A candle is 7 in. tall after burning for 1 h. The same candle is 5 1/2 in. tall after burning for 4 h. How tall will the candle be after burning for 6 h?
Answer: 4 1/2 in
Step-by-step explanation: correct on gradpoint
Jana blows up the same number of balloons as jeremy, places half of them in the living room, and ties the rest to the mailbox. jeremy places some of his balloons in the kitchen and the rest in the dining room. which equation represents how many balloons were placed in each location?
a.2 + 6 = 5 + 4
b.3 + 5 = 6 + 3
c.3 + 4 = 1 + 7 eliminate
d.4 + 4 = 3 + 5
To find the initial number of chocolates Jenny had, we solve the equation (x - 2)/2 = 6, which results in x = 14. Therefore, Jenny had 14 chocolates initially.
The question asks to determine how many chocolates Jenny had in the beginning if she eats two and gives half of the remainder to Lisa, who ends up with six chocolates. To solve this, we let x represent the initial number of chocolates Jenny had. After eating two chocolates, Jenny has x - 2 left. She gives half of this remainder to Lisa, which means Lisa receives (x - 2)/2 chocolates. Since Lisa has six chocolates, we set up the equation (x - 2)/2 = 6. Solving this gives us x - 2 = 12 and therefore, x = 14. Hence, Jenny had 14 chocolates in the beginning. The correct answer is option C. 14.
he coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .
Which statement correctly describes the relationship between △JKL and △J′K′L′ ?
△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a translation 1 unit up followed by a reflection across the y-axis, which is a sequence of rigid motions.
△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a reflection across the x-axis followed by a reflection across the y-axis, which is a sequence of rigid motions.
△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.
△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.
Answer:
As Given :The coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .
⇒As we can see the two triangles are congruent because length of sides are equal.i.e By SSS ΔJKL and ΔJ'K'L' are congruent.
⇒ As you can see from the figure depicted below the triangle JKL is rotated by an angle of 180° then translation of y coordinate by 1 unit up has taken place.
So , Option (3) is correct which is :△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.
A couch, a love seat, and a chair cost $1565. The couch costs twice as much as the chair, and the live seat costs $400 more than the couch. Find the cost of the love seat, the couch, and the chair.
To find the cost of the love seat, couch, and chair, set up a system of equations and solve for the variables.
Explanation:To find the cost of the love seat, the couch, and the chair, we need to set up a system of equations based on the given information. Let's represent the cost of the chair as x. Since the couch costs twice as much as the chair, its cost will be 2x. The love seat costs $400 more than the couch, so its cost will be 2x + $400. The sum of the costs of all three pieces of furniture is $1565. Using these equations, we can solve for x, and then find the costs of the love seat, the couch, and the chair.
Equations:
x + 2x + (2x + $400) = $15655x + $400 = $15655x = $1165x = $233Cost of the Chair: $233
Cost of the Couch: 2x = 2($233) = $466
Cost of the Love Seat: 2x + $400 = 2($233) + $400 = $466 + $400 = $866
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Need help with number 7
what will be the result of substituting 2 for x in both expressions below?
Answer:
the anwser is A
Step-by-step explanation:
if you didnt understand the top
Mr. Scott rented a bicycle for 6 hours on Saturday and then several more hours on Sunday. It cost $4 per hour to rent the bicycle, and he paid a total of $48. For how many hours did Mr. Scott rent the bicycle on Sunday? Choose two answers: one for the equation that models this situation and one for the correct answer. A. Equation: 6(4 + x) = 48 B. Equation: 4(6 + x) = 48 C. Answer: 4 hours
Answer:
The equation that models this situation : [tex]4\times (6+x)=48[/tex]
Duration of bicycle rented on Sunday was of 6 hours.
Step-by-step explanation:
Cost of per hour to rent the bicycle = $4
Duration of bicycle rented on Saturday = 6 hours
Duration of bicycle rented on Sunday = x
Total mount paid = $48
[tex]\$4\times (6+x)=$48[/tex]
[tex]4\times (6+x)=48[/tex]
For solving for x:
[tex]x=\frac{48}{4}-6= 6[/tex]
Duration of bicycle rented on Sunday was of 6 hours.
Ricky bought flowers for Susan he spent a total of $14.85 and bought 13 flowers if you knows Lillys cost $1.25 and tulips cost $.90 how many of each flower did he buy Susan
A line that passes through the points (2,1) and (k,5) is perpendicular to the line y=3x-9. Find the value of k
The value of k, which forms a line perpendicular to y=3x-9 passing through the points (2,1) and (k,5), is -2. This is determined by using the slope formula and the property that the slope of a line perpendicular to a given line is the negative reciprocal of the given line's slope.
Explanation:The subject of this question is linear equations in mathematics, specifically about finding the slope and working with perpendicular lines. The given equation, y=3x-9, represents a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this given equation, the slope (m) is 3 and the y-intercept (b) is -9.
If another line is perpendicular to this line, its slope is the negative reciprocal of the given line's slope. Therefore, the slope of the line that passes through the points (2,1) and (k,5) would be -1/3.
The slope formula, (m = (y2 - y1) / (x2 - x1)), can be used to find the value of k. So, we have -1/3 = (5 - 1) / (k - 2). From this, you can solve for k to find that k = -2.
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Write an expression for the sum of four consecutive odd integers where 2n +1 represents the smallest odd integer.
Given the statements, "A square root of 16 is 4," and "A square root of 9 is -3," complete the following blanks with the correct truth-values.
P is (true or false) and q is (true or false) , so the statement, "A square root of 16 is 4 or a square root of 9 is -3" is (true or false) .
Answer:
P is True and q true is , so the statement, "A square root of 16 is 4 or a square root of 9 is -3" is false .
Explanation:
The table of conjunctions show:
If p is true and q is true, then p & q are trueIf p is true and q is false, then p & q are falseIf p is false and q is true, then p & q are falseIf p is false and q is false, then p & q are falseThe first statement, "A square root of 16 is 4," (p), is true.
The second statement, "a square root of 9 is -3," (q), is true.
Therefore, p & q is true.The length of a train car is 50.6 feet. this is 5.8 feet less than six time the width. what is the width?
If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
A. (0, –2)
B. (1, –1)
C. (2, 0)
D. (3, 3)
Answer:
(3,3)
Step-by-step explanation:
Find the exact value of cot60°.
Answer:
The exact value is [tex]\cfrac{\sqrt{3}}3[/tex]
Step-by-step explanation:
Since 60 degrees is an angle we can find on the unit circle, the goal to get an exact value is to use the elements of the unit circle, which are exact values of sine and cosine.
Writing cotangent in terms of sine and cosine
We can use the trigonometric identity
[tex]\cot \theta = \cfrac{\cos \theta }{\sin \theta }[/tex]
Thus for the exercise we will have
[tex]\cot 60^\circ = \cfrac{\cos 60^\circ }{\sin 60^\circ }[/tex]
Identifying the known exact values.
From the unit circle that you can see on the attached image below, we have to identify the exact values of cosine and sine of 60 degrees.
So first try to look for the angle 60 degrees, there you will see a point that has a pair of values, those represent (cosine, sine), thus we get:
[tex]\cos 60^\circ=\cfrac 12 \\\\\sin 60^\circ = \cfrac{\sqrt3}2[/tex]
Finding the exact value of cot 60 degrees.
We can replace the exact values of sine and cosine on the trigonometric identity for cotangent.
[tex]\cot 60^\circ = \cfrac{\cfrac 12 }{\cfrac{\sqrt 3}2 }[/tex]
Working with the reciprocal we get
[tex]\cot 60^\circ = \cfrac 12\times \cfrac2{\sqrt 3}[/tex]
Simplifying we get
[tex]\cot 60^\circ = \cfrac 1{\sqrt 3}[/tex]
Rationalizing since we usually do not want square roots on the denominator we get
[tex]\cot 60^\circ = \cfrac 1{\sqrt 3} \times \cfrac{\sqrt 3}{\sqrt 3}\\\boxed{\cot 60^\circ = \cfrac {\sqrt 3}3}[/tex]
And that is the exact value of cotangent of 60 degrees.
The exact value of cot(60°) is √3 / 3.
How did we get the value?To find the exact value of cot(60°), we can use the identity:
cot(θ) = 1 / tan(θ)
Since tan(θ) = sin(θ) / cos(θ), we need to find the values of sin(60°) and cos(60°).
In a 30-60-90 degree triangle, the sides are in the ratio 1 : √3 : 2. Since the angle is 60°, the opposite side (opposite the 60° angle) has length √3 and the adjacent side (adjacent to the 60° angle) has length 1.
Using these values, we can calculate the sine and cosine of 60°:
sin(60°) = opposite/hypotenuse = √3/2
cos(60°) = adjacent/hypotenuse = 1/2
Now, we can find cot(60°):
cot(60°) = 1 / tan(60°)
= 1 / (sin(60°) / cos(60°))
= 1 / (√3/2 / 1/2)
= 1 / (√3/1)
= 1 / √3
= √3 / 3
Therefore, the exact value of cot(60°) is √3 / 3.
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Plz help me with this
What is 26.895 rounded to (2dp decimal points)
Given F= 9/5C+32, the conversion formula for Fahrenheit to Celsius, solve for C
Answer:
The required equation is [tex]C=\frac{5}{9}(F-32)[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]F= \frac{9}{5}C+32[/tex]
Solve the formula for C.
Subtract 32 from both sides.
[tex]F-32= \frac{9}{5}C+32-32[/tex]
[tex]F-32= \frac{9}{5}C[/tex]
Multiply both the sides by 5/9.
[tex]\frac{5}{9}(F-32)= \frac{9}{5}C\times \frac{5}{9}[/tex]
[tex]C=\frac{5}{9}(F-32)[/tex]
Hence the required equation is [tex]C=\frac{5}{9}(F-32)[/tex]
The formula to convert Fahrenheit to Celsius is C = 5/9( F - 32 ).
How to solve for a variable in an equation?Given the equation in the question:
F = (9/5)C + 32
To solve for C (Celsius) in the conversion formula F = (9/5)C + 32, first, isolate the terms that contain C on one side of the equation.
F = (9/5)C + 32
Subtract 32 from both sides of the equation:
F - 32 = (9/5)C + 32 - 32
F - 32 = (9/5)C
Next, multiply both sides by the reciprocal of the coefficient of C: 5/9:
5/9( F - 32 ) = 5/9 × (9/5)C
5/9( F - 32 ) = C
C = 5/9( F - 32 )
Therefore, C equals C = 5/9( F - 32 ).
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Find the parabola of the form y=ax2+b which best fits the points (−1,0), (5,5), (6,10) by minimizing the sum of squares, s, given by
The optimal least squares fit for the given data is y = 0.2732x² - 0.6452. This curve minimizes the sum of squared errors, providing an accurate representation of the data.
The provided data points are (-1, 0), (5, 5), and (6, 10), denoted as {x} = [-1, 5, 6] and {y} = [0, 5, 10]. The goal is to find the least squares fit for the curve y = ax² + b. To minimize the sum of squared errors between the data and the curve, the normal equations are derived.
The normal equations are given by:
(x₁⁴ + x₂⁴ + x₃⁴)a + (x₁² + x₂² + x₃²)b = x₁²y₁ + x₂²y₂ + x₃²y₃ (Equation 1)
(x₁² + x₂² + x₃²)a + 3b = y₁ + y₂ + y₃ (Equation 2)
By substituting the given data, the equations become:
1922a + 62b = 485
62a + 3b = 15
Solving these equations yields the values: a = 0.2732 and b = -0.6452. Therefore, the curve of the best least squares fit is y = 0.2732x² - 0.6452.
In conclusion, the curve that minimizes the sum of squared errors for the provided data points is y = 0.2732x² - 0.6452. The graph of this curve, along with the given data, visually represents the accuracy of the least squares fit.
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A two digit number is seven times the sum of its digits. the tens digit is 3 more than the units digit. what is the number
Final answer:
The two-digit number where the tens digit is three more than the units digit and the number is seven times the sum of its digits is 74.
Explanation:
The question involves finding a two-digit number that fits two conditions: it is seven times the sum of its digits, and its tens digit is three more than the units digit. To solve this, we set up the following equations. Let x represent the tens digit and y represent the units digit.
The number is 10x + y, because the value of the tens digit is ten times its face value.The first condition gives us the equation 10x + y = 7(x + y).The second condition gives the equation x = y + 3.Substituting x from the second equation into the first equation, we get 10(y + 3) + y = 7(y + 3 + y). Solving this, we find y = 4 and therefore x = 4 + 3, which gives x = 7. Thus, the number is 74.
The coordinates of the vertices of △RST are R(−3,1), S(−1,4), and T(3,1) .
Which statement correctly describes whether △RST is a right triangle?
△RST is a right triangle because RS¯¯ is perpendicular to RT¯¯ .
△RST is a right triangle because RS¯¯ is perpendicular to ST¯¯ .
△RST is a right triangle because ST¯¯ is perpendicular to RT¯¯.
△RST is not a right triangle because no two of its sides are perpendicular.
Final answer:
△RST is a right triangle because the slope of line RS is 3/2 and the slope of line RT is 0, indicating that RS is perpendicular to RT.
Explanation:
To determine whether △RST is a right triangle, we can calculate the slopes of the sides to check for perpendicularity. A right triangle will have one pair of sides that are perpendicular to each other, meaning their slopes will be negative reciprocals.
The slope of line RS is calculated using the coordinates R(-3,1) and S(-1,4) as:
Slope of RS = (4 - 1) / (-1 + 3) = 3 / 2
The slope of line RT is calculated using the coordinates R(-3,1) and T(3,1) as:
Slope of RT = (1 - 1) / (3 + 3) = 0 / 6 = 0
Since the slope of RS is a non-zero finite number and the slope of RT is zero, they are perpendicular to each other because the slope of a line perpendicular to a horizontal line (slope of 0) is undefined, which is the negative reciprocal of 0.
Therefore, the correct statement is:
△RST is a right triangle because RS‾ is perpendicular to RT‾.
Final answer:
Upon calculating the slopes of the sides of △RST, it is concluded that none of the sides are perpendicular to one another, which means that △RST is not a right triangle.
Explanation:
To determine if △RST is a right triangle, we need to calculate the slopes of the sides to check for perpendicularity because perpendicular lines have slopes that are negative reciprocals of each other. Let's calculate the slopes of line segments RS, ST, and RT.
Slope of RS is given by (4 - 1)/(-1 + 3) = 3/2.
Slope of ST is (4 - 1)/(-1 - 3) = 3/-4 = -3/4.
Slope of RT is (1 - 1)/(3 + 3) = 0/6 = 0.
Since the slope of RT is 0, it means that RT is a horizontal line. The slope of RS is 3/2, and the slope of ST is -3/4. These slopes are not negative reciprocals of each other. Hence, none of the lines are perpendicular to each other, and we can conclude that △RST is not a right triangle because no two of its sides are perpendicular.
the sum of a number and five is at least 5?
When x is divided by 3 the quotient is more than 7
Trey runs 4 miles in 30 minutes. at the same rate, how many miles would he run in 48 minutes?
Which of the following is NOT a typical method of payment for a job?
A. paycheck
B. money order
C. direct deposit
D. cash
Casey bought sandwiches and bags of chips. Each sandwich cost three times as much as a bag of chips. She bought 5 sandwiches for $6 each and spent $42. How many bags of chips b did she buy?
Answer:
She bought 6 bag of chips.
Step-by-step explanation:
Let the price of bag of chips be s.
Each sandwich cost three times as much as a bag of chips.
Cost of sandwich = 3s
She bought 5 sandwiches for $6.
That is cost of sandwich = 3s = 6
s = 2$
Cost of bag of chips = s = 2$
Price of 5 sandwiches = 5 x 6 = 30 $.
She spent $42, remaining money = 42 - 30 =12 $
Number of bag of chips can be bought with 12 $
[tex]n=\frac{12}{2}=6[/tex]
She bought 6 bag of chips.
Solve the inequality. g – 6 > –1
Answer:
g>5
Step-by-step explanation:
g-6>-1
+6 to both sides
g is left alone :)
Which expression is a difference of cubes?
A.9w^33 - y^12
B.18p^15 - q^21
C.36a^22 - b^16
D.64c^15 - d^27
The expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is 64c¹⁵-d²⁷. the expression will be written in the power of a cube as below:-
64c¹⁵-d²⁷ = (4c⁵)³ - (d⁹)³
Therefore, the expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.
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What is 1 tenth of 0.04
Find the area of triangle QRS. Round the answer to the nearest tenth. A. 19.4 square units B. 91.2 square units C. 1,040.5 square units D. 1,052.4 square unts
Answer: Letter B.
Step-by-step explanation:
Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 855 people, 47 people had hearing aids.