and pitched
3
33 innings. Felix allowed
4
44 runs and pitched
5
55 innings. Johan allowed
5
55 runs and pitched
7
77 innings.
Which pitcher has the lowest number of runs allowed per inning?
The pitcher that has the lowest number of runs allowed per inning is Randy.
Which pitcher has the lowest number of runs per inning?In order to determine the pitcher with the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.
Division is the process of determining the quotient of two or more numbers. It is the process of putting a number into equal groups using another number.
Number of runs per innings = number of runs / number of innings
Number of runs per innings for Randy : 2 / 3 = 0.667
Number of runs per innings for Felix : 4 / 5 = 0.80
Number of runs per innings for Johan: 5 / 7= 0.714
Here is the complete question:
A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.
Which pitcher has the lowest number of runs allowed per inning?
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Your friend uses the figure to say that all the exterior angles of any isosceles triangle are congruent. Is your friend correct? Explain your reasoning
Answer:
All the exterior angles of any isosceles triangle are congruent - FALSE statementStep-by-step explanation:
We know that the exterior angle of a triangle is the sum of remote interior angles.
If the triangle is equilateral then the sum of any two interior angles is same otherwise, with any isosceles triangle, we get different sums and therefore the friend is wrong.
Answer:
No.
Step-by-step explanation:
An isosceles triangle has two sides of equal length. Therefore, only two of its interior angles are congruent.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). Therefore, as not all of the three interior angles of an isosceles triangle are congruent, all the exterior angles will also not be congruent.
If WX equals to XY , what is the length of WZ?
Answer:
the length of WZ is 10
Step-by-step explanation:
I don’t know it and I need help. question is in picture
Pete's Convenience Store has a beginning inventory of 12 cans of soup at a cost of $.85 each. During the year, the store purchased 4 at $.95, 6 at $1.05, 7 at $1.35, and 8 at $1.50. By the end of the year, 18 cans were sold. Calculate (A) the number of cans of soup ending inventory and (B) the cost of ending inventory under LIFO, FIFO, and weighted average. (Round your final answers to the nearest cent.)
A) The number of cans of soup in ending inventory is 19.
B) The cost of the ending inventory under LIFO, FIFO, and the weighted average is as follows:
LIFO $17.15
FIFO $25.65
Weighted average $21.47
What are the inventory methods?The inventory methods include First-in, First-out (FIFO), Last-in, First-out (LIFO), Weighted Average, and Specific Identification.
FIFO assumes that the physical flow of goods during sales follows the chronological sequence of their acquisition.
LIFO assumes that the first goods acquired are the last to be sold.
The Weighted Average uses an average to determine the costs allocated to ending inventory and the cost of goods sold.
Specific Identification identifies the specific goods sold with their costs.
Description Units Unit Cost Total
Beginning inventory 12 $0.85 $10.20
Purchases 4 $0.95 $3.80
Purchases 6 $1.05 $6.30
Purchases 7 $1.35 $9.45
Purchases 8 $1.50 $12.00
Total 37 $41.75
Sales 18
Ending inventory 19 (37 - 18)
Average cost = $1.13 ($41.75/37)
LIFO:
Ending inventory = $17.15 ($10.20 + $3.80 + 3 x $1.05)
FIFO:
Ending inventory = $25.65 (4 x $1.05 + $9.45 + $12.00)
Weighted Average
Ending inventory = $21.47 (19 x $1.13)
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Pedro and Rebecca were trying to solve the equation:
0.1x^2 - 0.7x + 1.2 = 0
Pedro said, “I can multiply the entire equation by 10 and then factor. Then I can solve using the zero product property.”
Rebecca said, “I'll solve using the quadratic formula with a = 0.1 1, b = -0.7 and c = 1.2"
WHOs Strategy works?
A - Only Pedro's
B - Only Rebecca's
C - Both
D - Neither
The correct strategy between Pedro and Rebecca trying to solve the quadratic equation: 0.1x^2 - 0.7x + 1.2 = 0 is A - Only Pedro's
How to determine the correct strategyThe given function is a quadratic function which is solved by several method including the method both Pedro and Rebecca are trying to use
Pedro's method is the factorization method and the steps mentioned are correct
However Rebecca's method has some error
The equation is: 0.1x^2 - 0.7x + 1.2 = 0
factor of the leading coefficient a is 0.1, Rebecca is using 0.11
The error of using 0.11 instead of 0.1 will make the method ineffective
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Find the X-intercept for this please .
Answer: I believe both the x and y- intercepts are “(0,0)”
Step-by-step explanation: there is only one intercept and it is at the origin (0,0) making both the x and y - intercepts (0,0) :)
Can you guys awnser this ?
a. Jays total income is $93.50 and total spending is $103.25.
b. Jays Spending is greater than income.
c. Total saving is -9.75
d. Jays savings are negative. Since Jays spending is greater than income it does not make sense.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Jays Income:
Part time job: $83.50
Allowance: $10
Spending:
Clothing: $32.50
Lunches: $19.75
Entertainment: $29.00
Transportantion: $22.50
a. Jays total income and total spending
Total income = $83.50+$10.00
=$93.50
Total spending = $32.50+$19.75+$29.00+$22.50
=$103.25
b. Spending is greater than income.
c. Jays saving=Total income - Total spending
=93.50-103.25
=-9.75
d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.
