The value of the lesser integer is a = -7
How to find the value of the lesser integer?
Let an integer be = a
Let the next consecutive odd integer (b) = a+2
a + 5( b) = -32
a +5(a+2)= -32
a+ 5a +10 = - 32
6a = -32 -10
6a = -42
a = - 42 /6
a = - 7
The integer a = -7
The next consecutive odd integer (b) = a+2
= -7 + 2
b = -5
So, the value of the lesser integer is a = -7
What is an integer?
The integers are the smallest group and ring of natural numbers. In algebraic number theory, the integers are occasionally designated as rational integers to distinguish them from the algebraic integers, which are more broadly defined. Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The corresponding positive numbers' additive inverses are the negative numbers.To learn more about integers, refer:
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ln(x+2) + ln(2x-1) = 0
By solving a quadratic equation we will find two solutions, one is good and that is x = 0.62, and the other is extraneous and is x = -1.62
How to find the value of x?Here we have the following equation:
ln(x + 2) + ln(2x - 1) = 0
To solve this we need to know two things, first:
ln(a)+ ln(b) = ln(a*b)
ln(1) = 0
Using the first property, we can rewrite:
ln(x + 2) + ln(2x - 1) = ln( (x + 2)*(2x - 1)) = 0
And that can only be equal to zero if:
(x + 2)*(2x - 1) = 1
So we have a quadratic equation:
(x + 2)*(2x - 1) = 1
2x² - x + 4x - 2 = 1
2x² + 3x - 3 = 0
The solutions are:
[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*3*(-3)} }{2*3} \\\\x = \frac{-3 \pm 6.7 }{6}[/tex]
So we have:
x = (-3 + 6.7)/6 = 0.62
x = (-3 - 6.7)/6 = -1.62
The second solution when evaluated in the second term of the equation gives:
ln(2*(-1.62) - 1) = ln(-4.24)
And this is not defined, so x = -1.62 is an extraneous solution.
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A milk truck delivers 486 dozen gallons of milk to stores in 1 day. write and solve an equation to find g, the number of gallons of milk the milk truck delivers in 1 day
If a milk truck delivers 486 dozen gallons of milk to stores in 1 day, then equation to calculate "g", the number of gallons of milk the milk truck delivers in 1 day, can be written as [g = (486 * 12)]
As per the question statement, a milk truck delivers 486 dozen gallons of milk to stores in 1 day.
We are required to determine the equation that can best express "g", the number of gallons of milk the milk truck delivers in 1 day.
To solve this question, first we need to know what an equation is.
An equation is a mathematical statement, that determines the relation of equality among two separate expressions, each containing numbers or variables or both, and operators, by connecting them with an "equal to" sign in between.Here, We know that (1 dozen = a set of 12),
Then, [486 Dozen Gallons = (486 * 12)] gallons, which is the total number of gallons of milk the milk truck delivers in 1 day.
On the other hand, the variable "g" can also be used to determine the number of gallons of milk the milk truck delivers in 1 day.
Therefore, our required equation is [g = (486 * 12)].
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HELP QUICK plsplslpslpslspslsplspslspslspsls
Answer: 3,52 x 10²
Step-by-step explanation:
Answer:
3.5 x [tex]10^{2}[/tex]
Step-by-step explanation:
Multiply the numeric values times each other and add the exponents:
(3.2 x 1.1) x ([tex]10^{-7}[/tex] x [tex]10^{9}[/tex])
3.52 x [tex]10^{2}[/tex]
To one significant figure: 3.5 x [tex]10^{2}[/tex]
Witch answer gos in the box
The relationship between ∠7 and ∠8 are linear pair angles.
How to find the measure of angles?Line m and n intersect at point E.
When line intersects angle relationships are formed such as vertically opposite angles, linear angles etc.
Therefore, angles relationships are formed when the line m and line n intersect at point E.
Hence,
∠7 and ∠8 are linear pair angles.
Linear pair of angles are formed when two lines intersect each other at a single point.
Linear pair angles are supplementary.
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Rectangle A is a scaled version of rectangle B. The dimensions of rectangle B are twice the dimensions of rectangle A. The area of rectangle B is 512 sq cm. What is the area of rectangle A?
A. 256 sq cm
B. 192 sq cm
C. 128 sq cm
D. 64 sq cm
The area of rectangle A is (A) 256 cm².
What are Rectangles?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.So, the area of rectangle A:
The dimensions of rectangle B are twice the dimensions of rectangle A.So, rectangle A = 1/2 Rectangle BRectangle A = 512/2 = 256 cm²Therefore, the area of rectangle A is (A) 256 cm².
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Answer:
128 cm^2
Step-by-step explanation:
The area of rectangle B is 512 cm2. Since the dimensions of rectangle B are two times larger than the dimensions of rectangle A, the scale factor is 2.
To find the area of rectangle A, first square the scale factor, 2.
2^2 = 4
Next, divide the area of rectangle B by 4.
512 cm^2 ÷ 4 = 128 cm^2
the image of (6,12)(6,12) after a dilation by a scale factor of \frac{1}{2}
2
1
The image of the point after the dilation is (3, 6)
What is dilation?Dilation involves changing the side length of a shape or a function
How to determine the equation of g(x)?The given parameters are:
Point = (6, 12)
The scale factor of dilation is given as
Scale factor = 1/2
Mathematically, this transformation can be represented as
(x, y) = 1/2(x, y)
So, we have
(x, y) = (1/2x, 1/2y)
When represented as a function, we have
Image = 1/2 * Point
Substitute the equation Point = (6, 12) in the equation Image = 1/2 * Point
So, we have the following equation
Image = 1/2 * (6, 12)
Evaluate the product
Image = (3, 6)
Hence, the image is (3, 6)
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Put your answer as a decimal. In the accompanying diagram. AABC is similar to A DEF. ZALD, and 2BE LE IF AB = 3, BC = 12. DE = x+ 2. and ef=18 find the value of x.
Answer: x = 2.5
help
What is the relationship between Angle 1 and Angle 2
Any number of angles that add up to 180 are supplementary. Since a 180 degree angle is a straight line, these two angles, which lie on a straight line are supplementary.
Josie is participating in a charity bike ride. This table and graph represent her performance during the ride where x is the number of hours Josie rides and y is her distance from the finish line.
Match the quantity to the correct feature and interpretation.
Hours (x) 0 2 4 6
Kilometers away from finish line (y) 75 50 25 0
.The slope: the absolute value of the slope represents the speed Josie is riding in kilometers per hour.
.The x-intercept. The amount of time, in hours, that has passed when Josie completes the race.
.The y-intercept. Josie's distance, in kilometers, from the finish line when she begins the ride.
1. -25/2
2. 6
3. 75
Match the quantity to the correct feature and interpretation.
Answer:
Slope is -12.5
x-intercept is 75
y-intercept is 6
Step-by-step explanation:
See attached image
(7.22 x 10¹) (4.45 × 10³)
Answer:
[tex]3.2129 \times {10}^{5} [/tex]
Step-by-step explanation:
[tex](7.22 \times {10}^{1} )(4.45 \times {10}^{3} )[/tex]
[tex](7.22 \times 4.45) \times ( {10}^{1} \times {10}^{3} )[/tex]
[tex]32.129 \times {10}^{4} [/tex]
[tex]3.2129 \times {10}^{5} [/tex]
The regression equation y=3.610*1.194^x approximates the cost to go on a safari, y,given the number of years since it opened in 2005, X.What is the best estimate of the cost to go on a safari in 2,022 ? Round your answerto the nearest dollar.
Step 1:
Write the regression line equation.
[tex]y\text{ = 3.610 }\times1.194^x[/tex]Step 2:
y represents the cost and x represent the number of years.
From 2005 till 2022
x = 17 years
Step 3:
Let find the cost to go on a safari in 2022.
[tex]\begin{gathered} y\text{ = 3.610 }\times1.194^x \\ \text{Substitute x = 17} \\ y\text{ = 3.610 }\times1.194^{17} \\ y\text{ = 3.610 }\times\text{ 20.37387116} \\ y\text{ = 73.54967489} \\ y\text{ = \$74} \end{gathered}[/tex]Final answer
The cost to go on a safari in 2022 = $74
Jessie draws a marble from the bag shown and then, without replacing the first marble,
he draws a second one.
Which expression shows the probability that he drew a red marble both times?
O 3/10 3/10
O3/10 3/9
3/10 2/10
O3/102/9
Answer:
Last choice:
3/10 · 2/9
Step-by-step explanation:
The total number of marbles and the number of red marbles is not provided but only one answer fits the problem solution
3/10 x 2/9 which is the last choice
It can be deduced that there are 10 marbles totally and 3 of them are red
The probability of a red marble on first draw = 3/10
After the first draw given a red marble was drawn, there are 2 red marbles and total of marbles so the probability of a second red marble = 2/9
The combined probability is 3/10 x 2/9
.
Parcel A is heavier than parcel B by
2.5 kg. Parcel C is lighter than parcel
B by 4.86 kg. How heavy is parcel A if
parcel C is 6.2 kg?
Answer: 13.56 kg
Step-by-step explanation:
We can make two equations:
1) A = B + 2.5
2) C = B - 4.86
Replace C with 6.2.
(6.2) = B - 4.86 can be rewritten as 6.2 + 4.86 = B.
B = 11.06
Add 2.5 to 11.06 and you get 13.56 kg.
if 3x=5 what’s 3^4x=
Answer:
135
Step-by-step explanation:
If 3x = 5, x = 5/3
3^4 = 81
3^4 x = 81x = 81 x 5/3 = 135
Serkannur
15 minutes ago
Mathematics
High School
PLEASE help me this is due in 1 hour, please try to answer at least 2
1. How do you evaluate an expression involving a rational and negative exponent?
2. How do you simplify rational variable expressions? Add, subtract, multiply or divide 2 rational variable expressions and then simplify.
3. Why are there sometimes restrictions in a rational expression? How do you determine those restrictions?
1)Use the following rule to rewrite with only a positive exponent: [tex]x^{-n}[/tex] = 1 ÷ [tex]x^{n}[/tex] and apply the exponent to both the numerator and the denominator of the fractional base using the rule: [tex](\frac{a}{b} )^{n} = \frac{a^{n} }{b^{n} }[/tex].
2) Simply add or subtract the numerators of two arithmetic operations with the same denominator and write the result to the common factor.
3) Yes, reasonable expressions have limitations at times. Check for zero just on the denominator side to identify those constraints.
1) To evaluate an expression with a rational and negative exponent, follow these steps:
Use the following rule to rewrite with only a positive exponent: [tex]x^{-n}[/tex] = 1 ÷ [tex]x^{n}[/tex]Apply the exponent to both the numerator and the denominator of the fractional base using the rule: [tex](\frac{a}{b} )^{n} = \frac{a^{n} }{b^{n} }[/tex].Rewrite as the reciprocal of the denominator.Write the fractional exponent as a radical and an exponent.Evaluate the radicals.Evaluate the exponents.2) To simplify rational variable expressions,
Simply add or subtract the numerators of two arithmetic operations with the same denominator and write the result to the common factor. If the denominators do not match, they must be changed until they are equal. That is, we need to find a common denominator.
3) The denominator can be any number, even zero. However, there are constraints based on not reducing by zero inside the case of a denominator. There is a limit to the value that may be used to replace our variable and get a denominator of 0.
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Can someone solve this and put down the reason.
Based on the figure shown the lines that are parallel are
line sline tHow to show that line s and line t are parallelUsing the given figure
line s has tow angles 115 and 65line t has one angle which is 65line u has one angle which is 115From the alternate internal angle postulate it can be shown that angle in both line t and line s are equal. This angle is 65 degrees.
The alternate angle postulate hold true for parallel lines hence it shows that line s is parallel to line t while line m is the transversal line required to complete the postulate.
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Point U is on the line segment TV given TU = 4 UV =5x and TV =3x+6
I need help
Solving a linear equation that comes from the relation:
TV = TU + UV
We will see that the value of x is 1.
How to find the value of x?I'm answering the question you wrote.
We know that point U is on the line segment TV, then we can write:
TV = TU + UV
This says that the total length of TV is equal to the sum of the two segments in it.
It says:
"the length of segment TV is equal to the sum between the lengths of segments TU and UV"
Here we know that:
TU = 4
UV = 5x
TV = 3x + 6
Then we can write the linear equation:
3x + 6 = 4 + 5x
And solve this for x.
