The shaded sections of the trapezoid are triangles.
We know how to find the area of triangles
A = 1/2 bh
Lets start with the left triangle
The bases is 1.1 inches and the height is 3.8 inches
A left triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
The right triangle has the same dimensions
A right triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
Add the two triangles together
2.09+2.09 = 4.18 in^2
The area of the shaded region is 4.18 in^2
How many toys would Patricia build in 10 hours if she built 5 toys
every 6 minutes?
Answer:
500
Step-by-step explanation:
she can build 5 in 6 minutes. 6 × 10 is 1 hour
so you would do 5 × 10 = 50
then multiply 50 × 10 hours = 500 toys
Answer:
Patricia will build 500 toys in 10 hours
Step-by-step explanation:
5 toys ? toys
--------- = ----------
6 minutes 10 hours
so we would turn the hours into minutes which would be
600 minutes.
5 toys ? toys
--------- = ----------
6 minutes 600 mins
Then we would cross multiply and that will give us how many toys she can build in 10 hours, which is 500 toys.
help i dont understand this
Answer:
X= 15 is Undefined
Y= -3 is Zero
Y= 1/2x - 4 is a positive slope
what is a set of relations
The relation is the relationship between two or more sets of values. Suppose, x and y are two sets of ordered pairs. If set x has a relation with set y, then the values of set x are called domain whereas the values of set y are called range. A relation from a set A to a set B is a subset of A×B. Hence, a relation R consists of ordered pairs (a,b), where a∈A and b∈B. If (a,b)∈R, we say that is related to, and we also write aRb. A connection between the elements of two or more sets is a relation. The sets must be non-empty. A subset of the Cartesian product also forms a relation R. A relation may be represented either by the Roster method or by the Set-builder method.
Ray Horton is a laborer. He earns $16.25 per hour. How many hours per week must he work if
he wants to earn approximately $585.00 per week?
Directions: Write the slope form of the equation with the given information.
13) through (3,4) and (5,-2)
Answer:
y=-3x+13
Step-by-step explanation:
step one you will need to find the slope by the Y2 minus y1 all over x2 minus X1 formula. so you would have -2 - 4 all over 5 - 3 . you will get -6 over 2 which is equal to -3 . that means that -3 is the slope .
Step 2 you can find the equation with the point slope form formula . the point slope form formula is y-y1=m(x-x1). by substituting your values into these equation you can find the equation of this line . you can substitute any point into it as long as it is on the line . let's use (3,4) where 3=x1 and 4=y1.
step 3. simplify. you will get y-4=-3(x-3). keep in mind I substituted -3 into the equation because -3 is the slope.
you can simplify this if you want to . you will get y=-3(x-3)+4. it becomes through foiling, y=-3x+9+4. it simplifies to y=-3x+13.
use lagrange multipliers to find two positive numbers whose product is 196 and whose sum is a minimum. (enter your answers as a comma-separated list.)
Required Lagrange multipliers are 14,14.
What are Lagrange multipliers?
In multivariable calculus, Lagrange multipliers are used to locate the maximum and minimum of a function that is subject to restrictions.An approach for locating a function's maximum or minimum is the Lagrange multiplier method.The growth in the optimization problem (f(x, y)) that results from a marginal relaxation of the constraint is quantified by the Lagrange multiplier.We have to minimize f(x,y)=x+y'
subject to xy=196 ............(1)
x>0,y>0
Let L(x,y,d)= f(x,y)+d(XY-196)
∀L= [tex](\frac{Lx}{Ly} )=(\frac{1+dy}{1+dx} )[/tex]
For critical points,
∀L=0
⇒[tex](\frac{1+dy}{1+dx} )=\frac{0}{0}[/tex]
⇒ x,y= -1/d
Substituting in equation 1, we get,
d=±1/14
d=+1/14 ⇒ x=y=-14 (neglect)
d=-1/14 ⇒ x=y=+14
∵ x>0, y>0.
Hence, x=y=14
Function's maximum or minimum
f(x,y)=f(14,14)=28
Required Lagrange multipliers are 14,14.
