The addends 4, _ 37 + 1,28_ is completed so there will be need to regroup to add.
the addends. 4, 837 + 1,287
the sum is 6124
What is regrouping?Regrouping refers to rearranging numbers into groups according to place value to assist kids in handling greater numbers.
When performing operations like addition and subtraction on two-digit integers or bigger, regrouping is the process of forming groups of tens. Regrouping refers to the process of performing an operation by rearranging groups in place value.
Using regrouping for the addition problem
addend 4 8 3 7
addend 1 2 8 7
sum 4
1 regrouped to tens column
addend 4 8 3 7
addend 1 2 8 7
sum 2 4
1 regrouped to hundreds column
addend 4 8 3 7
addend 1 2 8 7
sum 1 2 4
1 regrouped to thousands column
addend 4 8 3 7
addend 1 2 8 7
sum 6 1 2 4
the sum is 6124
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Write an equation that passes through the point (4,-3) and is perpendicular to the line 4x+y=3
Answer:
y = 1/4x - 4
Step-by-step explanation:
4x + y = 3
y = -4x + 3
Perpendicular slope = 1/4
y = 1/4x + b
-3 = 1/4(4) + b
-3 = 1 + b
b = -4
y = 1/4x - 4
Find the inverse of f(x) = 2(x-2) ^2 +1
Find the inverse of y = ^3√x-3
Answer:
f^-1(x) = 2(x-2)^2 + 1
f^-1(x) = (x+3)^3
Step-by-step explanation:
The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.
3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.
The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.
Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.
To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace y with x in the original function to obtain x = ^3√y-3.
3. Solve for y in terms of x to obtain y = (x+3)^3.
The inverse function can then be written as f^-1(x) = (x+3)^3.
Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.
What are angle bisectors?Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.
According to the angle bisector theorem;
An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.
a point is equally far from both sides of an angle if it is on the angle's bisector.
According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.
The explanation with diagram is given in the image.
Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
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Given the side measures, which of the following could form a right triangle?
A. 61 m, 60 m, 11 m
B. 24 in, 34 in, 28 in
C. 55 ft, 45 ft, 35 ft
D. 48 cm, 46 cm, 15 cm
The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
What is the right triangle is triangle?
A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using this information, we can determine which of the given sets of side measures could form a right triangle:
A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:
(61 m)² = (60 m)² + (11 m)²
61² = 60² + 11²
61² ≠ 60² + 11²
Since the left side does not equal the right side, these sides cannot form a right triangle.
B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(34 in)² = (24 in)² + (28 in)²
34² = 24² + 28²
34² = 24² + 28²
The left side equals the right side, so these sides could form a right triangle.
C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(55 ft)² = (45 ft)² + (35 ft)²
55² = 45² + 35²
55² = 45² + 35²
The left side equals the right side, so these sides could form a right triangle.
D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:
(48 cm)² ≠ (46 cm)² + (15 cm)²
48² ≠ 46² + 15²
Since the left side does not equal the right side, these sides cannot form a right triangle.
Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
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HELP PLEASEEEE ASAP
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $29,521. The variable costs will be $12 per book. The publisher will sell the finished product to bookstores at a price of $25.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
2,228
Step-by-step explanation:
Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.
For what values of x, y, and z is this a parallelogram?
The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
What are the Properties of Angles of a Parallelogram?
A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.
The opposite angles of a parallelogram are congruent (equal). All the angles of a parallelogram add up to 360°. All the respective consecutive angles are supplementary.The consecutive angles are supplementary then,
5y + 7y - 24 = 180
12y = 180 + 24
12y = 204
y = 204/12
y = 17
The opposite angles of a parallelogram are congruent (equal) then,
5y = 4x + 7
5(17) = 4x + 7
85 = 4x + 7
85 -7 = 4x
4x = 78
x = 78/4 = 19.5
x = 19.5
the consecutive angles are supplementary, then
4x + 7 + 3z = 180
4(19.5) + 7 + 3z = 180
78 + 7 + 3z = 180
85 + 3z = 180
3z = 180 - 88
3z = 92
z = 92/3
z = 30.6
All the angles of a parallelogram add up to 360°, then:
4x + 7 + 3z + 5y +7y - 24 = 360
To check is this a parallelogram? put the values of x, y, and z in the above equation:
4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360
356.8 ≠ 360
hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
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Graph the line that has a slope of -4/3 and includes the point ( -6,2)
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
Slope intercept form:The slope-intercept form a line is given by
y = mx + c,where m is the slope of a line and c is the y-intercept.
Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line
Here we have
Slope of line = -4/3
The point of the line
As we know y = mx + c is the line Here m is the slope of the line
From the given data, m = -4/3
=> y = (-4/3)x + c
=> 3y = -4x + 3c
Given that the point on the line is (-6, 2)
=> 3(2) = -4(-6) + 3c
=> 6 = 24 + 3c
=> 3c = 18
=> c = 6
Therefore,
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
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Mikaela purchased a paddleboard originally priced at $699. If all merchandise was on sale for 40% off and the state tax rate is 7. 25%, what is the total amount that mikaela spent on the paddleboard?.
The total amount that Mikaela spent on the paddleboard will be $449.80.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths.
As per the given,
Original price = $699
The selling price = $699 - 40% of $699
⇒ $699 - 0.40 x $699 = $419.4
The state tax (assuming it applied to the selling price) will be as,
7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065
Final amount = $419.4 + $30.4065 = $449.80
Hence "Mikaela will have spent $449.80 in total on the paddleboard".
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The side of a cube has a length of 4x³y6 cm. The volume of the cube can be found using
the formula V = S³. What is the volume of the cube in cubic centimeters?
PLEASE HELP
Answer:
find my dad
Step-by-step explanation:
7. Use the Division Property of Equality to write an equation that is
equivalent to 5x = 14.
Answer: x = 14/5 or x = 2.8
Step-by-step explanation:
Step 1: Divide both sides of the equation by five: a common nonzero real number.
(5x)/5= 14/5
Step 2: Simplify
x = 14/5
A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?
Answer:
Step-by-step explanation:
Which of the following statements is correct for a triangle?
A. triangle can have two obtuse angles
B.The difference of two sides of a triangle is greater than any other side of the same triangle.
C.A triangle can have an obtuse angle and a right angle.
D.None of these
Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
The compound interest received by Matthew Westhoven is $51.80
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.
Given, the principal amount (P) = $925
Compound interest percentage (r) = 5.5% = 0.055
Time period (t) = 1
Since, it is semiannually compounded (n) = 2*t = 2
Amount (A) = P(1 + r/n)^nt
= 925(1 + 0.055/2)^2
= 925(1.0275)^2
= 925(1.056)
= 976.80
Thus, Interest amount (CI) = A - P
= $976.80 - $925
= $51.80
The compound interest received by Matthew Westhoven is $51.80
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What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
You mix 1 fourth cup of crisp wheat cereal with 1 1 half cups of crisp rice cereal. Find and interpret the value of the ratio of crisp wheat cereal to crisp rice cereal.
The amount of crisp wheat cereal is _____ the amount of crisp rice cereal
Response:
Answer:
The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.
Step-by-step explanation:
r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
What is sin(60) in degrees?
Answer:
(sqrt3)/2
Step-by-step explanation:
Sin(x)=opposite/hypotenuse
30, 60, 90 right triangle.
ratio of sides are 1, sqrt3, and 2.
Locate the 60 degree angle on the triangle
The opposite side is sqrt3
The hypotenuse is 2
so its (sqrt3)/2
Answer:
√3/2 or 0.866
Step-by-step explanation:
need help! can't figure it out :/
Answer:
please tell me if you get the answer. I need it too!
need help now i need to finish this delta
Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.
What do you mean by transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
What is reflection in mathematics?In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.
Figure H
Mapped onto figure I
The required transformation:
reflection along y=x.
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For which situation does one quantity change at a constant rate per unit interval relative to another quantity?
Responses
For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%
For every week that passes, a vine doubles in length 2 times a week.
.
For every year that passes, a population of insects increases by 6%
Answer:
(a) For every day that passes, a person drives 54 miles
Step-by-step explanation:
You want to know the situation in which one quantity changes relative to another at a constant rate.
DrivingThe rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.
SavingsWe assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.
VineIf the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.
PopulationAs with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.
The situation with a constant rate of change is ...
For every day that passes, a person drives 54 miles.
__
Additional comment
When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.
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Find the lengths of segments AD and BD. Then check your answers using a different method.
Answer: BD = 5
Step-by-step explanation:
Using the Pythagorean theorem [tex]a^{2} + b^{2} =c^{2}[/tex] where c is the hypotenuse, we can solve for BD[tex]a^{2} +12^{2} =13^{2}[/tex]
[tex]a^{2} =13^{2}-12^{2}[/tex]
[tex]a = \sqrt{25}[/tex]
[tex]a = 5[/tex]
Therefore BD = 5
Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407(-20, 12)
(17, 2)
(-11, 8)
(17, 8)
(11, 2)
Is this relation a function?
Answer:
No because x-coordinate 17 appears twice.
Step-by-step explanation:
In a function, no two ordered pairs can have the same x-coordinate.
Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.
The cost of a cake is twice that of a cup of tea.
1 cake and 5 cups of tea cost £21.
How much does a cake cost?
Answer:
The cake cost $6.00
Step-by-step explanation:
Let c = the cost of the cake
Let t = the cost of the tea
c = 2t
c + 5t = 21 Substitute 2t for c
2t + 5t = 21 Combine like terms
7t = 21 Divide both sides by 7
[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]
t = 3
A cup of tea costs $3.00
c = 2t Substitute 3 for t
c = 2(3)
c = 6
A cake costs $6.00
Answer:
Cake: £6
Step-by-step explanation:
1c = 2t Eq. 1
1c + 5t = 21 Eq. 2
c = cost of a cake
t = cost of a cup of tea
Replacing Eq. 1 in Eq 2:
2t + 5t = 21
7t = 21
t = 21/7
t = 3
From Eq. 1:
c = 2t
c = 2*3
c = 6
Check:
From Eq. 2:
c + 5t = 21
6 + 5*3 = 21
6 + 15 = 21
Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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In a video game, a player follows a certain path that can be partially modeled by the functionf(x)=x(x−5)(x−3) . This function can be graphed on a coordinate plane.
The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.
How to draw the sketch of the graph?To draw the sketch of the graph, we need to consider these three following features:
The x-intercepts.The y-intercept.The end behavior.The function in this problem is defined as follows:
f(x) = x(x - 5)(x - 3).
From the factor theorem, the x-intercepts are taken from the linear factors, as follows:
x = 0.x - 5 = 0 -> x = 5.x - 3 = 0 -> x = 3.The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:
f(0) = 0(0 - 5)(0 -3) = 0.
In the problem, we have a cube function, hence:
At the left tail(negative infinity) it goes to negative infinity.At the right tail(positive infinity) it goes to positive infinity.More can be learned about functions at https://brainly.com/question/24808124
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Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
Answers: 7 units
14 units
25 units
26 units
answer : 26
steps
get hypotenuse
a² + b² = c²
7² + 8² = c²
49 + 64 = c²
113 = c²
square root of c is √113 which 10.63
7 + 8 + 10.63 = 25.63
on the number line, the distance between x and y is greater than the distance between x and z. does z lie between x and y on the number line?
yes, z can lie between x and y but z can also lie on another side of x in Number lines.
With an example, define number line?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.
A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.
What does the math number line mean?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.
How a number is used—for example, to plot a point—depends on the question that goes with it.
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Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078A school is arranging a field trip to the zoo. The school spends 546.53 dollars on passes for 40 students and 3 teachers. The school also spends 351.60 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
There are $21.5 money was spent on a pass and lunch for each student.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that:
The amount spent by school on pass of 40 students and 3 teachers = $546.53
And, the amount spent for the lunch only for students = $351.60
Now,
The money spent for pass of 43 person = $546.53
Then, The amount of pass for each person = 546.53/43
= $12.71
Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40
⇒ $8.79
Therefore, amount of pass and lunch for each student = 12.71 + 8.79
= $21.5
Thus, $21.5 is the required answer.
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