Hence,
a. Jays total income is $93.50 and total spending is $103.25.
b. Jays Spending is greater than income.
c. Total saving is -9.75
d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.
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August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-seven guests attended the second party. What is the percentage increase of the number of guests from the first party to the second party?
A.
35%
B.
30%
C.
65%
D.
70%
Answer:
A 35%
Step-by-step explanation:
take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.
Answer:
a) 35%
Step-by-step explanation:
Given information,
→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.
Now we have to,
→ find the % increase of number of guests from first party to second party.
Let's solve the problem,
→ ((27 - 20)/20) × 100
→ (7/20) × 100
→ 0.35 × 100
→ 35%
Hence, the answer is 35%.
ms.folk at least 250 candies to reward her students she has 50 candies already and will buy more candy in bags with 20 candies in each write an inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies
50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies.
How to solve equations in word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:i) There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.(ii) Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Let x be the number of bags she bought:
50 + 20x ≥ 250
3x ≥ 200
x ≥ 200/3
x ≥ 66.67
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HELP PLEASE!! Dominique is selling merchandise for a school fundraiser. She is selling calendars for $8 each and coffee mugs for $12 each. She must sell at least $800 of merchandise, including at least 60 calendars, to meet her goals.
If x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario?
8x + 12y ≥ 800 and x ≥ 60
8x + 12y ≥ 800 and y ≥ 60
8x + 12y > 800 and y > 60
8x + 12y > 800 and x > 60
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
Given,
The cost for one calendar = $8
The cost for one coffee mug = $12
Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.
Here,
x be the number of calendars and y be the number of coffee mugs;
We have to find an inequality which represents the given situation;
So,
The inequality be;
8x + 12y ≥ 800 and x ≥ 60
That is,
The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.
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There are 207 public libaries in New York City. The population in New York City is 8.805 million. What was the rate of libraries per 100,000? Give your answer to the nearest hundredth.
The rate of libraries per 100000 is 88.05 .
In the question ,
it is given that ,
the number of public libraries in New York City = 207 libraries
the population of the New York City = 8.805 million
we have to find the rate of libraries per 100000 .
for this we first have to express the population in numbers .
the population 8.805 million expressed in numbers is 8805000 ,
the rate of libraries per 100000 is
= 8805000/100000
On further simplification ,
we get ,
= 88.05
Therefore , The rate of libraries per 100000 is 88.05 .
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The pH of solution measures its acidity and can be determined using the formula pH= -log(base of 10 )C, where is the concentration of hydronium ions in the solution. measured in moles per litre .A lower pH indicates a more acidic solution.
Determine whether the unknown liquid is more or less acidic then the coffee ( pH=-4.886)
if that liquid has 10 times the concentration ions of the coffee.
The pH of the liquid which is 3.886 indicates that it is more acidic than coffee.
What is the pH of a solution?The pH of a solution gives a measure of the concentration of hydronium ions in the solution, and therefore, indicates the level of acidity or basicity of the solution.
pH = -㏒₁₀CpH values ranges from 0 to 14, with solutions that are more acidic having a pH of less than 7, while basic solutions have a pH of more than 7.
The given pH of coffee = -4.886
The concentration of the liquid = 10 × The concentration of the ions in coffee
Which gives;
-㏒₁₀C = 4.886
Concentration of the hydronium ions in coffee, C = [tex]10^{(-4.886)}[/tex]
Concentration of ions in the unknown liquid = 10 × [tex]10^{(-4.886)}[/tex] = [tex]10^{(-3.886)}[/tex]
pH of the unknown liquid = [tex]-log_{10} \left(10^{(-3.886)}\right) = 3.886[/tex]
The pH of the unknown liquid indicates that it is more acidic than coffee
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Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 19, upper bound is 25.
The point estimate of the population mean is 22 and margin of error for the confidence interval is 3.
How to find the point estimate?1. Point estimate
Point estimate = Upper bound+ Lower bound/2
Point estimate = (25+19) /2
Point estimate = 44/2
Point estimate = 22
2. Margin error
Margin error = Upper bound - Lower bound/2
Margin error = ( 25-19) /2
Margin error = 6 /2
Margin error = 3
Therefore the point estimate is 22.
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x-intercept of (y+12) = 3(x - 9)
Answer: purple is the greatest
(2x²-3x+1)-(-x² + 2x − 2) - (2x - 3)² =
Answer:
6x^2-17x+12
Step-by-step explanation:
Distribute
2x^2-3x+1+x^2-2x+2(-2x+3)^2
Square (2x+3)
(-2x+3)(-2x+3)
FOIL
4x^2-6x-6x+9
Combine like terms
4x^2-12x+9
re-write equation
2x^2-3x+1+x^2-2x+2+4x^2-12x+9
Combine like terms
6x^2-17x+12
What is the equation of this graphed line
Answer: y = -9/8 + 7
Step-by-step explanation:
point a = (0,7), point b = (8,-2)
y = mx + b
b = 7
y = mx + 7
-2 = 8m + 7
-9 = 8m
m = -9/8
y = -9/8 + 7
Answer:
y= -9/8x+7
Step-by-step explanation:
find the slope
y2-y1/x2-x1
-2-7/8-0
-9/8
y=mx+b
m=slope
b=y intercept
y= - 9/8x + b
y= -9/8x+7
2.1 & 2.2 Assessment: Vertex & Standard Form of Quadratic Functions
What is the equation, written in vertex form, of a parabola with a vertex of (1, -9) that
passes through the point (2, -7)?
Work to Support Your Answer (Required for Credit!)
The equation of the parabola, in vertex form is
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]
f(x) = x^2+11x^2-15x-27 how to find the possibles
The solution for the function f(x) is x = 9/4 or -1.
What is function?Function is a combination of different types of variable and constants.
A function is denoted by f(x).
The given function is,
f(x) = x²+11x²-15x-27
⇒f(x) = 12x²-15x-27
To find solution of this function, find factor,
f(x) = 12x²-27x+12x-27
f(x) = 3x(4x-9) + 3(4x-9)
f(x) = (4x-9)(3x+3)
To find solutions substitute f(x)=0,
⇒(4x-9)(3x+3) =0
x=9/4 or -1
So the possible value of x is 9/4 or -1.
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right answers only please
Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Given,
In the question;
The equation is:
g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]
To find the is this the graph of g(x) or h(x).
Graph is given in the figure.
Now, According to the question;
g(x) = [tex]-x^{2} (x -2)[/tex] and h(x) = [tex]x^{2} (x -2)[/tex]
g(x) = 0 h(x) = 0
[tex]-x^{2} (x -2) = 0[/tex] [tex]x^{2} (x -2)[/tex] = 0
x = 0, 2 x = 0, 2
If we put x = 1 then,
g(1) = [tex]-(-1)^2(1-2)[/tex] and h(1) = [tex](1)^2(1-2)[/tex]
g(1) = -1 (-1) h(1) = 1(-1)
g(1) = 1 h(1) = -1
But as shown in graph, graph take positive value at x = 1
∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Hence, Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
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Drag the tiles to the correct boxes to complete the pairs.
Determine whether each pair of lines is perpendicular, parallel, or neither.
2y = 4x + 4
y=-2x-2
4y= 2x - 4
y=-2x+9
Perpendicular
Parallel
y = 2x+4
2y = 4x - 7
Neither
Answer:
neitherperpendicularparallelStep-by-step explanation:
You want to know whether the pairs of equations describe lines that are parallel, perpendicular, or neither.
ParallelParallel lines have the same slope. When the equations are written in slope-intercept form, the coefficients of x are identical.
PerpendicularPerpendicular lines have opposite reciprocal slopes. When the equations are written in slope-intercept form, the product of the x-coefficients is -1.
Application1. 2y = 4x +4; y = -2x -2Solving the first equation for y gives ...
y = 2x +2
The x-coefficients are 2 and -2, so the lines are neither parallel nor perpendicular.
2. 4y = 2x -4; y = -2x +9Solving the first equation for y gives ...
y = 2/4x -1 = 1/2x -1
The x-coefficients are 1/2 and -2, which have a product of -1. These lines are perpendicular.
3. y = 2x +4; 2y = 4x -7Solving the second equation for y gives ...
y = 2x -7/2
The x-coefficients are 2 and 2, which are identical. These lines are parallel.
Use the discriminant to determine the number of solutions for the following equation: \large 3x^2+4x-5=0 How many solutions does this equation have? a 1 real solution b 2 real solutions c infinite solutions d no real solutions
The number of solutions in the equation 3x² + 4x - 5=0 is (b) two real solutions
How to determine the number of solutions?The equation is given as:
3x² + 4x - 5=0
A quadratic equation is represented as:
ax² +bx + c=0
Where the discriminant is:
d = b² - 4ac
So, we have:
d = 4² - 4 * 3 * -5
Evaluate
d = 76
If the discriminant is greater than 0, then the equation has 2 real roots.
Hence, the number of solutions is (b) two real solutions
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Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Which equation could she use to determine how many marbles are in the bag? Select all that apply. (1.5)x + 1.5 = 30 30 – x = 2(1.5) (1.5)(30) = 1.5x 1.5 + x = 30 1.5x = 30 – 1.5
Answer:
1.5x = 30 - 1.5
Step-by-step explanation:
30 grams minus the weight of the bag 1.5
1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles