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8. the floor of a rectangular meeting room has raised platform that is the same length as the room. the whole room has an area of 46 14/15, ( 7 1 /3 yards )
Part B Suppose there are of the platform is 7 34/45 square yards. what fraction of the entire floor is the raised platform. P.s make sure to show your work
Answer:The width of the room is .
Step-by-step explanation:
Consider the provided information.
It is given that the whole room has an area 46 14/15 sq yd.
This can be written as:
yd.
Now consider the figure shown below:
From the figure we know that the length of the rectangular meeting room is yd.
The area of rectangle is
Let width of the rectangle is w yard.
Hence, the width of the room is .
active attachment
Step-by-step explanation:
The width of the room is .
Step-by-step explanation:
Consider the provided information.
It is given that the whole room has an area 46 14/15 sq yd.
This can be written as:
yd.
Now consider the figure shown below:
From the figure we know that the length of the rectangular meeting room is yd.
The area of rectangle is
Let width of the rectangle is w yard.
Hence, the width of the room is .
active attachment
Circle A is given by the equation (x-4) +(3-3)* = 25. Circle A is shifted up five units and left by six units. Then, its radius is doubled. What is the new equation for circle A? A. (x+2)+(y-2)* = 50 B. (x+2)+(y –8)* = 100 C. (x-2)* +(y+2) = 100 D. (x-2)+(+8)* = 50
The correct answer is B
Determined whether the relation is a function. If it is not a function, circle the ordered pairs that cause it not to be a function.
To be a function, each input can only go to one output
A. The input 1 goes to two different output values
(1,6) (1,7) causes it not to be a function
B. This is a function. Each input has only one output value
C. The input 0 goes to two different output values
(0,-5) snf (0,4) causes it not to be a function
Find the slope of the line that contains the given point
Answer:
(2, 1) and (4, 2): [tex]\frac{1}{2}[/tex]
(-4, 5) and (-3, -7): [tex]-12[/tex]
Step-by-step explanation:
Hello! Let's help you with that problem there!
So we know that in a slope intercept form, it is depicted as [tex]y=mx+b[/tex]. There are two ways to essentially find m, which is slope in this case. The first method is the [tex]\frac{rise}{run}[/tex] method. This is typically used when you have a graph to look off from and it's just a matter of counting the displacement from one point to another.
However, there is another way to find the slope given 2 points and that is what we are going to do here, since we have no graph to reference and have all the relevant information to find the slope using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
With this formula, we can plug in the coordinate values and solve for the slope!
(2, 1) and (4, 2):
[tex]m=\frac{2-1}{4-2}[/tex]
[tex]m=\frac{1}{2}[/tex]
Therefore, the slope of these points is [tex]m=\frac{1}{2}[/tex]
(-4, 5) and (-3, -7):
[tex]m=\frac{-7-5}{-3-(-4)}[/tex]
[tex]m=\frac{-12}{1}[/tex]
[tex]m=-12[/tex]
Therefore, the slope of these points is [tex]m=\frac{-12}{1}[/tex] or [tex]m=-12[/tex]
This double number line shows the distance a car travels over a period of time.
0
0
20
30
OB. 30
OC. 60
40
OD. 40
60 80 100
At what rate is the car traveling in maes per hour (mph)?
O A 20
Miles
60 90 120 150
Minutes
The rate at which the car is traveling is given as 1.5 miles/minute.
Given that,
This double-number line depicts the overall distance traveled by a car. It is necessary to determine the car's speed in miles per hour (mph).
What is Distance?Distance is referred to as an object moving between two points in time at a specific speed.
here,
The distance traveled = 150 miles
Time taken = 100 minutes
Rate = distance/time
Rate = 150 / 100
Rate = 1.5 miles per minute
Thus, The rate at which the car is traveling is given as 1.5 miles/minute.
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Graph the line with slope -3/4 and y-intercept 9.
The equation of the line with slope -3/4 and y intercept 9 is y=-3/4x+9.
Based on the conditions formulate:
m=-3/4
and b = 9
Write the equation of the linear function:
y=mx+b
substitute m=-3/4 and b=9 into y=mx+b:
y = -3/4x+9
A line's equation must be in the Slope-Intercept Form, y = mx + b, in order to be graphed using its slope and y-intercept.
This format makes it simple to read off the slope and y-intercept values. The y-intercept is the constant term b, whereas the slope is just the m coefficient of the variable x.
plot the y intercept (0,9) in the xy axis.
Use the slope to locate a different point beginning at the y-intercept. The direction you travel from one point to another is contained in the slope.
Hence the required graph is plotted.
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Roaring Zoo has 68 different species of birds. Because of cold weather, only 24 species stayed at the zoo, while the others were transported to the barn until warmer weather returned.
Which equation shows how many species of birds were transported?
b + 68 = 24
b − 68 = 24
b + 24 = 68
b − 24 = 68
Answer: b + 24 = 68
Step-by-step explanation:
we are told the zoo has 68 different species of birds so the equation will be = 28. The answers showing = 24 are already wrong.
transported means they are taken away, so we have to subtract 24 (animals that stayed in the zoo) to find b which are the remaining species moved to the barn.
b + 24 = 68
- 24 -24
b = 44 (transported to the barn)
24 ( stayed in the zoo)
68 ( total number of species of birds)
The correct expression to show the species of transported birds will be;
⇒ b + 24 = 68
Where, b is the number of transported birds.
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;
Total number of birds in Roaring Zoo = 68
Number of stayed birds in Zoo = 24
Let number of transported birds = b
Then, We can formulate;
Total number of birds = Stayed birds + Transported birds
Substitute all the values, we get;
⇒ 68 = 24 + b
Therefore,
The correct expression to show the species of transported birds will be;
⇒ b + 24 = 68
Where, b is the number of transported birds.
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Please please help! :)
Answer:
∠ 2 = 140°
Step-by-step explanation:
the left base angle in the triangle and 110° are a linear pair and sum to 180°
base angle + 110° = 180° ( subtract 110° from both sides )
base angle = 70°
the 2 sides of the triangle are congruent so Δ is isosceles with base angles congruent.
the vertex of the Δ is then
(180 - 70 - 70)° = 180° - 140° = 40°
the vertex and ∠ 2 are a linear pair and sum to 180° , that is
∠ 2 + 40° = 180° ( subtract 40° from both sides )
∠ 2 = 140°
Help me please is do today
The unknown variable, h of the equation is 18
How to find variable in an equation?A variable is a number represented by a letter in an equation.
The unknown variable in the equation is variable h.
Therefore, let's find the value of h.
A = 1 / 2 h(B + b)
where
A = 153B = 10b = 7Therefore, let's substitute the known values in the equation.
153 = 1 / 2h(10 + 7)
153 = 1 / 2 h(17)
153 = 17 / 2 h
cross multiply
153 × 2 = 17h
306 = 17h
divide both sides by 17
h = 306 / 17
Therefore,
h = 18
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A farmer has 80 animals on his farm.The animals consist of cows and chickens .Given there are 216 legs altogether among the animals, how many cows are there?
The farmer has 28 cows from a total of 80 animals in the farm.
How many cows and chickens does the farmer have in the farm?
Each chicken has two legs and each cow has four legs. The farmer has a total of 216 legs among all the animals, which are 80. Then, we can represent the situation with the following system of linear equations:
x + y = 80
4 · x + 2 · y = 216
Where:
x - The number of cows.y - The number of chickens.The system can be solved easily by some algebraic handling:
x = 80 - y
4 · (80 - y) + 2 · y = 216
320 - 4 · y + 2 · y = 216
320 - 2 · y = 216
2 · y = 320 - 216
2 · y = 104
y = 52
x = 80 - 52
x = 28
The farmer has 28 cows.
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$7.50x10 ANSWER PLEASE I FORGOT ABOUT THIS NOW IM LEARNING IT AGAIN
Answer:
$75
Step-by-step explanation:
basically 7.50 x 10
The chart below shows the approxinate distance from the Sun ti Earth, Mars, and Jupiter.
The speed of light is approximately 1.86 x 10^5 miles per second.
• The time it takes for a beam of light to travel from the Sun to the Earth is found by dividing the distance between the Sun and Earth by the speed of light. Find the amount of time it takes gir a beam if light fron the Sun to reach Earth. Show all work and express your answer in minutes.
• Explain or show how to use the numbers in scientific notation to calculate the difference in the distance from Jupiter to the Sun and the distance from Mars to the Sun. Then find the differences and express your answers in scientific notation.
• Explain ir show how to find the number if miles light will travel in 1/2 minute.
The amount of time it takes to reach the beam of sum from sun to earth is 200 seconds approximately
What is division?
Division is one of the basic arithmetic operation in which we find a number such the product of the number with the denominator is equal to the numerator.
We are given that the distant of earth from sun is 9.3 ×10^7
And the speed of light is 1.86×10^5
We divide the distance by the speed to get the value of time
[tex]\frac{9.3}{1.86}[/tex]×[tex]\frac{10^7}{10^5}[/tex]
On simplifying we get
200 seconds
Hence, The approximate time require to reach the beam of sun from sun to earth is 200 seconds
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What is the area of a triangle whose vertices are R(3, 4), S(6, 2), and T(7, 10)?
Enter your answer in the box.
[ ] units²
The area of the triangle is 13 square units.
We are given the coordinates of the vertices of a triangle.The coordinates of the vertices of the triangle are R(3, 4), S(6, 2), and T(7, 10).We need to find the area of the triangle.We know the coordinates of all the vertices.We will use the formula in coordinate geometry.Let the area of the triangle be "A".The equation can be written as given below :A = (1/2)[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]A = (1/2)[3(2 - 10) + 6(10 - 4) + 7(4 - 2)]A = (1/2)[3(-8) + 6(6) + 7(2)]A = (1/2)[-24 + 36 + 14]A = (1/2)(26)A = 13The area of the triangle is 13 square units.To learn more about equations, visit :
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Find g(x), where g(x) is the translation 6 units down of f(x)=6x+2.
Write your answer in the form mx+b, where m and b are integers.
Help please!
The image of the function after the translation is g(x) = 6x - 4
What is translation?Translation involves shifting a function across the coordinate plane
How to determine the equation of g(x)?The given parameters are:
f(x) = 6x + 2
The transformation is given as
Translation 6 units down
Mathematically, this transformation can be represented as
(x, y) = (x, y - 6)
When represented as a function, we have
g(x) = f(x) - 6
Substitute the equation f(x) = 6x + 2 in the equation g(x) = f(x) - 6
So, we have the following equation
g(x) = 6x + 2 - 6
Evaluate the like terms
g(x) = 6x - 4
Hence, the equation of g(x) is g(x) = 6x - 4
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A pet store clerk suggested 4 small fish for a 5-gallon fish tank. What size tank would be suggested to hold 60 small fish?
12-gallon tank
48-gallon tank
75-gallon tank
240-gallon tank
The size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
A pet store clerk suggested 4 small fish for a 5-gallon fish tank.
4 small fish = 5-gallon
60 small fish = x gallon
x = (5)(60)/4
x = 75 gallon-tank
Thus, the size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.
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If P=2500, r=6 %, and m=12, find the accumulated amount after 5 years.
hello
the question presented here related to compound interest and we can solve that using the formula
[tex]\begin{gathered} A=p(1+\frac{r}{n})^{nt}^{} \\ r=\text{rate}=6\text{ \% = 0.06} \\ n=12 \\ p=2500 \\ t=5 \\ \end{gathered}[/tex]let's proceed to substitute the values into the equation
[tex]\begin{gathered} A=2500(1+\frac{0.06}{12})^{12\times5} \\ A=2500(1+0.005)^{60} \\ A=2500(1.005)^{60} \\ A=2500\times1.005^{60}^{} \\ A=2500\times1.3488 \\ A=3375 \end{gathered}[/tex]the compounded interest compounded monthly at 6% for 5 years is 3375
The amount is 3250
The accumulated amount is calculated using the initial investment and interest earned in the given duration
The formula for simple interest is P×R×T and further, it is divided by 100
SI= 2500 × 6 × 5 =75000 ÷100 = 750
Now, for calculating the accumulated amount we will add the initial investment and the interest gained
ie, 2500+750 =3250
Here we are using the simple interest method to calculate the interest as it is assumed to be taken as simple interest when nothing is specified.
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Aislinn bought a new car. After 8 months, the odometer read 14,010 miles. How many miles did
Aislinn average per month on her car?
OA. Aislinn drove an average of 876 miles per month.
OB. Aislinn drove an average of 1,168 miles per month.
OC. Aislinn drove an average of 1,401 miles per month.
D. Aislinn drove an average of 1,751 miles per month.
When
out their o
19 milon
4
if their
d) Aislinn's average per month on her car is 1,751 miles per month.
How to find the average speed?The average speed is calculated by dividing the total distance traveled by the total time it took to travel that distance. Speed is the rate at which something moves at any given time.
Average speed is the average rate of speed over the course of a journey. Velocity exists as the directional speed of a moving object as an indication of its rate of change in position as observed from a specific frame of reference and measured by a specific time standard.
Given,
After 8 months, the odometer read 14,010 miles.
Solution:
t = 8,
d = 14,010 miles,
s = ?
s = d/t
s = 14,010/8
s = 1751 miles/month.
Aislinn drove an average of 1,751 miles per month.
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Is this a valid argument?
Given: If two points lie on the same plane, then they are coplanar.
Points X and Y both lie on plane R.
Conclusion: Points X and Y are coplanar.
Yes, this is a valid argument. This argument uses the Law of Detachment.
What is the Law of Detachment in logic?The Law of Detachment states that if the hypothesis of a true conditional statement is true, then the conclusion must be true as well. The Law of Detachment is the most often employed deductive reasoning theory.
Given:
Points X and Y both lie on plane R.
Conclusion: Points X and Y are coplanar.
The argument is true because,
The term "coplanar" refers to "being on the same plane." Coplanar points are points that are on the same plane. A group of points in space is said to be coplanar if there is a geometric plane that contains all of them.
Hence, the Conclusion is Points X and Y are coplanar.
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for a population with a standard deviation of σ = 6, what is the z-score corresponding to a score that is 12 points above the mean?
The z-score corresponding to a score that is 12 points above the mean is 2.
The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that
z-score = (x – μ) / σ
where x = sample data value
μ = mean
σ = standard deviation
If the sample score is 12 points above the mean, then (x – μ) = 12.
(x – μ) = 12
σ = 6
Substitute the values to the z-score formula.
z-score = (x – μ) / σ
z-score = 12/6
z-score = 2
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Look at the pic tell me what’s correct
Answer:
B
Step-by-step explanation:
V = 27(0.8)^1
V = 21.6
V = 27(0.8)^2
V = 17.28
And more
In math class, the girl to boy ratio is 8 to 6. If there are 24 girls in the class how many boys are there
Solve asap giving brainliest all the info you need is in the photo
Answer:
[tex]\textsf{C:}[/tex]
[tex]\begin{cases}s + h = 40\\18s + 14h = 700 \end{cases}[/tex]
Step-by-step explanation:
Given information:
40 = Total number of scarves and hats sold.$700 = Total amount made from the sale.$18 = Charge for each scarf.$14 = Charge for each hat.Define the variables:
Let s = number of scarves sold.Let h = number of hats sold.Create an equation for the total number of scarves and hats sold:
⇒ s + h = 40
Create an equation that represents the total amount made from sales considering the cost per item:
⇒ 18s + 14h = 700
Therefore, the system of equations that represents the given constraints is:
[tex]\begin{cases}s + h = 40\\18s + 14h = 700 \end{cases}[/tex]
Which is more 15% or 1/4
Answer: 1/4 is more
Step-by-step explanation:
1/4=25%
25%>15%
1/4>15%
1/4 is more than 15%
Quadrilateral MATH is congruent to quadrilateral WXYZ. Which
statement is always true?
(1) MA - XY
(2) m/H=mZW
(3) Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a
sequence of rigid motions.
(4) Quadrilateral MATH and quadrilateral WXYZ are the same shape, but
not necessarily the same size.
Answer:
2
Step-by-step explanation:
The true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.
What is Congruency?The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
Given:
MATH is congruent to quadrilateral WXYZ.
Then congruent sides are
MA= WX
AT = XY
TH = YZ
and, congruent angles are
<M = <W
<A = <X
<T= <Y
<H = <Z
So, if the quadrilateral is congruent then they equal in measure.
Hence, the true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.
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