Evaluating the square root expression -2√(2r + 5) = 6 gives r = 2
Evaluating the square root expressionFrom the question, we have the following expression that can be used in our computation:
-2 square root of 2r +5=6
Express properly
So, we have
-2√(2r + 5) = 6
Divide by -2
√(2r + 5) = -3
So, we have
2r + 5 = 9
Subtract 5 from both sides
2r = 4
Divide
r = 2
Hence, the solution is 2
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For questions 18-19, describe the end behavior of the graph for each function.
18. f(x) = x³ +2x² - 5x+1
19. g(x) = -2x³-8x2 +18x+72
Answer:
18. The end behavior of the graph of f(x) = x³ + 2x² - 5x + 1 is as follows: as x approaches negative infinity, the function f(x) approaches negative infinity, and as x approaches positive infinity, the function f(x) approaches positive infinity. This is because the leading term of the polynomial is x³, which has a positive coefficient, so the graph of the function will have a "smile" shape, with the ends of the graph pointing upwards.
19. The end behavior of the graph of g(x) = -2x³ - 8x² + 18x + 72 is as follows: as x approaches negative infinity, the function g(x) approaches negative infinity, and as x approaches positive infinity, the function g(x) approaches negative infinity. This is because the leading term of the polynomial is -2x³, which has a negative coefficient, so the graph of the function will have a "frown" shape, with the ends of the graph pointing downwards.
Step-by-step explanation:
PLEASE HELP ME PICK THE RIGHT ANSWER!!!!!
The meaning of the absolute value of -5.5 is given as follows:
The temperature decreases 5.5 degrees.
What is the absolute value of a number?The absolute value of a number is the number without the signal, for example:
|-2| = |2| = 2.
The number in this problem is given as follows:
-5.5.
Hence:
The negative sign means that the temperature decreased.The absolute value of 5.5 means that the temperature decreased by 5.5 degrees.Hence the second option is the correct option in the context of this problem.
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The volume of a rectangular prism is (x4 + 4x³ + 3x² + 8x + 4), and the area of its base is (x3 + 3x² + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? O X+1- Gere O X+1+ O X+1- 4 x4+4x³+3x²+8x+4 O X+1+ 4 X*+4x²+3x+8x+4 4 +³+3x²+8 4 +³+3x²+8
The Height of the given rectangular prism is: (x + 1) - 4/(x³ + 3x² + 8)
How to carry out polynomial division?In algebra, polynomial long division is defined as an algorithm used in dividing a polynomial by another particular polynomial of the same or even lower degree, which is a generalized version of the common arithmetic technique called long division. It can be done easily by hand, because it separates a supposedly complex division problem into smaller ones.
We are given:
Volume of a rectangular prism = (x⁴ + 4x³ + 3x² + 8x + 4), and the area of its base is (x³ + 3x² + 8)
Thus, height is:
x + 1
x³ + 3x² + 8|x⁴ + 4x³ + 3x² + 8x + 4
- x⁴ + 3x³ + 0 + 8x
x³ + 3x² + 4
- x³ + 3x² + 8
-4
Thus:
Height = (x + 1) - 4/(x³ + 3x² + 8)
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Which set of ordered pairs gives the polygon shown?
(-1, 0.5), (1.25, 0), (0.75, -0.75)
(0.75, -0.75), (-1, 0.5), (0, 1.25)
(-0.75, 0.75), (0.5, -1), (0, 1.25)
(-1, 0.75), (0, 1.5), (0.75, -0.75)
The set of ordered pairs of the polygon is:
(0.75, -0.75), (-1, 0.5), (0, 1.25)
Option B is the correct answer.
We have,
From the figure,
We have,
The polygon has three points.
The points are in ordered pairs.
We see that,
Each number has four units.
So,
1 unit = 0.25 units
Now,
The coordinates of the polygon are:
(3 units, -3 units) = (0.75, -0.75)
(0, 5 units) = (0, 1.25)
(-4 units, 2 units) = (-1, 0.50)
Thus,
The set of ordered pairs of the polygon is:
(0.75, -0.75), (-1, 0.5), (0, 1.25)
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will give brainliest!!!!!! Find the measure of each angle indicated.
Round to the nearest tenth.
6)
7)
A
0
C
A
0
12
()
6
5
B
B
10
C
Using trigonometric relations we can see that:
6) θ = 30°
7) θ = 60°
How to find the measure of the angle?We can see a right triangle where we want to find the value of θ, we know the hypotenuse and the opposite cathetus, then we can use the trigonometric relation:
sin(θ) = (opp cath)/hyp
Replacing what we know:
sin(θ) = 6/12 = 1/2
Then we know that θ = 30°
For the second one we know the adjacent cathetus and the hypotenuse, here we need to use the cosine relation:
cos(θ) = 5/10
cos(θ) = 1/2
then θ = 60°
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Is anyone good with Math or History
The probability of passing at least one will be 0.70.
We know that,
Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
here, we have,
Probability of passing history course = 0.59
Probability of passing math course = 0.60
Probability of passing both courses = 0.49
so, we get,
Probability of passing at least one will be
⇒ 0.59 + 0.60 – 0.49
⇒ 0.70
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complete question:
A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?
PLS HELP!
write an equation of the ellipse with foci at (0 ±10), and vertices at (0 ±11)
Find the missing angle
A
B
C
D
The solution is the missing angle is 74.
Here, we have,
The sum of all the angles of a triangle (of all types) is equal to 180°.
The sum of the length of the two sides of a triangle is greater than the length of the third side.
In the same way, the difference between the two sides of a triangle is less than the length of the third side.
here, we have,
from the given diagram, we get,
the given angles are 55 and 51
let, the missing angle be x
we know that,
The sum of all the angles of a triangle (of all types) is equal to 180°.
so, x+55+51 = 180
or, x + 106 = 180
or, x = 74
Hence, The solution is the missing angle is 74.
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The point J is a centroid for the triangle SZU. What is SV?
1. 21
2. 9
3. 6
4. 12
The value of SV, given that point J is the centroid, would be A. 9.
How to find the value of SV?Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:
JV = 1 / 3 x SV
Knowing this, we can make SV the subject of the formula to become:
(JV = 1 / 3 x SV ) / 1 / 3
3 x JV = SV
SV = 3 JV
SV would then be:
SV = 3 x JV
SV = 3 x 3
SV = 9
In conclusion, SV would be 9.
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Answer:
answer is B. 9 :)
Step-by-step explanation:
Claim: fewer than 7.4% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 13,323 homes 5.77% had landline phones without wireless phones. Complete parts (a) and (b).
There is sufficient evidence to suggest that the proportion of homes with only a landline phone is less than 7.4%.
Null hypothesis: p ≥ 0.074
proportion of homes with only a landline phone is greater than or equal to 7.4%
Alternative hypothesis: p < 0.074 (proportion of homes with only a landline phone is less than 7.4%)
where p is the true proportion of homes in the population that have only a landline phone.
(b) Compute the test statistic and p-value assuming the null hypothesis is true, using a significance level of α = 0.05.
To compute the test statistic, we first need to calculate the sample proportion:
p cap= 0.0577
The test statistic is given by:
z = (p cap - p) / √p(1-p)/n
where n is the sample size. Substituting the values, we get:
z = (0.0577 - 0.074) / √0.074(1-0.074)/13323)
= -12.28
the p-value is less than 0.0001, which is much smaller than the significance level of 0.05.
Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of homes with only a landline phone is less than 7.4%.
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Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z
x+3=y+12
z+13=x+8
y-7=z-11
PLS
Graph the line with slope 2/3 and y-intercept -6.
A line on the graph which could represent this scenario is shown in the image attached below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this line, it can be modeled by this equation:
y = mx + c
y = 2x/3 + (-6)
y = 2x/3 - 6
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What is the length of BC?
Answer:
18
Step-by-step explanation:
AC=AB
BC^2=AB^2+AC^2
162+162=324
Square root of 324 is 18.
you have negioated a vehcile purchase rice of $37,000, will make a $7,000 down payment and finance the remainder. The terms of the loan are: monthly payments, 6.00 percent annual rate of interest, and you will finance the loan for six years.
a. calculate the amount of your monthly payments
b. at the end of the six-year loan term, what is the total amount of interest you will have paid the lenders?
If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage e for a child of age a, pharmacists use the equation c = 0.0417D(a + 1).
Suppose the dosage for an adult is 150 mg.
(a) Find the slope of the graph of e. (Round your answer to two decimal places.)
What does it represent?
The slope represents the Select of the dosage for a child for each change of 1 year in age.
(b) What is the dosage for a newborn? (Round your answer to two decimal places.)
ma
a) The slope shows that the appropriate dose c for an older child increase by 6.225 mg if the child is one year older.
b) The dose for newborn baby is: 6.225 mg
The equation of a line in slope intercept form is:
y = mx + c
where: m is slope and c is y-intercept
(a) Let a be an age of an child in years. Then:
c = 0.0417Da + 0.0417D
Where D is a constant
Since D = 150 mg, then we have:
The slope of the graph = 0.0417(150)
= 6.225 mg/year
The slope shows that the appropriate dose c for an older child increase by 6.225 mg if the child is one year older.
(b) Newborn baby: a=0
Thus:
c(0) = 0 + 6.225
= 6.225 mg
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John paid $270 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 10% discount but still make 30% of the price he paid for. At what price should the bike be marked $?
John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.
If John wants to make a 30% profit on the price he paid for the bike, he needs to sell it for:
$270 + 30% of $270 = $270 + $81 = $351
To offer a 10% discount on the marked price, he needs to calculate the price that includes the discount. Let's call this price "x".
90% of the marked price "x" is the same as the price he wants to sell the bike for ($351):
0.9x = $351
x = $390
Therefore, John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.
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In which quadrant does the point (-25, 15) lie ?
The point (-25, 15) lies in the third quadrant above the x-axis and left to the y-axis.
The four quadrants are formed by the intersection of the x-axis and the y-axis on a Cartesian plane. The point (-25, 15) is represented by the coordinates (-25) and (15) on the x and y-axis, respectively. Since the x-coordinate is negative, the point lies to the left of the y-axis.
Similarly, since the y-coordinate is positive, the point lies above the x-axis. Therefore, the point (-25, 15) is located in the third quadrant, which is below the x-axis and to the left of the y-axis. In this quadrant, both the x and y-coordinates are negative.
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Please help me with this question giving brainliest and points
The category that had the highest relative frequency is given as follows:
Have chores.
How to obtain the relative frequencies?To obtain the relative frequencies for each item, we must add the rows/columns that represent the items in this problem.
Hence the relative frequencies for each item are given as follows:
Have chores: 9 + 7 = 16.Do not have chores: 8 + 6 = 14.Have a sibling: 7 + 8 = 15.Does not have a sibling: 9 + 6 = 15.More can be learned about relative frequencies at https://brainly.com/question/1809498
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Area of triangles
Look at the image below.
6
What is the area of the triangle?
units²
3
Answer:
Please help me by marking me the brainliest.
The area of the triangle is 9 units^2
Step-by-step explanation:
Area of triangle = 1/2(6*3)
=1/2(18)
=9
can someone solve and graph it
f(x)=|x+1|+2
Answer:
d y x+1
----- = (l x+1 l + 2) x -----------------------
d x (l x+1 l + 2) x lx+1l
After paying a 20% deposit on a $300,000 home, David and Kennah finance the rest of the home cost and the closing fees for their home purchase with a 30-year loan for
$247,249 that charges an annual percentage rate of 3.94%. Calculate the total sum (NOT A SINGLE MONTHLY PAYMENT) of all monthly payments required to pay off this loan.
Round to the nearest whole number.
Answer: The total sum of all monthly payments required to pay off this loan is $410,932.
To calculate this, we need to first find the amount of the loan that is not covered by the deposit. The deposit is 20% of $300,000, or $60,000, so the remaining amount of the loan is $300,000 - $60,000 = $240,000.
Next, we need to calculate the monthly payment on the loan. We can use the formula for a fixed-payment loan to do this:
Payment = (Loan amount x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
The monthly interest rate is the annual interest rate divided by 12, or 0.0394 / 12 = 0.003283.
The number of months is the number of years times 12, or 30 x 12 = 360.
Plugging these values into the formula gives:
Payment = ($247,249 x 0.003283) / (1 - (1 + 0.003283)^(-360)) = $1,151.80
Finally, we can find the total sum of all monthly payments by multiplying the monthly payment by the number of months:
Total payments = $1,151.80 x 360 = $410,932 (rounded to the nearest whole number).
Step-by-step explanation:
Need help fast I will rate
The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).
What is a polynomial graph?In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;
x = 5 ⇒ x - 5 = 0.
(x - 5)²
x = -3 ⇒ x + 3 = 0.
(x + 3)
In this context, an equation that represent the polynomial function is given by:
p(x) = a(x - 5)²(x + 3)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;
-7.5 = a(0 - 5)²(0 + 3)
-7.5 = a75
a = -7.5/75
a = -0.1.
Therefore, the required polynomial function is given by:
p(x) = -0.1(x - 5)²(x + 3)
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Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
PLEASE HELP FAST!
A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on the marble selected will be recorded as the outcome.
Consider the following events.
Event A: The marble selected has an ODD number.
Event B: The marble selected has a number from 3 to 6.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
The possible outcomes for each of the given events are:
A {1, 3, 5, 7}
B {3, 4, 5, 6}
How to identify the outcomes for the events?The possible outcomes for the experiment are {1, 2, 3, 4, 5, 6, 7, 8}.
The two given events are:
A "The marble selected is an odd number"
The outcomes for this event are the odd numbers that are outcomes for the experiment, then the outcomes here are {1, 3, 5, 7}
The second event is:
B "The marble selected has a number from 3 to 6."
The possible outcomes here are {3, 4, 5, 6}
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A school is constructing a rectangular play area against an exterior wall of the school building. It uses 120 feet of fencing material to enclose three sides of the play area.
Write an equation to represent l, the length of the play area in feet, as a function of w, the width in feet.
An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²
Here, we have,
According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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The ratio for the split is entered in cells B2 and C2. For example, the ratio of 2-for-1 would be entered as a 2 in B2 and a 1 in C2. The number of pre-split shares is entered in B3 and the pre-split price is entered in B4, Write the spreadsheet formula that will calculate the post-split number of outstanding shares in C3
The spreadsheet formula that will calculate the post-split number of outstanding shares in C3 will be C3*(B2/C2).
How to calculate the formulaAssuming the split ratio has been inputted in cells B2 and C2, one can easily ascertain the post-split number of outstanding shares in cell C3 by simply using the following formula:
=C3 × (B2/C2).
In this case, the equation multiplies the pre-split quantity of outstanding shares by the ratio written down in cells B2/C2 for the determination of resulting post-split number of outstanding shares that are in cell C3.
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if a small cup is 10 oz and cost 2.69 what is the cost per ounces
Answer:
The cost per ounce of the small cup is $0.269
Step-by-step explanation:
To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.
Cost per ounce = Cost of the cup ÷ Number of ounces in the cup
Cost of the cup = $2.69
Number of ounces in the cup = 10 oz
So,
Cost per ounce = $2.69 ÷ 10 oz
Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)
Therefore, the cost per ounce of the small cup is $0.269.
SIMPLIFY the expression: 12x - 7y - 8x + 3y
Answer:
the simplified expression is 4x - 4y
Step-by-step explanation:
1. Rewrite!
12x - 7y - 8x + 3y
2. Combine like terms:
12x - 8x - 7y + 3y
3. Solve both sides to simplify
12 x - 8x = 4x
and
-7y + 3y = -4y
So, 4x - 4y is your answer.
Find the value of
n so that the line that goes through the points
(8,n) and
(2,−2) is perpendicular to
y=2x+4.
Answer:
n = -5
Step-by-step explanation:
We know that when two lines are perpendicular, the slopes of the two lines are negative reciprocals as
[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we're usually not given, and m1 is the slope of the line we're given
Thus, we know that m2 must equal -1/2 from the formula since m1 is 2:
[tex]m_{2}=-\frac{1}{2}[/tex]
Of course, -1/2 is already simplified so m2 is the slope of the line passing through (8, n) and (2, -2)
To find n, we must use our knowledge of the slope formula that gives us the slope, m:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point on the line and x2 and y2 are another point on the line:
If we allow (8, n) to be our x1 and y1 point and allow (2, -2) to be our x1 and y2 point and -1/2 to be our m, we can now solve for m by plugging everything into the slope formula and solving for n (aka y1 in the formula:
[tex]-1/2=\frac{-2-n}{2-8}\\ \\-1/2=\frac{-2-n}{-6}\\ \\3=-2-n\\\\5=-n\\\\-5=n[/tex]
We can even check that we get -1/2 when we plug in -5 into the slope formula:
[tex]-1/2=(-2-(-5))/(2-8)\\-1/2=(-2+5)/(-6)\\-1/2=3/-6\\-1/2=-1/2[/tex]
I need these pages done quick! Can anyone give the answers?
Answer:
Step-by-step explanation: