The distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is [tex]3\sqrt{13}[/tex].
First, let us understand the distance formula:
The distance formula is the measurement of the distance between 2 points. It calculates the straight line distance between the given points.
The distance formula is given by:
Distance = [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]
Where A(a, b) and B(c, d) are the coordinates.
We are given;
The park entrance is located at (-3, 7).
Another point at (3, -2).
We need to find the distance from the entrance to the garden at another given point.
Substitute the given values in the distance formula, we will get;
Distance = [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]
Distance = [tex]\sqrt{(-3-3)^2+(7-(-2))^2}[/tex]
Distance = [tex]\sqrt{(6)^2+(9)^2}[/tex]
Distance = [tex]\sqrt{36+81}[/tex]
Distance = [tex]\sqrt{117}[/tex]
Distance = [tex]3\sqrt{13}[/tex]
So, the distance between the given points is [tex]3\sqrt{13}[/tex].
Thus, the distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is [tex]3\sqrt{13}[/tex].
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George wrote an integer. The opposite of George’s integer is -53. Which of these statements about George’s integer must be true?
I. The integer is 53.
II. The integer has an absolute value of -53.
III. The integer is -53.
IV. The integer has an absolute value of 53.
Answer
A
I and II
B
II and IV
C
II and III
D
I and IV NEED EXPLAINATION PLS
The George's integer must be true for option D)I and IV.
What is integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer . -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers. Integer, which means full or whole in Latin, is the root of the English term integer. A particular category of numbers called integers includes zero, positive numbers, and negative numbers. All whole numbers, both negative and positive, and 0 are considered integers.
Here the opposite of George integer is -53.
We know that opposite value of x is -x.
Then George integer is 53.
George integer must be true for The given options I. the integer is 53 and IV.The integer has absolute value of 53.
Therefore the correct option is D) I and IV.
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need help with this one
Number of solutions for the given linear quadratic equation y = x² and
y = 2x+ b is equal to 2.
b. As we change the value of b solution of the linear system of equation get modify. For example b = 0 it passes through origin.
As given in the question,
Given linear quadratic equations are:
y = x² and
y = 2x+ b
⇒ x² = 2x + b
⇒ x² -2x -b = 0
Number of solutions depends on :
Discriminant 'D' = b² -4ac
Here a = 1 , b = -2 , c= -b
D = (-2)² - 4(1)(-b)
= 4 + 4b
If D > 0 there are two real solutions.
If D = 0 there is only one solution.
If D < 0 there is no solution.
Value of D depends on the value of 'b' .
Linear quadratic equation has two solutions if D > 0.
Graph is attached for the given quadratic equations.
Therefore, number of solutions for the given linear quadratic equation y = x² and y = 2x+ b is equal to 2.
b. As we change the value of b solution of the linear system of equation get modify. For example b = 0 it passes through origin.
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It costs $0.75 each to make color copies at a copy
center. At this price, how many copies can be purchased with $60.00?
Answer: 80 copies can be purchased with $60.00.
Step-by-step explanation:
If it costs $0.75 for each color copy, then you would have to divide $60.00 by $0.75, which equals 80 copies.
an airplane flying with the wind can cover 560 miles in 2 hours. the return trip against the wind takes 2 1 2 hours. what is the speed of the plane? the speed of the plane is miles per hour. what is the speed of the air? the wind's speed is miles per hour.
The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
In the question ,
it is given that ,
the airplane covers the distance of 560 miles in 2 hours with the wind,
So , the speed of the airplane with the wind is 560/2 = 280 miles per hour
also given that
airplane covers the distance of 560 miles in 2.5 hours against the wind ,
So , the speed of the plane with the wind = 560/2.5 = 224 miles per hour .
let the speed of the airplane be "a" miles per hour ,
and let the speed of the wind be "b" miles per hour ,
So , equation of speed with the wind is denoted by
a + b = 280
and the equation of speed against the wind is denoted by
a - b = 224
Adding both the equations , we get
2a = 504
a = 504/2
a = 252 miles per hour
and b = 280 - 252 = 28 miles per hour .
Therefore , The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
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pls help!
Simplify the expression to a + bi form:
√4 + √−45 + √49 + √−45
Answer: 9+6i√5
Step-by-step explanation:
√4 + √−45 + √49 + √−45
2 + √45i + 7 + √45i
9 + 3i√5 + 3i√5
9+6i√5
Which expression represents the phrase? “The product of 8 and the quotient of 6 and and w.”
Answer:
B
Step-by-step explanation:
product means multiplication and quotient is division , then
product of 8 and the quotient of 6 and w is
8 ([tex]\frac{6}{w}[/tex] )
The community center has a pottery class each month each student pays $15 for the class and $27 for materials this month the pottery class brought in a total of $715 how many students are in the class the month?
Answer:17
Step-by-step explanation:
For his phone service, Alonzo pays a monthly fee of $17, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is $115.56. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m .
Answer:
at least 1,408 minutes
Step-by-step explanation:
Let m be the number of minutes.
[tex]17 + .07m \geqslant 115.56[/tex]
[tex].07m \geqslant 98.56[/tex]
[tex]m \geqslant 1408[/tex]
prime factorization for gcf and lcm for 25 and 60.
The gcf of 25 and 60 is 5
the lcm of 25 and 60 is 300
What is prime factorization?The process of determining which prime numbers combine to form the original number is known as prime factorization.
Prime factorization of 25 = 5 * 5
Prime factorization of 60 = 2 × 2 × 3 × 5
the greatest common factor, gcf of 25 and 60 is 5
The lowest common multiple, lcm of 25 and 60
= 2 * 2 * 3 * 5 * 5
= 300
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Madeline's account went into overdraft. To get back to a positive balance, she deposited mone at a steady rate of $29.06 per week. After 8 weeks, she had $190.69 in the account. What was the balance when the account went into overdraft?
Answer:
-41.79
Madeline was overdrawn $41.79.
Step-by-step explanation:
If she deposited $29.06 a week for 8 weeks, she put
8 × 29.06
= 232.48
$232.48 into her account. But they're saying she now has only $190.69. Some of the money went to payback the negative balance she had.
Balance+232.48=190.69
Balance=190.69-232.48
Balance = -41.79
Madeline had a negative balance of $41.79.
25 POINTS!! ANSWER FOR BRAINLIST AND SHOW WORK!!!
Answer:
See attached "Image 2" for graph
3 points that are in the system
[tex](6,1)\\(8,-2)\\(7,5)[/tex]
3 points that are not in the system:
[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]
Step-by-step explanation:
Start by writing the equation in slope-intercept form so they can be graphed.
[tex]\left \{ {{y+5 < 2x} \atop {3y\geq -2x+6}} \right. \\\\\left \{ {{y < 2x-5} \atop {y\geq -\frac{2}{3} x+2}} \right. \\\\[/tex]
Now, graph just the lines - LIGHTLY- on the coordinate plane. See the first attached image.
Now, you can shade the correct areas. In the first equation y is LESS THAN the function, so you would shade BELOW the line, and draw the line as a dashed line, not a solid line. This is because y is not EQUAL to the function.
In the second equation y is GREATER than or EQUAL to the function, so draw the line as a solid line and you would SHADE above the line.
In a system of inequalities, the correct area to shade is where the two shaded areas overlap. See the attached image 2 to see how that looks.
Some points that are in the system of inequalities are:
[tex](6,1)\\(8,-2)\\(7,5)[/tex]
These points are NOT in the system:
[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]
A coffee table is on sale for 20% off tej original price of $115.If there is a 7.5% sales tax, what is the final price of the coffee table
Answer:
$85.10
Step-by-step explanation:
115 * .20 = 23
115 - 23 = 92
92 * 0.075 = 6.9
92 - 6.9 + 85.10
please help me!!!!!!!!!!1
The value of x for the given equation is -20 .
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
(5/3)x+(1/3)x=13(1/3)+(8/3)x
Solve equation, to find the value of x,
(5/3+1/3)x=13(1/3)+(8/3)x
-13(1/3)=(8/3)x-(5/3+1/3)x
-40/3=(8/3-2)x
1.(-40/3)=1.(2/3)x
-20=x
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determine if the following orders pairs
The given ordered pair (x, y) represents a linear function
Consider first point (-1, -3) and (0, -1)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line.
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the value in the equation
The slope of the line = (-1-(-3)) / (0 -(-1)
= (-1+3) / 1
= 2
Consider the next set of points (1, 1) and (2, 3)
The slope of the line = (3-1) / (2-1)
= 2
Here slope of the line is same, therefore it is linear function
Hence, the given ordered pair (x, y) represents a linear function
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8.54÷0.35= what the answer
The required solution is 24.4 to the given numerical expression 8.54 ÷ 0.35.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
The numerical expression is given in the question as:
8.54 ÷ 0.35
We have to determine the solution to the given expression
As per the question,
8.54 ÷ 0.35
8.54 / 0.35
(854/100) / (35/100)
Reciprocal the terms of numerator
854/100 × 100/35
854/35
Apply the division operation to get the solution
24.4
Thus, the required solution is 24.4 to the given numerical expression.
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please help me with this
The inequality shown on the number line is -3 < x ≤ 2
Inequality means when the two values that are not equal is defined by inequalities. Inequality means unequal.
When two values are not equal we will greater than or less than sign .
" < " means less than
" >" means greater than
"≤ " means less than and equal to
"≥ " means greater than and equal to
(a) Inequality -4 < n ≤ 5
here , -4 is not included so, the Number line starts from -3
5 is included so, number line will end on 5
(b) The number line shows ,
line is starting from -3 but the dot is not filled means it is not included
The line ends at 2 so,
Inequality is -3 < n ≤ 2
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What is the length of AB
14
51
28
20
Answer:
51
Step-by-step explanation:
The segments are indicated to be congruent.
[tex]3x+9=5x-19 \\ \\ 9=2x-19 \\ \\ 2x=28 \\ \\ x=14 \\ \\ \implies AB=3(14)+9=51[/tex]
3x + 9 = 5x - 19
+ 19 + 19
3x +28 = 5x
- 3x -3x
28 = 2x
÷2 ÷2
14 = x
3x + 9
= 3(14) + 9
= 42 + 9
= 51Choose the expression that is equivalent to 1/4 x 12
Answer:
4%12
Step-by-step explanation:
SOLVES FOR 50 POINTS AND BARINLISTEST
Answer:
(-2, 3 1/3)
2nd one
Step-by-step explanation:
2/3*-3=-2 so x=-2
2/3*5=10/3= 3 1/3 so y= 3 1/3
(-2, 3 1/3)
Estimate a 25% tip on a bill of 68.37$ by first rounding the bill amount to the nearest ten dollars.
Answer:
20 dollar tip (rounded) assuming the bill is 68.37
Step-by-step explanation:
just multiply 68.37 by 0.25, and you get 17.09 or 20 dollars rounded to TENS place.
graph the system of inequalities shown i need this quick
x>1
y>x
Answer:
Graph
Step-by-step explanation:
graph the line x=1 (vertical line passing through point (1,0))with a dotted line and shade everything to the right of the line. Then graph the line y=x (line with slope 1 passing through origin) with a dotted line, shading everything above the line.
Write an equation in point-slope form that passes through (-4, -6) and is parallel to y= -7/2x+6. I'm stuck, please help.
Answer:
y= -7/2x-20
Step-by-step explanation:
parallel line so same slope
the equation given is in y=mx+b form so take out m:
m= -7/2
now input the coordinates and slope(m) given into y=mx+b to find b:
-6=-7/2(-4)+b
-6=28/2+b
-6=14+b
-6-14=b
b=-20
now write equation using slope(m) and y intercept(b)
y= -7/2x-20
Please mark as brainliesttt
The equation in point-slope pass through the given point will be y = -7/2x-20
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
The same slope due to a parallel line,
Take away m from the above equation since it is in the y = mx+b form:
m= -7/2
Now, enter the given coordinates and slope(m) into y=mx+b to determine b:
-6 =-7/2 (-4) + b
-6 = 28/2 + b
-6 = 14 + b
b = -20
Slope(m) and y-intercept are now used to create an equation (b),
y = -7/2x-20
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Factor the expression in the image please
To factorize this,the answer is [tex]\frac{1}{3} x^{4} y^{2} (\frac{1}{4} y^{} -\frac{1}{3} x)[/tex]
What is Factorization?Factorization is when you break a number down into smaller numbers that, when multiplied together, give you that original number.
The expression above can only be determined by looking at the common factors and using it to answer the question. [tex]\frac{1}{12} x^{4}y^{3} -\frac{1}{9}x^{5}y^{2}[/tex]
To factorize the fractions by looking at the common factor between the both[tex]\frac{1}{3} (\frac{1}{4} -\frac{1}{3} )[/tex]To factorize the indices by looking at the common factor[tex]x^{4}y^{2} (y-x)[/tex]
So, to factorize the expression above[tex]\frac{1}{3} x^{4} y^{2}(\frac{1}{4} y-\frac{1}{3} x)[/tex]
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which expression is equivalent to -24-12w
Answer:
Simplest form = -w - 2
Step-by-step explanation:
Given expression,
→ -24 - 12w
→ -12w - 24
Simplifying the expression,
→ -12w - 24
→ (-12w - 24)/12
→ -w - 2
Hence, the answer is -w -2.
Which of the following people likely pays the LEAST for health care?
a. Tanya, who has a Bronze level plan and goes to the doctor for an annual exam once all year
b. Alfred, who has a Bronze level plan and uses it for a few doctor appointments, an X-ray, and to fill
monthly prescriptions
c.
Marty, who does not sign up for health insurance and then has a 4-week hospital stay because he gets
pneumonia
d. Caroline, who has a Silver level plan and uses it frequently in the year, because she's pregnant and due
have a baby
Tanya, who has a Bronze level plan and only goes to the doctor once a year for an annual exam, is likely to pay the least for healthcare. The correct option is A.
What is health care?Health care refers to the maintenance or improvement of an individual's physical or mental health through the prevention, diagnosis, and treatment of illness, injury, or disease. It encompasses a range of services provided by healthcare professionals.
Based on the information provided, Tanya, who has a Bronze level plan and only goes to the doctor once a year for an annual exam, is likely to pay the least for healthcare.
Bronze level plans typically have lower monthly premiums but higher out-of-pocket costs for healthcare services, such as copays, deductibles, and coinsurance.
Since Tanya only goes to the doctor once a year, she is unlikely to meet her deductible or incur significant out-of-pocket costs.
In contrast, options B, C, and D involve more frequent or more serious healthcare needs, which would likely result in higher out-of-pocket costs for healthcare services.
Thus, the correct option is A.
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Simplify to a single power of 4:
(44) 5
Answer:
4²0=4×5=20=4²0 арлатат
Determine whether each number is an integer, a rational number that is not an integral or an irrational number
The integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.
A rational number is any number that can be written as a fraction, where both the numerator na demoninator that is the top and the bottom number are integers, and the denominator is cannot be zero
An irrational number is a type of real number which cannot be represented as a simple fraction.
A integer can always be a rational number but vice versa is not true.
Integer = 3√25 = 3x5 = 15
-185/5 = -37
rational = -1/4, 0.75, 3√25, -185/5, 4√8
irrational = √13,
Therefore, the integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
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a recent survey found that 70% of all adults wear sunglasses for driving. in a random sample of 10 adults, what is the probability that at least five wear sunglasses?
The probability that at least five wear sunglasses is 0.9464
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
In a random sample of 10 adults, the probability that at least five wear sunglasses
P(X ≥ 5) = P(X = 5) + P(X = 6 ) + P(X=7) + P(X=8) + P(X=9) + P(X=10)
P(X ≥ 5) = 10[tex]C_{5}[/tex] × [tex](0.7)^{5}[/tex]×[tex](0.3)^{5}[/tex] + 10[tex]C_{6}[/tex]×[tex](0.7)^{6}[/tex]× [tex](0.3)^{4}[/tex]+ 10[tex]C_{7}[/tex]×[tex](0.7)^{7}[/tex]×[tex](0.3)^{3}[/tex] + 10[tex]C_{8}[/tex]× [tex](0.7)^{8}[/tex]×[tex](0.3)^{2}[/tex] +10[tex]C_{9}[/tex] ×[tex](0.7)^{9}[/tex]×[tex](0.3)^{1}[/tex]+10[tex]C_{10}[/tex]×[tex](0.7)^{10}[/tex]×[tex](0.3)^{0}[/tex]
P(X ≥ 5) = 0.9464
The probability that at least five wear sunglasses is 0.9464
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The volume of a rectangular prism is represented by the function x3 9x2 6x − 16. the length of the box is x 2, while the height is x 8. find the expression representing the width of the box. x − 4 x − 1 x 1 x 4
The expression that represents the width of the box is (x - 1) , the correct option is (b) .
In the question ,
it is given that ,
the Volume of the rectangular prism is = x³ + 9x² + 6x – 16
the measure of the length of the box = x+2
the measure of the height of the box = x+8
formula for Volume of Prism is
Volume = l × w × h
where l = length of the prism,
w = width of the prism and
h = height of the prism.
Substituting the values ,
we get ,
x³ [tex]+[/tex] 9x² [tex]+[/tex] 6x – 16 [tex]=[/tex] (x [tex]+[/tex] 2) * (x [tex]+[/tex] 8) * width
On dividing the equation (x³ + 9x² + 6x – 16) with (x+2)
and then dividing the result with (x+8) , we get
width = (x-1) .
Therefore , The expression that represents the width of the box is (x - 1) , the correct option is (b) .
The given question is incomplete , the complete question is
The volume of a rectangular prism is represented by the function x³ + 9x² + 6x – 16. The length of the box is x + 2 while the height is x + 8. Find the expression representing the width of the box
(a) x - 4
(b) x - 1
(c) x + 1
(d) x + 4
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Answer:
B
Step-by-step explanation:
Asked my teacher to help me.
Bill started west on road u. S. 50, riding a bicycle at an average rate of 9 mph. Four hours later charles started after bill on a motor cycle and overtook him in 2 hours. What was charles' rate? which equation could be used to solve for charles' rate if it is represented by x? 6 x = 54 2 x = 54 2 x = 36.
The equation could be used to solve for charles' rate if it is represented by x is 2x=54.
In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.
Bill riding a bicycle at an average rate of 9 mph.
Charles' rate is x.
So the relative rate = x−9 mph
Distance traveled by Bill in 4 hours = 9*4 =36 mph
Charles' overtook Bill in 2 hours. So
Relative Rate = Distance/Time
x−9=36/2
Multiply by 2 on both side. We get
2(x−9)=36
Simplifying
2x−18=36
Add 18 on both side, we get
2x=36+18
2x=54
Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.
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