3x + 6 = 4 + 5x
6 - 4 = 5x - 3x
2 = 2x
2/2 = x
1 = x
The value of x is 1.
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Halp. me. e-x-p-l-a-i-n how you got your answer
The linear equation that passes through the anchor points (-3, -38) and (8, 61) is:
y = 9*x - 11
How to find the equation of the line?
The general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that for a line that passes through two points (x₁, y₁) and (x₂, y₂) can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Now, in this case we know that our line passes through the points (-3, -38) and (8, 61), then the slope will be:
a = (61 + 38)/(8 + 3) = 9
Replacing that we get:
y = 9*x + b
Now, using one of the points we can find the y-intercept, I will use (8, 61), replacing the values we get:
61 = 9*8 + b
61 = 72 + b
61 - 72 = b
-11 = b
The linear equation is:
y = 9*x - 11
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30 points for this if its correct (:
is the number 54.78 x 10 ^-8 written in scientific notation explain.
The number 0.0000005478 written in scientific notation is 54.78 x 10⁻⁸.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that,
the given number in its scientific notation is 0.0000005478.
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 ✕ 10^8 in scientific notation.
The decimal point must be moved till it is to the left of the first non-zero number in order to be written in scientific notation. The exponent is the number of places the decimal point advances since each movement signifies a "power of 10".
Thus, the number 0.0000005478 written in scientific notation is 54.78 x 10⁻⁸.
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-3, -6, -12, -24 Arithmetic Neither Geometric
An arithmetic succession, is defined by constant sums or substractions. A geometric succession, is defined by constant products. In this case, we can define this succession as a product
[tex]a_{n+1}=2a_n[/tex]It means this succession is geometric.
Please help!! I'm really bad at this and would appreciate some help on how to figure this out
The probability of either a dot or a dragon tile is 48/64
Number of dot tiles in Mahjong game = 36 tiles
Probability of a dot tile = 36/64
Number of wind tiles in Mahjong game = 16 tiles
Probability of a wind tile = 16/64
Number of dragon tiles in Mahjong game = 12 tiles
Probability of a dragon tile = 12/64
Total number of tiles in the Mahjong strategy game = 36+16+12 = 64 tiles
Probability of Grace's drawing a dot or a dragon tile:
(Number of dot tiles + Number of dragon tiles)/ Total number of tiles in the game
= (36+12)/64
= 48/64
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Question 14 (1 point)
Write the equation for the following graph.
Answer:
The correct equation is b, x = 4.
PLEASE ANSWER RIGHT (First and bottom are wrong
100 points
Answer:
[tex]36\frac{5}{9}[/tex]
Step-by-step explanation:
Given expression:
[tex]329 \div 9[/tex]
Solve using long division:
[tex]\large \begin{array}{r}36\phantom{)}\\9{\overline{\smash{\big)}\,329\phantom{)}}}\\{-~\phantom{(}\underline{0\phantom{)).)}}\\ {32\phantom{...}}\\{-~\phantom{(}\underline{27\phantom{...}}\\59\phantom{)}\\-~\phantom{()}\underline{54\phantom{)}}\\5\phantom{)}\\\end{array}[/tex]
Therefore, the solution to the given expression is:
[tex]\large\boxe36\frac{5}{9}[/tex]please help!!!!! SOS 15 points!!!
To calculate monthly charges, a cellphone provider uses the equation: C=0.25m+60, with C being dollars and m representing minutes used beyond the ones provided by the plan. Assuming the plan allowed for 60 minutes, what would the charge be for a client that used 55 minutes? Put your answer in terms of dollars.
Answer:
C = $60
Step-by-step explanation:
To calculate monthly charges, a cellphone provider uses the equation: C = 0.25m + 60, with C being dollars and m representing minutes used beyond the ones provided by the plan. Assuming the plan allowed for 60 minutes, what would the charge be for a client that used 55 minutes? Put your answer in terms of dollars.
The customer used 55 minutes and did not max out the phone plan, and therefore does not pay any over charges of m.
C = 0.25m + 60 when m = 0
C = 0.25m + 60
C = 0.25(0) + 60
C = 0 + 60
C = $60
Answer:
C = $60
Step-by-step explanation:
The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?
Answer: the volume of cube is 64 x6 + 144x4 + 108x2 + 27.
Step-by-step explanation: As given in the problem statement the volume
V = s3----- (1)
And
s = 4x2 + 3--------(2)
Hence,
the volume is obtained by substituting (2) in (1).
We get,
V = (4x2 + 3)3
= 64 x6 + 144x4 + 108x2 + 27
Therefore,
the volume of cube is 64 x6 + 144x4 + 108x2 + 27.
Answer:
121 units²
Step-by-step explanation:
The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?
Volume = s³
s = 4×2+3
so
(4 × 2 + 3)² = (remember PEMDAS)
(8 + 3)² =
11² =
121 units²
Zola is cutting a rope that is 3 yards long into pieces that are 4 inches long.
How many 4-inch pieces will Zola have in all? Enter the answer in the box.
Answer:
432. Zola will have 432 4-inch pieces of rope.
A dining hall had a total of 25 tables - some long rectangular tables and some round ones. Long tables can seat 8 people. Round tables can seat 6 people. on a Busy evening, all 190 seats at the tables are occupied. How many long tables, x, and how many round tables, y, are there?
Answer:
There are 20 long tables and 5 round tables y.
Step-by-step explanation:
Given:
long tables x + round tables y = total of 25 tables
8seats ·x +6seats ·y = 190 seats
Find x and y:
x+y= 25 so x= 25-y
8x+6y = 190, we substitute x for 25-y to find y
8(25-y) +6y = 190, we distribute 8 in parenthesis
200 -8y+6y = 190, combine like terms
200 -2y = 190, subtract 200 from both sides
-2y = 190-200, combine like terms
-2y = -10, divide both sides by -2
y = 5
x+y = 25, substitute y for 5
x+5 = 25, subtract 5 from both sides
x= 20
Conclusion:
There are 20 long tables and 5 round tables y.
Check :
20·8+5·6 = 160+30 = 190 seats
Can someone help please how do you solve (3x-5)(3x+5) It would be so much help high school is so stressful right now
Answer:
Step-by-step explanation:
(3x−5)(3x+5)
Multiplication can be transformed into difference of squares using the rule: (a−b)(a+b)=a
2
−b
2
.
(3x)
2
−5
2
Expand (3x)
2
.
3
2
x
2
−5
2
Calculate 3 to the power of 2 and get 9.
9x
2
−5
2
Calculate 5 to the power of 2 and get 25.
9x
2
−25
How many grains of sand are there in 6,300 kg of sand?
(only need an answer to the second part)
When one grain of sand weighs 7×10⁻⁵ g, then there are 9.0 × 10¹⁰ grains of sand in 6300 kg of sand.
Given, one grain of sand approximately weighs 7×10⁻⁵ g.
Then how many grains of sand are there in 6300 kg of sand = ?
we know that one grain of sand weighs = 7×10⁻⁵ g.
therefore, 6300 kg = 6300 × 10³ g sand contains
= 6300 × 10³/7×10⁻⁵
= 900×10³/10⁻⁵
= 900 × 10³ × 10⁵
= 9.00 × 10² × 10³ ×10⁵
= 9.0 × 10²⁺³⁺⁵
= 9.0 × 10¹⁰
Hence there are 9.0 × 10¹⁰ grains of sand in 6300 kg of sand.
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Help me please brainly to correct answer
Answer:
[tex]y - 3 = -\dfrac{1}{4}(x - 4)[/tex]
Step-by-step explanation:
This can be solved without too much calculation
First note that the lope of the graph is negative. If you look at the graph, as x increases, y decreases so that indicates a negative slope
We can safely eliminate the last two options because the coefficient of x in both is +1/4 indicating a positive slope
That leaves the first two for consideration
We can plug in the x, y values for the given point (4, 3) which lies on the line and see which of the equations is consistent, i.e whether the LHS and RHS of the equation match
Putting y = 3 and x = 4 in the first equation y - 4 = -1/4(x - 3) gives us
3 - 4 = -1/4(4-3) ??
-1 = -1/4(1) ?
-1 = -1/4? NO
So the correct choice is the second option and we can verify that by plugging in (4, 3) into y - 3 = -1/4(x - 4)
y - 3 = 3 - 3 = 0
x - 4 = 4 - 4 = 0
So 0 = -1/4(0) = 0
which is consistent
